premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
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sequencelengths 0
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stringlengths 684
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Everyone who is not rich is both not curious and not tall and vice versa. Everyone who is both quiet and not kind is not strong or brave and vice versa. Everyone who is both not curious and tall is not generous or curious and vice versa. Everyone who is both not brave and calm is both calm and not calm. Everyone who is both calm and not strong is both happy and creative. If someone is both not creative and funny then fred is either not strong or kind and vice versa. Everyone who is quiet is brave. If paul is both creative and not tall then someone is not brave. Everyone who is creative or brave is not brave and vice versa. Everyone who is not tall or wise is either tall or not strong and vice versa. Everyone who is both not quiet and not happy is both calm and not brave and vice versa. If someone is not creative then paul is not brave or not wise. Everyone who is both funny and not brave is patient or not rich and vice versa. If someone is either strong or funny then someone is either patient or not old and vice versa. Everyone who is both not curious and tall is curious or funny. Someone is creative or not tall. Fred is happy. Someone is both creative and patient. | Paul is not tall. | contradiction | (![X]:(~rich(X)<=>(~curious(X)&~tall(X))))&
(![X]:((quiet(X)&~kind(X))<=>(~strong(X)|brave(X))))&
(![X]:((~curious(X)&tall(X))<=>(~generous(X)|curious(X))))&
(![X]:((~brave(X)&calm(X))=>(calm(X)&~calm(X))))&
(![X]:((calm(X)&~strong(X))=>(happy(X)&creative(X))))&
((?[X]:((~creative(X)&funny(X))))<=>((~strong(fred)<~>kind(fred))))&
(![X]:(quiet(X)=>brave(X)))&
(((creative(paul)&~tall(paul)))=>(?[X]:(~brave(X))))&
(![X]:((creative(X)|brave(X))<=>~brave(X)))&
(![X]:((~tall(X)|wise(X))<=>(tall(X)<~>~strong(X))))&
(![X]:((~quiet(X)&~happy(X))<=>(calm(X)&~brave(X))))&
((?[X]:(~creative(X)))=>((~brave(paul)|~wise(paul))))&
(![X]:((funny(X)&~brave(X))<=>(patient(X)|~rich(X))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:((~curious(X)&tall(X))=>(curious(X)|funny(X))))&
(?[X]:((creative(X)|~tall(X))))&
(happy(fred))&
(?[X]:((creative(X)&patient(X)))) | ~tall(paul) | [
"p1",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4744533294331080093997633
% SZS output start Proof for 4744533294331080093997633
2. ! [X0] : ((~kind(X0) & quiet(X0)) <=> (brave(X0) | ~strong(X0))) [input p1]
7. ! [X0] : (quiet(X0) => brave(X0)) [input p6]
9. ! [X0] : ((brave(X0) | creative(X0)) <=> ~brave(X0)) [input p8]
10. ! [X0] : ((wise(X0) | ~tall(X0)) <=> (tall(X0) <~> ~strong(X0))) [input p9]
19. ~tall(paul) [input hypothesis]
25. ! [X0] : (brave(X0) | ~quiet(X0)) [ennf transformation 7]
34. ! [X0] : (((~kind(X0) & quiet(X0)) | (~brave(X0) & strong(X0))) & ((brave(X0) | ~strong(X0)) | (kind(X0) | ~quiet(X0)))) [nnf transformation 2]
35. ! [X0] : (((~kind(X0) & quiet(X0)) | (~brave(X0) & strong(X0))) & (brave(X0) | ~strong(X0) | kind(X0) | ~quiet(X0))) [flattening 34]
44. ! [X0] : (((brave(X0) | creative(X0)) | brave(X0)) & (~brave(X0) | (~brave(X0) & ~creative(X0)))) [nnf transformation 9]
45. ! [X0] : ((brave(X0) | creative(X0) | brave(X0)) & (~brave(X0) | (~brave(X0) & ~creative(X0)))) [flattening 44]
46. ! [X0] : (((wise(X0) | ~tall(X0)) | ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0)))) & (((strong(X0) | ~tall(X0)) & (~strong(X0) | tall(X0))) | (~wise(X0) & tall(X0)))) [nnf transformation 10]
47. ! [X0] : ((wise(X0) | ~tall(X0) | ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0)))) & (((strong(X0) | ~tall(X0)) & (~strong(X0) | tall(X0))) | (~wise(X0) & tall(X0)))) [flattening 46]
65. strong(X0) | quiet(X0) [cnf transformation 35]
84. ~quiet(X0) | brave(X0) [cnf transformation 25]
87. ~brave(X0) | ~brave(X0) [cnf transformation 45]
89. ~strong(X0) | tall(X0) | tall(X0) [cnf transformation 47]
118. ~tall(paul) [cnf transformation 19]
120. ~strong(X0) | tall(X0) [duplicate literal removal 89]
122. ~brave(X0) [duplicate literal removal 87]
161. 7 <=> tall(paul) [avatar definition]
162. ~tall(paul) <- (~7) [avatar component clause 161]
216. ~7 [avatar split clause 118,161]
224. quiet(X0) | tall(X0) [resolution 120,65]
312. tall(X0) | brave(X0) [resolution 224,84]
313. tall(X0) [subsumption resolution 312,122]
314. $false <- (~7) [resolution 313,162]
319. 7 [avatar contradiction clause 314]
320. $false [avatar sat refutation 216,319]
% SZS output end Proof for 4744533294331080093997633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then paul is not humble. Everyone who is both funny and not brave is both not old and creative and vice versa. Everyone who is both happy and tall is patient. If someone is both curious and generous then lucy is generous. If someone is old or not curious then john is old or not generous. Everyone who is rich is happy or funny and vice versa. If alice is both not curious and not brave then someone is either not patient or not rich. If paul is curious or funny then someone is wise or not generous and vice versa. If someone is not happy then someone is both calm and not brave. Everyone who is not humble is both funny and not brave. Everyone who is both not calm and happy is both patient and funny. Everyone who is either not curious or generous is not wise and vice versa. If someone is both generous and not creative then alice is both not humble and calm and vice versa. Everyone who is either patient or not rich is either not tall or not wise. If alice is not old then someone is humble or not creative and vice versa. Everyone who is quiet is not old and vice versa. John is quiet or curious. Someone is calm or not brave. Someone is either not curious or not funny. Someone is quiet. Mary is either brave or rich. Mary is not old. Someone is either humble or not creative. Someone is not calm. | Paul is rich. | entailment | ((?[X]:(quiet(X)))=>(~humble(paul)))&
(![X]:((funny(X)&~brave(X))<=>(~old(X)&creative(X))))&
(![X]:((happy(X)&tall(X))=>patient(X)))&
((?[X]:((curious(X)&generous(X))))=>(generous(lucy)))&
((?[X]:((old(X)|~curious(X))))=>((old(john)|~generous(john))))&
(![X]:(rich(X)<=>(happy(X)|funny(X))))&
(((~curious(alice)&~brave(alice)))=>(?[X]:((~patient(X)<~>~rich(X)))))&
(((curious(paul)|funny(paul)))<=>(?[X]:((wise(X)|~generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((calm(X)&~brave(X)))))&
(![X]:(~humble(X)=>(funny(X)&~brave(X))))&
(![X]:((~calm(X)&happy(X))=>(patient(X)&funny(X))))&
(![X]:((~curious(X)<~>generous(X))<=>~wise(X)))&
((?[X]:((generous(X)&~creative(X))))<=>((~humble(alice)&calm(alice))))&
(![X]:((patient(X)<~>~rich(X))=>(~tall(X)<~>~wise(X))))&
((~old(alice))<=>(?[X]:((humble(X)|~creative(X)))))&
(![X]:(quiet(X)<=>~old(X)))&
((quiet(john)|curious(john)))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
(?[X]:(quiet(X)))&
((brave(mary)<~>rich(mary)))&
(~old(mary))&
(?[X]:((humble(X)<~>~creative(X))))&
(?[X]:(~calm(X))) | rich(paul) | [
"p0",
"p5",
"p9",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3911677054315421769739914
% SZS output start Proof for 3911677054315421769739914
1. ? [X0] : quiet(X0) => ~humble(paul) [input p0]
6. ! [X0] : (rich(X0) <=> (funny(X0) | happy(X0))) [input p5]
10. ! [X0] : (~humble(X0) => (~brave(X0) & funny(X0))) [input p9]
16. ! [X0] : (quiet(X0) <=> ~old(X0)) [input p15]
22. ~old(mary) [input p21]
25. ~rich(paul) [input hypothesis]
27. ~humble(paul) | ! [X0] : ~quiet(X0) [ennf transformation 1]
36. ! [X0] : ((~brave(X0) & funny(X0)) | humble(X0)) [ennf transformation 10]
42. ! [X0] : ((rich(X0) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | ~rich(X0))) [nnf transformation 6]
43. ! [X0] : ((rich(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | ~rich(X0))) [flattening 42]
66. ! [X0] : ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0))) [nnf transformation 16]
80. ~humble(paul) | ~quiet(X0) [cnf transformation 27]
91. ~funny(X0) | rich(X0) [cnf transformation 43]
100. funny(X0) | humble(X0) [cnf transformation 36]
120. old(X0) | quiet(X0) [cnf transformation 66]
128. ~old(mary) [cnf transformation 22]
132. ~rich(paul) [cnf transformation 25]
134. 1 <=> ! [X0] : ~quiet(X0) [avatar definition]
135. ~quiet(X0) <- (1) [avatar component clause 134]
137. 2 <=> humble(paul) [avatar definition]
140. 1 | ~2 [avatar split clause 80,137,134]
320. rich(X0) | humble(X0) [resolution 100,91]
322. quiet(mary) [resolution 120,128]
329. humble(paul) [resolution 320,132]
333. 2 [avatar split clause 329,137]
336. $false <- (1) [resolution 135,322]
339. ~1 [avatar contradiction clause 336]
342. $false [avatar sat refutation 140,333,339]
% SZS output end Proof for 3911677054315421769739914
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and old is not rich and vice versa.
If someone is not quiet then alice is not tall.
If someone is not creative then someone is either strong or not creative.
Everyone who is brave is either not creative or not patient and vice versa.
If someone is either quiet or not curious then someone is not generous.
Everyone who is either happy or not brave is old and vice versa.
Everyone who is brave or not funny is not calm and vice versa.
Everyone who is humble or old is both rich and not curious.
If susan is not funny or not wise then alice is not calm.
If lucy is either wise or quiet then mary is not happy.
If someone is not curious then someone is not generous or not humble.
Everyone who is not happy is funny or not brave.
If someone is either tall or not kind then lucy is both not kind and rich.
Everyone who is either not humble or strong is curious or quiet and vice versa.
Everyone who is both not happy and old is not quiet and vice versa.
Everyone who is either not old or happy is either creative or funny and vice versa.
Mary is rich.
Someone is either brave or happy.
Lucy is either not happy or not rich.
Someone is not humble.
Susan is not strong.
Someone is not patient.
Alice is either not calm or wise.
Alice is both not tall and not funny. | Lucy is not happy. | entailment | (![X]:((strong(X)&old(X))<=>~rich(X)))&
((?[X]:(~quiet(X)))=>(~tall(alice)))&
((?[X]:(~creative(X)))=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:(brave(X)<=>(~creative(X)<~>~patient(X))))&
((?[X]:((quiet(X)<~>~curious(X))))=>(?[X]:(~generous(X))))&
(![X]:((happy(X)<~>~brave(X))<=>old(X)))&
(![X]:((brave(X)|~funny(X))<=>~calm(X)))&
(![X]:((humble(X)|old(X))=>(rich(X)&~curious(X))))&
(((~funny(susan)|~wise(susan)))=>(~calm(alice)))&
(((wise(lucy)<~>quiet(lucy)))=>(~happy(mary)))&
((?[X]:(~curious(X)))=>(?[X]:((~generous(X)|~humble(X)))))&
(![X]:(~happy(X)=>(funny(X)|~brave(X))))&
((?[X]:((tall(X)<~>~kind(X))))=>((~kind(lucy)&rich(lucy))))&
(![X]:((~humble(X)<~>strong(X))<=>(curious(X)|quiet(X))))&
(![X]:((~happy(X)&old(X))<=>~quiet(X)))&
(![X]:((~old(X)<~>happy(X))<=>(creative(X)<~>funny(X))))&
(rich(mary))&
(?[X]:((brave(X)<~>happy(X))))&
((~happy(lucy)<~>~rich(lucy)))&
(?[X]:(~humble(X)))&
(~strong(susan))&
(?[X]:(~patient(X)))&
((~calm(alice)<~>wise(alice)))&
((~tall(alice)&~funny(alice))) | ~happy(lucy) | [
"p0",
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6204661648415168241212620
% SZS output start Proof for 6204661648415168241212620
1. ! [X0] : ((old(X0) & strong(X0)) <=> ~rich(X0)) [input p0]
8. ! [X0] : ((old(X0) | humble(X0)) => (~curious(X0) & rich(X0))) [input p7]
19. ~happy(lucy) <~> ~rich(lucy) [input p18]
25. happy(lucy) [input hypothesis]
33. ! [X0] : ((~curious(X0) & rich(X0)) | (~old(X0) & ~humble(X0))) [ennf transformation 8]
39. ! [X0] : (((old(X0) & strong(X0)) | rich(X0)) & (~rich(X0) | (~old(X0) | ~strong(X0)))) [nnf transformation 1]
40. ! [X0] : (((old(X0) & strong(X0)) | rich(X0)) & (~rich(X0) | ~old(X0) | ~strong(X0))) [flattening 39]
59. (rich(lucy) | happy(lucy)) & (~rich(lucy) | ~happy(lucy)) [nnf transformation 19]
67. old(X0) | rich(X0) [cnf transformation 40]
83. rich(X0) | ~old(X0) [cnf transformation 33]
115. ~rich(lucy) | ~happy(lucy) [cnf transformation 59]
124. happy(lucy) [cnf transformation 25]
146. rich(X0) [subsumption resolution 83,67]
199. ~happy(lucy) [subsumption resolution 115,146]
207. $false [subsumption resolution 124,199]
% SZS output end Proof for 6204661648415168241212620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both not brave and curious then someone is creative and vice versa. Everyone who is not wise or brave is brave or not old and vice versa. Everyone who is funny or not generous is both patient and old. Everyone who is either not funny or wise is brave and vice versa. Everyone who is wise or not kind is not patient and vice versa. Everyone who is creative is patient. If someone is not generous or rich then someone is not patient or not funny. Everyone who is either quiet or not happy is generous or not generous and vice versa. Everyone who is curious or not patient is both not happy and happy and vice versa. Everyone who is quiet is not wise or not curious. If someone is not creative or quiet then someone is both happy and calm and vice versa. Everyone who is not calm or not quiet is happy. If alice is either not creative or tall then someone is not calm or not funny. Everyone who is not kind or creative is either not tall or funny. Everyone who is either not curious or brave is either funny or generous. If someone is tall or kind then susan is humble. Someone is either not strong or not old. Susan is either strong or not wise. Mary is either not wise or old. Someone is either calm or not tall. Someone is both calm and rich. Someone is tall or old. | John is not rich. | neutral | (((~brave(john)&curious(john)))<=>(?[X]:(creative(X))))&
(![X]:((~wise(X)|brave(X))<=>(brave(X)|~old(X))))&
(![X]:((funny(X)|~generous(X))=>(patient(X)&old(X))))&
(![X]:((~funny(X)<~>wise(X))<=>brave(X)))&
(![X]:((wise(X)|~kind(X))<=>~patient(X)))&
(![X]:(creative(X)=>patient(X)))&
((?[X]:((~generous(X)|rich(X))))=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:((quiet(X)<~>~happy(X))<=>(generous(X)|~generous(X))))&
(![X]:((curious(X)|~patient(X))<=>(~happy(X)&happy(X))))&
(![X]:(quiet(X)=>(~wise(X)|~curious(X))))&
((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((~calm(X)|~quiet(X))=>happy(X)))&
(((~creative(alice)<~>tall(alice)))=>(?[X]:((~calm(X)|~funny(X)))))&
(![X]:((~kind(X)|creative(X))=>(~tall(X)<~>funny(X))))&
(![X]:((~curious(X)<~>brave(X))=>(funny(X)<~>generous(X))))&
((?[X]:((tall(X)|kind(X))))=>(humble(susan)))&
(?[X]:((~strong(X)<~>~old(X))))&
((strong(susan)<~>~wise(susan)))&
((~wise(mary)<~>old(mary)))&
(?[X]:((calm(X)<~>~tall(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((tall(X)|old(X)))) | ~rich(john) | [] | null | 0 |
Everyone who is both quiet and happy is either not wise or not creative and vice versa.
Everyone who is quiet is either not patient or not happy and vice versa.
Everyone who is quiet or not curious is not wise.
Everyone who is either not wise or not kind is both funny and not kind.
If someone is not curious then someone is not old and vice versa.
Everyone who is both not humble and quiet is either happy or not calm and vice versa.
Everyone who is not patient is funny or humble.
Everyone who is strong or calm is not creative.
If someone is rich or not curious then paul is either generous or not patient.
If paul is both not humble and not tall then someone is either humble or rich and vice versa.
If someone is both not rich and not generous then paul is patient or not rich and vice versa.
Everyone who is both patient and not kind is both not strong and curious and vice versa.
Everyone who is both happy and not humble is either not happy or not kind and vice versa.
If someone is not calm or calm then fred is both old and not creative and vice versa.
Everyone who is both not patient and funny is both curious and strong and vice versa.
Everyone who is not funny is both funny and not brave.
Someone is strong or patient.
Paul is not happy.
Someone is both happy and not tall.
Someone is both brave and not wise.
Someone is either not humble or not funny.
Someone is either not strong or not patient.
John is both not strong and funny.
Someone is either not humble or generous. | John is calm. | neutral | (![X]:((quiet(X)&happy(X))<=>(~wise(X)<~>~creative(X))))&
(![X]:(quiet(X)<=>(~patient(X)<~>~happy(X))))&
(![X]:((quiet(X)|~curious(X))=>~wise(X)))&
(![X]:((~wise(X)<~>~kind(X))=>(funny(X)&~kind(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(~old(X))))&
(![X]:((~humble(X)&quiet(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(~patient(X)=>(funny(X)|humble(X))))&
(![X]:((strong(X)|calm(X))=>~creative(X)))&
((?[X]:((rich(X)|~curious(X))))=>((generous(paul)<~>~patient(paul))))&
(((~humble(paul)&~tall(paul)))<=>(?[X]:((humble(X)<~>rich(X)))))&
((?[X]:((~rich(X)&~generous(X))))<=>((patient(paul)|~rich(paul))))&
(![X]:((patient(X)&~kind(X))<=>(~strong(X)&curious(X))))&
(![X]:((happy(X)&~humble(X))<=>(~happy(X)<~>~kind(X))))&
((?[X]:((~calm(X)|calm(X))))<=>((old(fred)&~creative(fred))))&
(![X]:((~patient(X)&funny(X))<=>(curious(X)&strong(X))))&
(![X]:(~funny(X)=>(funny(X)&~brave(X))))&
(?[X]:((strong(X)|patient(X))))&
(~happy(paul))&
(?[X]:((happy(X)&~tall(X))))&
(?[X]:((brave(X)&~wise(X))))&
(?[X]:((~humble(X)<~>~funny(X))))&
(?[X]:((~strong(X)<~>~patient(X))))&
((~strong(john)&funny(john)))&
(?[X]:((~humble(X)<~>generous(X)))) | calm(john) | [] | null | 0 |
Everyone who is not tall or not calm is rich.
Everyone who is calm is brave and vice versa.
If someone is both not rich and not brave then john is not calm or quiet.
If paul is not generous then paul is not calm and vice versa.
If john is curious then someone is rich.
If someone is strong or brave then mary is either not strong or not curious and vice versa.
If paul is quiet then someone is either not strong or not rich.
If someone is either curious or not old then paul is either brave or generous and vice versa.
If fred is not old or happy then mary is curious or strong and vice versa.
If someone is rich then john is both not funny and not curious.
Everyone who is either not curious or happy is brave or old and vice versa.
If fred is creative or strong then john is either not patient or brave.
Everyone who is kind or not humble is both quiet and not brave and vice versa.
If someone is either strong or not curious then someone is either not tall or not humble and vice versa.
Everyone who is generous is either old or not happy and vice versa.
Paul is humble.
Mary is brave or wise.
John is humble or happy.
Someone is not happy.
Someone is either not generous or not happy.
Mary is both strong and not tall. | Paul is not old. | contradiction | (![X]:((~tall(X)|~calm(X))=>rich(X)))&
(![X]:(calm(X)<=>brave(X)))&
((?[X]:((~rich(X)&~brave(X))))=>((~calm(john)|quiet(john))))&
((~generous(paul))<=>(~calm(paul)))&
((curious(john))=>(?[X]:(rich(X))))&
((?[X]:((strong(X)|brave(X))))<=>((~strong(mary)<~>~curious(mary))))&
((quiet(paul))=>(?[X]:((~strong(X)<~>~rich(X)))))&
((?[X]:((curious(X)<~>~old(X))))<=>((brave(paul)<~>generous(paul))))&
(((~old(fred)|happy(fred)))<=>((curious(mary)|strong(mary))))&
((?[X]:(rich(X)))=>((~funny(john)&~curious(john))))&
(![X]:((~curious(X)<~>happy(X))<=>(brave(X)|old(X))))&
(((creative(fred)|strong(fred)))=>((~patient(john)<~>brave(john))))&
(![X]:((kind(X)|~humble(X))<=>(quiet(X)&~brave(X))))&
((?[X]:((strong(X)<~>~curious(X))))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:(generous(X)<=>(old(X)<~>~happy(X))))&
(humble(paul))&
((brave(mary)|wise(mary)))&
((humble(john)|happy(john)))&
(?[X]:(~happy(X)))&
(?[X]:((~generous(X)<~>~happy(X))))&
((strong(mary)&~tall(mary))) | ~old(paul) | [
"p1",
"p3",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4470097631044271559463739
% SZS output start Proof for 4470097631044271559463739
2. ! [X0] : (calm(X0) <=> brave(X0)) [input p1]
4. ~generous(paul) <=> ~calm(paul) [input p3]
8. ? [X0] : (curious(X0) <~> ~old(X0)) <=> (brave(paul) <~> generous(paul)) [input p7]
11. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (old(X0) | brave(X0))) [input p10]
15. ! [X0] : (generous(X0) <=> (old(X0) <~> ~happy(X0))) [input p14]
22. ~old(paul) [input hypothesis]
34. ! [X0] : ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0))) [nnf transformation 2]
35. (~generous(paul) | calm(paul)) & (~calm(paul) | generous(paul)) [nnf transformation 4]
45. (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) [nnf transformation 8]
46. (? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) [rectify 45]
47. ? [X0] : ((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) => ((old(sK3) | ~curious(sK3)) & (~old(sK3) | curious(sK3))) [choice axiom]
48. (((old(sK3) | ~curious(sK3)) & (~old(sK3) | curious(sK3))) | ((brave(paul) | ~generous(paul)) & (generous(paul) | ~brave(paul)))) & (((~generous(paul) | ~brave(paul)) & (generous(paul) | brave(paul))) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) [skolemisation 46,47]
51. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 11]
52. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 51]
61. ! [X0] : ((generous(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | ~generous(X0))) [nnf transformation 15]
69. ~calm(X0) | brave(X0) [cnf transformation 34]
70. ~brave(X0) | calm(X0) [cnf transformation 34]
72. ~calm(paul) | generous(paul) [cnf transformation 35]
73. ~generous(paul) | calm(paul) [cnf transformation 35]
84. generous(paul) | brave(paul) | curious(X1) | old(X1) [cnf transformation 48]
86. ~generous(paul) | ~brave(paul) | curious(X1) | old(X1) [cnf transformation 48]
97. ~happy(X0) | brave(X0) | ~curious(X0) | old(X0) [cnf transformation 52]
98. ~curious(X0) | happy(X0) | ~brave(X0) [cnf transformation 52]
117. ~happy(X0) | old(X0) | ~generous(X0) [cnf transformation 61]
120. happy(X0) | old(X0) | generous(X0) [cnf transformation 61]
128. ~old(paul) [cnf transformation 22]
142. 4 <=> calm(paul) [avatar definition]
143. ~calm(paul) <- (~4) [avatar component clause 142]
144. calm(paul) <- (4) [avatar component clause 142]
146. 5 <=> generous(paul) [avatar definition]
147. generous(paul) <- (5) [avatar component clause 146]
149. 4 | ~5 [avatar split clause 73,146,142]
150. 5 | ~4 [avatar split clause 72,142,146]
203. 17 <=> brave(paul) [avatar definition]
204. ~brave(paul) <- (~17) [avatar component clause 203]
205. brave(paul) <- (17) [avatar component clause 203]
219. 20 <=> ! [X1] : (curious(X1) | old(X1)) [avatar definition]
220. old(X1) | curious(X1) <- (20) [avatar component clause 219]
221. 20 | ~17 | ~5 [avatar split clause 86,146,203,219]
226. 20 | 17 | 5 [avatar split clause 84,146,203,219]
314. brave(paul) <- (4) [resolution 69,144]
315. $false <- (4, ~17) [subsumption resolution 314,204]
316. ~4 | 17 [avatar contradiction clause 315]
317. calm(paul) <- (17) [resolution 70,205]
318. $false <- (~4, 17) [subsumption resolution 317,143]
319. 4 | ~17 [avatar contradiction clause 318]
321. curious(paul) <- (20) [resolution 220,128]
329. happy(paul) | ~brave(paul) <- (20) [resolution 98,321]
378. brave(X1) | ~curious(X1) | old(X1) | old(X1) | generous(X1) [resolution 97,120]
379. brave(X1) | ~curious(X1) | old(X1) | generous(X1) [duplicate literal removal 378]
381. old(X1) | brave(X1) | generous(X1) <- (20) [subsumption resolution 379,220]
395. brave(paul) | generous(paul) <- (20) [resolution 381,128]
404. 5 | 17 | ~20 [avatar split clause 395,219,203,146]
406. 46 <=> happy(paul) [avatar definition]
408. happy(paul) <- (46) [avatar component clause 406]
409. ~17 | 46 | ~20 [avatar split clause 329,219,406,203]
420. old(paul) | ~generous(paul) <- (46) [resolution 408,117]
423. ~generous(paul) <- (46) [subsumption resolution 420,128]
424. $false <- (5, 46) [subsumption resolution 423,147]
425. ~5 | ~46 [avatar contradiction clause 424]
426. $false [avatar sat refutation 149,150,221,226,316,319,404,409,425]
% SZS output end Proof for 4470097631044271559463739
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or funny is both not generous and not quiet and vice versa.
If lucy is rich then paul is either tall or generous and vice versa.
Everyone who is not brave is patient or wise and vice versa.
If someone is generous then someone is both not humble and not patient and vice versa.
Everyone who is generous or not rich is either not creative or funny.
Everyone who is either rich or not humble is strong or brave.
Everyone who is not generous or creative is not strong or not happy and vice versa.
If mary is both not quiet and not funny then lucy is both not curious and not funny.
Everyone who is brave or kind is either patient or wise.
Everyone who is old or curious is rich and vice versa.
Everyone who is both kind and not happy is either not funny or happy.
If alice is both kind and not kind then paul is either happy or tall and vice versa.
Everyone who is both quiet and not happy is both creative and calm.
Everyone who is either curious or brave is not brave or not humble.
Everyone who is either curious or not happy is not quiet and vice versa.
Everyone who is old or tall is either not rich or brave and vice versa.
Someone is either generous or not calm.
Paul is wise.
Paul is rich or not old.
Alice is both not curious and not brave.
Someone is generous or not tall.
Someone is both not tall and not old.
Someone is both curious and kind.
Someone is not wise. | Lucy is kind. | neutral | (![X]:((old(X)|funny(X))<=>(~generous(X)&~quiet(X))))&
((rich(lucy))<=>((tall(paul)<~>generous(paul))))&
(![X]:(~brave(X)<=>(patient(X)|wise(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:((generous(X)|~rich(X))=>(~creative(X)<~>funny(X))))&
(![X]:((rich(X)<~>~humble(X))=>(strong(X)|brave(X))))&
(![X]:((~generous(X)|creative(X))<=>(~strong(X)|~happy(X))))&
(((~quiet(mary)&~funny(mary)))=>((~curious(lucy)&~funny(lucy))))&
(![X]:((brave(X)|kind(X))=>(patient(X)<~>wise(X))))&
(![X]:((old(X)|curious(X))<=>rich(X)))&
(![X]:((kind(X)&~happy(X))=>(~funny(X)<~>happy(X))))&
(((kind(alice)&~kind(alice)))<=>((happy(paul)<~>tall(paul))))&
(![X]:((quiet(X)&~happy(X))=>(creative(X)&calm(X))))&
(![X]:((curious(X)<~>brave(X))=>(~brave(X)|~humble(X))))&
(![X]:((curious(X)<~>~happy(X))<=>~quiet(X)))&
(![X]:((old(X)|tall(X))<=>(~rich(X)<~>brave(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
(wise(paul))&
((rich(paul)|~old(paul)))&
((~curious(alice)&~brave(alice)))&
(?[X]:((generous(X)|~tall(X))))&
(?[X]:((~tall(X)&~old(X))))&
(?[X]:((curious(X)&kind(X))))&
(?[X]:(~wise(X))) | kind(lucy) | [] | null | 0 |
Everyone who is quiet is not rich or not old and vice versa. Everyone who is funny or strong is generous. Everyone who is not calm is creative or not old. If someone is not happy then someone is either not brave or not humble and vice versa. If john is either not curious or not patient then susan is not calm. Everyone who is funny or not kind is either not generous or not wise. If susan is not humble or kind then mary is either tall or not generous. Everyone who is wise or rich is tall and vice versa. If fred is either generous or curious then susan is not strong. Everyone who is not funny or humble is both not curious and humble. If lucy is not quiet or creative then someone is either not funny or not brave. If susan is either creative or funny then john is both not tall and calm. Everyone who is creative is brave or not brave. Everyone who is quiet or funny is either generous or calm. Everyone who is both not humble and rich is not quiet and vice versa. If someone is brave then alice is wise or humble. Someone is not wise or not funny. John is not quiet or rich. Someone is not tall. Alice is not strong or tall. John is either not humble or quiet. Someone is both old and not kind. Lucy is not quiet. | Lucy is creative. | entailment | (![X]:(quiet(X)<=>(~rich(X)|~old(X))))&
(![X]:((funny(X)|strong(X))=>generous(X)))&
(![X]:(~calm(X)=>(creative(X)|~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(((~curious(john)<~>~patient(john)))=>(~calm(susan)))&
(![X]:((funny(X)|~kind(X))=>(~generous(X)<~>~wise(X))))&
(((~humble(susan)|kind(susan)))=>((tall(mary)<~>~generous(mary))))&
(![X]:((wise(X)|rich(X))<=>tall(X)))&
(((generous(fred)<~>curious(fred)))=>(~strong(susan)))&
(![X]:((~funny(X)|humble(X))=>(~curious(X)&humble(X))))&
(((~quiet(lucy)|creative(lucy)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(((creative(susan)<~>funny(susan)))=>((~tall(john)&calm(john))))&
(![X]:(creative(X)=>(brave(X)|~brave(X))))&
(![X]:((quiet(X)|funny(X))=>(generous(X)<~>calm(X))))&
(![X]:((~humble(X)&rich(X))<=>~quiet(X)))&
((?[X]:(brave(X)))=>((wise(alice)|humble(alice))))&
(?[X]:((~wise(X)|~funny(X))))&
((~quiet(john)|rich(john)))&
(?[X]:(~tall(X)))&
((~strong(alice)|tall(alice)))&
((~humble(john)<~>quiet(john)))&
(?[X]:((old(X)&~kind(X))))&
(~quiet(lucy)) | creative(lucy) | [
"p0",
"p1",
"p2",
"p9",
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7675546753465886807648423
% SZS output start Proof for 7675546753465886807648423
1. ! [X0] : (quiet(X0) <=> (~old(X0) | ~rich(X0))) [input p0]
2. ! [X0] : ((strong(X0) | funny(X0)) => generous(X0)) [input p1]
3. ! [X0] : (~calm(X0) => (~old(X0) | creative(X0))) [input p2]
10. ! [X0] : ((humble(X0) | ~funny(X0)) => (humble(X0) & ~curious(X0))) [input p9]
14. ! [X0] : ((funny(X0) | quiet(X0)) => (generous(X0) <~> calm(X0))) [input p13]
15. ! [X0] : ((rich(X0) & ~humble(X0)) <=> ~quiet(X0)) [input p14]
23. ~quiet(lucy) [input p22]
24. ~creative(lucy) [input hypothesis]
26. ! [X0] : (funny(X0) => generous(X0)) [pure predicate removal 2]
29. ! [X0] : (generous(X0) | ~funny(X0)) [ennf transformation 26]
30. ! [X0] : ((~old(X0) | creative(X0)) | calm(X0)) [ennf transformation 3]
31. ! [X0] : (~old(X0) | creative(X0) | calm(X0)) [flattening 30]
35. ! [X0] : ((humble(X0) & ~curious(X0)) | (~humble(X0) & funny(X0))) [ennf transformation 10]
40. ! [X0] : ((generous(X0) <~> calm(X0)) | (~funny(X0) & ~quiet(X0))) [ennf transformation 14]
43. ! [X0] : ((quiet(X0) | (old(X0) & rich(X0))) & ((~old(X0) | ~rich(X0)) | ~quiet(X0))) [nnf transformation 1]
44. ! [X0] : ((quiet(X0) | (old(X0) & rich(X0))) & (~old(X0) | ~rich(X0) | ~quiet(X0))) [flattening 43]
59. ! [X0] : (((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (~funny(X0) & ~quiet(X0))) [nnf transformation 40]
60. ! [X0] : (((rich(X0) & ~humble(X0)) | quiet(X0)) & (~quiet(X0) | (~rich(X0) | humble(X0)))) [nnf transformation 15]
61. ! [X0] : (((rich(X0) & ~humble(X0)) | quiet(X0)) & (~quiet(X0) | ~rich(X0) | humble(X0))) [flattening 60]
71. old(X0) | quiet(X0) [cnf transformation 44]
72. ~funny(X0) | generous(X0) [cnf transformation 29]
73. ~old(X0) | creative(X0) | calm(X0) [cnf transformation 31]
93. humble(X0) | funny(X0) [cnf transformation 35]
107. ~calm(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 59]
109. ~humble(X0) | quiet(X0) [cnf transformation 61]
119. ~quiet(lucy) [cnf transformation 23]
120. ~creative(lucy) [cnf transformation 24]
182. 14 <=> creative(lucy) [avatar definition]
184. ~creative(lucy) <- (~14) [avatar component clause 182]
195. 17 <=> quiet(lucy) [avatar definition]
196. ~quiet(lucy) <- (~17) [avatar component clause 195]
221. ~calm(X0) | ~funny(X0) [subsumption resolution 107,72]
244. ~17 [avatar split clause 119,195]
245. ~14 [avatar split clause 120,182]
258. funny(X0) | quiet(X0) [resolution 109,93]
273. creative(X0) | calm(X0) | quiet(X0) [resolution 73,71]
338. calm(lucy) | quiet(lucy) <- (~14) [resolution 273,184]
340. calm(lucy) <- (~14, ~17) [subsumption resolution 338,196]
349. ~funny(lucy) <- (~14, ~17) [resolution 340,221]
358. quiet(lucy) <- (~14, ~17) [resolution 349,258]
359. $false <- (~14, ~17) [subsumption resolution 358,196]
360. 14 | 17 [avatar contradiction clause 359]
361. $false [avatar sat refutation 244,245,360]
% SZS output end Proof for 7675546753465886807648423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is tall or curious and vice versa.
Everyone who is both not patient and not brave is old or not curious and vice versa.
Everyone who is both not brave and not humble is not humble.
Everyone who is either not quiet or old is not creative and vice versa.
Everyone who is both not strong and not quiet is both not strong and creative.
If someone is either kind or not patient then someone is both not old and generous and vice versa.
If someone is either happy or generous then susan is rich and vice versa.
If lucy is either happy or not patient then someone is either old or not kind and vice versa.
If someone is both quiet and not happy then paul is not creative or not strong and vice versa.
If someone is curious or happy then susan is not generous and vice versa.
If paul is not creative then susan is both not calm and kind.
If mary is not happy or kind then lucy is both not patient and brave and vice versa.
If someone is both funny and not curious then fred is both not generous and not brave.
Everyone who is either not rich or strong is funny and vice versa.
Everyone who is either rich or not creative is generous or not calm and vice versa.
If someone is either not humble or patient then someone is either not rich or rich.
Lucy is not funny.
Someone is rich or happy.
Someone is either not creative or not old.
Someone is both wise and rich.
Someone is not kind or tall.
Someone is both not curious and happy.
Someone is either not quiet or not tall. | Paul is not quiet. | neutral | (![X]:(quiet(X)<=>(tall(X)|curious(X))))&
(![X]:((~patient(X)&~brave(X))<=>(old(X)|~curious(X))))&
(![X]:((~brave(X)&~humble(X))=>~humble(X)))&
(![X]:((~quiet(X)<~>old(X))<=>~creative(X)))&
(![X]:((~strong(X)&~quiet(X))=>(~strong(X)&creative(X))))&
((?[X]:((kind(X)<~>~patient(X))))<=>(?[X]:((~old(X)&generous(X)))))&
((?[X]:((happy(X)<~>generous(X))))<=>(rich(susan)))&
(((happy(lucy)<~>~patient(lucy)))<=>(?[X]:((old(X)<~>~kind(X)))))&
((?[X]:((quiet(X)&~happy(X))))<=>((~creative(paul)|~strong(paul))))&
((?[X]:((curious(X)|happy(X))))<=>(~generous(susan)))&
((~creative(paul))=>((~calm(susan)&kind(susan))))&
(((~happy(mary)|kind(mary)))<=>((~patient(lucy)&brave(lucy))))&
((?[X]:((funny(X)&~curious(X))))=>((~generous(fred)&~brave(fred))))&
(![X]:((~rich(X)<~>strong(X))<=>funny(X)))&
(![X]:((rich(X)<~>~creative(X))<=>(generous(X)|~calm(X))))&
((?[X]:((~humble(X)<~>patient(X))))=>(?[X]:((~rich(X)<~>rich(X)))))&
(~funny(lucy))&
(?[X]:((rich(X)|happy(X))))&
(?[X]:((~creative(X)<~>~old(X))))&
(?[X]:((wise(X)&rich(X))))&
(?[X]:((~kind(X)|tall(X))))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:((~quiet(X)<~>~tall(X)))) | ~quiet(paul) | [] | null | 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. | John is not creative. | 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)))) | ~creative(john) | [] | null | 0 |
Everyone who is both not strong and not quiet is not creative.
Everyone who is not old or happy is both not funny and tall and vice versa.
If someone is both happy and old then fred is rich or tall.
If someone is either humble or not generous then someone is strong or not happy.
Everyone who is not kind is both not tall and not quiet.
Everyone who is generous is either not old or not quiet.
If someone is either rich or not funny then someone is not tall and vice versa.
Everyone who is happy is not wise or strong.
If lucy is quiet or not kind then someone is not calm or strong.
If lucy is not creative or creative then someone is happy and vice versa.
If lucy is either not happy or not wise then someone is either not rich or not funny.
Everyone who is not strong or wise is either humble or not old and vice versa.
If someone is both not old and not wise then mary is not funny or tall and vice versa.
If mary is quiet then someone is not happy.
If fred is creative then lucy is not humble.
Everyone who is not funny or quiet is happy.
John is either not strong or not rich.
Someone is quiet or not funny.
Fred is both brave and strong.
Someone is not wise or not funny.
Mary is not generous.
Someone is not strong or tall.
Someone is wise or not patient.
Mary is either not old or not calm. | Lucy is not wise. | neutral | (![X]:((~strong(X)&~quiet(X))=>~creative(X)))&
(![X]:((~old(X)|happy(X))<=>(~funny(X)&tall(X))))&
((?[X]:((happy(X)&old(X))))=>((rich(fred)|tall(fred))))&
((?[X]:((humble(X)<~>~generous(X))))=>(?[X]:((strong(X)|~happy(X)))))&
(![X]:(~kind(X)=>(~tall(X)&~quiet(X))))&
(![X]:(generous(X)=>(~old(X)<~>~quiet(X))))&
((?[X]:((rich(X)<~>~funny(X))))<=>(?[X]:(~tall(X))))&
(![X]:(happy(X)=>(~wise(X)|strong(X))))&
(((quiet(lucy)|~kind(lucy)))=>(?[X]:((~calm(X)|strong(X)))))&
(((~creative(lucy)|creative(lucy)))<=>(?[X]:(happy(X))))&
(((~happy(lucy)<~>~wise(lucy)))=>(?[X]:((~rich(X)<~>~funny(X)))))&
(![X]:((~strong(X)|wise(X))<=>(humble(X)<~>~old(X))))&
((?[X]:((~old(X)&~wise(X))))<=>((~funny(mary)|tall(mary))))&
((quiet(mary))=>(?[X]:(~happy(X))))&
((creative(fred))=>(~humble(lucy)))&
(![X]:((~funny(X)|quiet(X))=>happy(X)))&
((~strong(john)<~>~rich(john)))&
(?[X]:((quiet(X)|~funny(X))))&
((brave(fred)&strong(fred)))&
(?[X]:((~wise(X)|~funny(X))))&
(~generous(mary))&
(?[X]:((~strong(X)|tall(X))))&
(?[X]:((wise(X)|~patient(X))))&
((~old(mary)<~>~calm(mary))) | ~wise(lucy) | [] | null | 0 |
If mary is not quiet then someone is tall or not quiet and vice versa.
Everyone who is not humble or creative is either not tall or patient.
Everyone who is not quiet or not happy is calm and vice versa.
If fred is not kind or kind then susan is not brave and vice versa.
If someone is not wise then lucy is either not patient or wise and vice versa.
If alice is either not calm or funny then someone is not calm or not funny and vice versa.
Everyone who is not quiet or wise is both brave and old.
If lucy is rich or tall then paul is not humble and vice versa.
Everyone who is creative is not patient.
Everyone who is strong is rich or not kind and vice versa.
Everyone who is both not patient and generous is not brave or curious and vice versa.
Everyone who is generous or funny is both not old and funny.
If someone is either funny or brave then susan is curious or funny.
If someone is funny then paul is both not brave and not rich and vice versa.
Everyone who is either humble or curious is both not wise and patient and vice versa.
If paul is both old and curious then someone is either creative or funny.
Someone is either not funny or not brave.
Paul is not old.
Fred is not rich.
Lucy is not brave.
Someone is happy.
Susan is either not old or not calm.
Someone is rich or not creative.
Mary is either not creative or funny. | Paul is quiet. | entailment | ((~quiet(mary))<=>(?[X]:((tall(X)|~quiet(X)))))&
(![X]:((~humble(X)|creative(X))=>(~tall(X)<~>patient(X))))&
(![X]:((~quiet(X)|~happy(X))<=>calm(X)))&
(((~kind(fred)|kind(fred)))<=>(~brave(susan)))&
((?[X]:(~wise(X)))<=>((~patient(lucy)<~>wise(lucy))))&
(((~calm(alice)<~>funny(alice)))<=>(?[X]:((~calm(X)|~funny(X)))))&
(![X]:((~quiet(X)|wise(X))=>(brave(X)&old(X))))&
(((rich(lucy)|tall(lucy)))<=>(~humble(paul)))&
(![X]:(creative(X)=>~patient(X)))&
(![X]:(strong(X)<=>(rich(X)|~kind(X))))&
(![X]:((~patient(X)&generous(X))<=>(~brave(X)|curious(X))))&
(![X]:((generous(X)|funny(X))=>(~old(X)&funny(X))))&
((?[X]:((funny(X)<~>brave(X))))=>((curious(susan)|funny(susan))))&
((?[X]:(funny(X)))<=>((~brave(paul)&~rich(paul))))&
(![X]:((humble(X)<~>curious(X))<=>(~wise(X)&patient(X))))&
(((old(paul)&curious(paul)))=>(?[X]:((creative(X)<~>funny(X)))))&
(?[X]:((~funny(X)<~>~brave(X))))&
(~old(paul))&
(~rich(fred))&
(~brave(lucy))&
(?[X]:(happy(X)))&
((~old(susan)<~>~calm(susan)))&
(?[X]:((rich(X)|~creative(X))))&
((~creative(mary)<~>funny(mary))) | quiet(paul) | [
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3248574193340989785358980
% SZS output start Proof for 3248574193340989785358980
7. ! [X0] : ((wise(X0) | ~quiet(X0)) => (old(X0) & brave(X0))) [input p6]
18. ~old(paul) [input p17]
25. ~quiet(paul) [input hypothesis]
27. ! [X0] : ((old(X0) & brave(X0)) | (~wise(X0) & quiet(X0))) [ennf transformation 7]
100. old(X0) | quiet(X0) [cnf transformation 27]
130. ~old(paul) [cnf transformation 18]
139. ~quiet(paul) [cnf transformation 25]
270. 29 <=> old(paul) [avatar definition]
272. ~old(paul) <- (~29) [avatar component clause 270]
297. ~29 [avatar split clause 130,270]
341. quiet(paul) <- (~29) [resolution 100,272]
342. $false <- (~29) [subsumption resolution 341,139]
343. 29 [avatar contradiction clause 342]
344. $false [avatar sat refutation 297,343]
% SZS output end Proof for 3248574193340989785358980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not strong and not patient then someone is tall or not patient and vice versa. Everyone who is not rich or curious is either old or rich and vice versa. If susan is not calm then john is brave. Everyone who is not quiet or creative is either not tall or not creative and vice versa. If someone is not funny then alice is calm and vice versa. Everyone who is both creative and old is both not calm and not curious. If john is either not old or not tall then someone is not curious or old. Everyone who is both not brave and curious is not tall and vice versa. If fred is creative then mary is generous and vice versa. Everyone who is not tall or not quiet is either happy or not calm and vice versa. Everyone who is either patient or curious is generous or wise. If someone is both kind and rich then someone is both rich and not generous and vice versa. Everyone who is strong or not strong is patient or not tall and vice versa. If someone is either generous or kind then fred is calm or tall. If someone is not wise or not brave then john is both not happy and not calm. Everyone who is either old or brave is not kind. Someone is both not generous and calm. Someone is either patient or not generous. Someone is curious. John is either patient or not rich. Someone is either not generous or curious. Mary is both not creative and not rich. Paul is tall. Someone is quiet. | John is quiet. | entailment | (((~strong(john)&~patient(john)))<=>(?[X]:((tall(X)|~patient(X)))))&
(![X]:((~rich(X)|curious(X))<=>(old(X)<~>rich(X))))&
((~calm(susan))=>(brave(john)))&
(![X]:((~quiet(X)|creative(X))<=>(~tall(X)<~>~creative(X))))&
((?[X]:(~funny(X)))<=>(calm(alice)))&
(![X]:((creative(X)&old(X))=>(~calm(X)&~curious(X))))&
(((~old(john)<~>~tall(john)))=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((~brave(X)&curious(X))<=>~tall(X)))&
((creative(fred))<=>(generous(mary)))&
(![X]:((~tall(X)|~quiet(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((patient(X)<~>curious(X))=>(generous(X)|wise(X))))&
((?[X]:((kind(X)&rich(X))))<=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((strong(X)|~strong(X))<=>(patient(X)|~tall(X))))&
((?[X]:((generous(X)<~>kind(X))))=>((calm(fred)|tall(fred))))&
((?[X]:((~wise(X)|~brave(X))))=>((~happy(john)&~calm(john))))&
(![X]:((old(X)<~>brave(X))=>~kind(X)))&
(?[X]:((~generous(X)&calm(X))))&
(?[X]:((patient(X)<~>~generous(X))))&
(?[X]:(curious(X)))&
((patient(john)<~>~rich(john)))&
(?[X]:((~generous(X)<~>curious(X))))&
((~creative(mary)&~rich(mary)))&
(tall(paul))&
(?[X]:(quiet(X))) | quiet(john) | [
"p0",
"p1",
"p3",
"p5",
"p7",
"p12",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2138513758743714837459155
% SZS output start Proof for 2138513758743714837459155
1. (~patient(john) & ~strong(john)) <=> ? [X0] : (~patient(X0) | tall(X0)) [input p0]
2. ! [X0] : ((curious(X0) | ~rich(X0)) <=> (old(X0) <~> rich(X0))) [input p1]
4. ! [X0] : ((creative(X0) | ~quiet(X0)) <=> (~tall(X0) <~> ~creative(X0))) [input p3]
6. ! [X0] : ((old(X0) & creative(X0)) => (~curious(X0) & ~calm(X0))) [input p5]
8. ! [X0] : ((curious(X0) & ~brave(X0)) <=> ~tall(X0)) [input p7]
13. ! [X0] : ((~strong(X0) | strong(X0)) <=> (~tall(X0) | patient(X0))) [input p12]
20. patient(john) <~> ~rich(john) [input p19]
23. tall(paul) [input p22]
25. ~quiet(john) [input hypothesis]
30. ! [X0] : ((~curious(X0) & ~calm(X0)) | (~old(X0) | ~creative(X0))) [ennf transformation 6]
31. ! [X0] : ((~curious(X0) & ~calm(X0)) | ~old(X0) | ~creative(X0)) [flattening 30]
37. ((~patient(john) & ~strong(john)) | ! [X0] : (patient(X0) & ~tall(X0))) & (? [X0] : (~patient(X0) | tall(X0)) | (patient(john) | strong(john))) [nnf transformation 1]
38. ((~patient(john) & ~strong(john)) | ! [X0] : (patient(X0) & ~tall(X0))) & (? [X0] : (~patient(X0) | tall(X0)) | patient(john) | strong(john)) [flattening 37]
39. ((~patient(john) & ~strong(john)) | ! [X0] : (patient(X0) & ~tall(X0))) & (? [X1] : (~patient(X1) | tall(X1)) | patient(john) | strong(john)) [rectify 38]
40. ? [X1] : (~patient(X1) | tall(X1)) => (~patient(sK0) | tall(sK0)) [choice axiom]
41. ((~patient(john) & ~strong(john)) | ! [X0] : (patient(X0) & ~tall(X0))) & ((~patient(sK0) | tall(sK0)) | patient(john) | strong(john)) [skolemisation 39,40]
42. ! [X0] : (((curious(X0) | ~rich(X0)) | ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0)))) & (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (~curious(X0) & rich(X0)))) [nnf transformation 2]
43. ! [X0] : ((curious(X0) | ~rich(X0) | ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0)))) & (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (~curious(X0) & rich(X0)))) [flattening 42]
44. ! [X0] : (((creative(X0) | ~quiet(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~creative(X0) & quiet(X0)))) [nnf transformation 4]
45. ! [X0] : ((creative(X0) | ~quiet(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) & (((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~creative(X0) & quiet(X0)))) [flattening 44]
53. ! [X0] : (((curious(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | (~curious(X0) | brave(X0)))) [nnf transformation 8]
54. ! [X0] : (((curious(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | ~curious(X0) | brave(X0))) [flattening 53]
63. ! [X0] : (((~strong(X0) | strong(X0)) | (tall(X0) & ~patient(X0))) & ((~tall(X0) | patient(X0)) | (strong(X0) & ~strong(X0)))) [nnf transformation 13]
64. ! [X0] : ((~strong(X0) | strong(X0) | (tall(X0) & ~patient(X0))) & (~tall(X0) | patient(X0) | (strong(X0) & ~strong(X0)))) [flattening 63]
74. (rich(john) | ~patient(john)) & (~rich(john) | patient(john)) [nnf transformation 20]
83. ~patient(john) | ~tall(X0) [cnf transformation 41]
85. rich(X0) | old(X0) | rich(X0) [cnf transformation 43]
94. creative(X0) | tall(X0) | quiet(X0) [cnf transformation 45]
101. ~creative(X0) | ~old(X0) | ~curious(X0) [cnf transformation 31]
106. curious(X0) | tall(X0) [cnf transformation 54]
119. ~tall(X0) | patient(X0) | ~strong(X0) [cnf transformation 64]
120. ~tall(X0) | patient(X0) | strong(X0) [cnf transformation 64]
134. ~rich(john) | patient(john) [cnf transformation 74]
140. tall(paul) [cnf transformation 23]
142. ~quiet(john) [cnf transformation 25]
145. old(X0) | rich(X0) [duplicate literal removal 85]
151. 2 <=> patient(john) [avatar definition]
153. ~patient(john) <- (~2) [avatar component clause 151]
156. 3 <=> ! [X0] : ~tall(X0) [avatar definition]
157. ~tall(X0) <- (3) [avatar component clause 156]
158. 3 | ~2 [avatar split clause 83,151,156]
197. 12 <=> tall(john) [avatar definition]
199. tall(john) <- (12) [avatar component clause 197]
250. ~tall(X0) | patient(X0) [subsumption resolution 119,120]
291. 33 <=> rich(john) [avatar definition]
295. 2 | ~33 [avatar split clause 134,291,151]
336. ~old(X0) | ~curious(X0) | tall(X0) | quiet(X0) [resolution 101,94]
338. ~old(X0) | tall(X0) | quiet(X0) [subsumption resolution 336,106]
449. quiet(X0) | tall(X0) | rich(X0) [resolution 338,145]
459. tall(john) | rich(john) [resolution 449,142]
464. 33 | 12 [avatar split clause 459,197,291]
471. $false <- (3) [resolution 157,140]
476. ~3 [avatar contradiction clause 471]
484. patient(john) <- (12) [resolution 199,250]
488. $false <- (~2, 12) [subsumption resolution 484,153]
489. 2 | ~12 [avatar contradiction clause 488]
490. $false [avatar sat refutation 158,295,464,476,489]
% SZS output end Proof for 2138513758743714837459155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble and strong is both tall and not brave. If someone is funny or curious then lucy is not humble or patient and vice versa. If someone is kind or rich then someone is either wise or not creative and vice versa. If susan is humble or patient then someone is both happy and not curious. If someone is not calm then mary is either curious or not patient. Everyone who is creative or not patient is either brave or creative. Everyone who is generous or humble is tall. Everyone who is not rich or not old is patient and vice versa. If someone is not tall or brave then someone is either quiet or not calm. Everyone who is not creative is either patient or not creative and vice versa. If paul is both not curious and not creative then alice is both not funny and wise. If someone is either curious or old then someone is both not kind and not generous. Everyone who is tall is not generous and vice versa. Everyone who is either patient or not strong is both not funny and creative and vice versa. If lucy is both patient and strong then someone is either creative or not strong and vice versa. Everyone who is both happy and not funny is not strong or old and vice versa. Someone is not wise. Mary is either not old or not quiet. Lucy is both not kind and calm. Alice is not funny or humble. Someone is not quiet. Someone is kind or brave. | Susan is not patient. | entailment | (![X]:((~humble(X)&strong(X))=>(tall(X)&~brave(X))))&
((?[X]:((funny(X)|curious(X))))<=>((~humble(lucy)|patient(lucy))))&
((?[X]:((kind(X)|rich(X))))<=>(?[X]:((wise(X)<~>~creative(X)))))&
(((humble(susan)|patient(susan)))=>(?[X]:((happy(X)&~curious(X)))))&
((?[X]:(~calm(X)))=>((curious(mary)<~>~patient(mary))))&
(![X]:((creative(X)|~patient(X))=>(brave(X)<~>creative(X))))&
(![X]:((generous(X)|humble(X))=>tall(X)))&
(![X]:((~rich(X)|~old(X))<=>patient(X)))&
((?[X]:((~tall(X)|brave(X))))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:(~creative(X)<=>(patient(X)<~>~creative(X))))&
(((~curious(paul)&~creative(paul)))=>((~funny(alice)&wise(alice))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~funny(X)&creative(X))))&
(((patient(lucy)&strong(lucy)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(![X]:((happy(X)&~funny(X))<=>(~strong(X)|old(X))))&
(?[X]:(~wise(X)))&
((~old(mary)<~>~quiet(mary)))&
((~kind(lucy)&calm(lucy)))&
((~funny(alice)|humble(alice)))&
(?[X]:(~quiet(X)))&
(?[X]:((kind(X)|brave(X)))) | ~patient(susan) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5405492117350498917749808
% SZS output start Proof for 5405492117350498917749808
10. ! [X0] : (~creative(X0) <=> (patient(X0) <~> ~creative(X0))) [input p9]
23. patient(susan) [input hypothesis]
63. ! [X0] : ((~creative(X0) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) & (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | creative(X0))) [nnf transformation 10]
111. creative(X0) | ~patient(X0) | creative(X0) [cnf transformation 63]
112. ~creative(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 63]
143. patient(susan) [cnf transformation 23]
144. creative(X0) | ~patient(X0) [duplicate literal removal 111]
145. ~creative(X0) | ~patient(X0) [duplicate literal removal 112]
253. ~patient(X0) [subsumption resolution 144,145]
321. $false [subsumption resolution 143,253]
% SZS output end Proof for 5405492117350498917749808
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not rich is not happy or creative.
Everyone who is tall is not tall.
If john is either humble or not strong then fred is either patient or calm and vice versa.
Everyone who is either not kind or not humble is not kind.
If mary is both rich and funny then someone is not quiet or funny.
If someone is kind then someone is both not wise and happy.
If someone is either wise or happy then john is both quiet and not humble.
Everyone who is both not humble and strong is not curious.
Everyone who is not tall is both rich and quiet and vice versa.
If someone is both not generous and not wise then someone is either not kind or not quiet and vice versa.
If someone is both not patient and not tall then alice is both quiet and not brave and vice versa.
If lucy is either not humble or not funny then someone is strong and vice versa.
If john is both not tall and not generous then someone is strong or not rich.
If someone is not calm then someone is rich or kind.
Paul is funny.
Someone is both not happy and not old.
Paul is not patient.
Paul is old or not humble.
Someone is brave or not curious.
Someone is either funny or tall. | Fred is humble. | neutral | (![X]:((~strong(X)&~rich(X))=>(~happy(X)|creative(X))))&
(![X]:(tall(X)=>~tall(X)))&
(((humble(john)<~>~strong(john)))<=>((patient(fred)<~>calm(fred))))&
(![X]:((~kind(X)<~>~humble(X))=>~kind(X)))&
(((rich(mary)&funny(mary)))=>(?[X]:((~quiet(X)|funny(X)))))&
((?[X]:(kind(X)))=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:((wise(X)<~>happy(X))))=>((quiet(john)&~humble(john))))&
(![X]:((~humble(X)&strong(X))=>~curious(X)))&
(![X]:(~tall(X)<=>(rich(X)&quiet(X))))&
((?[X]:((~generous(X)&~wise(X))))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((?[X]:((~patient(X)&~tall(X))))<=>((quiet(alice)&~brave(alice))))&
(((~humble(lucy)<~>~funny(lucy)))<=>(?[X]:(strong(X))))&
(((~tall(john)&~generous(john)))=>(?[X]:((strong(X)|~rich(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(funny(paul))&
(?[X]:((~happy(X)&~old(X))))&
(~patient(paul))&
((old(paul)|~humble(paul)))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X)))) | humble(fred) | [] | null | 0 |
If someone is kind then someone is either wise or patient and vice versa. Everyone who is not creative is brave or not calm and vice versa. Everyone who is not generous or not creative is old or not humble. If someone is either not funny or creative then someone is not humble and vice versa. Everyone who is either kind or curious is both not creative and not kind. Everyone who is both not calm and not generous is both rich and not strong. Everyone who is not calm or not funny is both kind and rich and vice versa. Everyone who is not happy is not wise. If mary is both not tall and kind then lucy is tall. Everyone who is both not kind and old is generous and vice versa. Everyone who is both patient and not funny is old. If susan is not humble then someone is not tall or not kind. If someone is either humble or brave then someone is both not old and humble and vice versa. Everyone who is both funny and kind is not strong or not patient and vice versa. If paul is either not kind or not tall then someone is humble or not kind and vice versa. Everyone who is curious is either not old or not kind and vice versa. Someone is not quiet or funny. Someone is both quiet and funny. Someone is not creative. John is curious or not wise. Someone is not humble or old. Fred is either not curious or creative. Someone is old. Paul is not humble. | Fred is funny. | entailment | ((?[X]:(kind(X)))<=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:(~creative(X)<=>(brave(X)|~calm(X))))&
(![X]:((~generous(X)|~creative(X))=>(old(X)|~humble(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>(?[X]:(~humble(X))))&
(![X]:((kind(X)<~>curious(X))=>(~creative(X)&~kind(X))))&
(![X]:((~calm(X)&~generous(X))=>(rich(X)&~strong(X))))&
(![X]:((~calm(X)|~funny(X))<=>(kind(X)&rich(X))))&
(![X]:(~happy(X)=>~wise(X)))&
(((~tall(mary)&kind(mary)))=>(tall(lucy)))&
(![X]:((~kind(X)&old(X))<=>generous(X)))&
(![X]:((patient(X)&~funny(X))=>old(X)))&
((~humble(susan))=>(?[X]:((~tall(X)|~kind(X)))))&
((?[X]:((humble(X)<~>brave(X))))<=>(?[X]:((~old(X)&humble(X)))))&
(![X]:((funny(X)&kind(X))<=>(~strong(X)|~patient(X))))&
(((~kind(paul)<~>~tall(paul)))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:(curious(X)<=>(~old(X)<~>~kind(X))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:(~creative(X)))&
((curious(john)|~wise(john)))&
(?[X]:((~humble(X)|old(X))))&
((~curious(fred)<~>creative(fred)))&
(?[X]:(old(X)))&
(~humble(paul)) | funny(fred) | [
"p4",
"p6",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5007004273237308059427682
% SZS output start Proof for 5007004273237308059427682
5. ! [X0] : ((kind(X0) <~> curious(X0)) => (~kind(X0) & ~creative(X0))) [input p4]
7. ! [X0] : ((~funny(X0) | ~calm(X0)) <=> (rich(X0) & kind(X0))) [input p6]
11. ! [X0] : ((~funny(X0) & patient(X0)) => old(X0)) [input p10]
14. ! [X0] : ((kind(X0) & funny(X0)) <=> (~patient(X0) | ~strong(X0))) [input p13]
16. ! [X0] : (curious(X0) <=> (~old(X0) <~> ~kind(X0))) [input p15]
25. ~funny(fred) [input hypothesis]
33. ! [X0] : ((~kind(X0) & ~creative(X0)) | (kind(X0) <=> curious(X0))) [ennf transformation 5]
39. ! [X0] : (old(X0) | (funny(X0) | ~patient(X0))) [ennf transformation 11]
40. ! [X0] : (old(X0) | funny(X0) | ~patient(X0)) [flattening 39]
54. ! [X0] : ((~kind(X0) & ~creative(X0)) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0)))) [nnf transformation 33]
55. ! [X0] : (((~funny(X0) | ~calm(X0)) | (~rich(X0) | ~kind(X0))) & ((rich(X0) & kind(X0)) | (funny(X0) & calm(X0)))) [nnf transformation 7]
56. ! [X0] : ((~funny(X0) | ~calm(X0) | ~rich(X0) | ~kind(X0)) & ((rich(X0) & kind(X0)) | (funny(X0) & calm(X0)))) [flattening 55]
64. ! [X0] : (((kind(X0) & funny(X0)) | (patient(X0) & strong(X0))) & ((~patient(X0) | ~strong(X0)) | (~kind(X0) | ~funny(X0)))) [nnf transformation 14]
65. ! [X0] : (((kind(X0) & funny(X0)) | (patient(X0) & strong(X0))) & (~patient(X0) | ~strong(X0) | ~kind(X0) | ~funny(X0))) [flattening 64]
70. ! [X0] : ((curious(X0) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) & (((kind(X0) | old(X0)) & (~kind(X0) | ~old(X0))) | ~curious(X0))) [nnf transformation 16]
97. ~kind(X0) | curious(X0) | ~kind(X0) [cnf transformation 54]
102. funny(X0) | kind(X0) [cnf transformation 56]
109. ~patient(X0) | funny(X0) | old(X0) [cnf transformation 40]
119. funny(X0) | patient(X0) [cnf transformation 65]
128. ~kind(X0) | ~old(X0) | ~curious(X0) [cnf transformation 70]
131. curious(X0) | ~old(X0) | kind(X0) [cnf transformation 70]
142. ~funny(fred) [cnf transformation 25]
143. ~kind(X0) | curious(X0) [duplicate literal removal 97]
279. ~old(X0) | curious(X0) [subsumption resolution 131,143]
280. ~old(X0) | ~kind(X0) [subsumption resolution 128,279]
320. kind(fred) [resolution 102,142]
322. patient(fred) [resolution 119,142]
371. funny(fred) | old(fred) [resolution 109,322]
374. old(fred) [subsumption resolution 371,142]
383. ~kind(fred) [resolution 374,280]
385. $false [subsumption resolution 383,320]
% SZS output end Proof for 5007004273237308059427682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is tall or not patient then paul is not kind or happy and vice versa. Everyone who is quiet is kind. Everyone who is either rich or funny is either strong or generous and vice versa. Everyone who is either tall or creative is quiet or not strong. Everyone who is both not tall and wise is not curious and vice versa. Everyone who is generous is brave or old and vice versa. Everyone who is not rich or brave is either brave or not old and vice versa. Everyone who is not humble is kind. If alice is either not quiet or humble then someone is both tall and old and vice versa. Everyone who is creative is either not curious or not funny. Everyone who is both kind and generous is not brave or tall and vice versa. If fred is kind then susan is not curious. If someone is either strong or not quiet then someone is either brave or not rich. If someone is not creative or quiet then john is not generous and vice versa. Everyone who is both creative and not rich is both not wise and not curious and vice versa. If john is either funny or happy then someone is not humble and vice versa. Alice is either not patient or strong. Lucy is either not tall or not curious. Someone is not strong or generous. Alice is either not funny or funny. Someone is old. | Paul is not quiet. | entailment | (((tall(fred)|~patient(fred)))<=>((~kind(paul)|happy(paul))))&
(![X]:(quiet(X)=>kind(X)))&
(![X]:((rich(X)<~>funny(X))<=>(strong(X)<~>generous(X))))&
(![X]:((tall(X)<~>creative(X))=>(quiet(X)|~strong(X))))&
(![X]:((~tall(X)&wise(X))<=>~curious(X)))&
(![X]:(generous(X)<=>(brave(X)|old(X))))&
(![X]:((~rich(X)|brave(X))<=>(brave(X)<~>~old(X))))&
(![X]:(~humble(X)=>kind(X)))&
(((~quiet(alice)<~>humble(alice)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:(creative(X)=>(~curious(X)<~>~funny(X))))&
(![X]:((kind(X)&generous(X))<=>(~brave(X)|tall(X))))&
((kind(fred))=>(~curious(susan)))&
((?[X]:((strong(X)<~>~quiet(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
((?[X]:((~creative(X)|quiet(X))))<=>(~generous(john)))&
(![X]:((creative(X)&~rich(X))<=>(~wise(X)&~curious(X))))&
(((funny(john)<~>happy(john)))<=>(?[X]:(~humble(X))))&
((~patient(alice)<~>strong(alice)))&
((~tall(lucy)<~>~curious(lucy)))&
(?[X]:((~strong(X)|generous(X))))&
((~funny(alice)<~>funny(alice)))&
(?[X]:(old(X))) | ~quiet(paul) | [
"p5",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8712404688983749279995791
% SZS output start Proof for 8712404688983749279995791
6. ! [X0] : (generous(X0) <=> (old(X0) | brave(X0))) [input p5]
11. ! [X0] : ((generous(X0) & kind(X0)) <=> (tall(X0) | ~brave(X0))) [input p10]
14. ? [X0] : (quiet(X0) | ~creative(X0)) <=> ~generous(john) [input p13]
22. quiet(paul) [input hypothesis]
37. ! [X0] : ((generous(X0) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | ~generous(X0))) [nnf transformation 6]
38. ! [X0] : ((generous(X0) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ~generous(X0))) [flattening 37]
46. ! [X0] : (((generous(X0) & kind(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (~generous(X0) | ~kind(X0)))) [nnf transformation 11]
47. ! [X0] : (((generous(X0) & kind(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | ~generous(X0) | ~kind(X0))) [flattening 46]
52. (? [X0] : (quiet(X0) | ~creative(X0)) | generous(john)) & (~generous(john) | ! [X0] : (~quiet(X0) & creative(X0))) [nnf transformation 14]
53. (? [X0] : (quiet(X0) | ~creative(X0)) | generous(john)) & (~generous(john) | ! [X1] : (~quiet(X1) & creative(X1))) [rectify 52]
54. ? [X0] : (quiet(X0) | ~creative(X0)) => (quiet(sK2) | ~creative(sK2)) [choice axiom]
55. ((quiet(sK2) | ~creative(sK2)) | generous(john)) & (~generous(john) | ! [X1] : (~quiet(X1) & creative(X1))) [skolemisation 53,54]
88. generous(X0) | ~brave(X0) [cnf transformation 38]
108. generous(X0) | brave(X0) [cnf transformation 47]
116. ~generous(john) | ~quiet(X1) [cnf transformation 55]
134. quiet(paul) [cnf transformation 22]
182. generous(X0) [subsumption resolution 108,88]
211. ~quiet(X1) [subsumption resolution 116,182]
246. $false [subsumption resolution 134,211]
% SZS output end Proof for 8712404688983749279995791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not creative and not calm then someone is either old or not brave and vice versa.
Everyone who is either brave or not wise is not funny or strong and vice versa.
Everyone who is quiet is not funny and vice versa.
Everyone who is not creative is either strong or patient and vice versa.
Everyone who is both not wise and not brave is brave and vice versa.
Everyone who is both kind and not old is both not kind and humble.
If lucy is both not patient and creative then someone is tall or brave and vice versa.
Everyone who is not brave or not kind is curious or not rich and vice versa.
Everyone who is not calm or creative is not wise or brave and vice versa.
If someone is either rich or brave then lucy is both humble and calm and vice versa.
Everyone who is both not quiet and not wise is not old or strong and vice versa.
Everyone who is both not kind and not curious is brave.
If alice is not patient then someone is humble and vice versa.
If someone is either creative or not calm then someone is quiet or not rich.
Someone is wise or not happy.
Alice is calm or not creative.
Someone is either wise or brave.
Someone is both not brave and not tall.
John is either calm or rich. | Mary is brave. | contradiction | (((~creative(mary)&~calm(mary)))<=>(?[X]:((old(X)<~>~brave(X)))))&
(![X]:((brave(X)<~>~wise(X))<=>(~funny(X)|strong(X))))&
(![X]:(quiet(X)<=>~funny(X)))&
(![X]:(~creative(X)<=>(strong(X)<~>patient(X))))&
(![X]:((~wise(X)&~brave(X))<=>brave(X)))&
(![X]:((kind(X)&~old(X))=>(~kind(X)&humble(X))))&
(((~patient(lucy)&creative(lucy)))<=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~brave(X)|~kind(X))<=>(curious(X)|~rich(X))))&
(![X]:((~calm(X)|creative(X))<=>(~wise(X)|brave(X))))&
((?[X]:((rich(X)<~>brave(X))))<=>((humble(lucy)&calm(lucy))))&
(![X]:((~quiet(X)&~wise(X))<=>(~old(X)|strong(X))))&
(![X]:((~kind(X)&~curious(X))=>brave(X)))&
((~patient(alice))<=>(?[X]:(humble(X))))&
((?[X]:((creative(X)<~>~calm(X))))=>(?[X]:((quiet(X)|~rich(X)))))&
(?[X]:((wise(X)|~happy(X))))&
((calm(alice)|~creative(alice)))&
(?[X]:((wise(X)<~>brave(X))))&
(?[X]:((~brave(X)&~tall(X))))&
((calm(john)<~>rich(john))) | brave(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7689789864184120455200100
% SZS output start Proof for 7689789864184120455200100
5. ! [X0] : ((~brave(X0) & ~wise(X0)) <=> brave(X0)) [input p4]
20. brave(mary) [input hypothesis]
37. ! [X0] : (((~brave(X0) & ~wise(X0)) | ~brave(X0)) & (brave(X0) | (brave(X0) | wise(X0)))) [nnf transformation 5]
38. ! [X0] : (((~brave(X0) & ~wise(X0)) | ~brave(X0)) & (brave(X0) | brave(X0) | wise(X0))) [flattening 37]
89. ~brave(X0) | ~brave(X0) [cnf transformation 38]
128. brave(mary) [cnf transformation 20]
131. ~brave(X0) [duplicate literal removal 89]
218. $false [subsumption resolution 128,131]
% SZS output end Proof for 7689789864184120455200100
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or brave is both strong and not strong.
If alice is not generous or patient then someone is old or brave and vice versa.
Everyone who is not happy or not creative is both kind and generous and vice versa.
If someone is either not tall or calm then someone is both rich and creative.
If alice is either not brave or not rich then alice is either curious or not rich and vice versa.
If lucy is both not quiet and not strong then lucy is old.
Everyone who is both not old and patient is tall and vice versa.
If someone is either strong or rich then alice is patient.
If someone is either not strong or patient then alice is calm and vice versa.
Everyone who is not curious is both not curious and old and vice versa.
Everyone who is wise is creative or rich and vice versa.
Everyone who is either tall or not kind is not funny or tall and vice versa.
Everyone who is either not creative or not calm is old.
If paul is not quiet then someone is not curious or brave and vice versa.
Everyone who is not quiet or not brave is quiet.
If someone is not calm then fred is generous and vice versa.
Someone is both not happy and not creative.
Someone is kind.
Fred is not strong or curious.
Someone is wise or brave.
Someone is both not wise and curious.
Someone is generous. | Fred is not tall. | entailment | (![X]:((patient(X)<~>brave(X))=>(strong(X)&~strong(X))))&
(((~generous(alice)|patient(alice)))<=>(?[X]:((old(X)|brave(X)))))&
(![X]:((~happy(X)|~creative(X))<=>(kind(X)&generous(X))))&
((?[X]:((~tall(X)<~>calm(X))))=>(?[X]:((rich(X)&creative(X)))))&
(((~brave(alice)<~>~rich(alice)))<=>((curious(alice)<~>~rich(alice))))&
(((~quiet(lucy)&~strong(lucy)))=>(old(lucy)))&
(![X]:((~old(X)&patient(X))<=>tall(X)))&
((?[X]:((strong(X)<~>rich(X))))=>(patient(alice)))&
((?[X]:((~strong(X)<~>patient(X))))<=>(calm(alice)))&
(![X]:(~curious(X)<=>(~curious(X)&old(X))))&
(![X]:(wise(X)<=>(creative(X)|rich(X))))&
(![X]:((tall(X)<~>~kind(X))<=>(~funny(X)|tall(X))))&
(![X]:((~creative(X)<~>~calm(X))=>old(X)))&
((~quiet(paul))<=>(?[X]:((~curious(X)|brave(X)))))&
(![X]:((~quiet(X)|~brave(X))=>quiet(X)))&
((?[X]:(~calm(X)))<=>(generous(fred)))&
(?[X]:((~happy(X)&~creative(X))))&
(?[X]:(kind(X)))&
((~strong(fred)|curious(fred)))&
(?[X]:((wise(X)|brave(X))))&
(?[X]:((~wise(X)&curious(X))))&
(?[X]:(generous(X))) | ~tall(fred) | [
"p0",
"p6",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1084237079247401750925184
% SZS output start Proof for 1084237079247401750925184
1. ! [X0] : ((patient(X0) <~> brave(X0)) => (~strong(X0) & strong(X0))) [input p0]
7. ! [X0] : ((patient(X0) & ~old(X0)) <=> tall(X0)) [input p6]
14. ~quiet(paul) <=> ? [X0] : (brave(X0) | ~curious(X0)) [input p13]
15. ! [X0] : ((~brave(X0) | ~quiet(X0)) => quiet(X0)) [input p14]
23. tall(fred) [input hypothesis]
25. ! [X0] : ((~strong(X0) & strong(X0)) | (patient(X0) <=> brave(X0))) [ennf transformation 1]
31. ! [X0] : (quiet(X0) | (brave(X0) & quiet(X0))) [ennf transformation 15]
32. ! [X0] : ((~strong(X0) & strong(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) [nnf transformation 25]
45. ! [X0] : (((patient(X0) & ~old(X0)) | ~tall(X0)) & (tall(X0) | (~patient(X0) | old(X0)))) [nnf transformation 7]
46. ! [X0] : (((patient(X0) & ~old(X0)) | ~tall(X0)) & (tall(X0) | ~patient(X0) | old(X0))) [flattening 45]
59. (~quiet(paul) | ! [X0] : (~brave(X0) & curious(X0))) & (? [X0] : (brave(X0) | ~curious(X0)) | quiet(paul)) [nnf transformation 14]
60. (~quiet(paul) | ! [X0] : (~brave(X0) & curious(X0))) & (? [X1] : (brave(X1) | ~curious(X1)) | quiet(paul)) [rectify 59]
61. ? [X1] : (brave(X1) | ~curious(X1)) => (brave(sK3) | ~curious(sK3)) [choice axiom]
62. (~quiet(paul) | ! [X0] : (~brave(X0) & curious(X0))) & ((brave(sK3) | ~curious(sK3)) | quiet(paul)) [skolemisation 60,61]
77. strong(X0) | brave(X0) | ~patient(X0) [cnf transformation 32]
79. ~strong(X0) | brave(X0) | ~patient(X0) [cnf transformation 32]
105. ~tall(X0) | patient(X0) [cnf transformation 46]
128. ~quiet(paul) | ~brave(X0) [cnf transformation 62]
129. quiet(X0) | quiet(X0) [cnf transformation 31]
141. tall(fred) [cnf transformation 23]
142. quiet(X0) [duplicate literal removal 129]
150. ~patient(X0) | brave(X0) [subsumption resolution 77,79]
152. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
153. ~brave(X0) <- (1) [avatar component clause 152]
256. 24 <=> quiet(paul) [avatar definition]
258. ~quiet(paul) <- (~24) [avatar component clause 256]
259. 1 | ~24 [avatar split clause 128,256,152]
304. $false <- (~24) [subsumption resolution 258,142]
305. 24 [avatar contradiction clause 304]
311. patient(fred) [resolution 105,141]
315. brave(fred) [resolution 150,311]
318. $false <- (1) [subsumption resolution 315,153]
319. ~1 [avatar contradiction clause 318]
320. $false [avatar sat refutation 259,305,319]
% SZS output end Proof for 1084237079247401750925184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both quiet and not tall.
If alice is both not calm and old then someone is quiet and vice versa.
Everyone who is generous or not humble is either humble or strong and vice versa.
Everyone who is not happy or not patient is not quiet and vice versa.
Everyone who is both not brave and not curious is humble and vice versa.
Everyone who is not calm or not strong is both happy and not tall and vice versa.
If someone is quiet then fred is not generous or tall and vice versa.
Everyone who is both not tall and humble is both kind and curious and vice versa.
If fred is generous then someone is not wise and vice versa.
If someone is either not brave or curious then lucy is either not tall or not strong and vice versa.
Everyone who is either not generous or quiet is either old or not rich.
If someone is not funny then susan is both not patient and happy.
Everyone who is not quiet or kind is either happy or not creative and vice versa.
Everyone who is not kind or creative is not quiet and vice versa.
Everyone who is either not patient or not generous is either not creative or tall.
Someone is both tall and not happy.
Someone is either kind or not patient.
Someone is both rich and not patient.
Someone is not rich. | Alice is rich. | neutral | (![X]:((patient(X)<~>happy(X))=>(quiet(X)&~tall(X))))&
(((~calm(alice)&old(alice)))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)|~humble(X))<=>(humble(X)<~>strong(X))))&
(![X]:((~happy(X)|~patient(X))<=>~quiet(X)))&
(![X]:((~brave(X)&~curious(X))<=>humble(X)))&
(![X]:((~calm(X)|~strong(X))<=>(happy(X)&~tall(X))))&
((?[X]:(quiet(X)))<=>((~generous(fred)|tall(fred))))&
(![X]:((~tall(X)&humble(X))<=>(kind(X)&curious(X))))&
((generous(fred))<=>(?[X]:(~wise(X))))&
((?[X]:((~brave(X)<~>curious(X))))<=>((~tall(lucy)<~>~strong(lucy))))&
(![X]:((~generous(X)<~>quiet(X))=>(old(X)<~>~rich(X))))&
((?[X]:(~funny(X)))=>((~patient(susan)&happy(susan))))&
(![X]:((~quiet(X)|kind(X))<=>(happy(X)<~>~creative(X))))&
(![X]:((~kind(X)|creative(X))<=>~quiet(X)))&
(![X]:((~patient(X)<~>~generous(X))=>(~creative(X)<~>tall(X))))&
(?[X]:((tall(X)&~happy(X))))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((rich(X)&~patient(X))))&
(?[X]:(~rich(X))) | rich(alice) | [] | null | 0 |
If john is not funny then paul is calm or not old. Everyone who is curious or patient is old or curious and vice versa. Everyone who is either not creative or funny is generous and vice versa. Everyone who is humble is both calm and not humble. If someone is not generous or patient then susan is not tall and vice versa. If someone is both tall and kind then someone is either curious or not curious and vice versa. If someone is both strong and not creative then someone is not happy or not funny. Everyone who is either not rich or not patient is wise or not strong and vice versa. Everyone who is both calm and not humble is quiet or not old and vice versa. Everyone who is both not old and curious is rich. Everyone who is tall is generous or strong. Everyone who is either not brave or not humble is happy or not wise. Everyone who is funny is either old or not kind. Everyone who is both not patient and not rich is not quiet and vice versa. Lucy is either not kind or patient. Someone is either creative or not strong. Paul is not creative. Someone is both not humble and not creative. Someone is either strong or creative. Someone is either not tall or kind. Someone is not strong. | Susan is calm. | neutral | ((~funny(john))=>((calm(paul)|~old(paul))))&
(![X]:((curious(X)|patient(X))<=>(old(X)|curious(X))))&
(![X]:((~creative(X)<~>funny(X))<=>generous(X)))&
(![X]:(humble(X)=>(calm(X)&~humble(X))))&
((?[X]:((~generous(X)|patient(X))))<=>(~tall(susan)))&
((?[X]:((tall(X)&kind(X))))<=>(?[X]:((curious(X)<~>~curious(X)))))&
((?[X]:((strong(X)&~creative(X))))=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~rich(X)<~>~patient(X))<=>(wise(X)|~strong(X))))&
(![X]:((calm(X)&~humble(X))<=>(quiet(X)|~old(X))))&
(![X]:((~old(X)&curious(X))=>rich(X)))&
(![X]:(tall(X)=>(generous(X)|strong(X))))&
(![X]:((~brave(X)<~>~humble(X))=>(happy(X)|~wise(X))))&
(![X]:(funny(X)=>(old(X)<~>~kind(X))))&
(![X]:((~patient(X)&~rich(X))<=>~quiet(X)))&
((~kind(lucy)<~>patient(lucy)))&
(?[X]:((creative(X)<~>~strong(X))))&
(~creative(paul))&
(?[X]:((~humble(X)&~creative(X))))&
(?[X]:((strong(X)<~>creative(X))))&
(?[X]:((~tall(X)<~>kind(X))))&
(?[X]:(~strong(X))) | calm(susan) | [] | null | 0 |
If john is both humble and not humble then someone is either not quiet or happy and vice versa.
If john is curious or quiet then susan is humble.
Everyone who is both brave and curious is either patient or not quiet.
Everyone who is not patient is patient.
If lucy is both not calm and calm then someone is both not creative and not quiet.
Everyone who is not generous or not patient is both not happy and generous.
If susan is both wise and not kind then fred is either old or not creative.
If susan is both not happy and humble then someone is either old or strong.
Everyone who is kind or tall is both old and wise and vice versa.
If john is curious then mary is both not kind and not patient.
If paul is both not curious and not kind then alice is happy and vice versa.
If susan is creative then someone is either not happy or not rich and vice versa.
Everyone who is either kind or not old is either curious or not rich.
If someone is both not rich and not kind then mary is not old and vice versa.
If alice is either not creative or old then susan is both tall and not patient.
If someone is tall or not happy then fred is either not patient or creative and vice versa.
Fred is either humble or not rich.
Alice is brave or not funny.
Mary is either not old or not creative.
Someone is either happy or not rich.
Someone is either humble or creative.
Paul is either patient or not humble. | Alice is not generous. | contradiction | (((humble(john)&~humble(john)))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
(((curious(john)|quiet(john)))=>(humble(susan)))&
(![X]:((brave(X)&curious(X))=>(patient(X)<~>~quiet(X))))&
(![X]:(~patient(X)=>patient(X)))&
(((~calm(lucy)&calm(lucy)))=>(?[X]:((~creative(X)&~quiet(X)))))&
(![X]:((~generous(X)|~patient(X))=>(~happy(X)&generous(X))))&
(((wise(susan)&~kind(susan)))=>((old(fred)<~>~creative(fred))))&
(((~happy(susan)&humble(susan)))=>(?[X]:((old(X)<~>strong(X)))))&
(![X]:((kind(X)|tall(X))<=>(old(X)&wise(X))))&
((curious(john))=>((~kind(mary)&~patient(mary))))&
(((~curious(paul)&~kind(paul)))<=>(happy(alice)))&
((creative(susan))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
(![X]:((kind(X)<~>~old(X))=>(curious(X)<~>~rich(X))))&
((?[X]:((~rich(X)&~kind(X))))<=>(~old(mary)))&
(((~creative(alice)<~>old(alice)))=>((tall(susan)&~patient(susan))))&
((?[X]:((tall(X)|~happy(X))))<=>((~patient(fred)<~>creative(fred))))&
((humble(fred)<~>~rich(fred)))&
((brave(alice)|~funny(alice)))&
((~old(mary)<~>~creative(mary)))&
(?[X]:((happy(X)<~>~rich(X))))&
(?[X]:((humble(X)<~>creative(X))))&
((patient(paul)<~>~humble(paul))) | ~generous(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8508347921969032205801826
% SZS output start Proof for 8508347921969032205801826
6. ! [X0] : ((~patient(X0) | ~generous(X0)) => (generous(X0) & ~happy(X0))) [input p5]
23. ~generous(alice) [input hypothesis]
30. ! [X0] : ((generous(X0) & ~happy(X0)) | (patient(X0) & generous(X0))) [ennf transformation 6]
89. generous(X0) | generous(X0) [cnf transformation 30]
136. ~generous(alice) [cnf transformation 23]
137. generous(X0) [duplicate literal removal 89]
340. $false [subsumption resolution 136,137]
% SZS output end Proof for 8508347921969032205801826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both patient and curious then john is both tall and not old and vice versa. Everyone who is not tall or not strong is not brave and vice versa. If someone is not rich then someone is both wise and generous and vice versa. If fred is both not kind and calm then someone is both not strong and not funny. If someone is not funny or generous then mary is both curious and generous. If paul is happy then someone is strong or not quiet and vice versa. If someone is quiet then someone is not old and vice versa. If fred is brave or wise then someone is both calm and funny and vice versa. Everyone who is not calm is both not creative and not curious. If lucy is not happy or old then someone is humble. If someone is not old then someone is either not funny or not brave and vice versa. If someone is not curious or rich then john is either tall or old. If susan is either not patient or not creative then fred is either not patient or not wise. Everyone who is not kind or not patient is both not funny and happy and vice versa. Everyone who is both patient and not rich is both not old and tall and vice versa. Everyone who is not wise is tall or not funny and vice versa. Susan is both not old and patient. Someone is either not brave or brave. Someone is both not strong and not quiet. Alice is not curious. Paul is both not rich and quiet. Susan is brave or generous. Someone is curious or not happy. Fred is either not curious or quiet. | Lucy is not brave. | neutral | (((patient(fred)&curious(fred)))<=>((tall(john)&~old(john))))&
(![X]:((~tall(X)|~strong(X))<=>~brave(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((wise(X)&generous(X)))))&
(((~kind(fred)&calm(fred)))=>(?[X]:((~strong(X)&~funny(X)))))&
((?[X]:((~funny(X)|generous(X))))=>((curious(mary)&generous(mary))))&
((happy(paul))<=>(?[X]:((strong(X)|~quiet(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:(~old(X))))&
(((brave(fred)|wise(fred)))<=>(?[X]:((calm(X)&funny(X)))))&
(![X]:(~calm(X)=>(~creative(X)&~curious(X))))&
(((~happy(lucy)|old(lucy)))=>(?[X]:(humble(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~funny(X)<~>~brave(X)))))&
((?[X]:((~curious(X)|rich(X))))=>((tall(john)<~>old(john))))&
(((~patient(susan)<~>~creative(susan)))=>((~patient(fred)<~>~wise(fred))))&
(![X]:((~kind(X)|~patient(X))<=>(~funny(X)&happy(X))))&
(![X]:((patient(X)&~rich(X))<=>(~old(X)&tall(X))))&
(![X]:(~wise(X)<=>(tall(X)|~funny(X))))&
((~old(susan)&patient(susan)))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:((~strong(X)&~quiet(X))))&
(~curious(alice))&
((~rich(paul)&quiet(paul)))&
((brave(susan)|generous(susan)))&
(?[X]:((curious(X)|~happy(X))))&
((~curious(fred)<~>quiet(fred))) | ~brave(lucy) | [] | null | 0 |
If someone is both wise and not kind then someone is both not tall and not calm.
Everyone who is either wise or not quiet is both not quiet and not kind and vice versa.
If someone is both not tall and tall then someone is not humble or not rich.
Everyone who is not kind is both curious and not old.
Everyone who is either curious or not curious is both not patient and not strong and vice versa.
Everyone who is not creative or humble is not tall or not quiet.
Everyone who is old or not old is both not humble and not strong and vice versa.
If paul is curious or not generous then someone is strong or not humble and vice versa.
Everyone who is either not patient or happy is either not curious or funny and vice versa.
If mary is not strong or not generous then someone is either generous or not happy and vice versa.
If someone is both rich and not generous then paul is rich or not old and vice versa.
Everyone who is brave or not humble is not funny or not humble.
Everyone who is either old or humble is either strong or not calm.
Everyone who is either not old or not curious is both not creative and funny and vice versa.
If someone is not funny or not kind then someone is not strong and vice versa.
Everyone who is strong is tall and vice versa.
Someone is either not calm or creative.
Someone is happy.
Fred is not curious or not strong.
Someone is not wise.
John is brave or not generous.
Someone is funny or not rich.
Someone is both not generous and not curious. | Mary is not wise. | neutral | ((?[X]:((wise(X)&~kind(X))))=>(?[X]:((~tall(X)&~calm(X)))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~quiet(X)&~kind(X))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:((~humble(X)|~rich(X)))))&
(![X]:(~kind(X)=>(curious(X)&~old(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(~patient(X)&~strong(X))))&
(![X]:((~creative(X)|humble(X))=>(~tall(X)|~quiet(X))))&
(![X]:((old(X)|~old(X))<=>(~humble(X)&~strong(X))))&
(((curious(paul)|~generous(paul)))<=>(?[X]:((strong(X)|~humble(X)))))&
(![X]:((~patient(X)<~>happy(X))<=>(~curious(X)<~>funny(X))))&
(((~strong(mary)|~generous(mary)))<=>(?[X]:((generous(X)<~>~happy(X)))))&
((?[X]:((rich(X)&~generous(X))))<=>((rich(paul)|~old(paul))))&
(![X]:((brave(X)|~humble(X))=>(~funny(X)|~humble(X))))&
(![X]:((old(X)<~>humble(X))=>(strong(X)<~>~calm(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~creative(X)&funny(X))))&
((?[X]:((~funny(X)|~kind(X))))<=>(?[X]:(~strong(X))))&
(![X]:(strong(X)<=>tall(X)))&
(?[X]:((~calm(X)<~>creative(X))))&
(?[X]:(happy(X)))&
((~curious(fred)|~strong(fred)))&
(?[X]:(~wise(X)))&
((brave(john)|~generous(john)))&
(?[X]:((funny(X)|~rich(X))))&
(?[X]:((~generous(X)&~curious(X)))) | ~wise(mary) | [] | null | 0 |
Everyone who is both not rich and not generous is both not kind and wise and vice versa. If someone is happy then paul is both happy and not patient. If someone is both not patient and not curious then lucy is both not brave and quiet and vice versa. Everyone who is either wise or brave is not humble or brave and vice versa. Everyone who is both curious and humble is both not happy and brave. Everyone who is both not humble and not happy is not brave and vice versa. Everyone who is calm or not old is calm or not rich and vice versa. Everyone who is either funny or wise is either not strong or not calm and vice versa. Everyone who is not old is not happy or funny. If someone is either not old or not patient then someone is not wise. Everyone who is curious is not kind and vice versa. Everyone who is wise is both not rich and patient. Everyone who is rich or not happy is both not quiet and not curious. If someone is not kind then john is not old and vice versa. Everyone who is humble or calm is not funny or happy and vice versa. Everyone who is brave or kind is rich and vice versa. Paul is not quiet or brave. Fred is both not curious and generous. Someone is wise or not strong. Mary is either not old or not happy. Someone is humble. | Paul is rich. | entailment | (![X]:((~rich(X)&~generous(X))<=>(~kind(X)&wise(X))))&
((?[X]:(happy(X)))=>((happy(paul)&~patient(paul))))&
((?[X]:((~patient(X)&~curious(X))))<=>((~brave(lucy)&quiet(lucy))))&
(![X]:((wise(X)<~>brave(X))<=>(~humble(X)|brave(X))))&
(![X]:((curious(X)&humble(X))=>(~happy(X)&brave(X))))&
(![X]:((~humble(X)&~happy(X))<=>~brave(X)))&
(![X]:((calm(X)|~old(X))<=>(calm(X)|~rich(X))))&
(![X]:((funny(X)<~>wise(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:(~old(X)=>(~happy(X)|funny(X))))&
((?[X]:((~old(X)<~>~patient(X))))=>(?[X]:(~wise(X))))&
(![X]:(curious(X)<=>~kind(X)))&
(![X]:(wise(X)=>(~rich(X)&patient(X))))&
(![X]:((rich(X)|~happy(X))=>(~quiet(X)&~curious(X))))&
((?[X]:(~kind(X)))<=>(~old(john)))&
(![X]:((humble(X)|calm(X))<=>(~funny(X)|happy(X))))&
(![X]:((brave(X)|kind(X))<=>rich(X)))&
((~quiet(paul)|brave(paul)))&
((~curious(fred)&generous(fred)))&
(?[X]:((wise(X)|~strong(X))))&
((~old(mary)<~>~happy(mary)))&
(?[X]:(humble(X))) | rich(paul) | [
"p1",
"p5",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1820707776370089057556013
% SZS output start Proof for 1820707776370089057556013
2. ? [X0] : happy(X0) => (~patient(paul) & happy(paul)) [input p1]
6. ! [X0] : ((~happy(X0) & ~humble(X0)) <=> ~brave(X0)) [input p5]
11. ! [X0] : (curious(X0) <=> ~kind(X0)) [input p10]
13. ! [X0] : ((~happy(X0) | rich(X0)) => (~curious(X0) & ~quiet(X0))) [input p12]
16. ! [X0] : ((kind(X0) | brave(X0)) <=> rich(X0)) [input p15]
22. ~rich(paul) [input hypothesis]
24. (~patient(paul) & happy(paul)) | ! [X0] : ~happy(X0) [ennf transformation 2]
31. ! [X0] : ((~curious(X0) & ~quiet(X0)) | (happy(X0) & ~rich(X0))) [ennf transformation 13]
41. ! [X0] : (((~happy(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | (happy(X0) | humble(X0)))) [nnf transformation 6]
42. ! [X0] : (((~happy(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | happy(X0) | humble(X0))) [flattening 41]
50. ! [X0] : ((curious(X0) | kind(X0)) & (~kind(X0) | ~curious(X0))) [nnf transformation 11]
57. ! [X0] : (((kind(X0) | brave(X0)) | ~rich(X0)) & (rich(X0) | (~kind(X0) & ~brave(X0)))) [nnf transformation 16]
58. ! [X0] : ((kind(X0) | brave(X0) | ~rich(X0)) & (rich(X0) | (~kind(X0) & ~brave(X0)))) [flattening 57]
68. happy(paul) | ~happy(X0) [cnf transformation 24]
84. ~happy(X0) | brave(X0) [cnf transformation 42]
101. curious(X0) | kind(X0) [cnf transformation 50]
107. ~curious(X0) | happy(X0) [cnf transformation 31]
114. ~brave(X0) | rich(X0) [cnf transformation 58]
115. ~kind(X0) | rich(X0) [cnf transformation 58]
124. ~rich(paul) [cnf transformation 22]
128. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
129. ~happy(X0) <- (1) [avatar component clause 128]
136. 3 <=> happy(paul) [avatar definition]
138. happy(paul) <- (3) [avatar component clause 136]
139. 1 | 3 [avatar split clause 68,136,128]
186. 14 <=> ! [X1] : kind(X1) [avatar definition]
187. kind(X1) <- (14) [avatar component clause 186]
194. 16 <=> brave(paul) [avatar definition]
196. brave(paul) <- (16) [avatar component clause 194]
218. brave(paul) <- (3) [resolution 84,138]
219. 16 | ~3 [avatar split clause 218,136,194]
229. happy(X0) | kind(X0) [resolution 107,101]
231. rich(paul) <- (16) [resolution 114,196]
232. $false <- (16) [subsumption resolution 231,124]
233. ~16 [avatar contradiction clause 232]
297. kind(X0) <- (1) [resolution 229,129]
300. 14 | ~1 [avatar split clause 297,128,186]
303. rich(X1) <- (14) [resolution 187,115]
306. $false <- (14) [resolution 303,124]
308. ~14 [avatar contradiction clause 306]
309. $false [avatar sat refutation 139,219,233,300,308]
% SZS output end Proof for 1820707776370089057556013
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not old then lucy is both not happy and old.
Everyone who is either brave or rich is either tall or brave.
Everyone who is both not humble and not funny is either not humble or tall.
Everyone who is not patient is either patient or not humble and vice versa.
Everyone who is not calm or not happy is not wise or calm and vice versa.
Everyone who is either not funny or wise is both creative and not old and vice versa.
Everyone who is rich is both not brave and not tall.
If someone is either not brave or quiet then john is both rich and not creative and vice versa.
Everyone who is either not calm or not tall is not patient or not generous and vice versa.
Everyone who is both not creative and not old is not strong or not curious.
Everyone who is curious or tall is both rich and not generous.
If fred is quiet or not happy then susan is creative or kind.
Everyone who is not tall or rich is old or funny.
Everyone who is both rich and not calm is not strong.
Someone is either kind or patient.
John is quiet or calm.
Paul is not brave or not calm.
Paul is old or kind.
Susan is brave. | Lucy is creative. | neutral | ((?[X]:((happy(X)|~old(X))))=>((~happy(lucy)&old(lucy))))&
(![X]:((brave(X)<~>rich(X))=>(tall(X)<~>brave(X))))&
(![X]:((~humble(X)&~funny(X))=>(~humble(X)<~>tall(X))))&
(![X]:(~patient(X)<=>(patient(X)<~>~humble(X))))&
(![X]:((~calm(X)|~happy(X))<=>(~wise(X)|calm(X))))&
(![X]:((~funny(X)<~>wise(X))<=>(creative(X)&~old(X))))&
(![X]:(rich(X)=>(~brave(X)&~tall(X))))&
((?[X]:((~brave(X)<~>quiet(X))))<=>((rich(john)&~creative(john))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~patient(X)|~generous(X))))&
(![X]:((~creative(X)&~old(X))=>(~strong(X)|~curious(X))))&
(![X]:((curious(X)|tall(X))=>(rich(X)&~generous(X))))&
(((quiet(fred)|~happy(fred)))=>((creative(susan)|kind(susan))))&
(![X]:((~tall(X)|rich(X))=>(old(X)|funny(X))))&
(![X]:((rich(X)&~calm(X))=>~strong(X)))&
(?[X]:((kind(X)<~>patient(X))))&
((quiet(john)|calm(john)))&
((~brave(paul)|~calm(paul)))&
((old(paul)|kind(paul)))&
(brave(susan)) | creative(lucy) | [] | null | 0 |
If fred is happy then someone is either not creative or tall.
Everyone who is not happy is rich and vice versa.
If someone is either not creative or curious then someone is not generous or curious and vice versa.
If someone is strong or not rich then fred is either not wise or not happy and vice versa.
If lucy is rich then paul is either not calm or curious.
If fred is both calm and not creative then alice is either generous or not patient and vice versa.
Everyone who is both not rich and not patient is not brave or not curious and vice versa.
If john is either patient or tall then mary is happy or rich.
If lucy is both humble and not wise then paul is not kind or not wise.
Everyone who is funny or creative is both creative and not humble and vice versa.
If someone is either not tall or not rich then someone is either tall or patient.
If someone is generous then john is either not funny or rich.
If john is both kind and not creative then fred is both not generous and creative.
Everyone who is strong is both not patient and wise and vice versa.
Everyone who is not patient or not kind is both humble and not creative.
Everyone who is quiet or creative is not brave or happy and vice versa.
Paul is creative.
Someone is either generous or not tall.
Someone is both wise and not curious.
Fred is not strong or curious.
Mary is not brave.
Alice is not brave.
Someone is not creative. | Paul is not brave. | contradiction | ((happy(fred))=>(?[X]:((~creative(X)<~>tall(X)))))&
(![X]:(~happy(X)<=>rich(X)))&
((?[X]:((~creative(X)<~>curious(X))))<=>(?[X]:((~generous(X)|curious(X)))))&
((?[X]:((strong(X)|~rich(X))))<=>((~wise(fred)<~>~happy(fred))))&
((rich(lucy))=>((~calm(paul)<~>curious(paul))))&
(((calm(fred)&~creative(fred)))<=>((generous(alice)<~>~patient(alice))))&
(![X]:((~rich(X)&~patient(X))<=>(~brave(X)|~curious(X))))&
(((patient(john)<~>tall(john)))=>((happy(mary)|rich(mary))))&
(((humble(lucy)&~wise(lucy)))=>((~kind(paul)|~wise(paul))))&
(![X]:((funny(X)|creative(X))<=>(creative(X)&~humble(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>(?[X]:((tall(X)<~>patient(X)))))&
((?[X]:(generous(X)))=>((~funny(john)<~>rich(john))))&
(((kind(john)&~creative(john)))=>((~generous(fred)&creative(fred))))&
(![X]:(strong(X)<=>(~patient(X)&wise(X))))&
(![X]:((~patient(X)|~kind(X))=>(humble(X)&~creative(X))))&
(![X]:((quiet(X)|creative(X))<=>(~brave(X)|happy(X))))&
(creative(paul))&
(?[X]:((generous(X)<~>~tall(X))))&
(?[X]:((wise(X)&~curious(X))))&
((~strong(fred)|curious(fred)))&
(~brave(mary))&
(~brave(alice))&
(?[X]:(~creative(X))) | ~brave(paul) | [
"p6",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8939383156648416720826389
% SZS output start Proof for 8939383156648416720826389
7. ! [X0] : ((~patient(X0) & ~rich(X0)) <=> (~curious(X0) | ~brave(X0))) [input p6]
15. ! [X0] : ((~kind(X0) | ~patient(X0)) => (~creative(X0) & humble(X0))) [input p14]
17. creative(paul) [input p16]
24. ~brave(paul) [input hypothesis]
37. ! [X0] : ((~creative(X0) & humble(X0)) | (kind(X0) & patient(X0))) [ennf transformation 15]
54. ! [X0] : (((~patient(X0) & ~rich(X0)) | (curious(X0) & brave(X0))) & ((~curious(X0) | ~brave(X0)) | (patient(X0) | rich(X0)))) [nnf transformation 7]
55. ! [X0] : (((~patient(X0) & ~rich(X0)) | (curious(X0) & brave(X0))) & (~curious(X0) | ~brave(X0) | patient(X0) | rich(X0))) [flattening 54]
102. ~patient(X0) | brave(X0) [cnf transformation 55]
125. ~creative(X0) | patient(X0) [cnf transformation 37]
131. creative(paul) [cnf transformation 17]
140. ~brave(paul) [cnf transformation 24]
345. patient(paul) [resolution 125,131]
350. brave(paul) [resolution 345,102]
352. $false [subsumption resolution 350,140]
% SZS output end Proof for 8939383156648416720826389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and patient is strong or not generous and vice versa. Everyone who is both not old and calm is either not brave or not curious. If lucy is either not generous or not rich then lucy is not humble or strong. If someone is both not kind and wise then someone is both humble and tall and vice versa. Everyone who is funny or not rich is either creative or wise. If fred is not wise then paul is not rich and vice versa. If john is not rich or funny then mary is not creative. If someone is calm or not brave then mary is not calm or not quiet and vice versa. Everyone who is both not strong and generous is quiet or not patient. If someone is either creative or curious then lucy is both creative and curious and vice versa. If lucy is both strong and tall then someone is old and vice versa. If fred is not kind or humble then alice is wise or not generous. If alice is quiet then lucy is funny or not quiet. Everyone who is not happy is either not humble or patient and vice versa. If someone is both happy and not creative then someone is generous or not wise. Everyone who is not funny or happy is kind. Mary is both not brave and not quiet. Paul is both humble and not patient. John is not creative. Alice is either calm or kind. Someone is either generous or patient. Alice is old or not calm. Someone is tall. Someone is patient or not strong. | Alice is not old. | entailment | (![X]:((~tall(X)&patient(X))<=>(strong(X)|~generous(X))))&
(![X]:((~old(X)&calm(X))=>(~brave(X)<~>~curious(X))))&
(((~generous(lucy)<~>~rich(lucy)))=>((~humble(lucy)|strong(lucy))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((humble(X)&tall(X)))))&
(![X]:((funny(X)|~rich(X))=>(creative(X)<~>wise(X))))&
((~wise(fred))<=>(~rich(paul)))&
(((~rich(john)|funny(john)))=>(~creative(mary)))&
((?[X]:((calm(X)|~brave(X))))<=>((~calm(mary)|~quiet(mary))))&
(![X]:((~strong(X)&generous(X))=>(quiet(X)|~patient(X))))&
((?[X]:((creative(X)<~>curious(X))))<=>((creative(lucy)&curious(lucy))))&
(((strong(lucy)&tall(lucy)))<=>(?[X]:(old(X))))&
(((~kind(fred)|humble(fred)))=>((wise(alice)|~generous(alice))))&
((quiet(alice))=>((funny(lucy)|~quiet(lucy))))&
(![X]:(~happy(X)<=>(~humble(X)<~>patient(X))))&
((?[X]:((happy(X)&~creative(X))))=>(?[X]:((generous(X)|~wise(X)))))&
(![X]:((~funny(X)|happy(X))=>kind(X)))&
((~brave(mary)&~quiet(mary)))&
((humble(paul)&~patient(paul)))&
(~creative(john))&
((calm(alice)<~>kind(alice)))&
(?[X]:((generous(X)<~>patient(X))))&
((old(alice)|~calm(alice)))&
(?[X]:(tall(X)))&
(?[X]:((patient(X)|~strong(X)))) | ~old(alice) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1878098184373074399704176
% SZS output start Proof for 1878098184373074399704176
1. ! [X0] : ((patient(X0) & ~tall(X0)) <=> (~generous(X0) | strong(X0))) [input p0]
11. (tall(lucy) & strong(lucy)) <=> ? [X0] : old(X0) [input p10]
25. old(alice) [input hypothesis]
44. ! [X0] : (((patient(X0) & ~tall(X0)) | (generous(X0) & ~strong(X0))) & ((~generous(X0) | strong(X0)) | (~patient(X0) | tall(X0)))) [nnf transformation 1]
45. ! [X0] : (((patient(X0) & ~tall(X0)) | (generous(X0) & ~strong(X0))) & (~generous(X0) | strong(X0) | ~patient(X0) | tall(X0))) [flattening 44]
65. ((tall(lucy) & strong(lucy)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (~tall(lucy) | ~strong(lucy))) [nnf transformation 11]
66. ((tall(lucy) & strong(lucy)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | ~tall(lucy) | ~strong(lucy)) [flattening 65]
67. ((tall(lucy) & strong(lucy)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | ~tall(lucy) | ~strong(lucy)) [rectify 66]
68. ? [X1] : old(X1) => old(sK4) [choice axiom]
69. ((tall(lucy) & strong(lucy)) | ! [X0] : ~old(X0)) & (old(sK4) | ~tall(lucy) | ~strong(lucy)) [skolemisation 67,68]
83. ~strong(X0) | ~tall(X0) [cnf transformation 45]
115. strong(lucy) | ~old(X0) [cnf transformation 69]
116. tall(lucy) | ~old(X0) [cnf transformation 69]
137. old(alice) [cnf transformation 25]
151. 4 <=> strong(lucy) [avatar definition]
153. strong(lucy) <- (4) [avatar component clause 151]
261. 28 <=> ! [X0] : ~old(X0) [avatar definition]
262. ~old(X0) <- (28) [avatar component clause 261]
264. 29 <=> tall(lucy) [avatar definition]
266. tall(lucy) <- (29) [avatar component clause 264]
267. 28 | 29 [avatar split clause 116,264,261]
268. 28 | 4 [avatar split clause 115,151,261]
333. 44 <=> old(alice) [avatar definition]
335. old(alice) <- (44) [avatar component clause 333]
337. 44 [avatar split clause 137,333]
338. $false <- (28, 44) [resolution 335,262]
339. ~28 | ~44 [avatar contradiction clause 338]
340. ~tall(lucy) <- (4) [resolution 83,153]
341. $false <- (4, 29) [subsumption resolution 340,266]
342. ~4 | ~29 [avatar contradiction clause 341]
343. $false [avatar sat refutation 267,268,337,339,342]
% SZS output end Proof for 1878098184373074399704176
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not wise then alice is both not funny and creative.
If someone is kind then someone is not quiet.
If john is not wise then susan is both wise and patient.
Everyone who is not old is not happy or not wise and vice versa.
Everyone who is generous or not patient is not humble or quiet and vice versa.
Everyone who is strong or not patient is not brave.
If someone is not wise or not patient then alice is both wise and not creative and vice versa.
Everyone who is both not quiet and tall is either curious or funny.
If someone is either strong or happy then someone is not quiet or kind and vice versa.
Everyone who is not generous is both generous and strong.
Everyone who is either not generous or not strong is generous or wise and vice versa.
If someone is not patient then someone is either not wise or strong and vice versa.
Everyone who is not rich is not strong or not wise and vice versa.
Everyone who is both curious and creative is patient and vice versa.
If paul is both not happy and curious then someone is both not generous and not kind and vice versa.
Everyone who is not patient is old or creative.
Someone is both patient and kind.
John is not tall.
Alice is either humble or generous.
Alice is either patient or curious.
Lucy is either not strong or strong.
Someone is both not happy and not strong.
Paul is not generous or quiet. | Alice is old. | entailment | ((~wise(susan))=>((~funny(alice)&creative(alice))))&
((?[X]:(kind(X)))=>(?[X]:(~quiet(X))))&
((~wise(john))=>((wise(susan)&patient(susan))))&
(![X]:(~old(X)<=>(~happy(X)|~wise(X))))&
(![X]:((generous(X)|~patient(X))<=>(~humble(X)|quiet(X))))&
(![X]:((strong(X)|~patient(X))=>~brave(X)))&
((?[X]:((~wise(X)|~patient(X))))<=>((wise(alice)&~creative(alice))))&
(![X]:((~quiet(X)&tall(X))=>(curious(X)<~>funny(X))))&
((?[X]:((strong(X)<~>happy(X))))<=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:(~generous(X)=>(generous(X)&strong(X))))&
(![X]:((~generous(X)<~>~strong(X))<=>(generous(X)|wise(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:(~rich(X)<=>(~strong(X)|~wise(X))))&
(![X]:((curious(X)&creative(X))<=>patient(X)))&
(((~happy(paul)&curious(paul)))<=>(?[X]:((~generous(X)&~kind(X)))))&
(![X]:(~patient(X)=>(old(X)|creative(X))))&
(?[X]:((patient(X)&kind(X))))&
(~tall(john))&
((humble(alice)<~>generous(alice)))&
((patient(alice)<~>curious(alice)))&
((~strong(lucy)<~>strong(lucy)))&
(?[X]:((~happy(X)&~strong(X))))&
((~generous(paul)|quiet(paul))) | old(alice) | [
"p6",
"p9",
"p10",
"p11",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2019268387949424092725833
% SZS output start Proof for 2019268387949424092725833
7. ? [X0] : (~patient(X0) | ~wise(X0)) <=> (~creative(alice) & wise(alice)) [input p6]
10. ! [X0] : (~generous(X0) => (strong(X0) & generous(X0))) [input p9]
11. ! [X0] : ((~generous(X0) <~> ~strong(X0)) <=> (wise(X0) | generous(X0))) [input p10]
12. ? [X0] : ~patient(X0) <=> ? [X0] : (~wise(X0) <~> strong(X0)) [input p11]
14. ! [X0] : ((creative(X0) & curious(X0)) <=> patient(X0)) [input p13]
16. ! [X0] : (~patient(X0) => (creative(X0) | old(X0))) [input p15]
20. patient(alice) <~> curious(alice) [input p19]
24. ~old(alice) [input hypothesis]
27. ? [X0] : ~patient(X0) <=> ? [X1] : (~wise(X1) <~> strong(X1)) [rectify 12]
35. ! [X0] : ((strong(X0) & generous(X0)) | generous(X0)) [ennf transformation 10]
36. ! [X0] : ((creative(X0) | old(X0)) | patient(X0)) [ennf transformation 16]
37. ! [X0] : (creative(X0) | old(X0) | patient(X0)) [flattening 36]
45. (? [X0] : (~patient(X0) | ~wise(X0)) | (creative(alice) | ~wise(alice))) & ((~creative(alice) & wise(alice)) | ! [X0] : (patient(X0) & wise(X0))) [nnf transformation 7]
46. (? [X0] : (~patient(X0) | ~wise(X0)) | creative(alice) | ~wise(alice)) & ((~creative(alice) & wise(alice)) | ! [X0] : (patient(X0) & wise(X0))) [flattening 45]
47. (? [X0] : (~patient(X0) | ~wise(X0)) | creative(alice) | ~wise(alice)) & ((~creative(alice) & wise(alice)) | ! [X1] : (patient(X1) & wise(X1))) [rectify 46]
48. ? [X0] : (~patient(X0) | ~wise(X0)) => (~patient(sK1) | ~wise(sK1)) [choice axiom]
49. ((~patient(sK1) | ~wise(sK1)) | creative(alice) | ~wise(alice)) & ((~creative(alice) & wise(alice)) | ! [X1] : (patient(X1) & wise(X1))) [skolemisation 47,48]
55. ! [X0] : ((((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | (~wise(X0) & ~generous(X0))) & ((wise(X0) | generous(X0)) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))))) [nnf transformation 11]
56. ! [X0] : ((((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | (~wise(X0) & ~generous(X0))) & (wise(X0) | generous(X0) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))))) [flattening 55]
57. (? [X0] : ~patient(X0) | ! [X1] : ((~wise(X1) | ~strong(X1)) & (strong(X1) | wise(X1)))) & (? [X1] : ((~strong(X1) | wise(X1)) & (strong(X1) | ~wise(X1))) | ! [X0] : patient(X0)) [nnf transformation 27]
58. (? [X0] : ~patient(X0) | ! [X1] : ((~wise(X1) | ~strong(X1)) & (strong(X1) | wise(X1)))) & (? [X2] : ((~strong(X2) | wise(X2)) & (strong(X2) | ~wise(X2))) | ! [X3] : patient(X3)) [rectify 57]
59. ? [X0] : ~patient(X0) => ~patient(sK4) [choice axiom]
60. ? [X2] : ((~strong(X2) | wise(X2)) & (strong(X2) | ~wise(X2))) => ((~strong(sK5) | wise(sK5)) & (strong(sK5) | ~wise(sK5))) [choice axiom]
61. (~patient(sK4) | ! [X1] : ((~wise(X1) | ~strong(X1)) & (strong(X1) | wise(X1)))) & (((~strong(sK5) | wise(sK5)) & (strong(sK5) | ~wise(sK5))) | ! [X3] : patient(X3)) [skolemisation 58,60,59]
62. ! [X0] : (((creative(X0) & curious(X0)) | ~patient(X0)) & (patient(X0) | (~creative(X0) | ~curious(X0)))) [nnf transformation 14]
63. ! [X0] : (((creative(X0) & curious(X0)) | ~patient(X0)) & (patient(X0) | ~creative(X0) | ~curious(X0))) [flattening 62]
72. (~curious(alice) | ~patient(alice)) & (curious(alice) | patient(alice)) [nnf transformation 20]
89. ~creative(alice) | wise(X1) [cnf transformation 49]
98. generous(X0) | generous(X0) [cnf transformation 35]
102. ~strong(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 56]
106. strong(sK5) | ~wise(sK5) | patient(X3) [cnf transformation 61]
111. ~patient(X0) | curious(X0) [cnf transformation 63]
112. ~patient(X0) | creative(X0) [cnf transformation 63]
117. creative(X0) | old(X0) | patient(X0) [cnf transformation 37]
123. ~curious(alice) | ~patient(alice) [cnf transformation 72]
129. ~old(alice) [cnf transformation 24]
131. ~strong(X0) | ~generous(X0) [duplicate literal removal 102]
132. generous(X0) [duplicate literal removal 98]
138. 2 <=> creative(alice) [avatar definition]
139. ~creative(alice) <- (~2) [avatar component clause 138]
174. 10 <=> ! [X1] : patient(X1) [avatar definition]
175. patient(X1) <- (10) [avatar component clause 174]
178. 11 <=> ! [X1] : wise(X1) [avatar definition]
179. wise(X1) <- (11) [avatar component clause 178]
180. 11 | ~2 [avatar split clause 89,138,178]
215. ~strong(X0) [subsumption resolution 131,132]
222. ~wise(sK5) | patient(X3) [subsumption resolution 106,215]
224. 20 <=> wise(sK5) [avatar definition]
226. ~wise(sK5) <- (~20) [avatar component clause 224]
227. 10 | ~20 [avatar split clause 222,224,174]
243. old(X0) | creative(X0) [subsumption resolution 117,112]
245. ~patient(alice) [subsumption resolution 123,111]
250. $false <- (10) [resolution 245,175]
251. ~10 [avatar contradiction clause 250]
252. $false <- (11, ~20) [subsumption resolution 226,179]
253. ~11 | 20 [avatar contradiction clause 252]
260. creative(alice) [resolution 243,129]
263. $false <- (~2) [subsumption resolution 260,139]
264. 2 [avatar contradiction clause 263]
265. $false [avatar sat refutation 180,227,251,253,264]
% SZS output end Proof for 2019268387949424092725833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and humble is not old. If fred is not old then mary is either tall or not funny and vice versa. Everyone who is patient or generous is not calm and vice versa. Everyone who is either kind or not happy is both tall and curious and vice versa. If someone is both not patient and not strong then someone is both calm and rich and vice versa. Everyone who is not humble is not old or rich and vice versa. If someone is either old or generous then lucy is both humble and kind and vice versa. Everyone who is both not happy and creative is brave and vice versa. If mary is both not rich and not funny then someone is both rich and patient and vice versa. If someone is not wise then susan is either generous or creative. Everyone who is not tall or not generous is humble and vice versa. If someone is either funny or humble then john is both patient and not kind and vice versa. If john is either humble or brave then someone is not wise or rich. Everyone who is either not quiet or not happy is both funny and not creative. Everyone who is either brave or not old is both old and tall and vice versa. If fred is curious or not kind then alice is both humble and not rich and vice versa. Lucy is not humble. Someone is either not rich or quiet. Susan is not wise. Someone is both not creative and not calm. Someone is not tall. Someone is not generous or not wise. Someone is either happy or brave. Alice is either patient or creative. | Fred is generous. | entailment | (![X]:((~curious(X)&humble(X))=>~old(X)))&
((~old(fred))<=>((tall(mary)<~>~funny(mary))))&
(![X]:((patient(X)|generous(X))<=>~calm(X)))&
(![X]:((kind(X)<~>~happy(X))<=>(tall(X)&curious(X))))&
((?[X]:((~patient(X)&~strong(X))))<=>(?[X]:((calm(X)&rich(X)))))&
(![X]:(~humble(X)<=>(~old(X)|rich(X))))&
((?[X]:((old(X)<~>generous(X))))<=>((humble(lucy)&kind(lucy))))&
(![X]:((~happy(X)&creative(X))<=>brave(X)))&
(((~rich(mary)&~funny(mary)))<=>(?[X]:((rich(X)&patient(X)))))&
((?[X]:(~wise(X)))=>((generous(susan)<~>creative(susan))))&
(![X]:((~tall(X)|~generous(X))<=>humble(X)))&
((?[X]:((funny(X)<~>humble(X))))<=>((patient(john)&~kind(john))))&
(((humble(john)<~>brave(john)))=>(?[X]:((~wise(X)|rich(X)))))&
(![X]:((~quiet(X)<~>~happy(X))=>(funny(X)&~creative(X))))&
(![X]:((brave(X)<~>~old(X))<=>(old(X)&tall(X))))&
(((curious(fred)|~kind(fred)))<=>((humble(alice)&~rich(alice))))&
(~humble(lucy))&
(?[X]:((~rich(X)<~>quiet(X))))&
(~wise(susan))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~generous(X)|~wise(X))))&
(?[X]:((happy(X)<~>brave(X))))&
((patient(alice)<~>creative(alice))) | generous(fred) | [
"p5",
"p6",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 455966213413304396968101
% SZS output start Proof for 455966213413304396968101
6. ! [X0] : (~humble(X0) <=> (rich(X0) | ~old(X0))) [input p5]
7. ? [X0] : (old(X0) <~> generous(X0)) <=> (kind(lucy) & humble(lucy)) [input p6]
11. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> humble(X0)) [input p10]
17. ~humble(lucy) [input p16]
25. ~generous(fred) [input hypothesis]
42. ! [X0] : ((~humble(X0) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | humble(X0))) [nnf transformation 6]
43. ! [X0] : ((~humble(X0) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | humble(X0))) [flattening 42]
44. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (~kind(lucy) | ~humble(lucy))) & ((kind(lucy) & humble(lucy)) | ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [nnf transformation 7]
45. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [flattening 44]
46. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X1] : ((old(X1) | ~generous(X1)) & (generous(X1) | ~old(X1)))) [rectify 45]
47. ? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) => ((~generous(sK2) | ~old(sK2)) & (generous(sK2) | old(sK2))) [choice axiom]
48. (((~generous(sK2) | ~old(sK2)) & (generous(sK2) | old(sK2))) | ~kind(lucy) | ~humble(lucy)) & ((kind(lucy) & humble(lucy)) | ! [X1] : ((old(X1) | ~generous(X1)) & (generous(X1) | ~old(X1)))) [skolemisation 46,47]
57. ! [X0] : (((~generous(X0) | ~tall(X0)) | ~humble(X0)) & (humble(X0) | (generous(X0) & tall(X0)))) [nnf transformation 11]
58. ! [X0] : ((~generous(X0) | ~tall(X0) | ~humble(X0)) & (humble(X0) | (generous(X0) & tall(X0)))) [flattening 57]
104. ~humble(X0) | old(X0) [cnf transformation 43]
106. humble(lucy) | generous(X1) | ~old(X1) [cnf transformation 48]
107. humble(lucy) | old(X1) | ~generous(X1) [cnf transformation 48]
122. generous(X0) | humble(X0) [cnf transformation 58]
147. ~humble(lucy) [cnf transformation 17]
159. ~generous(fred) [cnf transformation 25]
205. 10 <=> humble(lucy) [avatar definition]
223. 14 <=> ! [X1] : (old(X1) | ~generous(X1)) [avatar definition]
224. ~generous(X1) | old(X1) <- (14) [avatar component clause 223]
227. 15 <=> ! [X1] : (generous(X1) | ~old(X1)) [avatar definition]
228. ~old(X1) | generous(X1) <- (15) [avatar component clause 227]
230. 14 | 10 [avatar split clause 107,205,223]
231. 15 | 10 [avatar split clause 106,205,227]
332. ~10 [avatar split clause 147,205]
391. old(X0) | humble(X0) <- (14) [resolution 224,122]
392. old(X0) <- (14) [subsumption resolution 391,104]
427. generous(X1) <- (14, 15) [resolution 392,228]
454. $false <- (14, 15) [resolution 427,159]
458. ~14 | ~15 [avatar contradiction clause 454]
459. $false [avatar sat refutation 230,231,332,458]
% SZS output end Proof for 455966213413304396968101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not wise or not old.
If someone is either brave or not funny then lucy is rich.
If someone is generous or creative then someone is both not tall and not kind and vice versa.
Everyone who is both not old and old is generous.
Everyone who is generous is not wise and vice versa.
Everyone who is old is not tall or not humble.
If john is both not kind and wise then someone is not rich.
Everyone who is not happy or not brave is not rich.
Everyone who is either humble or not generous is either not generous or not old.
If paul is either old or curious then susan is both quiet and not old.
Everyone who is not tall or not creative is both humble and wise.
Everyone who is tall is humble or wise and vice versa.
Everyone who is either creative or tall is humble.
Everyone who is either humble or curious is not rich or not tall.
Everyone who is old or not funny is funny or generous.
Everyone who is funny or brave is rich and vice versa.
Alice is not quiet or not happy.
Susan is not strong or not generous.
Someone is curious.
Someone is not old or curious. | Alice is happy. | entailment | (![X]:(~curious(X)=>(~wise(X)|~old(X))))&
((?[X]:((brave(X)<~>~funny(X))))=>(rich(lucy)))&
((?[X]:((generous(X)|creative(X))))<=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:((~old(X)&old(X))=>generous(X)))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:(old(X)=>(~tall(X)|~humble(X))))&
(((~kind(john)&wise(john)))=>(?[X]:(~rich(X))))&
(![X]:((~happy(X)|~brave(X))=>~rich(X)))&
(![X]:((humble(X)<~>~generous(X))=>(~generous(X)<~>~old(X))))&
(((old(paul)<~>curious(paul)))=>((quiet(susan)&~old(susan))))&
(![X]:((~tall(X)|~creative(X))=>(humble(X)&wise(X))))&
(![X]:(tall(X)<=>(humble(X)|wise(X))))&
(![X]:((creative(X)<~>tall(X))=>humble(X)))&
(![X]:((humble(X)<~>curious(X))=>(~rich(X)|~tall(X))))&
(![X]:((old(X)|~funny(X))=>(funny(X)|generous(X))))&
(![X]:((funny(X)|brave(X))<=>rich(X)))&
((~quiet(alice)|~happy(alice)))&
((~strong(susan)|~generous(susan)))&
(?[X]:(curious(X)))&
(?[X]:((~old(X)|curious(X)))) | happy(alice) | [
"p2",
"p4",
"p7",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6841601623066252750170030
% SZS output start Proof for 6841601623066252750170030
3. ? [X0] : (creative(X0) | generous(X0)) <=> ? [X0] : (~kind(X0) & ~tall(X0)) [input p2]
5. ! [X0] : (generous(X0) <=> ~wise(X0)) [input p4]
8. ! [X0] : ((~brave(X0) | ~happy(X0)) => ~rich(X0)) [input p7]
11. ! [X0] : ((~creative(X0) | ~tall(X0)) => (wise(X0) & humble(X0))) [input p10]
12. ! [X0] : (tall(X0) <=> (wise(X0) | humble(X0))) [input p11]
15. ! [X0] : ((~funny(X0) | old(X0)) => (generous(X0) | funny(X0))) [input p14]
16. ! [X0] : ((brave(X0) | funny(X0)) <=> rich(X0)) [input p15]
21. ~happy(alice) [input hypothesis]
22. ? [X0] : (creative(X0) | generous(X0)) <=> ? [X1] : (~kind(X1) & ~tall(X1)) [rectify 3]
33. ! [X0] : (~rich(X0) | (brave(X0) & happy(X0))) [ennf transformation 8]
36. ! [X0] : ((wise(X0) & humble(X0)) | (creative(X0) & tall(X0))) [ennf transformation 11]
40. ! [X0] : ((generous(X0) | funny(X0)) | (funny(X0) & ~old(X0))) [ennf transformation 15]
41. ! [X0] : (generous(X0) | funny(X0) | (funny(X0) & ~old(X0))) [flattening 40]
43. (? [X0] : (creative(X0) | generous(X0)) | ! [X1] : (kind(X1) | tall(X1))) & (? [X1] : (~kind(X1) & ~tall(X1)) | ! [X0] : (~creative(X0) & ~generous(X0))) [nnf transformation 22]
44. (? [X0] : (creative(X0) | generous(X0)) | ! [X1] : (kind(X1) | tall(X1))) & (? [X2] : (~kind(X2) & ~tall(X2)) | ! [X3] : (~creative(X3) & ~generous(X3))) [rectify 43]
45. ? [X0] : (creative(X0) | generous(X0)) => (creative(sK0) | generous(sK0)) [choice axiom]
46. ? [X2] : (~kind(X2) & ~tall(X2)) => (~kind(sK1) & ~tall(sK1)) [choice axiom]
47. ((creative(sK0) | generous(sK0)) | ! [X1] : (kind(X1) | tall(X1))) & ((~kind(sK1) & ~tall(sK1)) | ! [X3] : (~creative(X3) & ~generous(X3))) [skolemisation 44,46,45]
48. ! [X0] : ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0))) [nnf transformation 5]
53. ! [X0] : ((tall(X0) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | ~tall(X0))) [nnf transformation 12]
54. ! [X0] : ((tall(X0) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ~tall(X0))) [flattening 53]
57. ! [X0] : (((brave(X0) | funny(X0)) | ~rich(X0)) & (rich(X0) | (~brave(X0) & ~funny(X0)))) [nnf transformation 16]
58. ! [X0] : ((brave(X0) | funny(X0) | ~rich(X0)) & (rich(X0) | (~brave(X0) & ~funny(X0)))) [flattening 57]
66. ~tall(sK1) | ~generous(X3) [cnf transformation 47]
72. ~generous(X0) | ~wise(X0) [cnf transformation 48]
73. generous(X0) | wise(X0) [cnf transformation 48]
76. ~rich(X0) | happy(X0) [cnf transformation 33]
88. tall(X0) | wise(X0) [cnf transformation 36]
92. tall(X0) | ~wise(X0) [cnf transformation 54]
98. generous(X0) | funny(X0) | funny(X0) [cnf transformation 41]
99. ~funny(X0) | rich(X0) [cnf transformation 58]
105. ~happy(alice) [cnf transformation 21]
106. generous(X0) | funny(X0) [duplicate literal removal 98]
142. 9 <=> ! [X3] : ~generous(X3) [avatar definition]
143. ~generous(X3) <- (9) [avatar component clause 142]
146. 10 <=> tall(sK1) [avatar definition]
148. ~tall(sK1) <- (~10) [avatar component clause 146]
150. 9 | ~10 [avatar split clause 66,146,142]
184. tall(X0) [subsumption resolution 92,88]
193. 19 <=> happy(alice) [avatar definition]
195. ~happy(alice) <- (~19) [avatar component clause 193]
206. ~19 [avatar split clause 105,193]
207. $false <- (~10) [subsumption resolution 148,184]
208. 10 [avatar contradiction clause 207]
210. wise(X1) <- (9) [resolution 73,143]
215. funny(X0) | ~wise(X0) [resolution 106,72]
217. funny(X0) <- (9) [subsumption resolution 215,210]
218. rich(X0) <- (9) [resolution 217,99]
221. happy(X1) <- (9) [resolution 218,76]
234. $false <- (9, ~19) [resolution 221,195]
235. ~9 | 19 [avatar contradiction clause 234]
236. $false [avatar sat refutation 150,206,208,235]
% SZS output end Proof for 6841601623066252750170030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or creative then alice is not rich or curious and vice versa.
If susan is both rich and kind then someone is not kind.
Everyone who is old or not humble is patient and vice versa.
If alice is both rich and humble then someone is not creative and vice versa.
Everyone who is not patient or calm is either not creative or not curious.
If fred is both not patient and not wise then someone is happy or patient and vice versa.
If john is both wise and not funny then someone is both not rich and calm and vice versa.
Everyone who is brave or old is not creative or humble.
Everyone who is tall is funny or not generous and vice versa.
If someone is funny or quiet then someone is not quiet or not humble and vice versa.
If someone is not rich then someone is creative or not rich and vice versa.
If john is brave or not old then lucy is not quiet.
If paul is both curious and not funny then paul is both creative and wise and vice versa.
Everyone who is both not rich and not kind is humble.
If susan is quiet then someone is not patient or not strong.
Everyone who is not rich or generous is either happy or creative.
Someone is either funny or old.
Alice is either funny or curious.
John is not brave.
Alice is either calm or strong.
Alice is curious.
Lucy is either wise or patient.
Fred is curious or not happy.
Someone is old. | John is brave. | contradiction | ((?[X]:((~wise(X)<~>creative(X))))<=>((~rich(alice)|curious(alice))))&
(((rich(susan)&kind(susan)))=>(?[X]:(~kind(X))))&
(![X]:((old(X)|~humble(X))<=>patient(X)))&
(((rich(alice)&humble(alice)))<=>(?[X]:(~creative(X))))&
(![X]:((~patient(X)|calm(X))=>(~creative(X)<~>~curious(X))))&
(((~patient(fred)&~wise(fred)))<=>(?[X]:((happy(X)|patient(X)))))&
(((wise(john)&~funny(john)))<=>(?[X]:((~rich(X)&calm(X)))))&
(![X]:((brave(X)|old(X))=>(~creative(X)|humble(X))))&
(![X]:(tall(X)<=>(funny(X)|~generous(X))))&
((?[X]:((funny(X)|quiet(X))))<=>(?[X]:((~quiet(X)|~humble(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((creative(X)|~rich(X)))))&
(((brave(john)|~old(john)))=>(~quiet(lucy)))&
(((curious(paul)&~funny(paul)))<=>((creative(paul)&wise(paul))))&
(![X]:((~rich(X)&~kind(X))=>humble(X)))&
((quiet(susan))=>(?[X]:((~patient(X)|~strong(X)))))&
(![X]:((~rich(X)|generous(X))=>(happy(X)<~>creative(X))))&
(?[X]:((funny(X)<~>old(X))))&
((funny(alice)<~>curious(alice)))&
(~brave(john))&
((calm(alice)<~>strong(alice)))&
(curious(alice))&
((wise(lucy)<~>patient(lucy)))&
((curious(fred)|~happy(fred)))&
(?[X]:(old(X))) | brave(john) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 430497201679565248255526
% SZS output start Proof for 430497201679565248255526
19. ~brave(john) [input p18]
25. brave(john) [input hypothesis]
136. ~brave(john) [cnf transformation 19]
144. brave(john) [cnf transformation 25]
313. 39 <=> brave(john) [avatar definition]
366. ~39 [avatar split clause 136,313]
397. 39 [avatar split clause 144,313]
398. $false [avatar sat refutation 366,397]
% SZS output end Proof for 430497201679565248255526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is not generous or not strong and vice versa.
Everyone who is creative or not creative is funny or strong.
Everyone who is either not creative or patient is not wise or not calm and vice versa.
Everyone who is both not old and not generous is quiet.
Everyone who is both not funny and tall is kind and vice versa.
If fred is old then john is not patient or brave and vice versa.
If alice is both not calm and patient then mary is either curious or generous and vice versa.
If someone is either generous or old then fred is both not tall and not generous.
Everyone who is strong or not strong is not tall or not kind and vice versa.
If fred is either not old or not kind then someone is either not tall or creative.
Everyone who is both not generous and calm is both kind and not curious and vice versa.
Everyone who is both not curious and not creative is brave and vice versa.
Everyone who is humble or not generous is both not rich and curious and vice versa.
Everyone who is not happy or curious is creative or humble.
Everyone who is wise is either not patient or not curious and vice versa.
Everyone who is old is wise or not funny.
John is generous or creative.
Someone is either rich or not brave.
Someone is not humble.
Someone is not funny or strong.
John is either curious or not funny. | Fred is not creative. | neutral | (![X]:(strong(X)<=>(~generous(X)|~strong(X))))&
(![X]:((creative(X)|~creative(X))=>(funny(X)|strong(X))))&
(![X]:((~creative(X)<~>patient(X))<=>(~wise(X)|~calm(X))))&
(![X]:((~old(X)&~generous(X))=>quiet(X)))&
(![X]:((~funny(X)&tall(X))<=>kind(X)))&
((old(fred))<=>((~patient(john)|brave(john))))&
(((~calm(alice)&patient(alice)))<=>((curious(mary)<~>generous(mary))))&
((?[X]:((generous(X)<~>old(X))))=>((~tall(fred)&~generous(fred))))&
(![X]:((strong(X)|~strong(X))<=>(~tall(X)|~kind(X))))&
(((~old(fred)<~>~kind(fred)))=>(?[X]:((~tall(X)<~>creative(X)))))&
(![X]:((~generous(X)&calm(X))<=>(kind(X)&~curious(X))))&
(![X]:((~curious(X)&~creative(X))<=>brave(X)))&
(![X]:((humble(X)|~generous(X))<=>(~rich(X)&curious(X))))&
(![X]:((~happy(X)|curious(X))=>(creative(X)|humble(X))))&
(![X]:(wise(X)<=>(~patient(X)<~>~curious(X))))&
(![X]:(old(X)=>(wise(X)|~funny(X))))&
((generous(john)|creative(john)))&
(?[X]:((rich(X)<~>~brave(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~funny(X)|strong(X))))&
((curious(john)<~>~funny(john))) | ~creative(fred) | [] | null | 0 |
Everyone who is either not wise or curious is funny. Everyone who is quiet or generous is not funny and vice versa. If alice is tall then mary is both creative and old and vice versa. Everyone who is not kind or happy is either not calm or kind. Everyone who is kind is not strong. Everyone who is brave or calm is either not brave or not strong and vice versa. If alice is not quiet or tall then mary is both calm and wise and vice versa. If someone is either not happy or brave then someone is either generous or not patient and vice versa. If susan is tall or not funny then paul is rich. Everyone who is both curious and not humble is not creative or generous and vice versa. If john is not tall then john is both not creative and not rich and vice versa. Everyone who is either not happy or not kind is kind or quiet. Everyone who is not creative is not brave. If paul is quiet or rich then john is funny or generous and vice versa. Everyone who is happy is creative. If someone is funny then someone is either not generous or happy. Someone is both generous and not strong. Alice is funny. Fred is both not generous and not humble. Alice is not calm or funny. Alice is funny or not creative. Mary is wise. Someone is not patient or not wise. Someone is both not strong and not tall. | Paul is strong. | contradiction | (![X]:((~wise(X)<~>curious(X))=>funny(X)))&
(![X]:((quiet(X)|generous(X))<=>~funny(X)))&
((tall(alice))<=>((creative(mary)&old(mary))))&
(![X]:((~kind(X)|happy(X))=>(~calm(X)<~>kind(X))))&
(![X]:(kind(X)=>~strong(X)))&
(![X]:((brave(X)|calm(X))<=>(~brave(X)<~>~strong(X))))&
(((~quiet(alice)|tall(alice)))<=>((calm(mary)&wise(mary))))&
((?[X]:((~happy(X)<~>brave(X))))<=>(?[X]:((generous(X)<~>~patient(X)))))&
(((tall(susan)|~funny(susan)))=>(rich(paul)))&
(![X]:((curious(X)&~humble(X))<=>(~creative(X)|generous(X))))&
((~tall(john))<=>((~creative(john)&~rich(john))))&
(![X]:((~happy(X)<~>~kind(X))=>(kind(X)|quiet(X))))&
(![X]:(~creative(X)=>~brave(X)))&
(((quiet(paul)|rich(paul)))<=>((funny(john)|generous(john))))&
(![X]:(happy(X)=>creative(X)))&
((?[X]:(funny(X)))=>(?[X]:((~generous(X)<~>happy(X)))))&
(?[X]:((generous(X)&~strong(X))))&
(funny(alice))&
((~generous(fred)&~humble(fred)))&
((~calm(alice)|funny(alice)))&
((funny(alice)|~creative(alice)))&
(wise(mary))&
(?[X]:((~patient(X)|~wise(X))))&
(?[X]:((~strong(X)&~tall(X)))) | strong(paul) | [
"p3",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 391555666124830533475117
% SZS output start Proof for 391555666124830533475117
4. ! [X0] : ((happy(X0) | ~kind(X0)) => (~calm(X0) <~> kind(X0))) [input p3]
5. ! [X0] : (kind(X0) => ~strong(X0)) [input p4]
6. ! [X0] : ((calm(X0) | brave(X0)) <=> (~brave(X0) <~> ~strong(X0))) [input p5]
25. strong(paul) [input hypothesis]
29. ! [X0] : ((~calm(X0) <~> kind(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 4]
30. ! [X0] : (~strong(X0) | ~kind(X0)) [ennf transformation 5]
42. ! [X0] : (((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | (~happy(X0) & kind(X0))) [nnf transformation 29]
43. ! [X0] : (((calm(X0) | brave(X0)) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0)))) & (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (~calm(X0) & ~brave(X0)))) [nnf transformation 6]
44. ! [X0] : ((calm(X0) | brave(X0) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0)))) & (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (~calm(X0) & ~brave(X0)))) [flattening 43]
77. kind(X0) | ~calm(X0) | kind(X0) [cnf transformation 42]
81. ~strong(X0) | ~kind(X0) [cnf transformation 30]
82. ~strong(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 44]
86. calm(X0) | brave(X0) | ~strong(X0) | brave(X0) [cnf transformation 44]
132. strong(paul) [cnf transformation 25]
134. ~brave(X0) | ~strong(X0) [duplicate literal removal 82]
135. ~strong(X0) | brave(X0) | calm(X0) [duplicate literal removal 86]
136. ~calm(X0) | kind(X0) [duplicate literal removal 77]
274. ~kind(paul) [resolution 81,132]
374. brave(paul) | calm(paul) [resolution 135,132]
376. 41 <=> calm(paul) [avatar definition]
378. calm(paul) <- (41) [avatar component clause 376]
380. 42 <=> brave(paul) [avatar definition]
382. brave(paul) <- (42) [avatar component clause 380]
383. 41 | 42 [avatar split clause 374,380,376]
412. kind(paul) <- (41) [resolution 378,136]
414. $false <- (41) [subsumption resolution 412,274]
415. ~41 [avatar contradiction clause 414]
417. ~strong(paul) <- (42) [resolution 382,134]
419. $false <- (42) [subsumption resolution 417,132]
420. ~42 [avatar contradiction clause 419]
421. $false [avatar sat refutation 383,415,420]
% SZS output end Proof for 391555666124830533475117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or tall is not humble or patient and vice versa.
Everyone who is generous or kind is not kind and vice versa.
If john is not old then john is either not tall or not curious and vice versa.
If someone is not tall then someone is both not generous and patient and vice versa.
If lucy is strong or not wise then fred is brave or not strong.
If someone is both not curious and not quiet then susan is either rich or not happy and vice versa.
Everyone who is not quiet is both not wise and funny.
If someone is both not kind and calm then susan is both not generous and tall.
If someone is either creative or not humble then someone is quiet and vice versa.
If susan is not tall or not funny then someone is quiet.
Everyone who is not calm is either happy or not curious and vice versa.
Everyone who is both kind and not happy is not tall or patient.
If someone is brave or not quiet then someone is kind and vice versa.
If mary is both not curious and not old then someone is creative or curious.
If fred is both old and not happy then someone is either generous or not quiet.
Everyone who is not funny or happy is humble and vice versa.
Paul is curious or not humble.
Someone is rich or happy.
Alice is either not kind or strong.
Susan is not creative.
Alice is not wise.
Alice is brave or not wise.
Someone is not funny or not humble. | Mary is old. | neutral | (![X]:((quiet(X)|tall(X))<=>(~humble(X)|patient(X))))&
(![X]:((generous(X)|kind(X))<=>~kind(X)))&
((~old(john))<=>((~tall(john)<~>~curious(john))))&
((?[X]:(~tall(X)))<=>(?[X]:((~generous(X)&patient(X)))))&
(((strong(lucy)|~wise(lucy)))=>((brave(fred)|~strong(fred))))&
((?[X]:((~curious(X)&~quiet(X))))<=>((rich(susan)<~>~happy(susan))))&
(![X]:(~quiet(X)=>(~wise(X)&funny(X))))&
((?[X]:((~kind(X)&calm(X))))=>((~generous(susan)&tall(susan))))&
((?[X]:((creative(X)<~>~humble(X))))<=>(?[X]:(quiet(X))))&
(((~tall(susan)|~funny(susan)))=>(?[X]:(quiet(X))))&
(![X]:(~calm(X)<=>(happy(X)<~>~curious(X))))&
(![X]:((kind(X)&~happy(X))=>(~tall(X)|patient(X))))&
((?[X]:((brave(X)|~quiet(X))))<=>(?[X]:(kind(X))))&
(((~curious(mary)&~old(mary)))=>(?[X]:((creative(X)|curious(X)))))&
(((old(fred)&~happy(fred)))=>(?[X]:((generous(X)<~>~quiet(X)))))&
(![X]:((~funny(X)|happy(X))<=>humble(X)))&
((curious(paul)|~humble(paul)))&
(?[X]:((rich(X)|happy(X))))&
((~kind(alice)<~>strong(alice)))&
(~creative(susan))&
(~wise(alice))&
((brave(alice)|~wise(alice)))&
(?[X]:((~funny(X)|~humble(X)))) | old(mary) | [] | null | 0 |
Everyone who is not quiet or not strong is rich or funny and vice versa.
If someone is old or happy then paul is wise or brave.
Everyone who is either not old or not tall is generous or old and vice versa.
Everyone who is old is both not curious and quiet.
If someone is either quiet or not happy then someone is wise and vice versa.
Everyone who is both not humble and not tall is either not rich or tall.
Everyone who is rich or not quiet is both calm and happy.
Everyone who is calm is quiet and vice versa.
Everyone who is not strong is not funny and vice versa.
If someone is not strong then paul is humble.
Everyone who is either rich or not brave is either not old or creative and vice versa.
Everyone who is kind is both curious and not kind and vice versa.
If someone is either tall or quiet then someone is old.
Everyone who is either creative or not patient is both old and kind and vice versa.
Someone is not kind.
Someone is patient or funny.
Fred is not calm or patient.
Someone is either not curious or not creative.
Fred is not funny or generous. | Paul is happy. | entailment | (![X]:((~quiet(X)|~strong(X))<=>(rich(X)|funny(X))))&
((?[X]:((old(X)|happy(X))))=>((wise(paul)|brave(paul))))&
(![X]:((~old(X)<~>~tall(X))<=>(generous(X)|old(X))))&
(![X]:(old(X)=>(~curious(X)&quiet(X))))&
((?[X]:((quiet(X)<~>~happy(X))))<=>(?[X]:(wise(X))))&
(![X]:((~humble(X)&~tall(X))=>(~rich(X)<~>tall(X))))&
(![X]:((rich(X)|~quiet(X))=>(calm(X)&happy(X))))&
(![X]:(calm(X)<=>quiet(X)))&
(![X]:(~strong(X)<=>~funny(X)))&
((?[X]:(~strong(X)))=>(humble(paul)))&
(![X]:((rich(X)<~>~brave(X))<=>(~old(X)<~>creative(X))))&
(![X]:(kind(X)<=>(curious(X)&~kind(X))))&
((?[X]:((tall(X)<~>quiet(X))))=>(?[X]:(old(X))))&
(![X]:((creative(X)<~>~patient(X))<=>(old(X)&kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:((patient(X)|funny(X))))&
((~calm(fred)|patient(fred)))&
(?[X]:((~curious(X)<~>~creative(X))))&
((~funny(fred)|generous(fred))) | happy(paul) | [
"p0",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3614248019485457521843405
% SZS output start Proof for 3614248019485457521843405
1. ! [X0] : ((~strong(X0) | ~quiet(X0)) <=> (funny(X0) | rich(X0))) [input p0]
7. ! [X0] : ((~quiet(X0) | rich(X0)) => (happy(X0) & calm(X0))) [input p6]
8. ! [X0] : (calm(X0) <=> quiet(X0)) [input p7]
9. ! [X0] : (~strong(X0) <=> ~funny(X0)) [input p8]
20. ~happy(paul) [input hypothesis]
28. ! [X0] : ((happy(X0) & calm(X0)) | (quiet(X0) & ~rich(X0))) [ennf transformation 7]
30. ! [X0] : (((~strong(X0) | ~quiet(X0)) | (~funny(X0) & ~rich(X0))) & ((funny(X0) | rich(X0)) | (strong(X0) & quiet(X0)))) [nnf transformation 1]
31. ! [X0] : ((~strong(X0) | ~quiet(X0) | (~funny(X0) & ~rich(X0))) & (funny(X0) | rich(X0) | (strong(X0) & quiet(X0)))) [flattening 30]
39. ! [X0] : ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))) [nnf transformation 8]
40. ! [X0] : ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))) [nnf transformation 9]
58. funny(X0) | rich(X0) | strong(X0) [cnf transformation 31]
60. ~funny(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 31]
76. calm(X0) | quiet(X0) [cnf transformation 28]
77. ~rich(X0) | happy(X0) [cnf transformation 28]
79. quiet(X0) | ~calm(X0) [cnf transformation 39]
80. calm(X0) | ~quiet(X0) [cnf transformation 39]
81. ~funny(X0) | strong(X0) [cnf transformation 40]
82. ~strong(X0) | funny(X0) [cnf transformation 40]
108. ~happy(paul) [cnf transformation 20]
156. calm(X0) [subsumption resolution 80,76]
157. quiet(X0) [subsumption resolution 79,156]
217. rich(X0) | strong(X0) | strong(X0) [resolution 58,81]
218. rich(X0) | strong(X0) [duplicate literal removal 217]
267. 24 <=> rich(paul) [avatar definition]
268. rich(paul) <- (24) [avatar component clause 267]
269. ~rich(paul) <- (~24) [avatar component clause 267]
319. happy(paul) <- (24) [resolution 268,77]
322. $false <- (24) [subsumption resolution 319,108]
323. ~24 [avatar contradiction clause 322]
336. strong(paul) <- (~24) [resolution 218,269]
340. funny(paul) <- (~24) [resolution 336,82]
342. ~quiet(paul) | ~strong(paul) <- (~24) [resolution 340,60]
344. ~strong(paul) <- (~24) [subsumption resolution 342,157]
345. $false <- (~24) [subsumption resolution 344,336]
346. 24 [avatar contradiction clause 345]
347. $false [avatar sat refutation 323,346]
% SZS output end Proof for 3614248019485457521843405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or wise is both not quiet and not generous.
Everyone who is both not calm and not funny is both not funny and not old and vice versa.
Everyone who is not kind or not happy is both patient and not patient.
If john is brave or not generous then fred is both not generous and not funny and vice versa.
Everyone who is both not old and tall is either brave or not kind and vice versa.
If someone is quiet then someone is either humble or tall.
If someone is both curious and kind then someone is either old or humble.
If lucy is rich or not old then paul is both generous and quiet and vice versa.
Everyone who is either wise or not generous is happy or not brave.
Everyone who is either not tall or not humble is humble or not rich.
Everyone who is not quiet is both not strong and not tall.
Everyone who is either not calm or not strong is quiet and vice versa.
Everyone who is not brave is generous or not brave and vice versa.
If alice is kind then someone is kind and vice versa.
Everyone who is not kind or not calm is humble and vice versa.
Everyone who is not calm or not rich is not humble or not kind and vice versa.
Someone is not creative or wise.
Someone is calm.
Mary is not humble or not wise.
Someone is quiet or strong.
Alice is happy or creative.
Lucy is either not funny or not quiet.
Someone is curious or calm. | Mary is not humble. | entailment | (![X]:((tall(X)<~>wise(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~calm(X)&~funny(X))<=>(~funny(X)&~old(X))))&
(![X]:((~kind(X)|~happy(X))=>(patient(X)&~patient(X))))&
(((brave(john)|~generous(john)))<=>((~generous(fred)&~funny(fred))))&
(![X]:((~old(X)&tall(X))<=>(brave(X)<~>~kind(X))))&
((?[X]:(quiet(X)))=>(?[X]:((humble(X)<~>tall(X)))))&
((?[X]:((curious(X)&kind(X))))=>(?[X]:((old(X)<~>humble(X)))))&
(((rich(lucy)|~old(lucy)))<=>((generous(paul)&quiet(paul))))&
(![X]:((wise(X)<~>~generous(X))=>(happy(X)|~brave(X))))&
(![X]:((~tall(X)<~>~humble(X))=>(humble(X)|~rich(X))))&
(![X]:(~quiet(X)=>(~strong(X)&~tall(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>quiet(X)))&
(![X]:(~brave(X)<=>(generous(X)|~brave(X))))&
((kind(alice))<=>(?[X]:(kind(X))))&
(![X]:((~kind(X)|~calm(X))<=>humble(X)))&
(![X]:((~calm(X)|~rich(X))<=>(~humble(X)|~kind(X))))&
(?[X]:((~creative(X)|wise(X))))&
(?[X]:(calm(X)))&
((~humble(mary)|~wise(mary)))&
(?[X]:((quiet(X)|strong(X))))&
((happy(alice)|creative(alice)))&
((~funny(lucy)<~>~quiet(lucy)))&
(?[X]:((curious(X)|calm(X)))) | ~humble(mary) | [
"p2",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3045597532252866877804673
% SZS output start Proof for 3045597532252866877804673
3. ! [X0] : ((~happy(X0) | ~kind(X0)) => (~patient(X0) & patient(X0))) [input p2]
15. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> humble(X0)) [input p14]
16. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> (~kind(X0) | ~humble(X0))) [input p15]
24. humble(mary) [input hypothesis]
28. ! [X0] : (~kind(X0) => (~patient(X0) & patient(X0))) [pure predicate removal 3]
32. ! [X0] : ((~patient(X0) & patient(X0)) | kind(X0)) [ennf transformation 28]
63. ! [X0] : (((~calm(X0) | ~kind(X0)) | ~humble(X0)) & (humble(X0) | (calm(X0) & kind(X0)))) [nnf transformation 15]
64. ! [X0] : ((~calm(X0) | ~kind(X0) | ~humble(X0)) & (humble(X0) | (calm(X0) & kind(X0)))) [flattening 63]
65. ! [X0] : (((~rich(X0) | ~calm(X0)) | (kind(X0) & humble(X0))) & ((~kind(X0) | ~humble(X0)) | (rich(X0) & calm(X0)))) [nnf transformation 16]
66. ! [X0] : ((~rich(X0) | ~calm(X0) | (kind(X0) & humble(X0))) & (~kind(X0) | ~humble(X0) | (rich(X0) & calm(X0)))) [flattening 65]
82. patient(X0) | kind(X0) [cnf transformation 32]
83. ~patient(X0) | kind(X0) [cnf transformation 32]
119. ~calm(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 64]
120. ~kind(X0) | ~humble(X0) | calm(X0) [cnf transformation 66]
130. humble(mary) [cnf transformation 24]
132. kind(X0) [subsumption resolution 82,83]
208. ~calm(X0) | ~humble(X0) [subsumption resolution 119,132]
211. ~humble(X0) | calm(X0) [subsumption resolution 120,132]
212. ~humble(X0) [subsumption resolution 211,208]
233. $false [subsumption resolution 130,212]
% SZS output end Proof for 3045597532252866877804673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is both not strong and not happy. Everyone who is either not humble or not funny is both brave and funny. If someone is both not humble and curious then susan is kind and vice versa. If lucy is not happy or not creative then someone is either not curious or not brave. If someone is both curious and not brave then someone is both not rich and creative and vice versa. Everyone who is either funny or not brave is calm or not generous and vice versa. If fred is not rich then susan is either not creative or funny. If someone is wise or funny then fred is not old and vice versa. Everyone who is both not old and old is rich or not wise. If someone is not brave or tall then lucy is calm and vice versa. Everyone who is not humble is not rich or not creative. Everyone who is not rich is both humble and not rich and vice versa. If lucy is calm then mary is both creative and wise. Everyone who is both generous and kind is patient. If fred is not quiet or not strong then someone is both brave and not generous. Everyone who is quiet or not creative is either not tall or rich and vice versa. Someone is both calm and humble. Susan is not creative or rich. Someone is not humble. Lucy is humble or not creative. Someone is either not strong or rich. Susan is not curious or not old. Someone is both not patient and not brave. | Fred is not rich. | neutral | (![X]:(happy(X)=>(~strong(X)&~happy(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(brave(X)&funny(X))))&
((?[X]:((~humble(X)&curious(X))))<=>(kind(susan)))&
(((~happy(lucy)|~creative(lucy)))=>(?[X]:((~curious(X)<~>~brave(X)))))&
((?[X]:((curious(X)&~brave(X))))<=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:((funny(X)<~>~brave(X))<=>(calm(X)|~generous(X))))&
((~rich(fred))=>((~creative(susan)<~>funny(susan))))&
((?[X]:((wise(X)|funny(X))))<=>(~old(fred)))&
(![X]:((~old(X)&old(X))=>(rich(X)|~wise(X))))&
((?[X]:((~brave(X)|tall(X))))<=>(calm(lucy)))&
(![X]:(~humble(X)=>(~rich(X)|~creative(X))))&
(![X]:(~rich(X)<=>(humble(X)&~rich(X))))&
((calm(lucy))=>((creative(mary)&wise(mary))))&
(![X]:((generous(X)&kind(X))=>patient(X)))&
(((~quiet(fred)|~strong(fred)))=>(?[X]:((brave(X)&~generous(X)))))&
(![X]:((quiet(X)|~creative(X))<=>(~tall(X)<~>rich(X))))&
(?[X]:((calm(X)&humble(X))))&
((~creative(susan)|rich(susan)))&
(?[X]:(~humble(X)))&
((humble(lucy)|~creative(lucy)))&
(?[X]:((~strong(X)<~>rich(X))))&
((~curious(susan)|~old(susan)))&
(?[X]:((~patient(X)&~brave(X)))) | ~rich(fred) | [] | null | 0 |
Everyone who is both not strong and generous is either not generous or rich and vice versa. If someone is either not quiet or not tall then someone is both not tall and not humble. If someone is funny then someone is happy and vice versa. Everyone who is both wise and not rich is funny. Everyone who is humble or not rich is not humble and vice versa. Everyone who is both curious and brave is kind and vice versa. If susan is either not calm or not funny then someone is generous or curious. If susan is not old then alice is calm and vice versa. Everyone who is not old is both calm and not calm and vice versa. Everyone who is either not generous or kind is either rich or happy and vice versa. Everyone who is either not humble or not funny is either curious or not old. Everyone who is patient or creative is not generous. Everyone who is not old or not curious is either patient or not brave and vice versa. Everyone who is both funny and not strong is both humble and calm. If paul is kind or happy then susan is either brave or not patient and vice versa. Alice is old or not brave. Someone is not calm or brave. John is both not quiet and happy. Lucy is not rich. Someone is either happy or creative. Someone is humble or not rich. Alice is happy. John is not old or not wise. | Paul is wise. | neutral | (![X]:((~strong(X)&generous(X))<=>(~generous(X)<~>rich(X))))&
((?[X]:((~quiet(X)<~>~tall(X))))=>(?[X]:((~tall(X)&~humble(X)))))&
((?[X]:(funny(X)))<=>(?[X]:(happy(X))))&
(![X]:((wise(X)&~rich(X))=>funny(X)))&
(![X]:((humble(X)|~rich(X))<=>~humble(X)))&
(![X]:((curious(X)&brave(X))<=>kind(X)))&
(((~calm(susan)<~>~funny(susan)))=>(?[X]:((generous(X)|curious(X)))))&
((~old(susan))<=>(calm(alice)))&
(![X]:(~old(X)<=>(calm(X)&~calm(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(rich(X)<~>happy(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(curious(X)<~>~old(X))))&
(![X]:((patient(X)|creative(X))=>~generous(X)))&
(![X]:((~old(X)|~curious(X))<=>(patient(X)<~>~brave(X))))&
(![X]:((funny(X)&~strong(X))=>(humble(X)&calm(X))))&
(((kind(paul)|happy(paul)))<=>((brave(susan)<~>~patient(susan))))&
((old(alice)|~brave(alice)))&
(?[X]:((~calm(X)|brave(X))))&
((~quiet(john)&happy(john)))&
(~rich(lucy))&
(?[X]:((happy(X)<~>creative(X))))&
(?[X]:((humble(X)|~rich(X))))&
(happy(alice))&
((~old(john)|~wise(john))) | wise(paul) | [] | null | 0 |
Everyone who is not patient is generous or not kind and vice versa.
Everyone who is rich is happy or strong.
Everyone who is both not funny and not strong is quiet.
If someone is not creative then mary is not creative.
Everyone who is both quiet and not strong is not quiet and vice versa.
Everyone who is quiet or not humble is generous or kind.
If lucy is patient or not creative then someone is either not creative or strong.
If alice is both strong and not calm then alice is not generous or not strong and vice versa.
If john is either curious or patient then someone is both strong and not calm.
Everyone who is both not patient and tall is tall and vice versa.
Everyone who is both quiet and creative is not curious or strong and vice versa.
If fred is either rich or strong then someone is not old.
Everyone who is not quiet or patient is either calm or not humble.
If someone is not strong then paul is either not patient or not tall and vice versa.
Everyone who is not wise or not humble is not tall.
If fred is both wise and not calm then someone is not humble or not strong.
Someone is not funny.
John is not rich or not calm.
Someone is either not kind or curious.
Alice is funny.
Susan is not tall or quiet.
Fred is funny.
Susan is not kind. | John is patient. | neutral | (![X]:(~patient(X)<=>(generous(X)|~kind(X))))&
(![X]:(rich(X)=>(happy(X)|strong(X))))&
(![X]:((~funny(X)&~strong(X))=>quiet(X)))&
((?[X]:(~creative(X)))=>(~creative(mary)))&
(![X]:((quiet(X)&~strong(X))<=>~quiet(X)))&
(![X]:((quiet(X)|~humble(X))=>(generous(X)|kind(X))))&
(((patient(lucy)|~creative(lucy)))=>(?[X]:((~creative(X)<~>strong(X)))))&
(((strong(alice)&~calm(alice)))<=>((~generous(alice)|~strong(alice))))&
(((curious(john)<~>patient(john)))=>(?[X]:((strong(X)&~calm(X)))))&
(![X]:((~patient(X)&tall(X))<=>tall(X)))&
(![X]:((quiet(X)&creative(X))<=>(~curious(X)|strong(X))))&
(((rich(fred)<~>strong(fred)))=>(?[X]:(~old(X))))&
(![X]:((~quiet(X)|patient(X))=>(calm(X)<~>~humble(X))))&
((?[X]:(~strong(X)))<=>((~patient(paul)<~>~tall(paul))))&
(![X]:((~wise(X)|~humble(X))=>~tall(X)))&
(((wise(fred)&~calm(fred)))=>(?[X]:((~humble(X)|~strong(X)))))&
(?[X]:(~funny(X)))&
((~rich(john)|~calm(john)))&
(?[X]:((~kind(X)<~>curious(X))))&
(funny(alice))&
((~tall(susan)|quiet(susan)))&
(funny(fred))&
(~kind(susan)) | patient(john) | [] | null | 0 |
If someone is either not wise or patient then fred is either not curious or strong and vice versa. Everyone who is not kind or not happy is not creative. Everyone who is both not rich and happy is kind or funny and vice versa. If someone is not brave then alice is generous or not funny and vice versa. Everyone who is both not curious and not creative is not brave or tall. Everyone who is old or creative is not happy and vice versa. Everyone who is not curious is both funny and not generous. If someone is either strong or kind then someone is either not strong or rich and vice versa. If paul is either not funny or quiet then fred is not generous or not brave and vice versa. If someone is not generous then someone is either wise or old. If someone is not kind or patient then lucy is both old and not calm and vice versa. Everyone who is not generous is both not quiet and kind. Everyone who is wise or not patient is not brave. Everyone who is not wise or humble is not humble. Everyone who is not happy or funny is not curious. If john is creative then someone is not wise. Someone is not rich. Someone is not strong or not happy. Someone is either quiet or not generous. John is not calm. Paul is strong. Someone is both happy and not humble. Lucy is either old or strong. Someone is both generous and not calm. | Alice is not rich. | entailment | ((?[X]:((~wise(X)<~>patient(X))))<=>((~curious(fred)<~>strong(fred))))&
(![X]:((~kind(X)|~happy(X))=>~creative(X)))&
(![X]:((~rich(X)&happy(X))<=>(kind(X)|funny(X))))&
((?[X]:(~brave(X)))<=>((generous(alice)|~funny(alice))))&
(![X]:((~curious(X)&~creative(X))=>(~brave(X)|tall(X))))&
(![X]:((old(X)|creative(X))<=>~happy(X)))&
(![X]:(~curious(X)=>(funny(X)&~generous(X))))&
((?[X]:((strong(X)<~>kind(X))))<=>(?[X]:((~strong(X)<~>rich(X)))))&
(((~funny(paul)<~>quiet(paul)))<=>((~generous(fred)|~brave(fred))))&
((?[X]:(~generous(X)))=>(?[X]:((wise(X)<~>old(X)))))&
((?[X]:((~kind(X)|patient(X))))<=>((old(lucy)&~calm(lucy))))&
(![X]:(~generous(X)=>(~quiet(X)&kind(X))))&
(![X]:((wise(X)|~patient(X))=>~brave(X)))&
(![X]:((~wise(X)|humble(X))=>~humble(X)))&
(![X]:((~happy(X)|funny(X))=>~curious(X)))&
((creative(john))=>(?[X]:(~wise(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~strong(X)|~happy(X))))&
(?[X]:((quiet(X)<~>~generous(X))))&
(~calm(john))&
(strong(paul))&
(?[X]:((happy(X)&~humble(X))))&
((old(lucy)<~>strong(lucy)))&
(?[X]:((generous(X)&~calm(X)))) | ~rich(alice) | [
"p2",
"p5",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8740234833021130905648445
% SZS output start Proof for 8740234833021130905648445
3. ! [X0] : ((happy(X0) & ~rich(X0)) <=> (funny(X0) | kind(X0))) [input p2]
6. ! [X0] : ((creative(X0) | old(X0)) <=> ~happy(X0)) [input p5]
7. ! [X0] : (~curious(X0) => (~generous(X0) & funny(X0))) [input p6]
11. ? [X0] : (patient(X0) | ~kind(X0)) <=> (~calm(lucy) & old(lucy)) [input p10]
15. ! [X0] : ((funny(X0) | ~happy(X0)) => ~curious(X0)) [input p14]
25. rich(alice) [input hypothesis]
32. ! [X0] : ((~generous(X0) & funny(X0)) | curious(X0)) [ennf transformation 7]
36. ! [X0] : (~curious(X0) | (~funny(X0) & happy(X0))) [ennf transformation 15]
42. ! [X0] : (((happy(X0) & ~rich(X0)) | (~funny(X0) & ~kind(X0))) & ((funny(X0) | kind(X0)) | (~happy(X0) | rich(X0)))) [nnf transformation 3]
43. ! [X0] : (((happy(X0) & ~rich(X0)) | (~funny(X0) & ~kind(X0))) & (funny(X0) | kind(X0) | ~happy(X0) | rich(X0))) [flattening 42]
49. ! [X0] : (((creative(X0) | old(X0)) | happy(X0)) & (~happy(X0) | (~creative(X0) & ~old(X0)))) [nnf transformation 6]
50. ! [X0] : ((creative(X0) | old(X0) | happy(X0)) & (~happy(X0) | (~creative(X0) & ~old(X0)))) [flattening 49]
62. (? [X0] : (patient(X0) | ~kind(X0)) | (calm(lucy) | ~old(lucy))) & ((~calm(lucy) & old(lucy)) | ! [X0] : (~patient(X0) & kind(X0))) [nnf transformation 11]
63. (? [X0] : (patient(X0) | ~kind(X0)) | calm(lucy) | ~old(lucy)) & ((~calm(lucy) & old(lucy)) | ! [X0] : (~patient(X0) & kind(X0))) [flattening 62]
64. (? [X0] : (patient(X0) | ~kind(X0)) | calm(lucy) | ~old(lucy)) & ((~calm(lucy) & old(lucy)) | ! [X1] : (~patient(X1) & kind(X1))) [rectify 63]
65. ? [X0] : (patient(X0) | ~kind(X0)) => (patient(sK5) | ~kind(sK5)) [choice axiom]
66. ((patient(sK5) | ~kind(sK5)) | calm(lucy) | ~old(lucy)) & ((~calm(lucy) & old(lucy)) | ! [X1] : (~patient(X1) & kind(X1))) [skolemisation 64,65]
92. ~rich(X0) | ~kind(X0) [cnf transformation 43]
95. ~funny(X0) | happy(X0) [cnf transformation 43]
99. ~old(X0) | ~happy(X0) [cnf transformation 50]
102. funny(X0) | curious(X0) [cnf transformation 32]
120. old(lucy) | kind(X1) [cnf transformation 66]
129. ~curious(X0) | happy(X0) [cnf transformation 36]
143. rich(alice) [cnf transformation 25]
266. 26 <=> old(lucy) [avatar definition]
267. old(lucy) <- (26) [avatar component clause 266]
287. 31 <=> ! [X1] : kind(X1) [avatar definition]
288. kind(X1) <- (31) [avatar component clause 287]
291. 31 | 26 [avatar split clause 120,266,287]
320. ~kind(alice) [resolution 92,143]
321. ~happy(lucy) <- (26) [resolution 99,267]
324. curious(X0) | happy(X0) [resolution 102,95]
326. happy(X0) [subsumption resolution 324,129]
335. $false <- (26) [resolution 326,321]
336. ~26 [avatar contradiction clause 335]
339. $false <- (31) [resolution 288,320]
344. ~31 [avatar contradiction clause 339]
345. $false [avatar sat refutation 291,336,344]
% SZS output end Proof for 8740234833021130905648445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or tall is either brave or calm.
If someone is not generous or not humble then someone is calm and vice versa.
Everyone who is brave or patient is old or not calm and vice versa.
Everyone who is both patient and rich is tall.
If someone is either not wise or not old then someone is strong or humble.
If someone is funny or rich then someone is both humble and not patient and vice versa.
If someone is humble then paul is both not humble and funny.
Everyone who is not rich is not brave and vice versa.
Everyone who is either calm or quiet is rich and vice versa.
Everyone who is either wise or quiet is either not funny or not generous and vice versa.
Everyone who is happy or not kind is not patient or tall and vice versa.
Everyone who is both curious and not kind is either not quiet or strong and vice versa.
Everyone who is old or not patient is either tall or humble.
If fred is both not strong and not kind then john is not creative.
Everyone who is both not tall and not old is patient.
Everyone who is both funny and tall is strong or not rich and vice versa.
Someone is both curious and not funny.
John is funny.
Someone is both tall and funny.
Alice is not creative.
Fred is not patient.
Someone is patient.
Alice is not wise or not strong.
Susan is either old or brave. | Susan is not generous. | neutral | (![X]:((~quiet(X)<~>tall(X))=>(brave(X)<~>calm(X))))&
((?[X]:((~generous(X)|~humble(X))))<=>(?[X]:(calm(X))))&
(![X]:((brave(X)|patient(X))<=>(old(X)|~calm(X))))&
(![X]:((patient(X)&rich(X))=>tall(X)))&
((?[X]:((~wise(X)<~>~old(X))))=>(?[X]:((strong(X)|humble(X)))))&
((?[X]:((funny(X)|rich(X))))<=>(?[X]:((humble(X)&~patient(X)))))&
((?[X]:(humble(X)))=>((~humble(paul)&funny(paul))))&
(![X]:(~rich(X)<=>~brave(X)))&
(![X]:((calm(X)<~>quiet(X))<=>rich(X)))&
(![X]:((wise(X)<~>quiet(X))<=>(~funny(X)<~>~generous(X))))&
(![X]:((happy(X)|~kind(X))<=>(~patient(X)|tall(X))))&
(![X]:((curious(X)&~kind(X))<=>(~quiet(X)<~>strong(X))))&
(![X]:((old(X)|~patient(X))=>(tall(X)<~>humble(X))))&
(((~strong(fred)&~kind(fred)))=>(~creative(john)))&
(![X]:((~tall(X)&~old(X))=>patient(X)))&
(![X]:((funny(X)&tall(X))<=>(strong(X)|~rich(X))))&
(?[X]:((curious(X)&~funny(X))))&
(funny(john))&
(?[X]:((tall(X)&funny(X))))&
(~creative(alice))&
(~patient(fred))&
(?[X]:(patient(X)))&
((~wise(alice)|~strong(alice)))&
((old(susan)<~>brave(susan))) | ~generous(susan) | [] | null | 0 |
If john is brave then fred is both calm and curious. Everyone who is not rich is calm and vice versa. Everyone who is both not tall and creative is not curious. If fred is not wise or tall then mary is both not funny and happy and vice versa. Everyone who is both curious and rich is either not curious or not generous. If someone is either strong or not happy then lucy is generous and vice versa. If susan is old then someone is both humble and not patient and vice versa. If fred is both humble and not calm then someone is either not calm or quiet. If someone is old or not humble then john is not brave or patient and vice versa. Everyone who is both happy and not happy is either not happy or not quiet and vice versa. Everyone who is strong or quiet is not quiet. Everyone who is calm is either creative or patient. If someone is both calm and wise then paul is kind or humble and vice versa. Everyone who is not generous is not patient and vice versa. Everyone who is not brave or not quiet is both rich and not patient and vice versa. Lucy is both not old and not quiet. Fred is either rich or old. Someone is either not kind or not humble. Susan is old or curious. Someone is not tall. Alice is not calm. Someone is funny or not generous. | Mary is curious. | neutral | ((brave(john))=>((calm(fred)&curious(fred))))&
(![X]:(~rich(X)<=>calm(X)))&
(![X]:((~tall(X)&creative(X))=>~curious(X)))&
(((~wise(fred)|tall(fred)))<=>((~funny(mary)&happy(mary))))&
(![X]:((curious(X)&rich(X))=>(~curious(X)<~>~generous(X))))&
((?[X]:((strong(X)<~>~happy(X))))<=>(generous(lucy)))&
((old(susan))<=>(?[X]:((humble(X)&~patient(X)))))&
(((humble(fred)&~calm(fred)))=>(?[X]:((~calm(X)<~>quiet(X)))))&
((?[X]:((old(X)|~humble(X))))<=>((~brave(john)|patient(john))))&
(![X]:((happy(X)&~happy(X))<=>(~happy(X)<~>~quiet(X))))&
(![X]:((strong(X)|quiet(X))=>~quiet(X)))&
(![X]:(calm(X)=>(creative(X)<~>patient(X))))&
((?[X]:((calm(X)&wise(X))))<=>((kind(paul)|humble(paul))))&
(![X]:(~generous(X)<=>~patient(X)))&
(![X]:((~brave(X)|~quiet(X))<=>(rich(X)&~patient(X))))&
((~old(lucy)&~quiet(lucy)))&
((rich(fred)<~>old(fred)))&
(?[X]:((~kind(X)<~>~humble(X))))&
((old(susan)|curious(susan)))&
(?[X]:(~tall(X)))&
(~calm(alice))&
(?[X]:((funny(X)|~generous(X)))) | curious(mary) | [] | null | 0 |
Everyone who is not creative is either brave or not brave and vice versa.
Everyone who is not wise is not old or not humble and vice versa.
If someone is either not funny or not calm then someone is not tall or not kind.
Everyone who is not generous is both not kind and not funny and vice versa.
If alice is not kind or not old then someone is brave and vice versa.
Everyone who is curious is not humble or wise.
Everyone who is generous or not strong is not quiet and vice versa.
If john is either not old or old then someone is either not rich or strong.
Everyone who is not patient is both quiet and wise.
If mary is brave or wise then someone is both old and patient.
Everyone who is either not funny or kind is rich or not tall and vice versa.
If someone is either not happy or not kind then someone is either not tall or not strong and vice versa.
Everyone who is old or not tall is not old.
Everyone who is either not humble or curious is not creative or happy and vice versa.
If someone is not funny or not quiet then paul is generous and vice versa.
If someone is not kind or quiet then paul is both not brave and not tall.
Paul is both not happy and not calm.
Susan is not happy.
Paul is either not brave or kind.
Susan is either brave or rich.
Paul is generous or not rich.
John is both generous and rich.
Someone is both not humble and not strong.
Someone is either not calm or quiet. | Paul is not happy. | entailment | (![X]:(~creative(X)<=>(brave(X)<~>~brave(X))))&
(![X]:(~wise(X)<=>(~old(X)|~humble(X))))&
((?[X]:((~funny(X)<~>~calm(X))))=>(?[X]:((~tall(X)|~kind(X)))))&
(![X]:(~generous(X)<=>(~kind(X)&~funny(X))))&
(((~kind(alice)|~old(alice)))<=>(?[X]:(brave(X))))&
(![X]:(curious(X)=>(~humble(X)|wise(X))))&
(![X]:((generous(X)|~strong(X))<=>~quiet(X)))&
(((~old(john)<~>old(john)))=>(?[X]:((~rich(X)<~>strong(X)))))&
(![X]:(~patient(X)=>(quiet(X)&wise(X))))&
(((brave(mary)|wise(mary)))=>(?[X]:((old(X)&patient(X)))))&
(![X]:((~funny(X)<~>kind(X))<=>(rich(X)|~tall(X))))&
((?[X]:((~happy(X)<~>~kind(X))))<=>(?[X]:((~tall(X)<~>~strong(X)))))&
(![X]:((old(X)|~tall(X))=>~old(X)))&
(![X]:((~humble(X)<~>curious(X))<=>(~creative(X)|happy(X))))&
((?[X]:((~funny(X)|~quiet(X))))<=>(generous(paul)))&
((?[X]:((~kind(X)|quiet(X))))=>((~brave(paul)&~tall(paul))))&
((~happy(paul)&~calm(paul)))&
(~happy(susan))&
((~brave(paul)<~>kind(paul)))&
((brave(susan)<~>rich(susan)))&
((generous(paul)|~rich(paul)))&
((generous(john)&rich(john)))&
(?[X]:((~humble(X)&~strong(X))))&
(?[X]:((~calm(X)<~>quiet(X)))) | ~happy(paul) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5060557793426829524645759
% SZS output start Proof for 5060557793426829524645759
17. ~calm(paul) & ~happy(paul) [input p16]
25. happy(paul) [input hypothesis]
132. ~happy(paul) [cnf transformation 17]
146. happy(paul) [cnf transformation 25]
327. $false [subsumption resolution 146,132]
% SZS output end Proof for 5060557793426829524645759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and rich then fred is both not funny and humble and vice versa. Everyone who is not old or not tall is both generous and not brave and vice versa. Everyone who is generous or not funny is not funny and vice versa. If someone is either not rich or not generous then mary is happy and vice versa. Everyone who is funny is either not rich or kind and vice versa. Everyone who is both funny and curious is both wise and not tall and vice versa. Everyone who is calm is not calm or not generous and vice versa. If someone is either not kind or not generous then fred is either not wise or not quiet and vice versa. Everyone who is both rich and not humble is both not creative and not brave. Everyone who is either curious or not tall is old. If john is happy or humble then paul is both happy and rich and vice versa. Everyone who is rich is old or wise. If fred is both not humble and strong then paul is both generous and funny and vice versa. If someone is either not wise or kind then mary is calm and vice versa. Everyone who is not calm or old is either patient or not tall. Everyone who is both humble and not wise is either not creative or not strong. Paul is either strong or not rich. Lucy is both not funny and old. Alice is either not humble or not quiet. John is not brave. John is both not strong and happy. Paul is both patient and humble. Someone is either not generous or curious. | Fred is not generous. | entailment | ((?[X]:((curious(X)&rich(X))))<=>((~funny(fred)&humble(fred))))&
(![X]:((~old(X)|~tall(X))<=>(generous(X)&~brave(X))))&
(![X]:((generous(X)|~funny(X))<=>~funny(X)))&
((?[X]:((~rich(X)<~>~generous(X))))<=>(happy(mary)))&
(![X]:(funny(X)<=>(~rich(X)<~>kind(X))))&
(![X]:((funny(X)&curious(X))<=>(wise(X)&~tall(X))))&
(![X]:(calm(X)<=>(~calm(X)|~generous(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>((~wise(fred)<~>~quiet(fred))))&
(![X]:((rich(X)&~humble(X))=>(~creative(X)&~brave(X))))&
(![X]:((curious(X)<~>~tall(X))=>old(X)))&
(((happy(john)|humble(john)))<=>((happy(paul)&rich(paul))))&
(![X]:(rich(X)=>(old(X)|wise(X))))&
(((~humble(fred)&strong(fred)))<=>((generous(paul)&funny(paul))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(calm(mary)))&
(![X]:((~calm(X)|old(X))=>(patient(X)<~>~tall(X))))&
(![X]:((humble(X)&~wise(X))=>(~creative(X)<~>~strong(X))))&
((strong(paul)<~>~rich(paul)))&
((~funny(lucy)&old(lucy)))&
((~humble(alice)<~>~quiet(alice)))&
(~brave(john))&
((~strong(john)&happy(john)))&
((patient(paul)&humble(paul)))&
(?[X]:((~generous(X)<~>curious(X)))) | ~generous(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8173718379987943015208634
% SZS output start Proof for 8173718379987943015208634
7. ! [X0] : (calm(X0) <=> (~generous(X0) | ~calm(X0))) [input p6]
24. generous(fred) [input hypothesis]
49. ! [X0] : ((calm(X0) | (generous(X0) & calm(X0))) & ((~generous(X0) | ~calm(X0)) | ~calm(X0))) [nnf transformation 7]
50. ! [X0] : ((calm(X0) | (generous(X0) & calm(X0))) & (~generous(X0) | ~calm(X0) | ~calm(X0))) [flattening 49]
95. ~generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 50]
96. calm(X0) | calm(X0) [cnf transformation 50]
143. generous(fred) [cnf transformation 24]
144. ~generous(X0) | ~calm(X0) [duplicate literal removal 95]
145. calm(X0) [duplicate literal removal 96]
191. ~generous(X0) [subsumption resolution 144,145]
277. $false [subsumption resolution 143,191]
% SZS output end Proof for 8173718379987943015208634
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If alice is curious or generous then paul is not rich or not wise and vice versa. Everyone who is either not old or generous is both not old and not quiet and vice versa. Everyone who is both rich and not curious is curious and vice versa. If paul is both not happy and rich then someone is either generous or not rich. Everyone who is old is wise and vice versa. Everyone who is not funny or generous is both not happy and not creative. Everyone who is not tall or patient is either not strong or strong and vice versa. Everyone who is either funny or not funny is either not patient or happy and vice versa. Everyone who is not calm or not generous is not happy or creative and vice versa. If mary is generous then someone is not brave or not patient and vice versa. Everyone who is either not wise or not happy is kind or patient and vice versa. Everyone who is either not tall or not calm is not rich. Everyone who is both rich and not patient is tall or curious. If someone is brave or strong then someone is either not tall or happy and vice versa. Someone is either not funny or not generous. John is happy. Susan is not humble. | Alice is tall. | contradiction | (((curious(alice)|generous(alice)))<=>((~rich(paul)|~wise(paul))))&
(![X]:((~old(X)<~>generous(X))<=>(~old(X)&~quiet(X))))&
(![X]:((rich(X)&~curious(X))<=>curious(X)))&
(((~happy(paul)&rich(paul)))=>(?[X]:((generous(X)<~>~rich(X)))))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((~funny(X)|generous(X))=>(~happy(X)&~creative(X))))&
(![X]:((~tall(X)|patient(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((funny(X)<~>~funny(X))<=>(~patient(X)<~>happy(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~happy(X)|creative(X))))&
((generous(mary))<=>(?[X]:((~brave(X)|~patient(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(kind(X)|patient(X))))&
(![X]:((~tall(X)<~>~calm(X))=>~rich(X)))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(?[X]:((~funny(X)<~>~generous(X))))&
(happy(john))&
(~humble(susan)) | tall(alice) | [
"p0",
"p2",
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4516320528220709325807654
% SZS output start Proof for 4516320528220709325807654
1. (generous(alice) | curious(alice)) <=> (~wise(paul) | ~rich(paul)) [input p0]
3. ! [X0] : ((~curious(X0) & rich(X0)) <=> curious(X0)) [input p2]
6. ! [X0] : ((generous(X0) | ~funny(X0)) => (~creative(X0) & ~happy(X0))) [input p5]
7. ! [X0] : ((patient(X0) | ~tall(X0)) <=> (~strong(X0) <~> strong(X0))) [input p6]
8. ! [X0] : ((funny(X0) <~> ~funny(X0)) <=> (~patient(X0) <~> happy(X0))) [input p7]
18. tall(alice) [input hypothesis]
23. ! [X0] : ((~creative(X0) & ~happy(X0)) | (~generous(X0) & funny(X0))) [ennf transformation 6]
27. ((generous(alice) | curious(alice)) | (wise(paul) & rich(paul))) & ((~wise(paul) | ~rich(paul)) | (~generous(alice) & ~curious(alice))) [nnf transformation 1]
28. (generous(alice) | curious(alice) | (wise(paul) & rich(paul))) & (~wise(paul) | ~rich(paul) | (~generous(alice) & ~curious(alice))) [flattening 27]
31. ! [X0] : (((~curious(X0) & rich(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~rich(X0)))) [nnf transformation 3]
32. ! [X0] : (((~curious(X0) & rich(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~rich(X0))) [flattening 31]
37. ! [X0] : (((patient(X0) | ~tall(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~patient(X0) & tall(X0)))) [nnf transformation 7]
38. ! [X0] : ((patient(X0) | ~tall(X0) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~patient(X0) & tall(X0)))) [flattening 37]
39. ! [X0] : ((((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0)))) & (((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0))))) [nnf transformation 8]
59. generous(alice) | curious(alice) | rich(paul) [cnf transformation 28]
67. curious(X0) | curious(X0) | ~rich(X0) [cnf transformation 32]
69. ~curious(X0) | ~curious(X0) [cnf transformation 32]
74. ~happy(X0) | funny(X0) [cnf transformation 23]
75. ~happy(X0) | ~generous(X0) [cnf transformation 23]
82. patient(X0) | ~tall(X0) | strong(X0) | strong(X0) [cnf transformation 38]
83. patient(X0) | ~tall(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 38]
84. happy(X0) | ~patient(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 39]
85. happy(X0) | ~patient(X0) | funny(X0) | funny(X0) [cnf transformation 39]
117. tall(alice) [cnf transformation 18]
118. happy(X0) | ~patient(X0) | ~funny(X0) [duplicate literal removal 84]
119. happy(X0) | ~patient(X0) | funny(X0) [duplicate literal removal 85]
122. patient(X0) | ~tall(X0) | strong(X0) [duplicate literal removal 82]
123. patient(X0) | ~tall(X0) | ~strong(X0) [duplicate literal removal 83]
124. curious(X0) | ~rich(X0) [duplicate literal removal 67]
125. ~curious(X0) [duplicate literal removal 69]
133. 2 <=> curious(alice) [avatar definition]
135. curious(alice) <- (2) [avatar component clause 133]
137. 3 <=> generous(alice) [avatar definition]
142. 4 <=> rich(paul) [avatar definition]
144. rich(paul) <- (4) [avatar component clause 142]
145. 4 | 2 | 3 [avatar split clause 59,137,133,142]
148. ~rich(X0) [subsumption resolution 124,125]
149. ~tall(X0) | patient(X0) [subsumption resolution 122,123]
151. ~patient(X0) | funny(X0) [subsumption resolution 119,74]
152. ~patient(X0) | happy(X0) [subsumption resolution 118,151]
222. $false <- (2) [subsumption resolution 135,125]
223. ~2 [avatar contradiction clause 222]
226. patient(alice) [resolution 149,117]
230. happy(alice) [resolution 152,226]
233. ~generous(alice) [resolution 230,75]
237. ~3 [avatar split clause 233,137]
238. $false <- (4) [subsumption resolution 144,148]
239. ~4 [avatar contradiction clause 238]
240. $false [avatar sat refutation 145,223,237,239]
% SZS output end Proof for 4516320528220709325807654
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or not tall then someone is both not creative and not tall.
Everyone who is either not strong or creative is strong and vice versa.
If john is both not humble and tall then lucy is not quiet.
If someone is not rich then paul is either not brave or not humble.
Everyone who is happy is not curious.
If susan is either wise or tall then alice is both not humble and not funny and vice versa.
Everyone who is either not funny or not quiet is curious or not tall and vice versa.
Everyone who is both not calm and strong is both not strong and quiet and vice versa.
If paul is funny then someone is not happy or not creative.
If fred is either kind or brave then someone is not strong or not tall.
Everyone who is either not old or not wise is both not curious and old and vice versa.
If someone is both brave and kind then susan is either tall or not funny.
Everyone who is creative or generous is brave.
If paul is either old or wise then someone is either creative or calm and vice versa.
If someone is both generous and not strong then john is both strong and quiet and vice versa.
Everyone who is strong is not humble and vice versa.
John is not generous or quiet.
Someone is either brave or patient.
Alice is generous or patient.
Someone is quiet or not strong.
Someone is not rich.
John is both not calm and kind.
Mary is calm. | Alice is humble. | contradiction | ((?[X]:((~quiet(X)<~>~tall(X))))=>(?[X]:((~creative(X)&~tall(X)))))&
(![X]:((~strong(X)<~>creative(X))<=>strong(X)))&
(((~humble(john)&tall(john)))=>(~quiet(lucy)))&
((?[X]:(~rich(X)))=>((~brave(paul)<~>~humble(paul))))&
(![X]:(happy(X)=>~curious(X)))&
(((wise(susan)<~>tall(susan)))<=>((~humble(alice)&~funny(alice))))&
(![X]:((~funny(X)<~>~quiet(X))<=>(curious(X)|~tall(X))))&
(![X]:((~calm(X)&strong(X))<=>(~strong(X)&quiet(X))))&
((funny(paul))=>(?[X]:((~happy(X)|~creative(X)))))&
(((kind(fred)<~>brave(fred)))=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:((~old(X)<~>~wise(X))<=>(~curious(X)&old(X))))&
((?[X]:((brave(X)&kind(X))))=>((tall(susan)<~>~funny(susan))))&
(![X]:((creative(X)|generous(X))=>brave(X)))&
(((old(paul)<~>wise(paul)))<=>(?[X]:((creative(X)<~>calm(X)))))&
((?[X]:((generous(X)&~strong(X))))<=>((strong(john)&quiet(john))))&
(![X]:(strong(X)<=>~humble(X)))&
((~generous(john)|quiet(john)))&
(?[X]:((brave(X)<~>patient(X))))&
((generous(alice)|patient(alice)))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:(~rich(X)))&
((~calm(john)&kind(john)))&
(calm(mary)) | humble(alice) | [
"p0",
"p1",
"p5",
"p6",
"p10",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 782018789199971169954900
% SZS output start Proof for 782018789199971169954900
1. ? [X0] : (~quiet(X0) <~> ~tall(X0)) => ? [X0] : (~tall(X0) & ~creative(X0)) [input p0]
2. ! [X0] : ((~strong(X0) <~> creative(X0)) <=> strong(X0)) [input p1]
6. (wise(susan) <~> tall(susan)) <=> (~funny(alice) & ~humble(alice)) [input p5]
7. ! [X0] : ((~funny(X0) <~> ~quiet(X0)) <=> (~tall(X0) | curious(X0))) [input p6]
11. ! [X0] : ((~old(X0) <~> ~wise(X0)) <=> (old(X0) & ~curious(X0))) [input p10]
12. ? [X0] : (kind(X0) & brave(X0)) => (tall(susan) <~> ~funny(susan)) [input p11]
13. ! [X0] : ((generous(X0) | creative(X0)) => brave(X0)) [input p12]
22. kind(john) & ~calm(john) [input p21]
24. humble(alice) [input hypothesis]
25. ? [X0] : (~quiet(X0) <~> ~tall(X0)) => ? [X1] : (~tall(X1) & ~creative(X1)) [rectify 1]
28. ? [X1] : (~tall(X1) & ~creative(X1)) | ! [X0] : (~quiet(X0) <=> ~tall(X0)) [ennf transformation 25]
33. (tall(susan) <~> ~funny(susan)) | ! [X0] : (~kind(X0) | ~brave(X0)) [ennf transformation 12]
34. ! [X0] : (brave(X0) | (~generous(X0) & ~creative(X0))) [ennf transformation 13]
35. ? [X1] : (~tall(X1) & ~creative(X1)) | ! [X0] : ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))) [nnf transformation 28]
36. ? [X0] : (~tall(X0) & ~creative(X0)) | ! [X1] : ((~quiet(X1) | tall(X1)) & (~tall(X1) | quiet(X1))) [rectify 35]
37. ? [X0] : (~tall(X0) & ~creative(X0)) => (~tall(sK0) & ~creative(sK0)) [choice axiom]
38. (~tall(sK0) & ~creative(sK0)) | ! [X1] : ((~quiet(X1) | tall(X1)) & (~tall(X1) | quiet(X1))) [skolemisation 36,37]
39. ! [X0] : ((((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | ~strong(X0)) & (strong(X0) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0))))) [nnf transformation 2]
41. (((~tall(susan) | ~wise(susan)) & (tall(susan) | wise(susan))) | (funny(alice) | humble(alice))) & ((~funny(alice) & ~humble(alice)) | ((wise(susan) | ~tall(susan)) & (tall(susan) | ~wise(susan)))) [nnf transformation 6]
42. (((~tall(susan) | ~wise(susan)) & (tall(susan) | wise(susan))) | funny(alice) | humble(alice)) & ((~funny(alice) & ~humble(alice)) | ((wise(susan) | ~tall(susan)) & (tall(susan) | ~wise(susan)))) [flattening 41]
43. ! [X0] : ((((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | (tall(X0) & ~curious(X0))) & ((~tall(X0) | curious(X0)) | ((~funny(X0) | quiet(X0)) & (~quiet(X0) | funny(X0))))) [nnf transformation 7]
44. ! [X0] : ((((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | (tall(X0) & ~curious(X0))) & (~tall(X0) | curious(X0) | ((~funny(X0) | quiet(X0)) & (~quiet(X0) | funny(X0))))) [flattening 43]
50. ! [X0] : ((((wise(X0) | old(X0)) & (~wise(X0) | ~old(X0))) | (~old(X0) | curious(X0))) & ((old(X0) & ~curious(X0)) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0))))) [nnf transformation 11]
51. ! [X0] : ((((wise(X0) | old(X0)) & (~wise(X0) | ~old(X0))) | ~old(X0) | curious(X0)) & ((old(X0) & ~curious(X0)) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0))))) [flattening 50]
52. ((funny(susan) | ~tall(susan)) & (~funny(susan) | tall(susan))) | ! [X0] : (~kind(X0) | ~brave(X0)) [nnf transformation 33]
70. ~creative(sK0) | ~tall(X1) | quiet(X1) [cnf transformation 38]
71. ~creative(sK0) | ~quiet(X1) | tall(X1) [cnf transformation 38]
74. strong(X0) | creative(X0) | strong(X0) [cnf transformation 39]
76. creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 39]
82. ~humble(alice) | wise(susan) | ~tall(susan) [cnf transformation 42]
89. ~funny(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 44]
92. funny(X0) | quiet(X0) | tall(X0) [cnf transformation 44]
101. old(X0) | ~wise(X0) | old(X0) [cnf transformation 51]
103. ~wise(X0) | ~old(X0) | ~old(X0) | curious(X0) [cnf transformation 51]
105. ~funny(susan) | tall(susan) | ~kind(X0) | ~brave(X0) [cnf transformation 52]
106. funny(susan) | ~tall(susan) | ~kind(X0) | ~brave(X0) [cnf transformation 52]
107. brave(X0) | ~creative(X0) [cnf transformation 34]
130. kind(john) [cnf transformation 22]
132. humble(alice) [cnf transformation 24]
133. ~wise(X0) | old(X0) [duplicate literal removal 101]
134. ~old(X0) | ~wise(X0) | curious(X0) [duplicate literal removal 103]
137. strong(X0) | creative(X0) [duplicate literal removal 74]
138. ~strong(X0) | creative(X0) [duplicate literal removal 76]
140. 1 <=> ! [X1] : (~quiet(X1) | tall(X1)) [avatar definition]
141. ~quiet(X1) | tall(X1) <- (1) [avatar component clause 140]
148. 3 <=> ! [X1] : (~tall(X1) | quiet(X1)) [avatar definition]
149. ~tall(X1) | quiet(X1) <- (3) [avatar component clause 148]
152. 4 <=> creative(sK0) [avatar definition]
154. ~creative(sK0) <- (~4) [avatar component clause 152]
155. 1 | ~4 [avatar split clause 71,152,140]
156. 3 | ~4 [avatar split clause 70,152,148]
157. creative(X0) [subsumption resolution 137,138]
185. 11 <=> humble(alice) [avatar definition]
193. 13 <=> wise(susan) [avatar definition]
194. wise(susan) <- (13) [avatar component clause 193]
197. 14 <=> tall(susan) [avatar definition]
198. tall(susan) <- (14) [avatar component clause 197]
204. ~14 | 13 | ~11 [avatar split clause 82,185,193,197]
225. 19 <=> ! [X0] : (~kind(X0) | ~brave(X0)) [avatar definition]
226. ~kind(X0) | ~brave(X0) <- (19) [avatar component clause 225]
228. 20 <=> funny(susan) [avatar definition]
229. ~funny(susan) <- (~20) [avatar component clause 228]
230. funny(susan) <- (20) [avatar component clause 228]
231. 19 | ~14 | 20 [avatar split clause 106,228,197,225]
232. 19 | 14 | ~20 [avatar split clause 105,228,197,225]
233. brave(X0) [subsumption resolution 107,157]
306. 11 [avatar split clause 132,185]
307. $false <- (~4) [subsumption resolution 154,157]
308. 4 [avatar contradiction clause 307]
339. quiet(susan) | tall(susan) <- (~20) [resolution 92,229]
348. tall(susan) <- (1, ~20) [subsumption resolution 339,141]
349. 14 | ~1 | 20 [avatar split clause 348,228,140,197]
350. ~kind(X0) <- (19) [subsumption resolution 226,233]
351. old(susan) <- (13) [resolution 194,133]
352. quiet(susan) <- (3, 14) [resolution 198,149]
353. $false <- (19) [resolution 350,130]
354. ~19 [avatar contradiction clause 353]
356. ~quiet(susan) | ~curious(susan) <- (20) [resolution 230,89]
357. ~curious(susan) <- (3, 14, 20) [subsumption resolution 356,352]
366. ~wise(susan) | curious(susan) <- (13) [resolution 134,351]
367. curious(susan) <- (13) [subsumption resolution 366,194]
368. $false <- (3, 13, 14, 20) [subsumption resolution 367,357]
369. ~3 | ~13 | ~14 | ~20 [avatar contradiction clause 368]
370. $false [avatar sat refutation 155,156,204,231,232,306,308,349,354,369]
% SZS output end Proof for 782018789199971169954900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient or not patient then someone is not happy or patient.
If alice is not brave then john is both patient and happy.
Everyone who is generous is not funny.
If someone is not rich then someone is either not kind or not calm and vice versa.
Everyone who is both brave and not wise is wise or not wise and vice versa.
Everyone who is curious is either not wise or not creative and vice versa.
If someone is either not wise or not funny then someone is both not strong and generous.
If paul is either not humble or not happy then john is both not tall and not humble and vice versa.
If mary is both not patient and happy then john is kind or not kind.
If paul is old or happy then someone is either strong or brave and vice versa.
If paul is either old or rich then someone is curious or humble and vice versa.
If mary is happy then someone is either tall or not quiet.
If paul is happy then someone is both not calm and funny and vice versa.
Everyone who is kind is not creative or generous.
Everyone who is not patient is wise or quiet and vice versa.
Everyone who is not brave is either not quiet or quiet.
Paul is not curious or humble.
Someone is tall.
Someone is both calm and tall.
Paul is tall.
Susan is either funny or brave.
Someone is not calm or rich. | Paul is brave. | entailment | ((?[X]:((patient(X)|~patient(X))))=>(?[X]:((~happy(X)|patient(X)))))&
((~brave(alice))=>((patient(john)&happy(john))))&
(![X]:(generous(X)=>~funny(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:((brave(X)&~wise(X))<=>(wise(X)|~wise(X))))&
(![X]:(curious(X)<=>(~wise(X)<~>~creative(X))))&
((?[X]:((~wise(X)<~>~funny(X))))=>(?[X]:((~strong(X)&generous(X)))))&
(((~humble(paul)<~>~happy(paul)))<=>((~tall(john)&~humble(john))))&
(((~patient(mary)&happy(mary)))=>((kind(john)|~kind(john))))&
(((old(paul)|happy(paul)))<=>(?[X]:((strong(X)<~>brave(X)))))&
(((old(paul)<~>rich(paul)))<=>(?[X]:((curious(X)|humble(X)))))&
((happy(mary))=>(?[X]:((tall(X)<~>~quiet(X)))))&
((happy(paul))<=>(?[X]:((~calm(X)&funny(X)))))&
(![X]:(kind(X)=>(~creative(X)|generous(X))))&
(![X]:(~patient(X)<=>(wise(X)|quiet(X))))&
(![X]:(~brave(X)=>(~quiet(X)<~>quiet(X))))&
((~curious(paul)|humble(paul)))&
(?[X]:(tall(X)))&
(?[X]:((calm(X)&tall(X))))&
(tall(paul))&
((funny(susan)<~>brave(susan)))&
(?[X]:((~calm(X)|rich(X)))) | brave(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4009999333487900067617489
% SZS output start Proof for 4009999333487900067617489
5. ! [X0] : ((~wise(X0) & brave(X0)) <=> (~wise(X0) | wise(X0))) [input p4]
23. ~brave(paul) [input hypothesis]
45. ! [X0] : (((~wise(X0) & brave(X0)) | (wise(X0) & ~wise(X0))) & ((~wise(X0) | wise(X0)) | (wise(X0) | ~brave(X0)))) [nnf transformation 5]
46. ! [X0] : (((~wise(X0) & brave(X0)) | (wise(X0) & ~wise(X0))) & (~wise(X0) | wise(X0) | wise(X0) | ~brave(X0))) [flattening 45]
91. brave(X0) | wise(X0) [cnf transformation 46]
92. ~wise(X0) | ~wise(X0) [cnf transformation 46]
140. ~brave(paul) [cnf transformation 23]
142. ~wise(X0) [duplicate literal removal 92]
198. brave(X0) [subsumption resolution 91,142]
323. $false [subsumption resolution 140,198]
% SZS output end Proof for 4009999333487900067617489
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not quiet is both curious and calm.
If paul is not creative then paul is not curious or not rich.
Everyone who is either not creative or calm is not calm or not kind.
Everyone who is quiet is both not creative and not strong and vice versa.
If john is kind then someone is not generous.
If susan is funny then someone is tall or not patient.
Everyone who is not generous is not kind.
If someone is not humble then paul is both not rich and quiet and vice versa.
If alice is both humble and funny then mary is generous or creative.
Everyone who is either generous or not generous is either creative or not rich.
If paul is both rich and generous then someone is either not humble or not tall and vice versa.
Everyone who is not kind is either not tall or not happy.
If lucy is either funny or not brave then susan is either wise or not curious and vice versa.
Everyone who is either wise or not wise is not strong or not tall.
Everyone who is tall is not humble and vice versa.
If lucy is not funny then someone is calm and vice versa.
Susan is strong.
Someone is both strong and creative.
Mary is either not calm or generous.
Someone is both old and not calm.
Someone is either brave or not happy.
Paul is not wise or not brave.
Fred is curious or not funny. | Paul is tall. | contradiction | (![X]:((calm(X)<~>~quiet(X))=>(curious(X)&calm(X))))&
((~creative(paul))=>((~curious(paul)|~rich(paul))))&
(![X]:((~creative(X)<~>calm(X))=>(~calm(X)|~kind(X))))&
(![X]:(quiet(X)<=>(~creative(X)&~strong(X))))&
((kind(john))=>(?[X]:(~generous(X))))&
((funny(susan))=>(?[X]:((tall(X)|~patient(X)))))&
(![X]:(~generous(X)=>~kind(X)))&
((?[X]:(~humble(X)))<=>((~rich(paul)&quiet(paul))))&
(((humble(alice)&funny(alice)))=>((generous(mary)|creative(mary))))&
(![X]:((generous(X)<~>~generous(X))=>(creative(X)<~>~rich(X))))&
(((rich(paul)&generous(paul)))<=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(~kind(X)=>(~tall(X)<~>~happy(X))))&
(((funny(lucy)<~>~brave(lucy)))<=>((wise(susan)<~>~curious(susan))))&
(![X]:((wise(X)<~>~wise(X))=>(~strong(X)|~tall(X))))&
(![X]:(tall(X)<=>~humble(X)))&
((~funny(lucy))<=>(?[X]:(calm(X))))&
(strong(susan))&
(?[X]:((strong(X)&creative(X))))&
((~calm(mary)<~>generous(mary)))&
(?[X]:((old(X)&~calm(X))))&
(?[X]:((brave(X)<~>~happy(X))))&
((~wise(paul)|~brave(paul)))&
((curious(fred)|~funny(fred))) | tall(paul) | [
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2708440827981896767214077
% SZS output start Proof for 2708440827981896767214077
8. ? [X0] : ~humble(X0) <=> (quiet(paul) & ~rich(paul)) [input p7]
11. (generous(paul) & rich(paul)) <=> ? [X0] : (~humble(X0) <~> ~tall(X0)) [input p10]
15. ! [X0] : (tall(X0) <=> ~humble(X0)) [input p14]
24. tall(paul) [input hypothesis]
46. (? [X0] : ~humble(X0) | (~quiet(paul) | rich(paul))) & ((quiet(paul) & ~rich(paul)) | ! [X0] : humble(X0)) [nnf transformation 8]
47. (? [X0] : ~humble(X0) | ~quiet(paul) | rich(paul)) & ((quiet(paul) & ~rich(paul)) | ! [X0] : humble(X0)) [flattening 46]
48. (? [X0] : ~humble(X0) | ~quiet(paul) | rich(paul)) & ((quiet(paul) & ~rich(paul)) | ! [X1] : humble(X1)) [rectify 47]
49. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
50. (~humble(sK1) | ~quiet(paul) | rich(paul)) & ((quiet(paul) & ~rich(paul)) | ! [X1] : humble(X1)) [skolemisation 48,49]
52. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | (~generous(paul) | ~rich(paul))) [nnf transformation 11]
53. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | ~generous(paul) | ~rich(paul)) [flattening 52]
54. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X1] : ((tall(X1) | humble(X1)) & (~tall(X1) | ~humble(X1))) | ~generous(paul) | ~rich(paul)) [rectify 53]
55. ? [X1] : ((tall(X1) | humble(X1)) & (~tall(X1) | ~humble(X1))) => ((tall(sK2) | humble(sK2)) & (~tall(sK2) | ~humble(sK2))) [choice axiom]
56. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (((tall(sK2) | humble(sK2)) & (~tall(sK2) | ~humble(sK2))) | ~generous(paul) | ~rich(paul)) [skolemisation 54,55]
60. ! [X0] : ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))) [nnf transformation 15]
85. ~rich(paul) | humble(X1) [cnf transformation 50]
95. rich(paul) | ~tall(X0) | humble(X0) [cnf transformation 56]
111. ~humble(X0) | ~tall(X0) [cnf transformation 60]
112. tall(X0) | humble(X0) [cnf transformation 60]
125. tall(paul) [cnf transformation 24]
143. 3 <=> rich(paul) [avatar definition]
166. 8 <=> ! [X1] : humble(X1) [avatar definition]
167. humble(X1) <- (8) [avatar component clause 166]
169. 8 | ~3 [avatar split clause 85,143,166]
198. 15 <=> ! [X0] : (~tall(X0) | humble(X0)) [avatar definition]
199. ~tall(X0) | humble(X0) <- (15) [avatar component clause 198]
202. 15 | 3 [avatar split clause 95,143,198]
281. humble(X0) <- (15) [subsumption resolution 199,112]
282. 8 | ~15 [avatar split clause 281,198,166]
287. ~tall(X0) <- (8) [resolution 111,167]
290. $false <- (8) [resolution 287,125]
291. ~8 [avatar contradiction clause 290]
292. $false [avatar sat refutation 169,202,282,291]
% SZS output end Proof for 2708440827981896767214077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or not curious then john is both happy and not curious and vice versa. If someone is not curious or rich then someone is rich or wise. Everyone who is rich or creative is both happy and not strong and vice versa. If fred is both funny and not tall then someone is either brave or kind and vice versa. Everyone who is both calm and not happy is not happy and vice versa. If susan is either not old or old then alice is not funny or strong and vice versa. If someone is both tall and calm then paul is either humble or curious. If paul is rich or not tall then someone is rich. Everyone who is generous or wise is both not quiet and not wise and vice versa. Everyone who is not generous is either strong or not funny. If fred is not creative then someone is either old or not brave. Everyone who is not rich or not patient is not funny or calm. If someone is both tall and brave then susan is either not brave or patient and vice versa. If john is either humble or wise then someone is rich or kind and vice versa. Everyone who is either calm or not quiet is not patient and vice versa. Everyone who is both not curious and calm is curious or rich and vice versa. Someone is not humble. Lucy is both not quiet and rich. Susan is not funny. Susan is either not patient or calm. | Paul is not curious. | entailment | ((?[X]:((~old(X)<~>~curious(X))))<=>((happy(john)&~curious(john))))&
((?[X]:((~curious(X)|rich(X))))=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((rich(X)|creative(X))<=>(happy(X)&~strong(X))))&
(((funny(fred)&~tall(fred)))<=>(?[X]:((brave(X)<~>kind(X)))))&
(![X]:((calm(X)&~happy(X))<=>~happy(X)))&
(((~old(susan)<~>old(susan)))<=>((~funny(alice)|strong(alice))))&
((?[X]:((tall(X)&calm(X))))=>((humble(paul)<~>curious(paul))))&
(((rich(paul)|~tall(paul)))=>(?[X]:(rich(X))))&
(![X]:((generous(X)|wise(X))<=>(~quiet(X)&~wise(X))))&
(![X]:(~generous(X)=>(strong(X)<~>~funny(X))))&
((~creative(fred))=>(?[X]:((old(X)<~>~brave(X)))))&
(![X]:((~rich(X)|~patient(X))=>(~funny(X)|calm(X))))&
((?[X]:((tall(X)&brave(X))))<=>((~brave(susan)<~>patient(susan))))&
(((humble(john)<~>wise(john)))<=>(?[X]:((rich(X)|kind(X)))))&
(![X]:((calm(X)<~>~quiet(X))<=>~patient(X)))&
(![X]:((~curious(X)&calm(X))<=>(curious(X)|rich(X))))&
(?[X]:(~humble(X)))&
((~quiet(lucy)&rich(lucy)))&
(~funny(susan))&
((~patient(susan)<~>calm(susan))) | ~curious(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4287549984183397935196899
% SZS output start Proof for 4287549984183397935196899
16. ! [X0] : ((calm(X0) & ~curious(X0)) <=> (rich(X0) | curious(X0))) [input p15]
21. curious(paul) [input hypothesis]
67. ! [X0] : (((calm(X0) & ~curious(X0)) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | (~calm(X0) | curious(X0)))) [nnf transformation 16]
68. ! [X0] : (((calm(X0) & ~curious(X0)) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~calm(X0) | curious(X0))) [flattening 67]
132. ~curious(X0) | ~curious(X0) [cnf transformation 68]
142. curious(paul) [cnf transformation 21]
144. ~curious(X0) [duplicate literal removal 132]
329. $false [subsumption resolution 142,144]
% SZS output end Proof for 4287549984183397935196899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not calm is funny and vice versa.
If alice is not curious or not creative then susan is wise or old and vice versa.
Everyone who is either calm or not wise is both not calm and kind and vice versa.
If someone is generous then alice is both curious and rich and vice versa.
If someone is both not brave and kind then someone is not curious or not generous and vice versa.
If someone is not kind or strong then someone is both not old and not creative.
Everyone who is calm is patient or not happy.
Everyone who is patient is not wise or not old and vice versa.
Everyone who is either not rich or rich is not patient or strong and vice versa.
Everyone who is either creative or curious is humble or not quiet.
If someone is either humble or not kind then alice is not wise or wise and vice versa.
Everyone who is both funny and rich is either not quiet or not patient and vice versa.
Everyone who is tall or not generous is not calm or creative.
Everyone who is not strong is not quiet and vice versa.
If someone is either generous or not humble then susan is not old and vice versa.
Everyone who is either happy or funny is curious or happy and vice versa.
Someone is both happy and patient.
Someone is either wise or not brave.
Someone is both tall and not funny.
Susan is not generous or happy.
Someone is either not patient or not humble.
Someone is both patient and kind.
Paul is both old and tall.
Someone is both not funny and brave. | Alice is generous. | neutral | (![X]:((~humble(X)&~calm(X))<=>funny(X)))&
(((~curious(alice)|~creative(alice)))<=>((wise(susan)|old(susan))))&
(![X]:((calm(X)<~>~wise(X))<=>(~calm(X)&kind(X))))&
((?[X]:(generous(X)))<=>((curious(alice)&rich(alice))))&
((?[X]:((~brave(X)&kind(X))))<=>(?[X]:((~curious(X)|~generous(X)))))&
((?[X]:((~kind(X)|strong(X))))=>(?[X]:((~old(X)&~creative(X)))))&
(![X]:(calm(X)=>(patient(X)|~happy(X))))&
(![X]:(patient(X)<=>(~wise(X)|~old(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(~patient(X)|strong(X))))&
(![X]:((creative(X)<~>curious(X))=>(humble(X)|~quiet(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>((~wise(alice)|wise(alice))))&
(![X]:((funny(X)&rich(X))<=>(~quiet(X)<~>~patient(X))))&
(![X]:((tall(X)|~generous(X))=>(~calm(X)|creative(X))))&
(![X]:(~strong(X)<=>~quiet(X)))&
((?[X]:((generous(X)<~>~humble(X))))<=>(~old(susan)))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)|happy(X))))&
(?[X]:((happy(X)&patient(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((tall(X)&~funny(X))))&
((~generous(susan)|happy(susan)))&
(?[X]:((~patient(X)<~>~humble(X))))&
(?[X]:((patient(X)&kind(X))))&
((old(paul)&tall(paul)))&
(?[X]:((~funny(X)&brave(X)))) | generous(alice) | [] | null | 0 |
If susan is tall or kind then fred is brave or patient.
Everyone who is not happy is either generous or creative.
Everyone who is creative or tall is both old and happy and vice versa.
If someone is not funny or not tall then mary is either not patient or not happy.
If someone is not creative or happy then someone is both not calm and happy.
If someone is either creative or kind then paul is wise or creative.
If someone is tall then susan is both humble and not generous and vice versa.
Everyone who is not rich or not strong is either calm or not strong.
Everyone who is quiet is calm or strong.
If john is either not wise or not quiet then fred is either not happy or generous and vice versa.
Everyone who is old is both funny and kind and vice versa.
If someone is creative then paul is either creative or kind.
Everyone who is brave is creative or old and vice versa.
Everyone who is not humble or funny is both funny and not humble.
Everyone who is either brave or rich is brave and vice versa.
Everyone who is both tall and calm is old and vice versa.
Fred is not patient.
Fred is not generous.
Someone is kind or not rich.
Lucy is both not patient and not creative.
Someone is funny or not funny.
John is either not rich or kind. | Fred is happy. | entailment | (((tall(susan)|kind(susan)))=>((brave(fred)|patient(fred))))&
(![X]:(~happy(X)=>(generous(X)<~>creative(X))))&
(![X]:((creative(X)|tall(X))<=>(old(X)&happy(X))))&
((?[X]:((~funny(X)|~tall(X))))=>((~patient(mary)<~>~happy(mary))))&
((?[X]:((~creative(X)|happy(X))))=>(?[X]:((~calm(X)&happy(X)))))&
((?[X]:((creative(X)<~>kind(X))))=>((wise(paul)|creative(paul))))&
((?[X]:(tall(X)))<=>((humble(susan)&~generous(susan))))&
(![X]:((~rich(X)|~strong(X))=>(calm(X)<~>~strong(X))))&
(![X]:(quiet(X)=>(calm(X)|strong(X))))&
(((~wise(john)<~>~quiet(john)))<=>((~happy(fred)<~>generous(fred))))&
(![X]:(old(X)<=>(funny(X)&kind(X))))&
((?[X]:(creative(X)))=>((creative(paul)<~>kind(paul))))&
(![X]:(brave(X)<=>(creative(X)|old(X))))&
(![X]:((~humble(X)|funny(X))=>(funny(X)&~humble(X))))&
(![X]:((brave(X)<~>rich(X))<=>brave(X)))&
(![X]:((tall(X)&calm(X))<=>old(X)))&
(~patient(fred))&
(~generous(fred))&
(?[X]:((kind(X)|~rich(X))))&
((~patient(lucy)&~creative(lucy)))&
(?[X]:((funny(X)|~funny(X))))&
((~rich(john)<~>kind(john))) | happy(fred) | [
"p1",
"p2",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7008543409944100068963160
% SZS output start Proof for 7008543409944100068963160
2. ! [X0] : (~happy(X0) => (generous(X0) <~> creative(X0))) [input p1]
3. ! [X0] : ((tall(X0) | creative(X0)) <=> (happy(X0) & old(X0))) [input p2]
18. ~generous(fred) [input p17]
23. ~happy(fred) [input hypothesis]
27. ! [X0] : ((generous(X0) <~> creative(X0)) | happy(X0)) [ennf transformation 2]
37. ! [X0] : (((~creative(X0) | ~generous(X0)) & (creative(X0) | generous(X0))) | happy(X0)) [nnf transformation 27]
38. ! [X0] : (((tall(X0) | creative(X0)) | (~happy(X0) | ~old(X0))) & ((happy(X0) & old(X0)) | (~tall(X0) & ~creative(X0)))) [nnf transformation 3]
39. ! [X0] : ((tall(X0) | creative(X0) | ~happy(X0) | ~old(X0)) & ((happy(X0) & old(X0)) | (~tall(X0) & ~creative(X0)))) [flattening 38]
67. creative(X0) | generous(X0) | happy(X0) [cnf transformation 37]
71. ~creative(X0) | happy(X0) [cnf transformation 39]
120. ~generous(fred) [cnf transformation 18]
127. ~happy(fred) [cnf transformation 23]
221. 21 <=> generous(fred) [avatar definition]
223. ~generous(fred) <- (~21) [avatar component clause 221]
225. 22 <=> happy(fred) [avatar definition]
227. ~happy(fred) <- (~22) [avatar component clause 225]
256. ~21 [avatar split clause 120,221]
258. ~22 [avatar split clause 127,225]
279. generous(X2) | happy(X2) | happy(X2) [resolution 67,71]
281. generous(X2) | happy(X2) [duplicate literal removal 279]
301. happy(fred) <- (~21) [resolution 281,223]
302. $false <- (~21, ~22) [subsumption resolution 301,227]
303. 21 | 22 [avatar contradiction clause 302]
304. $false [avatar sat refutation 256,258,303]
% SZS output end Proof for 7008543409944100068963160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not humble or creative then paul is both not wise and not strong and vice versa.
Everyone who is both not calm and calm is not quiet and vice versa.
If someone is not wise or not curious then mary is not curious and vice versa.
Everyone who is not wise is either not tall or not kind.
Everyone who is not funny or funny is either not brave or old.
Everyone who is not generous is old and vice versa.
Everyone who is funny is not generous.
Everyone who is either not calm or curious is both generous and not kind and vice versa.
Everyone who is not wise is both not happy and generous and vice versa.
Everyone who is either happy or humble is both not kind and strong and vice versa.
If someone is either not creative or patient then someone is not quiet.
Everyone who is either not creative or not strong is either not old or not funny and vice versa.
If paul is either brave or quiet then someone is both not old and old.
Everyone who is not old or not rich is funny or old and vice versa.
If someone is not quiet then someone is generous or rich.
Everyone who is both not wise and tall is either not tall or patient.
Someone is both old and curious.
Fred is not patient or happy.
John is not quiet or brave.
Fred is strong.
John is either kind or happy.
Mary is wise or not rich.
Mary is calm or humble. | Mary is brave. | entailment | (((~humble(susan)<~>creative(susan)))<=>((~wise(paul)&~strong(paul))))&
(![X]:((~calm(X)&calm(X))<=>~quiet(X)))&
((?[X]:((~wise(X)|~curious(X))))<=>(~curious(mary)))&
(![X]:(~wise(X)=>(~tall(X)<~>~kind(X))))&
(![X]:((~funny(X)|funny(X))=>(~brave(X)<~>old(X))))&
(![X]:(~generous(X)<=>old(X)))&
(![X]:(funny(X)=>~generous(X)))&
(![X]:((~calm(X)<~>curious(X))<=>(generous(X)&~kind(X))))&
(![X]:(~wise(X)<=>(~happy(X)&generous(X))))&
(![X]:((happy(X)<~>humble(X))<=>(~kind(X)&strong(X))))&
((?[X]:((~creative(X)<~>patient(X))))=>(?[X]:(~quiet(X))))&
(![X]:((~creative(X)<~>~strong(X))<=>(~old(X)<~>~funny(X))))&
(((brave(paul)<~>quiet(paul)))=>(?[X]:((~old(X)&old(X)))))&
(![X]:((~old(X)|~rich(X))<=>(funny(X)|old(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((generous(X)|rich(X)))))&
(![X]:((~wise(X)&tall(X))=>(~tall(X)<~>patient(X))))&
(?[X]:((old(X)&curious(X))))&
((~patient(fred)|happy(fred)))&
((~quiet(john)|brave(john)))&
(strong(fred))&
((kind(john)<~>happy(john)))&
((wise(mary)|~rich(mary)))&
((calm(mary)|humble(mary))) | brave(mary) | [
"p4",
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5816938306340289772527987
% SZS output start Proof for 5816938306340289772527987
5. ! [X0] : ((funny(X0) | ~funny(X0)) => (~brave(X0) <~> old(X0))) [input p4]
6. ! [X0] : (~generous(X0) <=> old(X0)) [input p5]
7. ! [X0] : (funny(X0) => ~generous(X0)) [input p6]
14. ! [X0] : ((~rich(X0) | ~old(X0)) <=> (old(X0) | funny(X0))) [input p13]
24. ~brave(mary) [input hypothesis]
28. ! [X0] : ((~brave(X0) <~> old(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 5]
29. ! [X0] : (~generous(X0) | ~funny(X0)) [ennf transformation 7]
44. ! [X0] : (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | (~funny(X0) & funny(X0))) [nnf transformation 28]
45. ! [X0] : ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0))) [nnf transformation 6]
60. ! [X0] : (((~rich(X0) | ~old(X0)) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | (rich(X0) & old(X0)))) [nnf transformation 14]
61. ! [X0] : ((~rich(X0) | ~old(X0) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | (rich(X0) & old(X0)))) [flattening 60]
85. ~old(X0) | brave(X0) | funny(X0) [cnf transformation 44]
86. ~old(X0) | brave(X0) | ~funny(X0) [cnf transformation 44]
87. generous(X0) | old(X0) [cnf transformation 45]
89. ~generous(X0) | ~funny(X0) [cnf transformation 29]
119. old(X0) | funny(X0) | old(X0) [cnf transformation 61]
135. ~brave(mary) [cnf transformation 24]
137. old(X0) | funny(X0) [duplicate literal removal 119]
183. ~old(X0) | brave(X0) [subsumption resolution 85,86]
238. ~funny(X0) | old(X0) [resolution 89,87]
239. old(X0) [subsumption resolution 238,137]
248. brave(X1) [resolution 183,239]
252. $false [resolution 248,135]
% SZS output end Proof for 5816938306340289772527987
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and calm is both not wise and not rich.
If someone is either patient or not strong then someone is both not happy and brave and vice versa.
If john is not kind then someone is both kind and not calm and vice versa.
If someone is happy or kind then someone is either not kind or curious.
Everyone who is either not brave or strong is either strong or curious and vice versa.
If paul is not kind or brave then paul is both quiet and strong and vice versa.
Everyone who is not generous is funny and vice versa.
If someone is both rich and creative then someone is curious or not creative and vice versa.
Everyone who is not brave is patient and vice versa.
If someone is both not rich and not calm then someone is both not kind and not tall and vice versa.
Everyone who is either happy or not old is either tall or not funny.
Everyone who is creative is both brave and not happy.
Everyone who is funny or not funny is both not rich and not curious.
If someone is not brave or tall then someone is not funny or funny.
Everyone who is wise or brave is not funny.
Everyone who is both not old and curious is either not wise or patient.
Someone is both calm and generous.
John is brave or not quiet.
John is kind.
Someone is either not creative or not tall.
Someone is tall. | Paul is strong. | entailment | (![X]:((~generous(X)&calm(X))=>(~wise(X)&~rich(X))))&
((?[X]:((patient(X)<~>~strong(X))))<=>(?[X]:((~happy(X)&brave(X)))))&
((~kind(john))<=>(?[X]:((kind(X)&~calm(X)))))&
((?[X]:((happy(X)|kind(X))))=>(?[X]:((~kind(X)<~>curious(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(strong(X)<~>curious(X))))&
(((~kind(paul)|brave(paul)))<=>((quiet(paul)&strong(paul))))&
(![X]:(~generous(X)<=>funny(X)))&
((?[X]:((rich(X)&creative(X))))<=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:(~brave(X)<=>patient(X)))&
((?[X]:((~rich(X)&~calm(X))))<=>(?[X]:((~kind(X)&~tall(X)))))&
(![X]:((happy(X)<~>~old(X))=>(tall(X)<~>~funny(X))))&
(![X]:(creative(X)=>(brave(X)&~happy(X))))&
(![X]:((funny(X)|~funny(X))=>(~rich(X)&~curious(X))))&
((?[X]:((~brave(X)|tall(X))))=>(?[X]:((~funny(X)|funny(X)))))&
(![X]:((wise(X)|brave(X))=>~funny(X)))&
(![X]:((~old(X)&curious(X))=>(~wise(X)<~>patient(X))))&
(?[X]:((calm(X)&generous(X))))&
((brave(john)|~quiet(john)))&
(kind(john))&
(?[X]:((~creative(X)<~>~tall(X))))&
(?[X]:(tall(X))) | strong(paul) | [
"p5",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 510079940246136340096459
% SZS output start Proof for 510079940246136340096459
6. (brave(paul) | ~kind(paul)) <=> (strong(paul) & quiet(paul)) [input p5]
8. ? [X0] : (creative(X0) & rich(X0)) <=> ? [X0] : (~creative(X0) | curious(X0)) [input p7]
12. ! [X0] : (creative(X0) => (~happy(X0) & brave(X0))) [input p11]
13. ! [X0] : ((~funny(X0) | funny(X0)) => (~curious(X0) & ~rich(X0))) [input p12]
22. ~strong(paul) [input hypothesis]
25. ? [X0] : (creative(X0) & rich(X0)) <=> ? [X1] : (~creative(X1) | curious(X1)) [rectify 8]
34. ! [X0] : ((~happy(X0) & brave(X0)) | ~creative(X0)) [ennf transformation 12]
35. ! [X0] : ((~curious(X0) & ~rich(X0)) | (funny(X0) & ~funny(X0))) [ennf transformation 13]
54. ((brave(paul) | ~kind(paul)) | (~strong(paul) | ~quiet(paul))) & ((strong(paul) & quiet(paul)) | (~brave(paul) & kind(paul))) [nnf transformation 6]
55. (brave(paul) | ~kind(paul) | ~strong(paul) | ~quiet(paul)) & ((strong(paul) & quiet(paul)) | (~brave(paul) & kind(paul))) [flattening 54]
56. (? [X0] : (creative(X0) & rich(X0)) | ! [X1] : (creative(X1) & ~curious(X1))) & (? [X1] : (~creative(X1) | curious(X1)) | ! [X0] : (~creative(X0) | ~rich(X0))) [nnf transformation 25]
57. (? [X0] : (creative(X0) & rich(X0)) | ! [X1] : (creative(X1) & ~curious(X1))) & (? [X2] : (~creative(X2) | curious(X2)) | ! [X3] : (~creative(X3) | ~rich(X3))) [rectify 56]
58. ? [X0] : (creative(X0) & rich(X0)) => (creative(sK4) & rich(sK4)) [choice axiom]
59. ? [X2] : (~creative(X2) | curious(X2)) => (~creative(sK5) | curious(sK5)) [choice axiom]
60. ((creative(sK4) & rich(sK4)) | ! [X1] : (creative(X1) & ~curious(X1))) & ((~creative(sK5) | curious(sK5)) | ! [X3] : (~creative(X3) | ~rich(X3))) [skolemisation 57,59,58]
105. strong(paul) | ~brave(paul) [cnf transformation 55]
110. rich(sK4) | creative(X1) [cnf transformation 60]
123. ~creative(X0) | brave(X0) [cnf transformation 34]
125. ~rich(X0) | ~funny(X0) [cnf transformation 35]
126. ~rich(X0) | funny(X0) [cnf transformation 35]
142. ~strong(paul) [cnf transformation 22]
221. 17 <=> strong(paul) [avatar definition]
229. 19 <=> brave(paul) [avatar definition]
230. ~brave(paul) <- (~19) [avatar component clause 229]
233. ~19 | 17 [avatar split clause 105,221,229]
238. 20 <=> ! [X1] : creative(X1) [avatar definition]
239. creative(X1) <- (20) [avatar component clause 238]
250. 23 <=> rich(sK4) [avatar definition]
252. rich(sK4) <- (23) [avatar component clause 250]
253. 20 | 23 [avatar split clause 110,250,238]
295. ~rich(X0) [subsumption resolution 125,126]
316. ~17 [avatar split clause 142,221]
319. $false <- (23) [subsumption resolution 252,295]
320. ~23 [avatar contradiction clause 319]
324. brave(X0) <- (20) [resolution 123,239]
333. $false <- (~19, 20) [resolution 324,230]
335. 19 | ~20 [avatar contradiction clause 333]
336. $false [avatar sat refutation 233,253,316,320,335]
% SZS output end Proof for 510079940246136340096459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or brave is not old.
If fred is not strong then john is not brave and vice versa.
Everyone who is not patient is both tall and not happy and vice versa.
If mary is wise or not quiet then paul is either not calm or brave and vice versa.
Everyone who is generous or not strong is both not quiet and kind and vice versa.
Everyone who is either tall or not funny is both not patient and not funny and vice versa.
Everyone who is either calm or curious is both not kind and not happy.
If someone is not kind or calm then mary is not wise or not funny and vice versa.
Everyone who is either not curious or wise is both not kind and not tall.
Everyone who is both not rich and happy is either not rich or not brave and vice versa.
Everyone who is either patient or not funny is not calm and vice versa.
Everyone who is not calm is both creative and not happy.
Everyone who is both happy and calm is both not quiet and strong.
Everyone who is both quiet and not creative is not kind or funny and vice versa.
If someone is either funny or creative then someone is both not kind and patient and vice versa.
Everyone who is both generous and humble is brave.
Someone is both not rich and not wise.
Lucy is either not generous or generous.
Alice is either generous or not old.
Paul is either not rich or old. | John is not kind. | contradiction | (![X]:((~creative(X)<~>brave(X))=>~old(X)))&
((~strong(fred))<=>(~brave(john)))&
(![X]:(~patient(X)<=>(tall(X)&~happy(X))))&
(((wise(mary)|~quiet(mary)))<=>((~calm(paul)<~>brave(paul))))&
(![X]:((generous(X)|~strong(X))<=>(~quiet(X)&kind(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(~patient(X)&~funny(X))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)&~happy(X))))&
((?[X]:((~kind(X)|calm(X))))<=>((~wise(mary)|~funny(mary))))&
(![X]:((~curious(X)<~>wise(X))=>(~kind(X)&~tall(X))))&
(![X]:((~rich(X)&happy(X))<=>(~rich(X)<~>~brave(X))))&
(![X]:((patient(X)<~>~funny(X))<=>~calm(X)))&
(![X]:(~calm(X)=>(creative(X)&~happy(X))))&
(![X]:((happy(X)&calm(X))=>(~quiet(X)&strong(X))))&
(![X]:((quiet(X)&~creative(X))<=>(~kind(X)|funny(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((generous(X)&humble(X))=>brave(X)))&
(?[X]:((~rich(X)&~wise(X))))&
((~generous(lucy)<~>generous(lucy)))&
((generous(alice)<~>~old(alice)))&
((~rich(paul)<~>old(paul))) | ~kind(john) | [
"p2",
"p5",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 803012714218927569992681
% SZS output start Proof for 803012714218927569992681
3. ! [X0] : (~patient(X0) <=> (~happy(X0) & tall(X0))) [input p2]
6. ! [X0] : ((tall(X0) <~> ~funny(X0)) <=> (~funny(X0) & ~patient(X0))) [input p5]
11. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> ~calm(X0)) [input p10]
12. ! [X0] : (~calm(X0) => (~happy(X0) & creative(X0))) [input p11]
13. ! [X0] : ((calm(X0) & happy(X0)) => (strong(X0) & ~quiet(X0))) [input p12]
14. ! [X0] : ((~creative(X0) & quiet(X0)) <=> (funny(X0) | ~kind(X0))) [input p13]
21. ~kind(john) [input hypothesis]
27. ! [X0] : ((~happy(X0) & creative(X0)) | calm(X0)) [ennf transformation 12]
28. ! [X0] : ((strong(X0) & ~quiet(X0)) | (~calm(X0) | ~happy(X0))) [ennf transformation 13]
29. ! [X0] : ((strong(X0) & ~quiet(X0)) | ~calm(X0) | ~happy(X0)) [flattening 28]
32. ! [X0] : ((~patient(X0) | (happy(X0) | ~tall(X0))) & ((~happy(X0) & tall(X0)) | patient(X0))) [nnf transformation 3]
33. ! [X0] : ((~patient(X0) | happy(X0) | ~tall(X0)) & ((~happy(X0) & tall(X0)) | patient(X0))) [flattening 32]
38. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | (funny(X0) | patient(X0))) & ((~funny(X0) & ~patient(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [nnf transformation 6]
39. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | funny(X0) | patient(X0)) & ((~funny(X0) & ~patient(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [flattening 38]
49. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | calm(X0)) & (~calm(X0) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 11]
50. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | (creative(X0) | ~quiet(X0)))) [nnf transformation 14]
51. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | creative(X0) | ~quiet(X0))) [flattening 50]
66. tall(X0) | patient(X0) [cnf transformation 33]
68. ~tall(X0) | happy(X0) | ~patient(X0) [cnf transformation 33]
81. ~patient(X0) | tall(X0) | funny(X0) [cnf transformation 39]
82. ~funny(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 39]
85. funny(X0) | ~tall(X0) | funny(X0) | patient(X0) [cnf transformation 39]
104. ~funny(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 49]
107. funny(X0) | ~patient(X0) | calm(X0) [cnf transformation 49]
108. calm(X0) | creative(X0) [cnf transformation 27]
109. ~happy(X0) | calm(X0) [cnf transformation 27]
110. ~quiet(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 29]
113. kind(X0) | quiet(X0) [cnf transformation 51]
116. ~funny(X0) | ~creative(X0) [cnf transformation 51]
131. ~kind(john) [cnf transformation 21]
134. ~funny(X0) | ~tall(X0) [duplicate literal removal 82]
135. funny(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 85]
168. funny(X0) | patient(X0) [subsumption resolution 135,66]
169. funny(X0) | tall(X0) [subsumption resolution 81,168]
193. funny(X0) | calm(X0) [subsumption resolution 107,168]
196. ~quiet(X0) | ~happy(X0) [subsumption resolution 110,109]
255. quiet(john) [resolution 113,131]
262. patient(X0) | ~tall(X0) [resolution 168,134]
265. patient(X0) [subsumption resolution 262,66]
270. calm(X1) | ~creative(X1) [resolution 193,116]
272. calm(X1) [subsumption resolution 270,108]
277. ~happy(john) [resolution 196,255]
318. ~calm(X1) | ~patient(X1) | tall(X1) [resolution 104,169]
321. ~patient(X1) | tall(X1) [subsumption resolution 318,272]
322. tall(X1) [subsumption resolution 321,265]
333. happy(X2) | ~patient(X2) [resolution 322,68]
334. happy(X2) [subsumption resolution 333,265]
350. $false [resolution 334,277]
% SZS output end Proof for 803012714218927569992681
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is not calm and vice versa.
If someone is not curious then someone is not brave or not happy and vice versa.
Everyone who is not strong or kind is either old or not generous.
Everyone who is wise is either not rich or old and vice versa.
Everyone who is either brave or patient is either not kind or not patient and vice versa.
Everyone who is wise or not brave is not strong or funny and vice versa.
If fred is not old then paul is both kind and rich and vice versa.
Everyone who is calm or not happy is happy or generous.
Everyone who is quiet or not curious is not happy and vice versa.
Everyone who is either not patient or happy is either tall or strong and vice versa.
If someone is not funny or not patient then someone is not creative.
Everyone who is tall or not rich is both not funny and funny and vice versa.
If lucy is not creative then fred is not old and vice versa.
If susan is both not patient and patient then someone is either not wise or generous and vice versa.
If lucy is not quiet then someone is quiet.
If fred is either not rich or old then someone is both not happy and rich and vice versa.
Someone is not kind.
Paul is either kind or not humble.
Someone is either funny or wise.
Someone is either not quiet or brave.
Paul is either not wise or funny.
Paul is not tall.
Susan is curious or not happy.
Someone is not generous or not humble. | Fred is patient. | entailment | (![X]:(~old(X)<=>~calm(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((~brave(X)|~happy(X)))))&
(![X]:((~strong(X)|kind(X))=>(old(X)<~>~generous(X))))&
(![X]:(wise(X)<=>(~rich(X)<~>old(X))))&
(![X]:((brave(X)<~>patient(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((wise(X)|~brave(X))<=>(~strong(X)|funny(X))))&
((~old(fred))<=>((kind(paul)&rich(paul))))&
(![X]:((calm(X)|~happy(X))=>(happy(X)|generous(X))))&
(![X]:((quiet(X)|~curious(X))<=>~happy(X)))&
(![X]:((~patient(X)<~>happy(X))<=>(tall(X)<~>strong(X))))&
((?[X]:((~funny(X)|~patient(X))))=>(?[X]:(~creative(X))))&
(![X]:((tall(X)|~rich(X))<=>(~funny(X)&funny(X))))&
((~creative(lucy))<=>(~old(fred)))&
(((~patient(susan)&patient(susan)))<=>(?[X]:((~wise(X)<~>generous(X)))))&
((~quiet(lucy))=>(?[X]:(quiet(X))))&
(((~rich(fred)<~>old(fred)))<=>(?[X]:((~happy(X)&rich(X)))))&
(?[X]:(~kind(X)))&
((kind(paul)<~>~humble(paul)))&
(?[X]:((funny(X)<~>wise(X))))&
(?[X]:((~quiet(X)<~>brave(X))))&
((~wise(paul)<~>funny(paul)))&
(~tall(paul))&
((curious(susan)|~happy(susan)))&
(?[X]:((~generous(X)|~humble(X)))) | patient(fred) | [
"p2",
"p3",
"p7",
"p8",
"p9",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8524052374379481132760050
% SZS output start Proof for 8524052374379481132760050
3. ! [X0] : ((kind(X0) | ~strong(X0)) => (old(X0) <~> ~generous(X0))) [input p2]
4. ! [X0] : (wise(X0) <=> (~rich(X0) <~> old(X0))) [input p3]
8. ! [X0] : ((~happy(X0) | calm(X0)) => (generous(X0) | happy(X0))) [input p7]
9. ! [X0] : ((~curious(X0) | quiet(X0)) <=> ~happy(X0)) [input p8]
10. ! [X0] : ((~patient(X0) <~> happy(X0)) <=> (tall(X0) <~> strong(X0))) [input p9]
12. ! [X0] : ((~rich(X0) | tall(X0)) <=> (funny(X0) & ~funny(X0))) [input p11]
14. (patient(susan) & ~patient(susan)) <=> ? [X0] : (~wise(X0) <~> generous(X0)) [input p13]
15. ~quiet(lucy) => ? [X0] : quiet(X0) [input p14]
16. (~rich(fred) <~> old(fred)) <=> ? [X0] : (rich(X0) & ~happy(X0)) [input p15]
25. ~patient(fred) [input hypothesis]
28. ! [X0] : ((old(X0) <~> ~generous(X0)) | (~kind(X0) & strong(X0))) [ennf transformation 3]
29. ! [X0] : ((generous(X0) | happy(X0)) | (happy(X0) & ~calm(X0))) [ennf transformation 8]
30. ! [X0] : (generous(X0) | happy(X0) | (happy(X0) & ~calm(X0))) [flattening 29]
32. ? [X0] : quiet(X0) | quiet(lucy) [ennf transformation 15]
39. ! [X0] : (((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | (~kind(X0) & strong(X0))) [nnf transformation 28]
40. ! [X0] : ((wise(X0) | ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0)))) & (((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | ~wise(X0))) [nnf transformation 4]
46. ! [X0] : (((~curious(X0) | quiet(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & ~quiet(X0)))) [nnf transformation 9]
47. ! [X0] : ((~curious(X0) | quiet(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & ~quiet(X0)))) [flattening 46]
48. ! [X0] : ((((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | ((tall(X0) | ~strong(X0)) & (strong(X0) | ~tall(X0)))) & (((~strong(X0) | ~tall(X0)) & (strong(X0) | tall(X0))) | ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0))))) [nnf transformation 10]
52. ! [X0] : (((~rich(X0) | tall(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (rich(X0) & ~tall(X0)))) [nnf transformation 12]
53. ! [X0] : ((~rich(X0) | tall(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (rich(X0) & ~tall(X0)))) [flattening 52]
55. ((patient(susan) & ~patient(susan)) | ! [X0] : ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (? [X0] : ((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (~patient(susan) | patient(susan))) [nnf transformation 14]
56. ((patient(susan) & ~patient(susan)) | ! [X0] : ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (? [X0] : ((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | ~patient(susan) | patient(susan)) [flattening 55]
57. ((patient(susan) & ~patient(susan)) | ! [X0] : ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (? [X1] : ((~generous(X1) | wise(X1)) & (generous(X1) | ~wise(X1))) | ~patient(susan) | patient(susan)) [rectify 56]
58. ? [X1] : ((~generous(X1) | wise(X1)) & (generous(X1) | ~wise(X1))) => ((~generous(sK3) | wise(sK3)) & (generous(sK3) | ~wise(sK3))) [choice axiom]
59. ((patient(susan) & ~patient(susan)) | ! [X0] : ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0)))) & (((~generous(sK3) | wise(sK3)) & (generous(sK3) | ~wise(sK3))) | ~patient(susan) | patient(susan)) [skolemisation 57,58]
60. ? [X0] : quiet(X0) => quiet(sK4) [choice axiom]
61. quiet(sK4) | quiet(lucy) [skolemisation 32,60]
62. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | happy(X0))) & (? [X0] : (rich(X0) & ~happy(X0)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [nnf transformation 16]
63. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | happy(X0))) & (? [X1] : (rich(X1) & ~happy(X1)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [rectify 62]
64. ? [X1] : (rich(X1) & ~happy(X1)) => (rich(sK5) & ~happy(sK5)) [choice axiom]
65. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | happy(X0))) & ((rich(sK5) & ~happy(sK5)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [skolemisation 63,64]
85. ~old(X0) | generous(X0) | strong(X0) [cnf transformation 39]
90. ~rich(X0) | wise(X0) | ~old(X0) [cnf transformation 40]
107. generous(X0) | happy(X0) | happy(X0) [cnf transformation 30]
108. ~quiet(X0) | ~happy(X0) [cnf transformation 47]
118. ~strong(X0) | patient(X0) | tall(X0) | ~happy(X0) [cnf transformation 48]
121. ~funny(X0) | ~tall(X0) [cnf transformation 53]
122. ~funny(X0) | rich(X0) [cnf transformation 53]
123. ~tall(X0) | funny(X0) [cnf transformation 53]
124. funny(X0) | rich(X0) [cnf transformation 53]
131. ~patient(susan) | ~wise(X0) | ~generous(X0) [cnf transformation 59]
133. patient(susan) | ~wise(X0) | ~generous(X0) [cnf transformation 59]
134. quiet(sK4) | quiet(lucy) [cnf transformation 61]
139. old(fred) | ~rich(fred) | ~rich(X0) | happy(X0) [cnf transformation 65]
153. ~patient(fred) [cnf transformation 25]
154. generous(X0) | happy(X0) [duplicate literal removal 107]
160. 1 <=> ! [X1] : happy(X1) [avatar definition]
161. happy(X1) <- (1) [avatar component clause 160]
194. 9 <=> old(fred) [avatar definition]
195. old(fred) <- (9) [avatar component clause 194]
212. rich(X0) [subsumption resolution 122,124]
213. ~tall(X0) [subsumption resolution 121,123]
221. 14 <=> ! [X0] : (~wise(X0) | ~generous(X0)) [avatar definition]
222. ~wise(X0) | ~generous(X0) <- (14) [avatar component clause 221]
224. 15 <=> patient(susan) [avatar definition]
227. 14 | 15 [avatar split clause 133,224,221]
232. 14 | ~15 [avatar split clause 131,224,221]
235. 17 <=> quiet(lucy) [avatar definition]
237. quiet(lucy) <- (17) [avatar component clause 235]
239. 18 <=> quiet(sK4) [avatar definition]
241. quiet(sK4) <- (18) [avatar component clause 239]
242. 17 | 18 [avatar split clause 134,239,235]
243. old(fred) | ~rich(X0) | happy(X0) [subsumption resolution 139,212]
244. old(fred) | happy(X0) [subsumption resolution 243,212]
245. 1 | 9 [avatar split clause 244,194,160]
299. ~happy(lucy) <- (17) [resolution 108,237]
332. generous(fred) | strong(fred) <- (9) [resolution 85,195]
334. 33 <=> strong(fred) [avatar definition]
336. strong(fred) <- (33) [avatar component clause 334]
338. 34 <=> generous(fred) [avatar definition]
339. ~generous(fred) <- (~34) [avatar component clause 338]
341. 33 | 34 | ~9 [avatar split clause 332,194,338,334]
343. $false <- (1, 17) [resolution 161,299]
345. ~1 | ~17 [avatar contradiction clause 343]
356. ~happy(sK4) <- (18) [resolution 241,108]
357. $false <- (1, 18) [subsumption resolution 356,161]
358. ~1 | ~18 [avatar contradiction clause 357]
388. ~old(X1) | wise(X1) [resolution 90,212]
464. patient(fred) | tall(fred) | ~happy(fred) <- (33) [resolution 118,336]
466. tall(fred) | ~happy(fred) <- (33) [subsumption resolution 464,153]
467. ~happy(fred) <- (33) [subsumption resolution 466,213]
477. wise(fred) <- (9) [resolution 388,195]
553. ~generous(fred) <- (9, 14) [resolution 477,222]
558. ~34 | ~9 | ~14 [avatar split clause 553,221,194,338]
560. happy(fred) <- (~34) [resolution 339,154]
561. $false <- (33, ~34) [subsumption resolution 560,467]
562. ~33 | 34 [avatar contradiction clause 561]
563. $false [avatar sat refutation 227,232,242,245,341,345,358,558,562]
% SZS output end Proof for 8524052374379481132760050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and generous is happy or not old.
Everyone who is both rich and not tall is kind.
If someone is both patient and brave then someone is both not kind and happy and vice versa.
Everyone who is not patient is not calm or not old and vice versa.
Everyone who is either not happy or funny is rich.
Everyone who is generous or kind is not old or not quiet and vice versa.
Everyone who is quiet or happy is not calm.
Everyone who is humble or not wise is either patient or not old and vice versa.
Everyone who is both creative and patient is either not curious or not patient and vice versa.
If john is not rich or not generous then fred is both not happy and not humble and vice versa.
Everyone who is both strong and creative is both not rich and not funny.
If someone is either not curious or creative then someone is tall and vice versa.
Everyone who is either not brave or not curious is either quiet or old and vice versa.
Everyone who is both not strong and not creative is wise or creative.
Everyone who is both not humble and not strong is strong or brave and vice versa.
Everyone who is both not quiet and calm is both not happy and not old and vice versa.
Mary is either not old or not generous.
Someone is either not creative or not patient.
Someone is either kind or not quiet.
Lucy is either happy or not patient.
Fred is calm.
Mary is both kind and calm.
Alice is both not patient and not kind.
Susan is not old. | John is not rich. | contradiction | (![X]:((patient(X)&generous(X))=>(happy(X)|~old(X))))&
(![X]:((rich(X)&~tall(X))=>kind(X)))&
((?[X]:((patient(X)&brave(X))))<=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:(~patient(X)<=>(~calm(X)|~old(X))))&
(![X]:((~happy(X)<~>funny(X))=>rich(X)))&
(![X]:((generous(X)|kind(X))<=>(~old(X)|~quiet(X))))&
(![X]:((quiet(X)|happy(X))=>~calm(X)))&
(![X]:((humble(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:((creative(X)&patient(X))<=>(~curious(X)<~>~patient(X))))&
(((~rich(john)|~generous(john)))<=>((~happy(fred)&~humble(fred))))&
(![X]:((strong(X)&creative(X))=>(~rich(X)&~funny(X))))&
((?[X]:((~curious(X)<~>creative(X))))<=>(?[X]:(tall(X))))&
(![X]:((~brave(X)<~>~curious(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~strong(X)&~creative(X))=>(wise(X)|creative(X))))&
(![X]:((~humble(X)&~strong(X))<=>(strong(X)|brave(X))))&
(![X]:((~quiet(X)&calm(X))<=>(~happy(X)&~old(X))))&
((~old(mary)<~>~generous(mary)))&
(?[X]:((~creative(X)<~>~patient(X))))&
(?[X]:((kind(X)<~>~quiet(X))))&
((happy(lucy)<~>~patient(lucy)))&
(calm(fred))&
((kind(mary)&calm(mary)))&
((~patient(alice)&~kind(alice)))&
(~old(susan)) | ~rich(john) | [
"p2",
"p3",
"p6",
"p8",
"p9",
"p12",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7502754541644498530300042
% SZS output start Proof for 7502754541644498530300042
3. ? [X0] : (brave(X0) & patient(X0)) <=> ? [X0] : (happy(X0) & ~kind(X0)) [input p2]
4. ! [X0] : (~patient(X0) <=> (~old(X0) | ~calm(X0))) [input p3]
7. ! [X0] : ((happy(X0) | quiet(X0)) => ~calm(X0)) [input p6]
9. ! [X0] : ((patient(X0) & creative(X0)) <=> (~curious(X0) <~> ~patient(X0))) [input p8]
10. (~generous(john) | ~rich(john)) <=> (~humble(fred) & ~happy(fred)) [input p9]
13. ! [X0] : ((~brave(X0) <~> ~curious(X0)) <=> (quiet(X0) <~> old(X0))) [input p12]
15. ! [X0] : ((~strong(X0) & ~humble(X0)) <=> (brave(X0) | strong(X0))) [input p14]
16. ! [X0] : ((calm(X0) & ~quiet(X0)) <=> (~old(X0) & ~happy(X0))) [input p15]
21. calm(fred) [input p20]
25. ~rich(john) [input hypothesis]
26. ? [X0] : (brave(X0) & patient(X0)) <=> ? [X1] : (happy(X1) & ~kind(X1)) [rectify 3]
33. ! [X0] : (~calm(X0) | (~happy(X0) & ~quiet(X0))) [ennf transformation 7]
38. (? [X0] : (brave(X0) & patient(X0)) | ! [X1] : (~happy(X1) | kind(X1))) & (? [X1] : (happy(X1) & ~kind(X1)) | ! [X0] : (~brave(X0) | ~patient(X0))) [nnf transformation 26]
39. (? [X0] : (brave(X0) & patient(X0)) | ! [X1] : (~happy(X1) | kind(X1))) & (? [X2] : (happy(X2) & ~kind(X2)) | ! [X3] : (~brave(X3) | ~patient(X3))) [rectify 38]
40. ? [X0] : (brave(X0) & patient(X0)) => (brave(sK0) & patient(sK0)) [choice axiom]
41. ? [X2] : (happy(X2) & ~kind(X2)) => (happy(sK1) & ~kind(sK1)) [choice axiom]
42. ((brave(sK0) & patient(sK0)) | ! [X1] : (~happy(X1) | kind(X1))) & ((happy(sK1) & ~kind(sK1)) | ! [X3] : (~brave(X3) | ~patient(X3))) [skolemisation 39,41,40]
43. ! [X0] : ((~patient(X0) | (old(X0) & calm(X0))) & ((~old(X0) | ~calm(X0)) | patient(X0))) [nnf transformation 4]
44. ! [X0] : ((~patient(X0) | (old(X0) & calm(X0))) & (~old(X0) | ~calm(X0) | patient(X0))) [flattening 43]
50. ! [X0] : (((patient(X0) & creative(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | (~patient(X0) | ~creative(X0)))) [nnf transformation 9]
51. ! [X0] : (((patient(X0) & creative(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | ~patient(X0) | ~creative(X0))) [flattening 50]
52. ((~generous(john) | ~rich(john)) | (humble(fred) | happy(fred))) & ((~humble(fred) & ~happy(fred)) | (generous(john) & rich(john))) [nnf transformation 10]
53. (~generous(john) | ~rich(john) | humble(fred) | happy(fred)) & ((~humble(fred) & ~happy(fred)) | (generous(john) & rich(john))) [flattening 52]
59. ! [X0] : ((((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0)))) & (((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))))) [nnf transformation 13]
60. ! [X0] : (((~strong(X0) & ~humble(X0)) | (~brave(X0) & ~strong(X0))) & ((brave(X0) | strong(X0)) | (strong(X0) | humble(X0)))) [nnf transformation 15]
61. ! [X0] : (((~strong(X0) & ~humble(X0)) | (~brave(X0) & ~strong(X0))) & (brave(X0) | strong(X0) | strong(X0) | humble(X0))) [flattening 60]
62. ! [X0] : (((calm(X0) & ~quiet(X0)) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | (~calm(X0) | quiet(X0)))) [nnf transformation 16]
63. ! [X0] : (((calm(X0) & ~quiet(X0)) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | ~calm(X0) | quiet(X0))) [flattening 62]
74. ~kind(sK1) | ~brave(X3) | ~patient(X3) [cnf transformation 42]
75. happy(sK1) | ~brave(X3) | ~patient(X3) [cnf transformation 42]
76. patient(sK0) | ~happy(X1) | kind(X1) [cnf transformation 42]
79. ~patient(X0) | calm(X0) [cnf transformation 44]
80. ~patient(X0) | old(X0) [cnf transformation 44]
87. ~quiet(X0) | ~calm(X0) [cnf transformation 33]
100. patient(X0) | ~curious(X0) | patient(X0) [cnf transformation 51]
103. ~humble(fred) | rich(john) [cnf transformation 53]
113. ~brave(X0) | quiet(X0) | old(X0) | curious(X0) [cnf transformation 59]
121. brave(X0) | strong(X0) | strong(X0) | humble(X0) [cnf transformation 61]
124. ~strong(X0) | ~strong(X0) [cnf transformation 61]
127. ~old(X0) | ~calm(X0) | quiet(X0) [cnf transformation 63]
138. calm(fred) [cnf transformation 21]
144. ~rich(john) [cnf transformation 25]
145. brave(X0) | strong(X0) | humble(X0) [duplicate literal removal 121]
146. ~strong(X0) [duplicate literal removal 124]
149. ~curious(X0) | patient(X0) [duplicate literal removal 100]
151. 1 <=> ! [X1] : (~happy(X1) | kind(X1)) [avatar definition]
152. ~happy(X1) | kind(X1) <- (1) [avatar component clause 151]
159. 3 <=> patient(sK0) [avatar definition]
161. patient(sK0) <- (3) [avatar component clause 159]
162. 1 | 3 [avatar split clause 76,159,151]
164. 4 <=> ! [X3] : (~brave(X3) | ~patient(X3)) [avatar definition]
165. ~brave(X3) | ~patient(X3) <- (4) [avatar component clause 164]
167. 5 <=> happy(sK1) [avatar definition]
169. happy(sK1) <- (5) [avatar component clause 167]
170. 4 | 5 [avatar split clause 75,167,164]
172. 6 <=> kind(sK1) [avatar definition]
174. ~kind(sK1) <- (~6) [avatar component clause 172]
175. 4 | ~6 [avatar split clause 74,172,164]
184. 8 <=> humble(fred) [avatar definition]
185. ~humble(fred) <- (~8) [avatar component clause 184]
188. 9 <=> rich(john) [avatar definition]
197. 9 | ~8 [avatar split clause 103,184,188]
223. humble(X0) | brave(X0) [subsumption resolution 145,146]
224. ~calm(X0) | ~old(X0) [subsumption resolution 127,87]
265. ~9 [avatar split clause 144,188]
266. calm(sK0) <- (3) [resolution 79,161]
267. old(sK0) <- (3) [resolution 80,161]
283. brave(fred) <- (~8) [resolution 223,185]
285. ~patient(fred) <- (4, ~8) [resolution 283,165]
286. ~old(fred) [resolution 224,138]
288. ~old(sK0) <- (3) [resolution 224,266]
291. $false <- (3) [subsumption resolution 288,267]
292. ~3 [avatar contradiction clause 291]
357. quiet(fred) | old(fred) | curious(fred) <- (~8) [resolution 113,283]
358. quiet(fred) | curious(fred) <- (~8) [subsumption resolution 357,286]
360. 30 <=> curious(fred) [avatar definition]
362. curious(fred) <- (30) [avatar component clause 360]
364. 31 <=> quiet(fred) [avatar definition]
366. quiet(fred) <- (31) [avatar component clause 364]
367. 30 | 31 | 8 [avatar split clause 358,184,364,360]
374. ~calm(fred) <- (31) [resolution 366,87]
378. $false <- (31) [subsumption resolution 374,138]
379. ~31 [avatar contradiction clause 378]
385. patient(fred) <- (30) [resolution 362,149]
386. $false <- (4, ~8, 30) [subsumption resolution 385,285]
387. ~4 | 8 | ~30 [avatar contradiction clause 386]
388. kind(sK1) <- (1, 5) [resolution 169,152]
389. $false <- (1, 5, ~6) [subsumption resolution 388,174]
390. ~1 | ~5 | 6 [avatar contradiction clause 389]
391. $false [avatar sat refutation 162,170,175,197,265,292,367,379,387,390]
% SZS output end Proof for 7502754541644498530300042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or not rich is wise or quiet and vice versa. Everyone who is tall is rich and vice versa. Everyone who is patient is tall or not generous. If mary is old then lucy is both humble and tall and vice versa. Everyone who is either humble or not brave is both not patient and curious and vice versa. Everyone who is either not humble or not rich is both rich and not rich and vice versa. Everyone who is not funny is not calm. Everyone who is not wise is either patient or tall. Everyone who is both strong and wise is both not strong and generous and vice versa. If susan is either funny or creative then someone is tall. If someone is either not rich or funny then fred is either patient or not creative and vice versa. If paul is both not old and brave then susan is humble or not wise and vice versa. If someone is happy then someone is not calm. Everyone who is both generous and wise is not wise and vice versa. If paul is tall then someone is patient or curious. If alice is both funny and not brave then mary is either not patient or not rich. Someone is funny or creative. Fred is brave or calm. Someone is both not generous and calm. Fred is happy or patient. Someone is both not curious and not quiet. Someone is not brave or funny. Someone is either calm or not funny. | Paul is creative. | neutral | (![X]:((rich(X)<~>~rich(X))<=>(wise(X)|quiet(X))))&
(![X]:(tall(X)<=>rich(X)))&
(![X]:(patient(X)=>(tall(X)|~generous(X))))&
((old(mary))<=>((humble(lucy)&tall(lucy))))&
(![X]:((humble(X)<~>~brave(X))<=>(~patient(X)&curious(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(rich(X)&~rich(X))))&
(![X]:(~funny(X)=>~calm(X)))&
(![X]:(~wise(X)=>(patient(X)<~>tall(X))))&
(![X]:((strong(X)&wise(X))<=>(~strong(X)&generous(X))))&
(((funny(susan)<~>creative(susan)))=>(?[X]:(tall(X))))&
((?[X]:((~rich(X)<~>funny(X))))<=>((patient(fred)<~>~creative(fred))))&
(((~old(paul)&brave(paul)))<=>((humble(susan)|~wise(susan))))&
((?[X]:(happy(X)))=>(?[X]:(~calm(X))))&
(![X]:((generous(X)&wise(X))<=>~wise(X)))&
((tall(paul))=>(?[X]:((patient(X)|curious(X)))))&
(((funny(alice)&~brave(alice)))=>((~patient(mary)<~>~rich(mary))))&
(?[X]:((funny(X)|creative(X))))&
((brave(fred)|calm(fred)))&
(?[X]:((~generous(X)&calm(X))))&
((happy(fred)|patient(fred)))&
(?[X]:((~curious(X)&~quiet(X))))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((calm(X)<~>~funny(X)))) | creative(paul) | [] | null | 0 |
If someone is both not kind and creative then someone is old or kind and vice versa.
If someone is either not patient or strong then someone is not humble.
Everyone who is not funny or happy is either not kind or strong.
Everyone who is both happy and tall is either not kind or old and vice versa.
Everyone who is not brave is not calm.
Everyone who is tall is rich or wise and vice versa.
If someone is humble or quiet then fred is not wise.
Everyone who is both calm and not happy is brave or strong and vice versa.
Everyone who is both not creative and funny is not calm or happy.
If someone is both tall and not funny then someone is humble or rich and vice versa.
Everyone who is rich is calm or brave.
If someone is both creative and strong then mary is both not kind and happy and vice versa.
If susan is not brave or kind then fred is either not old or not funny.
If lucy is both not patient and happy then paul is not generous or not calm.
If someone is creative then paul is both brave and rich and vice versa.
If someone is not humble then paul is both quiet and wise.
Someone is not brave.
Someone is not kind or not funny.
Someone is not humble or generous.
Someone is old.
Lucy is funny.
Someone is not rich or not old.
Someone is either humble or not calm. | Paul is not calm. | contradiction | ((?[X]:((~kind(X)&creative(X))))<=>(?[X]:((old(X)|kind(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:(~humble(X))))&
(![X]:((~funny(X)|happy(X))=>(~kind(X)<~>strong(X))))&
(![X]:((happy(X)&tall(X))<=>(~kind(X)<~>old(X))))&
(![X]:(~brave(X)=>~calm(X)))&
(![X]:(tall(X)<=>(rich(X)|wise(X))))&
((?[X]:((humble(X)|quiet(X))))=>(~wise(fred)))&
(![X]:((calm(X)&~happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~creative(X)&funny(X))=>(~calm(X)|happy(X))))&
((?[X]:((tall(X)&~funny(X))))<=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(rich(X)=>(calm(X)|brave(X))))&
((?[X]:((creative(X)&strong(X))))<=>((~kind(mary)&happy(mary))))&
(((~brave(susan)|kind(susan)))=>((~old(fred)<~>~funny(fred))))&
(((~patient(lucy)&happy(lucy)))=>((~generous(paul)|~calm(paul))))&
((?[X]:(creative(X)))<=>((brave(paul)&rich(paul))))&
((?[X]:(~humble(X)))=>((quiet(paul)&wise(paul))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)|~funny(X))))&
(?[X]:((~humble(X)|generous(X))))&
(?[X]:(old(X)))&
(funny(lucy))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((humble(X)<~>~calm(X)))) | ~calm(paul) | [
"p0",
"p7",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3873212248550274834637272
% SZS output start Proof for 3873212248550274834637272
1. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X0] : (kind(X0) | old(X0)) [input p0]
8. ! [X0] : ((~happy(X0) & calm(X0)) <=> (strong(X0) | brave(X0))) [input p7]
15. ? [X0] : creative(X0) <=> (rich(paul) & brave(paul)) [input p14]
20. ? [X0] : old(X0) [input p19]
24. ~calm(paul) [input hypothesis]
25. ? [X0] : (creative(X0) & ~kind(X0)) <=> ? [X1] : (kind(X1) | old(X1)) [rectify 1]
40. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~kind(X1) & ~old(X1))) & (? [X1] : (kind(X1) | old(X1)) | ! [X0] : (~creative(X0) | kind(X0))) [nnf transformation 25]
41. (? [X0] : (creative(X0) & ~kind(X0)) | ! [X1] : (~kind(X1) & ~old(X1))) & (? [X2] : (kind(X2) | old(X2)) | ! [X3] : (~creative(X3) | kind(X3))) [rectify 40]
42. ? [X0] : (creative(X0) & ~kind(X0)) => (creative(sK0) & ~kind(sK0)) [choice axiom]
43. ? [X2] : (kind(X2) | old(X2)) => (kind(sK1) | old(sK1)) [choice axiom]
44. ((creative(sK0) & ~kind(sK0)) | ! [X1] : (~kind(X1) & ~old(X1))) & ((kind(sK1) | old(sK1)) | ! [X3] : (~creative(X3) | kind(X3))) [skolemisation 41,43,42]
54. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & ((strong(X0) | brave(X0)) | (happy(X0) | ~calm(X0)))) [nnf transformation 8]
55. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & (strong(X0) | brave(X0) | happy(X0) | ~calm(X0))) [flattening 54]
67. (? [X0] : creative(X0) | (~rich(paul) | ~brave(paul))) & ((rich(paul) & brave(paul)) | ! [X0] : ~creative(X0)) [nnf transformation 15]
68. (? [X0] : creative(X0) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X0] : ~creative(X0)) [flattening 67]
69. (? [X0] : creative(X0) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X1] : ~creative(X1)) [rectify 68]
70. ? [X0] : creative(X0) => creative(sK6) [choice axiom]
71. (creative(sK6) | ~rich(paul) | ~brave(paul)) & ((rich(paul) & brave(paul)) | ! [X1] : ~creative(X1)) [skolemisation 69,70]
78. ? [X0] : old(X0) => old(sK10) [choice axiom]
79. old(sK10) [skolemisation 20,78]
88. creative(sK0) | ~old(X1) [cnf transformation 44]
109. ~brave(X0) | calm(X0) [cnf transformation 55]
129. brave(paul) | ~creative(X1) [cnf transformation 71]
137. old(sK10) [cnf transformation 79]
142. ~calm(paul) [cnf transformation 24]
147. 2 <=> creative(sK0) [avatar definition]
149. creative(sK0) <- (2) [avatar component clause 147]
152. 3 <=> ! [X1] : ~old(X1) [avatar definition]
153. ~old(X1) <- (3) [avatar component clause 152]
154. 3 | 2 [avatar split clause 88,147,152]
281. 32 <=> calm(paul) [avatar definition]
283. ~calm(paul) <- (~32) [avatar component clause 281]
286. 33 <=> brave(paul) [avatar definition]
287. brave(paul) <- (33) [avatar component clause 286]
299. 36 <=> ! [X1] : ~creative(X1) [avatar definition]
300. ~creative(X1) <- (36) [avatar component clause 299]
302. 36 | 33 [avatar split clause 129,286,299]
353. ~32 [avatar split clause 142,281]
364. calm(paul) <- (33) [resolution 109,287]
365. $false <- (~32, 33) [subsumption resolution 364,283]
366. 32 | ~33 [avatar contradiction clause 365]
367. $false <- (2, 36) [resolution 300,149]
372. ~2 | ~36 [avatar contradiction clause 367]
373. $false <- (3) [resolution 153,137]
376. ~3 [avatar contradiction clause 373]
377. $false [avatar sat refutation 154,302,353,366,372,376]
% SZS output end Proof for 3873212248550274834637272
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not curious is not quiet and vice versa.
If someone is not calm then someone is either not funny or calm and vice versa.
Everyone who is either quiet or rich is not wise and vice versa.
Everyone who is calm is not humble or not tall and vice versa.
If susan is not rich or not funny then fred is not calm.
Everyone who is brave is kind and vice versa.
If alice is both happy and not quiet then alice is not tall or not brave and vice versa.
Everyone who is not rich is not creative.
Everyone who is not quiet or kind is either not creative or kind and vice versa.
If someone is not funny or not old then susan is either calm or not kind.
Everyone who is either funny or not creative is both not rich and humble.
If someone is rich then someone is not strong and vice versa.
Everyone who is either not humble or creative is either calm or not wise and vice versa.
Everyone who is not creative or strong is not creative and vice versa.
Fred is humble or not humble.
Someone is either not wise or not kind.
Someone is creative.
John is either not old or not happy.
Susan is either curious or not funny. | Fred is not curious. | entailment | (![X]:((kind(X)&~curious(X))<=>~quiet(X)))&
((?[X]:(~calm(X)))<=>(?[X]:((~funny(X)<~>calm(X)))))&
(![X]:((quiet(X)<~>rich(X))<=>~wise(X)))&
(![X]:(calm(X)<=>(~humble(X)|~tall(X))))&
(((~rich(susan)|~funny(susan)))=>(~calm(fred)))&
(![X]:(brave(X)<=>kind(X)))&
(((happy(alice)&~quiet(alice)))<=>((~tall(alice)|~brave(alice))))&
(![X]:(~rich(X)=>~creative(X)))&
(![X]:((~quiet(X)|kind(X))<=>(~creative(X)<~>kind(X))))&
((?[X]:((~funny(X)|~old(X))))=>((calm(susan)<~>~kind(susan))))&
(![X]:((funny(X)<~>~creative(X))=>(~rich(X)&humble(X))))&
((?[X]:(rich(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~humble(X)<~>creative(X))<=>(calm(X)<~>~wise(X))))&
(![X]:((~creative(X)|strong(X))<=>~creative(X)))&
((humble(fred)|~humble(fred)))&
(?[X]:((~wise(X)<~>~kind(X))))&
(?[X]:(creative(X)))&
((~old(john)<~>~happy(john)))&
((curious(susan)<~>~funny(susan))) | ~curious(fred) | [
"p0",
"p2",
"p3",
"p4",
"p7",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7258230941555182367897763
% SZS output start Proof for 7258230941555182367897763
1. ! [X0] : ((~curious(X0) & kind(X0)) <=> ~quiet(X0)) [input p0]
3. ! [X0] : ((quiet(X0) <~> rich(X0)) <=> ~wise(X0)) [input p2]
4. ! [X0] : (calm(X0) <=> (~tall(X0) | ~humble(X0))) [input p3]
5. (~funny(susan) | ~rich(susan)) => ~calm(fred) [input p4]
8. ! [X0] : (~rich(X0) => ~creative(X0)) [input p7]
9. ! [X0] : ((kind(X0) | ~quiet(X0)) <=> (~creative(X0) <~> kind(X0))) [input p8]
11. ! [X0] : ((funny(X0) <~> ~creative(X0)) => (humble(X0) & ~rich(X0))) [input p10]
13. ! [X0] : ((~humble(X0) <~> creative(X0)) <=> (calm(X0) <~> ~wise(X0))) [input p12]
20. curious(fred) [input hypothesis]
23. ~calm(fred) | (funny(susan) & rich(susan)) [ennf transformation 5]
24. ! [X0] : (~creative(X0) | rich(X0)) [ennf transformation 8]
26. ! [X0] : ((humble(X0) & ~rich(X0)) | (funny(X0) <=> ~creative(X0))) [ennf transformation 11]
27. ! [X0] : (((~curious(X0) & kind(X0)) | quiet(X0)) & (~quiet(X0) | (curious(X0) | ~kind(X0)))) [nnf transformation 1]
28. ! [X0] : (((~curious(X0) & kind(X0)) | quiet(X0)) & (~quiet(X0) | curious(X0) | ~kind(X0))) [flattening 27]
34. ! [X0] : ((((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | wise(X0)) & (~wise(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))))) [nnf transformation 3]
35. ! [X0] : ((calm(X0) | (tall(X0) & humble(X0))) & ((~tall(X0) | ~humble(X0)) | ~calm(X0))) [nnf transformation 4]
36. ! [X0] : ((calm(X0) | (tall(X0) & humble(X0))) & (~tall(X0) | ~humble(X0) | ~calm(X0))) [flattening 35]
40. ! [X0] : (((kind(X0) | ~quiet(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) & (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (~kind(X0) & quiet(X0)))) [nnf transformation 9]
41. ! [X0] : ((kind(X0) | ~quiet(X0) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) & (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (~kind(X0) & quiet(X0)))) [flattening 40]
43. ! [X0] : ((humble(X0) & ~rich(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) [nnf transformation 26]
49. ! [X0] : ((((~creative(X0) | humble(X0)) & (creative(X0) | ~humble(X0))) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0))))) [nnf transformation 13]
60. quiet(X0) | kind(X0) [cnf transformation 28]
61. ~curious(X0) | quiet(X0) [cnf transformation 28]
69. ~rich(X0) | ~quiet(X0) | wise(X0) [cnf transformation 34]
71. humble(X0) | calm(X0) [cnf transformation 36]
74. ~calm(fred) | funny(susan) [cnf transformation 23]
82. ~creative(X0) | rich(X0) [cnf transformation 24]
86. ~kind(X0) | creative(X0) | ~kind(X0) [cnf transformation 41]
87. kind(X0) | ~quiet(X0) | kind(X0) | creative(X0) [cnf transformation 41]
93. ~rich(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 43]
100. ~wise(X0) | calm(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 49]
105. ~creative(X0) | humble(X0) | ~wise(X0) | ~calm(X0) [cnf transformation 49]
118. curious(fred) [cnf transformation 20]
119. ~kind(X0) | creative(X0) [duplicate literal removal 86]
120. kind(X0) | ~quiet(X0) | creative(X0) [duplicate literal removal 87]
147. 7 <=> funny(susan) [avatar definition]
149. funny(susan) <- (7) [avatar component clause 147]
151. 8 <=> calm(fred) [avatar definition]
154. 7 | ~8 [avatar split clause 74,151,147]
181. creative(X0) | kind(X0) [subsumption resolution 120,60]
182. creative(X0) [subsumption resolution 119,181]
202. ~rich(X0) | ~funny(X0) [subsumption resolution 93,182]
219. humble(X0) | ~wise(X0) | ~calm(X0) [subsumption resolution 105,182]
220. ~wise(X0) | humble(X0) [subsumption resolution 219,71]
222. ~wise(X0) | calm(X0) | ~humble(X0) [subsumption resolution 100,182]
223. ~wise(X0) | calm(X0) [subsumption resolution 222,220]
253. quiet(fred) [resolution 61,118]
256. rich(X0) [resolution 82,182]
259. ~funny(X0) [resolution 202,256]
275. ~quiet(X0) | wise(X0) [resolution 69,256]
301. wise(fred) [resolution 275,253]
306. calm(fred) [resolution 301,223]
310. 8 [avatar split clause 306,151]
311. $false <- (7) [subsumption resolution 149,259]
312. ~7 [avatar contradiction clause 311]
313. $false [avatar sat refutation 154,310,312]
% SZS output end Proof for 7258230941555182367897763
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and humble is not humble or happy. Everyone who is both not calm and not quiet is not brave. If susan is old or not creative then lucy is both not kind and curious and vice versa. Everyone who is happy or old is not old and vice versa. Everyone who is either not happy or tall is not creative. Everyone who is either not happy or curious is kind or not generous. Everyone who is not kind or not creative is either rich or not rich and vice versa. Everyone who is kind or not strong is not funny or not happy. Everyone who is both old and patient is old or generous. Everyone who is either not old or funny is quiet or generous and vice versa. Everyone who is patient is both not wise and not rich. If someone is either tall or not calm then mary is not kind. If alice is not quiet or creative then someone is either not curious or not funny. If someone is either brave or not humble then paul is either quiet or creative. If someone is either generous or not patient then alice is either not old or old and vice versa. If someone is not creative or not strong then paul is either not patient or happy. Alice is wise or brave. Someone is either not generous or not humble. Alice is either strong or not happy. Someone is not calm. Someone is not wise. Fred is not creative. Someone is both not strong and not humble. Paul is brave or creative. | Susan is old. | contradiction | (![X]:((~brave(X)&humble(X))=>(~humble(X)|happy(X))))&
(![X]:((~calm(X)&~quiet(X))=>~brave(X)))&
(((old(susan)|~creative(susan)))<=>((~kind(lucy)&curious(lucy))))&
(![X]:((happy(X)|old(X))<=>~old(X)))&
(![X]:((~happy(X)<~>tall(X))=>~creative(X)))&
(![X]:((~happy(X)<~>curious(X))=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)|~creative(X))<=>(rich(X)<~>~rich(X))))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)|~happy(X))))&
(![X]:((old(X)&patient(X))=>(old(X)|generous(X))))&
(![X]:((~old(X)<~>funny(X))<=>(quiet(X)|generous(X))))&
(![X]:(patient(X)=>(~wise(X)&~rich(X))))&
((?[X]:((tall(X)<~>~calm(X))))=>(~kind(mary)))&
(((~quiet(alice)|creative(alice)))=>(?[X]:((~curious(X)<~>~funny(X)))))&
((?[X]:((brave(X)<~>~humble(X))))=>((quiet(paul)<~>creative(paul))))&
((?[X]:((generous(X)<~>~patient(X))))<=>((~old(alice)<~>old(alice))))&
((?[X]:((~creative(X)|~strong(X))))=>((~patient(paul)<~>happy(paul))))&
((wise(alice)|brave(alice)))&
(?[X]:((~generous(X)<~>~humble(X))))&
((strong(alice)<~>~happy(alice)))&
(?[X]:(~calm(X)))&
(?[X]:(~wise(X)))&
(~creative(fred))&
(?[X]:((~strong(X)&~humble(X))))&
((brave(paul)|creative(paul))) | old(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 407484295765651956274692
% SZS output start Proof for 407484295765651956274692
4. ! [X0] : ((old(X0) | happy(X0)) <=> ~old(X0)) [input p3]
25. old(susan) [input hypothesis]
44. ! [X0] : (((old(X0) | happy(X0)) | old(X0)) & (~old(X0) | (~old(X0) & ~happy(X0)))) [nnf transformation 4]
45. ! [X0] : ((old(X0) | happy(X0) | old(X0)) & (~old(X0) | (~old(X0) & ~happy(X0)))) [flattening 44]
80. ~old(X0) | ~old(X0) [cnf transformation 45]
136. old(susan) [cnf transformation 25]
143. ~old(X0) [duplicate literal removal 80]
285. $false [subsumption resolution 136,143]
% SZS output end Proof for 407484295765651956274692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If susan is either not creative or calm then mary is both brave and not quiet and vice versa.
If mary is either not kind or generous then someone is happy.
If someone is both tall and funny then john is either not tall or not wise and vice versa.
If someone is not strong or creative then mary is not old and vice versa.
If fred is both not brave and not kind then john is generous or brave.
Everyone who is both not humble and tall is both wise and humble and vice versa.
Everyone who is generous is either brave or funny and vice versa.
If someone is either not strong or calm then someone is either not tall or strong.
Everyone who is both brave and not quiet is strong or not humble.
If someone is not kind or not old then someone is not quiet.
Everyone who is not quiet or not wise is old and vice versa.
Everyone who is not patient or generous is not kind.
Everyone who is both curious and happy is humble or not happy.
Everyone who is either brave or not calm is both not funny and not strong and vice versa.
Everyone who is not tall is both not quiet and curious.
If john is either wise or happy then alice is both not kind and not wise and vice versa.
Mary is patient.
Someone is not wise or wise.
Someone is either not curious or kind.
Someone is not happy.
Mary is either not patient or calm.
Susan is both funny and wise. | John is creative. | contradiction | (((~creative(susan)<~>calm(susan)))<=>((brave(mary)&~quiet(mary))))&
(((~kind(mary)<~>generous(mary)))=>(?[X]:(happy(X))))&
((?[X]:((tall(X)&funny(X))))<=>((~tall(john)<~>~wise(john))))&
((?[X]:((~strong(X)|creative(X))))<=>(~old(mary)))&
(((~brave(fred)&~kind(fred)))=>((generous(john)|brave(john))))&
(![X]:((~humble(X)&tall(X))<=>(wise(X)&humble(X))))&
(![X]:(generous(X)<=>(brave(X)<~>funny(X))))&
((?[X]:((~strong(X)<~>calm(X))))=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((brave(X)&~quiet(X))=>(strong(X)|~humble(X))))&
((?[X]:((~kind(X)|~old(X))))=>(?[X]:(~quiet(X))))&
(![X]:((~quiet(X)|~wise(X))<=>old(X)))&
(![X]:((~patient(X)|generous(X))=>~kind(X)))&
(![X]:((curious(X)&happy(X))=>(humble(X)|~happy(X))))&
(![X]:((brave(X)<~>~calm(X))<=>(~funny(X)&~strong(X))))&
(![X]:(~tall(X)=>(~quiet(X)&curious(X))))&
(((wise(john)<~>happy(john)))<=>((~kind(alice)&~wise(alice))))&
(patient(mary))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:((~curious(X)<~>kind(X))))&
(?[X]:(~happy(X)))&
((~patient(mary)<~>calm(mary)))&
((funny(susan)&wise(susan))) | creative(john) | [
"p3",
"p5",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 86948172403179196143239
% SZS output start Proof for 86948172403179196143239
4. ? [X0] : (creative(X0) | ~strong(X0)) <=> ~old(mary) [input p3]
6. ! [X0] : ((tall(X0) & ~humble(X0)) <=> (humble(X0) & wise(X0))) [input p5]
11. ! [X0] : ((~wise(X0) | ~quiet(X0)) <=> old(X0)) [input p10]
15. ! [X0] : (~tall(X0) => (curious(X0) & ~quiet(X0))) [input p14]
23. creative(john) [input hypothesis]
36. ! [X0] : ((curious(X0) & ~quiet(X0)) | tall(X0)) [ennf transformation 15]
46. (? [X0] : (creative(X0) | ~strong(X0)) | old(mary)) & (~old(mary) | ! [X0] : (~creative(X0) & strong(X0))) [nnf transformation 4]
47. (? [X0] : (creative(X0) | ~strong(X0)) | old(mary)) & (~old(mary) | ! [X1] : (~creative(X1) & strong(X1))) [rectify 46]
48. ? [X0] : (creative(X0) | ~strong(X0)) => (creative(sK2) | ~strong(sK2)) [choice axiom]
49. ((creative(sK2) | ~strong(sK2)) | old(mary)) & (~old(mary) | ! [X1] : (~creative(X1) & strong(X1))) [skolemisation 47,48]
50. ! [X0] : (((tall(X0) & ~humble(X0)) | (~humble(X0) | ~wise(X0))) & ((humble(X0) & wise(X0)) | (~tall(X0) | humble(X0)))) [nnf transformation 6]
51. ! [X0] : (((tall(X0) & ~humble(X0)) | ~humble(X0) | ~wise(X0)) & ((humble(X0) & wise(X0)) | ~tall(X0) | humble(X0))) [flattening 50]
60. ! [X0] : (((~wise(X0) | ~quiet(X0)) | ~old(X0)) & (old(X0) | (wise(X0) & quiet(X0)))) [nnf transformation 11]
61. ! [X0] : ((~wise(X0) | ~quiet(X0) | ~old(X0)) & (old(X0) | (wise(X0) & quiet(X0)))) [flattening 60]
89. ~old(mary) | ~creative(X1) [cnf transformation 49]
93. humble(X0) | ~tall(X0) | humble(X0) [cnf transformation 51]
94. ~humble(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 51]
107. old(X0) | quiet(X0) [cnf transformation 61]
108. old(X0) | wise(X0) [cnf transformation 61]
119. ~quiet(X0) | tall(X0) [cnf transformation 36]
136. creative(john) [cnf transformation 23]
138. ~tall(X0) | humble(X0) [duplicate literal removal 93]
139. ~humble(X0) | ~wise(X0) [duplicate literal removal 94]
145. 2 <=> quiet(mary) [avatar definition]
147. quiet(mary) <- (2) [avatar component clause 145]
202. 13 <=> old(mary) [avatar definition]
203. ~old(mary) <- (~13) [avatar component clause 202]
215. 16 <=> ! [X1] : ~creative(X1) [avatar definition]
216. ~creative(X1) <- (16) [avatar component clause 215]
217. 16 | ~13 [avatar split clause 89,202,215]
298. quiet(mary) <- (~13) [resolution 107,203]
299. 2 | 13 [avatar split clause 298,202,145]
300. $false <- (16) [resolution 216,136]
303. ~16 [avatar contradiction clause 300]
309. wise(mary) <- (~13) [resolution 108,203]
311. tall(mary) <- (2) [resolution 119,147]
314. humble(mary) <- (2) [resolution 138,311]
319. ~wise(mary) <- (2) [resolution 314,139]
320. $false <- (2, ~13) [subsumption resolution 319,309]
321. ~2 | 13 [avatar contradiction clause 320]
322. $false [avatar sat refutation 217,299,303,321]
% SZS output end Proof for 86948172403179196143239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is old. Everyone who is wise or not wise is both funny and not old. If someone is both not creative and not humble then mary is not happy or not old. If someone is happy or not wise then lucy is not generous. If alice is both not creative and not calm then mary is strong. Everyone who is old or not humble is wise or humble and vice versa. Everyone who is either strong or not happy is either quiet or not old and vice versa. If someone is old or not funny then someone is kind and vice versa. Everyone who is rich or not kind is rich or not humble and vice versa. If someone is either not old or tall then someone is both generous and not humble. Everyone who is either happy or wise is either patient or not funny. Everyone who is either brave or funny is not happy or brave and vice versa. If someone is kind or not tall then someone is both humble and creative. Everyone who is either generous or not happy is either not calm or rich and vice versa. Everyone who is not tall is either not old or not kind. Everyone who is both not creative and curious is both not brave and not calm and vice versa. Someone is both not old and quiet. Mary is generous or not strong. John is rich. Susan is not kind or old. | Mary is not funny. | contradiction | (![X]:(~creative(X)=>old(X)))&
(![X]:((wise(X)|~wise(X))=>(funny(X)&~old(X))))&
((?[X]:((~creative(X)&~humble(X))))=>((~happy(mary)|~old(mary))))&
((?[X]:((happy(X)|~wise(X))))=>(~generous(lucy)))&
(((~creative(alice)&~calm(alice)))=>(strong(mary)))&
(![X]:((old(X)|~humble(X))<=>(wise(X)|humble(X))))&
(![X]:((strong(X)<~>~happy(X))<=>(quiet(X)<~>~old(X))))&
((?[X]:((old(X)|~funny(X))))<=>(?[X]:(kind(X))))&
(![X]:((rich(X)|~kind(X))<=>(rich(X)|~humble(X))))&
((?[X]:((~old(X)<~>tall(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((happy(X)<~>wise(X))=>(patient(X)<~>~funny(X))))&
(![X]:((brave(X)<~>funny(X))<=>(~happy(X)|brave(X))))&
((?[X]:((kind(X)|~tall(X))))=>(?[X]:((humble(X)&creative(X)))))&
(![X]:((generous(X)<~>~happy(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~tall(X)=>(~old(X)<~>~kind(X))))&
(![X]:((~creative(X)&curious(X))<=>(~brave(X)&~calm(X))))&
(?[X]:((~old(X)&quiet(X))))&
((generous(mary)|~strong(mary)))&
(rich(john))&
((~kind(susan)|old(susan))) | ~funny(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6477092047972079023495471
% SZS output start Proof for 6477092047972079023495471
2. ! [X0] : ((~wise(X0) | wise(X0)) => (~old(X0) & funny(X0))) [input p1]
21. ~funny(mary) [input hypothesis]
26. ! [X0] : ((~old(X0) & funny(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 2]
63. funny(X0) | ~wise(X0) [cnf transformation 26]
64. funny(X0) | wise(X0) [cnf transformation 26]
127. ~funny(mary) [cnf transformation 21]
133. funny(X0) [subsumption resolution 63,64]
200. $false [subsumption resolution 127,133]
% SZS output end Proof for 6477092047972079023495471
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not brave is either happy or tall.
If someone is not creative then fred is not wise.
If someone is happy or not wise then someone is both old and kind and vice versa.
Everyone who is both not happy and not quiet is old or tall and vice versa.
Everyone who is not humble or not brave is funny.
If john is not wise then someone is either rich or patient.
Everyone who is calm or not rich is not patient.
Everyone who is both not strong and not old is not quiet or not kind and vice versa.
Everyone who is not patient is creative and vice versa.
Everyone who is humble or quiet is not generous or quiet.
If someone is old or not patient then susan is either funny or not curious and vice versa.
If someone is not brave then someone is not humble and vice versa.
Everyone who is not humble or calm is either humble or not wise.
Lucy is both not quiet and rich.
Paul is happy or not happy.
Mary is both not kind and tall.
John is calm.
John is not patient or humble.
Fred is not old. | Lucy is tall. | entailment | (![X]:((brave(X)|~brave(X))=>(happy(X)<~>tall(X))))&
((?[X]:(~creative(X)))=>(~wise(fred)))&
((?[X]:((happy(X)|~wise(X))))<=>(?[X]:((old(X)&kind(X)))))&
(![X]:((~happy(X)&~quiet(X))<=>(old(X)|tall(X))))&
(![X]:((~humble(X)|~brave(X))=>funny(X)))&
((~wise(john))=>(?[X]:((rich(X)<~>patient(X)))))&
(![X]:((calm(X)|~rich(X))=>~patient(X)))&
(![X]:((~strong(X)&~old(X))<=>(~quiet(X)|~kind(X))))&
(![X]:(~patient(X)<=>creative(X)))&
(![X]:((humble(X)|quiet(X))=>(~generous(X)|quiet(X))))&
((?[X]:((old(X)|~patient(X))))<=>((funny(susan)<~>~curious(susan))))&
((?[X]:(~brave(X)))<=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)|calm(X))=>(humble(X)<~>~wise(X))))&
((~quiet(lucy)&rich(lucy)))&
((happy(paul)|~happy(paul)))&
((~kind(mary)&tall(mary)))&
(calm(john))&
((~patient(john)|humble(john)))&
(~old(fred)) | tall(lucy) | [
"p0",
"p2",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8050196332773601217444241
% SZS output start Proof for 8050196332773601217444241
1. ! [X0] : ((~brave(X0) | brave(X0)) => (happy(X0) <~> tall(X0))) [input p0]
3. ? [X0] : (~wise(X0) | happy(X0)) <=> ? [X0] : (kind(X0) & old(X0)) [input p2]
4. ! [X0] : ((~quiet(X0) & ~happy(X0)) <=> (tall(X0) | old(X0))) [input p3]
8. ! [X0] : ((~old(X0) & ~strong(X0)) <=> (~kind(X0) | ~quiet(X0))) [input p7]
20. ~tall(lucy) [input hypothesis]
21. ? [X0] : (~wise(X0) | happy(X0)) <=> ? [X1] : (kind(X1) & old(X1)) [rectify 3]
24. ! [X0] : ((happy(X0) <~> tall(X0)) | (brave(X0) & ~brave(X0))) [ennf transformation 1]
30. ! [X0] : (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | (brave(X0) & ~brave(X0))) [nnf transformation 24]
31. (? [X0] : (~wise(X0) | happy(X0)) | ! [X1] : (~kind(X1) | ~old(X1))) & (? [X1] : (kind(X1) & old(X1)) | ! [X0] : (wise(X0) & ~happy(X0))) [nnf transformation 21]
32. (? [X0] : (~wise(X0) | happy(X0)) | ! [X1] : (~kind(X1) | ~old(X1))) & (? [X2] : (kind(X2) & old(X2)) | ! [X3] : (wise(X3) & ~happy(X3))) [rectify 31]
33. ? [X0] : (~wise(X0) | happy(X0)) => (~wise(sK0) | happy(sK0)) [choice axiom]
34. ? [X2] : (kind(X2) & old(X2)) => (kind(sK1) & old(sK1)) [choice axiom]
35. ((~wise(sK0) | happy(sK0)) | ! [X1] : (~kind(X1) | ~old(X1))) & ((kind(sK1) & old(sK1)) | ! [X3] : (wise(X3) & ~happy(X3))) [skolemisation 32,34,33]
36. ! [X0] : (((~quiet(X0) & ~happy(X0)) | (~tall(X0) & ~old(X0))) & ((tall(X0) | old(X0)) | (quiet(X0) | happy(X0)))) [nnf transformation 4]
37. ! [X0] : (((~quiet(X0) & ~happy(X0)) | (~tall(X0) & ~old(X0))) & (tall(X0) | old(X0) | quiet(X0) | happy(X0))) [flattening 36]
41. ! [X0] : (((~old(X0) & ~strong(X0)) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | (old(X0) | strong(X0)))) [nnf transformation 8]
42. ! [X0] : (((~old(X0) & ~strong(X0)) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | old(X0) | strong(X0))) [flattening 41]
54. tall(X0) | happy(X0) | ~brave(X0) [cnf transformation 30]
55. tall(X0) | happy(X0) | brave(X0) [cnf transformation 30]
59. old(sK1) | ~happy(X3) [cnf transformation 35]
67. ~quiet(X0) | ~old(X0) [cnf transformation 37]
78. ~old(X0) | quiet(X0) [cnf transformation 42]
102. ~tall(lucy) [cnf transformation 20]
105. tall(X0) | happy(X0) [subsumption resolution 54,55]
135. 8 <=> ! [X3] : ~happy(X3) [avatar definition]
136. ~happy(X3) <- (8) [avatar component clause 135]
139. 9 <=> old(sK1) [avatar definition]
141. old(sK1) <- (9) [avatar component clause 139]
143. 8 | 9 [avatar split clause 59,139,135]
158. ~old(X0) [subsumption resolution 78,67]
210. $false <- (9) [subsumption resolution 141,158]
211. ~9 [avatar contradiction clause 210]
233. happy(lucy) [resolution 105,102]
235. $false <- (8) [subsumption resolution 233,136]
236. ~8 [avatar contradiction clause 235]
237. $false [avatar sat refutation 143,211,236]
% SZS output end Proof for 8050196332773601217444241
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not creative is not strong or not old and vice versa. If alice is old or funny then fred is not humble and vice versa. If fred is either not generous or not tall then paul is either not wise or not quiet. Everyone who is wise is both not generous and not rich. If someone is both not quiet and wise then someone is either tall or not brave and vice versa. If john is either not curious or happy then mary is not humble and vice versa. If mary is both brave and not creative then john is either curious or not quiet. If someone is not curious then someone is rich. If alice is either curious or wise then susan is humble and vice versa. Everyone who is not quiet or not old is kind or funny and vice versa. If someone is not creative or not funny then john is not quiet and vice versa. If someone is brave or not creative then someone is rich or not quiet and vice versa. If john is either not tall or not quiet then someone is either generous or not creative and vice versa. If susan is either not brave or funny then mary is both not kind and not patient and vice versa. If someone is both brave and not rich then someone is not tall or not patient. If someone is not strong then susan is both strong and wise and vice versa. Susan is either not tall or creative. Lucy is not old. Alice is not wise. Lucy is either quiet or not quiet. Fred is either not patient or old. Susan is both generous and kind. Paul is not humble. Lucy is rich. | Alice is not old. | entailment | (![X]:((~wise(X)|~creative(X))<=>(~strong(X)|~old(X))))&
(((old(alice)|funny(alice)))<=>(~humble(fred)))&
(((~generous(fred)<~>~tall(fred)))=>((~wise(paul)<~>~quiet(paul))))&
(![X]:(wise(X)=>(~generous(X)&~rich(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>(?[X]:((tall(X)<~>~brave(X)))))&
(((~curious(john)<~>happy(john)))<=>(~humble(mary)))&
(((brave(mary)&~creative(mary)))=>((curious(john)<~>~quiet(john))))&
((?[X]:(~curious(X)))=>(?[X]:(rich(X))))&
(((curious(alice)<~>wise(alice)))<=>(humble(susan)))&
(![X]:((~quiet(X)|~old(X))<=>(kind(X)|funny(X))))&
((?[X]:((~creative(X)|~funny(X))))<=>(~quiet(john)))&
((?[X]:((brave(X)|~creative(X))))<=>(?[X]:((rich(X)|~quiet(X)))))&
(((~tall(john)<~>~quiet(john)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
(((~brave(susan)<~>funny(susan)))<=>((~kind(mary)&~patient(mary))))&
((?[X]:((brave(X)&~rich(X))))=>(?[X]:((~tall(X)|~patient(X)))))&
((?[X]:(~strong(X)))<=>((strong(susan)&wise(susan))))&
((~tall(susan)<~>creative(susan)))&
(~old(lucy))&
(~wise(alice))&
((quiet(lucy)<~>~quiet(lucy)))&
((~patient(fred)<~>old(fred)))&
((generous(susan)&kind(susan)))&
(~humble(paul))&
(rich(lucy)) | ~old(alice) | [
"p0",
"p3",
"p15",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5283584993781454136350856
% SZS output start Proof for 5283584993781454136350856
1. ! [X0] : ((~creative(X0) | ~wise(X0)) <=> (~old(X0) | ~strong(X0))) [input p0]
4. ! [X0] : (wise(X0) => (~rich(X0) & ~generous(X0))) [input p3]
16. ? [X0] : ~strong(X0) <=> (wise(susan) & strong(susan)) [input p15]
19. ~wise(alice) [input p18]
22. kind(susan) & generous(susan) [input p21]
25. old(alice) [input hypothesis]
31. ! [X0] : ((~rich(X0) & ~generous(X0)) | ~wise(X0)) [ennf transformation 4]
36. ! [X0] : (((~creative(X0) | ~wise(X0)) | (old(X0) & strong(X0))) & ((~old(X0) | ~strong(X0)) | (creative(X0) & wise(X0)))) [nnf transformation 1]
37. ! [X0] : ((~creative(X0) | ~wise(X0) | (old(X0) & strong(X0))) & (~old(X0) | ~strong(X0) | (creative(X0) & wise(X0)))) [flattening 36]
72. (? [X0] : ~strong(X0) | (~wise(susan) | ~strong(susan))) & ((wise(susan) & strong(susan)) | ! [X0] : strong(X0)) [nnf transformation 16]
73. (? [X0] : ~strong(X0) | ~wise(susan) | ~strong(susan)) & ((wise(susan) & strong(susan)) | ! [X0] : strong(X0)) [flattening 72]
74. (? [X0] : ~strong(X0) | ~wise(susan) | ~strong(susan)) & ((wise(susan) & strong(susan)) | ! [X1] : strong(X1)) [rectify 73]
75. ? [X0] : ~strong(X0) => ~strong(sK8) [choice axiom]
76. (~strong(sK8) | ~wise(susan) | ~strong(susan)) & ((wise(susan) & strong(susan)) | ! [X1] : strong(X1)) [skolemisation 74,75]
80. ~old(X0) | ~strong(X0) | wise(X0) [cnf transformation 37]
91. ~generous(X0) | ~wise(X0) [cnf transformation 31]
137. wise(susan) | strong(X1) [cnf transformation 76]
142. ~wise(alice) [cnf transformation 19]
147. generous(susan) [cnf transformation 22]
151. old(alice) [cnf transformation 25]
157. 2 <=> old(alice) [avatar definition]
159. old(alice) <- (2) [avatar component clause 157]
265. 25 <=> wise(alice) [avatar definition]
267. ~wise(alice) <- (~25) [avatar component clause 265]
383. 50 <=> wise(susan) [avatar definition]
392. 52 <=> ! [X1] : strong(X1) [avatar definition]
393. strong(X1) <- (52) [avatar component clause 392]
394. 52 | 50 [avatar split clause 137,383,392]
406. ~25 [avatar split clause 142,265]
417. 2 [avatar split clause 151,157]
430. ~wise(susan) [resolution 91,147]
433. ~50 [avatar split clause 430,383]
438. ~strong(alice) | wise(alice) <- (2) [resolution 80,159]
439. wise(alice) <- (2, 52) [subsumption resolution 438,393]
440. $false <- (2, ~25, 52) [subsumption resolution 439,267]
441. ~2 | 25 | ~52 [avatar contradiction clause 440]
442. $false [avatar sat refutation 394,406,417,433,441]
% SZS output end Proof for 5283584993781454136350856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is old and vice versa. Everyone who is both not happy and not wise is both not old and not brave and vice versa. If john is either not rich or not calm then mary is rich or not rich. If someone is curious or tall then susan is curious or funny and vice versa. Everyone who is either not brave or funny is either patient or not creative. Everyone who is not generous is brave. If susan is creative then john is tall or generous and vice versa. Everyone who is both not brave and not rich is either not patient or not funny. If someone is not strong or not curious then john is either brave or not creative and vice versa. Everyone who is either not kind or strong is not rich or patient and vice versa. If john is not generous or kind then someone is not tall and vice versa. If someone is not creative then someone is both humble and not curious and vice versa. If someone is both not creative and not humble then fred is quiet or strong and vice versa. If fred is rich or quiet then fred is both patient and kind. Everyone who is either humble or patient is calm. Everyone who is both calm and patient is both curious and not rich and vice versa. Lucy is kind or generous. Someone is either calm or happy. Someone is both funny and not kind. Someone is not funny or wise. Fred is old or kind. Paul is both patient and not creative. Susan is not quiet. Alice is not strong. | Fred is not curious. | neutral | (![X]:(curious(X)<=>old(X)))&
(![X]:((~happy(X)&~wise(X))<=>(~old(X)&~brave(X))))&
(((~rich(john)<~>~calm(john)))=>((rich(mary)|~rich(mary))))&
((?[X]:((curious(X)|tall(X))))<=>((curious(susan)|funny(susan))))&
(![X]:((~brave(X)<~>funny(X))=>(patient(X)<~>~creative(X))))&
(![X]:(~generous(X)=>brave(X)))&
((creative(susan))<=>((tall(john)|generous(john))))&
(![X]:((~brave(X)&~rich(X))=>(~patient(X)<~>~funny(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>((brave(john)<~>~creative(john))))&
(![X]:((~kind(X)<~>strong(X))<=>(~rich(X)|patient(X))))&
(((~generous(john)|kind(john)))<=>(?[X]:(~tall(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((humble(X)&~curious(X)))))&
((?[X]:((~creative(X)&~humble(X))))<=>((quiet(fred)|strong(fred))))&
(((rich(fred)|quiet(fred)))=>((patient(fred)&kind(fred))))&
(![X]:((humble(X)<~>patient(X))=>calm(X)))&
(![X]:((calm(X)&patient(X))<=>(curious(X)&~rich(X))))&
((kind(lucy)|generous(lucy)))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((funny(X)&~kind(X))))&
(?[X]:((~funny(X)|wise(X))))&
((old(fred)|kind(fred)))&
((patient(paul)&~creative(paul)))&
(~quiet(susan))&
(~strong(alice)) | ~curious(fred) | [] | null | 0 |
Everyone who is either generous or curious is generous or not creative and vice versa.
Everyone who is both not creative and not brave is not creative or curious and vice versa.
Everyone who is curious is not old and vice versa.
If alice is either not tall or kind then someone is not kind and vice versa.
Everyone who is both generous and quiet is either curious or not quiet and vice versa.
Everyone who is either not kind or tall is not funny or not curious.
If mary is either creative or quiet then susan is wise.
If paul is both creative and wise then mary is funny and vice versa.
Everyone who is either not calm or humble is kind or funny and vice versa.
Everyone who is not rich is either not generous or not humble.
Everyone who is not generous or curious is either funny or not creative.
If someone is either curious or generous then someone is either calm or not rich.
Everyone who is curious is wise and vice versa.
If fred is either not curious or kind then mary is both patient and not quiet and vice versa.
If someone is creative or rich then someone is both calm and old and vice versa.
Everyone who is both brave and not wise is patient.
Someone is not rich or not patient.
Someone is not generous or not tall.
Susan is tall.
Someone is both not strong and quiet.
John is creative.
Someone is either happy or not rich. | Mary is not curious. | contradiction | (![X]:((generous(X)<~>curious(X))<=>(generous(X)|~creative(X))))&
(![X]:((~creative(X)&~brave(X))<=>(~creative(X)|curious(X))))&
(![X]:(curious(X)<=>~old(X)))&
(((~tall(alice)<~>kind(alice)))<=>(?[X]:(~kind(X))))&
(![X]:((generous(X)&quiet(X))<=>(curious(X)<~>~quiet(X))))&
(![X]:((~kind(X)<~>tall(X))=>(~funny(X)|~curious(X))))&
(((creative(mary)<~>quiet(mary)))=>(wise(susan)))&
(((creative(paul)&wise(paul)))<=>(funny(mary)))&
(![X]:((~calm(X)<~>humble(X))<=>(kind(X)|funny(X))))&
(![X]:(~rich(X)=>(~generous(X)<~>~humble(X))))&
(![X]:((~generous(X)|curious(X))=>(funny(X)<~>~creative(X))))&
((?[X]:((curious(X)<~>generous(X))))=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:(curious(X)<=>wise(X)))&
(((~curious(fred)<~>kind(fred)))<=>((patient(mary)&~quiet(mary))))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:((calm(X)&old(X)))))&
(![X]:((brave(X)&~wise(X))=>patient(X)))&
(?[X]:((~rich(X)|~patient(X))))&
(?[X]:((~generous(X)|~tall(X))))&
(tall(susan))&
(?[X]:((~strong(X)&quiet(X))))&
(creative(john))&
(?[X]:((happy(X)<~>~rich(X)))) | ~curious(mary) | [
"p0",
"p4",
"p7",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3318900827051346852734113
% SZS output start Proof for 3318900827051346852734113
1. ! [X0] : ((generous(X0) <~> curious(X0)) <=> (~creative(X0) | generous(X0))) [input p0]
5. ! [X0] : ((quiet(X0) & generous(X0)) <=> (curious(X0) <~> ~quiet(X0))) [input p4]
8. (wise(paul) & creative(paul)) <=> funny(mary) [input p7]
11. ! [X0] : ((curious(X0) | ~generous(X0)) => (funny(X0) <~> ~creative(X0))) [input p10]
13. ! [X0] : (curious(X0) <=> wise(X0)) [input p12]
23. ~curious(mary) [input hypothesis]
31. ! [X0] : ((funny(X0) <~> ~creative(X0)) | (~curious(X0) & generous(X0))) [ennf transformation 11]
35. ! [X0] : ((((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (creative(X0) & ~generous(X0))) & ((~creative(X0) | generous(X0)) | ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (creative(X0) & ~generous(X0))) & (~creative(X0) | generous(X0) | ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0))))) [flattening 35]
44. ! [X0] : (((quiet(X0) & generous(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | (~quiet(X0) | ~generous(X0)))) [nnf transformation 5]
45. ! [X0] : (((quiet(X0) & generous(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) & (((quiet(X0) | ~curious(X0)) & (~quiet(X0) | curious(X0))) | ~quiet(X0) | ~generous(X0))) [flattening 44]
48. ((wise(paul) & creative(paul)) | ~funny(mary)) & (funny(mary) | (~wise(paul) | ~creative(paul))) [nnf transformation 8]
49. ((wise(paul) & creative(paul)) | ~funny(mary)) & (funny(mary) | ~wise(paul) | ~creative(paul)) [flattening 48]
53. ! [X0] : (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | (~curious(X0) & generous(X0))) [nnf transformation 31]
58. ! [X0] : ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))) [nnf transformation 13]
76. ~creative(X0) | generous(X0) | generous(X0) | ~curious(X0) [cnf transformation 36]
78. creative(X0) | generous(X0) | curious(X0) [cnf transformation 36]
79. ~curious(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 36]
92. ~quiet(X0) | curious(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 45]
97. quiet(X0) | curious(X0) | quiet(X0) [cnf transformation 45]
103. creative(paul) | ~funny(mary) [cnf transformation 49]
104. wise(paul) | ~funny(mary) [cnf transformation 49]
113. ~creative(X0) | funny(X0) | generous(X0) [cnf transformation 53]
122. ~wise(X0) | curious(X0) [cnf transformation 58]
142. ~curious(mary) [cnf transformation 23]
143. ~quiet(X0) | curious(X0) | ~generous(X0) [duplicate literal removal 92]
144. quiet(X0) | curious(X0) [duplicate literal removal 97]
145. ~creative(X0) | generous(X0) | ~curious(X0) [duplicate literal removal 76]
146. ~curious(X0) | ~generous(X0) [duplicate literal removal 79]
147. ~creative(X0) | ~curious(X0) [subsumption resolution 145,146]
168. ~quiet(X0) | ~generous(X0) [subsumption resolution 143,146]
170. 5 <=> quiet(mary) [avatar definition]
171. quiet(mary) <- (5) [avatar component clause 170]
172. ~quiet(mary) <- (~5) [avatar component clause 170]
174. 6 <=> creative(mary) [avatar definition]
175. ~creative(mary) <- (~6) [avatar component clause 174]
176. creative(mary) <- (6) [avatar component clause 174]
184. 8 <=> funny(mary) [avatar definition]
188. 9 <=> wise(paul) [avatar definition]
190. wise(paul) <- (9) [avatar component clause 188]
191. ~8 | 9 [avatar split clause 104,188,184]
193. 10 <=> creative(paul) [avatar definition]
195. creative(paul) <- (10) [avatar component clause 193]
196. ~8 | 10 [avatar split clause 103,193,184]
301. curious(mary) <- (~5) [resolution 144,172]
302. $false <- (~5) [subsumption resolution 301,142]
303. 5 [avatar contradiction clause 302]
316. ~generous(mary) <- (5) [resolution 168,171]
323. generous(mary) | curious(mary) <- (~6) [resolution 78,175]
325. curious(mary) <- (5, ~6) [subsumption resolution 323,316]
326. $false <- (5, ~6) [subsumption resolution 325,142]
327. ~5 | 6 [avatar contradiction clause 326]
354. funny(mary) | generous(mary) <- (6) [resolution 113,176]
364. funny(mary) <- (5, 6) [subsumption resolution 354,316]
365. 8 | ~5 | ~6 [avatar split clause 364,174,170,184]
367. curious(paul) <- (9) [resolution 190,122]
369. ~curious(paul) <- (10) [resolution 195,147]
371. $false <- (9, 10) [subsumption resolution 369,367]
372. ~9 | ~10 [avatar contradiction clause 371]
373. $false [avatar sat refutation 191,196,303,327,365,372]
% SZS output end Proof for 3318900827051346852734113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not wise or tall is either not curious or not happy and vice versa. If someone is kind or not old then mary is rich. If alice is either not kind or wise then someone is both not creative and kind and vice versa. Everyone who is not kind or creative is not funny. Everyone who is either not quiet or not funny is tall or not curious and vice versa. If someone is funny then someone is curious or not quiet and vice versa. Everyone who is not happy or quiet is not happy or curious and vice versa. Everyone who is both quiet and patient is not old and vice versa. If paul is either rich or calm then someone is both strong and not creative. Everyone who is not brave or kind is quiet or not calm. If someone is rich then paul is both not creative and not tall and vice versa. If john is kind or not kind then paul is not strong. Everyone who is strong or humble is not calm and vice versa. If john is brave or wise then someone is not generous. If paul is both not calm and not curious then fred is both quiet and not funny and vice versa. Everyone who is not happy or not funny is either quiet or not curious. Fred is either calm or not quiet. Someone is not wise. Someone is both not calm and not patient. Someone is curious or tall. John is both wise and tall. Someone is either not humble or creative. Someone is not curious. Lucy is both not humble and curious. | Alice is kind. | neutral | (![X]:((~wise(X)<~>tall(X))<=>(~curious(X)<~>~happy(X))))&
((?[X]:((kind(X)|~old(X))))=>(rich(mary)))&
(((~kind(alice)<~>wise(alice)))<=>(?[X]:((~creative(X)&kind(X)))))&
(![X]:((~kind(X)|creative(X))=>~funny(X)))&
(![X]:((~quiet(X)<~>~funny(X))<=>(tall(X)|~curious(X))))&
((?[X]:(funny(X)))<=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:((~happy(X)|quiet(X))<=>(~happy(X)|curious(X))))&
(![X]:((quiet(X)&patient(X))<=>~old(X)))&
(((rich(paul)<~>calm(paul)))=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((~brave(X)|kind(X))=>(quiet(X)|~calm(X))))&
((?[X]:(rich(X)))<=>((~creative(paul)&~tall(paul))))&
(((kind(john)|~kind(john)))=>(~strong(paul)))&
(![X]:((strong(X)|humble(X))<=>~calm(X)))&
(((brave(john)|wise(john)))=>(?[X]:(~generous(X))))&
(((~calm(paul)&~curious(paul)))<=>((quiet(fred)&~funny(fred))))&
(![X]:((~happy(X)|~funny(X))=>(quiet(X)<~>~curious(X))))&
((calm(fred)<~>~quiet(fred)))&
(?[X]:(~wise(X)))&
(?[X]:((~calm(X)&~patient(X))))&
(?[X]:((curious(X)|tall(X))))&
((wise(john)&tall(john)))&
(?[X]:((~humble(X)<~>creative(X))))&
(?[X]:(~curious(X)))&
((~humble(lucy)&curious(lucy))) | kind(alice) | [] | null | 0 |
Everyone who is not funny is both not generous and strong.
If paul is either happy or not wise then someone is calm or old.
Everyone who is either brave or generous is both not funny and curious.
Everyone who is calm or not calm is either not old or calm.
If someone is both not humble and generous then john is not generous and vice versa.
Everyone who is both strong and creative is either not humble or creative.
If someone is both quiet and rich then someone is not creative or not generous and vice versa.
Everyone who is both old and not creative is not quiet or creative and vice versa.
Everyone who is either not humble or not tall is not generous and vice versa.
If mary is either brave or not generous then fred is either happy or not strong and vice versa.
Everyone who is not generous or not rich is either not old or happy.
Everyone who is not kind is not wise and vice versa.
Everyone who is both quiet and funny is either not brave or patient.
If alice is both humble and not generous then someone is tall.
Everyone who is wise is both not humble and not funny.
Lucy is not humble.
Susan is either not brave or patient.
Someone is either not funny or tall.
Fred is both happy and not rich.
Alice is not generous or not strong.
Fred is both not funny and not rich.
Someone is both not old and not wise.
Someone is wise or not kind. | Fred is old. | entailment | (![X]:(~funny(X)=>(~generous(X)&strong(X))))&
(((happy(paul)<~>~wise(paul)))=>(?[X]:((calm(X)|old(X)))))&
(![X]:((brave(X)<~>generous(X))=>(~funny(X)&curious(X))))&
(![X]:((calm(X)|~calm(X))=>(~old(X)<~>calm(X))))&
((?[X]:((~humble(X)&generous(X))))<=>(~generous(john)))&
(![X]:((strong(X)&creative(X))=>(~humble(X)<~>creative(X))))&
((?[X]:((quiet(X)&rich(X))))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((old(X)&~creative(X))<=>(~quiet(X)|creative(X))))&
(![X]:((~humble(X)<~>~tall(X))<=>~generous(X)))&
(((brave(mary)<~>~generous(mary)))<=>((happy(fred)<~>~strong(fred))))&
(![X]:((~generous(X)|~rich(X))=>(~old(X)<~>happy(X))))&
(![X]:(~kind(X)<=>~wise(X)))&
(![X]:((quiet(X)&funny(X))=>(~brave(X)<~>patient(X))))&
(((humble(alice)&~generous(alice)))=>(?[X]:(tall(X))))&
(![X]:(wise(X)=>(~humble(X)&~funny(X))))&
(~humble(lucy))&
((~brave(susan)<~>patient(susan)))&
(?[X]:((~funny(X)<~>tall(X))))&
((happy(fred)&~rich(fred)))&
((~generous(alice)|~strong(alice)))&
((~funny(fred)&~rich(fred)))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:((wise(X)|~kind(X)))) | old(fred) | [
"p0",
"p10",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1925555907201510092191590
% SZS output start Proof for 1925555907201510092191590
1. ! [X0] : (~funny(X0) => (strong(X0) & ~generous(X0))) [input p0]
11. ! [X0] : ((~rich(X0) | ~generous(X0)) => (~old(X0) <~> happy(X0))) [input p10]
19. ~rich(fred) & happy(fred) [input p18]
21. ~rich(fred) & ~funny(fred) [input p20]
24. ~old(fred) [input hypothesis]
28. ! [X0] : ((strong(X0) & ~generous(X0)) | funny(X0)) [ennf transformation 1]
34. ! [X0] : ((~old(X0) <~> happy(X0)) | (rich(X0) & generous(X0))) [ennf transformation 11]
60. ! [X0] : (((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | (rich(X0) & generous(X0))) [nnf transformation 34]
72. ~generous(X0) | funny(X0) [cnf transformation 28]
111. ~happy(X0) | old(X0) | generous(X0) [cnf transformation 60]
124. happy(fred) [cnf transformation 19]
127. ~funny(fred) [cnf transformation 21]
132. ~old(fred) [cnf transformation 24]
211. 17 <=> happy(fred) [avatar definition]
213. happy(fred) <- (17) [avatar component clause 211]
265. 17 [avatar split clause 124,211]
313. old(fred) | generous(fred) <- (17) [resolution 111,213]
323. generous(fred) <- (17) [subsumption resolution 313,132]
346. funny(fred) <- (17) [resolution 323,72]
347. $false <- (17) [subsumption resolution 346,127]
348. ~17 [avatar contradiction clause 347]
349. $false [avatar sat refutation 265,348]
% SZS output end Proof for 1925555907201510092191590
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and curious is either kind or happy and vice versa.
If alice is not calm then john is both not curious and not patient.
If lucy is wise then someone is either not patient or not quiet.
Everyone who is not happy or quiet is either tall or not kind and vice versa.
If someone is both creative and not funny then susan is either old or calm and vice versa.
If john is generous or not curious then susan is either happy or strong and vice versa.
If someone is both not kind and creative then someone is either not brave or not humble.
Everyone who is not old or funny is old or not funny and vice versa.
If someone is not happy or old then susan is both generous and strong and vice versa.
If john is not wise or not calm then john is not tall and vice versa.
If fred is rich then someone is patient or not strong and vice versa.
Everyone who is not patient or not generous is happy and vice versa.
Everyone who is both tall and not calm is tall or happy and vice versa.
Everyone who is either not tall or calm is either wise or not kind and vice versa.
Everyone who is either kind or not kind is humble or curious.
Everyone who is not strong or not rich is not happy and vice versa.
Susan is not wise.
Someone is both kind and curious.
Someone is patient or not patient.
Fred is both creative and happy.
Someone is either curious or brave.
Someone is both not strong and wise.
Someone is either not brave or not patient.
Someone is old. | Susan is happy. | contradiction | (![X]:((~funny(X)&curious(X))<=>(kind(X)<~>happy(X))))&
((~calm(alice))=>((~curious(john)&~patient(john))))&
((wise(lucy))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(![X]:((~happy(X)|quiet(X))<=>(tall(X)<~>~kind(X))))&
((?[X]:((creative(X)&~funny(X))))<=>((old(susan)<~>calm(susan))))&
(((generous(john)|~curious(john)))<=>((happy(susan)<~>strong(susan))))&
((?[X]:((~kind(X)&creative(X))))=>(?[X]:((~brave(X)<~>~humble(X)))))&
(![X]:((~old(X)|funny(X))<=>(old(X)|~funny(X))))&
((?[X]:((~happy(X)|old(X))))<=>((generous(susan)&strong(susan))))&
(((~wise(john)|~calm(john)))<=>(~tall(john)))&
((rich(fred))<=>(?[X]:((patient(X)|~strong(X)))))&
(![X]:((~patient(X)|~generous(X))<=>happy(X)))&
(![X]:((tall(X)&~calm(X))<=>(tall(X)|happy(X))))&
(![X]:((~tall(X)<~>calm(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((kind(X)<~>~kind(X))=>(humble(X)|curious(X))))&
(![X]:((~strong(X)|~rich(X))<=>~happy(X)))&
(~wise(susan))&
(?[X]:((kind(X)&curious(X))))&
(?[X]:((patient(X)|~patient(X))))&
((creative(fred)&happy(fred)))&
(?[X]:((curious(X)<~>brave(X))))&
(?[X]:((~strong(X)&wise(X))))&
(?[X]:((~brave(X)<~>~patient(X))))&
(?[X]:(old(X))) | happy(susan) | [
"p5",
"p8",
"p9",
"p11",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 550914142288885116480317
% SZS output start Proof for 550914142288885116480317
6. (~curious(john) | generous(john)) <=> (happy(susan) <~> strong(susan)) [input p5]
9. ? [X0] : (old(X0) | ~happy(X0)) <=> (strong(susan) & generous(susan)) [input p8]
10. (~calm(john) | ~wise(john)) <=> ~tall(john) [input p9]
12. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> happy(X0)) [input p11]
13. ! [X0] : ((~calm(X0) & tall(X0)) <=> (happy(X0) | tall(X0))) [input p12]
24. ? [X0] : old(X0) [input p23]
25. happy(susan) [input hypothesis]
43. ((~curious(john) | generous(john)) | ((happy(susan) | ~strong(susan)) & (strong(susan) | ~happy(susan)))) & (((~strong(susan) | ~happy(susan)) & (strong(susan) | happy(susan))) | (curious(john) & ~generous(john))) [nnf transformation 6]
44. (~curious(john) | generous(john) | ((happy(susan) | ~strong(susan)) & (strong(susan) | ~happy(susan)))) & (((~strong(susan) | ~happy(susan)) & (strong(susan) | happy(susan))) | (curious(john) & ~generous(john))) [flattening 43]
51. (? [X0] : (old(X0) | ~happy(X0)) | (~strong(susan) | ~generous(susan))) & ((strong(susan) & generous(susan)) | ! [X0] : (~old(X0) & happy(X0))) [nnf transformation 9]
52. (? [X0] : (old(X0) | ~happy(X0)) | ~strong(susan) | ~generous(susan)) & ((strong(susan) & generous(susan)) | ! [X0] : (~old(X0) & happy(X0))) [flattening 51]
53. (? [X0] : (old(X0) | ~happy(X0)) | ~strong(susan) | ~generous(susan)) & ((strong(susan) & generous(susan)) | ! [X1] : (~old(X1) & happy(X1))) [rectify 52]
54. ? [X0] : (old(X0) | ~happy(X0)) => (old(sK3) | ~happy(sK3)) [choice axiom]
55. ((old(sK3) | ~happy(sK3)) | ~strong(susan) | ~generous(susan)) & ((strong(susan) & generous(susan)) | ! [X1] : (~old(X1) & happy(X1))) [skolemisation 53,54]
56. ((~calm(john) | ~wise(john)) | tall(john)) & (~tall(john) | (calm(john) & wise(john))) [nnf transformation 10]
57. (~calm(john) | ~wise(john) | tall(john)) & (~tall(john) | (calm(john) & wise(john))) [flattening 56]
62. ! [X0] : (((~generous(X0) | ~patient(X0)) | ~happy(X0)) & (happy(X0) | (generous(X0) & patient(X0)))) [nnf transformation 12]
63. ! [X0] : ((~generous(X0) | ~patient(X0) | ~happy(X0)) & (happy(X0) | (generous(X0) & patient(X0)))) [flattening 62]
64. ! [X0] : (((~calm(X0) & tall(X0)) | (~happy(X0) & ~tall(X0))) & ((happy(X0) | tall(X0)) | (calm(X0) | ~tall(X0)))) [nnf transformation 13]
65. ! [X0] : (((~calm(X0) & tall(X0)) | (~happy(X0) & ~tall(X0))) & (happy(X0) | tall(X0) | calm(X0) | ~tall(X0))) [flattening 64]
82. ? [X0] : old(X0) => old(sK10) [choice axiom]
83. old(sK10) [skolemisation 24,82]
108. ~strong(susan) | ~happy(susan) | ~generous(john) [cnf transformation 44]
121. strong(susan) | ~old(X1) [cnf transformation 55]
124. ~tall(john) | calm(john) [cnf transformation 57]
130. generous(X0) | happy(X0) [cnf transformation 63]
134. ~happy(X0) | tall(X0) [cnf transformation 65]
135. ~tall(X0) | ~calm(X0) [cnf transformation 65]
162. old(sK10) [cnf transformation 83]
163. happy(susan) [cnf transformation 25]
224. 12 <=> strong(susan) [avatar definition]
228. 13 <=> happy(susan) [avatar definition]
232. 14 <=> generous(john) [avatar definition]
233. ~generous(john) <- (~14) [avatar component clause 232]
238. ~14 | ~13 | ~12 [avatar split clause 108,224,228,232]
268. 21 <=> ! [X1] : ~old(X1) [avatar definition]
269. ~old(X1) <- (21) [avatar component clause 268]
270. 21 | 12 [avatar split clause 121,224,268]
278. 23 <=> tall(john) [avatar definition]
280. tall(john) <- (23) [avatar component clause 278]
286. 25 <=> calm(john) [avatar definition]
287. calm(john) <- (25) [avatar component clause 286]
290. 25 | ~23 [avatar split clause 124,278,286]
338. 13 [avatar split clause 163,228]
339. $false <- (21) [resolution 269,162]
340. ~21 [avatar contradiction clause 339]
345. happy(john) <- (~14) [resolution 130,233]
369. tall(john) <- (~14) [resolution 345,134]
372. 23 | 14 [avatar split clause 369,232,278]
373. ~calm(john) <- (23) [resolution 280,135]
374. $false <- (23, 25) [subsumption resolution 373,287]
375. ~23 | ~25 [avatar contradiction clause 374]
376. $false [avatar sat refutation 238,270,290,338,340,372,375]
% SZS output end Proof for 550914142288885116480317
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or old is humble or generous.
If someone is either not calm or not rich then lucy is both generous and happy.
Everyone who is both calm and not patient is not tall and vice versa.
If mary is not happy or not strong then lucy is either strong or generous and vice versa.
If mary is not tall then someone is curious and vice versa.
If john is either not quiet or patient then susan is not creative or generous.
If mary is not calm or not old then someone is not creative.
Everyone who is strong or not happy is happy and vice versa.
If someone is not generous then lucy is old and vice versa.
Everyone who is patient or not generous is strong.
Everyone who is not happy is either calm or rich and vice versa.
If paul is either not quiet or funny then someone is creative.
If john is not happy then john is both not strong and wise.
If someone is not rich or rich then someone is not humble or calm and vice versa.
Everyone who is not patient or not creative is either funny or not rich and vice versa.
Everyone who is both not curious and rich is both curious and not happy.
Paul is not quiet or not rich.
Fred is either curious or not humble.
Alice is not funny.
Someone is both not brave and patient.
Someone is not creative.
John is either not strong or humble.
Fred is tall.
Alice is either not wise or not strong. | Lucy is happy. | entailment | (![X]:((curious(X)|old(X))=>(humble(X)|generous(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>((generous(lucy)&happy(lucy))))&
(![X]:((calm(X)&~patient(X))<=>~tall(X)))&
(((~happy(mary)|~strong(mary)))<=>((strong(lucy)<~>generous(lucy))))&
((~tall(mary))<=>(?[X]:(curious(X))))&
(((~quiet(john)<~>patient(john)))=>((~creative(susan)|generous(susan))))&
(((~calm(mary)|~old(mary)))=>(?[X]:(~creative(X))))&
(![X]:((strong(X)|~happy(X))<=>happy(X)))&
((?[X]:(~generous(X)))<=>(old(lucy)))&
(![X]:((patient(X)|~generous(X))=>strong(X)))&
(![X]:(~happy(X)<=>(calm(X)<~>rich(X))))&
(((~quiet(paul)<~>funny(paul)))=>(?[X]:(creative(X))))&
((~happy(john))=>((~strong(john)&wise(john))))&
((?[X]:((~rich(X)|rich(X))))<=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(funny(X)<~>~rich(X))))&
(![X]:((~curious(X)&rich(X))=>(curious(X)&~happy(X))))&
((~quiet(paul)|~rich(paul)))&
((curious(fred)<~>~humble(fred)))&
(~funny(alice))&
(?[X]:((~brave(X)&patient(X))))&
(?[X]:(~creative(X)))&
((~strong(john)<~>humble(john)))&
(tall(fred))&
((~wise(alice)<~>~strong(alice))) | happy(lucy) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 64611766020602856374450
% SZS output start Proof for 64611766020602856374450
8. ! [X0] : ((~happy(X0) | strong(X0)) <=> happy(X0)) [input p7]
25. ~happy(lucy) [input hypothesis]
51. ! [X0] : (((~happy(X0) | strong(X0)) | ~happy(X0)) & (happy(X0) | (happy(X0) & ~strong(X0)))) [nnf transformation 8]
52. ! [X0] : ((~happy(X0) | strong(X0) | ~happy(X0)) & (happy(X0) | (happy(X0) & ~strong(X0)))) [flattening 51]
97. happy(X0) | happy(X0) [cnf transformation 52]
134. ~happy(lucy) [cnf transformation 25]
136. happy(X0) [duplicate literal removal 97]
302. $false [subsumption resolution 134,136]
% SZS output end Proof for 64611766020602856374450
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or not patient then someone is either not kind or not patient and vice versa.
Everyone who is not patient or tall is calm and vice versa.
Everyone who is not patient or not wise is rich or not humble.
Everyone who is old is both patient and not patient.
Everyone who is either quiet or generous is not humble.
If paul is either funny or not creative then someone is not wise and vice versa.
Everyone who is either calm or funny is kind and vice versa.
If someone is patient or humble then alice is both not rich and wise.
If someone is both rich and not wise then john is either rich or not happy.
Everyone who is curious or not funny is not patient or patient and vice versa.
Everyone who is not patient or not rich is funny or not brave.
Everyone who is not curious is both creative and kind.
If alice is both not humble and not happy then paul is curious or quiet and vice versa.
If paul is not brave or calm then someone is both not strong and generous.
If someone is either not quiet or not curious then susan is not wise or not happy.
Everyone who is both generous and not quiet is either not strong or not calm.
Mary is not calm or not humble.
Someone is not humble.
Alice is not quiet or not rich.
Someone is either creative or calm.
Alice is not generous.
Lucy is calm.
Alice is either funny or quiet.
Someone is either not old or funny. | Lucy is not old. | entailment | ((?[X]:((old(X)|~patient(X))))<=>(?[X]:((~kind(X)<~>~patient(X)))))&
(![X]:((~patient(X)|tall(X))<=>calm(X)))&
(![X]:((~patient(X)|~wise(X))=>(rich(X)|~humble(X))))&
(![X]:(old(X)=>(patient(X)&~patient(X))))&
(![X]:((quiet(X)<~>generous(X))=>~humble(X)))&
(((funny(paul)<~>~creative(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((calm(X)<~>funny(X))<=>kind(X)))&
((?[X]:((patient(X)|humble(X))))=>((~rich(alice)&wise(alice))))&
((?[X]:((rich(X)&~wise(X))))=>((rich(john)<~>~happy(john))))&
(![X]:((curious(X)|~funny(X))<=>(~patient(X)|patient(X))))&
(![X]:((~patient(X)|~rich(X))=>(funny(X)|~brave(X))))&
(![X]:(~curious(X)=>(creative(X)&kind(X))))&
(((~humble(alice)&~happy(alice)))<=>((curious(paul)|quiet(paul))))&
(((~brave(paul)|calm(paul)))=>(?[X]:((~strong(X)&generous(X)))))&
((?[X]:((~quiet(X)<~>~curious(X))))=>((~wise(susan)|~happy(susan))))&
(![X]:((generous(X)&~quiet(X))=>(~strong(X)<~>~calm(X))))&
((~calm(mary)|~humble(mary)))&
(?[X]:(~humble(X)))&
((~quiet(alice)|~rich(alice)))&
(?[X]:((creative(X)<~>calm(X))))&
(~generous(alice))&
(calm(lucy))&
((funny(alice)<~>quiet(alice)))&
(?[X]:((~old(X)<~>funny(X)))) | ~old(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5369768147073982009100771
% SZS output start Proof for 5369768147073982009100771
4. ! [X0] : (old(X0) => (~patient(X0) & patient(X0))) [input p3]
25. old(lucy) [input hypothesis]
29. ! [X0] : ((~patient(X0) & patient(X0)) | ~old(X0)) [ennf transformation 4]
83. patient(X0) | ~old(X0) [cnf transformation 29]
84. ~patient(X0) | ~old(X0) [cnf transformation 29]
133. old(lucy) [cnf transformation 25]
163. 8 <=> ! [X3] : ~old(X3) [avatar definition]
164. ~old(X3) <- (8) [avatar component clause 163]
168. ~old(X0) [subsumption resolution 83,84]
169. 8 [avatar split clause 168,163]
320. $false <- (8) [resolution 164,133]
321. ~8 [avatar contradiction clause 320]
322. $false [avatar sat refutation 169,321]
% SZS output end Proof for 5369768147073982009100771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both not calm and brave and vice versa.
If someone is rich or not patient then alice is generous.
If someone is old or not brave then someone is not old.
Everyone who is either not creative or not funny is not curious.
If someone is both creative and not wise then someone is both not funny and creative and vice versa.
If someone is not curious then john is both not happy and not creative and vice versa.
Everyone who is tall is both not curious and kind and vice versa.
Everyone who is kind or not old is both not kind and not brave and vice versa.
If fred is either old or not happy then someone is old.
Everyone who is funny or not old is not curious.
Everyone who is both patient and calm is old or not old.
If someone is not quiet then someone is curious and vice versa.
Everyone who is either not creative or not tall is both strong and generous and vice versa.
Everyone who is not generous or not funny is funny and vice versa.
Someone is either wise or not old.
Someone is either not funny or not brave.
Lucy is both not tall and not generous.
Mary is either not strong or not calm.
Mary is happy or not rich.
Someone is not strong or not wise. | Lucy is not patient. | contradiction | (![X]:(happy(X)<=>(~calm(X)&brave(X))))&
((?[X]:((rich(X)|~patient(X))))=>(generous(alice)))&
((?[X]:((old(X)|~brave(X))))=>(?[X]:(~old(X))))&
(![X]:((~creative(X)<~>~funny(X))=>~curious(X)))&
((?[X]:((creative(X)&~wise(X))))<=>(?[X]:((~funny(X)&creative(X)))))&
((?[X]:(~curious(X)))<=>((~happy(john)&~creative(john))))&
(![X]:(tall(X)<=>(~curious(X)&kind(X))))&
(![X]:((kind(X)|~old(X))<=>(~kind(X)&~brave(X))))&
(((old(fred)<~>~happy(fred)))=>(?[X]:(old(X))))&
(![X]:((funny(X)|~old(X))=>~curious(X)))&
(![X]:((patient(X)&calm(X))=>(old(X)|~old(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(curious(X))))&
(![X]:((~creative(X)<~>~tall(X))<=>(strong(X)&generous(X))))&
(![X]:((~generous(X)|~funny(X))<=>funny(X)))&
(?[X]:((wise(X)<~>~old(X))))&
(?[X]:((~funny(X)<~>~brave(X))))&
((~tall(lucy)&~generous(lucy)))&
((~strong(mary)<~>~calm(mary)))&
((happy(mary)|~rich(mary)))&
(?[X]:((~strong(X)|~wise(X)))) | ~patient(lucy) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 83894360072950157443310
% SZS output start Proof for 83894360072950157443310
2. ? [X0] : (~patient(X0) | rich(X0)) => generous(alice) [input p1]
14. ! [X0] : ((~funny(X0) | ~generous(X0)) <=> funny(X0)) [input p13]
21. ~patient(lucy) [input hypothesis]
25. ? [X0] : ~patient(X0) => generous(alice) [pure predicate removal 2]
27. generous(alice) | ! [X0] : patient(X0) [ennf transformation 25]
64. ! [X0] : (((~funny(X0) | ~generous(X0)) | ~funny(X0)) & (funny(X0) | (funny(X0) & generous(X0)))) [nnf transformation 14]
65. ! [X0] : ((~funny(X0) | ~generous(X0) | ~funny(X0)) & (funny(X0) | (funny(X0) & generous(X0)))) [flattening 64]
78. generous(alice) | patient(X0) [cnf transformation 27]
112. funny(X0) | funny(X0) [cnf transformation 65]
113. ~funny(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 65]
123. ~patient(lucy) [cnf transformation 21]
124. funny(X0) [duplicate literal removal 112]
125. ~funny(X0) | ~generous(X0) [duplicate literal removal 113]
129. 1 <=> ! [X0] : patient(X0) [avatar definition]
130. patient(X0) <- (1) [avatar component clause 129]
132. 2 <=> generous(alice) [avatar definition]
134. generous(alice) <- (2) [avatar component clause 132]
135. 1 | 2 [avatar split clause 78,132,129]
258. ~generous(X0) [resolution 125,124]
259. $false <- (2) [resolution 258,134]
260. ~2 [avatar contradiction clause 259]
261. $false <- (1) [resolution 130,123]
262. ~1 [avatar contradiction clause 261]
263. $false [avatar sat refutation 135,260,262]
% SZS output end Proof for 83894360072950157443310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or wise is not funny or tall and vice versa.
Everyone who is not calm or not kind is humble or not old and vice versa.
If someone is humble then alice is creative or not wise.
If someone is both funny and not calm then lucy is either wise or patient and vice versa.
Everyone who is either creative or not calm is either creative or not funny and vice versa.
If someone is not tall or not creative then someone is both generous and quiet and vice versa.
Everyone who is both happy and not generous is not calm or funny and vice versa.
Everyone who is either not old or not funny is not humble and vice versa.
If someone is calm then someone is not brave and vice versa.
Everyone who is either not kind or not generous is either humble or creative.
Everyone who is both wise and not curious is either not humble or not patient.
Everyone who is not funny or curious is either not strong or creative and vice versa.
If fred is old or not strong then someone is either not calm or not tall.
If someone is either not strong or not humble then alice is either old or funny and vice versa.
If paul is wise or not happy then someone is patient and vice versa.
Everyone who is either patient or not calm is not strong and vice versa.
Someone is either not quiet or not old.
John is either not wise or humble.
Alice is calm or not humble.
Alice is not funny or not quiet.
Someone is tall or strong. | Paul is patient. | contradiction | (![X]:((creative(X)<~>wise(X))<=>(~funny(X)|tall(X))))&
(![X]:((~calm(X)|~kind(X))<=>(humble(X)|~old(X))))&
((?[X]:(humble(X)))=>((creative(alice)|~wise(alice))))&
((?[X]:((funny(X)&~calm(X))))<=>((wise(lucy)<~>patient(lucy))))&
(![X]:((creative(X)<~>~calm(X))<=>(creative(X)<~>~funny(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:((happy(X)&~generous(X))<=>(~calm(X)|funny(X))))&
(![X]:((~old(X)<~>~funny(X))<=>~humble(X)))&
((?[X]:(calm(X)))<=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(humble(X)<~>creative(X))))&
(![X]:((wise(X)&~curious(X))=>(~humble(X)<~>~patient(X))))&
(![X]:((~funny(X)|curious(X))<=>(~strong(X)<~>creative(X))))&
(((old(fred)|~strong(fred)))=>(?[X]:((~calm(X)<~>~tall(X)))))&
((?[X]:((~strong(X)<~>~humble(X))))<=>((old(alice)<~>funny(alice))))&
(((wise(paul)|~happy(paul)))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)<~>~calm(X))<=>~strong(X)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~wise(john)<~>humble(john)))&
((calm(alice)|~humble(alice)))&
((~funny(alice)|~quiet(alice)))&
(?[X]:((tall(X)|strong(X)))) | patient(paul) | [
"p0",
"p4",
"p5",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4752675010960243111501540
% SZS output start Proof for 4752675010960243111501540
1. ! [X0] : ((creative(X0) <~> wise(X0)) <=> (tall(X0) | ~funny(X0))) [input p0]
5. ! [X0] : ((creative(X0) <~> ~calm(X0)) <=> (creative(X0) <~> ~funny(X0))) [input p4]
6. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X0] : (quiet(X0) & generous(X0)) [input p5]
7. ! [X0] : ((~generous(X0) & happy(X0)) <=> (funny(X0) | ~calm(X0))) [input p6]
15. (~happy(paul) | wise(paul)) <=> ? [X0] : patient(X0) [input p14]
22. patient(paul) [input hypothesis]
23. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X1] : (quiet(X1) & generous(X1)) [rectify 6]
31. ! [X0] : ((((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))))) [nnf transformation 1]
32. ! [X0] : ((((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))))) [flattening 31]
39. ! [X0] : ((((calm(X0) | ~creative(X0)) & (~calm(X0) | creative(X0))) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0)))) & (((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0))))) [nnf transformation 5]
40. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & (? [X1] : (quiet(X1) & generous(X1)) | ! [X0] : (creative(X0) & tall(X0))) [nnf transformation 23]
41. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & (? [X2] : (quiet(X2) & generous(X2)) | ! [X3] : (creative(X3) & tall(X3))) [rectify 40]
42. ? [X0] : (~creative(X0) | ~tall(X0)) => (~creative(sK1) | ~tall(sK1)) [choice axiom]
43. ? [X2] : (quiet(X2) & generous(X2)) => (quiet(sK2) & generous(sK2)) [choice axiom]
44. ((~creative(sK1) | ~tall(sK1)) | ! [X1] : (~quiet(X1) | ~generous(X1))) & ((quiet(sK2) & generous(sK2)) | ! [X3] : (creative(X3) & tall(X3))) [skolemisation 41,43,42]
45. ! [X0] : (((~generous(X0) & happy(X0)) | (~funny(X0) & calm(X0))) & ((funny(X0) | ~calm(X0)) | (generous(X0) | ~happy(X0)))) [nnf transformation 7]
46. ! [X0] : (((~generous(X0) & happy(X0)) | (~funny(X0) & calm(X0))) & (funny(X0) | ~calm(X0) | generous(X0) | ~happy(X0))) [flattening 45]
64. ((~happy(paul) | wise(paul)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (happy(paul) & ~wise(paul))) [nnf transformation 15]
65. (~happy(paul) | wise(paul) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (happy(paul) & ~wise(paul))) [flattening 64]
66. (~happy(paul) | wise(paul) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | (happy(paul) & ~wise(paul))) [rectify 65]
67. ? [X1] : patient(X1) => patient(sK7) [choice axiom]
68. (~happy(paul) | wise(paul) | ! [X0] : ~patient(X0)) & (patient(sK7) | (happy(paul) & ~wise(paul))) [skolemisation 66,67]
81. ~tall(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 32]
95. funny(X0) | ~creative(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 39]
98. ~calm(X0) | creative(X0) | creative(X0) | funny(X0) [cnf transformation 39]
101. generous(sK2) | tall(X3) [cnf transformation 44]
102. generous(sK2) | creative(X3) [cnf transformation 44]
107. happy(X0) | calm(X0) [cnf transformation 46]
108. ~funny(X0) | happy(X0) [cnf transformation 46]
109. ~generous(X0) | calm(X0) [cnf transformation 46]
110. ~generous(X0) | ~funny(X0) [cnf transformation 46]
143. ~happy(paul) | wise(paul) | ~patient(X0) [cnf transformation 68]
155. patient(paul) [cnf transformation 22]
157. funny(X0) | ~creative(X0) | ~calm(X0) [duplicate literal removal 95]
158. ~calm(X0) | creative(X0) | funny(X0) [duplicate literal removal 98]
197. ~calm(X0) | funny(X0) [subsumption resolution 157,158]
213. 12 <=> ! [X3] : creative(X3) [avatar definition]
214. creative(X3) <- (12) [avatar component clause 213]
221. 14 <=> ! [X3] : tall(X3) [avatar definition]
222. tall(X3) <- (14) [avatar component clause 221]
225. 15 <=> generous(sK2) [avatar definition]
227. generous(sK2) <- (15) [avatar component clause 225]
228. 12 | 15 [avatar split clause 102,225,213]
229. 14 | 15 [avatar split clause 101,225,221]
297. 30 <=> ! [X0] : ~patient(X0) [avatar definition]
298. ~patient(X0) <- (30) [avatar component clause 297]
300. 31 <=> wise(paul) [avatar definition]
302. wise(paul) <- (31) [avatar component clause 300]
304. 32 <=> happy(paul) [avatar definition]
306. ~happy(paul) <- (~32) [avatar component clause 304]
307. 30 | 31 | ~32 [avatar split clause 143,304,300,297]
363. $false <- (30) [resolution 298,155]
364. ~30 [avatar contradiction clause 363]
365. calm(paul) <- (~32) [resolution 107,306]
372. funny(paul) <- (~32) [resolution 197,365]
382. happy(paul) <- (~32) [resolution 372,108]
383. $false <- (~32) [subsumption resolution 382,306]
384. 32 [avatar contradiction clause 383]
389. ~creative(X0) | ~wise(X0) <- (14) [resolution 81,222]
391. ~wise(X0) <- (12, 14) [subsumption resolution 389,214]
392. $false <- (12, 14, 31) [resolution 391,302]
393. ~12 | ~14 | ~31 [avatar contradiction clause 392]
416. ~funny(sK2) <- (15) [resolution 227,110]
417. calm(sK2) <- (15) [resolution 227,109]
419. funny(sK2) <- (15) [resolution 417,197]
420. $false <- (15) [subsumption resolution 419,416]
421. ~15 [avatar contradiction clause 420]
422. $false [avatar sat refutation 228,229,307,364,384,393,421]
% SZS output end Proof for 4752675010960243111501540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is either not kind or strong.
If paul is not curious or not quiet then fred is both wise and kind and vice versa.
If someone is not patient then susan is not patient and vice versa.
Everyone who is both not funny and not rich is both quiet and not rich and vice versa.
Everyone who is both happy and creative is quiet or not calm and vice versa.
If paul is not curious then alice is brave.
If someone is not brave or not curious then paul is brave or not quiet.
Everyone who is not old or not calm is not happy.
Everyone who is kind is both not wise and not patient and vice versa.
Everyone who is either not brave or strong is both not generous and rich.
Everyone who is both not creative and not quiet is not old or creative.
Everyone who is not tall or not kind is either not funny or quiet.
Everyone who is not happy or generous is either not kind or not creative and vice versa.
Everyone who is not humble or not old is kind or not wise and vice versa.
Everyone who is not calm or tall is not calm or not humble and vice versa.
Everyone who is happy is either not strong or not creative.
Paul is not curious or curious.
Someone is not curious.
Fred is not wise.
Someone is either not brave or not tall.
Lucy is not quiet or funny.
Someone is not kind or funny.
Susan is not brave or funny.
Alice is either not rich or kind. | Paul is not brave. | contradiction | (![X]:(quiet(X)=>(~kind(X)<~>strong(X))))&
(((~curious(paul)|~quiet(paul)))<=>((wise(fred)&kind(fred))))&
((?[X]:(~patient(X)))<=>(~patient(susan)))&
(![X]:((~funny(X)&~rich(X))<=>(quiet(X)&~rich(X))))&
(![X]:((happy(X)&creative(X))<=>(quiet(X)|~calm(X))))&
((~curious(paul))=>(brave(alice)))&
((?[X]:((~brave(X)|~curious(X))))=>((brave(paul)|~quiet(paul))))&
(![X]:((~old(X)|~calm(X))=>~happy(X)))&
(![X]:(kind(X)<=>(~wise(X)&~patient(X))))&
(![X]:((~brave(X)<~>strong(X))=>(~generous(X)&rich(X))))&
(![X]:((~creative(X)&~quiet(X))=>(~old(X)|creative(X))))&
(![X]:((~tall(X)|~kind(X))=>(~funny(X)<~>quiet(X))))&
(![X]:((~happy(X)|generous(X))<=>(~kind(X)<~>~creative(X))))&
(![X]:((~humble(X)|~old(X))<=>(kind(X)|~wise(X))))&
(![X]:((~calm(X)|tall(X))<=>(~calm(X)|~humble(X))))&
(![X]:(happy(X)=>(~strong(X)<~>~creative(X))))&
((~curious(paul)|curious(paul)))&
(?[X]:(~curious(X)))&
(~wise(fred))&
(?[X]:((~brave(X)<~>~tall(X))))&
((~quiet(lucy)|funny(lucy)))&
(?[X]:((~kind(X)|funny(X))))&
((~brave(susan)|funny(susan)))&
((~rich(alice)<~>kind(alice))) | ~brave(paul) | [
"p1",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8916121710599448041583741
% SZS output start Proof for 8916121710599448041583741
2. (~quiet(paul) | ~curious(paul)) <=> (kind(fred) & wise(fred)) [input p1]
7. ? [X0] : (~curious(X0) | ~brave(X0)) => (~quiet(paul) | brave(paul)) [input p6]
19. ~wise(fred) [input p18]
25. ~brave(paul) [input hypothesis]
28. (~quiet(paul) | brave(paul)) | ! [X0] : (curious(X0) & brave(X0)) [ennf transformation 7]
29. ~quiet(paul) | brave(paul) | ! [X0] : (curious(X0) & brave(X0)) [flattening 28]
37. ((~quiet(paul) | ~curious(paul)) | (~kind(fred) | ~wise(fred))) & ((kind(fred) & wise(fred)) | (quiet(paul) & curious(paul))) [nnf transformation 2]
38. (~quiet(paul) | ~curious(paul) | ~kind(fred) | ~wise(fred)) & ((kind(fred) & wise(fred)) | (quiet(paul) & curious(paul))) [flattening 37]
69. wise(fred) | quiet(paul) [cnf transformation 38]
85. ~quiet(paul) | brave(paul) | brave(X0) [cnf transformation 29]
119. ~wise(fred) [cnf transformation 19]
127. ~brave(paul) [cnf transformation 25]
130. 1 <=> wise(fred) [avatar definition]
142. 4 <=> quiet(paul) [avatar definition]
148. 4 | 1 [avatar split clause 69,130,142]
172. 10 <=> brave(paul) [avatar definition]
173. ~brave(paul) <- (~10) [avatar component clause 172]
177. 11 <=> ! [X0] : brave(X0) [avatar definition]
178. brave(X0) <- (11) [avatar component clause 177]
179. 11 | 10 | ~4 [avatar split clause 85,142,172,177]
186. ~1 [avatar split clause 119,130]
234. ~10 [avatar split clause 127,172]
235. $false <- (~10, 11) [subsumption resolution 173,178]
236. 10 | ~11 [avatar contradiction clause 235]
237. $false [avatar sat refutation 148,179,186,234,236]
% SZS output end Proof for 8916121710599448041583741
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not rich is old.
Everyone who is not wise is both rich and not quiet and vice versa.
Everyone who is both patient and happy is both tall and happy.
Everyone who is generous is not generous or quiet and vice versa.
If someone is either strong or not generous then john is either not happy or quiet and vice versa.
If someone is not patient then someone is either wise or not happy and vice versa.
Everyone who is not generous is either not kind or not happy.
If alice is either brave or wise then someone is either not creative or not happy.
If someone is both old and not generous then paul is either not creative or not humble and vice versa.
If someone is humble or not kind then someone is not curious or not quiet and vice versa.
If john is not funny then someone is either not rich or not funny.
If john is rich then someone is either happy or old.
Everyone who is curious is generous and vice versa.
If mary is patient then someone is creative or curious and vice versa.
If someone is not kind or tall then john is not old and vice versa.
If someone is not rich then alice is calm or generous and vice versa.
Someone is curious or not wise.
Paul is not wise or not happy.
Fred is funny.
Paul is strong or quiet.
John is not wise or tall.
Someone is both not humble and not patient.
Someone is funny or not old. | Mary is generous. | entailment | (![X]:((~happy(X)|~rich(X))=>old(X)))&
(![X]:(~wise(X)<=>(rich(X)&~quiet(X))))&
(![X]:((patient(X)&happy(X))=>(tall(X)&happy(X))))&
(![X]:(generous(X)<=>(~generous(X)|quiet(X))))&
((?[X]:((strong(X)<~>~generous(X))))<=>((~happy(john)<~>quiet(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:(~generous(X)=>(~kind(X)<~>~happy(X))))&
(((brave(alice)<~>wise(alice)))=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:((old(X)&~generous(X))))<=>((~creative(paul)<~>~humble(paul))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~curious(X)|~quiet(X)))))&
((~funny(john))=>(?[X]:((~rich(X)<~>~funny(X)))))&
((rich(john))=>(?[X]:((happy(X)<~>old(X)))))&
(![X]:(curious(X)<=>generous(X)))&
((patient(mary))<=>(?[X]:((creative(X)|curious(X)))))&
((?[X]:((~kind(X)|tall(X))))<=>(~old(john)))&
((?[X]:(~rich(X)))<=>((calm(alice)|generous(alice))))&
(?[X]:((curious(X)|~wise(X))))&
((~wise(paul)|~happy(paul)))&
(funny(fred))&
((strong(paul)|quiet(paul)))&
((~wise(john)|tall(john)))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((funny(X)|~old(X)))) | generous(mary) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3218761916920638480982181
% SZS output start Proof for 3218761916920638480982181
4. ! [X0] : (generous(X0) <=> (quiet(X0) | ~generous(X0))) [input p3]
24. ~generous(mary) [input hypothesis]
36. ! [X0] : ((generous(X0) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | ~generous(X0))) [nnf transformation 4]
37. ! [X0] : ((generous(X0) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | ~generous(X0))) [flattening 36]
94. generous(X0) | generous(X0) [cnf transformation 37]
147. ~generous(mary) [cnf transformation 24]
149. generous(X0) [duplicate literal removal 94]
362. $false [subsumption resolution 147,149]
% SZS output end Proof for 3218761916920638480982181
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then someone is rich and vice versa.
Everyone who is not brave is both not kind and strong.
If fred is not creative then lucy is both old and not generous.
Everyone who is quiet is tall.
Everyone who is brave is both happy and rich.
Everyone who is not patient is both not humble and patient and vice versa.
If someone is both quiet and not kind then john is both tall and not rich.
Everyone who is both strong and not kind is either brave or not wise.
Everyone who is not funny or not kind is both generous and old and vice versa.
If susan is not calm then paul is both happy and old and vice versa.
If fred is either happy or not generous then susan is both tall and not happy.
If susan is both not brave and happy then someone is both not tall and not quiet.
If paul is either humble or creative then paul is not brave or humble.
If someone is not brave then susan is creative and vice versa.
Paul is either funny or rich.
Lucy is not curious.
Someone is either not patient or strong.
Alice is curious or not rich.
Fred is either not patient or not kind.
Alice is calm. | Fred is not creative. | contradiction | ((~patient(lucy))<=>(?[X]:(rich(X))))&
(![X]:(~brave(X)=>(~kind(X)&strong(X))))&
((~creative(fred))=>((old(lucy)&~generous(lucy))))&
(![X]:(quiet(X)=>tall(X)))&
(![X]:(brave(X)=>(happy(X)&rich(X))))&
(![X]:(~patient(X)<=>(~humble(X)&patient(X))))&
((?[X]:((quiet(X)&~kind(X))))=>((tall(john)&~rich(john))))&
(![X]:((strong(X)&~kind(X))=>(brave(X)<~>~wise(X))))&
(![X]:((~funny(X)|~kind(X))<=>(generous(X)&old(X))))&
((~calm(susan))<=>((happy(paul)&old(paul))))&
(((happy(fred)<~>~generous(fred)))=>((tall(susan)&~happy(susan))))&
(((~brave(susan)&happy(susan)))=>(?[X]:((~tall(X)&~quiet(X)))))&
(((humble(paul)<~>creative(paul)))=>((~brave(paul)|humble(paul))))&
((?[X]:(~brave(X)))<=>(creative(susan)))&
((funny(paul)<~>rich(paul)))&
(~curious(lucy))&
(?[X]:((~patient(X)<~>strong(X))))&
((curious(alice)|~rich(alice)))&
((~patient(fred)<~>~kind(fred)))&
(calm(alice)) | ~creative(fred) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7530928034295509790336277
% SZS output start Proof for 7530928034295509790336277
1. ~patient(lucy) <=> ? [X0] : rich(X0) [input p0]
2. ! [X0] : (~brave(X0) => (strong(X0) & ~kind(X0))) [input p1]
3. ~creative(fred) => (~generous(lucy) & old(lucy)) [input p2]
5. ! [X0] : (brave(X0) => (rich(X0) & happy(X0))) [input p4]
6. ! [X0] : (~patient(X0) <=> (patient(X0) & ~humble(X0))) [input p5]
9. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (old(X0) & generous(X0))) [input p8]
21. ~creative(fred) [input hypothesis]
25. ! [X0] : ((strong(X0) & ~kind(X0)) | brave(X0)) [ennf transformation 2]
26. (~generous(lucy) & old(lucy)) | creative(fred) [ennf transformation 3]
27. ! [X0] : ((rich(X0) & happy(X0)) | ~brave(X0)) [ennf transformation 5]
35. (~patient(lucy) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | patient(lucy)) [nnf transformation 1]
36. (~patient(lucy) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | patient(lucy)) [rectify 35]
37. ? [X1] : rich(X1) => rich(sK0) [choice axiom]
38. (~patient(lucy) | ! [X0] : ~rich(X0)) & (rich(sK0) | patient(lucy)) [skolemisation 36,37]
39. ! [X0] : ((~patient(X0) | (~patient(X0) | humble(X0))) & ((patient(X0) & ~humble(X0)) | patient(X0))) [nnf transformation 6]
40. ! [X0] : ((~patient(X0) | ~patient(X0) | humble(X0)) & ((patient(X0) & ~humble(X0)) | patient(X0))) [flattening 39]
42. ! [X0] : (((~kind(X0) | ~funny(X0)) | (~old(X0) | ~generous(X0))) & ((old(X0) & generous(X0)) | (kind(X0) & funny(X0)))) [nnf transformation 9]
43. ! [X0] : ((~kind(X0) | ~funny(X0) | ~old(X0) | ~generous(X0)) & ((old(X0) & generous(X0)) | (kind(X0) & funny(X0)))) [flattening 42]
60. ~patient(lucy) | ~rich(X0) [cnf transformation 38]
61. ~kind(X0) | brave(X0) [cnf transformation 25]
64. ~generous(lucy) | creative(fred) [cnf transformation 26]
66. ~brave(X0) | rich(X0) [cnf transformation 27]
68. patient(X0) | patient(X0) [cnf transformation 40]
73. generous(X0) | kind(X0) [cnf transformation 43]
98. ~creative(fred) [cnf transformation 21]
100. patient(X0) [duplicate literal removal 68]
103. 1 <=> ! [X0] : ~rich(X0) [avatar definition]
104. ~rich(X0) <- (1) [avatar component clause 103]
106. 2 <=> patient(lucy) [avatar definition]
108. ~patient(lucy) <- (~2) [avatar component clause 106]
109. 1 | ~2 [avatar split clause 60,106,103]
116. 4 <=> creative(fred) [avatar definition]
120. 5 <=> generous(lucy) [avatar definition]
122. ~generous(lucy) <- (~5) [avatar component clause 120]
123. 4 | ~5 [avatar split clause 64,120,116]
222. ~4 [avatar split clause 98,116]
223. $false <- (~2) [subsumption resolution 108,100]
224. 2 [avatar contradiction clause 223]
227. kind(lucy) <- (~5) [resolution 73,122]
228. brave(lucy) <- (~5) [resolution 227,61]
229. rich(lucy) <- (~5) [resolution 228,66]
231. $false <- (1, ~5) [subsumption resolution 229,104]
232. ~1 | 5 [avatar contradiction clause 231]
233. $false [avatar sat refutation 109,123,222,224,232]
% SZS output end Proof for 7530928034295509790336277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is generous then someone is old.
If someone is both not generous and not rich then mary is not generous and vice versa.
If someone is both kind and not brave then lucy is both not calm and not brave.
If mary is either not creative or calm then someone is either strong or not strong and vice versa.
Everyone who is both rich and patient is quiet or creative.
Everyone who is not calm is either not patient or not funny.
If john is either creative or old then someone is not old.
Everyone who is both not quiet and humble is not calm.
Everyone who is either tall or not patient is either not kind or not wise.
Everyone who is brave is both tall and calm and vice versa.
Everyone who is either not wise or calm is not wise and vice versa.
If fred is both not rich and not tall then someone is not strong.
If someone is strong then someone is wise or not funny.
Everyone who is both not kind and not humble is calm or old.
If someone is not rich or patient then fred is either not rich or not wise and vice versa.
If someone is either not quiet or brave then paul is both creative and not wise and vice versa.
Someone is both not calm and creative.
Fred is both humble and not old.
Someone is funny or not old.
Someone is not brave or not generous.
John is either not brave or wise.
Someone is kind.
Someone is curious.
Someone is either funny or curious. | Mary is not calm. | entailment | ((generous(paul))=>(?[X]:(old(X))))&
((?[X]:((~generous(X)&~rich(X))))<=>(~generous(mary)))&
((?[X]:((kind(X)&~brave(X))))=>((~calm(lucy)&~brave(lucy))))&
(((~creative(mary)<~>calm(mary)))<=>(?[X]:((strong(X)<~>~strong(X)))))&
(![X]:((rich(X)&patient(X))=>(quiet(X)|creative(X))))&
(![X]:(~calm(X)=>(~patient(X)<~>~funny(X))))&
(((creative(john)<~>old(john)))=>(?[X]:(~old(X))))&
(![X]:((~quiet(X)&humble(X))=>~calm(X)))&
(![X]:((tall(X)<~>~patient(X))=>(~kind(X)<~>~wise(X))))&
(![X]:(brave(X)<=>(tall(X)&calm(X))))&
(![X]:((~wise(X)<~>calm(X))<=>~wise(X)))&
(((~rich(fred)&~tall(fred)))=>(?[X]:(~strong(X))))&
((?[X]:(strong(X)))=>(?[X]:((wise(X)|~funny(X)))))&
(![X]:((~kind(X)&~humble(X))=>(calm(X)|old(X))))&
((?[X]:((~rich(X)|patient(X))))<=>((~rich(fred)<~>~wise(fred))))&
((?[X]:((~quiet(X)<~>brave(X))))<=>((creative(paul)&~wise(paul))))&
(?[X]:((~calm(X)&creative(X))))&
((humble(fred)&~old(fred)))&
(?[X]:((funny(X)|~old(X))))&
(?[X]:((~brave(X)|~generous(X))))&
((~brave(john)<~>wise(john)))&
(?[X]:(kind(X)))&
(?[X]:(curious(X)))&
(?[X]:((funny(X)<~>curious(X)))) | ~calm(mary) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 78886898597287459602898
% SZS output start Proof for 78886898597287459602898
11. ! [X0] : ((~wise(X0) <~> calm(X0)) <=> ~wise(X0)) [input p10]
25. calm(mary) [input hypothesis]
58. ! [X0] : ((((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | wise(X0)) & (~wise(X0) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0))))) [nnf transformation 11]
115. ~wise(X0) | ~wise(X0) | ~calm(X0) [cnf transformation 58]
117. ~calm(X0) | wise(X0) | wise(X0) [cnf transformation 58]
145. calm(mary) [cnf transformation 25]
146. ~wise(X0) | ~calm(X0) [duplicate literal removal 115]
147. ~calm(X0) | wise(X0) [duplicate literal removal 117]
224. ~calm(X0) [subsumption resolution 146,147]
338. $false [subsumption resolution 145,224]
% SZS output end Proof for 78886898597287459602898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is both not rich and tall and vice versa. If mary is brave or wise then paul is not tall and vice versa. If someone is humble then paul is brave or not generous and vice versa. If someone is not kind then alice is both not brave and curious. If alice is both not quiet and old then someone is patient and vice versa. If alice is both strong and rich then lucy is not rich. If fred is either tall or not brave then someone is humble or not calm. Everyone who is both not kind and rich is not curious and vice versa. Everyone who is both not quiet and not curious is wise or creative. If someone is either not tall or happy then susan is either calm or not kind. If john is creative then someone is not calm or not creative. Everyone who is not rich is either not rich or not funny. If john is not patient then paul is not old or creative. Everyone who is both not creative and not tall is not kind or not humble. If someone is both wise and funny then someone is both tall and not strong. Mary is both tall and not wise. Someone is either not happy or generous. Someone is either not brave or wise. Someone is humble or not tall. Someone is tall. Susan is both old and not curious. Someone is both wise and tall. | Alice is not brave. | entailment | (![X]:(~tall(X)<=>(~rich(X)&tall(X))))&
(((brave(mary)|wise(mary)))<=>(~tall(paul)))&
((?[X]:(humble(X)))<=>((brave(paul)|~generous(paul))))&
((?[X]:(~kind(X)))=>((~brave(alice)&curious(alice))))&
(((~quiet(alice)&old(alice)))<=>(?[X]:(patient(X))))&
(((strong(alice)&rich(alice)))=>(~rich(lucy)))&
(((tall(fred)<~>~brave(fred)))=>(?[X]:((humble(X)|~calm(X)))))&
(![X]:((~kind(X)&rich(X))<=>~curious(X)))&
(![X]:((~quiet(X)&~curious(X))=>(wise(X)|creative(X))))&
((?[X]:((~tall(X)<~>happy(X))))=>((calm(susan)<~>~kind(susan))))&
((creative(john))=>(?[X]:((~calm(X)|~creative(X)))))&
(![X]:(~rich(X)=>(~rich(X)<~>~funny(X))))&
((~patient(john))=>((~old(paul)|creative(paul))))&
(![X]:((~creative(X)&~tall(X))=>(~kind(X)|~humble(X))))&
((?[X]:((wise(X)&funny(X))))=>(?[X]:((tall(X)&~strong(X)))))&
((tall(mary)&~wise(mary)))&
(?[X]:((~happy(X)<~>generous(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:(tall(X)))&
((old(susan)&~curious(susan)))&
(?[X]:((wise(X)&tall(X)))) | ~brave(alice) | [
"p3",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8559114509638540798785667
% SZS output start Proof for 8559114509638540798785667
4. ? [X0] : ~kind(X0) => (curious(alice) & ~brave(alice)) [input p3]
8. ! [X0] : ((rich(X0) & ~kind(X0)) <=> ~curious(X0)) [input p7]
21. ~curious(susan) & old(susan) [input p20]
23. brave(alice) [input hypothesis]
27. (curious(alice) & ~brave(alice)) | ! [X0] : kind(X0) [ennf transformation 4]
56. ! [X0] : (((rich(X0) & ~kind(X0)) | curious(X0)) & (~curious(X0) | (~rich(X0) | kind(X0)))) [nnf transformation 8]
57. ! [X0] : (((rich(X0) & ~kind(X0)) | curious(X0)) & (~curious(X0) | ~rich(X0) | kind(X0))) [flattening 56]
86. ~brave(alice) | kind(X0) [cnf transformation 27]
94. ~kind(X0) | curious(X0) [cnf transformation 57]
116. ~curious(susan) [cnf transformation 21]
119. brave(alice) [cnf transformation 23]
144. 5 <=> ! [X0] : kind(X0) [avatar definition]
145. kind(X0) <- (5) [avatar component clause 144]
152. 7 <=> brave(alice) [avatar definition]
155. 5 | ~7 [avatar split clause 86,152,144]
250. 7 [avatar split clause 119,152]
253. curious(X0) <- (5) [resolution 94,145]
254. $false <- (5) [resolution 253,116]
255. ~5 [avatar contradiction clause 254]
256. $false [avatar sat refutation 155,250,255]
% SZS output end Proof for 8559114509638540798785667
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or humble is not quiet.
Everyone who is not happy or not old is both not humble and generous and vice versa.
Everyone who is either not wise or wise is both funny and not creative.
If someone is kind or not funny then someone is calm and vice versa.
If someone is not curious then susan is either curious or old.
Everyone who is strong is both not funny and not curious and vice versa.
If mary is both not happy and not creative then lucy is not brave.
Everyone who is both not old and patient is kind.
Everyone who is either patient or not patient is tall.
If paul is either not wise or not kind then fred is both not calm and patient.
If susan is tall then mary is either not quiet or brave.
Everyone who is not curious is not strong or quiet and vice versa.
Everyone who is either not wise or wise is old.
Everyone who is either not strong or not creative is not patient or not brave.
If fred is both old and brave then fred is both kind and funny and vice versa.
Everyone who is humble or wise is both not humble and curious.
Someone is both not humble and rich.
Lucy is either not humble or happy.
Someone is either not funny or not kind.
Someone is both not brave and rich.
Alice is tall or brave.
Susan is brave or patient.
Someone is not patient. | Alice is strong. | contradiction | (![X]:((kind(X)|humble(X))=>~quiet(X)))&
(![X]:((~happy(X)|~old(X))<=>(~humble(X)&generous(X))))&
(![X]:((~wise(X)<~>wise(X))=>(funny(X)&~creative(X))))&
((?[X]:((kind(X)|~funny(X))))<=>(?[X]:(calm(X))))&
((?[X]:(~curious(X)))=>((curious(susan)<~>old(susan))))&
(![X]:(strong(X)<=>(~funny(X)&~curious(X))))&
(((~happy(mary)&~creative(mary)))=>(~brave(lucy)))&
(![X]:((~old(X)&patient(X))=>kind(X)))&
(![X]:((patient(X)<~>~patient(X))=>tall(X)))&
(((~wise(paul)<~>~kind(paul)))=>((~calm(fred)&patient(fred))))&
((tall(susan))=>((~quiet(mary)<~>brave(mary))))&
(![X]:(~curious(X)<=>(~strong(X)|quiet(X))))&
(![X]:((~wise(X)<~>wise(X))=>old(X)))&
(![X]:((~strong(X)<~>~creative(X))=>(~patient(X)|~brave(X))))&
(((old(fred)&brave(fred)))<=>((kind(fred)&funny(fred))))&
(![X]:((humble(X)|wise(X))=>(~humble(X)&curious(X))))&
(?[X]:((~humble(X)&rich(X))))&
((~humble(lucy)<~>happy(lucy)))&
(?[X]:((~funny(X)<~>~kind(X))))&
(?[X]:((~brave(X)&rich(X))))&
((tall(alice)|brave(alice)))&
((brave(susan)|patient(susan)))&
(?[X]:(~patient(X))) | strong(alice) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 137705238721403374706162
% SZS output start Proof for 137705238721403374706162
3. ! [X0] : ((~wise(X0) <~> wise(X0)) => (~creative(X0) & funny(X0))) [input p2]
6. ! [X0] : (strong(X0) <=> (~curious(X0) & ~funny(X0))) [input p5]
24. strong(alice) [input hypothesis]
29. ! [X0] : ((~creative(X0) & funny(X0)) | (~wise(X0) <=> wise(X0))) [ennf transformation 3]
44. ! [X0] : ((~creative(X0) & funny(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 29]
51. ! [X0] : ((strong(X0) | (curious(X0) | funny(X0))) & ((~curious(X0) & ~funny(X0)) | ~strong(X0))) [nnf transformation 6]
52. ! [X0] : ((strong(X0) | curious(X0) | funny(X0)) & ((~curious(X0) & ~funny(X0)) | ~strong(X0))) [flattening 51]
79. funny(X0) | wise(X0) | wise(X0) [cnf transformation 44]
80. funny(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 44]
88. ~funny(X0) | ~strong(X0) [cnf transformation 52]
125. strong(alice) [cnf transformation 24]
131. funny(X0) | wise(X0) [duplicate literal removal 79]
132. funny(X0) | ~wise(X0) [duplicate literal removal 80]
136. funny(X0) [subsumption resolution 131,132]
167. ~strong(X0) [subsumption resolution 88,136]
238. $false [subsumption resolution 125,167]
% SZS output end Proof for 137705238721403374706162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both not kind and not strong. If lucy is either creative or rich then someone is humble. Everyone who is both calm and not humble is both curious and calm and vice versa. If john is either not funny or tall then susan is both brave and rich. Everyone who is either humble or tall is both wise and not strong and vice versa. Everyone who is not curious or not strong is curious. If someone is both not tall and not calm then someone is both not curious and not happy and vice versa. Everyone who is both not kind and not quiet is both not generous and calm. Everyone who is either funny or not humble is not tall or not generous. Everyone who is not patient is both old and not tall and vice versa. If someone is either not creative or wise then john is not creative and vice versa. If fred is not brave then someone is not kind or not old. If fred is both wise and not old then mary is creative and vice versa. Everyone who is either creative or not patient is wise or old. Everyone who is either not strong or not old is both tall and creative and vice versa. Everyone who is both curious and not humble is humble or kind and vice versa. Someone is happy. Mary is not patient or wise. Paul is either not rich or happy. Paul is not humble. Fred is either creative or not patient. Susan is tall. Susan is both creative and brave. Fred is not brave. | John is brave. | neutral | (![X]:(~wise(X)=>(~kind(X)&~strong(X))))&
(((creative(lucy)<~>rich(lucy)))=>(?[X]:(humble(X))))&
(![X]:((calm(X)&~humble(X))<=>(curious(X)&calm(X))))&
(((~funny(john)<~>tall(john)))=>((brave(susan)&rich(susan))))&
(![X]:((humble(X)<~>tall(X))<=>(wise(X)&~strong(X))))&
(![X]:((~curious(X)|~strong(X))=>curious(X)))&
((?[X]:((~tall(X)&~calm(X))))<=>(?[X]:((~curious(X)&~happy(X)))))&
(![X]:((~kind(X)&~quiet(X))=>(~generous(X)&calm(X))))&
(![X]:((funny(X)<~>~humble(X))=>(~tall(X)|~generous(X))))&
(![X]:(~patient(X)<=>(old(X)&~tall(X))))&
((?[X]:((~creative(X)<~>wise(X))))<=>(~creative(john)))&
((~brave(fred))=>(?[X]:((~kind(X)|~old(X)))))&
(((wise(fred)&~old(fred)))<=>(creative(mary)))&
(![X]:((creative(X)<~>~patient(X))=>(wise(X)|old(X))))&
(![X]:((~strong(X)<~>~old(X))<=>(tall(X)&creative(X))))&
(![X]:((curious(X)&~humble(X))<=>(humble(X)|kind(X))))&
(?[X]:(happy(X)))&
((~patient(mary)|wise(mary)))&
((~rich(paul)<~>happy(paul)))&
(~humble(paul))&
((creative(fred)<~>~patient(fred)))&
(tall(susan))&
((creative(susan)&brave(susan)))&
(~brave(fred)) | brave(john) | [] | null | 0 |
If lucy is not strong or wise then alice is not happy.
Everyone who is not old or not happy is not humble or not rich and vice versa.
Everyone who is not humble is either patient or quiet and vice versa.
Everyone who is strong is both not wise and strong.
Everyone who is not humble is not quiet or not old.
Everyone who is curious or creative is tall.
Everyone who is generous is curious and vice versa.
Everyone who is both not generous and not calm is not happy or not generous and vice versa.
Everyone who is not generous or not old is both quiet and calm.
If alice is both not calm and wise then paul is old.
If someone is either not patient or tall then someone is not tall or not curious and vice versa.
Everyone who is either not tall or generous is not calm or not generous.
Everyone who is both not strong and not tall is funny or not humble and vice versa.
If someone is both generous and not calm then someone is either not funny or not wise and vice versa.
If lucy is not generous then mary is not rich or not funny.
Everyone who is either generous or rich is either creative or old.
John is either brave or not calm.
Mary is strong or not happy.
John is rich or creative.
Someone is either not tall or not patient.
Fred is brave or not humble. | Alice is not humble. | contradiction | (((~strong(lucy)|wise(lucy)))=>(~happy(alice)))&
(![X]:((~old(X)|~happy(X))<=>(~humble(X)|~rich(X))))&
(![X]:(~humble(X)<=>(patient(X)<~>quiet(X))))&
(![X]:(strong(X)=>(~wise(X)&strong(X))))&
(![X]:(~humble(X)=>(~quiet(X)|~old(X))))&
(![X]:((curious(X)|creative(X))=>tall(X)))&
(![X]:(generous(X)<=>curious(X)))&
(![X]:((~generous(X)&~calm(X))<=>(~happy(X)|~generous(X))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&calm(X))))&
(((~calm(alice)&wise(alice)))=>(old(paul)))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((~tall(X)<~>generous(X))=>(~calm(X)|~generous(X))))&
(![X]:((~strong(X)&~tall(X))<=>(funny(X)|~humble(X))))&
((?[X]:((generous(X)&~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
((~generous(lucy))=>((~rich(mary)|~funny(mary))))&
(![X]:((generous(X)<~>rich(X))=>(creative(X)<~>old(X))))&
((brave(john)<~>~calm(john)))&
((strong(mary)|~happy(mary)))&
((rich(john)|creative(john)))&
(?[X]:((~tall(X)<~>~patient(X))))&
((brave(fred)|~humble(fred))) | ~humble(alice) | [
"p5",
"p6",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4161037646453534456777070
% SZS output start Proof for 4161037646453534456777070
6. ! [X0] : ((creative(X0) | curious(X0)) => tall(X0)) [input p5]
7. ! [X0] : (generous(X0) <=> curious(X0)) [input p6]
8. ! [X0] : ((~calm(X0) & ~generous(X0)) <=> (~generous(X0) | ~happy(X0))) [input p7]
9. ! [X0] : ((~old(X0) | ~generous(X0)) => (calm(X0) & quiet(X0))) [input p8]
13. ! [X0] : ((~tall(X0) & ~strong(X0)) <=> (~humble(X0) | funny(X0))) [input p12]
22. ~humble(alice) [input hypothesis]
29. ! [X0] : (tall(X0) | (~creative(X0) & ~curious(X0))) [ennf transformation 6]
30. ! [X0] : ((calm(X0) & quiet(X0)) | (old(X0) & generous(X0))) [ennf transformation 9]
41. ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0))) [nnf transformation 7]
42. ! [X0] : (((~calm(X0) & ~generous(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (calm(X0) | generous(X0)))) [nnf transformation 8]
43. ! [X0] : (((~calm(X0) & ~generous(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | calm(X0) | generous(X0))) [flattening 42]
50. ! [X0] : (((~tall(X0) & ~strong(X0)) | (humble(X0) & ~funny(X0))) & ((~humble(X0) | funny(X0)) | (tall(X0) | strong(X0)))) [nnf transformation 13]
51. ! [X0] : (((~tall(X0) & ~strong(X0)) | (humble(X0) & ~funny(X0))) & (~humble(X0) | funny(X0) | tall(X0) | strong(X0))) [flattening 50]
75. ~curious(X0) | tall(X0) [cnf transformation 29]
77. ~generous(X0) | curious(X0) [cnf transformation 41]
83. ~calm(X0) | generous(X0) [cnf transformation 43]
86. calm(X0) | generous(X0) [cnf transformation 30]
101. ~tall(X0) | humble(X0) [cnf transformation 51]
120. ~humble(alice) [cnf transformation 22]
136. generous(X0) [subsumption resolution 86,83]
151. 7 <=> ! [X1] : curious(X1) [avatar definition]
152. curious(X1) <- (7) [avatar component clause 151]
163. 10 <=> ! [X1] : tall(X1) [avatar definition]
164. tall(X1) <- (10) [avatar component clause 163]
263. curious(X0) [resolution 77,136]
264. 7 [avatar split clause 263,151]
266. tall(X0) <- (7) [resolution 152,75]
268. 10 | ~7 [avatar split clause 266,151,163]
290. humble(X0) <- (10) [resolution 101,164]
295. $false <- (10) [resolution 290,120]
298. ~10 [avatar contradiction clause 295]
299. $false [avatar sat refutation 264,268,298]
% SZS output end Proof for 4161037646453534456777070
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not funny and generous then alice is either strong or brave.
Everyone who is either not wise or not quiet is both not curious and rich and vice versa.
Everyone who is either not funny or old is both not strong and generous.
If someone is both not creative and rich then someone is either quiet or not calm.
Everyone who is old is not rich or old and vice versa.
Everyone who is both not rich and quiet is brave or tall.
Everyone who is both not strong and not patient is either not kind or not humble and vice versa.
If john is quiet then mary is either brave or not quiet and vice versa.
If susan is either wise or not rich then susan is wise and vice versa.
Everyone who is both not funny and not creative is both creative and not creative.
Everyone who is not generous or humble is not happy or not curious and vice versa.
Everyone who is happy or not wise is either not creative or strong.
If mary is wise then someone is tall or curious.
If fred is either not creative or strong then paul is either not brave or calm.
Everyone who is not strong or not brave is strong and vice versa.
Everyone who is both calm and old is not curious.
Someone is both not funny and not generous.
Mary is curious.
Alice is not brave or funny.
Mary is either not curious or not rich.
Someone is either not kind or humble.
Someone is not brave or funny.
Someone is both not wise and not kind.
Mary is both not kind and quiet. | Mary is humble. | contradiction | (((~funny(susan)&generous(susan)))=>((strong(alice)<~>brave(alice))))&
(![X]:((~wise(X)<~>~quiet(X))<=>(~curious(X)&rich(X))))&
(![X]:((~funny(X)<~>old(X))=>(~strong(X)&generous(X))))&
((?[X]:((~creative(X)&rich(X))))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:(old(X)<=>(~rich(X)|old(X))))&
(![X]:((~rich(X)&quiet(X))=>(brave(X)|tall(X))))&
(![X]:((~strong(X)&~patient(X))<=>(~kind(X)<~>~humble(X))))&
((quiet(john))<=>((brave(mary)<~>~quiet(mary))))&
(((wise(susan)<~>~rich(susan)))<=>(wise(susan)))&
(![X]:((~funny(X)&~creative(X))=>(creative(X)&~creative(X))))&
(![X]:((~generous(X)|humble(X))<=>(~happy(X)|~curious(X))))&
(![X]:((happy(X)|~wise(X))=>(~creative(X)<~>strong(X))))&
((wise(mary))=>(?[X]:((tall(X)|curious(X)))))&
(((~creative(fred)<~>strong(fred)))=>((~brave(paul)<~>calm(paul))))&
(![X]:((~strong(X)|~brave(X))<=>strong(X)))&
(![X]:((calm(X)&old(X))=>~curious(X)))&
(?[X]:((~funny(X)&~generous(X))))&
(curious(mary))&
((~brave(alice)|funny(alice)))&
((~curious(mary)<~>~rich(mary)))&
(?[X]:((~kind(X)<~>humble(X))))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((~wise(X)&~kind(X))))&
((~kind(mary)&quiet(mary))) | humble(mary) | [
"p6",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8975947797436539263873316
% SZS output start Proof for 8975947797436539263873316
7. ! [X0] : ((~patient(X0) & ~strong(X0)) <=> (~kind(X0) <~> ~humble(X0))) [input p6]
15. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> strong(X0)) [input p14]
24. quiet(mary) & ~kind(mary) [input p23]
25. humble(mary) [input hypothesis]
49. ! [X0] : (((~patient(X0) & ~strong(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | (patient(X0) | strong(X0)))) [nnf transformation 7]
50. ! [X0] : (((~patient(X0) & ~strong(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | patient(X0) | strong(X0))) [flattening 49]
57. ! [X0] : (((~brave(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (brave(X0) & strong(X0)))) [nnf transformation 15]
58. ! [X0] : ((~brave(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (brave(X0) & strong(X0)))) [flattening 57]
88. ~humble(X0) | ~strong(X0) | kind(X0) [cnf transformation 50]
114. strong(X0) | strong(X0) [cnf transformation 58]
129. ~kind(mary) [cnf transformation 24]
131. humble(mary) [cnf transformation 25]
132. strong(X0) [duplicate literal removal 114]
261. ~strong(mary) | kind(mary) [resolution 88,131]
262. kind(mary) [subsumption resolution 261,132]
263. $false [subsumption resolution 262,129]
% SZS output end Proof for 8975947797436539263873316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not creative or funny then paul is not curious and vice versa.
If susan is not happy then fred is not patient or not strong and vice versa.
Everyone who is not old is either not curious or old.
If someone is both not rich and not generous then alice is not strong.
Everyone who is happy or not curious is either brave or not humble and vice versa.
If lucy is quiet or not wise then someone is not brave or kind.
Everyone who is not creative or quiet is both not creative and quiet and vice versa.
Everyone who is brave or not wise is both not rich and creative and vice versa.
Everyone who is curious is either curious or humble and vice versa.
If alice is either not creative or curious then mary is quiet.
If someone is either not humble or not kind then lucy is both generous and not quiet and vice versa.
Everyone who is both calm and strong is both quiet and wise.
If lucy is both rich and not generous then paul is either creative or not tall and vice versa.
If someone is rich then paul is both not old and strong.
If someone is not creative or wise then fred is humble.
Everyone who is not kind or funny is either patient or tall and vice versa.
Paul is not strong.
Someone is not humble or humble.
Someone is both not rich and creative.
Someone is both kind and funny.
Lucy is not happy or not strong.
Lucy is either not brave or creative.
Paul is either rich or creative.
Someone is not old or curious. | Paul is strong. | contradiction | (((~creative(alice)|funny(alice)))<=>(~curious(paul)))&
((~happy(susan))<=>((~patient(fred)|~strong(fred))))&
(![X]:(~old(X)=>(~curious(X)<~>old(X))))&
((?[X]:((~rich(X)&~generous(X))))=>(~strong(alice)))&
(![X]:((happy(X)|~curious(X))<=>(brave(X)<~>~humble(X))))&
(((quiet(lucy)|~wise(lucy)))=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((~creative(X)|quiet(X))<=>(~creative(X)&quiet(X))))&
(![X]:((brave(X)|~wise(X))<=>(~rich(X)&creative(X))))&
(![X]:(curious(X)<=>(curious(X)<~>humble(X))))&
(((~creative(alice)<~>curious(alice)))=>(quiet(mary)))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((generous(lucy)&~quiet(lucy))))&
(![X]:((calm(X)&strong(X))=>(quiet(X)&wise(X))))&
(((rich(lucy)&~generous(lucy)))<=>((creative(paul)<~>~tall(paul))))&
((?[X]:(rich(X)))=>((~old(paul)&strong(paul))))&
((?[X]:((~creative(X)|wise(X))))=>(humble(fred)))&
(![X]:((~kind(X)|funny(X))<=>(patient(X)<~>tall(X))))&
(~strong(paul))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:((~rich(X)&creative(X))))&
(?[X]:((kind(X)&funny(X))))&
((~happy(lucy)|~strong(lucy)))&
((~brave(lucy)<~>creative(lucy)))&
((rich(paul)<~>creative(paul)))&
(?[X]:((~old(X)|curious(X)))) | strong(paul) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 345897606401299062387336
% SZS output start Proof for 345897606401299062387336
17. ~strong(paul) [input p16]
25. strong(paul) [input hypothesis]
122. ~strong(paul) [cnf transformation 17]
134. strong(paul) [cnf transformation 25]
244. 22 <=> strong(paul) [avatar definition]
255. ~22 [avatar split clause 122,244]
276. 22 [avatar split clause 134,244]
277. $false [avatar sat refutation 255,276]
% SZS output end Proof for 345897606401299062387336
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then mary is brave or not rich and vice versa. If someone is both not brave and humble then someone is not strong or not humble. Everyone who is either patient or creative is both old and quiet. Everyone who is both not happy and generous is not calm and vice versa. Everyone who is not strong is kind or old and vice versa. Everyone who is kind or old is quiet and vice versa. Everyone who is both not humble and funny is either not generous or creative and vice versa. Everyone who is funny or generous is not quiet. If someone is either tall or kind then fred is calm. Everyone who is wise or not patient is not generous. If fred is both quiet and not quiet then mary is happy and vice versa. Everyone who is both rich and not wise is either not calm or not old and vice versa. If lucy is brave or old then lucy is either rich or humble. Everyone who is strong is humble and vice versa. If mary is both not calm and rich then someone is not old and vice versa. Everyone who is calm is either old or kind. Fred is both tall and not strong. Someone is not strong or happy. Someone is not wise or strong. Someone is curious. Someone is either generous or calm. Someone is either not happy or strong. | Mary is strong. | contradiction | ((?[X]:(generous(X)))<=>((brave(mary)|~rich(mary))))&
((?[X]:((~brave(X)&humble(X))))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((patient(X)<~>creative(X))=>(old(X)&quiet(X))))&
(![X]:((~happy(X)&generous(X))<=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
(((brave(lucy)|old(lucy)))=>((rich(lucy)<~>humble(lucy))))&
(![X]:(strong(X)<=>humble(X)))&
(((~calm(mary)&rich(mary)))<=>(?[X]:(~old(X))))&
(![X]:(calm(X)=>(old(X)<~>kind(X))))&
((tall(fred)&~strong(fred)))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((~wise(X)|strong(X))))&
(?[X]:(curious(X)))&
(?[X]:((generous(X)<~>calm(X))))&
(?[X]:((~happy(X)<~>strong(X)))) | strong(mary) | [
"p2",
"p3",
"p4",
"p6",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1978825090492019724789787
% SZS output start Proof for 1978825090492019724789787
3. ! [X0] : ((patient(X0) <~> creative(X0)) => (quiet(X0) & old(X0))) [input p2]
4. ! [X0] : ((generous(X0) & ~happy(X0)) <=> ~calm(X0)) [input p3]
5. ! [X0] : (~strong(X0) <=> (old(X0) | kind(X0))) [input p4]
7. ! [X0] : ((funny(X0) & ~humble(X0)) <=> (~generous(X0) <~> creative(X0))) [input p6]
10. ! [X0] : ((~patient(X0) | wise(X0)) => ~generous(X0)) [input p9]
14. ! [X0] : (strong(X0) <=> humble(X0)) [input p13]
15. (rich(mary) & ~calm(mary)) <=> ? [X0] : ~old(X0) [input p14]
23. strong(mary) [input hypothesis]
27. ! [X0] : ((quiet(X0) & old(X0)) | (patient(X0) <=> creative(X0))) [ennf transformation 3]
30. ! [X0] : (~generous(X0) | (patient(X0) & ~wise(X0))) [ennf transformation 10]
41. ! [X0] : ((quiet(X0) & old(X0)) | ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0)))) [nnf transformation 27]
42. ! [X0] : (((generous(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | (~generous(X0) | happy(X0)))) [nnf transformation 4]
43. ! [X0] : (((generous(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | ~generous(X0) | happy(X0))) [flattening 42]
44. ! [X0] : ((~strong(X0) | (~old(X0) & ~kind(X0))) & ((old(X0) | kind(X0)) | strong(X0))) [nnf transformation 5]
45. ! [X0] : ((~strong(X0) | (~old(X0) & ~kind(X0))) & (old(X0) | kind(X0) | strong(X0))) [flattening 44]
48. ! [X0] : (((funny(X0) & ~humble(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | (~funny(X0) | humble(X0)))) [nnf transformation 7]
49. ! [X0] : (((funny(X0) & ~humble(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | ~funny(X0) | humble(X0))) [flattening 48]
56. ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))) [nnf transformation 14]
57. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | (~rich(mary) | calm(mary))) [nnf transformation 15]
58. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~rich(mary) | calm(mary)) [flattening 57]
59. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~rich(mary) | calm(mary)) [rectify 58]
60. ? [X1] : ~old(X1) => ~old(sK2) [choice axiom]
61. ((rich(mary) & ~calm(mary)) | ! [X0] : old(X0)) & (~old(sK2) | ~rich(mary) | calm(mary)) [skolemisation 59,60]
77. ~patient(X0) | creative(X0) | old(X0) [cnf transformation 41]
83. calm(X0) | generous(X0) [cnf transformation 43]
86. ~old(X0) | ~strong(X0) [cnf transformation 45]
93. ~creative(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 49]
101. ~generous(X0) | patient(X0) [cnf transformation 30]
115. ~strong(X0) | humble(X0) [cnf transformation 56]
118. ~calm(mary) | old(X0) [cnf transformation 61]
130. strong(mary) [cnf transformation 23]
204. 17 <=> ! [X0] : old(X0) [avatar definition]
205. old(X0) <- (17) [avatar component clause 204]
208. 18 <=> calm(mary) [avatar definition]
210. ~calm(mary) <- (~18) [avatar component clause 208]
211. 17 | ~18 [avatar split clause 118,208,204]
258. ~strong(X0) <- (17) [resolution 86,205]
259. $false <- (17) [resolution 258,130]
260. ~17 [avatar contradiction clause 259]
262. generous(mary) <- (~18) [resolution 210,83]
267. patient(mary) <- (~18) [resolution 101,262]
268. humble(mary) [resolution 115,130]
290. creative(mary) | old(mary) <- (~18) [resolution 267,77]
292. 32 <=> old(mary) [avatar definition]
294. old(mary) <- (32) [avatar component clause 292]
296. 33 <=> creative(mary) [avatar definition]
298. creative(mary) <- (33) [avatar component clause 296]
299. 32 | 33 | 18 [avatar split clause 290,208,296,292]
310. ~strong(mary) <- (32) [resolution 294,86]
312. $false <- (32) [subsumption resolution 310,130]
313. ~32 [avatar contradiction clause 312]
342. ~generous(mary) | ~humble(mary) <- (33) [resolution 93,298]
343. ~humble(mary) <- (~18, 33) [subsumption resolution 342,262]
344. $false <- (~18, 33) [subsumption resolution 343,268]
345. 18 | ~33 [avatar contradiction clause 344]
346. $false [avatar sat refutation 211,260,299,313,345]
% SZS output end Proof for 1978825090492019724789787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or calm then susan is generous or happy. Everyone who is both not humble and patient is both not happy and strong and vice versa. Everyone who is not patient is both not funny and strong. If someone is either patient or not curious then someone is kind and vice versa. If someone is either not old or not funny then fred is either not creative or not rich. Everyone who is either rich or not rich is not creative and vice versa. If susan is patient then someone is funny or not creative. If someone is either curious or funny then someone is both not kind and happy. Everyone who is both curious and rich is not funny or not creative and vice versa. If john is brave or old then john is both not strong and kind and vice versa. If mary is either creative or not quiet then lucy is both generous and not calm and vice versa. Everyone who is either creative or not quiet is both brave and not funny and vice versa. If someone is both tall and not patient then someone is both not rich and not quiet and vice versa. Everyone who is funny is not brave and vice versa. Everyone who is not wise or curious is kind. Everyone who is not humble or curious is generous. Someone is not humble or calm. Alice is not tall. Someone is not brave. Someone is both humble and calm. Alice is either not humble or not calm. Fred is both curious and generous. Someone is not old. Someone is both not brave and not old. | Mary is not brave. | entailment | ((?[X]:((rich(X)|calm(X))))=>((generous(susan)|happy(susan))))&
(![X]:((~humble(X)&patient(X))<=>(~happy(X)&strong(X))))&
(![X]:(~patient(X)=>(~funny(X)&strong(X))))&
((?[X]:((patient(X)<~>~curious(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~old(X)<~>~funny(X))))=>((~creative(fred)<~>~rich(fred))))&
(![X]:((rich(X)<~>~rich(X))<=>~creative(X)))&
((patient(susan))=>(?[X]:((funny(X)|~creative(X)))))&
((?[X]:((curious(X)<~>funny(X))))=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((curious(X)&rich(X))<=>(~funny(X)|~creative(X))))&
(((brave(john)|old(john)))<=>((~strong(john)&kind(john))))&
(((creative(mary)<~>~quiet(mary)))<=>((generous(lucy)&~calm(lucy))))&
(![X]:((creative(X)<~>~quiet(X))<=>(brave(X)&~funny(X))))&
((?[X]:((tall(X)&~patient(X))))<=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:(funny(X)<=>~brave(X)))&
(![X]:((~wise(X)|curious(X))=>kind(X)))&
(![X]:((~humble(X)|curious(X))=>generous(X)))&
(?[X]:((~humble(X)|calm(X))))&
(~tall(alice))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)&calm(X))))&
((~humble(alice)<~>~calm(alice)))&
((curious(fred)&generous(fred)))&
(?[X]:(~old(X)))&
(?[X]:((~brave(X)&~old(X)))) | ~brave(mary) | [
"p5",
"p7",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3351551244573003400110305
% SZS output start Proof for 3351551244573003400110305
6. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> ~creative(X0)) [input p5]
8. ? [X0] : (curious(X0) <~> funny(X0)) => ? [X0] : (happy(X0) & ~kind(X0)) [input p7]
9. ! [X0] : ((rich(X0) & curious(X0)) <=> (~creative(X0) | ~funny(X0))) [input p8]
14. ! [X0] : (funny(X0) <=> ~brave(X0)) [input p13]
15. ! [X0] : ((curious(X0) | ~wise(X0)) => kind(X0)) [input p14]
25. brave(mary) [input hypothesis]
27. ? [X0] : (curious(X0) <~> funny(X0)) => ? [X1] : (happy(X1) & ~kind(X1)) [rectify 8]
29. ! [X0] : (curious(X0) => kind(X0)) [pure predicate removal 15]
35. ? [X1] : (happy(X1) & ~kind(X1)) | ! [X0] : (curious(X0) <=> funny(X0)) [ennf transformation 27]
36. ! [X0] : (kind(X0) | ~curious(X0)) [ennf transformation 29]
46. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | creative(X0)) & (~creative(X0) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 6]
49. ? [X1] : (happy(X1) & ~kind(X1)) | ! [X0] : ((curious(X0) | ~funny(X0)) & (funny(X0) | ~curious(X0))) [nnf transformation 35]
50. ? [X0] : (happy(X0) & ~kind(X0)) | ! [X1] : ((curious(X1) | ~funny(X1)) & (funny(X1) | ~curious(X1))) [rectify 49]
51. ? [X0] : (happy(X0) & ~kind(X0)) => (happy(sK3) & ~kind(sK3)) [choice axiom]
52. (happy(sK3) & ~kind(sK3)) | ! [X1] : ((curious(X1) | ~funny(X1)) & (funny(X1) | ~curious(X1))) [skolemisation 50,51]
53. ! [X0] : (((rich(X0) & curious(X0)) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | (~rich(X0) | ~curious(X0)))) [nnf transformation 9]
54. ! [X0] : (((rich(X0) & curious(X0)) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~rich(X0) | ~curious(X0))) [flattening 53]
66. ! [X0] : ((funny(X0) | brave(X0)) & (~brave(X0) | ~funny(X0))) [nnf transformation 14]
94. ~creative(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 46]
95. ~creative(X0) | rich(X0) | rich(X0) [cnf transformation 46]
99. ~kind(sK3) | funny(X1) | ~curious(X1) [cnf transformation 52]
105. curious(X0) | creative(X0) [cnf transformation 54]
129. ~brave(X0) | ~funny(X0) [cnf transformation 66]
131. kind(X0) | ~curious(X0) [cnf transformation 36]
146. brave(mary) [cnf transformation 25]
147. ~creative(X0) | ~rich(X0) [duplicate literal removal 94]
148. ~creative(X0) | rich(X0) [duplicate literal removal 95]
208. ~creative(X0) [subsumption resolution 147,148]
218. 17 <=> ! [X1] : (funny(X1) | ~curious(X1)) [avatar definition]
219. funny(X1) | ~curious(X1) <- (17) [avatar component clause 218]
222. 18 <=> kind(sK3) [avatar definition]
224. ~kind(sK3) <- (~18) [avatar component clause 222]
226. 17 | ~18 [avatar split clause 99,222,218]
228. curious(X0) [subsumption resolution 105,208]
281. kind(X0) [subsumption resolution 131,228]
304. $false <- (~18) [subsumption resolution 224,281]
305. 18 [avatar contradiction clause 304]
312. funny(X1) <- (17) [subsumption resolution 219,228]
316. ~funny(mary) [resolution 129,146]
317. $false <- (17) [subsumption resolution 316,312]
318. ~17 [avatar contradiction clause 317]
319. $false [avatar sat refutation 226,305,318]
% SZS output end Proof for 3351551244573003400110305
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or quiet then alice is either not happy or not calm and vice versa. If someone is brave or not humble then someone is calm and vice versa. If paul is both humble and calm then paul is not humble or rich. Everyone who is kind is either humble or rich. Everyone who is both tall and not humble is not patient or patient and vice versa. Everyone who is either not humble or humble is both curious and calm and vice versa. If fred is not happy or not curious then alice is generous or calm and vice versa. If someone is either generous or rich then someone is not humble or old and vice versa. Everyone who is old is generous. Everyone who is both not calm and kind is both humble and not old. If someone is funny then lucy is curious or not strong and vice versa. If someone is either not patient or quiet then someone is both curious and creative and vice versa. Everyone who is not funny is creative or not generous and vice versa. If mary is both brave and not generous then someone is both not humble and not happy and vice versa. Everyone who is both not wise and not patient is not creative and vice versa. If someone is not calm or not curious then someone is not quiet and vice versa. Paul is curious. Someone is either humble or kind. Someone is either not brave or not old. Someone is either kind or not wise. Alice is either brave or tall. Alice is not humble or creative. John is not patient or not happy. | Mary is old. | contradiction | ((?[X]:((~old(X)<~>quiet(X))))<=>((~happy(alice)<~>~calm(alice))))&
((?[X]:((brave(X)|~humble(X))))<=>(?[X]:(calm(X))))&
(((humble(paul)&calm(paul)))=>((~humble(paul)|rich(paul))))&
(![X]:(kind(X)=>(humble(X)<~>rich(X))))&
(![X]:((tall(X)&~humble(X))<=>(~patient(X)|patient(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(curious(X)&calm(X))))&
(((~happy(fred)|~curious(fred)))<=>((generous(alice)|calm(alice))))&
((?[X]:((generous(X)<~>rich(X))))<=>(?[X]:((~humble(X)|old(X)))))&
(![X]:(old(X)=>generous(X)))&
(![X]:((~calm(X)&kind(X))=>(humble(X)&~old(X))))&
((?[X]:(funny(X)))<=>((curious(lucy)|~strong(lucy))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((curious(X)&creative(X)))))&
(![X]:(~funny(X)<=>(creative(X)|~generous(X))))&
(((brave(mary)&~generous(mary)))<=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((~wise(X)&~patient(X))<=>~creative(X)))&
((?[X]:((~calm(X)|~curious(X))))<=>(?[X]:(~quiet(X))))&
(curious(paul))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:((~brave(X)<~>~old(X))))&
(?[X]:((kind(X)<~>~wise(X))))&
((brave(alice)<~>tall(alice)))&
((~humble(alice)|creative(alice)))&
((~patient(john)|~happy(john))) | old(mary) | [
"p0",
"p4",
"p5",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8995406784071626822217059
% SZS output start Proof for 8995406784071626822217059
1. ? [X0] : (~old(X0) <~> quiet(X0)) <=> (~happy(alice) <~> ~calm(alice)) [input p0]
5. ! [X0] : ((~humble(X0) & tall(X0)) <=> (patient(X0) | ~patient(X0))) [input p4]
6. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (calm(X0) & curious(X0))) [input p5]
9. ! [X0] : (old(X0) => generous(X0)) [input p8]
14. (~generous(mary) & brave(mary)) <=> ? [X0] : (~happy(X0) & ~humble(X0)) [input p13]
16. ? [X0] : (~curious(X0) | ~calm(X0)) <=> ? [X0] : ~quiet(X0) [input p15]
24. old(mary) [input hypothesis]
28. ? [X0] : (~curious(X0) | ~calm(X0)) <=> ? [X1] : ~quiet(X1) [rectify 16]
32. ! [X0] : (generous(X0) | ~old(X0)) [ennf transformation 9]
35. (? [X0] : ((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | ((~happy(alice) | calm(alice)) & (~calm(alice) | happy(alice)))) & (((calm(alice) | happy(alice)) & (~calm(alice) | ~happy(alice))) | ! [X0] : ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0)))) [nnf transformation 1]
36. (? [X0] : ((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | ((~happy(alice) | calm(alice)) & (~calm(alice) | happy(alice)))) & (((calm(alice) | happy(alice)) & (~calm(alice) | ~happy(alice))) | ! [X1] : ((~old(X1) | ~quiet(X1)) & (quiet(X1) | old(X1)))) [rectify 35]
37. ? [X0] : ((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) => ((~quiet(sK0) | old(sK0)) & (quiet(sK0) | ~old(sK0))) [choice axiom]
38. (((~quiet(sK0) | old(sK0)) & (quiet(sK0) | ~old(sK0))) | ((~happy(alice) | calm(alice)) & (~calm(alice) | happy(alice)))) & (((calm(alice) | happy(alice)) & (~calm(alice) | ~happy(alice))) | ! [X1] : ((~old(X1) | ~quiet(X1)) & (quiet(X1) | old(X1)))) [skolemisation 36,37]
45. ! [X0] : (((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0))) & ((patient(X0) | ~patient(X0)) | (humble(X0) | ~tall(X0)))) [nnf transformation 5]
46. ! [X0] : (((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0))) & (patient(X0) | ~patient(X0) | humble(X0) | ~tall(X0))) [flattening 45]
47. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (~calm(X0) | ~curious(X0))) & ((calm(X0) & curious(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 6]
48. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~calm(X0) | ~curious(X0)) & ((calm(X0) & curious(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 47]
68. ((~generous(mary) & brave(mary)) | ! [X0] : (happy(X0) | humble(X0))) & (? [X0] : (~happy(X0) & ~humble(X0)) | (generous(mary) | ~brave(mary))) [nnf transformation 14]
69. ((~generous(mary) & brave(mary)) | ! [X0] : (happy(X0) | humble(X0))) & (? [X0] : (~happy(X0) & ~humble(X0)) | generous(mary) | ~brave(mary)) [flattening 68]
70. ((~generous(mary) & brave(mary)) | ! [X0] : (happy(X0) | humble(X0))) & (? [X1] : (~happy(X1) & ~humble(X1)) | generous(mary) | ~brave(mary)) [rectify 69]
71. ? [X1] : (~happy(X1) & ~humble(X1)) => (~happy(sK8) & ~humble(sK8)) [choice axiom]
72. ((~generous(mary) & brave(mary)) | ! [X0] : (happy(X0) | humble(X0))) & ((~happy(sK8) & ~humble(sK8)) | generous(mary) | ~brave(mary)) [skolemisation 70,71]
75. (? [X0] : (~curious(X0) | ~calm(X0)) | ! [X1] : quiet(X1)) & (? [X1] : ~quiet(X1) | ! [X0] : (curious(X0) & calm(X0))) [nnf transformation 28]
76. (? [X0] : (~curious(X0) | ~calm(X0)) | ! [X1] : quiet(X1)) & (? [X2] : ~quiet(X2) | ! [X3] : (curious(X3) & calm(X3))) [rectify 75]
77. ? [X0] : (~curious(X0) | ~calm(X0)) => (~curious(sK9) | ~calm(sK9)) [choice axiom]
78. ? [X2] : ~quiet(X2) => ~quiet(sK10) [choice axiom]
79. ((~curious(sK9) | ~calm(sK9)) | ! [X1] : quiet(X1)) & (~quiet(sK10) | ! [X3] : (curious(X3) & calm(X3))) [skolemisation 76,78,77]
91. ~calm(alice) | ~happy(alice) | ~old(X1) | ~quiet(X1) [cnf transformation 38]
107. ~humble(X0) | patient(X0) [cnf transformation 46]
108. ~patient(X0) | ~humble(X0) [cnf transformation 46]
109. curious(X0) | humble(X0) | humble(X0) [cnf transformation 48]
111. calm(X0) | humble(X0) | humble(X0) [cnf transformation 48]
125. ~old(X0) | generous(X0) [cnf transformation 32]
143. ~generous(mary) | happy(X0) | humble(X0) [cnf transformation 72]
149. ~curious(sK9) | ~calm(sK9) | quiet(X1) [cnf transformation 79]
161. old(mary) [cnf transformation 24]
162. curious(X0) | humble(X0) [duplicate literal removal 109]
164. calm(X0) | humble(X0) [duplicate literal removal 111]
168. 1 <=> calm(alice) [avatar definition]
169. ~calm(alice) <- (~1) [avatar component clause 168]
172. 2 <=> happy(alice) [avatar definition]
174. ~happy(alice) <- (~2) [avatar component clause 172]
188. 5 <=> ! [X1] : (~old(X1) | ~quiet(X1)) [avatar definition]
189. ~old(X1) | ~quiet(X1) <- (5) [avatar component clause 188]
195. 5 | ~2 | ~1 [avatar split clause 91,168,172,188]
234. ~humble(X0) [subsumption resolution 107,108]
236. calm(X0) [subsumption resolution 164,234]
237. curious(X0) [subsumption resolution 162,234]
241. 16 <=> ! [X1] : ~old(X1) [avatar definition]
242. ~old(X1) <- (16) [avatar component clause 241]
295. ~generous(mary) | happy(X0) [subsumption resolution 143,234]
297. 27 <=> ! [X0] : happy(X0) [avatar definition]
298. happy(X0) <- (27) [avatar component clause 297]
300. 28 <=> generous(mary) [avatar definition]
302. ~generous(mary) <- (~28) [avatar component clause 300]
303. 27 | ~28 [avatar split clause 295,300,297]
315. ~calm(sK9) | quiet(X1) [subsumption resolution 149,237]
316. quiet(X1) [subsumption resolution 315,236]
354. $false <- (~1) [subsumption resolution 169,236]
355. 1 [avatar contradiction clause 354]
356. ~old(X1) <- (5) [subsumption resolution 189,316]
357. 16 | ~5 [avatar split clause 356,188,241]
358. $false <- (16) [resolution 242,161]
359. ~16 [avatar contradiction clause 358]
360. $false <- (~2, 27) [subsumption resolution 174,298]
361. 2 | ~27 [avatar contradiction clause 360]
366. generous(mary) [resolution 125,161]
368. $false <- (~28) [subsumption resolution 366,302]
369. 28 [avatar contradiction clause 368]
370. $false [avatar sat refutation 195,303,355,357,359,361,369]
% SZS output end Proof for 8995406784071626822217059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or not wise then fred is not patient or rich and vice versa.
If lucy is quiet or generous then someone is creative and vice versa.
Everyone who is either not happy or old is funny.
If alice is both kind and not patient then john is calm or quiet.
Everyone who is both not wise and quiet is either not strong or strong.
Everyone who is both creative and quiet is old or not strong and vice versa.
Everyone who is not creative or quiet is either not curious or not old and vice versa.
If mary is both not old and not brave then someone is not funny or happy.
Everyone who is both humble and not tall is either brave or patient.
If someone is creative then someone is strong.
Everyone who is not strong is kind and vice versa.
Everyone who is both not curious and kind is not old and vice versa.
Everyone who is either humble or not happy is calm or not kind.
Everyone who is both not old and not funny is patient and vice versa.
If someone is not happy then someone is not creative.
Everyone who is both strong and patient is not wise.
Alice is both not brave and wise.
Someone is calm or not brave.
Someone is either not funny or not patient.
Someone is tall or not happy.
Alice is not calm or kind.
John is either happy or not happy. | Alice is not strong. | contradiction | ((?[X]:((~kind(X)|~wise(X))))<=>((~patient(fred)|rich(fred))))&
(((quiet(lucy)|generous(lucy)))<=>(?[X]:(creative(X))))&
(![X]:((~happy(X)<~>old(X))=>funny(X)))&
(((kind(alice)&~patient(alice)))=>((calm(john)|quiet(john))))&
(![X]:((~wise(X)&quiet(X))=>(~strong(X)<~>strong(X))))&
(![X]:((creative(X)&quiet(X))<=>(old(X)|~strong(X))))&
(![X]:((~creative(X)|quiet(X))<=>(~curious(X)<~>~old(X))))&
(((~old(mary)&~brave(mary)))=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((humble(X)&~tall(X))=>(brave(X)<~>patient(X))))&
((?[X]:(creative(X)))=>(?[X]:(strong(X))))&
(![X]:(~strong(X)<=>kind(X)))&
(![X]:((~curious(X)&kind(X))<=>~old(X)))&
(![X]:((humble(X)<~>~happy(X))=>(calm(X)|~kind(X))))&
(![X]:((~old(X)&~funny(X))<=>patient(X)))&
((?[X]:(~happy(X)))=>(?[X]:(~creative(X))))&
(![X]:((strong(X)&patient(X))=>~wise(X)))&
((~brave(alice)&wise(alice)))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:((~funny(X)<~>~patient(X))))&
(?[X]:((tall(X)|~happy(X))))&
((~calm(alice)|kind(alice)))&
((happy(john)<~>~happy(john))) | ~strong(alice) | [
"p5",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5657162761455987958166105
% SZS output start Proof for 5657162761455987958166105
6. ! [X0] : ((quiet(X0) & creative(X0)) <=> (~strong(X0) | old(X0))) [input p5]
7. ! [X0] : ((quiet(X0) | ~creative(X0)) <=> (~curious(X0) <~> ~old(X0))) [input p6]
11. ! [X0] : (~strong(X0) <=> kind(X0)) [input p10]
12. ! [X0] : ((kind(X0) & ~curious(X0)) <=> ~old(X0)) [input p11]
23. ~strong(alice) [input hypothesis]
53. ! [X0] : (((quiet(X0) & creative(X0)) | (strong(X0) & ~old(X0))) & ((~strong(X0) | old(X0)) | (~quiet(X0) | ~creative(X0)))) [nnf transformation 6]
54. ! [X0] : (((quiet(X0) & creative(X0)) | (strong(X0) & ~old(X0))) & (~strong(X0) | old(X0) | ~quiet(X0) | ~creative(X0))) [flattening 53]
55. ! [X0] : (((quiet(X0) | ~creative(X0)) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (~quiet(X0) & creative(X0)))) [nnf transformation 7]
56. ! [X0] : ((quiet(X0) | ~creative(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (~quiet(X0) & creative(X0)))) [flattening 55]
62. ! [X0] : ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))) [nnf transformation 11]
63. ! [X0] : (((kind(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | (~kind(X0) | curious(X0)))) [nnf transformation 12]
64. ! [X0] : (((kind(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | ~kind(X0) | curious(X0))) [flattening 63]
92. ~old(X0) | quiet(X0) [cnf transformation 54]
93. strong(X0) | quiet(X0) [cnf transformation 54]
95. ~old(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 56]
97. ~quiet(X0) | curious(X0) | old(X0) [cnf transformation 56]
102. strong(X0) | kind(X0) [cnf transformation 62]
104. ~old(X0) | ~kind(X0) | curious(X0) [cnf transformation 64]
105. ~curious(X0) | old(X0) [cnf transformation 64]
122. ~strong(alice) [cnf transformation 23]
168. 11 <=> kind(alice) [avatar definition]
169. kind(alice) <- (11) [avatar component clause 168]
186. ~curious(X0) | ~old(X0) [subsumption resolution 95,92]
209. ~curious(X0) [subsumption resolution 105,186]
210. ~old(X0) | ~kind(X0) [subsumption resolution 104,209]
245. quiet(alice) [resolution 93,122]
246. kind(alice) [resolution 102,122]
249. 11 [avatar split clause 246,168]
273. curious(alice) | old(alice) [resolution 97,245]
276. old(alice) [subsumption resolution 273,209]
287. ~kind(alice) [resolution 276,210]
292. $false <- (11) [subsumption resolution 287,169]
293. ~11 [avatar contradiction clause 292]
296. $false [avatar sat refutation 249,293]
% SZS output end Proof for 5657162761455987958166105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or funny is old.
Everyone who is either not old or quiet is not humble.
Everyone who is either wise or not tall is brave or happy and vice versa.
If john is not patient or rich then someone is not tall and vice versa.
Everyone who is either funny or wise is tall or not humble.
If someone is old or brave then someone is humble or not old.
If someone is both not creative and calm then mary is not calm.
Everyone who is not kind is either not old or wise.
If john is not wise then alice is generous.
Everyone who is not brave or tall is generous and vice versa.
Everyone who is not creative is both kind and not generous and vice versa.
If someone is strong then someone is creative or not tall and vice versa.
If paul is both curious and kind then someone is both not creative and not wise and vice versa.
If someone is patient or brave then someone is not patient and vice versa.
Everyone who is calm or not kind is both funny and not tall.
Everyone who is both wise and not funny is both old and brave and vice versa.
Alice is either not strong or not calm.
Someone is either not wise or tall.
Paul is generous.
Alice is both patient and strong.
Someone is not rich.
John is both rich and strong.
Mary is curious.
Susan is calm or wise. | Paul is kind. | neutral | (![X]:((quiet(X)<~>funny(X))=>old(X)))&
(![X]:((~old(X)<~>quiet(X))=>~humble(X)))&
(![X]:((wise(X)<~>~tall(X))<=>(brave(X)|happy(X))))&
(((~patient(john)|rich(john)))<=>(?[X]:(~tall(X))))&
(![X]:((funny(X)<~>wise(X))=>(tall(X)|~humble(X))))&
((?[X]:((old(X)|brave(X))))=>(?[X]:((humble(X)|~old(X)))))&
((?[X]:((~creative(X)&calm(X))))=>(~calm(mary)))&
(![X]:(~kind(X)=>(~old(X)<~>wise(X))))&
((~wise(john))=>(generous(alice)))&
(![X]:((~brave(X)|tall(X))<=>generous(X)))&
(![X]:(~creative(X)<=>(kind(X)&~generous(X))))&
((?[X]:(strong(X)))<=>(?[X]:((creative(X)|~tall(X)))))&
(((curious(paul)&kind(paul)))<=>(?[X]:((~creative(X)&~wise(X)))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:(~patient(X))))&
(![X]:((calm(X)|~kind(X))=>(funny(X)&~tall(X))))&
(![X]:((wise(X)&~funny(X))<=>(old(X)&brave(X))))&
((~strong(alice)<~>~calm(alice)))&
(?[X]:((~wise(X)<~>tall(X))))&
(generous(paul))&
((patient(alice)&strong(alice)))&
(?[X]:(~rich(X)))&
((rich(john)&strong(john)))&
(curious(mary))&
((calm(susan)|wise(susan))) | kind(paul) | [] | null | 0 |
Everyone who is either not humble or not old is both tall and not happy.
Everyone who is both not generous and not curious is both not funny and wise.
If mary is either tall or rich then paul is brave and vice versa.
If someone is not old then lucy is both not calm and creative and vice versa.
Everyone who is both not wise and strong is both tall and kind and vice versa.
If lucy is either not funny or patient then someone is either not strong or rich and vice versa.
If lucy is both not wise and old then susan is tall or patient.
Everyone who is quiet or not creative is not quiet or brave and vice versa.
Everyone who is both patient and not kind is curious.
If john is both not rich and not humble then someone is either calm or not brave and vice versa.
Everyone who is old is both calm and generous and vice versa.
If susan is both not funny and not rich then someone is either not kind or not generous and vice versa.
If someone is not strong or brave then someone is both not strong and wise and vice versa.
Everyone who is curious or not kind is strong.
Everyone who is both not kind and not patient is not rich or rich and vice versa.
Everyone who is not funny is brave or not happy.
Someone is strong.
Someone is both funny and curious.
Alice is not calm or not quiet.
John is both not tall and not funny.
Someone is not calm or not humble.
Someone is either not creative or not rich. | Mary is not wise. | contradiction | (![X]:((~humble(X)<~>~old(X))=>(tall(X)&~happy(X))))&
(![X]:((~generous(X)&~curious(X))=>(~funny(X)&wise(X))))&
(((tall(mary)<~>rich(mary)))<=>(brave(paul)))&
((?[X]:(~old(X)))<=>((~calm(lucy)&creative(lucy))))&
(![X]:((~wise(X)&strong(X))<=>(tall(X)&kind(X))))&
(((~funny(lucy)<~>patient(lucy)))<=>(?[X]:((~strong(X)<~>rich(X)))))&
(((~wise(lucy)&old(lucy)))=>((tall(susan)|patient(susan))))&
(![X]:((quiet(X)|~creative(X))<=>(~quiet(X)|brave(X))))&
(![X]:((patient(X)&~kind(X))=>curious(X)))&
(((~rich(john)&~humble(john)))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:(old(X)<=>(calm(X)&generous(X))))&
(((~funny(susan)&~rich(susan)))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
((?[X]:((~strong(X)|brave(X))))<=>(?[X]:((~strong(X)&wise(X)))))&
(![X]:((curious(X)|~kind(X))=>strong(X)))&
(![X]:((~kind(X)&~patient(X))<=>(~rich(X)|rich(X))))&
(![X]:(~funny(X)=>(brave(X)|~happy(X))))&
(?[X]:(strong(X)))&
(?[X]:((funny(X)&curious(X))))&
((~calm(alice)|~quiet(alice)))&
((~tall(john)&~funny(john)))&
(?[X]:((~calm(X)|~humble(X))))&
(?[X]:((~creative(X)<~>~rich(X)))) | ~wise(mary) | [
"p4",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1376551549580692803386057
% SZS output start Proof for 1376551549580692803386057
5. ! [X0] : ((strong(X0) & ~wise(X0)) <=> (kind(X0) & tall(X0))) [input p4]
14. ! [X0] : ((~kind(X0) | curious(X0)) => strong(X0)) [input p13]
15. ! [X0] : ((~patient(X0) & ~kind(X0)) <=> (rich(X0) | ~rich(X0))) [input p14]
23. ~wise(mary) [input hypothesis]
34. ! [X0] : (strong(X0) | (kind(X0) & ~curious(X0))) [ennf transformation 14]
42. ! [X0] : (((strong(X0) & ~wise(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (~strong(X0) | wise(X0)))) [nnf transformation 5]
43. ! [X0] : (((strong(X0) & ~wise(X0)) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | ~strong(X0) | wise(X0))) [flattening 42]
67. ! [X0] : (((~patient(X0) & ~kind(X0)) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | (patient(X0) | kind(X0)))) [nnf transformation 15]
68. ! [X0] : (((~patient(X0) & ~kind(X0)) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | patient(X0) | kind(X0))) [flattening 67]
90. ~strong(X0) | kind(X0) | wise(X0) [cnf transformation 43]
128. kind(X0) | strong(X0) [cnf transformation 34]
130. ~kind(X0) | rich(X0) [cnf transformation 68]
131. ~kind(X0) | ~rich(X0) [cnf transformation 68]
143. ~wise(mary) [cnf transformation 23]
304. 35 <=> ! [X3] : strong(X3) [avatar definition]
305. strong(X3) <- (35) [avatar component clause 304]
314. ~kind(X0) [subsumption resolution 130,131]
345. strong(X0) [resolution 128,314]
346. 35 [avatar split clause 345,304]
416. kind(X0) | wise(X0) <- (35) [resolution 90,305]
417. wise(X0) <- (35) [subsumption resolution 416,314]
418. $false <- (35) [resolution 417,143]
419. ~35 [avatar contradiction clause 418]
420. $false [avatar sat refutation 346,419]
% SZS output end Proof for 1376551549580692803386057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or not curious then fred is both quiet and old and vice versa. Everyone who is not generous or calm is either happy or brave and vice versa. Everyone who is both funny and not funny is kind and vice versa. Everyone who is not calm or calm is either kind or not calm and vice versa. If susan is both not quiet and curious then someone is either strong or tall and vice versa. If susan is not quiet then someone is both not strong and brave. If someone is humble then someone is both not patient and generous and vice versa. If susan is either happy or not old then someone is either not rich or not quiet. If fred is not old or kind then lucy is both old and curious. If someone is not patient or not wise then fred is both not funny and not quiet. Everyone who is generous is not happy. If someone is both not strong and calm then someone is either not brave or generous and vice versa. If someone is either not funny or not rich then fred is not rich. If someone is not quiet then fred is happy or kind. Mary is not happy or curious. Someone is generous or not funny. Someone is generous or not quiet. Someone is either brave or not humble. Lucy is either not kind or not rich. Someone is not quiet or not brave. | Fred is not humble. | entailment | ((?[X]:((strong(X)|~curious(X))))<=>((quiet(fred)&old(fred))))&
(![X]:((~generous(X)|calm(X))<=>(happy(X)<~>brave(X))))&
(![X]:((funny(X)&~funny(X))<=>kind(X)))&
(![X]:((~calm(X)|calm(X))<=>(kind(X)<~>~calm(X))))&
(((~quiet(susan)&curious(susan)))<=>(?[X]:((strong(X)<~>tall(X)))))&
((~quiet(susan))=>(?[X]:((~strong(X)&brave(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~patient(X)&generous(X)))))&
(((happy(susan)<~>~old(susan)))=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(((~old(fred)|kind(fred)))=>((old(lucy)&curious(lucy))))&
((?[X]:((~patient(X)|~wise(X))))=>((~funny(fred)&~quiet(fred))))&
(![X]:(generous(X)=>~happy(X)))&
((?[X]:((~strong(X)&calm(X))))<=>(?[X]:((~brave(X)<~>generous(X)))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(~rich(fred)))&
((?[X]:(~quiet(X)))=>((happy(fred)|kind(fred))))&
((~happy(mary)|curious(mary)))&
(?[X]:((generous(X)|~funny(X))))&
(?[X]:((generous(X)|~quiet(X))))&
(?[X]:((brave(X)<~>~humble(X))))&
((~kind(lucy)<~>~rich(lucy)))&
(?[X]:((~quiet(X)|~brave(X)))) | ~humble(fred) | [
"p1",
"p2",
"p3",
"p6",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5627047108350287939742258
% SZS output start Proof for 5627047108350287939742258
2. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (happy(X0) <~> brave(X0))) [input p1]
3. ! [X0] : ((~funny(X0) & funny(X0)) <=> kind(X0)) [input p2]
4. ! [X0] : ((calm(X0) | ~calm(X0)) <=> (kind(X0) <~> ~calm(X0))) [input p3]
7. ? [X0] : humble(X0) <=> ? [X0] : (generous(X0) & ~patient(X0)) [input p6]
10. ? [X0] : (~wise(X0) | ~patient(X0)) => (~quiet(fred) & ~funny(fred)) [input p9]
11. ! [X0] : (generous(X0) => ~happy(X0)) [input p10]
12. ? [X0] : (calm(X0) & ~strong(X0)) <=> ? [X0] : (~brave(X0) <~> generous(X0)) [input p11]
14. ? [X0] : ~quiet(X0) => (kind(fred) | happy(fred)) [input p13]
21. humble(fred) [input hypothesis]
22. ? [X0] : humble(X0) <=> ? [X1] : (generous(X1) & ~patient(X1)) [rectify 7]
23. ? [X0] : (calm(X0) & ~strong(X0)) <=> ? [X1] : (~brave(X1) <~> generous(X1)) [rectify 12]
24. ? [X0] : ~patient(X0) => (~quiet(fred) & ~funny(fred)) [pure predicate removal 10]
28. (~quiet(fred) & ~funny(fred)) | ! [X0] : patient(X0) [ennf transformation 24]
29. ! [X0] : (~happy(X0) | ~generous(X0)) [ennf transformation 11]
31. (kind(fred) | happy(fred)) | ! [X0] : quiet(X0) [ennf transformation 14]
32. kind(fred) | happy(fred) | ! [X0] : quiet(X0) [flattening 31]
38. ! [X0] : (((calm(X0) | ~generous(X0)) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | (~calm(X0) & generous(X0)))) [nnf transformation 2]
39. ! [X0] : ((calm(X0) | ~generous(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | (~calm(X0) & generous(X0)))) [flattening 38]
40. ! [X0] : (((~funny(X0) & funny(X0)) | ~kind(X0)) & (kind(X0) | (funny(X0) | ~funny(X0)))) [nnf transformation 3]
41. ! [X0] : (((~funny(X0) & funny(X0)) | ~kind(X0)) & (kind(X0) | funny(X0) | ~funny(X0))) [flattening 40]
42. ! [X0] : (((calm(X0) | ~calm(X0)) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0)))) & (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~calm(X0) & calm(X0)))) [nnf transformation 4]
43. ! [X0] : ((calm(X0) | ~calm(X0) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0)))) & (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~calm(X0) & calm(X0)))) [flattening 42]
51. (? [X0] : humble(X0) | ! [X1] : (~generous(X1) | patient(X1))) & (? [X1] : (generous(X1) & ~patient(X1)) | ! [X0] : ~humble(X0)) [nnf transformation 22]
52. (? [X0] : humble(X0) | ! [X1] : (~generous(X1) | patient(X1))) & (? [X2] : (generous(X2) & ~patient(X2)) | ! [X3] : ~humble(X3)) [rectify 51]
53. ? [X0] : humble(X0) => humble(sK3) [choice axiom]
54. ? [X2] : (generous(X2) & ~patient(X2)) => (generous(sK4) & ~patient(sK4)) [choice axiom]
55. (humble(sK3) | ! [X1] : (~generous(X1) | patient(X1))) & ((generous(sK4) & ~patient(sK4)) | ! [X3] : ~humble(X3)) [skolemisation 52,54,53]
59. (? [X0] : (calm(X0) & ~strong(X0)) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) & (? [X1] : ((~generous(X1) | brave(X1)) & (generous(X1) | ~brave(X1))) | ! [X0] : (~calm(X0) | strong(X0))) [nnf transformation 23]
60. (? [X0] : (calm(X0) & ~strong(X0)) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) & (? [X2] : ((~generous(X2) | brave(X2)) & (generous(X2) | ~brave(X2))) | ! [X3] : (~calm(X3) | strong(X3))) [rectify 59]
61. ? [X0] : (calm(X0) & ~strong(X0)) => (calm(sK6) & ~strong(sK6)) [choice axiom]
62. ? [X2] : ((~generous(X2) | brave(X2)) & (generous(X2) | ~brave(X2))) => ((~generous(sK7) | brave(sK7)) & (generous(sK7) | ~brave(sK7))) [choice axiom]
63. ((calm(sK6) & ~strong(sK6)) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) & (((~generous(sK7) | brave(sK7)) & (generous(sK7) | ~brave(sK7))) | ! [X3] : (~calm(X3) | strong(X3))) [skolemisation 60,62,61]
82. ~brave(X0) | ~happy(X0) | generous(X0) [cnf transformation 39]
87. funny(X0) | ~kind(X0) [cnf transformation 41]
88. ~kind(X0) | ~funny(X0) [cnf transformation 41]
90. ~calm(X0) | kind(X0) | ~calm(X0) [cnf transformation 43]
103. ~patient(sK4) | ~humble(X3) [cnf transformation 55]
115. ~quiet(fred) | patient(X0) [cnf transformation 28]
116. ~happy(X0) | ~generous(X0) [cnf transformation 29]
121. calm(sK6) | generous(X1) | brave(X1) [cnf transformation 63]
125. kind(fred) | happy(fred) | quiet(X0) [cnf transformation 32]
134. humble(fred) [cnf transformation 21]
135. ~calm(X0) | kind(X0) [duplicate literal removal 90]
140. 1 <=> quiet(fred) [avatar definition]
142. ~quiet(fred) <- (~1) [avatar component clause 140]
166. ~kind(X0) [subsumption resolution 87,88]
167. ~calm(X0) [subsumption resolution 135,166]
215. 17 <=> ! [X3] : ~humble(X3) [avatar definition]
216. ~humble(X3) <- (17) [avatar component clause 215]
223. 19 <=> patient(sK4) [avatar definition]
225. ~patient(sK4) <- (~19) [avatar component clause 223]
226. 17 | ~19 [avatar split clause 103,223,215]
258. 26 <=> ! [X0] : patient(X0) [avatar definition]
259. patient(X0) <- (26) [avatar component clause 258]
260. 26 | ~1 [avatar split clause 115,140,258]
267. brave(X1) | generous(X1) [subsumption resolution 121,167]
280. happy(fred) | quiet(X0) [subsumption resolution 125,166]
282. 31 <=> ! [X0] : quiet(X0) [avatar definition]
283. quiet(X0) <- (31) [avatar component clause 282]
285. 32 <=> happy(fred) [avatar definition]
287. happy(fred) <- (32) [avatar component clause 285]
288. 31 | 32 [avatar split clause 280,285,282]
336. $false <- (~1, 31) [subsumption resolution 142,283]
337. 1 | ~31 [avatar contradiction clause 336]
338. $false <- (17) [resolution 216,134]
339. ~17 [avatar contradiction clause 338]
351. ~happy(X1) | generous(X1) | generous(X1) [resolution 82,267]
352. ~happy(X1) | generous(X1) [duplicate literal removal 351]
354. ~happy(X1) [subsumption resolution 352,116]
357. $false <- (32) [resolution 354,287]
358. ~32 [avatar contradiction clause 357]
361. $false <- (~19, 26) [resolution 259,225]
362. 19 | ~26 [avatar contradiction clause 361]
363. $false [avatar sat refutation 226,260,288,337,339,358,362]
% SZS output end Proof for 5627047108350287939742258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both not wise and strong and vice versa.
Everyone who is not creative is both humble and tall and vice versa.
If someone is old or not quiet then someone is either not happy or not curious.
Everyone who is both quiet and patient is either not kind or not patient and vice versa.
If john is both calm and not strong then paul is not humble or funny.
If someone is not happy or not quiet then fred is both not happy and old and vice versa.
Everyone who is not calm is quiet or strong and vice versa.
If fred is either not tall or curious then lucy is either not brave or not tall and vice versa.
If lucy is either not calm or happy then mary is not kind and vice versa.
Everyone who is creative is not humble.
Everyone who is either not rich or not curious is happy.
If mary is curious then john is both curious and humble.
Everyone who is either patient or happy is creative or not kind and vice versa.
If alice is both not wise and not patient then fred is happy.
If someone is not happy or not curious then someone is both not brave and not rich and vice versa.
Everyone who is either quiet or not kind is not quiet.
Lucy is both not curious and not tall.
Lucy is wise or not tall.
Someone is either not humble or funny.
Someone is either wise or not old.
Someone is kind or quiet.
John is either not curious or funny.
Someone is not rich or not funny. | Paul is calm. | neutral | (![X]:(~curious(X)<=>(~wise(X)&strong(X))))&
(![X]:(~creative(X)<=>(humble(X)&tall(X))))&
((?[X]:((old(X)|~quiet(X))))=>(?[X]:((~happy(X)<~>~curious(X)))))&
(![X]:((quiet(X)&patient(X))<=>(~kind(X)<~>~patient(X))))&
(((calm(john)&~strong(john)))=>((~humble(paul)|funny(paul))))&
((?[X]:((~happy(X)|~quiet(X))))<=>((~happy(fred)&old(fred))))&
(![X]:(~calm(X)<=>(quiet(X)|strong(X))))&
(((~tall(fred)<~>curious(fred)))<=>((~brave(lucy)<~>~tall(lucy))))&
(((~calm(lucy)<~>happy(lucy)))<=>(~kind(mary)))&
(![X]:(creative(X)=>~humble(X)))&
(![X]:((~rich(X)<~>~curious(X))=>happy(X)))&
((curious(mary))=>((curious(john)&humble(john))))&
(![X]:((patient(X)<~>happy(X))<=>(creative(X)|~kind(X))))&
(((~wise(alice)&~patient(alice)))=>(happy(fred)))&
((?[X]:((~happy(X)|~curious(X))))<=>(?[X]:((~brave(X)&~rich(X)))))&
(![X]:((quiet(X)<~>~kind(X))=>~quiet(X)))&
((~curious(lucy)&~tall(lucy)))&
((wise(lucy)|~tall(lucy)))&
(?[X]:((~humble(X)<~>funny(X))))&
(?[X]:((wise(X)<~>~old(X))))&
(?[X]:((kind(X)|quiet(X))))&
((~curious(john)<~>funny(john)))&
(?[X]:((~rich(X)|~funny(X)))) | calm(paul) | [] | null | 0 |
Everyone who is either funny or not tall is not happy or not patient.
If someone is generous then lucy is old and vice versa.
If someone is kind then someone is not calm or creative.
If someone is both not kind and wise then someone is both not generous and not quiet.
Everyone who is not calm is rich.
Everyone who is both quiet and patient is brave or happy and vice versa.
Everyone who is either wise or not curious is not brave or not quiet.
Everyone who is either not kind or not humble is humble or strong.
Everyone who is either calm or happy is happy or quiet.
Everyone who is either curious or brave is not humble or not funny.
If fred is creative or kind then john is strong or brave and vice versa.
Everyone who is either strong or happy is not strong or calm.
If someone is not brave then mary is either wise or not happy.
Everyone who is either rich or not strong is quiet.
If someone is not wise then someone is either funny or not funny.
Everyone who is not old is quiet and vice versa.
Fred is either wise or not happy.
Lucy is not rich.
Someone is both not strong and not brave.
Paul is both humble and rich.
Fred is not happy.
Someone is either not generous or not patient.
Alice is old. | Alice is calm. | contradiction | (![X]:((funny(X)<~>~tall(X))=>(~happy(X)|~patient(X))))&
((?[X]:(generous(X)))<=>(old(lucy)))&
((?[X]:(kind(X)))=>(?[X]:((~calm(X)|creative(X)))))&
((?[X]:((~kind(X)&wise(X))))=>(?[X]:((~generous(X)&~quiet(X)))))&
(![X]:(~calm(X)=>rich(X)))&
(![X]:((quiet(X)&patient(X))<=>(brave(X)|happy(X))))&
(![X]:((wise(X)<~>~curious(X))=>(~brave(X)|~quiet(X))))&
(![X]:((~kind(X)<~>~humble(X))=>(humble(X)|strong(X))))&
(![X]:((calm(X)<~>happy(X))=>(happy(X)|quiet(X))))&
(![X]:((curious(X)<~>brave(X))=>(~humble(X)|~funny(X))))&
(((creative(fred)|kind(fred)))<=>((strong(john)|brave(john))))&
(![X]:((strong(X)<~>happy(X))=>(~strong(X)|calm(X))))&
((?[X]:(~brave(X)))=>((wise(mary)<~>~happy(mary))))&
(![X]:((rich(X)<~>~strong(X))=>quiet(X)))&
((?[X]:(~wise(X)))=>(?[X]:((funny(X)<~>~funny(X)))))&
(![X]:(~old(X)<=>quiet(X)))&
((wise(fred)<~>~happy(fred)))&
(~rich(lucy))&
(?[X]:((~strong(X)&~brave(X))))&
((humble(paul)&rich(paul)))&
(~happy(fred))&
(?[X]:((~generous(X)<~>~patient(X))))&
(old(alice)) | calm(alice) | [
"p5",
"p8",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6628997654163098199656728
% SZS output start Proof for 6628997654163098199656728
6. ! [X0] : ((patient(X0) & quiet(X0)) <=> (happy(X0) | brave(X0))) [input p5]
9. ! [X0] : ((calm(X0) <~> happy(X0)) => (quiet(X0) | happy(X0))) [input p8]
16. ! [X0] : (~old(X0) <=> quiet(X0)) [input p15]
23. old(alice) [input p22]
24. calm(alice) [input hypothesis]
37. ! [X0] : ((quiet(X0) | happy(X0)) | (calm(X0) <=> happy(X0))) [ennf transformation 9]
38. ! [X0] : (quiet(X0) | happy(X0) | (calm(X0) <=> happy(X0))) [flattening 37]
57. ! [X0] : (((patient(X0) & quiet(X0)) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | (~patient(X0) | ~quiet(X0)))) [nnf transformation 6]
58. ! [X0] : (((patient(X0) & quiet(X0)) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ~patient(X0) | ~quiet(X0))) [flattening 57]
61. ! [X0] : (quiet(X0) | happy(X0) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0)))) [nnf transformation 38]
72. ! [X0] : ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0))) [nnf transformation 16]
89. ~happy(X0) | quiet(X0) [cnf transformation 58]
96. quiet(X0) | happy(X0) | happy(X0) | ~calm(X0) [cnf transformation 61]
113. ~quiet(X0) | ~old(X0) [cnf transformation 72]
124. old(alice) [cnf transformation 23]
125. calm(alice) [cnf transformation 24]
127. quiet(X0) | happy(X0) | ~calm(X0) [duplicate literal removal 96]
169. ~calm(X0) | quiet(X0) [subsumption resolution 127,89]
229. quiet(alice) [resolution 169,125]
231. ~old(alice) [resolution 229,113]
232. $false [subsumption resolution 231,124]
% SZS output end Proof for 6628997654163098199656728
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not humble is both old and not tall. Everyone who is strong or old is both not wise and rich and vice versa. If lucy is either not tall or generous then john is either generous or happy. Everyone who is brave is not kind. Everyone who is either not patient or patient is either not old or old and vice versa. Everyone who is both old and funny is both not calm and old. Everyone who is not wise is not tall. Everyone who is not brave or strong is generous or not curious and vice versa. Everyone who is either wise or not funny is both not humble and not patient and vice versa. Everyone who is both not creative and creative is both not funny and wise and vice versa. If someone is tall or not curious then fred is wise and vice versa. If john is not patient then someone is both wise and happy. If someone is either not humble or not old then someone is both not tall and not creative. Everyone who is strong or patient is not calm. Everyone who is not creative is not happy or kind and vice versa. Someone is either tall or not brave. Susan is either calm or old. Someone is not quiet. Someone is both kind and not brave. Lucy is not rich or patient. Someone is rich. Fred is funny or not patient. Someone is strong or not brave. | Fred is not tall. | entailment | (![X]:((kind(X)|~humble(X))=>(old(X)&~tall(X))))&
(![X]:((strong(X)|old(X))<=>(~wise(X)&rich(X))))&
(((~tall(lucy)<~>generous(lucy)))=>((generous(john)<~>happy(john))))&
(![X]:(brave(X)=>~kind(X)))&
(![X]:((~patient(X)<~>patient(X))<=>(~old(X)<~>old(X))))&
(![X]:((old(X)&funny(X))=>(~calm(X)&old(X))))&
(![X]:(~wise(X)=>~tall(X)))&
(![X]:((~brave(X)|strong(X))<=>(generous(X)|~curious(X))))&
(![X]:((wise(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~creative(X)&creative(X))<=>(~funny(X)&wise(X))))&
((?[X]:((tall(X)|~curious(X))))<=>(wise(fred)))&
((~patient(john))=>(?[X]:((wise(X)&happy(X)))))&
((?[X]:((~humble(X)<~>~old(X))))=>(?[X]:((~tall(X)&~creative(X)))))&
(![X]:((strong(X)|patient(X))=>~calm(X)))&
(![X]:(~creative(X)<=>(~happy(X)|kind(X))))&
(?[X]:((tall(X)<~>~brave(X))))&
((calm(susan)<~>old(susan)))&
(?[X]:(~quiet(X)))&
(?[X]:((kind(X)&~brave(X))))&
((~rich(lucy)|patient(lucy)))&
(?[X]:(rich(X)))&
((funny(fred)|~patient(fred)))&
(?[X]:((strong(X)|~brave(X)))) | ~tall(fred) | [
"p0",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5330265683622287498730006
% SZS output start Proof for 5330265683622287498730006
1. ! [X0] : ((~humble(X0) | kind(X0)) => (~tall(X0) & old(X0))) [input p0]
7. ! [X0] : (~wise(X0) => ~tall(X0)) [input p6]
9. ! [X0] : ((wise(X0) <~> ~funny(X0)) <=> (~patient(X0) & ~humble(X0))) [input p8]
10. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (wise(X0) & ~funny(X0))) [input p9]
24. tall(fred) [input hypothesis]
27. ! [X0] : ((~tall(X0) & old(X0)) | (humble(X0) & ~kind(X0))) [ennf transformation 1]
32. ! [X0] : (~tall(X0) | wise(X0)) [ennf transformation 7]
42. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (patient(X0) | humble(X0))) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [nnf transformation 9]
43. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | patient(X0) | humble(X0)) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [flattening 42]
44. ! [X0] : (((creative(X0) & ~creative(X0)) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 10]
45. ! [X0] : (((creative(X0) & ~creative(X0)) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ~creative(X0) | creative(X0))) [flattening 44]
71. ~tall(X0) | humble(X0) [cnf transformation 27]
92. ~tall(X0) | wise(X0) [cnf transformation 32]
97. ~funny(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 43]
105. ~creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 45]
106. creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 45]
131. tall(fred) [cnf transformation 24]
160. ~wise(X0) | funny(X0) [subsumption resolution 105,106]
162. 5 <=> wise(fred) [avatar definition]
163. wise(fred) <- (5) [avatar component clause 162]
248. 23 <=> funny(fred) [avatar definition]
250. funny(fred) <- (23) [avatar component clause 248]
269. humble(fred) [resolution 71,131]
276. wise(fred) [resolution 92,131]
283. funny(fred) <- (5) [resolution 160,163]
285. 23 | ~5 [avatar split clause 283,162,248]
286. 5 [avatar split clause 276,162]
301. ~humble(fred) | ~wise(fred) <- (23) [resolution 97,250]
303. ~wise(fred) <- (23) [subsumption resolution 301,269]
304. $false <- (5, 23) [subsumption resolution 303,163]
305. ~5 | ~23 [avatar contradiction clause 304]
309. $false [avatar sat refutation 285,286,305]
% SZS output end Proof for 5330265683622287498730006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not strong then lucy is either not tall or rich.
Everyone who is old or not calm is tall or quiet.
Everyone who is both not wise and old is either not rich or funny and vice versa.
Everyone who is either calm or not generous is not old or calm and vice versa.
Everyone who is brave is both kind and wise.
Everyone who is tall or patient is both old and not quiet.
If someone is either not tall or not generous then someone is happy or funny and vice versa.
If alice is tall then someone is both old and creative.
If someone is not kind then john is both not creative and not curious and vice versa.
Everyone who is either not creative or generous is both not calm and not tall.
If mary is generous then someone is either not quiet or quiet and vice versa.
Everyone who is both generous and humble is not brave or not kind and vice versa.
Everyone who is not old or not happy is generous and vice versa.
If someone is either brave or not rich then susan is either not creative or not generous and vice versa.
Everyone who is not tall is either not generous or strong.
If paul is not tall or not strong then someone is not curious and vice versa.
Someone is both strong and curious.
Mary is both calm and tall.
John is either not curious or not wise.
Fred is generous.
Someone is both not curious and patient.
Someone is either not old or wise.
Fred is wise or generous. | Mary is curious. | neutral | ((?[X]:((brave(X)<~>~strong(X))))=>((~tall(lucy)<~>rich(lucy))))&
(![X]:((old(X)|~calm(X))=>(tall(X)|quiet(X))))&
(![X]:((~wise(X)&old(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(~old(X)|calm(X))))&
(![X]:(brave(X)=>(kind(X)&wise(X))))&
(![X]:((tall(X)|patient(X))=>(old(X)&~quiet(X))))&
((?[X]:((~tall(X)<~>~generous(X))))<=>(?[X]:((happy(X)|funny(X)))))&
((tall(alice))=>(?[X]:((old(X)&creative(X)))))&
((?[X]:(~kind(X)))<=>((~creative(john)&~curious(john))))&
(![X]:((~creative(X)<~>generous(X))=>(~calm(X)&~tall(X))))&
((generous(mary))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((generous(X)&humble(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~old(X)|~happy(X))<=>generous(X)))&
((?[X]:((brave(X)<~>~rich(X))))<=>((~creative(susan)<~>~generous(susan))))&
(![X]:(~tall(X)=>(~generous(X)<~>strong(X))))&
(((~tall(paul)|~strong(paul)))<=>(?[X]:(~curious(X))))&
(?[X]:((strong(X)&curious(X))))&
((calm(mary)&tall(mary)))&
((~curious(john)<~>~wise(john)))&
(generous(fred))&
(?[X]:((~curious(X)&patient(X))))&
(?[X]:((~old(X)<~>wise(X))))&
((wise(fred)|generous(fred))) | curious(mary) | [] | null | 0 |
If someone is quiet then fred is either creative or generous.
Everyone who is both patient and calm is both not rich and not happy and vice versa.
If alice is both humble and not tall then someone is humble.
Everyone who is both happy and not curious is not happy or curious.
Everyone who is not curious is both not generous and not humble.
If someone is either patient or funny then someone is either brave or wise and vice versa.
Everyone who is not creative is not patient.
If someone is not old then someone is both not brave and not tall.
Everyone who is both calm and not old is either brave or not tall.
Everyone who is both not generous and not rich is either not creative or rich and vice versa.
Everyone who is both not quiet and kind is creative or not generous.
If someone is old or not tall then alice is both patient and calm and vice versa.
Everyone who is either tall or calm is not tall or not rich and vice versa.
Everyone who is humble or not funny is either not tall or not kind and vice versa.
If someone is both creative and generous then someone is either calm or rich and vice versa.
Everyone who is either not wise or not brave is old.
Alice is not happy or kind.
Someone is either not kind or quiet.
Someone is not rich or brave.
Someone is not happy.
Mary is not patient.
Someone is quiet or old.
Alice is not quiet.
Someone is either not funny or not wise. | Alice is not tall. | entailment | ((?[X]:(quiet(X)))=>((creative(fred)<~>generous(fred))))&
(![X]:((patient(X)&calm(X))<=>(~rich(X)&~happy(X))))&
(((humble(alice)&~tall(alice)))=>(?[X]:(humble(X))))&
(![X]:((happy(X)&~curious(X))=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~generous(X)&~humble(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((calm(X)&~old(X))=>(brave(X)<~>~tall(X))))&
(![X]:((~generous(X)&~rich(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((~quiet(X)&kind(X))=>(creative(X)|~generous(X))))&
((?[X]:((old(X)|~tall(X))))<=>((patient(alice)&calm(alice))))&
(![X]:((tall(X)<~>calm(X))<=>(~tall(X)|~rich(X))))&
(![X]:((humble(X)|~funny(X))<=>(~tall(X)<~>~kind(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>old(X)))&
((~happy(alice)|kind(alice)))&
(?[X]:((~kind(X)<~>quiet(X))))&
(?[X]:((~rich(X)|brave(X))))&
(?[X]:(~happy(X)))&
(~patient(mary))&
(?[X]:((quiet(X)|old(X))))&
(~quiet(alice))&
(?[X]:((~funny(X)<~>~wise(X)))) | ~tall(alice) | [
"p1",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8662871972802406541998745
% SZS output start Proof for 8662871972802406541998745
2. ! [X0] : ((calm(X0) & patient(X0)) <=> (~happy(X0) & ~rich(X0))) [input p1]
8. ? [X0] : ~old(X0) => ? [X0] : (~tall(X0) & ~brave(X0)) [input p7]
12. ? [X0] : (~tall(X0) | old(X0)) <=> (calm(alice) & patient(alice)) [input p11]
13. ! [X0] : ((tall(X0) <~> calm(X0)) <=> (~rich(X0) | ~tall(X0))) [input p12]
25. tall(alice) [input hypothesis]
27. ? [X0] : ~old(X0) => ? [X1] : (~tall(X1) & ~brave(X1)) [rectify 8]
35. ? [X1] : (~tall(X1) & ~brave(X1)) | ! [X0] : old(X0) [ennf transformation 27]
42. ! [X0] : (((calm(X0) & patient(X0)) | (happy(X0) | rich(X0))) & ((~happy(X0) & ~rich(X0)) | (~calm(X0) | ~patient(X0)))) [nnf transformation 2]
43. ! [X0] : (((calm(X0) & patient(X0)) | happy(X0) | rich(X0)) & ((~happy(X0) & ~rich(X0)) | ~calm(X0) | ~patient(X0))) [flattening 42]
51. ? [X0] : (~tall(X0) & ~brave(X0)) | ! [X1] : old(X1) [rectify 35]
52. ? [X0] : (~tall(X0) & ~brave(X0)) => (~tall(sK3) & ~brave(sK3)) [choice axiom]
53. (~tall(sK3) & ~brave(sK3)) | ! [X1] : old(X1) [skolemisation 51,52]
57. (? [X0] : (~tall(X0) | old(X0)) | (~calm(alice) | ~patient(alice))) & ((calm(alice) & patient(alice)) | ! [X0] : (tall(X0) & ~old(X0))) [nnf transformation 12]
58. (? [X0] : (~tall(X0) | old(X0)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X0] : (tall(X0) & ~old(X0))) [flattening 57]
59. (? [X0] : (~tall(X0) | old(X0)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X1] : (tall(X1) & ~old(X1))) [rectify 58]
60. ? [X0] : (~tall(X0) | old(X0)) => (~tall(sK4) | old(sK4)) [choice axiom]
61. ((~tall(sK4) | old(sK4)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X1] : (tall(X1) & ~old(X1))) [skolemisation 59,60]
62. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (rich(X0) & tall(X0))) & ((~rich(X0) | ~tall(X0)) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [nnf transformation 13]
63. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (rich(X0) & tall(X0))) & (~rich(X0) | ~tall(X0) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [flattening 62]
86. ~rich(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 43]
101. ~tall(sK3) | old(X1) [cnf transformation 53]
111. patient(alice) | ~old(X1) [cnf transformation 61]
112. patient(alice) | tall(X1) [cnf transformation 61]
113. calm(alice) | ~old(X1) [cnf transformation 61]
114. calm(alice) | tall(X1) [cnf transformation 61]
121. ~tall(X0) | ~calm(X0) | rich(X0) [cnf transformation 63]
146. tall(alice) [cnf transformation 25]
169. 5 <=> tall(alice) [avatar definition]
171. tall(alice) <- (5) [avatar component clause 169]
214. 15 <=> ! [X1] : old(X1) [avatar definition]
215. old(X1) <- (15) [avatar component clause 214]
217. 16 <=> tall(sK3) [avatar definition]
219. ~tall(sK3) <- (~16) [avatar component clause 217]
220. 15 | ~16 [avatar split clause 101,217,214]
228. 18 <=> patient(alice) [avatar definition]
232. 19 <=> calm(alice) [avatar definition]
233. calm(alice) <- (19) [avatar component clause 232]
245. 22 <=> ! [X1] : tall(X1) [avatar definition]
246. tall(X1) <- (22) [avatar component clause 245]
247. 22 | 19 [avatar split clause 114,232,245]
249. 23 <=> ! [X1] : ~old(X1) [avatar definition]
250. ~old(X1) <- (23) [avatar component clause 249]
251. 23 | 19 [avatar split clause 113,232,249]
252. 22 | 18 [avatar split clause 112,228,245]
253. 23 | 18 [avatar split clause 111,228,249]
332. 5 [avatar split clause 146,169]
386. ~calm(alice) | rich(alice) <- (5) [resolution 121,171]
390. rich(alice) <- (5, 19) [subsumption resolution 386,233]
391. ~calm(alice) | ~patient(alice) <- (5, 19) [resolution 390,86]
394. ~patient(alice) <- (5, 19) [subsumption resolution 391,233]
399. ~18 | ~5 | ~19 [avatar split clause 394,232,169,228]
400. $false <- (~16, 22) [resolution 246,219]
404. 16 | ~22 [avatar contradiction clause 400]
411. $false <- (15, 23) [subsumption resolution 215,250]
412. ~15 | ~23 [avatar contradiction clause 411]
413. $false [avatar sat refutation 220,247,251,252,253,332,399,404,412]
% SZS output end Proof for 8662871972802406541998745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then someone is not strong and vice versa.
If someone is either not creative or not wise then someone is both curious and humble and vice versa.
If someone is not strong then john is not creative or generous and vice versa.
Everyone who is old or brave is both not kind and not brave and vice versa.
If susan is not quiet or strong then john is not tall.
If paul is either not creative or not brave then paul is not wise or strong and vice versa.
If someone is both patient and brave then susan is not kind or old.
Everyone who is quiet is calm and vice versa.
If someone is not strong or calm then someone is not quiet or funny and vice versa.
Everyone who is generous or not funny is both not kind and brave and vice versa.
Everyone who is either kind or not generous is humble.
If john is creative or not rich then someone is both not rich and not humble.
Everyone who is both not brave and quiet is quiet or not funny and vice versa.
Everyone who is not wise or not curious is both happy and kind and vice versa.
If someone is both not strong and not happy then someone is either not kind or humble.
If alice is either funny or calm then john is not strong or strong and vice versa.
John is both strong and not rich.
Susan is not patient.
Mary is tall or curious.
Someone is either creative or not strong.
Fred is not brave. | Paul is not brave. | entailment | ((?[X]:(humble(X)))<=>(?[X]:(~strong(X))))&
((?[X]:((~creative(X)<~>~wise(X))))<=>(?[X]:((curious(X)&humble(X)))))&
((?[X]:(~strong(X)))<=>((~creative(john)|generous(john))))&
(![X]:((old(X)|brave(X))<=>(~kind(X)&~brave(X))))&
(((~quiet(susan)|strong(susan)))=>(~tall(john)))&
(((~creative(paul)<~>~brave(paul)))<=>((~wise(paul)|strong(paul))))&
((?[X]:((patient(X)&brave(X))))=>((~kind(susan)|old(susan))))&
(![X]:(quiet(X)<=>calm(X)))&
((?[X]:((~strong(X)|calm(X))))<=>(?[X]:((~quiet(X)|funny(X)))))&
(![X]:((generous(X)|~funny(X))<=>(~kind(X)&brave(X))))&
(![X]:((kind(X)<~>~generous(X))=>humble(X)))&
(((creative(john)|~rich(john)))=>(?[X]:((~rich(X)&~humble(X)))))&
(![X]:((~brave(X)&quiet(X))<=>(quiet(X)|~funny(X))))&
(![X]:((~wise(X)|~curious(X))<=>(happy(X)&kind(X))))&
((?[X]:((~strong(X)&~happy(X))))=>(?[X]:((~kind(X)<~>humble(X)))))&
(((funny(alice)<~>calm(alice)))<=>((~strong(john)|strong(john))))&
((strong(john)&~rich(john)))&
(~patient(susan))&
((tall(mary)|curious(mary)))&
(?[X]:((creative(X)<~>~strong(X))))&
(~brave(fred)) | ~brave(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3118303220831463023779066
% SZS output start Proof for 3118303220831463023779066
4. ! [X0] : ((brave(X0) | old(X0)) <=> (~brave(X0) & ~kind(X0))) [input p3]
22. brave(paul) [input hypothesis]
48. ! [X0] : (((brave(X0) | old(X0)) | (brave(X0) | kind(X0))) & ((~brave(X0) & ~kind(X0)) | (~brave(X0) & ~old(X0)))) [nnf transformation 4]
49. ! [X0] : ((brave(X0) | old(X0) | brave(X0) | kind(X0)) & ((~brave(X0) & ~kind(X0)) | (~brave(X0) & ~old(X0)))) [flattening 48]
90. ~brave(X0) | ~brave(X0) [cnf transformation 49]
141. brave(paul) [cnf transformation 22]
142. ~brave(X0) [duplicate literal removal 90]
334. $false [subsumption resolution 141,142]
% SZS output end Proof for 3118303220831463023779066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then someone is both not brave and not happy. If fred is both not old and not funny then susan is old or not old. Everyone who is not old or generous is both kind and not generous and vice versa. If someone is both not quiet and not creative then fred is quiet or happy and vice versa. If alice is either not humble or not calm then john is not curious. Everyone who is both not humble and funny is not humble or creative. If fred is not wise or generous then paul is happy. Everyone who is either not brave or funny is creative. If susan is happy then someone is not wise. If someone is both kind and not generous then mary is not funny and vice versa. Everyone who is either not calm or not happy is both not funny and old. If someone is both not kind and not wise then someone is both not kind and not creative and vice versa. Everyone who is happy is not strong and vice versa. If someone is either patient or not wise then someone is strong. If susan is not quiet then fred is both strong and old and vice versa. Everyone who is kind or not curious is not curious or curious. Someone is kind. Someone is either creative or patient. Paul is strong. Someone is happy or not generous. Paul is curious. Someone is not rich or not happy. Fred is brave or not funny. Lucy is either patient or generous. | Fred is wise. | entailment | ((~rich(lucy))=>(?[X]:((~brave(X)&~happy(X)))))&
(((~old(fred)&~funny(fred)))=>((old(susan)|~old(susan))))&
(![X]:((~old(X)|generous(X))<=>(kind(X)&~generous(X))))&
((?[X]:((~quiet(X)&~creative(X))))<=>((quiet(fred)|happy(fred))))&
(((~humble(alice)<~>~calm(alice)))=>(~curious(john)))&
(![X]:((~humble(X)&funny(X))=>(~humble(X)|creative(X))))&
(((~wise(fred)|generous(fred)))=>(happy(paul)))&
(![X]:((~brave(X)<~>funny(X))=>creative(X)))&
((happy(susan))=>(?[X]:(~wise(X))))&
((?[X]:((kind(X)&~generous(X))))<=>(~funny(mary)))&
(![X]:((~calm(X)<~>~happy(X))=>(~funny(X)&old(X))))&
((?[X]:((~kind(X)&~wise(X))))<=>(?[X]:((~kind(X)&~creative(X)))))&
(![X]:(happy(X)<=>~strong(X)))&
((?[X]:((patient(X)<~>~wise(X))))=>(?[X]:(strong(X))))&
((~quiet(susan))<=>((strong(fred)&old(fred))))&
(![X]:((kind(X)|~curious(X))=>(~curious(X)|curious(X))))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)<~>patient(X))))&
(strong(paul))&
(?[X]:((happy(X)|~generous(X))))&
(curious(paul))&
(?[X]:((~rich(X)|~happy(X))))&
((brave(fred)|~funny(fred)))&
((patient(lucy)<~>generous(lucy))) | wise(fred) | [
"p6",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6583651151134810493998742
% SZS output start Proof for 6583651151134810493998742
7. (generous(fred) | ~wise(fred)) => happy(paul) [input p6]
13. ! [X0] : (happy(X0) <=> ~strong(X0)) [input p12]
19. strong(paul) [input p18]
25. ~wise(fred) [input hypothesis]
34. happy(paul) | (~generous(fred) & wise(fred)) [ennf transformation 7]
64. ! [X0] : ((happy(X0) | strong(X0)) & (~strong(X0) | ~happy(X0))) [nnf transformation 13]
97. happy(paul) | wise(fred) [cnf transformation 34]
113. ~strong(X0) | ~happy(X0) [cnf transformation 64]
125. strong(paul) [cnf transformation 19]
132. ~wise(fred) [cnf transformation 25]
189. 12 <=> wise(fred) [avatar definition]
193. 13 <=> happy(paul) [avatar definition]
195. happy(paul) <- (13) [avatar component clause 193]
196. 12 | 13 [avatar split clause 97,193,189]
302. ~12 [avatar split clause 132,189]
305. ~happy(paul) [resolution 113,125]
308. $false <- (13) [subsumption resolution 305,195]
309. ~13 [avatar contradiction clause 308]
312. $false [avatar sat refutation 196,302,309]
% SZS output end Proof for 6583651151134810493998742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not curious or not patient and vice versa. Everyone who is happy is not generous. If someone is both not funny and creative then mary is calm or not strong. Everyone who is both curious and not kind is creative and vice versa. If susan is not kind then john is both tall and calm. If mary is both happy and not patient then paul is either not creative or not generous. If fred is happy then fred is either tall or not quiet. If susan is wise then someone is both calm and happy and vice versa. If susan is not humble or not old then mary is either tall or humble and vice versa. Everyone who is not creative is not happy or not wise. If someone is not patient or rich then someone is quiet. If someone is not happy or kind then john is old. Everyone who is either happy or not strong is either patient or quiet. Everyone who is old is brave. Everyone who is both kind and not wise is both not old and not quiet and vice versa. Everyone who is quiet or calm is not patient or calm and vice versa. Someone is either not happy or not humble. Susan is kind. Susan is not creative. Someone is not strong or not quiet. John is not wise or wise. Susan is strong. Susan is not generous. Someone is curious. | Paul is generous. | neutral | (![X]:(generous(X)<=>(~curious(X)|~patient(X))))&
(![X]:(happy(X)=>~generous(X)))&
((?[X]:((~funny(X)&creative(X))))=>((calm(mary)|~strong(mary))))&
(![X]:((curious(X)&~kind(X))<=>creative(X)))&
((~kind(susan))=>((tall(john)&calm(john))))&
(((happy(mary)&~patient(mary)))=>((~creative(paul)<~>~generous(paul))))&
((happy(fred))=>((tall(fred)<~>~quiet(fred))))&
((wise(susan))<=>(?[X]:((calm(X)&happy(X)))))&
(((~humble(susan)|~old(susan)))<=>((tall(mary)<~>humble(mary))))&
(![X]:(~creative(X)=>(~happy(X)|~wise(X))))&
((?[X]:((~patient(X)|rich(X))))=>(?[X]:(quiet(X))))&
((?[X]:((~happy(X)|kind(X))))=>(old(john)))&
(![X]:((happy(X)<~>~strong(X))=>(patient(X)<~>quiet(X))))&
(![X]:(old(X)=>brave(X)))&
(![X]:((kind(X)&~wise(X))<=>(~old(X)&~quiet(X))))&
(![X]:((quiet(X)|calm(X))<=>(~patient(X)|calm(X))))&
(?[X]:((~happy(X)<~>~humble(X))))&
(kind(susan))&
(~creative(susan))&
(?[X]:((~strong(X)|~quiet(X))))&
((~wise(john)|wise(john)))&
(strong(susan))&
(~generous(susan))&
(?[X]:(curious(X))) | generous(paul) | [] | null | 0 |
If susan is both not patient and not rich then fred is kind and vice versa. If paul is not rich then someone is either not quiet or not wise and vice versa. Everyone who is both calm and rich is either not old or not patient and vice versa. Everyone who is happy is either not quiet or not tall. If someone is either not rich or creative then lucy is both brave and not humble and vice versa. Everyone who is funny or not calm is both not kind and not patient and vice versa. If someone is both wise and not wise then john is kind or not calm and vice versa. If paul is not creative then mary is quiet or wise. Everyone who is either happy or quiet is both not creative and not brave and vice versa. Everyone who is either not old or humble is both not calm and not brave. If lucy is not curious or wise then someone is both not funny and wise. If someone is either tall or brave then john is patient. Everyone who is either not happy or not quiet is rich or not rich and vice versa. Everyone who is both patient and not curious is rich or old. Everyone who is both not old and funny is both rich and not strong and vice versa. If lucy is either not brave or kind then mary is brave or not curious. Alice is both not patient and not happy. Someone is not generous. Someone is either not rich or old. Paul is not patient or creative. Mary is not rich or not patient. Someone is either funny or not humble. | Mary is not calm. | neutral | (((~patient(susan)&~rich(susan)))<=>(kind(fred)))&
((~rich(paul))<=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(![X]:((calm(X)&rich(X))<=>(~old(X)<~>~patient(X))))&
(![X]:(happy(X)=>(~quiet(X)<~>~tall(X))))&
((?[X]:((~rich(X)<~>creative(X))))<=>((brave(lucy)&~humble(lucy))))&
(![X]:((funny(X)|~calm(X))<=>(~kind(X)&~patient(X))))&
((?[X]:((wise(X)&~wise(X))))<=>((kind(john)|~calm(john))))&
((~creative(paul))=>((quiet(mary)|wise(mary))))&
(![X]:((happy(X)<~>quiet(X))<=>(~creative(X)&~brave(X))))&
(![X]:((~old(X)<~>humble(X))=>(~calm(X)&~brave(X))))&
(((~curious(lucy)|wise(lucy)))=>(?[X]:((~funny(X)&wise(X)))))&
((?[X]:((tall(X)<~>brave(X))))=>(patient(john)))&
(![X]:((~happy(X)<~>~quiet(X))<=>(rich(X)|~rich(X))))&
(![X]:((patient(X)&~curious(X))=>(rich(X)|old(X))))&
(![X]:((~old(X)&funny(X))<=>(rich(X)&~strong(X))))&
(((~brave(lucy)<~>kind(lucy)))=>((brave(mary)|~curious(mary))))&
((~patient(alice)&~happy(alice)))&
(?[X]:(~generous(X)))&
(?[X]:((~rich(X)<~>old(X))))&
((~patient(paul)|creative(paul)))&
((~rich(mary)|~patient(mary)))&
(?[X]:((funny(X)<~>~humble(X)))) | ~calm(mary) | [] | null | 0 |
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