premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is either generous or humble is both curious and patient and vice versa. Everyone who is either humble or kind is both not old and happy. Everyone who is both not creative and not kind is not quiet and vice versa. Everyone who is wise is not generous and vice versa. Everyone who is both not tall and not rich is not calm and vice versa. If someone is not creative or not strong then someone is both kind and not humble and vice versa. Everyone who is tall is either brave or generous. Everyone who is not humble is not happy or brave and vice versa. If susan is not tall then someone is funny and vice versa. If paul is not old or calm then alice is not humble or not calm. If someone is both old and not happy then alice is not quiet and vice versa. If someone is not old then mary is either rich or not humble and vice versa. If someone is either not curious or not wise then paul is creative or funny and vice versa. Everyone who is not happy is kind and vice versa. If paul is brave then mary is either strong or tall. If mary is either not happy or kind then someone is both not humble and not wise. Mary is not brave. Someone is either patient or curious. Someone is either generous or not old. Fred is either humble or funny. Someone is not patient. Someone is rich or old. Someone is either old or not strong. Alice is either not kind or not happy. | Fred is not quiet. | contradiction | (![X]:((generous(X)<~>humble(X))<=>(curious(X)&patient(X))))&
(![X]:((humble(X)<~>kind(X))=>(~old(X)&happy(X))))&
(![X]:((~creative(X)&~kind(X))<=>~quiet(X)))&
(![X]:(wise(X)<=>~generous(X)))&
(![X]:((~tall(X)&~rich(X))<=>~calm(X)))&
((?[X]:((~creative(X)|~strong(X))))<=>(?[X]:((kind(X)&~humble(X)))))&
(![X]:(tall(X)=>(brave(X)<~>generous(X))))&
(![X]:(~humble(X)<=>(~happy(X)|brave(X))))&
((~tall(susan))<=>(?[X]:(funny(X))))&
(((~old(paul)|calm(paul)))=>((~humble(alice)|~calm(alice))))&
((?[X]:((old(X)&~happy(X))))<=>(~quiet(alice)))&
((?[X]:(~old(X)))<=>((rich(mary)<~>~humble(mary))))&
((?[X]:((~curious(X)<~>~wise(X))))<=>((creative(paul)|funny(paul))))&
(![X]:(~happy(X)<=>kind(X)))&
((brave(paul))=>((strong(mary)<~>tall(mary))))&
(((~happy(mary)<~>kind(mary)))=>(?[X]:((~humble(X)&~wise(X)))))&
(~brave(mary))&
(?[X]:((patient(X)<~>curious(X))))&
(?[X]:((generous(X)<~>~old(X))))&
((humble(fred)<~>funny(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)|old(X))))&
(?[X]:((old(X)<~>~strong(X))))&
((~kind(alice)<~>~happy(alice))) | ~quiet(fred) | [
"p1",
"p2",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4227194162732475479635106
% SZS output start Proof for 4227194162732475479635106
2. ! [X0] : ((humble(X0) <~> kind(X0)) => (happy(X0) & ~old(X0))) [input p1]
3. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> ~quiet(X0)) [input p2]
6. ? [X0] : (~strong(X0) | ~creative(X0)) <=> ? [X0] : (~humble(X0) & kind(X0)) [input p5]
14. ! [X0] : (~happy(X0) <=> kind(X0)) [input p13]
25. ~quiet(fred) [input hypothesis]
26. ? [X0] : (~strong(X0) | ~creative(X0)) <=> ? [X1] : (~humble(X1) & kind(X1)) [rectify 6]
28. ! [X0] : ((happy(X0) & ~old(X0)) | (humble(X0) <=> kind(X0))) [ennf transformation 2]
37. ! [X0] : ((happy(X0) & ~old(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) [nnf transformation 28]
38. ! [X0] : (((~kind(X0) & ~creative(X0)) | quiet(X0)) & (~quiet(X0) | (kind(X0) | creative(X0)))) [nnf transformation 3]
39. ! [X0] : (((~kind(X0) & ~creative(X0)) | quiet(X0)) & (~quiet(X0) | kind(X0) | creative(X0))) [flattening 38]
41. (? [X0] : (~strong(X0) | ~creative(X0)) | ! [X1] : (humble(X1) | ~kind(X1))) & (? [X1] : (~humble(X1) & kind(X1)) | ! [X0] : (strong(X0) & creative(X0))) [nnf transformation 26]
42. (? [X0] : (~strong(X0) | ~creative(X0)) | ! [X1] : (humble(X1) | ~kind(X1))) & (? [X2] : (~humble(X2) & kind(X2)) | ! [X3] : (strong(X3) & creative(X3))) [rectify 41]
43. ? [X0] : (~strong(X0) | ~creative(X0)) => (~strong(sK0) | ~creative(sK0)) [choice axiom]
44. ? [X2] : (~humble(X2) & kind(X2)) => (~humble(sK1) & kind(sK1)) [choice axiom]
45. ((~strong(sK0) | ~creative(sK0)) | ! [X1] : (humble(X1) | ~kind(X1))) & ((~humble(sK1) & kind(sK1)) | ! [X3] : (strong(X3) & creative(X3))) [skolemisation 42,44,43]
66. ! [X0] : ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))) [nnf transformation 14]
95. ~kind(X0) | humble(X0) | happy(X0) [cnf transformation 37]
97. ~creative(X0) | quiet(X0) [cnf transformation 39]
103. kind(sK1) | creative(X3) [cnf transformation 45]
105. ~humble(sK1) | creative(X3) [cnf transformation 45]
131. ~happy(X0) | ~kind(X0) [cnf transformation 66]
151. ~quiet(fred) [cnf transformation 25]
168. 5 <=> humble(sK1) [avatar definition]
170. ~humble(sK1) <- (~5) [avatar component clause 168]
173. 6 <=> ! [X3] : creative(X3) [avatar definition]
174. creative(X3) <- (6) [avatar component clause 173]
175. 6 | ~5 [avatar split clause 105,168,173]
177. 7 <=> kind(sK1) [avatar definition]
179. kind(sK1) <- (7) [avatar component clause 177]
181. 6 | 7 [avatar split clause 103,177,173]
394. humble(sK1) | happy(sK1) <- (7) [resolution 95,179]
396. happy(sK1) <- (~5, 7) [subsumption resolution 394,170]
430. ~kind(sK1) <- (~5, 7) [resolution 396,131]
431. $false <- (~5, 7) [subsumption resolution 430,179]
432. 5 | ~7 [avatar contradiction clause 431]
435. quiet(X0) <- (6) [resolution 174,97]
438. $false <- (6) [resolution 435,151]
440. ~6 [avatar contradiction clause 438]
441. $false [avatar sat refutation 175,181,432,440]
% SZS output end Proof for 4227194162732475479635106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and patient is not calm or funny.
If someone is both old and not curious then someone is either not funny or not rich and vice versa.
If someone is not happy or not wise then alice is both tall and generous.
Everyone who is not wise or quiet is both not tall and not wise and vice versa.
Everyone who is both curious and brave is both curious and not creative and vice versa.
Everyone who is not generous is both not happy and not calm and vice versa.
Everyone who is patient is not brave or not old and vice versa.
Everyone who is kind is curious.
If fred is not patient or brave then susan is both not rich and rich.
If fred is both not rich and tall then someone is both quiet and not strong and vice versa.
If someone is not tall or not creative then someone is not generous and vice versa.
Everyone who is either humble or not kind is either happy or tall and vice versa.
Everyone who is both not quiet and not strong is both not kind and not patient.
If lucy is both creative and strong then john is not brave or not funny and vice versa.
Everyone who is not creative is either rich or funny and vice versa.
Someone is not funny or rich.
Fred is either not kind or funny.
Someone is not happy or funny.
Fred is both not old and not humble.
Someone is either not curious or not funny.
Someone is not humble.
Someone is not happy or creative. | Susan is brave. | neutral | (![X]:((calm(X)&patient(X))=>(~calm(X)|funny(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:((~funny(X)<~>~rich(X)))))&
((?[X]:((~happy(X)|~wise(X))))=>((tall(alice)&generous(alice))))&
(![X]:((~wise(X)|quiet(X))<=>(~tall(X)&~wise(X))))&
(![X]:((curious(X)&brave(X))<=>(curious(X)&~creative(X))))&
(![X]:(~generous(X)<=>(~happy(X)&~calm(X))))&
(![X]:(patient(X)<=>(~brave(X)|~old(X))))&
(![X]:(kind(X)=>curious(X)))&
(((~patient(fred)|brave(fred)))=>((~rich(susan)&rich(susan))))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)&~strong(X)))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:(~generous(X))))&
(![X]:((humble(X)<~>~kind(X))<=>(happy(X)<~>tall(X))))&
(![X]:((~quiet(X)&~strong(X))=>(~kind(X)&~patient(X))))&
(((creative(lucy)&strong(lucy)))<=>((~brave(john)|~funny(john))))&
(![X]:(~creative(X)<=>(rich(X)<~>funny(X))))&
(?[X]:((~funny(X)|rich(X))))&
((~kind(fred)<~>funny(fred)))&
(?[X]:((~happy(X)|funny(X))))&
((~old(fred)&~humble(fred)))&
(?[X]:((~curious(X)<~>~funny(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)|creative(X)))) | brave(susan) | [] | null | 0 |
Everyone who is old is happy or not kind and vice versa.
If someone is not calm or tall then someone is either not humble or not strong and vice versa.
Everyone who is not kind is both wise and not strong.
Everyone who is either old or not curious is either not strong or generous and vice versa.
If someone is either not funny or not creative then someone is either not brave or brave and vice versa.
If someone is either not rich or not wise then paul is either not curious or not brave and vice versa.
If someone is curious or not tall then someone is kind and vice versa.
Everyone who is either not patient or creative is either not patient or not curious and vice versa.
Everyone who is either not patient or quiet is wise or humble and vice versa.
Everyone who is not strong is not old.
Everyone who is either strong or tall is quiet or happy.
Everyone who is either not happy or not strong is both curious and not humble and vice versa.
Everyone who is generous or not brave is either not patient or funny and vice versa.
If fred is both not creative and old then fred is strong or quiet and vice versa.
Everyone who is generous is either not creative or patient.
Everyone who is both not wise and not creative is happy.
Someone is not rich.
Mary is either not strong or not humble.
Someone is not rich or not funny.
Someone is both old and not brave.
Mary is not tall or not kind.
Paul is not quiet.
Someone is not strong.
Someone is either not funny or not old. | Mary is not happy. | neutral | (![X]:(old(X)<=>(happy(X)|~kind(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:(~kind(X)=>(wise(X)&~strong(X))))&
(![X]:((old(X)<~>~curious(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>(?[X]:((~brave(X)<~>brave(X)))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>((~curious(paul)<~>~brave(paul))))&
((?[X]:((curious(X)|~tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((~patient(X)<~>creative(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((~patient(X)<~>quiet(X))<=>(wise(X)|humble(X))))&
(![X]:(~strong(X)=>~old(X)))&
(![X]:((strong(X)<~>tall(X))=>(quiet(X)|happy(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>(curious(X)&~humble(X))))&
(![X]:((generous(X)|~brave(X))<=>(~patient(X)<~>funny(X))))&
(((~creative(fred)&old(fred)))<=>((strong(fred)|quiet(fred))))&
(![X]:(generous(X)=>(~creative(X)<~>patient(X))))&
(![X]:((~wise(X)&~creative(X))=>happy(X)))&
(?[X]:(~rich(X)))&
((~strong(mary)<~>~humble(mary)))&
(?[X]:((~rich(X)|~funny(X))))&
(?[X]:((old(X)&~brave(X))))&
((~tall(mary)|~kind(mary)))&
(~quiet(paul))&
(?[X]:(~strong(X)))&
(?[X]:((~funny(X)<~>~old(X)))) | ~happy(mary) | [] | null | 0 |
If someone is both tall and happy then someone is not strong.
If alice is either funny or curious then mary is curious.
Everyone who is brave or kind is strong or happy and vice versa.
Everyone who is not humble or not tall is either not generous or not creative and vice versa.
Everyone who is both wise and not funny is both curious and not old and vice versa.
If john is both wise and not happy then alice is not funny or old and vice versa.
Everyone who is both not curious and tall is both funny and old and vice versa.
If someone is either not quiet or not humble then someone is either kind or creative.
If mary is funny then someone is both creative and quiet and vice versa.
Everyone who is either not patient or rich is both kind and calm and vice versa.
If someone is either humble or not humble then someone is either not humble or not creative.
If lucy is both not curious and not patient then someone is not brave or not funny.
Everyone who is either not wise or wise is not generous and vice versa.
Everyone who is not tall is either not humble or kind and vice versa.
Everyone who is not quiet or brave is both not curious and not strong.
Everyone who is kind is either not tall or not kind and vice versa.
Someone is both not calm and not happy.
Someone is either not calm or not tall.
Someone is both not curious and brave.
Someone is both humble and brave.
Alice is both rich and not happy.
Someone is brave.
Paul is not curious. | Paul is not rich. | neutral | ((?[X]:((tall(X)&happy(X))))=>(?[X]:(~strong(X))))&
(((funny(alice)<~>curious(alice)))=>(curious(mary)))&
(![X]:((brave(X)|kind(X))<=>(strong(X)|happy(X))))&
(![X]:((~humble(X)|~tall(X))<=>(~generous(X)<~>~creative(X))))&
(![X]:((wise(X)&~funny(X))<=>(curious(X)&~old(X))))&
(((wise(john)&~happy(john)))<=>((~funny(alice)|old(alice))))&
(![X]:((~curious(X)&tall(X))<=>(funny(X)&old(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>(?[X]:((kind(X)<~>creative(X)))))&
((funny(mary))<=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~patient(X)<~>rich(X))<=>(kind(X)&calm(X))))&
((?[X]:((humble(X)<~>~humble(X))))=>(?[X]:((~humble(X)<~>~creative(X)))))&
(((~curious(lucy)&~patient(lucy)))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((~wise(X)<~>wise(X))<=>~generous(X)))&
(![X]:(~tall(X)<=>(~humble(X)<~>kind(X))))&
(![X]:((~quiet(X)|brave(X))=>(~curious(X)&~strong(X))))&
(![X]:(kind(X)<=>(~tall(X)<~>~kind(X))))&
(?[X]:((~calm(X)&~happy(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:((humble(X)&brave(X))))&
((rich(alice)&~happy(alice)))&
(?[X]:(brave(X)))&
(~curious(paul)) | ~rich(paul) | [] | null | 0 |
Everyone who is strong or not curious is either happy or not curious and vice versa. If someone is both not strong and not patient then someone is not creative. Everyone who is both kind and not kind is both old and not wise. If someone is either quiet or not patient then someone is both generous and not brave and vice versa. If someone is calm or curious then paul is kind or rich. If someone is not quiet or wise then someone is both strong and brave. If mary is both happy and curious then susan is not curious. Everyone who is not patient or not old is either generous or rich and vice versa. If mary is either creative or humble then someone is patient or not funny. Everyone who is wise or not humble is either old or not brave and vice versa. Everyone who is old or not old is both not generous and not curious. Everyone who is humble or generous is either not generous or not strong. If someone is either not patient or rich then mary is both not quiet and not strong. Everyone who is both not curious and not old is not quiet and vice versa. Everyone who is old is kind. If mary is not patient or old then paul is not happy or strong. Someone is not strong or not tall. Mary is both rich and not humble. Fred is not strong or creative. Someone is either quiet or generous. Mary is not wise or calm. Someone is either humble or strong. Lucy is kind or not rich. | Fred is rich. | entailment | (![X]:((strong(X)|~curious(X))<=>(happy(X)<~>~curious(X))))&
((?[X]:((~strong(X)&~patient(X))))=>(?[X]:(~creative(X))))&
(![X]:((kind(X)&~kind(X))=>(old(X)&~wise(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((calm(X)|curious(X))))=>((kind(paul)|rich(paul))))&
((?[X]:((~quiet(X)|wise(X))))=>(?[X]:((strong(X)&brave(X)))))&
(((happy(mary)&curious(mary)))=>(~curious(susan)))&
(![X]:((~patient(X)|~old(X))<=>(generous(X)<~>rich(X))))&
(((creative(mary)<~>humble(mary)))=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((wise(X)|~humble(X))<=>(old(X)<~>~brave(X))))&
(![X]:((old(X)|~old(X))=>(~generous(X)&~curious(X))))&
(![X]:((humble(X)|generous(X))=>(~generous(X)<~>~strong(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~quiet(mary)&~strong(mary))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
(![X]:(old(X)=>kind(X)))&
(((~patient(mary)|old(mary)))=>((~happy(paul)|strong(paul))))&
(?[X]:((~strong(X)|~tall(X))))&
((rich(mary)&~humble(mary)))&
((~strong(fred)|creative(fred)))&
(?[X]:((quiet(X)<~>generous(X))))&
((~wise(mary)|calm(mary)))&
(?[X]:((humble(X)<~>strong(X))))&
((kind(lucy)|~rich(lucy))) | rich(fred) | [
"p3",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5805088026360485466292588
% SZS output start Proof for 5805088026360485466292588
4. ? [X0] : (quiet(X0) <~> ~patient(X0)) <=> ? [X0] : (~brave(X0) & generous(X0)) [input p3]
8. ! [X0] : ((~old(X0) | ~patient(X0)) <=> (generous(X0) <~> rich(X0))) [input p7]
11. ! [X0] : ((~old(X0) | old(X0)) => (~curious(X0) & ~generous(X0))) [input p10]
14. ! [X0] : ((~old(X0) & ~curious(X0)) <=> ~quiet(X0)) [input p13]
24. ~rich(fred) [input hypothesis]
26. ? [X0] : (quiet(X0) <~> ~patient(X0)) <=> ? [X1] : (~brave(X1) & generous(X1)) [rectify 4]
38. ! [X0] : ((~curious(X0) & ~generous(X0)) | (old(X0) & ~old(X0))) [ennf transformation 11]
49. (? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | ! [X1] : (brave(X1) | ~generous(X1))) & (? [X1] : (~brave(X1) & generous(X1)) | ! [X0] : ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) [nnf transformation 26]
50. (? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | ! [X1] : (brave(X1) | ~generous(X1))) & (? [X2] : (~brave(X2) & generous(X2)) | ! [X3] : ((quiet(X3) | patient(X3)) & (~patient(X3) | ~quiet(X3)))) [rectify 49]
51. ? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) => ((patient(sK1) | ~quiet(sK1)) & (~patient(sK1) | quiet(sK1))) [choice axiom]
52. ? [X2] : (~brave(X2) & generous(X2)) => (~brave(sK2) & generous(sK2)) [choice axiom]
53. (((patient(sK1) | ~quiet(sK1)) & (~patient(sK1) | quiet(sK1))) | ! [X1] : (brave(X1) | ~generous(X1))) & ((~brave(sK2) & generous(sK2)) | ! [X3] : ((quiet(X3) | patient(X3)) & (~patient(X3) | ~quiet(X3)))) [skolemisation 50,52,51]
57. ! [X0] : (((~old(X0) | ~patient(X0)) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0)))) & (((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | (old(X0) & patient(X0)))) [nnf transformation 8]
58. ! [X0] : ((~old(X0) | ~patient(X0) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0)))) & (((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | (old(X0) & patient(X0)))) [flattening 57]
63. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | (old(X0) | curious(X0)))) [nnf transformation 14]
64. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | old(X0) | curious(X0))) [flattening 63]
80. generous(sK2) | ~patient(X3) | ~quiet(X3) [cnf transformation 53]
93. rich(X0) | generous(X0) | patient(X0) [cnf transformation 58]
94. rich(X0) | generous(X0) | old(X0) [cnf transformation 58]
105. ~generous(X0) | ~old(X0) [cnf transformation 38]
106. ~generous(X0) | old(X0) [cnf transformation 38]
119. ~old(X0) | quiet(X0) [cnf transformation 64]
132. ~rich(fred) [cnf transformation 24]
166. 8 <=> ! [X3] : (~patient(X3) | ~quiet(X3)) [avatar definition]
167. ~quiet(X3) | ~patient(X3) <- (8) [avatar component clause 166]
170. 9 <=> generous(sK2) [avatar definition]
172. generous(sK2) <- (9) [avatar component clause 170]
174. 8 | 9 [avatar split clause 80,170,166]
221. ~generous(X0) [subsumption resolution 105,106]
295. $false <- (9) [subsumption resolution 172,221]
296. ~9 [avatar contradiction clause 295]
318. generous(fred) | patient(fred) [resolution 93,132]
323. generous(fred) | old(fred) [resolution 94,132]
326. old(fred) [subsumption resolution 323,221]
344. quiet(fred) [resolution 326,119]
414. ~patient(fred) <- (8) [resolution 344,167]
418. patient(fred) [subsumption resolution 318,221]
419. $false <- (8) [subsumption resolution 418,414]
420. ~8 [avatar contradiction clause 419]
421. $false [avatar sat refutation 174,296,420]
% SZS output end Proof for 5805088026360485466292588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and calm is generous.
Everyone who is not tall is both happy and quiet.
Everyone who is not patient is not quiet or not generous.
Everyone who is not strong is both not happy and not rich and vice versa.
If fred is both creative and not happy then someone is either calm or old.
If someone is both not old and old then someone is both humble and not quiet and vice versa.
If susan is not brave or curious then someone is not happy and vice versa.
If lucy is both not kind and not patient then someone is both wise and not wise and vice versa.
If susan is kind or not strong then susan is not wise.
Everyone who is not rich is brave and vice versa.
Everyone who is not wise is either not brave or strong.
Everyone who is both patient and calm is not calm or rich and vice versa.
Everyone who is wise is both not quiet and tall and vice versa.
Everyone who is happy or not tall is either not rich or not strong and vice versa.
If paul is either not strong or curious then someone is not calm or happy.
Someone is either not tall or not kind.
Someone is both not patient and not curious.
Someone is both curious and not patient.
Fred is either kind or not creative.
Someone is humble.
Someone is not old or not wise. | Paul is not happy. | neutral | (![X]:((kind(X)&calm(X))=>generous(X)))&
(![X]:(~tall(X)=>(happy(X)&quiet(X))))&
(![X]:(~patient(X)=>(~quiet(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~happy(X)&~rich(X))))&
(((creative(fred)&~happy(fred)))=>(?[X]:((calm(X)<~>old(X)))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:((humble(X)&~quiet(X)))))&
(((~brave(susan)|curious(susan)))<=>(?[X]:(~happy(X))))&
(((~kind(lucy)&~patient(lucy)))<=>(?[X]:((wise(X)&~wise(X)))))&
(((kind(susan)|~strong(susan)))=>(~wise(susan)))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:(~wise(X)=>(~brave(X)<~>strong(X))))&
(![X]:((patient(X)&calm(X))<=>(~calm(X)|rich(X))))&
(![X]:(wise(X)<=>(~quiet(X)&tall(X))))&
(![X]:((happy(X)|~tall(X))<=>(~rich(X)<~>~strong(X))))&
(((~strong(paul)<~>curious(paul)))=>(?[X]:((~calm(X)|happy(X)))))&
(?[X]:((~tall(X)<~>~kind(X))))&
(?[X]:((~patient(X)&~curious(X))))&
(?[X]:((curious(X)&~patient(X))))&
((kind(fred)<~>~creative(fred)))&
(?[X]:(humble(X)))&
(?[X]:((~old(X)|~wise(X)))) | ~happy(paul) | [] | null | 0 |
If fred is either creative or kind then alice is both not rich and generous and vice versa.
Everyone who is both creative and calm is both not curious and not humble and vice versa.
Everyone who is not old or not happy is both calm and not quiet and vice versa.
Everyone who is either not funny or not humble is curious or not tall and vice versa.
If alice is not creative or not calm then someone is both wise and not generous and vice versa.
Everyone who is brave or not creative is either not curious or not quiet.
If paul is both not creative and tall then someone is both not generous and not strong and vice versa.
Everyone who is not happy is either not old or not creative.
Everyone who is humble or patient is both creative and not strong.
Everyone who is funny is both not happy and not strong.
If susan is creative or not quiet then someone is calm and vice versa.
If john is not old then someone is both brave and not tall and vice versa.
If someone is both not old and not quiet then paul is not kind.
Everyone who is not tall or not quiet is either not strong or not old.
Everyone who is not quiet is not funny or creative and vice versa.
Paul is not wise.
Susan is not brave or calm.
Paul is generous.
Someone is either strong or curious. | Paul is funny. | contradiction | (((creative(fred)<~>kind(fred)))<=>((~rich(alice)&generous(alice))))&
(![X]:((creative(X)&calm(X))<=>(~curious(X)&~humble(X))))&
(![X]:((~old(X)|~happy(X))<=>(calm(X)&~quiet(X))))&
(![X]:((~funny(X)<~>~humble(X))<=>(curious(X)|~tall(X))))&
(((~creative(alice)|~calm(alice)))<=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:((brave(X)|~creative(X))=>(~curious(X)<~>~quiet(X))))&
(((~creative(paul)&tall(paul)))<=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:(~happy(X)=>(~old(X)<~>~creative(X))))&
(![X]:((humble(X)|patient(X))=>(creative(X)&~strong(X))))&
(![X]:(funny(X)=>(~happy(X)&~strong(X))))&
(((creative(susan)|~quiet(susan)))<=>(?[X]:(calm(X))))&
((~old(john))<=>(?[X]:((brave(X)&~tall(X)))))&
((?[X]:((~old(X)&~quiet(X))))=>(~kind(paul)))&
(![X]:((~tall(X)|~quiet(X))=>(~strong(X)<~>~old(X))))&
(![X]:(~quiet(X)<=>(~funny(X)|creative(X))))&
(~wise(paul))&
((~brave(susan)|calm(susan)))&
(generous(paul))&
(?[X]:((strong(X)<~>curious(X)))) | funny(paul) | [
"p2",
"p7",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7869229152356227956631426
% SZS output start Proof for 7869229152356227956631426
3. ! [X0] : ((~happy(X0) | ~old(X0)) <=> (~quiet(X0) & calm(X0))) [input p2]
8. ! [X0] : (~happy(X0) => (~old(X0) <~> ~creative(X0))) [input p7]
10. ! [X0] : (funny(X0) => (~strong(X0) & ~happy(X0))) [input p9]
14. ! [X0] : ((~quiet(X0) | ~tall(X0)) => (~strong(X0) <~> ~old(X0))) [input p13]
15. ! [X0] : (~quiet(X0) <=> (creative(X0) | ~funny(X0))) [input p14]
20. funny(paul) [input hypothesis]
23. ! [X0] : ((~old(X0) <~> ~creative(X0)) | happy(X0)) [ennf transformation 8]
25. ! [X0] : ((~strong(X0) & ~happy(X0)) | ~funny(X0)) [ennf transformation 10]
27. ! [X0] : ((~strong(X0) <~> ~old(X0)) | (quiet(X0) & tall(X0))) [ennf transformation 14]
32. ! [X0] : (((~happy(X0) | ~old(X0)) | (quiet(X0) | ~calm(X0))) & ((~quiet(X0) & calm(X0)) | (happy(X0) & old(X0)))) [nnf transformation 3]
33. ! [X0] : ((~happy(X0) | ~old(X0) | quiet(X0) | ~calm(X0)) & ((~quiet(X0) & calm(X0)) | (happy(X0) & old(X0)))) [flattening 32]
47. ! [X0] : (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | happy(X0)) [nnf transformation 23]
57. ! [X0] : (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | (quiet(X0) & tall(X0))) [nnf transformation 27]
58. ! [X0] : ((~quiet(X0) | (~creative(X0) & funny(X0))) & ((creative(X0) | ~funny(X0)) | quiet(X0))) [nnf transformation 15]
59. ! [X0] : ((~quiet(X0) | (~creative(X0) & funny(X0))) & (creative(X0) | ~funny(X0) | quiet(X0))) [flattening 58]
75. ~quiet(X0) | old(X0) [cnf transformation 33]
76. ~quiet(X0) | happy(X0) [cnf transformation 33]
97. ~old(X0) | ~creative(X0) | happy(X0) [cnf transformation 47]
101. ~funny(X0) | ~happy(X0) [cnf transformation 25]
102. ~strong(X0) | ~funny(X0) [cnf transformation 25]
113. old(X0) | strong(X0) | quiet(X0) [cnf transformation 57]
114. ~funny(X0) | creative(X0) | quiet(X0) [cnf transformation 59]
122. funny(paul) [cnf transformation 20]
178. 12 <=> creative(paul) [avatar definition]
180. ~creative(paul) <- (~12) [avatar component clause 178]
237. strong(X0) | old(X0) [subsumption resolution 113,75]
262. ~happy(paul) [resolution 101,122]
277. ~funny(X0) | old(X0) [resolution 237,102]
285. old(paul) [resolution 277,122]
332. ~creative(paul) | happy(paul) [resolution 97,285]
345. ~creative(paul) [subsumption resolution 332,262]
346. ~12 [avatar split clause 345,178]
367. creative(paul) | quiet(paul) [resolution 114,122]
370. quiet(paul) <- (~12) [subsumption resolution 367,180]
374. happy(paul) <- (~12) [resolution 370,76]
379. $false <- (~12) [subsumption resolution 374,262]
380. 12 [avatar contradiction clause 379]
381. $false [avatar sat refutation 346,380]
% SZS output end Proof for 7869229152356227956631426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both generous and not curious then lucy is not tall and vice versa. If fred is either not creative or curious then paul is either not happy or not tall and vice versa. If lucy is either old or quiet then someone is not funny. Everyone who is both not rich and not tall is not strong or funny and vice versa. Everyone who is both humble and not kind is kind and vice versa. Everyone who is patient is creative or not generous. Everyone who is brave or old is either not brave or not rich and vice versa. Everyone who is not kind is both not funny and not old and vice versa. Everyone who is not quiet is not patient or not kind. Everyone who is both not calm and not brave is both wise and rich and vice versa. Everyone who is both wise and happy is not creative. Everyone who is either strong or not old is either brave or strong. Everyone who is tall is not creative or wise. Everyone who is not strong or calm is not strong. Everyone who is not happy or creative is not curious or wise. Everyone who is either not creative or calm is either patient or not generous and vice versa. Someone is both quiet and tall. Someone is curious. Fred is either happy or tall. Paul is not curious. Someone is both patient and creative. Fred is either not calm or generous. | Alice is not kind. | entailment | (((generous(alice)&~curious(alice)))<=>(~tall(lucy)))&
(((~creative(fred)<~>curious(fred)))<=>((~happy(paul)<~>~tall(paul))))&
(((old(lucy)<~>quiet(lucy)))=>(?[X]:(~funny(X))))&
(![X]:((~rich(X)&~tall(X))<=>(~strong(X)|funny(X))))&
(![X]:((humble(X)&~kind(X))<=>kind(X)))&
(![X]:(patient(X)=>(creative(X)|~generous(X))))&
(![X]:((brave(X)|old(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:(~kind(X)<=>(~funny(X)&~old(X))))&
(![X]:(~quiet(X)=>(~patient(X)|~kind(X))))&
(![X]:((~calm(X)&~brave(X))<=>(wise(X)&rich(X))))&
(![X]:((wise(X)&happy(X))=>~creative(X)))&
(![X]:((strong(X)<~>~old(X))=>(brave(X)<~>strong(X))))&
(![X]:(tall(X)=>(~creative(X)|wise(X))))&
(![X]:((~strong(X)|calm(X))=>~strong(X)))&
(![X]:((~happy(X)|creative(X))=>(~curious(X)|wise(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(patient(X)<~>~generous(X))))&
(?[X]:((quiet(X)&tall(X))))&
(?[X]:(curious(X)))&
((happy(fred)<~>tall(fred)))&
(~curious(paul))&
(?[X]:((patient(X)&creative(X))))&
((~calm(fred)<~>generous(fred))) | ~kind(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 2384824916888782535549721
% SZS output start Proof for 2384824916888782535549721
5. ! [X0] : ((~kind(X0) & humble(X0)) <=> kind(X0)) [input p4]
23. kind(alice) [input hypothesis]
45. ! [X0] : (((~kind(X0) & humble(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | ~humble(X0)))) [nnf transformation 5]
46. ! [X0] : (((~kind(X0) & humble(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | ~humble(X0))) [flattening 45]
83. ~kind(X0) | ~kind(X0) [cnf transformation 46]
127. kind(alice) [cnf transformation 23]
133. ~kind(X0) [duplicate literal removal 83]
214. $false [subsumption resolution 127,133]
% SZS output end Proof for 2384824916888782535549721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both calm and wise then someone is either not brave or not happy.
If someone is brave or old then fred is either brave or not kind.
Everyone who is not humble or calm is either not funny or not creative.
If someone is both funny and not strong then susan is either not humble or curious.
Everyone who is funny is not quiet or not tall and vice versa.
Everyone who is both not kind and funny is either not old or quiet.
Everyone who is quiet is either not funny or not rich.
If someone is not strong or not curious then someone is either kind or not quiet and vice versa.
Everyone who is calm or quiet is both not patient and patient and vice versa.
If lucy is either curious or not strong then fred is not creative and vice versa.
Everyone who is calm or tall is old or generous.
If alice is both not patient and not brave then someone is either funny or not strong.
If someone is not patient or patient then someone is either strong or not tall.
If someone is not brave or wise then someone is old or not rich and vice versa.
If susan is not curious then someone is not brave or tall.
Everyone who is both not brave and not tall is generous and vice versa.
Susan is both brave and not quiet.
Susan is both not old and rich.
Mary is either not wise or not generous.
Someone is not humble or calm.
Mary is creative.
Lucy is brave.
Someone is both not brave and old.
Paul is both old and generous. | Fred is not funny. | contradiction | (((calm(lucy)&wise(lucy)))=>(?[X]:((~brave(X)<~>~happy(X)))))&
((?[X]:((brave(X)|old(X))))=>((brave(fred)<~>~kind(fred))))&
(![X]:((~humble(X)|calm(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:((funny(X)&~strong(X))))=>((~humble(susan)<~>curious(susan))))&
(![X]:(funny(X)<=>(~quiet(X)|~tall(X))))&
(![X]:((~kind(X)&funny(X))=>(~old(X)<~>quiet(X))))&
(![X]:(quiet(X)=>(~funny(X)<~>~rich(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&patient(X))))&
(((curious(lucy)<~>~strong(lucy)))<=>(~creative(fred)))&
(![X]:((calm(X)|tall(X))=>(old(X)|generous(X))))&
(((~patient(alice)&~brave(alice)))=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:((~patient(X)|patient(X))))=>(?[X]:((strong(X)<~>~tall(X)))))&
((?[X]:((~brave(X)|wise(X))))<=>(?[X]:((old(X)|~rich(X)))))&
((~curious(susan))=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:((~brave(X)&~tall(X))<=>generous(X)))&
((brave(susan)&~quiet(susan)))&
((~old(susan)&rich(susan)))&
((~wise(mary)<~>~generous(mary)))&
(?[X]:((~humble(X)|calm(X))))&
(creative(mary))&
(brave(lucy))&
(?[X]:((~brave(X)&old(X))))&
((old(paul)&generous(paul))) | ~funny(fred) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 962372947502760895168837
% SZS output start Proof for 962372947502760895168837
5. ! [X0] : (funny(X0) <=> (~tall(X0) | ~quiet(X0))) [input p4]
9. ! [X0] : ((quiet(X0) | calm(X0)) <=> (patient(X0) & ~patient(X0))) [input p8]
25. ~funny(fred) [input hypothesis]
49. ! [X0] : ((funny(X0) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | ~funny(X0))) [nnf transformation 5]
50. ! [X0] : ((funny(X0) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | ~funny(X0))) [flattening 49]
58. ! [X0] : (((quiet(X0) | calm(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 9]
59. ! [X0] : ((quiet(X0) | calm(X0) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 58]
95. quiet(X0) | funny(X0) [cnf transformation 50]
108. ~patient(X0) | ~quiet(X0) [cnf transformation 59]
110. patient(X0) | ~quiet(X0) [cnf transformation 59]
145. ~funny(fred) [cnf transformation 25]
231. ~quiet(X0) [subsumption resolution 108,110]
334. funny(X0) [resolution 95,231]
335. $false [resolution 334,145]
% SZS output end Proof for 962372947502760895168837
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not old is not quiet and vice versa.
If susan is not quiet then mary is either creative or not strong and vice versa.
Everyone who is not old is patient.
If alice is either old or not patient then someone is not strong and vice versa.
If someone is either not patient or not rich then someone is not rich and vice versa.
Everyone who is either not quiet or not funny is both not creative and humble.
Everyone who is either tall or calm is not wise or not funny.
Everyone who is both not funny and kind is not quiet.
Everyone who is kind or patient is both happy and not humble.
Everyone who is patient or not strong is not tall or quiet and vice versa.
Everyone who is either not happy or not old is both happy and not strong and vice versa.
If alice is either calm or creative then someone is not creative and vice versa.
Everyone who is not kind or rich is both old and not creative.
If paul is both calm and not patient then someone is both curious and not rich and vice versa.
Everyone who is either not wise or not humble is rich and vice versa.
Fred is either old or not kind.
Fred is not generous or brave.
Someone is both wise and strong.
John is not calm or patient.
John is calm or old.
Someone is rich or not humble. | Alice is not brave. | neutral | (![X]:((happy(X)<~>~old(X))<=>~quiet(X)))&
((~quiet(susan))<=>((creative(mary)<~>~strong(mary))))&
(![X]:(~old(X)=>patient(X)))&
(((old(alice)<~>~patient(alice)))<=>(?[X]:(~strong(X))))&
((?[X]:((~patient(X)<~>~rich(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~quiet(X)<~>~funny(X))=>(~creative(X)&humble(X))))&
(![X]:((tall(X)<~>calm(X))=>(~wise(X)|~funny(X))))&
(![X]:((~funny(X)&kind(X))=>~quiet(X)))&
(![X]:((kind(X)|patient(X))=>(happy(X)&~humble(X))))&
(![X]:((patient(X)|~strong(X))<=>(~tall(X)|quiet(X))))&
(![X]:((~happy(X)<~>~old(X))<=>(happy(X)&~strong(X))))&
(((calm(alice)<~>creative(alice)))<=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)|rich(X))=>(old(X)&~creative(X))))&
(((calm(paul)&~patient(paul)))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:((~wise(X)<~>~humble(X))<=>rich(X)))&
((old(fred)<~>~kind(fred)))&
((~generous(fred)|brave(fred)))&
(?[X]:((wise(X)&strong(X))))&
((~calm(john)|patient(john)))&
((calm(john)|old(john)))&
(?[X]:((rich(X)|~humble(X)))) | ~brave(alice) | [] | null | 0 |
If someone is not humble then someone is tall or not tall.
If john is creative then paul is not old or funny and vice versa.
Everyone who is either curious or not generous is not wise.
If someone is not funny or happy then someone is either humble or not happy.
If susan is both rich and not happy then someone is generous or not calm and vice versa.
Everyone who is either strong or not wise is both strong and not wise and vice versa.
If lucy is not creative or not tall then someone is funny or not kind.
Everyone who is both curious and not rich is generous or not calm.
Everyone who is both not quiet and happy is either happy or strong and vice versa.
Everyone who is either wise or calm is rich or not tall and vice versa.
If john is both tall and kind then john is both curious and generous and vice versa.
If mary is not tall then someone is brave and vice versa.
Everyone who is not generous or not kind is both kind and not patient and vice versa.
Everyone who is either rich or not curious is not rich or calm.
If fred is either curious or not curious then susan is humble and vice versa.
Paul is both not humble and tall.
Lucy is calm or not strong.
Paul is either old or quiet.
Mary is strong or old.
Mary is either not wise or happy. | Paul is not kind. | contradiction | ((?[X]:(~humble(X)))=>(?[X]:((tall(X)|~tall(X)))))&
((creative(john))<=>((~old(paul)|funny(paul))))&
(![X]:((curious(X)<~>~generous(X))=>~wise(X)))&
((?[X]:((~funny(X)|happy(X))))=>(?[X]:((humble(X)<~>~happy(X)))))&
(((rich(susan)&~happy(susan)))<=>(?[X]:((generous(X)|~calm(X)))))&
(![X]:((strong(X)<~>~wise(X))<=>(strong(X)&~wise(X))))&
(((~creative(lucy)|~tall(lucy)))=>(?[X]:((funny(X)|~kind(X)))))&
(![X]:((curious(X)&~rich(X))=>(generous(X)|~calm(X))))&
(![X]:((~quiet(X)&happy(X))<=>(happy(X)<~>strong(X))))&
(![X]:((wise(X)<~>calm(X))<=>(rich(X)|~tall(X))))&
(((tall(john)&kind(john)))<=>((curious(john)&generous(john))))&
((~tall(mary))<=>(?[X]:(brave(X))))&
(![X]:((~generous(X)|~kind(X))<=>(kind(X)&~patient(X))))&
(![X]:((rich(X)<~>~curious(X))=>(~rich(X)|calm(X))))&
(((curious(fred)<~>~curious(fred)))<=>(humble(susan)))&
((~humble(paul)&tall(paul)))&
((calm(lucy)|~strong(lucy)))&
((old(paul)<~>quiet(paul)))&
((strong(mary)|old(mary)))&
((~wise(mary)<~>happy(mary))) | ~kind(paul) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4820015202587175830815160
% SZS output start Proof for 4820015202587175830815160
13. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (~patient(X0) & kind(X0))) [input p12]
21. ~kind(paul) [input hypothesis]
61. ! [X0] : (((~kind(X0) | ~generous(X0)) | (patient(X0) | ~kind(X0))) & ((~patient(X0) & kind(X0)) | (kind(X0) & generous(X0)))) [nnf transformation 13]
62. ! [X0] : ((~kind(X0) | ~generous(X0) | patient(X0) | ~kind(X0)) & ((~patient(X0) & kind(X0)) | (kind(X0) & generous(X0)))) [flattening 61]
110. kind(X0) | kind(X0) [cnf transformation 62]
128. ~kind(paul) [cnf transformation 21]
132. kind(X0) [duplicate literal removal 110]
275. $false [subsumption resolution 128,132]
% SZS output end Proof for 4820015202587175830815160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is not old or not brave and vice versa. Everyone who is not brave is happy or old. Everyone who is not quiet is both creative and curious and vice versa. If paul is strong then paul is both not calm and not curious and vice versa. If john is not calm then someone is creative and vice versa. Everyone who is rich or kind is both old and not kind and vice versa. Everyone who is either not happy or rich is not kind or not calm and vice versa. Everyone who is funny is both not kind and strong and vice versa. If someone is both not humble and tall then someone is curious. Everyone who is both brave and not creative is both not brave and wise and vice versa. If someone is either not generous or generous then fred is both not old and not funny. If someone is either not tall or not brave then mary is curious and vice versa. Everyone who is both rich and not brave is both rich and not wise and vice versa. If susan is not wise then someone is not strong and vice versa. If john is not calm or not old then someone is happy or humble and vice versa. If paul is not happy or not quiet then fred is brave or not funny and vice versa. Fred is not humble. Someone is not calm. Mary is strong. Susan is not quiet or not rich. Paul is both curious and wise. Someone is both humble and funny. Mary is either not wise or humble. Someone is old or not happy. | Susan is wise. | contradiction | (![X]:(~wise(X)<=>(~old(X)|~brave(X))))&
(![X]:(~brave(X)=>(happy(X)|old(X))))&
(![X]:(~quiet(X)<=>(creative(X)&curious(X))))&
((strong(paul))<=>((~calm(paul)&~curious(paul))))&
((~calm(john))<=>(?[X]:(creative(X))))&
(![X]:((rich(X)|kind(X))<=>(old(X)&~kind(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~kind(X)|~calm(X))))&
(![X]:(funny(X)<=>(~kind(X)&strong(X))))&
((?[X]:((~humble(X)&tall(X))))=>(?[X]:(curious(X))))&
(![X]:((brave(X)&~creative(X))<=>(~brave(X)&wise(X))))&
((?[X]:((~generous(X)<~>generous(X))))=>((~old(fred)&~funny(fred))))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(curious(mary)))&
(![X]:((rich(X)&~brave(X))<=>(rich(X)&~wise(X))))&
((~wise(susan))<=>(?[X]:(~strong(X))))&
(((~calm(john)|~old(john)))<=>(?[X]:((happy(X)|humble(X)))))&
(((~happy(paul)|~quiet(paul)))<=>((brave(fred)|~funny(fred))))&
(~humble(fred))&
(?[X]:(~calm(X)))&
(strong(mary))&
((~quiet(susan)|~rich(susan)))&
((curious(paul)&wise(paul)))&
(?[X]:((humble(X)&funny(X))))&
((~wise(mary)<~>humble(mary)))&
(?[X]:((old(X)|~happy(X)))) | wise(susan) | [
"p3",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6126925964839629779428462
% SZS output start Proof for 6126925964839629779428462
4. strong(paul) <=> (~curious(paul) & ~calm(paul)) [input p3]
14. ~wise(susan) <=> ? [X0] : ~strong(X0) [input p13]
21. wise(paul) & curious(paul) [input p20]
25. wise(susan) [input hypothesis]
35. (strong(paul) | (curious(paul) | calm(paul))) & ((~curious(paul) & ~calm(paul)) | ~strong(paul)) [nnf transformation 4]
36. (strong(paul) | curious(paul) | calm(paul)) & ((~curious(paul) & ~calm(paul)) | ~strong(paul)) [flattening 35]
59. (~wise(susan) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | wise(susan)) [nnf transformation 14]
60. (~wise(susan) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | wise(susan)) [rectify 59]
61. ? [X1] : ~strong(X1) => ~strong(sK3) [choice axiom]
62. (~wise(susan) | ! [X0] : strong(X0)) & (~strong(sK3) | wise(susan)) [skolemisation 60,61]
85. ~curious(paul) | ~strong(paul) [cnf transformation 36]
121. ~wise(susan) | strong(X0) [cnf transformation 62]
134. curious(paul) [cnf transformation 21]
141. wise(susan) [cnf transformation 25]
155. 2 <=> curious(paul) [avatar definition]
159. 3 <=> strong(paul) [avatar definition]
160. ~strong(paul) <- (~3) [avatar component clause 159]
163. ~3 | ~2 [avatar split clause 85,155,159]
230. 18 <=> ! [X0] : strong(X0) [avatar definition]
231. strong(X0) <- (18) [avatar component clause 230]
233. 19 <=> wise(susan) [avatar definition]
236. 18 | ~19 [avatar split clause 121,233,230]
289. 2 [avatar split clause 134,155]
309. 19 [avatar split clause 141,233]
311. $false <- (~3, 18) [subsumption resolution 160,231]
312. 3 | ~18 [avatar contradiction clause 311]
313. $false [avatar sat refutation 163,236,289,309,312]
% SZS output end Proof for 6126925964839629779428462
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and funny is not patient and vice versa. If someone is either not patient or curious then alice is either not kind or rich. Everyone who is old is either quiet or tall and vice versa. If someone is both not calm and old then someone is tall. If fred is happy or creative then alice is either calm or not kind and vice versa. Everyone who is either not generous or not humble is both not old and brave. Everyone who is either patient or wise is humble or not curious and vice versa. If susan is humble or tall then someone is not tall. Everyone who is not funny is not strong and vice versa. If susan is not old or old then alice is not wise or rich. Everyone who is happy or not rich is strong and vice versa. If mary is both calm and not wise then fred is either not rich or not strong and vice versa. If fred is humble or not happy then mary is both not calm and not brave and vice versa. If someone is either not rich or not humble then alice is both rich and strong and vice versa. Everyone who is either strong or funny is both curious and quiet and vice versa. Everyone who is funny or not wise is either not strong or not kind and vice versa. Mary is either rich or not wise. Fred is not kind. Someone is both not creative and brave. Paul is creative. Paul is both patient and not happy. Alice is both tall and not humble. Someone is not happy. | Alice is creative. | neutral | (![X]:((~quiet(X)&funny(X))<=>~patient(X)))&
((?[X]:((~patient(X)<~>curious(X))))=>((~kind(alice)<~>rich(alice))))&
(![X]:(old(X)<=>(quiet(X)<~>tall(X))))&
((?[X]:((~calm(X)&old(X))))=>(?[X]:(tall(X))))&
(((happy(fred)|creative(fred)))<=>((calm(alice)<~>~kind(alice))))&
(![X]:((~generous(X)<~>~humble(X))=>(~old(X)&brave(X))))&
(![X]:((patient(X)<~>wise(X))<=>(humble(X)|~curious(X))))&
(((humble(susan)|tall(susan)))=>(?[X]:(~tall(X))))&
(![X]:(~funny(X)<=>~strong(X)))&
(((~old(susan)|old(susan)))=>((~wise(alice)|rich(alice))))&
(![X]:((happy(X)|~rich(X))<=>strong(X)))&
(((calm(mary)&~wise(mary)))<=>((~rich(fred)<~>~strong(fred))))&
(((humble(fred)|~happy(fred)))<=>((~calm(mary)&~brave(mary))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>((rich(alice)&strong(alice))))&
(![X]:((strong(X)<~>funny(X))<=>(curious(X)&quiet(X))))&
(![X]:((funny(X)|~wise(X))<=>(~strong(X)<~>~kind(X))))&
((rich(mary)<~>~wise(mary)))&
(~kind(fred))&
(?[X]:((~creative(X)&brave(X))))&
(creative(paul))&
((patient(paul)&~happy(paul)))&
((tall(alice)&~humble(alice)))&
(?[X]:(~happy(X))) | creative(alice) | [] | null | 0 |
Everyone who is not quiet is both not brave and creative.
Everyone who is not rich is old.
Everyone who is both quiet and not calm is either not rich or humble and vice versa.
If lucy is humble then lucy is either creative or quiet and vice versa.
If john is both not patient and tall then susan is not curious or not funny.
If lucy is both not kind and not tall then someone is either generous or not creative.
If someone is either not wise or not humble then susan is generous.
If someone is creative then fred is both not brave and not humble.
Everyone who is patient or not tall is happy or generous.
Everyone who is both not brave and patient is not patient or not rich.
Everyone who is funny is not kind or not generous and vice versa.
If susan is either not patient or not humble then alice is not tall.
Everyone who is both not happy and happy is both tall and not patient.
If someone is both happy and not generous then alice is both rich and kind and vice versa.
Everyone who is either tall or not brave is quiet or not wise and vice versa.
If lucy is either curious or not wise then someone is both kind and not rich and vice versa.
Alice is both not tall and not wise.
John is not generous.
Someone is kind or not calm.
Lucy is either funny or not strong.
Someone is both old and not rich.
Fred is either wise or not generous.
Someone is not generous or funny.
Someone is calm. | Alice is kind. | neutral | (![X]:(~quiet(X)=>(~brave(X)&creative(X))))&
(![X]:(~rich(X)=>old(X)))&
(![X]:((quiet(X)&~calm(X))<=>(~rich(X)<~>humble(X))))&
((humble(lucy))<=>((creative(lucy)<~>quiet(lucy))))&
(((~patient(john)&tall(john)))=>((~curious(susan)|~funny(susan))))&
(((~kind(lucy)&~tall(lucy)))=>(?[X]:((generous(X)<~>~creative(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(generous(susan)))&
((?[X]:(creative(X)))=>((~brave(fred)&~humble(fred))))&
(![X]:((patient(X)|~tall(X))=>(happy(X)|generous(X))))&
(![X]:((~brave(X)&patient(X))=>(~patient(X)|~rich(X))))&
(![X]:(funny(X)<=>(~kind(X)|~generous(X))))&
(((~patient(susan)<~>~humble(susan)))=>(~tall(alice)))&
(![X]:((~happy(X)&happy(X))=>(tall(X)&~patient(X))))&
((?[X]:((happy(X)&~generous(X))))<=>((rich(alice)&kind(alice))))&
(![X]:((tall(X)<~>~brave(X))<=>(quiet(X)|~wise(X))))&
(((curious(lucy)<~>~wise(lucy)))<=>(?[X]:((kind(X)&~rich(X)))))&
((~tall(alice)&~wise(alice)))&
(~generous(john))&
(?[X]:((kind(X)|~calm(X))))&
((funny(lucy)<~>~strong(lucy)))&
(?[X]:((old(X)&~rich(X))))&
((wise(fred)<~>~generous(fred)))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:(calm(X))) | kind(alice) | [] | null | 0 |
Everyone who is rich or strong is calm.
Everyone who is both not brave and patient is either not strong or not creative and vice versa.
If susan is both strong and brave then someone is either creative or not calm and vice versa.
If someone is kind then alice is both happy and not funny and vice versa.
Everyone who is not curious is both old and calm and vice versa.
Everyone who is brave is not quiet and vice versa.
Everyone who is wise is either patient or rich.
If someone is funny then lucy is not tall or curious.
Everyone who is either old or happy is not funny or generous and vice versa.
If someone is not kind then lucy is both not strong and not brave.
Everyone who is both calm and curious is both not curious and brave and vice versa.
If someone is both funny and not old then mary is both not funny and not kind.
Everyone who is brave or not tall is either old or brave and vice versa.
If someone is both not creative and not funny then someone is either not strong or not funny.
If alice is either not old or not brave then someone is both tall and old and vice versa.
Everyone who is strong or not funny is not wise or generous.
Lucy is not kind or creative.
Someone is both not generous and funny.
Mary is either not strong or not patient.
John is kind.
Someone is either happy or not brave.
Paul is strong.
Someone is not wise or generous.
Susan is not wise or brave. | Alice is not strong. | entailment | (![X]:((rich(X)|strong(X))=>calm(X)))&
(![X]:((~brave(X)&patient(X))<=>(~strong(X)<~>~creative(X))))&
(((strong(susan)&brave(susan)))<=>(?[X]:((creative(X)<~>~calm(X)))))&
((?[X]:(kind(X)))<=>((happy(alice)&~funny(alice))))&
(![X]:(~curious(X)<=>(old(X)&calm(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
(![X]:(wise(X)=>(patient(X)<~>rich(X))))&
((?[X]:(funny(X)))=>((~tall(lucy)|curious(lucy))))&
(![X]:((old(X)<~>happy(X))<=>(~funny(X)|generous(X))))&
((?[X]:(~kind(X)))=>((~strong(lucy)&~brave(lucy))))&
(![X]:((calm(X)&curious(X))<=>(~curious(X)&brave(X))))&
((?[X]:((funny(X)&~old(X))))=>((~funny(mary)&~kind(mary))))&
(![X]:((brave(X)|~tall(X))<=>(old(X)<~>brave(X))))&
((?[X]:((~creative(X)&~funny(X))))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~old(alice)<~>~brave(alice)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:((strong(X)|~funny(X))=>(~wise(X)|generous(X))))&
((~kind(lucy)|creative(lucy)))&
(?[X]:((~generous(X)&funny(X))))&
((~strong(mary)<~>~patient(mary)))&
(kind(john))&
(?[X]:((happy(X)<~>~brave(X))))&
(strong(paul))&
(?[X]:((~wise(X)|generous(X))))&
((~wise(susan)|brave(susan))) | ~strong(alice) | [
"p0",
"p3",
"p4",
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1317832464548990548622250
% SZS output start Proof for 1317832464548990548622250
1. ! [X0] : ((strong(X0) | rich(X0)) => calm(X0)) [input p0]
4. ? [X0] : kind(X0) <=> (~funny(alice) & happy(alice)) [input p3]
5. ! [X0] : (~curious(X0) <=> (calm(X0) & old(X0))) [input p4]
9. ! [X0] : ((old(X0) <~> happy(X0)) <=> (generous(X0) | ~funny(X0))) [input p8]
11. ! [X0] : ((curious(X0) & calm(X0)) <=> (brave(X0) & ~curious(X0))) [input p10]
20. kind(john) [input p19]
25. strong(alice) [input hypothesis]
31. ! [X0] : (strong(X0) => calm(X0)) [pure predicate removal 1]
32. ! [X0] : (calm(X0) | ~strong(X0)) [ennf transformation 31]
45. (? [X0] : kind(X0) | (funny(alice) | ~happy(alice))) & ((~funny(alice) & happy(alice)) | ! [X0] : ~kind(X0)) [nnf transformation 4]
46. (? [X0] : kind(X0) | funny(alice) | ~happy(alice)) & ((~funny(alice) & happy(alice)) | ! [X0] : ~kind(X0)) [flattening 45]
47. (? [X0] : kind(X0) | funny(alice) | ~happy(alice)) & ((~funny(alice) & happy(alice)) | ! [X1] : ~kind(X1)) [rectify 46]
48. ? [X0] : kind(X0) => kind(sK1) [choice axiom]
49. (kind(sK1) | funny(alice) | ~happy(alice)) & ((~funny(alice) & happy(alice)) | ! [X1] : ~kind(X1)) [skolemisation 47,48]
50. ! [X0] : ((~curious(X0) | (~calm(X0) | ~old(X0))) & ((calm(X0) & old(X0)) | curious(X0))) [nnf transformation 5]
51. ! [X0] : ((~curious(X0) | ~calm(X0) | ~old(X0)) & ((calm(X0) & old(X0)) | curious(X0))) [flattening 50]
53. ! [X0] : ((((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (~generous(X0) & funny(X0))) & ((generous(X0) | ~funny(X0)) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))))) [nnf transformation 9]
54. ! [X0] : ((((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (~generous(X0) & funny(X0))) & (generous(X0) | ~funny(X0) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))))) [flattening 53]
55. ! [X0] : (((curious(X0) & calm(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (~curious(X0) | ~calm(X0)))) [nnf transformation 11]
56. ! [X0] : (((curious(X0) & calm(X0)) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | ~curious(X0) | ~calm(X0))) [flattening 55]
73. ~strong(X0) | calm(X0) [cnf transformation 32]
86. happy(alice) | ~kind(X1) [cnf transformation 49]
87. ~funny(alice) | ~kind(X1) [cnf transformation 49]
89. old(X0) | curious(X0) [cnf transformation 51]
99. ~old(X0) | ~happy(X0) | funny(X0) [cnf transformation 54]
103. ~curious(X0) | ~curious(X0) | ~calm(X0) [cnf transformation 56]
128. kind(john) [cnf transformation 20]
132. strong(alice) [cnf transformation 25]
135. ~curious(X0) | ~calm(X0) [duplicate literal removal 103]
166. 7 <=> happy(alice) [avatar definition]
167. happy(alice) <- (7) [avatar component clause 166]
170. 8 <=> funny(alice) [avatar definition]
171. ~funny(alice) <- (~8) [avatar component clause 170]
179. 10 <=> ! [X1] : ~kind(X1) [avatar definition]
180. ~kind(X1) <- (10) [avatar component clause 179]
181. 10 | ~8 [avatar split clause 87,170,179]
182. 10 | 7 [avatar split clause 86,166,179]
238. 24 <=> old(alice) [avatar definition]
239. ~old(alice) <- (~24) [avatar component clause 238]
240. old(alice) <- (24) [avatar component clause 238]
292. calm(alice) [resolution 73,132]
295. curious(alice) <- (~24) [resolution 89,239]
299. ~calm(alice) <- (~24) [resolution 135,295]
300. $false <- (~24) [subsumption resolution 299,292]
301. 24 [avatar contradiction clause 300]
318. $false <- (10) [resolution 180,128]
321. ~10 [avatar contradiction clause 318]
390. ~happy(alice) | funny(alice) <- (24) [resolution 99,240]
393. funny(alice) <- (7, 24) [subsumption resolution 390,167]
394. $false <- (7, ~8, 24) [subsumption resolution 393,171]
395. ~7 | 8 | ~24 [avatar contradiction clause 394]
405. $false [avatar sat refutation 181,182,301,321,395]
% SZS output end Proof for 1317832464548990548622250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not patient or not calm then fred is brave or humble. Everyone who is not kind is either not generous or quiet. If fred is tall then paul is strong or not quiet. Everyone who is not funny is not curious and vice versa. Everyone who is either rich or calm is not generous or curious. Everyone who is old or wise is both quiet and not wise and vice versa. If someone is both old and not funny then fred is both not generous and not wise and vice versa. If someone is humble or quiet then someone is creative or funny and vice versa. If alice is both not generous and not tall then someone is both not patient and strong. Everyone who is wise or not wise is both not generous and not humble and vice versa. If john is both not calm and strong then someone is both tall and humble. If alice is either not curious or not humble then someone is either strong or not wise. If mary is both not brave and strong then someone is old or not happy and vice versa. Everyone who is either curious or tall is either funny or not generous and vice versa. Everyone who is both quiet and not creative is wise or tall and vice versa. If paul is both not creative and wise then john is either humble or not kind and vice versa. Lucy is both not creative and calm. Someone is not happy. Paul is tall or not brave. Someone is both strong and not curious. John is wise or not patient. Someone is either not kind or not curious. Someone is not patient or humble. | Paul is not wise. | entailment | (((~patient(alice)|~calm(alice)))=>((brave(fred)|humble(fred))))&
(![X]:(~kind(X)=>(~generous(X)<~>quiet(X))))&
((tall(fred))=>((strong(paul)|~quiet(paul))))&
(![X]:(~funny(X)<=>~curious(X)))&
(![X]:((rich(X)<~>calm(X))=>(~generous(X)|curious(X))))&
(![X]:((old(X)|wise(X))<=>(quiet(X)&~wise(X))))&
((?[X]:((old(X)&~funny(X))))<=>((~generous(fred)&~wise(fred))))&
((?[X]:((humble(X)|quiet(X))))<=>(?[X]:((creative(X)|funny(X)))))&
(((~generous(alice)&~tall(alice)))=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:((wise(X)|~wise(X))<=>(~generous(X)&~humble(X))))&
(((~calm(john)&strong(john)))=>(?[X]:((tall(X)&humble(X)))))&
(((~curious(alice)<~>~humble(alice)))=>(?[X]:((strong(X)<~>~wise(X)))))&
(((~brave(mary)&strong(mary)))<=>(?[X]:((old(X)|~happy(X)))))&
(![X]:((curious(X)<~>tall(X))<=>(funny(X)<~>~generous(X))))&
(![X]:((quiet(X)&~creative(X))<=>(wise(X)|tall(X))))&
(((~creative(paul)&wise(paul)))<=>((humble(john)<~>~kind(john))))&
((~creative(lucy)&calm(lucy)))&
(?[X]:(~happy(X)))&
((tall(paul)|~brave(paul)))&
(?[X]:((strong(X)&~curious(X))))&
((wise(john)|~patient(john)))&
(?[X]:((~kind(X)<~>~curious(X))))&
(?[X]:((~patient(X)|humble(X)))) | ~wise(paul) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4501187449406964624267188
% SZS output start Proof for 4501187449406964624267188
6. ! [X0] : ((wise(X0) | old(X0)) <=> (~wise(X0) & quiet(X0))) [input p5]
24. wise(paul) [input hypothesis]
41. ! [X0] : (((wise(X0) | old(X0)) | (wise(X0) | ~quiet(X0))) & ((~wise(X0) & quiet(X0)) | (~wise(X0) & ~old(X0)))) [nnf transformation 6]
42. ! [X0] : ((wise(X0) | old(X0) | wise(X0) | ~quiet(X0)) & ((~wise(X0) & quiet(X0)) | (~wise(X0) & ~old(X0)))) [flattening 41]
93. ~wise(X0) | ~wise(X0) [cnf transformation 42]
150. wise(paul) [cnf transformation 24]
151. ~wise(X0) [duplicate literal removal 93]
364. $false [subsumption resolution 150,151]
% SZS output end Proof for 4501187449406964624267188
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall or not patient then fred is funny or not tall.
If someone is not calm or not patient then someone is wise and vice versa.
Everyone who is both not funny and not creative is either generous or quiet and vice versa.
Everyone who is tall or rich is either not wise or wise and vice versa.
If someone is brave then someone is both not brave and not curious and vice versa.
Everyone who is either not brave or not patient is brave and vice versa.
Everyone who is both creative and not strong is either not old or not wise and vice versa.
Everyone who is both not funny and quiet is both creative and happy.
Everyone who is both happy and not creative is both not kind and not wise and vice versa.
If someone is either humble or not happy then someone is not generous and vice versa.
Everyone who is both creative and patient is not humble or not curious.
If alice is not old or curious then someone is not tall and vice versa.
If alice is patient then mary is not happy and vice versa.
Everyone who is wise is not patient or not funny.
Everyone who is generous or not brave is not calm or not creative and vice versa.
If susan is funny or not old then someone is both tall and not kind and vice versa.
Someone is either not tall or not brave.
Alice is both strong and not happy.
Someone is not happy or happy.
Someone is not creative or not quiet.
Someone is either strong or wise.
Someone is either wise or not kind.
Mary is kind. | Susan is not kind. | neutral | ((?[X]:((~tall(X)|~patient(X))))=>((funny(fred)|~tall(fred))))&
((?[X]:((~calm(X)|~patient(X))))<=>(?[X]:(wise(X))))&
(![X]:((~funny(X)&~creative(X))<=>(generous(X)<~>quiet(X))))&
(![X]:((tall(X)|rich(X))<=>(~wise(X)<~>wise(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~brave(X)&~curious(X)))))&
(![X]:((~brave(X)<~>~patient(X))<=>brave(X)))&
(![X]:((creative(X)&~strong(X))<=>(~old(X)<~>~wise(X))))&
(![X]:((~funny(X)&quiet(X))=>(creative(X)&happy(X))))&
(![X]:((happy(X)&~creative(X))<=>(~kind(X)&~wise(X))))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:(~generous(X))))&
(![X]:((creative(X)&patient(X))=>(~humble(X)|~curious(X))))&
(((~old(alice)|curious(alice)))<=>(?[X]:(~tall(X))))&
((patient(alice))<=>(~happy(mary)))&
(![X]:(wise(X)=>(~patient(X)|~funny(X))))&
(![X]:((generous(X)|~brave(X))<=>(~calm(X)|~creative(X))))&
(((funny(susan)|~old(susan)))<=>(?[X]:((tall(X)&~kind(X)))))&
(?[X]:((~tall(X)<~>~brave(X))))&
((strong(alice)&~happy(alice)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((~creative(X)|~quiet(X))))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:((wise(X)<~>~kind(X))))&
(kind(mary)) | ~kind(susan) | [] | null | 0 |
If susan is both not happy and kind then someone is either not calm or wise and vice versa.
Everyone who is either happy or not humble is humble or tall and vice versa.
Everyone who is kind or calm is both patient and not quiet and vice versa.
Everyone who is not rich or happy is not kind.
Everyone who is either patient or generous is both kind and happy and vice versa.
If john is either not rich or old then paul is either humble or rich and vice versa.
If someone is both creative and quiet then someone is rich and vice versa.
Everyone who is calm is kind.
If someone is either not funny or happy then paul is both rich and not old and vice versa.
If someone is both not old and tall then paul is generous and vice versa.
If someone is not humble or brave then susan is rich or not curious.
Everyone who is happy is calm and vice versa.
Everyone who is both not patient and old is strong and vice versa.
Everyone who is not strong is both funny and not strong.
If paul is either not kind or not creative then fred is both calm and tall.
If someone is old then john is both kind and strong and vice versa.
Someone is not strong or quiet.
Someone is not brave or not tall.
Lucy is either not wise or not happy.
Mary is not happy.
Someone is not wise. | Susan is not rich. | contradiction | (((~happy(susan)&kind(susan)))<=>(?[X]:((~calm(X)<~>wise(X)))))&
(![X]:((happy(X)<~>~humble(X))<=>(humble(X)|tall(X))))&
(![X]:((kind(X)|calm(X))<=>(patient(X)&~quiet(X))))&
(![X]:((~rich(X)|happy(X))=>~kind(X)))&
(![X]:((patient(X)<~>generous(X))<=>(kind(X)&happy(X))))&
(((~rich(john)<~>old(john)))<=>((humble(paul)<~>rich(paul))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:(rich(X))))&
(![X]:(calm(X)=>kind(X)))&
((?[X]:((~funny(X)<~>happy(X))))<=>((rich(paul)&~old(paul))))&
((?[X]:((~old(X)&tall(X))))<=>(generous(paul)))&
((?[X]:((~humble(X)|brave(X))))=>((rich(susan)|~curious(susan))))&
(![X]:(happy(X)<=>calm(X)))&
(![X]:((~patient(X)&old(X))<=>strong(X)))&
(![X]:(~strong(X)=>(funny(X)&~strong(X))))&
(((~kind(paul)<~>~creative(paul)))=>((calm(fred)&tall(fred))))&
((?[X]:(old(X)))<=>((kind(john)&strong(john))))&
(?[X]:((~strong(X)|quiet(X))))&
(?[X]:((~brave(X)|~tall(X))))&
((~wise(lucy)<~>~happy(lucy)))&
(~happy(mary))&
(?[X]:(~wise(X))) | ~rich(susan) | [
"p0",
"p3",
"p7",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 141697683510189338577860
% SZS output start Proof for 141697683510189338577860
1. (kind(susan) & ~happy(susan)) <=> ? [X0] : (~calm(X0) <~> wise(X0)) [input p0]
4. ! [X0] : ((happy(X0) | ~rich(X0)) => ~kind(X0)) [input p3]
8. ! [X0] : (calm(X0) => kind(X0)) [input p7]
12. ! [X0] : (happy(X0) <=> calm(X0)) [input p11]
21. ? [X0] : ~wise(X0) [input p20]
22. ~rich(susan) [input hypothesis]
26. ! [X0] : (~kind(X0) | (~happy(X0) & rich(X0))) [ennf transformation 4]
27. ! [X0] : (kind(X0) | ~calm(X0)) [ennf transformation 8]
30. ((kind(susan) & ~happy(susan)) | ! [X0] : ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) & (? [X0] : ((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | (~kind(susan) | happy(susan))) [nnf transformation 1]
31. ((kind(susan) & ~happy(susan)) | ! [X0] : ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) & (? [X0] : ((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | ~kind(susan) | happy(susan)) [flattening 30]
32. ((kind(susan) & ~happy(susan)) | ! [X0] : ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) & (? [X1] : ((~wise(X1) | calm(X1)) & (wise(X1) | ~calm(X1))) | ~kind(susan) | happy(susan)) [rectify 31]
33. ? [X1] : ((~wise(X1) | calm(X1)) & (wise(X1) | ~calm(X1))) => ((~wise(sK0) | calm(sK0)) & (wise(sK0) | ~calm(sK0))) [choice axiom]
34. ((kind(susan) & ~happy(susan)) | ! [X0] : ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) & (((~wise(sK0) | calm(sK0)) & (wise(sK0) | ~calm(sK0))) | ~kind(susan) | happy(susan)) [skolemisation 32,33]
56. ! [X0] : ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))) [nnf transformation 12]
68. ? [X0] : ~wise(X0) => ~wise(sK7) [choice axiom]
69. ~wise(sK7) [skolemisation 21,68]
74. kind(susan) | wise(X0) | calm(X0) [cnf transformation 34]
87. ~kind(X0) | rich(X0) [cnf transformation 26]
88. ~kind(X0) | ~happy(X0) [cnf transformation 26]
106. ~calm(X0) | kind(X0) [cnf transformation 27]
117. ~calm(X0) | happy(X0) [cnf transformation 56]
134. ~wise(sK7) [cnf transformation 69]
135. ~rich(susan) [cnf transformation 22]
142. 2 <=> kind(susan) [avatar definition]
144. kind(susan) <- (2) [avatar component clause 142]
147. 3 <=> ! [X0] : (wise(X0) | calm(X0)) [avatar definition]
148. wise(X0) | calm(X0) <- (3) [avatar component clause 147]
149. 3 | 2 [avatar split clause 74,142,147]
318. rich(susan) <- (2) [resolution 87,144]
320. $false <- (2) [subsumption resolution 318,135]
321. ~2 [avatar contradiction clause 320]
342. calm(sK7) <- (3) [resolution 148,134]
365. happy(sK7) <- (3) [resolution 342,117]
366. kind(sK7) <- (3) [resolution 342,106]
399. ~happy(sK7) <- (3) [resolution 366,88]
402. $false <- (3) [subsumption resolution 399,365]
403. ~3 [avatar contradiction clause 402]
404. $false [avatar sat refutation 149,321,403]
% SZS output end Proof for 141697683510189338577860
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous or wise then someone is both not brave and humble and vice versa. Everyone who is not creative or creative is either rich or not tall and vice versa. Everyone who is not quiet or not humble is both not calm and old and vice versa. Everyone who is rich is old and vice versa. If alice is not happy or wise then fred is not funny. Everyone who is humble or patient is both not funny and funny and vice versa. Everyone who is quiet or rich is not patient and vice versa. Everyone who is not wise or not tall is not creative. If someone is not generous or not humble then someone is not curious. Everyone who is patient is not humble. Everyone who is happy or curious is not generous and vice versa. Everyone who is both not happy and not kind is either calm or not kind and vice versa. If someone is either not wise or not humble then someone is tall. Mary is not humble. Someone is strong or not calm. Mary is either strong or not calm. Someone is either quiet or creative. | Fred is not rich. | contradiction | ((?[X]:((~generous(X)|wise(X))))<=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:((~creative(X)|creative(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(~calm(X)&old(X))))&
(![X]:(rich(X)<=>old(X)))&
(((~happy(alice)|wise(alice)))=>(~funny(fred)))&
(![X]:((humble(X)|patient(X))<=>(~funny(X)&funny(X))))&
(![X]:((quiet(X)|rich(X))<=>~patient(X)))&
(![X]:((~wise(X)|~tall(X))=>~creative(X)))&
((?[X]:((~generous(X)|~humble(X))))=>(?[X]:(~curious(X))))&
(![X]:(patient(X)=>~humble(X)))&
(![X]:((happy(X)|curious(X))<=>~generous(X)))&
(![X]:((~happy(X)&~kind(X))<=>(calm(X)<~>~kind(X))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(tall(X))))&
(~humble(mary))&
(?[X]:((strong(X)|~calm(X))))&
((strong(mary)<~>~calm(mary)))&
(?[X]:((quiet(X)<~>creative(X)))) | ~rich(fred) | [
"p2",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2543267644960927627726171
% SZS output start Proof for 2543267644960927627726171
3. ! [X0] : ((~humble(X0) | ~quiet(X0)) <=> (old(X0) & ~calm(X0))) [input p2]
4. ! [X0] : (rich(X0) <=> old(X0)) [input p3]
6. ! [X0] : ((patient(X0) | humble(X0)) <=> (funny(X0) & ~funny(X0))) [input p5]
18. ~rich(fred) [input hypothesis]
34. ! [X0] : (((~humble(X0) | ~quiet(X0)) | (~old(X0) | calm(X0))) & ((old(X0) & ~calm(X0)) | (humble(X0) & quiet(X0)))) [nnf transformation 3]
35. ! [X0] : ((~humble(X0) | ~quiet(X0) | ~old(X0) | calm(X0)) & ((old(X0) & ~calm(X0)) | (humble(X0) & quiet(X0)))) [flattening 34]
36. ! [X0] : ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))) [nnf transformation 4]
37. ! [X0] : (((patient(X0) | humble(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (~patient(X0) & ~humble(X0)))) [nnf transformation 6]
38. ! [X0] : ((patient(X0) | humble(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (~patient(X0) & ~humble(X0)))) [flattening 37]
72. old(X0) | humble(X0) [cnf transformation 35]
75. ~old(X0) | rich(X0) [cnf transformation 36]
78. ~funny(X0) | ~humble(X0) [cnf transformation 38]
80. funny(X0) | ~humble(X0) [cnf transformation 38]
108. ~rich(fred) [cnf transformation 18]
158. ~humble(X0) [subsumption resolution 78,80]
203. rich(X0) | humble(X0) [resolution 75,72]
205. rich(X0) [subsumption resolution 203,158]
206. $false [resolution 205,108]
% SZS output end Proof for 2543267644960927627726171
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not brave or not rich then fred is both not brave and not wise.
Everyone who is patient or brave is not brave or not wise and vice versa.
Everyone who is either not kind or not creative is generous or not old.
Everyone who is both funny and not quiet is either generous or not curious.
Everyone who is not creative or old is kind or strong and vice versa.
If paul is creative then someone is both happy and not old and vice versa.
Everyone who is either not patient or funny is not happy.
Everyone who is either calm or not quiet is brave or not quiet and vice versa.
Everyone who is strong is funny.
If someone is old or not wise then paul is both creative and strong.
Everyone who is either quiet or creative is both patient and rich and vice versa.
Everyone who is either kind or not strong is both tall and creative.
If someone is either not old or not rich then someone is strong or patient and vice versa.
If someone is both quiet and not patient then lucy is funny or not strong and vice versa.
If lucy is either patient or not curious then fred is not kind or generous and vice versa.
Everyone who is both not curious and not strong is generous and vice versa.
Someone is both funny and old.
Fred is both strong and not generous.
Someone is old.
Someone is both kind and not calm.
Mary is either quiet or patient.
Someone is both happy and not tall.
Someone is either not creative or not strong. | Fred is tall. | neutral | (((~brave(alice)<~>~rich(alice)))=>((~brave(fred)&~wise(fred))))&
(![X]:((patient(X)|brave(X))<=>(~brave(X)|~wise(X))))&
(![X]:((~kind(X)<~>~creative(X))=>(generous(X)|~old(X))))&
(![X]:((funny(X)&~quiet(X))=>(generous(X)<~>~curious(X))))&
(![X]:((~creative(X)|old(X))<=>(kind(X)|strong(X))))&
((creative(paul))<=>(?[X]:((happy(X)&~old(X)))))&
(![X]:((~patient(X)<~>funny(X))=>~happy(X)))&
(![X]:((calm(X)<~>~quiet(X))<=>(brave(X)|~quiet(X))))&
(![X]:(strong(X)=>funny(X)))&
((?[X]:((old(X)|~wise(X))))=>((creative(paul)&strong(paul))))&
(![X]:((quiet(X)<~>creative(X))<=>(patient(X)&rich(X))))&
(![X]:((kind(X)<~>~strong(X))=>(tall(X)&creative(X))))&
((?[X]:((~old(X)<~>~rich(X))))<=>(?[X]:((strong(X)|patient(X)))))&
((?[X]:((quiet(X)&~patient(X))))<=>((funny(lucy)|~strong(lucy))))&
(((patient(lucy)<~>~curious(lucy)))<=>((~kind(fred)|generous(fred))))&
(![X]:((~curious(X)&~strong(X))<=>generous(X)))&
(?[X]:((funny(X)&old(X))))&
((strong(fred)&~generous(fred)))&
(?[X]:(old(X)))&
(?[X]:((kind(X)&~calm(X))))&
((quiet(mary)<~>patient(mary)))&
(?[X]:((happy(X)&~tall(X))))&
(?[X]:((~creative(X)<~>~strong(X)))) | tall(fred) | [] | null | 0 |
Everyone who is either not happy or tall is tall and vice versa.
Everyone who is either not quiet or not patient is both not tall and rich.
If someone is both not brave and kind then susan is brave.
If someone is either not calm or quiet then someone is wise or not tall and vice versa.
If mary is either tall or kind then mary is patient and vice versa.
Everyone who is not patient is not kind or not tall.
If someone is both quiet and humble then someone is not humble or creative.
Everyone who is not calm is not funny or rich and vice versa.
If mary is not curious or not rich then mary is not creative.
If someone is both funny and not patient then someone is old.
Everyone who is not old is not creative or not kind.
Everyone who is brave is either not rich or not quiet.
Everyone who is happy or tall is both not funny and not quiet and vice versa.
Everyone who is not brave or not happy is strong.
Everyone who is both tall and not tall is either not funny or not creative.
Susan is both not quiet and old.
John is both brave and not wise.
Mary is either not rich or calm.
Someone is humble or not strong.
Susan is not funny.
Someone is not humble or tall.
Someone is not humble. | John is not old. | neutral | (![X]:((~happy(X)<~>tall(X))<=>tall(X)))&
(![X]:((~quiet(X)<~>~patient(X))=>(~tall(X)&rich(X))))&
((?[X]:((~brave(X)&kind(X))))=>(brave(susan)))&
((?[X]:((~calm(X)<~>quiet(X))))<=>(?[X]:((wise(X)|~tall(X)))))&
(((tall(mary)<~>kind(mary)))<=>(patient(mary)))&
(![X]:(~patient(X)=>(~kind(X)|~tall(X))))&
((?[X]:((quiet(X)&humble(X))))=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:(~calm(X)<=>(~funny(X)|rich(X))))&
(((~curious(mary)|~rich(mary)))=>(~creative(mary)))&
((?[X]:((funny(X)&~patient(X))))=>(?[X]:(old(X))))&
(![X]:(~old(X)=>(~creative(X)|~kind(X))))&
(![X]:(brave(X)=>(~rich(X)<~>~quiet(X))))&
(![X]:((happy(X)|tall(X))<=>(~funny(X)&~quiet(X))))&
(![X]:((~brave(X)|~happy(X))=>strong(X)))&
(![X]:((tall(X)&~tall(X))=>(~funny(X)<~>~creative(X))))&
((~quiet(susan)&old(susan)))&
((brave(john)&~wise(john)))&
((~rich(mary)<~>calm(mary)))&
(?[X]:((humble(X)|~strong(X))))&
(~funny(susan))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:(~humble(X))) | ~old(john) | [] | null | 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. | Lucy is not happy. | neutral | (![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))) | ~happy(lucy) | [] | null | 0 |
If alice is not funny or not happy then susan is not calm and vice versa.
If john is not kind then paul is wise and vice versa.
Everyone who is not wise is either generous or not patient and vice versa.
Everyone who is brave is either not quiet or not patient and vice versa.
Everyone who is both not patient and quiet is both not old and not tall and vice versa.
If john is both not curious and not funny then lucy is either brave or creative and vice versa.
Everyone who is tall or creative is both old and not tall and vice versa.
If paul is generous then someone is funny or not quiet and vice versa.
If someone is either brave or not brave then susan is either not brave or happy.
If someone is not creative or not wise then someone is tall or not rich and vice versa.
Everyone who is either not old or not wise is either creative or humble.
Everyone who is curious is both not patient and happy and vice versa.
Everyone who is humble is not wise or calm.
If someone is generous then someone is either funny or quiet and vice versa.
If someone is either not patient or tall then someone is either not humble or happy and vice versa.
If susan is both humble and not wise then mary is old or quiet and vice versa.
Someone is not strong or humble.
Someone is both not creative and wise.
Someone is generous or not curious.
Someone is either not happy or not brave.
Paul is creative.
Someone is either funny or not humble.
Fred is not curious.
Someone is kind. | Susan is not happy. | contradiction | (((~funny(alice)|~happy(alice)))<=>(~calm(susan)))&
((~kind(john))<=>(wise(paul)))&
(![X]:(~wise(X)<=>(generous(X)<~>~patient(X))))&
(![X]:(brave(X)<=>(~quiet(X)<~>~patient(X))))&
(![X]:((~patient(X)&quiet(X))<=>(~old(X)&~tall(X))))&
(((~curious(john)&~funny(john)))<=>((brave(lucy)<~>creative(lucy))))&
(![X]:((tall(X)|creative(X))<=>(old(X)&~tall(X))))&
((generous(paul))<=>(?[X]:((funny(X)|~quiet(X)))))&
((?[X]:((brave(X)<~>~brave(X))))=>((~brave(susan)<~>happy(susan))))&
((?[X]:((~creative(X)|~wise(X))))<=>(?[X]:((tall(X)|~rich(X)))))&
(![X]:((~old(X)<~>~wise(X))=>(creative(X)<~>humble(X))))&
(![X]:(curious(X)<=>(~patient(X)&happy(X))))&
(![X]:(humble(X)=>(~wise(X)|calm(X))))&
((?[X]:(generous(X)))<=>(?[X]:((funny(X)<~>quiet(X)))))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((~humble(X)<~>happy(X)))))&
(((humble(susan)&~wise(susan)))<=>((old(mary)|quiet(mary))))&
(?[X]:((~strong(X)|humble(X))))&
(?[X]:((~creative(X)&wise(X))))&
(?[X]:((generous(X)|~curious(X))))&
(?[X]:((~happy(X)<~>~brave(X))))&
(creative(paul))&
(?[X]:((funny(X)<~>~humble(X))))&
(~curious(fred))&
(?[X]:(kind(X))) | ~happy(susan) | [
"p3",
"p4",
"p6",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8514230471632761961106131
% SZS output start Proof for 8514230471632761961106131
4. ! [X0] : (brave(X0) <=> (~quiet(X0) <~> ~patient(X0))) [input p3]
5. ! [X0] : ((quiet(X0) & ~patient(X0)) <=> (~tall(X0) & ~old(X0))) [input p4]
7. ! [X0] : ((creative(X0) | tall(X0)) <=> (~tall(X0) & old(X0))) [input p6]
9. ? [X0] : (brave(X0) <~> ~brave(X0)) => (~brave(susan) <~> happy(susan)) [input p8]
11. ! [X0] : ((~old(X0) <~> ~wise(X0)) => (creative(X0) <~> humble(X0))) [input p10]
16. (~wise(susan) & humble(susan)) <=> (quiet(mary) | old(mary)) [input p15]
25. ~happy(susan) [input hypothesis]
30. (~brave(susan) <~> happy(susan)) | ! [X0] : (brave(X0) <=> ~brave(X0)) [ennf transformation 9]
31. ! [X0] : ((creative(X0) <~> humble(X0)) | (~old(X0) <=> ~wise(X0))) [ennf transformation 11]
38. ! [X0] : ((brave(X0) | ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0)))) & (((patient(X0) | quiet(X0)) & (~patient(X0) | ~quiet(X0))) | ~brave(X0))) [nnf transformation 4]
39. ! [X0] : (((quiet(X0) & ~patient(X0)) | (tall(X0) | old(X0))) & ((~tall(X0) & ~old(X0)) | (~quiet(X0) | patient(X0)))) [nnf transformation 5]
40. ! [X0] : (((quiet(X0) & ~patient(X0)) | tall(X0) | old(X0)) & ((~tall(X0) & ~old(X0)) | ~quiet(X0) | patient(X0))) [flattening 39]
43. ! [X0] : (((creative(X0) | tall(X0)) | (tall(X0) | ~old(X0))) & ((~tall(X0) & old(X0)) | (~creative(X0) & ~tall(X0)))) [nnf transformation 7]
44. ! [X0] : ((creative(X0) | tall(X0) | tall(X0) | ~old(X0)) & ((~tall(X0) & old(X0)) | (~creative(X0) & ~tall(X0)))) [flattening 43]
49. ((~happy(susan) | brave(susan)) & (happy(susan) | ~brave(susan))) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0))) [nnf transformation 30]
55. ! [X0] : (((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0)))) [nnf transformation 31]
68. ((~wise(susan) & humble(susan)) | (~quiet(mary) & ~old(mary))) & ((quiet(mary) | old(mary)) | (wise(susan) | ~humble(susan))) [nnf transformation 16]
69. ((~wise(susan) & humble(susan)) | (~quiet(mary) & ~old(mary))) & (quiet(mary) | old(mary) | wise(susan) | ~humble(susan)) [flattening 68]
94. ~quiet(X0) | brave(X0) | patient(X0) [cnf transformation 38]
97. ~patient(X0) | tall(X0) | old(X0) [cnf transformation 40]
98. tall(X0) | quiet(X0) | old(X0) [cnf transformation 40]
106. ~creative(X0) | old(X0) [cnf transformation 44]
107. ~tall(X0) | ~tall(X0) [cnf transformation 44]
109. creative(X0) | tall(X0) | tall(X0) | ~old(X0) [cnf transformation 44]
113. happy(susan) | ~brave(susan) | ~brave(X0) | ~brave(X0) [cnf transformation 49]
124. ~humble(X0) | ~creative(X0) | ~old(X0) | wise(X0) [cnf transformation 55]
142. humble(susan) | ~old(mary) [cnf transformation 69]
143. humble(susan) | ~quiet(mary) [cnf transformation 69]
144. ~wise(susan) | ~old(mary) [cnf transformation 69]
145. ~wise(susan) | ~quiet(mary) [cnf transformation 69]
156. ~happy(susan) [cnf transformation 25]
157. happy(susan) | ~brave(susan) | ~brave(X0) [duplicate literal removal 113]
161. ~tall(X0) [duplicate literal removal 107]
162. ~old(X0) | tall(X0) | creative(X0) [duplicate literal removal 109]
235. 16 <=> brave(susan) [avatar definition]
236. ~brave(susan) <- (~16) [avatar component clause 235]
237. brave(susan) <- (16) [avatar component clause 235]
239. 17 <=> happy(susan) [avatar definition]
244. 18 <=> ! [X0] : ~brave(X0) [avatar definition]
245. ~brave(X0) <- (18) [avatar component clause 244]
248. 18 | ~16 | 17 [avatar split clause 157,239,235,244]
275. ~humble(X0) | ~creative(X0) | wise(X0) [subsumption resolution 124,106]
332. 37 <=> quiet(mary) [avatar definition]
336. 38 <=> wise(susan) [avatar definition]
338. ~wise(susan) <- (~38) [avatar component clause 336]
339. ~37 | ~38 [avatar split clause 145,336,332]
341. 39 <=> old(mary) [avatar definition]
343. ~old(mary) <- (~39) [avatar component clause 341]
344. ~39 | ~38 [avatar split clause 144,336,341]
346. 40 <=> humble(susan) [avatar definition]
348. humble(susan) <- (40) [avatar component clause 346]
349. ~37 | 40 [avatar split clause 143,346,332]
350. ~39 | 40 [avatar split clause 142,346,341]
381. ~17 [avatar split clause 156,239]
516. old(X1) | quiet(X1) [resolution 98,161]
579. quiet(mary) <- (~39) [resolution 516,343]
581. quiet(X1) | tall(X1) | creative(X1) [resolution 516,162]
586. creative(X1) | quiet(X1) [subsumption resolution 581,161]
589. 37 | 39 [avatar split clause 579,341,332]
603. ~creative(susan) | wise(susan) <- (40) [resolution 348,275]
605. ~creative(susan) <- (~38, 40) [subsumption resolution 603,338]
650. quiet(susan) <- (~38, 40) [resolution 586,605]
658. brave(susan) | patient(susan) <- (~38, 40) [resolution 650,94]
660. patient(susan) <- (~16, ~38, 40) [subsumption resolution 658,236]
661. tall(susan) | old(susan) <- (~16, ~38, 40) [resolution 660,97]
665. old(susan) <- (~16, ~38, 40) [subsumption resolution 661,161]
668. tall(susan) | creative(susan) <- (~16, ~38, 40) [resolution 665,162]
670. creative(susan) <- (~16, ~38, 40) [subsumption resolution 668,161]
671. $false <- (~16, ~38, 40) [subsumption resolution 670,605]
672. 16 | 38 | ~40 [avatar contradiction clause 671]
679. $false <- (16, 18) [subsumption resolution 237,245]
680. ~16 | ~18 [avatar contradiction clause 679]
683. $false [avatar sat refutation 248,339,344,349,350,381,589,672,680]
% SZS output end Proof for 8514230471632761961106131
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then someone is both old and not kind.
If someone is not patient or not strong then alice is wise and vice versa.
Everyone who is both not calm and quiet is both not quiet and quiet.
If alice is both brave and old then someone is not quiet or not calm.
If someone is not funny or funny then someone is happy and vice versa.
Everyone who is either not funny or brave is either kind or curious and vice versa.
If susan is both calm and not happy then lucy is curious.
If john is both not tall and brave then fred is not patient or tall and vice versa.
If mary is brave then susan is either not old or not brave.
Everyone who is not old is both brave and not creative and vice versa.
Everyone who is either calm or wise is either funny or not humble.
If someone is not kind then john is either not strong or calm and vice versa.
Everyone who is strong is either not patient or funny and vice versa.
If alice is not old or not humble then someone is calm or not happy.
Everyone who is either patient or not quiet is strong.
Everyone who is not wise or patient is both curious and not funny.
Mary is either wise or not rich.
Susan is brave or not humble.
Lucy is wise.
Someone is creative.
Someone is both happy and curious.
Lucy is both calm and not old.
John is both not tall and kind.
Someone is both kind and calm. | John is kind. | entailment | ((?[X]:(~quiet(X)))=>(?[X]:((old(X)&~kind(X)))))&
((?[X]:((~patient(X)|~strong(X))))<=>(wise(alice)))&
(![X]:((~calm(X)&quiet(X))=>(~quiet(X)&quiet(X))))&
(((brave(alice)&old(alice)))=>(?[X]:((~quiet(X)|~calm(X)))))&
((?[X]:((~funny(X)|funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((~funny(X)<~>brave(X))<=>(kind(X)<~>curious(X))))&
(((calm(susan)&~happy(susan)))=>(curious(lucy)))&
(((~tall(john)&brave(john)))<=>((~patient(fred)|tall(fred))))&
((brave(mary))=>((~old(susan)<~>~brave(susan))))&
(![X]:(~old(X)<=>(brave(X)&~creative(X))))&
(![X]:((calm(X)<~>wise(X))=>(funny(X)<~>~humble(X))))&
((?[X]:(~kind(X)))<=>((~strong(john)<~>calm(john))))&
(![X]:(strong(X)<=>(~patient(X)<~>funny(X))))&
(((~old(alice)|~humble(alice)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((patient(X)<~>~quiet(X))=>strong(X)))&
(![X]:((~wise(X)|patient(X))=>(curious(X)&~funny(X))))&
((wise(mary)<~>~rich(mary)))&
((brave(susan)|~humble(susan)))&
(wise(lucy))&
(?[X]:(creative(X)))&
(?[X]:((happy(X)&curious(X))))&
((calm(lucy)&~old(lucy)))&
((~tall(john)&kind(john)))&
(?[X]:((kind(X)&calm(X)))) | kind(john) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6021748758168323188634503
% SZS output start Proof for 6021748758168323188634503
23. kind(john) & ~tall(john) [input p22]
25. ~kind(john) [input hypothesis]
136. kind(john) [cnf transformation 23]
139. ~kind(john) [cnf transformation 25]
298. $false [subsumption resolution 139,136]
% SZS output end Proof for 6021748758168323188634503
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then fred is either kind or happy and vice versa.
Everyone who is not generous or not calm is not old or wise.
Everyone who is both tall and curious is either funny or not humble and vice versa.
Everyone who is both creative and curious is not happy and vice versa.
Everyone who is both not rich and happy is creative and vice versa.
If someone is both not brave and not funny then someone is either not brave or curious and vice versa.
Everyone who is either generous or not quiet is not funny or rich and vice versa.
Everyone who is both not calm and calm is not old.
Everyone who is either not generous or not kind is not quiet or curious.
Everyone who is wise or quiet is either not happy or not old and vice versa.
If lucy is either not calm or strong then alice is wise or not kind.
If mary is either patient or wise then someone is not kind or not generous and vice versa.
Everyone who is both not kind and kind is both old and curious.
If susan is both not creative and brave then someone is not calm and vice versa.
Everyone who is not rich or happy is generous and vice versa.
If someone is not kind then john is either not generous or not tall and vice versa.
John is not calm or calm.
Someone is not funny or tall.
Someone is calm or not rich.
Someone is not calm or calm.
Someone is both not tall and curious.
Someone is both not calm and not old.
Paul is not tall or not creative. | John is wise. | neutral | ((?[X]:(calm(X)))<=>((kind(fred)<~>happy(fred))))&
(![X]:((~generous(X)|~calm(X))=>(~old(X)|wise(X))))&
(![X]:((tall(X)&curious(X))<=>(funny(X)<~>~humble(X))))&
(![X]:((creative(X)&curious(X))<=>~happy(X)))&
(![X]:((~rich(X)&happy(X))<=>creative(X)))&
((?[X]:((~brave(X)&~funny(X))))<=>(?[X]:((~brave(X)<~>curious(X)))))&
(![X]:((generous(X)<~>~quiet(X))<=>(~funny(X)|rich(X))))&
(![X]:((~calm(X)&calm(X))=>~old(X)))&
(![X]:((~generous(X)<~>~kind(X))=>(~quiet(X)|curious(X))))&
(![X]:((wise(X)|quiet(X))<=>(~happy(X)<~>~old(X))))&
(((~calm(lucy)<~>strong(lucy)))=>((wise(alice)|~kind(alice))))&
(((patient(mary)<~>wise(mary)))<=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:((~kind(X)&kind(X))=>(old(X)&curious(X))))&
(((~creative(susan)&brave(susan)))<=>(?[X]:(~calm(X))))&
(![X]:((~rich(X)|happy(X))<=>generous(X)))&
((?[X]:(~kind(X)))<=>((~generous(john)<~>~tall(john))))&
((~calm(john)|calm(john)))&
(?[X]:((~funny(X)|tall(X))))&
(?[X]:((calm(X)|~rich(X))))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((~tall(X)&curious(X))))&
(?[X]:((~calm(X)&~old(X))))&
((~tall(paul)|~creative(paul))) | wise(john) | [] | null | 0 |
Everyone who is both not curious and old is both calm and creative and vice versa. Everyone who is both not calm and calm is either not quiet or not happy. If fred is not humble then fred is humble. Everyone who is either brave or not creative is both not creative and wise and vice versa. If susan is both not strong and not happy then someone is both generous and kind and vice versa. Everyone who is generous is either old or creative and vice versa. Everyone who is either creative or not old is either not brave or not tall and vice versa. If fred is both generous and funny then someone is both not creative and kind and vice versa. If someone is both not tall and old then paul is not generous or not strong and vice versa. If someone is patient or generous then paul is not rich or curious and vice versa. Everyone who is not humble or not calm is both not brave and quiet. Everyone who is either not quiet or not curious is both generous and not calm and vice versa. If mary is not generous then alice is not funny and vice versa. If someone is generous then lucy is either not calm or curious. Everyone who is both creative and kind is not humble or not creative. Everyone who is both not brave and tall is both not tall and not strong. Alice is tall. Paul is not wise. Someone is both curious and not patient. Someone is not wise or not funny. Someone is either curious or not wise. Someone is either not humble or creative. Someone is creative. Fred is funny. | Alice is creative. | contradiction | (![X]:((~curious(X)&old(X))<=>(calm(X)&creative(X))))&
(![X]:((~calm(X)&calm(X))=>(~quiet(X)<~>~happy(X))))&
((~humble(fred))=>(humble(fred)))&
(![X]:((brave(X)<~>~creative(X))<=>(~creative(X)&wise(X))))&
(((~strong(susan)&~happy(susan)))<=>(?[X]:((generous(X)&kind(X)))))&
(![X]:(generous(X)<=>(old(X)<~>creative(X))))&
(![X]:((creative(X)<~>~old(X))<=>(~brave(X)<~>~tall(X))))&
(((generous(fred)&funny(fred)))<=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:((~tall(X)&old(X))))<=>((~generous(paul)|~strong(paul))))&
((?[X]:((patient(X)|generous(X))))<=>((~rich(paul)|curious(paul))))&
(![X]:((~humble(X)|~calm(X))=>(~brave(X)&quiet(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(generous(X)&~calm(X))))&
((~generous(mary))<=>(~funny(alice)))&
((?[X]:(generous(X)))=>((~calm(lucy)<~>curious(lucy))))&
(![X]:((creative(X)&kind(X))=>(~humble(X)|~creative(X))))&
(![X]:((~brave(X)&tall(X))=>(~tall(X)&~strong(X))))&
(tall(alice))&
(~wise(paul))&
(?[X]:((curious(X)&~patient(X))))&
(?[X]:((~wise(X)|~funny(X))))&
(?[X]:((curious(X)<~>~wise(X))))&
(?[X]:((~humble(X)<~>creative(X))))&
(?[X]:(creative(X)))&
(funny(fred)) | creative(alice) | [
"p3",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 120401689794819445871808
% SZS output start Proof for 120401689794819445871808
4. ! [X0] : ((brave(X0) <~> ~creative(X0)) <=> (wise(X0) & ~creative(X0))) [input p3]
16. ! [X0] : ((tall(X0) & ~brave(X0)) => (~strong(X0) & ~tall(X0))) [input p15]
17. tall(alice) [input p16]
25. creative(alice) [input hypothesis]
33. ! [X0] : ((~strong(X0) & ~tall(X0)) | (~tall(X0) | brave(X0))) [ennf transformation 16]
34. ! [X0] : ((~strong(X0) & ~tall(X0)) | ~tall(X0) | brave(X0)) [flattening 33]
38. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | (~wise(X0) | creative(X0))) & ((wise(X0) & ~creative(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [nnf transformation 4]
39. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | ~wise(X0) | creative(X0)) & ((wise(X0) & ~creative(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [flattening 38]
85. ~creative(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 39]
135. ~tall(X0) | ~tall(X0) | brave(X0) [cnf transformation 34]
137. tall(alice) [cnf transformation 17]
148. creative(alice) [cnf transformation 25]
149. ~tall(X0) | brave(X0) [duplicate literal removal 135]
151. ~brave(X0) | ~creative(X0) [duplicate literal removal 85]
307. brave(alice) [resolution 149,137]
308. ~creative(alice) [resolution 307,151]
311. $false [subsumption resolution 308,148]
% SZS output end Proof for 120401689794819445871808
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not rich or wise then someone is either quiet or not calm. If mary is calm then someone is happy or rich and vice versa. If john is either brave or old then someone is either old or not curious and vice versa. Everyone who is old or not brave is both not patient and curious. If someone is not creative or calm then someone is both strong and not creative. Everyone who is not tall or funny is either calm or not happy. Everyone who is both creative and brave is both creative and not kind and vice versa. If someone is both happy and not calm then john is both not humble and not rich. Everyone who is calm is both old and patient and vice versa. Everyone who is both generous and quiet is either not brave or tall. Everyone who is both kind and brave is both not patient and not tall. Everyone who is either not funny or rich is either not curious or not kind. Everyone who is not brave or not quiet is funny or not calm and vice versa. Everyone who is not rich or humble is strong or humble. Everyone who is both funny and not curious is curious and vice versa. If someone is both not strong and wise then alice is happy and vice versa. John is both not curious and not funny. Someone is not creative or not happy. Someone is either not kind or not wise. Lucy is not curious. Someone is not calm. | Mary is not tall. | entailment | (((~rich(susan)<~>wise(susan)))=>(?[X]:((quiet(X)<~>~calm(X)))))&
((calm(mary))<=>(?[X]:((happy(X)|rich(X)))))&
(((brave(john)<~>old(john)))<=>(?[X]:((old(X)<~>~curious(X)))))&
(![X]:((old(X)|~brave(X))=>(~patient(X)&curious(X))))&
((?[X]:((~creative(X)|calm(X))))=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((~tall(X)|funny(X))=>(calm(X)<~>~happy(X))))&
(![X]:((creative(X)&brave(X))<=>(creative(X)&~kind(X))))&
((?[X]:((happy(X)&~calm(X))))=>((~humble(john)&~rich(john))))&
(![X]:(calm(X)<=>(old(X)&patient(X))))&
(![X]:((generous(X)&quiet(X))=>(~brave(X)<~>tall(X))))&
(![X]:((kind(X)&brave(X))=>(~patient(X)&~tall(X))))&
(![X]:((~funny(X)<~>rich(X))=>(~curious(X)<~>~kind(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(funny(X)|~calm(X))))&
(![X]:((~rich(X)|humble(X))=>(strong(X)|humble(X))))&
(![X]:((funny(X)&~curious(X))<=>curious(X)))&
((?[X]:((~strong(X)&wise(X))))<=>(happy(alice)))&
((~curious(john)&~funny(john)))&
(?[X]:((~creative(X)|~happy(X))))&
(?[X]:((~kind(X)<~>~wise(X))))&
(~curious(lucy))&
(?[X]:(~calm(X))) | ~tall(mary) | [
"p1",
"p3",
"p8",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1397217714883554171653938
% SZS output start Proof for 1397217714883554171653938
2. calm(mary) <=> ? [X0] : (rich(X0) | happy(X0)) [input p1]
4. ! [X0] : ((~brave(X0) | old(X0)) => (curious(X0) & ~patient(X0))) [input p3]
9. ! [X0] : (calm(X0) <=> (patient(X0) & old(X0))) [input p8]
11. ! [X0] : ((brave(X0) & kind(X0)) => (~tall(X0) & ~patient(X0))) [input p10]
12. ! [X0] : ((~funny(X0) <~> rich(X0)) => (~curious(X0) <~> ~kind(X0))) [input p11]
15. ! [X0] : ((~curious(X0) & funny(X0)) <=> curious(X0)) [input p14]
22. tall(mary) [input hypothesis]
26. ! [X0] : ((curious(X0) & ~patient(X0)) | (brave(X0) & ~old(X0))) [ennf transformation 4]
30. ! [X0] : ((~tall(X0) & ~patient(X0)) | (~brave(X0) | ~kind(X0))) [ennf transformation 11]
31. ! [X0] : ((~tall(X0) & ~patient(X0)) | ~brave(X0) | ~kind(X0)) [flattening 30]
32. ! [X0] : ((~curious(X0) <~> ~kind(X0)) | (~funny(X0) <=> rich(X0))) [ennf transformation 12]
38. (calm(mary) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X0] : (rich(X0) | happy(X0)) | ~calm(mary)) [nnf transformation 2]
39. (calm(mary) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X1] : (rich(X1) | happy(X1)) | ~calm(mary)) [rectify 38]
40. ? [X1] : (rich(X1) | happy(X1)) => (rich(sK1) | happy(sK1)) [choice axiom]
41. (calm(mary) | ! [X0] : (~rich(X0) & ~happy(X0))) & ((rich(sK1) | happy(sK1)) | ~calm(mary)) [skolemisation 39,40]
52. ! [X0] : ((calm(X0) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ~calm(X0))) [nnf transformation 9]
53. ! [X0] : ((calm(X0) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ~calm(X0))) [flattening 52]
54. ! [X0] : (((kind(X0) | curious(X0)) & (~kind(X0) | ~curious(X0))) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) [nnf transformation 32]
57. ! [X0] : (((~curious(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~funny(X0)))) [nnf transformation 15]
58. ! [X0] : (((~curious(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~funny(X0))) [flattening 57]
76. calm(mary) | ~rich(X0) [cnf transformation 41]
87. ~old(X0) | curious(X0) [cnf transformation 26]
88. curious(X0) | brave(X0) [cnf transformation 26]
103. ~calm(X0) | old(X0) [cnf transformation 53]
107. ~kind(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 31]
110. kind(X0) | curious(X0) | rich(X0) | funny(X0) [cnf transformation 54]
118. curious(X0) | curious(X0) | ~funny(X0) [cnf transformation 58]
120. ~curious(X0) | ~curious(X0) [cnf transformation 58]
131. tall(mary) [cnf transformation 22]
132. curious(X0) | ~funny(X0) [duplicate literal removal 118]
133. ~curious(X0) [duplicate literal removal 120]
155. 5 <=> ! [X0] : ~rich(X0) [avatar definition]
156. ~rich(X0) <- (5) [avatar component clause 155]
158. 6 <=> calm(mary) [avatar definition]
160. calm(mary) <- (6) [avatar component clause 158]
161. 5 | 6 [avatar split clause 76,158,155]
237. ~funny(X0) [subsumption resolution 132,133]
281. brave(X0) [resolution 88,133]
282. old(mary) <- (6) [resolution 103,160]
283. curious(mary) <- (6) [resolution 282,87]
284. $false <- (6) [subsumption resolution 283,133]
285. ~6 [avatar contradiction clause 284]
313. curious(X2) | rich(X2) | funny(X2) | ~brave(X2) | ~tall(X2) [resolution 110,107]
317. rich(X2) | funny(X2) | ~brave(X2) | ~tall(X2) [subsumption resolution 313,133]
318. funny(X2) | ~brave(X2) | ~tall(X2) <- (5) [subsumption resolution 317,156]
319. ~brave(X2) | ~tall(X2) <- (5) [subsumption resolution 318,237]
320. ~tall(X2) <- (5) [subsumption resolution 319,281]
328. $false <- (5) [resolution 320,131]
329. ~5 [avatar contradiction clause 328]
330. $false [avatar sat refutation 161,285,329]
% SZS output end Proof for 1397217714883554171653938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not humble then susan is both funny and not happy and vice versa. Everyone who is both not curious and rich is either calm or not brave. Everyone who is either funny or curious is both creative and not old and vice versa. Everyone who is both old and kind is both generous and not curious. If someone is not calm then fred is calm or not humble. Everyone who is both not calm and wise is brave or not wise. If someone is not happy then someone is either wise or old and vice versa. Everyone who is both not rich and patient is both not generous and generous and vice versa. If someone is either not curious or not happy then alice is both patient and funny. Everyone who is both not quiet and brave is both humble and tall and vice versa. If someone is both not humble and rich then someone is patient or generous. Everyone who is either not brave or not old is not creative. Everyone who is not old or patient is both not curious and not creative and vice versa. Everyone who is both strong and old is quiet or not humble. Everyone who is either curious or calm is both not brave and not quiet. Everyone who is not old or brave is both curious and old and vice versa. Susan is not quiet. Someone is either rich or curious. Someone is either not brave or old. Someone is kind. John is not funny or not creative. Mary is both not patient and not strong. Fred is either patient or humble. | Fred is funny. | entailment | ((~humble(fred))<=>((funny(susan)&~happy(susan))))&
(![X]:((~curious(X)&rich(X))=>(calm(X)<~>~brave(X))))&
(![X]:((funny(X)<~>curious(X))<=>(creative(X)&~old(X))))&
(![X]:((old(X)&kind(X))=>(generous(X)&~curious(X))))&
((?[X]:(~calm(X)))=>((calm(fred)|~humble(fred))))&
(![X]:((~calm(X)&wise(X))=>(brave(X)|~wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((~rich(X)&patient(X))<=>(~generous(X)&generous(X))))&
((?[X]:((~curious(X)<~>~happy(X))))=>((patient(alice)&funny(alice))))&
(![X]:((~quiet(X)&brave(X))<=>(humble(X)&tall(X))))&
((?[X]:((~humble(X)&rich(X))))=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~brave(X)<~>~old(X))=>~creative(X)))&
(![X]:((~old(X)|patient(X))<=>(~curious(X)&~creative(X))))&
(![X]:((strong(X)&old(X))=>(quiet(X)|~humble(X))))&
(![X]:((curious(X)<~>calm(X))=>(~brave(X)&~quiet(X))))&
(![X]:((~old(X)|brave(X))<=>(curious(X)&old(X))))&
(~quiet(susan))&
(?[X]:((rich(X)<~>curious(X))))&
(?[X]:((~brave(X)<~>old(X))))&
(?[X]:(kind(X)))&
((~funny(john)|~creative(john)))&
((~patient(mary)&~strong(mary)))&
((patient(fred)<~>humble(fred))) | funny(fred) | [
"p0",
"p2",
"p8",
"p11",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6565927815483852660498479
% SZS output start Proof for 6565927815483852660498479
1. ~humble(fred) <=> (~happy(susan) & funny(susan)) [input p0]
3. ! [X0] : ((funny(X0) <~> curious(X0)) <=> (~old(X0) & creative(X0))) [input p2]
9. ? [X0] : (~curious(X0) <~> ~happy(X0)) => (funny(alice) & patient(alice)) [input p8]
12. ! [X0] : ((~brave(X0) <~> ~old(X0)) => ~creative(X0)) [input p11]
13. ! [X0] : ((patient(X0) | ~old(X0)) <=> (~creative(X0) & ~curious(X0))) [input p12]
16. ! [X0] : ((brave(X0) | ~old(X0)) <=> (old(X0) & curious(X0))) [input p15]
23. patient(fred) <~> humble(fred) [input p22]
24. ~funny(fred) [input hypothesis]
37. (funny(alice) & patient(alice)) | ! [X0] : (~curious(X0) <=> ~happy(X0)) [ennf transformation 9]
39. ! [X0] : (~creative(X0) | (~brave(X0) <=> ~old(X0))) [ennf transformation 12]
41. (~humble(fred) | (happy(susan) | ~funny(susan))) & ((~happy(susan) & funny(susan)) | humble(fred)) [nnf transformation 1]
42. (~humble(fred) | happy(susan) | ~funny(susan)) & ((~happy(susan) & funny(susan)) | humble(fred)) [flattening 41]
44. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | (old(X0) | ~creative(X0))) & ((~old(X0) & creative(X0)) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 3]
45. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | old(X0) | ~creative(X0)) & ((~old(X0) & creative(X0)) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [flattening 44]
53. (funny(alice) & patient(alice)) | ! [X0] : ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0))) [nnf transformation 37]
59. ! [X0] : (~creative(X0) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) [nnf transformation 39]
60. ! [X0] : (((patient(X0) | ~old(X0)) | (creative(X0) | curious(X0))) & ((~creative(X0) & ~curious(X0)) | (~patient(X0) & old(X0)))) [nnf transformation 13]
61. ! [X0] : ((patient(X0) | ~old(X0) | creative(X0) | curious(X0)) & ((~creative(X0) & ~curious(X0)) | (~patient(X0) & old(X0)))) [flattening 60]
63. ! [X0] : (((brave(X0) | ~old(X0)) | (~old(X0) | ~curious(X0))) & ((old(X0) & curious(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 16]
64. ! [X0] : ((brave(X0) | ~old(X0) | ~old(X0) | ~curious(X0)) & ((old(X0) & curious(X0)) | (~brave(X0) & old(X0)))) [flattening 63]
73. (~humble(fred) | ~patient(fred)) & (humble(fred) | patient(fred)) [nnf transformation 23]
74. funny(susan) | humble(fred) [cnf transformation 42]
75. ~happy(susan) | humble(fred) [cnf transformation 42]
81. ~old(X0) | curious(X0) | ~funny(X0) [cnf transformation 45]
82. ~old(X0) | funny(X0) | ~curious(X0) [cnf transformation 45]
98. patient(alice) | ~curious(X0) | happy(X0) [cnf transformation 53]
100. funny(alice) | ~curious(X0) | happy(X0) [cnf transformation 53]
106. ~old(X0) | ~creative(X0) | brave(X0) [cnf transformation 59]
109. ~patient(X0) | ~curious(X0) [cnf transformation 61]
112. ~old(X0) | patient(X0) | creative(X0) | curious(X0) [cnf transformation 61]
118. ~brave(X0) | curious(X0) [cnf transformation 64]
119. old(X0) | old(X0) [cnf transformation 64]
131. ~humble(fred) | ~patient(fred) [cnf transformation 73]
132. ~funny(fred) [cnf transformation 24]
133. old(X0) [duplicate literal removal 119]
137. 1 <=> funny(susan) [avatar definition]
138. funny(susan) <- (1) [avatar component clause 137]
141. 2 <=> happy(susan) [avatar definition]
142. ~happy(susan) <- (~2) [avatar component clause 141]
145. 3 <=> humble(fred) [avatar definition]
149. 3 | ~2 [avatar split clause 75,141,145]
150. 3 | 1 [avatar split clause 74,137,145]
186. 12 <=> ! [X0] : (~curious(X0) | happy(X0)) [avatar definition]
187. ~curious(X0) | happy(X0) <- (12) [avatar component clause 186]
189. 13 <=> funny(alice) [avatar definition]
191. funny(alice) <- (13) [avatar component clause 189]
192. 12 | 13 [avatar split clause 100,189,186]
198. 15 <=> patient(alice) [avatar definition]
200. patient(alice) <- (15) [avatar component clause 198]
201. 12 | 15 [avatar split clause 98,198,186]
237. 23 <=> patient(fred) [avatar definition]
239. ~patient(fred) <- (~23) [avatar component clause 237]
240. ~23 | ~3 [avatar split clause 131,145,237]
272. ~funny(X0) | curious(X0) [resolution 81,133]
273. ~curious(X0) | funny(X0) [resolution 82,133]
293. ~creative(X0) | brave(X0) [resolution 106,133]
345. patient(X0) | creative(X0) | curious(X0) [resolution 112,133]
348. creative(fred) | curious(fred) <- (~23) [resolution 345,239]
363. 33 <=> curious(fred) [avatar definition]
364. ~curious(fred) <- (~33) [avatar component clause 363]
365. curious(fred) <- (33) [avatar component clause 363]
367. 34 <=> creative(fred) [avatar definition]
369. creative(fred) <- (34) [avatar component clause 367]
370. 33 | 34 | 23 [avatar split clause 348,237,367,363]
378. funny(fred) <- (33) [resolution 365,273]
383. $false <- (33) [subsumption resolution 378,132]
384. ~33 [avatar contradiction clause 383]
389. brave(fred) <- (34) [resolution 369,293]
437. curious(fred) <- (34) [resolution 389,118]
451. $false <- (~33, 34) [subsumption resolution 437,364]
452. 33 | ~34 [avatar contradiction clause 451]
453. curious(susan) <- (1) [resolution 138,272]
477. happy(susan) <- (1, 12) [resolution 453,187]
479. $false <- (1, ~2, 12) [subsumption resolution 477,142]
480. ~1 | 2 | ~12 [avatar contradiction clause 479]
481. curious(alice) <- (13) [resolution 191,272]
486. ~curious(alice) <- (15) [resolution 200,109]
497. $false <- (13, 15) [subsumption resolution 486,481]
498. ~13 | ~15 [avatar contradiction clause 497]
499. $false [avatar sat refutation 149,150,192,201,240,370,384,452,480,498]
% SZS output end Proof for 6565927815483852660498479
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or calm is either curious or wise and vice versa.
Everyone who is not curious is either curious or brave and vice versa.
If paul is both not patient and not calm then fred is either not wise or rich.
If alice is either not rich or rich then fred is both not curious and not strong and vice versa.
Everyone who is either not happy or funny is strong and vice versa.
Everyone who is both not tall and not old is patient or not patient.
Everyone who is either not brave or patient is either patient or not happy.
Everyone who is either not calm or funny is either not tall or curious and vice versa.
Everyone who is either curious or humble is quiet or not rich.
If mary is not old then someone is either not creative or creative and vice versa.
Everyone who is brave is either tall or not calm and vice versa.
Everyone who is either not tall or rich is either wise or not tall and vice versa.
Everyone who is either not happy or not creative 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.
Fred is either not kind or not tall.
Someone is either not happy or wise.
Someone is not curious or kind.
Mary is both humble and not wise.
Someone is not kind or not strong.
Fred is not quiet. | Paul is not patient. | neutral | (![X]:((old(X)<~>calm(X))<=>(curious(X)<~>wise(X))))&
(![X]:(~curious(X)<=>(curious(X)<~>brave(X))))&
(((~patient(paul)&~calm(paul)))=>((~wise(fred)<~>rich(fred))))&
(((~rich(alice)<~>rich(alice)))<=>((~curious(fred)&~strong(fred))))&
(![X]:((~happy(X)<~>funny(X))<=>strong(X)))&
(![X]:((~tall(X)&~old(X))=>(patient(X)|~patient(X))))&
(![X]:((~brave(X)<~>patient(X))=>(patient(X)<~>~happy(X))))&
(![X]:((~calm(X)<~>funny(X))<=>(~tall(X)<~>curious(X))))&
(![X]:((curious(X)<~>humble(X))=>(quiet(X)|~rich(X))))&
((~old(mary))<=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:(brave(X)<=>(tall(X)<~>~calm(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(wise(X)<~>~tall(X))))&
(![X]:((~happy(X)<~>~creative(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))))&
((~kind(fred)<~>~tall(fred)))&
(?[X]:((~happy(X)<~>wise(X))))&
(?[X]:((~curious(X)|kind(X))))&
((humble(mary)&~wise(mary)))&
(?[X]:((~kind(X)|~strong(X))))&
(~quiet(fred)) | ~patient(paul) | [] | null | 0 |
If fred is not calm or not curious then someone is both strong and quiet and vice versa.
If alice is either not wise or strong then paul is not patient.
Everyone who is not humble or calm is rich or humble and vice versa.
Everyone who is both not humble and not brave is humble and vice versa.
If alice is tall then someone is both kind and patient and vice versa.
If lucy is either wise or tall then mary is both curious and not funny.
If someone is both quiet and not generous then someone is either calm or not humble.
If someone is both not funny and humble then someone is either not rich or curious.
Everyone who is either not kind or rich is either rich or kind.
If someone is tall or patient then lucy is curious and vice versa.
Everyone who is both curious and not strong is both calm and creative.
If paul is either calm or not tall then lucy is rich or not humble and vice versa.
Everyone who is not wise is either not quiet or funny.
Everyone who is humble is either strong or kind.
Everyone who is not humble is not strong.
Everyone who is either not old or creative is either not humble or patient.
Someone is both old and calm.
Someone is both not generous and not kind.
Paul is not funny.
Someone is not humble.
Someone is not kind.
Fred is either not old or not wise. | Alice is curious. | neutral | (((~calm(fred)|~curious(fred)))<=>(?[X]:((strong(X)&quiet(X)))))&
(((~wise(alice)<~>strong(alice)))=>(~patient(paul)))&
(![X]:((~humble(X)|calm(X))<=>(rich(X)|humble(X))))&
(![X]:((~humble(X)&~brave(X))<=>humble(X)))&
((tall(alice))<=>(?[X]:((kind(X)&patient(X)))))&
(((wise(lucy)<~>tall(lucy)))=>((curious(mary)&~funny(mary))))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:((~funny(X)&humble(X))))=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:((~kind(X)<~>rich(X))=>(rich(X)<~>kind(X))))&
((?[X]:((tall(X)|patient(X))))<=>(curious(lucy)))&
(![X]:((curious(X)&~strong(X))=>(calm(X)&creative(X))))&
(((calm(paul)<~>~tall(paul)))<=>((rich(lucy)|~humble(lucy))))&
(![X]:(~wise(X)=>(~quiet(X)<~>funny(X))))&
(![X]:(humble(X)=>(strong(X)<~>kind(X))))&
(![X]:(~humble(X)=>~strong(X)))&
(![X]:((~old(X)<~>creative(X))=>(~humble(X)<~>patient(X))))&
(?[X]:((old(X)&calm(X))))&
(?[X]:((~generous(X)&~kind(X))))&
(~funny(paul))&
(?[X]:(~humble(X)))&
(?[X]:(~kind(X)))&
((~old(fred)<~>~wise(fred))) | curious(alice) | [] | null | 0 |
Everyone who is generous or not wise is either not humble or old.
Everyone who is both not rich and creative is either not tall or not humble and vice versa.
If susan is both not brave and not curious then someone is humble and vice versa.
If alice is either not creative or quiet then paul is both calm and humble.
Everyone who is not rich or not funny is either not kind or not old.
If john is 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.
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.
Someone is not patient.
Someone is quiet or wise.
Someone is creative.
Someone is not patient or not wise.
Someone is not generous.
Someone is both not brave and not funny.
Mary is brave. | Fred is happy. | contradiction | (![X]:((generous(X)|~wise(X))=>(~humble(X)<~>old(X))))&
(![X]:((~rich(X)&creative(X))<=>(~tall(X)<~>~humble(X))))&
(((~brave(susan)&~curious(susan)))<=>(?[X]:(humble(X))))&
(((~creative(alice)<~>quiet(alice)))=>((calm(paul)&humble(paul))))&
(![X]:((~rich(X)|~funny(X))=>(~kind(X)<~>~old(X))))&
(((~old(john)|quiet(john)))<=>((~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]:((~calm(X)&kind(X))=>(humble(X)&~old(X))))&
((?[X]:(funny(X)))<=>((curious(lucy)|~strong(lucy))))&
(?[X]:(~patient(X)))&
(?[X]:((quiet(X)|wise(X))))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)|~wise(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~brave(X)&~funny(X))))&
(brave(mary)) | happy(fred) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4035631080883023641897031
% SZS output start Proof for 4035631080883023641897031
11. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (calm(X0) & curious(X0))) [input p10]
12. (~curious(fred) | ~happy(fred)) <=> (calm(alice) | generous(alice)) [input p11]
22. happy(fred) [input hypothesis]
52. ! [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 11]
53. ! [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 52]
54. ((~curious(fred) | ~happy(fred)) | (~calm(alice) & ~generous(alice))) & ((calm(alice) | generous(alice)) | (curious(fred) & happy(fred))) [nnf transformation 12]
55. (~curious(fred) | ~happy(fred) | (~calm(alice) & ~generous(alice))) & (calm(alice) | generous(alice) | (curious(fred) & happy(fred))) [flattening 54]
111. curious(X0) | humble(X0) | humble(X0) [cnf transformation 53]
112. curious(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 53]
113. calm(X0) | humble(X0) | humble(X0) [cnf transformation 53]
114. calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 53]
120. ~curious(fred) | ~happy(fred) | ~calm(alice) [cnf transformation 55]
134. happy(fred) [cnf transformation 22]
135. curious(X0) | humble(X0) [duplicate literal removal 111]
136. curious(X0) | ~humble(X0) [duplicate literal removal 112]
137. calm(X0) | humble(X0) [duplicate literal removal 113]
138. calm(X0) | ~humble(X0) [duplicate literal removal 114]
232. calm(X0) [subsumption resolution 137,138]
233. curious(X0) [subsumption resolution 135,136]
234. ~happy(fred) | ~calm(alice) [subsumption resolution 120,233]
235. ~happy(fred) [subsumption resolution 234,232]
265. $false [subsumption resolution 134,235]
% SZS output end Proof for 4035631080883023641897031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not old or tall then fred is patient or not quiet and vice versa.
If john is both not tall and not generous then someone is not tall.
If someone is humble then someone is either curious or tall.
If mary is either not calm or funny then lucy is not old or strong and vice versa.
If someone is not happy or not old then susan is both generous and curious and vice versa.
If someone is both not kind and brave then fred is wise and vice versa.
Everyone who is patient is both humble and not humble and vice versa.
Everyone who is not strong is either not patient or not strong.
If mary is both creative and funny then mary is not creative and vice versa.
If paul is brave or calm then someone is either not curious or wise and vice versa.
If someone is not curious or old then lucy is old or generous and vice versa.
Everyone who is both not patient and happy is both happy and kind and vice versa.
If someone is not humble then paul is either not rich or kind.
If someone is both not rich and not kind then john is not funny.
If someone is either not quiet or generous then fred is not creative or quiet and vice versa.
Everyone who is both not kind and not generous is either humble or tall and vice versa.
Someone is either not creative or not funny.
Paul is strong.
John is calm or not rich.
Someone is either strong or kind.
Paul is not generous.
Mary is not humble. | Mary is not calm. | entailment | (((~old(fred)|tall(fred)))<=>((patient(fred)|~quiet(fred))))&
(((~tall(john)&~generous(john)))=>(?[X]:(~tall(X))))&
((?[X]:(humble(X)))=>(?[X]:((curious(X)<~>tall(X)))))&
(((~calm(mary)<~>funny(mary)))<=>((~old(lucy)|strong(lucy))))&
((?[X]:((~happy(X)|~old(X))))<=>((generous(susan)&curious(susan))))&
((?[X]:((~kind(X)&brave(X))))<=>(wise(fred)))&
(![X]:(patient(X)<=>(humble(X)&~humble(X))))&
(![X]:(~strong(X)=>(~patient(X)<~>~strong(X))))&
(((creative(mary)&funny(mary)))<=>(~creative(mary)))&
(((brave(paul)|calm(paul)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
((?[X]:((~curious(X)|old(X))))<=>((old(lucy)|generous(lucy))))&
(![X]:((~patient(X)&happy(X))<=>(happy(X)&kind(X))))&
((?[X]:(~humble(X)))=>((~rich(paul)<~>kind(paul))))&
((?[X]:((~rich(X)&~kind(X))))=>(~funny(john)))&
((?[X]:((~quiet(X)<~>generous(X))))<=>((~creative(fred)|quiet(fred))))&
(![X]:((~kind(X)&~generous(X))<=>(humble(X)<~>tall(X))))&
(?[X]:((~creative(X)<~>~funny(X))))&
(strong(paul))&
((calm(john)|~rich(john)))&
(?[X]:((strong(X)<~>kind(X))))&
(~generous(paul))&
(~humble(mary)) | ~calm(mary) | [
"p3",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2659004780971989955160111
% SZS output start Proof for 2659004780971989955160111
4. (~calm(mary) <~> funny(mary)) <=> (strong(lucy) | ~old(lucy)) [input p3]
7. ! [X0] : (patient(X0) <=> (~humble(X0) & humble(X0))) [input p6]
8. ! [X0] : (~strong(X0) => (~patient(X0) <~> ~strong(X0))) [input p7]
9. (funny(mary) & creative(mary)) <=> ~creative(mary) [input p8]
23. calm(mary) [input hypothesis]
28. ! [X0] : ((~patient(X0) <~> ~strong(X0)) | strong(X0)) [ennf transformation 8]
39. (((~funny(mary) | calm(mary)) & (funny(mary) | ~calm(mary))) | (~strong(lucy) & old(lucy))) & ((strong(lucy) | ~old(lucy)) | ((~calm(mary) | ~funny(mary)) & (funny(mary) | calm(mary)))) [nnf transformation 4]
40. (((~funny(mary) | calm(mary)) & (funny(mary) | ~calm(mary))) | (~strong(lucy) & old(lucy))) & (strong(lucy) | ~old(lucy) | ((~calm(mary) | ~funny(mary)) & (funny(mary) | calm(mary)))) [flattening 39]
50. ! [X0] : ((patient(X0) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | ~patient(X0))) [nnf transformation 7]
51. ! [X0] : ((patient(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | ~patient(X0))) [flattening 50]
52. ! [X0] : (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | strong(X0)) [nnf transformation 28]
53. ((funny(mary) & creative(mary)) | creative(mary)) & (~creative(mary) | (~funny(mary) | ~creative(mary))) [nnf transformation 9]
54. ((funny(mary) & creative(mary)) | creative(mary)) & (~creative(mary) | ~funny(mary) | ~creative(mary)) [flattening 53]
91. funny(mary) | ~calm(mary) | ~strong(lucy) [cnf transformation 40]
102. humble(X0) | ~patient(X0) [cnf transformation 51]
103. ~humble(X0) | ~patient(X0) [cnf transformation 51]
106. strong(X0) | patient(X0) | strong(X0) [cnf transformation 52]
107. ~creative(mary) | ~funny(mary) | ~creative(mary) [cnf transformation 54]
108. creative(mary) | creative(mary) [cnf transformation 54]
147. calm(mary) [cnf transformation 23]
148. ~creative(mary) | ~funny(mary) [duplicate literal removal 107]
149. creative(mary) [duplicate literal removal 108]
150. strong(X0) | patient(X0) [duplicate literal removal 106]
198. 11 <=> strong(lucy) [avatar definition]
200. ~strong(lucy) <- (~11) [avatar component clause 198]
202. 12 <=> calm(mary) [avatar definition]
206. 13 <=> funny(mary) [avatar definition]
215. ~11 | ~12 | 13 [avatar split clause 91,206,202,198]
264. ~patient(X0) [subsumption resolution 102,103]
265. strong(X0) [subsumption resolution 150,264]
267. 25 <=> creative(mary) [avatar definition]
271. 25 [avatar split clause 149,267]
272. ~13 | ~25 [avatar split clause 148,267,206]
389. 12 [avatar split clause 147,202]
390. $false <- (~11) [subsumption resolution 200,265]
391. 11 [avatar contradiction clause 390]
392. $false [avatar sat refutation 215,271,272,389,391]
% SZS output end Proof for 2659004780971989955160111
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and kind is both curious and not tall and vice versa. If paul is not happy then paul is either quiet or not kind and vice versa. Everyone who is either not tall or not creative is not brave and vice versa. Everyone who is both patient and not patient is rich and vice versa. Everyone who is either patient or creative is either not creative or funny. If someone is not patient or generous then someone is funny or tall. If susan is not calm then someone is either humble or not creative and vice versa. Everyone who is not kind or curious is either creative or not happy and vice versa. Everyone who is either calm or wise is brave or patient. Everyone who is both brave and curious is both not humble and not generous and vice versa. If someone is both not humble and brave then fred is not rich. If susan is both curious and funny then someone is both brave and wise. Everyone who is both rich and not quiet is not wise. Everyone who is generous is not quiet and vice versa. Everyone who is happy is both not rich and not brave and vice versa. Everyone who is not old or not wise is not old and vice versa. Susan is not curious or rich. Lucy is either not humble or not patient. Someone is either strong or not patient. Someone is either wise or strong. Someone is not generous. Paul is either not old or strong. Mary is both curious and not rich. Someone is not generous or not curious. | Lucy is not patient. | neutral | (![X]:((~humble(X)&kind(X))<=>(curious(X)&~tall(X))))&
((~happy(paul))<=>((quiet(paul)<~>~kind(paul))))&
(![X]:((~tall(X)<~>~creative(X))<=>~brave(X)))&
(![X]:((patient(X)&~patient(X))<=>rich(X)))&
(![X]:((patient(X)<~>creative(X))=>(~creative(X)<~>funny(X))))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:((funny(X)|tall(X)))))&
((~calm(susan))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((~kind(X)|curious(X))<=>(creative(X)<~>~happy(X))))&
(![X]:((calm(X)<~>wise(X))=>(brave(X)|patient(X))))&
(![X]:((brave(X)&curious(X))<=>(~humble(X)&~generous(X))))&
((?[X]:((~humble(X)&brave(X))))=>(~rich(fred)))&
(((curious(susan)&funny(susan)))=>(?[X]:((brave(X)&wise(X)))))&
(![X]:((rich(X)&~quiet(X))=>~wise(X)))&
(![X]:(generous(X)<=>~quiet(X)))&
(![X]:(happy(X)<=>(~rich(X)&~brave(X))))&
(![X]:((~old(X)|~wise(X))<=>~old(X)))&
((~curious(susan)|rich(susan)))&
((~humble(lucy)<~>~patient(lucy)))&
(?[X]:((strong(X)<~>~patient(X))))&
(?[X]:((wise(X)<~>strong(X))))&
(?[X]:(~generous(X)))&
((~old(paul)<~>strong(paul)))&
((curious(mary)&~rich(mary)))&
(?[X]:((~generous(X)|~curious(X)))) | ~patient(lucy) | [] | null | 0 |
If susan is both old and calm then someone is not calm.
If fred is both patient and funny then someone is not brave.
Everyone who is either not tall or not generous is either patient or not quiet and vice versa.
If john is curious then john is not strong or not generous and vice versa.
If someone is not generous or not strong then someone is either not creative or happy and vice versa.
Everyone who is not humble or not calm is old or generous and vice versa.
If paul is not happy or not tall then someone is not tall and vice versa.
Everyone who is either humble or rich is both tall and generous and vice versa.
Everyone who is patient is either funny or curious and vice versa.
Everyone who is either not strong or not curious is kind and vice versa.
Everyone who is both not strong and old is not curious or brave.
If alice is both quiet and creative then john is kind and vice versa.
If mary is not patient then someone is kind and vice versa.
Everyone who is both not old and not kind is either tall or not quiet and vice versa.
If someone is either curious or not old then fred is both not generous and not old and vice versa.
If someone is both not old and brave then paul is quiet and vice versa.
Lucy is not happy or humble.
Lucy is not curious.
Lucy is not old.
Someone is not tall or tall.
John is curious.
Lucy is both funny and not humble.
Someone is either wise or humble.
Susan is not patient or strong. | Mary is patient. | contradiction | (((old(susan)&calm(susan)))=>(?[X]:(~calm(X))))&
(((patient(fred)&funny(fred)))=>(?[X]:(~brave(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(patient(X)<~>~quiet(X))))&
((curious(john))<=>((~strong(john)|~generous(john))))&
((?[X]:((~generous(X)|~strong(X))))<=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:((~humble(X)|~calm(X))<=>(old(X)|generous(X))))&
(((~happy(paul)|~tall(paul)))<=>(?[X]:(~tall(X))))&
(![X]:((humble(X)<~>rich(X))<=>(tall(X)&generous(X))))&
(![X]:(patient(X)<=>(funny(X)<~>curious(X))))&
(![X]:((~strong(X)<~>~curious(X))<=>kind(X)))&
(![X]:((~strong(X)&old(X))=>(~curious(X)|brave(X))))&
(((quiet(alice)&creative(alice)))<=>(kind(john)))&
((~patient(mary))<=>(?[X]:(kind(X))))&
(![X]:((~old(X)&~kind(X))<=>(tall(X)<~>~quiet(X))))&
((?[X]:((curious(X)<~>~old(X))))<=>((~generous(fred)&~old(fred))))&
((?[X]:((~old(X)&brave(X))))<=>(quiet(paul)))&
((~happy(lucy)|humble(lucy)))&
(~curious(lucy))&
(~old(lucy))&
(?[X]:((~tall(X)|tall(X))))&
(curious(john))&
((funny(lucy)&~humble(lucy)))&
(?[X]:((wise(X)<~>humble(X))))&
((~patient(susan)|strong(susan))) | patient(mary) | [
"p2",
"p5",
"p8",
"p12",
"p13",
"p17",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3593971902115916346695516
% SZS output start Proof for 3593971902115916346695516
3. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (patient(X0) <~> ~quiet(X0))) [input p2]
6. ! [X0] : ((~calm(X0) | ~humble(X0)) <=> (generous(X0) | old(X0))) [input p5]
9. ! [X0] : (patient(X0) <=> (funny(X0) <~> curious(X0))) [input p8]
13. ~patient(mary) <=> ? [X0] : kind(X0) [input p12]
14. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (tall(X0) <~> ~quiet(X0))) [input p13]
18. ~curious(lucy) [input p17]
19. ~old(lucy) [input p18]
22. ~humble(lucy) & funny(lucy) [input p21]
25. patient(mary) [input hypothesis]
37. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | ((patient(X0) | quiet(X0)) & (~quiet(X0) | ~patient(X0)))) & (((quiet(X0) | ~patient(X0)) & (~quiet(X0) | patient(X0))) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 3]
45. ! [X0] : (((~calm(X0) | ~humble(X0)) | (~generous(X0) & ~old(X0))) & ((generous(X0) | old(X0)) | (calm(X0) & humble(X0)))) [nnf transformation 6]
46. ! [X0] : ((~calm(X0) | ~humble(X0) | (~generous(X0) & ~old(X0))) & (generous(X0) | old(X0) | (calm(X0) & humble(X0)))) [flattening 45]
54. ! [X0] : ((patient(X0) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0)))) & (((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | ~patient(X0))) [nnf transformation 9]
58. (~patient(mary) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | patient(mary)) [nnf transformation 13]
59. (~patient(mary) | ! [X0] : ~kind(X0)) & (? [X1] : kind(X1) | patient(mary)) [rectify 58]
60. ? [X1] : kind(X1) => kind(sK5) [choice axiom]
61. (~patient(mary) | ! [X0] : ~kind(X0)) & (kind(sK5) | patient(mary)) [skolemisation 59,60]
62. ! [X0] : (((~kind(X0) & ~old(X0)) | ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) & (((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | (kind(X0) | old(X0)))) [nnf transformation 14]
63. ! [X0] : (((~kind(X0) & ~old(X0)) | ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) & (((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | kind(X0) | old(X0))) [flattening 62]
82. ~generous(X0) | ~patient(X0) | quiet(X0) | tall(X0) [cnf transformation 37]
84. ~quiet(X0) | ~tall(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 37]
97. humble(X0) | old(X0) | generous(X0) [cnf transformation 46]
112. ~funny(X0) | curious(X0) | patient(X0) [cnf transformation 54]
123. ~patient(mary) | ~kind(X0) [cnf transformation 61]
124. ~quiet(X0) | tall(X0) | kind(X0) | old(X0) [cnf transformation 63]
125. ~tall(X0) | quiet(X0) | kind(X0) | old(X0) [cnf transformation 63]
140. ~curious(lucy) [cnf transformation 18]
141. ~old(lucy) [cnf transformation 19]
144. funny(lucy) [cnf transformation 22]
145. ~humble(lucy) [cnf transformation 22]
149. patient(mary) [cnf transformation 25]
259. 25 <=> ! [X0] : ~kind(X0) [avatar definition]
260. ~kind(X0) <- (25) [avatar component clause 259]
262. 26 <=> patient(mary) [avatar definition]
265. 25 | ~26 [avatar split clause 123,262,259]
322. 39 <=> humble(lucy) [avatar definition]
323. ~humble(lucy) <- (~39) [avatar component clause 322]
327. ~39 [avatar split clause 145,322]
347. 26 [avatar split clause 149,262]
348. old(lucy) | generous(lucy) <- (~39) [resolution 97,323]
350. generous(lucy) <- (~39) [subsumption resolution 348,141]
422. curious(lucy) | patient(lucy) [resolution 112,144]
423. patient(lucy) [subsumption resolution 422,140]
479. ~patient(lucy) | quiet(lucy) | tall(lucy) <- (~39) [resolution 82,350]
483. quiet(lucy) | tall(lucy) <- (~39) [subsumption resolution 479,423]
485. 61 <=> tall(lucy) [avatar definition]
487. tall(lucy) <- (61) [avatar component clause 485]
489. 62 <=> quiet(lucy) [avatar definition]
491. quiet(lucy) <- (62) [avatar component clause 489]
492. 61 | 62 | 39 [avatar split clause 483,322,489,485]
618. quiet(lucy) | kind(lucy) | old(lucy) <- (61) [resolution 125,487]
619. quiet(lucy) | old(lucy) <- (25, 61) [subsumption resolution 618,260]
620. quiet(lucy) <- (25, 61) [subsumption resolution 619,141]
621. 62 | ~25 | ~61 [avatar split clause 620,485,259,489]
622. tall(lucy) | kind(lucy) | old(lucy) <- (62) [resolution 491,124]
624. ~tall(lucy) | ~generous(lucy) | ~patient(lucy) <- (62) [resolution 491,84]
632. ~tall(lucy) | ~patient(lucy) <- (~39, 62) [subsumption resolution 624,350]
633. ~tall(lucy) <- (~39, 62) [subsumption resolution 632,423]
634. ~61 | 39 | ~62 [avatar split clause 633,489,322,485]
635. tall(lucy) | old(lucy) <- (25, 62) [subsumption resolution 622,260]
636. tall(lucy) <- (25, 62) [subsumption resolution 635,141]
637. 61 | ~25 | ~62 [avatar split clause 636,489,259,485]
643. $false [avatar sat refutation 265,327,347,492,621,634,637]
% SZS output end Proof for 3593971902115916346695516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or not patient then lucy is calm or curious and vice versa.
If john is both not patient and not quiet then john is both not generous and rich.
Everyone who is both not patient and curious is not old and vice versa.
If someone is generous then someone is quiet or not strong.
If someone is strong or kind then fred is both old and not patient and vice versa.
If someone is kind or rich then someone is quiet.
Everyone who is curious or creative is wise.
If someone is not strong or brave then someone is generous or strong.
Everyone who is not tall is both not brave and not happy.
Everyone who is both calm and tall is not generous and vice versa.
Everyone who is both not wise and not generous is generous and vice versa.
If someone is both curious and wise then alice is rich and vice versa.
Everyone who is not curious is either rich or humble.
Everyone who is both tall and curious is either not humble or not rich.
If someone is either not patient or not old then alice is both funny and kind and vice versa.
Everyone who is either not brave or kind is not happy and vice versa.
Someone is not kind or patient.
Someone is patient or tall.
Mary is both not creative and not brave.
Someone is either kind or old.
Fred is not funny or strong.
Fred is not happy.
Paul is curious or wise.
Alice is both not patient and not happy. | Fred is funny. | neutral | ((?[X]:((~calm(X)<~>~patient(X))))<=>((calm(lucy)|curious(lucy))))&
(((~patient(john)&~quiet(john)))=>((~generous(john)&rich(john))))&
(![X]:((~patient(X)&curious(X))<=>~old(X)))&
((?[X]:(generous(X)))=>(?[X]:((quiet(X)|~strong(X)))))&
((?[X]:((strong(X)|kind(X))))<=>((old(fred)&~patient(fred))))&
((?[X]:((kind(X)|rich(X))))=>(?[X]:(quiet(X))))&
(![X]:((curious(X)|creative(X))=>wise(X)))&
((?[X]:((~strong(X)|brave(X))))=>(?[X]:((generous(X)|strong(X)))))&
(![X]:(~tall(X)=>(~brave(X)&~happy(X))))&
(![X]:((calm(X)&tall(X))<=>~generous(X)))&
(![X]:((~wise(X)&~generous(X))<=>generous(X)))&
((?[X]:((curious(X)&wise(X))))<=>(rich(alice)))&
(![X]:(~curious(X)=>(rich(X)<~>humble(X))))&
(![X]:((tall(X)&curious(X))=>(~humble(X)<~>~rich(X))))&
((?[X]:((~patient(X)<~>~old(X))))<=>((funny(alice)&kind(alice))))&
(![X]:((~brave(X)<~>kind(X))<=>~happy(X)))&
(?[X]:((~kind(X)|patient(X))))&
(?[X]:((patient(X)|tall(X))))&
((~creative(mary)&~brave(mary)))&
(?[X]:((kind(X)<~>old(X))))&
((~funny(fred)|strong(fred)))&
(~happy(fred))&
((curious(paul)|wise(paul)))&
((~patient(alice)&~happy(alice))) | funny(fred) | [] | null | 0 |
Everyone who is funny or not strong is both happy and patient and vice versa. Everyone who is both old and happy is tall. Everyone who is either not kind or quiet is either not kind or generous. Everyone who is either not wise or not quiet is kind and vice versa. Everyone who is kind or not generous is both not strong and wise. Everyone who is creative or quiet is either strong or not generous. Everyone who is not kind or not happy is both not curious and not happy and vice versa. If mary is happy or patient then someone is either brave or not brave and vice versa. Everyone who is both patient and quiet is both not calm and happy and vice versa. If someone is not old then someone is generous or kind and vice versa. If paul is strong or not patient then fred is both not creative and not strong. If alice is not brave or wise then someone is not tall and vice versa. Everyone who is not quiet or not rich is not brave. Lucy is either not wise or not patient. Mary is humble or not tall. Someone is either not brave or brave. Someone is humble. Lucy is not humble. Alice is either rich or quiet. John is not tall or not kind. Lucy is both not curious and not creative. | Paul is tall. | neutral | (![X]:((funny(X)|~strong(X))<=>(happy(X)&patient(X))))&
(![X]:((old(X)&happy(X))=>tall(X)))&
(![X]:((~kind(X)<~>quiet(X))=>(~kind(X)<~>generous(X))))&
(![X]:((~wise(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((kind(X)|~generous(X))=>(~strong(X)&wise(X))))&
(![X]:((creative(X)|quiet(X))=>(strong(X)<~>~generous(X))))&
(![X]:((~kind(X)|~happy(X))<=>(~curious(X)&~happy(X))))&
(((happy(mary)|patient(mary)))<=>(?[X]:((brave(X)<~>~brave(X)))))&
(![X]:((patient(X)&quiet(X))<=>(~calm(X)&happy(X))))&
((?[X]:(~old(X)))<=>(?[X]:((generous(X)|kind(X)))))&
(((strong(paul)|~patient(paul)))=>((~creative(fred)&~strong(fred))))&
(((~brave(alice)|wise(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((~quiet(X)|~rich(X))=>~brave(X)))&
((~wise(lucy)<~>~patient(lucy)))&
((humble(mary)|~tall(mary)))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:(humble(X)))&
(~humble(lucy))&
((rich(alice)<~>quiet(alice)))&
((~tall(john)|~kind(john)))&
((~curious(lucy)&~creative(lucy))) | tall(paul) | [] | null | 0 |
If someone is not patient then fred is old and vice versa.
Everyone who is not creative or not curious is not brave or not rich and vice versa.
Everyone who is patient is not wise.
If alice is either brave or not brave then john is not tall or humble and vice versa.
If someone is either not funny or not rich then lucy is funny and vice versa.
Everyone who is funny is both tall and humble.
Everyone who is not strong is not curious or happy.
If alice is not rich then someone is both not old and old.
If someone is not wise then mary is either not brave or curious and vice versa.
Everyone who is either brave or not brave is not patient and vice versa.
If someone is either creative or not wise then john is wise or not happy and vice versa.
Everyone who is quiet or tall is both not quiet and happy and vice versa.
Everyone who is generous is either tall or not humble.
If someone is both kind and curious then susan is not strong and vice versa.
Everyone who is calm or not humble is humble or not wise and vice versa.
Everyone who is either not calm or not old is either tall or old and vice versa.
Someone is not curious or calm.
Someone is not rich.
Someone is not humble.
Paul is not creative.
Someone is both not curious and not humble.
Someone is either curious or not creative.
Someone is either not patient or funny. | Susan is not creative. | neutral | ((?[X]:(~patient(X)))<=>(old(fred)))&
(![X]:((~creative(X)|~curious(X))<=>(~brave(X)|~rich(X))))&
(![X]:(patient(X)=>~wise(X)))&
(((brave(alice)<~>~brave(alice)))<=>((~tall(john)|humble(john))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>(funny(lucy)))&
(![X]:(funny(X)=>(tall(X)&humble(X))))&
(![X]:(~strong(X)=>(~curious(X)|happy(X))))&
((~rich(alice))=>(?[X]:((~old(X)&old(X)))))&
((?[X]:(~wise(X)))<=>((~brave(mary)<~>curious(mary))))&
(![X]:((brave(X)<~>~brave(X))<=>~patient(X)))&
((?[X]:((creative(X)<~>~wise(X))))<=>((wise(john)|~happy(john))))&
(![X]:((quiet(X)|tall(X))<=>(~quiet(X)&happy(X))))&
(![X]:(generous(X)=>(tall(X)<~>~humble(X))))&
((?[X]:((kind(X)&curious(X))))<=>(~strong(susan)))&
(![X]:((calm(X)|~humble(X))<=>(humble(X)|~wise(X))))&
(![X]:((~calm(X)<~>~old(X))<=>(tall(X)<~>old(X))))&
(?[X]:((~curious(X)|calm(X))))&
(?[X]:(~rich(X)))&
(?[X]:(~humble(X)))&
(~creative(paul))&
(?[X]:((~curious(X)&~humble(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
(?[X]:((~patient(X)<~>funny(X)))) | ~creative(susan) | [] | null | 0 |
If alice is both old and not brave then someone is both happy and not funny.
Everyone who is not rich is either calm or creative and vice versa.
Everyone who is either old or not patient is either not funny or calm.
Everyone who is either not happy or not kind is not rich or not old.
Everyone who is either not calm or not humble is humble or not wise.
If lucy is both strong and not quiet then paul is not humble or rich.
Everyone who is either not funny or not curious is not kind or tall and vice versa.
Everyone who is old or creative is old and vice versa.
Everyone who is both kind and not curious is not patient and vice versa.
If fred is either funny or not old then someone is not patient and vice versa.
Everyone who is either quiet or not funny is both not brave and quiet.
Everyone who is either not happy or happy is either wise or happy and vice versa.
Everyone who is both strong and not kind is both not kind and wise and vice versa.
Everyone who is old is both not rich and not happy.
Everyone who is either not curious or happy is not happy or happy and vice versa.
If someone is both not patient and not calm then someone is both generous and not funny.
Paul is both not old and kind.
Alice is not patient.
Lucy is curious.
Someone is either rich or old.
Mary is wise or humble.
Fred is funny.
Mary is not tall or generous.
Mary is either kind or not kind. | Fred is curious. | contradiction | (((old(alice)&~brave(alice)))=>(?[X]:((happy(X)&~funny(X)))))&
(![X]:(~rich(X)<=>(calm(X)<~>creative(X))))&
(![X]:((old(X)<~>~patient(X))=>(~funny(X)<~>calm(X))))&
(![X]:((~happy(X)<~>~kind(X))=>(~rich(X)|~old(X))))&
(![X]:((~calm(X)<~>~humble(X))=>(humble(X)|~wise(X))))&
(((strong(lucy)&~quiet(lucy)))=>((~humble(paul)|rich(paul))))&
(![X]:((~funny(X)<~>~curious(X))<=>(~kind(X)|tall(X))))&
(![X]:((old(X)|creative(X))<=>old(X)))&
(![X]:((kind(X)&~curious(X))<=>~patient(X)))&
(((funny(fred)<~>~old(fred)))<=>(?[X]:(~patient(X))))&
(![X]:((quiet(X)<~>~funny(X))=>(~brave(X)&quiet(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(wise(X)<~>happy(X))))&
(![X]:((strong(X)&~kind(X))<=>(~kind(X)&wise(X))))&
(![X]:(old(X)=>(~rich(X)&~happy(X))))&
(![X]:((~curious(X)<~>happy(X))<=>(~happy(X)|happy(X))))&
((?[X]:((~patient(X)&~calm(X))))=>(?[X]:((generous(X)&~funny(X)))))&
((~old(paul)&kind(paul)))&
(~patient(alice))&
(curious(lucy))&
(?[X]:((rich(X)<~>old(X))))&
((wise(mary)|humble(mary)))&
(funny(fred))&
((~tall(mary)|generous(mary)))&
((kind(mary)<~>~kind(mary))) | curious(fred) | [
"p9",
"p13",
"p14",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5821787596612916726275374
% SZS output start Proof for 5821787596612916726275374
10. (funny(fred) <~> ~old(fred)) <=> ? [X0] : ~patient(X0) [input p9]
14. ! [X0] : (old(X0) => (~happy(X0) & ~rich(X0))) [input p13]
15. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (happy(X0) | ~happy(X0))) [input p14]
18. ~patient(alice) [input p17]
22. funny(fred) [input p21]
25. curious(fred) [input hypothesis]
39. ! [X0] : ((~happy(X0) & ~rich(X0)) | ~old(X0)) [ennf transformation 14]
53. (((old(fred) | ~funny(fred)) & (~old(fred) | funny(fred))) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | ((funny(fred) | old(fred)) & (~old(fred) | ~funny(fred)))) [nnf transformation 10]
54. (((old(fred) | ~funny(fred)) & (~old(fred) | funny(fred))) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | ((funny(fred) | old(fred)) & (~old(fred) | ~funny(fred)))) [rectify 53]
55. ? [X1] : ~patient(X1) => ~patient(sK1) [choice axiom]
56. (((old(fred) | ~funny(fred)) & (~old(fred) | funny(fred))) | ! [X0] : patient(X0)) & (~patient(sK1) | ((funny(fred) | old(fred)) & (~old(fred) | ~funny(fred)))) [skolemisation 54,55]
61. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 15]
62. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 61]
100. old(fred) | ~funny(fred) | patient(X0) [cnf transformation 56]
118. ~happy(X0) | ~old(X0) [cnf transformation 39]
121. happy(X0) | ~curious(X0) | happy(X0) [cnf transformation 62]
128. ~patient(alice) [cnf transformation 18]
133. funny(fred) [cnf transformation 22]
136. curious(fred) [cnf transformation 25]
139. ~curious(X0) | happy(X0) [duplicate literal removal 121]
187. 9 <=> ! [X0] : patient(X0) [avatar definition]
188. patient(X0) <- (9) [avatar component clause 187]
190. 10 <=> funny(fred) [avatar definition]
194. 11 <=> old(fred) [avatar definition]
196. old(fred) <- (11) [avatar component clause 194]
197. 9 | ~10 | 11 [avatar split clause 100,194,190,187]
231. 10 [avatar split clause 133,190]
232. $false <- (9) [resolution 188,128]
233. ~9 [avatar contradiction clause 232]
239. happy(fred) [resolution 139,136]
243. ~old(fred) [resolution 239,118]
244. $false <- (11) [subsumption resolution 243,196]
245. ~11 [avatar contradiction clause 244]
246. $false [avatar sat refutation 197,231,233,245]
% SZS output end Proof for 5821787596612916726275374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and quiet is not creative or not tall. Everyone who is either not patient or old is either old or curious and vice versa. Everyone who is either not creative or brave is both not creative and strong and vice versa. Everyone who is not curious is either rich or creative. Everyone who is either funny or kind is not curious or creative. If susan is not brave then someone is not happy or not rich. If susan is strong or tall then paul is not strong or not tall and vice versa. Everyone who is both not kind and not tall is not tall. Everyone who is generous or rich is not funny and vice versa. Everyone who is either not calm or brave is either happy or not quiet and vice versa. If susan is both not tall and humble then someone is patient and vice versa. If fred is both brave and not rich then fred is patient. Everyone who is either not creative or curious is generous or quiet and vice versa. Everyone who is both not humble and not old is both happy and not curious and vice versa. If alice is not strong or curious then lucy is either kind or tall. Everyone who is old or not strong is quiet and vice versa. Fred is humble. Paul is not old or not tall. Someone is both not generous and not creative. Someone is kind. Lucy is patient. Someone is either brave or not curious. Someone is both creative and not happy. Alice is curious. | Paul is humble. | neutral | (![X]:((strong(X)&quiet(X))=>(~creative(X)|~tall(X))))&
(![X]:((~patient(X)<~>old(X))<=>(old(X)<~>curious(X))))&
(![X]:((~creative(X)<~>brave(X))<=>(~creative(X)&strong(X))))&
(![X]:(~curious(X)=>(rich(X)<~>creative(X))))&
(![X]:((funny(X)<~>kind(X))=>(~curious(X)|creative(X))))&
((~brave(susan))=>(?[X]:((~happy(X)|~rich(X)))))&
(((strong(susan)|tall(susan)))<=>((~strong(paul)|~tall(paul))))&
(![X]:((~kind(X)&~tall(X))=>~tall(X)))&
(![X]:((generous(X)|rich(X))<=>~funny(X)))&
(![X]:((~calm(X)<~>brave(X))<=>(happy(X)<~>~quiet(X))))&
(((~tall(susan)&humble(susan)))<=>(?[X]:(patient(X))))&
(((brave(fred)&~rich(fred)))=>(patient(fred)))&
(![X]:((~creative(X)<~>curious(X))<=>(generous(X)|quiet(X))))&
(![X]:((~humble(X)&~old(X))<=>(happy(X)&~curious(X))))&
(((~strong(alice)|curious(alice)))=>((kind(lucy)<~>tall(lucy))))&
(![X]:((old(X)|~strong(X))<=>quiet(X)))&
(humble(fred))&
((~old(paul)|~tall(paul)))&
(?[X]:((~generous(X)&~creative(X))))&
(?[X]:(kind(X)))&
(patient(lucy))&
(?[X]:((brave(X)<~>~curious(X))))&
(?[X]:((creative(X)&~happy(X))))&
(curious(alice)) | humble(paul) | [] | null | 0 |
Everyone who is either humble or happy is both not strong and patient and vice versa.
Everyone who is either not brave or not creative is both wise and strong and vice versa.
If alice is both not calm and humble then someone is both curious and strong and vice versa.
Everyone who is either not calm or not generous is either brave or not strong.
Everyone who is patient is both curious and kind.
If fred is both calm and brave then someone is not humble or old.
Everyone who is either not kind or rich is both funny and patient.
Everyone who is either not curious or quiet is both strong and wise and vice versa.
If someone is either not quiet or happy then john is kind or not kind and vice versa.
Everyone who is either patient or kind is either funny or tall and vice versa.
If john is brave or not happy then paul is not happy or not kind and vice versa.
If alice is both wise and calm then someone is creative or not quiet.
Everyone who is wise is not old.
If john is old or brave then alice is rich or not old and vice versa.
If someone is not humble then someone is both funny and creative and vice versa.
Everyone who is both brave and happy is both strong and not kind.
Alice is both strong and creative.
Someone is both not quiet and not tall.
Someone is both patient and old.
John is not calm or humble.
Someone is not brave.
Someone is both happy and not calm.
Paul is not patient.
Lucy is both strong and wise. | Lucy is tall. | neutral | (![X]:((humble(X)<~>happy(X))<=>(~strong(X)&patient(X))))&
(![X]:((~brave(X)<~>~creative(X))<=>(wise(X)&strong(X))))&
(((~calm(alice)&humble(alice)))<=>(?[X]:((curious(X)&strong(X)))))&
(![X]:((~calm(X)<~>~generous(X))=>(brave(X)<~>~strong(X))))&
(![X]:(patient(X)=>(curious(X)&kind(X))))&
(((calm(fred)&brave(fred)))=>(?[X]:((~humble(X)|old(X)))))&
(![X]:((~kind(X)<~>rich(X))=>(funny(X)&patient(X))))&
(![X]:((~curious(X)<~>quiet(X))<=>(strong(X)&wise(X))))&
((?[X]:((~quiet(X)<~>happy(X))))<=>((kind(john)|~kind(john))))&
(![X]:((patient(X)<~>kind(X))<=>(funny(X)<~>tall(X))))&
(((brave(john)|~happy(john)))<=>((~happy(paul)|~kind(paul))))&
(((wise(alice)&calm(alice)))=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:(wise(X)=>~old(X)))&
(((old(john)|brave(john)))<=>((rich(alice)|~old(alice))))&
((?[X]:(~humble(X)))<=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((brave(X)&happy(X))=>(strong(X)&~kind(X))))&
((strong(alice)&creative(alice)))&
(?[X]:((~quiet(X)&~tall(X))))&
(?[X]:((patient(X)&old(X))))&
((~calm(john)|humble(john)))&
(?[X]:(~brave(X)))&
(?[X]:((happy(X)&~calm(X))))&
(~patient(paul))&
((strong(lucy)&wise(lucy))) | tall(lucy) | [] | null | 0 |
Everyone who is both calm and not wise is either strong or not humble and vice versa.
Everyone who is either not funny or wise is curious or not brave and vice versa.
Everyone who is not funny is strong or old.
Everyone who is either not quiet or not old is rich or wise.
If lucy is either not funny or brave then alice is both patient and not generous.
If someone is both curious and rich then susan is patient or not wise.
Everyone who is both not happy and not old is not old or not creative.
Everyone who is both wise and not rich is old or tall.
Everyone who is both generous and humble is both curious and creative and vice versa.
If someone is not curious or not old then someone is both calm and happy and vice versa.
If mary is both generous and not rich then someone is either not old or not quiet.
Everyone who is both not wise and wise is not tall or not happy.
Everyone who is either not quiet or humble is either rich or tall.
Everyone who is not old or patient is quiet or not strong.
Everyone who is either patient or not strong is both patient and not strong and vice versa.
Everyone who is either not curious or curious is not humble and vice versa.
Someone is both creative and rich.
Mary is either curious or kind.
Someone is not humble or not creative.
Someone is rich.
Mary is patient or not patient.
Alice is both not calm and not patient.
Lucy is both not kind and not creative. | Susan is patient. | contradiction | (![X]:((calm(X)&~wise(X))<=>(strong(X)<~>~humble(X))))&
(![X]:((~funny(X)<~>wise(X))<=>(curious(X)|~brave(X))))&
(![X]:(~funny(X)=>(strong(X)|old(X))))&
(![X]:((~quiet(X)<~>~old(X))=>(rich(X)|wise(X))))&
(((~funny(lucy)<~>brave(lucy)))=>((patient(alice)&~generous(alice))))&
((?[X]:((curious(X)&rich(X))))=>((patient(susan)|~wise(susan))))&
(![X]:((~happy(X)&~old(X))=>(~old(X)|~creative(X))))&
(![X]:((wise(X)&~rich(X))=>(old(X)|tall(X))))&
(![X]:((generous(X)&humble(X))<=>(curious(X)&creative(X))))&
((?[X]:((~curious(X)|~old(X))))<=>(?[X]:((calm(X)&happy(X)))))&
(((generous(mary)&~rich(mary)))=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:((~wise(X)&wise(X))=>(~tall(X)|~happy(X))))&
(![X]:((~quiet(X)<~>humble(X))=>(rich(X)<~>tall(X))))&
(![X]:((~old(X)|patient(X))=>(quiet(X)|~strong(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(patient(X)&~strong(X))))&
(![X]:((~curious(X)<~>curious(X))<=>~humble(X)))&
(?[X]:((creative(X)&rich(X))))&
((curious(mary)<~>kind(mary)))&
(?[X]:((~humble(X)|~creative(X))))&
(?[X]:(rich(X)))&
((patient(mary)|~patient(mary)))&
((~calm(alice)&~patient(alice)))&
((~kind(lucy)&~creative(lucy))) | patient(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7391883715844411396192503
% SZS output start Proof for 7391883715844411396192503
15. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (~strong(X0) & patient(X0))) [input p14]
24. patient(susan) [input hypothesis]
61. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (strong(X0) | ~patient(X0))) & ((~strong(X0) & patient(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 15]
62. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | strong(X0) | ~patient(X0)) & ((~strong(X0) & patient(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 61]
113. ~strong(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 62]
116. strong(X0) | ~patient(X0) | strong(X0) | ~patient(X0) [cnf transformation 62]
132. patient(susan) [cnf transformation 24]
136. ~strong(X0) | ~patient(X0) [duplicate literal removal 113]
137. strong(X0) | ~patient(X0) [duplicate literal removal 116]
218. ~patient(X0) [subsumption resolution 136,137]
231. $false [subsumption resolution 132,218]
% SZS output end Proof for 7391883715844411396192503
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both generous and brave then alice is not wise or not kind and vice versa.
If someone is both not rich and quiet then paul is old and vice versa.
Everyone who is both not funny and not humble is both not strong and wise and vice versa.
If someone is both strong and not generous then someone is not patient or quiet and vice versa.
Everyone who is either not strong or not quiet is strong and vice versa.
Everyone who is calm or not wise is not wise or strong and vice versa.
Everyone who is both kind and generous is calm.
Everyone who is both wise and creative is not tall or tall and vice versa.
If someone is not humble then someone is not strong or strong.
Everyone who is funny is either not rich or not curious.
If someone is both not calm and happy then someone is not tall or not funny and vice versa.
Everyone who is not humble is both funny and not kind and vice versa.
If susan is both not brave and not quiet then lucy is both not generous and not tall and vice versa.
If fred is both old and calm then someone is either not tall or not wise and vice versa.
If someone is both brave and rich then fred is humble and vice versa.
Mary is either creative or rich.
Paul is either generous or not old.
Someone is creative or not happy.
Mary is both not kind and calm.
Someone is both generous and not kind. | Susan is not tall. | contradiction | (((generous(mary)&brave(mary)))<=>((~wise(alice)|~kind(alice))))&
((?[X]:((~rich(X)&quiet(X))))<=>(old(paul)))&
(![X]:((~funny(X)&~humble(X))<=>(~strong(X)&wise(X))))&
((?[X]:((strong(X)&~generous(X))))<=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((~strong(X)<~>~quiet(X))<=>strong(X)))&
(![X]:((calm(X)|~wise(X))<=>(~wise(X)|strong(X))))&
(![X]:((kind(X)&generous(X))=>calm(X)))&
(![X]:((wise(X)&creative(X))<=>(~tall(X)|tall(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~strong(X)|strong(X)))))&
(![X]:(funny(X)=>(~rich(X)<~>~curious(X))))&
((?[X]:((~calm(X)&happy(X))))<=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:(~humble(X)<=>(funny(X)&~kind(X))))&
(((~brave(susan)&~quiet(susan)))<=>((~generous(lucy)&~tall(lucy))))&
(((old(fred)&calm(fred)))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((brave(X)&rich(X))))<=>(humble(fred)))&
((creative(mary)<~>rich(mary)))&
((generous(paul)<~>~old(paul)))&
(?[X]:((creative(X)|~happy(X))))&
((~kind(mary)&calm(mary)))&
(?[X]:((generous(X)&~kind(X)))) | ~tall(susan) | [
"p2",
"p5",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4681549830047995020339349
% SZS output start Proof for 4681549830047995020339349
3. ! [X0] : ((~humble(X0) & ~funny(X0)) <=> (wise(X0) & ~strong(X0))) [input p2]
6. ! [X0] : ((~wise(X0) | calm(X0)) <=> (strong(X0) | ~wise(X0))) [input p5]
8. ! [X0] : ((creative(X0) & wise(X0)) <=> (tall(X0) | ~tall(X0))) [input p7]
11. ? [X0] : (happy(X0) & ~calm(X0)) <=> ? [X0] : (~funny(X0) | ~tall(X0)) [input p10]
12. ! [X0] : (~humble(X0) <=> (~kind(X0) & funny(X0))) [input p11]
21. ~tall(susan) [input hypothesis]
24. ? [X0] : (happy(X0) & ~calm(X0)) <=> ? [X1] : (~funny(X1) | ~tall(X1)) [rectify 11]
35. ! [X0] : (((~humble(X0) & ~funny(X0)) | (~wise(X0) | strong(X0))) & ((wise(X0) & ~strong(X0)) | (humble(X0) | funny(X0)))) [nnf transformation 3]
36. ! [X0] : (((~humble(X0) & ~funny(X0)) | ~wise(X0) | strong(X0)) & ((wise(X0) & ~strong(X0)) | humble(X0) | funny(X0))) [flattening 35]
43. ! [X0] : (((~wise(X0) | calm(X0)) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | (wise(X0) & ~calm(X0)))) [nnf transformation 6]
44. ! [X0] : ((~wise(X0) | calm(X0) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | (wise(X0) & ~calm(X0)))) [flattening 43]
45. ! [X0] : (((creative(X0) & wise(X0)) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | (~creative(X0) | ~wise(X0)))) [nnf transformation 8]
46. ! [X0] : (((creative(X0) & wise(X0)) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | ~creative(X0) | ~wise(X0))) [flattening 45]
51. (? [X0] : (happy(X0) & ~calm(X0)) | ! [X1] : (funny(X1) & tall(X1))) & (? [X1] : (~funny(X1) | ~tall(X1)) | ! [X0] : (~happy(X0) | calm(X0))) [nnf transformation 24]
52. (? [X0] : (happy(X0) & ~calm(X0)) | ! [X1] : (funny(X1) & tall(X1))) & (? [X2] : (~funny(X2) | ~tall(X2)) | ! [X3] : (~happy(X3) | calm(X3))) [rectify 51]
53. ? [X0] : (happy(X0) & ~calm(X0)) => (happy(sK4) & ~calm(sK4)) [choice axiom]
54. ? [X2] : (~funny(X2) | ~tall(X2)) => (~funny(sK5) | ~tall(sK5)) [choice axiom]
55. ((happy(sK4) & ~calm(sK4)) | ! [X1] : (funny(X1) & tall(X1))) & ((~funny(sK5) | ~tall(sK5)) | ! [X3] : (~happy(X3) | calm(X3))) [skolemisation 52,54,53]
56. ! [X0] : ((~humble(X0) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | humble(X0))) [nnf transformation 12]
57. ! [X0] : ((~humble(X0) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | humble(X0))) [flattening 56]
85. ~funny(X0) | ~wise(X0) | strong(X0) [cnf transformation 36]
86. ~humble(X0) | ~wise(X0) | strong(X0) [cnf transformation 36]
99. ~strong(X0) | calm(X0) | ~wise(X0) [cnf transformation 44]
102. wise(X0) | tall(X0) [cnf transformation 46]
103. ~tall(X0) | wise(X0) [cnf transformation 46]
110. ~calm(sK4) | tall(X1) [cnf transformation 55]
114. humble(X0) | funny(X0) [cnf transformation 57]
139. ~tall(susan) [cnf transformation 21]
214. wise(X0) [subsumption resolution 102,103]
224. 18 <=> ! [X1] : tall(X1) [avatar definition]
225. tall(X1) <- (18) [avatar component clause 224]
228. 19 <=> calm(sK4) [avatar definition]
230. ~calm(sK4) <- (~19) [avatar component clause 228]
232. 18 | ~19 [avatar split clause 110,228,224]
312. $false <- (18) [resolution 225,139]
313. ~18 [avatar contradiction clause 312]
320. ~wise(X1) | strong(X1) | funny(X1) [resolution 86,114]
322. strong(X1) | funny(X1) [subsumption resolution 320,214]
335. funny(X0) | calm(X0) | ~wise(X0) [resolution 322,99]
339. calm(X0) | funny(X0) [subsumption resolution 335,214]
340. funny(sK4) <- (~19) [resolution 339,230]
343. ~wise(sK4) | strong(sK4) <- (~19) [resolution 340,85]
353. strong(sK4) <- (~19) [subsumption resolution 343,214]
369. calm(sK4) | ~wise(sK4) <- (~19) [resolution 353,99]
372. ~wise(sK4) <- (~19) [subsumption resolution 369,230]
373. $false <- (~19) [subsumption resolution 372,214]
374. 19 [avatar contradiction clause 373]
375. $false [avatar sat refutation 232,313,374]
% SZS output end Proof for 4681549830047995020339349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is both generous and creative.
Everyone who is either calm or not happy is not wise.
Everyone who is old is patient.
If mary is generous then someone is both not tall and kind and vice versa.
Everyone who is both not strong and not humble is quiet.
Everyone who is not funny is both funny and not kind and vice versa.
Everyone who is both rich and curious is not generous and vice versa.
Everyone who is either old or not brave is happy or not generous.
Everyone who is strong or wise is wise.
Everyone who is not kind is either funny or not creative.
If john is both not creative and not generous then someone is both wise and not strong and vice versa.
If someone is either not strong or not humble then mary is either not patient or quiet and vice versa.
If john is either generous or not old then paul is not creative and vice versa.
Everyone who is both quiet and not happy is not tall.
Everyone who is both curious and calm is happy.
Everyone who is generous is both not patient and not tall.
Someone is both creative and not generous.
Someone is either creative or patient.
Alice is not humble or rich.
Someone is patient.
John is tall or creative.
John is either not tall or not funny.
Someone is humble or old.
Alice is either calm or brave. | Mary is funny. | entailment | (![X]:(~rich(X)=>(generous(X)&creative(X))))&
(![X]:((calm(X)<~>~happy(X))=>~wise(X)))&
(![X]:(old(X)=>patient(X)))&
((generous(mary))<=>(?[X]:((~tall(X)&kind(X)))))&
(![X]:((~strong(X)&~humble(X))=>quiet(X)))&
(![X]:(~funny(X)<=>(funny(X)&~kind(X))))&
(![X]:((rich(X)&curious(X))<=>~generous(X)))&
(![X]:((old(X)<~>~brave(X))=>(happy(X)|~generous(X))))&
(![X]:((strong(X)|wise(X))=>wise(X)))&
(![X]:(~kind(X)=>(funny(X)<~>~creative(X))))&
(((~creative(john)&~generous(john)))<=>(?[X]:((wise(X)&~strong(X)))))&
((?[X]:((~strong(X)<~>~humble(X))))<=>((~patient(mary)<~>quiet(mary))))&
(((generous(john)<~>~old(john)))<=>(~creative(paul)))&
(![X]:((quiet(X)&~happy(X))=>~tall(X)))&
(![X]:((curious(X)&calm(X))=>happy(X)))&
(![X]:(generous(X)=>(~patient(X)&~tall(X))))&
(?[X]:((creative(X)&~generous(X))))&
(?[X]:((creative(X)<~>patient(X))))&
((~humble(alice)|rich(alice)))&
(?[X]:(patient(X)))&
((tall(john)|creative(john)))&
((~tall(john)<~>~funny(john)))&
(?[X]:((humble(X)|old(X))))&
((calm(alice)<~>brave(alice))) | funny(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7804616801820806676886718
% SZS output start Proof for 7804616801820806676886718
6. ! [X0] : (~funny(X0) <=> (~kind(X0) & funny(X0))) [input p5]
25. ~funny(mary) [input hypothesis]
45. ! [X0] : ((~funny(X0) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | funny(X0))) [nnf transformation 6]
46. ! [X0] : ((~funny(X0) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | funny(X0))) [flattening 45]
81. funny(X0) | funny(X0) [cnf transformation 46]
125. ~funny(mary) [cnf transformation 25]
126. funny(X0) [duplicate literal removal 81]
256. $false [subsumption resolution 125,126]
% SZS output end Proof for 7804616801820806676886718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | John is humble. | 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)))) | humble(john) | [
"p0",
"p4",
"p5",
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4886019955279818933272249
% SZS output start Proof for 4886019955279818933272249
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]
18. ~wise(john) <~> humble(john) [input p17]
22. humble(john) [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]
73. (~humble(john) | wise(john)) & (humble(john) | ~wise(john)) [nnf transformation 18]
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]
109. ~generous(X0) | calm(X0) [cnf transformation 46]
110. ~generous(X0) | ~funny(X0) [cnf transformation 46]
151. ~humble(john) | wise(john) [cnf transformation 73]
155. humble(john) [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]
325. 36 <=> wise(john) [avatar definition]
327. wise(john) <- (36) [avatar component clause 325]
329. 37 <=> humble(john) [avatar definition]
332. 36 | ~37 [avatar split clause 151,329,325]
357. 37 [avatar split clause 155,329]
382. ~creative(X0) | ~wise(X0) <- (14) [resolution 81,222]
384. ~wise(X0) <- (12, 14) [subsumption resolution 382,214]
385. $false <- (12, 14, 36) [resolution 384,327]
386. ~12 | ~14 | ~36 [avatar contradiction clause 385]
394. ~funny(sK2) <- (15) [resolution 227,110]
395. calm(sK2) <- (15) [resolution 227,109]
399. funny(sK2) <- (15) [resolution 395,197]
400. $false <- (15) [subsumption resolution 399,394]
401. ~15 [avatar contradiction clause 400]
402. $false [avatar sat refutation 228,229,332,357,386,401]
% SZS output end Proof for 4886019955279818933272249
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not calm is both old and not patient.
If someone is funny then alice is humble or rich and vice versa.
If susan is either not happy or calm then alice is old or not curious and vice versa.
Everyone who is both not calm and generous is either not rich or not curious.
Everyone who is both tall and not curious is both not old and creative and vice versa.
Everyone who is not calm is either brave or not tall and vice versa.
If paul is both rich and not calm then mary is calm and vice versa.
Everyone who is not calm or not rich is both not wise and not strong and vice versa.
Everyone who is both not quiet and not humble is not tall.
Everyone who is either brave or curious is both not humble and humble and vice versa.
If someone is not old or not quiet then someone is not happy.
Everyone who is both curious and brave is either not humble or not old and vice versa.
If alice is rich then paul is both old and calm.
If mary is either generous or rich then alice is either not generous or calm.
If someone is either patient or not humble then susan is both not brave and not kind and vice versa.
If someone is not quiet then someone is either not calm or old and vice versa.
Someone is both not tall and creative.
John is creative or generous.
Lucy is not quiet.
Lucy is either not funny or not old.
Paul is not strong.
Lucy is brave.
Alice is both kind and rich. | Mary is strong. | contradiction | (![X]:((patient(X)|~calm(X))=>(old(X)&~patient(X))))&
((?[X]:(funny(X)))<=>((humble(alice)|rich(alice))))&
(((~happy(susan)<~>calm(susan)))<=>((old(alice)|~curious(alice))))&
(![X]:((~calm(X)&generous(X))=>(~rich(X)<~>~curious(X))))&
(![X]:((tall(X)&~curious(X))<=>(~old(X)&creative(X))))&
(![X]:(~calm(X)<=>(brave(X)<~>~tall(X))))&
(((rich(paul)&~calm(paul)))<=>(calm(mary)))&
(![X]:((~calm(X)|~rich(X))<=>(~wise(X)&~strong(X))))&
(![X]:((~quiet(X)&~humble(X))=>~tall(X)))&
(![X]:((brave(X)<~>curious(X))<=>(~humble(X)&humble(X))))&
((?[X]:((~old(X)|~quiet(X))))=>(?[X]:(~happy(X))))&
(![X]:((curious(X)&brave(X))<=>(~humble(X)<~>~old(X))))&
((rich(alice))=>((old(paul)&calm(paul))))&
(((generous(mary)<~>rich(mary)))=>((~generous(alice)<~>calm(alice))))&
((?[X]:((patient(X)<~>~humble(X))))<=>((~brave(susan)&~kind(susan))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~calm(X)<~>old(X)))))&
(?[X]:((~tall(X)&creative(X))))&
((creative(john)|generous(john)))&
(~quiet(lucy))&
((~funny(lucy)<~>~old(lucy)))&
(~strong(paul))&
(brave(lucy))&
((kind(alice)&rich(alice))) | strong(mary) | [
"p6",
"p7",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8293847442795023856809721
% SZS output start Proof for 8293847442795023856809721
7. (~calm(paul) & rich(paul)) <=> calm(mary) [input p6]
8. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> (~strong(X0) & ~wise(X0))) [input p7]
13. rich(alice) => (calm(paul) & old(paul)) [input p12]
23. rich(alice) & kind(alice) [input p22]
24. strong(mary) [input hypothesis]
33. (calm(paul) & old(paul)) | ~rich(alice) [ennf transformation 13]
46. ((~calm(paul) & rich(paul)) | ~calm(mary)) & (calm(mary) | (calm(paul) | ~rich(paul))) [nnf transformation 7]
47. ((~calm(paul) & rich(paul)) | ~calm(mary)) & (calm(mary) | calm(paul) | ~rich(paul)) [flattening 46]
48. ! [X0] : (((~rich(X0) | ~calm(X0)) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | (rich(X0) & calm(X0)))) [nnf transformation 8]
49. ! [X0] : ((~rich(X0) | ~calm(X0) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | (rich(X0) & calm(X0)))) [flattening 48]
96. ~calm(paul) | ~calm(mary) [cnf transformation 47]
99. ~strong(X0) | calm(X0) [cnf transformation 49]
118. calm(paul) | ~rich(alice) [cnf transformation 33]
142. rich(alice) [cnf transformation 23]
143. strong(mary) [cnf transformation 24]
146. 1 <=> rich(alice) [avatar definition]
186. 9 <=> calm(mary) [avatar definition]
188. ~calm(mary) <- (~9) [avatar component clause 186]
190. 10 <=> calm(paul) [avatar definition]
193. ~9 | ~10 [avatar split clause 96,190,186]
216. ~1 | 10 [avatar split clause 118,190,146]
302. 1 [avatar split clause 142,146]
306. calm(mary) [resolution 99,143]
307. $false <- (~9) [subsumption resolution 306,188]
308. 9 [avatar contradiction clause 307]
309. $false [avatar sat refutation 193,216,302,308]
% SZS output end Proof for 8293847442795023856809721
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or not patient then alice is either happy or tall and vice versa.
If someone is not kind then lucy is patient or old.
If someone is not brave or not funny then someone is either wise or not rich and vice versa.
Everyone who is either not quiet or rich is both rich and humble.
If paul is both not kind and not curious then susan is either not brave or not funny.
Everyone who is either not rich or not creative is not calm.
Everyone who is not tall is both wise and generous and vice versa.
If someone is both tall and not brave then alice is not funny and vice versa.
If someone is calm or not patient then paul is both not wise and creative.
If someone is both not quiet and happy then someone is humble or curious.
Everyone who is not patient or creative is not kind.
If lucy is either not brave or not strong then paul is both creative and calm and vice versa.
If john is wise or not old then someone is not generous or not rich.
Everyone who is either not patient or not kind is either not quiet or not rich and vice versa.
Everyone who is funny is not quiet and vice versa.
Everyone who is not patient is either not wise or rich.
Alice is not old or rich.
Someone is tall or not patient.
Someone is not quiet.
Lucy is not rich.
Someone is both not wise and not funny.
John is both generous and calm.
Susan is patient or not humble.
Someone is not happy. | Paul is wise. | contradiction | ((?[X]:((~wise(X)<~>~patient(X))))<=>((happy(alice)<~>tall(alice))))&
((?[X]:(~kind(X)))=>((patient(lucy)|old(lucy))))&
((?[X]:((~brave(X)|~funny(X))))<=>(?[X]:((wise(X)<~>~rich(X)))))&
(![X]:((~quiet(X)<~>rich(X))=>(rich(X)&humble(X))))&
(((~kind(paul)&~curious(paul)))=>((~brave(susan)<~>~funny(susan))))&
(![X]:((~rich(X)<~>~creative(X))=>~calm(X)))&
(![X]:(~tall(X)<=>(wise(X)&generous(X))))&
((?[X]:((tall(X)&~brave(X))))<=>(~funny(alice)))&
((?[X]:((calm(X)|~patient(X))))=>((~wise(paul)&creative(paul))))&
((?[X]:((~quiet(X)&happy(X))))=>(?[X]:((humble(X)|curious(X)))))&
(![X]:((~patient(X)|creative(X))=>~kind(X)))&
(((~brave(lucy)<~>~strong(lucy)))<=>((creative(paul)&calm(paul))))&
(((wise(john)|~old(john)))=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~patient(X)<~>~kind(X))<=>(~quiet(X)<~>~rich(X))))&
(![X]:(funny(X)<=>~quiet(X)))&
(![X]:(~patient(X)=>(~wise(X)<~>rich(X))))&
((~old(alice)|rich(alice)))&
(?[X]:((tall(X)|~patient(X))))&
(?[X]:(~quiet(X)))&
(~rich(lucy))&
(?[X]:((~wise(X)&~funny(X))))&
((generous(john)&calm(john)))&
((patient(susan)|~humble(susan)))&
(?[X]:(~happy(X))) | wise(paul) | [
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8750674405665455046711399
% SZS output start Proof for 8750674405665455046711399
9. ? [X0] : (~patient(X0) | calm(X0)) => (creative(paul) & ~wise(paul)) [input p8]
22. calm(john) & generous(john) [input p21]
25. wise(paul) [input hypothesis]
34. (creative(paul) & ~wise(paul)) | ! [X0] : (patient(X0) & ~calm(X0)) [ennf transformation 9]
97. ~wise(paul) | ~calm(X0) [cnf transformation 34]
130. calm(john) [cnf transformation 22]
133. wise(paul) [cnf transformation 25]
238. 24 <=> ! [X0] : ~calm(X0) [avatar definition]
239. ~calm(X0) <- (24) [avatar component clause 238]
242. 25 <=> wise(paul) [avatar definition]
246. 24 | ~25 [avatar split clause 97,242,238]
319. 25 [avatar split clause 133,242]
323. $false <- (24) [resolution 239,130]
324. ~24 [avatar contradiction clause 323]
325. $false [avatar sat refutation 246,319,324]
% SZS output end Proof for 8750674405665455046711399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not patient is not kind or funny and vice versa. If susan is not curious or tall then fred is both strong and not happy. Everyone who is not funny or not generous is either not patient or not funny. Everyone who is both calm and not quiet is both tall and generous. Everyone who is humble or not humble is kind or rich. Everyone who is generous is both not generous and wise and vice versa. If someone is either tall or old then someone is old. If someone is both kind and generous then fred is both not kind and generous and vice versa. Everyone who is both not calm and quiet is not strong or old. If someone is funny or wise then someone is both tall and funny and vice versa. Everyone who is either quiet or not creative is curious or old. If fred is either generous or happy then paul is strong or not tall and vice versa. If mary is funny or tall then someone is both curious and kind. Everyone who is calm is not creative or generous. Everyone who is rich or not brave is patient. Mary is both old and not curious. Someone is either not kind or not quiet. Someone is creative or not humble. Someone is tall or strong. Someone is both not curious and humble. Someone is old or calm. | Susan is kind. | entailment | (![X]:((~rich(X)<~>~patient(X))<=>(~kind(X)|funny(X))))&
(((~curious(susan)|tall(susan)))=>((strong(fred)&~happy(fred))))&
(![X]:((~funny(X)|~generous(X))=>(~patient(X)<~>~funny(X))))&
(![X]:((calm(X)&~quiet(X))=>(tall(X)&generous(X))))&
(![X]:((humble(X)|~humble(X))=>(kind(X)|rich(X))))&
(![X]:(generous(X)<=>(~generous(X)&wise(X))))&
((?[X]:((tall(X)<~>old(X))))=>(?[X]:(old(X))))&
((?[X]:((kind(X)&generous(X))))<=>((~kind(fred)&generous(fred))))&
(![X]:((~calm(X)&quiet(X))=>(~strong(X)|old(X))))&
((?[X]:((funny(X)|wise(X))))<=>(?[X]:((tall(X)&funny(X)))))&
(![X]:((quiet(X)<~>~creative(X))=>(curious(X)|old(X))))&
(((generous(fred)<~>happy(fred)))<=>((strong(paul)|~tall(paul))))&
(((funny(mary)|tall(mary)))=>(?[X]:((curious(X)&kind(X)))))&
(![X]:(calm(X)=>(~creative(X)|generous(X))))&
(![X]:((rich(X)|~brave(X))=>patient(X)))&
((old(mary)&~curious(mary)))&
(?[X]:((~kind(X)<~>~quiet(X))))&
(?[X]:((creative(X)|~humble(X))))&
(?[X]:((tall(X)|strong(X))))&
(?[X]:((~curious(X)&humble(X))))&
(?[X]:((old(X)|calm(X)))) | kind(susan) | [
"p0",
"p2",
"p4",
"p5",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1840032730120640896429686
% SZS output start Proof for 1840032730120640896429686
1. ! [X0] : ((~rich(X0) <~> ~patient(X0)) <=> (funny(X0) | ~kind(X0))) [input p0]
3. ! [X0] : ((~generous(X0) | ~funny(X0)) => (~patient(X0) <~> ~funny(X0))) [input p2]
5. ! [X0] : ((~humble(X0) | humble(X0)) => (rich(X0) | kind(X0))) [input p4]
6. ! [X0] : (generous(X0) <=> (wise(X0) & ~generous(X0))) [input p5]
10. ? [X0] : (wise(X0) | funny(X0)) <=> ? [X0] : (funny(X0) & tall(X0)) [input p9]
15. ! [X0] : ((~brave(X0) | rich(X0)) => patient(X0)) [input p14]
22. ~kind(susan) [input hypothesis]
24. ? [X0] : (wise(X0) | funny(X0)) <=> ? [X1] : (funny(X1) & tall(X1)) [rectify 10]
25. ! [X0] : (rich(X0) => patient(X0)) [pure predicate removal 15]
27. ! [X0] : ((~patient(X0) <~> ~funny(X0)) | (generous(X0) & funny(X0))) [ennf transformation 3]
30. ! [X0] : ((rich(X0) | kind(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 5]
31. ! [X0] : (rich(X0) | kind(X0) | (humble(X0) & ~humble(X0))) [flattening 30]
40. ! [X0] : (patient(X0) | ~rich(X0)) [ennf transformation 25]
41. ! [X0] : ((((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))))) [nnf transformation 1]
42. ! [X0] : ((((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))))) [flattening 41]
43. ! [X0] : (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (generous(X0) & funny(X0))) [nnf transformation 27]
44. ! [X0] : ((generous(X0) | (~wise(X0) | generous(X0))) & ((wise(X0) & ~generous(X0)) | ~generous(X0))) [nnf transformation 6]
45. ! [X0] : ((generous(X0) | ~wise(X0) | generous(X0)) & ((wise(X0) & ~generous(X0)) | ~generous(X0))) [flattening 44]
55. (? [X0] : (wise(X0) | funny(X0)) | ! [X1] : (~funny(X1) | ~tall(X1))) & (? [X1] : (funny(X1) & tall(X1)) | ! [X0] : (~wise(X0) & ~funny(X0))) [nnf transformation 24]
56. (? [X0] : (wise(X0) | funny(X0)) | ! [X1] : (~funny(X1) | ~tall(X1))) & (? [X2] : (funny(X2) & tall(X2)) | ! [X3] : (~wise(X3) & ~funny(X3))) [rectify 55]
57. ? [X0] : (wise(X0) | funny(X0)) => (wise(sK2) | funny(sK2)) [choice axiom]
58. ? [X2] : (funny(X2) & tall(X2)) => (funny(sK3) & tall(sK3)) [choice axiom]
59. ((wise(sK2) | funny(sK2)) | ! [X1] : (~funny(X1) | ~tall(X1))) & ((funny(sK3) & tall(sK3)) | ! [X3] : (~wise(X3) & ~funny(X3))) [skolemisation 56,58,57]
78. ~patient(X0) | ~rich(X0) | kind(X0) [cnf transformation 42]
81. ~funny(X0) | rich(X0) | patient(X0) [cnf transformation 42]
87. ~funny(X0) | ~patient(X0) | generous(X0) [cnf transformation 43]
88. funny(X0) | patient(X0) | funny(X0) [cnf transformation 43]
92. rich(X0) | kind(X0) | ~humble(X0) [cnf transformation 31]
93. rich(X0) | kind(X0) | humble(X0) [cnf transformation 31]
94. ~generous(X0) | ~generous(X0) [cnf transformation 45]
106. funny(sK3) | ~funny(X3) [cnf transformation 59]
122. ~rich(X0) | patient(X0) [cnf transformation 40]
132. ~kind(susan) [cnf transformation 22]
133. ~generous(X0) [duplicate literal removal 94]
135. funny(X0) | patient(X0) [duplicate literal removal 88]
156. kind(X0) | rich(X0) [subsumption resolution 92,93]
185. 12 <=> funny(sK3) [avatar definition]
187. funny(sK3) <- (12) [avatar component clause 185]
190. 13 <=> ! [X3] : ~funny(X3) [avatar definition]
191. ~funny(X3) <- (13) [avatar component clause 190]
192. 13 | 12 [avatar split clause 106,185,190]
271. patient(X0) <- (13) [resolution 135,191]
275. ~rich(X0) | kind(X0) <- (13) [resolution 78,271]
276. kind(X0) <- (13) [subsumption resolution 275,156]
278. $false <- (13) [resolution 276,132]
279. ~13 [avatar contradiction clause 278]
291. rich(X0) | patient(X0) | patient(X0) [resolution 81,135]
294. rich(X0) | patient(X0) [duplicate literal removal 291]
295. patient(X0) [subsumption resolution 294,122]
297. ~patient(sK3) | generous(sK3) <- (12) [resolution 87,187]
299. generous(sK3) <- (12) [subsumption resolution 297,295]
300. $false <- (12) [subsumption resolution 299,133]
301. ~12 [avatar contradiction clause 300]
305. $false [avatar sat refutation 192,279,301]
% SZS output end Proof for 1840032730120640896429686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either not rich or not old and vice versa. Everyone who is either not creative or not tall is either rich or not old. Everyone who is either not generous or not calm is calm or not kind and vice versa. If john is either curious or generous then someone is either funny or not brave and vice versa. If susan is not tall then john is not creative or creative. Everyone who is both quiet and brave is not funny and vice versa. If someone is calm then someone is either wise or not brave. Everyone who is generous is both not rich and strong and vice versa. If alice is creative or not humble then someone is both strong and not old and vice versa. If alice is not wise or not rich then john is either calm or not curious. Everyone who is both not rich and not curious is not funny and vice versa. Everyone who is not strong is wise and vice versa. If john is either not strong or happy then someone is either not calm or not curious. Everyone who is not quiet is not old or humble and vice versa. Everyone who is generous or not quiet is funny. If lucy is both not calm and not humble then alice is brave or rich. Someone is both old and not wise. Someone is generous or not funny. Someone is strong or not patient. Paul is not brave. Susan is both happy and not curious. Fred is either not wise or funny. | Lucy is not patient. | neutral | (![X]:(~quiet(X)<=>(~rich(X)<~>~old(X))))&
(![X]:((~creative(X)<~>~tall(X))=>(rich(X)<~>~old(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(calm(X)|~kind(X))))&
(((curious(john)<~>generous(john)))<=>(?[X]:((funny(X)<~>~brave(X)))))&
((~tall(susan))=>((~creative(john)|creative(john))))&
(![X]:((quiet(X)&brave(X))<=>~funny(X)))&
((?[X]:(calm(X)))=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:(generous(X)<=>(~rich(X)&strong(X))))&
(((creative(alice)|~humble(alice)))<=>(?[X]:((strong(X)&~old(X)))))&
(((~wise(alice)|~rich(alice)))=>((calm(john)<~>~curious(john))))&
(![X]:((~rich(X)&~curious(X))<=>~funny(X)))&
(![X]:(~strong(X)<=>wise(X)))&
(((~strong(john)<~>happy(john)))=>(?[X]:((~calm(X)<~>~curious(X)))))&
(![X]:(~quiet(X)<=>(~old(X)|humble(X))))&
(![X]:((generous(X)|~quiet(X))=>funny(X)))&
(((~calm(lucy)&~humble(lucy)))=>((brave(alice)|rich(alice))))&
(?[X]:((old(X)&~wise(X))))&
(?[X]:((generous(X)|~funny(X))))&
(?[X]:((strong(X)|~patient(X))))&
(~brave(paul))&
((happy(susan)&~curious(susan)))&
((~wise(fred)<~>funny(fred))) | ~patient(lucy) | [] | null | 0 |
Everyone who is wise or kind is either not wise or creative and vice versa. If paul is humble then someone is wise and vice versa. If susan is kind then susan is either tall or funny and vice versa. If someone is not rich then someone is not brave or old. If paul is not patient or humble then mary is both not strong and not quiet and vice versa. Everyone who is either creative or kind is either wise or not patient and vice versa. If someone is not wise or kind then mary is curious. Everyone who is both not creative and generous is not humble or not wise and vice versa. If lucy is either calm or curious then lucy is both strong and old. If john is either strong or wise then susan is either kind or generous and vice versa. Everyone who is brave is not patient or not happy and vice versa. If someone is both not brave and tall then paul is either kind or not quiet and vice versa. Everyone who is not happy is both not strong and quiet and vice versa. Everyone who is both generous and not quiet is not old and vice versa. If lucy is not creative then paul is creative or strong. If paul is quiet or strong then someone is not old or not wise. Paul is not happy. Someone is either not curious or humble. Someone is old or not creative. Someone is rich or not wise. John is tall. John is either tall or not brave. Someone is not wise. Someone is either not humble or rich. | Paul is not quiet. | contradiction | (![X]:((wise(X)|kind(X))<=>(~wise(X)<~>creative(X))))&
((humble(paul))<=>(?[X]:(wise(X))))&
((kind(susan))<=>((tall(susan)<~>funny(susan))))&
((?[X]:(~rich(X)))=>(?[X]:((~brave(X)|old(X)))))&
(((~patient(paul)|humble(paul)))<=>((~strong(mary)&~quiet(mary))))&
(![X]:((creative(X)<~>kind(X))<=>(wise(X)<~>~patient(X))))&
((?[X]:((~wise(X)|kind(X))))=>(curious(mary)))&
(![X]:((~creative(X)&generous(X))<=>(~humble(X)|~wise(X))))&
(((calm(lucy)<~>curious(lucy)))=>((strong(lucy)&old(lucy))))&
(((strong(john)<~>wise(john)))<=>((kind(susan)<~>generous(susan))))&
(![X]:(brave(X)<=>(~patient(X)|~happy(X))))&
((?[X]:((~brave(X)&tall(X))))<=>((kind(paul)<~>~quiet(paul))))&
(![X]:(~happy(X)<=>(~strong(X)&quiet(X))))&
(![X]:((generous(X)&~quiet(X))<=>~old(X)))&
((~creative(lucy))=>((creative(paul)|strong(paul))))&
(((quiet(paul)|strong(paul)))=>(?[X]:((~old(X)|~wise(X)))))&
(~happy(paul))&
(?[X]:((~curious(X)<~>humble(X))))&
(?[X]:((old(X)|~creative(X))))&
(?[X]:((rich(X)|~wise(X))))&
(tall(john))&
((tall(john)<~>~brave(john)))&
(?[X]:(~wise(X)))&
(?[X]:((~humble(X)<~>rich(X)))) | ~quiet(paul) | [
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 382066661681299793107386
% SZS output start Proof for 382066661681299793107386
13. ! [X0] : (~happy(X0) <=> (quiet(X0) & ~strong(X0))) [input p12]
17. ~happy(paul) [input p16]
25. ~quiet(paul) [input hypothesis]
56. ! [X0] : ((~happy(X0) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | happy(X0))) [nnf transformation 13]
57. ! [X0] : ((~happy(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | happy(X0))) [flattening 56]
130. happy(X0) | quiet(X0) [cnf transformation 57]
138. ~happy(paul) [cnf transformation 17]
149. ~quiet(paul) [cnf transformation 25]
267. 23 <=> quiet(paul) [avatar definition]
268. ~quiet(paul) <- (~23) [avatar component clause 267]
353. ~23 [avatar split clause 149,267]
359. quiet(paul) [resolution 130,138]
360. $false <- (~23) [subsumption resolution 359,268]
361. 23 [avatar contradiction clause 360]
362. $false [avatar sat refutation 353,361]
% SZS output end Proof for 382066661681299793107386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not happy is patient or not rich.
If someone is not curious then alice is creative and vice versa.
Everyone who is both tall and curious is both not calm and generous and vice versa.
Everyone who is either not tall or brave is both not rich and not calm and vice versa.
Everyone who is wise is either creative or not happy.
If alice is curious or wise then alice is not kind or not brave and vice versa.
If someone is either not funny or funny then someone is funny and vice versa.
Everyone who is strong or humble is both quiet and not funny and vice versa.
Everyone who is not tall is either not curious or quiet and vice versa.
Everyone who is either not funny or not tall is both not calm and creative and vice versa.
If someone is both not strong and generous then fred is kind and vice versa.
Everyone who is both humble and not humble is generous and vice versa.
If someone is both not creative and humble then someone is not tall.
If someone is either strong or humble then someone is either not calm or happy.
Everyone who is wise is kind or not old.
Everyone who is humble is happy or not curious and vice versa.
John is either creative or curious.
Someone is either not quiet or tall.
Susan is not creative.
Someone is both humble and happy.
Mary is both not old and wise.
Someone is creative. | Alice is quiet. | entailment | (![X]:((~old(X)<~>~happy(X))=>(patient(X)|~rich(X))))&
((?[X]:(~curious(X)))<=>(creative(alice)))&
(![X]:((tall(X)&curious(X))<=>(~calm(X)&generous(X))))&
(![X]:((~tall(X)<~>brave(X))<=>(~rich(X)&~calm(X))))&
(![X]:(wise(X)=>(creative(X)<~>~happy(X))))&
(((curious(alice)|wise(alice)))<=>((~kind(alice)|~brave(alice))))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((strong(X)|humble(X))<=>(quiet(X)&~funny(X))))&
(![X]:(~tall(X)<=>(~curious(X)<~>quiet(X))))&
(![X]:((~funny(X)<~>~tall(X))<=>(~calm(X)&creative(X))))&
((?[X]:((~strong(X)&generous(X))))<=>(kind(fred)))&
(![X]:((humble(X)&~humble(X))<=>generous(X)))&
((?[X]:((~creative(X)&humble(X))))=>(?[X]:(~tall(X))))&
((?[X]:((strong(X)<~>humble(X))))=>(?[X]:((~calm(X)<~>happy(X)))))&
(![X]:(wise(X)=>(kind(X)|~old(X))))&
(![X]:(humble(X)<=>(happy(X)|~curious(X))))&
((creative(john)<~>curious(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(~creative(susan))&
(?[X]:((humble(X)&happy(X))))&
((~old(mary)&wise(mary)))&
(?[X]:(creative(X))) | quiet(alice) | [
"p2",
"p7",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2001942666464196410260132
% SZS output start Proof for 2001942666464196410260132
3. ! [X0] : ((curious(X0) & tall(X0)) <=> (generous(X0) & ~calm(X0))) [input p2]
8. ! [X0] : ((humble(X0) | strong(X0)) <=> (~funny(X0) & quiet(X0))) [input p7]
9. ! [X0] : (~tall(X0) <=> (~curious(X0) <~> quiet(X0))) [input p8]
12. ! [X0] : ((~humble(X0) & humble(X0)) <=> generous(X0)) [input p11]
16. ! [X0] : (humble(X0) <=> (~curious(X0) | happy(X0))) [input p15]
23. ~quiet(alice) [input hypothesis]
37. ! [X0] : (((curious(X0) & tall(X0)) | (~generous(X0) | calm(X0))) & ((generous(X0) & ~calm(X0)) | (~curious(X0) | ~tall(X0)))) [nnf transformation 3]
38. ! [X0] : (((curious(X0) & tall(X0)) | ~generous(X0) | calm(X0)) & ((generous(X0) & ~calm(X0)) | ~curious(X0) | ~tall(X0))) [flattening 37]
49. ! [X0] : (((humble(X0) | strong(X0)) | (funny(X0) | ~quiet(X0))) & ((~funny(X0) & quiet(X0)) | (~humble(X0) & ~strong(X0)))) [nnf transformation 8]
50. ! [X0] : ((humble(X0) | strong(X0) | funny(X0) | ~quiet(X0)) & ((~funny(X0) & quiet(X0)) | (~humble(X0) & ~strong(X0)))) [flattening 49]
51. ! [X0] : ((~tall(X0) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0)))) & (((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | tall(X0))) [nnf transformation 9]
58. ! [X0] : (((~humble(X0) & humble(X0)) | ~generous(X0)) & (generous(X0) | (humble(X0) | ~humble(X0)))) [nnf transformation 12]
59. ! [X0] : (((~humble(X0) & humble(X0)) | ~generous(X0)) & (generous(X0) | humble(X0) | ~humble(X0))) [flattening 58]
67. ! [X0] : ((humble(X0) | (curious(X0) & ~happy(X0))) & ((~curious(X0) | happy(X0)) | ~humble(X0))) [nnf transformation 16]
68. ! [X0] : ((humble(X0) | (curious(X0) & ~happy(X0))) & (~curious(X0) | happy(X0) | ~humble(X0))) [flattening 67]
80. ~tall(X0) | ~curious(X0) | generous(X0) [cnf transformation 38]
100. ~humble(X0) | quiet(X0) [cnf transformation 50]
104. ~curious(X0) | quiet(X0) | tall(X0) [cnf transformation 51]
118. humble(X0) | ~generous(X0) [cnf transformation 59]
119. ~humble(X0) | ~generous(X0) [cnf transformation 59]
127. humble(X0) | curious(X0) [cnf transformation 68]
137. ~quiet(alice) [cnf transformation 23]
158. 5 <=> curious(alice) [avatar definition]
159. ~curious(alice) <- (~5) [avatar component clause 158]
160. curious(alice) <- (5) [avatar component clause 158]
203. ~generous(X0) [subsumption resolution 118,119]
260. quiet(X2) | curious(X2) [resolution 127,100]
275. quiet(alice) | tall(alice) <- (5) [resolution 104,160]
285. tall(alice) <- (5) [subsumption resolution 275,137]
307. ~curious(alice) | generous(alice) <- (5) [resolution 285,80]
308. generous(alice) <- (5) [subsumption resolution 307,160]
309. $false <- (5) [subsumption resolution 308,203]
310. ~5 [avatar contradiction clause 309]
472. curious(alice) [resolution 260,137]
477. $false <- (~5) [subsumption resolution 472,159]
478. 5 [avatar contradiction clause 477]
479. $false [avatar sat refutation 310,478]
% SZS output end Proof for 2001942666464196410260132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not strong is either happy or not happy and vice versa.
If someone is not old then john is either not calm or not creative.
Everyone who is strong is either happy or creative.
If fred is not wise or not kind then john is not quiet or humble and vice versa.
Everyone who is either old or calm is either not tall or not funny.
If someone is either old or rich then someone is both not generous and kind and vice versa.
If alice is either not funny or brave then someone is rich and vice versa.
Everyone who is creative or not funny is either quiet or strong and vice versa.
Everyone who is not brave or tall is both not tall and curious and vice versa.
Everyone who is not brave is both not funny and curious and vice versa.
Everyone who is not curious is either not happy or curious and vice versa.
If someone is either rich or not humble then someone is either not quiet or humble.
Everyone who is both not happy and rich is calm.
If someone is not tall then lucy is both not funny and creative.
Everyone who is both kind and humble is both kind and brave.
Everyone who is either not patient or old is either not rich or tall and vice versa.
Alice is both not patient and brave.
Mary is either rich or not patient.
Someone is both brave and not wise.
Someone is either not rich or not funny.
Someone is not happy.
Lucy is not humble. | Mary is funny. | neutral | (![X]:((~curious(X)&~strong(X))<=>(happy(X)<~>~happy(X))))&
((?[X]:(~old(X)))=>((~calm(john)<~>~creative(john))))&
(![X]:(strong(X)=>(happy(X)<~>creative(X))))&
(((~wise(fred)|~kind(fred)))<=>((~quiet(john)|humble(john))))&
(![X]:((old(X)<~>calm(X))=>(~tall(X)<~>~funny(X))))&
((?[X]:((old(X)<~>rich(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
(((~funny(alice)<~>brave(alice)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~funny(X))<=>(quiet(X)<~>strong(X))))&
(![X]:((~brave(X)|tall(X))<=>(~tall(X)&curious(X))))&
(![X]:(~brave(X)<=>(~funny(X)&curious(X))))&
(![X]:(~curious(X)<=>(~happy(X)<~>curious(X))))&
((?[X]:((rich(X)<~>~humble(X))))=>(?[X]:((~quiet(X)<~>humble(X)))))&
(![X]:((~happy(X)&rich(X))=>calm(X)))&
((?[X]:(~tall(X)))=>((~funny(lucy)&creative(lucy))))&
(![X]:((kind(X)&humble(X))=>(kind(X)&brave(X))))&
(![X]:((~patient(X)<~>old(X))<=>(~rich(X)<~>tall(X))))&
((~patient(alice)&brave(alice)))&
((rich(mary)<~>~patient(mary)))&
(?[X]:((brave(X)&~wise(X))))&
(?[X]:((~rich(X)<~>~funny(X))))&
(?[X]:(~happy(X)))&
(~humble(lucy)) | funny(mary) | [] | null | 0 |
Everyone who is either not wise or humble is not generous and vice versa. If john is both tall and strong then mary is not quiet or not humble and vice versa. If someone is funny or happy then alice is kind or rich. If someone is either tall or not quiet then mary is either old or not humble and vice versa. Everyone who is either happy or brave is either not creative or kind. Everyone who is not strong or brave is not humble or not happy and vice versa. If paul is either quiet or not old then susan is tall or not generous and vice versa. Everyone who is not curious is not kind or rich and vice versa. Everyone who is calm is both not humble and rich and vice versa. Everyone who is both brave and curious is both brave and not old and vice versa. Everyone who is not brave or brave is both not old and strong. Everyone who is strong is both not creative and not brave and vice versa. If lucy is either rich or calm then paul is not brave. Everyone who is not old is either wise or creative. Everyone who is both patient and humble is both humble and old. Everyone who is either tall or not patient is either not kind or wise and vice versa. Someone is not kind or creative. Lucy is not kind or not patient. John is either generous or wise. | Mary is quiet. | contradiction | (![X]:((~wise(X)<~>humble(X))<=>~generous(X)))&
(((tall(john)&strong(john)))<=>((~quiet(mary)|~humble(mary))))&
((?[X]:((funny(X)|happy(X))))=>((kind(alice)|rich(alice))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>((old(mary)<~>~humble(mary))))&
(![X]:((happy(X)<~>brave(X))=>(~creative(X)<~>kind(X))))&
(![X]:((~strong(X)|brave(X))<=>(~humble(X)|~happy(X))))&
(((quiet(paul)<~>~old(paul)))<=>((tall(susan)|~generous(susan))))&
(![X]:(~curious(X)<=>(~kind(X)|rich(X))))&
(![X]:(calm(X)<=>(~humble(X)&rich(X))))&
(![X]:((brave(X)&curious(X))<=>(brave(X)&~old(X))))&
(![X]:((~brave(X)|brave(X))=>(~old(X)&strong(X))))&
(![X]:(strong(X)<=>(~creative(X)&~brave(X))))&
(((rich(lucy)<~>calm(lucy)))=>(~brave(paul)))&
(![X]:(~old(X)=>(wise(X)<~>creative(X))))&
(![X]:((patient(X)&humble(X))=>(humble(X)&old(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(~kind(X)<~>wise(X))))&
(?[X]:((~kind(X)|creative(X))))&
((~kind(lucy)|~patient(lucy)))&
((generous(john)<~>wise(john))) | quiet(mary) | [
"p3",
"p4",
"p5",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1095918504940119844468088
% SZS output start Proof for 1095918504940119844468088
4. ? [X0] : (tall(X0) <~> ~quiet(X0)) <=> (old(mary) <~> ~humble(mary)) [input p3]
5. ! [X0] : ((happy(X0) <~> brave(X0)) => (~creative(X0) <~> kind(X0))) [input p4]
6. ! [X0] : ((brave(X0) | ~strong(X0)) <=> (~happy(X0) | ~humble(X0))) [input p5]
11. ! [X0] : ((brave(X0) | ~brave(X0)) => (strong(X0) & ~old(X0))) [input p10]
12. ! [X0] : (strong(X0) <=> (~brave(X0) & ~creative(X0))) [input p11]
14. ! [X0] : (~old(X0) => (wise(X0) <~> creative(X0))) [input p13]
15. ! [X0] : ((humble(X0) & patient(X0)) => (old(X0) & humble(X0))) [input p14]
16. ! [X0] : ((tall(X0) <~> ~patient(X0)) <=> (~kind(X0) <~> wise(X0))) [input p15]
20. quiet(mary) [input hypothesis]
24. ! [X0] : ((~creative(X0) <~> kind(X0)) | (happy(X0) <=> brave(X0))) [ennf transformation 5]
25. ! [X0] : ((strong(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 11]
27. ! [X0] : ((wise(X0) <~> creative(X0)) | old(X0)) [ennf transformation 14]
28. ! [X0] : ((old(X0) & humble(X0)) | (~humble(X0) | ~patient(X0))) [ennf transformation 15]
29. ! [X0] : ((old(X0) & humble(X0)) | ~humble(X0) | ~patient(X0)) [flattening 28]
33. (? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ((old(mary) | humble(mary)) & (~humble(mary) | ~old(mary)))) & (((humble(mary) | ~old(mary)) & (~humble(mary) | old(mary))) | ! [X0] : ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) [nnf transformation 4]
34. (? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ((old(mary) | humble(mary)) & (~humble(mary) | ~old(mary)))) & (((humble(mary) | ~old(mary)) & (~humble(mary) | old(mary))) | ! [X1] : ((tall(X1) | quiet(X1)) & (~quiet(X1) | ~tall(X1)))) [rectify 33]
35. ? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) => ((quiet(sK0) | ~tall(sK0)) & (~quiet(sK0) | tall(sK0))) [choice axiom]
36. (((quiet(sK0) | ~tall(sK0)) & (~quiet(sK0) | tall(sK0))) | ((old(mary) | humble(mary)) & (~humble(mary) | ~old(mary)))) & (((humble(mary) | ~old(mary)) & (~humble(mary) | old(mary))) | ! [X1] : ((tall(X1) | quiet(X1)) & (~quiet(X1) | ~tall(X1)))) [skolemisation 34,35]
37. ! [X0] : (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) [nnf transformation 24]
38. ! [X0] : (((brave(X0) | ~strong(X0)) | (happy(X0) & humble(X0))) & ((~happy(X0) | ~humble(X0)) | (~brave(X0) & strong(X0)))) [nnf transformation 6]
39. ! [X0] : ((brave(X0) | ~strong(X0) | (happy(X0) & humble(X0))) & (~happy(X0) | ~humble(X0) | (~brave(X0) & strong(X0)))) [flattening 38]
48. ! [X0] : ((strong(X0) | (brave(X0) | creative(X0))) & ((~brave(X0) & ~creative(X0)) | ~strong(X0))) [nnf transformation 12]
49. ! [X0] : ((strong(X0) | brave(X0) | creative(X0)) & ((~brave(X0) & ~creative(X0)) | ~strong(X0))) [flattening 48]
51. ! [X0] : (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | old(X0)) [nnf transformation 27]
52. ! [X0] : ((((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0)))) & (((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0))))) [nnf transformation 16]
66. ~humble(mary) | old(mary) | ~quiet(X1) | ~tall(X1) [cnf transformation 36]
76. ~kind(X0) | creative(X0) | brave(X0) | ~happy(X0) [cnf transformation 37]
80. ~strong(X0) | brave(X0) | humble(X0) [cnf transformation 39]
81. ~strong(X0) | brave(X0) | happy(X0) [cnf transformation 39]
98. ~old(X0) | brave(X0) [cnf transformation 25]
99. ~brave(X0) | ~old(X0) [cnf transformation 25]
100. strong(X0) | brave(X0) [cnf transformation 25]
101. ~brave(X0) | strong(X0) [cnf transformation 25]
102. ~creative(X0) | ~strong(X0) [cnf transformation 49]
103. ~brave(X0) | ~strong(X0) [cnf transformation 49]
107. creative(X0) | wise(X0) | old(X0) [cnf transformation 51]
110. old(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 29]
114. ~wise(X0) | kind(X0) | tall(X0) | patient(X0) [cnf transformation 52]
123. quiet(mary) [cnf transformation 20]
125. 1 <=> humble(mary) [avatar definition]
126. ~humble(mary) <- (~1) [avatar component clause 125]
134. 3 <=> quiet(mary) [avatar definition]
136. quiet(mary) <- (3) [avatar component clause 134]
158. 8 <=> old(mary) [avatar definition]
160. old(mary) <- (8) [avatar component clause 158]
178. 12 <=> ! [X1] : (~quiet(X1) | ~tall(X1)) [avatar definition]
179. ~quiet(X1) | ~tall(X1) <- (12) [avatar component clause 178]
182. 12 | 8 | ~1 [avatar split clause 66,125,158,178]
205. strong(X0) [subsumption resolution 100,101]
206. ~old(X0) [subsumption resolution 98,99]
207. ~brave(X0) [subsumption resolution 103,205]
208. ~creative(X0) [subsumption resolution 102,205]
209. wise(X0) | old(X0) [subsumption resolution 107,208]
210. wise(X0) [subsumption resolution 209,206]
211. ~patient(X0) | ~humble(X0) [subsumption resolution 110,206]
214. patient(X0) | tall(X0) | kind(X0) [subsumption resolution 114,210]
227. 3 [avatar split clause 123,134]
236. brave(X0) | humble(X0) [resolution 80,205]
237. humble(X0) [subsumption resolution 236,207]
238. brave(X0) | happy(X0) [resolution 81,205]
239. happy(X0) [subsumption resolution 238,207]
249. $false <- (~1) [resolution 237,126]
251. 1 [avatar contradiction clause 249]
252. $false <- (8) [subsumption resolution 160,206]
253. ~8 [avatar contradiction clause 252]
260. ~tall(mary) <- (3, 12) [resolution 179,136]
273. tall(X1) | kind(X1) | ~humble(X1) [resolution 214,211]
275. kind(X1) | tall(X1) [subsumption resolution 273,237]
286. creative(X0) | brave(X0) | ~happy(X0) | tall(X0) [resolution 76,275]
291. brave(X0) | ~happy(X0) | tall(X0) [subsumption resolution 286,208]
292. ~happy(X0) | tall(X0) [subsumption resolution 291,207]
293. tall(X0) [subsumption resolution 292,239]
296. $false <- (3, 12) [resolution 293,260]
299. ~3 | ~12 [avatar contradiction clause 296]
301. $false [avatar sat refutation 182,227,251,253,299]
% SZS output end Proof for 1095918504940119844468088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not wise then susan is both kind and not creative.
Everyone who is not humble is strong or generous and vice versa.
Everyone who is strong is not patient and vice versa.
Everyone who is not funny is both not quiet and tall.
Everyone who is kind is both not generous and not happy.
Everyone who is quiet or not quiet is both not rich and not kind and vice versa.
If someone is both not generous and funny then someone is both not kind and humble and vice versa.
Everyone who is both not calm and funny is patient and vice versa.
If lucy is happy then paul is not creative.
Everyone who is both not creative and not kind is both strong and humble and vice versa.
Everyone who is either quiet or not wise is both not quiet and not curious.
If mary is either not kind or humble then lucy is not calm.
If someone is either not happy or not old then lucy is either not calm or calm and vice versa.
Everyone who is either old or wise is not generous or wise and vice versa.
Someone is either brave or not brave.
Susan is not strong or curious.
Someone is not calm.
Fred is not patient or not calm.
Someone is both not kind and wise.
John is happy. | Fred is not kind. | entailment | ((?[X]:((~humble(X)|~wise(X))))=>((kind(susan)&~creative(susan))))&
(![X]:(~humble(X)<=>(strong(X)|generous(X))))&
(![X]:(strong(X)<=>~patient(X)))&
(![X]:(~funny(X)=>(~quiet(X)&tall(X))))&
(![X]:(kind(X)=>(~generous(X)&~happy(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~rich(X)&~kind(X))))&
((?[X]:((~generous(X)&funny(X))))<=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:((~calm(X)&funny(X))<=>patient(X)))&
((happy(lucy))=>(~creative(paul)))&
(![X]:((~creative(X)&~kind(X))<=>(strong(X)&humble(X))))&
(![X]:((quiet(X)<~>~wise(X))=>(~quiet(X)&~curious(X))))&
(((~kind(mary)<~>humble(mary)))=>(~calm(lucy)))&
((?[X]:((~happy(X)<~>~old(X))))<=>((~calm(lucy)<~>calm(lucy))))&
(![X]:((old(X)<~>wise(X))<=>(~generous(X)|wise(X))))&
(?[X]:((brave(X)<~>~brave(X))))&
((~strong(susan)|curious(susan)))&
(?[X]:(~calm(X)))&
((~patient(fred)|~calm(fred)))&
(?[X]:((~kind(X)&wise(X))))&
(happy(john)) | ~kind(fred) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7924380160909086708589757
% SZS output start Proof for 7924380160909086708589757
6. ! [X0] : ((~quiet(X0) | quiet(X0)) <=> (~kind(X0) & ~rich(X0))) [input p5]
21. kind(fred) [input hypothesis]
33. ! [X0] : (((~quiet(X0) | quiet(X0)) | (kind(X0) | rich(X0))) & ((~kind(X0) & ~rich(X0)) | (quiet(X0) & ~quiet(X0)))) [nnf transformation 6]
34. ! [X0] : ((~quiet(X0) | quiet(X0) | kind(X0) | rich(X0)) & ((~kind(X0) & ~rich(X0)) | (quiet(X0) & ~quiet(X0)))) [flattening 33]
73. ~kind(X0) | ~quiet(X0) [cnf transformation 34]
74. ~kind(X0) | quiet(X0) [cnf transformation 34]
116. kind(fred) [cnf transformation 21]
142. ~kind(X0) [subsumption resolution 73,74]
210. $false [subsumption resolution 116,142]
% SZS output end Proof for 7924380160909086708589757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and generous is both rich and not creative and vice versa.
Everyone who is creative or not curious is both not humble and not kind.
If someone is curious or not quiet then someone is not kind.
Everyone who is wise is both curious and creative.
If mary is happy or not quiet then someone is both not old and old.
If someone is both not wise and not calm then john is either not wise or curious.
If someone is not quiet or humble then lucy is both tall and not patient and vice versa.
Everyone who is calm or brave is strong.
Everyone who is both not rich and rich is either not creative or not tall and vice versa.
If lucy is quiet or not rich then fred is strong and vice versa.
If lucy is either creative or brave then susan is humble.
If john is not curious or patient then someone is rich and vice versa.
Everyone who is not kind or not old is both not wise and happy.
If paul is funny or not creative then fred is either not brave or generous and vice versa.
Everyone who is brave is rich or not calm and vice versa.
Everyone who is wise is both happy and not rich and vice versa.
Alice is either creative or not creative.
Lucy is not tall or not rich.
Alice is either wise or tall.
John is either brave or curious.
Someone is brave or wise.
Someone is both kind and not patient.
Fred is calm or curious. | Fred is quiet. | entailment | (![X]:((wise(X)&generous(X))<=>(rich(X)&~creative(X))))&
(![X]:((creative(X)|~curious(X))=>(~humble(X)&~kind(X))))&
((?[X]:((curious(X)|~quiet(X))))=>(?[X]:(~kind(X))))&
(![X]:(wise(X)=>(curious(X)&creative(X))))&
(((happy(mary)|~quiet(mary)))=>(?[X]:((~old(X)&old(X)))))&
((?[X]:((~wise(X)&~calm(X))))=>((~wise(john)<~>curious(john))))&
((?[X]:((~quiet(X)|humble(X))))<=>((tall(lucy)&~patient(lucy))))&
(![X]:((calm(X)|brave(X))=>strong(X)))&
(![X]:((~rich(X)&rich(X))<=>(~creative(X)<~>~tall(X))))&
(((quiet(lucy)|~rich(lucy)))<=>(strong(fred)))&
(((creative(lucy)<~>brave(lucy)))=>(humble(susan)))&
(((~curious(john)|patient(john)))<=>(?[X]:(rich(X))))&
(![X]:((~kind(X)|~old(X))=>(~wise(X)&happy(X))))&
(((funny(paul)|~creative(paul)))<=>((~brave(fred)<~>generous(fred))))&
(![X]:(brave(X)<=>(rich(X)|~calm(X))))&
(![X]:(wise(X)<=>(happy(X)&~rich(X))))&
((creative(alice)<~>~creative(alice)))&
((~tall(lucy)|~rich(lucy)))&
((wise(alice)<~>tall(alice)))&
((brave(john)<~>curious(john)))&
(?[X]:((brave(X)|wise(X))))&
(?[X]:((kind(X)&~patient(X))))&
((calm(fred)|curious(fred))) | quiet(fred) | [
"p1",
"p6",
"p8",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 313023858358286765718601
% SZS output start Proof for 313023858358286765718601
2. ! [X0] : ((~curious(X0) | creative(X0)) => (~kind(X0) & ~humble(X0))) [input p1]
7. ? [X0] : (humble(X0) | ~quiet(X0)) <=> (~patient(lucy) & tall(lucy)) [input p6]
9. ! [X0] : ((rich(X0) & ~rich(X0)) <=> (~creative(X0) <~> ~tall(X0))) [input p8]
13. ! [X0] : ((~old(X0) | ~kind(X0)) => (happy(X0) & ~wise(X0))) [input p12]
16. ! [X0] : (wise(X0) <=> (~rich(X0) & happy(X0))) [input p15]
18. ~rich(lucy) | ~tall(lucy) [input p17]
24. ~quiet(fred) [input hypothesis]
26. ! [X0] : ((~kind(X0) & ~humble(X0)) | (curious(X0) & ~creative(X0))) [ennf transformation 2]
33. ! [X0] : ((happy(X0) & ~wise(X0)) | (old(X0) & kind(X0))) [ennf transformation 13]
42. (? [X0] : (humble(X0) | ~quiet(X0)) | (patient(lucy) | ~tall(lucy))) & ((~patient(lucy) & tall(lucy)) | ! [X0] : (~humble(X0) & quiet(X0))) [nnf transformation 7]
43. (? [X0] : (humble(X0) | ~quiet(X0)) | patient(lucy) | ~tall(lucy)) & ((~patient(lucy) & tall(lucy)) | ! [X0] : (~humble(X0) & quiet(X0))) [flattening 42]
44. (? [X0] : (humble(X0) | ~quiet(X0)) | patient(lucy) | ~tall(lucy)) & ((~patient(lucy) & tall(lucy)) | ! [X1] : (~humble(X1) & quiet(X1))) [rectify 43]
45. ? [X0] : (humble(X0) | ~quiet(X0)) => (humble(sK2) | ~quiet(sK2)) [choice axiom]
46. ((humble(sK2) | ~quiet(sK2)) | patient(lucy) | ~tall(lucy)) & ((~patient(lucy) & tall(lucy)) | ! [X1] : (~humble(X1) & quiet(X1))) [skolemisation 44,45]
47. ! [X0] : (((rich(X0) & ~rich(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (~rich(X0) | rich(X0)))) [nnf transformation 9]
48. ! [X0] : (((rich(X0) & ~rich(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | ~rich(X0) | rich(X0))) [flattening 47]
61. ! [X0] : ((wise(X0) | (rich(X0) | ~happy(X0))) & ((~rich(X0) & happy(X0)) | ~wise(X0))) [nnf transformation 16]
62. ! [X0] : ((wise(X0) | rich(X0) | ~happy(X0)) & ((~rich(X0) & happy(X0)) | ~wise(X0))) [flattening 61]
76. ~kind(X0) | ~creative(X0) [cnf transformation 26]
88. tall(lucy) | quiet(X1) [cnf transformation 46]
97. ~rich(X0) | ~tall(X0) | creative(X0) [cnf transformation 48]
99. ~tall(X0) | rich(X0) | creative(X0) [cnf transformation 48]
109. ~wise(X0) | kind(X0) [cnf transformation 33]
111. happy(X0) | kind(X0) [cnf transformation 33]
124. ~happy(X0) | rich(X0) | wise(X0) [cnf transformation 62]
127. ~rich(lucy) | ~tall(lucy) [cnf transformation 18]
136. ~quiet(fred) [cnf transformation 24]
138. 1 <=> ! [X1] : quiet(X1) [avatar definition]
139. quiet(X1) <- (1) [avatar component clause 138]
178. 10 <=> tall(lucy) [avatar definition]
179. tall(lucy) <- (10) [avatar component clause 178]
200. 1 | 10 [avatar split clause 88,178,138]
202. ~tall(X0) | creative(X0) [subsumption resolution 97,99]
212. 17 <=> rich(lucy) [avatar definition]
214. ~rich(lucy) <- (~17) [avatar component clause 212]
223. 19 <=> creative(lucy) [avatar definition]
225. creative(lucy) <- (19) [avatar component clause 223]
268. ~10 | ~17 [avatar split clause 127,212,178]
326. creative(lucy) <- (10) [resolution 202,179]
330. 19 | ~10 [avatar split clause 326,178,223]
354. rich(X0) | wise(X0) | kind(X0) [resolution 124,111]
368. kind(X0) | rich(X0) [subsumption resolution 354,109]
398. $false <- (1) [resolution 139,136]
401. ~1 [avatar contradiction clause 398]
461. ~creative(X1) | rich(X1) [resolution 368,76]
494. rich(lucy) <- (19) [resolution 461,225]
498. $false <- (~17, 19) [subsumption resolution 494,214]
499. 17 | ~19 [avatar contradiction clause 498]
500. $false [avatar sat refutation 200,268,330,401,499]
% SZS output end Proof for 313023858358286765718601
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or not quiet is brave or not old and vice versa.
If someone is old then someone is both brave and not brave and vice versa.
Everyone who is tall or not rich is patient.
Everyone who is either rich or brave is both not generous and not creative and vice versa.
If susan is not quiet or not funny then someone is both generous and not quiet and vice versa.
Everyone who is not generous or generous is either not brave or not humble and vice versa.
Everyone who is not happy or not humble is quiet.
Everyone who is both not funny and not brave is wise and vice versa.
If someone is both not patient and not happy then someone is both not creative and not wise.
Everyone who is either not rich or not calm is both not generous and not rich.
Everyone who is either not funny or not tall is not curious and vice versa.
If paul is either not curious or tall then mary is both old and strong and vice versa.
If someone is creative or not happy then someone is strong or not old.
Everyone who is not old or not generous is both not creative and not brave.
Everyone who is both curious and quiet is not tall.
If someone is brave or not happy then someone is not strong or kind and vice versa.
Someone is either not creative or not humble.
John is creative or generous.
John is either quiet or generous.
Someone is creative or not tall.
Alice is quiet.
Someone is either calm or tall.
Fred is not creative. | Alice is generous. | contradiction | (![X]:((rich(X)|~quiet(X))<=>(brave(X)|~old(X))))&
((?[X]:(old(X)))<=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:((tall(X)|~rich(X))=>patient(X)))&
(![X]:((rich(X)<~>brave(X))<=>(~generous(X)&~creative(X))))&
(((~quiet(susan)|~funny(susan)))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~generous(X)|generous(X))<=>(~brave(X)<~>~humble(X))))&
(![X]:((~happy(X)|~humble(X))=>quiet(X)))&
(![X]:((~funny(X)&~brave(X))<=>wise(X)))&
((?[X]:((~patient(X)&~happy(X))))=>(?[X]:((~creative(X)&~wise(X)))))&
(![X]:((~rich(X)<~>~calm(X))=>(~generous(X)&~rich(X))))&
(![X]:((~funny(X)<~>~tall(X))<=>~curious(X)))&
(((~curious(paul)<~>tall(paul)))<=>((old(mary)&strong(mary))))&
((?[X]:((creative(X)|~happy(X))))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((~old(X)|~generous(X))=>(~creative(X)&~brave(X))))&
(![X]:((curious(X)&quiet(X))=>~tall(X)))&
((?[X]:((brave(X)|~happy(X))))<=>(?[X]:((~strong(X)|kind(X)))))&
(?[X]:((~creative(X)<~>~humble(X))))&
((creative(john)|generous(john)))&
((quiet(john)<~>generous(john)))&
(?[X]:((creative(X)|~tall(X))))&
(quiet(alice))&
(?[X]:((calm(X)<~>tall(X))))&
(~creative(fred)) | generous(alice) | [
"p0",
"p1",
"p3",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 734396200015989164161726
% SZS output start Proof for 734396200015989164161726
1. ! [X0] : ((~quiet(X0) | rich(X0)) <=> (~old(X0) | brave(X0))) [input p0]
2. ? [X0] : old(X0) <=> ? [X0] : (~brave(X0) & brave(X0)) [input p1]
4. ! [X0] : ((rich(X0) <~> brave(X0)) <=> (~creative(X0) & ~generous(X0))) [input p3]
14. ! [X0] : ((~generous(X0) | ~old(X0)) => (~brave(X0) & ~creative(X0))) [input p13]
21. quiet(alice) [input p20]
24. generous(alice) [input hypothesis]
25. ? [X0] : old(X0) <=> ? [X1] : (~brave(X1) & brave(X1)) [rectify 2]
36. ! [X0] : ((~brave(X0) & ~creative(X0)) | (generous(X0) & old(X0))) [ennf transformation 14]
39. ! [X0] : (((~quiet(X0) | rich(X0)) | (old(X0) & ~brave(X0))) & ((~old(X0) | brave(X0)) | (quiet(X0) & ~rich(X0)))) [nnf transformation 1]
40. ! [X0] : ((~quiet(X0) | rich(X0) | (old(X0) & ~brave(X0))) & (~old(X0) | brave(X0) | (quiet(X0) & ~rich(X0)))) [flattening 39]
41. (? [X0] : old(X0) | ! [X1] : (brave(X1) | ~brave(X1))) & (? [X1] : (~brave(X1) & brave(X1)) | ! [X0] : ~old(X0)) [nnf transformation 25]
42. (? [X0] : old(X0) | ! [X1] : (brave(X1) | ~brave(X1))) & (? [X2] : (~brave(X2) & brave(X2)) | ! [X3] : ~old(X3)) [rectify 41]
43. ? [X0] : old(X0) => old(sK0) [choice axiom]
44. ? [X2] : (~brave(X2) & brave(X2)) => (~brave(sK1) & brave(sK1)) [choice axiom]
45. (old(sK0) | ! [X1] : (brave(X1) | ~brave(X1))) & ((~brave(sK1) & brave(sK1)) | ! [X3] : ~old(X3)) [skolemisation 42,44,43]
46. ! [X0] : ((((~brave(X0) | ~rich(X0)) & (brave(X0) | rich(X0))) | (creative(X0) | generous(X0))) & ((~creative(X0) & ~generous(X0)) | ((rich(X0) | ~brave(X0)) & (brave(X0) | ~rich(X0))))) [nnf transformation 4]
47. ! [X0] : ((((~brave(X0) | ~rich(X0)) & (brave(X0) | rich(X0))) | creative(X0) | generous(X0)) & ((~creative(X0) & ~generous(X0)) | ((rich(X0) | ~brave(X0)) & (brave(X0) | ~rich(X0))))) [flattening 46]
79. ~quiet(X0) | rich(X0) | old(X0) [cnf transformation 40]
80. brave(sK1) | ~old(X3) [cnf transformation 45]
81. ~brave(sK1) | ~old(X3) [cnf transformation 45]
83. ~generous(X0) | brave(X0) | ~rich(X0) [cnf transformation 47]
120. ~brave(X0) | old(X0) [cnf transformation 36]
133. quiet(alice) [cnf transformation 21]
137. generous(alice) [cnf transformation 24]
140. 1 <=> ! [X3] : ~old(X3) [avatar definition]
141. ~old(X3) <- (1) [avatar component clause 140]
143. 2 <=> brave(sK1) [avatar definition]
146. 1 | ~2 [avatar split clause 81,143,140]
147. 1 | 2 [avatar split clause 80,143,140]
286. rich(alice) | old(alice) [resolution 79,133]
289. rich(alice) <- (1) [subsumption resolution 286,141]
293. brave(alice) | ~rich(alice) [resolution 83,137]
296. brave(alice) <- (1) [subsumption resolution 293,289]
326. old(alice) <- (1) [resolution 296,120]
327. $false <- (1) [subsumption resolution 326,141]
328. ~1 [avatar contradiction clause 327]
329. $false [avatar sat refutation 146,147,328]
% SZS output end Proof for 734396200015989164161726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or generous is both tall and creative.
Everyone who is not old or not curious is not quiet.
If someone is not brave then alice is patient and vice versa.
Everyone who is either not tall or quiet is not kind or kind and vice versa.
Everyone who is not curious is not happy or quiet.
If someone is not tall then alice is rich and vice versa.
If someone is both wise and creative then someone is not brave or not curious and vice versa.
If someone is not creative then lucy is either funny or generous.
Everyone who is either not happy or old is both not rich and creative.
Everyone who is not happy or not strong is both calm and not curious.
Everyone who is both funny and patient is not brave.
Everyone who is not rich is not strong or not rich and vice versa.
Everyone who is both funny and calm is not brave and vice versa.
If someone is brave or kind then someone is not calm or not kind and vice versa.
If lucy is either patient or rich then mary is either not rich or not brave.
Everyone who is both wise and not calm is not generous or rich and vice versa.
Alice is humble.
Lucy is either not kind or happy.
Fred is either happy or not patient.
Lucy is not patient.
John is either humble or not kind.
Someone is not patient or tall.
Someone is both not calm and wise. | John is not happy. | contradiction | (![X]:((quiet(X)|generous(X))=>(tall(X)&creative(X))))&
(![X]:((~old(X)|~curious(X))=>~quiet(X)))&
((?[X]:(~brave(X)))<=>(patient(alice)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~kind(X)|kind(X))))&
(![X]:(~curious(X)=>(~happy(X)|quiet(X))))&
((?[X]:(~tall(X)))<=>(rich(alice)))&
((?[X]:((wise(X)&creative(X))))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:(~creative(X)))=>((funny(lucy)<~>generous(lucy))))&
(![X]:((~happy(X)<~>old(X))=>(~rich(X)&creative(X))))&
(![X]:((~happy(X)|~strong(X))=>(calm(X)&~curious(X))))&
(![X]:((funny(X)&patient(X))=>~brave(X)))&
(![X]:(~rich(X)<=>(~strong(X)|~rich(X))))&
(![X]:((funny(X)&calm(X))<=>~brave(X)))&
((?[X]:((brave(X)|kind(X))))<=>(?[X]:((~calm(X)|~kind(X)))))&
(((patient(lucy)<~>rich(lucy)))=>((~rich(mary)<~>~brave(mary))))&
(![X]:((wise(X)&~calm(X))<=>(~generous(X)|rich(X))))&
(humble(alice))&
((~kind(lucy)<~>happy(lucy)))&
((happy(fred)<~>~patient(fred)))&
(~patient(lucy))&
((humble(john)<~>~kind(john)))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((~calm(X)&wise(X)))) | ~happy(john) | [
"p0",
"p1",
"p3",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8512465371928027031469286
% SZS output start Proof for 8512465371928027031469286
1. ! [X0] : ((generous(X0) | quiet(X0)) => (creative(X0) & tall(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | ~old(X0)) => ~quiet(X0)) [input p1]
4. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (kind(X0) | ~kind(X0))) [input p3]
10. ! [X0] : ((~strong(X0) | ~happy(X0)) => (~curious(X0) & calm(X0))) [input p9]
16. ! [X0] : ((~calm(X0) & wise(X0)) <=> (rich(X0) | ~generous(X0))) [input p15]
24. ~happy(john) [input hypothesis]
27. ! [X0] : ((creative(X0) & tall(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 1]
28. ! [X0] : (~quiet(X0) | (curious(X0) & old(X0))) [ennf transformation 2]
33. ! [X0] : ((~curious(X0) & calm(X0)) | (strong(X0) & happy(X0))) [ennf transformation 10]
41. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [flattening 41]
64. ! [X0] : (((~calm(X0) & wise(X0)) | (~rich(X0) & generous(X0))) & ((rich(X0) | ~generous(X0)) | (calm(X0) | ~wise(X0)))) [nnf transformation 16]
65. ! [X0] : (((~calm(X0) & wise(X0)) | (~rich(X0) & generous(X0))) & (rich(X0) | ~generous(X0) | calm(X0) | ~wise(X0))) [flattening 64]
74. ~generous(X0) | tall(X0) [cnf transformation 27]
78. ~quiet(X0) | curious(X0) [cnf transformation 28]
83. quiet(X0) | ~tall(X0) | kind(X0) [cnf transformation 42]
84. ~kind(X0) | ~tall(X0) | quiet(X0) [cnf transformation 42]
101. calm(X0) | happy(X0) [cnf transformation 33]
103. ~curious(X0) | happy(X0) [cnf transformation 33]
123. ~calm(X0) | generous(X0) [cnf transformation 65]
136. ~happy(john) [cnf transformation 24]
150. ~tall(X0) | quiet(X0) [subsumption resolution 83,84]
311. happy(X2) | generous(X2) [resolution 123,101]
391. generous(john) [resolution 311,136]
400. tall(john) [resolution 391,74]
412. quiet(john) [resolution 400,150]
427. curious(john) [resolution 412,78]
441. happy(john) [resolution 427,103]
442. $false [subsumption resolution 441,136]
% SZS output end Proof for 8512465371928027031469286
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not humble is not patient or happy and vice versa.
Everyone who is both generous and happy is not creative or creative and vice versa.
If susan is kind or wise then susan is either funny or not tall.
Everyone who is not brave or not generous is not creative.
Everyone who is both not patient and not generous is wise and vice versa.
If someone is either not calm or curious then paul is both not old and not happy.
Everyone who is either not humble or quiet is either not creative or not strong.
If lucy is both not rich and not humble then mary is not patient and vice versa.
Everyone who is funny or not rich is not quiet or not old.
Everyone who is not creative or patient is either wise or not wise.
Everyone who is not tall or rich is not calm.
If someone is not tall or humble then paul is both not happy and not generous.
If fred is either patient or old then someone is quiet or not patient and vice versa.
Everyone who is not quiet is either wise or not humble and vice versa.
Everyone who is either creative or strong is funny or generous.
If someone is both quiet and not tall then susan is not patient and vice versa.
Someone is either not patient or quiet.
Alice is either curious or not wise.
Mary is both strong and tall.
Fred is humble or not rich.
Fred is old or humble.
Someone is not curious.
Alice is both tall and not rich. | Paul is not wise. | entailment | (![X]:((creative(X)|~humble(X))<=>(~patient(X)|happy(X))))&
(![X]:((generous(X)&happy(X))<=>(~creative(X)|creative(X))))&
(((kind(susan)|wise(susan)))=>((funny(susan)<~>~tall(susan))))&
(![X]:((~brave(X)|~generous(X))=>~creative(X)))&
(![X]:((~patient(X)&~generous(X))<=>wise(X)))&
((?[X]:((~calm(X)<~>curious(X))))=>((~old(paul)&~happy(paul))))&
(![X]:((~humble(X)<~>quiet(X))=>(~creative(X)<~>~strong(X))))&
(((~rich(lucy)&~humble(lucy)))<=>(~patient(mary)))&
(![X]:((funny(X)|~rich(X))=>(~quiet(X)|~old(X))))&
(![X]:((~creative(X)|patient(X))=>(wise(X)<~>~wise(X))))&
(![X]:((~tall(X)|rich(X))=>~calm(X)))&
((?[X]:((~tall(X)|humble(X))))=>((~happy(paul)&~generous(paul))))&
(((patient(fred)<~>old(fred)))<=>(?[X]:((quiet(X)|~patient(X)))))&
(![X]:(~quiet(X)<=>(wise(X)<~>~humble(X))))&
(![X]:((creative(X)<~>strong(X))=>(funny(X)|generous(X))))&
((?[X]:((quiet(X)&~tall(X))))<=>(~patient(susan)))&
(?[X]:((~patient(X)<~>quiet(X))))&
((curious(alice)<~>~wise(alice)))&
((strong(mary)&tall(mary)))&
((humble(fred)|~rich(fred)))&
((old(fred)|humble(fred)))&
(?[X]:(~curious(X)))&
((tall(alice)&~rich(alice))) | ~wise(paul) | [
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7734021399752784275834052
% SZS output start Proof for 7734021399752784275834052
2. ! [X0] : ((happy(X0) & generous(X0)) <=> (creative(X0) | ~creative(X0))) [input p1]
5. ! [X0] : ((~generous(X0) & ~patient(X0)) <=> wise(X0)) [input p4]
24. wise(paul) [input hypothesis]
40. ! [X0] : (((happy(X0) & generous(X0)) | (~creative(X0) & creative(X0))) & ((creative(X0) | ~creative(X0)) | (~happy(X0) | ~generous(X0)))) [nnf transformation 2]
41. ! [X0] : (((happy(X0) & generous(X0)) | (~creative(X0) & creative(X0))) & (creative(X0) | ~creative(X0) | ~happy(X0) | ~generous(X0))) [flattening 40]
43. ! [X0] : (((~generous(X0) & ~patient(X0)) | ~wise(X0)) & (wise(X0) | (generous(X0) | patient(X0)))) [nnf transformation 5]
44. ! [X0] : (((~generous(X0) & ~patient(X0)) | ~wise(X0)) & (wise(X0) | generous(X0) | patient(X0))) [flattening 43]
71. generous(X0) | creative(X0) [cnf transformation 41]
72. generous(X0) | ~creative(X0) [cnf transformation 41]
80. ~generous(X0) | ~wise(X0) [cnf transformation 44]
130. wise(paul) [cnf transformation 24]
132. generous(X0) [subsumption resolution 71,72]
147. ~wise(X0) [subsumption resolution 80,132]
213. $false [subsumption resolution 130,147]
% SZS output end Proof for 7734021399752784275834052
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is generous or not generous then someone is both not kind and generous. If someone is not rich then mary is both curious and patient and vice versa. Everyone who is both not creative and funny is either wise or kind. Everyone who is not rich is either creative or not creative. If someone is either not strong or not funny then someone is brave and vice versa. If someone is humble then mary is not wise. Everyone who is both funny and not wise is not curious. If someone is both tall and generous then someone is either curious or calm and vice versa. If fred is old then someone is funny and vice versa. Everyone who is quiet is not rich or quiet. If susan is both not happy and rich then someone is both not quiet and creative. Everyone who is both old and quiet is either curious or old. Everyone who is tall or kind is both curious and not tall and vice versa. Everyone who is either not quiet or calm is both not funny and patient and vice versa. Everyone who is either not calm or not old is both not quiet and not brave. Everyone who is either not kind or quiet is creative and vice versa. Lucy is either happy or not quiet. Someone is creative. Paul is not old. Paul is either patient or strong. Fred is brave or kind. Paul is either generous or not rich. Someone is not rich or not humble. Paul is either not curious or not creative. | Fred is not tall. | entailment | (((generous(paul)|~generous(paul)))=>(?[X]:((~kind(X)&generous(X)))))&
((?[X]:(~rich(X)))<=>((curious(mary)&patient(mary))))&
(![X]:((~creative(X)&funny(X))=>(wise(X)<~>kind(X))))&
(![X]:(~rich(X)=>(creative(X)<~>~creative(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>(?[X]:(brave(X))))&
((?[X]:(humble(X)))=>(~wise(mary)))&
(![X]:((funny(X)&~wise(X))=>~curious(X)))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((curious(X)<~>calm(X)))))&
((old(fred))<=>(?[X]:(funny(X))))&
(![X]:(quiet(X)=>(~rich(X)|quiet(X))))&
(((~happy(susan)&rich(susan)))=>(?[X]:((~quiet(X)&creative(X)))))&
(![X]:((old(X)&quiet(X))=>(curious(X)<~>old(X))))&
(![X]:((tall(X)|kind(X))<=>(curious(X)&~tall(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(~funny(X)&patient(X))))&
(![X]:((~calm(X)<~>~old(X))=>(~quiet(X)&~brave(X))))&
(![X]:((~kind(X)<~>quiet(X))<=>creative(X)))&
((happy(lucy)<~>~quiet(lucy)))&
(?[X]:(creative(X)))&
(~old(paul))&
((patient(paul)<~>strong(paul)))&
((brave(fred)|kind(fred)))&
((generous(paul)<~>~rich(paul)))&
(?[X]:((~rich(X)|~humble(X))))&
((~curious(paul)<~>~creative(paul))) | ~tall(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7563063368982513696898616
% SZS output start Proof for 7563063368982513696898616
13. ! [X0] : ((kind(X0) | tall(X0)) <=> (~tall(X0) & curious(X0))) [input p12]
25. tall(fred) [input hypothesis]
69. ! [X0] : (((kind(X0) | tall(X0)) | (tall(X0) | ~curious(X0))) & ((~tall(X0) & curious(X0)) | (~kind(X0) & ~tall(X0)))) [nnf transformation 13]
70. ! [X0] : ((kind(X0) | tall(X0) | tall(X0) | ~curious(X0)) & ((~tall(X0) & curious(X0)) | (~kind(X0) & ~tall(X0)))) [flattening 69]
112. ~tall(X0) | ~tall(X0) [cnf transformation 70]
140. tall(fred) [cnf transformation 25]
141. ~tall(X0) [duplicate literal removal 112]
310. $false [subsumption resolution 140,141]
% SZS output end Proof for 7563063368982513696898616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious then alice is curious and vice versa. If someone is not rich then fred is both not funny and patient. If someone is either rich or not strong then someone is not wise or not quiet. Everyone who is either not humble or not kind is either quiet or not quiet and vice versa. If someone is both not rich and quiet then lucy is not calm or not rich. Everyone who is old or not brave is either happy or not wise. Everyone who is either not brave or not happy is not rich. Everyone who is wise is both strong and generous. If someone is not happy then someone is brave or not calm and vice versa. Everyone who is both strong and rich is creative. Everyone who is both kind and happy is both not curious and happy and vice versa. Everyone who is not quiet or not funny is either not funny or funny. Everyone who is either humble or not strong is happy or not brave and vice versa. Everyone who is rich is quiet or patient and vice versa. If someone is not generous then lucy is old or not happy. If someone is both funny and strong then john is rich. Mary is both not curious and not strong. Susan is not curious. Susan is both not strong and not generous. Someone is either not humble or strong. Mary is either creative or strong. Mary is both not humble and quiet. Susan is either not humble or not brave. Alice is either wise or patient. | Susan is happy. | entailment | ((?[X]:(~curious(X)))<=>(curious(alice)))&
((?[X]:(~rich(X)))=>((~funny(fred)&patient(fred))))&
((?[X]:((rich(X)<~>~strong(X))))=>(?[X]:((~wise(X)|~quiet(X)))))&
(![X]:((~humble(X)<~>~kind(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:((~rich(X)&quiet(X))))=>((~calm(lucy)|~rich(lucy))))&
(![X]:((old(X)|~brave(X))=>(happy(X)<~>~wise(X))))&
(![X]:((~brave(X)<~>~happy(X))=>~rich(X)))&
(![X]:(wise(X)=>(strong(X)&generous(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:((strong(X)&rich(X))=>creative(X)))&
(![X]:((kind(X)&happy(X))<=>(~curious(X)&happy(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~funny(X)<~>funny(X))))&
(![X]:((humble(X)<~>~strong(X))<=>(happy(X)|~brave(X))))&
(![X]:(rich(X)<=>(quiet(X)|patient(X))))&
((?[X]:(~generous(X)))=>((old(lucy)|~happy(lucy))))&
((?[X]:((funny(X)&strong(X))))=>(rich(john)))&
((~curious(mary)&~strong(mary)))&
(~curious(susan))&
((~strong(susan)&~generous(susan)))&
(?[X]:((~humble(X)<~>strong(X))))&
((creative(mary)<~>strong(mary)))&
((~humble(mary)&quiet(mary)))&
((~humble(susan)<~>~brave(susan)))&
((wise(alice)<~>patient(alice))) | happy(susan) | [
"p12",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7790217244307101124136840
% SZS output start Proof for 7790217244307101124136840
13. ! [X0] : ((humble(X0) <~> ~strong(X0)) <=> (~brave(X0) | happy(X0))) [input p12]
19. ~generous(susan) & ~strong(susan) [input p18]
23. ~humble(susan) <~> ~brave(susan) [input p22]
25. ~happy(susan) [input hypothesis]
60. ! [X0] : ((((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | (brave(X0) & ~happy(X0))) & ((~brave(X0) | happy(X0)) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0))))) [nnf transformation 13]
61. ! [X0] : ((((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | (brave(X0) & ~happy(X0))) & (~brave(X0) | happy(X0) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0))))) [flattening 60]
68. (brave(susan) | humble(susan)) & (~brave(susan) | ~humble(susan)) [nnf transformation 23]
106. ~brave(X0) | happy(X0) | humble(X0) | strong(X0) [cnf transformation 61]
110. ~humble(X0) | strong(X0) | brave(X0) [cnf transformation 61]
119. ~strong(susan) [cnf transformation 19]
127. ~brave(susan) | ~humble(susan) [cnf transformation 68]
128. brave(susan) | humble(susan) [cnf transformation 68]
131. ~happy(susan) [cnf transformation 25]
251. 27 <=> humble(susan) [avatar definition]
252. ~humble(susan) <- (~27) [avatar component clause 251]
253. humble(susan) <- (27) [avatar component clause 251]
255. 28 <=> brave(susan) [avatar definition]
256. ~brave(susan) <- (~28) [avatar component clause 255]
257. brave(susan) <- (28) [avatar component clause 255]
258. 27 | 28 [avatar split clause 128,255,251]
259. ~27 | ~28 [avatar split clause 127,255,251]
290. strong(susan) | brave(susan) <- (27) [resolution 110,253]
291. brave(susan) <- (27) [subsumption resolution 290,119]
292. $false <- (27, ~28) [subsumption resolution 291,256]
293. ~27 | 28 [avatar contradiction clause 292]
308. happy(susan) | humble(susan) | strong(susan) <- (28) [resolution 106,257]
309. humble(susan) | strong(susan) <- (28) [subsumption resolution 308,131]
310. strong(susan) <- (~27, 28) [subsumption resolution 309,252]
311. $false <- (~27, 28) [subsumption resolution 310,119]
312. 27 | ~28 [avatar contradiction clause 311]
313. $false [avatar sat refutation 258,259,293,312]
% SZS output end Proof for 7790217244307101124136840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or old then someone is either humble or curious and vice versa.
Everyone who is both calm and not happy is calm and vice versa.
Everyone who is calm or generous is both brave and not tall and vice versa.
If someone is either not tall or not strong then someone is both happy and not quiet and vice versa.
Everyone who is not strong or old is both creative and patient.
If mary is either quiet or patient then fred is either not patient or not calm.
If john is both not quiet and not patient then fred is both patient and not strong and vice versa.
Everyone who is rich or patient is either not kind or not happy and vice versa.
If alice is both curious and not kind then alice is not humble or tall and vice versa.
If someone is both not calm and not happy then john is either not old or strong.
If mary is either not funny or not creative then mary is not humble and vice versa.
Everyone who is not old is both not humble and funny and vice versa.
If susan is either not creative or not humble then paul is curious and vice versa.
Everyone who is either not quiet or wise is wise and vice versa.
Everyone who is not wise or not funny is not calm and vice versa.
Everyone who is either not happy or wise is both creative and wise and vice versa.
Someone is either not kind or not happy.
Lucy is not kind or funny.
Someone is not patient or quiet.
John is both quiet and kind.
Someone is not calm.
Someone is both generous and rich.
Someone is both brave and curious. | Fred is generous. | contradiction | ((?[X]:((~strong(X)<~>old(X))))<=>(?[X]:((humble(X)<~>curious(X)))))&
(![X]:((calm(X)&~happy(X))<=>calm(X)))&
(![X]:((calm(X)|generous(X))<=>(brave(X)&~tall(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:((~strong(X)|old(X))=>(creative(X)&patient(X))))&
(((quiet(mary)<~>patient(mary)))=>((~patient(fred)<~>~calm(fred))))&
(((~quiet(john)&~patient(john)))<=>((patient(fred)&~strong(fred))))&
(![X]:((rich(X)|patient(X))<=>(~kind(X)<~>~happy(X))))&
(((curious(alice)&~kind(alice)))<=>((~humble(alice)|tall(alice))))&
((?[X]:((~calm(X)&~happy(X))))=>((~old(john)<~>strong(john))))&
(((~funny(mary)<~>~creative(mary)))<=>(~humble(mary)))&
(![X]:(~old(X)<=>(~humble(X)&funny(X))))&
(((~creative(susan)<~>~humble(susan)))<=>(curious(paul)))&
(![X]:((~quiet(X)<~>wise(X))<=>wise(X)))&
(![X]:((~wise(X)|~funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(creative(X)&wise(X))))&
(?[X]:((~kind(X)<~>~happy(X))))&
((~kind(lucy)|funny(lucy)))&
(?[X]:((~patient(X)|quiet(X))))&
((quiet(john)&kind(john)))&
(?[X]:(~calm(X)))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((brave(X)&curious(X)))) | generous(fred) | [
"p2",
"p3",
"p4",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8460171999914658958564366
% SZS output start Proof for 8460171999914658958564366
3. ! [X0] : ((generous(X0) | calm(X0)) <=> (~tall(X0) & brave(X0))) [input p2]
4. ? [X0] : (~tall(X0) <~> ~strong(X0)) <=> ? [X0] : (~quiet(X0) & happy(X0)) [input p3]
5. ! [X0] : ((old(X0) | ~strong(X0)) => (patient(X0) & creative(X0))) [input p4]
7. (~patient(john) & ~quiet(john)) <=> (~strong(fred) & patient(fred)) [input p6]
14. ! [X0] : ((~quiet(X0) <~> wise(X0)) <=> wise(X0)) [input p13]
24. generous(fred) [input hypothesis]
26. ? [X0] : (~tall(X0) <~> ~strong(X0)) <=> ? [X1] : (~quiet(X1) & happy(X1)) [rectify 4]
27. ! [X0] : ((patient(X0) & creative(X0)) | (~old(X0) & strong(X0))) [ennf transformation 5]
37. ! [X0] : (((generous(X0) | calm(X0)) | (tall(X0) | ~brave(X0))) & ((~tall(X0) & brave(X0)) | (~generous(X0) & ~calm(X0)))) [nnf transformation 3]
38. ! [X0] : ((generous(X0) | calm(X0) | tall(X0) | ~brave(X0)) & ((~tall(X0) & brave(X0)) | (~generous(X0) & ~calm(X0)))) [flattening 37]
39. (? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | ! [X1] : (quiet(X1) | ~happy(X1))) & (? [X1] : (~quiet(X1) & happy(X1)) | ! [X0] : ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) [nnf transformation 26]
40. (? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | ! [X1] : (quiet(X1) | ~happy(X1))) & (? [X2] : (~quiet(X2) & happy(X2)) | ! [X3] : ((~tall(X3) | strong(X3)) & (~strong(X3) | tall(X3)))) [rectify 39]
41. ? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) => ((strong(sK2) | tall(sK2)) & (~strong(sK2) | ~tall(sK2))) [choice axiom]
42. ? [X2] : (~quiet(X2) & happy(X2)) => (~quiet(sK3) & happy(sK3)) [choice axiom]
43. (((strong(sK2) | tall(sK2)) & (~strong(sK2) | ~tall(sK2))) | ! [X1] : (quiet(X1) | ~happy(X1))) & ((~quiet(sK3) & happy(sK3)) | ! [X3] : ((~tall(X3) | strong(X3)) & (~strong(X3) | tall(X3)))) [skolemisation 40,42,41]
45. ((~patient(john) & ~quiet(john)) | (strong(fred) | ~patient(fred))) & ((~strong(fred) & patient(fred)) | (patient(john) | quiet(john))) [nnf transformation 7]
46. ((~patient(john) & ~quiet(john)) | strong(fred) | ~patient(fred)) & ((~strong(fred) & patient(fred)) | patient(john) | quiet(john)) [flattening 45]
56. ! [X0] : ((((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~wise(X0)) & (wise(X0) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))))) [nnf transformation 14]
86. ~tall(X0) | ~generous(X0) [cnf transformation 38]
90. ~quiet(sK3) | ~strong(X3) | tall(X3) [cnf transformation 43]
96. patient(X0) | strong(X0) [cnf transformation 27]
104. ~quiet(john) | strong(fred) | ~patient(fred) [cnf transformation 46]
130. wise(X0) | wise(X0) | quiet(X0) [cnf transformation 56]
133. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 56]
154. generous(fred) [cnf transformation 24]
157. wise(X0) | quiet(X0) [duplicate literal removal 130]
158. ~wise(X0) | quiet(X0) [duplicate literal removal 133]
212. 13 <=> quiet(sK3) [avatar definition]
214. ~quiet(sK3) <- (~13) [avatar component clause 212]
217. 14 <=> ! [X3] : (~strong(X3) | tall(X3)) [avatar definition]
218. ~strong(X3) | tall(X3) <- (14) [avatar component clause 217]
219. 14 | ~13 [avatar split clause 90,212,217]
248. 20 <=> strong(fred) [avatar definition]
250. strong(fred) <- (20) [avatar component clause 248]
256. ~quiet(john) | strong(fred) [subsumption resolution 104,96]
258. 22 <=> quiet(john) [avatar definition]
260. ~quiet(john) <- (~22) [avatar component clause 258]
261. 20 | ~22 [avatar split clause 256,258,248]
330. quiet(X0) [subsumption resolution 157,158]
350. $false <- (~22) [subsumption resolution 260,330]
351. 22 [avatar contradiction clause 350]
373. tall(fred) <- (14, 20) [resolution 218,250]
377. ~generous(fred) <- (14, 20) [resolution 373,86]
379. $false <- (14, 20) [subsumption resolution 377,154]
380. ~14 | ~20 [avatar contradiction clause 379]
381. $false <- (~13) [subsumption resolution 214,330]
382. 13 [avatar contradiction clause 381]
383. $false [avatar sat refutation 219,261,351,380,382]
% SZS output end Proof for 8460171999914658958564366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not wise or strong then someone is generous and vice versa. Everyone who is both not rich and not happy is both not patient and not calm and vice versa. Everyone who is not kind or not generous is happy and vice versa. If someone is quiet then susan is either old or strong. If someone is wise then someone is not creative. Everyone who is both not old and wise is old or wise. If fred is both tall and not rich then someone is quiet. Everyone who is either funny or not tall is not happy or generous and vice versa. If susan is not kind or not old then john is not kind or not curious. Everyone who is both funny and not patient is not creative or not patient and vice versa. If someone is both funny and not quiet then lucy is not old and vice versa. Everyone who is either not happy or brave is either not humble or quiet and vice versa. Everyone who is curious is not kind. Everyone who is humble or not humble is either brave or old. Everyone who is not creative is either patient or not curious and vice versa. If someone is brave or strong then paul is both quiet and brave and vice versa. Someone is either not kind or not creative. Someone is either not patient or not brave. Paul is both quiet and generous. Mary is not curious. John is either not strong or not quiet. John is both tall and strong. Someone is curious. | John is tall. | entailment | (((~wise(fred)|strong(fred)))<=>(?[X]:(generous(X))))&
(![X]:((~rich(X)&~happy(X))<=>(~patient(X)&~calm(X))))&
(![X]:((~kind(X)|~generous(X))<=>happy(X)))&
((?[X]:(quiet(X)))=>((old(susan)<~>strong(susan))))&
((?[X]:(wise(X)))=>(?[X]:(~creative(X))))&
(![X]:((~old(X)&wise(X))=>(old(X)|wise(X))))&
(((tall(fred)&~rich(fred)))=>(?[X]:(quiet(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(~happy(X)|generous(X))))&
(((~kind(susan)|~old(susan)))=>((~kind(john)|~curious(john))))&
(![X]:((funny(X)&~patient(X))<=>(~creative(X)|~patient(X))))&
((?[X]:((funny(X)&~quiet(X))))<=>(~old(lucy)))&
(![X]:((~happy(X)<~>brave(X))<=>(~humble(X)<~>quiet(X))))&
(![X]:(curious(X)=>~kind(X)))&
(![X]:((humble(X)|~humble(X))=>(brave(X)<~>old(X))))&
(![X]:(~creative(X)<=>(patient(X)<~>~curious(X))))&
((?[X]:((brave(X)|strong(X))))<=>((quiet(paul)&brave(paul))))&
(?[X]:((~kind(X)<~>~creative(X))))&
(?[X]:((~patient(X)<~>~brave(X))))&
((quiet(paul)&generous(paul)))&
(~curious(mary))&
((~strong(john)<~>~quiet(john)))&
((tall(john)&strong(john)))&
(?[X]:(curious(X))) | tall(john) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4982436265470030632456895
% SZS output start Proof for 4982436265470030632456895
22. strong(john) & tall(john) [input p21]
24. ~tall(john) [input hypothesis]
138. tall(john) [cnf transformation 22]
141. ~tall(john) [cnf transformation 24]
292. $false [subsumption resolution 141,138]
% SZS output end Proof for 4982436265470030632456895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or brave is both brave and not creative and vice versa.
Everyone who is either old or not strong is either not creative or creative and vice versa.
If fred is not brave or curious then someone is not tall or not patient.
Everyone who is kind or not brave is both not funny and not creative.
Everyone who is happy or curious is not happy.
Everyone who is generous or old is not old or rich and vice versa.
Everyone who is either wise or funny is kind or patient and vice versa.
If someone is both old and not creative then alice is not old.
Everyone who is either creative or tall is not tall.
Everyone who is both tall and creative is not humble or not brave.
Everyone who is not old or not funny is both generous and not tall.
If someone is not brave then someone is not strong or curious and vice versa.
If someone is both happy and not humble then paul is either quiet or funny.
Everyone who is strong or not kind is either not brave or not patient and vice versa.
If alice is both not funny and not wise then fred is calm or not brave.
Everyone who is funny or kind is either happy or not tall.
Mary is not creative or calm.
Someone is old or not humble.
John is not happy.
Susan is both not quiet and not patient.
Someone is not creative or humble. | Paul is not kind. | entailment | (![X]:((wise(X)<~>brave(X))<=>(brave(X)&~creative(X))))&
(![X]:((old(X)<~>~strong(X))<=>(~creative(X)<~>creative(X))))&
(((~brave(fred)|curious(fred)))=>(?[X]:((~tall(X)|~patient(X)))))&
(![X]:((kind(X)|~brave(X))=>(~funny(X)&~creative(X))))&
(![X]:((happy(X)|curious(X))=>~happy(X)))&
(![X]:((generous(X)|old(X))<=>(~old(X)|rich(X))))&
(![X]:((wise(X)<~>funny(X))<=>(kind(X)|patient(X))))&
((?[X]:((old(X)&~creative(X))))=>(~old(alice)))&
(![X]:((creative(X)<~>tall(X))=>~tall(X)))&
(![X]:((tall(X)&creative(X))=>(~humble(X)|~brave(X))))&
(![X]:((~old(X)|~funny(X))=>(generous(X)&~tall(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((~strong(X)|curious(X)))))&
((?[X]:((happy(X)&~humble(X))))=>((quiet(paul)<~>funny(paul))))&
(![X]:((strong(X)|~kind(X))<=>(~brave(X)<~>~patient(X))))&
(((~funny(alice)&~wise(alice)))=>((calm(fred)|~brave(fred))))&
(![X]:((funny(X)|kind(X))=>(happy(X)<~>~tall(X))))&
((~creative(mary)|calm(mary)))&
(?[X]:((old(X)|~humble(X))))&
(~happy(john))&
((~quiet(susan)&~patient(susan)))&
(?[X]:((~creative(X)|humble(X)))) | ~kind(paul) | [
"p0",
"p1",
"p3",
"p6",
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4116886639205246929217113
% SZS output start Proof for 4116886639205246929217113
1. ! [X0] : ((wise(X0) <~> brave(X0)) <=> (~creative(X0) & brave(X0))) [input p0]
2. ! [X0] : ((old(X0) <~> ~strong(X0)) <=> (~creative(X0) <~> creative(X0))) [input p1]
4. ! [X0] : ((~brave(X0) | kind(X0)) => (~creative(X0) & ~funny(X0))) [input p3]
7. ! [X0] : ((wise(X0) <~> funny(X0)) <=> (patient(X0) | kind(X0))) [input p6]
8. ? [X0] : (~creative(X0) & old(X0)) => ~old(alice) [input p7]
12. ? [X0] : ~brave(X0) <=> ? [X0] : (curious(X0) | ~strong(X0)) [input p11]
14. ! [X0] : ((~kind(X0) | strong(X0)) <=> (~brave(X0) <~> ~patient(X0))) [input p13]
22. kind(paul) [input hypothesis]
23. ? [X0] : ~brave(X0) <=> ? [X1] : (curious(X1) | ~strong(X1)) [rectify 12]
27. ! [X0] : ((~creative(X0) & ~funny(X0)) | (brave(X0) & ~kind(X0))) [ennf transformation 4]
29. ~old(alice) | ! [X0] : (creative(X0) | ~old(X0)) [ennf transformation 8]
36. ! [X0] : ((((~brave(X0) | ~wise(X0)) & (brave(X0) | wise(X0))) | (creative(X0) | ~brave(X0))) & ((~creative(X0) & brave(X0)) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~brave(X0) | ~wise(X0)) & (brave(X0) | wise(X0))) | creative(X0) | ~brave(X0)) & ((~creative(X0) & brave(X0)) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))))) [flattening 36]
38. ! [X0] : ((((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0))))) [nnf transformation 2]
43. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 7]
44. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [flattening 43]
46. (? [X0] : ~brave(X0) | ! [X1] : (~curious(X1) & strong(X1))) & (? [X1] : (curious(X1) | ~strong(X1)) | ! [X0] : brave(X0)) [nnf transformation 23]
47. (? [X0] : ~brave(X0) | ! [X1] : (~curious(X1) & strong(X1))) & (? [X2] : (curious(X2) | ~strong(X2)) | ! [X3] : brave(X3)) [rectify 46]
48. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
49. ? [X2] : (curious(X2) | ~strong(X2)) => (curious(sK2) | ~strong(sK2)) [choice axiom]
50. (~brave(sK1) | ! [X1] : (~curious(X1) & strong(X1))) & ((curious(sK2) | ~strong(sK2)) | ! [X3] : brave(X3)) [skolemisation 47,49,48]
52. ! [X0] : (((~kind(X0) | strong(X0)) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) & (((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | (kind(X0) & ~strong(X0)))) [nnf transformation 14]
53. ! [X0] : ((~kind(X0) | strong(X0) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) & (((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | (kind(X0) & ~strong(X0)))) [flattening 52]
59. brave(X0) | brave(X0) | ~wise(X0) [cnf transformation 37]
69. ~strong(X0) | old(X0) | creative(X0) | creative(X0) [cnf transformation 38]
70. ~strong(X0) | old(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 38]
75. ~funny(X0) | ~kind(X0) [cnf transformation 27]
76. ~funny(X0) | brave(X0) [cnf transformation 27]
77. ~kind(X0) | ~creative(X0) [cnf transformation 27]
87. funny(X0) | wise(X0) | ~kind(X0) [cnf transformation 44]
88. ~patient(X0) | wise(X0) | funny(X0) [cnf transformation 44]
91. ~old(alice) | creative(X0) | ~old(X0) [cnf transformation 29]
100. ~brave(sK1) | strong(X1) [cnf transformation 50]
107. kind(X0) | brave(X0) | patient(X0) [cnf transformation 53]
119. kind(paul) [cnf transformation 22]
124. ~strong(X0) | old(X0) | creative(X0) [duplicate literal removal 69]
125. ~strong(X0) | old(X0) | ~creative(X0) [duplicate literal removal 70]
128. ~wise(X0) | brave(X0) [duplicate literal removal 59]
131. ~strong(X0) | old(X0) [subsumption resolution 124,125]
150. ~kind(X0) | wise(X0) [subsumption resolution 87,75]
153. 5 <=> ! [X0] : (creative(X0) | ~old(X0)) [avatar definition]
154. creative(X0) | ~old(X0) <- (5) [avatar component clause 153]
156. 6 <=> old(alice) [avatar definition]
158. ~old(alice) <- (~6) [avatar component clause 156]
159. 5 | ~6 [avatar split clause 91,156,153]
165. 8 <=> brave(sK1) [avatar definition]
167. ~brave(sK1) <- (~8) [avatar component clause 165]
170. 9 <=> ! [X1] : strong(X1) [avatar definition]
171. strong(X1) <- (9) [avatar component clause 170]
172. 9 | ~8 [avatar split clause 100,165,170]
174. 10 <=> ! [X3] : brave(X3) [avatar definition]
175. brave(X3) <- (10) [avatar component clause 174]
206. ~creative(paul) [resolution 77,119]
211. brave(X1) | patient(X1) | wise(X1) [resolution 107,150]
213. patient(X1) | brave(X1) [subsumption resolution 211,128]
217. brave(X2) | wise(X2) | funny(X2) [resolution 213,88]
218. brave(X2) | funny(X2) [subsumption resolution 217,128]
219. brave(X2) [subsumption resolution 218,76]
220. 10 [avatar split clause 219,174]
221. $false <- (~8, 10) [resolution 175,167]
222. 8 | ~10 [avatar contradiction clause 221]
225. old(X1) <- (9) [resolution 171,131]
227. $false <- (~6, 9) [resolution 225,158]
230. 6 | ~9 [avatar contradiction clause 227]
231. creative(X0) <- (5, 9) [subsumption resolution 154,225]
236. $false <- (5, 9) [resolution 231,206]
237. ~5 | ~9 [avatar contradiction clause 236]
240. $false [avatar sat refutation 159,172,220,222,230,237]
% SZS output end Proof for 4116886639205246929217113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or tall then someone is either rich or not old. If fred is both not creative and not patient then someone is not funny and vice versa. If john is brave or humble then someone is generous or kind. If someone is either creative or not patient then someone is both not humble and patient and vice versa. If alice is both not rich and quiet then someone is not tall. Everyone who is both not patient and not creative is rich or not kind. Everyone who is either creative or tall is either not tall or rich. Everyone who is creative is both not rich and old. If someone is either not curious or humble then someone is either brave or wise. Everyone who is either wise or not rich is strong. If john is either not funny or kind then someone is both not wise and strong. If john is either not wise or not generous then someone is both not brave and not curious and vice versa. Everyone who is humble or old is both not humble and not quiet and vice versa. Everyone who is either not rich or quiet is both not funny and not tall. If lucy is both not generous and tall then someone is both calm and not humble and vice versa. Everyone who is not brave is not happy or not creative. John is either not curious or calm. Someone is humble or tall. Paul is funny or old. Someone is brave or not generous. Someone is both quiet and not humble. Someone is rich or not strong. Alice is not creative. Someone is strong or not brave. | Fred is not humble. | entailment | ((?[X]:((~calm(X)|tall(X))))=>(?[X]:((rich(X)<~>~old(X)))))&
(((~creative(fred)&~patient(fred)))<=>(?[X]:(~funny(X))))&
(((brave(john)|humble(john)))=>(?[X]:((generous(X)|kind(X)))))&
((?[X]:((creative(X)<~>~patient(X))))<=>(?[X]:((~humble(X)&patient(X)))))&
(((~rich(alice)&quiet(alice)))=>(?[X]:(~tall(X))))&
(![X]:((~patient(X)&~creative(X))=>(rich(X)|~kind(X))))&
(![X]:((creative(X)<~>tall(X))=>(~tall(X)<~>rich(X))))&
(![X]:(creative(X)=>(~rich(X)&old(X))))&
((?[X]:((~curious(X)<~>humble(X))))=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:((wise(X)<~>~rich(X))=>strong(X)))&
(((~funny(john)<~>kind(john)))=>(?[X]:((~wise(X)&strong(X)))))&
(((~wise(john)<~>~generous(john)))<=>(?[X]:((~brave(X)&~curious(X)))))&
(![X]:((humble(X)|old(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(~funny(X)&~tall(X))))&
(((~generous(lucy)&tall(lucy)))<=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:(~brave(X)=>(~happy(X)|~creative(X))))&
((~curious(john)<~>calm(john)))&
(?[X]:((humble(X)|tall(X))))&
((funny(paul)|old(paul)))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((rich(X)|~strong(X))))&
(~creative(alice))&
(?[X]:((strong(X)|~brave(X)))) | ~humble(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7147823464099231999335996
% SZS output start Proof for 7147823464099231999335996
13. ! [X0] : ((old(X0) | humble(X0)) <=> (~quiet(X0) & ~humble(X0))) [input p12]
25. humble(fred) [input hypothesis]
73. ! [X0] : (((old(X0) | humble(X0)) | (quiet(X0) | humble(X0))) & ((~quiet(X0) & ~humble(X0)) | (~old(X0) & ~humble(X0)))) [nnf transformation 13]
74. ! [X0] : ((old(X0) | humble(X0) | quiet(X0) | humble(X0)) & ((~quiet(X0) & ~humble(X0)) | (~old(X0) & ~humble(X0)))) [flattening 73]
131. ~humble(X0) | ~humble(X0) [cnf transformation 74]
154. humble(fred) [cnf transformation 25]
155. ~humble(X0) [duplicate literal removal 131]
387. $false [subsumption resolution 154,155]
% SZS output end Proof for 7147823464099231999335996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or patient is either not kind or not strong and vice versa.
If john is both happy and not creative then alice is not old or tall and vice versa.
If someone is either not generous or not quiet then alice is not funny or not tall.
Everyone who is not wise is both not calm and not funny and vice versa.
Everyone who is both not kind and strong is either not rich or kind.
Everyone who is either strong or not brave is both old and not generous.
Everyone who is both not strong and not generous is both not quiet and not old.
Everyone who is not patient or funny is both strong and quiet.
Everyone who is either creative or not patient is both not brave and rich.
If john is both not calm and not wise then someone is either funny or not strong and vice versa.
If someone is not curious then paul is either wise or calm and vice versa.
If john is wise then john is either not strong or not funny and vice versa.
If alice is either not strong or brave then fred is curious and vice versa.
If someone is generous then lucy is not patient and vice versa.
Everyone who is either not rich or not wise is not creative and vice versa.
If susan is not funny or humble then lucy is funny or not rich.
Someone is not funny.
Someone is not generous or quiet.
Alice is both old and not wise.
Someone is happy.
Someone is not patient.
Susan is kind or brave. | Fred is not happy. | neutral | (![X]:((~patient(X)<~>patient(X))<=>(~kind(X)<~>~strong(X))))&
(((happy(john)&~creative(john)))<=>((~old(alice)|tall(alice))))&
((?[X]:((~generous(X)<~>~quiet(X))))=>((~funny(alice)|~tall(alice))))&
(![X]:(~wise(X)<=>(~calm(X)&~funny(X))))&
(![X]:((~kind(X)&strong(X))=>(~rich(X)<~>kind(X))))&
(![X]:((strong(X)<~>~brave(X))=>(old(X)&~generous(X))))&
(![X]:((~strong(X)&~generous(X))=>(~quiet(X)&~old(X))))&
(![X]:((~patient(X)|funny(X))=>(strong(X)&quiet(X))))&
(![X]:((creative(X)<~>~patient(X))=>(~brave(X)&rich(X))))&
(((~calm(john)&~wise(john)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:(~curious(X)))<=>((wise(paul)<~>calm(paul))))&
((wise(john))<=>((~strong(john)<~>~funny(john))))&
(((~strong(alice)<~>brave(alice)))<=>(curious(fred)))&
((?[X]:(generous(X)))<=>(~patient(lucy)))&
(![X]:((~rich(X)<~>~wise(X))<=>~creative(X)))&
(((~funny(susan)|humble(susan)))=>((funny(lucy)|~rich(lucy))))&
(?[X]:(~funny(X)))&
(?[X]:((~generous(X)|quiet(X))))&
((old(alice)&~wise(alice)))&
(?[X]:(happy(X)))&
(?[X]:(~patient(X)))&
((kind(susan)|brave(susan))) | ~happy(fred) | [] | null | 0 |
Everyone who is both not strong and not old is both rich and not funny. Everyone who is both not humble and kind is either not rich or not funny and vice versa. If fred is both funny and not rich then someone is both wise and not wise and vice versa. Everyone who is not old is funny or not wise. If john is either not old or wise then fred is either not funny or not strong. If someone is both calm and not calm then john is both tall and calm. If fred is both strong and happy then john is curious or strong and vice versa. If john is not happy then someone is both wise and not happy. Everyone who is kind or not tall is both strong and funny. Everyone who is tall is rich or not humble. Everyone who is both not brave and not curious is happy and vice versa. Everyone who is not strong or quiet is old or not patient and vice versa. If someone is both not humble and happy then lucy is not quiet or not humble and vice versa. Everyone who is patient or happy is not creative or rich and vice versa. If someone is both not kind and not happy then mary is not old or wise. Someone is not generous. Someone is both old and not quiet. Lucy is both creative and wise. John is not calm. Someone is both old and not rich. Paul is not patient or not funny. Someone is both not creative and not strong. John is both not happy and wise. | Lucy is not curious. | neutral | (![X]:((~strong(X)&~old(X))=>(rich(X)&~funny(X))))&
(![X]:((~humble(X)&kind(X))<=>(~rich(X)<~>~funny(X))))&
(((funny(fred)&~rich(fred)))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~old(X)=>(funny(X)|~wise(X))))&
(((~old(john)<~>wise(john)))=>((~funny(fred)<~>~strong(fred))))&
((?[X]:((calm(X)&~calm(X))))=>((tall(john)&calm(john))))&
(((strong(fred)&happy(fred)))<=>((curious(john)|strong(john))))&
((~happy(john))=>(?[X]:((wise(X)&~happy(X)))))&
(![X]:((kind(X)|~tall(X))=>(strong(X)&funny(X))))&
(![X]:(tall(X)=>(rich(X)|~humble(X))))&
(![X]:((~brave(X)&~curious(X))<=>happy(X)))&
(![X]:((~strong(X)|quiet(X))<=>(old(X)|~patient(X))))&
((?[X]:((~humble(X)&happy(X))))<=>((~quiet(lucy)|~humble(lucy))))&
(![X]:((patient(X)|happy(X))<=>(~creative(X)|rich(X))))&
((?[X]:((~kind(X)&~happy(X))))=>((~old(mary)|wise(mary))))&
(?[X]:(~generous(X)))&
(?[X]:((old(X)&~quiet(X))))&
((creative(lucy)&wise(lucy)))&
(~calm(john))&
(?[X]:((old(X)&~rich(X))))&
((~patient(paul)|~funny(paul)))&
(?[X]:((~creative(X)&~strong(X))))&
((~happy(john)&wise(john))) | ~curious(lucy) | [] | null | 0 |
If someone is either not tall or not creative then fred is either tall or strong and vice versa.
If someone is either not old or not tall then someone is both not humble and tall.
Everyone who is either funny or kind is both happy and not humble.
Everyone who is either brave or not creative is both creative and not rich.
If susan is both not patient and not quiet then john is both not patient and curious.
If someone is brave then someone is not humble.
If john is old or funny then mary is either not old or tall.
Everyone who is patient is both not humble and humble.
Everyone who is both calm and funny is both quiet and strong and vice versa.
If someone is not patient or rich then alice is funny or not quiet.
Everyone who is either patient or not strong is quiet and vice versa.
If someone is not strong or humble then susan is either patient or wise and vice versa.
Everyone who is either strong or quiet is not creative.
If someone is curious or humble then someone is brave or not old and vice versa.
Everyone who is not old is curious or not funny.
If someone is creative then someone is curious and vice versa.
Fred is quiet.
Alice is both not funny and rich.
Someone is either humble or old.
Alice is not funny or not strong.
Someone is not tall or old.
Someone is both tall and not humble.
Mary is either not rich or funny.
John is both not humble and not strong. | John is curious. | contradiction | ((?[X]:((~tall(X)<~>~creative(X))))<=>((tall(fred)<~>strong(fred))))&
((?[X]:((~old(X)<~>~tall(X))))=>(?[X]:((~humble(X)&tall(X)))))&
(![X]:((funny(X)<~>kind(X))=>(happy(X)&~humble(X))))&
(![X]:((brave(X)<~>~creative(X))=>(creative(X)&~rich(X))))&
(((~patient(susan)&~quiet(susan)))=>((~patient(john)&curious(john))))&
((?[X]:(brave(X)))=>(?[X]:(~humble(X))))&
(((old(john)|funny(john)))=>((~old(mary)<~>tall(mary))))&
(![X]:(patient(X)=>(~humble(X)&humble(X))))&
(![X]:((calm(X)&funny(X))<=>(quiet(X)&strong(X))))&
((?[X]:((~patient(X)|rich(X))))=>((funny(alice)|~quiet(alice))))&
(![X]:((patient(X)<~>~strong(X))<=>quiet(X)))&
((?[X]:((~strong(X)|humble(X))))<=>((patient(susan)<~>wise(susan))))&
(![X]:((strong(X)<~>quiet(X))=>~creative(X)))&
((?[X]:((curious(X)|humble(X))))<=>(?[X]:((brave(X)|~old(X)))))&
(![X]:(~old(X)=>(curious(X)|~funny(X))))&
((?[X]:(creative(X)))<=>(?[X]:(curious(X))))&
(quiet(fred))&
((~funny(alice)&rich(alice)))&
(?[X]:((humble(X)<~>old(X))))&
((~funny(alice)|~strong(alice)))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((tall(X)&~humble(X))))&
((~rich(mary)<~>funny(mary)))&
((~humble(john)&~strong(john))) | curious(john) | [
"p7",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6790242816482307421402757
% SZS output start Proof for 6790242816482307421402757
8. ! [X0] : (patient(X0) => (humble(X0) & ~humble(X0))) [input p7]
11. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> quiet(X0)) [input p10]
13. ! [X0] : ((strong(X0) <~> quiet(X0)) => ~creative(X0)) [input p12]
16. ? [X0] : creative(X0) <=> ? [X0] : curious(X0) [input p15]
25. curious(john) [input hypothesis]
29. ? [X0] : creative(X0) <=> ? [X1] : curious(X1) [rectify 16]
38. ! [X0] : ((humble(X0) & ~humble(X0)) | ~patient(X0)) [ennf transformation 8]
41. ! [X0] : (~creative(X0) | (strong(X0) <=> quiet(X0))) [ennf transformation 13]
60. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~quiet(X0)) & (quiet(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 11]
65. ! [X0] : (~creative(X0) | ((strong(X0) | ~quiet(X0)) & (quiet(X0) | ~strong(X0)))) [nnf transformation 41]
71. (? [X0] : creative(X0) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : ~creative(X0)) [nnf transformation 29]
72. (? [X0] : creative(X0) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : ~creative(X3)) [rectify 71]
73. ? [X0] : creative(X0) => creative(sK6) [choice axiom]
74. ? [X2] : curious(X2) => curious(sK7) [choice axiom]
75. (creative(sK6) | ! [X1] : ~curious(X1)) & (curious(sK7) | ! [X3] : ~creative(X3)) [skolemisation 72,74,73]
109. ~humble(X0) | ~patient(X0) [cnf transformation 38]
110. ~patient(X0) | humble(X0) [cnf transformation 38]
118. quiet(X0) | patient(X0) | strong(X0) [cnf transformation 60]
119. ~strong(X0) | patient(X0) | ~quiet(X0) [cnf transformation 60]
127. ~creative(X0) | quiet(X0) | ~strong(X0) [cnf transformation 65]
128. ~creative(X0) | strong(X0) | ~quiet(X0) [cnf transformation 65]
135. creative(sK6) | ~curious(X1) [cnf transformation 75]
149. curious(john) [cnf transformation 25]
208. 13 <=> curious(john) [avatar definition]
210. curious(john) <- (13) [avatar component clause 208]
245. ~patient(X0) [subsumption resolution 109,110]
260. ~quiet(X0) | ~strong(X0) [subsumption resolution 119,245]
261. quiet(X0) | strong(X0) [subsumption resolution 118,245]
286. ~quiet(X0) | ~creative(X0) [subsumption resolution 128,260]
287. ~creative(X0) | ~strong(X0) [subsumption resolution 127,286]
311. 34 <=> ! [X3] : ~curious(X3) [avatar definition]
312. ~curious(X3) <- (34) [avatar component clause 311]
315. 35 <=> creative(sK6) [avatar definition]
317. creative(sK6) <- (35) [avatar component clause 315]
318. 34 | 35 [avatar split clause 135,315,311]
320. 36 <=> ! [X3] : ~creative(X3) [avatar definition]
321. ~creative(X3) <- (36) [avatar component clause 320]
362. 13 [avatar split clause 149,208]
365. $false <- (13, 34) [subsumption resolution 210,312]
366. ~13 | ~34 [avatar contradiction clause 365]
367. $false <- (35, 36) [subsumption resolution 317,321]
368. ~35 | ~36 [avatar contradiction clause 367]
391. ~creative(X0) | strong(X0) [resolution 286,261]
392. ~creative(X0) [subsumption resolution 391,287]
393. 36 [avatar split clause 392,320]
394. $false [avatar sat refutation 318,362,366,368,393]
% SZS output end Proof for 6790242816482307421402757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not brave and rich then someone is not brave or not humble and vice versa.
If someone is not generous then someone is both not humble and not rich.
Everyone who is brave or not kind is not tall and vice versa.
If someone is both generous and not creative then someone is either not strong or humble.
Everyone who is calm is not quiet.
If fred is not rich or not happy then mary is either funny or rich.
Everyone who is not calm or strong is either not humble or humble and vice versa.
Everyone who is old is either kind or tall and vice versa.
If someone is both not rich and not funny then someone is strong and vice versa.
Everyone who is both generous and strong is not strong or not kind.
If mary is calm then someone is not creative and vice versa.
Everyone who is not funny or creative is either kind or calm.
Everyone who is not rich is either not calm or not strong.
Everyone who is not wise is either not funny or not strong.
Everyone who is not humble is both not kind and kind.
If susan is either tall or generous then lucy is not rich or not quiet and vice versa.
Lucy is not humble or not brave.
Alice is not strong or old.
Alice is humble.
Someone is tall. | Susan is not creative. | contradiction | ((?[X]:((~brave(X)&rich(X))))<=>(?[X]:((~brave(X)|~humble(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((brave(X)|~kind(X))<=>~tall(X)))&
((?[X]:((generous(X)&~creative(X))))=>(?[X]:((~strong(X)<~>humble(X)))))&
(![X]:(calm(X)=>~quiet(X)))&
(((~rich(fred)|~happy(fred)))=>((funny(mary)<~>rich(mary))))&
(![X]:((~calm(X)|strong(X))<=>(~humble(X)<~>humble(X))))&
(![X]:(old(X)<=>(kind(X)<~>tall(X))))&
((?[X]:((~rich(X)&~funny(X))))<=>(?[X]:(strong(X))))&
(![X]:((generous(X)&strong(X))=>(~strong(X)|~kind(X))))&
((calm(mary))<=>(?[X]:(~creative(X))))&
(![X]:((~funny(X)|creative(X))=>(kind(X)<~>calm(X))))&
(![X]:(~rich(X)=>(~calm(X)<~>~strong(X))))&
(![X]:(~wise(X)=>(~funny(X)<~>~strong(X))))&
(![X]:(~humble(X)=>(~kind(X)&kind(X))))&
(((tall(susan)<~>generous(susan)))<=>((~rich(lucy)|~quiet(lucy))))&
((~humble(lucy)|~brave(lucy)))&
((~strong(alice)|old(alice)))&
(humble(alice))&
(?[X]:(tall(X))) | ~creative(susan) | [
"p1",
"p6",
"p8",
"p9",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 73757398307752481428259
% SZS output start Proof for 73757398307752481428259
2. ? [X0] : ~generous(X0) => ? [X0] : (~rich(X0) & ~humble(X0)) [input p1]
7. ! [X0] : ((strong(X0) | ~calm(X0)) <=> (~humble(X0) <~> humble(X0))) [input p6]
9. ? [X0] : (~funny(X0) & ~rich(X0)) <=> ? [X0] : strong(X0) [input p8]
10. ! [X0] : ((strong(X0) & generous(X0)) => (~kind(X0) | ~strong(X0))) [input p9]
11. calm(mary) <=> ? [X0] : ~creative(X0) [input p10]
12. ! [X0] : ((creative(X0) | ~funny(X0)) => (kind(X0) <~> calm(X0))) [input p11]
13. ! [X0] : (~rich(X0) => (~calm(X0) <~> ~strong(X0))) [input p12]
15. ! [X0] : (~humble(X0) => (kind(X0) & ~kind(X0))) [input p14]
21. ~creative(susan) [input hypothesis]
23. ? [X0] : ~generous(X0) => ? [X1] : (~rich(X1) & ~humble(X1)) [rectify 2]
25. ? [X0] : (~funny(X0) & ~rich(X0)) <=> ? [X1] : strong(X1) [rectify 9]
29. ? [X1] : (~rich(X1) & ~humble(X1)) | ! [X0] : generous(X0) [ennf transformation 23]
34. ! [X0] : ((~kind(X0) | ~strong(X0)) | (~strong(X0) | ~generous(X0))) [ennf transformation 10]
35. ! [X0] : (~kind(X0) | ~strong(X0) | ~strong(X0) | ~generous(X0)) [flattening 34]
36. ! [X0] : ((kind(X0) <~> calm(X0)) | (~creative(X0) & funny(X0))) [ennf transformation 12]
37. ! [X0] : ((~calm(X0) <~> ~strong(X0)) | rich(X0)) [ennf transformation 13]
38. ! [X0] : ((kind(X0) & ~kind(X0)) | humble(X0)) [ennf transformation 15]
44. ? [X0] : (~rich(X0) & ~humble(X0)) | ! [X1] : generous(X1) [rectify 29]
45. ? [X0] : (~rich(X0) & ~humble(X0)) => (~rich(sK2) & ~humble(sK2)) [choice axiom]
46. (~rich(sK2) & ~humble(sK2)) | ! [X1] : generous(X1) [skolemisation 44,45]
54. ! [X0] : (((strong(X0) | ~calm(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (~strong(X0) & calm(X0)))) [nnf transformation 7]
55. ! [X0] : ((strong(X0) | ~calm(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (~strong(X0) & calm(X0)))) [flattening 54]
57. (? [X0] : (~funny(X0) & ~rich(X0)) | ! [X1] : ~strong(X1)) & (? [X1] : strong(X1) | ! [X0] : (funny(X0) | rich(X0))) [nnf transformation 25]
58. (? [X0] : (~funny(X0) & ~rich(X0)) | ! [X1] : ~strong(X1)) & (? [X2] : strong(X2) | ! [X3] : (funny(X3) | rich(X3))) [rectify 57]
59. ? [X0] : (~funny(X0) & ~rich(X0)) => (~funny(sK4) & ~rich(sK4)) [choice axiom]
60. ? [X2] : strong(X2) => strong(sK5) [choice axiom]
61. ((~funny(sK4) & ~rich(sK4)) | ! [X1] : ~strong(X1)) & (strong(sK5) | ! [X3] : (funny(X3) | rich(X3))) [skolemisation 58,60,59]
62. (calm(mary) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | ~calm(mary)) [nnf transformation 11]
63. (calm(mary) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | ~calm(mary)) [rectify 62]
64. ? [X1] : ~creative(X1) => ~creative(sK6) [choice axiom]
65. (calm(mary) | ! [X0] : creative(X0)) & (~creative(sK6) | ~calm(mary)) [skolemisation 63,64]
66. ! [X0] : (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~creative(X0) & funny(X0))) [nnf transformation 36]
67. ! [X0] : (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | rich(X0)) [nnf transformation 37]
77. ~humble(sK2) | generous(X1) [cnf transformation 46]
91. strong(X0) | ~calm(X0) | humble(X0) | humble(X0) [cnf transformation 55]
92. strong(X0) | ~calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 55]
96. ~rich(sK4) | ~strong(X1) [cnf transformation 61]
97. ~funny(sK4) | ~strong(X1) [cnf transformation 61]
98. ~kind(X0) | ~strong(X0) | ~strong(X0) | ~generous(X0) [cnf transformation 35]
100. calm(mary) | creative(X0) [cnf transformation 65]
101. funny(X0) | kind(X0) | calm(X0) [cnf transformation 66]
105. ~strong(X0) | ~calm(X0) | rich(X0) [cnf transformation 67]
106. strong(X0) | calm(X0) | rich(X0) [cnf transformation 67]
107. ~kind(X0) | humble(X0) [cnf transformation 38]
108. kind(X0) | humble(X0) [cnf transformation 38]
119. ~creative(susan) [cnf transformation 21]
120. ~strong(X0) | ~kind(X0) | ~generous(X0) [duplicate literal removal 98]
121. strong(X0) | ~calm(X0) | humble(X0) [duplicate literal removal 91]
122. ~calm(X0) | strong(X0) | ~humble(X0) [duplicate literal removal 92]
124. 1 <=> ! [X1] : humble(X1) [avatar definition]
125. humble(X1) <- (1) [avatar component clause 124]
154. 8 <=> ! [X1] : generous(X1) [avatar definition]
155. generous(X1) <- (8) [avatar component clause 154]
162. 10 <=> humble(sK2) [avatar definition]
164. ~humble(sK2) <- (~10) [avatar component clause 162]
165. 8 | ~10 [avatar split clause 77,162,154]
193. ~calm(X0) | strong(X0) [subsumption resolution 121,122]
197. 17 <=> ! [X1] : ~strong(X1) [avatar definition]
198. ~strong(X1) <- (17) [avatar component clause 197]
200. 18 <=> funny(sK4) [avatar definition]
202. ~funny(sK4) <- (~18) [avatar component clause 200]
203. 17 | ~18 [avatar split clause 97,200,197]
205. 19 <=> rich(sK4) [avatar definition]
207. ~rich(sK4) <- (~19) [avatar component clause 205]
208. 17 | ~19 [avatar split clause 96,205,197]
218. 22 <=> ! [X0] : creative(X0) [avatar definition]
219. creative(X0) <- (22) [avatar component clause 218]
221. 23 <=> calm(mary) [avatar definition]
223. calm(mary) <- (23) [avatar component clause 221]
224. 22 | 23 [avatar split clause 100,221,218]
230. strong(X0) | rich(X0) [subsumption resolution 106,193]
231. ~calm(X0) | rich(X0) [subsumption resolution 105,193]
232. humble(X0) [subsumption resolution 107,108]
233. 1 [avatar split clause 232,124]
278. $false <- (1, ~10) [resolution 164,125]
279. ~1 | 10 [avatar contradiction clause 278]
282. $false <- (22) [resolution 219,119]
283. ~22 [avatar contradiction clause 282]
298. strong(mary) <- (23) [resolution 193,223]
303. $false <- (17, 23) [resolution 198,298]
304. ~17 | ~23 [avatar contradiction clause 303]
311. kind(sK4) | calm(sK4) <- (~18) [resolution 101,202]
313. 33 <=> calm(sK4) [avatar definition]
315. calm(sK4) <- (33) [avatar component clause 313]
317. 34 <=> kind(sK4) [avatar definition]
319. kind(sK4) <- (34) [avatar component clause 317]
320. 33 | 34 | 18 [avatar split clause 311,200,317,313]
321. rich(sK4) <- (33) [resolution 315,231]
323. $false <- (~19, 33) [subsumption resolution 321,207]
324. 19 | ~33 [avatar contradiction clause 323]
343. ~kind(X0) | ~generous(X0) | rich(X0) [resolution 120,230]
347. ~kind(X0) | rich(X0) <- (8) [subsumption resolution 343,155]
355. rich(sK4) <- (8, 34) [resolution 347,319]
356. $false <- (8, ~19, 34) [subsumption resolution 355,207]
357. ~8 | 19 | ~34 [avatar contradiction clause 356]
358. $false [avatar sat refutation 165,203,208,224,233,279,283,304,320,324,357]
% SZS output end Proof for 73757398307752481428259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or rich.
If someone is either patient or not patient then fred is not strong or not old.
Everyone who is not kind is either not kind or generous and vice versa.
If someone is not curious or not kind then someone is either funny or not old and vice versa.
Everyone who is not patient or generous is either strong or not calm and vice versa.
If someone is both creative and not brave then someone is both not calm and calm and vice versa.
If someone is creative then fred is not wise or generous and vice versa.
Everyone who is both not creative and patient is both curious and not funny.
Everyone who is kind or not rich is either not funny or not strong and vice versa.
If john is both not creative and not generous then someone is funny and vice versa.
If someone is rich or strong then someone is both calm and not curious and vice versa.
Everyone who is kind or rich is humble or patient.
If susan is not curious or not old then someone is either not generous or not curious and vice versa.
If someone is both not rich and funny then paul is funny.
Everyone who is not tall or not patient is not happy.
If fred is generous then john is either funny or not patient.
Someone is patient.
Lucy is both wise and quiet.
Lucy is either not brave or not calm.
Someone is both brave and not curious.
Someone is both not generous and calm.
Mary is not quiet or not rich.
Someone is quiet. | Fred is not strong. | neutral | (![X]:(happy(X)=>(generous(X)|rich(X))))&
((?[X]:((patient(X)<~>~patient(X))))=>((~strong(fred)|~old(fred))))&
(![X]:(~kind(X)<=>(~kind(X)<~>generous(X))))&
((?[X]:((~curious(X)|~kind(X))))<=>(?[X]:((funny(X)<~>~old(X)))))&
(![X]:((~patient(X)|generous(X))<=>(strong(X)<~>~calm(X))))&
((?[X]:((creative(X)&~brave(X))))<=>(?[X]:((~calm(X)&calm(X)))))&
((?[X]:(creative(X)))<=>((~wise(fred)|generous(fred))))&
(![X]:((~creative(X)&patient(X))=>(curious(X)&~funny(X))))&
(![X]:((kind(X)|~rich(X))<=>(~funny(X)<~>~strong(X))))&
(((~creative(john)&~generous(john)))<=>(?[X]:(funny(X))))&
((?[X]:((rich(X)|strong(X))))<=>(?[X]:((calm(X)&~curious(X)))))&
(![X]:((kind(X)|rich(X))=>(humble(X)|patient(X))))&
(((~curious(susan)|~old(susan)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((~rich(X)&funny(X))))=>(funny(paul)))&
(![X]:((~tall(X)|~patient(X))=>~happy(X)))&
((generous(fred))=>((funny(john)<~>~patient(john))))&
(?[X]:(patient(X)))&
((wise(lucy)&quiet(lucy)))&
((~brave(lucy)<~>~calm(lucy)))&
(?[X]:((brave(X)&~curious(X))))&
(?[X]:((~generous(X)&calm(X))))&
((~quiet(mary)|~rich(mary)))&
(?[X]:(quiet(X))) | ~strong(fred) | [] | null | 0 |
Everyone who is funny is either not wise or calm and vice versa.
If someone is kind or not strong then paul is either not quiet or not strong.
Everyone who is both quiet and kind is both funny and not tall.
If someone is either not brave or not curious then someone is not calm.
If lucy is either wise or humble then someone is either humble or not curious.
If someone is not quiet then someone is generous.
If someone is not quiet then paul is both quiet and not rich and vice versa.
If someone is tall then someone is both not wise and generous and vice versa.
If someone is either not wise or not humble then someone is wise.
If someone is not wise then someone is not rich or humble and vice versa.
Everyone who is patient is either brave or not patient and vice versa.
If paul is funny then fred is strong and vice versa.
Everyone who is either not humble or not rich is not strong or not humble and vice versa.
Everyone who is rich or not old is both tall and old.
Everyone who is both patient and calm is humble or not happy.
If someone is not creative then susan is not rich or happy.
John is kind.
Someone is either tall or rich.
Mary is not kind.
Someone is both not kind and patient.
Someone is not kind.
Someone is both not wise and not creative.
John is either tall or generous.
Someone is quiet or not kind. | John is brave. | entailment | (![X]:(funny(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((kind(X)|~strong(X))))=>((~quiet(paul)<~>~strong(paul))))&
(![X]:((quiet(X)&kind(X))=>(funny(X)&~tall(X))))&
((?[X]:((~brave(X)<~>~curious(X))))=>(?[X]:(~calm(X))))&
(((wise(lucy)<~>humble(lucy)))=>(?[X]:((humble(X)<~>~curious(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:(generous(X))))&
((?[X]:(~quiet(X)))<=>((quiet(paul)&~rich(paul))))&
((?[X]:(tall(X)))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:(patient(X)<=>(brave(X)<~>~patient(X))))&
((funny(paul))<=>(strong(fred)))&
(![X]:((~humble(X)<~>~rich(X))<=>(~strong(X)|~humble(X))))&
(![X]:((rich(X)|~old(X))=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(kind(john))&
(?[X]:((tall(X)<~>rich(X))))&
(~kind(mary))&
(?[X]:((~kind(X)&patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~creative(X))))&
((tall(john)<~>generous(john)))&
(?[X]:((quiet(X)|~kind(X)))) | brave(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6165844808735654394427933
% SZS output start Proof for 6165844808735654394427933
11. ! [X0] : (patient(X0) <=> (brave(X0) <~> ~patient(X0))) [input p10]
25. ~brave(john) [input hypothesis]
75. ! [X0] : ((patient(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~patient(X0))) [nnf transformation 11]
119. ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 75]
122. patient(X0) | brave(X0) | patient(X0) [cnf transformation 75]
146. ~brave(john) [cnf transformation 25]
149. ~patient(X0) | brave(X0) [duplicate literal removal 119]
150. patient(X0) | brave(X0) [duplicate literal removal 122]
277. brave(X0) [subsumption resolution 149,150]
322. $false [subsumption resolution 146,277]
% SZS output end Proof for 6165844808735654394427933
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and humble is both happy and tall and vice versa.
Everyone who is calm is either not wise or happy and vice versa.
Everyone who is kind or not calm is not generous and vice versa.
If someone is not happy then paul is creative or not creative.
If someone is creative or not curious then someone is both humble and strong.
Everyone who is both kind and not generous is creative.
If someone is both calm and wise then someone is both curious and not calm and vice versa.
If mary is both creative and not creative then someone is either not strong or calm and vice versa.
Everyone who is not rich is rich.
If someone is both patient and not old then someone is both not wise and kind and vice versa.
Everyone who is wise or patient is both not wise and not generous.
Everyone who is either not funny or calm is both funny and not rich.
Everyone who is both brave and not quiet is both generous and not calm and vice versa.
If susan is not tall then someone is either not happy or not old and vice versa.
Everyone who is not calm or not old is not happy.
If someone is humble or old then someone is both happy and not calm and vice versa.
Fred is quiet.
Someone is either not quiet or strong.
Mary is tall or not funny.
Paul is either curious or humble. | Paul is funny. | contradiction | (![X]:((~patient(X)&humble(X))<=>(happy(X)&tall(X))))&
(![X]:(calm(X)<=>(~wise(X)<~>happy(X))))&
(![X]:((kind(X)|~calm(X))<=>~generous(X)))&
((?[X]:(~happy(X)))=>((creative(paul)|~creative(paul))))&
((?[X]:((creative(X)|~curious(X))))=>(?[X]:((humble(X)&strong(X)))))&
(![X]:((kind(X)&~generous(X))=>creative(X)))&
((?[X]:((calm(X)&wise(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(((creative(mary)&~creative(mary)))<=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:(~rich(X)=>rich(X)))&
((?[X]:((patient(X)&~old(X))))<=>(?[X]:((~wise(X)&kind(X)))))&
(![X]:((wise(X)|patient(X))=>(~wise(X)&~generous(X))))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(quiet(fred))&
(?[X]:((~quiet(X)<~>strong(X))))&
((tall(mary)|~funny(mary)))&
((curious(paul)<~>humble(paul))) | funny(paul) | [
"p4",
"p6",
"p8",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2989099403334167476452098
% SZS output start Proof for 2989099403334167476452098
5. ? [X0] : (~curious(X0) | creative(X0)) => ? [X0] : (strong(X0) & humble(X0)) [input p4]
7. ? [X0] : (wise(X0) & calm(X0)) <=> ? [X0] : (~calm(X0) & curious(X0)) [input p6]
9. ! [X0] : (~rich(X0) => rich(X0)) [input p8]
11. ! [X0] : ((patient(X0) | wise(X0)) => (~generous(X0) & ~wise(X0))) [input p10]
12. ! [X0] : ((~funny(X0) <~> calm(X0)) => (~rich(X0) & funny(X0))) [input p11]
15. ! [X0] : ((~old(X0) | ~calm(X0)) => ~happy(X0)) [input p14]
16. ? [X0] : (old(X0) | humble(X0)) <=> ? [X0] : (~calm(X0) & happy(X0)) [input p15]
21. funny(paul) [input hypothesis]
22. ? [X0] : (~curious(X0) | creative(X0)) => ? [X1] : (strong(X1) & humble(X1)) [rectify 5]
23. ? [X0] : (wise(X0) & calm(X0)) <=> ? [X1] : (~calm(X1) & curious(X1)) [rectify 7]
25. ? [X0] : (old(X0) | humble(X0)) <=> ? [X1] : (~calm(X1) & happy(X1)) [rectify 16]
28. ? [X1] : (strong(X1) & humble(X1)) | ! [X0] : (curious(X0) & ~creative(X0)) [ennf transformation 22]
31. ! [X0] : (rich(X0) | rich(X0)) [ennf transformation 9]
32. ! [X0] : ((~generous(X0) & ~wise(X0)) | (~patient(X0) & ~wise(X0))) [ennf transformation 11]
33. ! [X0] : ((~rich(X0) & funny(X0)) | (~funny(X0) <=> calm(X0))) [ennf transformation 12]
34. ! [X0] : (~happy(X0) | (old(X0) & calm(X0))) [ennf transformation 15]
40. ? [X0] : (strong(X0) & humble(X0)) | ! [X1] : (curious(X1) & ~creative(X1)) [rectify 28]
41. ? [X0] : (strong(X0) & humble(X0)) => (strong(sK0) & humble(sK0)) [choice axiom]
42. (strong(sK0) & humble(sK0)) | ! [X1] : (curious(X1) & ~creative(X1)) [skolemisation 40,41]
43. (? [X0] : (wise(X0) & calm(X0)) | ! [X1] : (calm(X1) | ~curious(X1))) & (? [X1] : (~calm(X1) & curious(X1)) | ! [X0] : (~wise(X0) | ~calm(X0))) [nnf transformation 23]
44. (? [X0] : (wise(X0) & calm(X0)) | ! [X1] : (calm(X1) | ~curious(X1))) & (? [X2] : (~calm(X2) & curious(X2)) | ! [X3] : (~wise(X3) | ~calm(X3))) [rectify 43]
45. ? [X0] : (wise(X0) & calm(X0)) => (wise(sK1) & calm(sK1)) [choice axiom]
46. ? [X2] : (~calm(X2) & curious(X2)) => (~calm(sK2) & curious(sK2)) [choice axiom]
47. ((wise(sK1) & calm(sK1)) | ! [X1] : (calm(X1) | ~curious(X1))) & ((~calm(sK2) & curious(sK2)) | ! [X3] : (~wise(X3) | ~calm(X3))) [skolemisation 44,46,45]
58. ! [X0] : ((~rich(X0) & funny(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) [nnf transformation 33]
65. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X1] : (~calm(X1) & happy(X1)) | ! [X0] : (~old(X0) & ~humble(X0))) [nnf transformation 25]
66. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X2] : (~calm(X2) & happy(X2)) | ! [X3] : (~old(X3) & ~humble(X3))) [rectify 65]
67. ? [X0] : (old(X0) | humble(X0)) => (old(sK7) | humble(sK7)) [choice axiom]
68. ? [X2] : (~calm(X2) & happy(X2)) => (~calm(sK8) & happy(sK8)) [choice axiom]
69. ((old(sK7) | humble(sK7)) | ! [X1] : (calm(X1) | ~happy(X1))) & ((~calm(sK8) & happy(sK8)) | ! [X3] : (~old(X3) & ~humble(X3))) [skolemisation 66,68,67]
87. humble(sK0) | curious(X1) [cnf transformation 42]
94. wise(sK1) | calm(X1) | ~curious(X1) [cnf transformation 47]
101. rich(X0) | rich(X0) [cnf transformation 31]
106. ~wise(X0) | ~wise(X0) [cnf transformation 32]
113. ~rich(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 58]
122. ~happy(X0) | calm(X0) [cnf transformation 34]
124. happy(sK8) | ~humble(X3) [cnf transformation 69]
126. ~calm(sK8) | ~humble(X3) [cnf transformation 69]
135. funny(paul) [cnf transformation 21]
137. ~wise(X0) [duplicate literal removal 106]
138. rich(X0) [duplicate literal removal 101]
140. 1 <=> ! [X1] : curious(X1) [avatar definition]
141. curious(X1) <- (1) [avatar component clause 140]
152. 4 <=> humble(sK0) [avatar definition]
154. humble(sK0) <- (4) [avatar component clause 152]
155. 1 | 4 [avatar split clause 87,152,140]
159. 5 <=> ! [X1] : (calm(X1) | ~curious(X1)) [avatar definition]
160. ~curious(X1) | calm(X1) <- (5) [avatar component clause 159]
162. 6 <=> wise(sK1) [avatar definition]
164. wise(sK1) <- (6) [avatar component clause 162]
165. 5 | 6 [avatar split clause 94,162,159]
224. ~funny(X0) | ~calm(X0) [subsumption resolution 113,138]
253. 26 <=> calm(sK8) [avatar definition]
255. ~calm(sK8) <- (~26) [avatar component clause 253]
258. 27 <=> ! [X3] : ~humble(X3) [avatar definition]
259. ~humble(X3) <- (27) [avatar component clause 258]
260. 27 | ~26 [avatar split clause 126,253,258]
262. 28 <=> happy(sK8) [avatar definition]
264. happy(sK8) <- (28) [avatar component clause 262]
266. 27 | 28 [avatar split clause 124,262,258]
299. $false <- (4, 27) [subsumption resolution 154,259]
300. ~4 | ~27 [avatar contradiction clause 299]
301. calm(X0) <- (1, 5) [resolution 160,141]
309. ~calm(paul) [resolution 224,135]
310. $false <- (1, 5) [subsumption resolution 309,301]
311. ~1 | ~5 [avatar contradiction clause 310]
312. $false <- (6) [subsumption resolution 164,137]
313. ~6 [avatar contradiction clause 312]
317. calm(sK8) <- (28) [resolution 264,122]
318. $false <- (~26, 28) [subsumption resolution 317,255]
319. 26 | ~28 [avatar contradiction clause 318]
320. $false [avatar sat refutation 155,165,260,266,300,311,313,319]
% SZS output end Proof for 2989099403334167476452098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or curious. If susan is both not curious and not calm then susan is both not strong and not creative and vice versa. Everyone who is wise is not tall. Everyone who is both calm and not kind is either funny or humble and vice versa. If mary is not patient then someone is both not strong and not rich. If someone is both creative and not humble then someone is not funny and vice versa. Everyone who is not humble is not brave or not old and vice versa. If mary is not curious then alice is both not tall and not curious and vice versa. Everyone who is humble or old is either not wise or not curious and vice versa. Everyone who is either not calm or not humble is tall. Everyone who is both not strong and humble is happy or old. Everyone who is kind is either brave or generous. If mary is not quiet or not brave then paul is not kind or not generous and vice versa. Everyone who is not happy or not patient is either wise or tall and vice versa. If john is either wise or calm then lucy is either not tall or brave and vice versa. Everyone who is old is kind or old and vice versa. Alice is wise. Someone is tall or old. Someone is both not brave and not quiet. Susan is funny or not happy. Lucy is either not wise or kind. Susan is wise. Paul is not old. | Mary is not kind. | neutral | (![X]:((~tall(X)&patient(X))=>(humble(X)|curious(X))))&
(((~curious(susan)&~calm(susan)))<=>((~strong(susan)&~creative(susan))))&
(![X]:(wise(X)=>~tall(X)))&
(![X]:((calm(X)&~kind(X))<=>(funny(X)<~>humble(X))))&
((~patient(mary))=>(?[X]:((~strong(X)&~rich(X)))))&
((?[X]:((creative(X)&~humble(X))))<=>(?[X]:(~funny(X))))&
(![X]:(~humble(X)<=>(~brave(X)|~old(X))))&
((~curious(mary))<=>((~tall(alice)&~curious(alice))))&
(![X]:((humble(X)|old(X))<=>(~wise(X)<~>~curious(X))))&
(![X]:((~calm(X)<~>~humble(X))=>tall(X)))&
(![X]:((~strong(X)&humble(X))=>(happy(X)|old(X))))&
(![X]:(kind(X)=>(brave(X)<~>generous(X))))&
(((~quiet(mary)|~brave(mary)))<=>((~kind(paul)|~generous(paul))))&
(![X]:((~happy(X)|~patient(X))<=>(wise(X)<~>tall(X))))&
(((wise(john)<~>calm(john)))<=>((~tall(lucy)<~>brave(lucy))))&
(![X]:(old(X)<=>(kind(X)|old(X))))&
(wise(alice))&
(?[X]:((tall(X)|old(X))))&
(?[X]:((~brave(X)&~quiet(X))))&
((funny(susan)|~happy(susan)))&
((~wise(lucy)<~>kind(lucy)))&
(wise(susan))&
(~old(paul)) | ~kind(mary) | [] | null | 0 |
If someone is kind then fred is not quiet or humble and vice versa.
Everyone who is not generous is not generous or old and vice versa.
If susan is generous then alice is both not kind and not wise and vice versa.
Everyone who is either not quiet or funny is rich.
If someone is either old or curious then lucy is either not brave or strong and vice versa.
If someone is both strong and brave then someone is curious and vice versa.
Everyone who is either funny or not calm is not humble.
If fred is either not humble or quiet then fred is strong and vice versa.
Everyone who is humble is either not curious or not brave.
Everyone who is not generous is both not old and not curious and vice versa.
Everyone who is patient is not creative or wise.
If alice is funny or not tall then someone is generous or brave.
Everyone who is not wise or tall is patient.
Everyone who is not calm or not kind is both humble and strong.
Everyone who is not curious or strong is wise and vice versa.
Everyone who is both not brave and not patient is brave or humble and vice versa.
Someone is either not old or brave.
Alice is both not creative and strong.
Someone is generous or not old.
Someone is both not brave and quiet.
John is not strong or not quiet.
Paul is generous or not generous. | Alice is brave. | contradiction | ((?[X]:(kind(X)))<=>((~quiet(fred)|humble(fred))))&
(![X]:(~generous(X)<=>(~generous(X)|old(X))))&
((generous(susan))<=>((~kind(alice)&~wise(alice))))&
(![X]:((~quiet(X)<~>funny(X))=>rich(X)))&
((?[X]:((old(X)<~>curious(X))))<=>((~brave(lucy)<~>strong(lucy))))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((funny(X)<~>~calm(X))=>~humble(X)))&
(((~humble(fred)<~>quiet(fred)))<=>(strong(fred)))&
(![X]:(humble(X)=>(~curious(X)<~>~brave(X))))&
(![X]:(~generous(X)<=>(~old(X)&~curious(X))))&
(![X]:(patient(X)=>(~creative(X)|wise(X))))&
(((funny(alice)|~tall(alice)))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~wise(X)|tall(X))=>patient(X)))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)&strong(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
(?[X]:((~old(X)<~>brave(X))))&
((~creative(alice)&strong(alice)))&
(?[X]:((generous(X)|~old(X))))&
(?[X]:((~brave(X)&quiet(X))))&
((~strong(john)|~quiet(john)))&
((generous(paul)|~generous(paul))) | brave(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 225706766288647880273971
% SZS output start Proof for 225706766288647880273971
16. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p15]
23. brave(alice) [input hypothesis]
60. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (patient(X0) | brave(X0)))) [nnf transformation 16]
61. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | patient(X0) | brave(X0))) [flattening 60]
112. ~brave(X0) | ~brave(X0) [cnf transformation 61]
124. brave(alice) [cnf transformation 23]
126. ~brave(X0) [duplicate literal removal 112]
249. $false [subsumption resolution 124,126]
% SZS output end Proof for 225706766288647880273971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not generous is both rich and not funny and vice versa. Everyone who is curious or not wise is creative or tall. Everyone who is both not kind and not calm is both strong and not quiet. Everyone who is rich is not patient or happy and vice versa. If someone is both curious and not old then alice is calm or not brave and vice versa. Everyone who is brave is either not brave or not generous and vice versa. If someone is both not strong and patient then someone is calm or not rich and vice versa. Everyone who is rich is either funny or not curious and vice versa. If alice is both kind and generous then someone is either not quiet or strong and vice versa. If someone is rich then paul is both humble and not happy. If someone is kind then fred is either not funny or rich and vice versa. If someone is not kind or wise then someone is not curious. Everyone who is both old and not kind is rich. Everyone who is either generous or not patient is both patient and tall and vice versa. Everyone who is both patient and not happy is not rich or not creative and vice versa. Alice is old. Someone is both not wise and brave. Someone is either rich or tall. Someone is not curious or not happy. John is both not creative and not generous. Someone is humble. Alice is both not rich and not generous. Someone is either humble or quiet. | John is quiet. | entailment | (![X]:((~quiet(X)&~generous(X))<=>(rich(X)&~funny(X))))&
(![X]:((curious(X)|~wise(X))=>(creative(X)|tall(X))))&
(![X]:((~kind(X)&~calm(X))=>(strong(X)&~quiet(X))))&
(![X]:(rich(X)<=>(~patient(X)|happy(X))))&
((?[X]:((curious(X)&~old(X))))<=>((calm(alice)|~brave(alice))))&
(![X]:(brave(X)<=>(~brave(X)<~>~generous(X))))&
((?[X]:((~strong(X)&patient(X))))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(rich(X)<=>(funny(X)<~>~curious(X))))&
(((kind(alice)&generous(alice)))<=>(?[X]:((~quiet(X)<~>strong(X)))))&
((?[X]:(rich(X)))=>((humble(paul)&~happy(paul))))&
((?[X]:(kind(X)))<=>((~funny(fred)<~>rich(fred))))&
((?[X]:((~kind(X)|wise(X))))=>(?[X]:(~curious(X))))&
(![X]:((old(X)&~kind(X))=>rich(X)))&
(![X]:((generous(X)<~>~patient(X))<=>(patient(X)&tall(X))))&
(![X]:((patient(X)&~happy(X))<=>(~rich(X)|~creative(X))))&
(old(alice))&
(?[X]:((~wise(X)&brave(X))))&
(?[X]:((rich(X)<~>tall(X))))&
(?[X]:((~curious(X)|~happy(X))))&
((~creative(john)&~generous(john)))&
(?[X]:(humble(X)))&
((~rich(alice)&~generous(alice)))&
(?[X]:((humble(X)<~>quiet(X)))) | quiet(john) | [
"p0",
"p1",
"p3",
"p5",
"p7",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8629947006537410011783065
% SZS output start Proof for 8629947006537410011783065
1. ! [X0] : ((~generous(X0) & ~quiet(X0)) <=> (~funny(X0) & rich(X0))) [input p0]
2. ! [X0] : ((~wise(X0) | curious(X0)) => (tall(X0) | creative(X0))) [input p1]
4. ! [X0] : (rich(X0) <=> (happy(X0) | ~patient(X0))) [input p3]
6. ! [X0] : (brave(X0) <=> (~brave(X0) <~> ~generous(X0))) [input p5]
8. ! [X0] : (rich(X0) <=> (funny(X0) <~> ~curious(X0))) [input p7]
14. ! [X0] : ((generous(X0) <~> ~patient(X0)) <=> (tall(X0) & patient(X0))) [input p13]
15. ! [X0] : ((~happy(X0) & patient(X0)) <=> (~creative(X0) | ~rich(X0))) [input p14]
20. ~generous(john) & ~creative(john) [input p19]
24. ~quiet(john) [input hypothesis]
27. ! [X0] : ((tall(X0) | creative(X0)) | (wise(X0) & ~curious(X0))) [ennf transformation 2]
28. ! [X0] : (tall(X0) | creative(X0) | (wise(X0) & ~curious(X0))) [flattening 27]
35. ! [X0] : (((~generous(X0) & ~quiet(X0)) | (funny(X0) | ~rich(X0))) & ((~funny(X0) & rich(X0)) | (generous(X0) | quiet(X0)))) [nnf transformation 1]
36. ! [X0] : (((~generous(X0) & ~quiet(X0)) | funny(X0) | ~rich(X0)) & ((~funny(X0) & rich(X0)) | generous(X0) | quiet(X0))) [flattening 35]
37. ! [X0] : ((rich(X0) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | ~rich(X0))) [nnf transformation 4]
38. ! [X0] : ((rich(X0) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | ~rich(X0))) [flattening 37]
44. ! [X0] : ((brave(X0) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | ~brave(X0))) [nnf transformation 6]
50. ! [X0] : ((rich(X0) | ((funny(X0) | curious(X0)) & (~curious(X0) | ~funny(X0)))) & (((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | ~rich(X0))) [nnf transformation 8]
63. ! [X0] : ((((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | (~tall(X0) | ~patient(X0))) & ((tall(X0) & patient(X0)) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0))))) [nnf transformation 14]
64. ! [X0] : ((((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | ~tall(X0) | ~patient(X0)) & ((tall(X0) & patient(X0)) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0))))) [flattening 63]
65. ! [X0] : (((~happy(X0) & patient(X0)) | (creative(X0) & rich(X0))) & ((~creative(X0) | ~rich(X0)) | (happy(X0) | ~patient(X0)))) [nnf transformation 15]
66. ! [X0] : (((~happy(X0) & patient(X0)) | (creative(X0) & rich(X0))) & (~creative(X0) | ~rich(X0) | happy(X0) | ~patient(X0))) [flattening 65]
80. ~funny(X0) | generous(X0) | quiet(X0) [cnf transformation 36]
83. ~curious(X0) | creative(X0) | tall(X0) [cnf transformation 28]
87. ~patient(X0) | happy(X0) | ~rich(X0) [cnf transformation 38]
95. ~generous(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 44]
97. brave(X0) | ~generous(X0) | brave(X0) [cnf transformation 44]
107. curious(X0) | funny(X0) | rich(X0) [cnf transformation 50]
124. patient(X0) | generous(X0) | patient(X0) [cnf transformation 64]
126. tall(X0) | generous(X0) | patient(X0) [cnf transformation 64]
127. ~patient(X0) | generous(X0) | ~tall(X0) | ~patient(X0) [cnf transformation 64]
133. ~happy(X0) | creative(X0) [cnf transformation 66]
140. ~creative(john) [cnf transformation 20]
147. ~quiet(john) [cnf transformation 24]
148. patient(X0) | generous(X0) [duplicate literal removal 124]
149. ~patient(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 127]
150. ~generous(X0) | ~brave(X0) [duplicate literal removal 95]
151. ~generous(X0) | brave(X0) [duplicate literal removal 97]
176. ~generous(X0) [subsumption resolution 150,151]
253. ~patient(X0) | ~tall(X0) [subsumption resolution 149,176]
254. patient(X0) | tall(X0) [subsumption resolution 126,176]
255. patient(X0) [subsumption resolution 148,176]
292. ~tall(X1) [resolution 253,255]
336. happy(X0) | ~rich(X0) | tall(X0) [resolution 87,254]
339. ~rich(X0) | happy(X0) [subsumption resolution 336,292]
359. funny(X2) | rich(X2) | creative(X2) | tall(X2) [resolution 107,83]
380. creative(X2) | rich(X2) | funny(X2) [subsumption resolution 359,292]
407. rich(john) | funny(john) [resolution 380,140]
409. 40 <=> funny(john) [avatar definition]
411. funny(john) <- (40) [avatar component clause 409]
413. 41 <=> rich(john) [avatar definition]
415. rich(john) <- (41) [avatar component clause 413]
416. 40 | 41 [avatar split clause 407,413,409]
421. generous(john) | quiet(john) <- (40) [resolution 411,80]
427. quiet(john) <- (40) [subsumption resolution 421,176]
428. $false <- (40) [subsumption resolution 427,147]
429. ~40 [avatar contradiction clause 428]
430. happy(john) <- (41) [resolution 415,339]
437. creative(john) <- (41) [resolution 430,133]
439. $false <- (41) [subsumption resolution 437,140]
440. ~41 [avatar contradiction clause 439]
441. $false [avatar sat refutation 416,429,440]
% SZS output end Proof for 8629947006537410011783065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not happy is strong or not calm.
If susan is wise or generous then susan is not rich.
If alice is either brave or not tall then someone is both not tall and generous.
If someone is not old or old then lucy is either funny or not wise and vice versa.
Everyone who is not wise is either not humble or wise.
If alice is both not patient and brave then someone is generous.
Everyone who is creative is not brave and vice versa.
Everyone who is not generous is rich or not kind.
Everyone who is calm or quiet is not wise or humble.
Everyone who is both rich and wise is not curious or not humble and vice versa.
Everyone who is not curious or rich is both tall and not tall and vice versa.
If someone is either creative or not brave then someone is either not happy or brave and vice versa.
Everyone who is both not calm and not humble is both not curious and humble.
If susan is both not patient and not creative then alice is both happy and calm and vice versa.
If someone is either not wise or generous then susan is either funny or quiet and vice versa.
Everyone who is patient is strong or creative.
Lucy is either not brave or humble.
Lucy is curious.
Susan is both patient and creative.
Lucy is not generous or happy.
Someone is funny.
Paul is either not quiet or rich. | Alice is not quiet. | neutral | (![X]:((~wise(X)&~happy(X))=>(strong(X)|~calm(X))))&
(((wise(susan)|generous(susan)))=>(~rich(susan)))&
(((brave(alice)<~>~tall(alice)))=>(?[X]:((~tall(X)&generous(X)))))&
((?[X]:((~old(X)|old(X))))<=>((funny(lucy)<~>~wise(lucy))))&
(![X]:(~wise(X)=>(~humble(X)<~>wise(X))))&
(((~patient(alice)&brave(alice)))=>(?[X]:(generous(X))))&
(![X]:(creative(X)<=>~brave(X)))&
(![X]:(~generous(X)=>(rich(X)|~kind(X))))&
(![X]:((calm(X)|quiet(X))=>(~wise(X)|humble(X))))&
(![X]:((rich(X)&wise(X))<=>(~curious(X)|~humble(X))))&
(![X]:((~curious(X)|rich(X))<=>(tall(X)&~tall(X))))&
((?[X]:((creative(X)<~>~brave(X))))<=>(?[X]:((~happy(X)<~>brave(X)))))&
(![X]:((~calm(X)&~humble(X))=>(~curious(X)&humble(X))))&
(((~patient(susan)&~creative(susan)))<=>((happy(alice)&calm(alice))))&
((?[X]:((~wise(X)<~>generous(X))))<=>((funny(susan)<~>quiet(susan))))&
(![X]:(patient(X)=>(strong(X)|creative(X))))&
((~brave(lucy)<~>humble(lucy)))&
(curious(lucy))&
((patient(susan)&creative(susan)))&
((~generous(lucy)|happy(lucy)))&
(?[X]:(funny(X)))&
((~quiet(paul)<~>rich(paul))) | ~quiet(alice) | [] | null | 0 |
Everyone who is either not tall or not rich is either brave or not kind and vice versa.
If lucy is creative then someone is both not tall and not humble.
Everyone who is not tall is humble or tall.
If someone is either not calm or not brave then mary is not brave.
Everyone who is tall is both not happy and generous and vice versa.
If someone is not kind then fred is wise or not creative.
Everyone who is either not creative or strong is funny and vice versa.
If someone is not generous or not strong then someone is either not rich or humble.
Everyone who is not wise or not tall is both not curious and not creative.
Everyone who is both wise and not creative is both not patient and happy and vice versa.
If someone is either tall or not quiet then susan is creative and vice versa.
Everyone who is not patient or creative is not quiet and vice versa.
Everyone who is not kind or tall is quiet.
If someone is funny then someone is creative.
If lucy is both creative and not generous then someone is either rich or happy.
Everyone who is both not patient and not old is not kind or not happy and vice versa.
Someone is either curious or brave.
Someone is curious or not curious.
Someone is either not funny or not generous. | Lucy is humble. | entailment | (![X]:((~tall(X)<~>~rich(X))<=>(brave(X)<~>~kind(X))))&
((creative(lucy))=>(?[X]:((~tall(X)&~humble(X)))))&
(![X]:(~tall(X)=>(humble(X)|tall(X))))&
((?[X]:((~calm(X)<~>~brave(X))))=>(~brave(mary)))&
(![X]:(tall(X)<=>(~happy(X)&generous(X))))&
((?[X]:(~kind(X)))=>((wise(fred)|~creative(fred))))&
(![X]:((~creative(X)<~>strong(X))<=>funny(X)))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((~wise(X)|~tall(X))=>(~curious(X)&~creative(X))))&
(![X]:((wise(X)&~creative(X))<=>(~patient(X)&happy(X))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>(creative(susan)))&
(![X]:((~patient(X)|creative(X))<=>~quiet(X)))&
(![X]:((~kind(X)|tall(X))=>quiet(X)))&
((?[X]:(funny(X)))=>(?[X]:(creative(X))))&
(((creative(lucy)&~generous(lucy)))=>(?[X]:((rich(X)<~>happy(X)))))&
(![X]:((~patient(X)&~old(X))<=>(~kind(X)|~happy(X))))&
(?[X]:((curious(X)<~>brave(X))))&
(?[X]:((curious(X)|~curious(X))))&
(?[X]:((~funny(X)<~>~generous(X)))) | humble(lucy) | [
"p2",
"p8",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 274759157896672735554069
% SZS output start Proof for 274759157896672735554069
3. ! [X0] : (~tall(X0) => (tall(X0) | humble(X0))) [input p2]
9. ! [X0] : ((~tall(X0) | ~wise(X0)) => (~creative(X0) & ~curious(X0))) [input p8]
11. ? [X0] : (tall(X0) <~> ~quiet(X0)) <=> creative(susan) [input p10]
12. ! [X0] : ((creative(X0) | ~patient(X0)) <=> ~quiet(X0)) [input p11]
13. ! [X0] : ((tall(X0) | ~kind(X0)) => quiet(X0)) [input p12]
20. ~humble(lucy) [input hypothesis]
24. ! [X0] : ((tall(X0) | humble(X0)) | tall(X0)) [ennf transformation 3]
25. ! [X0] : (tall(X0) | humble(X0) | tall(X0)) [flattening 24]
30. ! [X0] : ((~creative(X0) & ~curious(X0)) | (tall(X0) & wise(X0))) [ennf transformation 9]
31. ! [X0] : (quiet(X0) | (~tall(X0) & kind(X0))) [ennf transformation 13]
48. (? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ~creative(susan)) & (creative(susan) | ! [X0] : ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) [nnf transformation 11]
49. (? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ~creative(susan)) & (creative(susan) | ! [X1] : ((tall(X1) | quiet(X1)) & (~quiet(X1) | ~tall(X1)))) [rectify 48]
50. ? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) => ((quiet(sK2) | ~tall(sK2)) & (~quiet(sK2) | tall(sK2))) [choice axiom]
51. (((quiet(sK2) | ~tall(sK2)) & (~quiet(sK2) | tall(sK2))) | ~creative(susan)) & (creative(susan) | ! [X1] : ((tall(X1) | quiet(X1)) & (~quiet(X1) | ~tall(X1)))) [skolemisation 49,50]
52. ! [X0] : (((creative(X0) | ~patient(X0)) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & patient(X0)))) [nnf transformation 12]
53. ! [X0] : ((creative(X0) | ~patient(X0) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & patient(X0)))) [flattening 52]
80. tall(X0) | humble(X0) | tall(X0) [cnf transformation 25]
98. ~creative(X0) | tall(X0) [cnf transformation 30]
103. creative(susan) | ~quiet(X1) | ~tall(X1) [cnf transformation 51]
108. ~quiet(X0) | ~creative(X0) [cnf transformation 53]
111. ~tall(X0) | quiet(X0) [cnf transformation 31]
125. ~humble(lucy) [cnf transformation 20]
126. humble(X0) | tall(X0) [duplicate literal removal 80]
184. 14 <=> creative(susan) [avatar definition]
185. creative(susan) <- (14) [avatar component clause 184]
202. 18 <=> ! [X1] : (~quiet(X1) | ~tall(X1)) [avatar definition]
203. ~quiet(X1) | ~tall(X1) <- (18) [avatar component clause 202]
204. 18 | 14 [avatar split clause 103,184,202]
254. tall(susan) <- (14) [resolution 98,185]
264. quiet(susan) <- (14) [resolution 111,254]
268. tall(lucy) [resolution 126,125]
279. ~creative(susan) <- (14) [resolution 264,108]
281. $false <- (14) [subsumption resolution 279,185]
282. ~14 [avatar contradiction clause 281]
283. ~tall(X1) <- (18) [subsumption resolution 203,111]
285. $false <- (18) [resolution 283,268]
292. ~18 [avatar contradiction clause 285]
293. $false [avatar sat refutation 204,282,292]
% SZS output end Proof for 274759157896672735554069
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or curious is not curious. Everyone who is brave is either calm or not happy. Everyone who is tall or curious is not tall. Everyone who is not humble or not old is both creative and quiet. If fred is both not patient and not quiet then someone is either curious or not patient and vice versa. Everyone who is not funny is either not kind or old. Everyone who is strong is not curious or not calm. Everyone who is not humble is wise. Everyone who is not creative is not humble or not kind and vice versa. Everyone who is not brave is calm or not happy. Everyone who is not funny or patient is both not strong and not generous and vice versa. If someone is either generous or curious then fred is funny or creative. If lucy is not tall then alice is either not kind or not patient and vice versa. Everyone who is not creative is not curious or not wise and vice versa. If someone is creative or calm then fred is not strong or not brave and vice versa. Everyone who is humble or calm is not rich and vice versa. Mary is brave. Mary is not tall or not calm. Alice is both curious and not creative. Someone is not happy. John is humble. John is either old or not generous. Someone is either wise or funny. | Mary is not wise. | neutral | (![X]:((happy(X)<~>curious(X))=>~curious(X)))&
(![X]:(brave(X)=>(calm(X)<~>~happy(X))))&
(![X]:((tall(X)|curious(X))=>~tall(X)))&
(![X]:((~humble(X)|~old(X))=>(creative(X)&quiet(X))))&
(((~patient(fred)&~quiet(fred)))<=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:(~funny(X)=>(~kind(X)<~>old(X))))&
(![X]:(strong(X)=>(~curious(X)|~calm(X))))&
(![X]:(~humble(X)=>wise(X)))&
(![X]:(~creative(X)<=>(~humble(X)|~kind(X))))&
(![X]:(~brave(X)=>(calm(X)|~happy(X))))&
(![X]:((~funny(X)|patient(X))<=>(~strong(X)&~generous(X))))&
((?[X]:((generous(X)<~>curious(X))))=>((funny(fred)|creative(fred))))&
((~tall(lucy))<=>((~kind(alice)<~>~patient(alice))))&
(![X]:(~creative(X)<=>(~curious(X)|~wise(X))))&
((?[X]:((creative(X)|calm(X))))<=>((~strong(fred)|~brave(fred))))&
(![X]:((humble(X)|calm(X))<=>~rich(X)))&
(brave(mary))&
((~tall(mary)|~calm(mary)))&
((curious(alice)&~creative(alice)))&
(?[X]:(~happy(X)))&
(humble(john))&
((old(john)<~>~generous(john)))&
(?[X]:((wise(X)<~>funny(X)))) | ~wise(mary) | [] | null | 0 |
Everyone who is strong is not brave. Everyone who is both tall and quiet is either not generous or not curious and vice versa. Everyone who is either not humble or tall is both rich and not humble and vice versa. Everyone who is not funny or patient is either not old or patient and vice versa. Everyone who is either calm or funny is not calm. Everyone who is generous or humble is happy and vice versa. Everyone who is both not happy and kind is happy or wise. Everyone who is both kind and patient is old or not tall and vice versa. Everyone who is not quiet or rich is curious or not wise. Everyone who is generous or not brave is both quiet and generous. If fred is either generous or patient then paul is either not old or not patient and vice versa. If someone is not quiet then someone is brave and vice versa. If lucy is either humble or calm then someone is either curious or not quiet. Everyone who is not old is either humble or creative. Everyone who is not happy or not tall is brave or not funny. Someone is not humble. Someone is not rich. Alice is humble. Someone is creative or not humble. John is wise. Someone is not brave or happy. Someone is both creative and funny. | Alice is quiet. | neutral | (![X]:(strong(X)=>~brave(X)))&
(![X]:((tall(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
(![X]:((~humble(X)<~>tall(X))<=>(rich(X)&~humble(X))))&
(![X]:((~funny(X)|patient(X))<=>(~old(X)<~>patient(X))))&
(![X]:((calm(X)<~>funny(X))=>~calm(X)))&
(![X]:((generous(X)|humble(X))<=>happy(X)))&
(![X]:((~happy(X)&kind(X))=>(happy(X)|wise(X))))&
(![X]:((kind(X)&patient(X))<=>(old(X)|~tall(X))))&
(![X]:((~quiet(X)|rich(X))=>(curious(X)|~wise(X))))&
(![X]:((generous(X)|~brave(X))=>(quiet(X)&generous(X))))&
(((generous(fred)<~>patient(fred)))<=>((~old(paul)<~>~patient(paul))))&
((?[X]:(~quiet(X)))<=>(?[X]:(brave(X))))&
(((humble(lucy)<~>calm(lucy)))=>(?[X]:((curious(X)<~>~quiet(X)))))&
(![X]:(~old(X)=>(humble(X)<~>creative(X))))&
(![X]:((~happy(X)|~tall(X))=>(brave(X)|~funny(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~rich(X)))&
(humble(alice))&
(?[X]:((creative(X)|~humble(X))))&
(wise(john))&
(?[X]:((~brave(X)|happy(X))))&
(?[X]:((creative(X)&funny(X)))) | quiet(alice) | [] | null | 0 |
If someone is not humble or not brave then someone is not kind.
If fred is strong then someone is both kind and not strong.
Everyone who is both not rich and curious is not strong and vice versa.
Everyone who is either humble or quiet is not kind and vice versa.
Everyone who is both funny and not patient is both patient and brave.
Everyone who is not tall is generous.
If fred is patient then someone is kind or tall and vice versa.
Everyone who is either old or not generous is both not rich and quiet and vice versa.
Everyone who is both calm and wise is either patient or tall and vice versa.
Everyone who is not generous is not rich.
If paul is not quiet or not rich then someone is not generous or not patient and vice versa.
Everyone who is both happy and not strong is strong.
If lucy is either curious or not happy then someone is wise and vice versa.
If someone is strong or curious then mary is both not patient and not calm.
If someone is curious then fred is happy or old and vice versa.
Everyone who is not curious is not funny or generous and vice versa.
Lucy is both tall and not rich.
Someone is either generous or not humble.
Someone is not creative.
Someone is both generous and not brave.
Someone is not calm.
Someone is both not curious and not patient. | Lucy is old. | neutral | ((?[X]:((~humble(X)|~brave(X))))=>(?[X]:(~kind(X))))&
((strong(fred))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((~rich(X)&curious(X))<=>~strong(X)))&
(![X]:((humble(X)<~>quiet(X))<=>~kind(X)))&
(![X]:((funny(X)&~patient(X))=>(patient(X)&brave(X))))&
(![X]:(~tall(X)=>generous(X)))&
((patient(fred))<=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((old(X)<~>~generous(X))<=>(~rich(X)&quiet(X))))&
(![X]:((calm(X)&wise(X))<=>(patient(X)<~>tall(X))))&
(![X]:(~generous(X)=>~rich(X)))&
(((~quiet(paul)|~rich(paul)))<=>(?[X]:((~generous(X)|~patient(X)))))&
(![X]:((happy(X)&~strong(X))=>strong(X)))&
(((curious(lucy)<~>~happy(lucy)))<=>(?[X]:(wise(X))))&
((?[X]:((strong(X)|curious(X))))=>((~patient(mary)&~calm(mary))))&
((?[X]:(curious(X)))<=>((happy(fred)|old(fred))))&
(![X]:(~curious(X)<=>(~funny(X)|generous(X))))&
((tall(lucy)&~rich(lucy)))&
(?[X]:((generous(X)<~>~humble(X))))&
(?[X]:(~creative(X)))&
(?[X]:((generous(X)&~brave(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~curious(X)&~patient(X)))) | old(lucy) | [] | null | 0 |
Everyone who is either patient or not happy is either not brave or kind.
If someone is not tall or not old then alice is both not happy and not calm and vice versa.
If lucy is both not calm and not tall then alice is either not wise or generous and vice versa.
Everyone who is old or not funny is not strong or patient and vice versa.
If someone is both old and strong then someone is either creative or calm and vice versa.
Everyone who is either kind or wise is not funny and vice versa.
Everyone who is both curious and not funny is both not patient and old and vice versa.
Everyone who is creative or old is both calm and not funny.
If fred is both humble and tall then someone is tall and vice versa.
Everyone who is either not brave or funny is both not funny and kind and vice versa.
Everyone who is both calm and quiet is either not creative or not wise.
Everyone who is generous or patient is not tall and vice versa.
Everyone who is not rich is both not humble and not happy.
Everyone who is both not rich and not old is strong or quiet.
Everyone who is either strong or not brave is either not patient or not strong and vice versa.
Everyone who is not generous or old is either not calm or humble.
Alice is tall or funny.
Susan is either patient or rich.
Mary is either not humble or not funny. | Susan is rich. | entailment | (![X]:((patient(X)<~>~happy(X))=>(~brave(X)<~>kind(X))))&
((?[X]:((~tall(X)|~old(X))))<=>((~happy(alice)&~calm(alice))))&
(((~calm(lucy)&~tall(lucy)))<=>((~wise(alice)<~>generous(alice))))&
(![X]:((old(X)|~funny(X))<=>(~strong(X)|patient(X))))&
((?[X]:((old(X)&strong(X))))<=>(?[X]:((creative(X)<~>calm(X)))))&
(![X]:((kind(X)<~>wise(X))<=>~funny(X)))&
(![X]:((curious(X)&~funny(X))<=>(~patient(X)&old(X))))&
(![X]:((creative(X)|old(X))=>(calm(X)&~funny(X))))&
(((humble(fred)&tall(fred)))<=>(?[X]:(tall(X))))&
(![X]:((~brave(X)<~>funny(X))<=>(~funny(X)&kind(X))))&
(![X]:((calm(X)&quiet(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((generous(X)|patient(X))<=>~tall(X)))&
(![X]:(~rich(X)=>(~humble(X)&~happy(X))))&
(![X]:((~rich(X)&~old(X))=>(strong(X)|quiet(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(~patient(X)<~>~strong(X))))&
(![X]:((~generous(X)|old(X))=>(~calm(X)<~>humble(X))))&
((tall(alice)|funny(alice)))&
((patient(susan)<~>rich(susan)))&
((~humble(mary)<~>~funny(mary))) | rich(susan) | [
"p0",
"p1",
"p3",
"p7",
"p9",
"p11",
"p14",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 936565259967694961858011
% SZS output start Proof for 936565259967694961858011
1. ! [X0] : ((patient(X0) <~> ~happy(X0)) => (~brave(X0) <~> kind(X0))) [input p0]
2. ? [X0] : (~old(X0) | ~tall(X0)) <=> (~calm(alice) & ~happy(alice)) [input p1]
4. ! [X0] : ((~funny(X0) | old(X0)) <=> (patient(X0) | ~strong(X0))) [input p3]
8. ! [X0] : ((old(X0) | creative(X0)) => (~funny(X0) & calm(X0))) [input p7]
10. ! [X0] : ((~brave(X0) <~> funny(X0)) <=> (kind(X0) & ~funny(X0))) [input p9]
12. ! [X0] : ((patient(X0) | generous(X0)) <=> ~tall(X0)) [input p11]
15. ! [X0] : ((strong(X0) <~> ~brave(X0)) <=> (~patient(X0) <~> ~strong(X0))) [input p14]
17. funny(alice) | tall(alice) [input p16]
18. patient(susan) <~> rich(susan) [input p17]
20. ~rich(susan) [input hypothesis]
22. ! [X0] : ((~brave(X0) <~> kind(X0)) | (patient(X0) <=> ~happy(X0))) [ennf transformation 1]
23. ! [X0] : ((~funny(X0) & calm(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 8]
30. ! [X0] : (((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) [nnf transformation 22]
31. (? [X0] : (~old(X0) | ~tall(X0)) | (calm(alice) | happy(alice))) & ((~calm(alice) & ~happy(alice)) | ! [X0] : (old(X0) & tall(X0))) [nnf transformation 2]
32. (? [X0] : (~old(X0) | ~tall(X0)) | calm(alice) | happy(alice)) & ((~calm(alice) & ~happy(alice)) | ! [X0] : (old(X0) & tall(X0))) [flattening 31]
33. (? [X0] : (~old(X0) | ~tall(X0)) | calm(alice) | happy(alice)) & ((~calm(alice) & ~happy(alice)) | ! [X1] : (old(X1) & tall(X1))) [rectify 32]
34. ? [X0] : (~old(X0) | ~tall(X0)) => (~old(sK0) | ~tall(sK0)) [choice axiom]
35. ((~old(sK0) | ~tall(sK0)) | calm(alice) | happy(alice)) & ((~calm(alice) & ~happy(alice)) | ! [X1] : (old(X1) & tall(X1))) [skolemisation 33,34]
38. ! [X0] : (((~funny(X0) | old(X0)) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | (funny(X0) & ~old(X0)))) [nnf transformation 4]
39. ! [X0] : ((~funny(X0) | old(X0) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | (funny(X0) & ~old(X0)))) [flattening 38]
53. ! [X0] : ((((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | (~kind(X0) | funny(X0))) & ((kind(X0) & ~funny(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0))))) [nnf transformation 10]
54. ! [X0] : ((((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | ~kind(X0) | funny(X0)) & ((kind(X0) & ~funny(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0))))) [flattening 53]
56. ! [X0] : (((patient(X0) | generous(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) & ~generous(X0)))) [nnf transformation 12]
57. ! [X0] : ((patient(X0) | generous(X0) | tall(X0)) & (~tall(X0) | (~patient(X0) & ~generous(X0)))) [flattening 56]
58. ! [X0] : ((((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0))))) [nnf transformation 15]
60. (~rich(susan) | ~patient(susan)) & (rich(susan) | patient(susan)) [nnf transformation 18]
63. ~brave(X0) | kind(X0) | patient(X0) | happy(X0) [cnf transformation 30]
66. ~happy(alice) | tall(X1) [cnf transformation 35]
80. ~funny(X0) | old(X0) | ~patient(X0) [cnf transformation 39]
98. ~funny(X0) | ~old(X0) [cnf transformation 23]
103. ~funny(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 54]
106. funny(X0) | ~brave(X0) | ~kind(X0) | funny(X0) [cnf transformation 54]
111. ~tall(X0) | ~patient(X0) [cnf transformation 57]
119. strong(X0) | patient(X0) | strong(X0) | brave(X0) [cnf transformation 58]
122. brave(X0) | ~strong(X0) | ~strong(X0) | patient(X0) [cnf transformation 58]
128. funny(alice) | tall(alice) [cnf transformation 17]
129. rich(susan) | patient(susan) [cnf transformation 60]
133. ~rich(susan) [cnf transformation 20]
135. strong(X0) | patient(X0) | brave(X0) [duplicate literal removal 119]
137. ~strong(X0) | brave(X0) | patient(X0) [duplicate literal removal 122]
138. ~funny(X0) | ~brave(X0) [duplicate literal removal 103]
139. ~kind(X0) | ~brave(X0) | funny(X0) [duplicate literal removal 106]
141. 1 <=> happy(alice) [avatar definition]
162. 6 <=> ! [X1] : tall(X1) [avatar definition]
163. tall(X1) <- (6) [avatar component clause 162]
166. 6 | ~1 [avatar split clause 66,141,162]
239. brave(X0) | patient(X0) [subsumption resolution 135,137]
243. 22 <=> tall(alice) [avatar definition]
245. tall(alice) <- (22) [avatar component clause 243]
247. 23 <=> funny(alice) [avatar definition]
248. ~funny(alice) <- (~23) [avatar component clause 247]
249. funny(alice) <- (23) [avatar component clause 247]
250. 22 | 23 [avatar split clause 128,247,243]
252. 24 <=> patient(susan) [avatar definition]
253. patient(susan) <- (24) [avatar component clause 252]
256. 25 <=> rich(susan) [avatar definition]
260. 24 | 25 [avatar split clause 129,256,252]
271. ~25 [avatar split clause 133,256]
367. 37 <=> patient(alice) [avatar definition]
368. ~patient(alice) <- (~37) [avatar component clause 367]
389. old(alice) | ~patient(alice) <- (23) [resolution 249,80]
393. ~old(alice) <- (23) [resolution 249,98]
395. ~brave(alice) <- (23) [resolution 249,138]
401. 41 <=> old(alice) [avatar definition]
405. ~37 | 41 | ~23 [avatar split clause 389,247,401,367]
408. ~41 | ~23 [avatar split clause 393,247,401]
429. kind(X0) | patient(X0) | happy(X0) | patient(X0) [resolution 63,239]
430. kind(X0) | patient(X0) | happy(X0) [duplicate literal removal 429]
456. 45 <=> kind(alice) [avatar definition]
457. ~kind(alice) <- (~45) [avatar component clause 456]
458. kind(alice) <- (45) [avatar component clause 456]
463. ~patient(alice) <- (22) [resolution 245,111]
464. patient(alice) <- (23) [resolution 395,239]
465. $false <- (23, ~37) [subsumption resolution 464,368]
466. ~23 | 37 [avatar contradiction clause 465]
556. patient(alice) | happy(alice) <- (~45) [resolution 430,457]
576. ~patient(X0) <- (6) [resolution 163,111]
595. $false <- (6, 24) [resolution 576,253]
596. ~6 | ~24 [avatar contradiction clause 595]
600. 1 | 37 | 45 [avatar split clause 556,456,367,141]
604. ~37 | ~22 [avatar split clause 463,243,367]
612. 55 <=> brave(alice) [avatar definition]
613. ~brave(alice) <- (~55) [avatar component clause 612]
634. ~brave(alice) | funny(alice) <- (45) [resolution 458,139]
635. ~brave(alice) <- (~23, 45) [subsumption resolution 634,248]
636. ~55 | 23 | ~45 [avatar split clause 635,456,247,612]
637. patient(alice) <- (~55) [resolution 613,239]
638. $false <- (~37, ~55) [subsumption resolution 637,368]
639. 37 | 55 [avatar contradiction clause 638]
640. $false [avatar sat refutation 166,250,260,271,405,408,466,596,600,604,636,639]
% SZS output end Proof for 936565259967694961858011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or humble then someone is both not brave and humble.
Everyone who is not tall is humble or kind and vice versa.
Everyone who is both not kind and brave is not wise.
Everyone who is either not curious or not creative is not strong.
Everyone who is either not happy or not kind is creative or not kind and vice versa.
Everyone who is wise is either humble or happy.
Everyone who is either wise or calm is both not curious and not wise and vice versa.
Everyone who is either not old or not funny is both not calm and funny and vice versa.
If someone is curious then someone is either not calm or tall.
Everyone who is either not patient or quiet is not generous.
Everyone who is not kind or rich is both not tall and not old and vice versa.
If alice is patient or calm then fred is both not happy and funny.
Everyone who is either quiet or not old is both creative and not wise and vice versa.
Everyone who is both brave and old is either strong or curious and vice versa.
If someone is either tall or quiet then paul is kind or humble and vice versa.
If someone is not curious or not patient then someone is both patient and not strong and vice versa.
Someone is both funny and not quiet.
Someone is not wise.
John is either calm or not strong.
Someone is both brave and kind.
Someone is humble or brave.
Lucy is curious.
Fred is not generous. | Paul is kind. | neutral | ((?[X]:((brave(X)<~>humble(X))))=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:(~tall(X)<=>(humble(X)|kind(X))))&
(![X]:((~kind(X)&brave(X))=>~wise(X)))&
(![X]:((~curious(X)<~>~creative(X))=>~strong(X)))&
(![X]:((~happy(X)<~>~kind(X))<=>(creative(X)|~kind(X))))&
(![X]:(wise(X)=>(humble(X)<~>happy(X))))&
(![X]:((wise(X)<~>calm(X))<=>(~curious(X)&~wise(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(~calm(X)&funny(X))))&
((?[X]:(curious(X)))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:((~patient(X)<~>quiet(X))=>~generous(X)))&
(![X]:((~kind(X)|rich(X))<=>(~tall(X)&~old(X))))&
(((patient(alice)|calm(alice)))=>((~happy(fred)&funny(fred))))&
(![X]:((quiet(X)<~>~old(X))<=>(creative(X)&~wise(X))))&
(![X]:((brave(X)&old(X))<=>(strong(X)<~>curious(X))))&
((?[X]:((tall(X)<~>quiet(X))))<=>((kind(paul)|humble(paul))))&
((?[X]:((~curious(X)|~patient(X))))<=>(?[X]:((patient(X)&~strong(X)))))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:(~wise(X)))&
((calm(john)<~>~strong(john)))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((humble(X)|brave(X))))&
(curious(lucy))&
(~generous(fred)) | kind(paul) | [] | null | 0 |
If lucy is generous or rich then someone is not kind and vice versa.
If someone is wise or patient then lucy is not rich and vice versa.
If paul is curious or not brave then someone is either not tall or calm and vice versa.
Everyone who is either not wise or not happy is both wise and humble and vice versa.
If fred is old then mary is either wise or calm and vice versa.
If paul is both not calm and kind then someone is either calm or wise.
If fred is both not funny and happy then someone is kind and vice versa.
If someone is either not tall or rich then someone is both old and not funny.
If someone is not strong or strong then someone is either not happy or not patient and vice versa.
Everyone who is generous is kind and vice versa.
If fred is brave then someone is not brave or brave and vice versa.
If someone is either happy or not curious then paul is strong or patient.
Everyone who is both not funny and not wise is happy or rich.
If alice is patient then someone is either creative or calm.
If someone is creative then mary is either not quiet or not humble and vice versa.
If someone is funny then mary is strong or quiet.
Mary is not kind or creative.
Someone is wise.
Alice is quiet.
Paul is both not happy and kind.
Someone is not quiet or not humble.
Mary is funny or not strong.
Someone is humble or rich.
Mary is either not rich or rich. | Fred is wise. | entailment | (((generous(lucy)|rich(lucy)))<=>(?[X]:(~kind(X))))&
((?[X]:((wise(X)|patient(X))))<=>(~rich(lucy)))&
(((curious(paul)|~brave(paul)))<=>(?[X]:((~tall(X)<~>calm(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(wise(X)&humble(X))))&
((old(fred))<=>((wise(mary)<~>calm(mary))))&
(((~calm(paul)&kind(paul)))=>(?[X]:((calm(X)<~>wise(X)))))&
(((~funny(fred)&happy(fred)))<=>(?[X]:(kind(X))))&
((?[X]:((~tall(X)<~>rich(X))))=>(?[X]:((old(X)&~funny(X)))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:(generous(X)<=>kind(X)))&
((brave(fred))<=>(?[X]:((~brave(X)|brave(X)))))&
((?[X]:((happy(X)<~>~curious(X))))=>((strong(paul)|patient(paul))))&
(![X]:((~funny(X)&~wise(X))=>(happy(X)|rich(X))))&
((patient(alice))=>(?[X]:((creative(X)<~>calm(X)))))&
((?[X]:(creative(X)))<=>((~quiet(mary)<~>~humble(mary))))&
((?[X]:(funny(X)))=>((strong(mary)|quiet(mary))))&
((~kind(mary)|creative(mary)))&
(?[X]:(wise(X)))&
(quiet(alice))&
((~happy(paul)&kind(paul)))&
(?[X]:((~quiet(X)|~humble(X))))&
((funny(mary)|~strong(mary)))&
(?[X]:((humble(X)|rich(X))))&
((~rich(mary)<~>rich(mary))) | wise(fred) | [
"p3",
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7158155977062883625641774
% SZS output start Proof for 7158155977062883625641774
4. ! [X0] : ((~wise(X0) <~> ~happy(X0)) <=> (humble(X0) & wise(X0))) [input p3]
7. (happy(fred) & ~funny(fred)) <=> ? [X0] : kind(X0) [input p6]
20. kind(paul) & ~happy(paul) [input p19]
25. ~wise(fred) [input hypothesis]
52. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (~humble(X0) | ~wise(X0))) & ((humble(X0) & wise(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [nnf transformation 4]
53. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | ~humble(X0) | ~wise(X0)) & ((humble(X0) & wise(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [flattening 52]
58. ((happy(fred) & ~funny(fred)) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | (~happy(fred) | funny(fred))) [nnf transformation 7]
59. ((happy(fred) & ~funny(fred)) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | ~happy(fred) | funny(fred)) [flattening 58]
60. ((happy(fred) & ~funny(fred)) | ! [X0] : ~kind(X0)) & (? [X1] : kind(X1) | ~happy(fred) | funny(fred)) [rectify 59]
61. ? [X1] : kind(X1) => kind(sK4) [choice axiom]
62. ((happy(fred) & ~funny(fred)) | ! [X0] : ~kind(X0)) & (kind(sK4) | ~happy(fred) | funny(fred)) [skolemisation 60,61]
104. wise(X0) | ~happy(X0) | wise(X0) [cnf transformation 53]
118. happy(fred) | ~kind(X0) [cnf transformation 62]
148. kind(paul) [cnf transformation 20]
154. ~wise(fred) [cnf transformation 25]
155. ~happy(X0) | wise(X0) [duplicate literal removal 104]
241. 19 <=> kind(paul) [avatar definition]
242. kind(paul) <- (19) [avatar component clause 241]
255. 22 <=> ! [X0] : ~kind(X0) [avatar definition]
256. ~kind(X0) <- (22) [avatar component clause 255]
258. 23 <=> happy(fred) [avatar definition]
260. happy(fred) <- (23) [avatar component clause 258]
261. 22 | 23 [avatar split clause 118,258,255]
387. 19 [avatar split clause 148,241]
411. $false <- (19, 22) [subsumption resolution 242,256]
412. ~19 | ~22 [avatar contradiction clause 411]
418. wise(fred) <- (23) [resolution 155,260]
420. $false <- (23) [subsumption resolution 418,154]
421. ~23 [avatar contradiction clause 420]
422. $false [avatar sat refutation 261,387,412,421]
% SZS output end Proof for 7158155977062883625641774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is patient or not strong then someone is both not happy and kind and vice versa.
Everyone who is both calm and strong is either not wise or old.
If someone is tall or not humble then someone is either creative or generous.
Everyone who is not tall or not rich is both old and not curious.
If john is either not funny or creative then paul is humble or curious and vice versa.
Everyone who is wise is old or strong.
Everyone who is not funny or brave is curious and vice versa.
Everyone who is humble is both not curious and not kind and vice versa.
Everyone who is either not tall or old is both not creative and patient.
If someone is kind then someone is curious and vice versa.
Everyone who is not kind is humble or not generous.
Everyone who is either not generous or calm is not quiet or not tall and vice versa.
Everyone who is both brave and not happy is old or not creative and vice versa.
Everyone who is not old is curious.
Everyone who is happy or old is not old and vice versa.
Someone is both generous and curious.
Mary is rich or curious.
John is creative or not curious.
Someone is rich or strong.
Mary is both generous and not brave.
Someone is either kind or not funny. | Lucy is tall. | entailment | (((patient(lucy)|~strong(lucy)))<=>(?[X]:((~happy(X)&kind(X)))))&
(![X]:((calm(X)&strong(X))=>(~wise(X)<~>old(X))))&
((?[X]:((tall(X)|~humble(X))))=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((~tall(X)|~rich(X))=>(old(X)&~curious(X))))&
(((~funny(john)<~>creative(john)))<=>((humble(paul)|curious(paul))))&
(![X]:(wise(X)=>(old(X)|strong(X))))&
(![X]:((~funny(X)|brave(X))<=>curious(X)))&
(![X]:(humble(X)<=>(~curious(X)&~kind(X))))&
(![X]:((~tall(X)<~>old(X))=>(~creative(X)&patient(X))))&
((?[X]:(kind(X)))<=>(?[X]:(curious(X))))&
(![X]:(~kind(X)=>(humble(X)|~generous(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(~quiet(X)|~tall(X))))&
(![X]:((brave(X)&~happy(X))<=>(old(X)|~creative(X))))&
(![X]:(~old(X)=>curious(X)))&
(![X]:((happy(X)|old(X))<=>~old(X)))&
(?[X]:((generous(X)&curious(X))))&
((rich(mary)|curious(mary)))&
((creative(john)|~curious(john)))&
(?[X]:((rich(X)|strong(X))))&
((generous(mary)&~brave(mary)))&
(?[X]:((kind(X)<~>~funny(X)))) | tall(lucy) | [
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8852111580209003131221519
% SZS output start Proof for 8852111580209003131221519
4. ! [X0] : ((~rich(X0) | ~tall(X0)) => (~curious(X0) & old(X0))) [input p3]
15. ! [X0] : ((old(X0) | happy(X0)) <=> ~old(X0)) [input p14]
22. ~tall(lucy) [input hypothesis]
26. ! [X0] : (~tall(X0) => (~curious(X0) & old(X0))) [pure predicate removal 4]
31. ! [X0] : ((~curious(X0) & old(X0)) | tall(X0)) [ennf transformation 26]
64. ! [X0] : (((old(X0) | happy(X0)) | old(X0)) & (~old(X0) | (~old(X0) & ~happy(X0)))) [nnf transformation 15]
65. ! [X0] : ((old(X0) | happy(X0) | old(X0)) & (~old(X0) | (~old(X0) & ~happy(X0)))) [flattening 64]
82. tall(X0) | old(X0) [cnf transformation 31]
117. ~old(X0) | ~old(X0) [cnf transformation 65]
126. ~tall(lucy) [cnf transformation 22]
127. ~old(X0) [duplicate literal removal 117]
230. old(lucy) [resolution 82,126]
231. $false [subsumption resolution 230,127]
% SZS output end Proof for 8852111580209003131221519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or tall is both calm and not calm and vice versa.
Everyone who is either not humble or rich is wise or not tall.
Everyone who is not quiet is either quiet or strong.
Everyone who is either not wise or funny is generous and vice versa.
Everyone who is either not generous or brave is either tall or not kind.
If someone is not old or not wise then lucy is both not patient and not funny.
If someone is not happy or curious then someone is both not brave and not creative.
Everyone who is either not generous or not humble is either not brave or not generous and vice versa.
Everyone who is either not wise or funny is both not brave and not curious and vice versa.
If lucy is either funny or not happy then alice is both patient and strong and vice versa.
If someone is both not patient and not kind then mary is not happy or strong and vice versa.
If someone is not curious then susan is brave and vice versa.
Everyone who is either generous or brave is either curious or rich.
Everyone who is wise is both not humble and not tall and vice versa.
If someone is creative or not quiet then alice is both tall and not calm.
Everyone who is both not old and calm is not wise.
Alice is not curious.
Someone is either tall or humble.
Mary is not tall.
Someone is not wise.
Mary is rich or creative.
Alice is both wise and not strong.
Someone is generous or happy.
John is not funny. | Susan is not funny. | contradiction | (![X]:((~funny(X)<~>tall(X))<=>(calm(X)&~calm(X))))&
(![X]:((~humble(X)<~>rich(X))=>(wise(X)|~tall(X))))&
(![X]:(~quiet(X)=>(quiet(X)<~>strong(X))))&
(![X]:((~wise(X)<~>funny(X))<=>generous(X)))&
(![X]:((~generous(X)<~>brave(X))=>(tall(X)<~>~kind(X))))&
((?[X]:((~old(X)|~wise(X))))=>((~patient(lucy)&~funny(lucy))))&
((?[X]:((~happy(X)|curious(X))))=>(?[X]:((~brave(X)&~creative(X)))))&
(![X]:((~generous(X)<~>~humble(X))<=>(~brave(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>funny(X))<=>(~brave(X)&~curious(X))))&
(((funny(lucy)<~>~happy(lucy)))<=>((patient(alice)&strong(alice))))&
((?[X]:((~patient(X)&~kind(X))))<=>((~happy(mary)|strong(mary))))&
((?[X]:(~curious(X)))<=>(brave(susan)))&
(![X]:((generous(X)<~>brave(X))=>(curious(X)<~>rich(X))))&
(![X]:(wise(X)<=>(~humble(X)&~tall(X))))&
((?[X]:((creative(X)|~quiet(X))))=>((tall(alice)&~calm(alice))))&
(![X]:((~old(X)&calm(X))=>~wise(X)))&
(~curious(alice))&
(?[X]:((tall(X)<~>humble(X))))&
(~tall(mary))&
(?[X]:(~wise(X)))&
((rich(mary)|creative(mary)))&
((wise(alice)&~strong(alice)))&
(?[X]:((generous(X)|happy(X))))&
(~funny(john)) | ~funny(susan) | [
"p7",
"p8",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2119287458552887265581683
% SZS output start Proof for 2119287458552887265581683
8. ! [X0] : ((~generous(X0) <~> ~humble(X0)) <=> (~brave(X0) <~> ~generous(X0))) [input p7]
9. ! [X0] : ((~wise(X0) <~> funny(X0)) <=> (~curious(X0) & ~brave(X0))) [input p8]
12. ? [X0] : ~curious(X0) <=> brave(susan) [input p11]
14. ! [X0] : (wise(X0) <=> (~tall(X0) & ~humble(X0))) [input p13]
17. ~curious(alice) [input p16]
25. ~funny(susan) [input hypothesis]
46. ! [X0] : ((((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0))))) [nnf transformation 8]
47. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (curious(X0) | brave(X0))) & ((~curious(X0) & ~brave(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [nnf transformation 9]
48. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | curious(X0) | brave(X0)) & ((~curious(X0) & ~brave(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [flattening 47]
56. (? [X0] : ~curious(X0) | ~brave(susan)) & (brave(susan) | ! [X0] : curious(X0)) [nnf transformation 12]
57. (? [X0] : ~curious(X0) | ~brave(susan)) & (brave(susan) | ! [X1] : curious(X1)) [rectify 56]
58. ? [X0] : ~curious(X0) => ~curious(sK2) [choice axiom]
59. (~curious(sK2) | ~brave(susan)) & (brave(susan) | ! [X1] : curious(X1)) [skolemisation 57,58]
61. ! [X0] : ((wise(X0) | (tall(X0) | humble(X0))) & ((~tall(X0) & ~humble(X0)) | ~wise(X0))) [nnf transformation 14]
62. ! [X0] : ((wise(X0) | tall(X0) | humble(X0)) & ((~tall(X0) & ~humble(X0)) | ~wise(X0))) [flattening 61]
95. ~generous(X0) | ~brave(X0) | ~generous(X0) | humble(X0) [cnf transformation 46]
101. humble(X0) | generous(X0) | ~brave(X0) | generous(X0) [cnf transformation 46]
102. ~brave(X0) | funny(X0) | wise(X0) [cnf transformation 48]
119. brave(susan) | curious(X1) [cnf transformation 59]
125. ~wise(X0) | ~humble(X0) [cnf transformation 62]
132. ~curious(alice) [cnf transformation 17]
142. ~funny(susan) [cnf transformation 25]
143. ~generous(X0) | ~brave(X0) | humble(X0) [duplicate literal removal 95]
146. humble(X0) | generous(X0) | ~brave(X0) [duplicate literal removal 101]
182. ~brave(X0) | humble(X0) [subsumption resolution 143,146]
226. 16 <=> brave(susan) [avatar definition]
227. brave(susan) <- (16) [avatar component clause 226]
235. 18 <=> ! [X1] : curious(X1) [avatar definition]
236. curious(X1) <- (18) [avatar component clause 235]
237. 18 | 16 [avatar split clause 119,226,235]
293. humble(susan) <- (16) [resolution 182,227]
316. funny(susan) | wise(susan) <- (16) [resolution 102,227]
317. wise(susan) <- (16) [subsumption resolution 316,142]
321. ~humble(susan) <- (16) [resolution 317,125]
322. $false <- (16) [subsumption resolution 321,293]
323. ~16 [avatar contradiction clause 322]
324. $false <- (18) [resolution 236,132]
327. ~18 [avatar contradiction clause 324]
328. $false [avatar sat refutation 237,323,327]
% SZS output end Proof for 2119287458552887265581683
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not calm or kind then paul is old or calm.
Everyone who is happy is both funny and not old.
Everyone who is humble is either strong or not patient.
Everyone who is either not happy or brave is not old or funny and vice versa.
Everyone who is either brave or not old is wise or kind and vice versa.
Everyone who is either funny or creative is both rich and humble and vice versa.
If mary is not generous or not rich then someone is wise.
If alice is both happy and humble then alice is both tall and not old.
Everyone who is either calm or wise is not old or not generous and vice versa.
Everyone who is rich is both not brave and funny.
If someone is either strong or not kind then lucy is both funny and patient.
If someone is both patient and creative then mary is not humble and vice versa.
Everyone who is both patient and not quiet is either humble or not calm.
Everyone who is not creative is both curious and strong.
Everyone who is either not curious or not old is both generous and not funny and vice versa.
Everyone who is kind or not generous is both not creative and not tall and vice versa.
Someone is both wise and brave.
Someone is both kind and curious.
Fred is both rich and wise.
Alice is both creative and not rich.
Mary is both funny and not humble.
Someone is either not generous or not tall.
Someone is not calm or not patient.
Someone is both not kind and not strong. | Paul is not quiet. | neutral | (((~calm(john)|kind(john)))=>((old(paul)|calm(paul))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
(![X]:((funny(X)<~>creative(X))<=>(rich(X)&humble(X))))&
(((~generous(mary)|~rich(mary)))=>(?[X]:(wise(X))))&
(((happy(alice)&humble(alice)))=>((tall(alice)&~old(alice))))&
(![X]:((calm(X)<~>wise(X))<=>(~old(X)|~generous(X))))&
(![X]:(rich(X)=>(~brave(X)&funny(X))))&
((?[X]:((strong(X)<~>~kind(X))))=>((funny(lucy)&patient(lucy))))&
((?[X]:((patient(X)&creative(X))))<=>(~humble(mary)))&
(![X]:((patient(X)&~quiet(X))=>(humble(X)<~>~calm(X))))&
(![X]:(~creative(X)=>(curious(X)&strong(X))))&
(![X]:((~curious(X)<~>~old(X))<=>(generous(X)&~funny(X))))&
(![X]:((kind(X)|~generous(X))<=>(~creative(X)&~tall(X))))&
(?[X]:((wise(X)&brave(X))))&
(?[X]:((kind(X)&curious(X))))&
((rich(fred)&wise(fred)))&
((creative(alice)&~rich(alice)))&
((funny(mary)&~humble(mary)))&
(?[X]:((~generous(X)<~>~tall(X))))&
(?[X]:((~calm(X)|~patient(X))))&
(?[X]:((~kind(X)&~strong(X)))) | ~quiet(paul) | [] | null | 0 |
If someone is not calm or brave then lucy is not funny.
Everyone who is either not strong or tall is either not happy or not quiet.
Everyone who is rich or generous is not patient and vice versa.
Everyone who is either not patient or not tall is not kind and vice versa.
Everyone who is rich is both not patient and not kind and vice versa.
If someone is rich or not patient then someone is either not wise or not rich and vice versa.
If someone is either happy or not patient then paul is not rich and vice versa.
Everyone who is not kind is either not old or tall and vice versa.
Everyone who is either wise or creative is not funny.
Everyone who is not generous or generous is not kind and vice versa.
If lucy is funny then someone is both not generous and not happy and vice versa.
Everyone who is either patient or not old is both not funny and generous.
Everyone who is not humble or not calm is either strong or happy.
Everyone who is not generous is not brave or quiet and vice versa.
Everyone who is either not happy or kind is either calm or humble and vice versa.
Someone is either not patient or patient.
Someone is not creative.
Someone is both calm and not humble.
Susan is either not curious or funny.
Alice is strong or not funny.
Lucy is either not creative or curious. | Alice is calm. | entailment | ((?[X]:((~calm(X)|brave(X))))=>(~funny(lucy)))&
(![X]:((~strong(X)<~>tall(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((rich(X)|generous(X))<=>~patient(X)))&
(![X]:((~patient(X)<~>~tall(X))<=>~kind(X)))&
(![X]:(rich(X)<=>(~patient(X)&~kind(X))))&
((?[X]:((rich(X)|~patient(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
((?[X]:((happy(X)<~>~patient(X))))<=>(~rich(paul)))&
(![X]:(~kind(X)<=>(~old(X)<~>tall(X))))&
(![X]:((wise(X)<~>creative(X))=>~funny(X)))&
(![X]:((~generous(X)|generous(X))<=>~kind(X)))&
((funny(lucy))<=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:((patient(X)<~>~old(X))=>(~funny(X)&generous(X))))&
(![X]:((~humble(X)|~calm(X))=>(strong(X)<~>happy(X))))&
(![X]:(~generous(X)<=>(~brave(X)|quiet(X))))&
(![X]:((~happy(X)<~>kind(X))<=>(calm(X)<~>humble(X))))&
(?[X]:((~patient(X)<~>patient(X))))&
(?[X]:(~creative(X)))&
(?[X]:((calm(X)&~humble(X))))&
((~curious(susan)<~>funny(susan)))&
((strong(alice)|~funny(alice)))&
((~creative(lucy)<~>curious(lucy))) | calm(alice) | [
"p0",
"p1",
"p2",
"p3",
"p9",
"p10",
"p12",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3998683778714328672318388
% SZS output start Proof for 3998683778714328672318388
1. ? [X0] : (brave(X0) | ~calm(X0)) => ~funny(lucy) [input p0]
2. ! [X0] : ((~strong(X0) <~> tall(X0)) => (~happy(X0) <~> ~quiet(X0))) [input p1]
3. ! [X0] : ((generous(X0) | rich(X0)) <=> ~patient(X0)) [input p2]
4. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> ~kind(X0)) [input p3]
10. ! [X0] : ((generous(X0) | ~generous(X0)) <=> ~kind(X0)) [input p9]
11. funny(lucy) <=> ? [X0] : (~happy(X0) & ~generous(X0)) [input p10]
13. ! [X0] : ((~calm(X0) | ~humble(X0)) => (strong(X0) <~> happy(X0))) [input p12]
14. ! [X0] : (~generous(X0) <=> (quiet(X0) | ~brave(X0))) [input p13]
15. ! [X0] : ((~happy(X0) <~> kind(X0)) <=> (calm(X0) <~> humble(X0))) [input p14]
18. ? [X0] : (~humble(X0) & calm(X0)) [input p17]
22. ~calm(alice) [input hypothesis]
24. ~funny(lucy) | ! [X0] : (~brave(X0) & calm(X0)) [ennf transformation 1]
25. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) | (~strong(X0) <=> tall(X0))) [ennf transformation 2]
28. ! [X0] : ((strong(X0) <~> happy(X0)) | (calm(X0) & humble(X0))) [ennf transformation 13]
29. ! [X0] : (((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) [nnf transformation 25]
30. ! [X0] : (((generous(X0) | rich(X0)) | patient(X0)) & (~patient(X0) | (~generous(X0) & ~rich(X0)))) [nnf transformation 3]
31. ! [X0] : ((generous(X0) | rich(X0) | patient(X0)) & (~patient(X0) | (~generous(X0) & ~rich(X0)))) [flattening 30]
32. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | kind(X0)) & (~kind(X0) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 4]
46. ! [X0] : (((generous(X0) | ~generous(X0)) | kind(X0)) & (~kind(X0) | (~generous(X0) & generous(X0)))) [nnf transformation 10]
47. ! [X0] : ((generous(X0) | ~generous(X0) | kind(X0)) & (~kind(X0) | (~generous(X0) & generous(X0)))) [flattening 46]
48. (funny(lucy) | ! [X0] : (happy(X0) | generous(X0))) & (? [X0] : (~happy(X0) & ~generous(X0)) | ~funny(lucy)) [nnf transformation 11]
49. (funny(lucy) | ! [X0] : (happy(X0) | generous(X0))) & (? [X1] : (~happy(X1) & ~generous(X1)) | ~funny(lucy)) [rectify 48]
50. ? [X1] : (~happy(X1) & ~generous(X1)) => (~happy(sK3) & ~generous(sK3)) [choice axiom]
51. (funny(lucy) | ! [X0] : (happy(X0) | generous(X0))) & ((~happy(sK3) & ~generous(sK3)) | ~funny(lucy)) [skolemisation 49,50]
53. ! [X0] : (((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | (calm(X0) & humble(X0))) [nnf transformation 28]
54. ! [X0] : ((~generous(X0) | (~quiet(X0) & brave(X0))) & ((quiet(X0) | ~brave(X0)) | generous(X0))) [nnf transformation 14]
55. ! [X0] : ((~generous(X0) | (~quiet(X0) & brave(X0))) & (quiet(X0) | ~brave(X0) | generous(X0))) [flattening 54]
56. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) & (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [nnf transformation 15]
62. ? [X0] : (~humble(X0) & calm(X0)) => (~humble(sK6) & calm(sK6)) [choice axiom]
63. ~humble(sK6) & calm(sK6) [skolemisation 18,62]
66. ~funny(lucy) | calm(X0) [cnf transformation 24]
71. ~tall(X0) | happy(X0) | ~strong(X0) | quiet(X0) [cnf transformation 29]
73. ~patient(X0) | ~generous(X0) [cnf transformation 31]
78. kind(X0) | patient(X0) | tall(X0) [cnf transformation 32]
98. ~kind(X0) | generous(X0) [cnf transformation 47]
99. ~kind(X0) | ~generous(X0) [cnf transformation 47]
103. funny(lucy) | happy(X0) | generous(X0) [cnf transformation 51]
108. humble(X0) | strong(X0) | happy(X0) [cnf transformation 53]
114. ~generous(X0) | ~quiet(X0) [cnf transformation 55]
119. kind(X0) | ~happy(X0) | humble(X0) | ~calm(X0) [cnf transformation 56]
126. calm(sK6) [cnf transformation 63]
127. ~humble(sK6) [cnf transformation 63]
133. ~calm(alice) [cnf transformation 22]
138. 2 <=> funny(lucy) [avatar definition]
143. 3 <=> ! [X0] : calm(X0) [avatar definition]
144. calm(X0) <- (3) [avatar component clause 143]
145. 3 | ~2 [avatar split clause 66,138,143]
200. ~kind(X0) [subsumption resolution 98,99]
202. 16 <=> ! [X0] : (happy(X0) | generous(X0)) [avatar definition]
203. generous(X0) | happy(X0) <- (16) [avatar component clause 202]
204. 16 | 2 [avatar split clause 103,138,202]
217. ~happy(X0) | humble(X0) | ~calm(X0) [subsumption resolution 119,200]
294. patient(X2) | tall(X2) | ~generous(X2) [resolution 78,99]
299. ~generous(X2) | tall(X2) [subsumption resolution 294,73]
335. strong(sK6) | happy(sK6) [resolution 108,127]
337. 31 <=> happy(sK6) [avatar definition]
338. ~happy(sK6) <- (~31) [avatar component clause 337]
339. happy(sK6) <- (31) [avatar component clause 337]
341. 32 <=> strong(sK6) [avatar definition]
343. strong(sK6) <- (32) [avatar component clause 341]
344. 31 | 32 [avatar split clause 335,341,337]
380. humble(sK6) | ~calm(sK6) <- (31) [resolution 217,339]
386. ~calm(sK6) <- (31) [subsumption resolution 380,127]
387. $false <- (31) [subsumption resolution 386,126]
388. ~31 [avatar contradiction clause 387]
411. 38 <=> generous(sK6) [avatar definition]
412. ~generous(sK6) <- (~38) [avatar component clause 411]
413. generous(sK6) <- (38) [avatar component clause 411]
415. 39 <=> quiet(sK6) [avatar definition]
416. ~quiet(sK6) <- (~39) [avatar component clause 415]
431. $false <- (3) [resolution 144,133]
434. ~3 [avatar contradiction clause 431]
479. tall(sK6) <- (38) [resolution 413,299]
480. ~quiet(sK6) <- (38) [resolution 413,114]
482. ~39 | ~38 [avatar split clause 480,411,415]
510. happy(sK6) | ~strong(sK6) | quiet(sK6) <- (38) [resolution 479,71]
512. ~strong(sK6) | quiet(sK6) <- (~31, 38) [subsumption resolution 510,338]
513. quiet(sK6) <- (~31, 32, 38) [subsumption resolution 512,343]
514. $false <- (~31, 32, 38, ~39) [subsumption resolution 513,416]
515. 31 | ~32 | ~38 | 39 [avatar contradiction clause 514]
518. happy(sK6) <- (16, ~38) [resolution 412,203]
519. $false <- (16, ~31, ~38) [subsumption resolution 518,338]
520. ~16 | 31 | 38 [avatar contradiction clause 519]
521. $false [avatar sat refutation 145,204,344,388,434,482,515,520]
% SZS output end Proof for 3998683778714328672318388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not brave is both not calm and strong. Everyone who is either funny or rich is both funny and not humble and vice versa. If john is not old or creative then alice is either not kind or not quiet. Everyone who is either not strong or not old is funny or quiet. Everyone who is both generous and not quiet is either patient or brave. If someone is either not tall or wise then paul is brave. If someone is either tall or not quiet then susan is both calm and not kind. Everyone who is not happy or not creative is brave or creative and vice versa. If paul is both humble and old then paul is either not calm or funny. Everyone who is either old or quiet is either calm or humble. Everyone who is both tall and not humble is not happy or not creative and vice versa. Everyone who is not strong or not curious is rich and vice versa. If lucy is either creative or brave then someone is either not calm or not patient and vice versa. If someone is funny or creative then someone is kind and vice versa. If someone is not humble then someone is both generous and not creative and vice versa. Everyone who is both calm and not funny is both old and quiet and vice versa. Someone is not funny or patient. Someone is either humble or funny. Someone is not quiet or not humble. Someone is not old. Paul is both happy and tall. Someone is rich or strong. | John is old. | contradiction | (![X]:((brave(X)<~>~brave(X))=>(~calm(X)&strong(X))))&
(![X]:((funny(X)<~>rich(X))<=>(funny(X)&~humble(X))))&
(((~old(john)|creative(john)))=>((~kind(alice)<~>~quiet(alice))))&
(![X]:((~strong(X)<~>~old(X))=>(funny(X)|quiet(X))))&
(![X]:((generous(X)&~quiet(X))=>(patient(X)<~>brave(X))))&
((?[X]:((~tall(X)<~>wise(X))))=>(brave(paul)))&
((?[X]:((tall(X)<~>~quiet(X))))=>((calm(susan)&~kind(susan))))&
(![X]:((~happy(X)|~creative(X))<=>(brave(X)|creative(X))))&
(((humble(paul)&old(paul)))=>((~calm(paul)<~>funny(paul))))&
(![X]:((old(X)<~>quiet(X))=>(calm(X)<~>humble(X))))&
(![X]:((tall(X)&~humble(X))<=>(~happy(X)|~creative(X))))&
(![X]:((~strong(X)|~curious(X))<=>rich(X)))&
(((creative(lucy)<~>brave(lucy)))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
((?[X]:((funny(X)|creative(X))))<=>(?[X]:(kind(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((generous(X)&~creative(X)))))&
(![X]:((calm(X)&~funny(X))<=>(old(X)&quiet(X))))&
(?[X]:((~funny(X)|patient(X))))&
(?[X]:((humble(X)<~>funny(X))))&
(?[X]:((~quiet(X)|~humble(X))))&
(?[X]:(~old(X)))&
((happy(paul)&tall(paul)))&
(?[X]:((rich(X)|strong(X)))) | old(john) | [
"p0",
"p6",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2280150672433535390953202
% SZS output start Proof for 2280150672433535390953202
1. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (strong(X0) & ~calm(X0))) [input p0]
7. ? [X0] : (tall(X0) <~> ~quiet(X0)) => (~kind(susan) & calm(susan)) [input p6]
8. ! [X0] : ((~creative(X0) | ~happy(X0)) <=> (creative(X0) | brave(X0))) [input p7]
10. ! [X0] : ((old(X0) <~> quiet(X0)) => (calm(X0) <~> humble(X0))) [input p9]
11. ! [X0] : ((~humble(X0) & tall(X0)) <=> (~creative(X0) | ~happy(X0))) [input p10]
23. old(john) [input hypothesis]
26. ! [X0] : ((strong(X0) & ~calm(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 1]
33. (~kind(susan) & calm(susan)) | ! [X0] : (tall(X0) <=> ~quiet(X0)) [ennf transformation 7]
36. ! [X0] : ((calm(X0) <~> humble(X0)) | (old(X0) <=> quiet(X0))) [ennf transformation 10]
37. ! [X0] : ((strong(X0) & ~calm(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 26]
44. (~kind(susan) & calm(susan)) | ! [X0] : ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0))) [nnf transformation 33]
45. ! [X0] : (((~creative(X0) | ~happy(X0)) | (~creative(X0) & ~brave(X0))) & ((creative(X0) | brave(X0)) | (creative(X0) & happy(X0)))) [nnf transformation 8]
46. ! [X0] : ((~creative(X0) | ~happy(X0) | (~creative(X0) & ~brave(X0))) & (creative(X0) | brave(X0) | (creative(X0) & happy(X0)))) [flattening 45]
48. ! [X0] : (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | ((old(X0) | ~quiet(X0)) & (quiet(X0) | ~old(X0)))) [nnf transformation 36]
49. ! [X0] : (((~humble(X0) & tall(X0)) | (creative(X0) & happy(X0))) & ((~creative(X0) | ~happy(X0)) | (humble(X0) | ~tall(X0)))) [nnf transformation 11]
50. ! [X0] : (((~humble(X0) & tall(X0)) | (creative(X0) & happy(X0))) & (~creative(X0) | ~happy(X0) | humble(X0) | ~tall(X0))) [flattening 49]
80. ~calm(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 37]
81. ~calm(X0) | brave(X0) | brave(X0) [cnf transformation 37]
100. calm(susan) | ~quiet(X0) | ~tall(X0) [cnf transformation 44]
107. ~creative(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 46]
110. humble(X0) | calm(X0) | quiet(X0) | ~old(X0) [cnf transformation 48]
115. happy(X0) | tall(X0) [cnf transformation 50]
116. tall(X0) | creative(X0) [cnf transformation 50]
117. ~humble(X0) | happy(X0) [cnf transformation 50]
118. ~humble(X0) | creative(X0) [cnf transformation 50]
148. old(john) [cnf transformation 23]
150. ~happy(X0) | ~creative(X0) [duplicate literal removal 107]
153. ~calm(X0) | ~brave(X0) [duplicate literal removal 80]
154. ~calm(X0) | brave(X0) [duplicate literal removal 81]
158. ~calm(X0) [subsumption resolution 153,154]
160. 1 <=> creative(john) [avatar definition]
161. creative(john) <- (1) [avatar component clause 160]
173. 4 <=> old(john) [avatar definition]
175. old(john) <- (4) [avatar component clause 173]
201. 10 <=> ! [X0] : (~quiet(X0) | ~tall(X0)) [avatar definition]
202. ~tall(X0) | ~quiet(X0) <- (10) [avatar component clause 201]
206. ~quiet(X0) | ~tall(X0) [subsumption resolution 100,158]
207. 10 [avatar split clause 206,201]
223. ~old(X0) | quiet(X0) | humble(X0) [subsumption resolution 110,158]
322. 4 [avatar split clause 148,173]
339. ~creative(X0) | tall(X0) [resolution 150,115]
343. tall(X0) [subsumption resolution 339,116]
353. ~quiet(X1) <- (10) [resolution 202,343]
368. quiet(john) | humble(john) <- (4) [resolution 223,175]
371. humble(john) <- (4, 10) [subsumption resolution 368,353]
379. creative(john) <- (4, 10) [resolution 371,118]
380. happy(john) <- (4, 10) [resolution 371,117]
392. 1 | ~4 | ~10 [avatar split clause 379,201,173,160]
396. ~creative(john) <- (4, 10) [resolution 380,150]
397. $false <- (1, 4, 10) [subsumption resolution 396,161]
398. ~1 | ~4 | ~10 [avatar contradiction clause 397]
399. $false [avatar sat refutation 207,322,392,398]
% SZS output end Proof for 2280150672433535390953202
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or humble then someone is not generous and vice versa.
Everyone who is both not calm and patient is not curious or not brave.
Everyone who is not humble is old.
Everyone who is not calm or quiet is either not brave or not creative and vice versa.
Everyone who is funny or curious is either strong or curious.
If john is either happy or curious then someone is both not tall and generous.
Everyone who is not curious or funny is calm or not happy.
If someone is not strong then someone is generous and vice versa.
If fred is humble then lucy is not quiet.
Everyone who is old or not brave is both humble and not funny.
Everyone who is both not patient and tall is both not happy and not humble.
If john is both not old and not funny then mary is either happy or wise.
If fred is not tall or wise then mary is not curious or rich.
If someone is either not calm or calm then someone is either not kind or funny.
Everyone who is either not wise or quiet is not humble.
If john is patient then lucy is generous and vice versa.
Someone is calm or rich.
Fred is curious or not curious.
Someone is not patient.
Someone is both rich and not quiet.
Paul is both old and calm.
Someone is both not tall and creative.
Someone is generous.
Alice is not quiet or generous. | Lucy is wise. | entailment | ((?[X]:((old(X)<~>humble(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~calm(X)&patient(X))=>(~curious(X)|~brave(X))))&
(![X]:(~humble(X)=>old(X)))&
(![X]:((~calm(X)|quiet(X))<=>(~brave(X)<~>~creative(X))))&
(![X]:((funny(X)|curious(X))=>(strong(X)<~>curious(X))))&
(((happy(john)<~>curious(john)))=>(?[X]:((~tall(X)&generous(X)))))&
(![X]:((~curious(X)|funny(X))=>(calm(X)|~happy(X))))&
((?[X]:(~strong(X)))<=>(?[X]:(generous(X))))&
((humble(fred))=>(~quiet(lucy)))&
(![X]:((old(X)|~brave(X))=>(humble(X)&~funny(X))))&
(![X]:((~patient(X)&tall(X))=>(~happy(X)&~humble(X))))&
(((~old(john)&~funny(john)))=>((happy(mary)<~>wise(mary))))&
(((~tall(fred)|wise(fred)))=>((~curious(mary)|rich(mary))))&
((?[X]:((~calm(X)<~>calm(X))))=>(?[X]:((~kind(X)<~>funny(X)))))&
(![X]:((~wise(X)<~>quiet(X))=>~humble(X)))&
((patient(john))<=>(generous(lucy)))&
(?[X]:((calm(X)|rich(X))))&
((curious(fred)|~curious(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)&~quiet(X))))&
((old(paul)&calm(paul)))&
(?[X]:((~tall(X)&creative(X))))&
(?[X]:(generous(X)))&
((~quiet(alice)|generous(alice))) | wise(lucy) | [
"p2",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6987231599037029104592859
% SZS output start Proof for 6987231599037029104592859
3. ! [X0] : (~humble(X0) => old(X0)) [input p2]
9. humble(fred) => ~quiet(lucy) [input p8]
10. ! [X0] : ((~brave(X0) | old(X0)) => (~funny(X0) & humble(X0))) [input p9]
15. ! [X0] : ((~wise(X0) <~> quiet(X0)) => ~humble(X0)) [input p14]
25. ~wise(lucy) [input hypothesis]
37. ! [X0] : (old(X0) | humble(X0)) [ennf transformation 3]
42. ~quiet(lucy) | ~humble(fred) [ennf transformation 9]
43. ! [X0] : ((~funny(X0) & humble(X0)) | (brave(X0) & ~old(X0))) [ennf transformation 10]
47. ! [X0] : (~humble(X0) | (~wise(X0) <=> quiet(X0))) [ennf transformation 15]
69. ! [X0] : (~humble(X0) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) [nnf transformation 47]
84. humble(X0) | old(X0) [cnf transformation 37]
101. ~quiet(lucy) | ~humble(fred) [cnf transformation 42]
102. humble(X0) | ~old(X0) [cnf transformation 43]
112. ~humble(X0) | quiet(X0) | wise(X0) [cnf transformation 69]
124. ~wise(lucy) [cnf transformation 25]
186. 14 <=> humble(fred) [avatar definition]
188. ~humble(fred) <- (~14) [avatar component clause 186]
190. 15 <=> quiet(lucy) [avatar definition]
192. ~quiet(lucy) <- (~15) [avatar component clause 190]
193. ~14 | ~15 [avatar split clause 101,190,186]
194. humble(X0) [subsumption resolution 102,84]
232. wise(X0) | quiet(X0) [subsumption resolution 112,194]
252. $false <- (~14) [subsumption resolution 188,194]
253. 14 [avatar contradiction clause 252]
265. quiet(lucy) [resolution 232,124]
267. $false <- (~15) [subsumption resolution 265,192]
268. 15 [avatar contradiction clause 267]
269. $false [avatar sat refutation 193,253,268]
% SZS output end Proof for 6987231599037029104592859
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is not creative or funny and vice versa.
Everyone who is not happy is creative.
Everyone who is either not patient or not curious is generous or not tall.
If john is rich or brave then susan is both strong and not generous and vice versa.
Everyone who is not old is not generous.
Everyone who is strong or humble is creative or strong.
Everyone who is both humble and old is both not rich and tall.
If someone is not old then paul is not brave and vice versa.
Everyone who is either not strong or quiet is not strong or not old.
If someone is not happy then paul is both not funny and not old and vice versa.
Everyone who is humble or strong is either quiet or calm.
Everyone who is both not calm and brave is not wise and vice versa.
Everyone who is either humble or wise is not kind or calm.
If paul is either not kind or not strong then paul is not happy or not old and vice versa.
Everyone who is both happy and not old is both not quiet and generous.
Everyone who is either generous or not humble is both not happy and brave.
Someone is either creative or tall.
Fred is not strong.
John is either quiet or not rich.
Susan is not happy or not old.
Paul is either not kind or not wise.
Alice is both patient and not wise.
Someone is either not humble or tall.
Someone is both not wise and generous. | Paul is not creative. | contradiction | (![X]:(~humble(X)<=>(~creative(X)|funny(X))))&
(![X]:(~happy(X)=>creative(X)))&
(![X]:((~patient(X)<~>~curious(X))=>(generous(X)|~tall(X))))&
(((rich(john)|brave(john)))<=>((strong(susan)&~generous(susan))))&
(![X]:(~old(X)=>~generous(X)))&
(![X]:((strong(X)|humble(X))=>(creative(X)|strong(X))))&
(![X]:((humble(X)&old(X))=>(~rich(X)&tall(X))))&
((?[X]:(~old(X)))<=>(~brave(paul)))&
(![X]:((~strong(X)<~>quiet(X))=>(~strong(X)|~old(X))))&
((?[X]:(~happy(X)))<=>((~funny(paul)&~old(paul))))&
(![X]:((humble(X)|strong(X))=>(quiet(X)<~>calm(X))))&
(![X]:((~calm(X)&brave(X))<=>~wise(X)))&
(![X]:((humble(X)<~>wise(X))=>(~kind(X)|calm(X))))&
(((~kind(paul)<~>~strong(paul)))<=>((~happy(paul)|~old(paul))))&
(![X]:((happy(X)&~old(X))=>(~quiet(X)&generous(X))))&
(![X]:((generous(X)<~>~humble(X))=>(~happy(X)&brave(X))))&
(?[X]:((creative(X)<~>tall(X))))&
(~strong(fred))&
((quiet(john)<~>~rich(john)))&
((~happy(susan)|~old(susan)))&
((~kind(paul)<~>~wise(paul)))&
((patient(alice)&~wise(alice)))&
(?[X]:((~humble(X)<~>tall(X))))&
(?[X]:((~wise(X)&generous(X)))) | ~creative(paul) | [
"p1",
"p4",
"p9",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4951280705630346949643657
% SZS output start Proof for 4951280705630346949643657
2. ! [X0] : (~happy(X0) => creative(X0)) [input p1]
5. ! [X0] : (~old(X0) => ~generous(X0)) [input p4]
10. ? [X0] : ~happy(X0) <=> (~old(paul) & ~funny(paul)) [input p9]
15. ! [X0] : ((~old(X0) & happy(X0)) => (generous(X0) & ~quiet(X0))) [input p14]
20. ~old(susan) | ~happy(susan) [input p19]
25. ~creative(paul) [input hypothesis]
26. ! [X0] : (creative(X0) | happy(X0)) [ennf transformation 2]
29. ! [X0] : (~generous(X0) | old(X0)) [ennf transformation 5]
39. ! [X0] : ((generous(X0) & ~quiet(X0)) | (old(X0) | ~happy(X0))) [ennf transformation 15]
40. ! [X0] : ((generous(X0) & ~quiet(X0)) | old(X0) | ~happy(X0)) [flattening 39]
52. (? [X0] : ~happy(X0) | (old(paul) | funny(paul))) & ((~old(paul) & ~funny(paul)) | ! [X0] : happy(X0)) [nnf transformation 10]
53. (? [X0] : ~happy(X0) | old(paul) | funny(paul)) & ((~old(paul) & ~funny(paul)) | ! [X0] : happy(X0)) [flattening 52]
54. (? [X0] : ~happy(X0) | old(paul) | funny(paul)) & ((~old(paul) & ~funny(paul)) | ! [X1] : happy(X1)) [rectify 53]
55. ? [X0] : ~happy(X0) => ~happy(sK1) [choice axiom]
56. (~happy(sK1) | old(paul) | funny(paul)) & ((~old(paul) & ~funny(paul)) | ! [X1] : happy(X1)) [skolemisation 54,55]
77. happy(X0) | creative(X0) [cnf transformation 26]
85. ~generous(X0) | old(X0) [cnf transformation 29]
95. ~old(paul) | happy(X1) [cnf transformation 56]
113. generous(X0) | old(X0) | ~happy(X0) [cnf transformation 40]
123. ~old(susan) | ~happy(susan) [cnf transformation 20]
132. ~creative(paul) [cnf transformation 25]
173. 9 <=> old(paul) [avatar definition]
174. ~old(paul) <- (~9) [avatar component clause 173]
182. 11 <=> ! [X1] : happy(X1) [avatar definition]
183. happy(X1) <- (11) [avatar component clause 182]
184. 11 | ~9 [avatar split clause 95,173,182]
197. 14 <=> happy(paul) [avatar definition]
198. ~happy(paul) <- (~14) [avatar component clause 197]
199. happy(paul) <- (14) [avatar component clause 197]
205. ~happy(X0) | old(X0) [subsumption resolution 113,85]
222. ~happy(susan) [subsumption resolution 123,205]
284. $false <- (11) [resolution 183,222]
285. ~11 [avatar contradiction clause 284]
288. creative(paul) <- (~14) [resolution 198,77]
289. $false <- (~14) [subsumption resolution 288,132]
290. 14 [avatar contradiction clause 289]
291. old(paul) <- (14) [resolution 199,205]
292. $false <- (~9, 14) [subsumption resolution 291,174]
293. 9 | ~14 [avatar contradiction clause 292]
294. $false [avatar sat refutation 184,285,290,293]
% SZS output end Proof for 4951280705630346949643657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not generous and not strong then mary is not patient or not kind and vice versa. If someone is generous or calm then someone is both not humble and funny. Everyone who is not old or not brave is both not calm and not kind and vice versa. Everyone who is brave is not funny. If lucy is not happy or patient then fred is humble. Everyone who is both tall and old is both generous and not funny. If john is either strong or not generous then alice is either not curious or calm and vice versa. Everyone who is wise is not humble and vice versa. If lucy is either rich or not curious then someone is brave or not quiet and vice versa. Everyone who is strong is both not curious and brave. If paul is both quiet and not wise then someone is both not patient and brave and vice versa. If paul is both wise and not old then someone is creative or curious and vice versa. If someone is not funny then mary is either funny or wise and vice versa. If lucy is both humble and not curious then someone is curious or not humble and vice versa. Everyone who is not humble or not brave is either quiet or not rich. Everyone who is wise or kind is both not patient and not brave. Someone is not old. Someone is not patient. Alice is both not strong and quiet. John is curious. Someone is strong. Someone is not creative or generous. Alice is curious. Susan is generous or not wise. | Paul is not strong. | entailment | (((~generous(susan)&~strong(susan)))<=>((~patient(mary)|~kind(mary))))&
((?[X]:((generous(X)|calm(X))))=>(?[X]:((~humble(X)&funny(X)))))&
(![X]:((~old(X)|~brave(X))<=>(~calm(X)&~kind(X))))&
(![X]:(brave(X)=>~funny(X)))&
(((~happy(lucy)|patient(lucy)))=>(humble(fred)))&
(![X]:((tall(X)&old(X))=>(generous(X)&~funny(X))))&
(((strong(john)<~>~generous(john)))<=>((~curious(alice)<~>calm(alice))))&
(![X]:(wise(X)<=>~humble(X)))&
(((rich(lucy)<~>~curious(lucy)))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:(strong(X)=>(~curious(X)&brave(X))))&
(((quiet(paul)&~wise(paul)))<=>(?[X]:((~patient(X)&brave(X)))))&
(((wise(paul)&~old(paul)))<=>(?[X]:((creative(X)|curious(X)))))&
((?[X]:(~funny(X)))<=>((funny(mary)<~>wise(mary))))&
(((humble(lucy)&~curious(lucy)))<=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((~humble(X)|~brave(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((wise(X)|kind(X))=>(~patient(X)&~brave(X))))&
(?[X]:(~old(X)))&
(?[X]:(~patient(X)))&
((~strong(alice)&quiet(alice)))&
(curious(john))&
(?[X]:(strong(X)))&
(?[X]:((~creative(X)|generous(X))))&
(curious(alice))&
((generous(susan)|~wise(susan))) | ~strong(paul) | [
"p9",
"p11",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1801301693039048871247755
% SZS output start Proof for 1801301693039048871247755
10. ! [X0] : (strong(X0) => (brave(X0) & ~curious(X0))) [input p9]
12. (~old(paul) & wise(paul)) <=> ? [X0] : (curious(X0) | creative(X0)) [input p11]
16. ! [X0] : ((kind(X0) | wise(X0)) => (~brave(X0) & ~patient(X0))) [input p15]
23. curious(alice) [input p22]
25. strong(paul) [input hypothesis]
32. ! [X0] : ((brave(X0) & ~curious(X0)) | ~strong(X0)) [ennf transformation 10]
34. ! [X0] : ((~brave(X0) & ~patient(X0)) | (~kind(X0) & ~wise(X0))) [ennf transformation 16]
53. ((~old(paul) & wise(paul)) | ! [X0] : (~curious(X0) & ~creative(X0))) & (? [X0] : (curious(X0) | creative(X0)) | (old(paul) | ~wise(paul))) [nnf transformation 12]
54. ((~old(paul) & wise(paul)) | ! [X0] : (~curious(X0) & ~creative(X0))) & (? [X0] : (curious(X0) | creative(X0)) | old(paul) | ~wise(paul)) [flattening 53]
55. ((~old(paul) & wise(paul)) | ! [X0] : (~curious(X0) & ~creative(X0))) & (? [X1] : (curious(X1) | creative(X1)) | old(paul) | ~wise(paul)) [rectify 54]
56. ? [X1] : (curious(X1) | creative(X1)) => (curious(sK3) | creative(sK3)) [choice axiom]
57. ((~old(paul) & wise(paul)) | ! [X0] : (~curious(X0) & ~creative(X0))) & ((curious(sK3) | creative(sK3)) | old(paul) | ~wise(paul)) [skolemisation 55,56]
109. ~strong(X0) | brave(X0) [cnf transformation 32]
116. wise(paul) | ~curious(X0) [cnf transformation 57]
134. ~wise(X0) | ~brave(X0) [cnf transformation 34]
143. curious(alice) [cnf transformation 23]
145. strong(paul) [cnf transformation 25]
199. 12 <=> curious(alice) [avatar definition]
200. curious(alice) <- (12) [avatar component clause 199]
250. 22 <=> wise(paul) [avatar definition]
251. wise(paul) <- (22) [avatar component clause 250]
270. 26 <=> ! [X0] : ~curious(X0) [avatar definition]
271. ~curious(X0) <- (26) [avatar component clause 270]
281. 26 | 22 [avatar split clause 116,250,270]
341. 12 [avatar split clause 143,199]
347. $false <- (12, 26) [subsumption resolution 200,271]
348. ~12 | ~26 [avatar contradiction clause 347]
361. brave(paul) [resolution 109,145]
366. ~brave(paul) <- (22) [resolution 134,251]
369. $false <- (22) [subsumption resolution 366,361]
370. ~22 [avatar contradiction clause 369]
371. $false [avatar sat refutation 281,341,348,370]
% SZS output end Proof for 1801301693039048871247755
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not wise is not brave. Everyone who is not patient is either brave or funny. Everyone who is not happy or not old is not curious and vice versa. If someone is both quiet and not patient then mary is not kind or not tall and vice versa. If someone is not calm or not quiet then someone is old or tall and vice versa. If john is not kind or calm then john is not humble and vice versa. If paul is not generous or not happy then someone is both not brave and not calm. If someone is both humble and brave then mary is either not curious or kind. Everyone who is both tall and not happy is both not happy and humble and vice versa. If lucy is both curious and quiet then someone is both not calm and calm and vice versa. If someone is happy or patient then susan is both brave and not patient. If john is both not funny and funny then someone is both not humble and not tall and vice versa. Everyone who is strong or not funny is humble. If someone is both not strong and not patient then susan is not humble or not curious and vice versa. Everyone who is not quiet or rich is either not humble or tall and vice versa. Everyone who is wise or quiet is wise and vice versa. Someone is not rich or patient. Lucy is not wise. Fred is either quiet or not quiet. John is creative or tall. Someone is calm. | Paul is tall. | entailment | (![X]:((~funny(X)|~wise(X))=>~brave(X)))&
(![X]:(~patient(X)=>(brave(X)<~>funny(X))))&
(![X]:((~happy(X)|~old(X))<=>~curious(X)))&
((?[X]:((quiet(X)&~patient(X))))<=>((~kind(mary)|~tall(mary))))&
((?[X]:((~calm(X)|~quiet(X))))<=>(?[X]:((old(X)|tall(X)))))&
(((~kind(john)|calm(john)))<=>(~humble(john)))&
(((~generous(paul)|~happy(paul)))=>(?[X]:((~brave(X)&~calm(X)))))&
((?[X]:((humble(X)&brave(X))))=>((~curious(mary)<~>kind(mary))))&
(![X]:((tall(X)&~happy(X))<=>(~happy(X)&humble(X))))&
(((curious(lucy)&quiet(lucy)))<=>(?[X]:((~calm(X)&calm(X)))))&
((?[X]:((happy(X)|patient(X))))=>((brave(susan)&~patient(susan))))&
(((~funny(john)&funny(john)))<=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((strong(X)|~funny(X))=>humble(X)))&
((?[X]:((~strong(X)&~patient(X))))<=>((~humble(susan)|~curious(susan))))&
(![X]:((~quiet(X)|rich(X))<=>(~humble(X)<~>tall(X))))&
(![X]:((wise(X)|quiet(X))<=>wise(X)))&
(?[X]:((~rich(X)|patient(X))))&
(~wise(lucy))&
((quiet(fred)<~>~quiet(fred)))&
((creative(john)|tall(john)))&
(?[X]:(calm(X))) | tall(paul) | [
"p0",
"p1",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1709671916430145484957686
% SZS output start Proof for 1709671916430145484957686
1. ! [X0] : ((~wise(X0) | ~funny(X0)) => ~brave(X0)) [input p0]
2. ! [X0] : (~patient(X0) => (brave(X0) <~> funny(X0))) [input p1]
9. ! [X0] : ((~happy(X0) & tall(X0)) <=> (humble(X0) & ~happy(X0))) [input p8]
11. ? [X0] : (patient(X0) | happy(X0)) => (~patient(susan) & brave(susan)) [input p10]
12. (funny(john) & ~funny(john)) <=> ? [X0] : (~tall(X0) & ~humble(X0)) [input p11]
22. ~tall(paul) [input hypothesis]
26. ! [X0] : (~brave(X0) | (wise(X0) & funny(X0))) [ennf transformation 1]
27. ! [X0] : ((brave(X0) <~> funny(X0)) | patient(X0)) [ennf transformation 2]
30. (~patient(susan) & brave(susan)) | ! [X0] : (~patient(X0) & ~happy(X0)) [ennf transformation 11]
32. ! [X0] : (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | patient(X0)) [nnf transformation 27]
50. ! [X0] : (((~happy(X0) & tall(X0)) | (~humble(X0) | happy(X0))) & ((humble(X0) & ~happy(X0)) | (happy(X0) | ~tall(X0)))) [nnf transformation 9]
51. ! [X0] : (((~happy(X0) & tall(X0)) | ~humble(X0) | happy(X0)) & ((humble(X0) & ~happy(X0)) | happy(X0) | ~tall(X0))) [flattening 50]
57. ((funny(john) & ~funny(john)) | ! [X0] : (tall(X0) | humble(X0))) & (? [X0] : (~tall(X0) & ~humble(X0)) | (~funny(john) | funny(john))) [nnf transformation 12]
58. ((funny(john) & ~funny(john)) | ! [X0] : (tall(X0) | humble(X0))) & (? [X0] : (~tall(X0) & ~humble(X0)) | ~funny(john) | funny(john)) [flattening 57]
59. ((funny(john) & ~funny(john)) | ! [X0] : (tall(X0) | humble(X0))) & (? [X1] : (~tall(X1) & ~humble(X1)) | ~funny(john) | funny(john)) [rectify 58]
60. ? [X1] : (~tall(X1) & ~humble(X1)) => (~tall(sK5) & ~humble(sK5)) [choice axiom]
61. ((funny(john) & ~funny(john)) | ! [X0] : (tall(X0) | humble(X0))) & ((~tall(sK5) & ~humble(sK5)) | ~funny(john) | funny(john)) [skolemisation 59,60]
76. ~brave(X0) | funny(X0) [cnf transformation 26]
79. ~funny(X0) | ~brave(X0) | patient(X0) [cnf transformation 32]
101. ~humble(X0) | tall(X0) | happy(X0) [cnf transformation 51]
107. brave(susan) | ~happy(X0) [cnf transformation 30]
109. ~patient(susan) | ~happy(X0) [cnf transformation 30]
113. ~funny(john) | tall(X0) | humble(X0) [cnf transformation 61]
114. funny(john) | tall(X0) | humble(X0) [cnf transformation 61]
136. ~tall(paul) [cnf transformation 22]
137. ~brave(X0) | patient(X0) [subsumption resolution 79,76]
251. 26 <=> patient(susan) [avatar definition]
256. 27 <=> ! [X0] : ~happy(X0) [avatar definition]
257. ~happy(X0) <- (27) [avatar component clause 256]
258. 27 | ~26 [avatar split clause 109,251,256]
260. 28 <=> brave(susan) [avatar definition]
262. brave(susan) <- (28) [avatar component clause 260]
264. 27 | 28 [avatar split clause 107,260,256]
266. 29 <=> ! [X0] : (tall(X0) | humble(X0)) [avatar definition]
267. humble(X0) | tall(X0) <- (29) [avatar component clause 266]
269. 30 <=> funny(john) [avatar definition]
272. 29 | 30 [avatar split clause 114,269,266]
273. 29 | ~30 [avatar split clause 113,269,266]
329. patient(susan) <- (28) [resolution 262,137]
334. 26 | ~28 [avatar split clause 329,260,251]
338. tall(X0) | happy(X0) | tall(X0) <- (29) [resolution 101,267]
342. tall(X0) | happy(X0) <- (29) [duplicate literal removal 338]
343. tall(X0) <- (27, 29) [subsumption resolution 342,257]
349. $false <- (27, 29) [resolution 343,136]
352. ~27 | ~29 [avatar contradiction clause 349]
354. $false [avatar sat refutation 258,264,272,273,334,352]
% SZS output end Proof for 1709671916430145484957686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and funny is both brave and not creative. Everyone who is both not rich and creative is both quiet and strong. Everyone who is patient is creative or not old. Everyone who is not kind is curious or not funny and vice versa. If someone is both not strong and strong then someone is funny or creative and vice versa. Everyone who is quiet is both not wise and generous and vice versa. If lucy is either not happy or not generous then someone is not tall or not generous and vice versa. If alice is not funny or not wise then someone is either creative or old. If alice is both happy and rich then someone is not humble or wise and vice versa. If someone is happy or curious then lucy is either not brave or wise. Everyone who is either tall or not rich is either not happy or not brave and vice versa. Everyone who is brave is either happy or not kind. If lucy is both not curious and not tall then alice is not strong and vice versa. Everyone who is both quiet and tall is either patient or rich and vice versa. Everyone who is kind is tall. Everyone who is either not kind or funny is old and vice versa. Lucy is either tall or happy. Alice is happy. John is not wise. Fred is either not brave or curious. Someone is both not happy and curious. Someone is either not happy or rich. Someone is not wise. | Alice is not brave. | entailment | (![X]:((creative(X)&funny(X))=>(brave(X)&~creative(X))))&
(![X]:((~rich(X)&creative(X))=>(quiet(X)&strong(X))))&
(![X]:(patient(X)=>(creative(X)|~old(X))))&
(![X]:(~kind(X)<=>(curious(X)|~funny(X))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((funny(X)|creative(X)))))&
(![X]:(quiet(X)<=>(~wise(X)&generous(X))))&
(((~happy(lucy)<~>~generous(lucy)))<=>(?[X]:((~tall(X)|~generous(X)))))&
(((~funny(alice)|~wise(alice)))=>(?[X]:((creative(X)<~>old(X)))))&
(((happy(alice)&rich(alice)))<=>(?[X]:((~humble(X)|wise(X)))))&
((?[X]:((happy(X)|curious(X))))=>((~brave(lucy)<~>wise(lucy))))&
(![X]:((tall(X)<~>~rich(X))<=>(~happy(X)<~>~brave(X))))&
(![X]:(brave(X)=>(happy(X)<~>~kind(X))))&
(((~curious(lucy)&~tall(lucy)))<=>(~strong(alice)))&
(![X]:((quiet(X)&tall(X))<=>(patient(X)<~>rich(X))))&
(![X]:(kind(X)=>tall(X)))&
(![X]:((~kind(X)<~>funny(X))<=>old(X)))&
((tall(lucy)<~>happy(lucy)))&
(happy(alice))&
(~wise(john))&
((~brave(fred)<~>curious(fred)))&
(?[X]:((~happy(X)&curious(X))))&
(?[X]:((~happy(X)<~>rich(X))))&
(?[X]:(~wise(X))) | ~brave(alice) | [
"p3",
"p4",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6909845800318204700922006
% SZS output start Proof for 6909845800318204700922006
4. ! [X0] : (~kind(X0) <=> (~funny(X0) | curious(X0))) [input p3]
5. ? [X0] : (strong(X0) & ~strong(X0)) <=> ? [X0] : (creative(X0) | funny(X0)) [input p4]
12. ! [X0] : (brave(X0) => (happy(X0) <~> ~kind(X0))) [input p11]
18. happy(alice) [input p17]
24. brave(alice) [input hypothesis]
25. ? [X0] : (strong(X0) & ~strong(X0)) <=> ? [X1] : (creative(X1) | funny(X1)) [rectify 5]
34. ! [X0] : ((happy(X0) <~> ~kind(X0)) | ~brave(X0)) [ennf transformation 12]
36. ! [X0] : ((~kind(X0) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | kind(X0))) [nnf transformation 4]
37. ! [X0] : ((~kind(X0) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | kind(X0))) [flattening 36]
38. (? [X0] : (strong(X0) & ~strong(X0)) | ! [X1] : (~creative(X1) & ~funny(X1))) & (? [X1] : (creative(X1) | funny(X1)) | ! [X0] : (~strong(X0) | strong(X0))) [nnf transformation 25]
39. (? [X0] : (strong(X0) & ~strong(X0)) | ! [X1] : (~creative(X1) & ~funny(X1))) & (? [X2] : (creative(X2) | funny(X2)) | ! [X3] : (~strong(X3) | strong(X3))) [rectify 38]
40. ? [X0] : (strong(X0) & ~strong(X0)) => (strong(sK0) & ~strong(sK0)) [choice axiom]
41. ? [X2] : (creative(X2) | funny(X2)) => (creative(sK1) | funny(sK1)) [choice axiom]
42. ((strong(sK0) & ~strong(sK0)) | ! [X1] : (~creative(X1) & ~funny(X1))) & ((creative(sK1) | funny(sK1)) | ! [X3] : (~strong(X3) | strong(X3))) [skolemisation 39,41,40]
59. ! [X0] : (((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | ~brave(X0)) [nnf transformation 34]
81. ~kind(X0) | funny(X0) [cnf transformation 37]
83. ~strong(sK0) | ~funny(X1) [cnf transformation 42]
85. strong(sK0) | ~funny(X1) [cnf transformation 42]
118. ~happy(X0) | kind(X0) | ~brave(X0) [cnf transformation 59]
135. happy(alice) [cnf transformation 18]
144. brave(alice) [cnf transformation 24]
150. 2 <=> strong(sK0) [avatar definition]
155. 3 <=> ! [X1] : ~funny(X1) [avatar definition]
156. ~funny(X1) <- (3) [avatar component clause 155]
157. 3 | 2 [avatar split clause 85,150,155]
159. 3 | ~2 [avatar split clause 83,150,155]
221. 17 <=> happy(alice) [avatar definition]
223. happy(alice) <- (17) [avatar component clause 221]
272. 17 [avatar split clause 135,221]
305. kind(alice) | ~brave(alice) <- (17) [resolution 118,223]
306. kind(alice) <- (17) [subsumption resolution 305,144]
310. funny(alice) <- (17) [resolution 306,81]
311. $false <- (3, 17) [subsumption resolution 310,156]
312. ~3 | ~17 [avatar contradiction clause 311]
313. $false [avatar sat refutation 157,159,272,312]
% SZS output end Proof for 6909845800318204700922006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not rich is both not old and old. Everyone who is both not curious and not happy is generous or not wise. Everyone who is both not strong and not generous is calm and vice versa. Everyone who is not humble or patient is not wise or brave and vice versa. If someone is not quiet or not wise then mary is both not humble and humble. If someone is both not old and tall then someone is either brave or not tall and vice versa. If someone is either kind or not happy then someone is curious. If someone is curious or rich then alice is curious or not strong. Everyone who is patient or humble is not kind. Everyone who is not funny or wise is either not old or not generous. Everyone who is either strong or not calm is not humble and vice versa. If someone is either humble or kind then mary is both not quiet and not creative and vice versa. If john is either tall or kind then lucy is not wise or not generous and vice versa. Everyone who is either humble or calm is strong or not strong. Everyone who is creative or not rich is both generous and old. Someone is patient or not rich. Susan is not calm or not rich. Lucy is not funny or strong. Someone is not kind. | Lucy is rich. | entailment | (![X]:((creative(X)<~>~rich(X))=>(~old(X)&old(X))))&
(![X]:((~curious(X)&~happy(X))=>(generous(X)|~wise(X))))&
(![X]:((~strong(X)&~generous(X))<=>calm(X)))&
(![X]:((~humble(X)|patient(X))<=>(~wise(X)|brave(X))))&
((?[X]:((~quiet(X)|~wise(X))))=>((~humble(mary)&humble(mary))))&
((?[X]:((~old(X)&tall(X))))<=>(?[X]:((brave(X)<~>~tall(X)))))&
((?[X]:((kind(X)<~>~happy(X))))=>(?[X]:(curious(X))))&
((?[X]:((curious(X)|rich(X))))=>((curious(alice)|~strong(alice))))&
(![X]:((patient(X)|humble(X))=>~kind(X)))&
(![X]:((~funny(X)|wise(X))=>(~old(X)<~>~generous(X))))&
(![X]:((strong(X)<~>~calm(X))<=>~humble(X)))&
((?[X]:((humble(X)<~>kind(X))))<=>((~quiet(mary)&~creative(mary))))&
(((tall(john)<~>kind(john)))<=>((~wise(lucy)|~generous(lucy))))&
(![X]:((humble(X)<~>calm(X))=>(strong(X)|~strong(X))))&
(![X]:((creative(X)|~rich(X))=>(generous(X)&old(X))))&
(?[X]:((patient(X)|~rich(X))))&
((~calm(susan)|~rich(susan)))&
((~funny(lucy)|strong(lucy)))&
(?[X]:(~kind(X))) | rich(lucy) | [
"p0",
"p2",
"p4",
"p8",
"p9",
"p10",
"p11",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 124495670501656092199843
% SZS output start Proof for 124495670501656092199843
1. ! [X0] : ((creative(X0) <~> ~rich(X0)) => (old(X0) & ~old(X0))) [input p0]
3. ! [X0] : ((~generous(X0) & ~strong(X0)) <=> calm(X0)) [input p2]
5. ? [X0] : (~wise(X0) | ~quiet(X0)) => (humble(mary) & ~humble(mary)) [input p4]
9. ! [X0] : ((humble(X0) | patient(X0)) => ~kind(X0)) [input p8]
10. ! [X0] : ((wise(X0) | ~funny(X0)) => (~old(X0) <~> ~generous(X0))) [input p9]
11. ! [X0] : ((strong(X0) <~> ~calm(X0)) <=> ~humble(X0)) [input p10]
12. ? [X0] : (humble(X0) <~> kind(X0)) <=> (~creative(mary) & ~quiet(mary)) [input p11]
15. ! [X0] : ((~rich(X0) | creative(X0)) => (old(X0) & generous(X0))) [input p14]
18. strong(lucy) | ~funny(lucy) [input p17]
20. ~rich(lucy) [input hypothesis]
23. ! [X0] : ((old(X0) & ~old(X0)) | (creative(X0) <=> ~rich(X0))) [ennf transformation 1]
26. (humble(mary) & ~humble(mary)) | ! [X0] : (wise(X0) & quiet(X0)) [ennf transformation 5]
30. ! [X0] : (~kind(X0) | (~humble(X0) & ~patient(X0))) [ennf transformation 9]
31. ! [X0] : ((~old(X0) <~> ~generous(X0)) | (~wise(X0) & funny(X0))) [ennf transformation 10]
34. ! [X0] : ((old(X0) & generous(X0)) | (rich(X0) & ~creative(X0))) [ennf transformation 15]
35. ! [X0] : ((old(X0) & ~old(X0)) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [nnf transformation 23]
36. ! [X0] : (((~generous(X0) & ~strong(X0)) | ~calm(X0)) & (calm(X0) | (generous(X0) | strong(X0)))) [nnf transformation 3]
37. ! [X0] : (((~generous(X0) & ~strong(X0)) | ~calm(X0)) & (calm(X0) | generous(X0) | strong(X0))) [flattening 36]
49. ! [X0] : (((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | (~wise(X0) & funny(X0))) [nnf transformation 31]
50. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | humble(X0)) & (~humble(X0) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [nnf transformation 11]
51. (? [X0] : ((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (creative(mary) | quiet(mary))) & ((~creative(mary) & ~quiet(mary)) | ! [X0] : ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) [nnf transformation 12]
52. (? [X0] : ((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | creative(mary) | quiet(mary)) & ((~creative(mary) & ~quiet(mary)) | ! [X0] : ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) [flattening 51]
53. (? [X0] : ((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | creative(mary) | quiet(mary)) & ((~creative(mary) & ~quiet(mary)) | ! [X1] : ((humble(X1) | ~kind(X1)) & (kind(X1) | ~humble(X1)))) [rectify 52]
54. ? [X0] : ((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) => ((~kind(sK3) | ~humble(sK3)) & (kind(sK3) | humble(sK3))) [choice axiom]
55. (((~kind(sK3) | ~humble(sK3)) & (kind(sK3) | humble(sK3))) | creative(mary) | quiet(mary)) & ((~creative(mary) & ~quiet(mary)) | ! [X1] : ((humble(X1) | ~kind(X1)) & (kind(X1) | ~humble(X1)))) [skolemisation 53,54]
64. ~old(X0) | creative(X0) | rich(X0) [cnf transformation 35]
66. old(X0) | creative(X0) | rich(X0) [cnf transformation 35]
69. ~calm(X0) | ~strong(X0) [cnf transformation 37]
75. ~humble(mary) | quiet(X0) [cnf transformation 26]
77. humble(mary) | quiet(X0) [cnf transformation 26]
90. ~kind(X0) | ~humble(X0) [cnf transformation 30]
91. ~generous(X0) | ~old(X0) | funny(X0) [cnf transformation 49]
98. calm(X0) | ~strong(X0) | humble(X0) [cnf transformation 50]
99. ~quiet(mary) | kind(X1) | ~humble(X1) [cnf transformation 55]
114. generous(X0) | rich(X0) [cnf transformation 34]
115. ~creative(X0) | old(X0) [cnf transformation 34]
119. strong(lucy) | ~funny(lucy) [cnf transformation 18]
121. ~rich(lucy) [cnf transformation 20]
122. rich(X0) | creative(X0) [subsumption resolution 64,66]
128. 2 <=> humble(mary) [avatar definition]
133. 3 <=> ! [X0] : quiet(X0) [avatar definition]
134. quiet(X0) <- (3) [avatar component clause 133]
135. 3 | 2 [avatar split clause 77,128,133]
137. 3 | ~2 [avatar split clause 75,128,133]
197. ~strong(X0) | humble(X0) [subsumption resolution 98,69]
200. 18 <=> quiet(mary) [avatar definition]
201. ~quiet(mary) <- (~18) [avatar component clause 200]
223. 23 <=> ! [X1] : ~humble(X1) [avatar definition]
224. ~humble(X1) <- (23) [avatar component clause 223]
228. ~quiet(mary) | ~humble(X1) [subsumption resolution 99,90]
229. 23 | ~18 [avatar split clause 228,200,223]
231. 24 <=> generous(lucy) [avatar definition]
232. ~generous(lucy) <- (~24) [avatar component clause 231]
233. generous(lucy) <- (24) [avatar component clause 231]
271. 32 <=> funny(lucy) [avatar definition]
275. 33 <=> strong(lucy) [avatar definition]
277. strong(lucy) <- (33) [avatar component clause 275]
278. ~32 | 33 [avatar split clause 119,275,271]
279. $false <- (3, ~18) [resolution 201,134]
280. ~3 | 18 [avatar contradiction clause 279]
283. rich(lucy) <- (~24) [resolution 114,232]
284. $false <- (~24) [subsumption resolution 283,121]
285. 24 [avatar contradiction clause 284]
289. creative(lucy) [resolution 122,121]
293. old(lucy) [resolution 289,115]
331. ~old(lucy) | funny(lucy) <- (24) [resolution 91,233]
334. funny(lucy) <- (24) [subsumption resolution 331,293]
338. 32 | ~24 [avatar split clause 334,231,271]
339. humble(lucy) <- (33) [resolution 277,197]
340. $false <- (23, 33) [subsumption resolution 339,224]
341. ~23 | ~33 [avatar contradiction clause 340]
342. $false [avatar sat refutation 135,137,229,278,280,285,338,341]
% SZS output end Proof for 124495670501656092199843
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is both brave and not rich. Everyone who is both not tall and quiet is tall and vice versa. Everyone who is happy is not quiet and vice versa. Everyone who is not patient or happy is both not rich and creative and vice versa. If susan is not curious or not brave then john is both not brave and old. If susan is generous or not strong then someone is not old and vice versa. If someone is both generous and not humble then someone is either not brave or happy and vice versa. If alice is not creative or rich then someone is not curious or strong and vice versa. If someone is either funny or not quiet then fred is not patient and vice versa. Everyone who is either happy or calm is both not tall and generous and vice versa. Everyone who is humble is either generous or not humble and vice versa. Everyone who is both calm and not tall is not patient and vice versa. If someone is either not brave or not humble then someone is not calm or humble and vice versa. If alice is not creative then someone is both rich and curious. Susan is both curious and not kind. John is not tall or patient. Someone is creative or not generous. Alice is either not happy or creative. Susan is not brave or quiet. Someone is patient or strong. Fred is both old and curious. | John is not calm. | entailment | (![X]:(brave(X)=>(brave(X)&~rich(X))))&
(![X]:((~tall(X)&quiet(X))<=>tall(X)))&
(![X]:(happy(X)<=>~quiet(X)))&
(![X]:((~patient(X)|happy(X))<=>(~rich(X)&creative(X))))&
(((~curious(susan)|~brave(susan)))=>((~brave(john)&old(john))))&
(((generous(susan)|~strong(susan)))<=>(?[X]:(~old(X))))&
((?[X]:((generous(X)&~humble(X))))<=>(?[X]:((~brave(X)<~>happy(X)))))&
(((~creative(alice)|rich(alice)))<=>(?[X]:((~curious(X)|strong(X)))))&
((?[X]:((funny(X)<~>~quiet(X))))<=>(~patient(fred)))&
(![X]:((happy(X)<~>calm(X))<=>(~tall(X)&generous(X))))&
(![X]:(humble(X)<=>(generous(X)<~>~humble(X))))&
(![X]:((calm(X)&~tall(X))<=>~patient(X)))&
((?[X]:((~brave(X)<~>~humble(X))))<=>(?[X]:((~calm(X)|humble(X)))))&
((~creative(alice))=>(?[X]:((rich(X)&curious(X)))))&
((curious(susan)&~kind(susan)))&
((~tall(john)|patient(john)))&
(?[X]:((creative(X)|~generous(X))))&
((~happy(alice)<~>creative(alice)))&
((~brave(susan)|quiet(susan)))&
(?[X]:((patient(X)|strong(X))))&
((old(fred)&curious(fred))) | ~calm(john) | [
"p1",
"p2",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3579224605403930635244626
% SZS output start Proof for 3579224605403930635244626
2. ! [X0] : ((quiet(X0) & ~tall(X0)) <=> tall(X0)) [input p1]
3. ! [X0] : (happy(X0) <=> ~quiet(X0)) [input p2]
10. ! [X0] : ((happy(X0) <~> calm(X0)) <=> (generous(X0) & ~tall(X0))) [input p9]
11. ! [X0] : (humble(X0) <=> (generous(X0) <~> ~humble(X0))) [input p10]
22. calm(john) [input hypothesis]
29. ! [X0] : (((quiet(X0) & ~tall(X0)) | ~tall(X0)) & (tall(X0) | (~quiet(X0) | tall(X0)))) [nnf transformation 2]
30. ! [X0] : (((quiet(X0) & ~tall(X0)) | ~tall(X0)) & (tall(X0) | ~quiet(X0) | tall(X0))) [flattening 29]
31. ! [X0] : ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))) [nnf transformation 3]
53. ! [X0] : ((((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))))) [nnf transformation 10]
54. ! [X0] : ((((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))))) [flattening 53]
55. ! [X0] : ((humble(X0) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0)))) & (((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | ~humble(X0))) [nnf transformation 11]
72. tall(X0) | ~quiet(X0) | tall(X0) [cnf transformation 30]
73. ~tall(X0) | ~tall(X0) [cnf transformation 30]
76. happy(X0) | quiet(X0) [cnf transformation 31]
108. ~calm(X0) | ~happy(X0) | ~generous(X0) | tall(X0) [cnf transformation 54]
109. ~humble(X0) | generous(X0) | ~humble(X0) [cnf transformation 55]
112. humble(X0) | generous(X0) | humble(X0) [cnf transformation 55]
133. calm(john) [cnf transformation 22]
134. ~humble(X0) | generous(X0) [duplicate literal removal 109]
135. humble(X0) | generous(X0) [duplicate literal removal 112]
136. tall(X0) | ~quiet(X0) [duplicate literal removal 72]
137. ~tall(X0) [duplicate literal removal 73]
138. ~quiet(X0) [subsumption resolution 136,137]
139. happy(X0) [subsumption resolution 76,138]
223. ~calm(X0) | ~generous(X0) | tall(X0) [subsumption resolution 108,139]
224. ~calm(X0) | ~generous(X0) [subsumption resolution 223,137]
226. generous(X0) [subsumption resolution 134,135]
273. ~generous(john) [resolution 224,133]
275. $false [subsumption resolution 273,226]
% SZS output end Proof for 3579224605403930635244626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then paul is humble. If john is not tall then alice is both not curious and creative. Everyone who is not strong or not old is either tall or not rich and vice versa. Everyone who is either generous or not strong is both not funny and not humble. If john is both quiet and not curious then someone is curious and vice versa. If someone is not patient then someone is both not funny and generous and vice versa. If someone is either not tall or brave then someone is both humble and curious. Everyone who is not patient or not generous is funny or curious and vice versa. If alice is either calm or brave then someone is old and vice versa. If alice is both not generous and not creative then someone is either not tall or not humble. Everyone who is not strong or generous is both tall and not humble and vice versa. If alice is curious then someone is both happy and not wise and vice versa. If john is both not creative and not funny then fred is either not tall or strong. If someone is humble or not curious then someone is not curious and vice versa. If someone is happy or funny then mary is not strong and vice versa. If someone is either tall or not curious then john is not quiet. Alice is either creative or brave. Alice is not creative. John is not brave or not humble. Someone is brave. Fred is both not wise and not rich. Lucy is not humble. Someone is happy. Someone is either not patient or wise. | Fred is not strong. | contradiction | ((?[X]:(~happy(X)))=>(humble(paul)))&
((~tall(john))=>((~curious(alice)&creative(alice))))&
(![X]:((~strong(X)|~old(X))<=>(tall(X)<~>~rich(X))))&
(![X]:((generous(X)<~>~strong(X))=>(~funny(X)&~humble(X))))&
(((quiet(john)&~curious(john)))<=>(?[X]:(curious(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~funny(X)&generous(X)))))&
((?[X]:((~tall(X)<~>brave(X))))=>(?[X]:((humble(X)&curious(X)))))&
(![X]:((~patient(X)|~generous(X))<=>(funny(X)|curious(X))))&
(((calm(alice)<~>brave(alice)))<=>(?[X]:(old(X))))&
(((~generous(alice)&~creative(alice)))=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((~strong(X)|generous(X))<=>(tall(X)&~humble(X))))&
((curious(alice))<=>(?[X]:((happy(X)&~wise(X)))))&
(((~creative(john)&~funny(john)))=>((~tall(fred)<~>strong(fred))))&
((?[X]:((humble(X)|~curious(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((happy(X)|funny(X))))<=>(~strong(mary)))&
((?[X]:((tall(X)<~>~curious(X))))=>(~quiet(john)))&
((creative(alice)<~>brave(alice)))&
(~creative(alice))&
((~brave(john)|~humble(john)))&
(?[X]:(brave(X)))&
((~wise(fred)&~rich(fred)))&
(~humble(lucy))&
(?[X]:(happy(X)))&
(?[X]:((~patient(X)<~>wise(X)))) | ~strong(fred) | [
"p2",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1311722460971091931718735
% SZS output start Proof for 1311722460971091931718735
3. ! [X0] : ((~old(X0) | ~strong(X0)) <=> (tall(X0) <~> ~rich(X0))) [input p2]
11. ! [X0] : ((generous(X0) | ~strong(X0)) <=> (~humble(X0) & tall(X0))) [input p10]
21. ~rich(fred) & ~wise(fred) [input p20]
25. ~strong(fred) [input hypothesis]
38. ! [X0] : (((~old(X0) | ~strong(X0)) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) & (((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | (old(X0) & strong(X0)))) [nnf transformation 3]
39. ! [X0] : ((~old(X0) | ~strong(X0) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) & (((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | (old(X0) & strong(X0)))) [flattening 38]
64. ! [X0] : (((generous(X0) | ~strong(X0)) | (humble(X0) | ~tall(X0))) & ((~humble(X0) & tall(X0)) | (~generous(X0) & strong(X0)))) [nnf transformation 11]
65. ! [X0] : ((generous(X0) | ~strong(X0) | humble(X0) | ~tall(X0)) & ((~humble(X0) & tall(X0)) | (~generous(X0) & strong(X0)))) [flattening 64]
94. ~tall(X0) | rich(X0) | strong(X0) [cnf transformation 39]
122. strong(X0) | tall(X0) [cnf transformation 65]
146. ~rich(fred) [cnf transformation 21]
151. ~strong(fred) [cnf transformation 25]
288. 31 <=> tall(fred) [avatar definition]
290. tall(fred) <- (31) [avatar component clause 288]
294. 32 <=> strong(fred) [avatar definition]
295. ~strong(fred) <- (~32) [avatar component clause 294]
370. ~32 [avatar split clause 151,294]
375. tall(fred) <- (~32) [resolution 122,295]
377. 31 | 32 [avatar split clause 375,294,288]
400. rich(fred) | strong(fred) <- (31) [resolution 94,290]
413. strong(fred) <- (31) [subsumption resolution 400,146]
414. $false <- (31, ~32) [subsumption resolution 413,295]
415. ~31 | 32 [avatar contradiction clause 414]
435. $false [avatar sat refutation 370,377,415]
% SZS output end Proof for 1311722460971091931718735
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not creative is both not funny and not rich and vice versa.
Everyone who is not brave or generous is old or happy.
Everyone who is both generous and not kind is either not tall or generous.
If alice is curious or not quiet then mary is either not calm or creative and vice versa.
If lucy is both not curious and not tall then someone is both tall and kind.
If someone is kind or not calm then someone is strong or humble and vice versa.
Everyone who is generous is both not brave and not creative.
Everyone who is both not wise and not calm is both not rich and calm.
If susan is both humble and not generous then mary is both generous and not happy.
If alice is either quiet or not happy then someone is not tall and vice versa.
Everyone who is both not happy and not humble is both not wise and happy and vice versa.
If someone is both not creative and not old then fred is not old or happy and vice versa.
Everyone who is calm or kind is both not wise and humble.
Everyone who is both not kind and calm is not brave or patient and vice versa.
Everyone who is calm or brave is both wise and old.
If john is not patient then someone is both not calm and old and vice versa.
Lucy is both not happy and not curious.
Lucy is not brave or not curious.
Someone is both strong and not tall.
Mary is either not brave or quiet.
Paul is not quiet or tall.
Fred is either not wise or creative. | Mary is generous. | contradiction | (![X]:((tall(X)&~creative(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~brave(X)|generous(X))=>(old(X)|happy(X))))&
(![X]:((generous(X)&~kind(X))=>(~tall(X)<~>generous(X))))&
(((curious(alice)|~quiet(alice)))<=>((~calm(mary)<~>creative(mary))))&
(((~curious(lucy)&~tall(lucy)))=>(?[X]:((tall(X)&kind(X)))))&
((?[X]:((kind(X)|~calm(X))))<=>(?[X]:((strong(X)|humble(X)))))&
(![X]:(generous(X)=>(~brave(X)&~creative(X))))&
(![X]:((~wise(X)&~calm(X))=>(~rich(X)&calm(X))))&
(((humble(susan)&~generous(susan)))=>((generous(mary)&~happy(mary))))&
(((quiet(alice)<~>~happy(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)&~humble(X))<=>(~wise(X)&happy(X))))&
((?[X]:((~creative(X)&~old(X))))<=>((~old(fred)|happy(fred))))&
(![X]:((calm(X)|kind(X))=>(~wise(X)&humble(X))))&
(![X]:((~kind(X)&calm(X))<=>(~brave(X)|patient(X))))&
(![X]:((calm(X)|brave(X))=>(wise(X)&old(X))))&
((~patient(john))<=>(?[X]:((~calm(X)&old(X)))))&
((~happy(lucy)&~curious(lucy)))&
((~brave(lucy)|~curious(lucy)))&
(?[X]:((strong(X)&~tall(X))))&
((~brave(mary)<~>quiet(mary)))&
((~quiet(paul)|tall(paul)))&
((~wise(fred)<~>creative(fred))) | generous(mary) | [
"p6",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4154493762939245588820443
% SZS output start Proof for 4154493762939245588820443
7. ! [X0] : (generous(X0) => (~creative(X0) & ~brave(X0))) [input p6]
8. ! [X0] : ((~calm(X0) & ~wise(X0)) => (calm(X0) & ~rich(X0))) [input p7]
13. ! [X0] : ((kind(X0) | calm(X0)) => (humble(X0) & ~wise(X0))) [input p12]
14. ! [X0] : ((calm(X0) & ~kind(X0)) <=> (patient(X0) | ~brave(X0))) [input p13]
15. ! [X0] : ((brave(X0) | calm(X0)) => (old(X0) & wise(X0))) [input p14]
23. generous(mary) [input hypothesis]
31. ! [X0] : ((~creative(X0) & ~brave(X0)) | ~generous(X0)) [ennf transformation 7]
32. ! [X0] : ((calm(X0) & ~rich(X0)) | (calm(X0) | wise(X0))) [ennf transformation 8]
33. ! [X0] : ((calm(X0) & ~rich(X0)) | calm(X0) | wise(X0)) [flattening 32]
36. ! [X0] : ((humble(X0) & ~wise(X0)) | (~kind(X0) & ~calm(X0))) [ennf transformation 13]
37. ! [X0] : ((old(X0) & wise(X0)) | (~brave(X0) & ~calm(X0))) [ennf transformation 15]
61. ! [X0] : (((calm(X0) & ~kind(X0)) | (~patient(X0) & brave(X0))) & ((patient(X0) | ~brave(X0)) | (~calm(X0) | kind(X0)))) [nnf transformation 14]
62. ! [X0] : (((calm(X0) & ~kind(X0)) | (~patient(X0) & brave(X0))) & (patient(X0) | ~brave(X0) | ~calm(X0) | kind(X0))) [flattening 61]
91. ~generous(X0) | ~brave(X0) [cnf transformation 31]
94. calm(X0) | calm(X0) | wise(X0) [cnf transformation 33]
110. ~wise(X0) | ~calm(X0) [cnf transformation 36]
117. calm(X0) | brave(X0) [cnf transformation 62]
119. wise(X0) | ~calm(X0) [cnf transformation 37]
136. generous(mary) [cnf transformation 23]
139. calm(X0) | wise(X0) [duplicate literal removal 94]
227. 20 <=> generous(mary) [avatar definition]
229. generous(mary) <- (20) [avatar component clause 227]
270. wise(X0) [subsumption resolution 119,139]
315. 20 [avatar split clause 136,227]
316. ~brave(mary) <- (20) [resolution 91,229]
318. ~calm(X0) [resolution 110,270]
324. brave(X0) [resolution 117,318]
330. $false <- (20) [subsumption resolution 316,324]
331. ~20 [avatar contradiction clause 330]
332. $false [avatar sat refutation 315,331]
% SZS output end Proof for 4154493762939245588820443
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and happy then someone is brave or quiet. Everyone who is not happy or not rich is not patient or curious and vice versa. Everyone who is not humble is either kind or humble. Everyone who is both humble and patient is quiet and vice versa. If someone is not rich then someone is either not curious or not old and vice versa. If john is not humble or quiet then someone is both funny and not kind and vice versa. Everyone who is both wise and patient is not wise and vice versa. If susan is both not wise and not rich then someone is old and vice versa. Everyone who is both not wise and quiet is quiet and vice versa. Everyone who is both patient and not old is both funny and not strong. Everyone who is not wise or tall is both not quiet and happy. If lucy is strong or not humble then mary is either old or brave and vice versa. Everyone who is either rich or strong is both happy and brave and vice versa. Everyone who is not calm is both funny and not patient. Everyone who is not happy is either not strong or not quiet. Everyone who is both curious and calm is both creative and strong and vice versa. Someone is strong or not brave. Lucy is curious. Fred is either not rich or kind. Someone is not rich or patient. Someone is both wise and brave. Someone is either not happy or not rich. Paul is either not brave or not quiet. | Lucy is quiet. | contradiction | ((?[X]:((patient(X)&happy(X))))=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:((~happy(X)|~rich(X))<=>(~patient(X)|curious(X))))&
(![X]:(~humble(X)=>(kind(X)<~>humble(X))))&
(![X]:((humble(X)&patient(X))<=>quiet(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((~curious(X)<~>~old(X)))))&
(((~humble(john)|quiet(john)))<=>(?[X]:((funny(X)&~kind(X)))))&
(![X]:((wise(X)&patient(X))<=>~wise(X)))&
(((~wise(susan)&~rich(susan)))<=>(?[X]:(old(X))))&
(![X]:((~wise(X)&quiet(X))<=>quiet(X)))&
(![X]:((patient(X)&~old(X))=>(funny(X)&~strong(X))))&
(![X]:((~wise(X)|tall(X))=>(~quiet(X)&happy(X))))&
(((strong(lucy)|~humble(lucy)))<=>((old(mary)<~>brave(mary))))&
(![X]:((rich(X)<~>strong(X))<=>(happy(X)&brave(X))))&
(![X]:(~calm(X)=>(funny(X)&~patient(X))))&
(![X]:(~happy(X)=>(~strong(X)<~>~quiet(X))))&
(![X]:((curious(X)&calm(X))<=>(creative(X)&strong(X))))&
(?[X]:((strong(X)|~brave(X))))&
(curious(lucy))&
((~rich(fred)<~>kind(fred)))&
(?[X]:((~rich(X)|patient(X))))&
(?[X]:((wise(X)&brave(X))))&
(?[X]:((~happy(X)<~>~rich(X))))&
((~brave(paul)<~>~quiet(paul))) | quiet(lucy) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 497857393890626847667297
% SZS output start Proof for 497857393890626847667297
7. ! [X0] : ((patient(X0) & wise(X0)) <=> ~wise(X0)) [input p6]
9. ! [X0] : ((quiet(X0) & ~wise(X0)) <=> quiet(X0)) [input p8]
24. quiet(lucy) [input hypothesis]
53. ! [X0] : (((patient(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | (~patient(X0) | ~wise(X0)))) [nnf transformation 7]
54. ! [X0] : (((patient(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | ~patient(X0) | ~wise(X0))) [flattening 53]
60. ! [X0] : (((quiet(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | (~quiet(X0) | wise(X0)))) [nnf transformation 9]
61. ! [X0] : (((quiet(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | ~quiet(X0) | wise(X0))) [flattening 60]
100. wise(X0) | wise(X0) [cnf transformation 54]
106. ~wise(X0) | ~quiet(X0) [cnf transformation 61]
143. quiet(lucy) [cnf transformation 24]
145. wise(X0) [duplicate literal removal 100]
219. ~quiet(X0) [subsumption resolution 106,145]
274. $false [subsumption resolution 143,219]
% SZS output end Proof for 497857393890626847667297
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is not creative or patient.
Everyone who is both not humble and not generous is either not calm or not kind and vice versa.
If fred is either humble or not old then someone is both generous and not rich and vice versa.
Everyone who is not creative is strong or tall and vice versa.
If someone is either not rich or not quiet then lucy is not kind and vice versa.
Everyone who is not quiet or not tall is either not kind or humble.
Everyone who is generous is both curious and tall and vice versa.
If alice is humble then lucy is either not creative or calm.
Everyone who is both not brave and kind is creative.
If alice is not wise then someone is not funny.
If someone is not creative then someone is not brave and vice versa.
Everyone who is both quiet and not quiet is both not creative and not brave and vice versa.
Everyone who is either not calm or not creative is either quiet or kind and vice versa.
If paul is not wise then paul is either not funny or wise and vice versa.
Everyone who is either kind or humble is either not strong or humble.
If someone is not happy or tall then john is brave or not creative.
Someone is either funny or generous.
Someone is brave.
Someone is patient.
Someone is funny.
Susan is both wise and generous.
Mary is not creative or quiet.
Someone is happy. | John is humble. | neutral | (![X]:(~rich(X)=>(~creative(X)|patient(X))))&
(![X]:((~humble(X)&~generous(X))<=>(~calm(X)<~>~kind(X))))&
(((humble(fred)<~>~old(fred)))<=>(?[X]:((generous(X)&~rich(X)))))&
(![X]:(~creative(X)<=>(strong(X)|tall(X))))&
((?[X]:((~rich(X)<~>~quiet(X))))<=>(~kind(lucy)))&
(![X]:((~quiet(X)|~tall(X))=>(~kind(X)<~>humble(X))))&
(![X]:(generous(X)<=>(curious(X)&tall(X))))&
((humble(alice))=>((~creative(lucy)<~>calm(lucy))))&
(![X]:((~brave(X)&kind(X))=>creative(X)))&
((~wise(alice))=>(?[X]:(~funny(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~brave(X))))&
(![X]:((quiet(X)&~quiet(X))<=>(~creative(X)&~brave(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(quiet(X)<~>kind(X))))&
((~wise(paul))<=>((~funny(paul)<~>wise(paul))))&
(![X]:((kind(X)<~>humble(X))=>(~strong(X)<~>humble(X))))&
((?[X]:((~happy(X)|tall(X))))=>((brave(john)|~creative(john))))&
(?[X]:((funny(X)<~>generous(X))))&
(?[X]:(brave(X)))&
(?[X]:(patient(X)))&
(?[X]:(funny(X)))&
((wise(susan)&generous(susan)))&
((~creative(mary)|quiet(mary)))&
(?[X]:(happy(X))) | humble(john) | [] | null | 0 |
Everyone who is either not old or wise is either generous or not generous.
Everyone who is rich is quiet or happy and vice versa.
Everyone who is either strong or not humble is both happy and strong.
If john is either not wise or not humble then paul is funny or humble.
Everyone who is both not rich and not happy is both not generous and rich.
Everyone who is both humble and curious is both patient and not brave.
Everyone who is not patient or not strong is not creative and vice versa.
If lucy is either not rich or not wise then paul is rich or old and vice versa.
If fred is either curious or funny then john is not brave.
Everyone who is either not calm or not strong is patient or not curious and vice versa.
If alice is strong or not calm then alice is both wise and not tall and vice versa.
If mary is not patient then fred is both patient and tall and vice versa.
If someone is not creative then fred is strong or not patient.
Everyone who is either strong or kind is not humble and vice versa.
Everyone who is not curious is either not wise or not tall and vice versa.
Someone is either patient or not patient.
Someone is either strong or not creative.
Susan is both not kind and not happy.
Someone is not creative.
Someone is old.
Someone is either not generous or tall.
Someone is both rich and quiet. | Mary is not rich. | contradiction | (![X]:((~old(X)<~>wise(X))=>(generous(X)<~>~generous(X))))&
(![X]:(rich(X)<=>(quiet(X)|happy(X))))&
(![X]:((strong(X)<~>~humble(X))=>(happy(X)&strong(X))))&
(((~wise(john)<~>~humble(john)))=>((funny(paul)|humble(paul))))&
(![X]:((~rich(X)&~happy(X))=>(~generous(X)&rich(X))))&
(![X]:((humble(X)&curious(X))=>(patient(X)&~brave(X))))&
(![X]:((~patient(X)|~strong(X))<=>~creative(X)))&
(((~rich(lucy)<~>~wise(lucy)))<=>((rich(paul)|old(paul))))&
(((curious(fred)<~>funny(fred)))=>(~brave(john)))&
(![X]:((~calm(X)<~>~strong(X))<=>(patient(X)|~curious(X))))&
(((strong(alice)|~calm(alice)))<=>((wise(alice)&~tall(alice))))&
((~patient(mary))<=>((patient(fred)&tall(fred))))&
((?[X]:(~creative(X)))=>((strong(fred)|~patient(fred))))&
(![X]:((strong(X)<~>kind(X))<=>~humble(X)))&
(![X]:(~curious(X)<=>(~wise(X)<~>~tall(X))))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:((strong(X)<~>~creative(X))))&
((~kind(susan)&~happy(susan)))&
(?[X]:(~creative(X)))&
(?[X]:(old(X)))&
(?[X]:((~generous(X)<~>tall(X))))&
(?[X]:((rich(X)&quiet(X)))) | ~rich(mary) | [
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4577728367075726781486440
% SZS output start Proof for 4577728367075726781486440
2. ! [X0] : (rich(X0) <=> (happy(X0) | quiet(X0))) [input p1]
5. ! [X0] : ((~happy(X0) & ~rich(X0)) => (rich(X0) & ~generous(X0))) [input p4]
23. ~rich(mary) [input hypothesis]
29. ! [X0] : ((rich(X0) & ~generous(X0)) | (happy(X0) | rich(X0))) [ennf transformation 5]
30. ! [X0] : ((rich(X0) & ~generous(X0)) | happy(X0) | rich(X0)) [flattening 29]
36. ! [X0] : ((rich(X0) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | ~rich(X0))) [nnf transformation 2]
37. ! [X0] : ((rich(X0) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~rich(X0))) [flattening 36]
72. rich(X0) | ~happy(X0) [cnf transformation 37]
78. rich(X0) | happy(X0) | rich(X0) [cnf transformation 30]
124. ~rich(mary) [cnf transformation 23]
125. rich(X0) | happy(X0) [duplicate literal removal 78]
127. rich(X0) [subsumption resolution 125,72]
206. $false [subsumption resolution 124,127]
% SZS output end Proof for 4577728367075726781486440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and wise is quiet or kind.
Everyone who is both not creative and not quiet is not strong or not humble and vice versa.
If paul is both strong and kind then someone is either funny or rich.
If someone is either not brave or not old then someone is both not brave and not generous.
Everyone who is either quiet or tall is either not happy or generous and vice versa.
If someone is generous or not funny then someone is both not tall and not funny.
Everyone who is calm or kind is both not brave and humble.
Everyone who is either curious or humble is either funny or brave.
Everyone who is both tall and creative is both not brave and not kind.
If alice is not creative then someone is old or patient.
If john is both not curious and not humble then someone is either creative or not kind and vice versa.
Everyone who is not patient or quiet is both not patient and creative and vice versa.
If mary is either not quiet or creative then john is not quiet and vice versa.
Everyone who is either not curious or not tall is not curious and vice versa.
Everyone who is not wise or funny is rich or generous.
Someone is both not kind and calm.
Someone is either not curious or not funny.
Someone is not generous or curious.
Someone is happy or strong.
Mary is not generous.
Someone is not wise or not happy.
Someone is not brave or not tall.
Someone is humble or not kind. | Paul is strong. | neutral | (![X]:((strong(X)&wise(X))=>(quiet(X)|kind(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(~strong(X)|~humble(X))))&
(((strong(paul)&kind(paul)))=>(?[X]:((funny(X)<~>rich(X)))))&
((?[X]:((~brave(X)<~>~old(X))))=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~happy(X)<~>generous(X))))&
((?[X]:((generous(X)|~funny(X))))=>(?[X]:((~tall(X)&~funny(X)))))&
(![X]:((calm(X)|kind(X))=>(~brave(X)&humble(X))))&
(![X]:((curious(X)<~>humble(X))=>(funny(X)<~>brave(X))))&
(![X]:((tall(X)&creative(X))=>(~brave(X)&~kind(X))))&
((~creative(alice))=>(?[X]:((old(X)|patient(X)))))&
(((~curious(john)&~humble(john)))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((~patient(X)|quiet(X))<=>(~patient(X)&creative(X))))&
(((~quiet(mary)<~>creative(mary)))<=>(~quiet(john)))&
(![X]:((~curious(X)<~>~tall(X))<=>~curious(X)))&
(![X]:((~wise(X)|funny(X))=>(rich(X)|generous(X))))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((happy(X)|strong(X))))&
(~generous(mary))&
(?[X]:((~wise(X)|~happy(X))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:((humble(X)|~kind(X)))) | strong(paul) | [] | null | 0 |
If someone is patient or not patient then alice is brave.
Everyone who is humble is generous.
Everyone who is both not happy and not humble is either calm or strong.
Everyone who is tall is strong or not curious and vice versa.
If someone is not humble or not calm then someone is patient.
Everyone who is wise is either not old or quiet.
Everyone who is both rich and curious is both brave and not strong.
Everyone who is both not funny and rich is either not creative or funny and vice versa.
If someone is creative or kind then fred is both not strong and not funny.
If paul is both not kind and funny then someone is curious.
Everyone who is creative or not kind is not humble and vice versa.
If paul is either wise or not humble then someone is funny.
If susan is both wise and not strong then alice is quiet and vice versa.
Everyone who is not strong is both not creative and curious and vice versa.
Everyone who is not calm is old or not creative and vice versa.
If paul is funny or not tall then paul is rich or happy.
Someone is both kind and tall.
Someone is either not brave or not humble.
Someone is either tall or generous.
Paul is both curious and not humble.
Someone is not patient or patient.
Someone is old or not strong.
Fred is wise. | Paul is funny. | neutral | ((?[X]:((patient(X)|~patient(X))))=>(brave(alice)))&
(![X]:(humble(X)=>generous(X)))&
(![X]:((~happy(X)&~humble(X))=>(calm(X)<~>strong(X))))&
(![X]:(tall(X)<=>(strong(X)|~curious(X))))&
((?[X]:((~humble(X)|~calm(X))))=>(?[X]:(patient(X))))&
(![X]:(wise(X)=>(~old(X)<~>quiet(X))))&
(![X]:((rich(X)&curious(X))=>(brave(X)&~strong(X))))&
(![X]:((~funny(X)&rich(X))<=>(~creative(X)<~>funny(X))))&
((?[X]:((creative(X)|kind(X))))=>((~strong(fred)&~funny(fred))))&
(((~kind(paul)&funny(paul)))=>(?[X]:(curious(X))))&
(![X]:((creative(X)|~kind(X))<=>~humble(X)))&
(((wise(paul)<~>~humble(paul)))=>(?[X]:(funny(X))))&
(((wise(susan)&~strong(susan)))<=>(quiet(alice)))&
(![X]:(~strong(X)<=>(~creative(X)&curious(X))))&
(![X]:(~calm(X)<=>(old(X)|~creative(X))))&
(((funny(paul)|~tall(paul)))=>((rich(paul)|happy(paul))))&
(?[X]:((kind(X)&tall(X))))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((tall(X)<~>generous(X))))&
((curious(paul)&~humble(paul)))&
(?[X]:((~patient(X)|patient(X))))&
(?[X]:((old(X)|~strong(X))))&
(wise(fred)) | funny(paul) | [] | null | 0 |
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