premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
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| hypothesis_tptp
stringclasses 224
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sequencelengths 0
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| proof
stringlengths 684
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|---|---|---|---|---|---|---|---|
If fred is brave then someone is rich or happy.
Everyone who is brave or humble is rich or not creative and vice versa.
If alice is not humble then paul is either not kind or humble.
Everyone who is both patient and not tall is brave or not strong and vice versa.
If lucy is old then someone is both not curious and creative and vice versa.
Everyone who is either kind or not generous is either calm or tall and vice versa.
If paul is either not wise or rich then alice is either brave or not funny and vice versa.
Everyone who is both humble and not calm is happy.
Everyone who is rich or not funny is either creative or not rich.
Everyone who is either curious or quiet is either kind or quiet and vice versa.
Everyone who is either not creative or not calm is both curious and brave.
Everyone who is not humble is both wise and not strong and vice versa.
Everyone who is not funny or kind is not quiet.
Everyone who is not rich or not old is kind or quiet.
Everyone who is kind is quiet.
Everyone who is quiet or not curious is both not old and not patient and vice versa.
Someone is rich or not tall.
Mary is not tall or not old.
Someone is either not old or brave.
Someone is either funny or wise.
Someone is either not rich or wise.
Alice is both not curious and quiet.
Susan is both not rich and funny. | Alice is not brave. | entailment | ((brave(fred))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((brave(X)|humble(X))<=>(rich(X)|~creative(X))))&
((~humble(alice))=>((~kind(paul)<~>humble(paul))))&
(![X]:((patient(X)&~tall(X))<=>(brave(X)|~strong(X))))&
((old(lucy))<=>(?[X]:((~curious(X)&creative(X)))))&
(![X]:((kind(X)<~>~generous(X))<=>(calm(X)<~>tall(X))))&
(((~wise(paul)<~>rich(paul)))<=>((brave(alice)<~>~funny(alice))))&
(![X]:((humble(X)&~calm(X))=>happy(X)))&
(![X]:((rich(X)|~funny(X))=>(creative(X)<~>~rich(X))))&
(![X]:((curious(X)<~>quiet(X))<=>(kind(X)<~>quiet(X))))&
(![X]:((~creative(X)<~>~calm(X))=>(curious(X)&brave(X))))&
(![X]:(~humble(X)<=>(wise(X)&~strong(X))))&
(![X]:((~funny(X)|kind(X))=>~quiet(X)))&
(![X]:((~rich(X)|~old(X))=>(kind(X)|quiet(X))))&
(![X]:(kind(X)=>quiet(X)))&
(![X]:((quiet(X)|~curious(X))<=>(~old(X)&~patient(X))))&
(?[X]:((rich(X)|~tall(X))))&
((~tall(mary)|~old(mary)))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:((funny(X)<~>wise(X))))&
(?[X]:((~rich(X)<~>wise(X))))&
((~curious(alice)&quiet(alice)))&
((~rich(susan)&funny(susan))) | ~brave(alice) | [
"p3",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 222932283866075557660179
% SZS output start Proof for 222932283866075557660179
4. ! [X0] : ((~tall(X0) & patient(X0)) <=> (~strong(X0) | brave(X0))) [input p3]
16. ! [X0] : ((~curious(X0) | quiet(X0)) <=> (~patient(X0) & ~old(X0))) [input p15]
22. quiet(alice) & ~curious(alice) [input p21]
24. brave(alice) [input hypothesis]
37. ! [X0] : (((~tall(X0) & patient(X0)) | (strong(X0) & ~brave(X0))) & ((~strong(X0) | brave(X0)) | (tall(X0) | ~patient(X0)))) [nnf transformation 4]
38. ! [X0] : (((~tall(X0) & patient(X0)) | (strong(X0) & ~brave(X0))) & (~strong(X0) | brave(X0) | tall(X0) | ~patient(X0))) [flattening 37]
50. ! [X0] : (((~curious(X0) | quiet(X0)) | (patient(X0) | old(X0))) & ((~patient(X0) & ~old(X0)) | (curious(X0) & ~quiet(X0)))) [nnf transformation 16]
51. ! [X0] : ((~curious(X0) | quiet(X0) | patient(X0) | old(X0)) & ((~patient(X0) & ~old(X0)) | (curious(X0) & ~quiet(X0)))) [flattening 50]
70. ~brave(X0) | patient(X0) [cnf transformation 38]
119. ~quiet(X0) | ~patient(X0) [cnf transformation 51]
131. quiet(alice) [cnf transformation 22]
134. brave(alice) [cnf transformation 24]
177. 9 <=> brave(alice) [avatar definition]
179. brave(alice) <- (9) [avatar component clause 177]
247. 9 [avatar split clause 134,177]
248. patient(alice) <- (9) [resolution 70,179]
261. ~patient(alice) [resolution 119,131]
262. $false <- (9) [subsumption resolution 261,248]
263. ~9 [avatar contradiction clause 262]
264. $false [avatar sat refutation 247,263]
% SZS output end Proof for 222932283866075557660179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not happy is either not happy or curious.
Everyone who is either quiet or kind is either not generous or calm and vice versa.
Everyone who is not old or not creative is both not brave and tall and vice versa.
Everyone who is not old or rich is not creative.
If paul is either tall or happy then someone is both brave and not funny.
If someone is rich or creative then someone is both happy and not funny and vice versa.
Everyone who is not strong is not creative or not humble and vice versa.
If someone is either wise or patient then mary is either not humble or not funny and vice versa.
Everyone who is not creative is not brave or tall and vice versa.
Everyone who is not curious is either calm or not creative.
Everyone who is both calm and old is either not rich or patient.
Everyone who is both not wise and not tall is both not humble and happy.
If someone is generous or not brave then someone is humble.
Everyone who is not tall or funny is happy or not humble.
If someone is either happy or not patient then someone is either brave or happy.
Everyone who is not quiet is either generous or old and vice versa.
Someone is both wise and not rich.
Someone is both not wise and not strong.
Paul is not strong.
John is both not calm and tall.
Someone is either creative or not funny.
Someone is either not generous or not calm.
John is kind or rich.
Lucy is kind or not tall. | Lucy is old. | neutral | (![X]:((old(X)<~>~happy(X))=>(~happy(X)<~>curious(X))))&
(![X]:((quiet(X)<~>kind(X))<=>(~generous(X)<~>calm(X))))&
(![X]:((~old(X)|~creative(X))<=>(~brave(X)&tall(X))))&
(![X]:((~old(X)|rich(X))=>~creative(X)))&
(((tall(paul)<~>happy(paul)))=>(?[X]:((brave(X)&~funny(X)))))&
((?[X]:((rich(X)|creative(X))))<=>(?[X]:((happy(X)&~funny(X)))))&
(![X]:(~strong(X)<=>(~creative(X)|~humble(X))))&
((?[X]:((wise(X)<~>patient(X))))<=>((~humble(mary)<~>~funny(mary))))&
(![X]:(~creative(X)<=>(~brave(X)|tall(X))))&
(![X]:(~curious(X)=>(calm(X)<~>~creative(X))))&
(![X]:((calm(X)&old(X))=>(~rich(X)<~>patient(X))))&
(![X]:((~wise(X)&~tall(X))=>(~humble(X)&happy(X))))&
((?[X]:((generous(X)|~brave(X))))=>(?[X]:(humble(X))))&
(![X]:((~tall(X)|funny(X))=>(happy(X)|~humble(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:(~quiet(X)<=>(generous(X)<~>old(X))))&
(?[X]:((wise(X)&~rich(X))))&
(?[X]:((~wise(X)&~strong(X))))&
(~strong(paul))&
((~calm(john)&tall(john)))&
(?[X]:((creative(X)<~>~funny(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
((kind(john)|rich(john)))&
((kind(lucy)|~tall(lucy))) | old(lucy) | [] | null | 0 |
Everyone who is both not generous and not strong is happy or not kind and vice versa.
If someone is brave or not old then someone is not generous and vice versa.
Everyone who is either kind or not patient is either kind or not old and vice versa.
If someone is brave or old then fred is either not humble or happy.
Everyone who is both not rich and not wise is brave and vice versa.
Everyone who is either brave or calm is either strong or brave and vice versa.
If someone is not wise then someone is both not humble and quiet.
If someone is not brave or not creative then susan is tall.
If paul is either generous or kind then someone is brave or not quiet.
Everyone who is either calm or not old is either not funny or not calm.
Everyone who is not kind is not generous and vice versa.
If someone is wise or not brave then john is not calm.
If someone is either not happy or quiet then john is either funny or not kind.
Everyone who is quiet is either wise or not tall and vice versa.
If mary is both not rich and not strong then someone is not patient or not curious and vice versa.
If paul is both curious and quiet then mary is brave or rich and vice versa.
Lucy is both not rich and strong.
Someone is calm or not humble.
Someone is happy.
Someone is either happy or rich.
Paul is strong.
Someone is calm.
Paul is both not old and creative.
Alice is not happy. | Mary is rich. | contradiction | (![X]:((~generous(X)&~strong(X))<=>(happy(X)|~kind(X))))&
((?[X]:((brave(X)|~old(X))))<=>(?[X]:(~generous(X))))&
(![X]:((kind(X)<~>~patient(X))<=>(kind(X)<~>~old(X))))&
((?[X]:((brave(X)|old(X))))=>((~humble(fred)<~>happy(fred))))&
(![X]:((~rich(X)&~wise(X))<=>brave(X)))&
(![X]:((brave(X)<~>calm(X))<=>(strong(X)<~>brave(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((~brave(X)|~creative(X))))=>(tall(susan)))&
(((generous(paul)<~>kind(paul)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((calm(X)<~>~old(X))=>(~funny(X)<~>~calm(X))))&
(![X]:(~kind(X)<=>~generous(X)))&
((?[X]:((wise(X)|~brave(X))))=>(~calm(john)))&
((?[X]:((~happy(X)<~>quiet(X))))=>((funny(john)<~>~kind(john))))&
(![X]:(quiet(X)<=>(wise(X)<~>~tall(X))))&
(((~rich(mary)&~strong(mary)))<=>(?[X]:((~patient(X)|~curious(X)))))&
(((curious(paul)&quiet(paul)))<=>((brave(mary)|rich(mary))))&
((~rich(lucy)&strong(lucy)))&
(?[X]:((calm(X)|~humble(X))))&
(?[X]:(happy(X)))&
(?[X]:((happy(X)<~>rich(X))))&
(strong(paul))&
(?[X]:(calm(X)))&
((~old(paul)&creative(paul)))&
(~happy(alice)) | rich(mary) | [
"p2",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4678968634888090981167072
% SZS output start Proof for 4678968634888090981167072
3. ! [X0] : ((kind(X0) <~> ~patient(X0)) <=> (kind(X0) <~> ~old(X0))) [input p2]
15. (~strong(mary) & ~rich(mary)) <=> ? [X0] : (~curious(X0) | ~patient(X0)) [input p14]
23. creative(paul) & ~old(paul) [input p22]
25. rich(mary) [input hypothesis]
29. ~old(paul) [pure predicate removal 23]
44. ! [X0] : ((((patient(X0) | ~kind(X0)) & (~patient(X0) | kind(X0))) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0))))) [nnf transformation 3]
59. ((~strong(mary) & ~rich(mary)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X0] : (~curious(X0) | ~patient(X0)) | (strong(mary) | rich(mary))) [nnf transformation 15]
60. ((~strong(mary) & ~rich(mary)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X0] : (~curious(X0) | ~patient(X0)) | strong(mary) | rich(mary)) [flattening 59]
61. ((~strong(mary) & ~rich(mary)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X1] : (~curious(X1) | ~patient(X1)) | strong(mary) | rich(mary)) [rectify 60]
62. ? [X1] : (~curious(X1) | ~patient(X1)) => (~curious(sK4) | ~patient(sK4)) [choice axiom]
63. ((~strong(mary) & ~rich(mary)) | ! [X0] : (curious(X0) & patient(X0))) & ((~curious(sK4) | ~patient(sK4)) | strong(mary) | rich(mary)) [skolemisation 61,62]
85. old(X0) | ~kind(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 44]
88. ~patient(X0) | kind(X0) | kind(X0) | old(X0) [cnf transformation 44]
128. ~rich(mary) | patient(X0) [cnf transformation 63]
145. ~old(paul) [cnf transformation 29]
147. rich(mary) [cnf transformation 25]
155. old(X0) | ~kind(X0) | ~patient(X0) [duplicate literal removal 85]
156. ~patient(X0) | kind(X0) | old(X0) [duplicate literal removal 88]
171. 4 <=> ! [X3] : old(X3) [avatar definition]
172. old(X3) <- (4) [avatar component clause 171]
182. ~patient(X0) | old(X0) [subsumption resolution 155,156]
275. 27 <=> ! [X0] : patient(X0) [avatar definition]
276. patient(X0) <- (27) [avatar component clause 275]
279. 28 <=> rich(mary) [avatar definition]
283. 27 | ~28 [avatar split clause 128,279,275]
329. 28 [avatar split clause 147,279]
346. old(X0) <- (27) [resolution 182,276]
347. 4 | ~27 [avatar split clause 346,275,171]
348. $false <- (4) [resolution 172,145]
351. ~4 [avatar contradiction clause 348]
352. $false [avatar sat refutation 283,329,347,351]
% SZS output end Proof for 4678968634888090981167072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is not humble then alice is either creative or curious.
If someone is either quiet or generous then john is patient and vice versa.
If susan is not creative then susan is both generous and not funny.
Everyone who is either not creative or brave is not patient or strong and vice versa.
If lucy is tall or not creative then someone is not tall.
Everyone who is happy or not old is either not creative or brave and vice versa.
If paul is either generous or not patient then susan is both not wise and not patient.
If someone is not rich then mary is not strong or not funny and vice versa.
Everyone who is not calm or happy is both humble and happy and vice versa.
If paul is either quiet or old then someone is not old.
Everyone who is both brave and not humble is not happy or creative and vice versa.
Everyone who is not patient or quiet is either not quiet or not creative and vice versa.
Everyone who is not funny or patient is both generous and not curious.
Everyone who is not creative or wise is both not wise and not patient.
Everyone who is happy or wise is either not brave or generous.
Someone is humble or not quiet.
Alice is strong or not rich.
Someone is funny.
Someone is tall or brave.
Someone is either not rich or rich.
Mary is kind. | Mary is old. | contradiction | ((~humble(john))=>((creative(alice)<~>curious(alice))))&
((?[X]:((quiet(X)<~>generous(X))))<=>(patient(john)))&
((~creative(susan))=>((generous(susan)&~funny(susan))))&
(![X]:((~creative(X)<~>brave(X))<=>(~patient(X)|strong(X))))&
(((tall(lucy)|~creative(lucy)))=>(?[X]:(~tall(X))))&
(![X]:((happy(X)|~old(X))<=>(~creative(X)<~>brave(X))))&
(((generous(paul)<~>~patient(paul)))=>((~wise(susan)&~patient(susan))))&
((?[X]:(~rich(X)))<=>((~strong(mary)|~funny(mary))))&
(![X]:((~calm(X)|happy(X))<=>(humble(X)&happy(X))))&
(((quiet(paul)<~>old(paul)))=>(?[X]:(~old(X))))&
(![X]:((brave(X)&~humble(X))<=>(~happy(X)|creative(X))))&
(![X]:((~patient(X)|quiet(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~funny(X)|patient(X))=>(generous(X)&~curious(X))))&
(![X]:((~creative(X)|wise(X))=>(~wise(X)&~patient(X))))&
(![X]:((happy(X)|wise(X))=>(~brave(X)<~>generous(X))))&
(?[X]:((humble(X)|~quiet(X))))&
((strong(alice)|~rich(alice)))&
(?[X]:(funny(X)))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((~rich(X)<~>rich(X))))&
(kind(mary)) | old(mary) | [
"p1",
"p3",
"p5",
"p8",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7470129878087270697383806
% SZS output start Proof for 7470129878087270697383806
2. ? [X0] : (quiet(X0) <~> generous(X0)) <=> patient(john) [input p1]
4. ! [X0] : ((~creative(X0) <~> brave(X0)) <=> (strong(X0) | ~patient(X0))) [input p3]
6. ! [X0] : ((~old(X0) | happy(X0)) <=> (~creative(X0) <~> brave(X0))) [input p5]
9. ! [X0] : ((happy(X0) | ~calm(X0)) <=> (happy(X0) & humble(X0))) [input p8]
11. ! [X0] : ((~humble(X0) & brave(X0)) <=> (creative(X0) | ~happy(X0))) [input p10]
12. ! [X0] : ((quiet(X0) | ~patient(X0)) <=> (~quiet(X0) <~> ~creative(X0))) [input p11]
14. ! [X0] : ((wise(X0) | ~creative(X0)) => (~patient(X0) & ~wise(X0))) [input p13]
15. ! [X0] : ((wise(X0) | happy(X0)) => (~brave(X0) <~> generous(X0))) [input p14]
22. old(mary) [input hypothesis]
25. ! [X0] : (~creative(X0) => ~patient(X0)) [pure predicate removal 14]
26. ! [X0] : (happy(X0) => (~brave(X0) <~> generous(X0))) [pure predicate removal 15]
33. ! [X0] : (~patient(X0) | creative(X0)) [ennf transformation 25]
34. ! [X0] : ((~brave(X0) <~> generous(X0)) | ~happy(X0)) [ennf transformation 26]
36. (? [X0] : ((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | ~patient(john)) & (patient(john) | ! [X0] : ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0)))) [nnf transformation 2]
37. (? [X0] : ((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | ~patient(john)) & (patient(john) | ! [X1] : ((quiet(X1) | ~generous(X1)) & (generous(X1) | ~quiet(X1)))) [rectify 36]
38. ? [X0] : ((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) => ((~generous(sK0) | ~quiet(sK0)) & (generous(sK0) | quiet(sK0))) [choice axiom]
39. (((~generous(sK0) | ~quiet(sK0)) & (generous(sK0) | quiet(sK0))) | ~patient(john)) & (patient(john) | ! [X1] : ((quiet(X1) | ~generous(X1)) & (generous(X1) | ~quiet(X1)))) [skolemisation 37,38]
40. ! [X0] : ((((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (~strong(X0) & patient(X0))) & ((strong(X0) | ~patient(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0))))) [nnf transformation 4]
41. ! [X0] : ((((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (~strong(X0) & patient(X0))) & (strong(X0) | ~patient(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0))))) [flattening 40]
44. ! [X0] : (((~old(X0) | happy(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (old(X0) & ~happy(X0)))) [nnf transformation 6]
45. ! [X0] : ((~old(X0) | happy(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (old(X0) & ~happy(X0)))) [flattening 44]
52. ! [X0] : (((happy(X0) | ~calm(X0)) | (~happy(X0) | ~humble(X0))) & ((happy(X0) & humble(X0)) | (~happy(X0) & calm(X0)))) [nnf transformation 9]
53. ! [X0] : ((happy(X0) | ~calm(X0) | ~happy(X0) | ~humble(X0)) & ((happy(X0) & humble(X0)) | (~happy(X0) & calm(X0)))) [flattening 52]
57. ! [X0] : (((~humble(X0) & brave(X0)) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | (humble(X0) | ~brave(X0)))) [nnf transformation 11]
58. ! [X0] : (((~humble(X0) & brave(X0)) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | humble(X0) | ~brave(X0))) [flattening 57]
59. ! [X0] : (((quiet(X0) | ~patient(X0)) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) & (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | (~quiet(X0) & patient(X0)))) [nnf transformation 12]
60. ! [X0] : ((quiet(X0) | ~patient(X0) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) & (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | (~quiet(X0) & patient(X0)))) [flattening 59]
61. ! [X0] : (((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | ~happy(X0)) [nnf transformation 34]
73. patient(john) | generous(X1) | ~quiet(X1) [cnf transformation 39]
83. ~brave(X0) | creative(X0) | patient(X0) [cnf transformation 41]
89. ~happy(X0) | creative(X0) | ~brave(X0) [cnf transformation 45]
92. ~old(X0) | happy(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 45]
99. ~happy(X0) | humble(X0) [cnf transformation 53]
106. happy(X0) | brave(X0) [cnf transformation 58]
107. ~creative(X0) | brave(X0) [cnf transformation 58]
108. ~humble(X0) | happy(X0) [cnf transformation 58]
109. ~creative(X0) | ~humble(X0) [cnf transformation 58]
111. ~creative(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 60]
112. patient(X0) | quiet(X0) | creative(X0) [cnf transformation 60]
114. quiet(X0) | ~patient(X0) | ~creative(X0) | quiet(X0) [cnf transformation 60]
120. ~patient(X0) | creative(X0) [cnf transformation 33]
122. ~generous(X0) | brave(X0) | ~happy(X0) [cnf transformation 61]
129. old(mary) [cnf transformation 22]
130. ~quiet(X0) | ~creative(X0) [duplicate literal removal 111]
131. ~patient(X0) | quiet(X0) | ~creative(X0) [duplicate literal removal 114]
147. 4 <=> patient(john) [avatar definition]
148. patient(john) <- (4) [avatar component clause 147]
165. 8 <=> ! [X1] : (generous(X1) | ~quiet(X1)) [avatar definition]
166. ~quiet(X1) | generous(X1) <- (8) [avatar component clause 165]
167. 8 | 4 [avatar split clause 73,147,165]
242. ~generous(X0) | brave(X0) [subsumption resolution 122,106]
270. brave(X0) | humble(X0) [resolution 106,99]
278. creative(john) <- (4) [resolution 120,148]
288. creative(X0) | patient(X0) | humble(X0) [resolution 83,270]
293. creative(X0) | humble(X0) [subsumption resolution 288,120]
322. quiet(X0) | creative(X0) | creative(X0) [resolution 112,120]
325. quiet(X0) | creative(X0) [duplicate literal removal 322]
352. quiet(john) | ~creative(john) <- (4) [resolution 131,148]
355. quiet(john) <- (4) [subsumption resolution 352,278]
391. ~creative(john) <- (4) [resolution 355,130]
392. $false <- (4) [subsumption resolution 391,278]
393. ~4 [avatar contradiction clause 392]
400. generous(X0) | creative(X0) <- (8) [resolution 166,325]
438. happy(mary) | ~creative(mary) | ~brave(mary) [resolution 92,129]
439. happy(mary) | ~creative(mary) [subsumption resolution 438,106]
441. 40 <=> creative(mary) [avatar definition]
442. creative(mary) <- (40) [avatar component clause 441]
443. ~creative(mary) <- (~40) [avatar component clause 441]
445. 41 <=> happy(mary) [avatar definition]
447. happy(mary) <- (41) [avatar component clause 445]
448. ~40 | 41 [avatar split clause 439,445,441]
449. humble(mary) <- (~40) [resolution 443,293]
464. creative(X1) | brave(X1) <- (8) [resolution 400,242]
465. brave(X1) <- (8) [subsumption resolution 464,107]
479. happy(mary) <- (~40) [resolution 449,108]
480. 41 | 40 [avatar split clause 479,441,445]
482. creative(mary) | ~brave(mary) <- (41) [resolution 447,89]
484. humble(mary) <- (41) [resolution 447,99]
489. creative(mary) <- (8, 41) [subsumption resolution 482,465]
490. 40 | ~8 | ~41 [avatar split clause 489,445,165,441]
493. ~humble(mary) <- (40) [resolution 442,109]
495. $false <- (40, 41) [subsumption resolution 493,484]
496. ~40 | ~41 [avatar contradiction clause 495]
497. $false [avatar sat refutation 167,393,448,480,490,496]
% SZS output end Proof for 7470129878087270697383806
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then lucy is not tall or happy.
If alice is not kind then alice is either strong or generous.
If someone is patient then someone is creative and vice versa.
Everyone who is wise is not old and vice versa.
If someone is humble or tall then alice is either not curious or humble.
Everyone who is strong is not generous or not old and vice versa.
Everyone who is brave is not humble or rich.
Everyone who is humble is either rich or generous and vice versa.
If someone is not old then susan is either not rich or curious.
If lucy is either tall or brave then someone is kind or not wise.
Everyone who is not funny or funny is both quiet and not brave.
If someone is tall then lucy is either not tall or patient.
If john is both not curious and not happy then someone is not calm or strong and vice versa.
Everyone who is either not tall or patient is old.
Everyone who is kind is curious or rich and vice versa.
If someone is both not calm and funny then susan is either not strong or not funny and vice versa.
Paul is either brave or not kind.
Someone is both not humble and calm.
Alice is either not happy or quiet.
Lucy is not generous or wise.
Mary is either old or not old.
Someone is both happy and quiet.
Lucy is not generous. | Alice is quiet. | entailment | ((?[X]:(generous(X)))=>((~tall(lucy)|happy(lucy))))&
((~kind(alice))=>((strong(alice)<~>generous(alice))))&
((?[X]:(patient(X)))<=>(?[X]:(creative(X))))&
(![X]:(wise(X)<=>~old(X)))&
((?[X]:((humble(X)|tall(X))))=>((~curious(alice)<~>humble(alice))))&
(![X]:(strong(X)<=>(~generous(X)|~old(X))))&
(![X]:(brave(X)=>(~humble(X)|rich(X))))&
(![X]:(humble(X)<=>(rich(X)<~>generous(X))))&
((?[X]:(~old(X)))=>((~rich(susan)<~>curious(susan))))&
(((tall(lucy)<~>brave(lucy)))=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((~funny(X)|funny(X))=>(quiet(X)&~brave(X))))&
((?[X]:(tall(X)))=>((~tall(lucy)<~>patient(lucy))))&
(((~curious(john)&~happy(john)))<=>(?[X]:((~calm(X)|strong(X)))))&
(![X]:((~tall(X)<~>patient(X))=>old(X)))&
(![X]:(kind(X)<=>(curious(X)|rich(X))))&
((?[X]:((~calm(X)&funny(X))))<=>((~strong(susan)<~>~funny(susan))))&
((brave(paul)<~>~kind(paul)))&
(?[X]:((~humble(X)&calm(X))))&
((~happy(alice)<~>quiet(alice)))&
((~generous(lucy)|wise(lucy)))&
((old(mary)<~>~old(mary)))&
(?[X]:((happy(X)&quiet(X))))&
(~generous(lucy)) | quiet(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1211469627157681705652762
% SZS output start Proof for 1211469627157681705652762
11. ! [X0] : ((funny(X0) | ~funny(X0)) => (~brave(X0) & quiet(X0))) [input p10]
24. ~quiet(alice) [input hypothesis]
34. ! [X0] : ((~brave(X0) & quiet(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 11]
95. quiet(X0) | funny(X0) [cnf transformation 34]
96. quiet(X0) | ~funny(X0) [cnf transformation 34]
129. ~quiet(alice) [cnf transformation 24]
218. quiet(X0) [subsumption resolution 95,96]
289. $false [subsumption resolution 129,218]
% SZS output end Proof for 1211469627157681705652762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not generous is rich and vice versa.
Everyone who is not brave or not strong is both not old and not wise and vice versa.
If someone is creative or patient then paul is brave and vice versa.
Everyone who is humble is both funny and not quiet.
Everyone who is funny is both happy and not tall and vice versa.
Everyone who is either not calm or not generous is either not wise or not rich and vice versa.
Everyone who is either not brave or curious is happy.
Everyone who is both not creative and quiet is not creative.
Everyone who is funny is not funny or curious and vice versa.
Everyone who is both curious and happy is both brave and kind and vice versa.
Everyone who is either not patient or not rich is either not brave or strong.
If mary is both not brave and calm then someone is either quiet or wise.
If someone is both not brave and humble then alice is both not strong and wise.
If paul is not strong then someone is not generous or rich.
If someone is not wise or patient then someone is either rich or creative and vice versa.
If someone is either rich or old then alice is both not rich and creative.
Someone is not calm or brave.
Alice is patient.
Someone is not patient.
Alice is not creative.
Someone is both not wise and funny. | Alice is not rich. | neutral | (![X]:((~creative(X)<~>~generous(X))<=>rich(X)))&
(![X]:((~brave(X)|~strong(X))<=>(~old(X)&~wise(X))))&
((?[X]:((creative(X)|patient(X))))<=>(brave(paul)))&
(![X]:(humble(X)=>(funny(X)&~quiet(X))))&
(![X]:(funny(X)<=>(happy(X)&~tall(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:((~brave(X)<~>curious(X))=>happy(X)))&
(![X]:((~creative(X)&quiet(X))=>~creative(X)))&
(![X]:(funny(X)<=>(~funny(X)|curious(X))))&
(![X]:((curious(X)&happy(X))<=>(brave(X)&kind(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(~brave(X)<~>strong(X))))&
(((~brave(mary)&calm(mary)))=>(?[X]:((quiet(X)<~>wise(X)))))&
((?[X]:((~brave(X)&humble(X))))=>((~strong(alice)&wise(alice))))&
((~strong(paul))=>(?[X]:((~generous(X)|rich(X)))))&
((?[X]:((~wise(X)|patient(X))))<=>(?[X]:((rich(X)<~>creative(X)))))&
((?[X]:((rich(X)<~>old(X))))=>((~rich(alice)&creative(alice))))&
(?[X]:((~calm(X)|brave(X))))&
(patient(alice))&
(?[X]:(~patient(X)))&
(~creative(alice))&
(?[X]:((~wise(X)&funny(X)))) | ~rich(alice) | [] | null | 0 |
If susan is both not calm and kind then mary is happy and vice versa.
Everyone who is both brave and strong is both curious and not humble and vice versa.
If mary is both not patient and not generous then paul is not funny or not kind.
If someone is funny or not generous then alice is both not humble and not happy and vice versa.
If alice is not funny then susan is not old.
If paul is tall then someone is not strong or not brave and vice versa.
Everyone who is strong is both not generous and funny and vice versa.
Everyone who is either not kind or kind is either not curious or not happy and vice versa.
Everyone who is curious or creative is either not wise or wise.
Everyone who is both wise and old is generous and vice versa.
Everyone who is either wise or not generous is both funny and rich and vice versa.
Everyone who is generous is not old.
Everyone who is both not brave and calm is both strong and tall.
Everyone who is old is either not patient or not strong.
Everyone who is not funny is either not kind or not quiet and vice versa.
Susan is either not calm or generous.
John is either not tall or not patient.
Someone is not funny or not creative.
Someone is rich.
Someone is quiet or calm.
John is both not strong and not curious. | John is not old. | entailment | (((~calm(susan)&kind(susan)))<=>(happy(mary)))&
(![X]:((brave(X)&strong(X))<=>(curious(X)&~humble(X))))&
(((~patient(mary)&~generous(mary)))=>((~funny(paul)|~kind(paul))))&
((?[X]:((funny(X)|~generous(X))))<=>((~humble(alice)&~happy(alice))))&
((~funny(alice))=>(~old(susan)))&
((tall(paul))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:(strong(X)<=>(~generous(X)&funny(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(~curious(X)<~>~happy(X))))&
(![X]:((curious(X)|creative(X))=>(~wise(X)<~>wise(X))))&
(![X]:((wise(X)&old(X))<=>generous(X)))&
(![X]:((wise(X)<~>~generous(X))<=>(funny(X)&rich(X))))&
(![X]:(generous(X)=>~old(X)))&
(![X]:((~brave(X)&calm(X))=>(strong(X)&tall(X))))&
(![X]:(old(X)=>(~patient(X)<~>~strong(X))))&
(![X]:(~funny(X)<=>(~kind(X)<~>~quiet(X))))&
((~calm(susan)<~>generous(susan)))&
((~tall(john)<~>~patient(john)))&
(?[X]:((~funny(X)|~creative(X))))&
(?[X]:(rich(X)))&
(?[X]:((quiet(X)|calm(X))))&
((~strong(john)&~curious(john))) | ~old(john) | [
"p6",
"p9",
"p10",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4698750721956998285841205
% SZS output start Proof for 4698750721956998285841205
7. ! [X0] : (strong(X0) <=> (funny(X0) & ~generous(X0))) [input p6]
10. ! [X0] : ((old(X0) & wise(X0)) <=> generous(X0)) [input p9]
11. ! [X0] : ((wise(X0) <~> ~generous(X0)) <=> (rich(X0) & funny(X0))) [input p10]
12. ! [X0] : (generous(X0) => ~old(X0)) [input p11]
21. ~curious(john) & ~strong(john) [input p20]
22. old(john) [input hypothesis]
29. ! [X0] : (~old(X0) | ~generous(X0)) [ennf transformation 12]
46. ! [X0] : ((strong(X0) | (~funny(X0) | generous(X0))) & ((funny(X0) & ~generous(X0)) | ~strong(X0))) [nnf transformation 7]
47. ! [X0] : ((strong(X0) | ~funny(X0) | generous(X0)) & ((funny(X0) & ~generous(X0)) | ~strong(X0))) [flattening 46]
50. ! [X0] : (((old(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | (~old(X0) | ~wise(X0)))) [nnf transformation 10]
51. ! [X0] : (((old(X0) & wise(X0)) | ~generous(X0)) & (generous(X0) | ~old(X0) | ~wise(X0))) [flattening 50]
52. ! [X0] : ((((generous(X0) | ~wise(X0)) & (~generous(X0) | wise(X0))) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | ((wise(X0) | generous(X0)) & (~generous(X0) | ~wise(X0))))) [nnf transformation 11]
53. ! [X0] : ((((generous(X0) | ~wise(X0)) & (~generous(X0) | wise(X0))) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | ((wise(X0) | generous(X0)) & (~generous(X0) | ~wise(X0))))) [flattening 52]
81. ~funny(X0) | strong(X0) | generous(X0) [cnf transformation 47]
92. ~wise(X0) | ~old(X0) | generous(X0) [cnf transformation 51]
93. ~generous(X0) | wise(X0) [cnf transformation 51]
94. ~generous(X0) | old(X0) [cnf transformation 51]
96. funny(X0) | wise(X0) | generous(X0) [cnf transformation 53]
101. ~old(X0) | ~generous(X0) [cnf transformation 29]
116. ~strong(john) [cnf transformation 21]
118. old(john) [cnf transformation 22]
216. wise(X0) | funny(X0) [subsumption resolution 96,93]
218. ~generous(X0) [subsumption resolution 101,94]
244. ~old(X0) | generous(X0) | funny(X0) [resolution 92,216]
245. ~old(X0) | funny(X0) [subsumption resolution 244,218]
246. funny(john) [resolution 245,118]
247. strong(john) | generous(john) [resolution 246,81]
248. generous(john) [subsumption resolution 247,116]
249. $false [subsumption resolution 248,218]
% SZS output end Proof for 4698750721956998285841205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not quiet is either generous or not creative and vice versa. If someone is not wise then alice is not patient and vice versa. If someone is not creative then someone is both brave and not old. Everyone who is quiet is curious. If mary is both strong and not curious then someone is not humble or not brave and vice versa. Everyone who is not happy or not brave is both not patient and not creative and vice versa. Everyone who is brave is not humble or calm and vice versa. Everyone who is either not old or not brave is kind and vice versa. If someone is both not strong and creative then lucy is both not calm and strong and vice versa. If someone is both not creative and not humble then someone is humble or quiet and vice versa. Everyone who is not curious is patient. If john is either creative or humble then lucy is kind and vice versa. Everyone who is both not generous and calm is not creative or generous. If someone is not generous then lucy is calm or old. If someone is both not strong and curious then lucy is both not calm and not patient and vice versa. Everyone who is not generous is humble or kind. John is not humble. Alice is either creative or not generous. Mary is both not tall and not calm. Alice is either old or not patient. Someone is kind. Someone is either not rich or not brave. Someone is either humble or wise. | Mary is not humble. | entailment | (![X]:((creative(X)|~quiet(X))<=>(generous(X)<~>~creative(X))))&
((?[X]:(~wise(X)))<=>(~patient(alice)))&
((?[X]:(~creative(X)))=>(?[X]:((brave(X)&~old(X)))))&
(![X]:(quiet(X)=>curious(X)))&
(((strong(mary)&~curious(mary)))<=>(?[X]:((~humble(X)|~brave(X)))))&
(![X]:((~happy(X)|~brave(X))<=>(~patient(X)&~creative(X))))&
(![X]:(brave(X)<=>(~humble(X)|calm(X))))&
(![X]:((~old(X)<~>~brave(X))<=>kind(X)))&
((?[X]:((~strong(X)&creative(X))))<=>((~calm(lucy)&strong(lucy))))&
((?[X]:((~creative(X)&~humble(X))))<=>(?[X]:((humble(X)|quiet(X)))))&
(![X]:(~curious(X)=>patient(X)))&
(((creative(john)<~>humble(john)))<=>(kind(lucy)))&
(![X]:((~generous(X)&calm(X))=>(~creative(X)|generous(X))))&
((?[X]:(~generous(X)))=>((calm(lucy)|old(lucy))))&
((?[X]:((~strong(X)&curious(X))))<=>((~calm(lucy)&~patient(lucy))))&
(![X]:(~generous(X)=>(humble(X)|kind(X))))&
(~humble(john))&
((creative(alice)<~>~generous(alice)))&
((~tall(mary)&~calm(mary)))&
((old(alice)<~>~patient(alice)))&
(?[X]:(kind(X)))&
(?[X]:((~rich(X)<~>~brave(X))))&
(?[X]:((humble(X)<~>wise(X)))) | ~humble(mary) | [
"p4",
"p5",
"p6",
"p9",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4039477387570353460982328
% SZS output start Proof for 4039477387570353460982328
5. (~curious(mary) & strong(mary)) <=> ? [X0] : (~brave(X0) | ~humble(X0)) [input p4]
6. ! [X0] : ((~brave(X0) | ~happy(X0)) <=> (~creative(X0) & ~patient(X0))) [input p5]
7. ! [X0] : (brave(X0) <=> (calm(X0) | ~humble(X0))) [input p6]
10. ? [X0] : (~humble(X0) & ~creative(X0)) <=> ? [X0] : (quiet(X0) | humble(X0)) [input p9]
11. ! [X0] : (~curious(X0) => patient(X0)) [input p10]
19. ~calm(mary) & ~tall(mary) [input p18]
24. humble(mary) [input hypothesis]
26. ? [X0] : (~humble(X0) & ~creative(X0)) <=> ? [X1] : (quiet(X1) | humble(X1)) [rectify 10]
27. ~calm(mary) [pure predicate removal 19]
30. ! [X0] : (patient(X0) | curious(X0)) [ennf transformation 11]
46. ((~curious(mary) & strong(mary)) | ! [X0] : (brave(X0) & humble(X0))) & (? [X0] : (~brave(X0) | ~humble(X0)) | (curious(mary) | ~strong(mary))) [nnf transformation 5]
47. ((~curious(mary) & strong(mary)) | ! [X0] : (brave(X0) & humble(X0))) & (? [X0] : (~brave(X0) | ~humble(X0)) | curious(mary) | ~strong(mary)) [flattening 46]
48. ((~curious(mary) & strong(mary)) | ! [X0] : (brave(X0) & humble(X0))) & (? [X1] : (~brave(X1) | ~humble(X1)) | curious(mary) | ~strong(mary)) [rectify 47]
49. ? [X1] : (~brave(X1) | ~humble(X1)) => (~brave(sK2) | ~humble(sK2)) [choice axiom]
50. ((~curious(mary) & strong(mary)) | ! [X0] : (brave(X0) & humble(X0))) & ((~brave(sK2) | ~humble(sK2)) | curious(mary) | ~strong(mary)) [skolemisation 48,49]
51. ! [X0] : (((~brave(X0) | ~happy(X0)) | (creative(X0) | patient(X0))) & ((~creative(X0) & ~patient(X0)) | (brave(X0) & happy(X0)))) [nnf transformation 6]
52. ! [X0] : ((~brave(X0) | ~happy(X0) | creative(X0) | patient(X0)) & ((~creative(X0) & ~patient(X0)) | (brave(X0) & happy(X0)))) [flattening 51]
53. ! [X0] : ((brave(X0) | (~calm(X0) & humble(X0))) & ((calm(X0) | ~humble(X0)) | ~brave(X0))) [nnf transformation 7]
54. ! [X0] : ((brave(X0) | (~calm(X0) & humble(X0))) & (calm(X0) | ~humble(X0) | ~brave(X0))) [flattening 53]
61. (? [X0] : (~humble(X0) & ~creative(X0)) | ! [X1] : (~quiet(X1) & ~humble(X1))) & (? [X1] : (quiet(X1) | humble(X1)) | ! [X0] : (humble(X0) | creative(X0))) [nnf transformation 26]
62. (? [X0] : (~humble(X0) & ~creative(X0)) | ! [X1] : (~quiet(X1) & ~humble(X1))) & (? [X2] : (quiet(X2) | humble(X2)) | ! [X3] : (humble(X3) | creative(X3))) [rectify 61]
63. ? [X0] : (~humble(X0) & ~creative(X0)) => (~humble(sK4) & ~creative(sK4)) [choice axiom]
64. ? [X2] : (quiet(X2) | humble(X2)) => (quiet(sK5) | humble(sK5)) [choice axiom]
65. ((~humble(sK4) & ~creative(sK4)) | ! [X1] : (~quiet(X1) & ~humble(X1))) & ((quiet(sK5) | humble(sK5)) | ! [X3] : (humble(X3) | creative(X3))) [skolemisation 62,64,63]
96. ~curious(mary) | humble(X0) [cnf transformation 50]
99. ~patient(X0) | brave(X0) [cnf transformation 52]
103. ~humble(X0) | calm(X0) | ~brave(X0) [cnf transformation 54]
117. ~humble(sK4) | ~humble(X1) [cnf transformation 65]
119. curious(X0) | patient(X0) [cnf transformation 30]
134. ~calm(mary) [cnf transformation 27]
142. humble(mary) [cnf transformation 24]
176. 8 <=> curious(mary) [avatar definition]
178. ~curious(mary) <- (~8) [avatar component clause 176]
181. 9 <=> ! [X0] : humble(X0) [avatar definition]
182. humble(X0) <- (9) [avatar component clause 181]
183. 9 | ~8 [avatar split clause 96,176,181]
226. 19 <=> humble(sK4) [avatar definition]
228. ~humble(sK4) <- (~19) [avatar component clause 226]
231. 20 <=> ! [X1] : ~humble(X1) [avatar definition]
232. ~humble(X1) <- (20) [avatar component clause 231]
233. 20 | ~19 [avatar split clause 117,226,231]
333. $false <- (9, ~19) [resolution 228,182]
334. ~9 | 19 [avatar contradiction clause 333]
337. $false <- (20) [resolution 232,142]
338. ~20 [avatar contradiction clause 337]
345. patient(mary) <- (~8) [resolution 119,178]
346. brave(mary) <- (~8) [resolution 345,99]
358. calm(mary) | ~brave(mary) [resolution 103,142]
361. ~brave(mary) [subsumption resolution 358,134]
362. $false <- (~8) [subsumption resolution 361,346]
363. 8 [avatar contradiction clause 362]
382. $false [avatar sat refutation 183,233,334,338,363]
% SZS output end Proof for 4039477387570353460982328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either creative or not tall then someone is not calm or tall. Everyone who is patient is not tall or tall and vice versa. If mary is not quiet then john is both curious and not funny and vice versa. If someone is not tall then someone is both not kind and rich. Everyone who is not funny is either generous or tall and vice versa. Everyone who is either old or not kind is either not patient or funny. If susan is strong then john is either funny or not brave and vice versa. If someone is either quiet or not rich then alice is either not kind or quiet and vice versa. If susan is both quiet and patient then someone is both not patient and wise and vice versa. Everyone who is patient or not generous is strong and vice versa. If paul is not rich or funny then paul is either not brave or not creative. Everyone who is patient or strong is strong and vice versa. If someone is both creative and not happy then someone is not old and vice versa. If someone is both not humble and quiet then lucy is rich and vice versa. Someone is old or not tall. Someone is both humble and curious. Fred is either not calm or not tall. Someone is funny or calm. Someone is generous or creative. John is generous or not creative. Susan is either quiet or happy. Paul is strong. | Lucy is not patient. | contradiction | (((creative(lucy)<~>~tall(lucy)))=>(?[X]:((~calm(X)|tall(X)))))&
(![X]:(patient(X)<=>(~tall(X)|tall(X))))&
((~quiet(mary))<=>((curious(john)&~funny(john))))&
((?[X]:(~tall(X)))=>(?[X]:((~kind(X)&rich(X)))))&
(![X]:(~funny(X)<=>(generous(X)<~>tall(X))))&
(![X]:((old(X)<~>~kind(X))=>(~patient(X)<~>funny(X))))&
((strong(susan))<=>((funny(john)<~>~brave(john))))&
((?[X]:((quiet(X)<~>~rich(X))))<=>((~kind(alice)<~>quiet(alice))))&
(((quiet(susan)&patient(susan)))<=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:((patient(X)|~generous(X))<=>strong(X)))&
(((~rich(paul)|funny(paul)))=>((~brave(paul)<~>~creative(paul))))&
(![X]:((patient(X)|strong(X))<=>strong(X)))&
((?[X]:((creative(X)&~happy(X))))<=>(?[X]:(~old(X))))&
((?[X]:((~humble(X)&quiet(X))))<=>(rich(lucy)))&
(?[X]:((old(X)|~tall(X))))&
(?[X]:((humble(X)&curious(X))))&
((~calm(fred)<~>~tall(fred)))&
(?[X]:((funny(X)|calm(X))))&
(?[X]:((generous(X)|creative(X))))&
((generous(john)|~creative(john)))&
((quiet(susan)<~>happy(susan)))&
(strong(paul)) | ~patient(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 975362595197054028986994
% SZS output start Proof for 975362595197054028986994
2. ! [X0] : (patient(X0) <=> (tall(X0) | ~tall(X0))) [input p1]
23. ~patient(lucy) [input hypothesis]
33. ! [X0] : ((patient(X0) | (~tall(X0) & tall(X0))) & ((tall(X0) | ~tall(X0)) | ~patient(X0))) [nnf transformation 2]
34. ! [X0] : ((patient(X0) | (~tall(X0) & tall(X0))) & (tall(X0) | ~tall(X0) | ~patient(X0))) [flattening 33]
79. patient(X0) | tall(X0) [cnf transformation 34]
80. patient(X0) | ~tall(X0) [cnf transformation 34]
137. ~patient(lucy) [cnf transformation 23]
156. patient(X0) [subsumption resolution 79,80]
354. $false [subsumption resolution 137,156]
% SZS output end Proof for 975362595197054028986994
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not generous then lucy is not happy or rich.
Everyone who is not quiet or rich is patient.
Everyone who is both not old and happy is both not wise and patient and vice versa.
If john is either not happy or creative then someone is not brave or not tall.
Everyone who is either not funny or not creative is either not brave or wise and vice versa.
If someone is rich or wise then someone is either not brave or not wise and vice versa.
If john is not curious then someone is wise.
If mary is both humble and kind then someone is quiet and vice versa.
Everyone who is both not quiet and not old is either old or not wise and vice versa.
Everyone who is strong or rich is kind.
Everyone who is rich or not curious is both not wise and calm.
Everyone who is both curious and kind is either not rich or brave and vice versa.
Everyone who is patient is not brave and vice versa.
If mary is kind or humble then someone is either happy or wise.
If lucy is not generous or strong then someone is both creative and curious.
If alice is both not funny and not curious then susan is generous or not quiet.
Someone is not rich.
Someone is strong.
Mary is not humble.
John is either not happy or calm.
Someone is funny.
Lucy is brave or tall.
Paul is either humble or not strong. | Susan is kind. | entailment | ((~generous(paul))=>((~happy(lucy)|rich(lucy))))&
(![X]:((~quiet(X)|rich(X))=>patient(X)))&
(![X]:((~old(X)&happy(X))<=>(~wise(X)&patient(X))))&
(((~happy(john)<~>creative(john)))=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~funny(X)<~>~creative(X))<=>(~brave(X)<~>wise(X))))&
((?[X]:((rich(X)|wise(X))))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((~curious(john))=>(?[X]:(wise(X))))&
(((humble(mary)&kind(mary)))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&~old(X))<=>(old(X)<~>~wise(X))))&
(![X]:((strong(X)|rich(X))=>kind(X)))&
(![X]:((rich(X)|~curious(X))=>(~wise(X)&calm(X))))&
(![X]:((curious(X)&kind(X))<=>(~rich(X)<~>brave(X))))&
(![X]:(patient(X)<=>~brave(X)))&
(((kind(mary)|humble(mary)))=>(?[X]:((happy(X)<~>wise(X)))))&
(((~generous(lucy)|strong(lucy)))=>(?[X]:((creative(X)&curious(X)))))&
(((~funny(alice)&~curious(alice)))=>((generous(susan)|~quiet(susan))))&
(?[X]:(~rich(X)))&
(?[X]:(strong(X)))&
(~humble(mary))&
((~happy(john)<~>calm(john)))&
(?[X]:(funny(X)))&
((brave(lucy)|tall(lucy)))&
((humble(paul)<~>~strong(paul))) | kind(susan) | [
"p1",
"p5",
"p7",
"p8",
"p9",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3875853129939890482318342
% SZS output start Proof for 3875853129939890482318342
2. ! [X0] : ((rich(X0) | ~quiet(X0)) => patient(X0)) [input p1]
6. ? [X0] : (wise(X0) | rich(X0)) <=> ? [X0] : (~brave(X0) <~> ~wise(X0)) [input p5]
8. (kind(mary) & humble(mary)) <=> ? [X0] : quiet(X0) [input p7]
9. ! [X0] : ((~old(X0) & ~quiet(X0)) <=> (old(X0) <~> ~wise(X0))) [input p8]
10. ! [X0] : ((rich(X0) | strong(X0)) => kind(X0)) [input p9]
12. ! [X0] : ((kind(X0) & curious(X0)) <=> (~rich(X0) <~> brave(X0))) [input p11]
13. ! [X0] : (patient(X0) <=> ~brave(X0)) [input p12]
19. ~humble(mary) [input p18]
24. ~kind(susan) [input hypothesis]
25. ? [X0] : (wise(X0) | rich(X0)) <=> ? [X1] : (~brave(X1) <~> ~wise(X1)) [rectify 6]
29. ! [X0] : (patient(X0) | (~rich(X0) & quiet(X0))) [ennf transformation 2]
32. ! [X0] : (kind(X0) | (~rich(X0) & ~strong(X0))) [ennf transformation 10]
42. (? [X0] : (wise(X0) | rich(X0)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (? [X1] : ((wise(X1) | brave(X1)) & (~wise(X1) | ~brave(X1))) | ! [X0] : (~wise(X0) & ~rich(X0))) [nnf transformation 25]
43. (? [X0] : (wise(X0) | rich(X0)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (? [X2] : ((wise(X2) | brave(X2)) & (~wise(X2) | ~brave(X2))) | ! [X3] : (~wise(X3) & ~rich(X3))) [rectify 42]
44. ? [X0] : (wise(X0) | rich(X0)) => (wise(sK1) | rich(sK1)) [choice axiom]
45. ? [X2] : ((wise(X2) | brave(X2)) & (~wise(X2) | ~brave(X2))) => ((wise(sK2) | brave(sK2)) & (~wise(sK2) | ~brave(sK2))) [choice axiom]
46. ((wise(sK1) | rich(sK1)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (((wise(sK2) | brave(sK2)) & (~wise(sK2) | ~brave(sK2))) | ! [X3] : (~wise(X3) & ~rich(X3))) [skolemisation 43,45,44]
49. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | (~kind(mary) | ~humble(mary))) [nnf transformation 8]
50. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | ~kind(mary) | ~humble(mary)) [flattening 49]
51. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | ~kind(mary) | ~humble(mary)) [rectify 50]
52. ? [X1] : quiet(X1) => quiet(sK4) [choice axiom]
53. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (quiet(sK4) | ~kind(mary) | ~humble(mary)) [skolemisation 51,52]
54. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | (old(X0) | quiet(X0)))) [nnf transformation 9]
55. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | old(X0) | quiet(X0))) [flattening 54]
56. ! [X0] : (((kind(X0) & curious(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~kind(X0) | ~curious(X0)))) [nnf transformation 12]
57. ! [X0] : (((kind(X0) & curious(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~kind(X0) | ~curious(X0))) [flattening 56]
58. ! [X0] : ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))) [nnf transformation 13]
72. patient(X0) | quiet(X0) [cnf transformation 29]
90. wise(sK2) | brave(sK2) | ~rich(X3) [cnf transformation 46]
91. wise(sK2) | brave(sK2) | ~wise(X3) [cnf transformation 46]
93. wise(sK1) | rich(sK1) | ~brave(X1) | wise(X1) [cnf transformation 46]
96. humble(mary) | ~quiet(X0) [cnf transformation 53]
98. ~wise(X0) | old(X0) | old(X0) | quiet(X0) [cnf transformation 55]
102. ~old(X0) | ~wise(X0) | ~old(X0) [cnf transformation 55]
105. ~rich(X0) | kind(X0) [cnf transformation 32]
114. kind(X0) | brave(X0) | rich(X0) [cnf transformation 57]
116. ~brave(X0) | ~patient(X0) [cnf transformation 58]
126. ~humble(mary) [cnf transformation 19]
133. ~kind(susan) [cnf transformation 24]
134. ~wise(X0) | old(X0) | quiet(X0) [duplicate literal removal 98]
135. ~wise(X0) | ~old(X0) [duplicate literal removal 102]
155. 5 <=> ! [X1] : (~brave(X1) | wise(X1)) [avatar definition]
156. ~brave(X1) | wise(X1) <- (5) [avatar component clause 155]
158. 6 <=> rich(sK1) [avatar definition]
160. rich(sK1) <- (6) [avatar component clause 158]
162. 7 <=> wise(sK1) [avatar definition]
164. wise(sK1) <- (7) [avatar component clause 162]
165. 5 | 6 | 7 [avatar split clause 93,162,158,155]
171. 9 <=> ! [X3] : ~wise(X3) [avatar definition]
172. ~wise(X3) <- (9) [avatar component clause 171]
174. 10 <=> brave(sK2) [avatar definition]
176. brave(sK2) <- (10) [avatar component clause 174]
178. 11 <=> wise(sK2) [avatar definition]
180. wise(sK2) <- (11) [avatar component clause 178]
181. 9 | 10 | 11 [avatar split clause 91,178,174,171]
183. 12 <=> ! [X3] : ~rich(X3) [avatar definition]
184. ~rich(X3) <- (12) [avatar component clause 183]
185. 12 | 10 | 11 [avatar split clause 90,178,174,183]
198. 15 <=> ! [X0] : ~quiet(X0) [avatar definition]
199. ~quiet(X0) <- (15) [avatar component clause 198]
206. 17 <=> humble(mary) [avatar definition]
209. 15 | 17 [avatar split clause 96,206,198]
215. ~wise(X0) | quiet(X0) [subsumption resolution 134,135]
216. kind(X0) | brave(X0) [subsumption resolution 114,105]
244. ~17 [avatar split clause 126,206]
275. ~patient(sK2) <- (10) [resolution 116,176]
278. quiet(sK2) <- (10) [resolution 275,72]
279. $false <- (10, 15) [subsumption resolution 278,199]
280. ~10 | ~15 [avatar contradiction clause 279]
289. quiet(sK2) <- (11) [resolution 215,180]
290. $false <- (11, 15) [subsumption resolution 289,199]
291. ~11 | ~15 [avatar contradiction clause 290]
292. $false <- (6, 12) [resolution 184,160]
293. ~6 | ~12 [avatar contradiction clause 292]
294. $false <- (7, 9) [subsumption resolution 164,172]
295. ~7 | ~9 [avatar contradiction clause 294]
296. ~brave(X1) <- (5, 9) [subsumption resolution 156,172]
298. brave(susan) [resolution 216,133]
300. $false <- (5, 9) [subsumption resolution 298,296]
301. ~5 | ~9 [avatar contradiction clause 300]
304. $false [avatar sat refutation 165,181,185,209,244,280,291,293,295,301]
% SZS output end Proof for 3875853129939890482318342
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not quiet and vice versa. Everyone who is both not happy and curious is either not funny or not patient and vice versa. Everyone who is both not calm and not tall is both kind and not quiet. Everyone who is either not happy or rich is both not curious and curious. Everyone who is either not rich or tall is funny or not happy and vice versa. Everyone who is either not kind or not humble is strong and vice versa. If someone is not old or not funny then lucy is either calm or not creative and vice versa. Everyone who is both not wise and generous is either not brave or not humble. If someone is not humble or not creative then mary is both not brave and not generous and vice versa. If someone is both not funny and not old then susan is both not generous and not quiet and vice versa. If someone is either tall or quiet then paul is both happy and not old and vice versa. If someone is not quiet or strong then someone is both kind and not kind. Everyone who is both not calm and not rich is not funny or not kind. Everyone who is either not rich or generous is both humble and not generous. Everyone who is both quiet and generous is both not generous and not patient and vice versa. If someone is calm or not kind then mary is brave and vice versa. Someone is either kind or not funny. Lucy is tall. Someone is both not happy and not generous. Mary is either not calm or quiet. | Paul is not quiet. | contradiction | (![X]:(~patient(X)<=>~quiet(X)))&
(![X]:((~happy(X)&curious(X))<=>(~funny(X)<~>~patient(X))))&
(![X]:((~calm(X)&~tall(X))=>(kind(X)&~quiet(X))))&
(![X]:((~happy(X)<~>rich(X))=>(~curious(X)&curious(X))))&
(![X]:((~rich(X)<~>tall(X))<=>(funny(X)|~happy(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>strong(X)))&
((?[X]:((~old(X)|~funny(X))))<=>((calm(lucy)<~>~creative(lucy))))&
(![X]:((~wise(X)&generous(X))=>(~brave(X)<~>~humble(X))))&
((?[X]:((~humble(X)|~creative(X))))<=>((~brave(mary)&~generous(mary))))&
((?[X]:((~funny(X)&~old(X))))<=>((~generous(susan)&~quiet(susan))))&
((?[X]:((tall(X)<~>quiet(X))))<=>((happy(paul)&~old(paul))))&
((?[X]:((~quiet(X)|strong(X))))=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((~calm(X)&~rich(X))=>(~funny(X)|~kind(X))))&
(![X]:((~rich(X)<~>generous(X))=>(humble(X)&~generous(X))))&
(![X]:((quiet(X)&generous(X))<=>(~generous(X)&~patient(X))))&
((?[X]:((calm(X)|~kind(X))))<=>(brave(mary)))&
(?[X]:((kind(X)<~>~funny(X))))&
(tall(lucy))&
(?[X]:((~happy(X)&~generous(X))))&
((~calm(mary)<~>quiet(mary))) | ~quiet(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3599049743854707085927924
% SZS output start Proof for 3599049743854707085927924
12. ? [X0] : (strong(X0) | ~quiet(X0)) => ? [X0] : (~kind(X0) & kind(X0)) [input p11]
21. ~quiet(paul) [input hypothesis]
22. ? [X0] : (strong(X0) | ~quiet(X0)) => ? [X1] : (~kind(X1) & kind(X1)) [rectify 12]
29. ? [X1] : (~kind(X1) & kind(X1)) | ! [X0] : (~strong(X0) & quiet(X0)) [ennf transformation 22]
59. ? [X0] : (~kind(X0) & kind(X0)) | ! [X1] : (~strong(X1) & quiet(X1)) [rectify 29]
60. ? [X0] : (~kind(X0) & kind(X0)) => (~kind(sK4) & kind(sK4)) [choice axiom]
61. (~kind(sK4) & kind(sK4)) | ! [X1] : (~strong(X1) & quiet(X1)) [skolemisation 59,60]
118. kind(sK4) | quiet(X1) [cnf transformation 61]
120. ~kind(sK4) | quiet(X1) [cnf transformation 61]
141. ~quiet(paul) [cnf transformation 21]
260. 25 <=> kind(sK4) [avatar definition]
265. 26 <=> ! [X1] : quiet(X1) [avatar definition]
266. quiet(X1) <- (26) [avatar component clause 265]
267. 26 | ~25 [avatar split clause 120,260,265]
269. 26 | 25 [avatar split clause 118,260,265]
314. $false <- (26) [resolution 266,141]
315. ~26 [avatar contradiction clause 314]
316. $false [avatar sat refutation 267,269,315]
% SZS output end Proof for 3599049743854707085927924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is happy or humble then someone is not rich and vice versa.
If paul is either humble or rich then paul is creative and vice versa.
Everyone who is happy is wise.
Everyone who is both not wise and kind is not calm or funny and vice versa.
If someone is old or not quiet then lucy is not brave and vice versa.
Everyone who is both not kind and not quiet is both not brave and not calm and vice versa.
Everyone who is old is both patient and wise.
Everyone who is both curious and humble is both tall and generous and vice versa.
Everyone who is either rich or generous is not happy or curious and vice versa.
If someone is both patient and not creative then someone is both not rich and not patient and vice versa.
If someone is both not creative and not generous then paul is both not kind and generous.
Everyone who is either not patient or not funny is both quiet and not brave.
If someone is both not rich and humble then someone is not quiet and vice versa.
If someone is wise or tall then someone is not tall or not quiet.
Everyone who is patient or not funny is both not strong and happy.
Everyone who is either patient or not generous is both humble and kind and vice versa.
Fred is not kind.
Paul is either happy or not kind.
Someone is both old and curious.
Someone is rich.
Someone is strong.
Paul is not curious.
Someone is tall or calm.
Someone is not curious. | Paul is creative. | neutral | (((happy(mary)|humble(mary)))<=>(?[X]:(~rich(X))))&
(((humble(paul)<~>rich(paul)))<=>(creative(paul)))&
(![X]:(happy(X)=>wise(X)))&
(![X]:((~wise(X)&kind(X))<=>(~calm(X)|funny(X))))&
((?[X]:((old(X)|~quiet(X))))<=>(~brave(lucy)))&
(![X]:((~kind(X)&~quiet(X))<=>(~brave(X)&~calm(X))))&
(![X]:(old(X)=>(patient(X)&wise(X))))&
(![X]:((curious(X)&humble(X))<=>(tall(X)&generous(X))))&
(![X]:((rich(X)<~>generous(X))<=>(~happy(X)|curious(X))))&
((?[X]:((patient(X)&~creative(X))))<=>(?[X]:((~rich(X)&~patient(X)))))&
((?[X]:((~creative(X)&~generous(X))))=>((~kind(paul)&generous(paul))))&
(![X]:((~patient(X)<~>~funny(X))=>(quiet(X)&~brave(X))))&
((?[X]:((~rich(X)&humble(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((wise(X)|tall(X))))=>(?[X]:((~tall(X)|~quiet(X)))))&
(![X]:((patient(X)|~funny(X))=>(~strong(X)&happy(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(humble(X)&kind(X))))&
(~kind(fred))&
((happy(paul)<~>~kind(paul)))&
(?[X]:((old(X)&curious(X))))&
(?[X]:(rich(X)))&
(?[X]:(strong(X)))&
(~curious(paul))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:(~curious(X))) | creative(paul) | [] | null | 0 |
If fred is not happy or rich then someone is not curious. Everyone who is old or not generous is either wise or funny and vice versa. If paul is quiet then someone is either creative or humble. Everyone who is not creative is not calm and vice versa. Everyone who is calm or not tall is both funny and wise. If someone is quiet then susan is both not creative and patient and vice versa. Everyone who is wise or not strong is either patient or funny. If someone is not happy or brave then paul is happy and vice versa. Everyone who is either kind or quiet is both not quiet and not strong and vice versa. If mary is wise or not rich then someone is either quiet or old. Everyone who is patient or humble is calm. If alice is both not humble and patient then john is either generous or tall and vice versa. Everyone who is either not quiet or not kind is either not strong or old. Everyone who is either strong or not funny is both not old and not calm. If paul is both kind and generous then someone is both not quiet and not funny. Everyone who is not wise is not strong and vice versa. Someone is either tall or not wise. Alice is both tall and generous. Paul is tall. Mary is happy or not rich. Lucy is not brave or old. Someone is either not strong or happy. | Lucy is not patient. | entailment | (((~happy(fred)|rich(fred)))=>(?[X]:(~curious(X))))&
(![X]:((old(X)|~generous(X))<=>(wise(X)<~>funny(X))))&
((quiet(paul))=>(?[X]:((creative(X)<~>humble(X)))))&
(![X]:(~creative(X)<=>~calm(X)))&
(![X]:((calm(X)|~tall(X))=>(funny(X)&wise(X))))&
((?[X]:(quiet(X)))<=>((~creative(susan)&patient(susan))))&
(![X]:((wise(X)|~strong(X))=>(patient(X)<~>funny(X))))&
((?[X]:((~happy(X)|brave(X))))<=>(happy(paul)))&
(![X]:((kind(X)<~>quiet(X))<=>(~quiet(X)&~strong(X))))&
(((wise(mary)|~rich(mary)))=>(?[X]:((quiet(X)<~>old(X)))))&
(![X]:((patient(X)|humble(X))=>calm(X)))&
(((~humble(alice)&patient(alice)))<=>((generous(john)<~>tall(john))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~strong(X)<~>old(X))))&
(![X]:((strong(X)<~>~funny(X))=>(~old(X)&~calm(X))))&
(((kind(paul)&generous(paul)))=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:(~wise(X)<=>~strong(X)))&
(?[X]:((tall(X)<~>~wise(X))))&
((tall(alice)&generous(alice)))&
(tall(paul))&
((happy(mary)|~rich(mary)))&
((~brave(lucy)|old(lucy)))&
(?[X]:((~strong(X)<~>happy(X)))) | ~patient(lucy) | [
"p4",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8856821831496236947204210
% SZS output start Proof for 8856821831496236947204210
5. ! [X0] : ((~tall(X0) | calm(X0)) => (wise(X0) & funny(X0))) [input p4]
7. ! [X0] : ((~strong(X0) | wise(X0)) => (patient(X0) <~> funny(X0))) [input p6]
11. ! [X0] : ((humble(X0) | patient(X0)) => calm(X0)) [input p10]
23. patient(lucy) [input hypothesis]
26. ! [X0] : ((wise(X0) & funny(X0)) | (tall(X0) & ~calm(X0))) [ennf transformation 5]
27. ! [X0] : ((patient(X0) <~> funny(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 7]
29. ! [X0] : (calm(X0) | (~humble(X0) & ~patient(X0))) [ennf transformation 11]
45. ! [X0] : (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | (strong(X0) & ~wise(X0))) [nnf transformation 27]
78. ~calm(X0) | funny(X0) [cnf transformation 26]
80. ~calm(X0) | wise(X0) [cnf transformation 26]
87. ~patient(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 45]
102. ~patient(X0) | calm(X0) [cnf transformation 29]
131. patient(lucy) [cnf transformation 23]
277. calm(lucy) [resolution 102,131]
279. wise(lucy) [resolution 277,80]
280. funny(lucy) [resolution 277,78]
361. ~funny(lucy) | ~wise(lucy) [resolution 87,131]
362. ~wise(lucy) [subsumption resolution 361,280]
363. $false [subsumption resolution 362,279]
% SZS output end Proof for 8856821831496236947204210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and old then someone is either not brave or not strong and vice versa.
If someone is both not kind and not strong then mary is both not creative and patient and vice versa.
Everyone who is old or not tall is happy or generous and vice versa.
Everyone who is not curious or not happy is happy.
Everyone who is both not funny and not humble is both humble and strong.
If john is both kind and brave then someone is brave or not quiet and vice versa.
Everyone who is both not wise and old is both calm and rich.
Everyone who is either not rich or not brave is both happy and not strong.
Everyone who is both strong and kind is old and vice versa.
Everyone who is generous or not funny is both creative and not kind and vice versa.
Everyone who is both not generous and not kind is not kind or not old.
Everyone who is humble or tall is patient and vice versa.
If john is calm then mary is not creative and vice versa.
Everyone who is not funny or wise is both rich and not kind and vice versa.
If lucy is not creative or patient then someone is both funny and quiet and vice versa.
If someone is creative then fred is both wise and humble.
Someone is either not strong or creative.
Someone is not humble or not wise.
John is not wise.
Alice is both not tall and not generous.
Paul is rich.
Susan is either funny or generous.
Someone is calm or not humble. | Susan is not creative. | neutral | ((?[X]:((~calm(X)&old(X))))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
((?[X]:((~kind(X)&~strong(X))))<=>((~creative(mary)&patient(mary))))&
(![X]:((old(X)|~tall(X))<=>(happy(X)|generous(X))))&
(![X]:((~curious(X)|~happy(X))=>happy(X)))&
(![X]:((~funny(X)&~humble(X))=>(humble(X)&strong(X))))&
(((kind(john)&brave(john)))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((~wise(X)&old(X))=>(calm(X)&rich(X))))&
(![X]:((~rich(X)<~>~brave(X))=>(happy(X)&~strong(X))))&
(![X]:((strong(X)&kind(X))<=>old(X)))&
(![X]:((generous(X)|~funny(X))<=>(creative(X)&~kind(X))))&
(![X]:((~generous(X)&~kind(X))=>(~kind(X)|~old(X))))&
(![X]:((humble(X)|tall(X))<=>patient(X)))&
((calm(john))<=>(~creative(mary)))&
(![X]:((~funny(X)|wise(X))<=>(rich(X)&~kind(X))))&
(((~creative(lucy)|patient(lucy)))<=>(?[X]:((funny(X)&quiet(X)))))&
((?[X]:(creative(X)))=>((wise(fred)&humble(fred))))&
(?[X]:((~strong(X)<~>creative(X))))&
(?[X]:((~humble(X)|~wise(X))))&
(~wise(john))&
((~tall(alice)&~generous(alice)))&
(rich(paul))&
((funny(susan)<~>generous(susan)))&
(?[X]:((calm(X)|~humble(X)))) | ~creative(susan) | [] | null | 0 |
If paul is not patient then paul is either not old or not funny.
Everyone who is either wise or brave is old and vice versa.
If someone is both calm and old then susan is either not strong or curious and vice versa.
If john is both happy and not brave then paul is either not tall or not quiet and vice versa.
Everyone who is not calm is both brave and kind.
If someone is not wise then alice is both kind and not kind.
If someone is kind then someone is either rich or not kind and vice versa.
Everyone who is brave is not brave.
Everyone who is either kind or not happy is both not creative and tall and vice versa.
Everyone who is kind is curious and vice versa.
Everyone who is calm is either not quiet or creative and vice versa.
If someone is strong then someone is curious.
Everyone who is not creative is generous and vice versa.
Everyone who is both tall and not quiet is both not brave and generous and vice versa.
If someone is humble or wise then lucy is both happy and calm.
Everyone who is not tall or funny is either not curious or not kind and vice versa.
Fred is either strong or happy.
Someone is either curious or not happy.
Paul is rich.
Paul is old.
Someone is not strong or not funny.
Someone is not curious.
Someone is both generous and tall. | Susan is not calm. | contradiction | ((~patient(paul))=>((~old(paul)<~>~funny(paul))))&
(![X]:((wise(X)<~>brave(X))<=>old(X)))&
((?[X]:((calm(X)&old(X))))<=>((~strong(susan)<~>curious(susan))))&
(((happy(john)&~brave(john)))<=>((~tall(paul)<~>~quiet(paul))))&
(![X]:(~calm(X)=>(brave(X)&kind(X))))&
((?[X]:(~wise(X)))=>((kind(alice)&~kind(alice))))&
((?[X]:(kind(X)))<=>(?[X]:((rich(X)<~>~kind(X)))))&
(![X]:(brave(X)=>~brave(X)))&
(![X]:((kind(X)<~>~happy(X))<=>(~creative(X)&tall(X))))&
(![X]:(kind(X)<=>curious(X)))&
(![X]:(calm(X)<=>(~quiet(X)<~>creative(X))))&
((?[X]:(strong(X)))=>(?[X]:(curious(X))))&
(![X]:(~creative(X)<=>generous(X)))&
(![X]:((tall(X)&~quiet(X))<=>(~brave(X)&generous(X))))&
((?[X]:((humble(X)|wise(X))))=>((happy(lucy)&calm(lucy))))&
(![X]:((~tall(X)|funny(X))<=>(~curious(X)<~>~kind(X))))&
((strong(fred)<~>happy(fred)))&
(?[X]:((curious(X)<~>~happy(X))))&
(rich(paul))&
(old(paul))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:(~curious(X)))&
(?[X]:((generous(X)&tall(X)))) | ~calm(susan) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2560718245472213076766499
% SZS output start Proof for 2560718245472213076766499
5. ! [X0] : (~calm(X0) => (kind(X0) & brave(X0))) [input p4]
8. ! [X0] : (brave(X0) => ~brave(X0)) [input p7]
24. ~calm(susan) [input hypothesis]
29. ! [X0] : ((kind(X0) & brave(X0)) | calm(X0)) [ennf transformation 5]
31. ! [X0] : (~brave(X0) | ~brave(X0)) [ennf transformation 8]
84. calm(X0) | brave(X0) [cnf transformation 29]
92. ~brave(X0) | ~brave(X0) [cnf transformation 31]
130. ~calm(susan) [cnf transformation 24]
131. ~brave(X0) [duplicate literal removal 92]
276. brave(susan) [resolution 84,130]
277. $false [subsumption resolution 276,131]
% SZS output end Proof for 2560718245472213076766499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and wise is curious and vice versa.
Everyone who is both not humble and not funny is not old.
If someone is either strong or not happy then someone is not wise and vice versa.
Everyone who is not tall or not creative is not curious or creative.
If fred is both tall and kind then someone is either strong or generous and vice versa.
If someone is both strong and brave then alice is either patient or happy.
If fred is either not wise or not funny then john is creative.
If paul is tall or not patient then someone is tall or not humble.
Everyone who is both humble and not wise is either creative or humble and vice versa.
If someone is not funny or funny then susan is either brave or creative.
If paul is either not quiet or quiet then susan is strong.
Everyone who is either not quiet or calm is generous.
Everyone who is both brave and not quiet is funny or wise and vice versa.
Everyone who is not wise is not quiet and vice versa.
If someone is calm then someone is both strong and wise.
Everyone who is either funny or tall is either generous or not kind.
Mary is either happy or patient.
Someone is humble.
Someone is not tall or quiet.
John is either tall or old.
Someone is not funny.
Someone is not brave or not tall. | Paul is not humble. | neutral | (![X]:((calm(X)&wise(X))<=>curious(X)))&
(![X]:((~humble(X)&~funny(X))=>~old(X)))&
((?[X]:((strong(X)<~>~happy(X))))<=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)|~creative(X))=>(~curious(X)|creative(X))))&
(((tall(fred)&kind(fred)))<=>(?[X]:((strong(X)<~>generous(X)))))&
((?[X]:((strong(X)&brave(X))))=>((patient(alice)<~>happy(alice))))&
(((~wise(fred)<~>~funny(fred)))=>(creative(john)))&
(((tall(paul)|~patient(paul)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((humble(X)&~wise(X))<=>(creative(X)<~>humble(X))))&
((?[X]:((~funny(X)|funny(X))))=>((brave(susan)<~>creative(susan))))&
(((~quiet(paul)<~>quiet(paul)))=>(strong(susan)))&
(![X]:((~quiet(X)<~>calm(X))=>generous(X)))&
(![X]:((brave(X)&~quiet(X))<=>(funny(X)|wise(X))))&
(![X]:(~wise(X)<=>~quiet(X)))&
((?[X]:(calm(X)))=>(?[X]:((strong(X)&wise(X)))))&
(![X]:((funny(X)<~>tall(X))=>(generous(X)<~>~kind(X))))&
((happy(mary)<~>patient(mary)))&
(?[X]:(humble(X)))&
(?[X]:((~tall(X)|quiet(X))))&
((tall(john)<~>old(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~brave(X)|~tall(X)))) | ~humble(paul) | [] | null | 0 |
Everyone who is not patient or not generous is not strong or generous. Everyone who is not patient or quiet is either not funny or creative and vice versa. Everyone who is either not kind or calm is not patient or not kind and vice versa. If someone is both patient and rich then fred is both not calm and old. If someone is both funny and not happy then someone is either not humble or quiet. Everyone who is not strong is not funny. If paul is rich or not old then paul is either not rich or wise and vice versa. If someone is both not humble and wise then someone is not brave or tall and vice versa. Everyone who is strong is either not patient or strong. Everyone who is both not rich and tall is both generous and happy and vice versa. Everyone who is not creative is either not generous or curious and vice versa. If someone is either not patient or generous then mary is either rich or generous and vice versa. Everyone who is either not generous or curious is both wise and curious. If fred is funny or not curious then john is both not old and calm. Everyone who is both not patient and not funny is not tall and vice versa. If mary is not wise or not strong then someone is either generous or not tall. Alice is both old and kind. Someone is either patient or not quiet. John is not humble or wise. Fred is kind. Alice is generous. Someone is both rich and patient. | John is humble. | neutral | (![X]:((~patient(X)|~generous(X))=>(~strong(X)|generous(X))))&
(![X]:((~patient(X)|quiet(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((~kind(X)<~>calm(X))<=>(~patient(X)|~kind(X))))&
((?[X]:((patient(X)&rich(X))))=>((~calm(fred)&old(fred))))&
((?[X]:((funny(X)&~happy(X))))=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:(~strong(X)=>~funny(X)))&
(((rich(paul)|~old(paul)))<=>((~rich(paul)<~>wise(paul))))&
((?[X]:((~humble(X)&wise(X))))<=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:(strong(X)=>(~patient(X)<~>strong(X))))&
(![X]:((~rich(X)&tall(X))<=>(generous(X)&happy(X))))&
(![X]:(~creative(X)<=>(~generous(X)<~>curious(X))))&
((?[X]:((~patient(X)<~>generous(X))))<=>((rich(mary)<~>generous(mary))))&
(![X]:((~generous(X)<~>curious(X))=>(wise(X)&curious(X))))&
(((funny(fred)|~curious(fred)))=>((~old(john)&calm(john))))&
(![X]:((~patient(X)&~funny(X))<=>~tall(X)))&
(((~wise(mary)|~strong(mary)))=>(?[X]:((generous(X)<~>~tall(X)))))&
((old(alice)&kind(alice)))&
(?[X]:((patient(X)<~>~quiet(X))))&
((~humble(john)|wise(john)))&
(kind(fred))&
(generous(alice))&
(?[X]:((rich(X)&patient(X)))) | humble(john) | [] | null | 0 |
Everyone who is both rich and not creative is either patient or not tall and vice versa. If someone is either not rich or creative then fred is either wise or calm and vice versa. Everyone who is both not rich and not curious is old or funny and vice versa. Everyone who is not wise is kind and vice versa. If fred is happy or creative then someone is not strong or not quiet. If susan is not funny then someone is either funny or not calm. If alice is either not kind or rich then someone is either not funny or not generous and vice versa. If lucy is not strong then someone is calm and vice versa. Everyone who is not strong or not humble is both not generous and generous. Everyone who is not calm is not happy or wise. Everyone who is both brave and not wise is either humble or not creative and vice versa. Everyone who is either wise or not rich is either not tall or not humble and vice versa. Everyone who is either not creative or not curious is not patient or old. If alice is funny then susan is either not strong or not quiet. If alice is brave then mary is both not humble and not quiet and vice versa. If lucy is both old and patient then someone is generous or not strong. Susan is either not kind or not quiet. Alice is either quiet or calm. Someone is either curious or not tall. Someone is both generous and wise. Mary is both not rich and happy. Someone is not curious or not happy. Someone is not curious or not kind. | Susan is calm. | contradiction | (![X]:((rich(X)&~creative(X))<=>(patient(X)<~>~tall(X))))&
((?[X]:((~rich(X)<~>creative(X))))<=>((wise(fred)<~>calm(fred))))&
(![X]:((~rich(X)&~curious(X))<=>(old(X)|funny(X))))&
(![X]:(~wise(X)<=>kind(X)))&
(((happy(fred)|creative(fred)))=>(?[X]:((~strong(X)|~quiet(X)))))&
((~funny(susan))=>(?[X]:((funny(X)<~>~calm(X)))))&
(((~kind(alice)<~>rich(alice)))<=>(?[X]:((~funny(X)<~>~generous(X)))))&
((~strong(lucy))<=>(?[X]:(calm(X))))&
(![X]:((~strong(X)|~humble(X))=>(~generous(X)&generous(X))))&
(![X]:(~calm(X)=>(~happy(X)|wise(X))))&
(![X]:((brave(X)&~wise(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((wise(X)<~>~rich(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((~creative(X)<~>~curious(X))=>(~patient(X)|old(X))))&
((funny(alice))=>((~strong(susan)<~>~quiet(susan))))&
((brave(alice))<=>((~humble(mary)&~quiet(mary))))&
(((old(lucy)&patient(lucy)))=>(?[X]:((generous(X)|~strong(X)))))&
((~kind(susan)<~>~quiet(susan)))&
((quiet(alice)<~>calm(alice)))&
(?[X]:((curious(X)<~>~tall(X))))&
(?[X]:((generous(X)&wise(X))))&
((~rich(mary)&happy(mary)))&
(?[X]:((~curious(X)|~happy(X))))&
(?[X]:((~curious(X)|~kind(X)))) | calm(susan) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 283127663304642349795646
% SZS output start Proof for 283127663304642349795646
8. ~strong(lucy) <=> ? [X0] : calm(X0) [input p7]
9. ! [X0] : ((~humble(X0) | ~strong(X0)) => (generous(X0) & ~generous(X0))) [input p8]
24. calm(susan) [input hypothesis]
27. ! [X0] : ((generous(X0) & ~generous(X0)) | (humble(X0) & strong(X0))) [ennf transformation 9]
53. (~strong(lucy) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | strong(lucy)) [nnf transformation 8]
54. (~strong(lucy) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | strong(lucy)) [rectify 53]
55. ? [X1] : calm(X1) => calm(sK4) [choice axiom]
56. (~strong(lucy) | ! [X0] : ~calm(X0)) & (calm(sK4) | strong(lucy)) [skolemisation 54,55]
111. ~strong(lucy) | ~calm(X0) [cnf transformation 56]
112. ~generous(X0) | strong(X0) [cnf transformation 27]
114. generous(X0) | strong(X0) [cnf transformation 27]
151. calm(susan) [cnf transformation 24]
245. 20 <=> ! [X0] : ~calm(X0) [avatar definition]
246. ~calm(X0) <- (20) [avatar component clause 245]
248. 21 <=> strong(lucy) [avatar definition]
250. ~strong(lucy) <- (~21) [avatar component clause 248]
251. 20 | ~21 [avatar split clause 111,248,245]
258. strong(X0) [subsumption resolution 112,114]
348. $false <- (20) [resolution 246,151]
349. ~20 [avatar contradiction clause 348]
350. $false <- (~21) [subsumption resolution 250,258]
351. 21 [avatar contradiction clause 350]
352. $false [avatar sat refutation 251,349,351]
% SZS output end Proof for 283127663304642349795646
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not generous or quiet then alice is humble or brave.
If lucy is both old and not curious then someone is not wise or not curious.
Everyone who is both not calm and not creative is either not kind or not rich.
If fred is not funny or not curious then someone is both not strong 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.
Everyone who is not curious or calm is not wise and vice versa.
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.
Lucy is generous.
Someone is not old or not wise.
Someone is both not quiet and not wise. | Fred is not curious. | contradiction | (((~generous(mary)<~>quiet(mary)))=>((humble(alice)|brave(alice))))&
(((old(lucy)&~curious(lucy)))=>(?[X]:((~wise(X)|~curious(X)))))&
(![X]:((~calm(X)&~creative(X))=>(~kind(X)<~>~rich(X))))&
(((~funny(fred)|~curious(fred)))<=>(?[X]:((~strong(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]:((~curious(X)|calm(X))<=>~wise(X)))&
(?[X]:((~tall(X)<~>~kind(X))))&
(?[X]:((~patient(X)&~curious(X))))&
(?[X]:((curious(X)&~patient(X))))&
((kind(fred)<~>~creative(fred)))&
(?[X]:(humble(X)))&
(generous(lucy))&
(?[X]:((~old(X)|~wise(X))))&
(?[X]:((~quiet(X)&~wise(X)))) | ~curious(fred) | [
"p3",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2060172558672534140771924
% SZS output start Proof for 2060172558672534140771924
4. (~curious(fred) | ~funny(fred)) <=> ? [X0] : (~rich(X0) & ~strong(X0)) [input p3]
10. ! [X0] : (~rich(X0) <=> brave(X0)) [input p9]
11. ! [X0] : (~wise(X0) => (~brave(X0) <~> strong(X0))) [input p10]
12. ! [X0] : ((calm(X0) & patient(X0)) <=> (rich(X0) | ~calm(X0))) [input p11]
16. ! [X0] : ((calm(X0) | ~curious(X0)) <=> ~wise(X0)) [input p15]
25. ~curious(fred) [input hypothesis]
36. ! [X0] : ((~brave(X0) <~> strong(X0)) | wise(X0)) [ennf transformation 11]
42. ((~curious(fred) | ~funny(fred)) | ! [X0] : (rich(X0) | strong(X0))) & (? [X0] : (~rich(X0) & ~strong(X0)) | (curious(fred) & funny(fred))) [nnf transformation 4]
43. (~curious(fred) | ~funny(fred) | ! [X0] : (rich(X0) | strong(X0))) & (? [X0] : (~rich(X0) & ~strong(X0)) | (curious(fred) & funny(fred))) [flattening 42]
44. (~curious(fred) | ~funny(fred) | ! [X0] : (rich(X0) | strong(X0))) & (? [X1] : (~rich(X1) & ~strong(X1)) | (curious(fred) & funny(fred))) [rectify 43]
45. ? [X1] : (~rich(X1) & ~strong(X1)) => (~rich(sK1) & ~strong(sK1)) [choice axiom]
46. (~curious(fred) | ~funny(fred) | ! [X0] : (rich(X0) | strong(X0))) & ((~rich(sK1) & ~strong(sK1)) | (curious(fred) & funny(fred))) [skolemisation 44,45]
65. ! [X0] : ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))) [nnf transformation 10]
66. ! [X0] : (((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | wise(X0)) [nnf transformation 36]
67. ! [X0] : (((calm(X0) & patient(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~calm(X0) | ~patient(X0)))) [nnf transformation 12]
68. ! [X0] : (((calm(X0) & patient(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~calm(X0) | ~patient(X0))) [flattening 67]
76. ! [X0] : (((calm(X0) | ~curious(X0)) | wise(X0)) & (~wise(X0) | (~calm(X0) & curious(X0)))) [nnf transformation 16]
77. ! [X0] : ((calm(X0) | ~curious(X0) | wise(X0)) & (~wise(X0) | (~calm(X0) & curious(X0)))) [flattening 76]
98. ~strong(sK1) | curious(fred) [cnf transformation 46]
100. ~rich(sK1) | curious(fred) [cnf transformation 46]
117. rich(X0) | brave(X0) [cnf transformation 65]
119. ~brave(X0) | strong(X0) | wise(X0) [cnf transformation 66]
124. calm(X0) | calm(X0) [cnf transformation 68]
138. ~wise(X0) | ~calm(X0) [cnf transformation 77]
153. ~curious(fred) [cnf transformation 25]
155. calm(X0) [duplicate literal removal 124]
199. 11 <=> curious(fred) [avatar definition]
204. 12 <=> rich(sK1) [avatar definition]
206. ~rich(sK1) <- (~12) [avatar component clause 204]
207. 11 | ~12 [avatar split clause 100,204,199]
210. 13 <=> strong(sK1) [avatar definition]
212. ~strong(sK1) <- (~13) [avatar component clause 210]
213. 11 | ~13 [avatar split clause 98,210,199]
305. ~wise(X0) [subsumption resolution 138,155]
322. ~11 [avatar split clause 153,199]
323. brave(sK1) <- (~12) [resolution 117,206]
328. strong(sK1) | wise(sK1) <- (~12) [resolution 119,323]
329. wise(sK1) <- (~12, ~13) [subsumption resolution 328,212]
330. $false <- (~12, ~13) [subsumption resolution 329,305]
331. 12 | 13 [avatar contradiction clause 330]
332. $false [avatar sat refutation 207,213,322,331]
% SZS output end Proof for 2060172558672534140771924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not funny then mary is kind.
Everyone who is quiet or not generous is not creative or happy and vice versa.
Everyone who is not generous or not brave is happy and vice versa.
If fred is both tall and not happy then mary is either not tall or not patient.
If someone is not patient or not happy then mary is both not happy and not funny.
Everyone who is either quiet or not tall is either not calm or funny.
If fred is not rich then someone is funny.
Everyone who is both quiet and wise is not brave.
Everyone who is either not creative or kind is either rich or tall.
Everyone who is humble or not quiet is not kind.
Everyone who is not patient or not creative is both not patient and not kind and vice versa.
If someone is not strong then lucy is strong or not tall.
Everyone who is not rich or funny is both not tall and not calm.
If alice is either not tall or funny then someone is either not funny or not patient.
Someone is either kind or not kind.
Someone is curious or not old.
John is not happy or quiet.
Someone is not creative or curious.
Mary is not tall.
Someone is not tall.
Someone is not brave. | Alice is happy. | entailment | ((?[X]:((~rich(X)|~funny(X))))=>(kind(mary)))&
(![X]:((quiet(X)|~generous(X))<=>(~creative(X)|happy(X))))&
(![X]:((~generous(X)|~brave(X))<=>happy(X)))&
(((tall(fred)&~happy(fred)))=>((~tall(mary)<~>~patient(mary))))&
((?[X]:((~patient(X)|~happy(X))))=>((~happy(mary)&~funny(mary))))&
(![X]:((quiet(X)<~>~tall(X))=>(~calm(X)<~>funny(X))))&
((~rich(fred))=>(?[X]:(funny(X))))&
(![X]:((quiet(X)&wise(X))=>~brave(X)))&
(![X]:((~creative(X)<~>kind(X))=>(rich(X)<~>tall(X))))&
(![X]:((humble(X)|~quiet(X))=>~kind(X)))&
(![X]:((~patient(X)|~creative(X))<=>(~patient(X)&~kind(X))))&
((?[X]:(~strong(X)))=>((strong(lucy)|~tall(lucy))))&
(![X]:((~rich(X)|funny(X))=>(~tall(X)&~calm(X))))&
(((~tall(alice)<~>funny(alice)))=>(?[X]:((~funny(X)<~>~patient(X)))))&
(?[X]:((kind(X)<~>~kind(X))))&
(?[X]:((curious(X)|~old(X))))&
((~happy(john)|quiet(john)))&
(?[X]:((~creative(X)|curious(X))))&
(~tall(mary))&
(?[X]:(~tall(X)))&
(?[X]:(~brave(X))) | happy(alice) | [
"p0",
"p1",
"p4",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8360366608133196404750540
% SZS output start Proof for 8360366608133196404750540
1. ? [X0] : (~funny(X0) | ~rich(X0)) => kind(mary) [input p0]
2. ! [X0] : ((~generous(X0) | quiet(X0)) <=> (happy(X0) | ~creative(X0))) [input p1]
5. ? [X0] : (~happy(X0) | ~patient(X0)) => (~funny(mary) & ~happy(mary)) [input p4]
10. ! [X0] : ((~quiet(X0) | humble(X0)) => ~kind(X0)) [input p9]
11. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (~kind(X0) & ~patient(X0))) [input p10]
22. ~happy(alice) [input hypothesis]
26. ! [X0] : (~quiet(X0) => ~kind(X0)) [pure predicate removal 10]
28. kind(mary) | ! [X0] : (funny(X0) & rich(X0)) [ennf transformation 1]
31. (~funny(mary) & ~happy(mary)) | ! [X0] : (happy(X0) & patient(X0)) [ennf transformation 5]
35. ! [X0] : (~kind(X0) | quiet(X0)) [ennf transformation 26]
38. ! [X0] : (((~generous(X0) | quiet(X0)) | (~happy(X0) & creative(X0))) & ((happy(X0) | ~creative(X0)) | (generous(X0) & ~quiet(X0)))) [nnf transformation 2]
39. ! [X0] : ((~generous(X0) | quiet(X0) | (~happy(X0) & creative(X0))) & (happy(X0) | ~creative(X0) | (generous(X0) & ~quiet(X0)))) [flattening 38]
47. ! [X0] : (((~creative(X0) | ~patient(X0)) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 11]
48. ! [X0] : ((~creative(X0) | ~patient(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | (creative(X0) & patient(X0)))) [flattening 47]
60. kind(mary) | funny(X0) [cnf transformation 28]
61. ~creative(X0) | happy(X0) | ~quiet(X0) [cnf transformation 39]
71. ~happy(mary) | happy(X0) [cnf transformation 31]
73. ~funny(mary) | happy(X0) [cnf transformation 31]
83. ~kind(X0) | quiet(X0) [cnf transformation 35]
85. ~patient(X0) | creative(X0) [cnf transformation 48]
86. ~kind(X0) | patient(X0) [cnf transformation 48]
103. ~happy(alice) [cnf transformation 22]
105. 1 <=> ! [X0] : funny(X0) [avatar definition]
106. funny(X0) <- (1) [avatar component clause 105]
108. 2 <=> kind(mary) [avatar definition]
110. kind(mary) <- (2) [avatar component clause 108]
111. 1 | 2 [avatar split clause 60,108,105]
129. 7 <=> patient(mary) [avatar definition]
131. patient(mary) <- (7) [avatar component clause 129]
135. 8 <=> ! [X0] : happy(X0) [avatar definition]
136. happy(X0) <- (8) [avatar component clause 135]
138. 9 <=> funny(mary) [avatar definition]
140. ~funny(mary) <- (~9) [avatar component clause 138]
141. 8 | ~9 [avatar split clause 73,138,135]
147. 11 <=> happy(mary) [avatar definition]
150. 8 | ~11 [avatar split clause 71,147,135]
193. quiet(mary) <- (2) [resolution 83,110]
194. patient(mary) <- (2) [resolution 86,110]
195. 7 | ~2 [avatar split clause 194,108,129]
196. creative(mary) <- (7) [resolution 131,85]
201. happy(mary) | ~quiet(mary) <- (7) [resolution 61,196]
205. happy(mary) <- (2, 7) [subsumption resolution 201,193]
206. 11 | ~2 | ~7 [avatar split clause 205,129,108,147]
207. $false <- (8) [resolution 136,103]
210. ~8 [avatar contradiction clause 207]
216. $false <- (1, ~9) [resolution 106,140]
219. ~1 | 9 [avatar contradiction clause 216]
220. $false [avatar sat refutation 111,141,150,195,206,210,219]
% SZS output end Proof for 8360366608133196404750540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then susan is creative.
Everyone who is quiet or not creative is either humble or brave and vice versa.
Everyone who is brave is not generous or not curious.
If someone is brave then someone is calm or funny and vice versa.
Everyone who is both brave and not funny is both not wise and humble.
Everyone who is both funny and not humble is old or wise and vice versa.
If someone is not tall or tall then someone is both strong and not creative.
Everyone who is both humble and not curious is either not rich or not strong and vice versa.
Everyone who is wise is both funny and creative and vice versa.
Everyone who is either wise or funny is either happy or not rich.
Everyone who is not quiet or not generous is funny or not happy.
If john is both not generous and old then someone is either happy or not calm.
Everyone who is calm is not curious or patient.
If someone is not curious or creative then lucy is not rich.
If someone is quiet or creative then paul is curious or strong.
If someone is not strong then fred is not happy or curious.
Someone is both quiet and not strong.
Someone is both not patient and creative.
Someone is either not tall or not quiet.
Fred is not quiet or curious.
Someone is tall.
Alice is either funny or tall.
Fred is not wise or not patient.
Someone is not humble. | Paul is curious. | neutral | ((?[X]:(humble(X)))=>(creative(susan)))&
(![X]:((quiet(X)|~creative(X))<=>(humble(X)<~>brave(X))))&
(![X]:(brave(X)=>(~generous(X)|~curious(X))))&
((?[X]:(brave(X)))<=>(?[X]:((calm(X)|funny(X)))))&
(![X]:((brave(X)&~funny(X))=>(~wise(X)&humble(X))))&
(![X]:((funny(X)&~humble(X))<=>(old(X)|wise(X))))&
((?[X]:((~tall(X)|tall(X))))=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((humble(X)&~curious(X))<=>(~rich(X)<~>~strong(X))))&
(![X]:(wise(X)<=>(funny(X)&creative(X))))&
(![X]:((wise(X)<~>funny(X))=>(happy(X)<~>~rich(X))))&
(![X]:((~quiet(X)|~generous(X))=>(funny(X)|~happy(X))))&
(((~generous(john)&old(john)))=>(?[X]:((happy(X)<~>~calm(X)))))&
(![X]:(calm(X)=>(~curious(X)|patient(X))))&
((?[X]:((~curious(X)|creative(X))))=>(~rich(lucy)))&
((?[X]:((quiet(X)|creative(X))))=>((curious(paul)|strong(paul))))&
((?[X]:(~strong(X)))=>((~happy(fred)|curious(fred))))&
(?[X]:((quiet(X)&~strong(X))))&
(?[X]:((~patient(X)&creative(X))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
((~quiet(fred)|curious(fred)))&
(?[X]:(tall(X)))&
((funny(alice)<~>tall(alice)))&
((~wise(fred)|~patient(fred)))&
(?[X]:(~humble(X))) | curious(paul) | [] | null | 0 |
If someone is both old and not funny then someone is either not old or humble. Everyone who is not old is either not quiet or curious. Everyone who is either wise or not generous is not brave and vice versa. Everyone who is generous is wise or brave. If someone is either not calm or calm then someone is curious. If someone is not generous then someone is both kind and old. If someone is strong or not humble then someone is strong and vice versa. Everyone who is either humble or happy is both rich and brave. Everyone who is either not strong or not wise is not generous. If someone is not generous or calm then lucy is either curious or not creative and vice versa. Everyone who is kind or not brave is both not tall and not patient and vice versa. If someone is both not creative and quiet then someone is either not rich or not funny and vice versa. Everyone who is either not humble or not calm is both not brave and happy. Everyone who is either not happy or curious is not quiet. If john is not humble then someone is either curious or tall and vice versa. Everyone who is either not kind or not wise is not rich. Someone is not curious. Someone is brave. Someone is either not calm or rich. Someone is either not strong or not patient. Someone is not creative. Someone is both not creative and quiet. Paul is either not funny or generous. Someone is either not old or funny. | Lucy is not humble. | neutral | ((?[X]:((old(X)&~funny(X))))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:(~old(X)=>(~quiet(X)<~>curious(X))))&
(![X]:((wise(X)<~>~generous(X))<=>~brave(X)))&
(![X]:(generous(X)=>(wise(X)|brave(X))))&
((?[X]:((~calm(X)<~>calm(X))))=>(?[X]:(curious(X))))&
((?[X]:(~generous(X)))=>(?[X]:((kind(X)&old(X)))))&
((?[X]:((strong(X)|~humble(X))))<=>(?[X]:(strong(X))))&
(![X]:((humble(X)<~>happy(X))=>(rich(X)&brave(X))))&
(![X]:((~strong(X)<~>~wise(X))=>~generous(X)))&
((?[X]:((~generous(X)|calm(X))))<=>((curious(lucy)<~>~creative(lucy))))&
(![X]:((kind(X)|~brave(X))<=>(~tall(X)&~patient(X))))&
((?[X]:((~creative(X)&quiet(X))))<=>(?[X]:((~rich(X)<~>~funny(X)))))&
(![X]:((~humble(X)<~>~calm(X))=>(~brave(X)&happy(X))))&
(![X]:((~happy(X)<~>curious(X))=>~quiet(X)))&
((~humble(john))<=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((~kind(X)<~>~wise(X))=>~rich(X)))&
(?[X]:(~curious(X)))&
(?[X]:(brave(X)))&
(?[X]:((~calm(X)<~>rich(X))))&
(?[X]:((~strong(X)<~>~patient(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~creative(X)&quiet(X))))&
((~funny(paul)<~>generous(paul)))&
(?[X]:((~old(X)<~>funny(X)))) | ~humble(lucy) | [] | null | 0 |
Everyone who is not happy is patient and vice versa. Everyone who is quiet or patient is both creative and not funny. Everyone who is both calm and not curious is either wise or not kind and vice versa. Everyone who is generous is both quiet and funny. Everyone who is not old or not funny is not creative or happy. Everyone who is both not patient and not wise is both creative and brave and vice versa. If someone is not strong or not old then someone is generous. Everyone who is not patient is both not curious and not wise. If paul is either not rich or not wise then someone is either wise or not brave. Everyone who is not patient or generous is not kind. Everyone who is both not old and humble is both not kind and curious and vice versa. If someone is either not brave or happy then someone is calm or not generous. Everyone who is not patient is humble and vice versa. If someone is both not tall and not wise then fred is both brave and not rich and vice versa. If someone is not creative then someone is both quiet and not creative and vice versa. Everyone who is either not brave or happy is not generous. Alice is kind or tall. Someone is not curious or not generous. Mary is either humble or curious. John is both not kind and creative. Someone is either funny or not creative. | Alice is rich. | neutral | (![X]:(~happy(X)<=>patient(X)))&
(![X]:((quiet(X)|patient(X))=>(creative(X)&~funny(X))))&
(![X]:((calm(X)&~curious(X))<=>(wise(X)<~>~kind(X))))&
(![X]:(generous(X)=>(quiet(X)&funny(X))))&
(![X]:((~old(X)|~funny(X))=>(~creative(X)|happy(X))))&
(![X]:((~patient(X)&~wise(X))<=>(creative(X)&brave(X))))&
((?[X]:((~strong(X)|~old(X))))=>(?[X]:(generous(X))))&
(![X]:(~patient(X)=>(~curious(X)&~wise(X))))&
(((~rich(paul)<~>~wise(paul)))=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((~patient(X)|generous(X))=>~kind(X)))&
(![X]:((~old(X)&humble(X))<=>(~kind(X)&curious(X))))&
((?[X]:((~brave(X)<~>happy(X))))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:(~patient(X)<=>humble(X)))&
((?[X]:((~tall(X)&~wise(X))))<=>((brave(fred)&~rich(fred))))&
((?[X]:(~creative(X)))<=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~brave(X)<~>happy(X))=>~generous(X)))&
((kind(alice)|tall(alice)))&
(?[X]:((~curious(X)|~generous(X))))&
((humble(mary)<~>curious(mary)))&
((~kind(john)&creative(john)))&
(?[X]:((funny(X)<~>~creative(X)))) | rich(alice) | [] | null | 0 |
Everyone who is happy or not patient is either not funny or creative and vice versa. Everyone who is not creative or not happy is wise and vice versa. Everyone who is generous or not creative is both calm and quiet and vice versa. Everyone who is either kind or creative is not brave or calm and vice versa. Everyone who is humble is either not humble or humble and vice versa. Everyone who is either old or strong is both not rich and not happy. Everyone who is not calm or not funny is either not happy or wise. If someone is either brave or calm then susan is both not quiet and not wise. If someone is either quiet or not generous then someone is not tall or quiet. If someone is not creative then someone is both not funny and brave and vice versa. Everyone who is not funny is both tall and not calm. If mary is not generous then susan is not curious. Everyone who is rich or generous is quiet. If mary is not old or quiet then someone is not tall and vice versa. If mary is either rich or not curious then someone is either not humble or funny. Everyone who is not calm or brave is either not funny or happy and vice versa. Paul is not old. Susan is brave or strong. Someone is old or generous. Someone is either rich or not generous. Someone is quiet. Alice is not happy. | Alice is not patient. | entailment | (![X]:((happy(X)|~patient(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((~creative(X)|~happy(X))<=>wise(X)))&
(![X]:((generous(X)|~creative(X))<=>(calm(X)&quiet(X))))&
(![X]:((kind(X)<~>creative(X))<=>(~brave(X)|calm(X))))&
(![X]:(humble(X)<=>(~humble(X)<~>humble(X))))&
(![X]:((old(X)<~>strong(X))=>(~rich(X)&~happy(X))))&
(![X]:((~calm(X)|~funny(X))=>(~happy(X)<~>wise(X))))&
((?[X]:((brave(X)<~>calm(X))))=>((~quiet(susan)&~wise(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:(~funny(X)=>(tall(X)&~calm(X))))&
((~generous(mary))=>(~curious(susan)))&
(![X]:((rich(X)|generous(X))=>quiet(X)))&
(((~old(mary)|quiet(mary)))<=>(?[X]:(~tall(X))))&
(((rich(mary)<~>~curious(mary)))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~calm(X)|brave(X))<=>(~funny(X)<~>happy(X))))&
(~old(paul))&
((brave(susan)|strong(susan)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:(quiet(X)))&
(~happy(alice)) | ~patient(alice) | [
"p0",
"p1",
"p6",
"p9",
"p10",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2728716001867083104897413
% SZS output start Proof for 2728716001867083104897413
1. ! [X0] : ((~patient(X0) | happy(X0)) <=> (~funny(X0) <~> creative(X0))) [input p0]
2. ! [X0] : ((~happy(X0) | ~creative(X0)) <=> wise(X0)) [input p1]
7. ! [X0] : ((~funny(X0) | ~calm(X0)) => (~happy(X0) <~> wise(X0))) [input p6]
10. ? [X0] : ~creative(X0) <=> ? [X0] : (brave(X0) & ~funny(X0)) [input p9]
11. ! [X0] : (~funny(X0) => (~calm(X0) & tall(X0))) [input p10]
16. ! [X0] : ((brave(X0) | ~calm(X0)) <=> (~funny(X0) <~> happy(X0))) [input p15]
22. ~happy(alice) [input p21]
23. patient(alice) [input hypothesis]
25. ? [X0] : ~creative(X0) <=> ? [X1] : (brave(X1) & ~funny(X1)) [rectify 10]
27. ! [X0] : ((~happy(X0) <~> wise(X0)) | (funny(X0) & calm(X0))) [ennf transformation 7]
30. ! [X0] : ((~calm(X0) & tall(X0)) | funny(X0)) [ennf transformation 11]
34. ! [X0] : (((~patient(X0) | happy(X0)) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0)))) & (((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | (patient(X0) & ~happy(X0)))) [nnf transformation 1]
35. ! [X0] : ((~patient(X0) | happy(X0) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0)))) & (((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | (patient(X0) & ~happy(X0)))) [flattening 34]
36. ! [X0] : (((~happy(X0) | ~creative(X0)) | ~wise(X0)) & (wise(X0) | (happy(X0) & creative(X0)))) [nnf transformation 2]
37. ! [X0] : ((~happy(X0) | ~creative(X0) | ~wise(X0)) & (wise(X0) | (happy(X0) & creative(X0)))) [flattening 36]
44. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (funny(X0) & calm(X0))) [nnf transformation 27]
50. (? [X0] : ~creative(X0) | ! [X1] : (~brave(X1) | funny(X1))) & (? [X1] : (brave(X1) & ~funny(X1)) | ! [X0] : creative(X0)) [nnf transformation 25]
51. (? [X0] : ~creative(X0) | ! [X1] : (~brave(X1) | funny(X1))) & (? [X2] : (brave(X2) & ~funny(X2)) | ! [X3] : creative(X3)) [rectify 50]
52. ? [X0] : ~creative(X0) => ~creative(sK1) [choice axiom]
53. ? [X2] : (brave(X2) & ~funny(X2)) => (brave(sK2) & ~funny(sK2)) [choice axiom]
54. (~creative(sK1) | ! [X1] : (~brave(X1) | funny(X1))) & ((brave(sK2) & ~funny(sK2)) | ! [X3] : creative(X3)) [skolemisation 51,53,52]
63. ! [X0] : (((brave(X0) | ~calm(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~brave(X0) & calm(X0)))) [nnf transformation 16]
64. ! [X0] : ((brave(X0) | ~calm(X0) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~brave(X0) & calm(X0)))) [flattening 63]
77. ~creative(X0) | happy(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 35]
79. wise(X0) | happy(X0) [cnf transformation 37]
102. ~wise(X0) | happy(X0) | calm(X0) [cnf transformation 44]
110. ~funny(sK2) | creative(X3) [cnf transformation 54]
114. ~calm(X0) | funny(X0) [cnf transformation 30]
127. ~happy(X0) | funny(X0) | calm(X0) [cnf transformation 64]
137. ~happy(alice) [cnf transformation 22]
138. patient(alice) [cnf transformation 23]
146. calm(X0) | happy(X0) [subsumption resolution 102,79]
194. 11 <=> ! [X3] : creative(X3) [avatar definition]
195. creative(X3) <- (11) [avatar component clause 194]
202. 13 <=> funny(sK2) [avatar definition]
204. ~funny(sK2) <- (~13) [avatar component clause 202]
205. 11 | ~13 [avatar split clause 110,202,194]
252. funny(X0) | calm(X0) [subsumption resolution 127,146]
253. funny(X0) [subsumption resolution 252,114]
381. $false <- (~13) [subsumption resolution 204,253]
382. 13 [avatar contradiction clause 381]
392. happy(X0) | ~funny(X0) | ~patient(X0) <- (11) [resolution 77,195]
393. ~patient(X0) | happy(X0) <- (11) [subsumption resolution 392,253]
437. happy(alice) <- (11) [resolution 393,138]
438. $false <- (11) [subsumption resolution 437,137]
439. ~11 [avatar contradiction clause 438]
440. $false [avatar sat refutation 205,382,439]
% SZS output end Proof for 2728716001867083104897413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is generous or not funny and vice versa.
Everyone who is either not humble or rich is either not brave or funny and vice versa.
Everyone who is both not old and not funny is either not strong or not old and vice versa.
If someone is either brave or not old then mary is either generous or tall and vice versa.
If someone is brave then someone is patient and vice versa.
If john is not happy or not kind then lucy is curious.
If paul is calm or not brave then lucy is both not calm and rich.
If someone is brave or not kind then someone is both humble and wise.
Everyone who is not funny or patient is both not happy and not generous and vice versa.
If paul is either not old or not wise then someone is not creative and vice versa.
If paul is not rich or kind then someone is either rich or not calm and vice versa.
Everyone who is brave or generous is both brave and not kind and vice versa.
If john is both not strong and humble then lucy is humble.
Everyone who is not humble or strong is both not funny and quiet.
Everyone who is quiet or not strong is both kind and not wise.
If someone is either not funny or generous then lucy is calm or not tall.
Someone is both curious and not patient.
Someone is not old.
Fred is either generous or humble.
Someone is not tall.
Someone is not happy.
John is not brave or not quiet.
Someone is either calm or not calm. | Paul is patient. | contradiction | (![X]:(old(X)<=>(generous(X)|~funny(X))))&
(![X]:((~humble(X)<~>rich(X))<=>(~brave(X)<~>funny(X))))&
(![X]:((~old(X)&~funny(X))<=>(~strong(X)<~>~old(X))))&
((?[X]:((brave(X)<~>~old(X))))<=>((generous(mary)<~>tall(mary))))&
((?[X]:(brave(X)))<=>(?[X]:(patient(X))))&
(((~happy(john)|~kind(john)))=>(curious(lucy)))&
(((calm(paul)|~brave(paul)))=>((~calm(lucy)&rich(lucy))))&
((?[X]:((brave(X)|~kind(X))))=>(?[X]:((humble(X)&wise(X)))))&
(![X]:((~funny(X)|patient(X))<=>(~happy(X)&~generous(X))))&
(((~old(paul)<~>~wise(paul)))<=>(?[X]:(~creative(X))))&
(((~rich(paul)|kind(paul)))<=>(?[X]:((rich(X)<~>~calm(X)))))&
(![X]:((brave(X)|generous(X))<=>(brave(X)&~kind(X))))&
(((~strong(john)&humble(john)))=>(humble(lucy)))&
(![X]:((~humble(X)|strong(X))=>(~funny(X)&quiet(X))))&
(![X]:((quiet(X)|~strong(X))=>(kind(X)&~wise(X))))&
((?[X]:((~funny(X)<~>generous(X))))=>((calm(lucy)|~tall(lucy))))&
(?[X]:((curious(X)&~patient(X))))&
(?[X]:(~old(X)))&
((generous(fred)<~>humble(fred)))&
(?[X]:(~tall(X)))&
(?[X]:(~happy(X)))&
((~brave(john)|~quiet(john)))&
(?[X]:((calm(X)<~>~calm(X)))) | patient(paul) | [
"p4",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6423255884420371807904475
% SZS output start Proof for 6423255884420371807904475
5. ? [X0] : brave(X0) <=> ? [X0] : patient(X0) [input p4]
8. ? [X0] : (~kind(X0) | brave(X0)) => ? [X0] : (wise(X0) & humble(X0)) [input p7]
14. ! [X0] : ((strong(X0) | ~humble(X0)) => (quiet(X0) & ~funny(X0))) [input p13]
15. ! [X0] : ((~strong(X0) | quiet(X0)) => (~wise(X0) & kind(X0))) [input p14]
24. patient(paul) [input hypothesis]
25. ? [X0] : brave(X0) <=> ? [X1] : patient(X1) [rectify 5]
26. ? [X0] : (~kind(X0) | brave(X0)) => ? [X1] : (wise(X1) & humble(X1)) [rectify 8]
30. ? [X1] : (wise(X1) & humble(X1)) | ! [X0] : (kind(X0) & ~brave(X0)) [ennf transformation 26]
33. ! [X0] : ((quiet(X0) & ~funny(X0)) | (~strong(X0) & humble(X0))) [ennf transformation 14]
34. ! [X0] : ((~wise(X0) & kind(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 15]
46. (? [X0] : brave(X0) | ! [X1] : ~patient(X1)) & (? [X1] : patient(X1) | ! [X0] : ~brave(X0)) [nnf transformation 25]
47. (? [X0] : brave(X0) | ! [X1] : ~patient(X1)) & (? [X2] : patient(X2) | ! [X3] : ~brave(X3)) [rectify 46]
48. ? [X0] : brave(X0) => brave(sK1) [choice axiom]
49. ? [X2] : patient(X2) => patient(sK2) [choice axiom]
50. (brave(sK1) | ! [X1] : ~patient(X1)) & (patient(sK2) | ! [X3] : ~brave(X3)) [skolemisation 47,49,48]
51. ? [X0] : (wise(X0) & humble(X0)) | ! [X1] : (kind(X1) & ~brave(X1)) [rectify 30]
52. ? [X0] : (wise(X0) & humble(X0)) => (wise(sK3) & humble(sK3)) [choice axiom]
53. (wise(sK3) & humble(sK3)) | ! [X1] : (kind(X1) & ~brave(X1)) [skolemisation 51,52]
106. brave(sK1) | ~patient(X1) [cnf transformation 50]
113. wise(sK3) | ~brave(X1) [cnf transformation 53]
139. ~strong(X0) | quiet(X0) [cnf transformation 33]
142. ~quiet(X0) | ~wise(X0) [cnf transformation 34]
143. ~wise(X0) | strong(X0) [cnf transformation 34]
155. patient(paul) [cnf transformation 24]
190. 7 <=> ! [X1] : ~patient(X1) [avatar definition]
191. ~patient(X1) <- (7) [avatar component clause 190]
193. 8 <=> brave(sK1) [avatar definition]
195. brave(sK1) <- (8) [avatar component clause 193]
196. 7 | 8 [avatar split clause 106,193,190]
198. 9 <=> ! [X3] : ~brave(X3) [avatar definition]
199. ~brave(X3) <- (9) [avatar component clause 198]
229. 16 <=> wise(sK3) [avatar definition]
231. wise(sK3) <- (16) [avatar component clause 229]
233. 9 | 16 [avatar split clause 113,229,198]
333. $false <- (7) [resolution 191,155]
334. ~7 [avatar contradiction clause 333]
335. $false <- (8, 9) [subsumption resolution 195,199]
336. ~8 | ~9 [avatar contradiction clause 335]
361. strong(sK3) <- (16) [resolution 143,231]
362. quiet(sK3) <- (16) [resolution 361,139]
381. ~wise(sK3) <- (16) [resolution 362,142]
383. $false <- (16) [subsumption resolution 381,231]
384. ~16 [avatar contradiction clause 383]
385. $false [avatar sat refutation 196,233,334,336,384]
% SZS output end Proof for 6423255884420371807904475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or tall then fred is not brave or not happy and vice versa.
Everyone who is not generous is not happy or strong.
Everyone who is both humble and not patient is not tall and vice versa.
Everyone who is not old is not rich and vice versa.
If someone is both strong and not calm then someone is strong and vice versa.
If susan is both not kind and not calm then someone is kind or funny and vice versa.
Everyone who is either not quiet or quiet is strong.
Everyone who is generous is old or not rich and vice versa.
If lucy is either quiet or kind then fred is not quiet or not brave and vice versa.
Everyone who is old is both humble and not happy and vice versa.
Everyone who is not calm or humble is both strong and not happy and vice versa.
If someone is either not old or not calm then paul is not strong or brave.
If someone is either not creative or tall then alice is not generous or not strong and vice versa.
If someone is not kind then someone is either not kind or quiet and vice versa.
Everyone who is brave or rich is both not brave and not patient.
Everyone who is either humble or creative is old or brave and vice versa.
Someone is creative or patient.
Someone is either not curious or old.
John is both not brave and not calm. | Susan is not strong. | contradiction | ((?[X]:((quiet(X)<~>tall(X))))<=>((~brave(fred)|~happy(fred))))&
(![X]:(~generous(X)=>(~happy(X)|strong(X))))&
(![X]:((humble(X)&~patient(X))<=>~tall(X)))&
(![X]:(~old(X)<=>~rich(X)))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:(strong(X))))&
(((~kind(susan)&~calm(susan)))<=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((~quiet(X)<~>quiet(X))=>strong(X)))&
(![X]:(generous(X)<=>(old(X)|~rich(X))))&
(((quiet(lucy)<~>kind(lucy)))<=>((~quiet(fred)|~brave(fred))))&
(![X]:(old(X)<=>(humble(X)&~happy(X))))&
(![X]:((~calm(X)|humble(X))<=>(strong(X)&~happy(X))))&
((?[X]:((~old(X)<~>~calm(X))))=>((~strong(paul)|brave(paul))))&
((?[X]:((~creative(X)<~>tall(X))))<=>((~generous(alice)|~strong(alice))))&
((?[X]:(~kind(X)))<=>(?[X]:((~kind(X)<~>quiet(X)))))&
(![X]:((brave(X)|rich(X))=>(~brave(X)&~patient(X))))&
(![X]:((humble(X)<~>creative(X))<=>(old(X)|brave(X))))&
(?[X]:((creative(X)|patient(X))))&
(?[X]:((~curious(X)<~>old(X))))&
((~brave(john)&~calm(john))) | ~strong(susan) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7233149393698975902835238
% SZS output start Proof for 7233149393698975902835238
7. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => strong(X0)) [input p6]
20. ~strong(susan) [input hypothesis]
25. ! [X0] : (strong(X0) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 7]
47. ! [X0] : (strong(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 25]
94. strong(X0) | quiet(X0) | quiet(X0) [cnf transformation 47]
95. strong(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 47]
140. ~strong(susan) [cnf transformation 20]
142. strong(X0) | quiet(X0) [duplicate literal removal 94]
143. strong(X0) | ~quiet(X0) [duplicate literal removal 95]
220. strong(X0) [subsumption resolution 142,143]
326. $false [subsumption resolution 140,220]
% SZS output end Proof for 7233149393698975902835238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or kind is both not tall and not brave and vice versa.
If someone is either patient or happy then lucy is not happy and vice versa.
Everyone who is patient is either creative or funny.
Everyone who is either calm or not calm is either wise or not brave and vice versa.
If someone is both happy and patient then paul is old.
If susan is tall then john is wise or not rich and vice versa.
If alice is happy or strong then someone is not old or patient.
If lucy is brave or not generous then someone is wise or creative and vice versa.
Everyone who is either happy or creative is generous or tall and vice versa.
If alice is either not tall or not strong then someone is either kind or not generous and vice versa.
Everyone who is quiet or calm is either happy or not calm and vice versa.
Everyone who is both not strong and funny is both rich and not quiet.
Everyone who is both not happy and brave is either funny or not wise and vice versa.
If someone is both not strong and kind then mary is not strong and vice versa.
If lucy is not rich then someone is not humble and vice versa.
Everyone who is kind or strong is both strong and not brave and vice versa.
Someone is strong.
Fred is either kind or funny.
Someone is not kind.
Someone is both not tall and not funny.
Paul is either not generous or not funny.
Someone is both tall and not funny.
Someone is not tall. | Lucy is not strong. | contradiction | (![X]:((curious(X)<~>kind(X))<=>(~tall(X)&~brave(X))))&
((?[X]:((patient(X)<~>happy(X))))<=>(~happy(lucy)))&
(![X]:(patient(X)=>(creative(X)<~>funny(X))))&
(![X]:((calm(X)<~>~calm(X))<=>(wise(X)<~>~brave(X))))&
((?[X]:((happy(X)&patient(X))))=>(old(paul)))&
((tall(susan))<=>((wise(john)|~rich(john))))&
(((happy(alice)|strong(alice)))=>(?[X]:((~old(X)|patient(X)))))&
(((brave(lucy)|~generous(lucy)))<=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((happy(X)<~>creative(X))<=>(generous(X)|tall(X))))&
(((~tall(alice)<~>~strong(alice)))<=>(?[X]:((kind(X)<~>~generous(X)))))&
(![X]:((quiet(X)|calm(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((~strong(X)&funny(X))=>(rich(X)&~quiet(X))))&
(![X]:((~happy(X)&brave(X))<=>(funny(X)<~>~wise(X))))&
((?[X]:((~strong(X)&kind(X))))<=>(~strong(mary)))&
((~rich(lucy))<=>(?[X]:(~humble(X))))&
(![X]:((kind(X)|strong(X))<=>(strong(X)&~brave(X))))&
(?[X]:(strong(X)))&
((kind(fred)<~>funny(fred)))&
(?[X]:(~kind(X)))&
(?[X]:((~tall(X)&~funny(X))))&
((~generous(paul)<~>~funny(paul)))&
(?[X]:((tall(X)&~funny(X))))&
(?[X]:(~tall(X))) | ~strong(lucy) | [
"p1",
"p2",
"p3",
"p8",
"p10",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 491206152588875680158815
% SZS output start Proof for 491206152588875680158815
2. ? [X0] : (patient(X0) <~> happy(X0)) <=> ~happy(lucy) [input p1]
3. ! [X0] : (patient(X0) => (creative(X0) <~> funny(X0))) [input p2]
4. ! [X0] : ((calm(X0) <~> ~calm(X0)) <=> (wise(X0) <~> ~brave(X0))) [input p3]
9. ! [X0] : ((happy(X0) <~> creative(X0)) <=> (tall(X0) | generous(X0))) [input p8]
11. ! [X0] : ((calm(X0) | quiet(X0)) <=> (happy(X0) <~> ~calm(X0))) [input p10]
12. ! [X0] : ((funny(X0) & ~strong(X0)) => (~quiet(X0) & rich(X0))) [input p11]
13. ! [X0] : ((brave(X0) & ~happy(X0)) <=> (funny(X0) <~> ~wise(X0))) [input p12]
22. ? [X0] : (~funny(X0) & tall(X0)) [input p21]
24. ~strong(lucy) [input hypothesis]
25. ! [X0] : ((creative(X0) <~> funny(X0)) | ~patient(X0)) [ennf transformation 3]
28. ! [X0] : ((~quiet(X0) & rich(X0)) | (~funny(X0) | strong(X0))) [ennf transformation 12]
29. ! [X0] : ((~quiet(X0) & rich(X0)) | ~funny(X0) | strong(X0)) [flattening 28]
32. (? [X0] : ((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | happy(lucy)) & (~happy(lucy) | ! [X0] : ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0)))) [nnf transformation 2]
33. (? [X0] : ((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | happy(lucy)) & (~happy(lucy) | ! [X1] : ((patient(X1) | ~happy(X1)) & (happy(X1) | ~patient(X1)))) [rectify 32]
34. ? [X0] : ((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) => ((~happy(sK0) | ~patient(sK0)) & (happy(sK0) | patient(sK0))) [choice axiom]
35. (((~happy(sK0) | ~patient(sK0)) & (happy(sK0) | patient(sK0))) | happy(lucy)) & (~happy(lucy) | ! [X1] : ((patient(X1) | ~happy(X1)) & (happy(X1) | ~patient(X1)))) [skolemisation 33,34]
36. ! [X0] : (((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | ~patient(X0)) [nnf transformation 25]
37. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [nnf transformation 4]
47. ! [X0] : ((((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | (~tall(X0) & ~generous(X0))) & ((tall(X0) | generous(X0)) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0))))) [nnf transformation 9]
48. ! [X0] : ((((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | (~tall(X0) & ~generous(X0))) & (tall(X0) | generous(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0))))) [flattening 47]
53. ! [X0] : (((calm(X0) | quiet(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (~calm(X0) & ~quiet(X0)))) [nnf transformation 11]
54. ! [X0] : ((calm(X0) | quiet(X0) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (~calm(X0) & ~quiet(X0)))) [flattening 53]
55. ! [X0] : (((brave(X0) & ~happy(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0)))) & (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (~brave(X0) | happy(X0)))) [nnf transformation 13]
56. ! [X0] : (((brave(X0) & ~happy(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0)))) & (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | ~brave(X0) | happy(X0))) [flattening 55]
75. ? [X0] : (~funny(X0) & tall(X0)) => (~funny(sK9) & tall(sK9)) [choice axiom]
76. ~funny(sK9) & tall(sK9) [skolemisation 22,75]
86. ~happy(lucy) | patient(X1) | ~happy(X1) [cnf transformation 35]
89. ~patient(X0) | creative(X0) | funny(X0) [cnf transformation 36]
91. ~brave(X0) | wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 37]
92. ~brave(X0) | wise(X0) | calm(X0) | calm(X0) [cnf transformation 37]
93. brave(X0) | ~wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 37]
94. brave(X0) | ~wise(X0) | calm(X0) | calm(X0) [cnf transformation 37]
114. ~creative(X0) | ~happy(X0) | ~tall(X0) [cnf transformation 48]
124. ~calm(X0) | happy(X0) | ~calm(X0) [cnf transformation 54]
128. calm(X0) | quiet(X0) | happy(X0) | calm(X0) [cnf transformation 54]
130. ~quiet(X0) | ~funny(X0) | strong(X0) [cnf transformation 29]
131. ~wise(X0) | funny(X0) | ~brave(X0) | happy(X0) [cnf transformation 56]
136. brave(X0) | funny(X0) | wise(X0) [cnf transformation 56]
155. tall(sK9) [cnf transformation 76]
156. ~funny(sK9) [cnf transformation 76]
158. ~strong(lucy) [cnf transformation 24]
159. ~calm(X0) | happy(X0) [duplicate literal removal 124]
160. quiet(X0) | calm(X0) | happy(X0) [duplicate literal removal 128]
161. ~brave(X0) | wise(X0) | ~calm(X0) [duplicate literal removal 91]
162. ~brave(X0) | wise(X0) | calm(X0) [duplicate literal removal 92]
163. brave(X0) | ~wise(X0) | ~calm(X0) [duplicate literal removal 93]
164. ~wise(X0) | brave(X0) | calm(X0) [duplicate literal removal 94]
166. 1 <=> happy(lucy) [avatar definition]
180. 4 <=> ! [X1] : (patient(X1) | ~happy(X1)) [avatar definition]
181. ~happy(X1) | patient(X1) <- (4) [avatar component clause 180]
182. 4 | ~1 [avatar split clause 86,166,180]
187. ~wise(X0) | brave(X0) [subsumption resolution 163,164]
188. ~brave(X0) | wise(X0) [subsumption resolution 161,162]
282. wise(X0) | funny(X0) [subsumption resolution 136,188]
283. ~wise(X0) | funny(X0) | happy(X0) [subsumption resolution 131,187]
284. funny(X0) | happy(X0) [subsumption resolution 283,282]
345. happy(sK9) [resolution 284,156]
423. calm(X0) | happy(X0) | ~funny(X0) | strong(X0) [resolution 160,130]
426. happy(X0) | ~funny(X0) | strong(X0) [subsumption resolution 423,159]
427. strong(X0) | happy(X0) [subsumption resolution 426,284]
629. happy(lucy) [resolution 427,158]
635. 1 [avatar split clause 629,166]
660. patient(sK9) <- (4) [resolution 181,345]
872. creative(sK9) | funny(sK9) <- (4) [resolution 660,89]
873. creative(sK9) <- (4) [subsumption resolution 872,156]
956. ~happy(sK9) | ~tall(sK9) <- (4) [resolution 873,114]
957. ~tall(sK9) <- (4) [subsumption resolution 956,345]
958. $false <- (4) [subsumption resolution 957,155]
959. ~4 [avatar contradiction clause 958]
960. $false [avatar sat refutation 182,635,959]
% SZS output end Proof for 491206152588875680158815
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is creative or old.
Everyone who is tall is not wise and vice versa.
Everyone who is not curious or creative is not calm or happy and vice versa.
Everyone who is both not happy and not generous is both curious and humble and vice versa.
If fred is calm or not tall then someone is rich or brave.
If someone is either not happy or patient then someone is not old or not generous and vice versa.
Everyone who is generous is not strong or not happy and vice versa.
Everyone who is funny is rich or not kind.
If paul is not rich then someone is either not brave or calm.
Everyone who is either not calm or wise is either kind or generous and vice versa.
Everyone who is either not generous or not humble is creative and vice versa.
If lucy is happy then mary is either calm or happy.
Everyone who is either tall or not generous is either not happy or humble and vice versa.
If lucy is both not creative and calm then someone is not brave and vice versa.
Everyone who is humble or creative is either humble or not calm and vice versa.
Everyone who is both not creative and brave is both not funny and curious and vice versa.
Fred is either not humble or strong.
Mary is both wise and kind.
Someone is either not quiet or not happy.
John is both generous and not tall.
John is not tall or not creative.
Someone is not quiet.
Someone is not humble or creative.
Someone is either not funny or not patient. | Fred is not creative. | contradiction | (![X]:(kind(X)=>(creative(X)|old(X))))&
(![X]:(tall(X)<=>~wise(X)))&
(![X]:((~curious(X)|creative(X))<=>(~calm(X)|happy(X))))&
(![X]:((~happy(X)&~generous(X))<=>(curious(X)&humble(X))))&
(((calm(fred)|~tall(fred)))=>(?[X]:((rich(X)|brave(X)))))&
((?[X]:((~happy(X)<~>patient(X))))<=>(?[X]:((~old(X)|~generous(X)))))&
(![X]:(generous(X)<=>(~strong(X)|~happy(X))))&
(![X]:(funny(X)=>(rich(X)|~kind(X))))&
((~rich(paul))=>(?[X]:((~brave(X)<~>calm(X)))))&
(![X]:((~calm(X)<~>wise(X))<=>(kind(X)<~>generous(X))))&
(![X]:((~generous(X)<~>~humble(X))<=>creative(X)))&
((happy(lucy))=>((calm(mary)<~>happy(mary))))&
(![X]:((tall(X)<~>~generous(X))<=>(~happy(X)<~>humble(X))))&
(((~creative(lucy)&calm(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((humble(X)|creative(X))<=>(humble(X)<~>~calm(X))))&
(![X]:((~creative(X)&brave(X))<=>(~funny(X)&curious(X))))&
((~humble(fred)<~>strong(fred)))&
((wise(mary)&kind(mary)))&
(?[X]:((~quiet(X)<~>~happy(X))))&
((generous(john)&~tall(john)))&
((~tall(john)|~creative(john)))&
(?[X]:(~quiet(X)))&
(?[X]:((~humble(X)|creative(X))))&
(?[X]:((~funny(X)<~>~patient(X)))) | ~creative(fred) | [
"p2",
"p3",
"p6",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5958175227740315522547064
% SZS output start Proof for 5958175227740315522547064
3. ! [X0] : ((creative(X0) | ~curious(X0)) <=> (happy(X0) | ~calm(X0))) [input p2]
4. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> (humble(X0) & curious(X0))) [input p3]
7. ! [X0] : (generous(X0) <=> (~happy(X0) | ~strong(X0))) [input p6]
11. ! [X0] : ((~generous(X0) <~> ~humble(X0)) <=> creative(X0)) [input p10]
15. ! [X0] : ((creative(X0) | humble(X0)) <=> (humble(X0) <~> ~calm(X0))) [input p14]
17. ~humble(fred) <~> strong(fred) [input p16]
25. ~creative(fred) [input hypothesis]
34. ! [X0] : (((creative(X0) | ~curious(X0)) | (~happy(X0) & calm(X0))) & ((happy(X0) | ~calm(X0)) | (~creative(X0) & curious(X0)))) [nnf transformation 3]
35. ! [X0] : ((creative(X0) | ~curious(X0) | (~happy(X0) & calm(X0))) & (happy(X0) | ~calm(X0) | (~creative(X0) & curious(X0)))) [flattening 34]
36. ! [X0] : (((~generous(X0) & ~happy(X0)) | (~humble(X0) | ~curious(X0))) & ((humble(X0) & curious(X0)) | (generous(X0) | happy(X0)))) [nnf transformation 4]
37. ! [X0] : (((~generous(X0) & ~happy(X0)) | ~humble(X0) | ~curious(X0)) & ((humble(X0) & curious(X0)) | generous(X0) | happy(X0))) [flattening 36]
43. ! [X0] : ((generous(X0) | (happy(X0) & strong(X0))) & ((~happy(X0) | ~strong(X0)) | ~generous(X0))) [nnf transformation 7]
44. ! [X0] : ((generous(X0) | (happy(X0) & strong(X0))) & (~happy(X0) | ~strong(X0) | ~generous(X0))) [flattening 43]
46. ! [X0] : ((((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ~creative(X0)) & (creative(X0) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0))))) [nnf transformation 11]
54. ! [X0] : (((creative(X0) | humble(X0)) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0)))) & (((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | (~creative(X0) & ~humble(X0)))) [nnf transformation 15]
55. ! [X0] : ((creative(X0) | humble(X0) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0)))) & (((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | (~creative(X0) & ~humble(X0)))) [flattening 54]
58. (~strong(fred) | humble(fred)) & (strong(fred) | ~humble(fred)) [nnf transformation 17]
72. ~calm(X0) | happy(X0) | curious(X0) [cnf transformation 35]
79. ~humble(X0) | ~generous(X0) | ~curious(X0) [cnf transformation 37]
86. ~strong(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 44]
87. strong(X0) | generous(X0) [cnf transformation 44]
97. ~humble(X0) | creative(X0) | generous(X0) [cnf transformation 46]
98. ~generous(X0) | creative(X0) | humble(X0) [cnf transformation 46]
116. calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 55]
124. strong(fred) | ~humble(fred) [cnf transformation 58]
125. ~strong(fred) | humble(fred) [cnf transformation 58]
137. ~creative(fred) [cnf transformation 25]
138. ~humble(X0) | calm(X0) [duplicate literal removal 116]
211. 16 <=> humble(fred) [avatar definition]
212. ~humble(fred) <- (~16) [avatar component clause 211]
213. humble(fred) <- (16) [avatar component clause 211]
215. 17 <=> strong(fred) [avatar definition]
216. strong(fred) <- (17) [avatar component clause 215]
217. ~strong(fred) <- (~17) [avatar component clause 215]
218. 16 | ~17 [avatar split clause 125,215,211]
219. ~16 | 17 [avatar split clause 124,215,211]
253. generous(fred) <- (~17) [resolution 87,217]
291. creative(fred) | humble(fred) <- (~17) [resolution 98,253]
301. humble(fred) <- (~17) [subsumption resolution 291,137]
302. $false <- (~16, ~17) [subsumption resolution 301,212]
303. 16 | 17 [avatar contradiction clause 302]
304. creative(fred) | generous(fred) <- (16) [resolution 213,97]
305. ~generous(fred) | ~curious(fred) <- (16) [resolution 213,79]
307. calm(fred) <- (16) [resolution 213,138]
308. generous(fred) <- (16) [subsumption resolution 304,137]
309. ~curious(fred) <- (16) [subsumption resolution 305,308]
310. ~happy(fred) | ~generous(fred) <- (17) [resolution 216,86]
311. ~happy(fred) <- (16, 17) [subsumption resolution 310,308]
323. happy(fred) | curious(fred) <- (16) [resolution 307,72]
324. curious(fred) <- (16, 17) [subsumption resolution 323,311]
325. $false <- (16, 17) [subsumption resolution 324,309]
326. ~16 | ~17 [avatar contradiction clause 325]
327. $false [avatar sat refutation 218,219,303,326]
% SZS output end Proof for 5958175227740315522547064
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.047 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not humble then paul is patient and vice versa. Everyone who is either happy or not old is both not happy and not quiet. Everyone who is old is either not kind or not quiet and vice versa. Everyone who is wise is both not strong and not calm. Everyone who is happy is not strong or patient and vice versa. If lucy is both quiet and kind then lucy is not calm or kind. Everyone who is either not quiet or not wise is either not funny or quiet and vice versa. If susan is both brave and not calm then paul is both tall and not creative and vice versa. Everyone who is both not funny and generous is not patient and vice versa. If someone is not calm or brave then someone is both not humble and rich and vice versa. Everyone who is rich is both not old and old and vice versa. Everyone who is both not humble and old is either not old or happy. If lucy is not generous then lucy is both not calm and tall and vice versa. Everyone who is happy or not kind is either creative or not kind and vice versa. If lucy is either not kind or quiet then alice is not rich. Susan is either curious or not generous. Someone is old or generous. Someone is patient or not calm. Someone is both humble and tall. Someone is happy. Lucy is not funny or quiet. | Paul is not humble. | neutral | ((~humble(susan))<=>(patient(paul)))&
(![X]:((happy(X)<~>~old(X))=>(~happy(X)&~quiet(X))))&
(![X]:(old(X)<=>(~kind(X)<~>~quiet(X))))&
(![X]:(wise(X)=>(~strong(X)&~calm(X))))&
(![X]:(happy(X)<=>(~strong(X)|patient(X))))&
(((quiet(lucy)&kind(lucy)))=>((~calm(lucy)|kind(lucy))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~funny(X)<~>quiet(X))))&
(((brave(susan)&~calm(susan)))<=>((tall(paul)&~creative(paul))))&
(![X]:((~funny(X)&generous(X))<=>~patient(X)))&
((?[X]:((~calm(X)|brave(X))))<=>(?[X]:((~humble(X)&rich(X)))))&
(![X]:(rich(X)<=>(~old(X)&old(X))))&
(![X]:((~humble(X)&old(X))=>(~old(X)<~>happy(X))))&
((~generous(lucy))<=>((~calm(lucy)&tall(lucy))))&
(![X]:((happy(X)|~kind(X))<=>(creative(X)<~>~kind(X))))&
(((~kind(lucy)<~>quiet(lucy)))=>(~rich(alice)))&
((curious(susan)<~>~generous(susan)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((patient(X)|~calm(X))))&
(?[X]:((humble(X)&tall(X))))&
(?[X]:(happy(X)))&
((~funny(lucy)|quiet(lucy))) | ~humble(paul) | [] | null | 0 |
If lucy is wise then mary is either brave or not happy.
If john is calm then someone is both not quiet and not old and vice versa.
If someone is funny then someone is quiet or calm and vice versa.
Everyone who is not creative is not humble or not tall and vice versa.
Everyone who is not quiet or not generous is either not humble or not curious and vice versa.
Everyone who is either not generous or not happy is either patient or not generous and vice versa.
If alice is both kind and not happy then john is tall or kind.
If alice is curious or brave then lucy is not funny and vice versa.
If susan is either not humble or old then someone is either wise or not old and vice versa.
Everyone who is not humble or not curious is not funny or old.
Everyone who is brave is patient or strong and vice versa.
Everyone who is quiet is kind and vice versa.
Everyone who is old or quiet is not generous and vice versa.
If someone is not patient or creative then lucy is both funny and creative.
Everyone who is either brave or not funny is both not patient and wise.
Everyone who is rich is both creative and not creative and vice versa.
Someone is not funny or not strong.
Someone is quiet or not brave.
Someone is both tall and humble.
Lucy is both calm and not kind.
John is not humble.
Paul is not calm.
Someone is either strong or not brave. | Alice is strong. | contradiction | ((wise(lucy))=>((brave(mary)<~>~happy(mary))))&
((calm(john))<=>(?[X]:((~quiet(X)&~old(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((quiet(X)|calm(X)))))&
(![X]:(~creative(X)<=>(~humble(X)|~tall(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~generous(X)<~>~happy(X))<=>(patient(X)<~>~generous(X))))&
(((kind(alice)&~happy(alice)))=>((tall(john)|kind(john))))&
(((curious(alice)|brave(alice)))<=>(~funny(lucy)))&
(((~humble(susan)<~>old(susan)))<=>(?[X]:((wise(X)<~>~old(X)))))&
(![X]:((~humble(X)|~curious(X))=>(~funny(X)|old(X))))&
(![X]:(brave(X)<=>(patient(X)|strong(X))))&
(![X]:(quiet(X)<=>kind(X)))&
(![X]:((old(X)|quiet(X))<=>~generous(X)))&
((?[X]:((~patient(X)|creative(X))))=>((funny(lucy)&creative(lucy))))&
(![X]:((brave(X)<~>~funny(X))=>(~patient(X)&wise(X))))&
(![X]:(rich(X)<=>(creative(X)&~creative(X))))&
(?[X]:((~funny(X)|~strong(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:((tall(X)&humble(X))))&
((calm(lucy)&~kind(lucy)))&
(~humble(john))&
(~calm(paul))&
(?[X]:((strong(X)<~>~brave(X)))) | strong(alice) | [
"p2",
"p7",
"p10",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7816274628921354017679891
% SZS output start Proof for 7816274628921354017679891
3. ? [X0] : funny(X0) <=> ? [X0] : (calm(X0) | quiet(X0)) [input p2]
8. (brave(alice) | curious(alice)) <=> ~funny(lucy) [input p7]
11. ! [X0] : (brave(X0) <=> (strong(X0) | patient(X0))) [input p10]
14. ? [X0] : (creative(X0) | ~patient(X0)) => (creative(lucy) & funny(lucy)) [input p13]
15. ! [X0] : ((brave(X0) <~> ~funny(X0)) => (wise(X0) & ~patient(X0))) [input p14]
20. ~kind(lucy) & calm(lucy) [input p19]
24. strong(alice) [input hypothesis]
25. ? [X0] : funny(X0) <=> ? [X1] : (calm(X1) | quiet(X1)) [rectify 3]
31. (creative(lucy) & funny(lucy)) | ! [X0] : (~creative(X0) & patient(X0)) [ennf transformation 14]
32. ! [X0] : ((wise(X0) & ~patient(X0)) | (brave(X0) <=> ~funny(X0))) [ennf transformation 15]
38. (? [X0] : funny(X0) | ! [X1] : (~calm(X1) & ~quiet(X1))) & (? [X1] : (calm(X1) | quiet(X1)) | ! [X0] : ~funny(X0)) [nnf transformation 25]
39. (? [X0] : funny(X0) | ! [X1] : (~calm(X1) & ~quiet(X1))) & (? [X2] : (calm(X2) | quiet(X2)) | ! [X3] : ~funny(X3)) [rectify 38]
40. ? [X0] : funny(X0) => funny(sK1) [choice axiom]
41. ? [X2] : (calm(X2) | quiet(X2)) => (calm(sK2) | quiet(sK2)) [choice axiom]
42. (funny(sK1) | ! [X1] : (~calm(X1) & ~quiet(X1))) & ((calm(sK2) | quiet(sK2)) | ! [X3] : ~funny(X3)) [skolemisation 39,41,40]
48. ((brave(alice) | curious(alice)) | funny(lucy)) & (~funny(lucy) | (~brave(alice) & ~curious(alice))) [nnf transformation 8]
49. (brave(alice) | curious(alice) | funny(lucy)) & (~funny(lucy) | (~brave(alice) & ~curious(alice))) [flattening 48]
54. ! [X0] : ((brave(X0) | (~strong(X0) & ~patient(X0))) & ((strong(X0) | patient(X0)) | ~brave(X0))) [nnf transformation 11]
55. ! [X0] : ((brave(X0) | (~strong(X0) & ~patient(X0))) & (strong(X0) | patient(X0) | ~brave(X0))) [flattening 54]
59. ! [X0] : ((wise(X0) & ~patient(X0)) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0)))) [nnf transformation 32]
76. funny(sK1) | ~calm(X1) [cnf transformation 42]
96. ~funny(lucy) | ~brave(alice) [cnf transformation 49]
109. ~patient(X0) | brave(X0) [cnf transformation 55]
110. ~strong(X0) | brave(X0) [cnf transformation 55]
116. funny(lucy) | patient(X0) [cnf transformation 31]
120. ~patient(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 59]
128. calm(lucy) [cnf transformation 20]
134. strong(alice) [cnf transformation 24]
172. 8 <=> ! [X1] : ~calm(X1) [avatar definition]
173. ~calm(X1) <- (8) [avatar component clause 172]
175. 9 <=> funny(sK1) [avatar definition]
177. funny(sK1) <- (9) [avatar component clause 175]
178. 8 | 9 [avatar split clause 76,175,172]
184. 11 <=> ! [X3] : ~funny(X3) [avatar definition]
185. ~funny(X3) <- (11) [avatar component clause 184]
215. 18 <=> funny(lucy) [avatar definition]
223. 20 <=> brave(alice) [avatar definition]
227. ~20 | ~18 [avatar split clause 96,215,223]
268. 29 <=> ! [X0] : patient(X0) [avatar definition]
269. patient(X0) <- (29) [avatar component clause 268]
272. 29 | 18 [avatar split clause 116,215,268]
273. ~patient(X0) | ~funny(X0) [subsumption resolution 120,109]
301. $false <- (9, 11) [subsumption resolution 177,185]
302. ~9 | ~11 [avatar contradiction clause 301]
303. $false <- (8) [resolution 173,128]
304. ~8 [avatar contradiction clause 303]
309. brave(alice) [resolution 110,134]
312. 20 [avatar split clause 309,223]
333. ~funny(X1) <- (29) [resolution 273,269]
336. 11 | ~29 [avatar split clause 333,268,184]
337. $false [avatar sat refutation 178,227,272,302,304,312,336]
% SZS output end Proof for 7816274628921354017679891
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is either not calm or brave and vice versa. Everyone who is not patient is not strong or not wise and vice versa. If paul is either not quiet or not strong then someone is both not kind and happy. Everyone who is not funny or old is either happy or not happy. If someone is not creative or not humble then john is either not funny or rich. If fred is not funny then susan is not humble or not wise and vice versa. Everyone who is creative or not rich is both not kind and not humble. If john is either wise or not tall then someone is either kind or not creative. If paul is not curious then someone is either not calm or wise. If someone is not quiet or not patient then someone is both wise and not happy and vice versa. Everyone who is both not calm and not patient is either not happy or not generous and vice versa. Everyone who is funny or not rich is not old or strong and vice versa. Everyone who is either not old or strong is strong. Everyone who is strong or happy is kind. Everyone who is either rich or not calm is either not rich or old and vice versa. Everyone who is either not strong or generous is humble and vice versa. Lucy is not kind. Someone is either generous or tall. Someone is both rich and curious. Someone is wise or not old. Mary is calm or not tall. Someone is calm or creative. Paul is not quiet or not strong. | Lucy is not creative. | entailment | (![X]:(~kind(X)<=>(~calm(X)<~>brave(X))))&
(![X]:(~patient(X)<=>(~strong(X)|~wise(X))))&
(((~quiet(paul)<~>~strong(paul)))=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:((~funny(X)|old(X))=>(happy(X)<~>~happy(X))))&
((?[X]:((~creative(X)|~humble(X))))=>((~funny(john)<~>rich(john))))&
((~funny(fred))<=>((~humble(susan)|~wise(susan))))&
(![X]:((creative(X)|~rich(X))=>(~kind(X)&~humble(X))))&
(((wise(john)<~>~tall(john)))=>(?[X]:((kind(X)<~>~creative(X)))))&
((~curious(paul))=>(?[X]:((~calm(X)<~>wise(X)))))&
((?[X]:((~quiet(X)|~patient(X))))<=>(?[X]:((wise(X)&~happy(X)))))&
(![X]:((~calm(X)&~patient(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((funny(X)|~rich(X))<=>(~old(X)|strong(X))))&
(![X]:((~old(X)<~>strong(X))=>strong(X)))&
(![X]:((strong(X)|happy(X))=>kind(X)))&
(![X]:((rich(X)<~>~calm(X))<=>(~rich(X)<~>old(X))))&
(![X]:((~strong(X)<~>generous(X))<=>humble(X)))&
(~kind(lucy))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((wise(X)|~old(X))))&
((calm(mary)|~tall(mary)))&
(?[X]:((calm(X)|creative(X))))&
((~quiet(paul)|~strong(paul))) | ~creative(lucy) | [
"p6",
"p10",
"p12",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4403586987859146884366468
% SZS output start Proof for 4403586987859146884366468
7. ! [X0] : ((~rich(X0) | creative(X0)) => (~humble(X0) & ~kind(X0))) [input p6]
11. ! [X0] : ((~patient(X0) & ~calm(X0)) <=> (~happy(X0) <~> ~generous(X0))) [input p10]
13. ! [X0] : ((~old(X0) <~> strong(X0)) => strong(X0)) [input p12]
14. ! [X0] : ((happy(X0) | strong(X0)) => kind(X0)) [input p13]
15. ! [X0] : ((rich(X0) <~> ~calm(X0)) <=> (~rich(X0) <~> old(X0))) [input p14]
16. ! [X0] : ((~strong(X0) <~> generous(X0)) <=> humble(X0)) [input p15]
17. ~kind(lucy) [input p16]
24. creative(lucy) [input hypothesis]
31. ! [X0] : ((~humble(X0) & ~kind(X0)) | (rich(X0) & ~creative(X0))) [ennf transformation 7]
33. ! [X0] : (strong(X0) | (~old(X0) <=> strong(X0))) [ennf transformation 13]
34. ! [X0] : (kind(X0) | (~happy(X0) & ~strong(X0))) [ennf transformation 14]
53. ! [X0] : (((~patient(X0) & ~calm(X0)) | ((~happy(X0) | generous(X0)) & (~generous(X0) | happy(X0)))) & (((generous(X0) | happy(X0)) & (~generous(X0) | ~happy(X0))) | (patient(X0) | calm(X0)))) [nnf transformation 11]
54. ! [X0] : (((~patient(X0) & ~calm(X0)) | ((~happy(X0) | generous(X0)) & (~generous(X0) | happy(X0)))) & (((generous(X0) | happy(X0)) & (~generous(X0) | ~happy(X0))) | patient(X0) | calm(X0))) [flattening 53]
57. ! [X0] : (strong(X0) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0)))) [nnf transformation 33]
58. ! [X0] : ((((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0)))) & (((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0))))) [nnf transformation 15]
59. ! [X0] : ((((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ~humble(X0)) & (humble(X0) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0))))) [nnf transformation 16]
93. ~humble(X0) | ~creative(X0) [cnf transformation 31]
106. ~generous(X0) | ~calm(X0) | happy(X0) [cnf transformation 54]
114. strong(X0) | strong(X0) | old(X0) [cnf transformation 57]
116. ~strong(X0) | kind(X0) [cnf transformation 34]
117. ~happy(X0) | kind(X0) [cnf transformation 34]
121. ~old(X0) | rich(X0) | rich(X0) | calm(X0) [cnf transformation 58]
125. calm(X0) | ~rich(X0) | ~rich(X0) | ~old(X0) [cnf transformation 58]
126. generous(X0) | humble(X0) | strong(X0) [cnf transformation 59]
130. ~kind(lucy) [cnf transformation 17]
138. creative(lucy) [cnf transformation 24]
140. ~old(X0) | rich(X0) | calm(X0) [duplicate literal removal 121]
142. ~rich(X0) | calm(X0) | ~old(X0) [duplicate literal removal 125]
143. old(X0) | strong(X0) [duplicate literal removal 114]
251. ~old(X0) | calm(X0) [subsumption resolution 140,142]
305. strong(X0) | calm(X0) [resolution 251,143]
421. humble(X1) | strong(X1) | ~calm(X1) | happy(X1) [resolution 126,106]
422. humble(X1) | strong(X1) | happy(X1) [subsumption resolution 421,305]
523. ~creative(X2) | happy(X2) | strong(X2) [resolution 422,93]
575. happy(lucy) | strong(lucy) [resolution 523,138]
578. 63 <=> strong(lucy) [avatar definition]
580. strong(lucy) <- (63) [avatar component clause 578]
582. 64 <=> happy(lucy) [avatar definition]
584. happy(lucy) <- (64) [avatar component clause 582]
585. 63 | 64 [avatar split clause 575,582,578]
679. kind(lucy) <- (63) [resolution 580,116]
680. $false <- (63) [subsumption resolution 679,130]
681. ~63 [avatar contradiction clause 680]
686. kind(lucy) <- (64) [resolution 584,117]
688. $false <- (64) [subsumption resolution 686,130]
689. ~64 [avatar contradiction clause 688]
690. $false [avatar sat refutation 585,681,689]
% SZS output end Proof for 4403586987859146884366468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not calm is both not quiet and quiet.
Everyone who is either strong or not happy is both not brave and not creative and vice versa.
If someone is both calm and not tall then someone is not patient or quiet and vice versa.
Everyone who is either happy or not quiet is not generous or happy and vice versa.
If someone is not quiet then someone is brave or not curious and vice versa.
If susan is not calm or strong then john is calm and vice versa.
If someone is either not brave or not kind then someone is both not brave and not generous.
Everyone who is kind is patient or not brave.
If paul is either not tall or not old then someone is kind and vice versa.
If fred is quiet then fred is both kind and humble.
If mary is not tall then someone is humble and vice versa.
If john is creative or curious then someone is not tall.
Everyone who is not wise or not happy is curious.
Everyone who is either not tall or humble is not old or curious.
If someone is wise then paul is either not old or funny.
Everyone who is not kind or not brave is both not strong and not wise and vice versa.
Someone is either brave or rich.
Lucy is either not brave or funny.
Someone is both not old and patient.
Susan is not wise or strong.
Fred is not strong or funny.
Fred is not quiet.
Someone is either not wise or strong. | Fred is generous. | contradiction | (![X]:((~wise(X)|~calm(X))=>(~quiet(X)&quiet(X))))&
(![X]:((strong(X)<~>~happy(X))<=>(~brave(X)&~creative(X))))&
((?[X]:((calm(X)&~tall(X))))<=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((happy(X)<~>~quiet(X))<=>(~generous(X)|happy(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((brave(X)|~curious(X)))))&
(((~calm(susan)|strong(susan)))<=>(calm(john)))&
((?[X]:((~brave(X)<~>~kind(X))))=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:(kind(X)=>(patient(X)|~brave(X))))&
(((~tall(paul)<~>~old(paul)))<=>(?[X]:(kind(X))))&
((quiet(fred))=>((kind(fred)&humble(fred))))&
((~tall(mary))<=>(?[X]:(humble(X))))&
(((creative(john)|curious(john)))=>(?[X]:(~tall(X))))&
(![X]:((~wise(X)|~happy(X))=>curious(X)))&
(![X]:((~tall(X)<~>humble(X))=>(~old(X)|curious(X))))&
((?[X]:(wise(X)))=>((~old(paul)<~>funny(paul))))&
(![X]:((~kind(X)|~brave(X))<=>(~strong(X)&~wise(X))))&
(?[X]:((brave(X)<~>rich(X))))&
((~brave(lucy)<~>funny(lucy)))&
(?[X]:((~old(X)&patient(X))))&
((~wise(susan)|strong(susan)))&
((~strong(fred)|funny(fred)))&
(~quiet(fred))&
(?[X]:((~wise(X)<~>strong(X)))) | generous(fred) | [
"p3",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5699877158130426344903357
% SZS output start Proof for 5699877158130426344903357
4. ! [X0] : ((happy(X0) <~> ~quiet(X0)) <=> (happy(X0) | ~generous(X0))) [input p3]
22. ~quiet(fred) [input p21]
24. generous(fred) [input hypothesis]
45. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (~happy(X0) & generous(X0))) & ((happy(X0) | ~generous(X0)) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [nnf transformation 4]
46. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (~happy(X0) & generous(X0))) & (happy(X0) | ~generous(X0) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [flattening 45]
97. happy(X0) | ~generous(X0) | happy(X0) | quiet(X0) [cnf transformation 46]
101. quiet(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 46]
142. ~quiet(fred) [cnf transformation 22]
145. generous(fred) [cnf transformation 24]
146. happy(X0) | ~generous(X0) | quiet(X0) [duplicate literal removal 97]
147. ~happy(X0) | quiet(X0) [duplicate literal removal 101]
175. ~generous(X0) | quiet(X0) [subsumption resolution 146,147]
240. 21 <=> quiet(fred) [avatar definition]
242. ~quiet(fred) <- (~21) [avatar component clause 240]
301. ~21 [avatar split clause 142,240]
313. quiet(fred) [resolution 175,145]
314. $false <- (~21) [subsumption resolution 313,242]
315. 21 [avatar contradiction clause 314]
316. $false [avatar sat refutation 301,315]
% SZS output end Proof for 5699877158130426344903357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is generous or not quiet then fred is kind or not rich. Everyone who is happy is not generous or quiet. Everyone who is not creative is generous or not wise and vice versa. Everyone who is either old or quiet is kind or not calm. If paul is either not happy or not quiet then paul is not tall or creative. Everyone who is creative or not wise is either wise or not calm. Everyone who is both not curious and tall is tall or creative and vice versa. Everyone who is not funny or generous is happy or not humble. If mary is not calm then susan is both not wise and patient and vice versa. If susan is either not curious or funny then paul is generous or quiet. Everyone who is both not old and happy is not patient or not humble. Everyone who is either not funny or creative is both old and happy and vice versa. Everyone who is not funny is both not curious and creative. If alice is either not brave or humble then someone is not kind or not strong and vice versa. If susan is not generous or not rich then john is not strong and vice versa. Everyone who is brave or not funny is not humble. Alice is both not wise and quiet. Lucy is not tall or not calm. Someone is creative or kind. Someone is not old. Paul is either curious or patient. Someone is not tall or not humble. Paul is humble. Someone is happy. | John is not kind. | neutral | (((generous(fred)|~quiet(fred)))=>((kind(fred)|~rich(fred))))&
(![X]:(happy(X)=>(~generous(X)|quiet(X))))&
(![X]:(~creative(X)<=>(generous(X)|~wise(X))))&
(![X]:((old(X)<~>quiet(X))=>(kind(X)|~calm(X))))&
(((~happy(paul)<~>~quiet(paul)))=>((~tall(paul)|creative(paul))))&
(![X]:((creative(X)|~wise(X))=>(wise(X)<~>~calm(X))))&
(![X]:((~curious(X)&tall(X))<=>(tall(X)|creative(X))))&
(![X]:((~funny(X)|generous(X))=>(happy(X)|~humble(X))))&
((~calm(mary))<=>((~wise(susan)&patient(susan))))&
(((~curious(susan)<~>funny(susan)))=>((generous(paul)|quiet(paul))))&
(![X]:((~old(X)&happy(X))=>(~patient(X)|~humble(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(old(X)&happy(X))))&
(![X]:(~funny(X)=>(~curious(X)&creative(X))))&
(((~brave(alice)<~>humble(alice)))<=>(?[X]:((~kind(X)|~strong(X)))))&
(((~generous(susan)|~rich(susan)))<=>(~strong(john)))&
(![X]:((brave(X)|~funny(X))=>~humble(X)))&
((~wise(alice)&quiet(alice)))&
((~tall(lucy)|~calm(lucy)))&
(?[X]:((creative(X)|kind(X))))&
(?[X]:(~old(X)))&
((curious(paul)<~>patient(paul)))&
(?[X]:((~tall(X)|~humble(X))))&
(humble(paul))&
(?[X]:(happy(X))) | ~kind(john) | [] | null | 0 |
Everyone who is either old or calm is creative or happy.
Everyone who is either old or not generous is not tall or not rich.
If paul is both brave and not generous then john is not curious and vice versa.
If someone is not funny then mary is not generous or not curious.
If someone is brave or not quiet then fred is both not patient and not happy and vice versa.
Everyone who is rich or not old is both not wise and not strong.
Everyone who is either not patient or kind is not creative or not generous and vice versa.
Everyone who is either not kind or kind is both not rich and not wise.
Everyone who is both not humble and kind is quiet or not patient.
If alice is both not brave and creative then alice is not calm and vice versa.
Everyone who is either patient or not kind is either calm or not wise.
If someone is strong then susan is generous or creative and vice versa.
Everyone who is either not happy or happy is not strong or patient and vice versa.
If mary is rich or not wise then someone is both not humble and curious and vice versa.
Everyone who is both funny and patient is not rich and vice versa.
Everyone who is wise or not patient is either kind or not strong and vice versa.
Fred is either generous or brave.
Someone is either not wise or not patient.
Someone is either not curious or not funny.
John is calm or strong. | Paul is brave. | contradiction | (![X]:((old(X)<~>calm(X))=>(creative(X)|happy(X))))&
(![X]:((old(X)<~>~generous(X))=>(~tall(X)|~rich(X))))&
(((brave(paul)&~generous(paul)))<=>(~curious(john)))&
((?[X]:(~funny(X)))=>((~generous(mary)|~curious(mary))))&
((?[X]:((brave(X)|~quiet(X))))<=>((~patient(fred)&~happy(fred))))&
(![X]:((rich(X)|~old(X))=>(~wise(X)&~strong(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~creative(X)|~generous(X))))&
(![X]:((~kind(X)<~>kind(X))=>(~rich(X)&~wise(X))))&
(![X]:((~humble(X)&kind(X))=>(quiet(X)|~patient(X))))&
(((~brave(alice)&creative(alice)))<=>(~calm(alice)))&
(![X]:((patient(X)<~>~kind(X))=>(calm(X)<~>~wise(X))))&
((?[X]:(strong(X)))<=>((generous(susan)|creative(susan))))&
(![X]:((~happy(X)<~>happy(X))<=>(~strong(X)|patient(X))))&
(((rich(mary)|~wise(mary)))<=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:((funny(X)&patient(X))<=>~rich(X)))&
(![X]:((wise(X)|~patient(X))<=>(kind(X)<~>~strong(X))))&
((generous(fred)<~>brave(fred)))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
((calm(john)|strong(john))) | brave(paul) | [
"p4",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8132281148425873350804522
% SZS output start Proof for 8132281148425873350804522
5. ? [X0] : (~quiet(X0) | brave(X0)) <=> (~happy(fred) & ~patient(fred)) [input p4]
8. ! [X0] : ((~kind(X0) <~> kind(X0)) => (~wise(X0) & ~rich(X0))) [input p7]
15. ! [X0] : ((patient(X0) & funny(X0)) <=> ~rich(X0)) [input p14]
21. brave(paul) [input hypothesis]
28. ! [X0] : ((~wise(X0) & ~rich(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 8]
35. (? [X0] : (~quiet(X0) | brave(X0)) | (happy(fred) | patient(fred))) & ((~happy(fred) & ~patient(fred)) | ! [X0] : (quiet(X0) & ~brave(X0))) [nnf transformation 5]
36. (? [X0] : (~quiet(X0) | brave(X0)) | happy(fred) | patient(fred)) & ((~happy(fred) & ~patient(fred)) | ! [X0] : (quiet(X0) & ~brave(X0))) [flattening 35]
37. (? [X0] : (~quiet(X0) | brave(X0)) | happy(fred) | patient(fred)) & ((~happy(fred) & ~patient(fred)) | ! [X1] : (quiet(X1) & ~brave(X1))) [rectify 36]
38. ? [X0] : (~quiet(X0) | brave(X0)) => (~quiet(sK0) | brave(sK0)) [choice axiom]
39. ((~quiet(sK0) | brave(sK0)) | happy(fred) | patient(fred)) & ((~happy(fred) & ~patient(fred)) | ! [X1] : (quiet(X1) & ~brave(X1))) [skolemisation 37,38]
42. ! [X0] : ((~wise(X0) & ~rich(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 28]
58. ! [X0] : (((patient(X0) & funny(X0)) | rich(X0)) & (~rich(X0) | (~patient(X0) | ~funny(X0)))) [nnf transformation 15]
59. ! [X0] : (((patient(X0) & funny(X0)) | rich(X0)) & (~rich(X0) | ~patient(X0) | ~funny(X0))) [flattening 58]
75. ~patient(fred) | ~brave(X1) [cnf transformation 39]
90. ~rich(X0) | kind(X0) | kind(X0) [cnf transformation 42]
91. ~rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
118. patient(X0) | rich(X0) [cnf transformation 59]
132. brave(paul) [cnf transformation 21]
135. ~rich(X0) | kind(X0) [duplicate literal removal 90]
136. ~rich(X0) | ~kind(X0) [duplicate literal removal 91]
149. 3 <=> brave(paul) [avatar definition]
151. brave(paul) <- (3) [avatar component clause 149]
167. 7 <=> patient(fred) [avatar definition]
168. ~patient(fred) <- (~7) [avatar component clause 167]
188. 12 <=> ! [X1] : ~brave(X1) [avatar definition]
189. ~brave(X1) <- (12) [avatar component clause 188]
192. 12 | ~7 [avatar split clause 75,167,188]
194. ~rich(X0) [subsumption resolution 135,136]
233. patient(X0) [subsumption resolution 118,194]
269. 3 [avatar split clause 132,149]
270. $false <- (~7) [subsumption resolution 168,233]
271. 7 [avatar contradiction clause 270]
274. $false <- (3, 12) [resolution 189,151]
275. ~3 | ~12 [avatar contradiction clause 274]
276. $false [avatar sat refutation 192,269,271,275]
% SZS output end Proof for 8132281148425873350804522
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and patient then someone is both wise and not brave and vice versa.
Everyone who is both rich and old is old or happy.
Everyone who is strong or funny is either not kind or not curious.
If john is both not wise and generous then john is both wise and not curious.
Everyone who is funny is not quiet or creative and vice versa.
Everyone who is either funny or not creative is generous or kind.
Everyone who is either not strong or not old is calm.
Everyone who is rich or not calm is not patient.
If mary is strong or generous then paul is either rich or not kind.
Everyone who is not patient or not rich is both not wise and not quiet.
Everyone who is not tall or calm is either not creative or not wise and vice versa.
If someone is patient or not funny then someone is not patient.
Everyone who is strong is humble.
If someone is not happy or funny then mary is not tall.
Everyone who is quiet is either not tall or not curious.
If someone is either rich or not generous then someone is not patient or rich and vice versa.
Alice is both not quiet and not tall.
Someone is either not calm or not creative.
Lucy is not humble or not rich.
Fred is not calm or patient.
John is both not happy and not rich.
Someone is patient or old.
Someone is either not quiet or not brave. | Mary is not quiet. | entailment | ((?[X]:((~happy(X)&patient(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((rich(X)&old(X))=>(old(X)|happy(X))))&
(![X]:((strong(X)|funny(X))=>(~kind(X)<~>~curious(X))))&
(((~wise(john)&generous(john)))=>((wise(john)&~curious(john))))&
(![X]:(funny(X)<=>(~quiet(X)|creative(X))))&
(![X]:((funny(X)<~>~creative(X))=>(generous(X)|kind(X))))&
(![X]:((~strong(X)<~>~old(X))=>calm(X)))&
(![X]:((rich(X)|~calm(X))=>~patient(X)))&
(((strong(mary)|generous(mary)))=>((rich(paul)<~>~kind(paul))))&
(![X]:((~patient(X)|~rich(X))=>(~wise(X)&~quiet(X))))&
(![X]:((~tall(X)|calm(X))<=>(~creative(X)<~>~wise(X))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:(~patient(X))))&
(![X]:(strong(X)=>humble(X)))&
((?[X]:((~happy(X)|funny(X))))=>(~tall(mary)))&
(![X]:(quiet(X)=>(~tall(X)<~>~curious(X))))&
((?[X]:((rich(X)<~>~generous(X))))<=>(?[X]:((~patient(X)|rich(X)))))&
((~quiet(alice)&~tall(alice)))&
(?[X]:((~calm(X)<~>~creative(X))))&
((~humble(lucy)|~rich(lucy)))&
((~calm(fred)|patient(fred)))&
((~happy(john)&~rich(john)))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((~quiet(X)<~>~brave(X)))) | ~quiet(mary) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3095707405044544702279345
% SZS output start Proof for 3095707405044544702279345
8. ! [X0] : ((~calm(X0) | rich(X0)) => ~patient(X0)) [input p7]
10. ! [X0] : ((~rich(X0) | ~patient(X0)) => (~quiet(X0) & ~wise(X0))) [input p9]
24. quiet(mary) [input hypothesis]
36. ! [X0] : (~patient(X0) | (calm(X0) & ~rich(X0))) [ennf transformation 8]
38. ! [X0] : ((~quiet(X0) & ~wise(X0)) | (rich(X0) & patient(X0))) [ennf transformation 10]
91. ~rich(X0) | ~patient(X0) [cnf transformation 36]
99. ~quiet(X0) | patient(X0) [cnf transformation 38]
100. ~quiet(X0) | rich(X0) [cnf transformation 38]
131. quiet(mary) [cnf transformation 24]
301. patient(mary) [resolution 99,131]
305. rich(mary) [resolution 100,131]
309. ~patient(mary) [resolution 305,91]
310. $false [subsumption resolution 309,301]
% SZS output end Proof for 3095707405044544702279345
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If lucy is not brave then someone is humble and vice versa.
If someone is either wise or not strong then someone is calm or rich.
Everyone who is not rich is not rich or happy and vice versa.
Everyone who is not generous is either curious or not curious and vice versa.
Everyone who is either rich or not calm is not old or happy and vice versa.
Everyone who is humble or not happy is not humble.
If alice is not curious then someone is both creative and not old.
Everyone who is not happy or not tall is not wise or wise and vice versa.
Everyone who is either not funny or patient is either not calm or not rich.
If susan is either not happy or not brave then fred is either humble or not tall and vice versa.
Everyone who is either not rich or tall is both not brave and generous.
Everyone who is either humble or rich is humble and vice versa.
If someone is both not creative and rich then someone is both happy and rich.
Everyone who is strong or kind is not curious.
If someone is either patient or not wise then someone is not quiet and vice versa.
Everyone who is quiet is not calm or not humble.
Someone is both not generous and tall.
Someone is either generous or not humble.
Someone is both not brave and not strong.
Fred is tall or brave.
Someone is not patient.
Someone is tall or strong. | Alice is old. | neutral | ((~brave(lucy))<=>(?[X]:(humble(X))))&
((?[X]:((wise(X)<~>~strong(X))))=>(?[X]:((calm(X)|rich(X)))))&
(![X]:(~rich(X)<=>(~rich(X)|happy(X))))&
(![X]:(~generous(X)<=>(curious(X)<~>~curious(X))))&
(![X]:((rich(X)<~>~calm(X))<=>(~old(X)|happy(X))))&
(![X]:((humble(X)|~happy(X))=>~humble(X)))&
((~curious(alice))=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((~happy(X)|~tall(X))<=>(~wise(X)|wise(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~calm(X)<~>~rich(X))))&
(((~happy(susan)<~>~brave(susan)))<=>((humble(fred)<~>~tall(fred))))&
(![X]:((~rich(X)<~>tall(X))=>(~brave(X)&generous(X))))&
(![X]:((humble(X)<~>rich(X))<=>humble(X)))&
((?[X]:((~creative(X)&rich(X))))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:((strong(X)|kind(X))=>~curious(X)))&
((?[X]:((patient(X)<~>~wise(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(quiet(X)=>(~calm(X)|~humble(X))))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((generous(X)<~>~humble(X))))&
(?[X]:((~brave(X)&~strong(X))))&
((tall(fred)|brave(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((tall(X)|strong(X)))) | old(alice) | [] | null | 0 |
If someone is not curious or happy then mary is not funny or not quiet and vice versa. Everyone who is not quiet is creative or happy and vice versa. Everyone who is brave or not creative is not humble and vice versa. Everyone who is both patient and not happy is calm or not funny. Everyone who is brave is either quiet or not kind. Everyone who is not humble or rich is either not generous or not creative. If alice is both not old and not happy then someone is calm and vice versa. Everyone who is both not brave and creative is both generous and rich. Everyone who is not patient is not wise and vice versa. Everyone who is generous or wise is not patient or curious and vice versa. If someone is either happy or not quiet then paul is either not curious or creative and vice versa. If susan is both creative and not kind then alice is not kind or tall. Everyone who is both rich and curious is either not kind or rich and vice versa. Everyone who is either not curious or happy is both not humble and not creative and vice versa. Everyone who is both brave and not generous is both funny and kind. Someone is either not rich or happy. Someone is generous. Someone is quiet or happy. Someone is generous or old. Someone is calm or generous. | Paul is not kind. | contradiction | ((?[X]:((~curious(X)|happy(X))))<=>((~funny(mary)|~quiet(mary))))&
(![X]:(~quiet(X)<=>(creative(X)|happy(X))))&
(![X]:((brave(X)|~creative(X))<=>~humble(X)))&
(![X]:((patient(X)&~happy(X))=>(calm(X)|~funny(X))))&
(![X]:(brave(X)=>(quiet(X)<~>~kind(X))))&
(![X]:((~humble(X)|rich(X))=>(~generous(X)<~>~creative(X))))&
(((~old(alice)&~happy(alice)))<=>(?[X]:(calm(X))))&
(![X]:((~brave(X)&creative(X))=>(generous(X)&rich(X))))&
(![X]:(~patient(X)<=>~wise(X)))&
(![X]:((generous(X)|wise(X))<=>(~patient(X)|curious(X))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>((~curious(paul)<~>creative(paul))))&
(((creative(susan)&~kind(susan)))=>((~kind(alice)|tall(alice))))&
(![X]:((rich(X)&curious(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((~curious(X)<~>happy(X))<=>(~humble(X)&~creative(X))))&
(![X]:((brave(X)&~generous(X))=>(funny(X)&kind(X))))&
(?[X]:((~rich(X)<~>happy(X))))&
(?[X]:(generous(X)))&
(?[X]:((quiet(X)|happy(X))))&
(?[X]:((generous(X)|old(X))))&
(?[X]:((calm(X)|generous(X)))) | ~kind(paul) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"p10",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 963883622880498105573696
% SZS output start Proof for 963883622880498105573696
2. ! [X0] : (~quiet(X0) <=> (happy(X0) | creative(X0))) [input p1]
3. ! [X0] : ((~creative(X0) | brave(X0)) <=> ~humble(X0)) [input p2]
5. ! [X0] : (brave(X0) => (quiet(X0) <~> ~kind(X0))) [input p4]
6. ! [X0] : ((rich(X0) | ~humble(X0)) => (~generous(X0) <~> ~creative(X0))) [input p5]
8. ! [X0] : ((creative(X0) & ~brave(X0)) => (rich(X0) & generous(X0))) [input p7]
11. ? [X0] : (happy(X0) <~> ~quiet(X0)) <=> (~curious(paul) <~> creative(paul)) [input p10]
13. ! [X0] : ((curious(X0) & rich(X0)) <=> (~kind(X0) <~> rich(X0))) [input p12]
14. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (~creative(X0) & ~humble(X0))) [input p13]
15. ! [X0] : ((~generous(X0) & brave(X0)) => (kind(X0) & funny(X0))) [input p14]
21. ~kind(paul) [input hypothesis]
25. ! [X0] : ((quiet(X0) <~> ~kind(X0)) | ~brave(X0)) [ennf transformation 5]
26. ! [X0] : ((~generous(X0) <~> ~creative(X0)) | (~rich(X0) & humble(X0))) [ennf transformation 6]
27. ! [X0] : ((rich(X0) & generous(X0)) | (~creative(X0) | brave(X0))) [ennf transformation 8]
28. ! [X0] : ((rich(X0) & generous(X0)) | ~creative(X0) | brave(X0)) [flattening 27]
29. ! [X0] : ((kind(X0) & funny(X0)) | (generous(X0) | ~brave(X0))) [ennf transformation 15]
30. ! [X0] : ((kind(X0) & funny(X0)) | generous(X0) | ~brave(X0)) [flattening 29]
36. ! [X0] : ((~quiet(X0) | (~happy(X0) & ~creative(X0))) & ((happy(X0) | creative(X0)) | quiet(X0))) [nnf transformation 2]
37. ! [X0] : ((~quiet(X0) | (~happy(X0) & ~creative(X0))) & (happy(X0) | creative(X0) | quiet(X0))) [flattening 36]
38. ! [X0] : (((~creative(X0) | brave(X0)) | humble(X0)) & (~humble(X0) | (creative(X0) & ~brave(X0)))) [nnf transformation 3]
39. ! [X0] : ((~creative(X0) | brave(X0) | humble(X0)) & (~humble(X0) | (creative(X0) & ~brave(X0)))) [flattening 38]
40. ! [X0] : (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | ~brave(X0)) [nnf transformation 25]
41. ! [X0] : (((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (~rich(X0) & humble(X0))) [nnf transformation 26]
50. (? [X0] : ((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | ((~curious(paul) | ~creative(paul)) & (creative(paul) | curious(paul)))) & (((~creative(paul) | curious(paul)) & (creative(paul) | ~curious(paul))) | ! [X0] : ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0)))) [nnf transformation 11]
51. (? [X0] : ((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | ((~curious(paul) | ~creative(paul)) & (creative(paul) | curious(paul)))) & (((~creative(paul) | curious(paul)) & (creative(paul) | ~curious(paul))) | ! [X1] : ((happy(X1) | quiet(X1)) & (~quiet(X1) | ~happy(X1)))) [rectify 50]
52. ? [X0] : ((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) => ((quiet(sK2) | ~happy(sK2)) & (~quiet(sK2) | happy(sK2))) [choice axiom]
53. (((quiet(sK2) | ~happy(sK2)) & (~quiet(sK2) | happy(sK2))) | ((~curious(paul) | ~creative(paul)) & (creative(paul) | curious(paul)))) & (((~creative(paul) | curious(paul)) & (creative(paul) | ~curious(paul))) | ! [X1] : ((happy(X1) | quiet(X1)) & (~quiet(X1) | ~happy(X1)))) [skolemisation 51,52]
54. ! [X0] : (((curious(X0) & rich(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (~curious(X0) | ~rich(X0)))) [nnf transformation 13]
55. ! [X0] : (((curious(X0) & rich(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | ~curious(X0) | ~rich(X0))) [flattening 54]
56. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (creative(X0) | humble(X0))) & ((~creative(X0) & ~humble(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 14]
57. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | creative(X0) | humble(X0)) & ((~creative(X0) & ~humble(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 56]
73. creative(X0) | happy(X0) | quiet(X0) [cnf transformation 37]
75. ~quiet(X0) | ~happy(X0) [cnf transformation 37]
77. ~humble(X0) | creative(X0) [cnf transformation 39]
80. ~kind(X0) | quiet(X0) | ~brave(X0) [cnf transformation 40]
83. ~generous(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 41]
84. creative(X0) | generous(X0) | humble(X0) [cnf transformation 41]
89. generous(X0) | ~creative(X0) | brave(X0) [cnf transformation 28]
90. ~creative(X0) | rich(X0) | brave(X0) [cnf transformation 28]
101. ~quiet(sK2) | happy(sK2) | creative(paul) | curious(paul) [cnf transformation 53]
103. quiet(sK2) | ~happy(sK2) | creative(paul) | curious(paul) [cnf transformation 53]
106. ~rich(X0) | kind(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 55]
107. rich(X0) | rich(X0) | kind(X0) [cnf transformation 55]
113. ~creative(X0) | happy(X0) | curious(X0) [cnf transformation 57]
115. happy(X0) | ~curious(X0) | creative(X0) | humble(X0) [cnf transformation 57]
118. kind(X0) | generous(X0) | ~brave(X0) [cnf transformation 30]
125. ~kind(paul) [cnf transformation 21]
126. ~rich(X0) | kind(X0) | ~curious(X0) [duplicate literal removal 106]
127. rich(X0) | kind(X0) [duplicate literal removal 107]
154. generous(X0) | creative(X0) [subsumption resolution 84,77]
173. generous(X0) | brave(X0) [subsumption resolution 89,154]
178. 11 <=> creative(paul) [avatar definition]
179. creative(paul) <- (11) [avatar component clause 178]
182. 12 <=> curious(paul) [avatar definition]
183. curious(paul) <- (12) [avatar component clause 182]
186. 13 <=> happy(sK2) [avatar definition]
188. ~happy(sK2) <- (~13) [avatar component clause 186]
190. ~happy(sK2) | creative(paul) | curious(paul) [subsumption resolution 103,75]
191. 12 | 11 | ~13 [avatar split clause 190,186,178,182]
194. 14 <=> quiet(sK2) [avatar definition]
196. ~quiet(sK2) <- (~14) [avatar component clause 194]
198. ~quiet(sK2) | creative(paul) | curious(paul) [subsumption resolution 101,75]
199. 12 | 11 | ~14 [avatar split clause 198,194,178,182]
205. ~curious(X0) | kind(X0) [subsumption resolution 126,127]
207. ~curious(X0) | happy(X0) | creative(X0) [subsumption resolution 115,77]
208. generous(X0) | kind(X0) [subsumption resolution 118,173]
267. kind(paul) <- (12) [resolution 183,205]
268. $false <- (12) [subsumption resolution 267,125]
269. ~12 [avatar contradiction clause 268]
339. ~creative(X2) | ~rich(X2) | kind(X2) [resolution 83,208]
340. ~creative(X3) | ~rich(X3) | brave(X3) [resolution 83,173]
343. ~creative(X2) | kind(X2) [subsumption resolution 339,127]
344. ~creative(X3) | brave(X3) [subsumption resolution 340,90]
437. happy(X0) | curious(X0) | happy(X0) | quiet(X0) [resolution 113,73]
438. quiet(X0) | curious(X0) | happy(X0) [duplicate literal removal 437]
462. curious(sK2) | happy(sK2) <- (~14) [resolution 438,196]
473. curious(sK2) <- (~13, ~14) [subsumption resolution 462,188]
494. happy(sK2) | creative(sK2) <- (~13, ~14) [resolution 473,207]
496. kind(sK2) <- (~13, ~14) [resolution 473,205]
497. creative(sK2) <- (~13, ~14) [subsumption resolution 494,188]
504. quiet(sK2) | ~brave(sK2) <- (~13, ~14) [resolution 496,80]
505. ~brave(sK2) <- (~13, ~14) [subsumption resolution 504,196]
519. brave(sK2) <- (~13, ~14) [resolution 497,344]
522. $false <- (~13, ~14) [subsumption resolution 519,505]
523. 13 | 14 [avatar contradiction clause 522]
532. kind(paul) <- (11) [resolution 179,343]
542. $false <- (11) [subsumption resolution 532,125]
543. ~11 [avatar contradiction clause 542]
545. $false [avatar sat refutation 191,199,269,523,543]
% SZS output end Proof for 963883622880498105573696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall or not humble is happy or calm and vice versa. Everyone who is rich is not kind. If mary is either not generous or rich then someone is kind or not creative. If someone is both not quiet and rich then alice is both tall and kind and vice versa. Everyone who is either funny or strong is either happy or not generous and vice versa. If john is creative or not happy then mary is wise and vice versa. If john is both not calm and old then someone is both not calm and not tall and vice versa. Everyone who is either not creative or not strong is either not happy or wise. Everyone who is both humble and not wise is not humble. Everyone who is not happy is not rich. Everyone who is either not strong or not creative is happy or curious and vice versa. If paul is either not patient or strong then mary is not humble and vice versa. If fred is either not tall or not wise then someone is not happy. Everyone who is both quiet and not happy is either not tall or not patient and vice versa. If lucy is happy then someone is both creative and not strong and vice versa. If someone is not strong or humble then fred is not quiet or generous and vice versa. Mary is both wise and quiet. Someone is not humble. Lucy is either brave or not quiet. Someone is not patient. Someone is rich or happy. Someone is strong. Susan is old or not brave. Paul is both calm and not generous. | Fred is patient. | neutral | (![X]:((~tall(X)|~humble(X))<=>(happy(X)|calm(X))))&
(![X]:(rich(X)=>~kind(X)))&
(((~generous(mary)<~>rich(mary)))=>(?[X]:((kind(X)|~creative(X)))))&
((?[X]:((~quiet(X)&rich(X))))<=>((tall(alice)&kind(alice))))&
(![X]:((funny(X)<~>strong(X))<=>(happy(X)<~>~generous(X))))&
(((creative(john)|~happy(john)))<=>(wise(mary)))&
(((~calm(john)&old(john)))<=>(?[X]:((~calm(X)&~tall(X)))))&
(![X]:((~creative(X)<~>~strong(X))=>(~happy(X)<~>wise(X))))&
(![X]:((humble(X)&~wise(X))=>~humble(X)))&
(![X]:(~happy(X)=>~rich(X)))&
(![X]:((~strong(X)<~>~creative(X))<=>(happy(X)|curious(X))))&
(((~patient(paul)<~>strong(paul)))<=>(~humble(mary)))&
(((~tall(fred)<~>~wise(fred)))=>(?[X]:(~happy(X))))&
(![X]:((quiet(X)&~happy(X))<=>(~tall(X)<~>~patient(X))))&
((happy(lucy))<=>(?[X]:((creative(X)&~strong(X)))))&
((?[X]:((~strong(X)|humble(X))))<=>((~quiet(fred)|generous(fred))))&
((wise(mary)&quiet(mary)))&
(?[X]:(~humble(X)))&
((brave(lucy)<~>~quiet(lucy)))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)|happy(X))))&
(?[X]:(strong(X)))&
((old(susan)|~brave(susan)))&
((calm(paul)&~generous(paul))) | patient(fred) | [] | null | 0 |
If paul is both not happy and not humble then someone is not humble. If fred is funny then paul is humble or not generous. Everyone who is not curious is curious or kind and vice versa. Everyone who is quiet is not old or not kind and vice versa. If mary is either brave or not humble then susan is creative. Everyone who is happy is both kind and calm and vice versa. Everyone who is kind is not wise or not old and vice versa. Everyone who is both quiet and funny is either tall or funny and vice versa. Everyone who is both humble and old is either tall or quiet. Everyone who is both not brave and not funny is kind and vice versa. If mary is happy or kind then someone is either patient or creative. Everyone who is patient or generous is old. If lucy is either humble or not curious then someone is generous or wise. Everyone who is either not curious or not generous is either not curious or not old and vice versa. Everyone who is both humble and creative is either creative or not humble and vice versa. Everyone who is both generous and not rich is either generous or creative. Alice is funny or not quiet. Someone is either not brave or not strong. Someone is not strong. Paul is calm or not creative. John is either curious or generous. Someone is rich. | John is creative. | entailment | (((~happy(paul)&~humble(paul)))=>(?[X]:(~humble(X))))&
((funny(fred))=>((humble(paul)|~generous(paul))))&
(![X]:(~curious(X)<=>(curious(X)|kind(X))))&
(![X]:(quiet(X)<=>(~old(X)|~kind(X))))&
(((brave(mary)<~>~humble(mary)))=>(creative(susan)))&
(![X]:(happy(X)<=>(kind(X)&calm(X))))&
(![X]:(kind(X)<=>(~wise(X)|~old(X))))&
(![X]:((quiet(X)&funny(X))<=>(tall(X)<~>funny(X))))&
(![X]:((humble(X)&old(X))=>(tall(X)<~>quiet(X))))&
(![X]:((~brave(X)&~funny(X))<=>kind(X)))&
(((happy(mary)|kind(mary)))=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((patient(X)|generous(X))=>old(X)))&
(((humble(lucy)<~>~curious(lucy)))=>(?[X]:((generous(X)|wise(X)))))&
(![X]:((~curious(X)<~>~generous(X))<=>(~curious(X)<~>~old(X))))&
(![X]:((humble(X)&creative(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((generous(X)&~rich(X))=>(generous(X)<~>creative(X))))&
((funny(alice)|~quiet(alice)))&
(?[X]:((~brave(X)<~>~strong(X))))&
(?[X]:(~strong(X)))&
((calm(paul)|~creative(paul)))&
((curious(john)<~>generous(john)))&
(?[X]:(rich(X))) | creative(john) | [
"p2",
"p3",
"p7",
"p8",
"p9",
"p11",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8202306853270647231256038
% SZS output start Proof for 8202306853270647231256038
3. ! [X0] : (~curious(X0) <=> (kind(X0) | curious(X0))) [input p2]
4. ! [X0] : (quiet(X0) <=> (~kind(X0) | ~old(X0))) [input p3]
8. ! [X0] : ((funny(X0) & quiet(X0)) <=> (tall(X0) <~> funny(X0))) [input p7]
9. ! [X0] : ((old(X0) & humble(X0)) => (tall(X0) <~> quiet(X0))) [input p8]
10. ! [X0] : ((~funny(X0) & ~brave(X0)) <=> kind(X0)) [input p9]
12. ! [X0] : ((generous(X0) | patient(X0)) => old(X0)) [input p11]
15. ! [X0] : ((creative(X0) & humble(X0)) <=> (creative(X0) <~> ~humble(X0))) [input p14]
21. curious(john) <~> generous(john) [input p20]
23. ~creative(john) [input hypothesis]
31. ! [X0] : ((tall(X0) <~> quiet(X0)) | (~old(X0) | ~humble(X0))) [ennf transformation 9]
32. ! [X0] : ((tall(X0) <~> quiet(X0)) | ~old(X0) | ~humble(X0)) [flattening 31]
34. ! [X0] : (old(X0) | (~generous(X0) & ~patient(X0))) [ennf transformation 12]
38. ! [X0] : ((~curious(X0) | (~kind(X0) & ~curious(X0))) & ((kind(X0) | curious(X0)) | curious(X0))) [nnf transformation 3]
39. ! [X0] : ((~curious(X0) | (~kind(X0) & ~curious(X0))) & (kind(X0) | curious(X0) | curious(X0))) [flattening 38]
40. ! [X0] : ((quiet(X0) | (kind(X0) & old(X0))) & ((~kind(X0) | ~old(X0)) | ~quiet(X0))) [nnf transformation 4]
41. ! [X0] : ((quiet(X0) | (kind(X0) & old(X0))) & (~kind(X0) | ~old(X0) | ~quiet(X0))) [flattening 40]
47. ! [X0] : (((funny(X0) & quiet(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 8]
48. ! [X0] : (((funny(X0) & quiet(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | ~funny(X0) | ~quiet(X0))) [flattening 47]
49. ! [X0] : (((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | ~old(X0) | ~humble(X0)) [nnf transformation 32]
50. ! [X0] : (((~funny(X0) & ~brave(X0)) | ~kind(X0)) & (kind(X0) | (funny(X0) | brave(X0)))) [nnf transformation 10]
51. ! [X0] : (((~funny(X0) & ~brave(X0)) | ~kind(X0)) & (kind(X0) | funny(X0) | brave(X0))) [flattening 50]
59. ! [X0] : (((creative(X0) & humble(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | (~creative(X0) | ~humble(X0)))) [nnf transformation 15]
60. ! [X0] : (((creative(X0) & humble(X0)) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | ~creative(X0) | ~humble(X0))) [flattening 59]
66. (~generous(john) | ~curious(john)) & (generous(john) | curious(john)) [nnf transformation 21]
69. kind(X0) | curious(X0) | curious(X0) [cnf transformation 39]
70. ~curious(X0) | ~curious(X0) [cnf transformation 39]
72. ~kind(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 41]
87. funny(X0) | funny(X0) | ~tall(X0) [cnf transformation 48]
89. quiet(X0) | tall(X0) | ~old(X0) | ~humble(X0) [cnf transformation 49]
93. ~funny(X0) | ~kind(X0) [cnf transformation 51]
99. ~generous(X0) | old(X0) [cnf transformation 34]
115. creative(X0) | creative(X0) | humble(X0) [cnf transformation 60]
121. generous(john) | curious(john) [cnf transformation 66]
123. ~creative(john) [cnf transformation 23]
127. creative(X0) | humble(X0) [duplicate literal removal 115]
133. ~tall(X0) | funny(X0) [duplicate literal removal 87]
134. kind(X0) | curious(X0) [duplicate literal removal 69]
135. ~curious(X0) [duplicate literal removal 70]
158. kind(X0) [subsumption resolution 134,135]
159. ~old(X0) | ~quiet(X0) [subsumption resolution 72,158]
177. ~old(X0) | tall(X0) | ~humble(X0) [subsumption resolution 89,159]
178. ~funny(X0) [subsumption resolution 93,158]
224. generous(john) [subsumption resolution 121,135]
227. old(john) [resolution 99,224]
228. humble(john) [resolution 127,123]
247. tall(john) | ~humble(john) [resolution 177,227]
249. tall(john) [subsumption resolution 247,228]
293. funny(john) [resolution 249,133]
294. $false [subsumption resolution 293,178]
% SZS output end Proof for 8202306853270647231256038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is both not patient and calm.
Everyone who is not patient or calm is both happy and tall and vice versa.
If someone is strong or not curious then paul is not brave and vice versa.
If alice is not old then someone is either patient or kind.
If someone is patient then mary is both rich and brave.
Everyone who is either old or not old is tall and vice versa.
Everyone who is either not patient or not happy is not brave and vice versa.
If fred is both not calm and not old then mary is both not quiet and strong and vice versa.
If someone is brave or tall then someone is both generous and strong and vice versa.
If someone is not happy or not generous then someone is both brave and not strong.
If lucy is quiet or not curious then fred is both brave and not patient.
If someone is tall then lucy is not patient or not tall and vice versa.
If fred is not tall or old then someone is creative or kind.
If someone is either curious or not calm then paul is not funny or generous.
Everyone who is not creative is quiet or creative.
Everyone who is not curious is not creative.
Lucy is both old and not rich.
Someone is not rich or old.
Paul is not happy or not patient.
Someone is not old.
Fred is both not calm and kind. | Mary is not creative. | neutral | (![X]:(~happy(X)=>(~patient(X)&calm(X))))&
(![X]:((~patient(X)|calm(X))<=>(happy(X)&tall(X))))&
((?[X]:((strong(X)|~curious(X))))<=>(~brave(paul)))&
((~old(alice))=>(?[X]:((patient(X)<~>kind(X)))))&
((?[X]:(patient(X)))=>((rich(mary)&brave(mary))))&
(![X]:((old(X)<~>~old(X))<=>tall(X)))&
(![X]:((~patient(X)<~>~happy(X))<=>~brave(X)))&
(((~calm(fred)&~old(fred)))<=>((~quiet(mary)&strong(mary))))&
((?[X]:((brave(X)|tall(X))))<=>(?[X]:((generous(X)&strong(X)))))&
((?[X]:((~happy(X)|~generous(X))))=>(?[X]:((brave(X)&~strong(X)))))&
(((quiet(lucy)|~curious(lucy)))=>((brave(fred)&~patient(fred))))&
((?[X]:(tall(X)))<=>((~patient(lucy)|~tall(lucy))))&
(((~tall(fred)|old(fred)))=>(?[X]:((creative(X)|kind(X)))))&
((?[X]:((curious(X)<~>~calm(X))))=>((~funny(paul)|generous(paul))))&
(![X]:(~creative(X)=>(quiet(X)|creative(X))))&
(![X]:(~curious(X)=>~creative(X)))&
((old(lucy)&~rich(lucy)))&
(?[X]:((~rich(X)|old(X))))&
((~happy(paul)|~patient(paul)))&
(?[X]:(~old(X)))&
((~calm(fred)&kind(fred))) | ~creative(mary) | [] | null | 0 |
Everyone who is not humble or curious is kind or generous. If someone is both not generous and quiet then someone is strong and vice versa. Everyone who is happy is quiet or creative and vice versa. If alice is either tall or brave then someone is not creative or wise. Everyone who is both not curious and happy is strong or not funny. Everyone who is creative is generous and vice versa. If lucy is either not rich or creative then someone is calm and vice versa. Everyone who is old or not patient is generous. If someone is either not rich or wise then someone is not happy and vice versa. If alice is both not old and rich then someone is not humble. Everyone who is either not tall or not generous is either creative or not rich and vice versa. Everyone who is not strong or not quiet is both brave and not humble and vice versa. Everyone who is strong or not creative is creative or not calm. Everyone who is either not curious or not old is either happy or not generous and vice versa. If someone is not patient or not brave then someone is not curious and vice versa. Everyone who is either strong or humble is both not strong and not kind. Someone is either not wise or not generous. Someone is not happy. Someone is not strong. Someone is either not kind or old. John is not patient. Someone is both quiet and not generous. Someone is both not happy and tall. | Lucy is quiet. | neutral | (![X]:((~humble(X)|curious(X))=>(kind(X)|generous(X))))&
((?[X]:((~generous(X)&quiet(X))))<=>(?[X]:(strong(X))))&
(![X]:(happy(X)<=>(quiet(X)|creative(X))))&
(((tall(alice)<~>brave(alice)))=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((~curious(X)&happy(X))=>(strong(X)|~funny(X))))&
(![X]:(creative(X)<=>generous(X)))&
(((~rich(lucy)<~>creative(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((old(X)|~patient(X))=>generous(X)))&
((?[X]:((~rich(X)<~>wise(X))))<=>(?[X]:(~happy(X))))&
(((~old(alice)&rich(alice)))=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((~strong(X)|~quiet(X))<=>(brave(X)&~humble(X))))&
(![X]:((strong(X)|~creative(X))=>(creative(X)|~calm(X))))&
(![X]:((~curious(X)<~>~old(X))<=>(happy(X)<~>~generous(X))))&
((?[X]:((~patient(X)|~brave(X))))<=>(?[X]:(~curious(X))))&
(![X]:((strong(X)<~>humble(X))=>(~strong(X)&~kind(X))))&
(?[X]:((~wise(X)<~>~generous(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~kind(X)<~>old(X))))&
(~patient(john))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((~happy(X)&tall(X)))) | quiet(lucy) | [] | null | 0 |
If someone is either curious or not tall then someone is humble and vice versa.
Everyone who is either not strong or not funny is wise or not calm and vice versa.
If someone is both not rich and old then someone is not funny and vice versa.
Everyone who is happy or calm is both not generous and patient.
Everyone who is not strong is tall or not wise.
Everyone who is not humble or quiet is not rich or calm and vice versa.
Everyone who is either not patient or wise is both creative and tall and vice versa.
Everyone who is both quiet and not funny is humble or not humble and vice versa.
Everyone who is both not brave and funny is either funny or not kind.
Everyone who is not patient is rich or creative.
If someone is either not wise or calm then someone is either rich or not quiet.
Everyone who is both not generous and kind is not funny.
If someone is both not funny and funny then someone is not generous.
If john is both happy and not rich then lucy is old or wise and vice versa.
Everyone who is either generous or patient is not old.
Everyone who is patient is either brave or wise and vice versa.
Mary is not tall or funny.
Someone is either brave or tall.
Susan is either not creative or not strong.
Someone is both quiet and not humble.
Someone is funny or kind.
Mary is not humble or not quiet.
Lucy is both not calm and generous.
John is either generous or not brave. | Susan is not wise. | entailment | ((?[X]:((curious(X)<~>~tall(X))))<=>(?[X]:(humble(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>(wise(X)|~calm(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:(~funny(X))))&
(![X]:((happy(X)|calm(X))=>(~generous(X)&patient(X))))&
(![X]:(~strong(X)=>(tall(X)|~wise(X))))&
(![X]:((~humble(X)|quiet(X))<=>(~rich(X)|calm(X))))&
(![X]:((~patient(X)<~>wise(X))<=>(creative(X)&tall(X))))&
(![X]:((quiet(X)&~funny(X))<=>(humble(X)|~humble(X))))&
(![X]:((~brave(X)&funny(X))=>(funny(X)<~>~kind(X))))&
(![X]:(~patient(X)=>(rich(X)|creative(X))))&
((?[X]:((~wise(X)<~>calm(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((~generous(X)&kind(X))=>~funny(X)))&
((?[X]:((~funny(X)&funny(X))))=>(?[X]:(~generous(X))))&
(((happy(john)&~rich(john)))<=>((old(lucy)|wise(lucy))))&
(![X]:((generous(X)<~>patient(X))=>~old(X)))&
(![X]:(patient(X)<=>(brave(X)<~>wise(X))))&
((~tall(mary)|funny(mary)))&
(?[X]:((brave(X)<~>tall(X))))&
((~creative(susan)<~>~strong(susan)))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((funny(X)|kind(X))))&
((~humble(mary)|~quiet(mary)))&
((~calm(lucy)&generous(lucy)))&
((generous(john)<~>~brave(john))) | ~wise(susan) | [
"p1",
"p3",
"p5",
"p6",
"p7",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7490740852358020794114680
% SZS output start Proof for 7490740852358020794114680
2. ! [X0] : ((~strong(X0) <~> ~funny(X0)) <=> (~calm(X0) | wise(X0))) [input p1]
4. ! [X0] : ((calm(X0) | happy(X0)) => (patient(X0) & ~generous(X0))) [input p3]
6. ! [X0] : ((quiet(X0) | ~humble(X0)) <=> (calm(X0) | ~rich(X0))) [input p5]
7. ! [X0] : ((~patient(X0) <~> wise(X0)) <=> (tall(X0) & creative(X0))) [input p6]
8. ! [X0] : ((~funny(X0) & quiet(X0)) <=> (~humble(X0) | humble(X0))) [input p7]
10. ! [X0] : (~patient(X0) => (creative(X0) | rich(X0))) [input p9]
19. ~creative(susan) <~> ~strong(susan) [input p18]
25. wise(susan) [input hypothesis]
30. ! [X0] : ((patient(X0) & ~generous(X0)) | (~calm(X0) & ~happy(X0))) [ennf transformation 4]
35. ! [X0] : ((creative(X0) | rich(X0)) | patient(X0)) [ennf transformation 10]
36. ! [X0] : (creative(X0) | rich(X0) | patient(X0)) [flattening 35]
47. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | (calm(X0) & ~wise(X0))) & ((~calm(X0) | wise(X0)) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [nnf transformation 2]
48. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | (calm(X0) & ~wise(X0))) & (~calm(X0) | wise(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [flattening 47]
54. ! [X0] : (((quiet(X0) | ~humble(X0)) | (~calm(X0) & rich(X0))) & ((calm(X0) | ~rich(X0)) | (~quiet(X0) & humble(X0)))) [nnf transformation 6]
55. ! [X0] : ((quiet(X0) | ~humble(X0) | (~calm(X0) & rich(X0))) & (calm(X0) | ~rich(X0) | (~quiet(X0) & humble(X0)))) [flattening 54]
56. ! [X0] : ((((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | (~tall(X0) | ~creative(X0))) & ((tall(X0) & creative(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0))))) [nnf transformation 7]
57. ! [X0] : ((((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | ~tall(X0) | ~creative(X0)) & ((tall(X0) & creative(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0))))) [flattening 56]
58. ! [X0] : (((~funny(X0) & quiet(X0)) | (humble(X0) & ~humble(X0))) & ((~humble(X0) | humble(X0)) | (funny(X0) | ~quiet(X0)))) [nnf transformation 8]
59. ! [X0] : (((~funny(X0) & quiet(X0)) | (humble(X0) & ~humble(X0))) & (~humble(X0) | humble(X0) | funny(X0) | ~quiet(X0))) [flattening 58]
75. (strong(susan) | creative(susan)) & (~strong(susan) | ~creative(susan)) [nnf transformation 19]
89. ~wise(X0) | strong(X0) | funny(X0) [cnf transformation 48]
97. ~calm(X0) | patient(X0) [cnf transformation 30]
100. ~quiet(X0) | ~rich(X0) | calm(X0) [cnf transformation 55]
104. ~patient(X0) | creative(X0) | ~wise(X0) [cnf transformation 57]
110. quiet(X0) | ~humble(X0) [cnf transformation 59]
111. quiet(X0) | humble(X0) [cnf transformation 59]
112. ~funny(X0) | ~humble(X0) [cnf transformation 59]
113. ~funny(X0) | humble(X0) [cnf transformation 59]
116. creative(X0) | rich(X0) | patient(X0) [cnf transformation 36]
137. ~strong(susan) | ~creative(susan) [cnf transformation 75]
147. wise(susan) [cnf transformation 25]
195. ~funny(X0) [subsumption resolution 112,113]
196. quiet(X0) [subsumption resolution 110,111]
244. 21 <=> creative(susan) [avatar definition]
245. ~creative(susan) <- (~21) [avatar component clause 244]
248. 22 <=> strong(susan) [avatar definition]
252. ~21 | ~22 [avatar split clause 137,248,244]
270. strong(susan) | funny(susan) [resolution 89,147]
274. strong(susan) [subsumption resolution 270,195]
275. 22 [avatar split clause 274,248]
303. ~rich(X1) | calm(X1) [resolution 100,196]
326. rich(susan) | patient(susan) <- (~21) [resolution 116,245]
328. 29 <=> patient(susan) [avatar definition]
329. ~patient(susan) <- (~29) [avatar component clause 328]
330. patient(susan) <- (29) [avatar component clause 328]
332. 30 <=> rich(susan) [avatar definition]
334. rich(susan) <- (30) [avatar component clause 332]
335. 29 | 30 | 21 [avatar split clause 326,244,332,328]
338. creative(susan) | ~wise(susan) <- (29) [resolution 330,104]
340. ~wise(susan) <- (~21, 29) [subsumption resolution 338,245]
341. $false <- (~21, 29) [subsumption resolution 340,147]
342. 21 | ~29 [avatar contradiction clause 341]
391. calm(susan) <- (30) [resolution 334,303]
448. patient(susan) <- (30) [resolution 391,97]
451. $false <- (~29, 30) [subsumption resolution 448,329]
452. 29 | ~30 [avatar contradiction clause 451]
453. $false [avatar sat refutation 252,275,335,342,452]
% SZS output end Proof for 7490740852358020794114680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both not patient and creative and vice versa. Everyone who is not generous or funny is funny or not brave. If someone is either quiet or humble then someone is not strong. Everyone who is both not calm and calm is generous and vice versa. Everyone who is either not patient or wise is not curious or not generous. Everyone who is both not brave and not curious is old or not quiet. If susan is quiet or not brave then someone is not calm or strong and vice versa. If mary is tall or not happy then someone is rich or wise and vice versa. Everyone who is strong or not generous is creative and vice versa. Everyone who is either brave or funny is either old or not curious. Everyone who is either strong or old is not old or not kind and vice versa. Everyone who is rich is both not funny and not rich and vice versa. Everyone who is either not calm or quiet is either happy or not tall. If someone is both kind and brave then someone is both not happy and funny. If someone is not quiet then someone is quiet and vice versa. If someone is either not funny or not humble then someone is both not tall and quiet and vice versa. Fred is not happy or creative. Mary is either old or wise. Someone is either not wise or patient. Someone is not old or not quiet. Someone is either not strong or strong. Someone is both not generous and happy. Someone is both not quiet and humble. | Susan is not happy. | neutral | (![X]:(~humble(X)<=>(~patient(X)&creative(X))))&
(![X]:((~generous(X)|funny(X))=>(funny(X)|~brave(X))))&
((?[X]:((quiet(X)<~>humble(X))))=>(?[X]:(~strong(X))))&
(![X]:((~calm(X)&calm(X))<=>generous(X)))&
(![X]:((~patient(X)<~>wise(X))=>(~curious(X)|~generous(X))))&
(![X]:((~brave(X)&~curious(X))=>(old(X)|~quiet(X))))&
(((quiet(susan)|~brave(susan)))<=>(?[X]:((~calm(X)|strong(X)))))&
(((tall(mary)|~happy(mary)))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((strong(X)|~generous(X))<=>creative(X)))&
(![X]:((brave(X)<~>funny(X))=>(old(X)<~>~curious(X))))&
(![X]:((strong(X)<~>old(X))<=>(~old(X)|~kind(X))))&
(![X]:(rich(X)<=>(~funny(X)&~rich(X))))&
(![X]:((~calm(X)<~>quiet(X))=>(happy(X)<~>~tall(X))))&
((?[X]:((kind(X)&brave(X))))=>(?[X]:((~happy(X)&funny(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:(quiet(X))))&
((?[X]:((~funny(X)<~>~humble(X))))<=>(?[X]:((~tall(X)&quiet(X)))))&
((~happy(fred)|creative(fred)))&
((old(mary)<~>wise(mary)))&
(?[X]:((~wise(X)<~>patient(X))))&
(?[X]:((~old(X)|~quiet(X))))&
(?[X]:((~strong(X)<~>strong(X))))&
(?[X]:((~generous(X)&happy(X))))&
(?[X]:((~quiet(X)&humble(X)))) | ~happy(susan) | [] | null | 0 |
If susan is humble then someone is not quiet or not humble and vice versa. If someone is either generous or funny then john is funny and vice versa. Everyone who is either not kind or not happy is patient and vice versa. If someone is strong or not happy then someone is generous or patient and vice versa. If mary is old then someone is both not brave and not humble and vice versa. If someone is quiet then someone is either tall or brave. Everyone who is both not patient and calm is either not calm or brave and vice versa. Everyone who is both humble and not rich is not creative and vice versa. Everyone who is not tall or not quiet is not old and vice versa. If someone is both quiet and funny then alice is either happy or not funny. If someone is not quiet then someone is either not quiet or not wise and vice versa. Everyone who is both not patient and calm is either happy or not creative. Everyone who is generous or not quiet is either tall or not kind. Everyone who is not patient or not tall is not brave and vice versa. Everyone who is not rich is both not creative and not humble and vice versa. If john is brave then someone is either kind or not humble and vice versa. Susan is both not old and curious. Susan is both tall and brave. Mary is either curious or humble. Someone is both curious and not wise. Someone is not brave. John is not happy or generous. Mary is calm or not wise. | Alice is not curious. | neutral | ((humble(susan))<=>(?[X]:((~quiet(X)|~humble(X)))))&
((?[X]:((generous(X)<~>funny(X))))<=>(funny(john)))&
(![X]:((~kind(X)<~>~happy(X))<=>patient(X)))&
((?[X]:((strong(X)|~happy(X))))<=>(?[X]:((generous(X)|patient(X)))))&
((old(mary))<=>(?[X]:((~brave(X)&~humble(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:((~patient(X)&calm(X))<=>(~calm(X)<~>brave(X))))&
(![X]:((humble(X)&~rich(X))<=>~creative(X)))&
(![X]:((~tall(X)|~quiet(X))<=>~old(X)))&
((?[X]:((quiet(X)&funny(X))))=>((happy(alice)<~>~funny(alice))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(![X]:((~patient(X)&calm(X))=>(happy(X)<~>~creative(X))))&
(![X]:((generous(X)|~quiet(X))=>(tall(X)<~>~kind(X))))&
(![X]:((~patient(X)|~tall(X))<=>~brave(X)))&
(![X]:(~rich(X)<=>(~creative(X)&~humble(X))))&
((brave(john))<=>(?[X]:((kind(X)<~>~humble(X)))))&
((~old(susan)&curious(susan)))&
((tall(susan)&brave(susan)))&
((curious(mary)<~>humble(mary)))&
(?[X]:((curious(X)&~wise(X))))&
(?[X]:(~brave(X)))&
((~happy(john)|generous(john)))&
((calm(mary)|~wise(mary))) | ~curious(alice) | [] | null | 0 |
If someone is both not strong and calm then paul is both not wise and not rich and vice versa.
Everyone who is both not wise and generous is brave or not funny and vice versa.
Everyone who is not tall is quiet or not happy and vice versa.
If paul is rich then mary is both wise and not kind.
Everyone who is not happy is generous and vice versa.
If someone is not strong or not brave then someone is both curious and not calm and vice versa.
Everyone who is either not brave or kind is either wise or old and vice versa.
If someone is calm then lucy is both quiet and creative.
Everyone who is either not old or humble is both quiet and curious.
Everyone who is curious is wise or not happy.
Everyone who is quiet or not patient is both old and strong.
Everyone who is rich is either tall or not curious and vice versa.
Everyone who is not humble is kind.
Everyone who is creative or rich is quiet and vice versa.
Everyone who is both old and not brave is not wise or brave and vice versa.
If someone is either funny or strong then john is either not rich or not kind and vice versa.
Fred is either patient or not tall.
Someone is funny or not generous.
Someone is either kind or happy.
Someone is both strong and not happy. | Lucy is rich. | contradiction | ((?[X]:((~strong(X)&calm(X))))<=>((~wise(paul)&~rich(paul))))&
(![X]:((~wise(X)&generous(X))<=>(brave(X)|~funny(X))))&
(![X]:(~tall(X)<=>(quiet(X)|~happy(X))))&
((rich(paul))=>((wise(mary)&~kind(mary))))&
(![X]:(~happy(X)<=>generous(X)))&
((?[X]:((~strong(X)|~brave(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((~brave(X)<~>kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:(calm(X)))=>((quiet(lucy)&creative(lucy))))&
(![X]:((~old(X)<~>humble(X))=>(quiet(X)&curious(X))))&
(![X]:(curious(X)=>(wise(X)|~happy(X))))&
(![X]:((quiet(X)|~patient(X))=>(old(X)&strong(X))))&
(![X]:(rich(X)<=>(tall(X)<~>~curious(X))))&
(![X]:(~humble(X)=>kind(X)))&
(![X]:((creative(X)|rich(X))<=>quiet(X)))&
(![X]:((old(X)&~brave(X))<=>(~wise(X)|brave(X))))&
((?[X]:((funny(X)<~>strong(X))))<=>((~rich(john)<~>~kind(john))))&
((patient(fred)<~>~tall(fred)))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:((kind(X)<~>happy(X))))&
(?[X]:((strong(X)&~happy(X)))) | rich(lucy) | [
"p2",
"p6",
"p8",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5882560839776216033800895
% SZS output start Proof for 5882560839776216033800895
3. ! [X0] : (~tall(X0) <=> (~happy(X0) | quiet(X0))) [input p2]
7. ! [X0] : ((~brave(X0) <~> kind(X0)) <=> (wise(X0) <~> old(X0))) [input p6]
9. ! [X0] : ((~old(X0) <~> humble(X0)) => (curious(X0) & quiet(X0))) [input p8]
11. ! [X0] : ((~patient(X0) | quiet(X0)) => (strong(X0) & old(X0))) [input p10]
12. ! [X0] : (rich(X0) <=> (tall(X0) <~> ~curious(X0))) [input p11]
13. ! [X0] : (~humble(X0) => kind(X0)) [input p12]
14. ! [X0] : ((rich(X0) | creative(X0)) <=> quiet(X0)) [input p13]
15. ! [X0] : ((~brave(X0) & old(X0)) <=> (brave(X0) | ~wise(X0))) [input p14]
21. rich(lucy) [input hypothesis]
25. ! [X0] : ((curious(X0) & quiet(X0)) | (~old(X0) <=> humble(X0))) [ennf transformation 9]
28. ! [X0] : ((strong(X0) & old(X0)) | (patient(X0) & ~quiet(X0))) [ennf transformation 11]
29. ! [X0] : (kind(X0) | humble(X0)) [ennf transformation 13]
37. ! [X0] : ((~tall(X0) | (happy(X0) & ~quiet(X0))) & ((~happy(X0) | quiet(X0)) | tall(X0))) [nnf transformation 3]
38. ! [X0] : ((~tall(X0) | (happy(X0) & ~quiet(X0))) & (~happy(X0) | quiet(X0) | tall(X0))) [flattening 37]
45. ! [X0] : ((((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))))) [nnf transformation 7]
46. ! [X0] : ((curious(X0) & quiet(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) [nnf transformation 25]
47. ! [X0] : ((rich(X0) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | ~rich(X0))) [nnf transformation 12]
48. ! [X0] : (((rich(X0) | creative(X0)) | ~quiet(X0)) & (quiet(X0) | (~rich(X0) & ~creative(X0)))) [nnf transformation 14]
49. ! [X0] : ((rich(X0) | creative(X0) | ~quiet(X0)) & (quiet(X0) | (~rich(X0) & ~creative(X0)))) [flattening 48]
50. ! [X0] : (((~brave(X0) & old(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (brave(X0) | ~old(X0)))) [nnf transformation 15]
51. ! [X0] : (((~brave(X0) & old(X0)) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | brave(X0) | ~old(X0))) [flattening 50]
74. ~quiet(X0) | ~tall(X0) [cnf transformation 38]
92. ~old(X0) | brave(X0) | wise(X0) | ~kind(X0) [cnf transformation 45]
98. ~humble(X0) | ~old(X0) | curious(X0) [cnf transformation 46]
100. ~quiet(X0) | old(X0) [cnf transformation 28]
104. ~curious(X0) | tall(X0) | ~rich(X0) [cnf transformation 47]
108. humble(X0) | kind(X0) [cnf transformation 29]
110. ~rich(X0) | quiet(X0) [cnf transformation 49]
112. brave(X0) | ~wise(X0) | brave(X0) | ~old(X0) [cnf transformation 51]
113. old(X0) | wise(X0) [cnf transformation 51]
116. ~brave(X0) | ~brave(X0) [cnf transformation 51]
132. rich(lucy) [cnf transformation 21]
133. brave(X0) | ~wise(X0) | ~old(X0) [duplicate literal removal 112]
134. ~brave(X0) [duplicate literal removal 116]
211. 17 <=> quiet(lucy) [avatar definition]
213. quiet(lucy) <- (17) [avatar component clause 211]
215. ~old(X0) | ~wise(X0) [subsumption resolution 133,134]
273. ~tall(lucy) <- (17) [resolution 74,213]
277. old(lucy) <- (17) [resolution 100,213]
282. quiet(lucy) [resolution 110,132]
283. ~wise(lucy) <- (17) [resolution 215,277]
293. ~old(X2) | curious(X2) | kind(X2) [resolution 98,108]
372. brave(X1) | wise(X1) | ~kind(X1) | wise(X1) [resolution 92,113]
377. brave(X1) | wise(X1) | ~kind(X1) [duplicate literal removal 372]
379. ~kind(X1) | wise(X1) [subsumption resolution 377,134]
441. curious(lucy) | kind(lucy) <- (17) [resolution 293,277]
448. 42 <=> kind(lucy) [avatar definition]
450. kind(lucy) <- (42) [avatar component clause 448]
452. 43 <=> curious(lucy) [avatar definition]
454. curious(lucy) <- (43) [avatar component clause 452]
455. 42 | 43 | ~17 [avatar split clause 441,211,452,448]
482. wise(lucy) <- (42) [resolution 450,379]
485. $false <- (17, 42) [subsumption resolution 482,283]
486. ~17 | ~42 [avatar contradiction clause 485]
488. tall(lucy) | ~rich(lucy) <- (43) [resolution 454,104]
490. ~rich(lucy) <- (17, 43) [subsumption resolution 488,273]
491. $false <- (17, 43) [subsumption resolution 490,132]
492. ~17 | ~43 [avatar contradiction clause 491]
494. 17 [avatar split clause 282,211]
496. $false [avatar sat refutation 455,486,492,494]
% SZS output end Proof for 5882560839776216033800895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or wise is kind and vice versa.
Everyone who is kind or old is not quiet or strong and vice versa.
Everyone who is either wise or not rich is not quiet.
If paul is either not quiet or creative then paul is both not wise and not strong.
If mary is generous then susan is either brave or humble.
If paul is not calm then someone is not strong and vice versa.
If someone is both patient and wise then mary is not curious.
Everyone who is either not wise or not tall is not tall and vice versa.
Everyone who is both rich and not creative is tall and vice versa.
If someone is kind or not happy then susan is not curious or not humble and vice versa.
Everyone who is both not strong and calm is rich or not strong and vice versa.
If susan is humble or not quiet then someone is both rich and not old and vice versa.
If someone is patient then alice is either not creative or not funny.
If someone is both not rich and not creative then paul is both happy and not brave.
If someone is not calm then john is not rich and vice versa.
If susan is both kind and not patient then someone is not patient and vice versa.
Someone is both old and tall.
John is either not creative or not kind.
Someone is strong or tall.
Someone is not calm.
Someone is not old or humble.
Lucy is both not humble and happy.
Fred is both not quiet and creative. | Fred is creative. | entailment | (![X]:((~curious(X)|wise(X))<=>kind(X)))&
(![X]:((kind(X)|old(X))<=>(~quiet(X)|strong(X))))&
(![X]:((wise(X)<~>~rich(X))=>~quiet(X)))&
(((~quiet(paul)<~>creative(paul)))=>((~wise(paul)&~strong(paul))))&
((generous(mary))=>((brave(susan)<~>humble(susan))))&
((~calm(paul))<=>(?[X]:(~strong(X))))&
((?[X]:((patient(X)&wise(X))))=>(~curious(mary)))&
(![X]:((~wise(X)<~>~tall(X))<=>~tall(X)))&
(![X]:((rich(X)&~creative(X))<=>tall(X)))&
((?[X]:((kind(X)|~happy(X))))<=>((~curious(susan)|~humble(susan))))&
(![X]:((~strong(X)&calm(X))<=>(rich(X)|~strong(X))))&
(((humble(susan)|~quiet(susan)))<=>(?[X]:((rich(X)&~old(X)))))&
((?[X]:(patient(X)))=>((~creative(alice)<~>~funny(alice))))&
((?[X]:((~rich(X)&~creative(X))))=>((happy(paul)&~brave(paul))))&
((?[X]:(~calm(X)))<=>(~rich(john)))&
(((kind(susan)&~patient(susan)))<=>(?[X]:(~patient(X))))&
(?[X]:((old(X)&tall(X))))&
((~creative(john)<~>~kind(john)))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~old(X)|humble(X))))&
((~humble(lucy)&happy(lucy)))&
((~quiet(fred)&creative(fred))) | creative(fred) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 746501924443965646869512
% SZS output start Proof for 746501924443965646869512
23. creative(fred) & ~quiet(fred) [input p22]
24. ~creative(fred) [input hypothesis]
131. creative(fred) [cnf transformation 23]
132. ~creative(fred) [cnf transformation 24]
303. $false [subsumption resolution 132,131]
% SZS output end Proof for 746501924443965646869512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not quiet is not brave.
If someone is not tall or not kind then someone is not kind or creative.
If someone is not funny then fred is not kind or strong.
If someone is both not patient and patient then someone is both not brave and not humble.
Everyone who is both wise and patient is both quiet and not happy and vice versa.
Everyone who is funny is either tall or rich and vice versa.
Everyone who is brave or not curious is not patient and vice versa.
Everyone who is not old or not strong is tall or curious and vice versa.
If someone is tall then someone is both not quiet and generous and vice versa.
If someone is both not strong and strong then someone is not calm or humble and vice versa.
Everyone who is both brave and not tall is either not wise or calm.
Everyone who is not curious or curious is both happy and not brave and vice versa.
Everyone who is either quiet or not patient is both not generous and not calm and vice versa.
Everyone who is happy or strong is both not patient and old.
Everyone who is either not brave or patient is either not rich or curious.
Someone is both calm and wise.
Lucy is rich or not tall.
Mary is wise or happy.
Someone is curious or old. | Lucy is not strong. | contradiction | (![X]:((~creative(X)|~quiet(X))=>~brave(X)))&
((?[X]:((~tall(X)|~kind(X))))=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:(~funny(X)))=>((~kind(fred)|strong(fred))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((wise(X)&patient(X))<=>(quiet(X)&~happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>rich(X))))&
(![X]:((brave(X)|~curious(X))<=>~patient(X)))&
(![X]:((~old(X)|~strong(X))<=>(tall(X)|curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~quiet(X)&generous(X)))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((brave(X)&~tall(X))=>(~wise(X)<~>calm(X))))&
(![X]:((~curious(X)|curious(X))<=>(happy(X)&~brave(X))))&
(![X]:((quiet(X)<~>~patient(X))<=>(~generous(X)&~calm(X))))&
(![X]:((happy(X)|strong(X))=>(~patient(X)&old(X))))&
(![X]:((~brave(X)<~>patient(X))=>(~rich(X)<~>curious(X))))&
(?[X]:((calm(X)&wise(X))))&
((rich(lucy)|~tall(lucy)))&
((wise(mary)|happy(mary)))&
(?[X]:((curious(X)|old(X)))) | ~strong(lucy) | [
"p6",
"p7",
"p11",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 41138631205070857989239
% SZS output start Proof for 41138631205070857989239
7. ! [X0] : ((~curious(X0) | brave(X0)) <=> ~patient(X0)) [input p6]
8. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (curious(X0) | tall(X0))) [input p7]
12. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~brave(X0) & happy(X0))) [input p11]
14. ! [X0] : ((strong(X0) | happy(X0)) => (old(X0) & ~patient(X0))) [input p13]
15. ! [X0] : ((~brave(X0) <~> patient(X0)) => (~rich(X0) <~> curious(X0))) [input p14]
17. ~tall(lucy) | rich(lucy) [input p16]
20. ~strong(lucy) [input hypothesis]
34. ! [X0] : ((old(X0) & ~patient(X0)) | (~strong(X0) & ~happy(X0))) [ennf transformation 14]
35. ! [X0] : ((~rich(X0) <~> curious(X0)) | (~brave(X0) <=> patient(X0))) [ennf transformation 15]
41. ! [X0] : (((~curious(X0) | brave(X0)) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [nnf transformation 7]
42. ! [X0] : ((~curious(X0) | brave(X0) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [flattening 41]
43. ! [X0] : (((~strong(X0) | ~old(X0)) | (~curious(X0) & ~tall(X0))) & ((curious(X0) | tall(X0)) | (strong(X0) & old(X0)))) [nnf transformation 8]
44. ! [X0] : ((~strong(X0) | ~old(X0) | (~curious(X0) & ~tall(X0))) & (curious(X0) | tall(X0) | (strong(X0) & old(X0)))) [flattening 43]
56. ! [X0] : (((curious(X0) | ~curious(X0)) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [nnf transformation 12]
57. ! [X0] : ((curious(X0) | ~curious(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [flattening 56]
60. ! [X0] : (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) [nnf transformation 35]
74. ~curious(X0) | brave(X0) | patient(X0) [cnf transformation 42]
76. curious(X0) | tall(X0) | strong(X0) [cnf transformation 44]
89. happy(X0) | curious(X0) [cnf transformation 57]
90. ~curious(X0) | happy(X0) [cnf transformation 57]
91. ~brave(X0) | curious(X0) [cnf transformation 57]
92. ~curious(X0) | ~brave(X0) [cnf transformation 57]
100. ~patient(X0) | ~happy(X0) [cnf transformation 34]
104. curious(X0) | ~rich(X0) | patient(X0) | brave(X0) [cnf transformation 60]
110. ~tall(lucy) | rich(lucy) [cnf transformation 17]
113. ~strong(lucy) [cnf transformation 20]
149. ~brave(X0) [subsumption resolution 91,92]
150. happy(X0) [subsumption resolution 89,90]
152. ~patient(X0) [subsumption resolution 100,150]
153. curious(X0) | ~rich(X0) | brave(X0) [subsumption resolution 104,152]
154. ~rich(X0) | curious(X0) [subsumption resolution 153,149]
156. 9 <=> rich(lucy) [avatar definition]
158. rich(lucy) <- (9) [avatar component clause 156]
160. 10 <=> tall(lucy) [avatar definition]
163. 9 | ~10 [avatar split clause 110,160,156]
166. tall(X0) | strong(X0) | brave(X0) | patient(X0) [resolution 76,74]
169. tall(X0) | strong(X0) | patient(X0) [subsumption resolution 166,149]
170. strong(X0) | tall(X0) [subsumption resolution 169,152]
171. tall(lucy) [resolution 170,113]
175. 10 [avatar split clause 171,160]
176. curious(lucy) <- (9) [resolution 158,154]
179. brave(lucy) | patient(lucy) <- (9) [resolution 176,74]
182. patient(lucy) <- (9) [subsumption resolution 179,149]
183. $false <- (9) [subsumption resolution 182,152]
184. ~9 [avatar contradiction clause 183]
185. $false [avatar sat refutation 163,175,184]
% SZS output end Proof for 41138631205070857989239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is strong then john is either kind or not calm.
Everyone who is either not patient or not funny is either not funny or strong.
Everyone who is both not curious and not brave is either not strong or curious.
If mary is patient then paul is not generous or wise and vice versa.
Everyone who is both not kind and generous is both tall and not calm and vice versa.
If lucy is both not calm and not curious then alice is not old or humble and vice versa.
If fred is either not humble or calm then someone is either not funny or not generous.
Everyone who is quiet or not strong is both not rich and calm.
If fred is both not creative and generous then someone is either not rich or not generous and vice versa.
If lucy is both old and creative then someone is humble or rich.
Everyone who is not brave is not creative and vice versa.
If paul is not tall or not curious then fred is not creative and vice versa.
Everyone who is strong or calm is either not patient or wise and vice versa.
If someone is wise then someone is both happy and quiet and vice versa.
Everyone who is not creative is both brave and humble and vice versa.
Everyone who is either strong or not patient is not rich and vice versa.
Susan is rich.
Paul is kind.
Susan is calm or not curious.
Susan is not quiet or happy.
Someone is quiet.
Susan is both not happy and not patient.
John is not curious or not wise. | Paul is quiet. | neutral | ((strong(john))=>((kind(john)<~>~calm(john))))&
(![X]:((~patient(X)<~>~funny(X))=>(~funny(X)<~>strong(X))))&
(![X]:((~curious(X)&~brave(X))=>(~strong(X)<~>curious(X))))&
((patient(mary))<=>((~generous(paul)|wise(paul))))&
(![X]:((~kind(X)&generous(X))<=>(tall(X)&~calm(X))))&
(((~calm(lucy)&~curious(lucy)))<=>((~old(alice)|humble(alice))))&
(((~humble(fred)<~>calm(fred)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
(![X]:((quiet(X)|~strong(X))=>(~rich(X)&calm(X))))&
(((~creative(fred)&generous(fred)))<=>(?[X]:((~rich(X)<~>~generous(X)))))&
(((old(lucy)&creative(lucy)))=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(~brave(X)<=>~creative(X)))&
(((~tall(paul)|~curious(paul)))<=>(~creative(fred)))&
(![X]:((strong(X)|calm(X))<=>(~patient(X)<~>wise(X))))&
((?[X]:(wise(X)))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:(~creative(X)<=>(brave(X)&humble(X))))&
(![X]:((strong(X)<~>~patient(X))<=>~rich(X)))&
(rich(susan))&
(kind(paul))&
((calm(susan)|~curious(susan)))&
((~quiet(susan)|happy(susan)))&
(?[X]:(quiet(X)))&
((~happy(susan)&~patient(susan)))&
((~curious(john)|~wise(john))) | quiet(paul) | [] | null | 0 |
If someone is not brave then someone is not brave or wise.
Everyone who is wise or not humble is not rich.
Everyone who is either not rich or rich is either creative or brave.
Everyone who is not creative is either not creative or wise.
Everyone who is both not creative and creative is creative and vice versa.
If paul is patient then someone is either happy or not curious.
If someone is not creative or not kind then someone is not tall.
If someone is both old and not calm then someone is not strong and vice versa.
If susan is old then lucy is either rich or happy.
Everyone who is not tall or patient is not calm.
Everyone who is not rich or not calm is either wise or not rich.
If alice is not humble or not quiet then lucy is tall or not humble and vice versa.
Everyone who is not calm or generous is not funny or not calm and vice versa.
Everyone who is either strong or not happy is either patient or not brave.
If alice is both humble and not brave then susan is either not wise or curious.
If someone is either not patient or curious then alice is kind and vice versa.
Paul is not generous.
Susan is either not funny or not curious.
Someone is not funny or not curious.
Mary is not patient or not rich.
Alice is not wise or not calm.
Someone is not old.
Alice is old.
Mary is both not humble and not tall. | Alice is creative. | contradiction | ((?[X]:(~brave(X)))=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((wise(X)|~humble(X))=>~rich(X)))&
(![X]:((~rich(X)<~>rich(X))=>(creative(X)<~>brave(X))))&
(![X]:(~creative(X)=>(~creative(X)<~>wise(X))))&
(![X]:((~creative(X)&creative(X))<=>creative(X)))&
((patient(paul))=>(?[X]:((happy(X)<~>~curious(X)))))&
((?[X]:((~creative(X)|~kind(X))))=>(?[X]:(~tall(X))))&
((?[X]:((old(X)&~calm(X))))<=>(?[X]:(~strong(X))))&
((old(susan))=>((rich(lucy)<~>happy(lucy))))&
(![X]:((~tall(X)|patient(X))=>~calm(X)))&
(![X]:((~rich(X)|~calm(X))=>(wise(X)<~>~rich(X))))&
(((~humble(alice)|~quiet(alice)))<=>((tall(lucy)|~humble(lucy))))&
(![X]:((~calm(X)|generous(X))<=>(~funny(X)|~calm(X))))&
(![X]:((strong(X)<~>~happy(X))=>(patient(X)<~>~brave(X))))&
(((humble(alice)&~brave(alice)))=>((~wise(susan)<~>curious(susan))))&
((?[X]:((~patient(X)<~>curious(X))))<=>(kind(alice)))&
(~generous(paul))&
((~funny(susan)<~>~curious(susan)))&
(?[X]:((~funny(X)|~curious(X))))&
((~patient(mary)|~rich(mary)))&
((~wise(alice)|~calm(alice)))&
(?[X]:(~old(X)))&
(old(alice))&
((~humble(mary)&~tall(mary))) | creative(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 790502069152005109932240
% SZS output start Proof for 790502069152005109932240
5. ! [X0] : ((creative(X0) & ~creative(X0)) <=> creative(X0)) [input p4]
25. creative(alice) [input hypothesis]
46. ! [X0] : (((creative(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | (~creative(X0) | creative(X0)))) [nnf transformation 5]
47. ! [X0] : (((creative(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | ~creative(X0) | creative(X0))) [flattening 46]
86. ~creative(X0) | ~creative(X0) [cnf transformation 47]
131. creative(alice) [cnf transformation 25]
134. ~creative(X0) [duplicate literal removal 86]
292. $false [subsumption resolution 131,134]
% SZS output end Proof for 790502069152005109932240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or not brave is either not tall or not old.
If john is both not generous and quiet then someone is patient or tall and vice versa.
If susan is either not kind or tall then susan is tall or not quiet and vice versa.
Everyone who is either not calm or not happy is either humble or kind.
Everyone who is not kind is strong or curious and vice versa.
If someone is not quiet then fred is both rich and not patient and vice versa.
If paul is not calm then mary is not patient or patient.
If susan is both generous and not calm then john is both rich and strong and vice versa.
If lucy is funny then someone is wise or strong and vice versa.
If someone is not happy then someone is both funny and not calm.
If someone is not brave then someone is rich or not strong and vice versa.
Everyone who is patient is either not humble or not generous.
Everyone who is either not calm or tall is both not old and not kind and vice versa.
Everyone who is brave or generous is either strong or quiet and vice versa.
Everyone who is both tall and quiet is both not happy and rich.
Everyone who is both patient and not calm is happy or not happy and vice versa.
Someone is both not tall and not strong.
Someone is either not wise or not brave.
Someone is not calm.
Alice is happy.
Someone is either not patient or quiet.
Someone is both not wise and not curious.
Mary is both funny and not curious. | Mary is not kind. | contradiction | (![X]:((tall(X)|~brave(X))=>(~tall(X)<~>~old(X))))&
(((~generous(john)&quiet(john)))<=>(?[X]:((patient(X)|tall(X)))))&
(((~kind(susan)<~>tall(susan)))<=>((tall(susan)|~quiet(susan))))&
(![X]:((~calm(X)<~>~happy(X))=>(humble(X)<~>kind(X))))&
(![X]:(~kind(X)<=>(strong(X)|curious(X))))&
((?[X]:(~quiet(X)))<=>((rich(fred)&~patient(fred))))&
((~calm(paul))=>((~patient(mary)|patient(mary))))&
(((generous(susan)&~calm(susan)))<=>((rich(john)&strong(john))))&
((funny(lucy))<=>(?[X]:((wise(X)|strong(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((funny(X)&~calm(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:((rich(X)|~strong(X)))))&
(![X]:(patient(X)=>(~humble(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>tall(X))<=>(~old(X)&~kind(X))))&
(![X]:((brave(X)|generous(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((tall(X)&quiet(X))=>(~happy(X)&rich(X))))&
(![X]:((patient(X)&~calm(X))<=>(happy(X)|~happy(X))))&
(?[X]:((~tall(X)&~strong(X))))&
(?[X]:((~wise(X)<~>~brave(X))))&
(?[X]:(~calm(X)))&
(happy(alice))&
(?[X]:((~patient(X)<~>quiet(X))))&
(?[X]:((~wise(X)&~curious(X))))&
((funny(mary)&~curious(mary))) | ~kind(mary) | [
"p0",
"p4",
"p5",
"p12",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7589980016407745779240499
% SZS output start Proof for 7589980016407745779240499
1. ! [X0] : ((~brave(X0) | tall(X0)) => (~tall(X0) <~> ~old(X0))) [input p0]
5. ! [X0] : (~kind(X0) <=> (curious(X0) | strong(X0))) [input p4]
6. ? [X0] : ~quiet(X0) <=> (~patient(fred) & rich(fred)) [input p5]
13. ! [X0] : ((~calm(X0) <~> tall(X0)) <=> (~kind(X0) & ~old(X0))) [input p12]
14. ! [X0] : ((generous(X0) | brave(X0)) <=> (strong(X0) <~> quiet(X0))) [input p13]
16. ! [X0] : ((~calm(X0) & patient(X0)) <=> (~happy(X0) | happy(X0))) [input p15]
23. ~curious(mary) & funny(mary) [input p22]
24. ~kind(mary) [input hypothesis]
27. ! [X0] : ((~tall(X0) <~> ~old(X0)) | (brave(X0) & ~tall(X0))) [ennf transformation 1]
35. ! [X0] : (((old(X0) | tall(X0)) & (~old(X0) | ~tall(X0))) | (brave(X0) & ~tall(X0))) [nnf transformation 27]
44. ! [X0] : ((~kind(X0) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | kind(X0))) [nnf transformation 5]
45. ! [X0] : ((~kind(X0) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | kind(X0))) [flattening 44]
46. (? [X0] : ~quiet(X0) | (patient(fred) | ~rich(fred))) & ((~patient(fred) & rich(fred)) | ! [X0] : quiet(X0)) [nnf transformation 6]
47. (? [X0] : ~quiet(X0) | patient(fred) | ~rich(fred)) & ((~patient(fred) & rich(fred)) | ! [X0] : quiet(X0)) [flattening 46]
48. (? [X0] : ~quiet(X0) | patient(fred) | ~rich(fred)) & ((~patient(fred) & rich(fred)) | ! [X1] : quiet(X1)) [rectify 47]
49. ? [X0] : ~quiet(X0) => ~quiet(sK1) [choice axiom]
50. (~quiet(sK1) | patient(fred) | ~rich(fred)) & ((~patient(fred) & rich(fred)) | ! [X1] : quiet(X1)) [skolemisation 48,49]
66. ! [X0] : ((((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0))))) [nnf transformation 13]
67. ! [X0] : ((((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0))))) [flattening 66]
68. ! [X0] : (((generous(X0) | brave(X0)) | ((strong(X0) | ~quiet(X0)) & (quiet(X0) | ~strong(X0)))) & (((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | (~generous(X0) & ~brave(X0)))) [nnf transformation 14]
69. ! [X0] : ((generous(X0) | brave(X0) | ((strong(X0) | ~quiet(X0)) & (quiet(X0) | ~strong(X0)))) & (((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | (~generous(X0) & ~brave(X0)))) [flattening 68]
70. ! [X0] : (((~calm(X0) & patient(X0)) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | (calm(X0) | ~patient(X0)))) [nnf transformation 16]
71. ! [X0] : (((~calm(X0) & patient(X0)) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | calm(X0) | ~patient(X0))) [flattening 70]
84. ~old(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 35]
87. old(X0) | tall(X0) | brave(X0) [cnf transformation 35]
103. curious(X0) | strong(X0) | kind(X0) [cnf transformation 45]
107. ~patient(fred) | quiet(X1) [cnf transformation 50]
124. ~old(X0) | tall(X0) | calm(X0) [cnf transformation 67]
129. ~tall(X0) | calm(X0) | kind(X0) | old(X0) [cnf transformation 67]
132. ~strong(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 69]
139. patient(X0) | ~happy(X0) [cnf transformation 71]
140. happy(X0) | patient(X0) [cnf transformation 71]
141. ~calm(X0) | ~happy(X0) [cnf transformation 71]
142. ~calm(X0) | happy(X0) [cnf transformation 71]
154. ~curious(mary) [cnf transformation 23]
155. ~kind(mary) [cnf transformation 24]
158. ~old(X0) | ~tall(X0) [duplicate literal removal 84]
207. 11 <=> patient(fred) [avatar definition]
208. ~patient(fred) <- (~11) [avatar component clause 207]
216. 13 <=> ! [X1] : quiet(X1) [avatar definition]
217. quiet(X1) <- (13) [avatar component clause 216]
218. 13 | ~11 [avatar split clause 107,207,216]
298. ~tall(X0) | calm(X0) | kind(X0) [subsumption resolution 129,158]
299. ~old(X0) | calm(X0) [subsumption resolution 124,158]
300. ~calm(X0) [subsumption resolution 141,142]
301. patient(X0) [subsumption resolution 139,140]
313. $false <- (~11) [subsumption resolution 208,301]
314. 11 [avatar contradiction clause 313]
322. tall(X1) | brave(X1) | calm(X1) [resolution 87,299]
325. brave(X1) | tall(X1) [subsumption resolution 322,300]
329. strong(mary) | kind(mary) [resolution 103,154]
335. strong(mary) [subsumption resolution 329,155]
357. ~quiet(mary) | ~brave(mary) [resolution 132,335]
358. ~brave(mary) <- (13) [subsumption resolution 357,217]
359. tall(mary) <- (13) [resolution 358,325]
401. calm(mary) | kind(mary) <- (13) [resolution 359,298]
402. kind(mary) <- (13) [subsumption resolution 401,300]
403. $false <- (13) [subsumption resolution 402,155]
404. ~13 [avatar contradiction clause 403]
405. $false [avatar sat refutation 218,314,404]
% SZS output end Proof for 7589980016407745779240499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is calm or tall. Everyone who is both not rich and not humble is both generous and wise and vice versa. Everyone who is generous is not curious and vice versa. Everyone who is not quiet or not old is calm and vice versa. If john is not wise or curious then someone is not patient. If paul is strong or old then paul is not tall and vice versa. If someone is wise or kind then someone is both quiet and calm and vice versa. If lucy is both happy and wise then susan is quiet and vice versa. If alice is curious or brave then someone is tall or not humble. Everyone who is not old or not humble is funny and vice versa. If someone is either funny or not humble then someone is either brave or not calm and vice versa. Everyone who is funny or not old is both wise and not strong and vice versa. Everyone who is either strong or not funny is either not tall or tall and vice versa. If fred is not tall or tall then someone is not curious and vice versa. If someone is both not curious and happy then someone is both not humble and not wise. If mary is not quiet or not strong then alice is kind or not tall. Someone is either not tall or humble. Mary is not wise. Alice is not tall. John is either not kind or not generous. | Lucy is not curious. | neutral | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~rich(X)&~humble(X))<=>(generous(X)&wise(X))))&
(![X]:(generous(X)<=>~curious(X)))&
(![X]:((~quiet(X)|~old(X))<=>calm(X)))&
(((~wise(john)|curious(john)))=>(?[X]:(~patient(X))))&
(((strong(paul)|old(paul)))<=>(~tall(paul)))&
((?[X]:((wise(X)|kind(X))))<=>(?[X]:((quiet(X)&calm(X)))))&
(((happy(lucy)&wise(lucy)))<=>(quiet(susan)))&
(((curious(alice)|brave(alice)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~old(X)|~humble(X))<=>funny(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((funny(X)|~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~tall(X)<~>tall(X))))&
(((~tall(fred)|tall(fred)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~humble(X)&~wise(X)))))&
(((~quiet(mary)|~strong(mary)))=>((kind(alice)|~tall(alice))))&
(?[X]:((~tall(X)<~>humble(X))))&
(~wise(mary))&
(~tall(alice))&
((~kind(john)<~>~generous(john))) | ~curious(lucy) | [] | null | 0 |
Everyone who is not patient is not quiet or old and vice versa.
Everyone who is both patient and kind is not rich and vice versa.
Everyone who is patient is both not happy and not old.
If john is wise or old then someone is either not brave or old and vice versa.
Everyone who is not creative or funny is both generous and not happy and vice versa.
If someone is either quiet or curious then susan is either kind or not rich.
If someone is funny then someone is both not curious and not funny and vice versa.
Everyone who is both rich and not curious is not happy and vice versa.
If someone is not quiet then someone is both tall and quiet.
Everyone who is not happy or not wise is rich or tall and vice versa.
If someone is either tall or not strong then mary is both not tall and funny.
If someone is not wise or not kind then someone is not rich.
If someone is brave or curious then fred is either not happy or not brave.
If john is both patient and not funny then someone is not old or not tall and vice versa.
Everyone who is both not brave and happy is humble or not tall and vice versa.
If john is both brave and generous then susan is not funny.
Susan is not rich or tall.
Someone is quiet or old.
Paul is both quiet and old.
Mary is both not happy and brave.
Someone is either not wise or not curious.
Someone is not tall or funny.
Susan is not strong. | Susan is funny. | neutral | (![X]:(~patient(X)<=>(~quiet(X)|old(X))))&
(![X]:((patient(X)&kind(X))<=>~rich(X)))&
(![X]:(patient(X)=>(~happy(X)&~old(X))))&
(((wise(john)|old(john)))<=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:((~creative(X)|funny(X))<=>(generous(X)&~happy(X))))&
((?[X]:((quiet(X)<~>curious(X))))=>((kind(susan)<~>~rich(susan))))&
((?[X]:(funny(X)))<=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:((rich(X)&~curious(X))<=>~happy(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((~happy(X)|~wise(X))<=>(rich(X)|tall(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>((~tall(mary)&funny(mary))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)|curious(X))))=>((~happy(fred)<~>~brave(fred))))&
(((patient(john)&~funny(john)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~brave(X)&happy(X))<=>(humble(X)|~tall(X))))&
(((brave(john)&generous(john)))=>(~funny(susan)))&
((~rich(susan)|tall(susan)))&
(?[X]:((quiet(X)|old(X))))&
((quiet(paul)&old(paul)))&
((~happy(mary)&brave(mary)))&
(?[X]:((~wise(X)<~>~curious(X))))&
(?[X]:((~tall(X)|funny(X))))&
(~strong(susan)) | funny(susan) | [] | null | 0 |
Everyone who is not quiet is both not brave and not calm.
If mary is not kind or rich then susan is either happy or wise and vice versa.
If someone is either humble or rich then susan is both not wise and not rich and vice versa.
Everyone who is wise is wise or not patient and vice versa.
If alice is calm then someone is quiet.
If lucy is both not calm and not brave then alice is funny or tall.
Everyone who is calm is both not kind and old.
Everyone who is funny is not strong.
Everyone who is either not patient or not old is both strong and tall.
Everyone who is not creative is either funny or not calm and vice versa.
If mary is rich then someone is not rich and vice versa.
If paul is not tall then paul is both rich and humble and vice versa.
If susan is creative then susan is quiet or not wise and vice versa.
If alice is not quiet then someone is kind or not creative and vice versa.
Everyone who is humble or quiet is not kind or not happy and vice versa.
If susan is humble then john is patient or not brave.
John is calm or not wise.
Alice is brave.
Someone is either rich or not creative.
Someone is both not curious and brave.
Fred is either not curious or not old.
Fred is both not humble and not patient.
Mary is not curious.
Lucy is curious or not kind. | Paul is not kind. | entailment | (![X]:(~quiet(X)=>(~brave(X)&~calm(X))))&
(((~kind(mary)|rich(mary)))<=>((happy(susan)<~>wise(susan))))&
((?[X]:((humble(X)<~>rich(X))))<=>((~wise(susan)&~rich(susan))))&
(![X]:(wise(X)<=>(wise(X)|~patient(X))))&
((calm(alice))=>(?[X]:(quiet(X))))&
(((~calm(lucy)&~brave(lucy)))=>((funny(alice)|tall(alice))))&
(![X]:(calm(X)=>(~kind(X)&old(X))))&
(![X]:(funny(X)=>~strong(X)))&
(![X]:((~patient(X)<~>~old(X))=>(strong(X)&tall(X))))&
(![X]:(~creative(X)<=>(funny(X)<~>~calm(X))))&
((rich(mary))<=>(?[X]:(~rich(X))))&
((~tall(paul))<=>((rich(paul)&humble(paul))))&
((creative(susan))<=>((quiet(susan)|~wise(susan))))&
((~quiet(alice))<=>(?[X]:((kind(X)|~creative(X)))))&
(![X]:((humble(X)|quiet(X))<=>(~kind(X)|~happy(X))))&
((humble(susan))=>((patient(john)|~brave(john))))&
((calm(john)|~wise(john)))&
(brave(alice))&
(?[X]:((rich(X)<~>~creative(X))))&
(?[X]:((~curious(X)&brave(X))))&
((~curious(fred)<~>~old(fred)))&
((~humble(fred)&~patient(fred)))&
(~curious(mary))&
((curious(lucy)|~kind(lucy))) | ~kind(paul) | [
"p0",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2432295877879007753538657
% SZS output start Proof for 2432295877879007753538657
1. ! [X0] : (~quiet(X0) => (~calm(X0) & ~brave(X0))) [input p0]
14. ~quiet(alice) <=> ? [X0] : (~creative(X0) | kind(X0)) [input p13]
18. brave(alice) [input p17]
25. kind(paul) [input hypothesis]
26. ! [X0] : ((~calm(X0) & ~brave(X0)) | quiet(X0)) [ennf transformation 1]
56. (~quiet(alice) | ! [X0] : (creative(X0) & ~kind(X0))) & (? [X0] : (~creative(X0) | kind(X0)) | quiet(alice)) [nnf transformation 14]
57. (~quiet(alice) | ! [X0] : (creative(X0) & ~kind(X0))) & (? [X1] : (~creative(X1) | kind(X1)) | quiet(alice)) [rectify 56]
58. ? [X1] : (~creative(X1) | kind(X1)) => (~creative(sK3) | kind(sK3)) [choice axiom]
59. (~quiet(alice) | ! [X0] : (creative(X0) & ~kind(X0))) & ((~creative(sK3) | kind(sK3)) | quiet(alice)) [skolemisation 57,58]
68. ~brave(X0) | quiet(X0) [cnf transformation 26]
107. ~quiet(alice) | ~kind(X0) [cnf transformation 59]
115. brave(alice) [cnf transformation 18]
126. kind(paul) [cnf transformation 25]
238. 24 <=> quiet(alice) [avatar definition]
243. 25 <=> ! [X0] : ~kind(X0) [avatar definition]
244. ~kind(X0) <- (25) [avatar component clause 243]
245. 25 | ~24 [avatar split clause 107,238,243]
306. quiet(alice) [resolution 68,115]
310. 24 [avatar split clause 306,238]
315. $false <- (25) [resolution 244,126]
316. ~25 [avatar contradiction clause 315]
317. $false [avatar sat refutation 245,310,316]
% SZS output end Proof for 2432295877879007753538657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or calm is either wise or strong.
If someone is patient or not old then someone is both not funny and not quiet.
Everyone who is not kind is either kind or not kind and vice versa.
Everyone who is not tall is both funny and strong.
Everyone who is not happy is both patient and brave and vice versa.
If alice is not rich then paul is both generous and curious.
Everyone who is not happy or quiet is generous and vice versa.
If someone is both not funny and not humble then someone is kind and vice versa.
Everyone who is not curious or rich is rich or brave.
Everyone who is not old or quiet is both wise and not generous and vice versa.
Everyone who is both wise and humble is quiet and vice versa.
If someone is rich then someone is both strong and not old.
If someone is not funny or generous then someone is both not generous and creative.
If someone is either funny or humble then someone is either not tall or not patient and vice versa.
If someone is both not old and not wise then someone is both not happy and happy.
If someone is either patient or tall then john is both not strong and not rich.
Fred is both not rich and not calm.
Someone is both wise and not generous.
Someone is both not generous and not tall.
Someone is not funny.
John is either not quiet or not generous.
Fred is either strong or not rich.
Someone is either quiet or humble. | John is not funny. | neutral | (![X]:((~happy(X)<~>calm(X))=>(wise(X)<~>strong(X))))&
((?[X]:((patient(X)|~old(X))))=>(?[X]:((~funny(X)&~quiet(X)))))&
(![X]:(~kind(X)<=>(kind(X)<~>~kind(X))))&
(![X]:(~tall(X)=>(funny(X)&strong(X))))&
(![X]:(~happy(X)<=>(patient(X)&brave(X))))&
((~rich(alice))=>((generous(paul)&curious(paul))))&
(![X]:((~happy(X)|quiet(X))<=>generous(X)))&
((?[X]:((~funny(X)&~humble(X))))<=>(?[X]:(kind(X))))&
(![X]:((~curious(X)|rich(X))=>(rich(X)|brave(X))))&
(![X]:((~old(X)|quiet(X))<=>(wise(X)&~generous(X))))&
(![X]:((wise(X)&humble(X))<=>quiet(X)))&
((?[X]:(rich(X)))=>(?[X]:((strong(X)&~old(X)))))&
((?[X]:((~funny(X)|generous(X))))=>(?[X]:((~generous(X)&creative(X)))))&
((?[X]:((funny(X)<~>humble(X))))<=>(?[X]:((~tall(X)<~>~patient(X)))))&
((?[X]:((~old(X)&~wise(X))))=>(?[X]:((~happy(X)&happy(X)))))&
((?[X]:((patient(X)<~>tall(X))))=>((~strong(john)&~rich(john))))&
((~rich(fred)&~calm(fred)))&
(?[X]:((wise(X)&~generous(X))))&
(?[X]:((~generous(X)&~tall(X))))&
(?[X]:(~funny(X)))&
((~quiet(john)<~>~generous(john)))&
((strong(fred)<~>~rich(fred)))&
(?[X]:((quiet(X)<~>humble(X)))) | ~funny(john) | [] | null | 0 |
If someone is both wise and not wise then someone is humble or not rich.
Everyone who is both tall and strong is either creative or not old.
Everyone who is not humble or not strong is creative or calm and vice versa.
Everyone who is either not brave or not funny is either old or not kind.
Everyone who is either wise or not generous is not generous or curious.
If paul is either not rich or funny then paul is creative and vice versa.
If alice is happy or humble then susan is both not patient and kind.
If paul is both rich and funny then lucy is either funny or patient and vice versa.
If mary is either not humble or rich then someone is both patient and not happy and vice versa.
Everyone who is strong is both not humble and kind and vice versa.
If paul is funny then alice is either not quiet or kind.
Everyone who is not tall is both kind and not old and vice versa.
Everyone who is either not old or curious is patient.
If susan is not happy or not patient then someone is either not old or not creative and vice versa.
Everyone who is not calm or not happy is both wise and not patient.
Everyone who is not generous or strong is both not creative and not rich and vice versa.
Someone is both rich and curious.
Someone is humble or patient.
Someone is both happy and strong.
Lucy is both strong and generous.
Mary is both tall and rich.
Susan is quiet.
Someone is either not brave or not rich.
Someone is either not strong or strong. | Mary is not kind. | entailment | ((?[X]:((wise(X)&~wise(X))))=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:((tall(X)&strong(X))=>(creative(X)<~>~old(X))))&
(![X]:((~humble(X)|~strong(X))<=>(creative(X)|calm(X))))&
(![X]:((~brave(X)<~>~funny(X))=>(old(X)<~>~kind(X))))&
(![X]:((wise(X)<~>~generous(X))=>(~generous(X)|curious(X))))&
(((~rich(paul)<~>funny(paul)))<=>(creative(paul)))&
(((happy(alice)|humble(alice)))=>((~patient(susan)&kind(susan))))&
(((rich(paul)&funny(paul)))<=>((funny(lucy)<~>patient(lucy))))&
(((~humble(mary)<~>rich(mary)))<=>(?[X]:((patient(X)&~happy(X)))))&
(![X]:(strong(X)<=>(~humble(X)&kind(X))))&
((funny(paul))=>((~quiet(alice)<~>kind(alice))))&
(![X]:(~tall(X)<=>(kind(X)&~old(X))))&
(![X]:((~old(X)<~>curious(X))=>patient(X)))&
(((~happy(susan)|~patient(susan)))<=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:((~calm(X)|~happy(X))=>(wise(X)&~patient(X))))&
(![X]:((~generous(X)|strong(X))<=>(~creative(X)&~rich(X))))&
(?[X]:((rich(X)&curious(X))))&
(?[X]:((humble(X)|patient(X))))&
(?[X]:((happy(X)&strong(X))))&
((strong(lucy)&generous(lucy)))&
((tall(mary)&rich(mary)))&
(quiet(susan))&
(?[X]:((~brave(X)<~>~rich(X))))&
(?[X]:((~strong(X)<~>strong(X)))) | ~kind(mary) | [
"p8",
"p9",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8966795359631805722230070
% SZS output start Proof for 8966795359631805722230070
9. (~humble(mary) <~> rich(mary)) <=> ? [X0] : (~happy(X0) & patient(X0)) [input p8]
10. ! [X0] : (strong(X0) <=> (kind(X0) & ~humble(X0))) [input p9]
15. ! [X0] : ((~happy(X0) | ~calm(X0)) => (~patient(X0) & wise(X0))) [input p14]
16. ! [X0] : ((strong(X0) | ~generous(X0)) <=> (~rich(X0) & ~creative(X0))) [input p15]
21. rich(mary) & tall(mary) [input p20]
25. kind(mary) [input hypothesis]
36. ! [X0] : ((~patient(X0) & wise(X0)) | (happy(X0) & calm(X0))) [ennf transformation 15]
48. (((~rich(mary) | humble(mary)) & (rich(mary) | ~humble(mary))) | ! [X0] : (happy(X0) | ~patient(X0))) & (? [X0] : (~happy(X0) & patient(X0)) | ((~humble(mary) | ~rich(mary)) & (rich(mary) | humble(mary)))) [nnf transformation 9]
49. (((~rich(mary) | humble(mary)) & (rich(mary) | ~humble(mary))) | ! [X0] : (happy(X0) | ~patient(X0))) & (? [X1] : (~happy(X1) & patient(X1)) | ((~humble(mary) | ~rich(mary)) & (rich(mary) | humble(mary)))) [rectify 48]
50. ? [X1] : (~happy(X1) & patient(X1)) => (~happy(sK1) & patient(sK1)) [choice axiom]
51. (((~rich(mary) | humble(mary)) & (rich(mary) | ~humble(mary))) | ! [X0] : (happy(X0) | ~patient(X0))) & ((~happy(sK1) & patient(sK1)) | ((~humble(mary) | ~rich(mary)) & (rich(mary) | humble(mary)))) [skolemisation 49,50]
52. ! [X0] : ((strong(X0) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | ~strong(X0))) [nnf transformation 10]
53. ! [X0] : ((strong(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | ~strong(X0))) [flattening 52]
63. ! [X0] : (((strong(X0) | ~generous(X0)) | (rich(X0) | creative(X0))) & ((~rich(X0) & ~creative(X0)) | (~strong(X0) & generous(X0)))) [nnf transformation 16]
64. ! [X0] : ((strong(X0) | ~generous(X0) | rich(X0) | creative(X0)) & ((~rich(X0) & ~creative(X0)) | (~strong(X0) & generous(X0)))) [flattening 63]
105. patient(sK1) | ~humble(mary) | ~rich(mary) [cnf transformation 51]
107. ~happy(sK1) | ~humble(mary) | ~rich(mary) [cnf transformation 51]
112. ~kind(X0) | strong(X0) | humble(X0) [cnf transformation 53]
129. ~patient(X0) | happy(X0) [cnf transformation 36]
133. ~strong(X0) | ~rich(X0) [cnf transformation 64]
143. rich(mary) [cnf transformation 21]
149. kind(mary) [cnf transformation 25]
202. 10 <=> ! [X0] : (happy(X0) | ~patient(X0)) [avatar definition]
203. ~patient(X0) | happy(X0) <- (10) [avatar component clause 202]
205. 11 <=> humble(mary) [avatar definition]
206. ~humble(mary) <- (~11) [avatar component clause 205]
209. 12 <=> rich(mary) [avatar definition]
210. rich(mary) <- (12) [avatar component clause 209]
215. 13 <=> happy(sK1) [avatar definition]
217. ~happy(sK1) <- (~13) [avatar component clause 215]
218. ~12 | ~11 | ~13 [avatar split clause 107,215,205,209]
221. 14 <=> patient(sK1) [avatar definition]
223. patient(sK1) <- (14) [avatar component clause 221]
224. ~12 | ~11 | 14 [avatar split clause 105,221,205,209]
260. 10 [avatar split clause 129,202]
270. 12 [avatar split clause 143,209]
299. strong(mary) | humble(mary) [resolution 112,149]
301. strong(mary) <- (~11) [subsumption resolution 299,206]
302. ~rich(mary) <- (~11) [resolution 301,133]
305. $false <- (~11, 12) [subsumption resolution 302,210]
306. 11 | ~12 [avatar contradiction clause 305]
313. happy(sK1) <- (10, 14) [resolution 223,203]
315. $false <- (10, ~13, 14) [subsumption resolution 313,217]
316. ~10 | 13 | ~14 [avatar contradiction clause 315]
317. $false [avatar sat refutation 218,224,260,270,306,316]
% SZS output end Proof for 8966795359631805722230070
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall is not humble or tall and vice versa.
If someone is kind then someone is either not humble or not generous and vice versa.
Everyone who is not creative is calm and vice versa.
If susan is both generous and calm then susan is either not kind or not strong.
Everyone who is both not brave and strong is both not patient and wise and vice versa.
Everyone who is patient is not patient.
Everyone who is both kind and tall is both brave and not kind.
If someone is either not calm or funny then someone is not tall or creative.
If paul is not quiet or not rich then someone is either happy or curious and vice versa.
If fred is either not brave or not tall then someone is either not curious or not tall and vice versa.
Everyone who is happy is kind.
If someone is not funny then alice is either not old or curious.
Everyone who is not wise or old is either not calm or not old.
Everyone who is not old or not wise is both not wise and not strong.
Everyone who is either not generous or humble is both patient and not happy.
Someone is not rich.
Lucy is not patient.
Someone is not patient.
Someone is not patient or curious.
Mary is either not tall or not wise.
Someone is not strong or tall.
Paul is either not funny or brave. | Paul is not funny. | neutral | (![X]:(~tall(X)<=>(~humble(X)|tall(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)<~>~generous(X)))))&
(![X]:(~creative(X)<=>calm(X)))&
(((generous(susan)&calm(susan)))=>((~kind(susan)<~>~strong(susan))))&
(![X]:((~brave(X)&strong(X))<=>(~patient(X)&wise(X))))&
(![X]:(patient(X)=>~patient(X)))&
(![X]:((kind(X)&tall(X))=>(brave(X)&~kind(X))))&
((?[X]:((~calm(X)<~>funny(X))))=>(?[X]:((~tall(X)|creative(X)))))&
(((~quiet(paul)|~rich(paul)))<=>(?[X]:((happy(X)<~>curious(X)))))&
(((~brave(fred)<~>~tall(fred)))<=>(?[X]:((~curious(X)<~>~tall(X)))))&
(![X]:(happy(X)=>kind(X)))&
((?[X]:(~funny(X)))=>((~old(alice)<~>curious(alice))))&
(![X]:((~wise(X)|old(X))=>(~calm(X)<~>~old(X))))&
(![X]:((~old(X)|~wise(X))=>(~wise(X)&~strong(X))))&
(![X]:((~generous(X)<~>humble(X))=>(patient(X)&~happy(X))))&
(?[X]:(~rich(X)))&
(~patient(lucy))&
(?[X]:(~patient(X)))&
(?[X]:((~patient(X)|curious(X))))&
((~tall(mary)<~>~wise(mary)))&
(?[X]:((~strong(X)|tall(X))))&
((~funny(paul)<~>brave(paul))) | ~funny(paul) | [] | null | 0 |
Everyone who is wise is both not calm and old.
If lucy is not rich or not tall then someone is both curious and not patient and vice versa.
Everyone who is not patient or not tall is wise and vice versa.
If someone is brave or not humble then alice is either not old or not happy.
If mary is strong then someone is brave or not old and vice versa.
If paul is not generous or humble then alice is not generous or not happy.
Everyone who is not tall is not curious.
Everyone who is not brave is not patient and vice versa.
If alice is not patient or not rich then someone is not wise and vice versa.
If someone is either not rich or strong then someone is either not kind or not calm and vice versa.
If alice is not calm then susan is calm and vice versa.
Everyone who is either not kind or not creative is tall and vice versa.
Everyone who is happy or curious is not old and vice versa.
Everyone who is not quiet is not generous and vice versa.
If susan is not rich or not strong then paul is quiet or not curious and vice versa.
Everyone who is kind or old is happy or funny and vice versa.
Fred is not patient or funny.
Someone is either happy or curious.
Someone is either creative or not patient.
Lucy is either not old or kind.
John is tall.
Someone is generous or not rich.
Lucy is not funny.
Someone is not strong. | Fred is funny. | entailment | (![X]:(wise(X)=>(~calm(X)&old(X))))&
(((~rich(lucy)|~tall(lucy)))<=>(?[X]:((curious(X)&~patient(X)))))&
(![X]:((~patient(X)|~tall(X))<=>wise(X)))&
((?[X]:((brave(X)|~humble(X))))=>((~old(alice)<~>~happy(alice))))&
((strong(mary))<=>(?[X]:((brave(X)|~old(X)))))&
(((~generous(paul)|humble(paul)))=>((~generous(alice)|~happy(alice))))&
(![X]:(~tall(X)=>~curious(X)))&
(![X]:(~brave(X)<=>~patient(X)))&
(((~patient(alice)|~rich(alice)))<=>(?[X]:(~wise(X))))&
((?[X]:((~rich(X)<~>strong(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
((~calm(alice))<=>(calm(susan)))&
(![X]:((~kind(X)<~>~creative(X))<=>tall(X)))&
(![X]:((happy(X)|curious(X))<=>~old(X)))&
(![X]:(~quiet(X)<=>~generous(X)))&
(((~rich(susan)|~strong(susan)))<=>((quiet(paul)|~curious(paul))))&
(![X]:((kind(X)|old(X))<=>(happy(X)|funny(X))))&
((~patient(fred)|funny(fred)))&
(?[X]:((happy(X)<~>curious(X))))&
(?[X]:((creative(X)<~>~patient(X))))&
((~old(lucy)<~>kind(lucy)))&
(tall(john))&
(?[X]:((generous(X)|~rich(X))))&
(~funny(lucy))&
(?[X]:(~strong(X))) | funny(fred) | [
"p0",
"p2",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 817202064603877204836658
% SZS output start Proof for 817202064603877204836658
1. ! [X0] : (wise(X0) => (old(X0) & ~calm(X0))) [input p0]
3. ! [X0] : ((~tall(X0) | ~patient(X0)) <=> wise(X0)) [input p2]
13. ! [X0] : ((curious(X0) | happy(X0)) <=> ~old(X0)) [input p12]
16. ! [X0] : ((old(X0) | kind(X0)) <=> (funny(X0) | happy(X0))) [input p15]
17. funny(fred) | ~patient(fred) [input p16]
25. ~funny(fred) [input hypothesis]
27. ! [X0] : ((old(X0) & ~calm(X0)) | ~wise(X0)) [ennf transformation 1]
37. ! [X0] : (((~tall(X0) | ~patient(X0)) | ~wise(X0)) & (wise(X0) | (tall(X0) & patient(X0)))) [nnf transformation 3]
38. ! [X0] : ((~tall(X0) | ~patient(X0) | ~wise(X0)) & (wise(X0) | (tall(X0) & patient(X0)))) [flattening 37]
57. ! [X0] : (((curious(X0) | happy(X0)) | old(X0)) & (~old(X0) | (~curious(X0) & ~happy(X0)))) [nnf transformation 13]
58. ! [X0] : ((curious(X0) | happy(X0) | old(X0)) & (~old(X0) | (~curious(X0) & ~happy(X0)))) [flattening 57]
62. ! [X0] : (((old(X0) | kind(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (~old(X0) & ~kind(X0)))) [nnf transformation 16]
63. ! [X0] : ((old(X0) | kind(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (~old(X0) & ~kind(X0)))) [flattening 62]
76. ~wise(X0) | old(X0) [cnf transformation 27]
82. patient(X0) | wise(X0) [cnf transformation 38]
114. ~happy(X0) | ~old(X0) [cnf transformation 58]
124. funny(X0) | happy(X0) | ~old(X0) [cnf transformation 63]
127. funny(fred) | ~patient(fred) [cnf transformation 17]
138. ~funny(fred) [cnf transformation 25]
298. ~old(X0) | funny(X0) [subsumption resolution 124,114]
300. 35 <=> patient(fred) [avatar definition]
302. ~patient(fred) <- (~35) [avatar component clause 300]
304. 36 <=> funny(fred) [avatar definition]
305. ~funny(fred) <- (~36) [avatar component clause 304]
307. ~35 | 36 [avatar split clause 127,304,300]
347. ~36 [avatar split clause 138,304]
354. wise(fred) <- (~35) [resolution 82,302]
360. old(fred) <- (~35) [resolution 354,76]
413. funny(fred) <- (~35) [resolution 360,298]
414. $false <- (~35, ~36) [subsumption resolution 413,305]
415. 35 | 36 [avatar contradiction clause 414]
416. $false [avatar sat refutation 307,347,415]
% SZS output end Proof for 817202064603877204836658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not tall then someone is not calm and vice versa. If someone is generous or not patient then alice is either not happy or humble and vice versa. If fred is either not old or not tall then fred is not creative and vice versa. Everyone who is funny is both not generous and not happy. Everyone who is not quiet or not rich is not old and vice versa. Everyone who is not quiet is strong. Everyone who is either generous or not wise is happy. Everyone who is curious or quiet is both old and creative. If someone is both tall and strong then someone is not quiet or not strong and vice versa. Everyone who is calm is both not wise and not curious. Everyone who is both funny and not tall is not patient or humble and vice versa. Everyone who is both strong and not quiet is both not patient and not wise. Everyone who is both not quiet and not wise is wise and vice versa. If john is both not rich and generous then someone is either not quiet or quiet. Susan is calm. Lucy is not strong or patient. Paul is not humble or not kind. | John is not patient. | contradiction | ((?[X]:((~wise(X)|~tall(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((generous(X)|~patient(X))))<=>((~happy(alice)<~>humble(alice))))&
(((~old(fred)<~>~tall(fred)))<=>(~creative(fred)))&
(![X]:(funny(X)=>(~generous(X)&~happy(X))))&
(![X]:((~quiet(X)|~rich(X))<=>~old(X)))&
(![X]:(~quiet(X)=>strong(X)))&
(![X]:((generous(X)<~>~wise(X))=>happy(X)))&
(![X]:((curious(X)|quiet(X))=>(old(X)&creative(X))))&
((?[X]:((tall(X)&strong(X))))<=>(?[X]:((~quiet(X)|~strong(X)))))&
(![X]:(calm(X)=>(~wise(X)&~curious(X))))&
(![X]:((funny(X)&~tall(X))<=>(~patient(X)|humble(X))))&
(![X]:((strong(X)&~quiet(X))=>(~patient(X)&~wise(X))))&
(![X]:((~quiet(X)&~wise(X))<=>wise(X)))&
(((~rich(john)&generous(john)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(calm(susan))&
((~strong(lucy)|patient(lucy)))&
((~humble(paul)|~kind(paul))) | ~patient(john) | [
"p3",
"p6",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3689972463695525991737214
% SZS output start Proof for 3689972463695525991737214
4. ! [X0] : (funny(X0) => (~happy(X0) & ~generous(X0))) [input p3]
7. ! [X0] : ((generous(X0) <~> ~wise(X0)) => happy(X0)) [input p6]
11. ! [X0] : ((~tall(X0) & funny(X0)) <=> (humble(X0) | ~patient(X0))) [input p10]
13. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> wise(X0)) [input p12]
18. ~patient(john) [input hypothesis]
24. ! [X0] : ((~happy(X0) & ~generous(X0)) | ~funny(X0)) [ennf transformation 4]
26. ! [X0] : (happy(X0) | (generous(X0) <=> ~wise(X0))) [ennf transformation 7]
45. ! [X0] : (happy(X0) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) [nnf transformation 26]
51. ! [X0] : (((~tall(X0) & funny(X0)) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | (tall(X0) | ~funny(X0)))) [nnf transformation 11]
52. ! [X0] : (((~tall(X0) & funny(X0)) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | tall(X0) | ~funny(X0))) [flattening 51]
53. ! [X0] : (((~wise(X0) & ~quiet(X0)) | ~wise(X0)) & (wise(X0) | (wise(X0) | quiet(X0)))) [nnf transformation 13]
54. ! [X0] : (((~wise(X0) & ~quiet(X0)) | ~wise(X0)) & (wise(X0) | wise(X0) | quiet(X0))) [flattening 53]
71. ~funny(X0) | ~generous(X0) [cnf transformation 24]
72. ~funny(X0) | ~happy(X0) [cnf transformation 24]
78. happy(X0) | generous(X0) | wise(X0) [cnf transformation 45]
88. funny(X0) | patient(X0) [cnf transformation 52]
96. ~wise(X0) | ~wise(X0) [cnf transformation 54]
101. ~patient(john) [cnf transformation 18]
103. ~wise(X0) [duplicate literal removal 96]
147. 11 <=> ! [X1] : patient(X1) [avatar definition]
148. patient(X1) <- (11) [avatar component clause 147]
230. ~happy(X0) | patient(X0) [resolution 88,72]
231. ~generous(X1) | patient(X1) [resolution 88,71]
238. generous(X0) | wise(X0) | patient(X0) [resolution 78,230]
240. generous(X0) | patient(X0) [subsumption resolution 238,103]
241. patient(X0) [subsumption resolution 240,231]
242. 11 [avatar split clause 241,147]
243. $false <- (11) [resolution 148,101]
247. ~11 [avatar contradiction clause 243]
248. $false [avatar sat refutation 242,247]
% SZS output end Proof for 3689972463695525991737214
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not generous then john is either wise or not brave and vice versa.
If someone is not rich or humble then john is creative.
Everyone who is both creative and not wise is not kind or not happy and vice versa.
If susan is both calm and not wise then mary is both not quiet and old.
If lucy is either rich or not tall then john is wise or patient.
If someone is rich then mary is not brave or tall and vice versa.
If someone is not calm then someone is generous or quiet and vice versa.
Everyone who is not brave or not humble is wise or not humble.
Everyone who is either patient or not quiet is both not brave and not tall and vice versa.
Everyone who is either kind or not old is either not kind or not quiet.
Everyone who is not happy is not generous or not strong.
Everyone who is not calm or not quiet is both kind and not happy and vice versa.
Everyone who is not curious is not creative or not humble and vice versa.
Everyone who is both kind and strong is quiet and vice versa.
If lucy is not wise or funny then john is either not brave or happy and vice versa.
Everyone who is both not old and old is either not funny or not happy and vice versa.
Someone is both humble and generous.
Someone is not generous.
Lucy is not brave or patient.
Alice is either rich or not brave.
Alice is either tall or happy.
Someone is not curious or not tall.
Alice is both not curious and not wise.
Paul is either rich or not funny. | Mary is kind. | entailment | ((?[X]:((~patient(X)|~generous(X))))<=>((wise(john)<~>~brave(john))))&
((?[X]:((~rich(X)|humble(X))))=>(creative(john)))&
(![X]:((creative(X)&~wise(X))<=>(~kind(X)|~happy(X))))&
(((calm(susan)&~wise(susan)))=>((~quiet(mary)&old(mary))))&
(((rich(lucy)<~>~tall(lucy)))=>((wise(john)|patient(john))))&
((?[X]:(rich(X)))<=>((~brave(mary)|tall(mary))))&
((?[X]:(~calm(X)))<=>(?[X]:((generous(X)|quiet(X)))))&
(![X]:((~brave(X)|~humble(X))=>(wise(X)|~humble(X))))&
(![X]:((patient(X)<~>~quiet(X))<=>(~brave(X)&~tall(X))))&
(![X]:((kind(X)<~>~old(X))=>(~kind(X)<~>~quiet(X))))&
(![X]:(~happy(X)=>(~generous(X)|~strong(X))))&
(![X]:((~calm(X)|~quiet(X))<=>(kind(X)&~happy(X))))&
(![X]:(~curious(X)<=>(~creative(X)|~humble(X))))&
(![X]:((kind(X)&strong(X))<=>quiet(X)))&
(((~wise(lucy)|funny(lucy)))<=>((~brave(john)<~>happy(john))))&
(![X]:((~old(X)&old(X))<=>(~funny(X)<~>~happy(X))))&
(?[X]:((humble(X)&generous(X))))&
(?[X]:(~generous(X)))&
((~brave(lucy)|patient(lucy)))&
((rich(alice)<~>~brave(alice)))&
((tall(alice)<~>happy(alice)))&
(?[X]:((~curious(X)|~tall(X))))&
((~curious(alice)&~wise(alice)))&
((rich(paul)<~>~funny(paul))) | kind(mary) | [
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2551718370647341375554490
% SZS output start Proof for 2551718370647341375554490
12. ! [X0] : ((~quiet(X0) | ~calm(X0)) <=> (~happy(X0) & kind(X0))) [input p11]
14. ! [X0] : ((strong(X0) & kind(X0)) <=> quiet(X0)) [input p13]
25. ~kind(mary) [input hypothesis]
60. ! [X0] : (((~quiet(X0) | ~calm(X0)) | (happy(X0) | ~kind(X0))) & ((~happy(X0) & kind(X0)) | (quiet(X0) & calm(X0)))) [nnf transformation 12]
61. ! [X0] : ((~quiet(X0) | ~calm(X0) | happy(X0) | ~kind(X0)) & ((~happy(X0) & kind(X0)) | (quiet(X0) & calm(X0)))) [flattening 60]
62. ! [X0] : (((strong(X0) & kind(X0)) | ~quiet(X0)) & (quiet(X0) | (~strong(X0) | ~kind(X0)))) [nnf transformation 14]
63. ! [X0] : (((strong(X0) & kind(X0)) | ~quiet(X0)) & (quiet(X0) | ~strong(X0) | ~kind(X0))) [flattening 62]
114. kind(X0) | quiet(X0) [cnf transformation 61]
120. kind(X0) | ~quiet(X0) [cnf transformation 63]
147. ~kind(mary) [cnf transformation 25]
264. kind(X0) [subsumption resolution 120,114]
334. $false [subsumption resolution 147,264]
% SZS output end Proof for 2551718370647341375554490
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and quiet is either not creative or funny.
If someone is not funny or rich then susan is either kind or not tall.
If alice is either not strong or tall then susan is not old and vice versa.
Everyone who is both not funny and patient is both not brave and not tall.
Everyone who is both not humble and not patient is both calm and not quiet.
Everyone who is humble is both creative and not strong.
Everyone who is old is both quiet and brave and vice versa.
If john is not generous then someone is quiet and vice versa.
If susan is not generous or funny then susan is not curious or not creative and vice versa.
Everyone who is not old or not curious is humble and vice versa.
If paul is not wise then someone is happy and vice versa.
Everyone who is old is strong or not calm.
Everyone who is not strong is either not calm or tall.
If lucy is not humble or brave then alice is not humble or not funny.
Everyone who is not wise or generous is both not kind and not happy.
Everyone who is rich is wise or not rich.
Someone is both not rich and not old.
Someone is both not patient and wise.
Alice is both not calm and tall.
Lucy is both not calm and strong.
Someone is both funny and not calm.
Someone is either not kind or old.
Mary is both not brave and humble. | Lucy is humble. | contradiction | (![X]:((~calm(X)&quiet(X))=>(~creative(X)<~>funny(X))))&
((?[X]:((~funny(X)|rich(X))))=>((kind(susan)<~>~tall(susan))))&
(((~strong(alice)<~>tall(alice)))<=>(~old(susan)))&
(![X]:((~funny(X)&patient(X))=>(~brave(X)&~tall(X))))&
(![X]:((~humble(X)&~patient(X))=>(calm(X)&~quiet(X))))&
(![X]:(humble(X)=>(creative(X)&~strong(X))))&
(![X]:(old(X)<=>(quiet(X)&brave(X))))&
((~generous(john))<=>(?[X]:(quiet(X))))&
(((~generous(susan)|funny(susan)))<=>((~curious(susan)|~creative(susan))))&
(![X]:((~old(X)|~curious(X))<=>humble(X)))&
((~wise(paul))<=>(?[X]:(happy(X))))&
(![X]:(old(X)=>(strong(X)|~calm(X))))&
(![X]:(~strong(X)=>(~calm(X)<~>tall(X))))&
(((~humble(lucy)|brave(lucy)))=>((~humble(alice)|~funny(alice))))&
(![X]:((~wise(X)|generous(X))=>(~kind(X)&~happy(X))))&
(![X]:(rich(X)=>(wise(X)|~rich(X))))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:((~patient(X)&wise(X))))&
((~calm(alice)&tall(alice)))&
((~calm(lucy)&strong(lucy)))&
(?[X]:((funny(X)&~calm(X))))&
(?[X]:((~kind(X)<~>old(X))))&
((~brave(mary)&humble(mary))) | humble(lucy) | [
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3427651286038602760945446
% SZS output start Proof for 3427651286038602760945446
6. ! [X0] : (humble(X0) => (~strong(X0) & creative(X0))) [input p5]
20. strong(lucy) & ~calm(lucy) [input p19]
24. humble(lucy) [input hypothesis]
35. ! [X0] : ((~strong(X0) & creative(X0)) | ~humble(X0)) [ennf transformation 6]
82. ~humble(X0) | ~strong(X0) [cnf transformation 35]
112. strong(lucy) [cnf transformation 20]
119. humble(lucy) [cnf transformation 24]
209. 20 <=> humble(lucy) [avatar definition]
211. humble(lucy) <- (20) [avatar component clause 209]
224. 20 [avatar split clause 119,209]
228. ~strong(lucy) <- (20) [resolution 82,211]
229. $false <- (20) [subsumption resolution 228,112]
230. ~20 [avatar contradiction clause 229]
231. $false [avatar sat refutation 224,230]
% SZS output end Proof for 3427651286038602760945446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not strong is either not kind or kind and vice versa.
If someone is either happy or not patient then someone is tall or funny.
Everyone who is not wise or not curious is generous and vice versa.
Everyone who is both not humble and not creative is both tall and not brave and vice versa.
If lucy is not rich then mary is either not funny or not generous.
If someone is happy then someone is brave or not quiet.
Everyone who is either old or generous is generous or not kind and vice versa.
Everyone who is both not tall and quiet is creative.
If someone is either wise or rich then paul is both not brave and rich and vice versa.
Everyone who is both not curious and not calm is not curious or not creative.
Everyone who is calm or kind is either not funny or not curious.
Everyone who is wise or not curious is both not funny and strong.
Everyone who is humble is not strong.
If john is not brave or rich then someone is both not patient and not tall.
If someone is not kind then someone is not kind or not curious.
If someone is not strong then alice is both not creative and not calm.
Someone is either not rich or kind.
Someone is wise.
Someone is both creative and strong.
Someone is either humble or kind.
Someone is not brave. | Lucy is not humble. | entailment | (![X]:((generous(X)<~>~strong(X))<=>(~kind(X)<~>kind(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:((~wise(X)|~curious(X))<=>generous(X)))&
(![X]:((~humble(X)&~creative(X))<=>(tall(X)&~brave(X))))&
((~rich(lucy))=>((~funny(mary)<~>~generous(mary))))&
((?[X]:(happy(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((old(X)<~>generous(X))<=>(generous(X)|~kind(X))))&
(![X]:((~tall(X)&quiet(X))=>creative(X)))&
((?[X]:((wise(X)<~>rich(X))))<=>((~brave(paul)&rich(paul))))&
(![X]:((~curious(X)&~calm(X))=>(~curious(X)|~creative(X))))&
(![X]:((calm(X)|kind(X))=>(~funny(X)<~>~curious(X))))&
(![X]:((wise(X)|~curious(X))=>(~funny(X)&strong(X))))&
(![X]:(humble(X)=>~strong(X)))&
(((~brave(john)|rich(john)))=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((~kind(X)|~curious(X)))))&
((?[X]:(~strong(X)))=>((~creative(alice)&~calm(alice))))&
(?[X]:((~rich(X)<~>kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)&strong(X))))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:(~brave(X))) | ~humble(lucy) | [
"p0",
"p2",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2100096480807985364475099
% SZS output start Proof for 2100096480807985364475099
1. ! [X0] : ((generous(X0) <~> ~strong(X0)) <=> (~kind(X0) <~> kind(X0))) [input p0]
3. ! [X0] : ((~curious(X0) | ~wise(X0)) <=> generous(X0)) [input p2]
12. ! [X0] : ((~curious(X0) | wise(X0)) => (strong(X0) & ~funny(X0))) [input p11]
13. ! [X0] : (humble(X0) => ~strong(X0)) [input p12]
22. humble(lucy) [input hypothesis]
33. ! [X0] : ((strong(X0) & ~funny(X0)) | (curious(X0) & ~wise(X0))) [ennf transformation 12]
34. ! [X0] : (~strong(X0) | ~humble(X0)) [ennf transformation 13]
38. ! [X0] : ((((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ((generous(X0) | strong(X0)) & (~strong(X0) | ~generous(X0))))) [nnf transformation 1]
43. ! [X0] : (((~curious(X0) | ~wise(X0)) | ~generous(X0)) & (generous(X0) | (curious(X0) & wise(X0)))) [nnf transformation 3]
44. ! [X0] : ((~curious(X0) | ~wise(X0) | ~generous(X0)) & (generous(X0) | (curious(X0) & wise(X0)))) [flattening 43]
77. ~strong(X0) | generous(X0) | kind(X0) | kind(X0) [cnf transformation 38]
78. ~strong(X0) | generous(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
79. strong(X0) | ~generous(X0) | kind(X0) | kind(X0) [cnf transformation 38]
80. strong(X0) | ~generous(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
83. wise(X0) | generous(X0) [cnf transformation 44]
111. ~wise(X0) | strong(X0) [cnf transformation 33]
113. ~humble(X0) | ~strong(X0) [cnf transformation 34]
129. humble(lucy) [cnf transformation 22]
132. ~strong(X0) | generous(X0) | kind(X0) [duplicate literal removal 77]
133. ~strong(X0) | generous(X0) | ~kind(X0) [duplicate literal removal 78]
134. strong(X0) | ~generous(X0) | kind(X0) [duplicate literal removal 79]
135. strong(X0) | ~generous(X0) | ~kind(X0) [duplicate literal removal 80]
136. ~generous(X0) | strong(X0) [subsumption resolution 134,135]
137. ~strong(X0) | generous(X0) [subsumption resolution 132,133]
230. 21 <=> ! [X0] : strong(X0) [avatar definition]
231. strong(X0) <- (21) [avatar component clause 230]
268. strong(X0) | generous(X0) [resolution 111,83]
269. generous(X0) [subsumption resolution 268,137]
271. ~strong(lucy) [resolution 113,129]
274. strong(X0) [resolution 136,269]
275. 21 [avatar split clause 274,230]
281. $false <- (21) [resolution 271,231]
282. ~21 [avatar contradiction clause 281]
283. $false [avatar sat refutation 275,282]
% SZS output end Proof for 2100096480807985364475099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not curious is kind or rich.
If john is both not old and not rich then paul is both quiet and rich and vice versa.
If someone is happy or humble then someone is kind.
Everyone who is both not funny and not strong is either calm or not calm and vice versa.
Everyone who is both tall and not kind is not creative or not tall.
Everyone who is either not calm or not wise is not strong or patient and vice versa.
Everyone who is kind is not curious and vice versa.
If someone is either not tall or humble then someone is wise or not funny and vice versa.
Everyone who is quiet is creative or not generous.
If paul is not kind then fred is both curious and not happy.
If someone is quiet or not generous then someone is both not old and not tall and vice versa.
Everyone who is curious or strong is both not wise and not humble and vice versa.
If someone is both not generous and not humble then susan is not generous.
If paul is creative or wise then lucy is rich or happy and vice versa.
Everyone who is both calm and not quiet is not rich or not wise.
Everyone who is patient or wise is quiet and vice versa.
Someone is tall.
Alice is brave.
Someone is generous.
Alice is either creative or not generous.
Fred is happy or not humble.
Mary is funny or not wise.
Someone is not curious.
Mary is both not wise and kind. | Alice is strong. | contradiction | (![X]:((~wise(X)&~curious(X))=>(kind(X)|rich(X))))&
(((~old(john)&~rich(john)))<=>((quiet(paul)&rich(paul))))&
((?[X]:((happy(X)|humble(X))))=>(?[X]:(kind(X))))&
(![X]:((~funny(X)&~strong(X))<=>(calm(X)<~>~calm(X))))&
(![X]:((tall(X)&~kind(X))=>(~creative(X)|~tall(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>(~strong(X)|patient(X))))&
(![X]:(kind(X)<=>~curious(X)))&
((?[X]:((~tall(X)<~>humble(X))))<=>(?[X]:((wise(X)|~funny(X)))))&
(![X]:(quiet(X)=>(creative(X)|~generous(X))))&
((~kind(paul))=>((curious(fred)&~happy(fred))))&
((?[X]:((quiet(X)|~generous(X))))<=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
(((creative(paul)|wise(paul)))<=>((rich(lucy)|happy(lucy))))&
(![X]:((calm(X)&~quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(?[X]:(tall(X)))&
(brave(alice))&
(?[X]:(generous(X)))&
((creative(alice)<~>~generous(alice)))&
((happy(fred)|~humble(fred)))&
((funny(mary)|~wise(mary)))&
(?[X]:(~curious(X)))&
((~wise(mary)&kind(mary))) | strong(alice) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6975333630060754983515660
% SZS output start Proof for 6975333630060754983515660
4. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (calm(X0) <~> ~calm(X0))) [input p3]
25. strong(alice) [input hypothesis]
48. ! [X0] : (((~strong(X0) & ~funny(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | (strong(X0) | funny(X0)))) [nnf transformation 4]
49. ! [X0] : (((~strong(X0) & ~funny(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | strong(X0) | funny(X0))) [flattening 48]
86. ~strong(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 49]
87. ~strong(X0) | calm(X0) | calm(X0) [cnf transformation 49]
133. strong(alice) [cnf transformation 25]
137. ~strong(X0) | ~calm(X0) [duplicate literal removal 86]
138. ~strong(X0) | calm(X0) [duplicate literal removal 87]
171. ~strong(X0) [subsumption resolution 137,138]
281. $false [subsumption resolution 133,171]
% SZS output end Proof for 6975333630060754983515660
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not brave or humble is not old and vice versa.
Everyone who is either old or not rich is not quiet and vice versa.
Everyone who is either wise or quiet is happy.
If lucy is either not happy or not quiet then fred is tall.
Everyone who is both patient and not funny is both not happy and quiet.
If lucy is either creative or tall then someone is not patient or patient and vice versa.
Everyone who is either humble or strong is both wise and not kind and vice versa.
Everyone who is either not creative or strong is not rich.
If someone is not humble then john is not creative or rich.
If someone is rich then lucy is not generous and vice versa.
Everyone who is wise is both not happy and not rich.
If someone is both funny and curious then fred is not strong or happy.
If lucy is both not calm and curious then someone is either patient or old.
Everyone who is both not rich and old is both not quiet and happy and vice versa.
Everyone who is humble is brave and vice versa.
Everyone who is both old and not quiet is either wise or not funny and vice versa.
Paul is either creative or not generous.
Lucy is not happy.
Mary is not happy.
Paul is not strong or rich.
Lucy is kind.
Someone is not humble or tall. | Lucy is wise. | contradiction | (![X]:((~brave(X)<~>humble(X))<=>~old(X)))&
(![X]:((old(X)<~>~rich(X))<=>~quiet(X)))&
(![X]:((wise(X)<~>quiet(X))=>happy(X)))&
(((~happy(lucy)<~>~quiet(lucy)))=>(tall(fred)))&
(![X]:((patient(X)&~funny(X))=>(~happy(X)&quiet(X))))&
(((creative(lucy)<~>tall(lucy)))<=>(?[X]:((~patient(X)|patient(X)))))&
(![X]:((humble(X)<~>strong(X))<=>(wise(X)&~kind(X))))&
(![X]:((~creative(X)<~>strong(X))=>~rich(X)))&
((?[X]:(~humble(X)))=>((~creative(john)|rich(john))))&
((?[X]:(rich(X)))<=>(~generous(lucy)))&
(![X]:(wise(X)=>(~happy(X)&~rich(X))))&
((?[X]:((funny(X)&curious(X))))=>((~strong(fred)|happy(fred))))&
(((~calm(lucy)&curious(lucy)))=>(?[X]:((patient(X)<~>old(X)))))&
(![X]:((~rich(X)&old(X))<=>(~quiet(X)&happy(X))))&
(![X]:(humble(X)<=>brave(X)))&
(![X]:((old(X)&~quiet(X))<=>(wise(X)<~>~funny(X))))&
((creative(paul)<~>~generous(paul)))&
(~happy(lucy))&
(~happy(mary))&
((~strong(paul)|rich(paul)))&
(kind(lucy))&
(?[X]:((~humble(X)|tall(X)))) | wise(lucy) | [
"p1",
"p2",
"p10",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6905606128862892383246348
% SZS output start Proof for 6905606128862892383246348
2. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> ~quiet(X0)) [input p1]
3. ! [X0] : ((wise(X0) <~> quiet(X0)) => happy(X0)) [input p2]
11. ! [X0] : (wise(X0) => (~rich(X0) & ~happy(X0))) [input p10]
14. ! [X0] : ((old(X0) & ~rich(X0)) <=> (happy(X0) & ~quiet(X0))) [input p13]
18. ~happy(lucy) [input p17]
23. wise(lucy) [input hypothesis]
26. ! [X0] : (happy(X0) | (wise(X0) <=> quiet(X0))) [ennf transformation 3]
33. ! [X0] : ((~rich(X0) & ~happy(X0)) | ~wise(X0)) [ennf transformation 11]
35. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | quiet(X0)) & (~quiet(X0) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 2]
36. ! [X0] : (happy(X0) | ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0)))) [nnf transformation 26]
49. ! [X0] : (((old(X0) & ~rich(X0)) | (~happy(X0) | quiet(X0))) & ((happy(X0) & ~quiet(X0)) | (~old(X0) | rich(X0)))) [nnf transformation 14]
50. ! [X0] : (((old(X0) & ~rich(X0)) | ~happy(X0) | quiet(X0)) & ((happy(X0) & ~quiet(X0)) | ~old(X0) | rich(X0))) [flattening 49]
62. ~quiet(X0) | old(X0) | rich(X0) [cnf transformation 35]
65. ~wise(X0) | quiet(X0) | happy(X0) [cnf transformation 36]
89. ~wise(X0) | ~rich(X0) [cnf transformation 33]
90. ~quiet(X0) | ~old(X0) | rich(X0) [cnf transformation 50]
104. ~happy(lucy) [cnf transformation 18]
109. wise(lucy) [cnf transformation 23]
111. 1 <=> quiet(lucy) [avatar definition]
113. quiet(lucy) <- (1) [avatar component clause 111]
115. 2 <=> happy(lucy) [avatar definition]
117. ~happy(lucy) <- (~2) [avatar component clause 115]
167. ~quiet(X0) | rich(X0) [subsumption resolution 90,62]
178. ~2 [avatar split clause 104,115]
197. ~rich(lucy) [resolution 89,109]
208. quiet(lucy) | happy(lucy) [resolution 65,109]
212. quiet(lucy) <- (~2) [subsumption resolution 208,117]
213. 1 | 2 [avatar split clause 212,115,111]
216. rich(lucy) <- (1) [resolution 113,167]
218. $false <- (1) [subsumption resolution 216,197]
219. ~1 [avatar contradiction clause 218]
220. $false [avatar sat refutation 178,213,219]
% SZS output end Proof for 6905606128862892383246348
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not tall is both not calm and patient. Everyone who is not strong or happy is calm. Everyone who is not happy is not generous or funny and vice versa. If someone is both creative and humble then someone is both generous and not generous. If someone is brave or not funny then paul is both tall and not rich. If someone is both not curious and not brave then john is wise. If someone is both wise and calm then john is not patient or not quiet and vice versa. Everyone who is not strong is either wise or not wise and vice versa. If alice is both generous and calm then someone is patient or not tall. If alice is not generous then paul is either not wise or kind. Everyone who is both not wise and not old is humble or not old and vice versa. If alice is both rich and wise then someone is wise or curious and vice versa. If someone is tall then someone is both rich and not wise and vice versa. If someone is either brave or strong then someone is either funny or creative. Everyone who is either brave or not generous is either generous or funny and vice versa. If lucy is either brave or not quiet then paul is either not happy or not funny. Mary is either kind or quiet. Someone is not rich. Someone is tall. Mary is both not creative and not happy. Someone is both not humble and not kind. Someone is not old. Fred is not calm or humble. | Paul is not funny. | contradiction | (![X]:((~funny(X)|~tall(X))=>(~calm(X)&patient(X))))&
(![X]:((~strong(X)|happy(X))=>calm(X)))&
(![X]:(~happy(X)<=>(~generous(X)|funny(X))))&
((?[X]:((creative(X)&humble(X))))=>(?[X]:((generous(X)&~generous(X)))))&
((?[X]:((brave(X)|~funny(X))))=>((tall(paul)&~rich(paul))))&
((?[X]:((~curious(X)&~brave(X))))=>(wise(john)))&
((?[X]:((wise(X)&calm(X))))<=>((~patient(john)|~quiet(john))))&
(![X]:(~strong(X)<=>(wise(X)<~>~wise(X))))&
(((generous(alice)&calm(alice)))=>(?[X]:((patient(X)|~tall(X)))))&
((~generous(alice))=>((~wise(paul)<~>kind(paul))))&
(![X]:((~wise(X)&~old(X))<=>(humble(X)|~old(X))))&
(((rich(alice)&wise(alice)))<=>(?[X]:((wise(X)|curious(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((rich(X)&~wise(X)))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((funny(X)<~>creative(X)))))&
(![X]:((brave(X)<~>~generous(X))<=>(generous(X)<~>funny(X))))&
(((brave(lucy)<~>~quiet(lucy)))=>((~happy(paul)<~>~funny(paul))))&
((kind(mary)<~>quiet(mary)))&
(?[X]:(~rich(X)))&
(?[X]:(tall(X)))&
((~creative(mary)&~happy(mary)))&
(?[X]:((~humble(X)&~kind(X))))&
(?[X]:(~old(X)))&
((~calm(fred)|humble(fred))) | ~funny(paul) | [
"p0",
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5892747583363031965468816
% SZS output start Proof for 5892747583363031965468816
1. ! [X0] : ((~tall(X0) | ~funny(X0)) => (patient(X0) & ~calm(X0))) [input p0]
2. ! [X0] : ((happy(X0) | ~strong(X0)) => calm(X0)) [input p1]
8. ! [X0] : (~strong(X0) <=> (wise(X0) <~> ~wise(X0))) [input p7]
24. ~funny(paul) [input hypothesis]
28. ! [X0] : ((patient(X0) & ~calm(X0)) | (tall(X0) & funny(X0))) [ennf transformation 1]
29. ! [X0] : (calm(X0) | (~happy(X0) & strong(X0))) [ennf transformation 2]
48. ! [X0] : ((~strong(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | strong(X0))) [nnf transformation 8]
79. ~calm(X0) | funny(X0) [cnf transformation 28]
83. strong(X0) | calm(X0) [cnf transformation 29]
102. ~strong(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 48]
103. ~strong(X0) | wise(X0) | wise(X0) [cnf transformation 48]
146. ~funny(paul) [cnf transformation 24]
151. ~strong(X0) | ~wise(X0) [duplicate literal removal 102]
152. ~strong(X0) | wise(X0) [duplicate literal removal 103]
163. 3 <=> ! [X0] : funny(X0) [avatar definition]
164. funny(X0) <- (3) [avatar component clause 163]
212. ~strong(X0) [subsumption resolution 151,152]
312. 35 <=> funny(paul) [avatar definition]
313. ~funny(paul) <- (~35) [avatar component clause 312]
336. ~35 [avatar split clause 146,312]
351. $false <- (3, ~35) [resolution 313,164]
352. ~3 | 35 [avatar contradiction clause 351]
355. calm(X0) [resolution 83,212]
358. funny(X1) [resolution 355,79]
360. 3 [avatar split clause 358,163]
361. $false [avatar sat refutation 336,352,360]
% SZS output end Proof for 5892747583363031965468816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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 not tall. | contradiction | (![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 2622571510945405880866992
% SZS output start Proof for 2622571510945405880866992
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 2622571510945405880866992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or kind is either not humble or not curious and vice versa.
If lucy is both not strong and patient then susan is both quiet and brave and vice versa.
Everyone who is wise or not kind is both not kind and not humble.
Everyone who is generous is not old or not curious.
Everyone who is either humble or not happy is funny and vice versa.
Everyone who is old is either not old or quiet.
Everyone who is curious or brave is both not funny and not calm.
Everyone who is both not wise and quiet is both rich and not rich.
If alice is both calm and not wise then someone is either not kind or humble.
If someone is either strong or tall then alice is humble.
Everyone who is both not calm and not curious is old or rich and vice versa.
If someone is funny or not brave then someone is not curious or not kind and vice versa.
If someone is not wise or not old then lucy is curious or not calm and vice versa.
If alice is both not humble and funny then someone is not curious and vice versa.
If susan is not strong then someone is not happy or curious and vice versa.
Mary is happy or not calm.
Lucy is not strong.
Someone is either calm or brave.
Someone is either happy or funny.
Someone is not quiet or strong. | Mary is strong. | neutral | (![X]:((~calm(X)<~>kind(X))<=>(~humble(X)<~>~curious(X))))&
(((~strong(lucy)&patient(lucy)))<=>((quiet(susan)&brave(susan))))&
(![X]:((wise(X)|~kind(X))=>(~kind(X)&~humble(X))))&
(![X]:(generous(X)=>(~old(X)|~curious(X))))&
(![X]:((humble(X)<~>~happy(X))<=>funny(X)))&
(![X]:(old(X)=>(~old(X)<~>quiet(X))))&
(![X]:((curious(X)|brave(X))=>(~funny(X)&~calm(X))))&
(![X]:((~wise(X)&quiet(X))=>(rich(X)&~rich(X))))&
(((calm(alice)&~wise(alice)))=>(?[X]:((~kind(X)<~>humble(X)))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((~strong(susan))<=>(?[X]:((~happy(X)|curious(X)))))&
((happy(mary)|~calm(mary)))&
(~strong(lucy))&
(?[X]:((calm(X)<~>brave(X))))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X)))) | strong(mary) | [] | null | 0 |
Everyone who is happy or brave is both funny and creative and vice versa.
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.
Everyone who is not happy or calm is strong or not curious.
Everyone who is both not humble and old is not brave and vice versa.
Everyone who is either curious or not curious is not happy.
If john is curious then someone is strong or not calm.
Everyone who is both quiet and strong is not strong or humble.
If someone is not wise then someone is both wise and not creative.
If paul is both happy and not rich then someone is not happy.
If someone is either creative or not brave then someone is both old and happy.
Everyone who is not rich or not calm is either tall or generous and vice versa.
Everyone who is either not tall or not humble is humble.
Everyone who is both curious and not generous is both not tall and happy.
Everyone who is either patient or funny is not humble or not patient.
Someone is either not happy or not strong.
Mary is either not patient or tall.
Someone is not quiet.
Alice is not calm or not brave.
Paul is kind.
Someone is either not curious or not patient.
Mary is either not brave or generous.
Susan is either not kind or rich. | Alice is tall. | contradiction | (![X]:((happy(X)|brave(X))<=>(funny(X)&creative(X))))&
(![X]:((kind(X)&humble(X))=>(kind(X)&brave(X))))&
(![X]:((~patient(X)<~>old(X))<=>(~rich(X)<~>tall(X))))&
(![X]:((~happy(X)|calm(X))=>(strong(X)|~curious(X))))&
(![X]:((~humble(X)&old(X))<=>~brave(X)))&
(![X]:((curious(X)<~>~curious(X))=>~happy(X)))&
((curious(john))=>(?[X]:((strong(X)|~calm(X)))))&
(![X]:((quiet(X)&strong(X))=>(~strong(X)|humble(X))))&
((?[X]:(~wise(X)))=>(?[X]:((wise(X)&~creative(X)))))&
(((happy(paul)&~rich(paul)))=>(?[X]:(~happy(X))))&
((?[X]:((creative(X)<~>~brave(X))))=>(?[X]:((old(X)&happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(tall(X)<~>generous(X))))&
(![X]:((~tall(X)<~>~humble(X))=>humble(X)))&
(![X]:((curious(X)&~generous(X))=>(~tall(X)&happy(X))))&
(![X]:((patient(X)<~>funny(X))=>(~humble(X)|~patient(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
((~patient(mary)<~>tall(mary)))&
(?[X]:(~quiet(X)))&
((~calm(alice)|~brave(alice)))&
(kind(paul))&
(?[X]:((~curious(X)<~>~patient(X))))&
((~brave(mary)<~>generous(mary)))&
((~kind(susan)<~>rich(susan))) | tall(alice) | [
"p0",
"p4",
"p5",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4624063374327487296407286
% SZS output start Proof for 4624063374327487296407286
1. ! [X0] : ((brave(X0) | happy(X0)) <=> (creative(X0) & funny(X0))) [input p0]
5. ! [X0] : ((old(X0) & ~humble(X0)) <=> ~brave(X0)) [input p4]
6. ! [X0] : ((curious(X0) <~> ~curious(X0)) => ~happy(X0)) [input p5]
11. ? [X0] : (creative(X0) <~> ~brave(X0)) => ? [X0] : (happy(X0) & old(X0)) [input p10]
13. ! [X0] : ((~tall(X0) <~> ~humble(X0)) => humble(X0)) [input p12]
24. tall(alice) [input hypothesis]
26. ? [X0] : (creative(X0) <~> ~brave(X0)) => ? [X1] : (happy(X1) & old(X1)) [rectify 11]
34. ! [X0] : (~happy(X0) | (curious(X0) <=> ~curious(X0))) [ennf transformation 6]
38. ? [X1] : (happy(X1) & old(X1)) | ! [X0] : (creative(X0) <=> ~brave(X0)) [ennf transformation 26]
39. ! [X0] : (humble(X0) | (~tall(X0) <=> ~humble(X0))) [ennf transformation 13]
44. ! [X0] : (((brave(X0) | happy(X0)) | (~creative(X0) | ~funny(X0))) & ((creative(X0) & funny(X0)) | (~brave(X0) & ~happy(X0)))) [nnf transformation 1]
45. ! [X0] : ((brave(X0) | happy(X0) | ~creative(X0) | ~funny(X0)) & ((creative(X0) & funny(X0)) | (~brave(X0) & ~happy(X0)))) [flattening 44]
47. ! [X0] : (((old(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | (~old(X0) | humble(X0)))) [nnf transformation 5]
48. ! [X0] : (((old(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | ~old(X0) | humble(X0))) [flattening 47]
49. ! [X0] : (~happy(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) [nnf transformation 34]
54. ? [X1] : (happy(X1) & old(X1)) | ! [X0] : ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))) [nnf transformation 38]
55. ? [X0] : (happy(X0) & old(X0)) | ! [X1] : ((creative(X1) | brave(X1)) & (~brave(X1) | ~creative(X1))) [rectify 54]
56. ? [X0] : (happy(X0) & old(X0)) => (happy(sK2) & old(sK2)) [choice axiom]
57. (happy(sK2) & old(sK2)) | ! [X1] : ((creative(X1) | brave(X1)) & (~brave(X1) | ~creative(X1))) [skolemisation 55,56]
60. ! [X0] : (humble(X0) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) [nnf transformation 39]
74. ~brave(X0) | creative(X0) [cnf transformation 45]
89. ~humble(X0) | brave(X0) [cnf transformation 48]
91. ~happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 49]
92. ~happy(X0) | curious(X0) | curious(X0) [cnf transformation 49]
97. happy(sK2) | ~brave(X1) | ~creative(X1) [cnf transformation 57]
98. happy(sK2) | creative(X1) | brave(X1) [cnf transformation 57]
106. humble(X0) | ~tall(X0) | humble(X0) [cnf transformation 60]
123. tall(alice) [cnf transformation 24]
125. ~tall(X0) | humble(X0) [duplicate literal removal 106]
126. ~happy(X0) | ~curious(X0) [duplicate literal removal 91]
127. ~happy(X0) | curious(X0) [duplicate literal removal 92]
128. ~happy(X0) [subsumption resolution 126,127]
142. creative(X1) | brave(X1) [subsumption resolution 98,128]
143. creative(X1) [subsumption resolution 142,74]
144. ~brave(X1) | ~creative(X1) [subsumption resolution 97,128]
145. ~brave(X1) [subsumption resolution 144,143]
179. humble(alice) [resolution 125,123]
180. brave(alice) [resolution 179,89]
181. $false [subsumption resolution 180,145]
% SZS output end Proof for 4624063374327487296407286
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not generous and strong then alice is either not wise or not generous and vice versa.
If john is both funny and strong then fred is curious or not strong.
Everyone who is wise or not rich is both patient and not patient and vice versa.
Everyone who is calm is curious or generous.
Everyone who is quiet or rich is either not wise or happy.
Everyone who is calm is either funny or not curious and vice versa.
Everyone who is either funny or not wise is both not happy and not calm and vice versa.
Everyone who is wise or not creative is either happy or not patient and vice versa.
Everyone who is either not curious or not quiet is either brave or funny and vice versa.
If lucy is creative then fred is calm and vice versa.
If paul is creative then someone is both not happy and not quiet.
Everyone who is not funny is both not tall and creative.
Everyone who is not happy or quiet is not humble.
If someone is both not old and not funny then someone is both not happy and not old.
If mary is not old or not quiet then someone is humble or not quiet and vice versa.
If lucy is old then someone is both not strong and not humble.
Someone is either strong or not tall.
Susan is either rich or quiet.
Paul is patient.
Susan is not humble or kind.
Fred is not strong.
Susan is either not rich or strong. | Alice is strong. | contradiction | (((~generous(alice)&strong(alice)))<=>((~wise(alice)<~>~generous(alice))))&
(((funny(john)&strong(john)))=>((curious(fred)|~strong(fred))))&
(![X]:((wise(X)|~rich(X))<=>(patient(X)&~patient(X))))&
(![X]:(calm(X)=>(curious(X)|generous(X))))&
(![X]:((quiet(X)|rich(X))=>(~wise(X)<~>happy(X))))&
(![X]:(calm(X)<=>(funny(X)<~>~curious(X))))&
(![X]:((funny(X)<~>~wise(X))<=>(~happy(X)&~calm(X))))&
(![X]:((wise(X)|~creative(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(brave(X)<~>funny(X))))&
((creative(lucy))<=>(calm(fred)))&
((creative(paul))=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:(~funny(X)=>(~tall(X)&creative(X))))&
(![X]:((~happy(X)|quiet(X))=>~humble(X)))&
((?[X]:((~old(X)&~funny(X))))=>(?[X]:((~happy(X)&~old(X)))))&
(((~old(mary)|~quiet(mary)))<=>(?[X]:((humble(X)|~quiet(X)))))&
((old(lucy))=>(?[X]:((~strong(X)&~humble(X)))))&
(?[X]:((strong(X)<~>~tall(X))))&
((rich(susan)<~>quiet(susan)))&
(patient(paul))&
((~humble(susan)|kind(susan)))&
(~strong(fred))&
((~rich(susan)<~>strong(susan))) | strong(alice) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 6488170154393688226839898
% SZS output start Proof for 6488170154393688226839898
1. (strong(alice) & ~generous(alice)) <=> (~wise(alice) <~> ~generous(alice)) [input p0]
3. ! [X0] : ((~rich(X0) | wise(X0)) <=> (~patient(X0) & patient(X0))) [input p2]
23. strong(alice) [input hypothesis]
36. ((strong(alice) & ~generous(alice)) | ((~wise(alice) | generous(alice)) & (~generous(alice) | wise(alice)))) & (((generous(alice) | wise(alice)) & (~generous(alice) | ~wise(alice))) | (~strong(alice) | generous(alice))) [nnf transformation 1]
37. ((strong(alice) & ~generous(alice)) | ((~wise(alice) | generous(alice)) & (~generous(alice) | wise(alice)))) & (((generous(alice) | wise(alice)) & (~generous(alice) | ~wise(alice))) | ~strong(alice) | generous(alice)) [flattening 36]
38. ! [X0] : (((~rich(X0) | wise(X0)) | (patient(X0) | ~patient(X0))) & ((~patient(X0) & patient(X0)) | (rich(X0) & ~wise(X0)))) [nnf transformation 3]
39. ! [X0] : ((~rich(X0) | wise(X0) | patient(X0) | ~patient(X0)) & ((~patient(X0) & patient(X0)) | (rich(X0) & ~wise(X0)))) [flattening 38]
66. generous(alice) | wise(alice) | ~strong(alice) | generous(alice) [cnf transformation 37]
67. ~generous(alice) | ~generous(alice) | wise(alice) [cnf transformation 37]
72. patient(X0) | ~wise(X0) [cnf transformation 39]
74. ~patient(X0) | ~wise(X0) [cnf transformation 39]
130. strong(alice) [cnf transformation 23]
131. generous(alice) | wise(alice) | ~strong(alice) [duplicate literal removal 66]
132. ~generous(alice) | wise(alice) [duplicate literal removal 67]
134. 1 <=> generous(alice) [avatar definition]
138. 2 <=> wise(alice) [avatar definition]
139. wise(alice) <- (2) [avatar component clause 138]
142. 3 <=> strong(alice) [avatar definition]
147. 2 | ~1 [avatar split clause 132,134,138]
148. ~3 | 2 | 1 [avatar split clause 131,134,138,142]
167. ~wise(X0) [subsumption resolution 72,74]
246. 3 [avatar split clause 130,142]
247. $false <- (2) [subsumption resolution 139,167]
248. ~2 [avatar contradiction clause 247]
249. $false [avatar sat refutation 147,148,246,248]
% SZS output end Proof for 6488170154393688226839898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not generous is both creative and generous and vice versa.
Everyone who is both not old and rich is generous.
Everyone who is either not strong or not creative is either not funny or not strong.
Everyone who is both not brave and not rich is not brave or not rich.
Everyone who is strong is quiet.
If alice is either rich or happy then alice is creative or calm.
If john is not old or rich then mary is wise or not kind and vice versa.
Everyone who is not rich or tall is not generous and vice versa.
If someone is either not quiet or not tall then someone is either kind or happy and vice versa.
Everyone who is both creative and not patient is both funny and not tall and vice versa.
Everyone who is not tall is not kind.
Everyone who is both not calm and not patient is patient and vice versa.
Everyone who is not tall or not creative is not quiet and vice versa.
If someone is not old or not kind then someone is either not generous or not curious and vice versa.
If someone is either not humble or strong then susan is either not curious or brave.
John is both not tall and not brave.
Someone is rich.
Susan is both calm and old.
Susan is curious or not old.
Someone is either not brave or not creative. | Susan is not quiet. | entailment | (![X]:((strong(X)<~>~generous(X))<=>(creative(X)&generous(X))))&
(![X]:((~old(X)&rich(X))=>generous(X)))&
(![X]:((~strong(X)<~>~creative(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((~brave(X)&~rich(X))=>(~brave(X)|~rich(X))))&
(![X]:(strong(X)=>quiet(X)))&
(((rich(alice)<~>happy(alice)))=>((creative(alice)|calm(alice))))&
(((~old(john)|rich(john)))<=>((wise(mary)|~kind(mary))))&
(![X]:((~rich(X)|tall(X))<=>~generous(X)))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((creative(X)&~patient(X))<=>(funny(X)&~tall(X))))&
(![X]:(~tall(X)=>~kind(X)))&
(![X]:((~calm(X)&~patient(X))<=>patient(X)))&
(![X]:((~tall(X)|~creative(X))<=>~quiet(X)))&
((?[X]:((~old(X)|~kind(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((~humble(X)<~>strong(X))))=>((~curious(susan)<~>brave(susan))))&
((~tall(john)&~brave(john)))&
(?[X]:(rich(X)))&
((calm(susan)&old(susan)))&
((curious(susan)|~old(susan)))&
(?[X]:((~brave(X)<~>~creative(X)))) | ~quiet(susan) | [
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5760616250996458356272534
% SZS output start Proof for 5760616250996458356272534
10. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~tall(X0) & funny(X0))) [input p9]
12. ! [X0] : ((~patient(X0) & ~calm(X0)) <=> patient(X0)) [input p11]
13. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> ~quiet(X0)) [input p12]
21. quiet(susan) [input hypothesis]
47. ! [X0] : (((~patient(X0) & creative(X0)) | (tall(X0) | ~funny(X0))) & ((~tall(X0) & funny(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 10]
48. ! [X0] : (((~patient(X0) & creative(X0)) | tall(X0) | ~funny(X0)) & ((~tall(X0) & funny(X0)) | patient(X0) | ~creative(X0))) [flattening 47]
49. ! [X0] : (((~patient(X0) & ~calm(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) | calm(X0)))) [nnf transformation 12]
50. ! [X0] : (((~patient(X0) & ~calm(X0)) | ~patient(X0)) & (patient(X0) | patient(X0) | calm(X0))) [flattening 49]
51. ! [X0] : (((~creative(X0) | ~tall(X0)) | quiet(X0)) & (~quiet(X0) | (creative(X0) & tall(X0)))) [nnf transformation 13]
52. ! [X0] : ((~creative(X0) | ~tall(X0) | quiet(X0)) & (~quiet(X0) | (creative(X0) & tall(X0)))) [flattening 51]
95. ~tall(X0) | patient(X0) | ~creative(X0) [cnf transformation 48]
101. ~patient(X0) | ~patient(X0) [cnf transformation 50]
102. ~quiet(X0) | tall(X0) [cnf transformation 52]
103. ~quiet(X0) | creative(X0) [cnf transformation 52]
123. quiet(susan) [cnf transformation 21]
125. ~patient(X0) [duplicate literal removal 101]
187. 13 <=> ! [X3] : (~quiet(X3) | tall(X3)) [avatar definition]
188. ~quiet(X3) | tall(X3) <- (13) [avatar component clause 187]
205. 13 [avatar split clause 102,187]
272. creative(susan) [resolution 103,123]
276. tall(susan) <- (13) [resolution 188,123]
316. patient(susan) | ~creative(susan) <- (13) [resolution 95,276]
320. ~creative(susan) <- (13) [subsumption resolution 316,125]
321. $false <- (13) [subsumption resolution 320,272]
322. ~13 [avatar contradiction clause 321]
326. $false [avatar sat refutation 205,322]
% SZS output end Proof for 5760616250996458356272534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and not humble then someone is either not wise or funny.
If paul is both not quiet and tall then susan is either not brave or not quiet.
If someone is both not generous and curious then paul is both calm and creative and vice versa.
Everyone who is both not happy and calm is wise and vice versa.
If fred is funny or wise then someone is not brave or funny and vice versa.
Everyone who is not strong is generous and vice versa.
Everyone who is both tall and generous is both not patient and kind and vice versa.
Everyone who is both calm and not patient is either not brave or happy.
Everyone who is both not generous and not creative is both not quiet and not strong.
Everyone who is wise or not quiet is funny and vice versa.
Everyone who is not rich is not tall or patient and vice versa.
If someone is not happy or not generous then lucy is either wise or not calm and vice versa.
If someone is not strong or creative then someone is curious or not wise and vice versa.
Everyone who is not creative is either patient or not old.
Everyone who is either patient or not curious is funny.
Everyone who is either rich or generous is either curious or not strong and vice versa.
Someone is humble or not strong.
Alice is either curious or not rich.
Someone is not kind or not old.
Mary is both not tall and not calm.
Paul is not kind or not calm.
Someone is calm.
Someone is kind or calm.
John is either not happy or not wise. | Mary is wise. | contradiction | ((?[X]:((quiet(X)&~humble(X))))=>(?[X]:((~wise(X)<~>funny(X)))))&
(((~quiet(paul)&tall(paul)))=>((~brave(susan)<~>~quiet(susan))))&
((?[X]:((~generous(X)&curious(X))))<=>((calm(paul)&creative(paul))))&
(![X]:((~happy(X)&calm(X))<=>wise(X)))&
(((funny(fred)|wise(fred)))<=>(?[X]:((~brave(X)|funny(X)))))&
(![X]:(~strong(X)<=>generous(X)))&
(![X]:((tall(X)&generous(X))<=>(~patient(X)&kind(X))))&
(![X]:((calm(X)&~patient(X))=>(~brave(X)<~>happy(X))))&
(![X]:((~generous(X)&~creative(X))=>(~quiet(X)&~strong(X))))&
(![X]:((wise(X)|~quiet(X))<=>funny(X)))&
(![X]:(~rich(X)<=>(~tall(X)|patient(X))))&
((?[X]:((~happy(X)|~generous(X))))<=>((wise(lucy)<~>~calm(lucy))))&
((?[X]:((~strong(X)|creative(X))))<=>(?[X]:((curious(X)|~wise(X)))))&
(![X]:(~creative(X)=>(patient(X)<~>~old(X))))&
(![X]:((patient(X)<~>~curious(X))=>funny(X)))&
(![X]:((rich(X)<~>generous(X))<=>(curious(X)<~>~strong(X))))&
(?[X]:((humble(X)|~strong(X))))&
((curious(alice)<~>~rich(alice)))&
(?[X]:((~kind(X)|~old(X))))&
((~tall(mary)&~calm(mary)))&
((~kind(paul)|~calm(paul)))&
(?[X]:(calm(X)))&
(?[X]:((kind(X)|calm(X))))&
((~happy(john)<~>~wise(john))) | wise(mary) | [
"p3",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 12362659324079616612893
% SZS output start Proof for 12362659324079616612893
4. ! [X0] : ((calm(X0) & ~happy(X0)) <=> wise(X0)) [input p3]
20. ~calm(mary) & ~tall(mary) [input p19]
25. wise(mary) [input hypothesis]
44. ! [X0] : (((calm(X0) & ~happy(X0)) | ~wise(X0)) & (wise(X0) | (~calm(X0) | happy(X0)))) [nnf transformation 4]
45. ! [X0] : (((calm(X0) & ~happy(X0)) | ~wise(X0)) & (wise(X0) | ~calm(X0) | happy(X0))) [flattening 44]
87. ~wise(X0) | calm(X0) [cnf transformation 45]
134. ~calm(mary) [cnf transformation 20]
140. wise(mary) [cnf transformation 25]
301. calm(mary) [resolution 87,140]
302. $false [subsumption resolution 301,134]
% SZS output end Proof for 12362659324079616612893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is curious then someone is not wise.
If alice is old then someone is both not brave and strong and vice versa.
If john is not tall then fred is not creative or old.
If someone is not rich or not calm then someone is both wise and not strong and vice versa.
Everyone who is not tall is both calm and tall and vice versa.
Everyone who is not rich is either patient or not kind.
If john is humble or funny then mary is either not patient or humble.
Everyone who is either wise or not rich is either tall or patient and vice versa.
If someone is either funny or not old then someone is wise and vice versa.
If john is both quiet and brave then someone is not happy or not patient and vice versa.
Everyone who is calm or generous is old.
If fred is brave or strong then someone is both not rich and funny and vice versa.
If someone is both happy and wise then susan is not patient or not humble.
Everyone who is both not rich and not calm is both not old and not wise and vice versa.
If alice is rich then susan is both humble and wise.
If someone is generous or calm then someone is both rich and tall and vice versa.
Mary is both not generous and not humble.
Someone is not strong.
Someone is brave.
Someone is both not old and creative.
Susan is either not patient or kind.
Someone is both curious and happy. | John is brave. | entailment | ((curious(fred))=>(?[X]:(~wise(X))))&
((old(alice))<=>(?[X]:((~brave(X)&strong(X)))))&
((~tall(john))=>((~creative(fred)|old(fred))))&
((?[X]:((~rich(X)|~calm(X))))<=>(?[X]:((wise(X)&~strong(X)))))&
(![X]:(~tall(X)<=>(calm(X)&tall(X))))&
(![X]:(~rich(X)=>(patient(X)<~>~kind(X))))&
(((humble(john)|funny(john)))=>((~patient(mary)<~>humble(mary))))&
(![X]:((wise(X)<~>~rich(X))<=>(tall(X)<~>patient(X))))&
((?[X]:((funny(X)<~>~old(X))))<=>(?[X]:(wise(X))))&
(((quiet(john)&brave(john)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((calm(X)|generous(X))=>old(X)))&
(((brave(fred)|strong(fred)))<=>(?[X]:((~rich(X)&funny(X)))))&
((?[X]:((happy(X)&wise(X))))=>((~patient(susan)|~humble(susan))))&
(![X]:((~rich(X)&~calm(X))<=>(~old(X)&~wise(X))))&
((rich(alice))=>((humble(susan)&wise(susan))))&
((?[X]:((generous(X)|calm(X))))<=>(?[X]:((rich(X)&tall(X)))))&
((~generous(mary)&~humble(mary)))&
(?[X]:(~strong(X)))&
(?[X]:(brave(X)))&
(?[X]:((~old(X)&creative(X))))&
((~patient(susan)<~>kind(susan)))&
(?[X]:((curious(X)&happy(X)))) | brave(john) | [
"p3",
"p4",
"p7",
"p8",
"p9",
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1702287689391023010250342
% SZS output start Proof for 1702287689391023010250342
4. ? [X0] : (~calm(X0) | ~rich(X0)) <=> ? [X0] : (~strong(X0) & wise(X0)) [input p3]
5. ! [X0] : (~tall(X0) <=> (tall(X0) & calm(X0))) [input p4]
8. ! [X0] : ((wise(X0) <~> ~rich(X0)) <=> (tall(X0) <~> patient(X0))) [input p7]
9. ? [X0] : (funny(X0) <~> ~old(X0)) <=> ? [X0] : wise(X0) [input p8]
10. (brave(john) & quiet(john)) <=> ? [X0] : (~patient(X0) | ~happy(X0)) [input p9]
11. ! [X0] : ((generous(X0) | calm(X0)) => old(X0)) [input p10]
14. ! [X0] : ((~calm(X0) & ~rich(X0)) <=> (~wise(X0) & ~old(X0))) [input p13]
20. ? [X0] : (creative(X0) & ~old(X0)) [input p19]
23. ~brave(john) [input hypothesis]
24. ? [X0] : (~calm(X0) | ~rich(X0)) <=> ? [X1] : (~strong(X1) & wise(X1)) [rectify 4]
25. ? [X0] : (funny(X0) <~> ~old(X0)) <=> ? [X1] : wise(X1) [rectify 9]
32. ! [X0] : (old(X0) | (~generous(X0) & ~calm(X0))) [ennf transformation 11]
42. (? [X0] : (~calm(X0) | ~rich(X0)) | ! [X1] : (strong(X1) | ~wise(X1))) & (? [X1] : (~strong(X1) & wise(X1)) | ! [X0] : (calm(X0) & rich(X0))) [nnf transformation 24]
43. (? [X0] : (~calm(X0) | ~rich(X0)) | ! [X1] : (strong(X1) | ~wise(X1))) & (? [X2] : (~strong(X2) & wise(X2)) | ! [X3] : (calm(X3) & rich(X3))) [rectify 42]
44. ? [X0] : (~calm(X0) | ~rich(X0)) => (~calm(sK2) | ~rich(sK2)) [choice axiom]
45. ? [X2] : (~strong(X2) & wise(X2)) => (~strong(sK3) & wise(sK3)) [choice axiom]
46. ((~calm(sK2) | ~rich(sK2)) | ! [X1] : (strong(X1) | ~wise(X1))) & ((~strong(sK3) & wise(sK3)) | ! [X3] : (calm(X3) & rich(X3))) [skolemisation 43,45,44]
47. ! [X0] : ((~tall(X0) | (~tall(X0) | ~calm(X0))) & ((tall(X0) & calm(X0)) | tall(X0))) [nnf transformation 5]
48. ! [X0] : ((~tall(X0) | ~tall(X0) | ~calm(X0)) & ((tall(X0) & calm(X0)) | tall(X0))) [flattening 47]
51. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [nnf transformation 8]
52. (? [X0] : ((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) | ! [X1] : ~wise(X1)) & (? [X1] : wise(X1) | ! [X0] : ((funny(X0) | old(X0)) & (~old(X0) | ~funny(X0)))) [nnf transformation 25]
53. (? [X0] : ((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) | ! [X1] : ~wise(X1)) & (? [X2] : wise(X2) | ! [X3] : ((funny(X3) | old(X3)) & (~old(X3) | ~funny(X3)))) [rectify 52]
54. ? [X0] : ((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) => ((old(sK4) | ~funny(sK4)) & (~old(sK4) | funny(sK4))) [choice axiom]
55. ? [X2] : wise(X2) => wise(sK5) [choice axiom]
56. (((old(sK4) | ~funny(sK4)) & (~old(sK4) | funny(sK4))) | ! [X1] : ~wise(X1)) & (wise(sK5) | ! [X3] : ((funny(X3) | old(X3)) & (~old(X3) | ~funny(X3)))) [skolemisation 53,55,54]
57. ((brave(john) & quiet(john)) | ! [X0] : (patient(X0) & happy(X0))) & (? [X0] : (~patient(X0) | ~happy(X0)) | (~brave(john) | ~quiet(john))) [nnf transformation 10]
58. ((brave(john) & quiet(john)) | ! [X0] : (patient(X0) & happy(X0))) & (? [X0] : (~patient(X0) | ~happy(X0)) | ~brave(john) | ~quiet(john)) [flattening 57]
59. ((brave(john) & quiet(john)) | ! [X0] : (patient(X0) & happy(X0))) & (? [X1] : (~patient(X1) | ~happy(X1)) | ~brave(john) | ~quiet(john)) [rectify 58]
60. ? [X1] : (~patient(X1) | ~happy(X1)) => (~patient(sK6) | ~happy(sK6)) [choice axiom]
61. ((brave(john) & quiet(john)) | ! [X0] : (patient(X0) & happy(X0))) & ((~patient(sK6) | ~happy(sK6)) | ~brave(john) | ~quiet(john)) [skolemisation 59,60]
67. ! [X0] : (((~calm(X0) & ~rich(X0)) | (wise(X0) | old(X0))) & ((~wise(X0) & ~old(X0)) | (calm(X0) | rich(X0)))) [nnf transformation 14]
68. ! [X0] : (((~calm(X0) & ~rich(X0)) | wise(X0) | old(X0)) & ((~wise(X0) & ~old(X0)) | calm(X0) | rich(X0))) [flattening 67]
78. ? [X0] : (creative(X0) & ~old(X0)) => (creative(sK12) & ~old(sK12)) [choice axiom]
79. creative(sK12) & ~old(sK12) [skolemisation 20,78]
89. wise(sK3) | calm(X3) [cnf transformation 46]
94. tall(X0) | tall(X0) [cnf transformation 48]
95. ~tall(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 48]
104. ~patient(X0) | ~tall(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 51]
110. wise(sK5) | ~old(X3) | ~funny(X3) [cnf transformation 56]
111. wise(sK5) | funny(X3) | old(X3) [cnf transformation 56]
112. ~old(sK4) | funny(sK4) | ~wise(X1) [cnf transformation 56]
113. old(sK4) | ~funny(sK4) | ~wise(X1) [cnf transformation 56]
118. brave(john) | patient(X0) [cnf transformation 61]
119. ~calm(X0) | old(X0) [cnf transformation 32]
128. ~wise(X0) | calm(X0) | rich(X0) [cnf transformation 68]
142. ~old(sK12) [cnf transformation 79]
148. ~brave(john) [cnf transformation 23]
149. tall(X0) [duplicate literal removal 94]
150. ~calm(X0) | ~tall(X0) [duplicate literal removal 95]
204. 13 <=> ! [X3] : calm(X3) [avatar definition]
205. calm(X3) <- (13) [avatar component clause 204]
216. 16 <=> wise(sK3) [avatar definition]
218. wise(sK3) <- (16) [avatar component clause 216]
219. 13 | 16 [avatar split clause 89,216,204]
244. ~patient(X0) | ~rich(X0) | ~wise(X0) [subsumption resolution 104,149]
246. 21 <=> ! [X1] : ~wise(X1) [avatar definition]
247. ~wise(X1) <- (21) [avatar component clause 246]
249. 22 <=> funny(sK4) [avatar definition]
250. funny(sK4) <- (22) [avatar component clause 249]
251. ~funny(sK4) <- (~22) [avatar component clause 249]
253. 23 <=> old(sK4) [avatar definition]
254. ~old(sK4) <- (~23) [avatar component clause 253]
255. old(sK4) <- (23) [avatar component clause 253]
256. 21 | ~22 | 23 [avatar split clause 113,253,249,246]
257. 21 | 22 | ~23 [avatar split clause 112,253,249,246]
259. 24 <=> ! [X3] : (funny(X3) | old(X3)) [avatar definition]
260. funny(X3) | old(X3) <- (24) [avatar component clause 259]
262. 25 <=> wise(sK5) [avatar definition]
264. wise(sK5) <- (25) [avatar component clause 262]
265. 24 | 25 [avatar split clause 111,262,259]
267. 26 <=> ! [X3] : (~old(X3) | ~funny(X3)) [avatar definition]
268. ~funny(X3) | ~old(X3) <- (26) [avatar component clause 267]
269. 26 | 25 [avatar split clause 110,262,267]
271. 27 <=> ! [X0] : patient(X0) [avatar definition]
272. patient(X0) <- (27) [avatar component clause 271]
274. 28 <=> brave(john) [avatar definition]
277. 27 | 28 [avatar split clause 118,274,271]
375. ~28 [avatar split clause 148,274]
387. old(X0) <- (13) [resolution 119,205]
388. $false <- (13) [resolution 387,142]
393. ~13 [avatar contradiction clause 388]
412. calm(sK5) | rich(sK5) <- (25) [resolution 128,264]
423. 53 <=> rich(sK5) [avatar definition]
425. rich(sK5) <- (53) [avatar component clause 423]
427. 54 <=> calm(sK5) [avatar definition]
429. calm(sK5) <- (54) [avatar component clause 427]
430. 53 | 54 | ~25 [avatar split clause 412,262,427,423]
443. ~tall(sK5) <- (54) [resolution 429,150]
445. $false <- (54) [subsumption resolution 443,149]
446. ~54 [avatar contradiction clause 445]
448. old(sK4) <- (~22, 24) [resolution 260,251]
450. $false <- (~22, ~23, 24) [subsumption resolution 448,254]
451. 22 | 23 | ~24 [avatar contradiction clause 450]
452. $false <- (16, 21) [resolution 247,218]
453. ~16 | ~21 [avatar contradiction clause 452]
457. ~old(sK4) <- (22, 26) [resolution 268,250]
458. $false <- (22, 23, 26) [subsumption resolution 457,255]
459. ~22 | ~23 | ~26 [avatar contradiction clause 458]
480. ~rich(X0) | ~wise(X0) <- (27) [resolution 244,272]
531. ~wise(sK5) <- (27, 53) [resolution 480,425]
536. $false <- (25, 27, 53) [subsumption resolution 531,264]
537. ~25 | ~27 | ~53 [avatar contradiction clause 536]
539. $false [avatar sat refutation 219,256,257,265,269,277,375,393,430,446,451,453,459,537]
% SZS output end Proof for 1702287689391023010250342
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then someone is both wise and not funny. Everyone who is not kind or tall is both not kind and kind. Everyone who is both quiet and old is both calm and not happy. If lucy is both quiet and not kind then john is either wise or not calm. Everyone who is curious is not happy or not quiet and vice versa. If someone is rich or funny then john is either not old or brave. Everyone who is creative is happy. If someone is strong then someone is calm or not strong and vice versa. If susan is wise or not kind then someone is not curious and vice versa. Everyone who is humble is not old or strong and vice versa. Everyone who is both not calm and not creative is not quiet and vice versa. Everyone who is both creative and not generous is either not kind or not wise and vice versa. If someone is either rich or not quiet then alice is either tall or not quiet and vice versa. Everyone who is either not rich or calm is not creative or not generous. If john is either happy or not calm then someone is not curious or not wise. Everyone who is strong is both funny and creative and vice versa. Someone is happy or quiet. Someone is not humble or not strong. Susan is either strong or not kind. Someone is funny. Someone is both calm and generous. Someone is either rich or generous. Someone is not wise or not kind. | Susan is not funny. | contradiction | ((?[X]:(kind(X)))=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:((~kind(X)|tall(X))=>(~kind(X)&kind(X))))&
(![X]:((quiet(X)&old(X))=>(calm(X)&~happy(X))))&
(((quiet(lucy)&~kind(lucy)))=>((wise(john)<~>~calm(john))))&
(![X]:(curious(X)<=>(~happy(X)|~quiet(X))))&
((?[X]:((rich(X)|funny(X))))=>((~old(john)<~>brave(john))))&
(![X]:(creative(X)=>happy(X)))&
((?[X]:(strong(X)))<=>(?[X]:((calm(X)|~strong(X)))))&
(((wise(susan)|~kind(susan)))<=>(?[X]:(~curious(X))))&
(![X]:(humble(X)<=>(~old(X)|strong(X))))&
(![X]:((~calm(X)&~creative(X))<=>~quiet(X)))&
(![X]:((creative(X)&~generous(X))<=>(~kind(X)<~>~wise(X))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>((tall(alice)<~>~quiet(alice))))&
(![X]:((~rich(X)<~>calm(X))=>(~creative(X)|~generous(X))))&
(((happy(john)<~>~calm(john)))=>(?[X]:((~curious(X)|~wise(X)))))&
(![X]:(strong(X)<=>(funny(X)&creative(X))))&
(?[X]:((happy(X)|quiet(X))))&
(?[X]:((~humble(X)|~strong(X))))&
((strong(susan)<~>~kind(susan)))&
(?[X]:(funny(X)))&
(?[X]:((calm(X)&generous(X))))&
(?[X]:((rich(X)<~>generous(X))))&
(?[X]:((~wise(X)|~kind(X)))) | ~funny(susan) | [
"p1",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7781170918184066665879330
% SZS output start Proof for 7781170918184066665879330
2. ! [X0] : ((tall(X0) | ~kind(X0)) => (kind(X0) & ~kind(X0))) [input p1]
16. ! [X0] : (strong(X0) <=> (creative(X0) & funny(X0))) [input p15]
19. strong(susan) <~> ~kind(susan) [input p18]
24. ~funny(susan) [input hypothesis]
29. ! [X0] : ((kind(X0) & ~kind(X0)) | (~tall(X0) & kind(X0))) [ennf transformation 2]
69. ! [X0] : ((strong(X0) | (~creative(X0) | ~funny(X0))) & ((creative(X0) & funny(X0)) | ~strong(X0))) [nnf transformation 16]
70. ! [X0] : ((strong(X0) | ~creative(X0) | ~funny(X0)) & ((creative(X0) & funny(X0)) | ~strong(X0))) [flattening 69]
75. (kind(susan) | ~strong(susan)) & (~kind(susan) | strong(susan)) [nnf transformation 19]
89. kind(X0) | kind(X0) [cnf transformation 29]
132. ~strong(X0) | funny(X0) [cnf transformation 70]
137. ~kind(susan) | strong(susan) [cnf transformation 75]
145. ~funny(susan) [cnf transformation 24]
146. kind(X0) [duplicate literal removal 89]
274. strong(susan) [subsumption resolution 137,146]
294. funny(susan) [resolution 132,274]
295. $false [subsumption resolution 294,145]
% SZS output end Proof for 7781170918184066665879330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and not tall is either not funny or not creative. Everyone who is not strong is kind or not tall and vice versa. If someone is creative or not curious then lucy is either not old or brave and vice versa. Everyone who is both calm and not happy is not generous and vice versa. If someone is not calm or not patient then someone is either creative or not humble. Everyone who is not curious is either brave or creative. Everyone who is tall is quiet and vice versa. If paul is either not creative or not quiet then john is not strong or not wise and vice versa. Everyone who is both not brave and not humble is both not funny and kind and vice versa. Everyone who is not tall or quiet is both rich and creative and vice versa. If mary is both not generous and not patient then alice is either not old or not quiet. If someone is not curious then someone is humble. If fred is either funny or strong then someone is wise. If someone is both quiet and curious then someone is both rich and not happy and vice versa. Everyone who is not strong or brave is both not calm and not patient and vice versa. Everyone who is either curious or funny is quiet and vice versa. Susan is either brave or humble. Someone is patient. Someone is patient or wise. Mary is either kind or not patient. Lucy is either funny or not humble. | Paul is creative. | entailment | (![X]:((kind(X)&~tall(X))=>(~funny(X)<~>~creative(X))))&
(![X]:(~strong(X)<=>(kind(X)|~tall(X))))&
((?[X]:((creative(X)|~curious(X))))<=>((~old(lucy)<~>brave(lucy))))&
(![X]:((calm(X)&~happy(X))<=>~generous(X)))&
((?[X]:((~calm(X)|~patient(X))))=>(?[X]:((creative(X)<~>~humble(X)))))&
(![X]:(~curious(X)=>(brave(X)<~>creative(X))))&
(![X]:(tall(X)<=>quiet(X)))&
(((~creative(paul)<~>~quiet(paul)))<=>((~strong(john)|~wise(john))))&
(![X]:((~brave(X)&~humble(X))<=>(~funny(X)&kind(X))))&
(![X]:((~tall(X)|quiet(X))<=>(rich(X)&creative(X))))&
(((~generous(mary)&~patient(mary)))=>((~old(alice)<~>~quiet(alice))))&
((?[X]:(~curious(X)))=>(?[X]:(humble(X))))&
(((funny(fred)<~>strong(fred)))=>(?[X]:(wise(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((rich(X)&~happy(X)))))&
(![X]:((~strong(X)|brave(X))<=>(~calm(X)&~patient(X))))&
(![X]:((curious(X)<~>funny(X))<=>quiet(X)))&
((brave(susan)<~>humble(susan)))&
(?[X]:(patient(X)))&
(?[X]:((patient(X)|wise(X))))&
((kind(mary)<~>~patient(mary)))&
((funny(lucy)<~>~humble(lucy))) | creative(paul) | [
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8245181955697689197855175
% SZS output start Proof for 8245181955697689197855175
7. ! [X0] : (tall(X0) <=> quiet(X0)) [input p6]
10. ! [X0] : ((quiet(X0) | ~tall(X0)) <=> (creative(X0) & rich(X0))) [input p9]
22. ~creative(paul) [input hypothesis]
49. ! [X0] : ((tall(X0) | ~quiet(X0)) & (quiet(X0) | ~tall(X0))) [nnf transformation 7]
54. ! [X0] : (((quiet(X0) | ~tall(X0)) | (~creative(X0) | ~rich(X0))) & ((creative(X0) & rich(X0)) | (~quiet(X0) & tall(X0)))) [nnf transformation 10]
55. ! [X0] : ((quiet(X0) | ~tall(X0) | ~creative(X0) | ~rich(X0)) & ((creative(X0) & rich(X0)) | (~quiet(X0) & tall(X0)))) [flattening 54]
96. ~tall(X0) | quiet(X0) [cnf transformation 49]
110. creative(X0) | tall(X0) [cnf transformation 55]
111. ~quiet(X0) | creative(X0) [cnf transformation 55]
139. ~creative(paul) [cnf transformation 22]
191. 12 <=> creative(paul) [avatar definition]
192. ~creative(paul) <- (~12) [avatar component clause 191]
195. 13 <=> quiet(paul) [avatar definition]
196. ~quiet(paul) <- (~13) [avatar component clause 195]
197. quiet(paul) <- (13) [avatar component clause 195]
306. ~12 [avatar split clause 139,191]
314. tall(paul) <- (~12) [resolution 110,192]
315. creative(paul) <- (13) [resolution 111,197]
316. $false <- (~12, 13) [subsumption resolution 315,192]
317. 12 | ~13 [avatar contradiction clause 316]
366. quiet(paul) <- (~12) [resolution 314,96]
376. $false <- (~12, ~13) [subsumption resolution 366,196]
377. 12 | 13 [avatar contradiction clause 376]
378. $false [avatar sat refutation 306,317,377]
% SZS output end Proof for 8245181955697689197855175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave or happy is both quiet and patient.
If mary is not kind or calm then someone is not brave or not wise.
Everyone who is not curious or calm is either strong or brave.
If someone is happy then someone is either happy or not old.
Everyone who is either funny or creative is not quiet.
If someone is tall then someone is not calm or not quiet and vice versa.
If alice is not humble then someone is not calm and vice versa.
Everyone who is both not strong and funny is both not old and not funny and vice versa.
Everyone who is both generous and not strong is both not wise and not old.
If fred is either not creative or not wise then someone is both rich and old.
Everyone who is either not brave or not curious is not brave and vice versa.
Everyone who is not generous or patient is either happy or generous and vice versa.
Everyone who is both not humble and not generous is not kind or not creative and vice versa.
If susan is both generous and not quiet then someone is either not calm or strong and vice versa.
Everyone who is both kind and not happy is patient or not kind.
Everyone who is either curious or not humble is either quiet or happy and vice versa.
Alice is both tall and strong.
Someone is either not tall or humble.
Susan is humble or not generous.
Someone is generous or not patient.
Susan is either not kind or tall.
Someone is not quiet or calm.
Fred is either happy or not rich. | Fred is not rich. | neutral | (![X]:((~brave(X)|happy(X))=>(quiet(X)&patient(X))))&
(((~kind(mary)|calm(mary)))=>(?[X]:((~brave(X)|~wise(X)))))&
(![X]:((~curious(X)|calm(X))=>(strong(X)<~>brave(X))))&
((?[X]:(happy(X)))=>(?[X]:((happy(X)<~>~old(X)))))&
(![X]:((funny(X)<~>creative(X))=>~quiet(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~calm(X)|~quiet(X)))))&
((~humble(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~strong(X)&funny(X))<=>(~old(X)&~funny(X))))&
(![X]:((generous(X)&~strong(X))=>(~wise(X)&~old(X))))&
(((~creative(fred)<~>~wise(fred)))=>(?[X]:((rich(X)&old(X)))))&
(![X]:((~brave(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((~generous(X)|patient(X))<=>(happy(X)<~>generous(X))))&
(![X]:((~humble(X)&~generous(X))<=>(~kind(X)|~creative(X))))&
(((generous(susan)&~quiet(susan)))<=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((kind(X)&~happy(X))=>(patient(X)|~kind(X))))&
(![X]:((curious(X)<~>~humble(X))<=>(quiet(X)<~>happy(X))))&
((tall(alice)&strong(alice)))&
(?[X]:((~tall(X)<~>humble(X))))&
((humble(susan)|~generous(susan)))&
(?[X]:((generous(X)|~patient(X))))&
((~kind(susan)<~>tall(susan)))&
(?[X]:((~quiet(X)|calm(X))))&
((happy(fred)<~>~rich(fred))) | ~rich(fred) | [] | null | 0 |
Everyone who is calm is patient and vice versa. Everyone who is brave is both not happy and not quiet. Everyone who is wise is either not strong or old and vice versa. If someone is either happy or humble then someone is both wise and not kind and vice versa. Everyone who is either curious or humble is tall. If someone is either not creative or humble then someone is brave and vice versa. Everyone who is either generous or not kind is not patient or not happy and vice versa. If mary is not quiet then john is both not old and not wise. If lucy is happy then someone is not calm. If mary is not strong or wise then susan is humble and vice versa. If lucy is not creative then fred is not wise or not happy. If someone is not old then fred is kind or strong. If someone is both not strong and kind then susan is not generous and vice versa. Everyone who is both not curious and not wise is either curious or funny. Everyone who is not quiet or not happy is tall or strong and vice versa. If john is both strong and not curious then someone is either creative or not creative and vice versa. Mary is not wise. Alice is both happy and not strong. Susan is tall. Someone is both kind and rich. Someone is both not calm and not happy. Someone is either creative or not funny. Susan is wise or not wise. | Susan is generous. | neutral | (![X]:(calm(X)<=>patient(X)))&
(![X]:(brave(X)=>(~happy(X)&~quiet(X))))&
(![X]:(wise(X)<=>(~strong(X)<~>old(X))))&
((?[X]:((happy(X)<~>humble(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((curious(X)<~>humble(X))=>tall(X)))&
((?[X]:((~creative(X)<~>humble(X))))<=>(?[X]:(brave(X))))&
(![X]:((generous(X)<~>~kind(X))<=>(~patient(X)|~happy(X))))&
((~quiet(mary))=>((~old(john)&~wise(john))))&
((happy(lucy))=>(?[X]:(~calm(X))))&
(((~strong(mary)|wise(mary)))<=>(humble(susan)))&
((~creative(lucy))=>((~wise(fred)|~happy(fred))))&
((?[X]:(~old(X)))=>((kind(fred)|strong(fred))))&
((?[X]:((~strong(X)&kind(X))))<=>(~generous(susan)))&
(![X]:((~curious(X)&~wise(X))=>(curious(X)<~>funny(X))))&
(![X]:((~quiet(X)|~happy(X))<=>(tall(X)|strong(X))))&
(((strong(john)&~curious(john)))<=>(?[X]:((creative(X)<~>~creative(X)))))&
(~wise(mary))&
((happy(alice)&~strong(alice)))&
(tall(susan))&
(?[X]:((kind(X)&rich(X))))&
(?[X]:((~calm(X)&~happy(X))))&
(?[X]:((creative(X)<~>~funny(X))))&
((wise(susan)|~wise(susan))) | generous(susan) | [] | null | 0 |
If john is wise or strong then someone is both not patient and rich and vice versa.
Everyone who is not brave or generous is either humble or happy.
Everyone who is both brave and wise is either old or not curious.
Everyone who is brave is both generous and creative and vice versa.
If mary is either not kind or not rich then john is both not funny and patient and vice versa.
Everyone who is not rich or not calm is not patient or not brave.
Everyone who is both not curious and creative is wise or kind and vice versa.
If someone is not funny or tall then someone is both not wise and not brave and vice versa.
If lucy is both brave and not brave then paul is strong or funny.
If fred is either kind or strong then susan is not wise.
If john is not generous then someone is either old or not kind and vice versa.
If fred is generous or humble then someone is either kind or not humble.
Everyone who is not quiet or not wise is both wise and not brave and vice versa.
Everyone who is not happy or rich is both happy and not strong and vice versa.
Everyone who is either brave or humble is not calm or not creative and vice versa.
Everyone who is both calm and patient is not brave and vice versa.
Fred is generous or not calm.
Someone is not tall.
Someone is either not patient or not tall.
Paul is quiet or happy. | Paul is happy. | entailment | (((wise(john)|strong(john)))<=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:((~brave(X)|generous(X))=>(humble(X)<~>happy(X))))&
(![X]:((brave(X)&wise(X))=>(old(X)<~>~curious(X))))&
(![X]:(brave(X)<=>(generous(X)&creative(X))))&
(((~kind(mary)<~>~rich(mary)))<=>((~funny(john)&patient(john))))&
(![X]:((~rich(X)|~calm(X))=>(~patient(X)|~brave(X))))&
(![X]:((~curious(X)&creative(X))<=>(wise(X)|kind(X))))&
((?[X]:((~funny(X)|tall(X))))<=>(?[X]:((~wise(X)&~brave(X)))))&
(((brave(lucy)&~brave(lucy)))=>((strong(paul)|funny(paul))))&
(((kind(fred)<~>strong(fred)))=>(~wise(susan)))&
((~generous(john))<=>(?[X]:((old(X)<~>~kind(X)))))&
(((generous(fred)|humble(fred)))=>(?[X]:((kind(X)<~>~humble(X)))))&
(![X]:((~quiet(X)|~wise(X))<=>(wise(X)&~brave(X))))&
(![X]:((~happy(X)|rich(X))<=>(happy(X)&~strong(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~calm(X)|~creative(X))))&
(![X]:((calm(X)&patient(X))<=>~brave(X)))&
((generous(fred)|~calm(fred)))&
(?[X]:(~tall(X)))&
(?[X]:((~patient(X)<~>~tall(X))))&
((quiet(paul)|happy(paul))) | happy(paul) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1334926223666881984762716
% SZS output start Proof for 1334926223666881984762716
14. ! [X0] : ((rich(X0) | ~happy(X0)) <=> (~strong(X0) & happy(X0))) [input p13]
21. ~happy(paul) [input hypothesis]
60. ! [X0] : (((rich(X0) | ~happy(X0)) | (strong(X0) | ~happy(X0))) & ((~strong(X0) & happy(X0)) | (~rich(X0) & happy(X0)))) [nnf transformation 14]
61. ! [X0] : ((rich(X0) | ~happy(X0) | strong(X0) | ~happy(X0)) & ((~strong(X0) & happy(X0)) | (~rich(X0) & happy(X0)))) [flattening 60]
119. happy(X0) | happy(X0) [cnf transformation 61]
138. ~happy(paul) [cnf transformation 21]
139. happy(X0) [duplicate literal removal 119]
293. $false [subsumption resolution 138,139]
% SZS output end Proof for 1334926223666881984762716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either curious or not humble then someone is not wise and vice versa.
If someone is not tall or not calm then susan is not happy.
If alice is both wise and not quiet then someone is wise and vice versa.
If someone is funny then lucy is either not happy or not tall and vice versa.
If someone is old then fred is both rich and not strong.
Everyone who is not kind or not generous is both old and not generous.
If alice is both not wise and not happy then john is either not quiet or not tall and vice versa.
If fred is either creative or patient then paul is both not happy and not brave.
Everyone who is patient or not creative is either generous or not old.
Everyone who is rich is not old or old and vice versa.
Everyone who is rich is both strong and kind and vice versa.
Everyone who is both generous and strong is either funny or old and vice versa.
Everyone who is either not old or wise is either rich or not old.
If lucy is both curious and wise then susan is old and vice versa.
Susan is curious or not quiet.
Someone is happy.
Someone is both rich and not calm.
John is both tall and not brave.
Paul is patient or not humble.
Someone is brave or not humble. | Paul is curious. | entailment | ((?[X]:((curious(X)<~>~humble(X))))<=>(?[X]:(~wise(X))))&
((?[X]:((~tall(X)|~calm(X))))=>(~happy(susan)))&
(((wise(alice)&~quiet(alice)))<=>(?[X]:(wise(X))))&
((?[X]:(funny(X)))<=>((~happy(lucy)<~>~tall(lucy))))&
((?[X]:(old(X)))=>((rich(fred)&~strong(fred))))&
(![X]:((~kind(X)|~generous(X))=>(old(X)&~generous(X))))&
(((~wise(alice)&~happy(alice)))<=>((~quiet(john)<~>~tall(john))))&
(((creative(fred)<~>patient(fred)))=>((~happy(paul)&~brave(paul))))&
(![X]:((patient(X)|~creative(X))=>(generous(X)<~>~old(X))))&
(![X]:(rich(X)<=>(~old(X)|old(X))))&
(![X]:(rich(X)<=>(strong(X)&kind(X))))&
(![X]:((generous(X)&strong(X))<=>(funny(X)<~>old(X))))&
(![X]:((~old(X)<~>wise(X))=>(rich(X)<~>~old(X))))&
(((curious(lucy)&wise(lucy)))<=>(old(susan)))&
((curious(susan)|~quiet(susan)))&
(?[X]:(happy(X)))&
(?[X]:((rich(X)&~calm(X))))&
((tall(john)&~brave(john)))&
((patient(paul)|~humble(paul)))&
(?[X]:((brave(X)|~humble(X)))) | curious(paul) | [
"p0",
"p4",
"p5",
"p8",
"p9",
"p10",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 533135469206505999375801
% SZS output start Proof for 533135469206505999375801
1. ? [X0] : (curious(X0) <~> ~humble(X0)) <=> ? [X0] : ~wise(X0) [input p0]
5. ? [X0] : old(X0) => (~strong(fred) & rich(fred)) [input p4]
6. ! [X0] : ((~generous(X0) | ~kind(X0)) => (~generous(X0) & old(X0))) [input p5]
9. ! [X0] : ((~creative(X0) | patient(X0)) => (generous(X0) <~> ~old(X0))) [input p8]
10. ! [X0] : (rich(X0) <=> (old(X0) | ~old(X0))) [input p9]
11. ! [X0] : (rich(X0) <=> (kind(X0) & strong(X0))) [input p10]
13. ! [X0] : ((~old(X0) <~> wise(X0)) => (rich(X0) <~> ~old(X0))) [input p12]
19. ~humble(paul) | patient(paul) [input p18]
21. ~curious(paul) [input hypothesis]
22. ? [X0] : (curious(X0) <~> ~humble(X0)) <=> ? [X1] : ~wise(X1) [rectify 1]
24. (~strong(fred) & rich(fred)) | ! [X0] : ~old(X0) [ennf transformation 5]
25. ! [X0] : ((~generous(X0) & old(X0)) | (generous(X0) & kind(X0))) [ennf transformation 6]
27. ! [X0] : ((generous(X0) <~> ~old(X0)) | (creative(X0) & ~patient(X0))) [ennf transformation 9]
28. ! [X0] : ((rich(X0) <~> ~old(X0)) | (~old(X0) <=> wise(X0))) [ennf transformation 13]
29. (? [X0] : ((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | ! [X1] : wise(X1)) & (? [X1] : ~wise(X1) | ! [X0] : ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0)))) [nnf transformation 22]
30. (? [X0] : ((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | ! [X1] : wise(X1)) & (? [X2] : ~wise(X2) | ! [X3] : ((curious(X3) | humble(X3)) & (~humble(X3) | ~curious(X3)))) [rectify 29]
31. ? [X0] : ((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) => ((humble(sK0) | ~curious(sK0)) & (~humble(sK0) | curious(sK0))) [choice axiom]
32. ? [X2] : ~wise(X2) => ~wise(sK1) [choice axiom]
33. (((humble(sK0) | ~curious(sK0)) & (~humble(sK0) | curious(sK0))) | ! [X1] : wise(X1)) & (~wise(sK1) | ! [X3] : ((curious(X3) | humble(X3)) & (~humble(X3) | ~curious(X3)))) [skolemisation 30,32,31]
46. ! [X0] : (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (creative(X0) & ~patient(X0))) [nnf transformation 27]
47. ! [X0] : ((rich(X0) | (~old(X0) & old(X0))) & ((old(X0) | ~old(X0)) | ~rich(X0))) [nnf transformation 10]
48. ! [X0] : ((rich(X0) | (~old(X0) & old(X0))) & (old(X0) | ~old(X0) | ~rich(X0))) [flattening 47]
49. ! [X0] : ((rich(X0) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | ~rich(X0))) [nnf transformation 11]
50. ! [X0] : ((rich(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | ~rich(X0))) [flattening 49]
53. ! [X0] : (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0)))) [nnf transformation 28]
63. ~wise(sK1) | curious(X3) | humble(X3) [cnf transformation 33]
76. ~strong(fred) | ~old(X0) [cnf transformation 24]
78. generous(X0) | old(X0) [cnf transformation 25]
93. old(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 46]
96. rich(X0) | old(X0) [cnf transformation 48]
97. ~old(X0) | rich(X0) [cnf transformation 48]
98. strong(X0) | ~rich(X0) [cnf transformation 50]
109. old(X0) | ~rich(X0) | wise(X0) | old(X0) [cnf transformation 53]
120. ~humble(paul) | patient(paul) [cnf transformation 19]
122. ~curious(paul) [cnf transformation 21]
124. old(X0) | ~rich(X0) | wise(X0) [duplicate literal removal 109]
126. 1 <=> ! [X1] : wise(X1) [avatar definition]
127. wise(X1) <- (1) [avatar component clause 126]
139. 4 <=> ! [X3] : (curious(X3) | humble(X3)) [avatar definition]
140. humble(X3) | curious(X3) <- (4) [avatar component clause 139]
142. 5 <=> wise(sK1) [avatar definition]
144. ~wise(sK1) <- (~5) [avatar component clause 142]
145. 4 | ~5 [avatar split clause 63,142,139]
200. 18 <=> ! [X0] : ~old(X0) [avatar definition]
201. ~old(X0) <- (18) [avatar component clause 200]
203. 19 <=> strong(fred) [avatar definition]
205. ~strong(fred) <- (~19) [avatar component clause 203]
206. 18 | ~19 [avatar split clause 76,203,200]
251. ~patient(X0) | old(X0) [subsumption resolution 93,78]
254. rich(X0) [subsumption resolution 96,97]
256. strong(X0) [subsumption resolution 98,254]
261. old(X0) | wise(X0) [subsumption resolution 124,254]
288. 33 <=> patient(paul) [avatar definition]
290. patient(paul) <- (33) [avatar component clause 288]
292. 34 <=> humble(paul) [avatar definition]
294. ~humble(paul) <- (~34) [avatar component clause 292]
295. 33 | ~34 [avatar split clause 120,292,288]
309. $false <- (~19) [subsumption resolution 205,256]
310. 19 [avatar contradiction clause 309]
315. wise(X0) <- (18) [resolution 261,201]
322. 1 | ~18 [avatar split clause 315,200,126]
325. $false <- (1, ~5) [resolution 144,127]
326. ~1 | 5 [avatar contradiction clause 325]
328. curious(paul) <- (4, ~34) [resolution 140,294]
332. $false <- (4, ~34) [subsumption resolution 328,122]
333. ~4 | 34 [avatar contradiction clause 332]
336. old(paul) <- (33) [resolution 290,251]
337. $false <- (18, 33) [subsumption resolution 336,201]
338. ~18 | ~33 [avatar contradiction clause 337]
339. $false [avatar sat refutation 145,206,295,310,322,326,333,338]
% SZS output end Proof for 533135469206505999375801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not kind or creative then alice is both quiet and not humble and vice versa. If susan is either wise or not generous then someone is either not brave or rich and vice versa. If alice is both not calm and not curious then someone is either happy or strong and vice versa. Everyone who is tall or not tall is both kind and humble. If someone is generous then john is both brave and curious. Everyone who is both old and not rich is either humble or not brave. If someone is not patient then lucy is calm and vice versa. Everyone who is both humble and not kind is rich or creative and vice versa. Everyone who is both not brave and not curious is either creative or not happy and vice versa. If someone is either generous or not tall then someone is not curious or curious and vice versa. If lucy is humble or funny then someone is both quiet and wise. If john is not old then someone is both not tall and not wise and vice versa. If someone is quiet or not curious then paul is not patient or not tall and vice versa. Everyone who is tall or generous is either funny or not funny and vice versa. If susan is generous or strong then lucy is either patient or old and vice versa. If someone is either happy or not happy then fred is old and vice versa. Someone is old. Susan is either creative or not patient. John is not patient or not funny. Someone is patient. Susan is either not rich or strong. Someone is both not happy and patient. | Lucy is not wise. | neutral | (((~kind(fred)<~>creative(fred)))<=>((quiet(alice)&~humble(alice))))&
(((wise(susan)<~>~generous(susan)))<=>(?[X]:((~brave(X)<~>rich(X)))))&
(((~calm(alice)&~curious(alice)))<=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:((tall(X)|~tall(X))=>(kind(X)&humble(X))))&
((?[X]:(generous(X)))=>((brave(john)&curious(john))))&
(![X]:((old(X)&~rich(X))=>(humble(X)<~>~brave(X))))&
((?[X]:(~patient(X)))<=>(calm(lucy)))&
(![X]:((humble(X)&~kind(X))<=>(rich(X)|creative(X))))&
(![X]:((~brave(X)&~curious(X))<=>(creative(X)<~>~happy(X))))&
((?[X]:((generous(X)<~>~tall(X))))<=>(?[X]:((~curious(X)|curious(X)))))&
(((humble(lucy)|funny(lucy)))=>(?[X]:((quiet(X)&wise(X)))))&
((~old(john))<=>(?[X]:((~tall(X)&~wise(X)))))&
((?[X]:((quiet(X)|~curious(X))))<=>((~patient(paul)|~tall(paul))))&
(![X]:((tall(X)|generous(X))<=>(funny(X)<~>~funny(X))))&
(((generous(susan)|strong(susan)))<=>((patient(lucy)<~>old(lucy))))&
((?[X]:((happy(X)<~>~happy(X))))<=>(old(fred)))&
(?[X]:(old(X)))&
((creative(susan)<~>~patient(susan)))&
((~patient(john)|~funny(john)))&
(?[X]:(patient(X)))&
((~rich(susan)<~>strong(susan)))&
(?[X]:((~happy(X)&patient(X)))) | ~wise(lucy) | [] | null | 0 |
If someone is either humble or not old then lucy is both wise and not tall. If someone is generous or old then someone is generous. If mary is not calm then susan is either rich or funny. Everyone who is strong is both calm and quiet. Everyone who is not patient or not strong is not happy or happy. If paul is both patient and old then paul is either not funny or quiet and vice versa. Everyone who is not curious is rich or funny. If lucy is patient then someone is both rich and funny. Everyone who is either curious or brave is both not rich and not happy and vice versa. Everyone who is curious is not humble. Everyone who is kind or patient is generous. If someone is either rich or wise then someone is either happy or not rich and vice versa. Everyone who is strong or kind is curious or creative and vice versa. If susan is not strong then fred is either not wise or not quiet and vice versa. If paul is brave then someone is not tall. If lucy is not strong or not patient then john is not rich or wise and vice versa. Someone is either rich or not brave. Paul is both humble and generous. Fred is either not humble or curious. Someone is not kind. Someone is either not rich or not patient. Lucy is either not humble or not calm. Someone is humble. Paul is quiet. | Paul is not quiet. | contradiction | ((?[X]:((humble(X)<~>~old(X))))=>((wise(lucy)&~tall(lucy))))&
((?[X]:((generous(X)|old(X))))=>(?[X]:(generous(X))))&
((~calm(mary))=>((rich(susan)<~>funny(susan))))&
(![X]:(strong(X)=>(calm(X)&quiet(X))))&
(![X]:((~patient(X)|~strong(X))=>(~happy(X)|happy(X))))&
(((patient(paul)&old(paul)))<=>((~funny(paul)<~>quiet(paul))))&
(![X]:(~curious(X)=>(rich(X)|funny(X))))&
((patient(lucy))=>(?[X]:((rich(X)&funny(X)))))&
(![X]:((curious(X)<~>brave(X))<=>(~rich(X)&~happy(X))))&
(![X]:(curious(X)=>~humble(X)))&
(![X]:((kind(X)|patient(X))=>generous(X)))&
((?[X]:((rich(X)<~>wise(X))))<=>(?[X]:((happy(X)<~>~rich(X)))))&
(![X]:((strong(X)|kind(X))<=>(curious(X)|creative(X))))&
((~strong(susan))<=>((~wise(fred)<~>~quiet(fred))))&
((brave(paul))=>(?[X]:(~tall(X))))&
(((~strong(lucy)|~patient(lucy)))<=>((~rich(john)|wise(john))))&
(?[X]:((rich(X)<~>~brave(X))))&
((humble(paul)&generous(paul)))&
((~humble(fred)<~>curious(fred)))&
(?[X]:(~kind(X)))&
(?[X]:((~rich(X)<~>~patient(X))))&
((~humble(lucy)<~>~calm(lucy)))&
(?[X]:(humble(X)))&
(quiet(paul)) | ~quiet(paul) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2899250561869314453281054
% SZS output start Proof for 2899250561869314453281054
24. quiet(paul) [input p23]
25. ~quiet(paul) [input hypothesis]
134. quiet(paul) [cnf transformation 24]
135. ~quiet(paul) [cnf transformation 25]
175. 10 <=> quiet(paul) [avatar definition]
310. 10 [avatar split clause 134,175]
311. ~10 [avatar split clause 135,175]
312. $false [avatar sat refutation 310,311]
% SZS output end Proof for 2899250561869314453281054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny then fred is both not curious and creative.
If john is either tall or quiet then someone is either not calm or not curious.
If fred is either not brave or tall then paul is calm.
Everyone who is not kind or not rich is either calm or wise.
Everyone who is either not generous or rich is both quiet and old.
If susan is both not kind and not calm then susan is either old or not happy.
Everyone who is both not funny and rich is both not happy and patient and vice versa.
If someone is both brave and tall then someone is quiet or not calm.
Everyone who is not rich or patient is both old and not happy and vice versa.
If someone is both quiet and strong then someone is not brave or old and vice versa.
If someone is not strong then alice is both happy and not brave.
Everyone who is both humble and funny is old.
Everyone who is either quiet or rich is happy and vice versa.
Everyone who is not happy or not wise is not strong or not quiet and vice versa.
Someone is not patient or creative.
Lucy is not brave or not old.
Lucy is not humble or happy.
Someone is either not wise or curious. | John is not generous. | entailment | ((~funny(alice))=>((~curious(fred)&creative(fred))))&
(((tall(john)<~>quiet(john)))=>(?[X]:((~calm(X)<~>~curious(X)))))&
(((~brave(fred)<~>tall(fred)))=>(calm(paul)))&
(![X]:((~kind(X)|~rich(X))=>(calm(X)<~>wise(X))))&
(![X]:((~generous(X)<~>rich(X))=>(quiet(X)&old(X))))&
(((~kind(susan)&~calm(susan)))=>((old(susan)<~>~happy(susan))))&
(![X]:((~funny(X)&rich(X))<=>(~happy(X)&patient(X))))&
((?[X]:((brave(X)&tall(X))))=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:((~rich(X)|patient(X))<=>(old(X)&~happy(X))))&
((?[X]:((quiet(X)&strong(X))))<=>(?[X]:((~brave(X)|old(X)))))&
((?[X]:(~strong(X)))=>((happy(alice)&~brave(alice))))&
(![X]:((humble(X)&funny(X))=>old(X)))&
(![X]:((quiet(X)<~>rich(X))<=>happy(X)))&
(![X]:((~happy(X)|~wise(X))<=>(~strong(X)|~quiet(X))))&
(?[X]:((~patient(X)|creative(X))))&
((~brave(lucy)|~old(lucy)))&
((~humble(lucy)|happy(lucy)))&
(?[X]:((~wise(X)<~>curious(X)))) | ~generous(john) | [
"p4",
"p8",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8498790081031146237531095
% SZS output start Proof for 8498790081031146237531095
5. ! [X0] : ((~generous(X0) <~> rich(X0)) => (old(X0) & quiet(X0))) [input p4]
9. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (~happy(X0) & old(X0))) [input p8]
10. ? [X0] : (strong(X0) & quiet(X0)) <=> ? [X0] : (old(X0) | ~brave(X0)) [input p9]
11. ? [X0] : ~strong(X0) => (~brave(alice) & happy(alice)) [input p10]
13. ! [X0] : ((quiet(X0) <~> rich(X0)) <=> happy(X0)) [input p12]
14. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> (~quiet(X0) | ~strong(X0))) [input p13]
19. generous(john) [input hypothesis]
21. ? [X0] : (strong(X0) & quiet(X0)) <=> ? [X1] : (old(X1) | ~brave(X1)) [rectify 10]
32. ! [X0] : ((old(X0) & quiet(X0)) | (~generous(X0) <=> rich(X0))) [ennf transformation 5]
34. (~brave(alice) & happy(alice)) | ! [X0] : strong(X0) [ennf transformation 11]
40. ! [X0] : ((old(X0) & quiet(X0)) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) [nnf transformation 32]
46. ! [X0] : (((patient(X0) | ~rich(X0)) | (happy(X0) | ~old(X0))) & ((~happy(X0) & old(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 9]
47. ! [X0] : ((patient(X0) | ~rich(X0) | happy(X0) | ~old(X0)) & ((~happy(X0) & old(X0)) | (~patient(X0) & rich(X0)))) [flattening 46]
48. (? [X0] : (strong(X0) & quiet(X0)) | ! [X1] : (~old(X1) & brave(X1))) & (? [X1] : (old(X1) | ~brave(X1)) | ! [X0] : (~strong(X0) | ~quiet(X0))) [nnf transformation 21]
49. (? [X0] : (strong(X0) & quiet(X0)) | ! [X1] : (~old(X1) & brave(X1))) & (? [X2] : (old(X2) | ~brave(X2)) | ! [X3] : (~strong(X3) | ~quiet(X3))) [rectify 48]
50. ? [X0] : (strong(X0) & quiet(X0)) => (strong(sK2) & quiet(sK2)) [choice axiom]
51. ? [X2] : (old(X2) | ~brave(X2)) => (old(sK3) | ~brave(sK3)) [choice axiom]
52. ((strong(sK2) & quiet(sK2)) | ! [X1] : (~old(X1) & brave(X1))) & ((old(sK3) | ~brave(sK3)) | ! [X3] : (~strong(X3) | ~quiet(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ~happy(X0)) & (happy(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))))) [nnf transformation 13]
54. ! [X0] : (((~wise(X0) | ~happy(X0)) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | (wise(X0) & happy(X0)))) [nnf transformation 14]
55. ! [X0] : ((~wise(X0) | ~happy(X0) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | (wise(X0) & happy(X0)))) [flattening 54]
69. ~generous(X0) | quiet(X0) | ~rich(X0) [cnf transformation 40]
77. old(X0) | rich(X0) [cnf transformation 47]
79. ~happy(X0) | rich(X0) [cnf transformation 47]
83. quiet(sK2) | brave(X1) [cnf transformation 52]
84. quiet(sK2) | ~old(X1) [cnf transformation 52]
85. strong(sK2) | brave(X1) [cnf transformation 52]
88. ~brave(alice) | strong(X0) [cnf transformation 34]
92. ~rich(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 53]
93. ~quiet(X0) | ~strong(X0) | happy(X0) [cnf transformation 55]
100. generous(john) [cnf transformation 19]
157. 13 <=> ! [X1] : ~old(X1) [avatar definition]
158. ~old(X1) <- (13) [avatar component clause 157]
160. 14 <=> strong(sK2) [avatar definition]
162. strong(sK2) <- (14) [avatar component clause 160]
165. 15 <=> ! [X1] : brave(X1) [avatar definition]
166. brave(X1) <- (15) [avatar component clause 165]
167. 15 | 14 [avatar split clause 85,160,165]
169. 16 <=> quiet(sK2) [avatar definition]
171. quiet(sK2) <- (16) [avatar component clause 169]
172. 13 | 16 [avatar split clause 84,169,157]
173. 15 | 16 [avatar split clause 83,169,165]
175. 17 <=> ! [X3] : (~strong(X3) | ~quiet(X3)) [avatar definition]
176. ~strong(X3) | ~quiet(X3) <- (17) [avatar component clause 175]
187. 20 <=> ! [X0] : strong(X0) [avatar definition]
188. strong(X0) <- (20) [avatar component clause 187]
190. 21 <=> brave(alice) [avatar definition]
192. ~brave(alice) <- (~21) [avatar component clause 190]
193. 20 | ~21 [avatar split clause 88,190,187]
199. ~happy(X0) | ~quiet(X0) [subsumption resolution 92,79]
202. ~quiet(X0) | ~strong(X0) [subsumption resolution 93,199]
203. 17 [avatar split clause 202,175]
223. ~quiet(X3) <- (17, 20) [subsumption resolution 176,188]
226. rich(X0) <- (13) [resolution 77,158]
231. quiet(john) | ~rich(john) [resolution 69,100]
234. ~rich(john) <- (17, 20) [subsumption resolution 231,223]
235. $false <- (13, 17, 20) [subsumption resolution 234,226]
236. ~13 | ~17 | ~20 [avatar contradiction clause 235]
246. $false <- (16, 17, 20) [subsumption resolution 171,223]
247. ~16 | ~17 | ~20 [avatar contradiction clause 246]
253. $false <- (15, ~21) [subsumption resolution 192,166]
254. ~15 | 21 [avatar contradiction clause 253]
261. ~quiet(sK2) <- (14, 17) [resolution 176,162]
262. $false <- (14, 16, 17) [subsumption resolution 261,171]
263. ~14 | ~16 | ~17 [avatar contradiction clause 262]
264. $false [avatar sat refutation 167,172,173,193,203,236,247,254,263]
% SZS output end Proof for 8498790081031146237531095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not funny is not kind or calm and vice versa.
Everyone who is either not wise or not generous is humble and vice versa.
Everyone who is not generous or calm is creative.
Everyone who is calm is not generous or not tall and vice versa.
Everyone who is rich is both not curious and not brave and vice versa.
Everyone who is curious or calm is both humble and generous and vice versa.
Everyone who is old or not kind is both not strong and not creative.
If someone is not creative then someone is rich and vice versa.
If someone is both not curious and not humble then someone is either brave or rich and vice versa.
Everyone who is tall or brave is both humble and not old and vice versa.
Everyone who is not kind or curious is not patient.
If someone is not curious then fred is either not humble or not brave.
If someone is both not happy and kind then susan is either not patient or not funny.
Everyone who is humble or not quiet is rich or quiet and vice versa.
Everyone who is both brave and funny is either brave or funny.
Alice is either not patient or not creative.
Someone is creative or not tall.
Someone is happy.
Paul is not old or kind. | Fred is patient. | contradiction | (![X]:((~wise(X)&~funny(X))<=>(~kind(X)|calm(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>humble(X)))&
(![X]:((~generous(X)|calm(X))=>creative(X)))&
(![X]:(calm(X)<=>(~generous(X)|~tall(X))))&
(![X]:(rich(X)<=>(~curious(X)&~brave(X))))&
(![X]:((curious(X)|calm(X))<=>(humble(X)&generous(X))))&
(![X]:((old(X)|~kind(X))=>(~strong(X)&~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(rich(X))))&
((?[X]:((~curious(X)&~humble(X))))<=>(?[X]:((brave(X)<~>rich(X)))))&
(![X]:((tall(X)|brave(X))<=>(humble(X)&~old(X))))&
(![X]:((~kind(X)|curious(X))=>~patient(X)))&
((?[X]:(~curious(X)))=>((~humble(fred)<~>~brave(fred))))&
((?[X]:((~happy(X)&kind(X))))=>((~patient(susan)<~>~funny(susan))))&
(![X]:((humble(X)|~quiet(X))<=>(rich(X)|quiet(X))))&
(![X]:((brave(X)&funny(X))=>(brave(X)<~>funny(X))))&
((~patient(alice)<~>~creative(alice)))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:(happy(X)))&
((~old(paul)|kind(paul))) | patient(fred) | [
"p3",
"p4",
"p5",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 272413696175389931483652
% SZS output start Proof for 272413696175389931483652
4. ! [X0] : (calm(X0) <=> (~tall(X0) | ~generous(X0))) [input p3]
5. ! [X0] : (rich(X0) <=> (~brave(X0) & ~curious(X0))) [input p4]
6. ! [X0] : ((calm(X0) | curious(X0)) <=> (generous(X0) & humble(X0))) [input p5]
9. ? [X0] : (~humble(X0) & ~curious(X0)) <=> ? [X0] : (brave(X0) <~> rich(X0)) [input p8]
10. ! [X0] : ((brave(X0) | tall(X0)) <=> (~old(X0) & humble(X0))) [input p9]
11. ! [X0] : ((curious(X0) | ~kind(X0)) => ~patient(X0)) [input p10]
20. patient(fred) [input hypothesis]
22. ? [X0] : (~humble(X0) & ~curious(X0)) <=> ? [X1] : (brave(X1) <~> rich(X1)) [rectify 9]
28. ! [X0] : (~patient(X0) | (~curious(X0) & kind(X0))) [ennf transformation 11]
35. ! [X0] : ((calm(X0) | (tall(X0) & generous(X0))) & ((~tall(X0) | ~generous(X0)) | ~calm(X0))) [nnf transformation 4]
36. ! [X0] : ((calm(X0) | (tall(X0) & generous(X0))) & (~tall(X0) | ~generous(X0) | ~calm(X0))) [flattening 35]
37. ! [X0] : ((rich(X0) | (brave(X0) | curious(X0))) & ((~brave(X0) & ~curious(X0)) | ~rich(X0))) [nnf transformation 5]
38. ! [X0] : ((rich(X0) | brave(X0) | curious(X0)) & ((~brave(X0) & ~curious(X0)) | ~rich(X0))) [flattening 37]
39. ! [X0] : (((calm(X0) | curious(X0)) | (~generous(X0) | ~humble(X0))) & ((generous(X0) & humble(X0)) | (~calm(X0) & ~curious(X0)))) [nnf transformation 6]
40. ! [X0] : ((calm(X0) | curious(X0) | ~generous(X0) | ~humble(X0)) & ((generous(X0) & humble(X0)) | (~calm(X0) & ~curious(X0)))) [flattening 39]
46. (? [X0] : (~humble(X0) & ~curious(X0)) | ! [X1] : ((brave(X1) | ~rich(X1)) & (rich(X1) | ~brave(X1)))) & (? [X1] : ((~rich(X1) | ~brave(X1)) & (rich(X1) | brave(X1))) | ! [X0] : (humble(X0) | curious(X0))) [nnf transformation 22]
47. (? [X0] : (~humble(X0) & ~curious(X0)) | ! [X1] : ((brave(X1) | ~rich(X1)) & (rich(X1) | ~brave(X1)))) & (? [X2] : ((~rich(X2) | ~brave(X2)) & (rich(X2) | brave(X2))) | ! [X3] : (humble(X3) | curious(X3))) [rectify 46]
48. ? [X0] : (~humble(X0) & ~curious(X0)) => (~humble(sK2) & ~curious(sK2)) [choice axiom]
49. ? [X2] : ((~rich(X2) | ~brave(X2)) & (rich(X2) | brave(X2))) => ((~rich(sK3) | ~brave(sK3)) & (rich(sK3) | brave(sK3))) [choice axiom]
50. ((~humble(sK2) & ~curious(sK2)) | ! [X1] : ((brave(X1) | ~rich(X1)) & (rich(X1) | ~brave(X1)))) & (((~rich(sK3) | ~brave(sK3)) & (rich(sK3) | brave(sK3))) | ! [X3] : (humble(X3) | curious(X3))) [skolemisation 47,49,48]
51. ! [X0] : (((brave(X0) | tall(X0)) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | (~brave(X0) & ~tall(X0)))) [nnf transformation 10]
52. ! [X0] : ((brave(X0) | tall(X0) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | (~brave(X0) & ~tall(X0)))) [flattening 51]
73. tall(X0) | calm(X0) [cnf transformation 36]
75. ~brave(X0) | ~rich(X0) [cnf transformation 38]
76. brave(X0) | rich(X0) | curious(X0) [cnf transformation 38]
78. ~calm(X0) | humble(X0) [cnf transformation 40]
90. ~humble(sK2) | rich(X1) | ~brave(X1) [cnf transformation 50]
91. ~humble(sK2) | brave(X1) | ~rich(X1) [cnf transformation 50]
92. ~tall(X0) | humble(X0) [cnf transformation 52]
98. ~patient(X0) | ~curious(X0) [cnf transformation 28]
111. patient(fred) [cnf transformation 20]
118. 1 <=> ! [X1] : ~rich(X1) [avatar definition]
119. ~rich(X1) <- (1) [avatar component clause 118]
133. ~humble(sK2) | ~rich(X1) [subsumption resolution 91,75]
135. 5 <=> humble(sK2) [avatar definition]
137. ~humble(sK2) <- (~5) [avatar component clause 135]
138. 1 | ~5 [avatar split clause 133,135,118]
139. ~humble(sK2) | ~brave(X1) [subsumption resolution 90,75]
141. 6 <=> ! [X1] : ~brave(X1) [avatar definition]
142. ~brave(X1) <- (6) [avatar component clause 141]
143. 6 | ~5 [avatar split clause 139,135,141]
154. 8 <=> ! [X3] : humble(X3) [avatar definition]
155. humble(X3) <- (8) [avatar component clause 154]
176. 13 <=> brave(fred) [avatar definition]
177. brave(fred) <- (13) [avatar component clause 176]
178. ~brave(fred) <- (~13) [avatar component clause 176]
210. $false <- (~5, 8) [subsumption resolution 137,155]
211. 5 | ~8 [avatar contradiction clause 210]
224. humble(X0) | calm(X0) [resolution 92,73]
225. humble(X0) [subsumption resolution 224,78]
226. 8 [avatar split clause 225,154]
230. ~curious(fred) [resolution 98,111]
243. rich(fred) | curious(fred) <- (~13) [resolution 76,178]
248. curious(fred) <- (1, ~13) [subsumption resolution 243,119]
249. $false <- (1, ~13) [subsumption resolution 248,230]
250. ~1 | 13 [avatar contradiction clause 249]
254. $false <- (6, 13) [subsumption resolution 177,142]
255. ~6 | ~13 [avatar contradiction clause 254]
256. $false [avatar sat refutation 138,143,211,226,250,255]
% SZS output end Proof for 272413696175389931483652
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not funny is patient. If someone is not old or not humble then fred is both old and humble. Everyone who is happy or humble is not funny or not happy. Everyone who is either not rich or quiet is not generous or happy and vice versa. Everyone who is not humble or humble is not creative and vice versa. Everyone who is both generous and not kind is not patient and vice versa. Everyone who is humble or strong is old. Everyone who is not kind or not calm is both creative and wise and vice versa. Everyone who is not curious or curious is generous and vice versa. Everyone who is not generous is either not quiet or rich. Everyone who is not happy or not quiet is both wise and not curious. Everyone who is both not patient and not funny is both not curious and generous and vice versa. If paul is not humble then someone is either wise or brave and vice versa. If someone is quiet then paul is generous and vice versa. Paul is not humble or quiet. Someone is either not humble or not quiet. Someone is not generous or not tall. | Paul is not curious. | contradiction | (![X]:((~strong(X)&~funny(X))=>patient(X)))&
((?[X]:((~old(X)|~humble(X))))=>((old(fred)&humble(fred))))&
(![X]:((happy(X)|humble(X))=>(~funny(X)|~happy(X))))&
(![X]:((~rich(X)<~>quiet(X))<=>(~generous(X)|happy(X))))&
(![X]:((~humble(X)|humble(X))<=>~creative(X)))&
(![X]:((generous(X)&~kind(X))<=>~patient(X)))&
(![X]:((humble(X)|strong(X))=>old(X)))&
(![X]:((~kind(X)|~calm(X))<=>(creative(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~happy(X)|~quiet(X))=>(wise(X)&~curious(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((~humble(paul))<=>(?[X]:((wise(X)<~>brave(X)))))&
((?[X]:(quiet(X)))<=>(generous(paul)))&
((~humble(paul)|quiet(paul)))&
(?[X]:((~humble(X)<~>~quiet(X))))&
(?[X]:((~generous(X)|~tall(X)))) | ~curious(paul) | [
"p4",
"p5",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7547234284894892577199550
% SZS output start Proof for 7547234284894892577199550
5. ! [X0] : ((humble(X0) | ~humble(X0)) <=> ~creative(X0)) [input p4]
6. ! [X0] : ((~kind(X0) & generous(X0)) <=> ~patient(X0)) [input p5]
8. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> (wise(X0) & creative(X0))) [input p7]
9. ! [X0] : ((curious(X0) | ~curious(X0)) <=> generous(X0)) [input p8]
12. ! [X0] : ((~funny(X0) & ~patient(X0)) <=> (generous(X0) & ~curious(X0))) [input p11]
18. ~curious(paul) [input hypothesis]
30. ! [X0] : (((humble(X0) | ~humble(X0)) | creative(X0)) & (~creative(X0) | (~humble(X0) & humble(X0)))) [nnf transformation 5]
31. ! [X0] : ((humble(X0) | ~humble(X0) | creative(X0)) & (~creative(X0) | (~humble(X0) & humble(X0)))) [flattening 30]
32. ! [X0] : (((~kind(X0) & generous(X0)) | patient(X0)) & (~patient(X0) | (kind(X0) | ~generous(X0)))) [nnf transformation 6]
33. ! [X0] : (((~kind(X0) & generous(X0)) | patient(X0)) & (~patient(X0) | kind(X0) | ~generous(X0))) [flattening 32]
34. ! [X0] : (((~calm(X0) | ~kind(X0)) | (~wise(X0) | ~creative(X0))) & ((wise(X0) & creative(X0)) | (calm(X0) & kind(X0)))) [nnf transformation 8]
35. ! [X0] : ((~calm(X0) | ~kind(X0) | ~wise(X0) | ~creative(X0)) & ((wise(X0) & creative(X0)) | (calm(X0) & kind(X0)))) [flattening 34]
36. ! [X0] : (((curious(X0) | ~curious(X0)) | ~generous(X0)) & (generous(X0) | (~curious(X0) & curious(X0)))) [nnf transformation 9]
37. ! [X0] : ((curious(X0) | ~curious(X0) | ~generous(X0)) & (generous(X0) | (~curious(X0) & curious(X0)))) [flattening 36]
39. ! [X0] : (((~funny(X0) & ~patient(X0)) | (~generous(X0) | curious(X0))) & ((generous(X0) & ~curious(X0)) | (funny(X0) | patient(X0)))) [nnf transformation 12]
40. ! [X0] : (((~funny(X0) & ~patient(X0)) | ~generous(X0) | curious(X0)) & ((generous(X0) & ~curious(X0)) | funny(X0) | patient(X0))) [flattening 39]
61. ~creative(X0) | humble(X0) [cnf transformation 31]
62. ~creative(X0) | ~humble(X0) [cnf transformation 31]
66. ~kind(X0) | patient(X0) [cnf transformation 33]
67. creative(X0) | kind(X0) [cnf transformation 35]
72. generous(X0) | curious(X0) [cnf transformation 37]
73. ~curious(X0) | generous(X0) [cnf transformation 37]
83. ~patient(X0) | ~generous(X0) | curious(X0) [cnf transformation 40]
94. ~curious(paul) [cnf transformation 18]
104. ~creative(X0) [subsumption resolution 61,62]
106. kind(X0) [subsumption resolution 67,104]
107. generous(X0) [subsumption resolution 72,73]
109. ~patient(X0) | curious(X0) [subsumption resolution 83,107]
148. patient(X0) [resolution 66,106]
149. curious(X0) [resolution 109,148]
150. $false [resolution 149,94]
% SZS output end Proof for 7547234284894892577199550
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and creative is happy or generous. If alice is not brave or not tall then someone is both not generous and not creative and vice versa. If john is not humble or old then alice is not creative or wise and vice versa. If john is rich or not creative then susan is generous or funny. Everyone who is not old is not curious. If someone is both not funny and not happy then someone is quiet and vice versa. If mary is both not funny and calm then john is rich. Everyone who is brave is not calm and vice versa. Everyone who is rich is not generous or not humble and vice versa. Everyone who is kind is not old. If someone is both strong and happy then someone is either creative or not quiet. Everyone who is either calm or not generous is generous or not humble. Everyone who is rich is not patient and vice versa. Everyone who is strong or wise is either not generous or not quiet and vice versa. Everyone who is both brave and curious is both quiet and not kind and vice versa. Everyone who is patient or not rich is not brave or quiet and vice versa. Mary is tall. Alice is both not kind and strong. Fred is old. Fred is either not rich or not happy. Paul is not strong or patient. Fred is humble. Lucy is not patient or patient. Someone is wise or not calm. | Alice is generous. | entailment | (![X]:((~creative(X)&creative(X))=>(happy(X)|generous(X))))&
(((~brave(alice)|~tall(alice)))<=>(?[X]:((~generous(X)&~creative(X)))))&
(((~humble(john)|old(john)))<=>((~creative(alice)|wise(alice))))&
(((rich(john)|~creative(john)))=>((generous(susan)|funny(susan))))&
(![X]:(~old(X)=>~curious(X)))&
((?[X]:((~funny(X)&~happy(X))))<=>(?[X]:(quiet(X))))&
(((~funny(mary)&calm(mary)))=>(rich(john)))&
(![X]:(brave(X)<=>~calm(X)))&
(![X]:(rich(X)<=>(~generous(X)|~humble(X))))&
(![X]:(kind(X)=>~old(X)))&
((?[X]:((strong(X)&happy(X))))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((calm(X)<~>~generous(X))=>(generous(X)|~humble(X))))&
(![X]:(rich(X)<=>~patient(X)))&
(![X]:((strong(X)|wise(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((brave(X)&curious(X))<=>(quiet(X)&~kind(X))))&
(![X]:((patient(X)|~rich(X))<=>(~brave(X)|quiet(X))))&
(tall(mary))&
((~kind(alice)&strong(alice)))&
(old(fred))&
((~rich(fred)<~>~happy(fred)))&
((~strong(paul)|patient(paul)))&
(humble(fred))&
((~patient(lucy)|patient(lucy)))&
(?[X]:((wise(X)|~calm(X)))) | generous(alice) | [
"p8",
"p12",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7680427356529734218262777
% SZS output start Proof for 7680427356529734218262777
9. ! [X0] : (rich(X0) <=> (~humble(X0) | ~generous(X0))) [input p8]
13. ! [X0] : (rich(X0) <=> ~patient(X0)) [input p12]
14. ! [X0] : ((wise(X0) | strong(X0)) <=> (~generous(X0) <~> ~quiet(X0))) [input p13]
16. ! [X0] : ((~rich(X0) | patient(X0)) <=> (quiet(X0) | ~brave(X0))) [input p15]
18. strong(alice) & ~kind(alice) [input p17]
25. ~generous(alice) [input hypothesis]
52. ! [X0] : ((rich(X0) | (humble(X0) & generous(X0))) & ((~humble(X0) | ~generous(X0)) | ~rich(X0))) [nnf transformation 9]
53. ! [X0] : ((rich(X0) | (humble(X0) & generous(X0))) & (~humble(X0) | ~generous(X0) | ~rich(X0))) [flattening 52]
59. ! [X0] : ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))) [nnf transformation 13]
60. ! [X0] : (((wise(X0) | strong(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (~wise(X0) & ~strong(X0)))) [nnf transformation 14]
61. ! [X0] : ((wise(X0) | strong(X0) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (~wise(X0) & ~strong(X0)))) [flattening 60]
64. ! [X0] : (((~rich(X0) | patient(X0)) | (~quiet(X0) & brave(X0))) & ((quiet(X0) | ~brave(X0)) | (rich(X0) & ~patient(X0)))) [nnf transformation 16]
65. ! [X0] : ((~rich(X0) | patient(X0) | (~quiet(X0) & brave(X0))) & (quiet(X0) | ~brave(X0) | (rich(X0) & ~patient(X0)))) [flattening 64]
89. rich(X0) | generous(X0) [cnf transformation 53]
96. ~patient(X0) | ~rich(X0) [cnf transformation 59]
97. patient(X0) | rich(X0) [cnf transformation 59]
100. ~strong(X0) | generous(X0) | quiet(X0) [cnf transformation 61]
111. ~rich(X0) | patient(X0) | ~quiet(X0) [cnf transformation 65]
114. strong(alice) [cnf transformation 18]
122. ~generous(alice) [cnf transformation 25]
229. ~quiet(X0) | patient(X0) [subsumption resolution 111,97]
281. generous(alice) | quiet(alice) [resolution 100,114]
282. quiet(alice) [subsumption resolution 281,122]
297. patient(alice) [resolution 282,229]
299. ~rich(alice) [resolution 297,96]
459. generous(alice) [resolution 299,89]
460. $false [subsumption resolution 459,122]
% SZS output end Proof for 7680427356529734218262777
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then someone is either not old or not rich and vice versa.
Everyone who is either tall or brave is both not humble and humble and vice versa.
If mary is either humble or kind then someone is both humble and generous.
If someone is not funny then paul is either not calm or not tall.
If fred is either brave or happy then someone is not funny or not generous and vice versa.
Everyone who is funny is both not funny and not generous and vice versa.
Everyone who is either curious or not strong is either not calm or old and vice versa.
Everyone who is not funny is either not curious or not happy.
If someone is happy or quiet then someone is both funny and calm and vice versa.
If mary is either funny or humble then susan is either not tall or not generous and vice versa.
If fred is not funny or patient then someone is not old and vice versa.
If paul is quiet or humble then someone is either not rich or not patient and vice versa.
Everyone who is not kind or rich is creative.
Everyone who is both calm and not creative is either generous or not calm.
Everyone who is either tall or wise is tall.
Everyone who is old or not rich is either wise or strong.
Alice is not old or not strong.
John is not funny.
Someone is either not rich or humble.
Someone is not humble.
Alice is wise.
Mary is calm. | Paul is not tall. | neutral | ((?[X]:(~old(X)))<=>(?[X]:((~old(X)<~>~rich(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(~humble(X)&humble(X))))&
(((humble(mary)<~>kind(mary)))=>(?[X]:((humble(X)&generous(X)))))&
((?[X]:(~funny(X)))=>((~calm(paul)<~>~tall(paul))))&
(((brave(fred)<~>happy(fred)))<=>(?[X]:((~funny(X)|~generous(X)))))&
(![X]:(funny(X)<=>(~funny(X)&~generous(X))))&
(![X]:((curious(X)<~>~strong(X))<=>(~calm(X)<~>old(X))))&
(![X]:(~funny(X)=>(~curious(X)<~>~happy(X))))&
((?[X]:((happy(X)|quiet(X))))<=>(?[X]:((funny(X)&calm(X)))))&
(((funny(mary)<~>humble(mary)))<=>((~tall(susan)<~>~generous(susan))))&
(((~funny(fred)|patient(fred)))<=>(?[X]:(~old(X))))&
(((quiet(paul)|humble(paul)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
(![X]:((~kind(X)|rich(X))=>creative(X)))&
(![X]:((calm(X)&~creative(X))=>(generous(X)<~>~calm(X))))&
(![X]:((tall(X)<~>wise(X))=>tall(X)))&
(![X]:((old(X)|~rich(X))=>(wise(X)<~>strong(X))))&
((~old(alice)|~strong(alice)))&
(~funny(john))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:(~humble(X)))&
(wise(alice))&
(calm(mary)) | ~tall(paul) | [] | null | 0 |
If someone is both not humble and patient then paul is both not calm and humble and vice versa.
Everyone who is patient is old.
Everyone who is both tall and not strong is brave.
Everyone who is both not rich and not calm is old or quiet.
If lucy is either creative or tall then someone is not creative or not brave.
Everyone who is not tall or rich is humble or old and vice versa.
Everyone who is not patient is either not happy or not generous.
If alice is wise or rich then someone is happy or not brave.
If lucy is either creative or not happy then someone is old and vice versa.
If paul is wise or happy then paul is both tall and not old.
Everyone who is either not tall or strong is rich or happy and vice versa.
Everyone who is old or creative is both not strong and not calm and vice versa.
Everyone who is both happy and generous is not quiet or not old.
Everyone who is either not old or not tall is funny or tall and vice versa.
Everyone who is both funny and not patient is not calm or humble.
Everyone who is rich is either humble or not brave and vice versa.
Lucy is rich.
Mary is both funny and generous.
Paul is quiet or tall.
Fred is brave or not happy.
Paul is not rich or tall.
Fred is not tall or quiet.
Someone is not happy.
Paul is either not old or wise. | Alice is humble. | neutral | ((?[X]:((~humble(X)&patient(X))))<=>((~calm(paul)&humble(paul))))&
(![X]:(patient(X)=>old(X)))&
(![X]:((tall(X)&~strong(X))=>brave(X)))&
(![X]:((~rich(X)&~calm(X))=>(old(X)|quiet(X))))&
(((creative(lucy)<~>tall(lucy)))=>(?[X]:((~creative(X)|~brave(X)))))&
(![X]:((~tall(X)|rich(X))<=>(humble(X)|old(X))))&
(![X]:(~patient(X)=>(~happy(X)<~>~generous(X))))&
(((wise(alice)|rich(alice)))=>(?[X]:((happy(X)|~brave(X)))))&
(((creative(lucy)<~>~happy(lucy)))<=>(?[X]:(old(X))))&
(((wise(paul)|happy(paul)))=>((tall(paul)&~old(paul))))&
(![X]:((~tall(X)<~>strong(X))<=>(rich(X)|happy(X))))&
(![X]:((old(X)|creative(X))<=>(~strong(X)&~calm(X))))&
(![X]:((happy(X)&generous(X))=>(~quiet(X)|~old(X))))&
(![X]:((~old(X)<~>~tall(X))<=>(funny(X)|tall(X))))&
(![X]:((funny(X)&~patient(X))=>(~calm(X)|humble(X))))&
(![X]:(rich(X)<=>(humble(X)<~>~brave(X))))&
(rich(lucy))&
((funny(mary)&generous(mary)))&
((quiet(paul)|tall(paul)))&
((brave(fred)|~happy(fred)))&
((~rich(paul)|tall(paul)))&
((~tall(fred)|quiet(fred)))&
(?[X]:(~happy(X)))&
((~old(paul)<~>wise(paul))) | humble(alice) | [] | null | 0 |
If someone is both generous and not calm then mary is either happy or not funny and vice versa.
Everyone who is either happy or not humble is both rich and not strong.
If someone is generous or not curious then someone is either old or generous.
Everyone who is funny is either not old or strong.
If fred is either not old or not creative then lucy is both not old and patient and vice versa.
Everyone who is both old and not kind is both brave and old and vice versa.
If lucy is wise then someone is old or not curious and vice versa.
Everyone who is not generous is either not generous or old and vice versa.
Everyone who is curious or humble is both not humble and calm.
Everyone who is not old or kind is both not patient and wise.
Everyone who is both not happy and curious is both not humble and kind and vice versa.
Everyone who is not funny is both not humble and quiet and vice versa.
If lucy is generous or not wise then someone is quiet or creative and vice versa.
Everyone who is brave is humble and vice versa.
Everyone who is not happy or rich is not kind or brave.
If someone is happy or not patient then fred is either not happy or patient.
Alice is not generous.
Mary is both wise and not curious.
Lucy is curious.
Paul is both not kind and not calm.
Lucy is patient or not tall.
Mary is not rich.
John is not brave. | Alice is kind. | contradiction | ((?[X]:((generous(X)&~calm(X))))<=>((happy(mary)<~>~funny(mary))))&
(![X]:((happy(X)<~>~humble(X))=>(rich(X)&~strong(X))))&
((?[X]:((generous(X)|~curious(X))))=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:(funny(X)=>(~old(X)<~>strong(X))))&
(((~old(fred)<~>~creative(fred)))<=>((~old(lucy)&patient(lucy))))&
(![X]:((old(X)&~kind(X))<=>(brave(X)&old(X))))&
((wise(lucy))<=>(?[X]:((old(X)|~curious(X)))))&
(![X]:(~generous(X)<=>(~generous(X)<~>old(X))))&
(![X]:((curious(X)|humble(X))=>(~humble(X)&calm(X))))&
(![X]:((~old(X)|kind(X))=>(~patient(X)&wise(X))))&
(![X]:((~happy(X)&curious(X))<=>(~humble(X)&kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)&quiet(X))))&
(((generous(lucy)|~wise(lucy)))<=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:(brave(X)<=>humble(X)))&
(![X]:((~happy(X)|rich(X))=>(~kind(X)|brave(X))))&
((?[X]:((happy(X)|~patient(X))))=>((~happy(fred)<~>patient(fred))))&
(~generous(alice))&
((wise(mary)&~curious(mary)))&
(curious(lucy))&
((~kind(paul)&~calm(paul)))&
((patient(lucy)|~tall(lucy)))&
(~rich(mary))&
(~brave(john)) | kind(alice) | [
"p8",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5267419124772649346238086
% SZS output start Proof for 5267419124772649346238086
9. ! [X0] : ((humble(X0) | curious(X0)) => (calm(X0) & ~humble(X0))) [input p8]
11. ! [X0] : ((curious(X0) & ~happy(X0)) <=> (kind(X0) & ~humble(X0))) [input p10]
14. ! [X0] : (brave(X0) <=> humble(X0)) [input p13]
15. ! [X0] : ((rich(X0) | ~happy(X0)) => (brave(X0) | ~kind(X0))) [input p14]
24. kind(alice) [input hypothesis]
30. ! [X0] : ((calm(X0) & ~humble(X0)) | (~humble(X0) & ~curious(X0))) [ennf transformation 9]
32. ! [X0] : ((brave(X0) | ~kind(X0)) | (~rich(X0) & happy(X0))) [ennf transformation 15]
33. ! [X0] : (brave(X0) | ~kind(X0) | (~rich(X0) & happy(X0))) [flattening 32]
54. ! [X0] : (((curious(X0) & ~happy(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (~curious(X0) | happy(X0)))) [nnf transformation 11]
55. ! [X0] : (((curious(X0) & ~happy(X0)) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | ~curious(X0) | happy(X0))) [flattening 54]
63. ! [X0] : ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0))) [nnf transformation 14]
99. ~humble(X0) | ~humble(X0) [cnf transformation 30]
108. ~happy(X0) | ~kind(X0) | humble(X0) [cnf transformation 55]
117. humble(X0) | ~brave(X0) [cnf transformation 63]
119. brave(X0) | ~kind(X0) | happy(X0) [cnf transformation 33]
133. kind(alice) [cnf transformation 24]
134. ~humble(X0) [duplicate literal removal 99]
223. ~happy(X0) | ~kind(X0) [subsumption resolution 108,134]
247. ~brave(X0) [subsumption resolution 117,134]
249. ~kind(X0) | happy(X0) [subsumption resolution 119,247]
250. ~kind(X0) [subsumption resolution 249,223]
269. $false [subsumption resolution 133,250]
% SZS output end Proof for 5267419124772649346238086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or not generous then alice is either wise or not patient. If someone is funny then someone is not quiet or quiet. Everyone who is either not kind or rich is not happy and vice versa. Everyone who is not patient is not happy and vice versa. Everyone who is either wise or not tall is not generous and vice versa. If someone is not generous then susan is both not curious and not strong and vice versa. Everyone who is both tall and curious is tall and vice versa. If mary is both calm and not humble then someone is not patient or not wise. Everyone who is not calm or kind is both not old and happy. Everyone who is either old or not humble is not calm or not strong. If someone is both not quiet and happy then john is rich. Everyone who is either rich or not creative is not creative. If paul is calm then paul is both not old and strong. Everyone who is either not funny or curious is generous or old. If lucy is not wise or not humble then john is either strong or not funny. Everyone who is either not quiet or creative is either not happy or curious and vice versa. Lucy is not creative. Someone is both brave and humble. Paul is curious or not creative. Someone is not humble. Someone is both humble and not generous. John is kind. Someone is either not brave or tall. Someone is both curious and generous. | John is rich. | contradiction | ((?[X]:((~kind(X)<~>~generous(X))))=>((wise(alice)<~>~patient(alice))))&
((?[X]:(funny(X)))=>(?[X]:((~quiet(X)|quiet(X)))))&
(![X]:((~kind(X)<~>rich(X))<=>~happy(X)))&
(![X]:(~patient(X)<=>~happy(X)))&
(![X]:((wise(X)<~>~tall(X))<=>~generous(X)))&
((?[X]:(~generous(X)))<=>((~curious(susan)&~strong(susan))))&
(![X]:((tall(X)&curious(X))<=>tall(X)))&
(((calm(mary)&~humble(mary)))=>(?[X]:((~patient(X)|~wise(X)))))&
(![X]:((~calm(X)|kind(X))=>(~old(X)&happy(X))))&
(![X]:((old(X)<~>~humble(X))=>(~calm(X)|~strong(X))))&
((?[X]:((~quiet(X)&happy(X))))=>(rich(john)))&
(![X]:((rich(X)<~>~creative(X))=>~creative(X)))&
((calm(paul))=>((~old(paul)&strong(paul))))&
(![X]:((~funny(X)<~>curious(X))=>(generous(X)|old(X))))&
(((~wise(lucy)|~humble(lucy)))=>((strong(john)<~>~funny(john))))&
(![X]:((~quiet(X)<~>creative(X))<=>(~happy(X)<~>curious(X))))&
(~creative(lucy))&
(?[X]:((brave(X)&humble(X))))&
((curious(paul)|~creative(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((humble(X)&~generous(X))))&
(kind(john))&
(?[X]:((~brave(X)<~>tall(X))))&
(?[X]:((curious(X)&generous(X)))) | rich(john) | [
"p2",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6477693554660326260581706
% SZS output start Proof for 6477693554660326260581706
3. ! [X0] : ((~kind(X0) <~> rich(X0)) <=> ~happy(X0)) [input p2]
9. ! [X0] : ((kind(X0) | ~calm(X0)) => (happy(X0) & ~old(X0))) [input p8]
22. kind(john) [input p21]
25. rich(john) [input hypothesis]
31. ! [X0] : ((happy(X0) & ~old(X0)) | (~kind(X0) & calm(X0))) [ennf transformation 9]
44. ! [X0] : ((((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | happy(X0)) & (~happy(X0) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))))) [nnf transformation 3]
78. ~happy(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 44]
97. ~kind(X0) | happy(X0) [cnf transformation 31]
126. kind(john) [cnf transformation 22]
131. rich(john) [cnf transformation 25]
191. 14 <=> rich(john) [avatar definition]
193. rich(john) <- (14) [avatar component clause 191]
244. 14 [avatar split clause 131,191]
246. happy(john) [resolution 97,126]
261. ~kind(john) | ~rich(john) [resolution 78,246]
262. ~rich(john) [subsumption resolution 261,126]
263. $false <- (14) [subsumption resolution 262,193]
264. ~14 [avatar contradiction clause 263]
265. $false [avatar sat refutation 244,264]
% SZS output end Proof for 6477693554660326260581706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not creative then lucy is not curious. If someone is patient then someone is not generous or not brave and vice versa. If john is strong or not patient then john is either rich or not wise and vice versa. Everyone who is both not kind and funny is both funny and not kind and vice versa. If someone is happy then someone is either not creative or not curious and vice versa. Everyone who is funny or not patient is both wise and not rich and vice versa. Everyone who is not rich is strong or not quiet and vice versa. If mary is not humble then susan is either wise or strong. If john is either quiet or not old then john is either kind or not curious and vice versa. If mary is either not tall or not rich then lucy is not creative. Everyone who is both tall and humble is not calm. Everyone who is curious or brave is not brave or not happy and vice versa. Everyone who is both quiet and not brave is either generous or not happy and vice versa. If someone is not generous then john is both creative and not funny and vice versa. Everyone who is generous or not creative is creative and vice versa. Everyone who is not creative is generous or not creative. Someone is either not rich or humble. Someone is not kind or tall. Mary is both not curious and not calm. Mary is not generous or wise. Someone is not quiet or wise. John is not humble or humble. | Lucy is not rich. | neutral | ((~creative(fred))=>(~curious(lucy)))&
((?[X]:(patient(X)))<=>(?[X]:((~generous(X)|~brave(X)))))&
(((strong(john)|~patient(john)))<=>((rich(john)<~>~wise(john))))&
(![X]:((~kind(X)&funny(X))<=>(funny(X)&~kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:((funny(X)|~patient(X))<=>(wise(X)&~rich(X))))&
(![X]:(~rich(X)<=>(strong(X)|~quiet(X))))&
((~humble(mary))=>((wise(susan)<~>strong(susan))))&
(((quiet(john)<~>~old(john)))<=>((kind(john)<~>~curious(john))))&
(((~tall(mary)<~>~rich(mary)))=>(~creative(lucy)))&
(![X]:((tall(X)&humble(X))=>~calm(X)))&
(![X]:((curious(X)|brave(X))<=>(~brave(X)|~happy(X))))&
(![X]:((quiet(X)&~brave(X))<=>(generous(X)<~>~happy(X))))&
((?[X]:(~generous(X)))<=>((creative(john)&~funny(john))))&
(![X]:((generous(X)|~creative(X))<=>creative(X)))&
(![X]:(~creative(X)=>(generous(X)|~creative(X))))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:((~kind(X)|tall(X))))&
((~curious(mary)&~calm(mary)))&
((~generous(mary)|wise(mary)))&
(?[X]:((~quiet(X)|wise(X))))&
((~humble(john)|humble(john))) | ~rich(lucy) | [] | null | 0 |
If someone is quiet or creative then mary is not creative or not generous and vice versa.
Everyone who is either not strong or creative is wise.
Everyone who is not calm is both not funny and calm and vice versa.
If alice is wise or patient then someone is wise or not quiet.
If someone is not quiet then mary is both not wise and kind.
If someone is either happy or not rich then someone is old or not kind and vice versa.
Everyone who is either rich or not wise is not generous or happy and vice versa.
Everyone who is either old or not quiet is either not quiet or not kind.
If john is both not curious and not generous then susan is not calm.
Everyone who is both kind and funny is rich.
Everyone who is rich is quiet or not funny.
If susan is tall then someone is either brave or generous and vice versa.
Everyone who is not funny is either strong or not humble.
Everyone who is not wise or kind is both not strong and tall and vice versa.
If someone is both strong and rich then mary is not rich or kind and vice versa.
Everyone who is old is not calm or curious.
Someone is not brave.
Someone is either humble or strong.
Someone is humble or tall.
Someone is wise.
Lucy is tall or calm.
Someone is either not happy or generous. | Mary is not patient. | neutral | ((?[X]:((quiet(X)|creative(X))))<=>((~creative(mary)|~generous(mary))))&
(![X]:((~strong(X)<~>creative(X))=>wise(X)))&
(![X]:(~calm(X)<=>(~funny(X)&calm(X))))&
(((wise(alice)|patient(alice)))=>(?[X]:((wise(X)|~quiet(X)))))&
((?[X]:(~quiet(X)))=>((~wise(mary)&kind(mary))))&
((?[X]:((happy(X)<~>~rich(X))))<=>(?[X]:((old(X)|~kind(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(~generous(X)|happy(X))))&
(![X]:((old(X)<~>~quiet(X))=>(~quiet(X)<~>~kind(X))))&
(((~curious(john)&~generous(john)))=>(~calm(susan)))&
(![X]:((kind(X)&funny(X))=>rich(X)))&
(![X]:(rich(X)=>(quiet(X)|~funny(X))))&
((tall(susan))<=>(?[X]:((brave(X)<~>generous(X)))))&
(![X]:(~funny(X)=>(strong(X)<~>~humble(X))))&
(![X]:((~wise(X)|kind(X))<=>(~strong(X)&tall(X))))&
((?[X]:((strong(X)&rich(X))))<=>((~rich(mary)|kind(mary))))&
(![X]:(old(X)=>(~calm(X)|curious(X))))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)<~>strong(X))))&
(?[X]:((humble(X)|tall(X))))&
(?[X]:(wise(X)))&
((tall(lucy)|calm(lucy)))&
(?[X]:((~happy(X)<~>generous(X)))) | ~patient(mary) | [] | null | 0 |
Everyone who is kind is not generous.
Everyone who is both patient and not patient is either not generous or not creative and vice versa.
Everyone who is happy is not strong or not funny.
Everyone who is not quiet or wise is both brave and old.
If lucy is rich or tall then paul is not humble and vice versa.
Everyone who is creative is not patient.
Everyone who is strong is rich or not kind and vice versa.
Everyone who is both not patient and generous is not brave or curious and vice versa.
Everyone who is generous or funny is both not old and funny.
If someone is either funny or brave then susan is curious or funny.
If someone is funny then paul is both not brave and not rich and vice versa.
Everyone who is either humble or curious is both not wise and patient and vice versa.
If paul is both old and curious then someone is either creative or funny.
If susan is either creative or not quiet then lucy is not tall or strong.
Mary is not humble.
Someone is humble.
Fred is not happy.
Susan is not generous or happy.
Someone is either not quiet or patient. | Paul is not humble. | neutral | (![X]:(kind(X)=>~generous(X)))&
(![X]:((patient(X)&~patient(X))<=>(~generous(X)<~>~creative(X))))&
(![X]:(happy(X)=>(~strong(X)|~funny(X))))&
(![X]:((~quiet(X)|wise(X))=>(brave(X)&old(X))))&
(((rich(lucy)|tall(lucy)))<=>(~humble(paul)))&
(![X]:(creative(X)=>~patient(X)))&
(![X]:(strong(X)<=>(rich(X)|~kind(X))))&
(![X]:((~patient(X)&generous(X))<=>(~brave(X)|curious(X))))&
(![X]:((generous(X)|funny(X))=>(~old(X)&funny(X))))&
((?[X]:((funny(X)<~>brave(X))))=>((curious(susan)|funny(susan))))&
((?[X]:(funny(X)))<=>((~brave(paul)&~rich(paul))))&
(![X]:((humble(X)<~>curious(X))<=>(~wise(X)&patient(X))))&
(((old(paul)&curious(paul)))=>(?[X]:((creative(X)<~>funny(X)))))&
(((creative(susan)<~>~quiet(susan)))=>((~tall(lucy)|strong(lucy))))&
(~humble(mary))&
(?[X]:(humble(X)))&
(~happy(fred))&
((~generous(susan)|happy(susan)))&
(?[X]:((~quiet(X)<~>patient(X)))) | ~humble(paul) | [] | null | 0 |
Everyone who is not strong or strong is both wise and rich and vice versa.
If alice is not creative then someone is generous and vice versa.
Everyone who is both curious and not strong is not wise.
If someone is either not patient or old then someone is not rich and vice versa.
Everyone who is either not brave or kind is either patient or generous and vice versa.
If someone is either brave or not brave then fred is either not patient or rich and vice versa.
If susan is either not brave or not wise then john is both not humble and humble.
Everyone who is both old and calm is either not rich or strong.
If someone is not tall or not creative then someone is both not patient and not old and vice versa.
If john is both strong and patient then someone is not calm or not wise.
Everyone who is both quiet and curious is not creative and vice versa.
If lucy is either not old or not generous then mary is both wise and calm and vice versa.
If fred is brave then someone is either tall or quiet and vice versa.
If someone is not calm then susan is both not brave and not patient and vice versa.
Everyone who is either humble or not happy is rich or not funny.
Everyone who is not tall or not quiet is not old or generous.
John is not funny.
John is not old.
Someone is patient.
Someone is either not strong or not wise. | Alice is generous. | contradiction | (![X]:((~strong(X)|strong(X))<=>(wise(X)&rich(X))))&
((~creative(alice))<=>(?[X]:(generous(X))))&
(![X]:((curious(X)&~strong(X))=>~wise(X)))&
((?[X]:((~patient(X)<~>old(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(patient(X)<~>generous(X))))&
((?[X]:((brave(X)<~>~brave(X))))<=>((~patient(fred)<~>rich(fred))))&
(((~brave(susan)<~>~wise(susan)))=>((~humble(john)&humble(john))))&
(![X]:((old(X)&calm(X))=>(~rich(X)<~>strong(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(((strong(john)&patient(john)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((quiet(X)&curious(X))<=>~creative(X)))&
(((~old(lucy)<~>~generous(lucy)))<=>((wise(mary)&calm(mary))))&
((brave(fred))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))<=>((~brave(susan)&~patient(susan))))&
(![X]:((humble(X)<~>~happy(X))=>(rich(X)|~funny(X))))&
(![X]:((~tall(X)|~quiet(X))=>(~old(X)|generous(X))))&
(~funny(john))&
(~old(john))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)<~>~wise(X)))) | generous(alice) | [
"p0",
"p1",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2445321386826730055175598
% SZS output start Proof for 2445321386826730055175598
1. ! [X0] : ((strong(X0) | ~strong(X0)) <=> (rich(X0) & wise(X0))) [input p0]
2. ~creative(alice) <=> ? [X0] : generous(X0) [input p1]
4. ? [X0] : (~patient(X0) <~> old(X0)) <=> ? [X0] : ~rich(X0) [input p3]
9. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X0] : (~old(X0) & ~patient(X0)) [input p8]
21. generous(alice) [input hypothesis]
22. ? [X0] : (~patient(X0) <~> old(X0)) <=> ? [X1] : ~rich(X1) [rectify 4]
23. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X1] : (~old(X1) & ~patient(X1)) [rectify 9]
35. ! [X0] : (((strong(X0) | ~strong(X0)) | (~rich(X0) | ~wise(X0))) & ((rich(X0) & wise(X0)) | (~strong(X0) & strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((strong(X0) | ~strong(X0) | ~rich(X0) | ~wise(X0)) & ((rich(X0) & wise(X0)) | (~strong(X0) & strong(X0)))) [flattening 35]
37. (~creative(alice) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | creative(alice)) [nnf transformation 2]
38. (~creative(alice) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | creative(alice)) [rectify 37]
39. ? [X1] : generous(X1) => generous(sK0) [choice axiom]
40. (~creative(alice) | ! [X0] : ~generous(X0)) & (generous(sK0) | creative(alice)) [skolemisation 38,39]
41. (? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ! [X1] : rich(X1)) & (? [X1] : ~rich(X1) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) [nnf transformation 22]
42. (? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ! [X1] : rich(X1)) & (? [X2] : ~rich(X2) | ! [X3] : ((~patient(X3) | ~old(X3)) & (old(X3) | patient(X3)))) [rectify 41]
43. ? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) => ((~old(sK1) | patient(sK1)) & (old(sK1) | ~patient(sK1))) [choice axiom]
44. ? [X2] : ~rich(X2) => ~rich(sK2) [choice axiom]
45. (((~old(sK1) | patient(sK1)) & (old(sK1) | ~patient(sK1))) | ! [X1] : rich(X1)) & (~rich(sK2) | ! [X3] : ((~patient(X3) | ~old(X3)) & (old(X3) | patient(X3)))) [skolemisation 42,44,43]
53. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (old(X1) | patient(X1))) & (? [X1] : (~old(X1) & ~patient(X1)) | ! [X0] : (creative(X0) & tall(X0))) [nnf transformation 23]
54. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (old(X1) | patient(X1))) & (? [X2] : (~old(X2) & ~patient(X2)) | ! [X3] : (creative(X3) & tall(X3))) [rectify 53]
55. ? [X0] : (~creative(X0) | ~tall(X0)) => (~creative(sK4) | ~tall(sK4)) [choice axiom]
56. ? [X2] : (~old(X2) & ~patient(X2)) => (~old(sK5) & ~patient(sK5)) [choice axiom]
57. ((~creative(sK4) | ~tall(sK4)) | ! [X1] : (old(X1) | patient(X1))) & ((~old(sK5) & ~patient(sK5)) | ! [X3] : (creative(X3) & tall(X3))) [skolemisation 54,56,55]
80. rich(X0) | strong(X0) [cnf transformation 36]
81. ~strong(X0) | rich(X0) [cnf transformation 36]
84. ~creative(alice) | ~generous(X0) [cnf transformation 40]
86. ~rich(sK2) | old(X3) | patient(X3) [cnf transformation 45]
113. ~patient(sK5) | creative(X3) [cnf transformation 57]
115. ~old(sK5) | creative(X3) [cnf transformation 57]
140. generous(alice) [cnf transformation 21]
145. rich(X0) [subsumption resolution 80,81]
148. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
149. ~generous(X0) <- (1) [avatar component clause 148]
151. 2 <=> creative(alice) [avatar definition]
153. ~creative(alice) <- (~2) [avatar component clause 151]
154. 1 | ~2 [avatar split clause 84,151,148]
162. old(X3) | patient(X3) [subsumption resolution 86,145]
191. 9 <=> ! [X3] : creative(X3) [avatar definition]
192. creative(X3) <- (9) [avatar component clause 191]
194. 10 <=> old(sK5) [avatar definition]
196. ~old(sK5) <- (~10) [avatar component clause 194]
197. 9 | ~10 [avatar split clause 115,194,191]
203. 12 <=> patient(sK5) [avatar definition]
205. ~patient(sK5) <- (~12) [avatar component clause 203]
206. 9 | ~12 [avatar split clause 113,203,191]
284. patient(sK5) <- (~10) [resolution 162,196]
287. $false <- (~10, ~12) [subsumption resolution 284,205]
288. 10 | 12 [avatar contradiction clause 287]
289. $false <- (~2, 9) [resolution 192,153]
290. 2 | ~9 [avatar contradiction clause 289]
291. $false <- (1) [resolution 149,140]
294. ~1 [avatar contradiction clause 291]
295. $false [avatar sat refutation 154,197,206,288,290,294]
% SZS output end Proof for 2445321386826730055175598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not strong is either funny or not wise and vice versa.
If john is either humble or generous then someone is both not funny and brave and vice versa.
Everyone who is either brave or not quiet is both generous and not curious and vice versa.
Everyone who is happy is not happy or quiet.
Everyone who is happy or wise is not patient or kind and vice versa.
Everyone who is not patient is quiet or not generous and vice versa.
If paul is both not quiet and old then someone is either wise or strong and vice versa.
Everyone who is old or rich is brave or not happy and vice versa.
If someone is both generous and not brave then someone is either patient or not happy.
Everyone who is not kind is either kind or wise.
Everyone who is both not kind and happy is kind or not happy.
If paul is kind or not patient then paul is brave or not wise and vice versa.
Everyone who is both humble and not humble is both funny and not humble and vice versa.
If someone is not patient or not quiet then someone is funny or wise.
Everyone who is not strong is humble or not patient.
Everyone who is not strong is not wise.
Someone is patient.
Someone is not calm.
Fred is both generous and not humble.
Paul is quiet.
Someone is both brave and rich.
Someone is both not generous and kind.
Someone is either not quiet or strong.
Someone is not funny or quiet. | John is funny. | neutral | (![X]:((~tall(X)|~strong(X))<=>(funny(X)<~>~wise(X))))&
(((humble(john)<~>generous(john)))<=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:((brave(X)<~>~quiet(X))<=>(generous(X)&~curious(X))))&
(![X]:(happy(X)=>(~happy(X)|quiet(X))))&
(![X]:((happy(X)|wise(X))<=>(~patient(X)|kind(X))))&
(![X]:(~patient(X)<=>(quiet(X)|~generous(X))))&
(((~quiet(paul)&old(paul)))<=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:((old(X)|rich(X))<=>(brave(X)|~happy(X))))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:((patient(X)<~>~happy(X)))))&
(![X]:(~kind(X)=>(kind(X)<~>wise(X))))&
(![X]:((~kind(X)&happy(X))=>(kind(X)|~happy(X))))&
(((kind(paul)|~patient(paul)))<=>((brave(paul)|~wise(paul))))&
(![X]:((humble(X)&~humble(X))<=>(funny(X)&~humble(X))))&
((?[X]:((~patient(X)|~quiet(X))))=>(?[X]:((funny(X)|wise(X)))))&
(![X]:(~strong(X)=>(humble(X)|~patient(X))))&
(![X]:(~strong(X)=>~wise(X)))&
(?[X]:(patient(X)))&
(?[X]:(~calm(X)))&
((generous(fred)&~humble(fred)))&
(quiet(paul))&
(?[X]:((brave(X)&rich(X))))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:((~quiet(X)<~>strong(X))))&
(?[X]:((~funny(X)|quiet(X)))) | funny(john) | [] | null | 0 |
Everyone who is either tall or not curious is both not kind and curious and vice versa.
Everyone who is both tall and not rich is both creative and curious.
Everyone who is kind is brave and vice versa.
If someone is funny or generous then mary is tall or not patient.
If someone is either humble or tall then alice is quiet and vice versa.
If alice is both not old and rich then someone is both patient and not quiet.
Everyone who is either rich or not humble is not calm and vice versa.
Everyone who is both humble and not curious is either humble or not calm.
If alice is either not funny or patient then someone is both brave and wise.
If mary is not patient then someone is tall and vice versa.
If fred is both kind and not curious then alice is both not quiet and creative and vice versa.
Everyone who is either not wise or not strong is not humble or tall.
Everyone who is curious or not humble is both not funny and old.
Everyone who is both not patient and not quiet is both strong and brave.
Everyone who is either rich or quiet is brave or kind and vice versa.
Everyone who is quiet or happy is both not old and rich and vice versa.
Paul is both calm and kind.
John is both not kind and curious.
Someone is calm.
Mary is either not humble or not brave.
Someone is either happy or wise.
Someone is not rich. | Mary is not humble. | entailment | (![X]:((tall(X)<~>~curious(X))<=>(~kind(X)&curious(X))))&
(![X]:((tall(X)&~rich(X))=>(creative(X)&curious(X))))&
(![X]:(kind(X)<=>brave(X)))&
((?[X]:((funny(X)|generous(X))))=>((tall(mary)|~patient(mary))))&
((?[X]:((humble(X)<~>tall(X))))<=>(quiet(alice)))&
(((~old(alice)&rich(alice)))=>(?[X]:((patient(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~humble(X))<=>~calm(X)))&
(![X]:((humble(X)&~curious(X))=>(humble(X)<~>~calm(X))))&
(((~funny(alice)<~>patient(alice)))=>(?[X]:((brave(X)&wise(X)))))&
((~patient(mary))<=>(?[X]:(tall(X))))&
(((kind(fred)&~curious(fred)))<=>((~quiet(alice)&creative(alice))))&
(![X]:((~wise(X)<~>~strong(X))=>(~humble(X)|tall(X))))&
(![X]:((curious(X)|~humble(X))=>(~funny(X)&old(X))))&
(![X]:((~patient(X)&~quiet(X))=>(strong(X)&brave(X))))&
(![X]:((rich(X)<~>quiet(X))<=>(brave(X)|kind(X))))&
(![X]:((quiet(X)|happy(X))<=>(~old(X)&rich(X))))&
((calm(paul)&kind(paul)))&
((~kind(john)&curious(john)))&
(?[X]:(calm(X)))&
((~humble(mary)<~>~brave(mary)))&
(?[X]:((happy(X)<~>wise(X))))&
(?[X]:(~rich(X))) | ~humble(mary) | [
"p0",
"p1",
"p2",
"p6",
"p7",
"p9",
"p12",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 77318722955339149045275
% SZS output start Proof for 77318722955339149045275
1. ! [X0] : ((tall(X0) <~> ~curious(X0)) <=> (curious(X0) & ~kind(X0))) [input p0]
2. ! [X0] : ((~rich(X0) & tall(X0)) => (curious(X0) & creative(X0))) [input p1]
3. ! [X0] : (kind(X0) <=> brave(X0)) [input p2]
7. ! [X0] : ((rich(X0) <~> ~humble(X0)) <=> ~calm(X0)) [input p6]
8. ! [X0] : ((~curious(X0) & humble(X0)) => (humble(X0) <~> ~calm(X0))) [input p7]
10. ~patient(mary) <=> ? [X0] : tall(X0) [input p9]
13. ! [X0] : ((~humble(X0) | curious(X0)) => (old(X0) & ~funny(X0))) [input p12]
14. ! [X0] : ((~quiet(X0) & ~patient(X0)) => (brave(X0) & strong(X0))) [input p13]
15. ! [X0] : ((rich(X0) <~> quiet(X0)) <=> (kind(X0) | brave(X0))) [input p14]
16. ! [X0] : ((happy(X0) | quiet(X0)) <=> (rich(X0) & ~old(X0))) [input p15]
20. ~humble(mary) <~> ~brave(mary) [input p19]
23. humble(mary) [input hypothesis]
25. ! [X0] : ((curious(X0) & creative(X0)) | (rich(X0) | ~tall(X0))) [ennf transformation 2]
26. ! [X0] : ((curious(X0) & creative(X0)) | rich(X0) | ~tall(X0)) [flattening 25]
31. ! [X0] : ((humble(X0) <~> ~calm(X0)) | (curious(X0) | ~humble(X0))) [ennf transformation 8]
32. ! [X0] : ((humble(X0) <~> ~calm(X0)) | curious(X0) | ~humble(X0)) [flattening 31]
36. ! [X0] : ((old(X0) & ~funny(X0)) | (humble(X0) & ~curious(X0))) [ennf transformation 13]
37. ! [X0] : ((brave(X0) & strong(X0)) | (quiet(X0) | patient(X0))) [ennf transformation 14]
38. ! [X0] : ((brave(X0) & strong(X0)) | quiet(X0) | patient(X0)) [flattening 37]
39. ! [X0] : ((((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (~curious(X0) | kind(X0))) & ((curious(X0) & ~kind(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))))) [nnf transformation 1]
40. ! [X0] : ((((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | ~curious(X0) | kind(X0)) & ((curious(X0) & ~kind(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))))) [flattening 39]
41. ! [X0] : ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0))) [nnf transformation 3]
48. ! [X0] : ((((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | calm(X0)) & (~calm(X0) | ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0))))) [nnf transformation 7]
49. ! [X0] : (((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | curious(X0) | ~humble(X0)) [nnf transformation 32]
53. (~patient(mary) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | patient(mary)) [nnf transformation 10]
54. (~patient(mary) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | patient(mary)) [rectify 53]
55. ? [X1] : tall(X1) => tall(sK3) [choice axiom]
56. (~patient(mary) | ! [X0] : ~tall(X0)) & (tall(sK3) | patient(mary)) [skolemisation 54,55]
60. ! [X0] : ((((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (~kind(X0) & ~brave(X0))) & ((kind(X0) | brave(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (~kind(X0) & ~brave(X0))) & (kind(X0) | brave(X0) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0))))) [flattening 60]
62. ! [X0] : (((happy(X0) | quiet(X0)) | (~rich(X0) | old(X0))) & ((rich(X0) & ~old(X0)) | (~happy(X0) & ~quiet(X0)))) [nnf transformation 16]
63. ! [X0] : ((happy(X0) | quiet(X0) | ~rich(X0) | old(X0)) & ((rich(X0) & ~old(X0)) | (~happy(X0) & ~quiet(X0)))) [flattening 62]
66. (brave(mary) | humble(mary)) & (~brave(mary) | ~humble(mary)) [nnf transformation 20]
75. curious(X0) | tall(X0) | curious(X0) [cnf transformation 40]
76. ~curious(X0) | tall(X0) | ~curious(X0) | kind(X0) [cnf transformation 40]
79. curious(X0) | rich(X0) | ~tall(X0) [cnf transformation 26]
80. ~kind(X0) | brave(X0) [cnf transformation 41]
89. ~calm(X0) | ~humble(X0) | ~rich(X0) [cnf transformation 48]
92. ~rich(X0) | humble(X0) | calm(X0) [cnf transformation 48]
94. calm(X0) | ~humble(X0) | curious(X0) | ~humble(X0) [cnf transformation 49]
100. ~patient(mary) | ~tall(X0) [cnf transformation 56]
109. ~curious(X0) | old(X0) [cnf transformation 36]
112. quiet(X0) | brave(X0) | patient(X0) [cnf transformation 38]
113. kind(X0) | brave(X0) | quiet(X0) | ~rich(X0) [cnf transformation 61]
119. ~old(X0) | ~quiet(X0) [cnf transformation 63]
121. ~quiet(X0) | rich(X0) [cnf transformation 63]
129. ~brave(mary) | ~humble(mary) [cnf transformation 66]
134. humble(mary) [cnf transformation 23]
135. ~humble(X0) | calm(X0) | curious(X0) [duplicate literal removal 94]
136. curious(X0) | tall(X0) [duplicate literal removal 75]
137. ~curious(X0) | tall(X0) | kind(X0) [duplicate literal removal 76]
138. rich(X0) | curious(X0) [subsumption resolution 79,136]
143. 2 <=> tall(mary) [avatar definition]
145. tall(mary) <- (2) [avatar component clause 143]
147. 3 <=> patient(mary) [avatar definition]
149. ~patient(mary) <- (~3) [avatar component clause 147]
212. 17 <=> ! [X0] : ~tall(X0) [avatar definition]
213. ~tall(X0) <- (17) [avatar component clause 212]
214. 17 | ~3 [avatar split clause 100,147,212]
237. ~rich(X0) | quiet(X0) | brave(X0) [subsumption resolution 113,80]
239. 22 <=> humble(mary) [avatar definition]
241. humble(mary) <- (22) [avatar component clause 239]
243. 23 <=> brave(mary) [avatar definition]
244. ~brave(mary) <- (~23) [avatar component clause 243]
247. ~22 | ~23 [avatar split clause 129,243,239]
258. 22 [avatar split clause 134,239]
259. $false <- (2, 17) [subsumption resolution 145,213]
260. ~2 | ~17 [avatar contradiction clause 259]
293. 29 <=> rich(mary) [avatar definition]
295. rich(mary) <- (29) [avatar component clause 293]
346. humble(X0) | calm(X0) | curious(X0) [resolution 92,138]
351. calm(X0) | curious(X0) [subsumption resolution 346,135]
372. patient(X0) | brave(X0) | rich(X0) [resolution 112,121]
403. tall(X0) | kind(X0) | tall(X0) [resolution 137,136]
407. kind(X0) | tall(X0) [duplicate literal removal 403]
415. quiet(mary) | brave(mary) <- (29) [resolution 237,295]
420. quiet(mary) <- (~23, 29) [subsumption resolution 415,244]
478. curious(X1) | ~humble(X1) | ~rich(X1) [resolution 351,89]
480. ~humble(X1) | curious(X1) [subsumption resolution 478,138]
489. brave(X2) | tall(X2) [resolution 407,80]
504. brave(mary) | rich(mary) <- (~3) [resolution 372,149]
580. curious(mary) <- (22) [resolution 480,241]
586. tall(mary) <- (~23) [resolution 489,244]
682. old(mary) <- (22) [resolution 580,109]
880. ~quiet(mary) <- (22) [resolution 682,119]
881. $false <- (22, ~23, 29) [subsumption resolution 880,420]
882. ~22 | 23 | ~29 [avatar contradiction clause 881]
883. rich(mary) <- (~3, ~23) [subsumption resolution 504,244]
884. 29 | 3 | 23 [avatar split clause 883,243,147,293]
891. 2 | 23 [avatar split clause 586,243,143]
898. $false [avatar sat refutation 214,247,258,260,882,884,891]
% SZS output end Proof for 77318722955339149045275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or quiet is brave and vice versa.
If someone is curious or not strong then alice is both not curious and curious.
Everyone who is either not wise or strong is patient.
If someone is humble or not curious then susan is both not patient and not kind and vice versa.
If someone is both not quiet and not generous then fred is not curious or not kind and vice versa.
If alice is brave then someone is both not humble and not rich.
Everyone who is both creative and brave is not curious and vice versa.
Everyone who is both tall and happy is both not funny and not patient.
If someone is both not kind and wise then someone is either not funny or wise and vice versa.
If john is not kind or happy then john is either humble or quiet.
If someone is both creative and not wise then someone is rich and vice versa.
Everyone who is quiet or not humble is happy.
Everyone who is not kind or not quiet is both not old and not kind.
If paul is either generous or curious then someone is calm or tall and vice versa.
Everyone who is either not funny or happy is happy and vice versa.
If fred is not happy then fred is funny.
Susan is either not brave or tall.
Someone is generous.
Someone is not patient or not curious.
Paul is humble or generous.
Lucy is not brave or not generous.
Paul is either patient or not happy.
Paul is either tall or funny.
Alice is not curious. | Paul is curious. | contradiction | (![X]:((creative(X)|quiet(X))<=>brave(X)))&
((?[X]:((curious(X)|~strong(X))))=>((~curious(alice)&curious(alice))))&
(![X]:((~wise(X)<~>strong(X))=>patient(X)))&
((?[X]:((humble(X)|~curious(X))))<=>((~patient(susan)&~kind(susan))))&
((?[X]:((~quiet(X)&~generous(X))))<=>((~curious(fred)|~kind(fred))))&
((brave(alice))=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((creative(X)&brave(X))<=>~curious(X)))&
(![X]:((tall(X)&happy(X))=>(~funny(X)&~patient(X))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((~funny(X)<~>wise(X)))))&
(((~kind(john)|happy(john)))=>((humble(john)<~>quiet(john))))&
((?[X]:((creative(X)&~wise(X))))<=>(?[X]:(rich(X))))&
(![X]:((quiet(X)|~humble(X))=>happy(X)))&
(![X]:((~kind(X)|~quiet(X))=>(~old(X)&~kind(X))))&
(((generous(paul)<~>curious(paul)))<=>(?[X]:((calm(X)|tall(X)))))&
(![X]:((~funny(X)<~>happy(X))<=>happy(X)))&
((~happy(fred))=>(funny(fred)))&
((~brave(susan)<~>tall(susan)))&
(?[X]:(generous(X)))&
(?[X]:((~patient(X)|~curious(X))))&
((humble(paul)|generous(paul)))&
((~brave(lucy)|~generous(lucy)))&
((patient(paul)<~>~happy(paul)))&
((tall(paul)<~>funny(paul)))&
(~curious(alice)) | curious(paul) | [
"p1",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2195021711521588286705465
% SZS output start Proof for 2195021711521588286705465
2. ? [X0] : (~strong(X0) | curious(X0)) => (curious(alice) & ~curious(alice)) [input p1]
24. ~curious(alice) [input p23]
25. curious(paul) [input hypothesis]
29. (curious(alice) & ~curious(alice)) | ! [X0] : (strong(X0) & ~curious(X0)) [ennf transformation 2]
83. curious(alice) | ~curious(X0) [cnf transformation 29]
142. ~curious(alice) [cnf transformation 24]
143. curious(paul) [cnf transformation 25]
150. 2 <=> curious(alice) [avatar definition]
155. 3 <=> ! [X0] : ~curious(X0) [avatar definition]
156. ~curious(X0) <- (3) [avatar component clause 155]
157. 3 | 2 [avatar split clause 83,150,155]
306. 36 <=> curious(paul) [avatar definition]
307. curious(paul) <- (36) [avatar component clause 306]
371. ~2 [avatar split clause 142,150]
372. 36 [avatar split clause 143,306]
375. $false <- (3, 36) [resolution 307,156]
376. ~3 | ~36 [avatar contradiction clause 375]
377. $false [avatar sat refutation 157,371,372,376]
% SZS output end Proof for 2195021711521588286705465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not brave then susan is funny or not calm and vice versa.
Everyone who is not happy or brave is either 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.
If john is patient or old then someone is both not tall and not rich and vice versa.
If paul is strong then john is either calm or funny and vice versa.
If paul is either calm or not old then someone is quiet.
Lucy is kind.
John is not old or not creative.
Mary is not creative.
Mary is patient.
Fred is patient or calm. | Susan is kind. | entailment | ((~brave(mary))<=>((funny(susan)|~calm(susan))))&
(![X]:((~happy(X)|brave(X))=>(wise(X)<~>~creative(X))))&
(![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))))&
(((patient(john)|old(john)))<=>(?[X]:((~tall(X)&~rich(X)))))&
((strong(paul))<=>((calm(john)<~>funny(john))))&
(((calm(paul)<~>~old(paul)))=>(?[X]:(quiet(X))))&
(kind(lucy))&
((~old(john)|~creative(john)))&
(~creative(mary))&
(patient(mary))&
((patient(fred)|calm(fred))) | kind(susan) | [
"p6",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1604941416758345942827408
% SZS output start Proof for 1604941416758345942827408
7. ? [X0] : (tall(X0) <~> ~quiet(X0)) <=> creative(susan) [input p6]
8. ! [X0] : ((creative(X0) | ~patient(X0)) <=> ~quiet(X0)) [input p7]
9. ! [X0] : ((tall(X0) | ~kind(X0)) => quiet(X0)) [input p8]
12. ! [X0] : ((~old(X0) & ~patient(X0)) <=> (~happy(X0) | ~kind(X0))) [input p11]
21. ~kind(susan) [input hypothesis]
30. ! [X0] : (quiet(X0) | (~tall(X0) & kind(X0))) [ennf transformation 9]
43. (? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ~creative(susan)) & (creative(susan) | ! [X0] : ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) [nnf transformation 7]
44. (? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ~creative(susan)) & (creative(susan) | ! [X1] : ((tall(X1) | quiet(X1)) & (~quiet(X1) | ~tall(X1)))) [rectify 43]
45. ? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) => ((quiet(sK1) | ~tall(sK1)) & (~quiet(sK1) | tall(sK1))) [choice axiom]
46. (((quiet(sK1) | ~tall(sK1)) & (~quiet(sK1) | tall(sK1))) | ~creative(susan)) & (creative(susan) | ! [X1] : ((tall(X1) | quiet(X1)) & (~quiet(X1) | ~tall(X1)))) [skolemisation 44,45]
47. ! [X0] : (((creative(X0) | ~patient(X0)) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & patient(X0)))) [nnf transformation 8]
48. ! [X0] : ((creative(X0) | ~patient(X0) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & patient(X0)))) [flattening 47]
52. ! [X0] : (((~old(X0) & ~patient(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (old(X0) | patient(X0)))) [nnf transformation 12]
53. ! [X0] : (((~old(X0) & ~patient(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | old(X0) | patient(X0))) [flattening 52]
82. creative(susan) | ~quiet(X1) | ~tall(X1) [cnf transformation 46]
83. creative(susan) | tall(X1) | quiet(X1) [cnf transformation 46]
86. ~quiet(X0) | patient(X0) [cnf transformation 48]
87. ~quiet(X0) | ~creative(X0) [cnf transformation 48]
89. kind(X0) | quiet(X0) [cnf transformation 30]
90. ~tall(X0) | quiet(X0) [cnf transformation 30]
93. ~patient(X0) | kind(X0) [cnf transformation 53]
113. ~kind(susan) [cnf transformation 21]
143. 7 <=> creative(susan) [avatar definition]
157. 10 <=> ! [X1] : (tall(X1) | quiet(X1)) [avatar definition]
158. tall(X1) | quiet(X1) <- (10) [avatar component clause 157]
159. 10 | 7 [avatar split clause 83,143,157]
161. 11 <=> ! [X1] : (~quiet(X1) | ~tall(X1)) [avatar definition]
162. ~quiet(X1) | ~tall(X1) <- (11) [avatar component clause 161]
163. 11 | 7 [avatar split clause 82,143,161]
242. quiet(susan) [resolution 89,113]
244. ~creative(susan) [resolution 242,87]
248. ~7 [avatar split clause 244,143]
249. ~tall(X1) <- (11) [subsumption resolution 162,90]
250. quiet(X1) <- (10, 11) [subsumption resolution 158,249]
253. patient(X1) <- (10, 11) [resolution 250,86]
258. kind(X0) <- (10, 11) [resolution 253,93]
274. $false <- (10, 11) [resolution 258,113]
275. ~10 | ~11 [avatar contradiction clause 274]
276. $false [avatar sat refutation 159,163,248,275]
% SZS output end Proof for 1604941416758345942827408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If john is rich then someone is both tall and not tall.
If fred is not humble then someone is not creative or not funny.
If someone is either not strong or happy then susan is both tall and calm.
If someone is either not brave or not humble then lucy is not humble.
Everyone who is not curious is either not curious or strong.
Everyone who is either not happy or not wise is humble.
Everyone who is both calm and not funny is both strong and tall.
Everyone who is both not brave and not old is patient.
If someone is creative or patient then fred is strong.
If fred is not kind then someone is not calm.
If paul is kind or not happy then alice is either not happy or not rich and vice versa.
Everyone who is either not quiet or not calm is funny or not generous and vice versa.
Everyone who is either rich or humble is both not tall and happy and vice versa.
Everyone who is either strong or not curious is either not creative or not strong and vice versa.
Everyone who is quiet or not funny is calm and vice versa.
Everyone who is not funny is not calm or not patient and vice versa.
Someone is both tall and generous.
Someone is both wise and not generous.
Fred is not curious or calm.
Someone is both wise and rich.
Lucy is both wise and tall.
Fred is either not tall or calm. | Lucy is not calm. | contradiction | ((rich(john))=>(?[X]:((tall(X)&~tall(X)))))&
((~humble(fred))=>(?[X]:((~creative(X)|~funny(X)))))&
((?[X]:((~strong(X)<~>happy(X))))=>((tall(susan)&calm(susan))))&
((?[X]:((~brave(X)<~>~humble(X))))=>(~humble(lucy)))&
(![X]:(~curious(X)=>(~curious(X)<~>strong(X))))&
(![X]:((~happy(X)<~>~wise(X))=>humble(X)))&
(![X]:((calm(X)&~funny(X))=>(strong(X)&tall(X))))&
(![X]:((~brave(X)&~old(X))=>patient(X)))&
((?[X]:((creative(X)|patient(X))))=>(strong(fred)))&
((~kind(fred))=>(?[X]:(~calm(X))))&
(((kind(paul)|~happy(paul)))<=>((~happy(alice)<~>~rich(alice))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(funny(X)|~generous(X))))&
(![X]:((rich(X)<~>humble(X))<=>(~tall(X)&happy(X))))&
(![X]:((strong(X)<~>~curious(X))<=>(~creative(X)<~>~strong(X))))&
(![X]:((quiet(X)|~funny(X))<=>calm(X)))&
(![X]:(~funny(X)<=>(~calm(X)|~patient(X))))&
(?[X]:((tall(X)&generous(X))))&
(?[X]:((wise(X)&~generous(X))))&
((~curious(fred)|calm(fred)))&
(?[X]:((wise(X)&rich(X))))&
((wise(lucy)&tall(lucy)))&
((~tall(fred)<~>calm(fred))) | ~calm(lucy) | [
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1764953915889155245960215
% SZS output start Proof for 1764953915889155245960215
15. ! [X0] : ((~funny(X0) | quiet(X0)) <=> calm(X0)) [input p14]
16. ! [X0] : (~funny(X0) <=> (~patient(X0) | ~calm(X0))) [input p15]
23. ~calm(lucy) [input hypothesis]
52. ! [X0] : (((~funny(X0) | quiet(X0)) | ~calm(X0)) & (calm(X0) | (funny(X0) & ~quiet(X0)))) [nnf transformation 15]
53. ! [X0] : ((~funny(X0) | quiet(X0) | ~calm(X0)) & (calm(X0) | (funny(X0) & ~quiet(X0)))) [flattening 52]
54. ! [X0] : ((~funny(X0) | (patient(X0) & calm(X0))) & ((~patient(X0) | ~calm(X0)) | funny(X0))) [nnf transformation 16]
55. ! [X0] : ((~funny(X0) | (patient(X0) & calm(X0))) & (~patient(X0) | ~calm(X0) | funny(X0))) [flattening 54]
108. calm(X0) | funny(X0) [cnf transformation 53]
111. ~funny(X0) | calm(X0) [cnf transformation 55]
124. ~calm(lucy) [cnf transformation 23]
229. calm(X0) [subsumption resolution 111,108]
232. $false [subsumption resolution 124,229]
% SZS output end Proof for 1764953915889155245960215
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not strong is curious and vice versa. Everyone who is not rich is funny. Everyone who is either not old or calm is humble. Everyone who is either not brave or kind is both wise and not wise. Everyone who is patient or creative is not happy and vice versa. Everyone who is both happy and rich is not wise or not tall and vice versa. Everyone who is not strong or not brave is both not kind and tall and vice versa. Everyone who is rich or not brave is tall and vice versa. Everyone who is not wise is either not tall or old and vice versa. Everyone who is either not kind or happy is not happy or not calm. If john is both tall and curious then someone is both rich and wise. If someone is creative then someone is happy and vice versa. Everyone who is not old or creative is wise. If mary is patient or not generous then paul is both not happy and creative and vice versa. If someone is kind or not humble then fred is either not kind or old and vice versa. If someone is both not wise and not humble then someone is patient or calm and vice versa. Mary is strong or tall. Alice is creative or not generous. Susan is not rich or not creative. John is not generous. Susan is strong or not patient. Someone is happy or wise. Alice is both generous and funny. | Paul is rich. | entailment | (![X]:((calm(X)|~strong(X))<=>curious(X)))&
(![X]:(~rich(X)=>funny(X)))&
(![X]:((~old(X)<~>calm(X))=>humble(X)))&
(![X]:((~brave(X)<~>kind(X))=>(wise(X)&~wise(X))))&
(![X]:((patient(X)|creative(X))<=>~happy(X)))&
(![X]:((happy(X)&rich(X))<=>(~wise(X)|~tall(X))))&
(![X]:((~strong(X)|~brave(X))<=>(~kind(X)&tall(X))))&
(![X]:((rich(X)|~brave(X))<=>tall(X)))&
(![X]:(~wise(X)<=>(~tall(X)<~>old(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~happy(X)|~calm(X))))&
(((tall(john)&curious(john)))=>(?[X]:((rich(X)&wise(X)))))&
((?[X]:(creative(X)))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)|creative(X))=>wise(X)))&
(((patient(mary)|~generous(mary)))<=>((~happy(paul)&creative(paul))))&
((?[X]:((kind(X)|~humble(X))))<=>((~kind(fred)<~>old(fred))))&
((?[X]:((~wise(X)&~humble(X))))<=>(?[X]:((patient(X)|calm(X)))))&
((strong(mary)|tall(mary)))&
((creative(alice)|~generous(alice)))&
((~rich(susan)|~creative(susan)))&
(~generous(john))&
((strong(susan)|~patient(susan)))&
(?[X]:((happy(X)|wise(X))))&
((generous(alice)&funny(alice))) | rich(paul) | [
"p3",
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3648323452760656262291907
% SZS output start Proof for 3648323452760656262291907
4. ! [X0] : ((~brave(X0) <~> kind(X0)) => (~wise(X0) & wise(X0))) [input p3]
6. ! [X0] : ((rich(X0) & happy(X0)) <=> (~tall(X0) | ~wise(X0))) [input p5]
7. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> (tall(X0) & ~kind(X0))) [input p6]
8. ! [X0] : ((~brave(X0) | rich(X0)) <=> tall(X0)) [input p7]
24. ~rich(paul) [input hypothesis]
32. ! [X0] : ((~wise(X0) & wise(X0)) | (~brave(X0) <=> kind(X0))) [ennf transformation 4]
39. ! [X0] : ((~wise(X0) & wise(X0)) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0)))) [nnf transformation 32]
42. ! [X0] : (((rich(X0) & happy(X0)) | (tall(X0) & wise(X0))) & ((~tall(X0) | ~wise(X0)) | (~rich(X0) | ~happy(X0)))) [nnf transformation 6]
43. ! [X0] : (((rich(X0) & happy(X0)) | (tall(X0) & wise(X0))) & (~tall(X0) | ~wise(X0) | ~rich(X0) | ~happy(X0))) [flattening 42]
44. ! [X0] : (((~brave(X0) | ~strong(X0)) | (~tall(X0) | kind(X0))) & ((tall(X0) & ~kind(X0)) | (brave(X0) & strong(X0)))) [nnf transformation 7]
45. ! [X0] : ((~brave(X0) | ~strong(X0) | ~tall(X0) | kind(X0)) & ((tall(X0) & ~kind(X0)) | (brave(X0) & strong(X0)))) [flattening 44]
46. ! [X0] : (((~brave(X0) | rich(X0)) | ~tall(X0)) & (tall(X0) | (brave(X0) & ~rich(X0)))) [nnf transformation 8]
47. ! [X0] : ((~brave(X0) | rich(X0) | ~tall(X0)) & (tall(X0) | (brave(X0) & ~rich(X0)))) [flattening 46]
74. wise(X0) | kind(X0) | brave(X0) [cnf transformation 39]
75. wise(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 39]
76. ~wise(X0) | kind(X0) | brave(X0) [cnf transformation 39]
77. ~wise(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 39]
85. tall(X0) | rich(X0) [cnf transformation 43]
87. ~kind(X0) | brave(X0) [cnf transformation 45]
93. ~brave(X0) | rich(X0) | ~tall(X0) [cnf transformation 47]
129. ~rich(paul) [cnf transformation 24]
131. ~kind(X0) | ~brave(X0) [subsumption resolution 75,77]
132. kind(X0) | brave(X0) [subsumption resolution 74,76]
134. ~kind(X0) [subsumption resolution 87,131]
135. ~brave(X0) | rich(X0) [subsumption resolution 93,85]
282. brave(X1) [resolution 132,134]
283. rich(X0) [resolution 135,282]
284. $false [resolution 283,129]
% SZS output end Proof for 3648323452760656262291907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is either not kind or not funny and vice versa. If fred is either kind or patient then fred is both not creative and not calm. Everyone who is not funny or not quiet is brave or not rich and vice versa. Everyone who is both funny and quiet is either not curious or old. Everyone who is not old or not rich is both not curious and not rich. If susan is not calm then susan is both not kind and not curious and vice versa. If lucy is rich or patient then susan is not rich and vice versa. If someone is both generous and not wise then john is not old and vice versa. If alice is funny or not rich then someone is humble. If lucy is both not creative and not tall then someone is wise or not happy and vice versa. Everyone who is funny or not tall is either not tall or funny. Everyone who is both not tall and not curious is patient. If alice is not funny then someone is both creative and brave. Everyone who is not quiet or not wise is both not creative and not brave. Everyone who is creative or not generous is both not brave and not kind and vice versa. Everyone who is old is both not funny and not humble. Someone is humble. Susan is quiet or brave. Someone is not calm or not happy. Someone is calm. Paul is both not quiet and patient. John is calm. Someone is both generous and happy. Someone is either not curious or not wise. | John is calm. | entailment | (![X]:(~strong(X)<=>(~kind(X)<~>~funny(X))))&
(((kind(fred)<~>patient(fred)))=>((~creative(fred)&~calm(fred))))&
(![X]:((~funny(X)|~quiet(X))<=>(brave(X)|~rich(X))))&
(![X]:((funny(X)&quiet(X))=>(~curious(X)<~>old(X))))&
(![X]:((~old(X)|~rich(X))=>(~curious(X)&~rich(X))))&
((~calm(susan))<=>((~kind(susan)&~curious(susan))))&
(((rich(lucy)|patient(lucy)))<=>(~rich(susan)))&
((?[X]:((generous(X)&~wise(X))))<=>(~old(john)))&
(((funny(alice)|~rich(alice)))=>(?[X]:(humble(X))))&
(((~creative(lucy)&~tall(lucy)))<=>(?[X]:((wise(X)|~happy(X)))))&
(![X]:((funny(X)|~tall(X))=>(~tall(X)<~>funny(X))))&
(![X]:((~tall(X)&~curious(X))=>patient(X)))&
((~funny(alice))=>(?[X]:((creative(X)&brave(X)))))&
(![X]:((~quiet(X)|~wise(X))=>(~creative(X)&~brave(X))))&
(![X]:((creative(X)|~generous(X))<=>(~brave(X)&~kind(X))))&
(![X]:(old(X)=>(~funny(X)&~humble(X))))&
(?[X]:(humble(X)))&
((quiet(susan)|brave(susan)))&
(?[X]:((~calm(X)|~happy(X))))&
(?[X]:(calm(X)))&
((~quiet(paul)&patient(paul)))&
(calm(john))&
(?[X]:((generous(X)&happy(X))))&
(?[X]:((~curious(X)<~>~wise(X)))) | calm(john) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8048272297927171004989292
% SZS output start Proof for 8048272297927171004989292
22. calm(john) [input p21]
25. ~calm(john) [input hypothesis]
126. calm(john) [cnf transformation 22]
131. ~calm(john) [cnf transformation 25]
273. $false [subsumption resolution 131,126]
% SZS output end Proof for 8048272297927171004989292
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both brave and tall then someone is strong and vice versa. Everyone who is calm or not happy is not strong and vice versa. Everyone who is tall or happy is humble or curious and vice versa. Everyone who is not humble is not curious and vice versa. Everyone who is not strong or strong is calm or wise. If someone is both not rich and old then someone is wise or calm and vice versa. If susan is both old and not tall then lucy is both not humble and strong. If paul is both quiet and not humble then someone is not brave or creative and vice versa. If someone is either happy or funny then lucy is not funny. If someone is both curious and not tall then someone is either brave or not calm and vice versa. If someone is happy then susan is tall or curious. Everyone who is creative is both humble and not creative. Everyone who is either creative or not generous is not funny. Everyone who is not calm is either tall or not quiet and vice versa. Everyone who is both kind and rich is not calm and vice versa. If someone is either rich or calm then susan is not curious and vice versa. Someone is either curious or not tall. Someone is both quiet and not strong. Mary is not curious or not calm. Someone is both not creative and quiet. Paul is not funny or not humble. Someone is either not funny or old. Someone is both not generous and not strong. Lucy is not rich. | Lucy is not happy. | entailment | (((brave(john)&tall(john)))<=>(?[X]:(strong(X))))&
(![X]:((calm(X)|~happy(X))<=>~strong(X)))&
(![X]:((tall(X)|happy(X))<=>(humble(X)|curious(X))))&
(![X]:(~humble(X)<=>~curious(X)))&
(![X]:((~strong(X)|strong(X))=>(calm(X)|wise(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:((wise(X)|calm(X)))))&
(((old(susan)&~tall(susan)))=>((~humble(lucy)&strong(lucy))))&
(((quiet(paul)&~humble(paul)))<=>(?[X]:((~brave(X)|creative(X)))))&
((?[X]:((happy(X)<~>funny(X))))=>(~funny(lucy)))&
((?[X]:((curious(X)&~tall(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
((?[X]:(happy(X)))=>((tall(susan)|curious(susan))))&
(![X]:(creative(X)=>(humble(X)&~creative(X))))&
(![X]:((creative(X)<~>~generous(X))=>~funny(X)))&
(![X]:(~calm(X)<=>(tall(X)<~>~quiet(X))))&
(![X]:((kind(X)&rich(X))<=>~calm(X)))&
((?[X]:((rich(X)<~>calm(X))))<=>(~curious(susan)))&
(?[X]:((curious(X)<~>~tall(X))))&
(?[X]:((quiet(X)&~strong(X))))&
((~curious(mary)|~calm(mary)))&
(?[X]:((~creative(X)&quiet(X))))&
((~funny(paul)|~humble(paul)))&
(?[X]:((~funny(X)<~>old(X))))&
(?[X]:((~generous(X)&~strong(X))))&
(~rich(lucy)) | ~happy(lucy) | [
"p2",
"p3",
"p10",
"p14",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4226996612400630451711056
% SZS output start Proof for 4226996612400630451711056
3. ! [X0] : ((happy(X0) | tall(X0)) <=> (curious(X0) | humble(X0))) [input p2]
4. ! [X0] : (~humble(X0) <=> ~curious(X0)) [input p3]
11. ? [X0] : happy(X0) => (curious(susan) | tall(susan)) [input p10]
15. ! [X0] : ((rich(X0) & kind(X0)) <=> ~calm(X0)) [input p14]
16. ? [X0] : (rich(X0) <~> calm(X0)) <=> ~curious(susan) [input p15]
24. ~rich(lucy) [input p23]
25. happy(lucy) [input hypothesis]
33. (curious(susan) | tall(susan)) | ! [X0] : ~happy(X0) [ennf transformation 11]
34. curious(susan) | tall(susan) | ! [X0] : ~happy(X0) [flattening 33]
44. ! [X0] : (((happy(X0) | tall(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (~happy(X0) & ~tall(X0)))) [nnf transformation 3]
45. ! [X0] : ((happy(X0) | tall(X0) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | (~happy(X0) & ~tall(X0)))) [flattening 44]
46. ! [X0] : ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0))) [nnf transformation 4]
65. ! [X0] : (((rich(X0) & kind(X0)) | calm(X0)) & (~calm(X0) | (~rich(X0) | ~kind(X0)))) [nnf transformation 15]
66. ! [X0] : (((rich(X0) & kind(X0)) | calm(X0)) & (~calm(X0) | ~rich(X0) | ~kind(X0))) [flattening 65]
67. (? [X0] : ((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | curious(susan)) & (~curious(susan) | ! [X0] : ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) [nnf transformation 16]
68. (? [X0] : ((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | curious(susan)) & (~curious(susan) | ! [X1] : ((rich(X1) | ~calm(X1)) & (calm(X1) | ~rich(X1)))) [rectify 67]
69. ? [X0] : ((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) => ((~calm(sK6) | ~rich(sK6)) & (calm(sK6) | rich(sK6))) [choice axiom]
70. (((~calm(sK6) | ~rich(sK6)) & (calm(sK6) | rich(sK6))) | curious(susan)) & (~curious(susan) | ! [X1] : ((rich(X1) | ~calm(X1)) & (calm(X1) | ~rich(X1)))) [skolemisation 68,69]
89. ~tall(X0) | humble(X0) | curious(X0) [cnf transformation 45]
94. ~humble(X0) | curious(X0) [cnf transformation 46]
117. curious(susan) | tall(susan) | ~happy(X0) [cnf transformation 34]
128. rich(X0) | calm(X0) [cnf transformation 66]
130. ~curious(susan) | rich(X1) | ~calm(X1) [cnf transformation 70]
145. ~rich(lucy) [cnf transformation 24]
146. happy(lucy) [cnf transformation 25]
191. 10 <=> tall(susan) [avatar definition]
193. tall(susan) <- (10) [avatar component clause 191]
275. 29 <=> ! [X0] : ~happy(X0) [avatar definition]
276. ~happy(X0) <- (29) [avatar component clause 275]
278. 30 <=> curious(susan) [avatar definition]
279. ~curious(susan) <- (~30) [avatar component clause 278]
281. 29 | 10 | 30 [avatar split clause 117,278,191,275]
292. ~curious(susan) | rich(X1) [subsumption resolution 130,128]
294. 33 <=> ! [X1] : rich(X1) [avatar definition]
295. rich(X1) <- (33) [avatar component clause 294]
296. 33 | ~30 [avatar split clause 292,278,294]
357. humble(susan) | curious(susan) <- (10) [resolution 89,193]
359. humble(susan) <- (10, ~30) [subsumption resolution 357,279]
365. curious(susan) <- (10, ~30) [resolution 359,94]
366. $false <- (10, ~30) [subsumption resolution 365,279]
367. ~10 | 30 [avatar contradiction clause 366]
368. $false <- (29) [resolution 276,146]
371. ~29 [avatar contradiction clause 368]
373. $false <- (33) [resolution 295,145]
376. ~33 [avatar contradiction clause 373]
377. $false [avatar sat refutation 281,296,367,371,376]
% SZS output end Proof for 4226996612400630451711056
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not patient is either not funny or creative and vice versa. Everyone who is not creative or not happy is wise and vice versa. Everyone who is generous or not creative is both calm and quiet and vice versa. Everyone who is either kind or creative is not brave or calm and vice versa. Everyone who is humble is either not humble or humble and vice versa. Everyone who is either old or strong is both not rich and not happy. Everyone who is not calm or not funny is either not happy or wise. If someone is either brave or calm then susan is both not quiet and not wise. If someone is either quiet or not generous then someone is not tall or quiet. If someone is not creative then someone is both not funny and brave and vice versa. Everyone who is not funny is both tall and not calm. If mary is not generous then susan is not curious. Everyone who is rich or generous is quiet. If mary is not old or quiet then someone is not tall and vice versa. If mary is either rich or not curious then someone is either not humble or funny. Everyone who is not calm or brave is either not funny or happy and vice versa. Paul is not old. Susan is brave or strong. Someone is old or generous. Someone is either rich or not generous. Someone is quiet. Alice is not happy. | Mary is funny. | entailment | (![X]:((happy(X)|~patient(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((~creative(X)|~happy(X))<=>wise(X)))&
(![X]:((generous(X)|~creative(X))<=>(calm(X)&quiet(X))))&
(![X]:((kind(X)<~>creative(X))<=>(~brave(X)|calm(X))))&
(![X]:(humble(X)<=>(~humble(X)<~>humble(X))))&
(![X]:((old(X)<~>strong(X))=>(~rich(X)&~happy(X))))&
(![X]:((~calm(X)|~funny(X))=>(~happy(X)<~>wise(X))))&
((?[X]:((brave(X)<~>calm(X))))=>((~quiet(susan)&~wise(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:(~funny(X)=>(tall(X)&~calm(X))))&
((~generous(mary))=>(~curious(susan)))&
(![X]:((rich(X)|generous(X))=>quiet(X)))&
(((~old(mary)|quiet(mary)))<=>(?[X]:(~tall(X))))&
(((rich(mary)<~>~curious(mary)))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~calm(X)|brave(X))<=>(~funny(X)<~>happy(X))))&
(~old(paul))&
((brave(susan)|strong(susan)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:(quiet(X)))&
(~happy(alice)) | funny(mary) | [
"p1",
"p6",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4971347201143876721909180
% SZS output start Proof for 4971347201143876721909180
2. ! [X0] : ((~happy(X0) | ~creative(X0)) <=> wise(X0)) [input p1]
7. ! [X0] : ((~funny(X0) | ~calm(X0)) => (~happy(X0) <~> wise(X0))) [input p6]
11. ! [X0] : (~funny(X0) => (~calm(X0) & tall(X0))) [input p10]
16. ! [X0] : ((brave(X0) | ~calm(X0)) <=> (~funny(X0) <~> happy(X0))) [input p15]
23. ~funny(mary) [input hypothesis]
27. ! [X0] : ((~happy(X0) <~> wise(X0)) | (funny(X0) & calm(X0))) [ennf transformation 7]
30. ! [X0] : ((~calm(X0) & tall(X0)) | funny(X0)) [ennf transformation 11]
36. ! [X0] : (((~happy(X0) | ~creative(X0)) | ~wise(X0)) & (wise(X0) | (happy(X0) & creative(X0)))) [nnf transformation 2]
37. ! [X0] : ((~happy(X0) | ~creative(X0) | ~wise(X0)) & (wise(X0) | (happy(X0) & creative(X0)))) [flattening 36]
44. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (funny(X0) & calm(X0))) [nnf transformation 27]
63. ! [X0] : (((brave(X0) | ~calm(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~brave(X0) & calm(X0)))) [nnf transformation 16]
64. ! [X0] : ((brave(X0) | ~calm(X0) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (~brave(X0) & calm(X0)))) [flattening 63]
79. wise(X0) | happy(X0) [cnf transformation 37]
102. ~wise(X0) | happy(X0) | calm(X0) [cnf transformation 44]
114. ~calm(X0) | funny(X0) [cnf transformation 30]
127. ~happy(X0) | funny(X0) | calm(X0) [cnf transformation 64]
138. ~funny(mary) [cnf transformation 23]
146. happy(X0) | calm(X0) [subsumption resolution 102,79]
252. funny(X0) | calm(X0) [subsumption resolution 127,146]
253. funny(X0) [subsumption resolution 252,114]
283. $false [subsumption resolution 138,253]
% SZS output end Proof for 4971347201143876721909180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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