premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not creative or not funny is both patient and not patient and vice versa.
Everyone who is both calm and not old is either old or wise and vice versa.
Everyone who is not happy or not funny is rich or happy.
If someone is not rich or humble then someone is either not quiet or kind.
If paul is both not creative and generous then someone is both old and not creative.
If someone is rich or wise then mary is both not old and kind.
If someone is not brave then mary is either old or not tall.
If someone is both quiet and not humble then someone is either not funny or not brave and vice versa.
If paul is not humble then john is both not old and not strong and vice versa.
If mary is not humble then lucy is both not tall and humble and vice versa.
If mary is not strong or funny then lucy is both curious and not tall.
If someone is either not creative or wise then someone is either not old or not tall and vice versa.
Everyone who is both patient and not happy is both not tall and not curious.
If someone is either funny or generous then someone is humble or not tall.
If mary is either not creative or calm then someone is not calm.
Someone is kind or humble.
Someone is both not humble and not kind.
Mary is not happy.
Someone is happy.
Someone is not kind or not generous.
Fred is not wise.
John is both creative and not happy.
Alice is either not generous or patient. | Mary is not old. | entailment | (![X]:((~creative(X)|~funny(X))<=>(patient(X)&~patient(X))))&
(![X]:((calm(X)&~old(X))<=>(old(X)<~>wise(X))))&
(![X]:((~happy(X)|~funny(X))=>(rich(X)|happy(X))))&
((?[X]:((~rich(X)|humble(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(((~creative(paul)&generous(paul)))=>(?[X]:((old(X)&~creative(X)))))&
((?[X]:((rich(X)|wise(X))))=>((~old(mary)&kind(mary))))&
((?[X]:(~brave(X)))=>((old(mary)<~>~tall(mary))))&
((?[X]:((quiet(X)&~humble(X))))<=>(?[X]:((~funny(X)<~>~brave(X)))))&
((~humble(paul))<=>((~old(john)&~strong(john))))&
((~humble(mary))<=>((~tall(lucy)&humble(lucy))))&
(((~strong(mary)|funny(mary)))=>((curious(lucy)&~tall(lucy))))&
((?[X]:((~creative(X)<~>wise(X))))<=>(?[X]:((~old(X)<~>~tall(X)))))&
(![X]:((patient(X)&~happy(X))=>(~tall(X)&~curious(X))))&
((?[X]:((funny(X)<~>generous(X))))=>(?[X]:((humble(X)|~tall(X)))))&
(((~creative(mary)<~>calm(mary)))=>(?[X]:(~calm(X))))&
(?[X]:((kind(X)|humble(X))))&
(?[X]:((~humble(X)&~kind(X))))&
(~happy(mary))&
(?[X]:(happy(X)))&
(?[X]:((~kind(X)|~generous(X))))&
(~wise(fred))&
((creative(john)&~happy(john)))&
((~generous(alice)<~>patient(alice))) | ~old(mary) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2573494822968672935372591
% SZS output start Proof for 2573494822968672935372591
2. ! [X0] : ((~old(X0) & calm(X0)) <=> (old(X0) <~> wise(X0))) [input p1]
6. ? [X0] : (wise(X0) | rich(X0)) => (kind(mary) & ~old(mary)) [input p5]
24. old(mary) [input hypothesis]
34. (kind(mary) & ~old(mary)) | ! [X0] : (~wise(X0) & ~rich(X0)) [ennf transformation 6]
43. ! [X0] : (((~old(X0) & calm(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0)))) & (((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | (old(X0) | ~calm(X0)))) [nnf transformation 2]
44. ! [X0] : (((~old(X0) & calm(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0)))) & (((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | old(X0) | ~calm(X0))) [flattening 43]
91. ~old(X0) | wise(X0) | ~old(X0) [cnf transformation 44]
102. ~old(mary) | ~wise(X0) [cnf transformation 34]
148. old(mary) [cnf transformation 24]
151. ~old(X0) | wise(X0) [duplicate literal removal 91]
174. 5 <=> ! [X0] : ~wise(X0) [avatar definition]
175. ~wise(X0) <- (5) [avatar component clause 174]
186. 8 <=> old(mary) [avatar definition]
187. old(mary) <- (8) [avatar component clause 186]
189. 5 | ~8 [avatar split clause 102,186,174]
336. 8 [avatar split clause 148,186]
342. wise(mary) <- (8) [resolution 151,187]
343. $false <- (5, 8) [subsumption resolution 342,175]
344. ~5 | ~8 [avatar contradiction clause 343]
345. $false [avatar sat refutation 189,336,344]
% SZS output end Proof for 2573494822968672935372591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is curious or brave and vice versa.
Everyone who is not curious or not generous is curious.
If lucy is both not wise and not quiet then john is both not curious and quiet.
Everyone who is both funny and not old is both not strong and creative.
Everyone who is both not brave and not patient is both brave and tall.
Everyone who is either creative or tall is not old or wise and vice versa.
Everyone who is either not rich or not strong is not wise.
If paul is both kind and tall then someone is not brave and vice versa.
Everyone who is either curious or old is not rich or rich.
Everyone who is not brave is either not strong or not wise and vice versa.
Everyone who is not humble is both humble and strong and vice versa.
If mary is not strong or old then someone is funny or brave.
Everyone who is both humble and not rich is either funny or kind.
Everyone who is rich or quiet is curious or strong.
If someone is both funny and strong then someone is both not tall and not kind.
Everyone who is humble is calm and vice versa.
Someone is patient.
Lucy is both not tall and not generous.
Mary is both not generous and old.
Alice is not creative or humble.
Someone is either funny or curious.
Someone is happy.
Paul is old.
Mary is either not quiet or not curious. | Paul is not creative. | entailment | (![X]:(~tall(X)<=>(curious(X)|brave(X))))&
(![X]:((~curious(X)|~generous(X))=>curious(X)))&
(((~wise(lucy)&~quiet(lucy)))=>((~curious(john)&quiet(john))))&
(![X]:((funny(X)&~old(X))=>(~strong(X)&creative(X))))&
(![X]:((~brave(X)&~patient(X))=>(brave(X)&tall(X))))&
(![X]:((creative(X)<~>tall(X))<=>(~old(X)|wise(X))))&
(![X]:((~rich(X)<~>~strong(X))=>~wise(X)))&
(((kind(paul)&tall(paul)))<=>(?[X]:(~brave(X))))&
(![X]:((curious(X)<~>old(X))=>(~rich(X)|rich(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~wise(X))))&
(![X]:(~humble(X)<=>(humble(X)&strong(X))))&
(((~strong(mary)|old(mary)))=>(?[X]:((funny(X)|brave(X)))))&
(![X]:((humble(X)&~rich(X))=>(funny(X)<~>kind(X))))&
(![X]:((rich(X)|quiet(X))=>(curious(X)|strong(X))))&
((?[X]:((funny(X)&strong(X))))=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:(humble(X)<=>calm(X)))&
(?[X]:(patient(X)))&
((~tall(lucy)&~generous(lucy)))&
((~generous(mary)&old(mary)))&
((~creative(alice)|humble(alice)))&
(?[X]:((funny(X)<~>curious(X))))&
(?[X]:(happy(X)))&
(old(paul))&
((~quiet(mary)<~>~curious(mary))) | ~creative(paul) | [
"p0",
"p1",
"p5",
"p7",
"p9",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2073612464108907437486338
% SZS output start Proof for 2073612464108907437486338
1. ! [X0] : (~tall(X0) <=> (brave(X0) | curious(X0))) [input p0]
2. ! [X0] : ((~generous(X0) | ~curious(X0)) => curious(X0)) [input p1]
6. ! [X0] : ((creative(X0) <~> tall(X0)) <=> (wise(X0) | ~old(X0))) [input p5]
8. (tall(paul) & kind(paul)) <=> ? [X0] : ~brave(X0) [input p7]
10. ! [X0] : (~brave(X0) <=> (~strong(X0) <~> ~wise(X0))) [input p9]
11. ! [X0] : (~humble(X0) <=> (strong(X0) & humble(X0))) [input p10]
23. old(paul) [input p22]
25. creative(paul) [input hypothesis]
30. ! [X0] : (curious(X0) | (generous(X0) & curious(X0))) [ennf transformation 2]
44. ! [X0] : ((~tall(X0) | (~brave(X0) & ~curious(X0))) & ((brave(X0) | curious(X0)) | tall(X0))) [nnf transformation 1]
45. ! [X0] : ((~tall(X0) | (~brave(X0) & ~curious(X0))) & (brave(X0) | curious(X0) | tall(X0))) [flattening 44]
46. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~wise(X0) & old(X0))) & ((wise(X0) | ~old(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [nnf transformation 6]
47. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~wise(X0) & old(X0))) & (wise(X0) | ~old(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [flattening 46]
49. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~tall(paul) | ~kind(paul))) [nnf transformation 8]
50. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~tall(paul) | ~kind(paul)) [flattening 49]
51. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~tall(paul) | ~kind(paul)) [rectify 50]
52. ? [X1] : ~brave(X1) => ~brave(sK0) [choice axiom]
53. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (~brave(sK0) | ~tall(paul) | ~kind(paul)) [skolemisation 51,52]
55. ! [X0] : ((~brave(X0) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) & (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | brave(X0))) [nnf transformation 10]
56. ! [X0] : ((~humble(X0) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | humble(X0))) [nnf transformation 11]
57. ! [X0] : ((~humble(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | humble(X0))) [flattening 56]
70. ~curious(X0) | ~tall(X0) [cnf transformation 45]
72. curious(X0) | curious(X0) [cnf transformation 30]
78. ~creative(X0) | ~old(X0) | tall(X0) | wise(X0) [cnf transformation 47]
88. tall(paul) | brave(X0) [cnf transformation 53]
93. ~wise(X0) | ~brave(X0) | strong(X0) [cnf transformation 55]
95. humble(X0) | humble(X0) [cnf transformation 57]
97. ~humble(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 57]
115. old(paul) [cnf transformation 23]
118. creative(paul) [cnf transformation 25]
119. humble(X0) [duplicate literal removal 95]
120. ~humble(X0) | ~strong(X0) [duplicate literal removal 97]
121. curious(X0) [duplicate literal removal 72]
138. 4 <=> ! [X0] : brave(X0) [avatar definition]
139. brave(X0) <- (4) [avatar component clause 138]
141. 5 <=> tall(paul) [avatar definition]
142. ~tall(paul) <- (~5) [avatar component clause 141]
143. tall(paul) <- (5) [avatar component clause 141]
144. 4 | 5 [avatar split clause 88,141,138]
192. ~tall(X0) [resolution 70,121]
197. ~strong(X1) [resolution 120,119]
235. ~old(paul) | tall(paul) | wise(paul) [resolution 78,118]
238. tall(paul) | wise(paul) [subsumption resolution 235,115]
239. wise(paul) <- (~5) [subsumption resolution 238,142]
242. ~brave(paul) | strong(paul) <- (~5) [resolution 239,93]
244. strong(paul) <- (4, ~5) [subsumption resolution 242,139]
245. $false <- (4, ~5) [subsumption resolution 244,197]
246. ~4 | 5 [avatar contradiction clause 245]
250. $false <- (5) [subsumption resolution 143,192]
251. ~5 [avatar contradiction clause 250]
252. $false [avatar sat refutation 144,246,251]
% SZS output end Proof for 2073612464108907437486338
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or quiet is either not happy or not generous. If john is calm or quiet then fred is not kind. Everyone who is not curious is rich or not rich and vice versa. Everyone who is brave is both brave and not strong. If someone is either happy or not curious then someone is not calm. Everyone who is funny is either humble or not humble and vice versa. If susan is not old then susan is not tall. Everyone who is both creative and not creative is not quiet or not patient and vice versa. If someone is either not generous or patient then someone is both not old and not funny. If john is both not patient and kind then john is both not generous and not wise and vice versa. Everyone who is both generous and not calm is either not old or calm. If someone is brave or not humble then john is calm. If someone is both rich and creative then fred is either not quiet or not rich and vice versa. Everyone who is not humble is not strong or wise. Everyone who is both quiet and wise is calm or curious and vice versa. Everyone who is wise is both calm and creative and vice versa. Susan is either funny or not old. Someone is not kind or strong. Susan is not generous or tall. Mary is both not humble and old. Someone is both strong and humble. Mary is not generous. Paul is both not strong and not generous. | Fred is patient. | entailment | (![X]:((brave(X)|quiet(X))=>(~happy(X)<~>~generous(X))))&
(((calm(john)|quiet(john)))=>(~kind(fred)))&
(![X]:(~curious(X)<=>(rich(X)|~rich(X))))&
(![X]:(brave(X)=>(brave(X)&~strong(X))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:(~calm(X))))&
(![X]:(funny(X)<=>(humble(X)<~>~humble(X))))&
((~old(susan))=>(~tall(susan)))&
(![X]:((creative(X)&~creative(X))<=>(~quiet(X)|~patient(X))))&
((?[X]:((~generous(X)<~>patient(X))))=>(?[X]:((~old(X)&~funny(X)))))&
(((~patient(john)&kind(john)))<=>((~generous(john)&~wise(john))))&
(![X]:((generous(X)&~calm(X))=>(~old(X)<~>calm(X))))&
((?[X]:((brave(X)|~humble(X))))=>(calm(john)))&
((?[X]:((rich(X)&creative(X))))<=>((~quiet(fred)<~>~rich(fred))))&
(![X]:(~humble(X)=>(~strong(X)|wise(X))))&
(![X]:((quiet(X)&wise(X))<=>(calm(X)|curious(X))))&
(![X]:(wise(X)<=>(calm(X)&creative(X))))&
((funny(susan)<~>~old(susan)))&
(?[X]:((~kind(X)|strong(X))))&
((~generous(susan)|tall(susan)))&
((~humble(mary)&old(mary)))&
(?[X]:((strong(X)&humble(X))))&
(~generous(mary))&
((~strong(paul)&~generous(paul))) | patient(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3048752925661883055935136
% SZS output start Proof for 3048752925661883055935136
8. ! [X0] : ((~creative(X0) & creative(X0)) <=> (~patient(X0) | ~quiet(X0))) [input p7]
24. ~patient(fred) [input hypothesis]
46. ! [X0] : (((~creative(X0) & creative(X0)) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | (creative(X0) | ~creative(X0)))) [nnf transformation 8]
47. ! [X0] : (((~creative(X0) & creative(X0)) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | creative(X0) | ~creative(X0))) [flattening 46]
88. creative(X0) | patient(X0) [cnf transformation 47]
90. ~creative(X0) | patient(X0) [cnf transformation 47]
129. ~patient(fred) [cnf transformation 24]
167. patient(X0) [subsumption resolution 88,90]
226. $false [subsumption resolution 129,167]
% SZS output end Proof for 3048752925661883055935136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then someone is both not calm and not tall.
If someone is not wise then fred is curious.
If someone is not patient then someone is both strong and not rich.
If someone is brave then fred is wise and vice versa.
If alice is humble or not tall then someone is not tall or happy and vice versa.
If someone is both not calm and kind then someone is both rich and not rich.
Everyone who is wise is either generous or not creative and vice versa.
Everyone who is both patient and not curious is brave or old and vice versa.
Everyone who is either not calm or not wise is both not old and rich.
If someone is either funny or not quiet then someone is both old and not wise.
Everyone who is both not kind and brave is not calm or rich.
Everyone who is not calm or not wise is both not brave and brave.
Everyone who is rich is calm or patient.
Everyone who is both not generous and old is wise or calm.
If john is either not old or kind then lucy is not happy and vice versa.
Everyone who is not old or wise is strong or not brave.
Paul is either rich or funny.
Someone is not kind or old.
John is either rich or not humble.
Mary is either not strong or humble.
Someone is not brave.
Alice is curious.
Someone is not generous.
Someone is wise. | Fred is not quiet. | contradiction | ((?[X]:(~quiet(X)))=>(?[X]:((~calm(X)&~tall(X)))))&
((?[X]:(~wise(X)))=>(curious(fred)))&
((?[X]:(~patient(X)))=>(?[X]:((strong(X)&~rich(X)))))&
((?[X]:(brave(X)))<=>(wise(fred)))&
(((humble(alice)|~tall(alice)))<=>(?[X]:((~tall(X)|happy(X)))))&
((?[X]:((~calm(X)&kind(X))))=>(?[X]:((rich(X)&~rich(X)))))&
(![X]:(wise(X)<=>(generous(X)<~>~creative(X))))&
(![X]:((patient(X)&~curious(X))<=>(brave(X)|old(X))))&
(![X]:((~calm(X)<~>~wise(X))=>(~old(X)&rich(X))))&
((?[X]:((funny(X)<~>~quiet(X))))=>(?[X]:((old(X)&~wise(X)))))&
(![X]:((~kind(X)&brave(X))=>(~calm(X)|rich(X))))&
(![X]:((~calm(X)|~wise(X))=>(~brave(X)&brave(X))))&
(![X]:(rich(X)=>(calm(X)|patient(X))))&
(![X]:((~generous(X)&old(X))=>(wise(X)|calm(X))))&
(((~old(john)<~>kind(john)))<=>(~happy(lucy)))&
(![X]:((~old(X)|wise(X))=>(strong(X)|~brave(X))))&
((rich(paul)<~>funny(paul)))&
(?[X]:((~kind(X)|old(X))))&
((rich(john)<~>~humble(john)))&
((~strong(mary)<~>humble(mary)))&
(?[X]:(~brave(X)))&
(curious(alice))&
(?[X]:(~generous(X)))&
(?[X]:(wise(X))) | ~quiet(fred) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7785713461926326263340516
% SZS output start Proof for 7785713461926326263340516
1. ? [X0] : ~quiet(X0) => ? [X0] : (~tall(X0) & ~calm(X0)) [input p0]
12. ! [X0] : ((~wise(X0) | ~calm(X0)) => (brave(X0) & ~brave(X0))) [input p11]
25. ~quiet(fred) [input hypothesis]
26. ? [X0] : ~quiet(X0) => ? [X1] : (~tall(X1) & ~calm(X1)) [rectify 1]
30. ? [X1] : (~tall(X1) & ~calm(X1)) | ! [X0] : quiet(X0) [ennf transformation 26]
38. ! [X0] : ((brave(X0) & ~brave(X0)) | (wise(X0) & calm(X0))) [ennf transformation 12]
45. ? [X0] : (~tall(X0) & ~calm(X0)) | ! [X1] : quiet(X1) [rectify 30]
46. ? [X0] : (~tall(X0) & ~calm(X0)) => (~tall(sK0) & ~calm(sK0)) [choice axiom]
47. (~tall(sK0) & ~calm(sK0)) | ! [X1] : quiet(X1) [skolemisation 45,46]
83. ~calm(sK0) | quiet(X1) [cnf transformation 47]
114. ~brave(X0) | calm(X0) [cnf transformation 38]
116. brave(X0) | calm(X0) [cnf transformation 38]
137. ~quiet(fred) [cnf transformation 25]
139. 1 <=> ! [X1] : quiet(X1) [avatar definition]
140. quiet(X1) <- (1) [avatar component clause 139]
147. 3 <=> calm(sK0) [avatar definition]
149. ~calm(sK0) <- (~3) [avatar component clause 147]
150. 1 | ~3 [avatar split clause 83,147,139]
240. calm(X0) [subsumption resolution 114,116]
296. $false <- (~3) [subsumption resolution 149,240]
297. 3 [avatar contradiction clause 296]
298. $false <- (1) [resolution 140,137]
299. ~1 [avatar contradiction clause 298]
300. $false [avatar sat refutation 150,297,299]
% SZS output end Proof for 7785713461926326263340516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not happy then alice is both not generous and not rich. If fred is both happy and strong then susan is not curious. If paul is either tall or not old then mary is not tall. If someone is either not funny or funny then someone is either not kind or old. Everyone who is either happy or brave is either not patient or not kind and vice versa. If someone is either wise or tall then someone is both happy and tall and vice versa. Everyone who is both not rich and wise is either creative or not creative and vice versa. Everyone who is either rich or not curious is not brave and vice versa. Everyone who is kind or brave is both not quiet and patient. Everyone who is both not tall and not curious is strong. Everyone who is not happy or brave is not tall or not humble and vice versa. Everyone who is not curious or not funny is both not brave and not humble and vice versa. Everyone who is both not patient and not funny is not old or not curious and vice versa. Everyone who is patient is both tall and quiet and vice versa. If susan is both not calm and not generous then susan is old or brave. If someone is either patient or quiet then someone is not rich or brave. Someone is either not creative or not kind. Someone is strong. Mary is either not generous or not old. Someone is both not quiet and not funny. Someone is happy or wise. | Fred is curious. | contradiction | ((?[X]:((~humble(X)|~happy(X))))=>((~generous(alice)&~rich(alice))))&
(((happy(fred)&strong(fred)))=>(~curious(susan)))&
(((tall(paul)<~>~old(paul)))=>(~tall(mary)))&
((?[X]:((~funny(X)<~>funny(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(~patient(X)<~>~kind(X))))&
((?[X]:((wise(X)<~>tall(X))))<=>(?[X]:((happy(X)&tall(X)))))&
(![X]:((~rich(X)&wise(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((rich(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((kind(X)|brave(X))=>(~quiet(X)&patient(X))))&
(![X]:((~tall(X)&~curious(X))=>strong(X)))&
(![X]:((~happy(X)|brave(X))<=>(~tall(X)|~humble(X))))&
(![X]:((~curious(X)|~funny(X))<=>(~brave(X)&~humble(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~old(X)|~curious(X))))&
(![X]:(patient(X)<=>(tall(X)&quiet(X))))&
(((~calm(susan)&~generous(susan)))=>((old(susan)|brave(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>(?[X]:((~rich(X)|brave(X)))))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:(strong(X)))&
((~generous(mary)<~>~old(mary)))&
(?[X]:((~quiet(X)&~funny(X))))&
(?[X]:((happy(X)|wise(X)))) | curious(fred) | [
"p6",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4025878976706923752494293
% SZS output start Proof for 4025878976706923752494293
7. ! [X0] : ((wise(X0) & ~rich(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p6]
8. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> ~brave(X0)) [input p7]
9. ! [X0] : ((brave(X0) | kind(X0)) => (patient(X0) & ~quiet(X0))) [input p8]
14. ! [X0] : (patient(X0) <=> (quiet(X0) & tall(X0))) [input p13]
22. curious(fred) [input hypothesis]
32. ! [X0] : ((patient(X0) & ~quiet(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 9]
47. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~wise(X0) | rich(X0)))) [nnf transformation 7]
48. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~wise(X0) | rich(X0))) [flattening 47]
49. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | brave(X0)) & (~brave(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 8]
56. ! [X0] : ((patient(X0) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [nnf transformation 14]
57. ! [X0] : ((patient(X0) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | ~patient(X0))) [flattening 56]
99. ~rich(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
100. ~rich(X0) | creative(X0) | creative(X0) [cnf transformation 48]
105. ~curious(X0) | rich(X0) | brave(X0) [cnf transformation 49]
108. ~quiet(X0) | ~brave(X0) [cnf transformation 32]
110. ~brave(X0) | patient(X0) [cnf transformation 32]
127. ~patient(X0) | quiet(X0) [cnf transformation 57]
139. curious(fred) [cnf transformation 22]
140. ~rich(X0) | ~creative(X0) [duplicate literal removal 99]
141. ~rich(X0) | creative(X0) [duplicate literal removal 100]
243. ~rich(X0) [subsumption resolution 140,141]
244. ~curious(X0) | brave(X0) [subsumption resolution 105,243]
272. brave(fred) [resolution 244,139]
274. patient(fred) [resolution 272,110]
278. quiet(fred) [resolution 274,127]
286. ~brave(fred) [resolution 278,108]
288. $false [subsumption resolution 286,272]
% SZS output end Proof for 4025878976706923752494293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is not curious or not tall and vice versa.
If susan is both not funny and old then someone is not generous.
Everyone who is wise or generous is both tall and not generous.
Everyone who is either tall or brave is old and vice versa.
If lucy is both humble and not humble then someone is not happy and vice versa.
If someone is both generous and not kind then someone is funny.
If someone is both not kind and humble then john is either not happy or humble and vice versa.
Everyone who is happy is both rich and not calm.
If someone is both kind and curious then alice is not happy or humble.
Everyone who is not happy or not quiet is either not humble or brave and vice versa.
If someone is either happy or funny then susan is either not funny or funny.
If someone is patient or not calm then paul is both kind and not patient.
Everyone who is not happy or kind is not curious or wise and vice versa.
Everyone who is not old or humble is brave or generous and vice versa.
If fred is not humble then alice is not humble and vice versa.
Everyone who is brave or wise is both not tall and creative and vice versa.
Alice is not wise.
Someone is both not humble and kind.
Fred is not calm.
Someone is not tall or funny.
Someone is happy or not strong.
Fred is not generous or creative. | Fred is not happy. | contradiction | (![X]:(~calm(X)<=>(~curious(X)|~tall(X))))&
(((~funny(susan)&old(susan)))=>(?[X]:(~generous(X))))&
(![X]:((wise(X)|generous(X))=>(tall(X)&~generous(X))))&
(![X]:((tall(X)<~>brave(X))<=>old(X)))&
(((humble(lucy)&~humble(lucy)))<=>(?[X]:(~happy(X))))&
((?[X]:((generous(X)&~kind(X))))=>(?[X]:(funny(X))))&
((?[X]:((~kind(X)&humble(X))))<=>((~happy(john)<~>humble(john))))&
(![X]:(happy(X)=>(rich(X)&~calm(X))))&
((?[X]:((kind(X)&curious(X))))=>((~happy(alice)|humble(alice))))&
(![X]:((~happy(X)|~quiet(X))<=>(~humble(X)<~>brave(X))))&
((?[X]:((happy(X)<~>funny(X))))=>((~funny(susan)<~>funny(susan))))&
((?[X]:((patient(X)|~calm(X))))=>((kind(paul)&~patient(paul))))&
(![X]:((~happy(X)|kind(X))<=>(~curious(X)|wise(X))))&
(![X]:((~old(X)|humble(X))<=>(brave(X)|generous(X))))&
((~humble(fred))<=>(~humble(alice)))&
(![X]:((brave(X)|wise(X))<=>(~tall(X)&creative(X))))&
(~wise(alice))&
(?[X]:((~humble(X)&kind(X))))&
(~calm(fred))&
(?[X]:((~tall(X)|funny(X))))&
(?[X]:((happy(X)|~strong(X))))&
((~generous(fred)|creative(fred))) | ~happy(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8188479817534483037840616
% SZS output start Proof for 8188479817534483037840616
5. (~humble(lucy) & humble(lucy)) <=> ? [X0] : ~happy(X0) [input p4]
23. ~happy(fred) [input hypothesis]
42. ((~humble(lucy) & humble(lucy)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (humble(lucy) | ~humble(lucy))) [nnf transformation 5]
43. ((~humble(lucy) & humble(lucy)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | humble(lucy) | ~humble(lucy)) [flattening 42]
44. ((~humble(lucy) & humble(lucy)) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | humble(lucy) | ~humble(lucy)) [rectify 43]
45. ? [X1] : ~happy(X1) => ~happy(sK1) [choice axiom]
46. ((~humble(lucy) & humble(lucy)) | ! [X0] : happy(X0)) & (~happy(sK1) | humble(lucy) | ~humble(lucy)) [skolemisation 44,45]
81. humble(lucy) | happy(X0) [cnf transformation 46]
82. ~humble(lucy) | happy(X0) [cnf transformation 46]
124. ~happy(fred) [cnf transformation 23]
140. 4 <=> ! [X0] : happy(X0) [avatar definition]
141. happy(X0) <- (4) [avatar component clause 140]
143. 5 <=> humble(lucy) [avatar definition]
146. 4 | ~5 [avatar split clause 82,143,140]
147. 4 | 5 [avatar split clause 81,143,140]
212. $false <- (4) [resolution 141,124]
213. ~4 [avatar contradiction clause 212]
214. $false [avatar sat refutation 146,147,213]
% SZS output end Proof for 8188479817534483037840616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both patient and rich then someone is not generous or funny. Everyone who is both strong and not kind is not tall or patient. Everyone who is both not patient and not funny is not tall and vice versa. Everyone who is not old is not patient or not quiet and vice versa. If someone is both not quiet and not brave then lucy is both rich and not patient. Everyone who is kind is both curious and not old and vice versa. Everyone who is not happy or humble is humble and vice versa. If someone is not rich or wise then someone is either strong or tall and vice versa. Everyone who is not funny is tall or not happy. Everyone who is both not funny and not curious is tall. If fred is both not patient and not tall then lucy is rich and vice versa. Everyone who is both calm and creative is tall or brave and vice versa. Everyone who is happy or calm is not generous and vice versa. Everyone who is both calm and not patient is both not old and tall. If fred is both old and not old then someone is not generous and vice versa. Susan is not strong or strong. Mary is either not old or rich. Someone is not calm or not brave. | Lucy is not old. | entailment | (((patient(paul)&rich(paul)))=>(?[X]:((~generous(X)|funny(X)))))&
(![X]:((strong(X)&~kind(X))=>(~tall(X)|patient(X))))&
(![X]:((~patient(X)&~funny(X))<=>~tall(X)))&
(![X]:(~old(X)<=>(~patient(X)|~quiet(X))))&
((?[X]:((~quiet(X)&~brave(X))))=>((rich(lucy)&~patient(lucy))))&
(![X]:(kind(X)<=>(curious(X)&~old(X))))&
(![X]:((~happy(X)|humble(X))<=>humble(X)))&
((?[X]:((~rich(X)|wise(X))))<=>(?[X]:((strong(X)<~>tall(X)))))&
(![X]:(~funny(X)=>(tall(X)|~happy(X))))&
(![X]:((~funny(X)&~curious(X))=>tall(X)))&
(((~patient(fred)&~tall(fred)))<=>(rich(lucy)))&
(![X]:((calm(X)&creative(X))<=>(tall(X)|brave(X))))&
(![X]:((happy(X)|calm(X))<=>~generous(X)))&
(![X]:((calm(X)&~patient(X))=>(~old(X)&tall(X))))&
(((old(fred)&~old(fred)))<=>(?[X]:(~generous(X))))&
((~strong(susan)|strong(susan)))&
((~old(mary)<~>rich(mary)))&
(?[X]:((~calm(X)|~brave(X)))) | ~old(lucy) | [
"p2",
"p3",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3155425152745538835655301
% SZS output start Proof for 3155425152745538835655301
3. ! [X0] : ((~funny(X0) & ~patient(X0)) <=> ~tall(X0)) [input p2]
4. ! [X0] : (~old(X0) <=> (~quiet(X0) | ~patient(X0))) [input p3]
12. ! [X0] : ((creative(X0) & calm(X0)) <=> (brave(X0) | tall(X0))) [input p11]
13. ! [X0] : ((calm(X0) | happy(X0)) <=> ~generous(X0)) [input p12]
15. (~old(fred) & old(fred)) <=> ? [X0] : ~generous(X0) [input p14]
19. old(lucy) [input hypothesis]
36. ! [X0] : (((~funny(X0) & ~patient(X0)) | tall(X0)) & (~tall(X0) | (funny(X0) | patient(X0)))) [nnf transformation 3]
37. ! [X0] : (((~funny(X0) & ~patient(X0)) | tall(X0)) & (~tall(X0) | funny(X0) | patient(X0))) [flattening 36]
38. ! [X0] : ((~old(X0) | (quiet(X0) & patient(X0))) & ((~quiet(X0) | ~patient(X0)) | old(X0))) [nnf transformation 4]
39. ! [X0] : ((~old(X0) | (quiet(X0) & patient(X0))) & (~quiet(X0) | ~patient(X0) | old(X0))) [flattening 38]
49. ! [X0] : (((creative(X0) & calm(X0)) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | (~creative(X0) | ~calm(X0)))) [nnf transformation 12]
50. ! [X0] : (((creative(X0) & calm(X0)) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | ~creative(X0) | ~calm(X0))) [flattening 49]
51. ! [X0] : (((calm(X0) | happy(X0)) | generous(X0)) & (~generous(X0) | (~calm(X0) & ~happy(X0)))) [nnf transformation 13]
52. ! [X0] : ((calm(X0) | happy(X0) | generous(X0)) & (~generous(X0) | (~calm(X0) & ~happy(X0)))) [flattening 51]
53. ((~old(fred) & old(fred)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (old(fred) | ~old(fred))) [nnf transformation 15]
54. ((~old(fred) & old(fred)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | old(fred) | ~old(fred)) [flattening 53]
55. ((~old(fred) & old(fred)) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | old(fred) | ~old(fred)) [rectify 54]
56. ? [X1] : ~generous(X1) => ~generous(sK3) [choice axiom]
57. ((~old(fred) & old(fred)) | ! [X0] : generous(X0)) & (~generous(sK3) | old(fred) | ~old(fred)) [skolemisation 55,56]
64. ~patient(X0) | tall(X0) [cnf transformation 37]
67. ~old(X0) | patient(X0) [cnf transformation 39]
86. ~tall(X0) | calm(X0) [cnf transformation 50]
91. ~calm(X0) | ~generous(X0) [cnf transformation 52]
96. old(fred) | generous(X0) [cnf transformation 57]
97. ~old(fred) | generous(X0) [cnf transformation 57]
102. old(lucy) [cnf transformation 19]
124. 6 <=> patient(lucy) [avatar definition]
125. patient(lucy) <- (6) [avatar component clause 124]
182. 18 <=> ! [X0] : generous(X0) [avatar definition]
183. generous(X0) <- (18) [avatar component clause 182]
185. 19 <=> old(fred) [avatar definition]
188. 18 | ~19 [avatar split clause 97,185,182]
189. 18 | 19 [avatar split clause 96,185,182]
203. patient(lucy) [resolution 67,102]
206. 6 [avatar split clause 203,124]
207. tall(lucy) <- (6) [resolution 125,64]
210. calm(lucy) <- (6) [resolution 86,207]
212. ~generous(lucy) <- (6) [resolution 91,210]
213. $false <- (6, 18) [subsumption resolution 212,183]
214. ~6 | ~18 [avatar contradiction clause 213]
215. $false [avatar sat refutation 188,189,206,214]
% SZS output end Proof for 3155425152745538835655301
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
Everyone who is humble is both happy and not wise.
Everyone who is either not happy or brave is either happy or not wise and vice versa.
If someone is tall then mary is both strong and not calm and vice versa.
Everyone who is old is strong or quiet.
Everyone who is either not curious or not happy is not kind and vice versa.
Everyone who is both not humble and not kind is both funny and not brave.
If mary is rich or brave then paul is quiet or not funny and vice versa.
If someone is quiet or not generous then lucy is either curious or not happy and vice versa.
If someone is creative then paul is either humble or not humble and vice versa.
Susan is creative or not wise.
Someone is brave or happy.
Alice is creative or funny.
Susan is curious or not brave.
Paul is either brave or not rich.
Alice is not funny or kind. | Lucy is curious. | entailment | ((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
(![X]:(humble(X)=>(happy(X)&~wise(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:(tall(X)))<=>((strong(mary)&~calm(mary))))&
(![X]:(old(X)=>(strong(X)|quiet(X))))&
(![X]:((~curious(X)<~>~happy(X))<=>~kind(X)))&
(![X]:((~humble(X)&~kind(X))=>(funny(X)&~brave(X))))&
(((rich(mary)|brave(mary)))<=>((quiet(paul)|~funny(paul))))&
((?[X]:((quiet(X)|~generous(X))))<=>((curious(lucy)<~>~happy(lucy))))&
((?[X]:(creative(X)))<=>((humble(paul)<~>~humble(paul))))&
((creative(susan)|~wise(susan)))&
(?[X]:((brave(X)|happy(X))))&
((creative(alice)|funny(alice)))&
((curious(susan)|~brave(susan)))&
((brave(paul)<~>~rich(paul)))&
((~funny(alice)|kind(alice))) | curious(lucy) | [
"p2",
"p5",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2163803107389117377964742
% SZS output start Proof for 2163803107389117377964742
3. ! [X0] : (generous(X0) <=> ~happy(X0)) [input p2]
6. ! [X0] : (~curious(X0) <=> (~kind(X0) & old(X0))) [input p5]
11. ! [X0] : ((~curious(X0) <~> ~happy(X0)) <=> ~kind(X0)) [input p10]
14. ? [X0] : (~generous(X0) | quiet(X0)) <=> (curious(lucy) <~> ~happy(lucy)) [input p13]
22. ~curious(lucy) [input hypothesis]
30. ! [X0] : ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))) [nnf transformation 3]
35. ! [X0] : ((~curious(X0) | (kind(X0) | ~old(X0))) & ((~kind(X0) & old(X0)) | curious(X0))) [nnf transformation 6]
36. ! [X0] : ((~curious(X0) | kind(X0) | ~old(X0)) & ((~kind(X0) & old(X0)) | curious(X0))) [flattening 35]
43. ! [X0] : ((((happy(X0) | curious(X0)) & (~happy(X0) | ~curious(X0))) | kind(X0)) & (~kind(X0) | ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0))))) [nnf transformation 11]
46. (? [X0] : (~generous(X0) | quiet(X0)) | ((curious(lucy) | happy(lucy)) & (~happy(lucy) | ~curious(lucy)))) & (((happy(lucy) | ~curious(lucy)) & (~happy(lucy) | curious(lucy))) | ! [X0] : (generous(X0) & ~quiet(X0))) [nnf transformation 14]
47. (? [X0] : (~generous(X0) | quiet(X0)) | ((curious(lucy) | happy(lucy)) & (~happy(lucy) | ~curious(lucy)))) & (((happy(lucy) | ~curious(lucy)) & (~happy(lucy) | curious(lucy))) | ! [X1] : (generous(X1) & ~quiet(X1))) [rectify 46]
48. ? [X0] : (~generous(X0) | quiet(X0)) => (~generous(sK1) | quiet(sK1)) [choice axiom]
49. ((~generous(sK1) | quiet(sK1)) | ((curious(lucy) | happy(lucy)) & (~happy(lucy) | ~curious(lucy)))) & (((happy(lucy) | ~curious(lucy)) & (~happy(lucy) | curious(lucy))) | ! [X1] : (generous(X1) & ~quiet(X1))) [skolemisation 47,48]
63. ~generous(X0) | ~happy(X0) [cnf transformation 30]
78. ~kind(X0) | curious(X0) [cnf transformation 36]
97. happy(X0) | curious(X0) | kind(X0) [cnf transformation 43]
105. ~happy(lucy) | curious(lucy) | generous(X1) [cnf transformation 49]
121. ~curious(lucy) [cnf transformation 22]
188. curious(X0) | happy(X0) [subsumption resolution 97,78]
211. 17 <=> curious(lucy) [avatar definition]
213. ~curious(lucy) <- (~17) [avatar component clause 211]
229. 21 <=> ! [X1] : generous(X1) [avatar definition]
230. generous(X1) <- (21) [avatar component clause 229]
237. curious(lucy) | generous(X1) [subsumption resolution 105,188]
238. 21 | 17 [avatar split clause 237,211,229]
298. ~17 [avatar split clause 121,211]
301. ~happy(X0) <- (21) [resolution 63,230]
312. happy(lucy) <- (~17) [resolution 188,213]
315. $false <- (~17, 21) [subsumption resolution 312,301]
316. 17 | ~21 [avatar contradiction clause 315]
317. $false [avatar sat refutation 238,298,316]
% SZS output end Proof for 2163803107389117377964742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either not happy or creative. Everyone who is both patient and kind is both quiet and not humble. If paul is both patient and not humble then someone is not quiet or not funny and vice versa. Everyone who is old is both not calm and not kind. If someone is both not humble and not kind then someone is curious. If lucy is not generous then someone is not humble. Everyone who is both not patient and quiet is not wise. Everyone who is not calm or humble is kind or not generous and vice versa. If fred is funny or old then john is both kind and not wise and vice versa. Everyone who is brave is both happy and calm. If someone is not wise or kind then alice is curious and vice versa. If lucy is creative or not tall then someone is either old or not tall. If john is either not kind or calm then someone is not generous or happy. Everyone who is not funny or not brave is creative. Everyone who is kind or humble is not kind. Everyone who is both quiet and not happy is both not generous and patient. Someone is either not curious or not funny. Someone is rich. Mary is both not brave and not rich. Alice is both wise and not rich. John is both patient and not quiet. Someone is either wise or not happy. Fred is both not patient and not strong. Susan is either not brave or kind. | Mary is creative. | entailment | (![X]:(happy(X)=>(~happy(X)<~>creative(X))))&
(![X]:((patient(X)&kind(X))=>(quiet(X)&~humble(X))))&
(((patient(paul)&~humble(paul)))<=>(?[X]:((~quiet(X)|~funny(X)))))&
(![X]:(old(X)=>(~calm(X)&~kind(X))))&
((?[X]:((~humble(X)&~kind(X))))=>(?[X]:(curious(X))))&
((~generous(lucy))=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)&quiet(X))=>~wise(X)))&
(![X]:((~calm(X)|humble(X))<=>(kind(X)|~generous(X))))&
(((funny(fred)|old(fred)))<=>((kind(john)&~wise(john))))&
(![X]:(brave(X)=>(happy(X)&calm(X))))&
((?[X]:((~wise(X)|kind(X))))<=>(curious(alice)))&
(((creative(lucy)|~tall(lucy)))=>(?[X]:((old(X)<~>~tall(X)))))&
(((~kind(john)<~>calm(john)))=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~funny(X)|~brave(X))=>creative(X)))&
(![X]:((kind(X)|humble(X))=>~kind(X)))&
(![X]:((quiet(X)&~happy(X))=>(~generous(X)&patient(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
(?[X]:(rich(X)))&
((~brave(mary)&~rich(mary)))&
((wise(alice)&~rich(alice)))&
((patient(john)&~quiet(john)))&
(?[X]:((wise(X)<~>~happy(X))))&
((~patient(fred)&~strong(fred)))&
((~brave(susan)<~>kind(susan))) | creative(mary) | [
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8699684266194783400532951
% SZS output start Proof for 8699684266194783400532951
14. ! [X0] : ((~brave(X0) | ~funny(X0)) => creative(X0)) [input p13]
19. ~rich(mary) & ~brave(mary) [input p18]
25. ~creative(mary) [input hypothesis]
39. ! [X0] : (creative(X0) | (brave(X0) & funny(X0))) [ennf transformation 14]
112. brave(X0) | creative(X0) [cnf transformation 39]
120. ~brave(mary) [cnf transformation 19]
131. ~creative(mary) [cnf transformation 25]
291. creative(mary) [resolution 112,120]
295. $false [subsumption resolution 291,131]
% SZS output end Proof for 8699684266194783400532951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not kind is not happy and vice versa.
Everyone who is creative is not humble.
Everyone who is wise is both not strong and not generous and vice versa.
Everyone who is both not creative and not kind is both brave and kind and vice versa.
Everyone who is not quiet or not patient is not rich and vice versa.
Everyone who is old is both not kind and curious.
If paul is rich or not kind then someone is both not happy and not humble and vice versa.
Everyone who is brave or not wise is happy or calm and vice versa.
If john is calm then someone is not rich or not old and vice versa.
If mary is creative then john is both not tall and not creative and vice versa.
If fred is both humble and happy then mary is either not patient or not strong and vice versa.
If fred is both not calm and curious then someone is calm or not rich and vice versa.
Everyone who is both brave and tall is not strong or generous.
If someone is creative then someone is either brave or not humble and vice versa.
Someone is old or brave.
Someone is not funny or not brave.
Someone is humble.
Someone is curious or not tall.
Someone is not happy or funny.
John is kind or strong. | Fred is not generous. | neutral | (![X]:((~wise(X)&~kind(X))<=>~happy(X)))&
(![X]:(creative(X)=>~humble(X)))&
(![X]:(wise(X)<=>(~strong(X)&~generous(X))))&
(![X]:((~creative(X)&~kind(X))<=>(brave(X)&kind(X))))&
(![X]:((~quiet(X)|~patient(X))<=>~rich(X)))&
(![X]:(old(X)=>(~kind(X)&curious(X))))&
(((rich(paul)|~kind(paul)))<=>(?[X]:((~happy(X)&~humble(X)))))&
(![X]:((brave(X)|~wise(X))<=>(happy(X)|calm(X))))&
((calm(john))<=>(?[X]:((~rich(X)|~old(X)))))&
((creative(mary))<=>((~tall(john)&~creative(john))))&
(((humble(fred)&happy(fred)))<=>((~patient(mary)<~>~strong(mary))))&
(((~calm(fred)&curious(fred)))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:((brave(X)&tall(X))=>(~strong(X)|generous(X))))&
((?[X]:(creative(X)))<=>(?[X]:((brave(X)<~>~humble(X)))))&
(?[X]:((old(X)|brave(X))))&
(?[X]:((~funny(X)|~brave(X))))&
(?[X]:(humble(X)))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((~happy(X)|funny(X))))&
((kind(john)|strong(john))) | ~generous(fred) | [] | null | 0 |
Everyone who is rich or not generous is curious or kind and vice versa.
Everyone who is either not curious or not creative is both not brave and tall.
Everyone who is either old or not patient is both not funny and rich.
Everyone who is either not strong or tall is either not curious or strong.
If someone is humble then lucy is both strong and curious.
If susan is not curious or not wise then someone is not wise and vice versa.
Everyone who is kind is either not generous or calm.
If lucy is not happy then someone is both tall and not patient and vice versa.
If someone is not calm or not creative then paul is not strong and vice versa.
Everyone who is not funny or not quiet is not calm or not funny and vice versa.
Everyone who is wise or not kind is either not strong or calm.
If mary is both strong and not tall then someone is strong or not brave.
If someone is tall then mary is not strong or not creative.
If susan is both not patient and not happy then someone is creative or not funny and vice versa.
Everyone who is not tall is both not wise and not patient and vice versa.
If paul is both old and curious then alice is creative and vice versa.
Susan is creative.
Someone is either not humble or not happy.
Mary is both curious and brave.
Susan is humble or not tall.
John is not quiet.
Alice is both quiet and tall.
Someone is both not happy and quiet.
John is both curious and not tall. | Mary is not tall. | contradiction | (![X]:((rich(X)|~generous(X))<=>(curious(X)|kind(X))))&
(![X]:((~curious(X)<~>~creative(X))=>(~brave(X)&tall(X))))&
(![X]:((old(X)<~>~patient(X))=>(~funny(X)&rich(X))))&
(![X]:((~strong(X)<~>tall(X))=>(~curious(X)<~>strong(X))))&
((?[X]:(humble(X)))=>((strong(lucy)&curious(lucy))))&
(((~curious(susan)|~wise(susan)))<=>(?[X]:(~wise(X))))&
(![X]:(kind(X)=>(~generous(X)<~>calm(X))))&
((~happy(lucy))<=>(?[X]:((tall(X)&~patient(X)))))&
((?[X]:((~calm(X)|~creative(X))))<=>(~strong(paul)))&
(![X]:((~funny(X)|~quiet(X))<=>(~calm(X)|~funny(X))))&
(![X]:((wise(X)|~kind(X))=>(~strong(X)<~>calm(X))))&
(((strong(mary)&~tall(mary)))=>(?[X]:((strong(X)|~brave(X)))))&
((?[X]:(tall(X)))=>((~strong(mary)|~creative(mary))))&
(((~patient(susan)&~happy(susan)))<=>(?[X]:((creative(X)|~funny(X)))))&
(![X]:(~tall(X)<=>(~wise(X)&~patient(X))))&
(((old(paul)&curious(paul)))<=>(creative(alice)))&
(creative(susan))&
(?[X]:((~humble(X)<~>~happy(X))))&
((curious(mary)&brave(mary)))&
((humble(susan)|~tall(susan)))&
(~quiet(john))&
((quiet(alice)&tall(alice)))&
(?[X]:((~happy(X)&quiet(X))))&
((curious(john)&~tall(john))) | ~tall(mary) | [
"p1",
"p3",
"p12",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1327797217620813074668041
% SZS output start Proof for 1327797217620813074668041
2. ! [X0] : ((~curious(X0) <~> ~creative(X0)) => (tall(X0) & ~brave(X0))) [input p1]
4. ! [X0] : ((~strong(X0) <~> tall(X0)) => (~curious(X0) <~> strong(X0))) [input p3]
13. ? [X0] : tall(X0) => (~creative(mary) | ~strong(mary)) [input p12]
19. brave(mary) & curious(mary) [input p18]
22. tall(alice) & quiet(alice) [input p21]
25. ~tall(mary) [input hypothesis]
26. ! [X0] : ((tall(X0) & ~brave(X0)) | (~curious(X0) <=> ~creative(X0))) [ennf transformation 2]
28. ! [X0] : ((~curious(X0) <~> strong(X0)) | (~strong(X0) <=> tall(X0))) [ennf transformation 4]
34. (~creative(mary) | ~strong(mary)) | ! [X0] : ~tall(X0) [ennf transformation 13]
35. ~creative(mary) | ~strong(mary) | ! [X0] : ~tall(X0) [flattening 34]
38. ! [X0] : ((tall(X0) & ~brave(X0)) | ((~curious(X0) | creative(X0)) & (~creative(X0) | curious(X0)))) [nnf transformation 26]
40. ! [X0] : (((~strong(X0) | curious(X0)) & (strong(X0) | ~curious(X0))) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) [nnf transformation 28]
79. ~brave(X0) | ~curious(X0) | creative(X0) [cnf transformation 38]
86. strong(X0) | ~curious(X0) | tall(X0) | strong(X0) [cnf transformation 40]
112. ~creative(mary) | ~strong(mary) | ~tall(X0) [cnf transformation 35]
127. curious(mary) [cnf transformation 19]
128. brave(mary) [cnf transformation 19]
132. tall(alice) [cnf transformation 22]
137. ~tall(mary) [cnf transformation 25]
138. ~curious(X0) | strong(X0) | tall(X0) [duplicate literal removal 86]
211. 17 <=> strong(mary) [avatar definition]
215. 18 <=> tall(mary) [avatar definition]
216. ~tall(mary) <- (~18) [avatar component clause 215]
228. 21 <=> ! [X0] : ~tall(X0) [avatar definition]
229. ~tall(X0) <- (21) [avatar component clause 228]
231. 22 <=> creative(mary) [avatar definition]
234. 21 | ~17 | ~22 [avatar split clause 112,231,211,228]
296. ~18 [avatar split clause 137,215]
331. ~curious(mary) | creative(mary) [resolution 79,128]
332. creative(mary) [subsumption resolution 331,127]
333. 22 [avatar split clause 332,231]
439. strong(mary) | tall(mary) [resolution 138,127]
446. strong(mary) <- (~18) [subsumption resolution 439,216]
447. 17 | 18 [avatar split clause 446,215,211]
458. $false <- (21) [resolution 229,132]
459. ~21 [avatar contradiction clause 458]
460. $false [avatar sat refutation 234,296,333,447,459]
% SZS output end Proof for 1327797217620813074668041
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not creative is not rich.
Everyone who is brave or not rich is not brave.
Everyone who is not old is both not kind and kind.
If someone is not wise or calm then paul is not patient.
If mary is both not strong and not calm then someone is tall or brave.
Everyone who is generous or kind is not funny.
If someone is both not strong and not happy then john is both not wise and patient and vice versa.
Everyone who is not curious or calm is old.
If someone is strong or wise then mary is both funny and generous and vice versa.
Everyone who is not quiet is either old or curious and vice versa.
Everyone who is not creative or not curious is both not wise and not strong.
Everyone who is not creative or happy is either not old or happy and vice versa.
Everyone who is not old or not brave is curious.
If paul is not old or patient then john is either calm or not creative and vice versa.
If john is not creative or not rich then alice is both tall and strong.
Everyone who is either not quiet or quiet is either happy or not generous and vice versa.
Someone is either not tall or wise.
Mary is not rich.
Someone is generous or not rich.
Someone is not funny or not tall.
Someone is both not rich and not wise.
Mary is not kind or not rich.
Someone is not calm or not strong. | Alice is generous. | neutral | (![X]:((brave(X)<~>~creative(X))=>~rich(X)))&
(![X]:((brave(X)|~rich(X))=>~brave(X)))&
(![X]:(~old(X)=>(~kind(X)&kind(X))))&
((?[X]:((~wise(X)|calm(X))))=>(~patient(paul)))&
(((~strong(mary)&~calm(mary)))=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((generous(X)|kind(X))=>~funny(X)))&
((?[X]:((~strong(X)&~happy(X))))<=>((~wise(john)&patient(john))))&
(![X]:((~curious(X)|calm(X))=>old(X)))&
((?[X]:((strong(X)|wise(X))))<=>((funny(mary)&generous(mary))))&
(![X]:(~quiet(X)<=>(old(X)<~>curious(X))))&
(![X]:((~creative(X)|~curious(X))=>(~wise(X)&~strong(X))))&
(![X]:((~creative(X)|happy(X))<=>(~old(X)<~>happy(X))))&
(![X]:((~old(X)|~brave(X))=>curious(X)))&
(((~old(paul)|patient(paul)))<=>((calm(john)<~>~creative(john))))&
(((~creative(john)|~rich(john)))=>((tall(alice)&strong(alice))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(happy(X)<~>~generous(X))))&
(?[X]:((~tall(X)<~>wise(X))))&
(~rich(mary))&
(?[X]:((generous(X)|~rich(X))))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((~rich(X)&~wise(X))))&
((~kind(mary)|~rich(mary)))&
(?[X]:((~calm(X)|~strong(X)))) | generous(alice) | [] | 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 not curious is kind or patient.
If fred is both not strong and not creative then someone is not calm or not wise.
Everyone who is curious or not happy is not humble and vice versa.
If alice is tall or strong then someone is not kind or curious.
If mary is funny then someone is not calm and vice versa.
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.
Paul is not tall or not quiet.
Alice is strong.
Someone is not kind or not happy.
Susan is both not old and not brave.
Paul is both tall and calm.
Someone is either not tall or funny. | John is not strong. | neutral | (![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]:(~curious(X)=>(kind(X)|patient(X))))&
(((~strong(fred)&~creative(fred)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((curious(X)|~happy(X))<=>~humble(X)))&
(((tall(alice)|strong(alice)))=>(?[X]:((~kind(X)|curious(X)))))&
((funny(mary))<=>(?[X]:(~calm(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))))&
((~tall(paul)|~quiet(paul)))&
(strong(alice))&
(?[X]:((~kind(X)|~happy(X))))&
((~old(susan)&~brave(susan)))&
((tall(paul)&calm(paul)))&
(?[X]:((~tall(X)<~>funny(X)))) | ~strong(john) | [] | null | 0 |
Everyone who is either not funny or not brave is not rich.
Everyone who is either kind or calm is not brave or humble.
If fred is not quiet or calm then someone is either old or patient.
Everyone who is happy or kind is not generous or wise.
If someone is not curious then mary is rich or not tall and vice versa.
If someone is not generous then someone is both not patient and strong and vice versa.
Everyone who is curious or not humble is not tall and vice versa.
Everyone who is either rich or curious is both tall and wise and vice versa.
Everyone who is brave or wise is not generous and vice versa.
If someone is kind then someone is both not rich and not humble and vice versa.
If paul is not humble or tall then someone is not calm or generous and vice versa.
Everyone who is not old or not curious is wise.
If susan is either not brave or happy then someone is either strong or happy.
If mary is generous or calm then someone is not happy or generous and vice versa.
If someone is not calm then someone is both old and not rich.
Everyone who is either not calm or kind is not brave and vice versa.
Someone is either tall or not tall.
Someone is either calm or kind.
Susan is patient or not patient.
Someone is tall.
Fred is calm or not generous.
Someone is both not humble and patient.
Someone is strong or not curious.
Alice is not humble. | Mary is generous. | neutral | (![X]:((~funny(X)<~>~brave(X))=>~rich(X)))&
(![X]:((kind(X)<~>calm(X))=>(~brave(X)|humble(X))))&
(((~quiet(fred)|calm(fred)))=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:((happy(X)|kind(X))=>(~generous(X)|wise(X))))&
((?[X]:(~curious(X)))<=>((rich(mary)|~tall(mary))))&
((?[X]:(~generous(X)))<=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:((curious(X)|~humble(X))<=>~tall(X)))&
(![X]:((rich(X)<~>curious(X))<=>(tall(X)&wise(X))))&
(![X]:((brave(X)|wise(X))<=>~generous(X)))&
((?[X]:(kind(X)))<=>(?[X]:((~rich(X)&~humble(X)))))&
(((~humble(paul)|tall(paul)))<=>(?[X]:((~calm(X)|generous(X)))))&
(![X]:((~old(X)|~curious(X))=>wise(X)))&
(((~brave(susan)<~>happy(susan)))=>(?[X]:((strong(X)<~>happy(X)))))&
(((generous(mary)|calm(mary)))<=>(?[X]:((~happy(X)|generous(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((old(X)&~rich(X)))))&
(![X]:((~calm(X)<~>kind(X))<=>~brave(X)))&
(?[X]:((tall(X)<~>~tall(X))))&
(?[X]:((calm(X)<~>kind(X))))&
((patient(susan)|~patient(susan)))&
(?[X]:(tall(X)))&
((calm(fred)|~generous(fred)))&
(?[X]:((~humble(X)&patient(X))))&
(?[X]:((strong(X)|~curious(X))))&
(~humble(alice)) | generous(mary) | [] | null | 0 |
Everyone who is both not kind and not rich is funny and vice versa.
Everyone who is happy is not strong or tall and vice versa.
If lucy is not humble then john is either rich or not funny.
If paul is both not wise and not rich then someone is not happy or not curious.
Everyone who is old is not humble.
If mary is quiet then someone is both not creative and not funny and vice versa.
Everyone who is not old or brave is both happy and not rich and vice versa.
Everyone who is both strong and kind is both not humble and humble.
Everyone who is either not rich or not funny is either not tall or not humble.
Everyone who is brave or not funny is not happy and vice versa.
Everyone who is both not patient and rich is brave or not brave.
If mary is not calm or happy then someone is either quiet or happy and vice versa.
Everyone who is either wise or strong is both curious and generous.
If susan is not happy or wise then lucy is both happy and rich and vice versa.
If fred is funny or not funny then someone is either not patient or kind and vice versa.
If someone is both calm and not tall then someone is not calm or not old.
Lucy is either wise or patient.
Susan is either not patient or not happy.
Someone is not strong.
Someone is either generous or not wise.
Someone is not funny or tall.
Lucy is quiet. | Susan is happy. | entailment | (![X]:((~kind(X)&~rich(X))<=>funny(X)))&
(![X]:(happy(X)<=>(~strong(X)|tall(X))))&
((~humble(lucy))=>((rich(john)<~>~funny(john))))&
(((~wise(paul)&~rich(paul)))=>(?[X]:((~happy(X)|~curious(X)))))&
(![X]:(old(X)=>~humble(X)))&
((quiet(mary))<=>(?[X]:((~creative(X)&~funny(X)))))&
(![X]:((~old(X)|brave(X))<=>(happy(X)&~rich(X))))&
(![X]:((strong(X)&kind(X))=>(~humble(X)&humble(X))))&
(![X]:((~rich(X)<~>~funny(X))=>(~tall(X)<~>~humble(X))))&
(![X]:((brave(X)|~funny(X))<=>~happy(X)))&
(![X]:((~patient(X)&rich(X))=>(brave(X)|~brave(X))))&
(((~calm(mary)|happy(mary)))<=>(?[X]:((quiet(X)<~>happy(X)))))&
(![X]:((wise(X)<~>strong(X))=>(curious(X)&generous(X))))&
(((~happy(susan)|wise(susan)))<=>((happy(lucy)&rich(lucy))))&
(((funny(fred)|~funny(fred)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
((?[X]:((calm(X)&~tall(X))))=>(?[X]:((~calm(X)|~old(X)))))&
((wise(lucy)<~>patient(lucy)))&
((~patient(susan)<~>~happy(susan)))&
(?[X]:(~strong(X)))&
(?[X]:((generous(X)<~>~wise(X))))&
(?[X]:((~funny(X)|tall(X))))&
(quiet(lucy)) | happy(susan) | [
"p0",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1583042736259148065919433
% SZS output start Proof for 1583042736259148065919433
1. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> funny(X0)) [input p0]
10. ! [X0] : ((~funny(X0) | brave(X0)) <=> ~happy(X0)) [input p9]
14. (wise(susan) | ~happy(susan)) <=> (rich(lucy) & happy(lucy)) [input p13]
23. ~happy(susan) [input hypothesis]
36. ! [X0] : (((~rich(X0) & ~kind(X0)) | ~funny(X0)) & (funny(X0) | (rich(X0) | kind(X0)))) [nnf transformation 1]
37. ! [X0] : (((~rich(X0) & ~kind(X0)) | ~funny(X0)) & (funny(X0) | rich(X0) | kind(X0))) [flattening 36]
50. ! [X0] : (((~funny(X0) | brave(X0)) | happy(X0)) & (~happy(X0) | (funny(X0) & ~brave(X0)))) [nnf transformation 10]
51. ! [X0] : ((~funny(X0) | brave(X0) | happy(X0)) & (~happy(X0) | (funny(X0) & ~brave(X0)))) [flattening 50]
58. ((wise(susan) | ~happy(susan)) | (~rich(lucy) | ~happy(lucy))) & ((rich(lucy) & happy(lucy)) | (~wise(susan) & happy(susan))) [nnf transformation 14]
59. (wise(susan) | ~happy(susan) | ~rich(lucy) | ~happy(lucy)) & ((rich(lucy) & happy(lucy)) | (~wise(susan) & happy(susan))) [flattening 58]
79. ~funny(X0) | ~rich(X0) [cnf transformation 37]
102. ~happy(X0) | funny(X0) [cnf transformation 51]
115. happy(lucy) | happy(susan) [cnf transformation 59]
117. rich(lucy) | happy(susan) [cnf transformation 59]
136. ~happy(susan) [cnf transformation 23]
224. 18 <=> happy(lucy) [avatar definition]
225. happy(lucy) <- (18) [avatar component clause 224]
228. 19 <=> rich(lucy) [avatar definition]
229. rich(lucy) <- (19) [avatar component clause 228]
232. 20 <=> happy(susan) [avatar definition]
241. 20 | 19 [avatar split clause 117,228,232]
243. 20 | 18 [avatar split clause 115,224,232]
307. ~20 [avatar split clause 136,232]
314. funny(lucy) <- (18) [resolution 102,225]
317. ~rich(lucy) <- (18) [resolution 314,79]
319. $false <- (18, 19) [subsumption resolution 317,229]
320. ~18 | ~19 [avatar contradiction clause 319]
321. $false [avatar sat refutation 241,243,307,320]
% SZS output end Proof for 1583042736259148065919433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not calm or happy.
Everyone who is strong is both rich and tall and vice versa.
If someone is either not curious or kind then someone is wise or strong.
Everyone who is rich is tall or not quiet.
Everyone who is tall or not calm is either calm or generous and vice versa.
Everyone who is both tall and creative is strong.
Everyone who is both not curious and happy is tall or wise.
Everyone who is strong or not generous is either tall or not curious and vice versa.
Everyone who is either not kind or not old is both not happy and not patient.
Everyone who is both brave and not funny is both rich and not happy and vice versa.
Everyone who is not strong or not calm is both curious and creative.
If fred is not quiet then susan is both calm and not funny and vice versa.
If someone is not strong or not brave then fred is both not curious and not wise and vice versa.
If lucy is both rich and not strong then paul is not curious or curious.
If someone is tall or humble then alice is either not humble or patient.
Lucy is not generous.
Susan is not patient.
Alice is either happy or not old.
Susan is either curious or creative.
Mary is not calm or not curious. | Mary is strong. | entailment | (![X]:(~brave(X)=>(~calm(X)<~>happy(X))))&
(![X]:(strong(X)<=>(rich(X)&tall(X))))&
((?[X]:((~curious(X)<~>kind(X))))=>(?[X]:((wise(X)|strong(X)))))&
(![X]:(rich(X)=>(tall(X)|~quiet(X))))&
(![X]:((tall(X)|~calm(X))<=>(calm(X)<~>generous(X))))&
(![X]:((tall(X)&creative(X))=>strong(X)))&
(![X]:((~curious(X)&happy(X))=>(tall(X)|wise(X))))&
(![X]:((strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~happy(X)&~patient(X))))&
(![X]:((brave(X)&~funny(X))<=>(rich(X)&~happy(X))))&
(![X]:((~strong(X)|~calm(X))=>(curious(X)&creative(X))))&
((~quiet(fred))<=>((calm(susan)&~funny(susan))))&
((?[X]:((~strong(X)|~brave(X))))<=>((~curious(fred)&~wise(fred))))&
(((rich(lucy)&~strong(lucy)))=>((~curious(paul)|curious(paul))))&
((?[X]:((tall(X)|humble(X))))=>((~humble(alice)<~>patient(alice))))&
(~generous(lucy))&
(~patient(susan))&
((happy(alice)<~>~old(alice)))&
((curious(susan)<~>creative(susan)))&
((~calm(mary)|~curious(mary))) | strong(mary) | [
"p1",
"p7",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 838864212261664284566245
% SZS output start Proof for 838864212261664284566245
2. ! [X0] : (strong(X0) <=> (tall(X0) & rich(X0))) [input p1]
8. ! [X0] : ((~generous(X0) | strong(X0)) <=> (tall(X0) <~> ~curious(X0))) [input p7]
11. ! [X0] : ((~calm(X0) | ~strong(X0)) => (creative(X0) & curious(X0))) [input p10]
13. ? [X0] : (~brave(X0) | ~strong(X0)) <=> (~wise(fred) & ~curious(fred)) [input p12]
21. ~strong(mary) [input hypothesis]
32. ! [X0] : ((creative(X0) & curious(X0)) | (calm(X0) & strong(X0))) [ennf transformation 11]
37. ! [X0] : ((strong(X0) | (~tall(X0) | ~rich(X0))) & ((tall(X0) & rich(X0)) | ~strong(X0))) [nnf transformation 2]
38. ! [X0] : ((strong(X0) | ~tall(X0) | ~rich(X0)) & ((tall(X0) & rich(X0)) | ~strong(X0))) [flattening 37]
45. ! [X0] : (((~generous(X0) | strong(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (generous(X0) & ~strong(X0)))) [nnf transformation 8]
46. ! [X0] : ((~generous(X0) | strong(X0) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (generous(X0) & ~strong(X0)))) [flattening 45]
52. (? [X0] : (~brave(X0) | ~strong(X0)) | (wise(fred) | curious(fred))) & ((~wise(fred) & ~curious(fred)) | ! [X0] : (brave(X0) & strong(X0))) [nnf transformation 13]
53. (? [X0] : (~brave(X0) | ~strong(X0)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X0] : (brave(X0) & strong(X0))) [flattening 52]
54. (? [X0] : (~brave(X0) | ~strong(X0)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X1] : (brave(X1) & strong(X1))) [rectify 53]
55. ? [X0] : (~brave(X0) | ~strong(X0)) => (~brave(sK1) | ~strong(sK1)) [choice axiom]
56. ((~brave(sK1) | ~strong(sK1)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X1] : (brave(X1) & strong(X1))) [skolemisation 54,55]
63. tall(X0) | ~strong(X0) [cnf transformation 38]
78. curious(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 46]
90. curious(X0) | strong(X0) [cnf transformation 32]
97. ~curious(fred) | strong(X1) [cnf transformation 56]
114. ~strong(mary) [cnf transformation 21]
134. curious(X0) | ~strong(X0) [subsumption resolution 78,63]
135. curious(X0) [subsumption resolution 90,134]
160. 10 <=> ! [X1] : strong(X1) [avatar definition]
161. strong(X1) <- (10) [avatar component clause 160]
165. strong(X1) [subsumption resolution 97,135]
166. 10 [avatar split clause 165,160]
197. $false <- (10) [resolution 161,114]
198. ~10 [avatar contradiction clause 197]
199. $false [avatar sat refutation 166,198]
% SZS output end Proof for 838864212261664284566245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either old or not tall then paul is not patient or not strong and vice versa.
If lucy is either curious or generous then someone is both not curious and not funny.
Everyone who is both happy and wise is both not quiet and quiet.
Everyone who is not wise or wise is not strong.
Everyone who is not kind or not creative is either kind or not funny.
Everyone who is not curious is both not creative and not funny.
Everyone who is both generous and rich is not happy and vice versa.
If mary is both not patient and not rich then mary is either tall or generous and vice versa.
If lucy is both curious and brave then someone is funny and vice versa.
Everyone who is both old and tall is both curious and kind and vice versa.
Everyone who is rich or kind is both not rich and strong and vice versa.
Everyone who is either not humble or tall is both funny and calm and vice versa.
If alice is both funny and kind then mary is patient and vice versa.
If alice is both not rich and brave then someone is either not brave or funny and vice versa.
If someone is either not quiet or not humble then alice is both not brave and curious.
If john is strong or calm then someone is both not generous and not curious and vice versa.
Alice is quiet.
Mary is both generous and not brave.
John is not brave.
Paul is not wise or generous.
Someone is tall or not happy. | Mary is not patient. | entailment | (((old(fred)<~>~tall(fred)))<=>((~patient(paul)|~strong(paul))))&
(((curious(lucy)<~>generous(lucy)))=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:((happy(X)&wise(X))=>(~quiet(X)&quiet(X))))&
(![X]:((~wise(X)|wise(X))=>~strong(X)))&
(![X]:((~kind(X)|~creative(X))=>(kind(X)<~>~funny(X))))&
(![X]:(~curious(X)=>(~creative(X)&~funny(X))))&
(![X]:((generous(X)&rich(X))<=>~happy(X)))&
(((~patient(mary)&~rich(mary)))<=>((tall(mary)<~>generous(mary))))&
(((curious(lucy)&brave(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((old(X)&tall(X))<=>(curious(X)&kind(X))))&
(![X]:((rich(X)|kind(X))<=>(~rich(X)&strong(X))))&
(![X]:((~humble(X)<~>tall(X))<=>(funny(X)&calm(X))))&
(((funny(alice)&kind(alice)))<=>(patient(mary)))&
(((~rich(alice)&brave(alice)))<=>(?[X]:((~brave(X)<~>funny(X)))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>((~brave(alice)&curious(alice))))&
(((strong(john)|calm(john)))<=>(?[X]:((~generous(X)&~curious(X)))))&
(quiet(alice))&
((generous(mary)&~brave(mary)))&
(~brave(john))&
((~wise(paul)|generous(paul)))&
(?[X]:((tall(X)|~happy(X)))) | ~patient(mary) | [
"p3",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1757942972590881556820438
% SZS output start Proof for 1757942972590881556820438
4. ! [X0] : ((wise(X0) | ~wise(X0)) => ~strong(X0)) [input p3]
11. ! [X0] : ((kind(X0) | rich(X0)) <=> (strong(X0) & ~rich(X0))) [input p10]
13. (kind(alice) & funny(alice)) <=> patient(mary) [input p12]
22. patient(mary) [input hypothesis]
27. ! [X0] : (~strong(X0) | (~wise(X0) & wise(X0))) [ennf transformation 4]
47. ! [X0] : (((kind(X0) | rich(X0)) | (~strong(X0) | rich(X0))) & ((strong(X0) & ~rich(X0)) | (~kind(X0) & ~rich(X0)))) [nnf transformation 11]
48. ! [X0] : ((kind(X0) | rich(X0) | ~strong(X0) | rich(X0)) & ((strong(X0) & ~rich(X0)) | (~kind(X0) & ~rich(X0)))) [flattening 47]
51. ((kind(alice) & funny(alice)) | ~patient(mary)) & (patient(mary) | (~kind(alice) | ~funny(alice))) [nnf transformation 13]
52. ((kind(alice) & funny(alice)) | ~patient(mary)) & (patient(mary) | ~kind(alice) | ~funny(alice)) [flattening 51]
78. ~strong(X0) | wise(X0) [cnf transformation 27]
79. ~strong(X0) | ~wise(X0) [cnf transformation 27]
104. strong(X0) | ~kind(X0) [cnf transformation 48]
114. kind(alice) | ~patient(mary) [cnf transformation 52]
136. patient(mary) [cnf transformation 22]
183. ~strong(X0) [subsumption resolution 78,79]
199. 12 <=> patient(mary) [avatar definition]
220. ~kind(X0) [subsumption resolution 104,183]
222. ~patient(mary) [subsumption resolution 114,220]
223. ~12 [avatar split clause 222,199]
305. 12 [avatar split clause 136,199]
306. $false [avatar sat refutation 223,305]
% SZS output end Proof for 1757942972590881556820438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both not strong and rich and vice versa.
Everyone who is both not generous and rich is not funny or not rich and vice versa.
Everyone who is not calm or not brave is creative and vice versa.
Everyone who is either not generous or not tall is quiet or wise and vice versa.
Everyone who is funny is rich or kind and vice versa.
If someone is not strong or not rich then john is either not wise or happy and vice versa.
If someone is brave or tall then john is both not old and creative and vice versa.
Everyone who is both not calm and not old is both not calm and not creative.
Everyone who is either old or not humble is both funny and tall.
If someone is both not old and funny then someone is both strong and tall and vice versa.
Everyone who is both wise and not calm is both not rich and strong and vice versa.
If john is either patient or generous then someone is either patient or not humble.
Everyone who is generous or not quiet is quiet.
Everyone who is both not curious and not kind is curious.
Everyone who is both strong and not curious is either tall or not wise.
Someone is not happy or kind.
Fred is tall or not kind.
Someone is either rich or not curious.
Mary is either rich or not happy.
Mary is not tall. | Fred is not strong. | contradiction | (![X]:(~funny(X)<=>(~strong(X)&rich(X))))&
(![X]:((~generous(X)&rich(X))<=>(~funny(X)|~rich(X))))&
(![X]:((~calm(X)|~brave(X))<=>creative(X)))&
(![X]:((~generous(X)<~>~tall(X))<=>(quiet(X)|wise(X))))&
(![X]:(funny(X)<=>(rich(X)|kind(X))))&
((?[X]:((~strong(X)|~rich(X))))<=>((~wise(john)<~>happy(john))))&
((?[X]:((brave(X)|tall(X))))<=>((~old(john)&creative(john))))&
(![X]:((~calm(X)&~old(X))=>(~calm(X)&~creative(X))))&
(![X]:((old(X)<~>~humble(X))=>(funny(X)&tall(X))))&
((?[X]:((~old(X)&funny(X))))<=>(?[X]:((strong(X)&tall(X)))))&
(![X]:((wise(X)&~calm(X))<=>(~rich(X)&strong(X))))&
(((patient(john)<~>generous(john)))=>(?[X]:((patient(X)<~>~humble(X)))))&
(![X]:((generous(X)|~quiet(X))=>quiet(X)))&
(![X]:((~curious(X)&~kind(X))=>curious(X)))&
(![X]:((strong(X)&~curious(X))=>(tall(X)<~>~wise(X))))&
(?[X]:((~happy(X)|kind(X))))&
((tall(fred)|~kind(fred)))&
(?[X]:((rich(X)<~>~curious(X))))&
((rich(mary)<~>~happy(mary)))&
(~tall(mary)) | ~strong(fred) | [
"p0",
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7542711063953396204359286
% SZS output start Proof for 7542711063953396204359286
1. ! [X0] : (~funny(X0) <=> (rich(X0) & ~strong(X0))) [input p0]
2. ! [X0] : ((rich(X0) & ~generous(X0)) <=> (~rich(X0) | ~funny(X0))) [input p1]
5. ! [X0] : (funny(X0) <=> (kind(X0) | rich(X0))) [input p4]
21. ~strong(fred) [input hypothesis]
32. ! [X0] : ((~funny(X0) | (~rich(X0) | strong(X0))) & ((rich(X0) & ~strong(X0)) | funny(X0))) [nnf transformation 1]
33. ! [X0] : ((~funny(X0) | ~rich(X0) | strong(X0)) & ((rich(X0) & ~strong(X0)) | funny(X0))) [flattening 32]
34. ! [X0] : (((rich(X0) & ~generous(X0)) | (rich(X0) & funny(X0))) & ((~rich(X0) | ~funny(X0)) | (~rich(X0) | generous(X0)))) [nnf transformation 2]
35. ! [X0] : (((rich(X0) & ~generous(X0)) | (rich(X0) & funny(X0))) & (~rich(X0) | ~funny(X0) | ~rich(X0) | generous(X0))) [flattening 34]
40. ! [X0] : ((funny(X0) | (~kind(X0) & ~rich(X0))) & ((kind(X0) | rich(X0)) | ~funny(X0))) [nnf transformation 5]
41. ! [X0] : ((funny(X0) | (~kind(X0) & ~rich(X0))) & (kind(X0) | rich(X0) | ~funny(X0))) [flattening 40]
71. ~rich(X0) | ~funny(X0) | strong(X0) [cnf transformation 33]
76. rich(X0) | rich(X0) [cnf transformation 35]
87. funny(X0) | ~rich(X0) [cnf transformation 41]
130. ~strong(fred) [cnf transformation 21]
134. rich(X0) [duplicate literal removal 76]
136. funny(X0) [subsumption resolution 87,134]
154. 4 <=> ! [X1] : strong(X1) [avatar definition]
155. strong(X1) <- (4) [avatar component clause 154]
261. ~funny(X1) | strong(X1) [resolution 71,134]
262. strong(X1) [subsumption resolution 261,136]
263. 4 [avatar split clause 262,154]
264. $false <- (4) [resolution 155,130]
268. ~4 [avatar contradiction clause 264]
269. $false [avatar sat refutation 263,268]
% SZS output end Proof for 7542711063953396204359286
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either not humble or not patient then someone is calm and vice versa.
If someone is either not strong or not patient then paul is both generous and rich and vice versa.
Everyone who is both not kind and tall is not calm or rich.
If someone is not humble then someone is kind or not tall.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
If paul is patient or not curious then susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Susan is not kind or curious.
Someone is old. | John is humble. | entailment | ((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:(calm(X))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>((generous(paul)&rich(paul))))&
(![X]:((~kind(X)&tall(X))=>(~calm(X)|rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
(((patient(paul)|~curious(paul)))=>((~happy(susan)|happy(susan))))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
((~kind(susan)|curious(susan)))&
(?[X]:(old(X))) | humble(john) | [
"p0",
"p1",
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6125913264082504404286197
% SZS output start Proof for 6125913264082504404286197
1. ? [X0] : (~humble(X0) <~> ~patient(X0)) <=> ? [X0] : calm(X0) [input p0]
2. ? [X0] : (~strong(X0) <~> ~patient(X0)) <=> (rich(paul) & generous(paul)) [input p1]
6. ! [X0] : ((~calm(X0) <~> ~curious(X0)) <=> (~strong(X0) | generous(X0))) [input p5]
9. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> strong(X0)) [input p8]
12. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X0] : curious(X0) [input p11]
21. ~humble(john) [input hypothesis]
22. ? [X0] : (~humble(X0) <~> ~patient(X0)) <=> ? [X1] : calm(X1) [rectify 1]
24. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X1] : curious(X1) [rectify 12]
38. (? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) [nnf transformation 22]
39. (? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : ((~humble(X3) | patient(X3)) & (~patient(X3) | humble(X3)))) [rectify 38]
40. ? [X0] : ((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) => ((patient(sK0) | humble(sK0)) & (~patient(sK0) | ~humble(sK0))) [choice axiom]
41. ? [X2] : calm(X2) => calm(sK1) [choice axiom]
42. (((patient(sK0) | humble(sK0)) & (~patient(sK0) | ~humble(sK0))) | ! [X1] : ~calm(X1)) & (calm(sK1) | ! [X3] : ((~humble(X3) | patient(X3)) & (~patient(X3) | humble(X3)))) [skolemisation 39,41,40]
43. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (~rich(paul) | ~generous(paul))) & ((rich(paul) & generous(paul)) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 2]
44. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [flattening 43]
45. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X1] : ((~strong(X1) | patient(X1)) & (~patient(X1) | strong(X1)))) [rectify 44]
46. ? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) => ((patient(sK2) | strong(sK2)) & (~patient(sK2) | ~strong(sK2))) [choice axiom]
47. (((patient(sK2) | strong(sK2)) & (~patient(sK2) | ~strong(sK2))) | ~rich(paul) | ~generous(paul)) & ((rich(paul) & generous(paul)) | ! [X1] : ((~strong(X1) | patient(X1)) & (~patient(X1) | strong(X1)))) [skolemisation 45,46]
49. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [nnf transformation 6]
50. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [flattening 49]
53. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [nnf transformation 9]
54. ! [X0] : ((~generous(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [flattening 53]
59. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (funny(X0) | ~generous(X0))) [nnf transformation 24]
60. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (funny(X3) | ~generous(X3))) [rectify 59]
61. ? [X0] : (~funny(X0) & generous(X0)) => (~funny(sK4) & generous(sK4)) [choice axiom]
62. ? [X2] : curious(X2) => curious(sK5) [choice axiom]
63. ((~funny(sK4) & generous(sK4)) | ! [X1] : ~curious(X1)) & (curious(sK5) | ! [X3] : (funny(X3) | ~generous(X3))) [skolemisation 60,62,61]
70. calm(sK1) | ~patient(X3) | humble(X3) [cnf transformation 42]
75. generous(paul) | ~strong(X1) | patient(X1) [cnf transformation 47]
83. ~strong(X0) | generous(X0) | ~calm(X0) | curious(X0) [cnf transformation 50]
95. strong(X0) | strong(X0) [cnf transformation 54]
97. ~generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 54]
106. generous(sK4) | ~curious(X1) [cnf transformation 63]
125. ~humble(john) [cnf transformation 21]
126. strong(X0) [duplicate literal removal 95]
127. ~generous(X0) | ~strong(X0) [duplicate literal removal 97]
147. 5 <=> calm(sK1) [avatar definition]
149. calm(sK1) <- (5) [avatar component clause 147]
152. 6 <=> ! [X3] : (~patient(X3) | humble(X3)) [avatar definition]
153. ~patient(X3) | humble(X3) <- (6) [avatar component clause 152]
154. 6 | 5 [avatar split clause 70,147,152]
156. 7 <=> generous(paul) [avatar definition]
157. generous(paul) <- (7) [avatar component clause 156]
174. 11 <=> ! [X1] : (~strong(X1) | patient(X1)) [avatar definition]
175. ~strong(X1) | patient(X1) <- (11) [avatar component clause 174]
181. 11 | 7 [avatar split clause 75,156,174]
209. 18 <=> ! [X1] : ~curious(X1) [avatar definition]
210. ~curious(X1) <- (18) [avatar component clause 209]
217. 20 <=> generous(sK4) [avatar definition]
219. generous(sK4) <- (20) [avatar component clause 217]
220. 18 | 20 [avatar split clause 106,217,209]
277. ~strong(paul) <- (7) [resolution 127,157]
279. $false <- (7) [subsumption resolution 277,126]
280. ~7 [avatar contradiction clause 279]
281. patient(X1) <- (11) [subsumption resolution 175,126]
303. generous(X0) | ~calm(X0) | curious(X0) [resolution 83,126]
304. ~calm(X0) | generous(X0) <- (18) [subsumption resolution 303,210]
305. generous(sK1) <- (5, 18) [resolution 304,149]
328. ~strong(sK1) <- (5, 18) [resolution 305,127]
329. $false <- (5, 18) [subsumption resolution 328,126]
330. ~5 | ~18 [avatar contradiction clause 329]
334. ~strong(sK4) <- (20) [resolution 219,127]
346. $false <- (20) [subsumption resolution 334,126]
347. ~20 [avatar contradiction clause 346]
348. humble(X3) <- (6, 11) [subsumption resolution 153,281]
351. $false <- (6, 11) [resolution 348,125]
358. ~6 | ~11 [avatar contradiction clause 351]
359. $false [avatar sat refutation 154,181,220,280,330,347,358]
% SZS output end Proof for 6125913264082504404286197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not brave then someone is both not rich and kind. Everyone who is either brave or not humble is both rich and not funny. If susan is both not patient and not old then alice is tall or not curious. If someone is happy or generous then alice is not patient or not tall and vice versa. If lucy is generous then susan is not funny. If fred is either strong or kind then someone is not generous or not old and vice versa. Everyone who is both not brave and not old is either not old or not patient and vice versa. Everyone who is brave or happy is both not patient and generous and vice versa. Everyone who is both funny and humble is not old or wise. Everyone who is both not patient and old is happy or generous. If mary is either not brave or calm then mary is both not wise and funny. Everyone who is either calm or not calm is either creative or not funny. Everyone who is not old is both old and wise and vice versa. Everyone who is not strong or not patient is either funny or brave. Someone is not happy. Someone is both calm and quiet. Someone is both not quiet and tall. Someone is patient. Fred is funny or tall. Someone is creative or not generous. | Susan is not patient. | contradiction | ((~brave(lucy))=>(?[X]:((~rich(X)&kind(X)))))&
(![X]:((brave(X)<~>~humble(X))=>(rich(X)&~funny(X))))&
(((~patient(susan)&~old(susan)))=>((tall(alice)|~curious(alice))))&
((?[X]:((happy(X)|generous(X))))<=>((~patient(alice)|~tall(alice))))&
((generous(lucy))=>(~funny(susan)))&
(((strong(fred)<~>kind(fred)))<=>(?[X]:((~generous(X)|~old(X)))))&
(![X]:((~brave(X)&~old(X))<=>(~old(X)<~>~patient(X))))&
(![X]:((brave(X)|happy(X))<=>(~patient(X)&generous(X))))&
(![X]:((funny(X)&humble(X))=>(~old(X)|wise(X))))&
(![X]:((~patient(X)&old(X))=>(happy(X)|generous(X))))&
(((~brave(mary)<~>calm(mary)))=>((~wise(mary)&funny(mary))))&
(![X]:((calm(X)<~>~calm(X))=>(creative(X)<~>~funny(X))))&
(![X]:(~old(X)<=>(old(X)&wise(X))))&
(![X]:((~strong(X)|~patient(X))=>(funny(X)<~>brave(X))))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)&quiet(X))))&
(?[X]:((~quiet(X)&tall(X))))&
(?[X]:(patient(X)))&
((funny(fred)|tall(fred)))&
(?[X]:((creative(X)|~generous(X)))) | ~patient(susan) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2082189244259125909168385
% SZS output start Proof for 2082189244259125909168385
7. ! [X0] : ((~old(X0) & ~brave(X0)) <=> (~old(X0) <~> ~patient(X0))) [input p6]
13. ! [X0] : (~old(X0) <=> (wise(X0) & old(X0))) [input p12]
21. ~patient(susan) [input hypothesis]
45. ! [X0] : (((~old(X0) & ~brave(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (old(X0) | brave(X0)))) [nnf transformation 7]
46. ! [X0] : (((~old(X0) & ~brave(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | old(X0) | brave(X0))) [flattening 45]
51. ! [X0] : ((~old(X0) | (~wise(X0) | ~old(X0))) & ((wise(X0) & old(X0)) | old(X0))) [nnf transformation 13]
52. ! [X0] : ((~old(X0) | ~wise(X0) | ~old(X0)) & ((wise(X0) & old(X0)) | old(X0))) [flattening 51]
86. ~old(X0) | ~old(X0) | patient(X0) [cnf transformation 46]
102. old(X0) | old(X0) [cnf transformation 52]
117. ~patient(susan) [cnf transformation 21]
118. old(X0) [duplicate literal removal 102]
125. ~old(X0) | patient(X0) [duplicate literal removal 86]
176. 12 <=> ! [X0] : old(X0) [avatar definition]
177. old(X0) <- (12) [avatar component clause 176]
226. 12 [avatar split clause 118,176]
253. patient(X0) <- (12) [resolution 125,177]
259. $false <- (12) [resolution 253,117]
264. ~12 [avatar contradiction clause 259]
265. $false [avatar sat refutation 226,264]
% SZS output end Proof for 2082189244259125909168385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not generous or creative then john is not strong and vice versa.
If someone is either not quiet or not funny then someone is brave and vice versa.
If someone is either not generous or calm then someone is either tall or curious and vice versa.
Everyone who is strong or generous is both not wise and not funny and vice versa.
Everyone who is strong is both not tall and calm and vice versa.
If someone is not strong or wise then someone is either kind or not strong and vice versa.
If someone is both not curious and generous then fred is both not old and not wise.
Everyone who is funny or not wise is not wise and vice versa.
Everyone who is both not kind and funny is either not strong or funny and vice versa.
Everyone who is kind or not quiet is not rich or not kind and vice versa.
Everyone who is either generous or not humble is either kind or quiet.
If someone is both not humble and not calm then someone is either not strong or curious and vice versa.
If john is either not humble or not curious then someone is either old or quiet and vice versa.
Everyone who is not generous is creative or not tall.
Someone is not strong or not funny.
Susan is either tall or not happy.
Someone is not kind or not humble.
Someone is both creative and patient.
Fred is funny or not tall. | Alice is not wise. | entailment | (((~generous(alice)|creative(alice)))<=>(~strong(john)))&
((?[X]:((~quiet(X)<~>~funny(X))))<=>(?[X]:(brave(X))))&
((?[X]:((~generous(X)<~>calm(X))))<=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:((strong(X)|generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:(strong(X)<=>(~tall(X)&calm(X))))&
((?[X]:((~strong(X)|wise(X))))<=>(?[X]:((kind(X)<~>~strong(X)))))&
((?[X]:((~curious(X)&generous(X))))=>((~old(fred)&~wise(fred))))&
(![X]:((funny(X)|~wise(X))<=>~wise(X)))&
(![X]:((~kind(X)&funny(X))<=>(~strong(X)<~>funny(X))))&
(![X]:((kind(X)|~quiet(X))<=>(~rich(X)|~kind(X))))&
(![X]:((generous(X)<~>~humble(X))=>(kind(X)<~>quiet(X))))&
((?[X]:((~humble(X)&~calm(X))))<=>(?[X]:((~strong(X)<~>curious(X)))))&
(((~humble(john)<~>~curious(john)))<=>(?[X]:((old(X)<~>quiet(X)))))&
(![X]:(~generous(X)=>(creative(X)|~tall(X))))&
(?[X]:((~strong(X)|~funny(X))))&
((tall(susan)<~>~happy(susan)))&
(?[X]:((~kind(X)|~humble(X))))&
(?[X]:((creative(X)&patient(X))))&
((funny(fred)|~tall(fred))) | ~wise(alice) | [
"p3",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7066563556549242803554689
% SZS output start Proof for 7066563556549242803554689
4. ! [X0] : ((generous(X0) | strong(X0)) <=> (~funny(X0) & ~wise(X0))) [input p3]
8. ! [X0] : ((~wise(X0) | funny(X0)) <=> ~wise(X0)) [input p7]
9. ! [X0] : ((funny(X0) & ~kind(X0)) <=> (~strong(X0) <~> funny(X0))) [input p8]
20. wise(alice) [input hypothesis]
42. ! [X0] : (((generous(X0) | strong(X0)) | (funny(X0) | wise(X0))) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & ~strong(X0)))) [nnf transformation 4]
43. ! [X0] : ((generous(X0) | strong(X0) | funny(X0) | wise(X0)) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & ~strong(X0)))) [flattening 42]
51. ! [X0] : (((~wise(X0) | funny(X0)) | wise(X0)) & (~wise(X0) | (wise(X0) & ~funny(X0)))) [nnf transformation 8]
52. ! [X0] : ((~wise(X0) | funny(X0) | wise(X0)) & (~wise(X0) | (wise(X0) & ~funny(X0)))) [flattening 51]
53. ! [X0] : (((funny(X0) & ~kind(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) & (((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~funny(X0) | kind(X0)))) [nnf transformation 9]
54. ! [X0] : (((funny(X0) & ~kind(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) & (((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | ~funny(X0) | kind(X0))) [flattening 53]
89. ~wise(X0) | ~strong(X0) [cnf transformation 43]
105. ~wise(X0) | ~funny(X0) [cnf transformation 52]
112. funny(X0) | funny(X0) | strong(X0) [cnf transformation 54]
143. wise(alice) [cnf transformation 20]
147. funny(X0) | strong(X0) [duplicate literal removal 112]
364. ~strong(alice) [resolution 89,143]
366. ~funny(alice) [resolution 105,143]
371. strong(alice) [resolution 147,366]
372. $false [subsumption resolution 371,364]
% SZS output end Proof for 7066563556549242803554689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not rich or generous then susan is both not creative and humble.
Everyone who is either wise or not brave is not generous.
If fred is both not quiet and not creative then someone is creative.
Everyone who is both old and brave is not curious or not rich and vice versa.
Everyone who is either not old or not curious is both old and patient.
Everyone who is either humble or quiet is either generous or happy.
Everyone who is both wise and not calm is either not patient or old and vice versa.
If mary is either not brave or not happy then fred is not generous.
Everyone who is patient or not wise is not old or generous and vice versa.
If someone is strong then someone is either not curious or funny and vice versa.
If someone is not quiet then someone is funny and vice versa.
Everyone who is both not creative and quiet is both not old and not kind and vice versa.
Everyone who is not calm is funny or old and vice versa.
Everyone who is not quiet is wise or old and vice versa.
Everyone who is kind is not strong or happy and vice versa.
Everyone who is not tall or strong is either generous or not wise and vice versa.
Someone is both not patient and not rich.
Lucy is happy.
Paul is not humble.
Susan is funny or not humble.
Mary is either not humble or wise.
Fred is either not kind or curious.
Someone is not old or brave. | Paul is not generous. | contradiction | (((~rich(alice)|generous(alice)))=>((~creative(susan)&humble(susan))))&
(![X]:((wise(X)<~>~brave(X))=>~generous(X)))&
(((~quiet(fred)&~creative(fred)))=>(?[X]:(creative(X))))&
(![X]:((old(X)&brave(X))<=>(~curious(X)|~rich(X))))&
(![X]:((~old(X)<~>~curious(X))=>(old(X)&patient(X))))&
(![X]:((humble(X)<~>quiet(X))=>(generous(X)<~>happy(X))))&
(![X]:((wise(X)&~calm(X))<=>(~patient(X)<~>old(X))))&
(((~brave(mary)<~>~happy(mary)))=>(~generous(fred)))&
(![X]:((patient(X)|~wise(X))<=>(~old(X)|generous(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~curious(X)<~>funny(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:(funny(X))))&
(![X]:((~creative(X)&quiet(X))<=>(~old(X)&~kind(X))))&
(![X]:(~calm(X)<=>(funny(X)|old(X))))&
(![X]:(~quiet(X)<=>(wise(X)|old(X))))&
(![X]:(kind(X)<=>(~strong(X)|happy(X))))&
(![X]:((~tall(X)|strong(X))<=>(generous(X)<~>~wise(X))))&
(?[X]:((~patient(X)&~rich(X))))&
(happy(lucy))&
(~humble(paul))&
((funny(susan)|~humble(susan)))&
((~humble(mary)<~>wise(mary)))&
((~kind(fred)<~>curious(fred)))&
(?[X]:((~old(X)|brave(X)))) | ~generous(paul) | [
"p3",
"p4",
"p6",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1192502150682324271350400
% SZS output start Proof for 1192502150682324271350400
4. ! [X0] : ((brave(X0) & old(X0)) <=> (~rich(X0) | ~curious(X0))) [input p3]
5. ! [X0] : ((~old(X0) <~> ~curious(X0)) => (patient(X0) & old(X0))) [input p4]
7. ! [X0] : ((~calm(X0) & wise(X0)) <=> (~patient(X0) <~> old(X0))) [input p6]
9. ! [X0] : ((~wise(X0) | patient(X0)) <=> (generous(X0) | ~old(X0))) [input p8]
13. ! [X0] : (~calm(X0) <=> (old(X0) | funny(X0))) [input p12]
24. ~generous(paul) [input hypothesis]
31. ! [X0] : ((patient(X0) & old(X0)) | (~old(X0) <=> ~curious(X0))) [ennf transformation 5]
37. ! [X0] : (((brave(X0) & old(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (~brave(X0) | ~old(X0)))) [nnf transformation 4]
38. ! [X0] : (((brave(X0) & old(X0)) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | ~brave(X0) | ~old(X0))) [flattening 37]
39. ! [X0] : ((patient(X0) & old(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) [nnf transformation 31]
41. ! [X0] : (((~calm(X0) & wise(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (calm(X0) | ~wise(X0)))) [nnf transformation 7]
42. ! [X0] : (((~calm(X0) & wise(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | calm(X0) | ~wise(X0))) [flattening 41]
44. ! [X0] : (((~wise(X0) | patient(X0)) | (~generous(X0) & old(X0))) & ((generous(X0) | ~old(X0)) | (wise(X0) & ~patient(X0)))) [nnf transformation 9]
45. ! [X0] : ((~wise(X0) | patient(X0) | (~generous(X0) & old(X0))) & (generous(X0) | ~old(X0) | (wise(X0) & ~patient(X0)))) [flattening 44]
58. ! [X0] : ((~calm(X0) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | calm(X0))) [nnf transformation 13]
59. ! [X0] : ((~calm(X0) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | calm(X0))) [flattening 58]
80. curious(X0) | old(X0) [cnf transformation 38]
84. old(X0) | ~curious(X0) | old(X0) [cnf transformation 39]
93. ~old(X0) | patient(X0) | calm(X0) | ~wise(X0) [cnf transformation 42]
100. generous(X0) | ~old(X0) | ~patient(X0) [cnf transformation 45]
101. generous(X0) | ~old(X0) | wise(X0) [cnf transformation 45]
116. ~calm(X0) | ~old(X0) [cnf transformation 59]
139. ~generous(paul) [cnf transformation 24]
140. old(X0) | ~curious(X0) [duplicate literal removal 84]
176. old(X0) [subsumption resolution 140,80]
179. ~wise(X0) | calm(X0) | patient(X0) [subsumption resolution 93,176]
194. wise(X0) | generous(X0) [subsumption resolution 101,176]
195. ~patient(X0) | generous(X0) [subsumption resolution 100,176]
238. ~calm(X0) [subsumption resolution 116,176]
362. calm(X0) | patient(X0) | generous(X0) [resolution 179,194]
364. patient(X0) | generous(X0) [subsumption resolution 362,238]
365. generous(X0) [subsumption resolution 364,195]
374. $false [resolution 365,139]
% SZS output end Proof for 1192502150682324271350400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then someone is both not rich and not patient and vice versa. If someone is either patient or not patient then someone is not calm or brave and vice versa. Everyone who is either calm or not wise is not kind or not old and vice versa. Everyone who is both creative and calm is not patient or patient. Everyone who is both not funny and not calm is both not funny and not curious and vice versa. Everyone who is not patient or humble is not creative and vice versa. Everyone who is both not happy and not old is either calm or not rich and vice versa. Everyone who is both quiet and rich is both strong and not funny and vice versa. Everyone who is both not curious and not tall is strong and vice versa. If mary is both not old and not tall then someone is both not funny and generous. Everyone who is both wise and old is either not creative or not rich and vice versa. Everyone who is both calm and not rich is not wise. Everyone who is either strong or kind is not calm or not happy and vice versa. If someone is both humble and not brave then lucy is brave or kind and vice versa. Everyone who is either strong or not kind is patient and vice versa. Everyone who is either not tall or not creative is happy and vice versa. Paul is both not generous and happy. Lucy is not calm. Someone is patient or not curious. Someone is both not humble and not patient. Someone is either not rich or happy. Someone is both not calm and funny. Fred is rich. | Paul is tall. | entailment | ((?[X]:(strong(X)))<=>(?[X]:((~rich(X)&~patient(X)))))&
((?[X]:((patient(X)<~>~patient(X))))<=>(?[X]:((~calm(X)|brave(X)))))&
(![X]:((calm(X)<~>~wise(X))<=>(~kind(X)|~old(X))))&
(![X]:((creative(X)&calm(X))=>(~patient(X)|patient(X))))&
(![X]:((~funny(X)&~calm(X))<=>(~funny(X)&~curious(X))))&
(![X]:((~patient(X)|humble(X))<=>~creative(X)))&
(![X]:((~happy(X)&~old(X))<=>(calm(X)<~>~rich(X))))&
(![X]:((quiet(X)&rich(X))<=>(strong(X)&~funny(X))))&
(![X]:((~curious(X)&~tall(X))<=>strong(X)))&
(((~old(mary)&~tall(mary)))=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:((wise(X)&old(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:((calm(X)&~rich(X))=>~wise(X)))&
(![X]:((strong(X)<~>kind(X))<=>(~calm(X)|~happy(X))))&
((?[X]:((humble(X)&~brave(X))))<=>((brave(lucy)|kind(lucy))))&
(![X]:((strong(X)<~>~kind(X))<=>patient(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>happy(X)))&
((~generous(paul)&happy(paul)))&
(~calm(lucy))&
(?[X]:((patient(X)|~curious(X))))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~rich(X)<~>happy(X))))&
(?[X]:((~calm(X)&funny(X))))&
(rich(fred)) | tall(paul) | [
"p2",
"p5",
"p6",
"p10",
"p11",
"p12",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3972571747223159722106359
% SZS output start Proof for 3972571747223159722106359
3. ! [X0] : ((calm(X0) <~> ~wise(X0)) <=> (~old(X0) | ~kind(X0))) [input p2]
6. ! [X0] : ((humble(X0) | ~patient(X0)) <=> ~creative(X0)) [input p5]
7. ! [X0] : ((~old(X0) & ~happy(X0)) <=> (calm(X0) <~> ~rich(X0))) [input p6]
11. ! [X0] : ((old(X0) & wise(X0)) <=> (~creative(X0) <~> ~rich(X0))) [input p10]
12. ! [X0] : ((~rich(X0) & calm(X0)) => ~wise(X0)) [input p11]
13. ! [X0] : ((strong(X0) <~> kind(X0)) <=> (~happy(X0) | ~calm(X0))) [input p12]
15. ! [X0] : ((strong(X0) <~> ~kind(X0)) <=> patient(X0)) [input p14]
16. ! [X0] : ((~tall(X0) <~> ~creative(X0)) <=> happy(X0)) [input p15]
17. happy(paul) & ~generous(paul) [input p16]
24. ~tall(paul) [input hypothesis]
31. ! [X0] : (~wise(X0) | (rich(X0) | ~calm(X0))) [ennf transformation 12]
32. ! [X0] : (~wise(X0) | rich(X0) | ~calm(X0)) [flattening 31]
43. ! [X0] : ((((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (old(X0) & kind(X0))) & ((~old(X0) | ~kind(X0)) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0))))) [nnf transformation 3]
44. ! [X0] : ((((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (old(X0) & kind(X0))) & (~old(X0) | ~kind(X0) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0))))) [flattening 43]
47. ! [X0] : (((humble(X0) | ~patient(X0)) | creative(X0)) & (~creative(X0) | (~humble(X0) & patient(X0)))) [nnf transformation 6]
48. ! [X0] : ((humble(X0) | ~patient(X0) | creative(X0)) & (~creative(X0) | (~humble(X0) & patient(X0)))) [flattening 47]
49. ! [X0] : (((~old(X0) & ~happy(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0)))) & (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | (old(X0) | happy(X0)))) [nnf transformation 7]
50. ! [X0] : (((~old(X0) & ~happy(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0)))) & (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | old(X0) | happy(X0))) [flattening 49]
57. ! [X0] : (((old(X0) & wise(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | (~old(X0) | ~wise(X0)))) [nnf transformation 11]
58. ! [X0] : (((old(X0) & wise(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ~old(X0) | ~wise(X0))) [flattening 57]
59. ! [X0] : ((((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (happy(X0) & calm(X0))) & ((~happy(X0) | ~calm(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0))))) [nnf transformation 13]
60. ! [X0] : ((((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (happy(X0) & calm(X0))) & (~happy(X0) | ~calm(X0) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0))))) [flattening 59]
66. ! [X0] : ((((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | ~patient(X0)) & (patient(X0) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0))))) [nnf transformation 15]
67. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | ~happy(X0)) & (happy(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [nnf transformation 16]
90. ~calm(X0) | wise(X0) | kind(X0) [cnf transformation 44]
97. ~creative(X0) | patient(X0) [cnf transformation 48]
102. ~happy(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 50]
118. ~creative(X0) | wise(X0) | rich(X0) [cnf transformation 58]
121. ~wise(X0) | rich(X0) | ~calm(X0) [cnf transformation 32]
123. ~happy(X0) | ~calm(X0) | strong(X0) | ~kind(X0) [cnf transformation 60]
124. kind(X0) | strong(X0) | calm(X0) [cnf transformation 60]
126. ~kind(X0) | ~strong(X0) | calm(X0) [cnf transformation 60]
135. ~kind(X0) | strong(X0) | ~patient(X0) [cnf transformation 66]
136. ~patient(X0) | ~strong(X0) | kind(X0) [cnf transformation 66]
140. ~happy(X0) | tall(X0) | creative(X0) [cnf transformation 67]
142. happy(paul) [cnf transformation 17]
152. ~tall(paul) [cnf transformation 24]
254. ~rich(paul) | ~calm(paul) [resolution 102,142]
256. 23 <=> calm(paul) [avatar definition]
257. calm(paul) <- (23) [avatar component clause 256]
260. 24 <=> rich(paul) [avatar definition]
263. ~23 | ~24 [avatar split clause 254,260,256]
270. wise(paul) | kind(paul) <- (23) [resolution 257,90]
285. 28 <=> wise(paul) [avatar definition]
287. wise(paul) <- (28) [avatar component clause 285]
290. 29 <=> kind(paul) [avatar definition]
292. kind(paul) <- (29) [avatar component clause 290]
293. 29 | 28 | ~23 [avatar split clause 270,256,285,290]
353. 39 <=> strong(paul) [avatar definition]
354. ~strong(paul) <- (~39) [avatar component clause 353]
355. strong(paul) <- (39) [avatar component clause 353]
376. 43 <=> creative(paul) [avatar definition]
378. creative(paul) <- (43) [avatar component clause 376]
424. wise(paul) | rich(paul) <- (43) [resolution 378,118]
425. patient(paul) <- (43) [resolution 378,97]
432. strong(X1) | ~patient(X1) | strong(X1) | calm(X1) [resolution 135,124]
436. ~patient(X1) | strong(X1) | calm(X1) [duplicate literal removal 432]
472. tall(paul) | creative(paul) [resolution 140,142]
487. ~strong(paul) | kind(paul) <- (43) [resolution 425,136]
495. ~strong(paul) | calm(paul) <- (29) [resolution 292,126]
496. calm(paul) <- (29, 39) [subsumption resolution 495,355]
499. 23 | ~29 | ~39 [avatar split clause 496,353,290,256]
500. 24 | 28 | ~43 [avatar split clause 424,376,285,260]
523. ~calm(paul) | strong(paul) | ~kind(paul) [resolution 123,142]
535. strong(paul) | calm(paul) <- (43) [resolution 436,425]
571. strong(paul) | ~kind(paul) <- (23) [subsumption resolution 523,257]
572. ~29 | 39 | ~23 [avatar split clause 571,256,353,290]
573. 29 | ~39 | ~43 [avatar split clause 487,376,353,290]
581. rich(paul) | ~calm(paul) <- (28) [resolution 287,121]
589. calm(paul) <- (~39, 43) [subsumption resolution 535,354]
590. 23 | 39 | ~43 [avatar split clause 589,376,353,256]
592. ~23 | 24 | ~28 [avatar split clause 581,285,260,256]
599. creative(paul) [subsumption resolution 472,152]
600. 43 [avatar split clause 599,376]
601. $false [avatar sat refutation 263,293,499,500,572,573,590,592,600]
% SZS output end Proof for 3972571747223159722106359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not funny is not kind or creative.
If fred is both generous and rich then paul is either funny or wise and vice versa.
If alice is either old or not calm then john is curious.
Everyone who is both not wise and not funny is either funny or generous and vice versa.
If mary is funny then someone is either patient or not funny and vice versa.
If someone is kind or not wise then paul is brave or not tall.
Everyone who is both not wise and quiet is not calm.
If someone is not generous then someone is either rich or not patient and vice versa.
Everyone who is calm or not generous is rich.
Everyone who is both not happy and not brave is either not calm or tall.
If john is not generous or not happy then paul is tall or not wise.
If someone is either curious or not kind then susan is wise or creative and vice versa.
Everyone who is creative is not creative.
Everyone who is both not happy and tall is calm or not old and vice versa.
Everyone who is either rich or not generous is both happy and not curious and vice versa.
Everyone who is curious is either not brave or curious.
Paul is both kind and not funny.
Susan is both not happy and not wise.
Someone is both not funny and humble.
Paul is either funny or calm.
Someone is funny or not rich.
Lucy is either not kind or quiet.
Someone is not patient or not tall. | Mary is not calm. | entailment | (![X]:((patient(X)&~funny(X))=>(~kind(X)|creative(X))))&
(((generous(fred)&rich(fred)))<=>((funny(paul)<~>wise(paul))))&
(((old(alice)<~>~calm(alice)))=>(curious(john)))&
(![X]:((~wise(X)&~funny(X))<=>(funny(X)<~>generous(X))))&
((funny(mary))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:((kind(X)|~wise(X))))=>((brave(paul)|~tall(paul))))&
(![X]:((~wise(X)&quiet(X))=>~calm(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((rich(X)<~>~patient(X)))))&
(![X]:((calm(X)|~generous(X))=>rich(X)))&
(![X]:((~happy(X)&~brave(X))=>(~calm(X)<~>tall(X))))&
(((~generous(john)|~happy(john)))=>((tall(paul)|~wise(paul))))&
((?[X]:((curious(X)<~>~kind(X))))<=>((wise(susan)|creative(susan))))&
(![X]:(creative(X)=>~creative(X)))&
(![X]:((~happy(X)&tall(X))<=>(calm(X)|~old(X))))&
(![X]:((rich(X)<~>~generous(X))<=>(happy(X)&~curious(X))))&
(![X]:(curious(X)=>(~brave(X)<~>curious(X))))&
((kind(paul)&~funny(paul)))&
((~happy(susan)&~wise(susan)))&
(?[X]:((~funny(X)&humble(X))))&
((funny(paul)<~>calm(paul)))&
(?[X]:((funny(X)|~rich(X))))&
((~kind(lucy)<~>quiet(lucy)))&
(?[X]:((~patient(X)|~tall(X)))) | ~calm(mary) | [
"p0",
"p3",
"p4",
"p8",
"p12",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7775596923602095572466931
% SZS output start Proof for 7775596923602095572466931
1. ! [X0] : ((~funny(X0) & patient(X0)) => (creative(X0) | ~kind(X0))) [input p0]
4. ! [X0] : ((~funny(X0) & ~wise(X0)) <=> (funny(X0) <~> generous(X0))) [input p3]
5. funny(mary) <=> ? [X0] : (patient(X0) <~> ~funny(X0)) [input p4]
9. ! [X0] : ((~generous(X0) | calm(X0)) => rich(X0)) [input p8]
13. ! [X0] : (creative(X0) => ~creative(X0)) [input p12]
14. ! [X0] : ((tall(X0) & ~happy(X0)) <=> (~old(X0) | calm(X0))) [input p13]
15. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> (~curious(X0) & happy(X0))) [input p14]
17. ~funny(paul) & kind(paul) [input p16]
24. calm(mary) [input hypothesis]
27. ! [X0] : ((creative(X0) | ~kind(X0)) | (funny(X0) | ~patient(X0))) [ennf transformation 1]
28. ! [X0] : (creative(X0) | ~kind(X0) | funny(X0) | ~patient(X0)) [flattening 27]
34. ! [X0] : (rich(X0) | (generous(X0) & ~calm(X0))) [ennf transformation 9]
39. ! [X0] : (~creative(X0) | ~creative(X0)) [ennf transformation 13]
44. ! [X0] : (((~funny(X0) & ~wise(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (funny(X0) | wise(X0)))) [nnf transformation 4]
45. ! [X0] : (((~funny(X0) & ~wise(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | funny(X0) | wise(X0))) [flattening 44]
46. (funny(mary) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (? [X0] : ((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ~funny(mary)) [nnf transformation 5]
47. (funny(mary) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (? [X1] : ((funny(X1) | ~patient(X1)) & (~funny(X1) | patient(X1))) | ~funny(mary)) [rectify 46]
48. ? [X1] : ((funny(X1) | ~patient(X1)) & (~funny(X1) | patient(X1))) => ((funny(sK0) | ~patient(sK0)) & (~funny(sK0) | patient(sK0))) [choice axiom]
49. (funny(mary) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0)))) & (((funny(sK0) | ~patient(sK0)) & (~funny(sK0) | patient(sK0))) | ~funny(mary)) [skolemisation 47,48]
61. ! [X0] : (((tall(X0) & ~happy(X0)) | (old(X0) & ~calm(X0))) & ((~old(X0) | calm(X0)) | (~tall(X0) | happy(X0)))) [nnf transformation 14]
62. ! [X0] : (((tall(X0) & ~happy(X0)) | (old(X0) & ~calm(X0))) & (~old(X0) | calm(X0) | ~tall(X0) | happy(X0))) [flattening 61]
63. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | (curious(X0) | ~happy(X0))) & ((~curious(X0) & happy(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 15]
64. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | curious(X0) | ~happy(X0)) & ((~curious(X0) & happy(X0)) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [flattening 63]
74. ~kind(X0) | creative(X0) | funny(X0) | ~patient(X0) [cnf transformation 28]
87. ~funny(X0) | generous(X0) | ~funny(X0) [cnf transformation 45]
92. funny(mary) | patient(X0) | funny(X0) [cnf transformation 49]
100. ~calm(X0) | rich(X0) [cnf transformation 34]
112. ~creative(X0) | ~creative(X0) [cnf transformation 39]
114. ~happy(X0) | ~calm(X0) [cnf transformation 62]
118. ~rich(X0) | ~generous(X0) | happy(X0) [cnf transformation 64]
126. kind(paul) [cnf transformation 17]
127. ~funny(paul) [cnf transformation 17]
137. calm(mary) [cnf transformation 24]
139. ~creative(X0) [duplicate literal removal 112]
141. ~funny(X0) | generous(X0) [duplicate literal removal 87]
147. 2 <=> funny(paul) [avatar definition]
148. ~funny(paul) <- (~2) [avatar component clause 147]
180. 8 <=> ! [X0] : (patient(X0) | funny(X0)) [avatar definition]
181. funny(X0) | patient(X0) <- (8) [avatar component clause 180]
183. 9 <=> funny(mary) [avatar definition]
185. funny(mary) <- (9) [avatar component clause 183]
186. 8 | 9 [avatar split clause 92,183,180]
282. ~2 [avatar split clause 127,147]
320. rich(mary) [resolution 100,137]
331. generous(mary) <- (9) [resolution 141,185]
345. ~generous(mary) | happy(mary) [resolution 118,320]
356. happy(mary) <- (9) [subsumption resolution 345,331]
391. creative(paul) | funny(paul) | ~patient(paul) [resolution 74,126]
392. funny(paul) | ~patient(paul) [subsumption resolution 391,139]
393. ~patient(paul) <- (~2) [subsumption resolution 392,148]
405. ~calm(mary) <- (9) [resolution 356,114]
406. $false <- (9) [subsumption resolution 405,137]
407. ~9 [avatar contradiction clause 406]
418. patient(paul) <- (~2, 8) [resolution 181,148]
422. $false <- (~2, 8) [subsumption resolution 418,393]
423. 2 | ~8 [avatar contradiction clause 422]
426. $false [avatar sat refutation 186,282,407,423]
% SZS output end Proof for 7775596923602095572466931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not curious and not creative then mary is either not generous or old.
Everyone who is quiet or not kind is both kind and not generous and vice versa.
Everyone who is not old or curious is creative or not kind.
If someone is either old or calm then someone is either not patient or not happy and vice versa.
If someone is either not wise or not quiet then mary is both not quiet and not funny and vice versa.
Everyone who is not old or not strong is not strong and vice versa.
If fred is not calm then someone is either not old or creative and vice versa.
Everyone who is either patient or rich is not creative or old.
If john is both not patient and not calm then someone is either not calm or not strong and vice versa.
If fred is not curious then someone is not generous.
Everyone who is either old or not old is funny or not old and vice versa.
If susan is not tall then someone is both not tall and old.
Everyone who is both old and not wise is either not old or not kind.
Everyone who is not strong or kind is wise or tall.
If someone is creative or curious then someone is rich.
If fred is not calm or curious then alice is wise or not patient and vice versa.
Someone is either brave or not happy.
Someone is both not strong and not creative.
Someone is not patient.
Someone is either not funny or not curious.
Paul is strong or wise.
Someone is either not quiet or not kind.
Mary is not old or rich. | Mary is not strong. | neutral | (((~curious(john)&~creative(john)))=>((~generous(mary)<~>old(mary))))&
(![X]:((quiet(X)|~kind(X))<=>(kind(X)&~generous(X))))&
(![X]:((~old(X)|curious(X))=>(creative(X)|~kind(X))))&
((?[X]:((old(X)<~>calm(X))))<=>(?[X]:((~patient(X)<~>~happy(X)))))&
((?[X]:((~wise(X)<~>~quiet(X))))<=>((~quiet(mary)&~funny(mary))))&
(![X]:((~old(X)|~strong(X))<=>~strong(X)))&
((~calm(fred))<=>(?[X]:((~old(X)<~>creative(X)))))&
(![X]:((patient(X)<~>rich(X))=>(~creative(X)|old(X))))&
(((~patient(john)&~calm(john)))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
((~curious(fred))=>(?[X]:(~generous(X))))&
(![X]:((old(X)<~>~old(X))<=>(funny(X)|~old(X))))&
((~tall(susan))=>(?[X]:((~tall(X)&old(X)))))&
(![X]:((old(X)&~wise(X))=>(~old(X)<~>~kind(X))))&
(![X]:((~strong(X)|kind(X))=>(wise(X)|tall(X))))&
((?[X]:((creative(X)|curious(X))))=>(?[X]:(rich(X))))&
(((~calm(fred)|curious(fred)))<=>((wise(alice)|~patient(alice))))&
(?[X]:((brave(X)<~>~happy(X))))&
(?[X]:((~strong(X)&~creative(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~funny(X)<~>~curious(X))))&
((strong(paul)|wise(paul)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
((~old(mary)|rich(mary))) | ~strong(mary) | [] | null | 0 |
Everyone who is happy is not curious or rich and vice versa.
Everyone who is either happy or not quiet is strong or not quiet and vice versa.
Everyone who is either happy or not old is either not calm or creative and vice versa.
Everyone who is either quiet or strong is not brave or wise.
Everyone who is not happy is both happy and curious and vice versa.
Everyone who is both not funny and patient is not generous or not creative.
If john is brave or rich then someone is not kind.
Everyone who is strong or old is either not patient or not quiet and vice versa.
Everyone who is patient is quiet or not calm.
Everyone who is both not quiet and not brave is kind or generous and vice versa.
If someone is curious then someone is not old.
Everyone who is either not brave or patient is not strong.
Everyone who is both patient and not patient is humble and vice versa.
If fred is calm then fred is strong or not old.
Everyone who is either not old or not creative is both brave and not generous.
John is either generous or creative.
Someone is brave.
Someone is quiet or creative.
Alice is either not kind or calm.
Someone is both not tall and creative.
Paul is not curious or not patient. | Fred is calm. | neutral | (![X]:(happy(X)<=>(~curious(X)|rich(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(strong(X)|~quiet(X))))&
(![X]:((happy(X)<~>~old(X))<=>(~calm(X)<~>creative(X))))&
(![X]:((quiet(X)<~>strong(X))=>(~brave(X)|wise(X))))&
(![X]:(~happy(X)<=>(happy(X)&curious(X))))&
(![X]:((~funny(X)&patient(X))=>(~generous(X)|~creative(X))))&
(((brave(john)|rich(john)))=>(?[X]:(~kind(X))))&
(![X]:((strong(X)|old(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:(patient(X)=>(quiet(X)|~calm(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(kind(X)|generous(X))))&
((?[X]:(curious(X)))=>(?[X]:(~old(X))))&
(![X]:((~brave(X)<~>patient(X))=>~strong(X)))&
(![X]:((patient(X)&~patient(X))<=>humble(X)))&
((calm(fred))=>((strong(fred)|~old(fred))))&
(![X]:((~old(X)<~>~creative(X))=>(brave(X)&~generous(X))))&
((generous(john)<~>creative(john)))&
(?[X]:(brave(X)))&
(?[X]:((quiet(X)|creative(X))))&
((~kind(alice)<~>calm(alice)))&
(?[X]:((~tall(X)&creative(X))))&
((~curious(paul)|~patient(paul))) | calm(fred) | [] | null | 0 |
If fred is both patient and not quiet then someone is not happy and vice versa.
Everyone who is not old or generous is either not creative or not rich.
If john is either not strong or not patient then paul is either not old or calm and vice versa.
Everyone who is both not quiet and patient is either not strong or quiet and vice versa.
If mary is both creative and not humble then mary is funny or happy.
Everyone who is either brave or not patient is generous and vice versa.
Everyone who is old or not curious is not old or not generous and vice versa.
Everyone who is both quiet and not funny is either happy or not patient and vice versa.
If someone is wise then someone is either kind or strong.
If someone is funny or not old then mary is not funny and vice versa.
Everyone who is both not brave and tall is not humble and vice versa.
If someone is either generous or not wise then lucy is either not curious or not funny and vice versa.
Everyone who is either not brave or calm is not funny or strong and vice versa.
Everyone who is funny is either not tall or happy and vice versa.
Everyone who is generous is either kind or rich and vice versa.
If someone is either not kind or tall then someone is not creative and vice versa.
Mary is either rich or not humble.
Someone is not curious.
Someone is either not patient or not generous.
Someone is not tall or humble.
Fred is not calm or brave.
Fred is calm or not happy.
Paul is both quiet and not tall. | Paul is not tall. | entailment | (((patient(fred)&~quiet(fred)))<=>(?[X]:(~happy(X))))&
(![X]:((~old(X)|generous(X))=>(~creative(X)<~>~rich(X))))&
(((~strong(john)<~>~patient(john)))<=>((~old(paul)<~>calm(paul))))&
(![X]:((~quiet(X)&patient(X))<=>(~strong(X)<~>quiet(X))))&
(((creative(mary)&~humble(mary)))=>((funny(mary)|happy(mary))))&
(![X]:((brave(X)<~>~patient(X))<=>generous(X)))&
(![X]:((old(X)|~curious(X))<=>(~old(X)|~generous(X))))&
(![X]:((quiet(X)&~funny(X))<=>(happy(X)<~>~patient(X))))&
((?[X]:(wise(X)))=>(?[X]:((kind(X)<~>strong(X)))))&
((?[X]:((funny(X)|~old(X))))<=>(~funny(mary)))&
(![X]:((~brave(X)&tall(X))<=>~humble(X)))&
((?[X]:((generous(X)<~>~wise(X))))<=>((~curious(lucy)<~>~funny(lucy))))&
(![X]:((~brave(X)<~>calm(X))<=>(~funny(X)|strong(X))))&
(![X]:(funny(X)<=>(~tall(X)<~>happy(X))))&
(![X]:(generous(X)<=>(kind(X)<~>rich(X))))&
((?[X]:((~kind(X)<~>tall(X))))<=>(?[X]:(~creative(X))))&
((rich(mary)<~>~humble(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:((~tall(X)|humble(X))))&
((~calm(fred)|brave(fred)))&
((calm(fred)|~happy(fred)))&
((quiet(paul)&~tall(paul))) | ~tall(paul) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3136906406094123530857272
% SZS output start Proof for 3136906406094123530857272
23. ~tall(paul) & quiet(paul) [input p22]
24. tall(paul) [input hypothesis]
155. ~tall(paul) [cnf transformation 23]
156. tall(paul) [cnf transformation 24]
337. $false [subsumption resolution 156,155]
% SZS output end Proof for 3136906406094123530857272
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is creative or not funny then lucy is patient and vice versa.
Everyone who is not strong or old is both tall and patient and vice versa.
Everyone who is funny or curious is not rich.
Everyone who is not happy or not patient is either rich or funny and vice versa.
If someone is kind then someone is wise or rich and vice versa.
If someone is either not curious or rich then someone is both kind and creative.
Everyone who is not wise is both quiet and patient.
Everyone who is either brave or not humble is both not humble and strong and vice versa.
Everyone who is either generous or tall is patient or calm and vice versa.
If lucy is either rich or not creative then someone is not strong or not old and vice versa.
If paul is humble or calm then someone is both kind and not patient.
Everyone who is rich or not curious is not funny and vice versa.
Everyone who is not brave or not strong is either rich or not curious.
If someone is generous or not happy then someone is rich or not tall.
Everyone who is quiet is both calm and brave.
Everyone who is either not kind or not old is both rich and not wise and vice versa.
Lucy is happy.
Susan is humble or brave.
Susan is both humble and not old.
Fred is patient.
Someone is kind.
Paul is humble or not brave. | Paul is not wise. | contradiction | (((creative(fred)|~funny(fred)))<=>(patient(lucy)))&
(![X]:((~strong(X)|old(X))<=>(tall(X)&patient(X))))&
(![X]:((funny(X)|curious(X))=>~rich(X)))&
(![X]:((~happy(X)|~patient(X))<=>(rich(X)<~>funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((wise(X)|rich(X)))))&
((?[X]:((~curious(X)<~>rich(X))))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:(~wise(X)=>(quiet(X)&patient(X))))&
(![X]:((brave(X)<~>~humble(X))<=>(~humble(X)&strong(X))))&
(![X]:((generous(X)<~>tall(X))<=>(patient(X)|calm(X))))&
(((rich(lucy)<~>~creative(lucy)))<=>(?[X]:((~strong(X)|~old(X)))))&
(((humble(paul)|calm(paul)))=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:((rich(X)|~curious(X))<=>~funny(X)))&
(![X]:((~brave(X)|~strong(X))=>(rich(X)<~>~curious(X))))&
((?[X]:((generous(X)|~happy(X))))=>(?[X]:((rich(X)|~tall(X)))))&
(![X]:(quiet(X)=>(calm(X)&brave(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(rich(X)&~wise(X))))&
(happy(lucy))&
((humble(susan)|brave(susan)))&
((humble(susan)&~old(susan)))&
(patient(fred))&
(?[X]:(kind(X)))&
((humble(paul)|~brave(paul))) | ~wise(paul) | [
"p6",
"p7",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5573438623580643727570855
% SZS output start Proof for 5573438623580643727570855
7. ! [X0] : (~wise(X0) => (patient(X0) & quiet(X0))) [input p6]
8. ! [X0] : ((brave(X0) <~> ~humble(X0)) <=> (strong(X0) & ~humble(X0))) [input p7]
15. ! [X0] : (quiet(X0) => (brave(X0) & calm(X0))) [input p14]
22. ~brave(paul) | humble(paul) [input p21]
23. ~wise(paul) [input hypothesis]
29. ! [X0] : ((patient(X0) & quiet(X0)) | wise(X0)) [ennf transformation 7]
33. ! [X0] : ((brave(X0) & calm(X0)) | ~quiet(X0)) [ennf transformation 15]
49. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (~strong(X0) | humble(X0))) & ((strong(X0) & ~humble(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [nnf transformation 8]
50. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | ~strong(X0) | humble(X0)) & ((strong(X0) & ~humble(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [flattening 49]
92. quiet(X0) | wise(X0) [cnf transformation 29]
94. ~humble(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 50]
126. ~quiet(X0) | brave(X0) [cnf transformation 33]
139. ~brave(paul) | humble(paul) [cnf transformation 22]
140. ~wise(paul) [cnf transformation 23]
141. ~humble(X0) | ~brave(X0) [duplicate literal removal 94]
276. ~brave(paul) [subsumption resolution 139,141]
283. brave(X0) | wise(X0) [resolution 126,92]
299. wise(paul) [resolution 283,276]
301. $false [subsumption resolution 299,140]
% SZS output end Proof for 5573438623580643727570855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not funny is either not creative or funny and vice versa.
Everyone who is both old and calm is either not strong or humble and vice versa.
If someone is either tall or not funny then alice is wise or not patient.
Everyone who is both not curious and humble is both not generous and brave and vice versa.
If someone is either not brave or not tall then lucy is either not kind or not patient.
If someone is curious then fred is both funny and not curious and vice versa.
If fred is creative or not strong then mary is not wise and vice versa.
If fred is either not tall or not old then someone is both not kind and not generous.
Everyone who is both strong and not strong is calm or tall and vice versa.
Everyone who is old or humble is either not curious or wise and vice versa.
If susan is either not humble or not quiet then someone is tall and vice versa.
Everyone who is either not strong or tall is not tall or not patient and vice versa.
If someone is both not strong and happy then lucy is not brave and vice versa.
If someone is not calm or not humble then someone is either not kind or not funny.
If someone is both patient and quiet then fred is either brave or generous.
Everyone who is not generous or not calm is not wise or rich and vice versa.
Someone is either not funny or calm.
Someone is either not generous or strong.
Someone is both quiet and not curious.
Lucy is either patient or humble.
Susan is not creative or wise.
Someone is both not old and not calm. | Mary is old. | neutral | (![X]:((~rich(X)|~funny(X))<=>(~creative(X)<~>funny(X))))&
(![X]:((old(X)&calm(X))<=>(~strong(X)<~>humble(X))))&
((?[X]:((tall(X)<~>~funny(X))))=>((wise(alice)|~patient(alice))))&
(![X]:((~curious(X)&humble(X))<=>(~generous(X)&brave(X))))&
((?[X]:((~brave(X)<~>~tall(X))))=>((~kind(lucy)<~>~patient(lucy))))&
((?[X]:(curious(X)))<=>((funny(fred)&~curious(fred))))&
(((creative(fred)|~strong(fred)))<=>(~wise(mary)))&
(((~tall(fred)<~>~old(fred)))=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:((strong(X)&~strong(X))<=>(calm(X)|tall(X))))&
(![X]:((old(X)|humble(X))<=>(~curious(X)<~>wise(X))))&
(((~humble(susan)<~>~quiet(susan)))<=>(?[X]:(tall(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(~tall(X)|~patient(X))))&
((?[X]:((~strong(X)&happy(X))))<=>(~brave(lucy)))&
((?[X]:((~calm(X)|~humble(X))))=>(?[X]:((~kind(X)<~>~funny(X)))))&
((?[X]:((patient(X)&quiet(X))))=>((brave(fred)<~>generous(fred))))&
(![X]:((~generous(X)|~calm(X))<=>(~wise(X)|rich(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:((~generous(X)<~>strong(X))))&
(?[X]:((quiet(X)&~curious(X))))&
((patient(lucy)<~>humble(lucy)))&
((~creative(susan)|wise(susan)))&
(?[X]:((~old(X)&~calm(X)))) | old(mary) | [] | null | 0 |
Everyone who is not strong or happy is either calm or not strong and vice versa.
Everyone who is generous is either quiet or not generous and vice versa.
Everyone who is both creative and not tall is either not funny or not strong.
Everyone who is either wise or patient is patient and vice versa.
Everyone who is happy or not quiet is both generous and not old and vice versa.
If susan is both wise and rich then lucy is either tall or not brave and vice versa.
If someone is generous or wise then someone is not calm and vice versa.
Everyone who is either strong or not kind is both not curious and strong.
If fred is either patient or not wise then susan is either not curious or tall.
If paul is strong or not rich then someone is not patient.
Everyone who is either not calm or quiet is both curious and kind and vice versa.
Everyone who is not quiet is kind and vice versa.
Everyone who is both rich and creative is both curious and not old and vice versa.
If susan is not quiet or calm then someone is both old and tall and vice versa.
If someone is both not funny and not calm then someone is funny.
Someone is old or curious.
Mary is not generous.
Paul is either not quiet or not wise.
Someone is either quiet or not brave.
Someone is curious or wise.
Fred is funny or not calm.
Someone is both rich and not patient. | Fred is not quiet. | contradiction | (![X]:((~strong(X)|happy(X))<=>(calm(X)<~>~strong(X))))&
(![X]:(generous(X)<=>(quiet(X)<~>~generous(X))))&
(![X]:((creative(X)&~tall(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((wise(X)<~>patient(X))<=>patient(X)))&
(![X]:((happy(X)|~quiet(X))<=>(generous(X)&~old(X))))&
(((wise(susan)&rich(susan)))<=>((tall(lucy)<~>~brave(lucy))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>~kind(X))=>(~curious(X)&strong(X))))&
(((patient(fred)<~>~wise(fred)))=>((~curious(susan)<~>tall(susan))))&
(((strong(paul)|~rich(paul)))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(curious(X)&kind(X))))&
(![X]:(~quiet(X)<=>kind(X)))&
(![X]:((rich(X)&creative(X))<=>(curious(X)&~old(X))))&
(((~quiet(susan)|calm(susan)))<=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~funny(X)&~calm(X))))=>(?[X]:(funny(X))))&
(?[X]:((old(X)|curious(X))))&
(~generous(mary))&
((~quiet(paul)<~>~wise(paul)))&
(?[X]:((quiet(X)<~>~brave(X))))&
(?[X]:((curious(X)|wise(X))))&
((funny(fred)|~calm(fred)))&
(?[X]:((rich(X)&~patient(X)))) | ~quiet(fred) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 7358973901187348383216459
% SZS output start Proof for 7358973901187348383216459
2. ! [X0] : (generous(X0) <=> (quiet(X0) <~> ~generous(X0))) [input p1]
23. ~quiet(fred) [input hypothesis]
34. ! [X0] : ((generous(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ~generous(X0))) [nnf transformation 2]
79. ~generous(X0) | quiet(X0) | ~generous(X0) [cnf transformation 34]
82. generous(X0) | quiet(X0) | generous(X0) [cnf transformation 34]
141. ~quiet(fred) [cnf transformation 23]
145. ~generous(X0) | quiet(X0) [duplicate literal removal 79]
146. generous(X0) | quiet(X0) [duplicate literal removal 82]
149. quiet(X0) [subsumption resolution 145,146]
268. $false [subsumption resolution 141,149]
% SZS output end Proof for 7358973901187348383216459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not creative then susan is both generous and not rich.
Everyone who is rich or strong is both not tall and funny.
Everyone who is not tall or happy is both not calm and curious and vice versa.
If someone is both not brave and old then john is both calm and rich.
Everyone who is curious is either not funny or not tall and vice versa.
Everyone who is both rich and not tall is not funny or kind and vice versa.
Everyone who is both not old and rich is both not rich and not curious.
If mary is both not calm and creative then susan is brave or curious and vice versa.
Everyone who is either not tall or generous is not generous or creative.
Everyone who is either not humble or funny is strong.
Everyone who is either brave or generous is both brave and quiet.
Everyone who is funny is either humble or tall.
If mary is either not kind or not creative then john is both not creative and not generous and vice versa.
Everyone who is not wise is either wise or generous and vice versa.
Everyone who is both curious and happy is strong or not brave and vice versa.
If someone is both not funny and curious then lucy is both not creative and not happy and vice versa.
Fred is happy.
Someone is rich or not old.
Someone is either calm or rich.
Someone is not patient or happy.
Someone is not calm.
Someone is not strong or not funny. | Mary is tall. | contradiction | ((?[X]:((kind(X)<~>~creative(X))))=>((generous(susan)&~rich(susan))))&
(![X]:((rich(X)|strong(X))=>(~tall(X)&funny(X))))&
(![X]:((~tall(X)|happy(X))<=>(~calm(X)&curious(X))))&
((?[X]:((~brave(X)&old(X))))=>((calm(john)&rich(john))))&
(![X]:(curious(X)<=>(~funny(X)<~>~tall(X))))&
(![X]:((rich(X)&~tall(X))<=>(~funny(X)|kind(X))))&
(![X]:((~old(X)&rich(X))=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
(![X]:(~wise(X)<=>(wise(X)<~>generous(X))))&
(![X]:((curious(X)&happy(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(happy(fred))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((~patient(X)|happy(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~strong(X)|~funny(X)))) | tall(mary) | [
"p5",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1544249142671114145244583
% SZS output start Proof for 1544249142671114145244583
6. ! [X0] : ((~tall(X0) & rich(X0)) <=> (kind(X0) | ~funny(X0))) [input p5]
8. (creative(mary) & ~calm(mary)) <=> (curious(susan) | brave(susan)) [input p7]
13. (~kind(mary) <~> ~creative(mary)) <=> (~generous(john) & ~creative(john)) [input p12]
14. ! [X0] : (~wise(X0) <=> (wise(X0) <~> generous(X0))) [input p13]
15. ! [X0] : ((happy(X0) & curious(X0)) <=> (~brave(X0) | strong(X0))) [input p14]
23. tall(mary) [input hypothesis]
40. ! [X0] : (((~tall(X0) & rich(X0)) | (~kind(X0) & funny(X0))) & ((kind(X0) | ~funny(X0)) | (tall(X0) | ~rich(X0)))) [nnf transformation 6]
41. ! [X0] : (((~tall(X0) & rich(X0)) | (~kind(X0) & funny(X0))) & (kind(X0) | ~funny(X0) | tall(X0) | ~rich(X0))) [flattening 40]
42. ((creative(mary) & ~calm(mary)) | (~curious(susan) & ~brave(susan))) & ((curious(susan) | brave(susan)) | (~creative(mary) | calm(mary))) [nnf transformation 8]
43. ((creative(mary) & ~calm(mary)) | (~curious(susan) & ~brave(susan))) & (curious(susan) | brave(susan) | ~creative(mary) | calm(mary)) [flattening 42]
48. (((creative(mary) | kind(mary)) & (~creative(mary) | ~kind(mary))) | (generous(john) | creative(john))) & ((~generous(john) & ~creative(john)) | ((~kind(mary) | creative(mary)) & (~creative(mary) | kind(mary)))) [nnf transformation 13]
49. (((creative(mary) | kind(mary)) & (~creative(mary) | ~kind(mary))) | generous(john) | creative(john)) & ((~generous(john) & ~creative(john)) | ((~kind(mary) | creative(mary)) & (~creative(mary) | kind(mary)))) [flattening 48]
50. ! [X0] : ((~wise(X0) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) & (((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | wise(X0))) [nnf transformation 14]
51. ! [X0] : (((happy(X0) & curious(X0)) | (brave(X0) & ~strong(X0))) & ((~brave(X0) | strong(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 15]
52. ! [X0] : (((happy(X0) & curious(X0)) | (brave(X0) & ~strong(X0))) & (~brave(X0) | strong(X0) | ~happy(X0) | ~curious(X0))) [flattening 51]
90. ~tall(X0) | ~kind(X0) [cnf transformation 41]
96. creative(mary) | ~brave(susan) [cnf transformation 43]
97. creative(mary) | ~curious(susan) [cnf transformation 43]
108. ~generous(john) | ~creative(mary) | kind(mary) [cnf transformation 49]
112. generous(X0) | wise(X0) | wise(X0) [cnf transformation 50]
114. ~wise(X0) | generous(X0) | ~wise(X0) [cnf transformation 50]
118. brave(X0) | curious(X0) [cnf transformation 52]
131. tall(mary) [cnf transformation 23]
132. generous(X0) | wise(X0) [duplicate literal removal 112]
133. ~wise(X0) | generous(X0) [duplicate literal removal 114]
174. 8 <=> curious(susan) [avatar definition]
176. ~curious(susan) <- (~8) [avatar component clause 174]
178. 9 <=> creative(mary) [avatar definition]
181. ~8 | 9 [avatar split clause 97,178,174]
183. 10 <=> brave(susan) [avatar definition]
185. ~brave(susan) <- (~10) [avatar component clause 183]
186. ~10 | 9 [avatar split clause 96,178,183]
202. 13 <=> generous(john) [avatar definition]
203. ~generous(john) <- (~13) [avatar component clause 202]
206. 14 <=> kind(mary) [avatar definition]
212. 14 | ~9 | ~13 [avatar split clause 108,202,178,206]
215. generous(X0) [subsumption resolution 132,133]
252. $false <- (~13) [subsumption resolution 203,215]
253. 13 [avatar contradiction clause 252]
264. ~kind(mary) [resolution 90,131]
267. curious(susan) <- (~10) [resolution 118,185]
268. $false <- (~8, ~10) [subsumption resolution 267,176]
269. 8 | 10 [avatar contradiction clause 268]
270. ~14 [avatar split clause 264,206]
271. $false [avatar sat refutation 181,186,212,253,269,270]
% SZS output end Proof for 1544249142671114145244583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then someone is either rich or happy and vice versa.
Everyone who is either not strong or kind is both curious and funny.
If john is not curious or not calm then someone is not old or not creative and vice versa.
If paul is not happy then someone is either generous or not tall.
Everyone who is wise or calm is not calm or old and vice versa.
Everyone who is quiet is either old or not tall.
If someone is either not calm or old then paul is not brave or wise and vice versa.
Everyone who is wise or not strong is either not strong or not wise and vice versa.
If someone is generous then someone is both not calm and not tall.
If paul is either calm or not wise then someone is funny or not curious.
If someone is tall or calm then someone is strong.
If paul is not happy or not creative then someone is either not tall or not rich.
If someone is brave then paul is not brave and vice versa.
Everyone who is not funny or rich is either brave or kind and vice versa.
If alice is not funny or not creative then alice is quiet or humble.
If lucy is either not tall or not generous then susan is brave or funny.
Fred is rich or not generous.
Susan is not funny or humble.
Paul is not happy.
Someone is either generous or curious.
Someone is both creative and not quiet.
Someone is happy or not creative.
Alice is either not strong or strong.
Someone is either not humble or kind. | Paul is not calm. | entailment | ((?[X]:((~rich(X)|~kind(X))))<=>(?[X]:((rich(X)<~>happy(X)))))&
(![X]:((~strong(X)<~>kind(X))=>(curious(X)&funny(X))))&
(((~curious(john)|~calm(john)))<=>(?[X]:((~old(X)|~creative(X)))))&
((~happy(paul))=>(?[X]:((generous(X)<~>~tall(X)))))&
(![X]:((wise(X)|calm(X))<=>(~calm(X)|old(X))))&
(![X]:(quiet(X)=>(old(X)<~>~tall(X))))&
((?[X]:((~calm(X)<~>old(X))))<=>((~brave(paul)|wise(paul))))&
(![X]:((wise(X)|~strong(X))<=>(~strong(X)<~>~wise(X))))&
((?[X]:(generous(X)))=>(?[X]:((~calm(X)&~tall(X)))))&
(((calm(paul)<~>~wise(paul)))=>(?[X]:((funny(X)|~curious(X)))))&
((?[X]:((tall(X)|calm(X))))=>(?[X]:(strong(X))))&
(((~happy(paul)|~creative(paul)))=>(?[X]:((~tall(X)<~>~rich(X)))))&
((?[X]:(brave(X)))<=>(~brave(paul)))&
(![X]:((~funny(X)|rich(X))<=>(brave(X)<~>kind(X))))&
(((~funny(alice)|~creative(alice)))=>((quiet(alice)|humble(alice))))&
(((~tall(lucy)<~>~generous(lucy)))=>((brave(susan)|funny(susan))))&
((rich(fred)|~generous(fred)))&
((~funny(susan)|humble(susan)))&
(~happy(paul))&
(?[X]:((generous(X)<~>curious(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(?[X]:((happy(X)|~creative(X))))&
((~strong(alice)<~>strong(alice)))&
(?[X]:((~humble(X)<~>kind(X)))) | ~calm(paul) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4754313732101950970936017
% SZS output start Proof for 4754313732101950970936017
8. ! [X0] : ((~strong(X0) | wise(X0)) <=> (~strong(X0) <~> ~wise(X0))) [input p7]
11. ? [X0] : (calm(X0) | tall(X0)) => ? [X0] : strong(X0) [input p10]
25. calm(paul) [input hypothesis]
28. ? [X0] : (calm(X0) | tall(X0)) => ? [X1] : strong(X1) [rectify 11]
34. ? [X1] : strong(X1) | ! [X0] : (~calm(X0) & ~tall(X0)) [ennf transformation 28]
62. ! [X0] : (((~strong(X0) | wise(X0)) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) & (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | (strong(X0) & ~wise(X0)))) [nnf transformation 8]
63. ! [X0] : ((~strong(X0) | wise(X0) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) & (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | (strong(X0) & ~wise(X0)))) [flattening 62]
70. ? [X0] : strong(X0) | ! [X1] : (~calm(X1) & ~tall(X1)) [rectify 34]
71. ? [X0] : strong(X0) => strong(sK7) [choice axiom]
72. strong(sK7) | ! [X1] : (~calm(X1) & ~tall(X1)) [skolemisation 70,71]
122. ~wise(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 63]
125. wise(X0) | strong(X0) | strong(X0) [cnf transformation 63]
127. ~strong(X0) | wise(X0) | ~strong(X0) | wise(X0) [cnf transformation 63]
133. strong(sK7) | ~calm(X1) [cnf transformation 72]
162. calm(paul) [cnf transformation 25]
163. ~wise(X0) | ~strong(X0) [duplicate literal removal 122]
164. wise(X0) | strong(X0) [duplicate literal removal 125]
165. ~strong(X0) | wise(X0) [duplicate literal removal 127]
262. 22 <=> ! [X1] : ~calm(X1) [avatar definition]
263. ~calm(X1) <- (22) [avatar component clause 262]
267. wise(X0) [subsumption resolution 164,165]
268. ~strong(X0) [subsumption resolution 163,267]
284. 26 <=> calm(paul) [avatar definition]
285. calm(paul) <- (26) [avatar component clause 284]
296. ~calm(X1) [subsumption resolution 133,268]
297. 22 [avatar split clause 296,262]
396. 26 [avatar split clause 162,284]
397. $false <- (22, 26) [resolution 285,263]
398. ~22 | ~26 [avatar contradiction clause 397]
399. $false [avatar sat refutation 297,396,398]
% SZS output end Proof for 4754313732101950970936017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then someone is either not happy or not rich and vice versa. Everyone who is either quiet or wise is tall. Everyone who is not brave or happy is both wise and not rich and vice versa. Everyone who is either strong or not curious is both not quiet and not tall. Everyone who is either not kind or strong is either humble or not generous. Everyone who is not funny is either not quiet or funny and vice versa. If mary is either strong or generous then susan is brave or not curious. If someone is not funny then someone is either not brave or brave. Everyone who is both not generous and not quiet is wise or generous and vice versa. If alice is humble or tall then john is either not rich or rich. Everyone who is either not kind or not wise is both not kind and kind and vice versa. Everyone who is both not wise and calm is either not curious or not strong. Everyone who is both wise and not curious is both not curious and tall. Everyone who is both kind and not wise is either patient or creative. If someone is not creative then someone is creative or wise and vice versa. Everyone who is either not happy or not wise is both humble and rich. Paul is brave. Someone is funny or not quiet. Someone is not wise or not rich. Mary is not rich or not kind. Someone is old or creative. | Susan is not wise. | contradiction | ((old(mary))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
(![X]:((quiet(X)<~>wise(X))=>tall(X)))&
(![X]:((~brave(X)|happy(X))<=>(wise(X)&~rich(X))))&
(![X]:((strong(X)<~>~curious(X))=>(~quiet(X)&~tall(X))))&
(![X]:((~kind(X)<~>strong(X))=>(humble(X)<~>~generous(X))))&
(![X]:(~funny(X)<=>(~quiet(X)<~>funny(X))))&
(((strong(mary)<~>generous(mary)))=>((brave(susan)|~curious(susan))))&
((?[X]:(~funny(X)))=>(?[X]:((~brave(X)<~>brave(X)))))&
(![X]:((~generous(X)&~quiet(X))<=>(wise(X)|generous(X))))&
(((humble(alice)|tall(alice)))=>((~rich(john)<~>rich(john))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~kind(X)&kind(X))))&
(![X]:((~wise(X)&calm(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((wise(X)&~curious(X))=>(~curious(X)&tall(X))))&
(![X]:((kind(X)&~wise(X))=>(patient(X)<~>creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((~happy(X)<~>~wise(X))=>(humble(X)&rich(X))))&
(brave(paul))&
(?[X]:((funny(X)|~quiet(X))))&
(?[X]:((~wise(X)|~rich(X))))&
((~rich(mary)|~kind(mary)))&
(?[X]:((old(X)|creative(X)))) | ~wise(susan) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2795497061434405587217876
% SZS output start Proof for 2795497061434405587217876
6. ! [X0] : (~funny(X0) <=> (~quiet(X0) <~> funny(X0))) [input p5]
9. ! [X0] : ((~quiet(X0) & ~generous(X0)) <=> (generous(X0) | wise(X0))) [input p8]
22. ~wise(susan) [input hypothesis]
47. ! [X0] : ((~funny(X0) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0)))) & (((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | funny(X0))) [nnf transformation 6]
53. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (~generous(X0) & ~wise(X0))) & ((generous(X0) | wise(X0)) | (quiet(X0) | generous(X0)))) [nnf transformation 9]
54. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (~generous(X0) & ~wise(X0))) & (generous(X0) | wise(X0) | quiet(X0) | generous(X0))) [flattening 53]
90. funny(X0) | ~quiet(X0) | funny(X0) [cnf transformation 47]
93. ~funny(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 47]
98. generous(X0) | wise(X0) | quiet(X0) | generous(X0) [cnf transformation 54]
100. ~generous(X0) | ~generous(X0) [cnf transformation 54]
129. ~wise(susan) [cnf transformation 22]
134. generous(X0) | wise(X0) | quiet(X0) [duplicate literal removal 98]
135. ~generous(X0) [duplicate literal removal 100]
136. funny(X0) | ~quiet(X0) [duplicate literal removal 90]
137. ~funny(X0) | ~quiet(X0) [duplicate literal removal 93]
160. ~quiet(X0) [subsumption resolution 136,137]
179. wise(X0) | quiet(X0) [subsumption resolution 134,135]
180. wise(X0) [subsumption resolution 179,160]
197. $false [subsumption resolution 129,180]
% SZS output end Proof for 2795497061434405587217876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not brave is both not strong and strong and vice versa. Everyone who is creative is not strong and vice versa. If someone is either humble or not calm then lucy is both not creative and not rich. If someone is not old or not happy then susan is not calm or happy. Everyone who is brave is not creative. Everyone who is either not brave or not tall is humble. Everyone who is quiet is not happy or not creative and vice versa. Everyone who is both happy and brave is not tall or quiet and vice versa. Everyone who is brave is calm or humble. Everyone who is either funny or not calm is humble or curious. Everyone who is not calm or not tall is rich and vice versa. If someone is not wise or happy then alice is both brave and wise and vice versa. If someone is either wise or patient then someone is not patient or not kind. If someone is generous or not generous then john is quiet. If john is not strong then someone is either quiet or humble and vice versa. Paul is either humble or generous. John is either curious or rich. Someone is not humble or tall. Someone is funny. Someone is strong. Susan is both humble and calm. Someone is not old or not curious. | Lucy is strong. | entailment | (![X]:((~calm(X)|~brave(X))<=>(~strong(X)&strong(X))))&
(![X]:(creative(X)<=>~strong(X)))&
((?[X]:((humble(X)<~>~calm(X))))=>((~creative(lucy)&~rich(lucy))))&
((?[X]:((~old(X)|~happy(X))))=>((~calm(susan)|happy(susan))))&
(![X]:(brave(X)=>~creative(X)))&
(![X]:((~brave(X)<~>~tall(X))=>humble(X)))&
(![X]:(quiet(X)<=>(~happy(X)|~creative(X))))&
(![X]:((happy(X)&brave(X))<=>(~tall(X)|quiet(X))))&
(![X]:(brave(X)=>(calm(X)|humble(X))))&
(![X]:((funny(X)<~>~calm(X))=>(humble(X)|curious(X))))&
(![X]:((~calm(X)|~tall(X))<=>rich(X)))&
((?[X]:((~wise(X)|happy(X))))<=>((brave(alice)&wise(alice))))&
((?[X]:((wise(X)<~>patient(X))))=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((generous(X)|~generous(X))))=>(quiet(john)))&
((~strong(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
((humble(paul)<~>generous(paul)))&
((curious(john)<~>rich(john)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:(funny(X)))&
(?[X]:(strong(X)))&
((humble(susan)&calm(susan)))&
(?[X]:((~old(X)|~curious(X)))) | strong(lucy) | [
"p0",
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5142990946694174761265229
% SZS output start Proof for 5142990946694174761265229
1. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (strong(X0) & ~strong(X0))) [input p0]
2. ! [X0] : (creative(X0) <=> ~strong(X0)) [input p1]
5. ! [X0] : (brave(X0) => ~creative(X0)) [input p4]
23. ~strong(lucy) [input hypothesis]
29. ! [X0] : (~creative(X0) | ~brave(X0)) [ennf transformation 5]
36. ! [X0] : (((~brave(X0) | ~calm(X0)) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 1]
37. ! [X0] : ((~brave(X0) | ~calm(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | (brave(X0) & calm(X0)))) [flattening 36]
38. ! [X0] : ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0))) [nnf transformation 2]
68. ~strong(X0) | brave(X0) [cnf transformation 37]
70. strong(X0) | brave(X0) [cnf transformation 37]
73. creative(X0) | strong(X0) [cnf transformation 38]
80. ~creative(X0) | ~brave(X0) [cnf transformation 29]
118. ~strong(lucy) [cnf transformation 23]
119. brave(X0) [subsumption resolution 68,70]
150. ~creative(X0) [subsumption resolution 80,119]
229. strong(X1) [resolution 73,150]
230. $false [resolution 229,118]
% SZS output end Proof for 5142990946694174761265229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not kind then someone is both generous and tall and vice versa. If john is brave or strong then someone is not quiet. Everyone who is either not quiet or not strong is either happy or not kind and vice versa. If someone is not generous then fred is rich. If someone is both not patient and tall then mary is both not humble and not generous. Everyone who is not calm or rich is both funny and not quiet and vice versa. Everyone who is funny is not quiet and vice versa. If someone is both strong and quiet then someone is not old and vice versa. Everyone who is both not creative and creative is tall and vice versa. If alice is creative or not tall then someone is both old and not humble and vice versa. Everyone who is not strong is both not tall and not humble and vice versa. Everyone who is either not quiet or not happy is rich or happy. Everyone who is not calm or not old is both wise and tall. If someone is both strong and not patient then john is either not quiet or not creative and vice versa. If fred is either funny or not creative then someone is both not calm and funny. If alice is kind or funny then fred is either not curious or not tall. Someone is either not generous or humble. John is either not tall or not brave. Fred is not funny or not brave. Fred is brave. Susan is both humble and generous. Someone is either humble or not wise. | John is happy. | neutral | ((?[X]:((wise(X)|~kind(X))))<=>(?[X]:((generous(X)&tall(X)))))&
(((brave(john)|strong(john)))=>(?[X]:(~quiet(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>(happy(X)<~>~kind(X))))&
((?[X]:(~generous(X)))=>(rich(fred)))&
((?[X]:((~patient(X)&tall(X))))=>((~humble(mary)&~generous(mary))))&
(![X]:((~calm(X)|rich(X))<=>(funny(X)&~quiet(X))))&
(![X]:(funny(X)<=>~quiet(X)))&
((?[X]:((strong(X)&quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)&creative(X))<=>tall(X)))&
(((creative(alice)|~tall(alice)))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:(~strong(X)<=>(~tall(X)&~humble(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>(rich(X)|happy(X))))&
(![X]:((~calm(X)|~old(X))=>(wise(X)&tall(X))))&
((?[X]:((strong(X)&~patient(X))))<=>((~quiet(john)<~>~creative(john))))&
(((funny(fred)<~>~creative(fred)))=>(?[X]:((~calm(X)&funny(X)))))&
(((kind(alice)|funny(alice)))=>((~curious(fred)<~>~tall(fred))))&
(?[X]:((~generous(X)<~>humble(X))))&
((~tall(john)<~>~brave(john)))&
((~funny(fred)|~brave(fred)))&
(brave(fred))&
((humble(susan)&generous(susan)))&
(?[X]:((humble(X)<~>~wise(X)))) | happy(john) | [] | null | 0 |
Everyone who is not wise or patient is both not rich and not humble and vice versa.
If someone is not happy or not humble then someone is either not brave or not humble.
If someone is not strong or calm then someone is either calm or not humble.
If someone is either not creative or not kind then lucy is strong and vice versa.
If fred is either not patient or not humble then alice is either not quiet or tall and vice versa.
If mary is happy then someone is not brave or patient and vice versa.
Everyone who is wise or not curious is both funny and generous.
Everyone who is both not wise and not tall is either not brave or rich.
If someone is either strong or not strong then lucy is either calm or not wise.
Everyone who is both not happy and not quiet is generous or brave.
Everyone who is either not curious or tall is either quiet or happy.
Everyone who is either happy or not patient is not curious or not creative and vice versa.
If lucy is both creative and not creative then someone is not curious or rich and vice versa.
Everyone who is not tall or not generous is not tall or patient.
If someone is either not creative or not old then someone is funny or old and vice versa.
If mary is either not creative or tall then john is funny or not patient.
Someone is either not happy or kind.
Fred is either rich or wise.
Someone is not generous or happy.
Lucy is either humble or generous.
Someone is either not old or kind.
Someone is either not wise or funny.
Paul is not brave.
Mary is either not patient or not happy. | Mary is happy. | entailment | (![X]:((~wise(X)|patient(X))<=>(~rich(X)&~humble(X))))&
((?[X]:((~happy(X)|~humble(X))))=>(?[X]:((~brave(X)<~>~humble(X)))))&
((?[X]:((~strong(X)|calm(X))))=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:((~creative(X)<~>~kind(X))))<=>(strong(lucy)))&
(((~patient(fred)<~>~humble(fred)))<=>((~quiet(alice)<~>tall(alice))))&
((happy(mary))<=>(?[X]:((~brave(X)|patient(X)))))&
(![X]:((wise(X)|~curious(X))=>(funny(X)&generous(X))))&
(![X]:((~wise(X)&~tall(X))=>(~brave(X)<~>rich(X))))&
((?[X]:((strong(X)<~>~strong(X))))=>((calm(lucy)<~>~wise(lucy))))&
(![X]:((~happy(X)&~quiet(X))=>(generous(X)|brave(X))))&
(![X]:((~curious(X)<~>tall(X))=>(quiet(X)<~>happy(X))))&
(![X]:((happy(X)<~>~patient(X))<=>(~curious(X)|~creative(X))))&
(((creative(lucy)&~creative(lucy)))<=>(?[X]:((~curious(X)|rich(X)))))&
(![X]:((~tall(X)|~generous(X))=>(~tall(X)|patient(X))))&
((?[X]:((~creative(X)<~>~old(X))))<=>(?[X]:((funny(X)|old(X)))))&
(((~creative(mary)<~>tall(mary)))=>((funny(john)|~patient(john))))&
(?[X]:((~happy(X)<~>kind(X))))&
((rich(fred)<~>wise(fred)))&
(?[X]:((~generous(X)|happy(X))))&
((humble(lucy)<~>generous(lucy)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:((~wise(X)<~>funny(X))))&
(~brave(paul))&
((~patient(mary)<~>~happy(mary))) | happy(mary) | [
"p5",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1435015007400512015139606
% SZS output start Proof for 1435015007400512015139606
6. happy(mary) <=> ? [X0] : (patient(X0) | ~brave(X0)) [input p5]
23. ~brave(paul) [input p22]
25. ~happy(mary) [input hypothesis]
57. (happy(mary) | ! [X0] : (~patient(X0) & brave(X0))) & (? [X0] : (patient(X0) | ~brave(X0)) | ~happy(mary)) [nnf transformation 6]
58. (happy(mary) | ! [X0] : (~patient(X0) & brave(X0))) & (? [X1] : (patient(X1) | ~brave(X1)) | ~happy(mary)) [rectify 57]
59. ? [X1] : (patient(X1) | ~brave(X1)) => (patient(sK3) | ~brave(sK3)) [choice axiom]
60. (happy(mary) | ! [X0] : (~patient(X0) & brave(X0))) & ((patient(sK3) | ~brave(sK3)) | ~happy(mary)) [skolemisation 58,59]
117. happy(mary) | brave(X0) [cnf transformation 60]
166. ~brave(paul) [cnf transformation 23]
169. ~happy(mary) [cnf transformation 25]
262. 19 <=> happy(mary) [avatar definition]
267. 20 <=> ! [X0] : brave(X0) [avatar definition]
268. brave(X0) <- (20) [avatar component clause 267]
269. 20 | 19 [avatar split clause 117,262,267]
417. ~19 [avatar split clause 169,262]
418. $false <- (20) [resolution 268,166]
419. ~20 [avatar contradiction clause 418]
420. $false [avatar sat refutation 269,417,419]
% SZS output end Proof for 1435015007400512015139606
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is both not wise and not funny.
Everyone who is both not creative and wise is not brave.
Everyone who is not rich is either not tall or not calm and vice versa.
Everyone who is either happy or not tall is either curious or happy and vice versa.
Everyone who is both not humble and not wise is either not funny or not wise and vice versa.
Everyone who is not humble is both not patient and kind and vice versa.
Everyone who is both not curious and calm is not tall or quiet and vice versa.
If alice is either wise or not quiet then paul is both strong and funny and vice versa.
Everyone who is both not quiet and not creative is either not funny or not strong and vice versa.
If fred is strong or wise then someone is either not humble or kind and vice versa.
Everyone who is not wise or happy is both not generous and not wise.
Everyone who is not tall or not quiet is strong and vice versa.
Everyone who is brave or creative is both not strong and not generous and vice versa.
If fred is both curious and not humble then lucy is not funny or not curious.
If fred is patient then someone is either patient or not rich.
If someone is humble or not brave then someone is not old and vice versa.
Someone is either not patient or patient.
Paul is either strong or not curious.
Someone is not quiet or creative.
Someone is rich or not kind.
Someone is happy or not tall.
Someone is either kind or rich.
Someone is not happy or old. | Alice is not rich. | contradiction | (![X]:(~tall(X)=>(~wise(X)&~funny(X))))&
(![X]:((~creative(X)&wise(X))=>~brave(X)))&
(![X]:(~rich(X)<=>(~tall(X)<~>~calm(X))))&
(![X]:((happy(X)<~>~tall(X))<=>(curious(X)<~>happy(X))))&
(![X]:((~humble(X)&~wise(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:(~humble(X)<=>(~patient(X)&kind(X))))&
(![X]:((~curious(X)&calm(X))<=>(~tall(X)|quiet(X))))&
(((wise(alice)<~>~quiet(alice)))<=>((strong(paul)&funny(paul))))&
(![X]:((~quiet(X)&~creative(X))<=>(~funny(X)<~>~strong(X))))&
(((strong(fred)|wise(fred)))<=>(?[X]:((~humble(X)<~>kind(X)))))&
(![X]:((~wise(X)|happy(X))=>(~generous(X)&~wise(X))))&
(![X]:((~tall(X)|~quiet(X))<=>strong(X)))&
(![X]:((brave(X)|creative(X))<=>(~strong(X)&~generous(X))))&
(((curious(fred)&~humble(fred)))=>((~funny(lucy)|~curious(lucy))))&
((patient(fred))=>(?[X]:((patient(X)<~>~rich(X)))))&
((?[X]:((humble(X)|~brave(X))))<=>(?[X]:(~old(X))))&
(?[X]:((~patient(X)<~>patient(X))))&
((strong(paul)<~>~curious(paul)))&
(?[X]:((~quiet(X)|creative(X))))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((happy(X)|~tall(X))))&
(?[X]:((kind(X)<~>rich(X))))&
(?[X]:((~happy(X)|old(X)))) | ~rich(alice) | [
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8927520762774715831711162
% SZS output start Proof for 8927520762774715831711162
3. ! [X0] : (~rich(X0) <=> (~tall(X0) <~> ~calm(X0))) [input p2]
4. ! [X0] : ((happy(X0) <~> ~tall(X0)) <=> (curious(X0) <~> happy(X0))) [input p3]
5. ! [X0] : ((~wise(X0) & ~humble(X0)) <=> (~funny(X0) <~> ~wise(X0))) [input p4]
7. ! [X0] : ((calm(X0) & ~curious(X0)) <=> (quiet(X0) | ~tall(X0))) [input p6]
8. (wise(alice) <~> ~quiet(alice)) <=> (funny(paul) & strong(paul)) [input p7]
9. ! [X0] : ((~creative(X0) & ~quiet(X0)) <=> (~funny(X0) <~> ~strong(X0))) [input p8]
12. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> strong(X0)) [input p11]
13. ! [X0] : ((creative(X0) | brave(X0)) <=> (~generous(X0) & ~strong(X0))) [input p12]
18. strong(paul) <~> ~curious(paul) [input p17]
24. ~rich(alice) [input hypothesis]
33. ! [X0] : ((~rich(X0) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0)))) & (((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | rich(X0))) [nnf transformation 3]
34. ! [X0] : ((((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0)))) & (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0))))) [nnf transformation 4]
35. ! [X0] : (((~wise(X0) & ~humble(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | (wise(X0) | humble(X0)))) [nnf transformation 5]
36. ! [X0] : (((~wise(X0) & ~humble(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | wise(X0) | humble(X0))) [flattening 35]
39. ! [X0] : (((calm(X0) & ~curious(X0)) | (~quiet(X0) & tall(X0))) & ((quiet(X0) | ~tall(X0)) | (~calm(X0) | curious(X0)))) [nnf transformation 7]
40. ! [X0] : (((calm(X0) & ~curious(X0)) | (~quiet(X0) & tall(X0))) & (quiet(X0) | ~tall(X0) | ~calm(X0) | curious(X0))) [flattening 39]
41. (((quiet(alice) | ~wise(alice)) & (~quiet(alice) | wise(alice))) | (~funny(paul) | ~strong(paul))) & ((funny(paul) & strong(paul)) | ((wise(alice) | quiet(alice)) & (~quiet(alice) | ~wise(alice)))) [nnf transformation 8]
42. (((quiet(alice) | ~wise(alice)) & (~quiet(alice) | wise(alice))) | ~funny(paul) | ~strong(paul)) & ((funny(paul) & strong(paul)) | ((wise(alice) | quiet(alice)) & (~quiet(alice) | ~wise(alice)))) [flattening 41]
43. ! [X0] : (((~creative(X0) & ~quiet(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (creative(X0) | quiet(X0)))) [nnf transformation 9]
44. ! [X0] : (((~creative(X0) & ~quiet(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | creative(X0) | quiet(X0))) [flattening 43]
50. ! [X0] : (((~quiet(X0) | ~tall(X0)) | ~strong(X0)) & (strong(X0) | (quiet(X0) & tall(X0)))) [nnf transformation 12]
51. ! [X0] : ((~quiet(X0) | ~tall(X0) | ~strong(X0)) & (strong(X0) | (quiet(X0) & tall(X0)))) [flattening 50]
52. ! [X0] : (((creative(X0) | brave(X0)) | (generous(X0) | strong(X0))) & ((~generous(X0) & ~strong(X0)) | (~creative(X0) & ~brave(X0)))) [nnf transformation 13]
53. ! [X0] : ((creative(X0) | brave(X0) | generous(X0) | strong(X0)) & ((~generous(X0) & ~strong(X0)) | (~creative(X0) & ~brave(X0)))) [flattening 52]
65. (curious(paul) | ~strong(paul)) & (~curious(paul) | strong(paul)) [nnf transformation 18]
80. ~calm(X0) | ~tall(X0) | rich(X0) [cnf transformation 33]
85. happy(X0) | curious(X0) | happy(X0) | tall(X0) [cnf transformation 34]
86. ~happy(X0) | ~curious(X0) | ~tall(X0) | ~happy(X0) [cnf transformation 34]
88. ~tall(X0) | happy(X0) | happy(X0) | ~curious(X0) [cnf transformation 34]
91. tall(X0) | ~happy(X0) | curious(X0) | ~happy(X0) [cnf transformation 34]
96. ~wise(X0) | ~wise(X0) | funny(X0) [cnf transformation 36]
102. ~curious(X0) | tall(X0) [cnf transformation 40]
105. ~quiet(X0) | calm(X0) [cnf transformation 40]
107. strong(paul) | wise(alice) | quiet(alice) [cnf transformation 42]
112. ~strong(X0) | ~funny(X0) | creative(X0) | quiet(X0) [cnf transformation 44]
129. strong(X0) | quiet(X0) [cnf transformation 51]
132. ~strong(X0) | ~creative(X0) [cnf transformation 53]
145. curious(paul) | ~strong(paul) [cnf transformation 65]
152. ~rich(alice) [cnf transformation 24]
154. ~wise(X0) | funny(X0) [duplicate literal removal 96]
155. happy(X0) | curious(X0) | tall(X0) [duplicate literal removal 85]
156. ~happy(X0) | ~curious(X0) | ~tall(X0) [duplicate literal removal 86]
157. ~curious(X0) | happy(X0) | ~tall(X0) [duplicate literal removal 88]
158. ~happy(X0) | tall(X0) | curious(X0) [duplicate literal removal 91]
159. ~curious(X0) | ~tall(X0) [subsumption resolution 156,157]
160. curious(X0) | tall(X0) [subsumption resolution 155,158]
162. ~curious(X0) [subsumption resolution 102,159]
165. 1 <=> strong(paul) [avatar definition]
173. 3 <=> wise(alice) [avatar definition]
174. wise(alice) <- (3) [avatar component clause 173]
177. 4 <=> quiet(alice) [avatar definition]
178. ~quiet(alice) <- (~4) [avatar component clause 177]
179. quiet(alice) <- (4) [avatar component clause 177]
184. 4 | 3 | 1 [avatar split clause 107,165,173,177]
252. ~strong(paul) [subsumption resolution 145,162]
253. ~1 [avatar split clause 252,165]
308. ~creative(X0) | quiet(X0) [resolution 132,129]
314. funny(alice) <- (3) [resolution 154,174]
317. tall(X1) [resolution 160,162]
370. ~funny(X0) | creative(X0) | quiet(X0) | quiet(X0) [resolution 112,129]
372. ~funny(X0) | creative(X0) | quiet(X0) [duplicate literal removal 370]
373. ~funny(X0) | quiet(X0) [subsumption resolution 372,308]
374. quiet(alice) <- (3) [resolution 373,314]
376. $false <- (3, ~4) [subsumption resolution 374,178]
377. ~3 | 4 [avatar contradiction clause 376]
379. calm(alice) <- (4) [resolution 179,105]
403. ~tall(alice) | rich(alice) <- (4) [resolution 379,80]
404. rich(alice) <- (4) [subsumption resolution 403,317]
405. $false <- (4) [subsumption resolution 404,152]
406. ~4 [avatar contradiction clause 405]
407. $false [avatar sat refutation 184,253,377,406]
% SZS output end Proof for 8927520762774715831711162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then someone is strong or quiet and vice versa. Everyone who is not rich or not strong is happy. If paul is patient then john is kind and vice versa. Everyone who is either not humble or rich is not old or not humble and vice versa. If someone is either kind or not kind then alice is curious or not happy and vice versa. Everyone who is either not humble or brave is either rich or strong. If alice is rich then someone is curious. If someone is either funny or not rich then paul is either humble or brave. If someone is either old or not brave then someone is both not patient and not wise and vice versa. If paul is either not patient or not strong then someone is kind and vice versa. Everyone who is either happy or quiet is calm and vice versa. If someone is either strong or generous then someone is both not strong and not curious. Everyone who is not calm is either not creative or rich and vice versa. If someone is not old or not rich then someone is both not tall and not patient. Everyone who is not humble is either not strong or not old. If someone is not tall then lucy is both old and creative and vice versa. Someone is both kind and not rich. Paul is not happy or rich. Someone is funny. Someone is either not old or not rich. Someone is both quiet and brave. Someone is old. Someone is both not funny and strong. Susan is not happy or happy. | Paul is not rich. | contradiction | ((?[X]:(~old(X)))<=>(?[X]:((strong(X)|quiet(X)))))&
(![X]:((~rich(X)|~strong(X))=>happy(X)))&
((patient(paul))<=>(kind(john)))&
(![X]:((~humble(X)<~>rich(X))<=>(~old(X)|~humble(X))))&
((?[X]:((kind(X)<~>~kind(X))))<=>((curious(alice)|~happy(alice))))&
(![X]:((~humble(X)<~>brave(X))=>(rich(X)<~>strong(X))))&
((rich(alice))=>(?[X]:(curious(X))))&
((?[X]:((funny(X)<~>~rich(X))))=>((humble(paul)<~>brave(paul))))&
((?[X]:((old(X)<~>~brave(X))))<=>(?[X]:((~patient(X)&~wise(X)))))&
(((~patient(paul)<~>~strong(paul)))<=>(?[X]:(kind(X))))&
(![X]:((happy(X)<~>quiet(X))<=>calm(X)))&
((?[X]:((strong(X)<~>generous(X))))=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:(~calm(X)<=>(~creative(X)<~>rich(X))))&
((?[X]:((~old(X)|~rich(X))))=>(?[X]:((~tall(X)&~patient(X)))))&
(![X]:(~humble(X)=>(~strong(X)<~>~old(X))))&
((?[X]:(~tall(X)))<=>((old(lucy)&creative(lucy))))&
(?[X]:((kind(X)&~rich(X))))&
((~happy(paul)|rich(paul)))&
(?[X]:(funny(X)))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:((quiet(X)&brave(X))))&
(?[X]:(old(X)))&
(?[X]:((~funny(X)&strong(X))))&
((~happy(susan)|happy(susan))) | ~rich(paul) | [
"p1",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 399749144424891802355116
% SZS output start Proof for 399749144424891802355116
2. ! [X0] : ((~strong(X0) | ~rich(X0)) => happy(X0)) [input p1]
18. rich(paul) | ~happy(paul) [input p17]
25. ~rich(paul) [input hypothesis]
30. ! [X0] : (happy(X0) | (strong(X0) & rich(X0))) [ennf transformation 2]
94. happy(X0) | rich(X0) [cnf transformation 30]
152. rich(paul) | ~happy(paul) [cnf transformation 18]
162. ~rich(paul) [cnf transformation 25]
341. rich(paul) [subsumption resolution 152,94]
351. $false [subsumption resolution 162,341]
% SZS output end Proof for 399749144424891802355116
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is wise or not strong then mary is both not calm and quiet and vice versa.
Everyone who is both funny and quiet is not kind or creative.
Everyone who is either patient or not tall is not humble or not wise.
If alice is not rich then someone is not rich or generous and vice versa.
Everyone who is strong is calm or not creative.
If lucy is both not brave and funny then someone is not kind.
If someone is either not kind or wise then john is either not tall or strong and vice versa.
If someone is not quiet or not calm then fred is not funny.
If alice is both wise and not curious then someone is both not old and happy.
Everyone who is old is generous.
Everyone who is both not generous and not strong is both not kind and happy.
If someone is kind or not calm then alice is not brave and vice versa.
If paul is calm then someone is both old and not humble.
If alice is quiet or calm then susan is not kind or curious and vice versa.
If someone is both humble and not wise then someone is both not rich and wise.
Everyone who is both not strong and happy is either kind or not kind and vice versa.
Someone is happy or not calm.
Fred is either not generous or not patient.
Alice is calm.
Someone is wise or not calm.
Someone is brave or creative.
Someone is both not patient and brave.
Someone is not quiet. | Mary is not quiet. | contradiction | (((wise(susan)|~strong(susan)))<=>((~calm(mary)&quiet(mary))))&
(![X]:((funny(X)&quiet(X))=>(~kind(X)|creative(X))))&
(![X]:((patient(X)<~>~tall(X))=>(~humble(X)|~wise(X))))&
((~rich(alice))<=>(?[X]:((~rich(X)|generous(X)))))&
(![X]:(strong(X)=>(calm(X)|~creative(X))))&
(((~brave(lucy)&funny(lucy)))=>(?[X]:(~kind(X))))&
((?[X]:((~kind(X)<~>wise(X))))<=>((~tall(john)<~>strong(john))))&
((?[X]:((~quiet(X)|~calm(X))))=>(~funny(fred)))&
(((wise(alice)&~curious(alice)))=>(?[X]:((~old(X)&happy(X)))))&
(![X]:(old(X)=>generous(X)))&
(![X]:((~generous(X)&~strong(X))=>(~kind(X)&happy(X))))&
((?[X]:((kind(X)|~calm(X))))<=>(~brave(alice)))&
((calm(paul))=>(?[X]:((old(X)&~humble(X)))))&
(((quiet(alice)|calm(alice)))<=>((~kind(susan)|curious(susan))))&
((?[X]:((humble(X)&~wise(X))))=>(?[X]:((~rich(X)&wise(X)))))&
(![X]:((~strong(X)&happy(X))<=>(kind(X)<~>~kind(X))))&
(?[X]:((happy(X)|~calm(X))))&
((~generous(fred)<~>~patient(fred)))&
(calm(alice))&
(?[X]:((wise(X)|~calm(X))))&
(?[X]:((brave(X)|creative(X))))&
(?[X]:((~patient(X)&brave(X))))&
(?[X]:(~quiet(X))) | ~quiet(mary) | [
"p0",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3260700026652208683152664
% SZS output start Proof for 3260700026652208683152664
1. (~strong(susan) | wise(susan)) <=> (quiet(mary) & ~calm(mary)) [input p0]
16. ! [X0] : ((happy(X0) & ~strong(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p15]
24. ~quiet(mary) [input hypothesis]
40. ((~strong(susan) | wise(susan)) | (~quiet(mary) | calm(mary))) & ((quiet(mary) & ~calm(mary)) | (strong(susan) & ~wise(susan))) [nnf transformation 1]
41. (~strong(susan) | wise(susan) | ~quiet(mary) | calm(mary)) & ((quiet(mary) & ~calm(mary)) | (strong(susan) & ~wise(susan))) [flattening 40]
60. ! [X0] : (((happy(X0) & ~strong(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | (~happy(X0) | strong(X0)))) [nnf transformation 16]
61. ! [X0] : (((happy(X0) & ~strong(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~happy(X0) | strong(X0))) [flattening 60]
76. quiet(mary) | strong(susan) [cnf transformation 41]
105. ~strong(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 61]
106. ~strong(X0) | kind(X0) | kind(X0) [cnf transformation 61]
118. ~quiet(mary) [cnf transformation 24]
119. ~strong(X0) | ~kind(X0) [duplicate literal removal 105]
120. ~strong(X0) | kind(X0) [duplicate literal removal 106]
128. 2 <=> quiet(mary) [avatar definition]
136. 4 <=> strong(susan) [avatar definition]
137. strong(susan) <- (4) [avatar component clause 136]
140. 4 | 2 [avatar split clause 76,128,136]
264. ~strong(X0) [subsumption resolution 119,120]
294. ~2 [avatar split clause 118,128]
295. $false <- (4) [subsumption resolution 137,264]
296. ~4 [avatar contradiction clause 295]
297. $false [avatar sat refutation 140,294,296]
% SZS output end Proof for 3260700026652208683152664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is happy then john is either not calm or kind and vice versa.
If alice is not funny or happy then john is wise.
If susan is both funny and quiet then someone is either brave or not tall and vice versa.
Everyone who is not calm is either not wise or not brave and vice versa.
If lucy is either humble or happy then susan is not rich or creative.
If susan is not calm or not generous then someone is both generous and quiet and vice versa.
Everyone who is not rich is not generous or creative and vice versa.
If susan is humble or creative then someone is creative and vice versa.
Everyone who is both brave and generous is not calm and vice versa.
Everyone who is not patient is both funny and strong.
If fred is generous then john is funny and vice versa.
Everyone who is not strong is creative or not generous and vice versa.
If someone is either kind or not old then mary is both tall and not calm.
Everyone who is both strong and not old is not happy or not generous and vice versa.
Everyone who is calm is not quiet.
Someone is quiet.
Someone is not funny.
Alice is both kind and not quiet.
John is either calm or patient.
Someone is either wise or not humble.
Someone is old.
Fred is not curious. | Susan is not generous. | contradiction | ((?[X]:(happy(X)))<=>((~calm(john)<~>kind(john))))&
(((~funny(alice)|happy(alice)))=>(wise(john)))&
(((funny(susan)&quiet(susan)))<=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:(~calm(X)<=>(~wise(X)<~>~brave(X))))&
(((humble(lucy)<~>happy(lucy)))=>((~rich(susan)|creative(susan))))&
(((~calm(susan)|~generous(susan)))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:(~rich(X)<=>(~generous(X)|creative(X))))&
(((humble(susan)|creative(susan)))<=>(?[X]:(creative(X))))&
(![X]:((brave(X)&generous(X))<=>~calm(X)))&
(![X]:(~patient(X)=>(funny(X)&strong(X))))&
((generous(fred))<=>(funny(john)))&
(![X]:(~strong(X)<=>(creative(X)|~generous(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~generous(X))))&
(![X]:(calm(X)=>~quiet(X)))&
(?[X]:(quiet(X)))&
(?[X]:(~funny(X)))&
((kind(alice)&~quiet(alice)))&
((calm(john)<~>patient(john)))&
(?[X]:((wise(X)<~>~humble(X))))&
(?[X]:(old(X)))&
(~curious(fred)) | ~generous(susan) | [
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 735186395638465964534689
% SZS output start Proof for 735186395638465964534689
12. ! [X0] : (~strong(X0) <=> (~generous(X0) | creative(X0))) [input p11]
14. ! [X0] : ((~old(X0) & strong(X0)) <=> (~generous(X0) | ~happy(X0))) [input p13]
23. ~generous(susan) [input hypothesis]
58. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | strong(X0))) [nnf transformation 12]
59. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | strong(X0))) [flattening 58]
61. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (old(X0) | ~strong(X0)))) [nnf transformation 14]
62. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0))) [flattening 61]
109. ~strong(X0) | generous(X0) [cnf transformation 59]
116. strong(X0) | generous(X0) [cnf transformation 62]
129. ~generous(susan) [cnf transformation 23]
275. generous(X0) [subsumption resolution 116,109]
293. $false [subsumption resolution 129,275]
% SZS output end Proof for 735186395638465964534689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or rich is both patient and not patient and vice versa.
If someone is generous or not strong then fred is both not rich and not happy.
Everyone who is either not generous or calm is either strong or quiet and vice versa.
Everyone who is happy is both quiet and not funny and vice versa.
If someone is creative then someone is both rich and creative and vice versa.
Everyone who is not kind or not curious is not quiet and vice versa.
Everyone who is not quiet or not generous is not brave or not patient and vice versa.
If someone is either old or kind then someone is not happy or not calm.
If lucy is not old then someone is both not old and patient and vice versa.
If john is either not brave or creative then someone is generous.
If susan is either kind or tall then paul is both wise and quiet and vice versa.
Everyone who is not happy is strong and vice versa.
If john is not generous then fred is either not curious or not patient.
Everyone who is either not kind or not rich is either happy or wise.
Everyone who is either curious or patient is not tall and vice versa.
Everyone who is either not funny or kind is rich or not old and vice versa.
Someone is either old or not humble.
John is curious.
Lucy is both quiet and tall.
Paul is happy.
Someone is creative or old.
Lucy is not old or not tall.
Alice is either happy or quiet. | Alice is old. | contradiction | (![X]:((calm(X)|rich(X))<=>(patient(X)&~patient(X))))&
((?[X]:((generous(X)|~strong(X))))=>((~rich(fred)&~happy(fred))))&
(![X]:((~generous(X)<~>calm(X))<=>(strong(X)<~>quiet(X))))&
(![X]:(happy(X)<=>(quiet(X)&~funny(X))))&
((?[X]:(creative(X)))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:((~kind(X)|~curious(X))<=>~quiet(X)))&
(![X]:((~quiet(X)|~generous(X))<=>(~brave(X)|~patient(X))))&
((?[X]:((old(X)<~>kind(X))))=>(?[X]:((~happy(X)|~calm(X)))))&
((~old(lucy))<=>(?[X]:((~old(X)&patient(X)))))&
(((~brave(john)<~>creative(john)))=>(?[X]:(generous(X))))&
(((kind(susan)<~>tall(susan)))<=>((wise(paul)&quiet(paul))))&
(![X]:(~happy(X)<=>strong(X)))&
((~generous(john))=>((~curious(fred)<~>~patient(fred))))&
(![X]:((~kind(X)<~>~rich(X))=>(happy(X)<~>wise(X))))&
(![X]:((curious(X)<~>patient(X))<=>~tall(X)))&
(![X]:((~funny(X)<~>kind(X))<=>(rich(X)|~old(X))))&
(?[X]:((old(X)<~>~humble(X))))&
(curious(john))&
((quiet(lucy)&tall(lucy)))&
(happy(paul))&
(?[X]:((creative(X)|old(X))))&
((~old(lucy)|~tall(lucy)))&
((happy(alice)<~>quiet(alice))) | old(alice) | [
"p0",
"p3",
"p5",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3540043851983354005694474
% SZS output start Proof for 3540043851983354005694474
1. ! [X0] : ((rich(X0) | calm(X0)) <=> (~patient(X0) & patient(X0))) [input p0]
4. ! [X0] : (happy(X0) <=> (~funny(X0) & quiet(X0))) [input p3]
6. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> ~quiet(X0)) [input p5]
16. ! [X0] : ((~funny(X0) <~> kind(X0)) <=> (~old(X0) | rich(X0))) [input p15]
23. happy(alice) <~> quiet(alice) [input p22]
24. old(alice) [input hypothesis]
32. ! [X0] : (((rich(X0) | calm(X0)) | (patient(X0) | ~patient(X0))) & ((~patient(X0) & patient(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 1]
33. ! [X0] : ((rich(X0) | calm(X0) | patient(X0) | ~patient(X0)) & ((~patient(X0) & patient(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 32]
35. ! [X0] : ((happy(X0) | (funny(X0) | ~quiet(X0))) & ((~funny(X0) & quiet(X0)) | ~happy(X0))) [nnf transformation 4]
36. ! [X0] : ((happy(X0) | funny(X0) | ~quiet(X0)) & ((~funny(X0) & quiet(X0)) | ~happy(X0))) [flattening 35]
42. ! [X0] : (((~curious(X0) | ~kind(X0)) | quiet(X0)) & (~quiet(X0) | (curious(X0) & kind(X0)))) [nnf transformation 6]
43. ! [X0] : ((~curious(X0) | ~kind(X0) | quiet(X0)) & (~quiet(X0) | (curious(X0) & kind(X0)))) [flattening 42]
63. ! [X0] : ((((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (old(X0) & ~rich(X0))) & ((~old(X0) | rich(X0)) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))))) [nnf transformation 16]
64. ! [X0] : ((((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (old(X0) & ~rich(X0))) & (~old(X0) | rich(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))))) [flattening 63]
70. (~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice)) [nnf transformation 23]
72. patient(X0) | ~rich(X0) [cnf transformation 33]
74. ~patient(X0) | ~rich(X0) [cnf transformation 33]
88. ~happy(X0) | quiet(X0) [cnf transformation 36]
90. ~quiet(X0) | funny(X0) | happy(X0) [cnf transformation 36]
94. ~quiet(X0) | kind(X0) [cnf transformation 43]
127. ~old(X0) | rich(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 64]
140. quiet(alice) | happy(alice) [cnf transformation 70]
141. ~quiet(alice) | ~happy(alice) [cnf transformation 70]
142. old(alice) [cnf transformation 24]
143. ~rich(X0) [subsumption resolution 72,74]
241. ~old(X0) | ~funny(X0) | ~kind(X0) [subsumption resolution 127,143]
264. ~happy(alice) [subsumption resolution 141,88]
265. quiet(alice) [subsumption resolution 140,264]
275. kind(alice) [resolution 94,265]
286. funny(alice) | happy(alice) [resolution 90,265]
297. funny(alice) [subsumption resolution 286,264]
480. ~funny(alice) | ~kind(alice) [resolution 241,142]
482. ~kind(alice) [subsumption resolution 480,297]
483. $false [subsumption resolution 482,275]
% SZS output end Proof for 3540043851983354005694474
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either happy or not kind then someone is not calm or patient. If someone is quiet then john is kind. Everyone who is both strong and not calm is both not humble and old. Everyone who is not brave or patient is either happy or not rich and vice versa. Everyone who is kind is creative and vice versa. Everyone who is both happy and not happy is creative or rich and vice versa. Everyone who is both not humble and creative is not generous or happy. Everyone who is both old and not brave is not creative or strong and vice versa. If someone is patient or quiet then someone is happy and vice versa. Everyone who is kind is both calm and brave and vice versa. If paul is either not wise or tall then someone is both not creative and patient. Everyone who is not quiet or strong is not strong. Everyone who is strong or not old is rich or not old. Everyone who is either not calm or old is not happy. If fred is both generous and not curious then someone is humble. If john is either brave or generous then susan is both tall and not rich and vice versa. Someone is not rich. Someone is not calm or not curious. Fred is funny or patient. John is not brave. Someone is both not quiet and wise. Paul is either calm or not old. Someone is not brave. | Fred is patient. | contradiction | (((happy(mary)<~>~kind(mary)))=>(?[X]:((~calm(X)|patient(X)))))&
((?[X]:(quiet(X)))=>(kind(john)))&
(![X]:((strong(X)&~calm(X))=>(~humble(X)&old(X))))&
(![X]:((~brave(X)|patient(X))<=>(happy(X)<~>~rich(X))))&
(![X]:(kind(X)<=>creative(X)))&
(![X]:((happy(X)&~happy(X))<=>(creative(X)|rich(X))))&
(![X]:((~humble(X)&creative(X))=>(~generous(X)|happy(X))))&
(![X]:((old(X)&~brave(X))<=>(~creative(X)|strong(X))))&
((?[X]:((patient(X)|quiet(X))))<=>(?[X]:(happy(X))))&
(![X]:(kind(X)<=>(calm(X)&brave(X))))&
(((~wise(paul)<~>tall(paul)))=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:((~quiet(X)|strong(X))=>~strong(X)))&
(![X]:((strong(X)|~old(X))=>(rich(X)|~old(X))))&
(![X]:((~calm(X)<~>old(X))=>~happy(X)))&
(((generous(fred)&~curious(fred)))=>(?[X]:(humble(X))))&
(((brave(john)<~>generous(john)))<=>((tall(susan)&~rich(susan))))&
(?[X]:(~rich(X)))&
(?[X]:((~calm(X)|~curious(X))))&
((funny(fred)|patient(fred)))&
(~brave(john))&
(?[X]:((~quiet(X)&wise(X))))&
((calm(paul)<~>~old(paul)))&
(?[X]:(~brave(X))) | patient(fred) | [
"p3",
"p5",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2965271382426558049566021
% SZS output start Proof for 2965271382426558049566021
4. ! [X0] : ((patient(X0) | ~brave(X0)) <=> (happy(X0) <~> ~rich(X0))) [input p3]
6. ! [X0] : ((~happy(X0) & happy(X0)) <=> (rich(X0) | creative(X0))) [input p5]
8. ! [X0] : ((~brave(X0) & old(X0)) <=> (strong(X0) | ~creative(X0))) [input p7]
9. ? [X0] : (quiet(X0) | patient(X0)) <=> ? [X0] : happy(X0) [input p8]
24. patient(fred) [input hypothesis]
25. ? [X0] : (quiet(X0) | patient(X0)) <=> ? [X1] : happy(X1) [rectify 9]
43. ! [X0] : (((patient(X0) | ~brave(X0)) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) & (((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | (~patient(X0) & brave(X0)))) [nnf transformation 4]
44. ! [X0] : ((patient(X0) | ~brave(X0) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0)))) & (((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | (~patient(X0) & brave(X0)))) [flattening 43]
46. ! [X0] : (((~happy(X0) & happy(X0)) | (~rich(X0) & ~creative(X0))) & ((rich(X0) | creative(X0)) | (happy(X0) | ~happy(X0)))) [nnf transformation 6]
47. ! [X0] : (((~happy(X0) & happy(X0)) | (~rich(X0) & ~creative(X0))) & (rich(X0) | creative(X0) | happy(X0) | ~happy(X0))) [flattening 46]
48. ! [X0] : (((~brave(X0) & old(X0)) | (~strong(X0) & creative(X0))) & ((strong(X0) | ~creative(X0)) | (brave(X0) | ~old(X0)))) [nnf transformation 8]
49. ! [X0] : (((~brave(X0) & old(X0)) | (~strong(X0) & creative(X0))) & (strong(X0) | ~creative(X0) | brave(X0) | ~old(X0))) [flattening 48]
50. (? [X0] : (quiet(X0) | patient(X0)) | ! [X1] : ~happy(X1)) & (? [X1] : happy(X1) | ! [X0] : (~quiet(X0) & ~patient(X0))) [nnf transformation 25]
51. (? [X0] : (quiet(X0) | patient(X0)) | ! [X1] : ~happy(X1)) & (? [X2] : happy(X2) | ! [X3] : (~quiet(X3) & ~patient(X3))) [rectify 50]
52. ? [X0] : (quiet(X0) | patient(X0)) => (quiet(sK1) | patient(sK1)) [choice axiom]
53. ? [X2] : happy(X2) => happy(sK2) [choice axiom]
54. ((quiet(sK1) | patient(sK1)) | ! [X1] : ~happy(X1)) & (happy(sK2) | ! [X3] : (~quiet(X3) & ~patient(X3))) [skolemisation 51,53,52]
81. ~happy(X0) | rich(X0) | brave(X0) [cnf transformation 44]
88. happy(X0) | ~creative(X0) [cnf transformation 47]
89. happy(X0) | ~rich(X0) [cnf transformation 47]
90. ~creative(X0) | ~happy(X0) [cnf transformation 47]
91. ~rich(X0) | ~happy(X0) [cnf transformation 47]
96. ~brave(X0) | creative(X0) [cnf transformation 49]
98. happy(sK2) | ~patient(X3) [cnf transformation 54]
129. patient(fred) [cnf transformation 24]
157. ~rich(X0) [subsumption resolution 89,91]
158. ~creative(X0) [subsumption resolution 88,90]
159. ~brave(X0) [subsumption resolution 96,158]
174. 10 <=> happy(sK2) [avatar definition]
176. happy(sK2) <- (10) [avatar component clause 174]
179. 11 <=> ! [X3] : ~patient(X3) [avatar definition]
180. ~patient(X3) <- (11) [avatar component clause 179]
181. 11 | 10 [avatar split clause 98,174,179]
237. rich(sK2) | brave(sK2) <- (10) [resolution 81,176]
238. brave(sK2) <- (10) [subsumption resolution 237,157]
239. $false <- (10) [subsumption resolution 238,159]
240. ~10 [avatar contradiction clause 239]
241. $false <- (11) [resolution 180,129]
244. ~11 [avatar contradiction clause 241]
245. $false [avatar sat refutation 181,240,244]
% SZS output end Proof for 2965271382426558049566021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not calm or not tall then someone is both generous and funny.
Everyone who is both not wise and not quiet is either creative or not rich.
Everyone who is either patient or not rich is either not calm or not curious.
Everyone who is happy or not patient is both not patient and not happy.
Everyone who is humble is both wise and curious.
Everyone who is not funny is generous or calm.
If susan is humble or not tall then alice is either not wise or curious.
If someone is either not generous or not tall then susan is curious and vice versa.
Everyone who is old or not happy is both not creative and not wise.
If someone is not kind then someone is not old or quiet.
Everyone who is not tall is both not happy and patient.
If someone is tall then lucy is quiet.
Everyone who is not generous or quiet is both not happy and tall and vice versa.
If someone is not creative then someone is not humble or not wise.
Everyone who is not humble or not brave is not old or rich and vice versa.
Everyone who is not rich is not humble and vice versa.
Mary is not quiet.
Someone is either creative or not strong.
Paul is quiet or strong.
Paul is either not patient or generous.
Someone is not wise or wise.
Someone is both not generous and not funny.
John is generous or tall.
Fred is either funny or old. | Lucy is quiet. | entailment | (((~calm(alice)<~>~tall(alice)))=>(?[X]:((generous(X)&funny(X)))))&
(![X]:((~wise(X)&~quiet(X))=>(creative(X)<~>~rich(X))))&
(![X]:((patient(X)<~>~rich(X))=>(~calm(X)<~>~curious(X))))&
(![X]:((happy(X)|~patient(X))=>(~patient(X)&~happy(X))))&
(![X]:(humble(X)=>(wise(X)&curious(X))))&
(![X]:(~funny(X)=>(generous(X)|calm(X))))&
(((humble(susan)|~tall(susan)))=>((~wise(alice)<~>curious(alice))))&
((?[X]:((~generous(X)<~>~tall(X))))<=>(curious(susan)))&
(![X]:((old(X)|~happy(X))=>(~creative(X)&~wise(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~old(X)|quiet(X)))))&
(![X]:(~tall(X)=>(~happy(X)&patient(X))))&
((?[X]:(tall(X)))=>(quiet(lucy)))&
(![X]:((~generous(X)|quiet(X))<=>(~happy(X)&tall(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:((~humble(X)|~brave(X))<=>(~old(X)|rich(X))))&
(![X]:(~rich(X)<=>~humble(X)))&
(~quiet(mary))&
(?[X]:((creative(X)<~>~strong(X))))&
((quiet(paul)|strong(paul)))&
((~patient(paul)<~>generous(paul)))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:((~generous(X)&~funny(X))))&
((generous(john)|tall(john)))&
((funny(fred)<~>old(fred))) | quiet(lucy) | [
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3278751132690077668957091
% SZS output start Proof for 3278751132690077668957091
12. ? [X0] : tall(X0) => quiet(lucy) [input p11]
13. ! [X0] : ((quiet(X0) | ~generous(X0)) <=> (tall(X0) & ~happy(X0))) [input p12]
22. ? [X0] : (~funny(X0) & ~generous(X0)) [input p21]
25. ~quiet(lucy) [input hypothesis]
40. quiet(lucy) | ! [X0] : ~tall(X0) [ennf transformation 12]
52. ! [X0] : (((quiet(X0) | ~generous(X0)) | (~tall(X0) | happy(X0))) & ((tall(X0) & ~happy(X0)) | (~quiet(X0) & generous(X0)))) [nnf transformation 13]
53. ! [X0] : ((quiet(X0) | ~generous(X0) | ~tall(X0) | happy(X0)) & ((tall(X0) & ~happy(X0)) | (~quiet(X0) & generous(X0)))) [flattening 52]
66. ? [X0] : (~funny(X0) & ~generous(X0)) => (~funny(sK5) & ~generous(sK5)) [choice axiom]
67. ~funny(sK5) & ~generous(sK5) [skolemisation 22,66]
100. quiet(lucy) | ~tall(X0) [cnf transformation 40]
103. generous(X0) | tall(X0) [cnf transformation 53]
120. ~generous(sK5) [cnf transformation 67]
125. ~quiet(lucy) [cnf transformation 25]
192. 14 <=> ! [X0] : ~tall(X0) [avatar definition]
193. ~tall(X0) <- (14) [avatar component clause 192]
195. 15 <=> quiet(lucy) [avatar definition]
198. 14 | 15 [avatar split clause 100,195,192]
230. ~15 [avatar split clause 125,195]
234. tall(sK5) [resolution 103,120]
235. $false <- (14) [subsumption resolution 234,193]
236. ~14 [avatar contradiction clause 235]
237. $false [avatar sat refutation 198,230,236]
% SZS output end Proof for 3278751132690077668957091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is funny then someone is either not curious or not wise.
Everyone who is both happy and not old is old.
If fred is either not rich or not calm then someone is either not quiet or rich and vice versa.
Everyone who is both not calm and brave is not tall or not quiet.
Everyone who is not quiet is both not happy and curious.
If someone is generous then someone is not patient or not old.
If someone is both rich and patient then someone is curious and vice versa.
If susan is both funny and calm then someone is both tall and calm.
If someone is either not wise or kind then lucy is either not generous or not funny and vice versa.
Everyone who is both not calm and not funny is not kind and vice versa.
Everyone who is not happy is not strong or curious and vice versa.
Everyone who is wise or humble is creative and vice versa.
Everyone who is not creative or kind is both not curious and happy.
If alice is either not brave or not calm then john is strong and vice versa.
If susan is both not calm and not creative then alice is both happy and wise and vice versa.
Everyone who is not strong or not kind is both not happy and tall.
Paul is either not patient or not calm.
Someone is not quiet.
Fred is not brave or calm.
Someone is not happy.
Someone is either not curious or not humble.
Susan is not old.
Someone is both brave and not calm.
Someone is generous. | Susan is tall. | entailment | ((funny(mary))=>(?[X]:((~curious(X)<~>~wise(X)))))&
(![X]:((happy(X)&~old(X))=>old(X)))&
(((~rich(fred)<~>~calm(fred)))<=>(?[X]:((~quiet(X)<~>rich(X)))))&
(![X]:((~calm(X)&brave(X))=>(~tall(X)|~quiet(X))))&
(![X]:(~quiet(X)=>(~happy(X)&curious(X))))&
((?[X]:(generous(X)))=>(?[X]:((~patient(X)|~old(X)))))&
((?[X]:((rich(X)&patient(X))))<=>(?[X]:(curious(X))))&
(((funny(susan)&calm(susan)))=>(?[X]:((tall(X)&calm(X)))))&
((?[X]:((~wise(X)<~>kind(X))))<=>((~generous(lucy)<~>~funny(lucy))))&
(![X]:((~calm(X)&~funny(X))<=>~kind(X)))&
(![X]:(~happy(X)<=>(~strong(X)|curious(X))))&
(![X]:((wise(X)|humble(X))<=>creative(X)))&
(![X]:((~creative(X)|kind(X))=>(~curious(X)&happy(X))))&
(((~brave(alice)<~>~calm(alice)))<=>(strong(john)))&
(((~calm(susan)&~creative(susan)))<=>((happy(alice)&wise(alice))))&
(![X]:((~strong(X)|~kind(X))=>(~happy(X)&tall(X))))&
((~patient(paul)<~>~calm(paul)))&
(?[X]:(~quiet(X)))&
((~brave(fred)|calm(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((~curious(X)<~>~humble(X))))&
(~old(susan))&
(?[X]:((brave(X)&~calm(X))))&
(?[X]:(generous(X))) | tall(susan) | [
"p1",
"p12",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6542432871560354241962704
% SZS output start Proof for 6542432871560354241962704
2. ! [X0] : ((~old(X0) & happy(X0)) => old(X0)) [input p1]
13. ! [X0] : ((kind(X0) | ~creative(X0)) => (happy(X0) & ~curious(X0))) [input p12]
16. ! [X0] : ((~kind(X0) | ~strong(X0)) => (tall(X0) & ~happy(X0))) [input p15]
22. ~old(susan) [input p21]
25. ~tall(susan) [input hypothesis]
29. ! [X0] : (old(X0) | (old(X0) | ~happy(X0))) [ennf transformation 2]
30. ! [X0] : (old(X0) | old(X0) | ~happy(X0)) [flattening 29]
37. ! [X0] : ((happy(X0) & ~curious(X0)) | (~kind(X0) & creative(X0))) [ennf transformation 13]
38. ! [X0] : ((tall(X0) & ~happy(X0)) | (kind(X0) & strong(X0))) [ennf transformation 16]
83. old(X0) | old(X0) | ~happy(X0) [cnf transformation 30]
121. ~kind(X0) | happy(X0) [cnf transformation 37]
133. kind(X0) | tall(X0) [cnf transformation 38]
141. ~old(susan) [cnf transformation 22]
145. ~tall(susan) [cnf transformation 25]
146. ~happy(X0) | old(X0) [duplicate literal removal 83]
344. tall(X0) | happy(X0) [resolution 133,121]
458. happy(susan) [resolution 344,145]
487. old(susan) [resolution 458,146]
492. $false [subsumption resolution 487,141]
% SZS output end Proof for 6542432871560354241962704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not happy and not creative is not tall or funny. Everyone who is both not generous and not rich is not strong and vice versa. Everyone who is brave is both humble and not curious. If alice is either not quiet or quiet then lucy is either not creative or humble. If someone is brave then someone is either wise or not rich and vice versa. If someone is both calm and not wise then someone is generous or creative. Everyone who is not brave or not strong is both kind and not brave. If alice is curious or creative then someone is not brave or generous. If mary is not curious or not funny then lucy is both brave and not humble and vice versa. Everyone who is either patient or not generous is either not creative or not tall. Everyone who is not happy is either not curious or creative and vice versa. Everyone who is either calm or generous is either quiet or rich. Everyone who is either not brave or not happy is either quiet or not creative and vice versa. Everyone who is either generous or not tall is both not curious and wise. If john is either quiet or not quiet then someone is either not curious or kind and vice versa. Everyone who is either not brave or strong is not kind or not tall and vice versa. Someone is not old or tall. Someone is not wise or humble. Alice is brave. Susan is either curious or not creative. Susan is both not funny and rich. Someone is both generous and not calm. | Susan is not brave. | neutral | (![X]:((~happy(X)&~creative(X))=>(~tall(X)|funny(X))))&
(![X]:((~generous(X)&~rich(X))<=>~strong(X)))&
(![X]:(brave(X)=>(humble(X)&~curious(X))))&
(((~quiet(alice)<~>quiet(alice)))=>((~creative(lucy)<~>humble(lucy))))&
((?[X]:(brave(X)))<=>(?[X]:((wise(X)<~>~rich(X)))))&
((?[X]:((calm(X)&~wise(X))))=>(?[X]:((generous(X)|creative(X)))))&
(![X]:((~brave(X)|~strong(X))=>(kind(X)&~brave(X))))&
(((curious(alice)|creative(alice)))=>(?[X]:((~brave(X)|generous(X)))))&
(((~curious(mary)|~funny(mary)))<=>((brave(lucy)&~humble(lucy))))&
(![X]:((patient(X)<~>~generous(X))=>(~creative(X)<~>~tall(X))))&
(![X]:(~happy(X)<=>(~curious(X)<~>creative(X))))&
(![X]:((calm(X)<~>generous(X))=>(quiet(X)<~>rich(X))))&
(![X]:((~brave(X)<~>~happy(X))<=>(quiet(X)<~>~creative(X))))&
(![X]:((generous(X)<~>~tall(X))=>(~curious(X)&wise(X))))&
(((quiet(john)<~>~quiet(john)))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(~kind(X)|~tall(X))))&
(?[X]:((~old(X)|tall(X))))&
(?[X]:((~wise(X)|humble(X))))&
(brave(alice))&
((curious(susan)<~>~creative(susan)))&
((~funny(susan)&rich(susan)))&
(?[X]:((generous(X)&~calm(X)))) | ~brave(susan) | [] | null | 0 |
Everyone who is calm is quiet or not creative and vice versa.
Everyone who is not humble is both funny and rich.
If someone is either humble or not curious then alice is both not humble and not curious and vice versa.
If someone is both not humble and not kind then john is not old or rich and vice versa.
Everyone who is rich is wise or not patient.
Everyone who is either patient or not patient is not generous or not wise and vice versa.
If susan is both not generous and not calm then fred is both rich and not wise.
Everyone who is not wise is rich or old and vice versa.
If lucy is not humble or not rich then someone is not quiet and vice versa.
Everyone who is both not rich and not kind is happy or rich and vice versa.
If someone is either not patient or old then lucy is not strong or humble.
If paul is not calm or brave then someone is both not old and not rich and vice versa.
Everyone who is brave or not wise is humble and vice versa.
Everyone who is not quiet or humble is both creative and not tall.
Everyone who is either not creative or generous is humble or not generous and vice versa.
Everyone who is either not funny or not quiet is either not old or curious.
Someone is not wise or calm.
Someone is either funny or not humble.
Mary is kind.
Someone is both happy and not patient.
Someone is creative or funny. | Lucy is humble. | entailment | (![X]:(calm(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~humble(X)=>(funny(X)&rich(X))))&
((?[X]:((humble(X)<~>~curious(X))))<=>((~humble(alice)&~curious(alice))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~old(john)|rich(john))))&
(![X]:(rich(X)=>(wise(X)|~patient(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~generous(X)|~wise(X))))&
(((~generous(susan)&~calm(susan)))=>((rich(fred)&~wise(fred))))&
(![X]:(~wise(X)<=>(rich(X)|old(X))))&
(((~humble(lucy)|~rich(lucy)))<=>(?[X]:(~quiet(X))))&
(![X]:((~rich(X)&~kind(X))<=>(happy(X)|rich(X))))&
((?[X]:((~patient(X)<~>old(X))))=>((~strong(lucy)|humble(lucy))))&
(((~calm(paul)|brave(paul)))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((brave(X)|~wise(X))<=>humble(X)))&
(![X]:((~quiet(X)|humble(X))=>(creative(X)&~tall(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(humble(X)|~generous(X))))&
(![X]:((~funny(X)<~>~quiet(X))=>(~old(X)<~>curious(X))))&
(?[X]:((~wise(X)|calm(X))))&
(?[X]:((funny(X)<~>~humble(X))))&
(kind(mary))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((creative(X)|funny(X)))) | humble(lucy) | [
"p1",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8005084828107090874914374
% SZS output start Proof for 8005084828107090874914374
2. ! [X0] : (~humble(X0) => (rich(X0) & funny(X0))) [input p1]
10. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (rich(X0) | happy(X0))) [input p9]
22. ~humble(lucy) [input hypothesis]
25. ! [X0] : ((rich(X0) & funny(X0)) | humble(X0)) [ennf transformation 2]
53. ! [X0] : (((~kind(X0) & ~rich(X0)) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 10]
54. ! [X0] : (((~kind(X0) & ~rich(X0)) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | kind(X0) | rich(X0))) [flattening 53]
78. rich(X0) | humble(X0) [cnf transformation 25]
107. ~rich(X0) | ~rich(X0) [cnf transformation 54]
137. ~humble(lucy) [cnf transformation 22]
141. ~rich(X0) [duplicate literal removal 107]
219. 17 <=> humble(lucy) [avatar definition]
221. ~humble(lucy) <- (~17) [avatar component clause 219]
274. ~17 [avatar split clause 137,219]
275. humble(X0) [resolution 78,141]
277. $false <- (~17) [resolution 275,221]
282. 17 [avatar contradiction clause 277]
284. $false [avatar sat refutation 274,282]
% SZS output end Proof for 8005084828107090874914374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or humble is both not rich and strong.
Everyone who is both humble and not calm is either not brave or calm and vice versa.
Everyone who is both not kind and curious is not old or happy.
Everyone who is not happy is not humble or not quiet.
If someone is either humble or not generous then paul is old and vice versa.
Everyone who is quiet or creative is not quiet and vice versa.
If someone is both not brave and calm then someone is both not old and patient and vice versa.
If susan is not rich then alice is generous and vice versa.
If someone is strong then someone is both old and not strong.
If alice is both not tall and not happy then someone is both not humble and not strong and vice versa.
If someone is either patient or old then someone is both not wise and not rich and vice versa.
If susan is not quiet then someone is either not generous or not tall.
Everyone who is tall is happy.
Everyone who is either strong or not generous is either not patient or wise.
If paul is old then paul is not patient or quiet and vice versa.
If someone is both humble and happy then someone is not tall or not strong and vice versa.
Someone is not humble.
Alice is either not generous or not rich.
John is patient.
Someone is either creative or generous.
Lucy is not generous or creative.
Susan is not old or not strong.
Paul is not old or not tall.
Paul is both curious and not brave. | Lucy is not creative. | contradiction | (![X]:((tall(X)<~>humble(X))=>(~rich(X)&strong(X))))&
(![X]:((humble(X)&~calm(X))<=>(~brave(X)<~>calm(X))))&
(![X]:((~kind(X)&curious(X))=>(~old(X)|happy(X))))&
(![X]:(~happy(X)=>(~humble(X)|~quiet(X))))&
((?[X]:((humble(X)<~>~generous(X))))<=>(old(paul)))&
(![X]:((quiet(X)|creative(X))<=>~quiet(X)))&
((?[X]:((~brave(X)&calm(X))))<=>(?[X]:((~old(X)&patient(X)))))&
((~rich(susan))<=>(generous(alice)))&
((?[X]:(strong(X)))=>(?[X]:((old(X)&~strong(X)))))&
(((~tall(alice)&~happy(alice)))<=>(?[X]:((~humble(X)&~strong(X)))))&
((?[X]:((patient(X)<~>old(X))))<=>(?[X]:((~wise(X)&~rich(X)))))&
((~quiet(susan))=>(?[X]:((~generous(X)<~>~tall(X)))))&
(![X]:(tall(X)=>happy(X)))&
(![X]:((strong(X)<~>~generous(X))=>(~patient(X)<~>wise(X))))&
((old(paul))<=>((~patient(paul)|quiet(paul))))&
((?[X]:((humble(X)&happy(X))))<=>(?[X]:((~tall(X)|~strong(X)))))&
(?[X]:(~humble(X)))&
((~generous(alice)<~>~rich(alice)))&
(patient(john))&
(?[X]:((creative(X)<~>generous(X))))&
((~generous(lucy)|creative(lucy)))&
((~old(susan)|~strong(susan)))&
((~old(paul)|~tall(paul)))&
((curious(paul)&~brave(paul))) | ~creative(lucy) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 738145035813011888138168
% SZS output start Proof for 738145035813011888138168
6. ! [X0] : ((creative(X0) | quiet(X0)) <=> ~quiet(X0)) [input p5]
25. ~creative(lucy) [input hypothesis]
46. ! [X0] : (((creative(X0) | quiet(X0)) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & ~quiet(X0)))) [nnf transformation 6]
47. ! [X0] : ((creative(X0) | quiet(X0) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & ~quiet(X0)))) [flattening 46]
99. ~quiet(X0) | ~quiet(X0) [cnf transformation 47]
101. creative(X0) | quiet(X0) | quiet(X0) [cnf transformation 47]
145. ~creative(lucy) [cnf transformation 25]
146. ~quiet(X0) [duplicate literal removal 99]
147. creative(X0) | quiet(X0) [duplicate literal removal 101]
345. 42 <=> creative(lucy) [avatar definition]
346. ~creative(lucy) <- (~42) [avatar component clause 345]
363. ~42 [avatar split clause 145,345]
376. quiet(lucy) <- (~42) [resolution 147,346]
378. $false <- (~42) [subsumption resolution 376,146]
379. 42 [avatar contradiction clause 378]
380. $false [avatar sat refutation 363,379]
% SZS output end Proof for 738145035813011888138168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is either not funny or not wise and vice versa. If someone is both kind and happy then fred is funny and vice versa. If mary is both not curious and not old then mary is not tall and vice versa. Everyone who is tall is patient. Everyone who is either not curious or kind is not curious or not wise. Everyone who is both not old and rich is both not calm and kind and vice versa. If someone is patient then someone is not old. If someone is not brave or old then mary is wise or tall and vice versa. Everyone who is both strong and quiet is both brave and humble and vice versa. Everyone who is either not tall or quiet is not strong or curious and vice versa. Everyone who is either strong or not wise is tall and vice versa. Everyone who is either not happy or creative is not generous or not creative. Everyone who is not quiet is either creative or happy. If john is both not curious and not calm then paul is happy or not tall and vice versa. If someone is not old then someone is not old or not calm. If susan is not wise then alice is not happy or not tall and vice versa. Someone is not rich or not generous. Someone is both curious and not funny. Alice is either not rich or happy. Fred is both rich and not happy. Someone is not strong. Susan is either kind or not humble. Someone is either kind or not happy. Susan is either not calm or not funny. | John is curious. | neutral | (![X]:(humble(X)<=>(~funny(X)<~>~wise(X))))&
((?[X]:((kind(X)&happy(X))))<=>(funny(fred)))&
(((~curious(mary)&~old(mary)))<=>(~tall(mary)))&
(![X]:(tall(X)=>patient(X)))&
(![X]:((~curious(X)<~>kind(X))=>(~curious(X)|~wise(X))))&
(![X]:((~old(X)&rich(X))<=>(~calm(X)&kind(X))))&
((?[X]:(patient(X)))=>(?[X]:(~old(X))))&
((?[X]:((~brave(X)|old(X))))<=>((wise(mary)|tall(mary))))&
(![X]:((strong(X)&quiet(X))<=>(brave(X)&humble(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~strong(X)|curious(X))))&
(![X]:((strong(X)<~>~wise(X))<=>tall(X)))&
(![X]:((~happy(X)<~>creative(X))=>(~generous(X)|~creative(X))))&
(![X]:(~quiet(X)=>(creative(X)<~>happy(X))))&
(((~curious(john)&~calm(john)))<=>((happy(paul)|~tall(paul))))&
((?[X]:(~old(X)))=>(?[X]:((~old(X)|~calm(X)))))&
((~wise(susan))<=>((~happy(alice)|~tall(alice))))&
(?[X]:((~rich(X)|~generous(X))))&
(?[X]:((curious(X)&~funny(X))))&
((~rich(alice)<~>happy(alice)))&
((rich(fred)&~happy(fred)))&
(?[X]:(~strong(X)))&
((kind(susan)<~>~humble(susan)))&
(?[X]:((kind(X)<~>~happy(X))))&
((~calm(susan)<~>~funny(susan))) | curious(john) | [] | null | 0 |
If paul is not creative then someone is either happy or brave and vice versa.
Everyone who is happy is both calm and not old and vice versa.
If susan is either generous or quiet then someone is either not old or happy and vice versa.
If someone is 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.
Everyone who is both creative and curious is both not strong and not calm.
Everyone who is both not quiet and happy is both rich and curious and vice versa.
Everyone who is either not humble or funny is both tall and generous and vice versa.
If paul is either rich or funny then susan is both wise and brave and vice versa.
If someone is humble or calm then lucy is either rich or happy.
Everyone who is either not kind or not curious is both generous and not kind and vice versa.
If mary is kind or not happy then paul is both kind and not funny and vice versa.
Everyone who is both not tall and curious is not rich.
Everyone who is both not creative and quiet is either creative or not rich.
Someone is both wise and not patient.
Mary is either strong or funny.
Someone is both rich and humble.
Someone is not strong.
Paul is either not patient or not generous.
Lucy is not curious.
Susan is funny or not strong.
John is happy. | John is calm. | entailment | ((~creative(paul))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:(happy(X)<=>(calm(X)&~old(X))))&
(((generous(susan)<~>quiet(susan)))<=>(?[X]:((~old(X)<~>happy(X)))))&
((?[X]:((humble(X)|~curious(X))))=>(?[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))))&
(![X]:((creative(X)&curious(X))=>(~strong(X)&~calm(X))))&
(![X]:((~quiet(X)&happy(X))<=>(rich(X)&curious(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(tall(X)&generous(X))))&
(((rich(paul)<~>funny(paul)))<=>((wise(susan)&brave(susan))))&
((?[X]:((humble(X)|calm(X))))=>((rich(lucy)<~>happy(lucy))))&
(![X]:((~kind(X)<~>~curious(X))<=>(generous(X)&~kind(X))))&
(((kind(mary)|~happy(mary)))<=>((kind(paul)&~funny(paul))))&
(![X]:((~tall(X)&curious(X))=>~rich(X)))&
(![X]:((~creative(X)&quiet(X))=>(creative(X)<~>~rich(X))))&
(?[X]:((wise(X)&~patient(X))))&
((strong(mary)<~>funny(mary)))&
(?[X]:((rich(X)&humble(X))))&
(?[X]:(~strong(X)))&
((~patient(paul)<~>~generous(paul)))&
(~curious(lucy))&
((funny(susan)|~strong(susan)))&
(happy(john)) | calm(john) | [
"p1",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3064512167101169610199585
% SZS output start Proof for 3064512167101169610199585
2. ! [X0] : (happy(X0) <=> (~old(X0) & calm(X0))) [input p1]
24. happy(john) [input p23]
25. ~calm(john) [input hypothesis]
41. ! [X0] : ((happy(X0) | (old(X0) | ~calm(X0))) & ((~old(X0) & calm(X0)) | ~happy(X0))) [nnf transformation 2]
42. ! [X0] : ((happy(X0) | old(X0) | ~calm(X0)) & ((~old(X0) & calm(X0)) | ~happy(X0))) [flattening 41]
78. ~happy(X0) | calm(X0) [cnf transformation 42]
154. happy(john) [cnf transformation 24]
155. ~calm(john) [cnf transformation 25]
324. calm(john) [resolution 78,154]
326. $false [subsumption resolution 324,155]
% SZS output end Proof for 3064512167101169610199585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or humble then john is both funny and calm.
Everyone who is humble is tall or not humble and vice versa.
Everyone who is not brave is not brave or not strong.
Everyone who is both not quiet and not old is both not calm and not creative.
Everyone who is not strong is calm and vice versa.
Everyone who is tall or not strong is creative.
If alice is not strong then john is both humble and not curious.
If someone is both not happy and quiet then someone is both brave and not old.
Everyone who is both not humble and generous is generous or patient.
If mary is both humble and wise then someone is both not rich and happy.
Everyone who is either not humble or not generous is not curious or not happy.
If someone is not quiet or not happy then john is not strong or kind.
If lucy is both funny and not rich then someone is both tall and not creative.
If alice is not quiet then someone is humble or generous and vice versa.
If someone is tall then someone is both funny and not curious and vice versa.
Everyone who is kind or not generous is either humble or quiet.
Lucy is both strong and creative.
Mary is both patient and not funny.
Mary is not wise.
Paul is rich.
Someone is not calm or not old.
Someone is either not generous or old.
Mary is both not quiet and not calm.
Someone is generous. | Mary is not old. | contradiction | ((?[X]:((~humble(X)|humble(X))))=>((funny(john)&calm(john))))&
(![X]:(humble(X)<=>(tall(X)|~humble(X))))&
(![X]:(~brave(X)=>(~brave(X)|~strong(X))))&
(![X]:((~quiet(X)&~old(X))=>(~calm(X)&~creative(X))))&
(![X]:(~strong(X)<=>calm(X)))&
(![X]:((tall(X)|~strong(X))=>creative(X)))&
((~strong(alice))=>((humble(john)&~curious(john))))&
((?[X]:((~happy(X)&quiet(X))))=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((~humble(X)&generous(X))=>(generous(X)|patient(X))))&
(((humble(mary)&wise(mary)))=>(?[X]:((~rich(X)&happy(X)))))&
(![X]:((~humble(X)<~>~generous(X))=>(~curious(X)|~happy(X))))&
((?[X]:((~quiet(X)|~happy(X))))=>((~strong(john)|kind(john))))&
(((funny(lucy)&~rich(lucy)))=>(?[X]:((tall(X)&~creative(X)))))&
((~quiet(alice))<=>(?[X]:((humble(X)|generous(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((funny(X)&~curious(X)))))&
(![X]:((kind(X)|~generous(X))=>(humble(X)<~>quiet(X))))&
((strong(lucy)&creative(lucy)))&
((patient(mary)&~funny(mary)))&
(~wise(mary))&
(rich(paul))&
(?[X]:((~calm(X)|~old(X))))&
(?[X]:((~generous(X)<~>old(X))))&
((~quiet(mary)&~calm(mary)))&
(?[X]:(generous(X))) | ~old(mary) | [
"p1",
"p3",
"p5",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 320723218804338815125351
% SZS output start Proof for 320723218804338815125351
2. ! [X0] : (humble(X0) <=> (~humble(X0) | tall(X0))) [input p1]
4. ! [X0] : ((~old(X0) & ~quiet(X0)) => (~creative(X0) & ~calm(X0))) [input p3]
6. ! [X0] : ((~strong(X0) | tall(X0)) => creative(X0)) [input p5]
23. ~calm(mary) & ~quiet(mary) [input p22]
25. ~old(mary) [input hypothesis]
37. ! [X0] : ((~creative(X0) & ~calm(X0)) | (old(X0) | quiet(X0))) [ennf transformation 4]
38. ! [X0] : ((~creative(X0) & ~calm(X0)) | old(X0) | quiet(X0)) [flattening 37]
39. ! [X0] : (creative(X0) | (strong(X0) & ~tall(X0))) [ennf transformation 6]
47. ! [X0] : ((humble(X0) | (humble(X0) & ~tall(X0))) & ((~humble(X0) | tall(X0)) | ~humble(X0))) [nnf transformation 2]
48. ! [X0] : ((humble(X0) | (humble(X0) & ~tall(X0))) & (~humble(X0) | tall(X0) | ~humble(X0))) [flattening 47]
75. ~humble(X0) | tall(X0) | ~humble(X0) [cnf transformation 48]
77. humble(X0) | humble(X0) [cnf transformation 48]
80. ~creative(X0) | old(X0) | quiet(X0) [cnf transformation 38]
83. ~tall(X0) | creative(X0) [cnf transformation 39]
109. ~quiet(mary) [cnf transformation 23]
112. ~old(mary) [cnf transformation 25]
113. ~humble(X0) | tall(X0) [duplicate literal removal 75]
114. humble(X0) [duplicate literal removal 77]
124. 3 <=> ! [X0] : humble(X0) [avatar definition]
125. humble(X0) <- (3) [avatar component clause 124]
133. 3 [avatar split clause 114,124]
239. tall(X0) <- (3) [resolution 113,125]
245. creative(X0) <- (3) [resolution 239,83]
269. old(X0) | quiet(X0) <- (3) [resolution 80,245]
294. quiet(mary) <- (3) [resolution 269,112]
297. $false <- (3) [subsumption resolution 294,109]
298. ~3 [avatar contradiction clause 297]
299. $false [avatar sat refutation 133,298]
% SZS output end Proof for 320723218804338815125351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or old then susan is wise and vice versa.
If mary is quiet then someone is either not rich or calm.
If someone is not generous then mary is either not tall or strong.
If someone is both not happy and not patient then fred is not kind or generous.
Everyone who is either not quiet or creative is not tall.
Everyone who is both not calm and not happy is tall or generous and vice versa.
If someone is not calm or not curious then someone is not patient and vice versa.
Everyone who is both not kind and not quiet is both humble and brave and vice versa.
Everyone who is either calm or quiet is both not patient and not humble.
Everyone who is both not curious and calm is patient and vice versa.
If someone is not creative then someone is tall.
Everyone who is not creative is humble and vice versa.
Everyone who is happy or not tall is not strong.
If someone is either calm or wise then someone is brave and vice versa.
Everyone who is both rich and humble is either old or not creative and vice versa.
Everyone who is funny or strong is not old or not patient and vice versa.
Someone is both not quiet and rich.
Mary is both patient and humble.
Someone is quiet.
Someone is not rich or calm.
Paul is quiet or not quiet.
Someone is both not rich and humble.
Someone is both calm and not wise.
Someone is patient or calm. | Mary is brave. | contradiction | ((?[X]:((~quiet(X)<~>old(X))))<=>(wise(susan)))&
((quiet(mary))=>(?[X]:((~rich(X)<~>calm(X)))))&
((?[X]:(~generous(X)))=>((~tall(mary)<~>strong(mary))))&
((?[X]:((~happy(X)&~patient(X))))=>((~kind(fred)|generous(fred))))&
(![X]:((~quiet(X)<~>creative(X))=>~tall(X)))&
(![X]:((~calm(X)&~happy(X))<=>(tall(X)|generous(X))))&
((?[X]:((~calm(X)|~curious(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~kind(X)&~quiet(X))<=>(humble(X)&brave(X))))&
(![X]:((calm(X)<~>quiet(X))=>(~patient(X)&~humble(X))))&
(![X]:((~curious(X)&calm(X))<=>patient(X)))&
((?[X]:(~creative(X)))=>(?[X]:(tall(X))))&
(![X]:(~creative(X)<=>humble(X)))&
(![X]:((happy(X)|~tall(X))=>~strong(X)))&
((?[X]:((calm(X)<~>wise(X))))<=>(?[X]:(brave(X))))&
(![X]:((rich(X)&humble(X))<=>(old(X)<~>~creative(X))))&
(![X]:((funny(X)|strong(X))<=>(~old(X)|~patient(X))))&
(?[X]:((~quiet(X)&rich(X))))&
((patient(mary)&humble(mary)))&
(?[X]:(quiet(X)))&
(?[X]:((~rich(X)|calm(X))))&
((quiet(paul)|~quiet(paul)))&
(?[X]:((~rich(X)&humble(X))))&
(?[X]:((calm(X)&~wise(X))))&
(?[X]:((patient(X)|calm(X)))) | brave(mary) | [
"p7",
"p8",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7486863425515557062552181
% SZS output start Proof for 7486863425515557062552181
8. ! [X0] : ((~quiet(X0) & ~kind(X0)) <=> (brave(X0) & humble(X0))) [input p7]
9. ! [X0] : ((calm(X0) <~> quiet(X0)) => (~humble(X0) & ~patient(X0))) [input p8]
10. ! [X0] : ((calm(X0) & ~curious(X0)) <=> patient(X0)) [input p9]
18. humble(mary) & patient(mary) [input p17]
25. brave(mary) [input hypothesis]
34. ! [X0] : ((~humble(X0) & ~patient(X0)) | (calm(X0) <=> quiet(X0))) [ennf transformation 9]
53. ! [X0] : (((~quiet(X0) & ~kind(X0)) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | (quiet(X0) | kind(X0)))) [nnf transformation 8]
54. ! [X0] : (((~quiet(X0) & ~kind(X0)) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | quiet(X0) | kind(X0))) [flattening 53]
55. ! [X0] : ((~humble(X0) & ~patient(X0)) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0)))) [nnf transformation 34]
56. ! [X0] : (((calm(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | (~calm(X0) | curious(X0)))) [nnf transformation 10]
57. ! [X0] : (((calm(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | ~calm(X0) | curious(X0))) [flattening 56]
105. ~brave(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 54]
106. ~patient(X0) | quiet(X0) | ~calm(X0) [cnf transformation 55]
112. ~patient(X0) | calm(X0) [cnf transformation 57]
134. patient(mary) [cnf transformation 18]
135. humble(mary) [cnf transformation 18]
144. brave(mary) [cnf transformation 25]
168. 6 <=> quiet(mary) [avatar definition]
277. calm(mary) [resolution 112,134]
311. ~quiet(mary) | ~humble(mary) [resolution 105,144]
322. quiet(mary) | ~calm(mary) [resolution 106,134]
326. quiet(mary) [subsumption resolution 322,277]
327. 6 [avatar split clause 326,168]
328. ~quiet(mary) [subsumption resolution 311,135]
329. ~6 [avatar split clause 328,168]
330. $false [avatar sat refutation 327,329]
% SZS output end Proof for 7486863425515557062552181
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not brave then someone is not kind.
If fred is strong then someone is both kind and not strong.
Everyone who is both not rich and curious is not strong and vice versa.
Everyone who is either humble or quiet is not kind and vice versa.
Everyone who is both funny and not patient is both patient and brave.
Everyone who is not tall is generous.
If fred is patient then someone is kind or tall and vice versa.
Everyone who is either old or not generous is both not rich and quiet and vice versa.
Everyone who is both calm and wise is either patient or tall and vice versa.
Everyone who is not generous is not rich.
If paul is not quiet or not rich then someone is not generous or not patient and vice versa.
Everyone who is both happy and not strong is strong.
If lucy is either curious or not happy then someone is wise and vice versa.
If someone is strong or curious then mary is both not patient and not calm.
If someone is curious then fred is happy or old and vice versa.
Everyone who is not curious is not funny or generous and vice versa.
Lucy is both tall and not rich.
Someone is either generous or not humble.
Someone is not creative.
Someone is both generous and not brave.
Someone is not calm.
Someone is both not curious and not patient. | Fred is not generous. | neutral | ((?[X]:((~humble(X)|~brave(X))))=>(?[X]:(~kind(X))))&
((strong(fred))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((~rich(X)&curious(X))<=>~strong(X)))&
(![X]:((humble(X)<~>quiet(X))<=>~kind(X)))&
(![X]:((funny(X)&~patient(X))=>(patient(X)&brave(X))))&
(![X]:(~tall(X)=>generous(X)))&
((patient(fred))<=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((old(X)<~>~generous(X))<=>(~rich(X)&quiet(X))))&
(![X]:((calm(X)&wise(X))<=>(patient(X)<~>tall(X))))&
(![X]:(~generous(X)=>~rich(X)))&
(((~quiet(paul)|~rich(paul)))<=>(?[X]:((~generous(X)|~patient(X)))))&
(![X]:((happy(X)&~strong(X))=>strong(X)))&
(((curious(lucy)<~>~happy(lucy)))<=>(?[X]:(wise(X))))&
((?[X]:((strong(X)|curious(X))))=>((~patient(mary)&~calm(mary))))&
((?[X]:(curious(X)))<=>((happy(fred)|old(fred))))&
(![X]:(~curious(X)<=>(~funny(X)|generous(X))))&
((tall(lucy)&~rich(lucy)))&
(?[X]:((generous(X)<~>~humble(X))))&
(?[X]:(~creative(X)))&
(?[X]:((generous(X)&~brave(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~curious(X)&~patient(X)))) | ~generous(fred) | [] | null | 0 |
Everyone who is either not curious or funny is both old and not creative. Everyone who is old or humble is creative. Everyone who is old or patient is both not old and not strong. Everyone who is not strong or not happy is both not happy and kind. Everyone who is not kind or generous is calm and vice versa. If john is both not quiet and tall then someone is tall or humble and vice versa. Everyone who is curious or quiet is both funny and rich. Everyone who is not patient is both not old and funny and vice versa. Everyone who is not curious or calm is both not humble and kind and vice versa. If john is humble then alice is either not rich or not quiet. If john is both creative and funny then susan is either not quiet or brave and vice versa. If mary is kind then paul is creative or curious and vice versa. Everyone who is both not generous and not kind is both not happy and not creative. If fred is both old and not humble then someone is either old or not tall and vice versa. Everyone who is quiet is both humble and not creative and vice versa. If paul is not creative or not strong then someone is strong and vice versa. John is not patient or humble. John is brave or not funny. Someone is not old. Lucy is both not old and not rich. Someone is brave. Lucy is patient or calm. | Fred is humble. | contradiction | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|humble(X))=>creative(X)))&
(![X]:((old(X)|patient(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
((~patient(john)|humble(john)))&
((brave(john)|~funny(john)))&
(?[X]:(~old(X)))&
((~old(lucy)&~rich(lucy)))&
(?[X]:(brave(X)))&
((patient(lucy)|calm(lucy))) | humble(fred) | [
"p0",
"p2",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 419393738756386574269156
% SZS output start Proof for 419393738756386574269156
1. ! [X0] : ((~curious(X0) <~> funny(X0)) => (~creative(X0) & old(X0))) [input p0]
3. ! [X0] : ((patient(X0) | old(X0)) => (~strong(X0) & ~old(X0))) [input p2]
7. ! [X0] : ((quiet(X0) | curious(X0)) => (rich(X0) & funny(X0))) [input p6]
9. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (kind(X0) & ~humble(X0))) [input p8]
23. humble(fred) [input hypothesis]
24. ! [X0] : ((~creative(X0) & old(X0)) | (~curious(X0) <=> funny(X0))) [ennf transformation 1]
26. ! [X0] : ((~strong(X0) & ~old(X0)) | (~patient(X0) & ~old(X0))) [ennf transformation 3]
28. ! [X0] : ((rich(X0) & funny(X0)) | (~quiet(X0) & ~curious(X0))) [ennf transformation 7]
32. ! [X0] : ((~creative(X0) & old(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) [nnf transformation 24]
42. ! [X0] : (((calm(X0) | ~curious(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [nnf transformation 9]
43. ! [X0] : ((calm(X0) | ~curious(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [flattening 42]
66. ~funny(X0) | ~curious(X0) | old(X0) [cnf transformation 32]
71. ~old(X0) | ~old(X0) [cnf transformation 26]
87. ~curious(X0) | funny(X0) [cnf transformation 28]
94. ~humble(X0) | curious(X0) [cnf transformation 43]
131. humble(fred) [cnf transformation 23]
132. ~old(X0) [duplicate literal removal 71]
216. 17 <=> humble(fred) [avatar definition]
217. humble(fred) <- (17) [avatar component clause 216]
256. 17 [avatar split clause 131,216]
276. curious(fred) <- (17) [resolution 94,217]
279. funny(fred) <- (17) [resolution 276,87]
298. ~curious(fred) | old(fred) <- (17) [resolution 66,279]
306. old(fred) <- (17) [subsumption resolution 298,276]
307. $false <- (17) [subsumption resolution 306,132]
308. ~17 [avatar contradiction clause 307]
310. $false [avatar sat refutation 256,308]
% SZS output end Proof for 419393738756386574269156
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and quiet is both not tall and not patient and vice versa.
If fred is either funny or not kind then someone is not tall or not brave.
If someone is both not wise and not calm then someone is old and vice versa.
Everyone who is both not patient and not brave is both brave and not humble.
Everyone who is not quiet is patient or generous and vice versa.
If lucy is either not tall or funny then someone is generous or not curious and vice versa.
Everyone who is either strong or patient is either brave or not strong and vice versa.
Everyone who is generous or not generous is both not tall and quiet and vice versa.
If susan is creative then someone is wise.
Everyone who is humble or happy is either brave or calm and vice versa.
If someone is both not quiet and old then someone is both brave and not old and vice versa.
Everyone who is brave or calm is either not patient or not kind.
Everyone who is both not funny and generous is both not happy and brave.
If mary is either creative or not old then mary is not curious or brave.
If someone is both humble and strong then alice is curious or not humble and vice versa.
Someone is either funny or calm.
Alice is either happy or curious.
Mary is both curious and brave.
Alice is not strong or not wise.
Someone is not happy or wise.
Someone is both not calm and not happy. | Alice is not patient. | entailment | (![X]:((~calm(X)&quiet(X))<=>(~tall(X)&~patient(X))))&
(((funny(fred)<~>~kind(fred)))=>(?[X]:((~tall(X)|~brave(X)))))&
((?[X]:((~wise(X)&~calm(X))))<=>(?[X]:(old(X))))&
(![X]:((~patient(X)&~brave(X))=>(brave(X)&~humble(X))))&
(![X]:(~quiet(X)<=>(patient(X)|generous(X))))&
(((~tall(lucy)<~>funny(lucy)))<=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((strong(X)<~>patient(X))<=>(brave(X)<~>~strong(X))))&
(![X]:((generous(X)|~generous(X))<=>(~tall(X)&quiet(X))))&
((creative(susan))=>(?[X]:(wise(X))))&
(![X]:((humble(X)|happy(X))<=>(brave(X)<~>calm(X))))&
((?[X]:((~quiet(X)&old(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((brave(X)|calm(X))=>(~patient(X)<~>~kind(X))))&
(![X]:((~funny(X)&generous(X))=>(~happy(X)&brave(X))))&
(((creative(mary)<~>~old(mary)))=>((~curious(mary)|brave(mary))))&
((?[X]:((humble(X)&strong(X))))<=>((curious(alice)|~humble(alice))))&
(?[X]:((funny(X)<~>calm(X))))&
((happy(alice)<~>curious(alice)))&
((curious(mary)&brave(mary)))&
((~strong(alice)|~wise(alice)))&
(?[X]:((~happy(X)|wise(X))))&
(?[X]:((~calm(X)&~happy(X)))) | ~patient(alice) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7787083628913923953213812
% SZS output start Proof for 7787083628913923953213812
5. ! [X0] : (~quiet(X0) <=> (generous(X0) | patient(X0))) [input p4]
8. ! [X0] : ((~generous(X0) | generous(X0)) <=> (quiet(X0) & ~tall(X0))) [input p7]
22. patient(alice) [input hypothesis]
44. ! [X0] : ((~quiet(X0) | (~generous(X0) & ~patient(X0))) & ((generous(X0) | patient(X0)) | quiet(X0))) [nnf transformation 5]
45. ! [X0] : ((~quiet(X0) | (~generous(X0) & ~patient(X0))) & (generous(X0) | patient(X0) | quiet(X0))) [flattening 44]
51. ! [X0] : (((~generous(X0) | generous(X0)) | (~quiet(X0) | tall(X0))) & ((quiet(X0) & ~tall(X0)) | (generous(X0) & ~generous(X0)))) [nnf transformation 8]
52. ! [X0] : ((~generous(X0) | generous(X0) | ~quiet(X0) | tall(X0)) & ((quiet(X0) & ~tall(X0)) | (generous(X0) & ~generous(X0)))) [flattening 51]
89. ~patient(X0) | ~quiet(X0) [cnf transformation 45]
90. ~generous(X0) | ~quiet(X0) [cnf transformation 45]
107. quiet(X0) | ~generous(X0) [cnf transformation 52]
108. generous(X0) | quiet(X0) [cnf transformation 52]
144. patient(alice) [cnf transformation 22]
202. 13 <=> ! [X0] : ~generous(X0) [avatar definition]
203. ~generous(X0) <- (13) [avatar component clause 202]
218. ~generous(X0) [subsumption resolution 107,90]
219. 13 [avatar split clause 218,202]
335. ~quiet(alice) [resolution 89,144]
337. quiet(X1) <- (13) [resolution 108,203]
338. $false <- (13) [resolution 337,335]
339. ~13 [avatar contradiction clause 338]
340. $false [avatar sat refutation 219,339]
% SZS output end Proof for 7787083628913923953213812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not calm is either happy or not funny and vice versa.
Everyone who is both not strong and not brave is either creative or not curious.
Everyone who is both not humble and patient is both creative and funny and vice versa.
Everyone who is rich or happy is not wise and vice versa.
Everyone who is not funny or old is both not wise and strong and vice versa.
Everyone who is humble or not humble is creative and vice versa.
If someone is either wise or not quiet then someone is patient or kind and vice versa.
If someone is not strong then mary is both not creative and funny.
Everyone who is not happy is not kind.
If someone is funny or calm then lucy is either not wise or old and vice versa.
Everyone who is patient is either generous or not generous and vice versa.
If someone is quiet then someone is either funny or brave.
If someone is not patient or curious then mary is both not tall and creative.
Everyone who is both not funny and not kind is either rich or not humble.
If fred is either patient or old then mary is both tall and happy and vice versa.
Someone is either rich or generous.
Alice is calm or not brave.
Someone is either not curious or not wise.
Fred is not calm or not generous.
Someone is both curious and not humble.
Mary is not calm.
Mary is generous. | Fred is not calm. | neutral | (![X]:((~curious(X)<~>~calm(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((~strong(X)&~brave(X))=>(creative(X)<~>~curious(X))))&
(![X]:((~humble(X)&patient(X))<=>(creative(X)&funny(X))))&
(![X]:((rich(X)|happy(X))<=>~wise(X)))&
(![X]:((~funny(X)|old(X))<=>(~wise(X)&strong(X))))&
(![X]:((humble(X)|~humble(X))<=>creative(X)))&
((?[X]:((wise(X)<~>~quiet(X))))<=>(?[X]:((patient(X)|kind(X)))))&
((?[X]:(~strong(X)))=>((~creative(mary)&funny(mary))))&
(![X]:(~happy(X)=>~kind(X)))&
((?[X]:((funny(X)|calm(X))))<=>((~wise(lucy)<~>old(lucy))))&
(![X]:(patient(X)<=>(generous(X)<~>~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((~patient(X)|curious(X))))=>((~tall(mary)&creative(mary))))&
(![X]:((~funny(X)&~kind(X))=>(rich(X)<~>~humble(X))))&
(((patient(fred)<~>old(fred)))<=>((tall(mary)&happy(mary))))&
(?[X]:((rich(X)<~>generous(X))))&
((calm(alice)|~brave(alice)))&
(?[X]:((~curious(X)<~>~wise(X))))&
((~calm(fred)|~generous(fred)))&
(?[X]:((curious(X)&~humble(X))))&
(~calm(mary))&
(generous(mary)) | ~calm(fred) | [] | null | 0 |
If someone is not calm then lucy is not curious or not brave and vice versa. If alice is not curious then someone is brave or not happy and vice versa. If paul is either not funny or humble then someone is either not funny or not happy. If someone is not creative or not tall then someone is both wise and not patient and vice versa. Everyone who is not generous is either funny or not old. Everyone who is either not brave or not funny is either quiet or strong. Everyone who is either not calm or creative is either not tall or not quiet. If someone is generous or funny then someone is not funny or not humble and vice versa. If alice is brave or not quiet then someone is strong and vice versa. Everyone who is not patient or not old is either brave or funny. If paul is both generous and brave then someone is both not quiet and kind. If susan is both strong and generous then fred is old or rich and vice versa. Everyone who is generous or not tall is tall. Everyone who is strong is both not generous and kind and vice versa. Everyone who is not generous or not quiet is either not kind or not tall and vice versa. Everyone who is creative or not funny is both kind and humble and vice versa. Paul is not quiet. Someone is not tall or not creative. Lucy is either not happy or patient. Someone is funny or not strong. Mary is either not old or patient. Alice is quiet or curious. Fred is not wise or not humble. Someone is tall or not curious. | Paul is not patient. | contradiction | ((?[X]:(~calm(X)))<=>((~curious(lucy)|~brave(lucy))))&
((~curious(alice))<=>(?[X]:((brave(X)|~happy(X)))))&
(((~funny(paul)<~>humble(paul)))=>(?[X]:((~funny(X)<~>~happy(X)))))&
((?[X]:((~creative(X)|~tall(X))))<=>(?[X]:((wise(X)&~patient(X)))))&
(![X]:(~generous(X)=>(funny(X)<~>~old(X))))&
(![X]:((~brave(X)<~>~funny(X))=>(quiet(X)<~>strong(X))))&
(![X]:((~calm(X)<~>creative(X))=>(~tall(X)<~>~quiet(X))))&
((?[X]:((generous(X)|funny(X))))<=>(?[X]:((~funny(X)|~humble(X)))))&
(((brave(alice)|~quiet(alice)))<=>(?[X]:(strong(X))))&
(![X]:((~patient(X)|~old(X))=>(brave(X)<~>funny(X))))&
(((generous(paul)&brave(paul)))=>(?[X]:((~quiet(X)&kind(X)))))&
(((strong(susan)&generous(susan)))<=>((old(fred)|rich(fred))))&
(![X]:((generous(X)|~tall(X))=>tall(X)))&
(![X]:(strong(X)<=>(~generous(X)&kind(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(~kind(X)<~>~tall(X))))&
(![X]:((creative(X)|~funny(X))<=>(kind(X)&humble(X))))&
(~quiet(paul))&
(?[X]:((~tall(X)|~creative(X))))&
((~happy(lucy)<~>patient(lucy)))&
(?[X]:((funny(X)|~strong(X))))&
((~old(mary)<~>patient(mary)))&
((quiet(alice)|curious(alice)))&
((~wise(fred)|~humble(fred)))&
(?[X]:((tall(X)|~curious(X)))) | ~patient(paul) | [
"p5",
"p8",
"p9",
"p12",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1031813016770346419888027
% SZS output start Proof for 1031813016770346419888027
6. ! [X0] : ((~brave(X0) <~> ~funny(X0)) => (quiet(X0) <~> strong(X0))) [input p5]
9. (~quiet(alice) | brave(alice)) <=> ? [X0] : strong(X0) [input p8]
10. ! [X0] : ((~old(X0) | ~patient(X0)) => (brave(X0) <~> funny(X0))) [input p9]
13. ! [X0] : ((~tall(X0) | generous(X0)) => tall(X0)) [input p12]
14. ! [X0] : (strong(X0) <=> (kind(X0) & ~generous(X0))) [input p13]
15. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (~kind(X0) <~> ~tall(X0))) [input p14]
16. ! [X0] : ((~funny(X0) | creative(X0)) <=> (humble(X0) & kind(X0))) [input p15]
17. ~quiet(paul) [input p16]
25. ~patient(paul) [input hypothesis]
30. ! [X0] : ((quiet(X0) <~> strong(X0)) | (~brave(X0) <=> ~funny(X0))) [ennf transformation 6]
32. ! [X0] : ((brave(X0) <~> funny(X0)) | (old(X0) & patient(X0))) [ennf transformation 10]
35. ! [X0] : (tall(X0) | (tall(X0) & ~generous(X0))) [ennf transformation 13]
54. ! [X0] : (((~strong(X0) | ~quiet(X0)) & (strong(X0) | quiet(X0))) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) [nnf transformation 30]
61. ((~quiet(alice) | brave(alice)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | (quiet(alice) & ~brave(alice))) [nnf transformation 9]
62. (~quiet(alice) | brave(alice) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | (quiet(alice) & ~brave(alice))) [flattening 61]
63. (~quiet(alice) | brave(alice) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | (quiet(alice) & ~brave(alice))) [rectify 62]
64. ? [X1] : strong(X1) => strong(sK7) [choice axiom]
65. (~quiet(alice) | brave(alice) | ! [X0] : ~strong(X0)) & (strong(sK7) | (quiet(alice) & ~brave(alice))) [skolemisation 63,64]
66. ! [X0] : (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | (old(X0) & patient(X0))) [nnf transformation 32]
71. ! [X0] : ((strong(X0) | (~kind(X0) | generous(X0))) & ((kind(X0) & ~generous(X0)) | ~strong(X0))) [nnf transformation 14]
72. ! [X0] : ((strong(X0) | ~kind(X0) | generous(X0)) & ((kind(X0) & ~generous(X0)) | ~strong(X0))) [flattening 71]
73. ! [X0] : (((~quiet(X0) | ~generous(X0)) | ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | (quiet(X0) & generous(X0)))) [nnf transformation 15]
74. ! [X0] : ((~quiet(X0) | ~generous(X0) | ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | (quiet(X0) & generous(X0)))) [flattening 73]
75. ! [X0] : (((~funny(X0) | creative(X0)) | (~humble(X0) | ~kind(X0))) & ((humble(X0) & kind(X0)) | (funny(X0) & ~creative(X0)))) [nnf transformation 16]
76. ! [X0] : ((~funny(X0) | creative(X0) | ~humble(X0) | ~kind(X0)) & ((humble(X0) & kind(X0)) | (funny(X0) & ~creative(X0)))) [flattening 75]
102. ~funny(X0) | quiet(X0) | strong(X0) | brave(X0) [cnf transformation 54]
114. strong(sK7) | ~brave(alice) [cnf transformation 65]
115. strong(sK7) | quiet(alice) [cnf transformation 65]
116. ~quiet(alice) | brave(alice) | ~strong(X0) [cnf transformation 65]
119. ~funny(X0) | ~brave(X0) | patient(X0) [cnf transformation 66]
129. tall(X0) | tall(X0) [cnf transformation 35]
130. ~strong(X0) | ~generous(X0) [cnf transformation 72]
131. ~strong(X0) | kind(X0) [cnf transformation 72]
133. ~kind(X0) | ~tall(X0) | generous(X0) [cnf transformation 74]
134. ~kind(X0) | ~tall(X0) | quiet(X0) [cnf transformation 74]
140. kind(X0) | funny(X0) [cnf transformation 76]
144. ~quiet(paul) [cnf transformation 17]
154. ~patient(paul) [cnf transformation 25]
155. tall(X0) [duplicate literal removal 129]
200. 11 <=> funny(paul) [avatar definition]
201. funny(paul) <- (11) [avatar component clause 200]
202. ~funny(paul) <- (~11) [avatar component clause 200]
228. 17 <=> ! [X3] : tall(X3) [avatar definition]
229. tall(X3) <- (17) [avatar component clause 228]
278. 29 <=> ! [X0] : ~strong(X0) [avatar definition]
279. ~strong(X0) <- (29) [avatar component clause 278]
281. 30 <=> brave(alice) [avatar definition]
285. 31 <=> quiet(alice) [avatar definition]
288. 29 | 30 | ~31 [avatar split clause 116,285,281,278]
290. 32 <=> strong(sK7) [avatar definition]
292. strong(sK7) <- (32) [avatar component clause 290]
293. 31 | 32 [avatar split clause 115,290,285]
294. ~30 | 32 [avatar split clause 114,290,281]
300. 34 <=> brave(paul) [avatar definition]
302. ~brave(paul) <- (~34) [avatar component clause 300]
334. 17 [avatar split clause 155,228]
482. ~brave(paul) | patient(paul) <- (11) [resolution 119,201]
485. ~brave(paul) <- (11) [subsumption resolution 482,154]
486. ~34 | ~11 [avatar split clause 485,200,300]
513. ~tall(X1) | quiet(X1) | funny(X1) [resolution 134,140]
514. quiet(X1) | funny(X1) <- (17) [subsumption resolution 513,229]
532. quiet(paul) | strong(paul) | brave(paul) <- (11) [resolution 102,201]
537. strong(paul) | brave(paul) <- (11) [subsumption resolution 532,144]
538. brave(paul) <- (11, 29) [subsumption resolution 537,279]
539. $false <- (11, 29, ~34) [subsumption resolution 538,302]
540. ~11 | ~29 | 34 [avatar contradiction clause 539]
577. kind(sK7) <- (32) [resolution 292,131]
578. ~generous(sK7) <- (32) [resolution 292,130]
615. ~tall(sK7) | generous(sK7) <- (32) [resolution 577,133]
619. generous(sK7) <- (17, 32) [subsumption resolution 615,229]
620. $false <- (17, 32) [subsumption resolution 619,578]
621. ~17 | ~32 [avatar contradiction clause 620]
686. funny(paul) <- (17) [resolution 514,144]
690. $false <- (~11, 17) [subsumption resolution 686,202]
691. 11 | ~17 [avatar contradiction clause 690]
694. $false [avatar sat refutation 288,293,294,334,486,540,621,691]
% SZS output end Proof for 1031813016770346419888027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If john is kind then john is both old and not rich and vice versa.
If susan is both calm and tall then alice is wise.
If someone is not calm then someone is not curious or wise and vice versa.
Everyone who is both not calm and quiet is both not rich and rich.
Everyone who is either curious or calm is both strong and creative.
If someone is old or tall then alice is either not generous or not funny.
Everyone who is not calm or not funny is either creative or not generous and vice versa.
Everyone who is not wise or not rich is both not old and kind and vice versa.
If fred is strong then someone is old or creative and vice versa.
Everyone who is calm is both calm and not happy.
If paul is either creative or funny then someone is either kind or rich and vice versa.
If someone is happy then someone is tall.
Everyone who is either not old or rich is both not happy and not old and vice versa.
Everyone who is not curious is calm or kind.
If lucy is both not brave and patient then someone is both kind and generous.
If paul is either not patient or not old then someone is both kind and not strong.
Someone is humble.
Someone is kind.
Mary is either not tall or quiet.
Someone is either funny or not strong.
Someone is both happy and not tall.
Paul is patient or kind.
Someone is kind or not happy. | John is not calm. | entailment | ((kind(john))<=>((old(john)&~rich(john))))&
(((calm(susan)&tall(susan)))=>(wise(alice)))&
((?[X]:(~calm(X)))<=>(?[X]:((~curious(X)|wise(X)))))&
(![X]:((~calm(X)&quiet(X))=>(~rich(X)&rich(X))))&
(![X]:((curious(X)<~>calm(X))=>(strong(X)&creative(X))))&
((?[X]:((old(X)|tall(X))))=>((~generous(alice)<~>~funny(alice))))&
(![X]:((~calm(X)|~funny(X))<=>(creative(X)<~>~generous(X))))&
(![X]:((~wise(X)|~rich(X))<=>(~old(X)&kind(X))))&
((strong(fred))<=>(?[X]:((old(X)|creative(X)))))&
(![X]:(calm(X)=>(calm(X)&~happy(X))))&
(((creative(paul)<~>funny(paul)))<=>(?[X]:((kind(X)<~>rich(X)))))&
((?[X]:(happy(X)))=>(?[X]:(tall(X))))&
(![X]:((~old(X)<~>rich(X))<=>(~happy(X)&~old(X))))&
(![X]:(~curious(X)=>(calm(X)|kind(X))))&
(((~brave(lucy)&patient(lucy)))=>(?[X]:((kind(X)&generous(X)))))&
(((~patient(paul)<~>~old(paul)))=>(?[X]:((kind(X)&~strong(X)))))&
(?[X]:(humble(X)))&
(?[X]:(kind(X)))&
((~tall(mary)<~>quiet(mary)))&
(?[X]:((funny(X)<~>~strong(X))))&
(?[X]:((happy(X)&~tall(X))))&
((patient(paul)|kind(paul)))&
(?[X]:((kind(X)|~happy(X)))) | ~calm(john) | [
"p0",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2414561918600246636310342
% SZS output start Proof for 2414561918600246636310342
1. kind(john) <=> (~rich(john) & old(john)) [input p0]
8. ! [X0] : ((~rich(X0) | ~wise(X0)) <=> (kind(X0) & ~old(X0))) [input p7]
10. ! [X0] : (calm(X0) => (~happy(X0) & calm(X0))) [input p9]
13. ! [X0] : ((~old(X0) <~> rich(X0)) <=> (~old(X0) & ~happy(X0))) [input p12]
24. calm(john) [input hypothesis]
35. ! [X0] : ((~happy(X0) & calm(X0)) | ~calm(X0)) [ennf transformation 10]
40. (kind(john) | (rich(john) | ~old(john))) & ((~rich(john) & old(john)) | ~kind(john)) [nnf transformation 1]
41. (kind(john) | rich(john) | ~old(john)) & ((~rich(john) & old(john)) | ~kind(john)) [flattening 40]
51. ! [X0] : (((~rich(X0) | ~wise(X0)) | (~kind(X0) | old(X0))) & ((kind(X0) & ~old(X0)) | (rich(X0) & wise(X0)))) [nnf transformation 8]
52. ! [X0] : ((~rich(X0) | ~wise(X0) | ~kind(X0) | old(X0)) & ((kind(X0) & ~old(X0)) | (rich(X0) & wise(X0)))) [flattening 51]
64. ! [X0] : ((((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))))) [nnf transformation 13]
65. ! [X0] : ((((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))))) [flattening 64]
79. old(john) | ~kind(john) [cnf transformation 41]
103. ~old(X0) | rich(X0) [cnf transformation 52]
105. rich(X0) | kind(X0) [cnf transformation 52]
111. ~happy(X0) | ~calm(X0) [cnf transformation 35]
124. ~old(X0) | ~old(X0) | ~rich(X0) [cnf transformation 65]
126. ~rich(X0) | old(X0) | old(X0) | happy(X0) [cnf transformation 65]
141. calm(john) [cnf transformation 24]
142. ~old(X0) | ~rich(X0) [duplicate literal removal 124]
143. ~rich(X0) | old(X0) | happy(X0) [duplicate literal removal 126]
145. 1 <=> old(john) [avatar definition]
146. old(john) <- (1) [avatar component clause 145]
153. 3 <=> kind(john) [avatar definition]
158. ~3 | 1 [avatar split clause 79,145,153]
210. 16 <=> ! [X0] : ~old(X0) [avatar definition]
211. ~old(X0) <- (16) [avatar component clause 210]
273. ~old(X0) [subsumption resolution 142,103]
274. 16 [avatar split clause 273,210]
429. old(X0) | happy(X0) | kind(X0) [resolution 143,105]
431. happy(X0) | kind(X0) <- (16) [subsumption resolution 429,211]
458. ~calm(X2) | kind(X2) <- (16) [resolution 431,111]
492. kind(john) <- (16) [resolution 458,141]
495. 3 | ~16 [avatar split clause 492,210,153]
496. $false <- (1, 16) [subsumption resolution 146,211]
497. ~1 | ~16 [avatar contradiction clause 496]
498. $false [avatar sat refutation 158,274,495,497]
% SZS output end Proof for 2414561918600246636310342
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not happy or quiet then someone is not wise or not quiet. Everyone who is not happy or not old is not kind or not patient and vice versa. If fred is not happy or calm then mary is both happy and patient and vice versa. Everyone who is either not funny or patient is both not funny and not curious. If someone is both humble and calm then someone is not calm or quiet and vice versa. Everyone who is both not creative and patient is both not brave and not creative. If someone is quiet then lucy is either creative or humble. If susan is either curious or not happy then someone is both old and kind. If mary is not kind or not happy then alice is wise. Everyone who is either brave or not funny is not kind and vice versa. If someone is both strong and kind then someone is generous or not curious and vice versa. If someone is tall or not tall then paul is not humble and vice versa. Everyone who is either not rich or not generous is not creative and vice versa. Everyone who is not generous or not tall is humble and vice versa. If someone is both curious and not quiet then paul is both not brave and not kind and vice versa. Everyone who is wise or tall is either not tall or not quiet and vice versa. Someone is either not patient or happy. Susan is not curious or tall. Lucy is not quiet. John is not kind or strong. Someone is brave or curious. Someone is humble or not rich. Someone is both rich and strong. | Paul is not quiet. | entailment | (((~happy(paul)|quiet(paul)))=>(?[X]:((~wise(X)|~quiet(X)))))&
(![X]:((~happy(X)|~old(X))<=>(~kind(X)|~patient(X))))&
(((~happy(fred)|calm(fred)))<=>((happy(mary)&patient(mary))))&
(![X]:((~funny(X)<~>patient(X))=>(~funny(X)&~curious(X))))&
((?[X]:((humble(X)&calm(X))))<=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:((~creative(X)&patient(X))=>(~brave(X)&~creative(X))))&
((?[X]:(quiet(X)))=>((creative(lucy)<~>humble(lucy))))&
(((curious(susan)<~>~happy(susan)))=>(?[X]:((old(X)&kind(X)))))&
(((~kind(mary)|~happy(mary)))=>(wise(alice)))&
(![X]:((brave(X)<~>~funny(X))<=>~kind(X)))&
((?[X]:((strong(X)&kind(X))))<=>(?[X]:((generous(X)|~curious(X)))))&
((?[X]:((tall(X)|~tall(X))))<=>(~humble(paul)))&
(![X]:((~rich(X)<~>~generous(X))<=>~creative(X)))&
(![X]:((~generous(X)|~tall(X))<=>humble(X)))&
((?[X]:((curious(X)&~quiet(X))))<=>((~brave(paul)&~kind(paul))))&
(![X]:((wise(X)|tall(X))<=>(~tall(X)<~>~quiet(X))))&
(?[X]:((~patient(X)<~>happy(X))))&
((~curious(susan)|tall(susan)))&
(~quiet(lucy))&
((~kind(john)|strong(john)))&
(?[X]:((brave(X)|curious(X))))&
(?[X]:((humble(X)|~rich(X))))&
(?[X]:((rich(X)&strong(X)))) | ~quiet(paul) | [
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4553293151428624157554578
% SZS output start Proof for 4553293151428624157554578
12. ? [X0] : (~tall(X0) | tall(X0)) <=> ~humble(paul) [input p11]
14. ! [X0] : ((~tall(X0) | ~generous(X0)) <=> humble(X0)) [input p13]
16. ! [X0] : ((tall(X0) | wise(X0)) <=> (~tall(X0) <~> ~quiet(X0))) [input p15]
24. quiet(paul) [input hypothesis]
56. (? [X0] : (~tall(X0) | tall(X0)) | humble(paul)) & (~humble(paul) | ! [X0] : (tall(X0) & ~tall(X0))) [nnf transformation 12]
57. (? [X0] : (~tall(X0) | tall(X0)) | humble(paul)) & (~humble(paul) | ! [X1] : (tall(X1) & ~tall(X1))) [rectify 56]
58. ? [X0] : (~tall(X0) | tall(X0)) => (~tall(sK6) | tall(sK6)) [choice axiom]
59. ((~tall(sK6) | tall(sK6)) | humble(paul)) & (~humble(paul) | ! [X1] : (tall(X1) & ~tall(X1))) [skolemisation 57,58]
61. ! [X0] : (((~tall(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (tall(X0) & generous(X0)))) [nnf transformation 14]
62. ! [X0] : ((~tall(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (tall(X0) & generous(X0)))) [flattening 61]
68. ! [X0] : (((tall(X0) | wise(X0)) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | (~tall(X0) & ~wise(X0)))) [nnf transformation 16]
69. ! [X0] : ((tall(X0) | wise(X0) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | (~tall(X0) & ~wise(X0)))) [flattening 68]
118. ~humble(paul) | ~tall(X1) [cnf transformation 59]
119. ~humble(paul) | tall(X1) [cnf transformation 59]
126. tall(X0) | humble(X0) [cnf transformation 62]
133. ~quiet(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 69]
147. quiet(paul) [cnf transformation 24]
148. ~tall(X0) | ~quiet(X0) [duplicate literal removal 133]
152. 1 <=> quiet(paul) [avatar definition]
153. quiet(paul) <- (1) [avatar component clause 152]
291. 31 <=> ! [X1] : tall(X1) [avatar definition]
292. tall(X1) <- (31) [avatar component clause 291]
294. 32 <=> humble(paul) [avatar definition]
297. 31 | ~32 [avatar split clause 119,294,291]
299. 33 <=> ! [X1] : ~tall(X1) [avatar definition]
300. ~tall(X1) <- (33) [avatar component clause 299]
301. 33 | ~32 [avatar split clause 118,294,299]
367. 1 [avatar split clause 147,152]
379. ~quiet(X0) | humble(X0) [resolution 148,126]
380. humble(paul) <- (1) [resolution 379,153]
383. 32 | ~1 [avatar split clause 380,152,294]
384. $false <- (31, 33) [subsumption resolution 292,300]
385. ~31 | ~33 [avatar contradiction clause 384]
386. $false [avatar sat refutation 297,301,367,383,385]
% SZS output end Proof for 4553293151428624157554578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If fred is quiet then someone is not brave or not creative and vice versa.
If someone is either not rich or calm then someone is either not kind or brave.
Everyone who is both old and not curious is both brave and wise and vice versa.
If someone is either not patient or rich then fred is calm.
Everyone who is not wise is both curious and wise and vice versa.
Everyone who is both generous and curious is not strong or not old and vice versa.
If fred is either not old or not quiet then fred is both not calm and not tall and vice versa.
If someone is rich then someone is both not quiet and not calm and vice versa.
If someone is either not rich or funny then someone is either curious or not rich.
Everyone who is either not strong or patient is either not generous or not strong.
If mary is strong then john is both not kind and not quiet and vice versa.
If mary is calm or quiet then someone is not creative.
Everyone who is both curious and patient is rich.
If someone is strong then someone is both not tall and old.
Everyone who is funny is old.
Someone is creative or not curious.
Someone is funny or not funny.
Someone is either humble or not wise.
Paul is not rich.
Susan is either funny or not curious.
Someone is both not curious and humble. | Susan is not rich. | neutral | ((quiet(fred))<=>(?[X]:((~brave(X)|~creative(X)))))&
((?[X]:((~rich(X)<~>calm(X))))=>(?[X]:((~kind(X)<~>brave(X)))))&
(![X]:((old(X)&~curious(X))<=>(brave(X)&wise(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>(calm(fred)))&
(![X]:(~wise(X)<=>(curious(X)&wise(X))))&
(![X]:((generous(X)&curious(X))<=>(~strong(X)|~old(X))))&
(((~old(fred)<~>~quiet(fred)))<=>((~calm(fred)&~tall(fred))))&
((?[X]:(rich(X)))<=>(?[X]:((~quiet(X)&~calm(X)))))&
((?[X]:((~rich(X)<~>funny(X))))=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:((~strong(X)<~>patient(X))=>(~generous(X)<~>~strong(X))))&
((strong(mary))<=>((~kind(john)&~quiet(john))))&
(((calm(mary)|quiet(mary)))=>(?[X]:(~creative(X))))&
(![X]:((curious(X)&patient(X))=>rich(X)))&
((?[X]:(strong(X)))=>(?[X]:((~tall(X)&old(X)))))&
(![X]:(funny(X)=>old(X)))&
(?[X]:((creative(X)|~curious(X))))&
(?[X]:((funny(X)|~funny(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
(~rich(paul))&
((funny(susan)<~>~curious(susan)))&
(?[X]:((~curious(X)&humble(X)))) | ~rich(susan) | [] | null | 0 |
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.
Everyone who is both calm and humble is both not calm and not creative and vice versa.
If someone is tall or rich then john is either calm or wise and vice versa.
If someone is brave or not kind then someone is humble or not creative and vice versa.
John is not patient or not happy.
Lucy is generous or not generous.
Alice is not happy or not funny.
Someone is either not calm or old. | Fred is not creative. | entailment | ((?[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)))&
(![X]:((calm(X)&humble(X))<=>(~calm(X)&~creative(X))))&
((?[X]:((tall(X)|rich(X))))<=>((calm(john)<~>wise(john))))&
((?[X]:((brave(X)|~kind(X))))<=>(?[X]:((humble(X)|~creative(X)))))&
((~patient(john)|~happy(john)))&
((generous(lucy)|~generous(lucy)))&
((~happy(alice)|~funny(alice)))&
(?[X]:((~calm(X)<~>old(X)))) | ~creative(fred) | [
"p2",
"p6",
"p8",
"p9",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2968364885267859128934780
% SZS output start Proof for 2968364885267859128934780
3. ! [X0] : ((~rich(X0) | creative(X0)) => (~humble(X0) & ~kind(X0))) [input p2]
7. ! [X0] : ((~patient(X0) & ~calm(X0)) <=> (~happy(X0) <~> ~generous(X0))) [input p6]
9. ! [X0] : ((~old(X0) <~> strong(X0)) => strong(X0)) [input p8]
10. ! [X0] : ((happy(X0) | strong(X0)) => kind(X0)) [input p9]
11. ! [X0] : ((rich(X0) <~> ~calm(X0)) <=> (~rich(X0) <~> old(X0))) [input p10]
12. ! [X0] : ((~strong(X0) <~> generous(X0)) <=> humble(X0)) [input p11]
13. ! [X0] : ((humble(X0) & calm(X0)) <=> (~creative(X0) & ~calm(X0))) [input p12]
20. creative(fred) [input hypothesis]
25. ! [X0] : ((~humble(X0) & ~kind(X0)) | (rich(X0) & ~creative(X0))) [ennf transformation 3]
27. ! [X0] : (strong(X0) | (~old(X0) <=> strong(X0))) [ennf transformation 9]
28. ! [X0] : (kind(X0) | (~happy(X0) & ~strong(X0))) [ennf transformation 10]
40. ! [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 7]
41. ! [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 40]
44. ! [X0] : (strong(X0) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0)))) [nnf transformation 27]
45. ! [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 11]
46. ! [X0] : ((((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ~humble(X0)) & (humble(X0) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0))))) [nnf transformation 12]
47. ! [X0] : (((humble(X0) & calm(X0)) | (creative(X0) | calm(X0))) & ((~creative(X0) & ~calm(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 13]
48. ! [X0] : (((humble(X0) & calm(X0)) | creative(X0) | calm(X0)) & ((~creative(X0) & ~calm(X0)) | ~humble(X0) | ~calm(X0))) [flattening 47]
68. ~kind(X0) | ~creative(X0) [cnf transformation 25]
70. ~humble(X0) | ~creative(X0) [cnf transformation 25]
83. ~generous(X0) | ~calm(X0) | happy(X0) [cnf transformation 41]
91. strong(X0) | strong(X0) | old(X0) [cnf transformation 44]
93. ~strong(X0) | kind(X0) [cnf transformation 28]
94. ~happy(X0) | kind(X0) [cnf transformation 28]
98. ~old(X0) | rich(X0) | rich(X0) | calm(X0) [cnf transformation 45]
102. calm(X0) | ~rich(X0) | ~rich(X0) | ~old(X0) [cnf transformation 45]
103. strong(X0) | generous(X0) | humble(X0) [cnf transformation 46]
107. ~calm(X0) | ~humble(X0) | ~calm(X0) [cnf transformation 48]
109. calm(X0) | creative(X0) | calm(X0) [cnf transformation 48]
126. creative(fred) [cnf transformation 20]
127. ~calm(X0) | ~humble(X0) [duplicate literal removal 107]
128. calm(X0) | creative(X0) [duplicate literal removal 109]
130. ~old(X0) | rich(X0) | calm(X0) [duplicate literal removal 98]
132. calm(X0) | ~rich(X0) | ~old(X0) [duplicate literal removal 102]
133. strong(X0) | old(X0) [duplicate literal removal 91]
221. ~old(X0) | calm(X0) [subsumption resolution 130,132]
257. 26 <=> ! [X1] : ~humble(X1) [avatar definition]
258. ~humble(X1) <- (26) [avatar component clause 257]
262. 27 <=> ! [X3] : kind(X3) [avatar definition]
263. kind(X3) <- (27) [avatar component clause 262]
293. creative(X0) | ~humble(X0) [resolution 128,127]
294. ~humble(X0) [subsumption resolution 293,70]
295. 26 [avatar split clause 294,257]
296. old(X0) | kind(X0) [resolution 133,93]
298. calm(X0) | kind(X0) [resolution 296,221]
341. generous(X1) | humble(X1) | kind(X1) [resolution 103,93]
344. generous(X1) | kind(X1) <- (26) [subsumption resolution 341,258]
361. kind(X2) | ~calm(X2) | happy(X2) <- (26) [resolution 344,83]
364. kind(X2) | happy(X2) <- (26) [subsumption resolution 361,298]
365. kind(X2) <- (26) [subsumption resolution 364,94]
366. 27 | ~26 [avatar split clause 365,257,262]
369. ~creative(X1) <- (27) [resolution 263,68]
373. $false <- (27) [resolution 369,126]
374. ~27 [avatar contradiction clause 373]
375. $false [avatar sat refutation 295,366,374]
% SZS output end Proof for 2968364885267859128934780
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If john is not brave then someone is not tall.
If fred is either creative or not calm then someone is quiet.
If someone is kind or tall then john is both not wise and not strong and vice versa.
If someone is not patient then someone is not rich or not calm and vice versa.
Everyone who is not kind or not curious is both creative and not calm and vice versa.
Everyone who is funny is not old.
Everyone who is patient is either not calm or not creative.
Everyone who is not tall is either not strong or not brave.
If lucy is not humble or not patient then lucy is not rich or not wise and vice versa.
Everyone who is strong is either not rich or calm and vice versa.
If alice is not calm or calm then lucy is not rich and vice versa.
If someone is both old and humble then someone is not generous or wise.
Everyone who is happy or calm is both not creative and kind.
Everyone who is both happy and kind is not curious.
Everyone who is kind is either not curious or not creative.
Everyone who is not quiet is calm.
Paul is not curious.
Paul is both generous and not wise.
Fred is not patient.
Someone is both funny and curious.
Alice is funny.
John is not wise or funny.
Mary is not creative. | Mary is not curious. | contradiction | ((~brave(john))=>(?[X]:(~tall(X))))&
(((creative(fred)<~>~calm(fred)))=>(?[X]:(quiet(X))))&
((?[X]:((kind(X)|tall(X))))<=>((~wise(john)&~strong(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((~rich(X)|~calm(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(creative(X)&~calm(X))))&
(![X]:(funny(X)=>~old(X)))&
(![X]:(patient(X)=>(~calm(X)<~>~creative(X))))&
(![X]:(~tall(X)=>(~strong(X)<~>~brave(X))))&
(((~humble(lucy)|~patient(lucy)))<=>((~rich(lucy)|~wise(lucy))))&
(![X]:(strong(X)<=>(~rich(X)<~>calm(X))))&
(((~calm(alice)|calm(alice)))<=>(~rich(lucy)))&
((?[X]:((old(X)&humble(X))))=>(?[X]:((~generous(X)|wise(X)))))&
(![X]:((happy(X)|calm(X))=>(~creative(X)&kind(X))))&
(![X]:((happy(X)&kind(X))=>~curious(X)))&
(![X]:(kind(X)=>(~curious(X)<~>~creative(X))))&
(![X]:(~quiet(X)=>calm(X)))&
(~curious(paul))&
((generous(paul)&~wise(paul)))&
(~patient(fred))&
(?[X]:((funny(X)&curious(X))))&
(funny(alice))&
((~wise(john)|funny(john)))&
(~creative(mary)) | ~curious(mary) | [
"p4",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7608109574332250020660644
% SZS output start Proof for 7608109574332250020660644
5. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> (~calm(X0) & creative(X0))) [input p4]
23. ~creative(mary) [input p22]
24. ~curious(mary) [input hypothesis]
54. ! [X0] : (((~curious(X0) | ~kind(X0)) | (calm(X0) | ~creative(X0))) & ((~calm(X0) & creative(X0)) | (curious(X0) & kind(X0)))) [nnf transformation 5]
55. ! [X0] : ((~curious(X0) | ~kind(X0) | calm(X0) | ~creative(X0)) & ((~calm(X0) & creative(X0)) | (curious(X0) & kind(X0)))) [flattening 54]
76. curious(X0) | creative(X0) [cnf transformation 55]
103. ~creative(mary) [cnf transformation 23]
104. ~curious(mary) [cnf transformation 24]
192. creative(mary) [resolution 76,104]
193. $false [subsumption resolution 192,103]
% SZS output end Proof for 7608109574332250020660644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then someone is not generous and vice versa.
Everyone who is not funny is either not patient or not tall.
Everyone who is either not patient or funny is not happy and vice versa.
If fred is tall or not tall then someone is kind.
If someone is either not patient or not wise then someone is either not calm or not old and vice versa.
If john is tall then someone is old or brave.
Everyone who is not strong or not brave is not humble and vice versa.
If someone is both not happy and not humble then someone is not brave and vice versa.
Everyone who is either not creative or generous is not brave and vice versa.
Everyone who is either not old or strong is both funny and calm and vice versa.
Everyone who is not strong is not funny and vice versa.
Everyone who is not wise is both not creative and not strong and vice versa.
If fred is either not generous or not wise then lucy is both old and not generous and vice versa.
Everyone who is funny or tall is funny and vice versa.
If paul is both not generous and rich then someone is quiet.
Mary is either not patient or not brave.
Someone is patient.
Lucy is not funny or brave.
Someone is either creative or not strong.
Lucy is tall.
Fred is humble. | Mary is happy. | neutral | ((?[X]:(kind(X)))<=>(?[X]:(~generous(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>~tall(X))))&
(![X]:((~patient(X)<~>funny(X))<=>~happy(X)))&
(((tall(fred)|~tall(fred)))=>(?[X]:(kind(X))))&
((?[X]:((~patient(X)<~>~wise(X))))<=>(?[X]:((~calm(X)<~>~old(X)))))&
((tall(john))=>(?[X]:((old(X)|brave(X)))))&
(![X]:((~strong(X)|~brave(X))<=>~humble(X)))&
((?[X]:((~happy(X)&~humble(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~creative(X)<~>generous(X))<=>~brave(X)))&
(![X]:((~old(X)<~>strong(X))<=>(funny(X)&calm(X))))&
(![X]:(~strong(X)<=>~funny(X)))&
(![X]:(~wise(X)<=>(~creative(X)&~strong(X))))&
(((~generous(fred)<~>~wise(fred)))<=>((old(lucy)&~generous(lucy))))&
(![X]:((funny(X)|tall(X))<=>funny(X)))&
(((~generous(paul)&rich(paul)))=>(?[X]:(quiet(X))))&
((~patient(mary)<~>~brave(mary)))&
(?[X]:(patient(X)))&
((~funny(lucy)|brave(lucy)))&
(?[X]:((creative(X)<~>~strong(X))))&
(tall(lucy))&
(humble(fred)) | happy(mary) | [] | null | 0 |
If someone is not wise then someone is not tall. Everyone who is quiet or patient is either not kind or not patient. Everyone who is either not wise or not generous is not rich or calm. Everyone who is both funny and kind is either wise or not rich and vice versa. If someone is both not curious and patient then fred is creative. Everyone who is brave is either humble or not patient. Everyone who is either old or not funny is not curious. Everyone who is both not rich and not wise is not kind and vice versa. If john is not calm then fred is either happy or not generous and vice versa. Everyone who is not funny is not calm or not kind and vice versa. Everyone who is rich is not creative. If someone is patient then someone is tall and vice versa. If john is both calm and not happy then paul is not creative or not strong. Everyone who is not generous or not old is both quiet and not quiet. If someone is not curious then someone is kind or not rich. If john is tall or brave then someone is both not quiet and not tall and vice versa. Alice is both curious and creative. Someone is either not humble or curious. Someone is not generous or quiet. Paul is either funny or not wise. Someone is not tall or humble. Fred is not curious or not calm. | Alice is not tall. | entailment | ((?[X]:(~wise(X)))=>(?[X]:(~tall(X))))&
(![X]:((quiet(X)|patient(X))=>(~kind(X)<~>~patient(X))))&
(![X]:((~wise(X)<~>~generous(X))=>(~rich(X)|calm(X))))&
(![X]:((funny(X)&kind(X))<=>(wise(X)<~>~rich(X))))&
((?[X]:((~curious(X)&patient(X))))=>(creative(fred)))&
(![X]:(brave(X)=>(humble(X)<~>~patient(X))))&
(![X]:((old(X)<~>~funny(X))=>~curious(X)))&
(![X]:((~rich(X)&~wise(X))<=>~kind(X)))&
((~calm(john))<=>((happy(fred)<~>~generous(fred))))&
(![X]:(~funny(X)<=>(~calm(X)|~kind(X))))&
(![X]:(rich(X)=>~creative(X)))&
((?[X]:(patient(X)))<=>(?[X]:(tall(X))))&
(((calm(john)&~happy(john)))=>((~creative(paul)|~strong(paul))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&~quiet(X))))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~rich(X)))))&
(((tall(john)|brave(john)))<=>(?[X]:((~quiet(X)&~tall(X)))))&
((curious(alice)&creative(alice)))&
(?[X]:((~humble(X)<~>curious(X))))&
(?[X]:((~generous(X)|quiet(X))))&
((funny(paul)<~>~wise(paul)))&
(?[X]:((~tall(X)|humble(X))))&
((~curious(fred)|~calm(fred))) | ~tall(alice) | [
"p1",
"p3",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1616174203003057237195858
% SZS output start Proof for 1616174203003057237195858
2. ! [X0] : ((patient(X0) | quiet(X0)) => (~kind(X0) <~> ~patient(X0))) [input p1]
4. ! [X0] : ((kind(X0) & funny(X0)) <=> (wise(X0) <~> ~rich(X0))) [input p3]
8. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> ~kind(X0)) [input p7]
12. ? [X0] : patient(X0) <=> ? [X0] : tall(X0) [input p11]
23. tall(alice) [input hypothesis]
25. ? [X0] : patient(X0) <=> ? [X1] : tall(X1) [rectify 12]
29. ! [X0] : ((~kind(X0) <~> ~patient(X0)) | (~patient(X0) & ~quiet(X0))) [ennf transformation 2]
41. ! [X0] : (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (~patient(X0) & ~quiet(X0))) [nnf transformation 29]
43. ! [X0] : (((kind(X0) & funny(X0)) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0)))) & (((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (~kind(X0) | ~funny(X0)))) [nnf transformation 4]
44. ! [X0] : (((kind(X0) & funny(X0)) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0)))) & (((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | ~kind(X0) | ~funny(X0))) [flattening 43]
47. ! [X0] : (((~wise(X0) & ~rich(X0)) | kind(X0)) & (~kind(X0) | (wise(X0) | rich(X0)))) [nnf transformation 8]
48. ! [X0] : (((~wise(X0) & ~rich(X0)) | kind(X0)) & (~kind(X0) | wise(X0) | rich(X0))) [flattening 47]
52. (? [X0] : patient(X0) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : ~patient(X0)) [nnf transformation 25]
53. (? [X0] : patient(X0) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : ~patient(X3)) [rectify 52]
54. ? [X0] : patient(X0) => patient(sK1) [choice axiom]
55. ? [X2] : tall(X2) => tall(sK2) [choice axiom]
56. (patient(sK1) | ! [X1] : ~tall(X1)) & (tall(sK2) | ! [X3] : ~patient(X3)) [skolemisation 53,55,54]
75. ~patient(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 41]
85. kind(X0) | wise(X0) | rich(X0) [cnf transformation 44]
91. ~kind(X0) | wise(X0) | rich(X0) [cnf transformation 48]
92. ~rich(X0) | kind(X0) [cnf transformation 48]
93. ~wise(X0) | kind(X0) [cnf transformation 48]
103. patient(sK1) | ~tall(X1) [cnf transformation 56]
123. tall(alice) [cnf transformation 23]
124. ~kind(X0) | ~patient(X0) [duplicate literal removal 75]
141. rich(X0) | wise(X0) [subsumption resolution 91,85]
159. 8 <=> ! [X1] : ~tall(X1) [avatar definition]
160. ~tall(X1) <- (8) [avatar component clause 159]
162. 9 <=> patient(sK1) [avatar definition]
164. patient(sK1) <- (9) [avatar component clause 162]
165. 8 | 9 [avatar split clause 103,162,159]
167. 10 <=> ! [X3] : ~patient(X3) [avatar definition]
168. ~patient(X3) <- (10) [avatar component clause 167]
241. $false <- (8) [resolution 160,123]
242. ~8 [avatar contradiction clause 241]
243. $false <- (9, 10) [subsumption resolution 164,168]
244. ~9 | ~10 [avatar contradiction clause 243]
249. wise(X0) | kind(X0) [resolution 141,92]
251. kind(X0) [subsumption resolution 249,93]
252. ~patient(X0) [resolution 251,124]
253. 10 [avatar split clause 252,167]
254. $false [avatar sat refutation 165,242,244,253]
% SZS output end Proof for 1616174203003057237195858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either not funny or not kind then john is calm and vice versa.
Everyone who is not old or not happy is not quiet and vice versa.
Everyone who is not curious or humble is either funny or not funny.
Everyone who is not kind is rich or not calm.
If lucy is both not curious and not tall then paul is either not rich or rich and vice versa.
Everyone who is either rich or funny is not rich or not kind.
If fred is both old and not brave then paul is both not brave and creative and vice versa.
Everyone who is either humble or funny is old or not tall and vice versa.
Everyone who is patient is not generous.
Everyone who is both not wise and not funny is funny or not brave.
If susan is not happy then someone is either kind or not generous.
If mary is creative or patient then mary is not brave and vice versa.
Everyone who is either not happy or not strong is not happy or quiet and vice versa.
If someone is humble then someone is either funny or not wise and vice versa.
If lucy is kind or rich then mary is curious and vice versa.
Everyone who is tall or brave is either wise or not quiet and vice versa.
Alice is both not kind and not calm.
Someone is both calm and wise.
Fred is either rich or not brave.
Paul is not funny.
Lucy is either not creative or not rich.
Alice is both not rich and not humble.
Paul is either strong or happy.
Someone is either curious or not quiet. | John is not wise. | neutral | (((~funny(susan)<~>~kind(susan)))<=>(calm(john)))&
(![X]:((~old(X)|~happy(X))<=>~quiet(X)))&
(![X]:((~curious(X)|humble(X))=>(funny(X)<~>~funny(X))))&
(![X]:(~kind(X)=>(rich(X)|~calm(X))))&
(((~curious(lucy)&~tall(lucy)))<=>((~rich(paul)<~>rich(paul))))&
(![X]:((rich(X)<~>funny(X))=>(~rich(X)|~kind(X))))&
(((old(fred)&~brave(fred)))<=>((~brave(paul)&creative(paul))))&
(![X]:((humble(X)<~>funny(X))<=>(old(X)|~tall(X))))&
(![X]:(patient(X)=>~generous(X)))&
(![X]:((~wise(X)&~funny(X))=>(funny(X)|~brave(X))))&
((~happy(susan))=>(?[X]:((kind(X)<~>~generous(X)))))&
(((creative(mary)|patient(mary)))<=>(~brave(mary)))&
(![X]:((~happy(X)<~>~strong(X))<=>(~happy(X)|quiet(X))))&
((?[X]:(humble(X)))<=>(?[X]:((funny(X)<~>~wise(X)))))&
(((kind(lucy)|rich(lucy)))<=>(curious(mary)))&
(![X]:((tall(X)|brave(X))<=>(wise(X)<~>~quiet(X))))&
((~kind(alice)&~calm(alice)))&
(?[X]:((calm(X)&wise(X))))&
((rich(fred)<~>~brave(fred)))&
(~funny(paul))&
((~creative(lucy)<~>~rich(lucy)))&
((~rich(alice)&~humble(alice)))&
((strong(paul)<~>happy(paul)))&
(?[X]:((curious(X)<~>~quiet(X)))) | ~wise(john) | [] | null | 0 |
If someone is calm then paul is both not rich and happy and vice versa. Everyone who is not kind is not curious. If someone is either patient or not humble then someone is either humble or not strong. If mary is not calm or creative then john is not brave or not rich. If susan is both funny and not funny then someone is either not curious or creative. Everyone who is creative or not creative is either not rich or old and vice versa. If mary is wise or not funny then fred is either brave or old. Everyone who is not brave or creative is both rich and not happy and vice versa. Everyone who is both brave and strong is either not tall or not quiet and vice versa. Everyone who is either not calm or old is not strong or wise and vice versa. Everyone who is not patient is not calm. Everyone who is not brave is either not patient or generous. If someone is either not creative or not old then john is wise. Everyone who is calm or happy is humble and vice versa. If lucy is creative or kind then paul is both not wise and not strong. Everyone who is not happy is both generous and not funny. Someone is both creative and not funny. Susan is either not brave or not tall. John is kind. Fred is either not tall or tall. John is either rich or not patient. Susan is tall or not brave. Fred is not rich or not quiet. | John is brave. | neutral | ((?[X]:(calm(X)))<=>((~rich(paul)&happy(paul))))&
(![X]:(~kind(X)=>~curious(X)))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((humble(X)<~>~strong(X)))))&
(((~calm(mary)|creative(mary)))=>((~brave(john)|~rich(john))))&
(((funny(susan)&~funny(susan)))=>(?[X]:((~curious(X)<~>creative(X)))))&
(![X]:((creative(X)|~creative(X))<=>(~rich(X)<~>old(X))))&
(((wise(mary)|~funny(mary)))=>((brave(fred)<~>old(fred))))&
(![X]:((~brave(X)|creative(X))<=>(rich(X)&~happy(X))))&
(![X]:((brave(X)&strong(X))<=>(~tall(X)<~>~quiet(X))))&
(![X]:((~calm(X)<~>old(X))<=>(~strong(X)|wise(X))))&
(![X]:(~patient(X)=>~calm(X)))&
(![X]:(~brave(X)=>(~patient(X)<~>generous(X))))&
((?[X]:((~creative(X)<~>~old(X))))=>(wise(john)))&
(![X]:((calm(X)|happy(X))<=>humble(X)))&
(((creative(lucy)|kind(lucy)))=>((~wise(paul)&~strong(paul))))&
(![X]:(~happy(X)=>(generous(X)&~funny(X))))&
(?[X]:((creative(X)&~funny(X))))&
((~brave(susan)<~>~tall(susan)))&
(kind(john))&
((~tall(fred)<~>tall(fred)))&
((rich(john)<~>~patient(john)))&
((tall(susan)|~brave(susan)))&
((~rich(fred)|~quiet(fred))) | brave(john) | [] | null | 0 |
If someone is both tall and happy then someone is not strong.
If alice is either funny or curious then mary is curious.
Everyone who is brave or kind is strong or happy and vice versa.
Everyone who is not humble or not tall is either not generous or not creative and vice versa.
Everyone who is both wise and not funny is both curious and not old and vice versa.
If john is both wise and not happy then alice is not funny or old and vice versa.
Everyone who is both not curious and tall is both funny and old and vice versa.
If someone is either not quiet or not humble then someone is either kind or creative.
If mary is funny then someone is both creative and quiet and vice versa.
Everyone who is either not patient or rich is both kind and calm and vice versa.
If someone is either humble or not humble then someone is either not humble or not creative.
If lucy is both not curious and not patient then someone is not brave or not funny.
Everyone who is either not wise or wise is not generous and vice versa.
Everyone who is not tall is either not humble or kind and vice versa.
Everyone who is not quiet or brave is both not curious and not strong.
Everyone who is kind is either not tall or not kind and vice versa.
Someone is both not calm and not happy.
Someone is either not calm or not tall.
Someone is both not curious and brave.
Someone is both humble and brave.
Alice is both rich and not happy.
Someone is brave.
Paul is not curious. | Lucy is rich. | neutral | ((?[X]:((tall(X)&happy(X))))=>(?[X]:(~strong(X))))&
(((funny(alice)<~>curious(alice)))=>(curious(mary)))&
(![X]:((brave(X)|kind(X))<=>(strong(X)|happy(X))))&
(![X]:((~humble(X)|~tall(X))<=>(~generous(X)<~>~creative(X))))&
(![X]:((wise(X)&~funny(X))<=>(curious(X)&~old(X))))&
(((wise(john)&~happy(john)))<=>((~funny(alice)|old(alice))))&
(![X]:((~curious(X)&tall(X))<=>(funny(X)&old(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>(?[X]:((kind(X)<~>creative(X)))))&
((funny(mary))<=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~patient(X)<~>rich(X))<=>(kind(X)&calm(X))))&
((?[X]:((humble(X)<~>~humble(X))))=>(?[X]:((~humble(X)<~>~creative(X)))))&
(((~curious(lucy)&~patient(lucy)))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((~wise(X)<~>wise(X))<=>~generous(X)))&
(![X]:(~tall(X)<=>(~humble(X)<~>kind(X))))&
(![X]:((~quiet(X)|brave(X))=>(~curious(X)&~strong(X))))&
(![X]:(kind(X)<=>(~tall(X)<~>~kind(X))))&
(?[X]:((~calm(X)&~happy(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:((humble(X)&brave(X))))&
((rich(alice)&~happy(alice)))&
(?[X]:(brave(X)))&
(~curious(paul)) | rich(lucy) | [] | null | 0 |
Everyone who is wise or not patient is not kind and vice versa.
Everyone who is not patient is not calm and vice versa.
Everyone who is humble is both tall and humble.
Everyone who is not tall is funny or not calm and vice versa.
Everyone who is either kind or not strong is either creative or not patient and vice versa.
Everyone who is either wise or not creative is either not humble or strong and vice versa.
If someone is both tall and funny then someone is not brave or not patient and vice versa.
Everyone who is patient is both rich and not strong.
If someone is either rich or not tall then someone is generous.
Everyone who is happy or not brave is not tall.
Everyone who is both not creative and not calm is both not wise and calm and vice versa.
Everyone who is not wise is either not happy or generous and vice versa.
If susan is either not quiet or happy then mary is not brave or not tall and vice versa.
If someone is kind or old then someone is not funny or humble and vice versa.
If someone is either brave or curious then someone is happy.
Everyone who is happy is both not old and calm.
Someone is either strong or not humble.
Fred is rich.
Lucy is either rich or happy.
John is both wise and calm.
Paul is both not quiet and tall.
Someone is either patient or not creative.
Someone is not tall. | Paul is not creative. | contradiction | (![X]:((wise(X)|~patient(X))<=>~kind(X)))&
(![X]:(~patient(X)<=>~calm(X)))&
(![X]:(humble(X)=>(tall(X)&humble(X))))&
(![X]:(~tall(X)<=>(funny(X)|~calm(X))))&
(![X]:((kind(X)<~>~strong(X))<=>(creative(X)<~>~patient(X))))&
(![X]:((wise(X)<~>~creative(X))<=>(~humble(X)<~>strong(X))))&
((?[X]:((tall(X)&funny(X))))<=>(?[X]:((~brave(X)|~patient(X)))))&
(![X]:(patient(X)=>(rich(X)&~strong(X))))&
((?[X]:((rich(X)<~>~tall(X))))=>(?[X]:(generous(X))))&
(![X]:((happy(X)|~brave(X))=>~tall(X)))&
(![X]:((~creative(X)&~calm(X))<=>(~wise(X)&calm(X))))&
(![X]:(~wise(X)<=>(~happy(X)<~>generous(X))))&
(((~quiet(susan)<~>happy(susan)))<=>((~brave(mary)|~tall(mary))))&
((?[X]:((kind(X)|old(X))))<=>(?[X]:((~funny(X)|humble(X)))))&
((?[X]:((brave(X)<~>curious(X))))=>(?[X]:(happy(X))))&
(![X]:(happy(X)=>(~old(X)&calm(X))))&
(?[X]:((strong(X)<~>~humble(X))))&
(rich(fred))&
((rich(lucy)<~>happy(lucy)))&
((wise(john)&calm(john)))&
((~quiet(paul)&tall(paul)))&
(?[X]:((patient(X)<~>~creative(X))))&
(?[X]:(~tall(X))) | ~creative(paul) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4846639428192546527877944
% SZS output start Proof for 4846639428192546527877944
1. ! [X0] : ((~patient(X0) | wise(X0)) <=> ~kind(X0)) [input p0]
2. ! [X0] : (~patient(X0) <=> ~calm(X0)) [input p1]
4. ! [X0] : (~tall(X0) <=> (~calm(X0) | funny(X0))) [input p3]
5. ! [X0] : ((kind(X0) <~> ~strong(X0)) <=> (creative(X0) <~> ~patient(X0))) [input p4]
7. ? [X0] : (funny(X0) & tall(X0)) <=> ? [X0] : (~patient(X0) | ~brave(X0)) [input p6]
8. ! [X0] : (patient(X0) => (~strong(X0) & rich(X0))) [input p7]
11. ! [X0] : ((~calm(X0) & ~creative(X0)) <=> (calm(X0) & ~wise(X0))) [input p10]
24. ~creative(paul) [input hypothesis]
25. ? [X0] : (funny(X0) & tall(X0)) <=> ? [X1] : (~patient(X1) | ~brave(X1)) [rectify 7]
30. ! [X0] : ((~strong(X0) & rich(X0)) | ~patient(X0)) [ennf transformation 8]
35. ! [X0] : (((~patient(X0) | wise(X0)) | kind(X0)) & (~kind(X0) | (patient(X0) & ~wise(X0)))) [nnf transformation 1]
36. ! [X0] : ((~patient(X0) | wise(X0) | kind(X0)) & (~kind(X0) | (patient(X0) & ~wise(X0)))) [flattening 35]
37. ! [X0] : ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0))) [nnf transformation 2]
38. ! [X0] : ((~tall(X0) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | tall(X0))) [nnf transformation 4]
39. ! [X0] : ((~tall(X0) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | tall(X0))) [flattening 38]
40. ! [X0] : ((((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0))))) [nnf transformation 5]
42. (? [X0] : (funny(X0) & tall(X0)) | ! [X1] : (patient(X1) & brave(X1))) & (? [X1] : (~patient(X1) | ~brave(X1)) | ! [X0] : (~funny(X0) | ~tall(X0))) [nnf transformation 25]
43. (? [X0] : (funny(X0) & tall(X0)) | ! [X1] : (patient(X1) & brave(X1))) & (? [X2] : (~patient(X2) | ~brave(X2)) | ! [X3] : (~funny(X3) | ~tall(X3))) [rectify 42]
44. ? [X0] : (funny(X0) & tall(X0)) => (funny(sK0) & tall(sK0)) [choice axiom]
45. ? [X2] : (~patient(X2) | ~brave(X2)) => (~patient(sK1) | ~brave(sK1)) [choice axiom]
46. ((funny(sK0) & tall(sK0)) | ! [X1] : (patient(X1) & brave(X1))) & ((~patient(sK1) | ~brave(sK1)) | ! [X3] : (~funny(X3) | ~tall(X3))) [skolemisation 43,45,44]
51. ! [X0] : (((~calm(X0) & ~creative(X0)) | (~calm(X0) | wise(X0))) & ((calm(X0) & ~wise(X0)) | (calm(X0) | creative(X0)))) [nnf transformation 11]
52. ! [X0] : (((~calm(X0) & ~creative(X0)) | ~calm(X0) | wise(X0)) & ((calm(X0) & ~wise(X0)) | calm(X0) | creative(X0))) [flattening 51]
74. ~kind(X0) | ~wise(X0) [cnf transformation 36]
78. ~patient(X0) | calm(X0) [cnf transformation 37]
82. ~funny(X0) | ~tall(X0) [cnf transformation 39]
85. ~patient(X0) | creative(X0) | kind(X0) | strong(X0) [cnf transformation 40]
102. tall(sK0) | patient(X1) [cnf transformation 46]
104. funny(sK0) | patient(X1) [cnf transformation 46]
106. ~strong(X0) | ~patient(X0) [cnf transformation 30]
114. ~calm(X0) | ~calm(X0) | wise(X0) [cnf transformation 52]
145. ~creative(paul) [cnf transformation 24]
147. ~calm(X0) | wise(X0) [duplicate literal removal 114]
153. 1 <=> ! [X1] : patient(X1) [avatar definition]
154. patient(X1) <- (1) [avatar component clause 153]
156. 2 <=> funny(sK0) [avatar definition]
158. funny(sK0) <- (2) [avatar component clause 156]
159. 1 | 2 [avatar split clause 104,156,153]
165. 4 <=> tall(sK0) [avatar definition]
167. tall(sK0) <- (4) [avatar component clause 165]
168. 1 | 4 [avatar split clause 102,165,153]
286. ~tall(sK0) <- (2) [resolution 82,158]
287. $false <- (2, 4) [subsumption resolution 286,167]
288. ~2 | ~4 [avatar contradiction clause 287]
290. calm(X0) <- (1) [resolution 154,78]
305. wise(X0) <- (1) [resolution 147,290]
367. creative(X0) | kind(X0) | strong(X0) <- (1) [resolution 85,154]
427. kind(paul) | strong(paul) <- (1) [resolution 367,145]
441. 40 <=> strong(paul) [avatar definition]
443. strong(paul) <- (40) [avatar component clause 441]
445. 41 <=> kind(paul) [avatar definition]
447. kind(paul) <- (41) [avatar component clause 445]
448. 40 | 41 | ~1 [avatar split clause 427,153,445,441]
451. ~wise(paul) <- (41) [resolution 447,74]
452. $false <- (1, 41) [subsumption resolution 451,305]
453. ~1 | ~41 [avatar contradiction clause 452]
458. ~patient(paul) <- (40) [resolution 443,106]
461. $false <- (1, 40) [subsumption resolution 458,154]
462. ~1 | ~40 [avatar contradiction clause 461]
463. $false [avatar sat refutation 159,168,288,448,453,462]
% SZS output end Proof for 4846639428192546527877944
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not tall is old and vice versa. If mary is either rich or not wise then susan is either not generous or not wise and vice versa. If someone is not brave or not generous then someone is not wise or not rich and vice versa. Everyone who is both creative and not tall is not quiet or not generous. If susan is both happy and not tall then alice is rich and vice versa. If someone is not creative or not wise then lucy is both not curious and patient. If paul is either not funny or not kind then paul is rich or not creative. Everyone who is tall or not happy is either curious or wise and vice versa. Everyone who is both not creative and wise is strong and vice versa. Everyone who is not funny or not happy is both not rich and not strong and vice versa. Everyone who is not patient or not quiet is old or calm and vice versa. Everyone who is happy is both funny and not old. Everyone who is humble is either strong or not patient. Everyone who is either not happy or brave is not old or funny and vice versa. Everyone who is either brave or not old is wise or kind and vice versa. Everyone who is either funny or creative is both rich and humble and vice versa. John is both not old and creative. Someone is either not curious or not quiet. Someone is both not wise and quiet. Someone is not rich or tall. Lucy is not old. Alice is not brave or not creative. Fred is both not funny and brave. | Fred is not curious. | contradiction | (![X]:((~calm(X)&~tall(X))<=>old(X)))&
(((rich(mary)<~>~wise(mary)))<=>((~generous(susan)<~>~wise(susan))))&
((?[X]:((~brave(X)|~generous(X))))<=>(?[X]:((~wise(X)|~rich(X)))))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~tall(susan)))<=>(rich(alice)))&
((?[X]:((~creative(X)|~wise(X))))=>((~curious(lucy)&patient(lucy))))&
(((~funny(paul)<~>~kind(paul)))=>((rich(paul)|~creative(paul))))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)&wise(X))<=>strong(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(old(X)|calm(X))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
(![X]:((funny(X)<~>creative(X))<=>(rich(X)&humble(X))))&
((~old(john)&creative(john)))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:((~wise(X)&quiet(X))))&
(?[X]:((~rich(X)|tall(X))))&
(~old(lucy))&
((~brave(alice)|~creative(alice)))&
((~funny(fred)&brave(fred))) | ~curious(fred) | [
"p7",
"p8",
"p9",
"p11",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6462259659405498640475446
% SZS output start Proof for 6462259659405498640475446
8. ! [X0] : ((~happy(X0) | tall(X0)) <=> (curious(X0) <~> wise(X0))) [input p7]
9. ! [X0] : ((wise(X0) & ~creative(X0)) <=> strong(X0)) [input p8]
10. ! [X0] : ((~happy(X0) | ~funny(X0)) <=> (~strong(X0) & ~rich(X0))) [input p9]
12. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p11]
16. ! [X0] : ((funny(X0) <~> creative(X0)) <=> (humble(X0) & rich(X0))) [input p15]
23. brave(fred) & ~funny(fred) [input p22]
24. ~curious(fred) [input hypothesis]
31. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 12]
44. ! [X0] : (((~happy(X0) | tall(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (happy(X0) & ~tall(X0)))) [nnf transformation 8]
45. ! [X0] : ((~happy(X0) | tall(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (happy(X0) & ~tall(X0)))) [flattening 44]
46. ! [X0] : (((wise(X0) & ~creative(X0)) | ~strong(X0)) & (strong(X0) | (~wise(X0) | creative(X0)))) [nnf transformation 9]
47. ! [X0] : (((wise(X0) & ~creative(X0)) | ~strong(X0)) & (strong(X0) | ~wise(X0) | creative(X0))) [flattening 46]
48. ! [X0] : (((~happy(X0) | ~funny(X0)) | (strong(X0) | rich(X0))) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [nnf transformation 10]
49. ! [X0] : ((~happy(X0) | ~funny(X0) | strong(X0) | rich(X0)) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [flattening 48]
57. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~humble(X0) | ~rich(X0))) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 16]
58. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ~humble(X0) | ~rich(X0)) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [flattening 57]
92. curious(X0) | wise(X0) | happy(X0) [cnf transformation 45]
97. ~wise(X0) | strong(X0) | creative(X0) [cnf transformation 47]
100. ~rich(X0) | funny(X0) [cnf transformation 49]
102. ~strong(X0) | funny(X0) [cnf transformation 49]
109. ~happy(X0) | funny(X0) [cnf transformation 31]
126. rich(X0) | funny(X0) | ~creative(X0) [cnf transformation 58]
140. ~funny(fred) [cnf transformation 23]
142. ~curious(fred) [cnf transformation 24]
250. ~creative(X0) | funny(X0) [subsumption resolution 126,100]
302. wise(fred) | happy(fred) [resolution 92,142]
305. 33 <=> happy(fred) [avatar definition]
307. happy(fred) <- (33) [avatar component clause 305]
309. 34 <=> wise(fred) [avatar definition]
311. wise(fred) <- (34) [avatar component clause 309]
312. 33 | 34 [avatar split clause 302,309,305]
353. funny(fred) <- (33) [resolution 307,109]
354. $false <- (33) [subsumption resolution 353,140]
355. ~33 [avatar contradiction clause 354]
356. strong(fred) | creative(fred) <- (34) [resolution 311,97]
358. 40 <=> creative(fred) [avatar definition]
360. creative(fred) <- (40) [avatar component clause 358]
362. 41 <=> strong(fred) [avatar definition]
364. strong(fred) <- (41) [avatar component clause 362]
365. 40 | 41 | ~34 [avatar split clause 356,309,362,358]
428. funny(fred) <- (40) [resolution 360,250]
429. $false <- (40) [subsumption resolution 428,140]
430. ~40 [avatar contradiction clause 429]
434. funny(fred) <- (41) [resolution 364,102]
439. $false <- (41) [subsumption resolution 434,140]
440. ~41 [avatar contradiction clause 439]
441. $false [avatar sat refutation 312,355,365,430,440]
% SZS output end Proof for 6462259659405498640475446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not strong is both patient and humble. If someone is funny or not generous then someone is not tall or brave. If someone is not quiet or not calm then someone is quiet and vice versa. If someone is either rich or curious then john is not curious. Everyone who is rich is both old and not quiet and vice versa. Everyone who is either not curious or curious is both not funny and not strong. Everyone who is creative or not kind is humble and vice versa. If someone is both not humble and not quiet then someone is either rich or strong and vice versa. If lucy is both happy and not humble then paul is both not happy and happy and vice versa. Everyone who is either not generous or not strong is rich. Everyone who is both old and not quiet is kind. Everyone who is both patient and not tall is old. Everyone who is either not wise or curious is either rich or not generous and vice versa. Everyone who is either curious or not humble is not rich. Everyone who is both not humble and not kind is kind. John is either not curious or kind. Lucy is generous. Susan is funny or not kind. Someone is not wise. Fred is both not strong and not calm. Susan is either not old or not kind. | Paul is brave. | neutral | (![X]:((~tall(X)<~>~strong(X))=>(patient(X)&humble(X))))&
((?[X]:((funny(X)|~generous(X))))=>(?[X]:((~tall(X)|brave(X)))))&
((?[X]:((~quiet(X)|~calm(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((rich(X)<~>curious(X))))=>(~curious(john)))&
(![X]:(rich(X)<=>(old(X)&~quiet(X))))&
(![X]:((~curious(X)<~>curious(X))=>(~funny(X)&~strong(X))))&
(![X]:((creative(X)|~kind(X))<=>humble(X)))&
((?[X]:((~humble(X)&~quiet(X))))<=>(?[X]:((rich(X)<~>strong(X)))))&
(((happy(lucy)&~humble(lucy)))<=>((~happy(paul)&happy(paul))))&
(![X]:((~generous(X)<~>~strong(X))=>rich(X)))&
(![X]:((old(X)&~quiet(X))=>kind(X)))&
(![X]:((patient(X)&~tall(X))=>old(X)))&
(![X]:((~wise(X)<~>curious(X))<=>(rich(X)<~>~generous(X))))&
(![X]:((curious(X)<~>~humble(X))=>~rich(X)))&
(![X]:((~humble(X)&~kind(X))=>kind(X)))&
((~curious(john)<~>kind(john)))&
(generous(lucy))&
((funny(susan)|~kind(susan)))&
(?[X]:(~wise(X)))&
((~strong(fred)&~calm(fred)))&
((~old(susan)<~>~kind(susan))) | brave(paul) | [] | null | 0 |
Everyone who is wise is not tall or funny and vice versa.
If someone is not wise or brave then someone is not strong or rich.
If someone is either kind or wise then fred is not brave and vice versa.
If mary is both happy and not kind then someone is not patient or brave and vice versa.
If someone is either curious or calm then john is not curious or rich.
If susan is either strong or old then john is patient and vice versa.
Everyone who is both generous and not calm is funny or tall.
Everyone who is both calm and strong is not patient and vice versa.
If someone is tall then fred is generous or brave.
Everyone who is either not wise or not brave is either not wise or not generous and vice versa.
If someone is quiet then someone is not strong or generous.
If someone is not generous or not funny then someone is either humble or brave and vice versa.
Everyone who is not tall is curious or not old.
Everyone who is not calm is both not rich and not curious.
If someone is both not old and curious then someone is either not funny or generous.
If someone is not calm then someone is not patient.
Someone is not curious.
Fred is not curious or not generous.
Someone is both not creative and calm.
Someone is both patient and not happy.
Fred is either kind or wise.
Someone is either not tall or not generous.
Fred is either funny or wise.
Someone is either wise or not calm. | Fred is curious. | neutral | (![X]:(wise(X)<=>(~tall(X)|funny(X))))&
((?[X]:((~wise(X)|brave(X))))=>(?[X]:((~strong(X)|rich(X)))))&
((?[X]:((kind(X)<~>wise(X))))<=>(~brave(fred)))&
(((happy(mary)&~kind(mary)))<=>(?[X]:((~patient(X)|brave(X)))))&
((?[X]:((curious(X)<~>calm(X))))=>((~curious(john)|rich(john))))&
(((strong(susan)<~>old(susan)))<=>(patient(john)))&
(![X]:((generous(X)&~calm(X))=>(funny(X)|tall(X))))&
(![X]:((calm(X)&strong(X))<=>~patient(X)))&
((?[X]:(tall(X)))=>((generous(fred)|brave(fred))))&
(![X]:((~wise(X)<~>~brave(X))<=>(~wise(X)<~>~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~strong(X)|generous(X)))))&
((?[X]:((~generous(X)|~funny(X))))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~tall(X)=>(curious(X)|~old(X))))&
(![X]:(~calm(X)=>(~rich(X)&~curious(X))))&
((?[X]:((~old(X)&curious(X))))=>(?[X]:((~funny(X)<~>generous(X)))))&
((?[X]:(~calm(X)))=>(?[X]:(~patient(X))))&
(?[X]:(~curious(X)))&
((~curious(fred)|~generous(fred)))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>wise(fred)))&
(?[X]:((~tall(X)<~>~generous(X))))&
((funny(fred)<~>wise(fred)))&
(?[X]:((wise(X)<~>~calm(X)))) | curious(fred) | [] | null | 0 |
Everyone who is not funny is curious or not tall. Everyone who is either not calm or rich is wise and vice versa. If susan is not generous then fred is both tall and not curious. If lucy is not generous then john is both not brave and creative. If paul is patient then someone is humble or patient and vice versa. Everyone who is generous is either not kind or not generous and vice versa. Everyone who is rich or wise is both brave and rich. Everyone who is either creative or not creative is not old or funny. If fred is both not tall and not humble then someone is brave or not rich and vice versa. Everyone who is both humble and funny is not funny or calm and vice versa. If someone is both calm and not funny then fred is patient or not generous and vice versa. Everyone who is not brave or not calm is curious and vice versa. Everyone who is both creative and not brave is either not tall or not humble. If mary is funny or not kind then someone is funny or not strong and vice versa. Someone is creative or not calm. Someone is either not patient or not creative. Lucy is curious or not calm. Someone is curious. Someone is calm. Someone is not brave. | Paul is not kind. | entailment | (![X]:(~funny(X)=>(curious(X)|~tall(X))))&
(![X]:((~calm(X)<~>rich(X))<=>wise(X)))&
((~generous(susan))=>((tall(fred)&~curious(fred))))&
((~generous(lucy))=>((~brave(john)&creative(john))))&
((patient(paul))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:(generous(X)<=>(~kind(X)<~>~generous(X))))&
(![X]:((rich(X)|wise(X))=>(brave(X)&rich(X))))&
(![X]:((creative(X)<~>~creative(X))=>(~old(X)|funny(X))))&
(((~tall(fred)&~humble(fred)))<=>(?[X]:((brave(X)|~rich(X)))))&
(![X]:((humble(X)&funny(X))<=>(~funny(X)|calm(X))))&
((?[X]:((calm(X)&~funny(X))))<=>((patient(fred)|~generous(fred))))&
(![X]:((~brave(X)|~calm(X))<=>curious(X)))&
(![X]:((creative(X)&~brave(X))=>(~tall(X)<~>~humble(X))))&
(((funny(mary)|~kind(mary)))<=>(?[X]:((funny(X)|~strong(X)))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((~patient(X)<~>~creative(X))))&
((curious(lucy)|~calm(lucy)))&
(?[X]:(curious(X)))&
(?[X]:(calm(X)))&
(?[X]:(~brave(X))) | ~kind(paul) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3692646733559838815382028
% SZS output start Proof for 3692646733559838815382028
6. ! [X0] : (generous(X0) <=> (~kind(X0) <~> ~generous(X0))) [input p5]
21. kind(paul) [input hypothesis]
37. ! [X0] : ((generous(X0) | ((~kind(X0) | generous(X0)) & (~generous(X0) | kind(X0)))) & (((generous(X0) | kind(X0)) & (~generous(X0) | ~kind(X0))) | ~generous(X0))) [nnf transformation 6]
79. ~generous(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 37]
82. generous(X0) | ~kind(X0) | generous(X0) [cnf transformation 37]
118. kind(paul) [cnf transformation 21]
121. ~generous(X0) | ~kind(X0) [duplicate literal removal 79]
122. generous(X0) | ~kind(X0) [duplicate literal removal 82]
172. ~kind(X0) [subsumption resolution 121,122]
210. $false [subsumption resolution 118,172]
% SZS output end Proof for 3692646733559838815382028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not curious then someone is strong or curious.
If someone is either generous or calm then fred is both not kind and rich and vice versa.
Everyone who is either wise or not strong is either calm or not calm.
If lucy is humble or not wise then susan is not funny or strong.
Everyone who is either not tall or curious is not tall.
If susan is generous then mary is quiet or not funny and vice versa.
Everyone who is patient is strong and vice versa.
Everyone who is either rich or calm is not quiet.
Everyone who is both not creative and patient is not brave and vice versa.
Everyone who is quiet is kind or strong and vice versa.
If someone is either quiet or not tall then someone is both not creative and not curious and vice versa.
If someone is either wise or not old then someone is either not tall or not happy and vice versa.
Everyone who is not brave or not old is both kind and not generous.
Everyone who is brave or happy is both humble and strong and vice versa.
Everyone who is both not generous and tall is both not patient and brave.
If someone is either quiet or not tall then fred is not old and vice versa.
Someone is kind or brave.
Someone is not happy or not brave.
Someone is funny.
Someone is either not brave or kind.
Paul is either not curious or tall. | Lucy is not patient. | contradiction | ((?[X]:((brave(X)<~>~curious(X))))=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((generous(X)<~>calm(X))))<=>((~kind(fred)&rich(fred))))&
(![X]:((wise(X)<~>~strong(X))=>(calm(X)<~>~calm(X))))&
(((humble(lucy)|~wise(lucy)))=>((~funny(susan)|strong(susan))))&
(![X]:((~tall(X)<~>curious(X))=>~tall(X)))&
((generous(susan))<=>((quiet(mary)|~funny(mary))))&
(![X]:(patient(X)<=>strong(X)))&
(![X]:((rich(X)<~>calm(X))=>~quiet(X)))&
(![X]:((~creative(X)&patient(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(kind(X)|strong(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(?[X]:((~creative(X)&~curious(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~brave(X)|~old(X))=>(kind(X)&~generous(X))))&
(![X]:((brave(X)|happy(X))<=>(humble(X)&strong(X))))&
(![X]:((~generous(X)&tall(X))=>(~patient(X)&brave(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(~old(fred)))&
(?[X]:((kind(X)|brave(X))))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
((~curious(paul)<~>tall(paul))) | ~patient(lucy) | [
"p6",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1439401666736041663760877
% SZS output start Proof for 1439401666736041663760877
7. ! [X0] : (patient(X0) <=> strong(X0)) [input p6]
9. ! [X0] : ((patient(X0) & ~creative(X0)) <=> ~brave(X0)) [input p8]
14. ! [X0] : ((happy(X0) | brave(X0)) <=> (strong(X0) & humble(X0))) [input p13]
22. ~patient(lucy) [input hypothesis]
48. ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 7]
50. ! [X0] : (((patient(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | (~patient(X0) | creative(X0)))) [nnf transformation 9]
51. ! [X0] : (((patient(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | ~patient(X0) | creative(X0))) [flattening 50]
64. ! [X0] : (((happy(X0) | brave(X0)) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | (~happy(X0) & ~brave(X0)))) [nnf transformation 14]
65. ! [X0] : ((happy(X0) | brave(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | (~happy(X0) & ~brave(X0)))) [flattening 64]
99. ~patient(X0) | strong(X0) [cnf transformation 48]
100. ~strong(X0) | patient(X0) [cnf transformation 48]
105. patient(X0) | brave(X0) [cnf transformation 51]
129. ~brave(X0) | strong(X0) [cnf transformation 65]
145. ~patient(lucy) [cnf transformation 22]
324. brave(X0) | strong(X0) [resolution 105,99]
325. strong(X0) [subsumption resolution 324,129]
327. patient(X0) [resolution 325,100]
348. $false [resolution 327,145]
% SZS output end Proof for 1439401666736041663760877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or creative is both happy and not old and vice versa.
If someone is not creative or wise then paul is either funny or not quiet and vice versa.
Everyone who is not patient or not strong is not quiet.
Everyone who is not happy is not strong or not happy and vice versa.
If someone is happy then someone is funny.
If someone is either calm or generous then someone is quiet.
If fred is rich then alice is not wise.
Everyone who is calm or not happy is happy or quiet and vice versa.
Everyone who is not kind or not generous is both not tall and not old and vice versa.
If someone is both funny and patient then lucy is not rich and vice versa.
Everyone who is creative is quiet or tall and vice versa.
Everyone who is wise or humble is not kind or not happy.
Everyone who is either not tall or not kind is either tall or not generous.
Everyone who is quiet or tall is either not rich or brave.
Everyone who is wise is both strong and funny.
Someone is both brave and not generous.
Someone is either old or not curious.
Lucy is not kind or kind.
Susan is both not curious and strong.
John is both not rich and humble. | Paul is not wise. | neutral | (![X]:((tall(X)|creative(X))<=>(happy(X)&~old(X))))&
((?[X]:((~creative(X)|wise(X))))<=>((funny(paul)<~>~quiet(paul))))&
(![X]:((~patient(X)|~strong(X))=>~quiet(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~happy(X))))&
((?[X]:(happy(X)))=>(?[X]:(funny(X))))&
((?[X]:((calm(X)<~>generous(X))))=>(?[X]:(quiet(X))))&
((rich(fred))=>(~wise(alice)))&
(![X]:((calm(X)|~happy(X))<=>(happy(X)|quiet(X))))&
(![X]:((~kind(X)|~generous(X))<=>(~tall(X)&~old(X))))&
((?[X]:((funny(X)&patient(X))))<=>(~rich(lucy)))&
(![X]:(creative(X)<=>(quiet(X)|tall(X))))&
(![X]:((wise(X)|humble(X))=>(~kind(X)|~happy(X))))&
(![X]:((~tall(X)<~>~kind(X))=>(tall(X)<~>~generous(X))))&
(![X]:((quiet(X)|tall(X))=>(~rich(X)<~>brave(X))))&
(![X]:(wise(X)=>(strong(X)&funny(X))))&
(?[X]:((brave(X)&~generous(X))))&
(?[X]:((old(X)<~>~curious(X))))&
((~kind(lucy)|kind(lucy)))&
((~curious(susan)&strong(susan)))&
((~rich(john)&humble(john))) | ~wise(paul) | [] | null | 0 |
If paul is wise or not old then fred is both quiet and not quiet and vice versa. Everyone who is either kind or generous is both not curious and not funny and vice versa. Everyone who is both not old and not quiet is either not old or not quiet and vice versa. Everyone who is generous is curious or old and vice versa. Everyone who is strong or not curious is either not kind or patient and vice versa. Everyone who is both funny and not patient is both old and not patient and vice versa. Everyone who is both quiet and not quiet is strong or calm and vice versa. If alice is happy then someone is both old and not quiet and vice versa. Everyone who is either rich or not curious is either not wise or not old and vice versa. Everyone who is either not patient or calm is either not tall or generous. Everyone who is both tall and not humble is both not patient and funny and vice versa. Everyone who is funny is not wise and vice versa. If fred is curious or brave then someone is either creative or not strong and vice versa. If mary is not wise or curious then fred is humble or not patient and vice versa. Everyone who is either funny or not brave is calm and vice versa. Fred is not kind or not curious. Someone is both generous and patient. Paul is humble. Someone is generous or not old. Mary is not brave. | Mary is not tall. | neutral | (((wise(paul)|~old(paul)))<=>((quiet(fred)&~quiet(fred))))&
(![X]:((kind(X)<~>generous(X))<=>(~curious(X)&~funny(X))))&
(![X]:((~old(X)&~quiet(X))<=>(~old(X)<~>~quiet(X))))&
(![X]:(generous(X)<=>(curious(X)|old(X))))&
(![X]:((strong(X)|~curious(X))<=>(~kind(X)<~>patient(X))))&
(![X]:((funny(X)&~patient(X))<=>(old(X)&~patient(X))))&
(![X]:((quiet(X)&~quiet(X))<=>(strong(X)|calm(X))))&
((happy(alice))<=>(?[X]:((old(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~curious(X))<=>(~wise(X)<~>~old(X))))&
(![X]:((~patient(X)<~>calm(X))=>(~tall(X)<~>generous(X))))&
(![X]:((tall(X)&~humble(X))<=>(~patient(X)&funny(X))))&
(![X]:(funny(X)<=>~wise(X)))&
(((curious(fred)|brave(fred)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(((~wise(mary)|curious(mary)))<=>((humble(fred)|~patient(fred))))&
(![X]:((funny(X)<~>~brave(X))<=>calm(X)))&
((~kind(fred)|~curious(fred)))&
(?[X]:((generous(X)&patient(X))))&
(humble(paul))&
(?[X]:((generous(X)|~old(X))))&
(~brave(mary)) | ~tall(mary) | [] | null | 0 |
If someone is both not old and rich then alice is not old or humble and vice versa.
Everyone who is both brave and not creative is not brave or not rich and vice versa.
If someone is both kind and happy then john is both curious and generous and vice versa.
Everyone who is not calm or curious is not humble or not curious.
If someone is either old or brave then someone is not rich or wise and vice versa.
If someone is both old and not calm then someone is funny or kind and vice versa.
Everyone who is both not patient and not brave is not humble or not rich and vice versa.
If mary is funny then someone is both not curious and not creative.
If fred is not calm then susan is quiet or curious and vice versa.
Everyone who is either quiet or creative is both generous and not funny and vice versa.
If someone is both not rich and not strong then someone is either not calm or tall and vice versa.
If susan is both not patient and not humble then fred is either not tall or calm and vice versa.
Everyone who is both brave and not quiet is either happy or not rich and vice versa.
If lucy is not happy then john is not rich and vice versa.
Everyone who is both kind and not calm is either quiet or generous.
Everyone who is not strong or humble is not calm or not funny and vice versa.
Alice is both tall and old.
John is either kind or not humble.
Someone is both not quiet and not curious.
John is not generous or not happy.
Someone is strong or not calm.
Paul is either not generous or strong. | Mary is humble. | entailment | ((?[X]:((~old(X)&rich(X))))<=>((~old(alice)|humble(alice))))&
(![X]:((brave(X)&~creative(X))<=>(~brave(X)|~rich(X))))&
((?[X]:((kind(X)&happy(X))))<=>((curious(john)&generous(john))))&
(![X]:((~calm(X)|curious(X))=>(~humble(X)|~curious(X))))&
((?[X]:((old(X)<~>brave(X))))<=>(?[X]:((~rich(X)|wise(X)))))&
((?[X]:((old(X)&~calm(X))))<=>(?[X]:((funny(X)|kind(X)))))&
(![X]:((~patient(X)&~brave(X))<=>(~humble(X)|~rich(X))))&
((funny(mary))=>(?[X]:((~curious(X)&~creative(X)))))&
((~calm(fred))<=>((quiet(susan)|curious(susan))))&
(![X]:((quiet(X)<~>creative(X))<=>(generous(X)&~funny(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:((~calm(X)<~>tall(X)))))&
(((~patient(susan)&~humble(susan)))<=>((~tall(fred)<~>calm(fred))))&
(![X]:((brave(X)&~quiet(X))<=>(happy(X)<~>~rich(X))))&
((~happy(lucy))<=>(~rich(john)))&
(![X]:((kind(X)&~calm(X))=>(quiet(X)<~>generous(X))))&
(![X]:((~strong(X)|humble(X))<=>(~calm(X)|~funny(X))))&
((tall(alice)&old(alice)))&
((kind(john)<~>~humble(john)))&
(?[X]:((~quiet(X)&~curious(X))))&
((~generous(john)|~happy(john)))&
(?[X]:((strong(X)|~calm(X))))&
((~generous(paul)<~>strong(paul))) | humble(mary) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 429303427594668103327978
% SZS output start Proof for 429303427594668103327978
2. ! [X0] : ((~creative(X0) & brave(X0)) <=> (~rich(X0) | ~brave(X0))) [input p1]
7. ! [X0] : ((~brave(X0) & ~patient(X0)) <=> (~rich(X0) | ~humble(X0))) [input p6]
23. ~humble(mary) [input hypothesis]
37. ! [X0] : (((~creative(X0) & brave(X0)) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | (creative(X0) | ~brave(X0)))) [nnf transformation 2]
38. ! [X0] : (((~creative(X0) & brave(X0)) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | creative(X0) | ~brave(X0))) [flattening 37]
54. ! [X0] : (((~brave(X0) & ~patient(X0)) | (rich(X0) & humble(X0))) & ((~rich(X0) | ~humble(X0)) | (brave(X0) | patient(X0)))) [nnf transformation 7]
55. ! [X0] : (((~brave(X0) & ~patient(X0)) | (rich(X0) & humble(X0))) & (~rich(X0) | ~humble(X0) | brave(X0) | patient(X0))) [flattening 54]
87. brave(X0) | brave(X0) [cnf transformation 38]
111. ~brave(X0) | humble(X0) [cnf transformation 55]
160. ~humble(mary) [cnf transformation 23]
163. brave(X0) [duplicate literal removal 87]
271. humble(X0) [subsumption resolution 111,163]
385. $false [subsumption resolution 160,271]
% SZS output end Proof for 429303427594668103327978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not wise is happy and vice versa. Everyone who is curious is calm. Everyone who is either curious or not brave is strong and vice versa. Everyone who is either not wise or not kind is both quiet and brave and vice versa. Everyone who is both curious and not creative is not funny or calm and vice versa. If fred is rich then someone is both not strong and kind. Everyone who is not brave or quiet is quiet and vice versa. If mary is not wise then someone is either not old or brave. Everyone who is not calm or not old is either not generous or calm and vice versa. If fred is calm or not kind then alice is old and vice versa. If someone is either generous or curious then someone is brave. Everyone who is not quiet or not funny is both strong and wise and vice versa. Everyone who is strong is brave and vice versa. If someone is both not happy and kind then someone is either not old or patient and vice versa. If alice is not funny or creative then someone is strong. Lucy is both brave and not kind. Susan is either not old or not happy. Someone is either humble or wise. Someone is not creative. Paul is not curious or not strong. John is both quiet and kind. | Alice is not wise. | neutral | (![X]:((strong(X)<~>~wise(X))<=>happy(X)))&
(![X]:(curious(X)=>calm(X)))&
(![X]:((curious(X)<~>~brave(X))<=>strong(X)))&
(![X]:((~wise(X)<~>~kind(X))<=>(quiet(X)&brave(X))))&
(![X]:((curious(X)&~creative(X))<=>(~funny(X)|calm(X))))&
((rich(fred))=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~brave(X)|quiet(X))<=>quiet(X)))&
((~wise(mary))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~old(X))<=>(~generous(X)<~>calm(X))))&
(((calm(fred)|~kind(fred)))<=>(old(alice)))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(strong(X)&wise(X))))&
(![X]:(strong(X)<=>brave(X)))&
((?[X]:((~happy(X)&kind(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~funny(alice)|creative(alice)))=>(?[X]:(strong(X))))&
((brave(lucy)&~kind(lucy)))&
((~old(susan)<~>~happy(susan)))&
(?[X]:((humble(X)<~>wise(X))))&
(?[X]:(~creative(X)))&
((~curious(paul)|~strong(paul)))&
((quiet(john)&kind(john))) | ~wise(alice) | [] | null | 0 |
Everyone who is either strong or funny is curious.
If lucy is both not calm and not creative then someone is either not generous or rich.
Everyone who is either patient or tall is either strong or rich.
Everyone who is quiet or creative is not kind and vice versa.
Everyone who is both happy and not funny is either not calm or not curious and vice versa.
Everyone who is both quiet and not generous is both not tall and not patient and vice versa.
If fred is not rich or calm then someone is not brave or creative and vice versa.
If someone is wise then someone is both generous and not quiet.
If someone is curious then fred is rich.
If lucy is not brave then paul is funny or calm.
Everyone who is brave is creative or not patient and vice versa.
Everyone who is either not calm or kind is either curious or not calm.
Everyone who is not quiet or tall is either not patient or brave.
If alice is not patient then alice is rich or old and vice versa.
Everyone who is either calm or not quiet is both not quiet and not happy and vice versa.
If lucy is both not patient and kind then someone is either not tall or patient.
Someone is both wise and not quiet.
John is either curious or not old.
Someone is both curious and generous.
Alice is both patient and not tall.
Someone is patient or not humble.
Someone is both old and tall.
Fred is either not wise or brave.
Fred is either not wise or not old. | Fred is old. | contradiction | (![X]:((strong(X)<~>funny(X))=>curious(X)))&
(((~calm(lucy)&~creative(lucy)))=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:((patient(X)<~>tall(X))=>(strong(X)<~>rich(X))))&
(![X]:((quiet(X)|creative(X))<=>~kind(X)))&
(![X]:((happy(X)&~funny(X))<=>(~calm(X)<~>~curious(X))))&
(![X]:((quiet(X)&~generous(X))<=>(~tall(X)&~patient(X))))&
(((~rich(fred)|calm(fred)))<=>(?[X]:((~brave(X)|creative(X)))))&
((?[X]:(wise(X)))=>(?[X]:((generous(X)&~quiet(X)))))&
((?[X]:(curious(X)))=>(rich(fred)))&
((~brave(lucy))=>((funny(paul)|calm(paul))))&
(![X]:(brave(X)<=>(creative(X)|~patient(X))))&
(![X]:((~calm(X)<~>kind(X))=>(curious(X)<~>~calm(X))))&
(![X]:((~quiet(X)|tall(X))=>(~patient(X)<~>brave(X))))&
((~patient(alice))<=>((rich(alice)|old(alice))))&
(![X]:((calm(X)<~>~quiet(X))<=>(~quiet(X)&~happy(X))))&
(((~patient(lucy)&kind(lucy)))=>(?[X]:((~tall(X)<~>patient(X)))))&
(?[X]:((wise(X)&~quiet(X))))&
((curious(john)<~>~old(john)))&
(?[X]:((curious(X)&generous(X))))&
((patient(alice)&~tall(alice)))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((old(X)&tall(X))))&
((~wise(fred)<~>brave(fred)))&
((~wise(fred)<~>~old(fred))) | old(fred) | [
"p6",
"p8",
"p10",
"p12",
"p14",
"p18",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1889900619453429676233903
% SZS output start Proof for 1889900619453429676233903
7. (calm(fred) | ~rich(fred)) <=> ? [X0] : (creative(X0) | ~brave(X0)) [input p6]
9. ? [X0] : curious(X0) => rich(fred) [input p8]
11. ! [X0] : (brave(X0) <=> (~patient(X0) | creative(X0))) [input p10]
13. ! [X0] : ((tall(X0) | ~quiet(X0)) => (~patient(X0) <~> brave(X0))) [input p12]
15. ! [X0] : ((calm(X0) <~> ~quiet(X0)) <=> (~happy(X0) & ~quiet(X0))) [input p14]
19. ? [X0] : (generous(X0) & curious(X0)) [input p18]
23. ~wise(fred) <~> brave(fred) [input p22]
24. ~wise(fred) <~> ~old(fred) [input p23]
25. old(fred) [input hypothesis]
33. rich(fred) | ! [X0] : ~curious(X0) [ennf transformation 9]
37. ! [X0] : ((~patient(X0) <~> brave(X0)) | (~tall(X0) & quiet(X0))) [ennf transformation 13]
51. ((calm(fred) | ~rich(fred)) | ! [X0] : (~creative(X0) & brave(X0))) & (? [X0] : (creative(X0) | ~brave(X0)) | (~calm(fred) & rich(fred))) [nnf transformation 7]
52. (calm(fred) | ~rich(fred) | ! [X0] : (~creative(X0) & brave(X0))) & (? [X0] : (creative(X0) | ~brave(X0)) | (~calm(fred) & rich(fred))) [flattening 51]
53. (calm(fred) | ~rich(fred) | ! [X0] : (~creative(X0) & brave(X0))) & (? [X1] : (creative(X1) | ~brave(X1)) | (~calm(fred) & rich(fred))) [rectify 52]
54. ? [X1] : (creative(X1) | ~brave(X1)) => (creative(sK1) | ~brave(sK1)) [choice axiom]
55. (calm(fred) | ~rich(fred) | ! [X0] : (~creative(X0) & brave(X0))) & ((creative(sK1) | ~brave(sK1)) | (~calm(fred) & rich(fred))) [skolemisation 53,54]
59. ! [X0] : ((brave(X0) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | ~brave(X0))) [nnf transformation 11]
60. ! [X0] : ((brave(X0) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | ~brave(X0))) [flattening 59]
62. ! [X0] : (((~brave(X0) | patient(X0)) & (brave(X0) | ~patient(X0))) | (~tall(X0) & quiet(X0))) [nnf transformation 37]
65. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (happy(X0) | quiet(X0))) & ((~happy(X0) & ~quiet(X0)) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [nnf transformation 15]
66. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | happy(X0) | quiet(X0)) & ((~happy(X0) & ~quiet(X0)) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [flattening 65]
73. ? [X0] : (generous(X0) & curious(X0)) => (generous(sK5) & curious(sK5)) [choice axiom]
74. generous(sK5) & curious(sK5) [skolemisation 19,73]
77. (~brave(fred) | wise(fred)) & (brave(fred) | ~wise(fred)) [nnf transformation 23]
78. (old(fred) | wise(fred)) & (~old(fred) | ~wise(fred)) [nnf transformation 24]
102. calm(fred) | ~rich(fred) | brave(X0) [cnf transformation 55]
106. rich(fred) | ~curious(X0) [cnf transformation 33]
110. brave(X0) | patient(X0) [cnf transformation 60]
115. brave(X0) | ~patient(X0) | quiet(X0) [cnf transformation 62]
117. ~brave(X0) | patient(X0) | quiet(X0) [cnf transformation 62]
122. ~quiet(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 66]
134. curious(sK5) [cnf transformation 74]
141. ~brave(fred) | wise(fred) [cnf transformation 77]
142. ~old(fred) | ~wise(fred) [cnf transformation 78]
144. old(fred) [cnf transformation 25]
145. ~quiet(X0) | ~calm(X0) [duplicate literal removal 122]
171. 6 <=> rich(fred) [avatar definition]
175. 7 <=> calm(fred) [avatar definition]
180. 8 <=> ! [X0] : brave(X0) [avatar definition]
181. brave(X0) <- (8) [avatar component clause 180]
182. 8 | ~6 | 7 [avatar split clause 102,175,171,180]
207. 14 <=> ! [X0] : ~curious(X0) [avatar definition]
208. ~curious(X0) <- (14) [avatar component clause 207]
209. 14 | 6 [avatar split clause 106,171,207]
224. quiet(X0) | patient(X0) [subsumption resolution 117,110]
226. brave(X0) | quiet(X0) [subsumption resolution 115,224]
271. 27 <=> wise(fred) [avatar definition]
275. 28 <=> brave(fred) [avatar definition]
277. ~brave(fred) <- (~28) [avatar component clause 275]
278. 27 | ~28 [avatar split clause 141,275,271]
281. 29 <=> old(fred) [avatar definition]
285. ~27 | ~29 [avatar split clause 142,281,271]
286. 29 [avatar split clause 144,281]
297. quiet(fred) <- (~28) [resolution 226,277]
301. ~calm(fred) <- (~28) [resolution 297,145]
304. ~7 | 28 [avatar split clause 301,275,175]
306. $false <- (8, ~28) [resolution 181,277]
307. ~8 | 28 [avatar contradiction clause 306]
309. $false <- (14) [resolution 208,134]
310. ~14 [avatar contradiction clause 309]
311. $false [avatar sat refutation 182,209,278,285,286,304,307,310]
% SZS output end Proof for 1889900619453429676233903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or creative is not kind and vice versa.
Everyone who is both not brave and funny is either quiet or patient and vice versa.
Everyone who is either not wise or not quiet is not generous or not curious.
Everyone who is not tall is curious and vice versa.
If fred is either tall or kind then someone is either not calm or kind.
Everyone who is either not creative or creative is brave or funny and vice versa.
Everyone who is either not strong or not quiet is both not tall and rich.
Everyone who is not generous is not creative or not happy and vice versa.
Everyone who is not humble or not rich is either not brave or not generous and vice versa.
Everyone who is either not wise or not kind is not old or funny and vice versa.
If someone is not kind then someone is both not creative and generous and vice versa.
Everyone who is either quiet or not brave is either not strong or not quiet and vice versa.
Everyone who is rich or not kind is either not rich or kind.
If lucy is either not curious or not quiet then someone is either strong or happy.
Everyone who is rich or not happy is both tall and old.
Someone is kind or happy.
Someone is not creative or strong.
Lucy is creative or funny.
Susan is wise or not brave.
John is both happy and calm. | Susan is not kind. | contradiction | (![X]:((brave(X)|creative(X))<=>~kind(X)))&
(![X]:((~brave(X)&funny(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>(~generous(X)|~curious(X))))&
(![X]:(~tall(X)<=>curious(X)))&
(((tall(fred)<~>kind(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)|funny(X))))&
(![X]:((~strong(X)<~>~quiet(X))=>(~tall(X)&rich(X))))&
(![X]:(~generous(X)<=>(~creative(X)|~happy(X))))&
(![X]:((~humble(X)|~rich(X))<=>(~brave(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>~kind(X))<=>(~old(X)|funny(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~creative(X)&generous(X)))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)<~>~quiet(X))))&
(![X]:((rich(X)|~kind(X))=>(~rich(X)<~>kind(X))))&
(((~curious(lucy)<~>~quiet(lucy)))=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:((rich(X)|~happy(X))=>(tall(X)&old(X))))&
(?[X]:((kind(X)|happy(X))))&
(?[X]:((~creative(X)|strong(X))))&
((creative(lucy)|funny(lucy)))&
((wise(susan)|~brave(susan)))&
((happy(john)&calm(john))) | ~kind(susan) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2721863256682778778659549
% SZS output start Proof for 2721863256682778778659549
8. ! [X0] : (~generous(X0) <=> (~happy(X0) | ~creative(X0))) [input p7]
11. ? [X0] : ~kind(X0) <=> ? [X0] : (generous(X0) & ~creative(X0)) [input p10]
21. ~kind(susan) [input hypothesis]
22. ? [X0] : ~kind(X0) <=> ? [X1] : (generous(X1) & ~creative(X1)) [rectify 11]
42. ! [X0] : ((~generous(X0) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | generous(X0))) [nnf transformation 8]
43. ! [X0] : ((~generous(X0) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | generous(X0))) [flattening 42]
48. (? [X0] : ~kind(X0) | ! [X1] : (~generous(X1) | creative(X1))) & (? [X1] : (generous(X1) & ~creative(X1)) | ! [X0] : kind(X0)) [nnf transformation 22]
49. (? [X0] : ~kind(X0) | ! [X1] : (~generous(X1) | creative(X1))) & (? [X2] : (generous(X2) & ~creative(X2)) | ! [X3] : kind(X3)) [rectify 48]
50. ? [X0] : ~kind(X0) => ~kind(sK1) [choice axiom]
51. ? [X2] : (generous(X2) & ~creative(X2)) => (generous(sK2) & ~creative(sK2)) [choice axiom]
52. (~kind(sK1) | ! [X1] : (~generous(X1) | creative(X1))) & ((generous(sK2) & ~creative(sK2)) | ! [X3] : kind(X3)) [skolemisation 49,51,50]
90. ~generous(X0) | creative(X0) [cnf transformation 43]
104. ~creative(sK2) | kind(X3) [cnf transformation 52]
105. generous(sK2) | kind(X3) [cnf transformation 52]
133. ~kind(susan) [cnf transformation 21]
164. 5 <=> ! [X3] : kind(X3) [avatar definition]
165. kind(X3) <- (5) [avatar component clause 164]
167. 6 <=> generous(sK2) [avatar definition]
169. generous(sK2) <- (6) [avatar component clause 167]
170. 5 | 6 [avatar split clause 105,167,164]
172. 7 <=> creative(sK2) [avatar definition]
175. 5 | ~7 [avatar split clause 104,172,164]
240. creative(sK2) <- (6) [resolution 90,169]
243. 7 | ~6 [avatar split clause 240,167,172]
247. $false <- (5) [resolution 165,133]
250. ~5 [avatar contradiction clause 247]
251. $false [avatar sat refutation 170,175,243,250]
% SZS output end Proof for 2721863256682778778659549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or old then lucy is not brave and vice versa. Everyone who is either curious or not old is not old or strong and vice versa. Everyone who is kind or calm is either not happy or brave and vice versa. If someone is both not brave and quiet then someone is kind or brave and vice versa. Everyone who is both kind and not happy is kind or patient and vice versa. If someone is both not strong and not curious then fred is calm. Everyone who is humble or not wise is both wise and not calm and vice versa. Everyone who is either creative or not patient is either not quiet or not wise and vice versa. If someone is quiet then someone is both calm and brave and vice versa. If someone is both humble and not humble then someone is both not quiet and kind. Everyone who is either rich or not wise is patient or not creative and vice versa. Everyone who is not curious is not quiet or tall and vice versa. Everyone who is either not happy or creative is not happy or kind. Everyone who is funny or creative is either not creative or patient. If susan is both not creative and not old then someone is either kind or happy and vice versa. Everyone who is both not funny and not tall is not generous and vice versa. Mary is tall. John is both humble and not tall. Mary is calm or not brave. Mary is not quiet. Alice is not funny. Mary is either curious or not funny. | Mary is creative. | neutral | ((?[X]:((creative(X)|old(X))))<=>(~brave(lucy)))&
(![X]:((curious(X)<~>~old(X))<=>(~old(X)|strong(X))))&
(![X]:((kind(X)|calm(X))<=>(~happy(X)<~>brave(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((kind(X)&~happy(X))<=>(kind(X)|patient(X))))&
((?[X]:((~strong(X)&~curious(X))))=>(calm(fred)))&
(![X]:((humble(X)|~wise(X))<=>(wise(X)&~calm(X))))&
(![X]:((creative(X)<~>~patient(X))<=>(~quiet(X)<~>~wise(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((calm(X)&brave(X)))))&
((?[X]:((humble(X)&~humble(X))))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(patient(X)|~creative(X))))&
(![X]:(~curious(X)<=>(~quiet(X)|tall(X))))&
(![X]:((~happy(X)<~>creative(X))=>(~happy(X)|kind(X))))&
(![X]:((funny(X)|creative(X))=>(~creative(X)<~>patient(X))))&
(((~creative(susan)&~old(susan)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((~funny(X)&~tall(X))<=>~generous(X)))&
(tall(mary))&
((humble(john)&~tall(john)))&
((calm(mary)|~brave(mary)))&
(~quiet(mary))&
(~funny(alice))&
((curious(mary)<~>~funny(mary))) | creative(mary) | [] | null | 0 |
Everyone who is not generous is either not creative or not funny and vice versa.
Everyone who is generous or happy is tall and vice versa.
If someone is either not tall or not creative then mary is both rich and not wise.
Everyone who is not humble is either happy or strong and vice versa.
If someone is both creative and not old then someone is either wise or generous and vice versa.
Everyone who is both curious and not curious is both rich and quiet and vice versa.
If mary is humble or happy then alice is not patient or not strong.
If alice is both calm and not kind then mary is not wise or creative and vice versa.
Everyone who is kind or not humble is rich and vice versa.
If paul is either kind or not strong then someone is rich or patient and vice versa.
Everyone who is not strong is not curious and vice versa.
If someone is either not brave or not curious then someone is either tall or happy and vice versa.
If someone is both not happy and brave then someone is rich or happy and vice versa.
Everyone who is either wise or kind is generous and vice versa.
Everyone who is both not old and not funny is not generous or humble and vice versa.
Everyone who is rich is not creative and vice versa.
Paul is generous.
Fred is happy or not funny.
Lucy is either generous or not humble.
Lucy is both not wise and not patient.
John is wise or happy.
Someone is not funny.
Someone is not happy or calm.
Alice is not wise. | Mary is not quiet. | entailment | (![X]:(~generous(X)<=>(~creative(X)<~>~funny(X))))&
(![X]:((generous(X)|happy(X))<=>tall(X)))&
((?[X]:((~tall(X)<~>~creative(X))))=>((rich(mary)&~wise(mary))))&
(![X]:(~humble(X)<=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)&~old(X))))<=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((curious(X)&~curious(X))<=>(rich(X)&quiet(X))))&
(((humble(mary)|happy(mary)))=>((~patient(alice)|~strong(alice))))&
(((calm(alice)&~kind(alice)))<=>((~wise(mary)|creative(mary))))&
(![X]:((kind(X)|~humble(X))<=>rich(X)))&
(((kind(paul)<~>~strong(paul)))<=>(?[X]:((rich(X)|patient(X)))))&
(![X]:(~strong(X)<=>~curious(X)))&
((?[X]:((~brave(X)<~>~curious(X))))<=>(?[X]:((tall(X)<~>happy(X)))))&
((?[X]:((~happy(X)&brave(X))))<=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((wise(X)<~>kind(X))<=>generous(X)))&
(![X]:((~old(X)&~funny(X))<=>(~generous(X)|humble(X))))&
(![X]:(rich(X)<=>~creative(X)))&
(generous(paul))&
((happy(fred)|~funny(fred)))&
((generous(lucy)<~>~humble(lucy)))&
((~wise(lucy)&~patient(lucy)))&
((wise(john)|happy(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~happy(X)|calm(X))))&
(~wise(alice)) | ~quiet(mary) | [
"p0",
"p1",
"p2",
"p5",
"p8",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2307403126182111514123101
% SZS output start Proof for 2307403126182111514123101
1. ! [X0] : (~generous(X0) <=> (~creative(X0) <~> ~funny(X0))) [input p0]
2. ! [X0] : ((happy(X0) | generous(X0)) <=> tall(X0)) [input p1]
3. ? [X0] : (~tall(X0) <~> ~creative(X0)) => (~wise(mary) & rich(mary)) [input p2]
6. ! [X0] : ((~curious(X0) & curious(X0)) <=> (quiet(X0) & rich(X0))) [input p5]
9. ! [X0] : ((~humble(X0) | kind(X0)) <=> rich(X0)) [input p8]
15. ! [X0] : ((~funny(X0) & ~old(X0)) <=> (humble(X0) | ~generous(X0))) [input p14]
16. ! [X0] : (rich(X0) <=> ~creative(X0)) [input p15]
17. generous(paul) [input p16]
25. quiet(mary) [input hypothesis]
29. (~wise(mary) & rich(mary)) | ! [X0] : (~tall(X0) <=> ~creative(X0)) [ennf transformation 3]
32. ! [X0] : ((~generous(X0) | ((~creative(X0) | funny(X0)) & (~funny(X0) | creative(X0)))) & (((funny(X0) | creative(X0)) & (~funny(X0) | ~creative(X0))) | generous(X0))) [nnf transformation 1]
33. ! [X0] : (((happy(X0) | generous(X0)) | ~tall(X0)) & (tall(X0) | (~happy(X0) & ~generous(X0)))) [nnf transformation 2]
34. ! [X0] : ((happy(X0) | generous(X0) | ~tall(X0)) & (tall(X0) | (~happy(X0) & ~generous(X0)))) [flattening 33]
35. (~wise(mary) & rich(mary)) | ! [X0] : ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))) [nnf transformation 29]
42. ! [X0] : (((~curious(X0) & curious(X0)) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | (curious(X0) | ~curious(X0)))) [nnf transformation 6]
43. ! [X0] : (((~curious(X0) & curious(X0)) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | curious(X0) | ~curious(X0))) [flattening 42]
46. ! [X0] : (((~humble(X0) | kind(X0)) | ~rich(X0)) & (rich(X0) | (humble(X0) & ~kind(X0)))) [nnf transformation 9]
47. ! [X0] : ((~humble(X0) | kind(X0) | ~rich(X0)) & (rich(X0) | (humble(X0) & ~kind(X0)))) [flattening 46]
64. ! [X0] : (((~funny(X0) & ~old(X0)) | (~humble(X0) & generous(X0))) & ((humble(X0) | ~generous(X0)) | (funny(X0) | old(X0)))) [nnf transformation 15]
65. ! [X0] : (((~funny(X0) & ~old(X0)) | (~humble(X0) & generous(X0))) & (humble(X0) | ~generous(X0) | funny(X0) | old(X0))) [flattening 64]
66. ! [X0] : ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))) [nnf transformation 16]
75. ~creative(X0) | ~generous(X0) | funny(X0) [cnf transformation 32]
76. ~generous(X0) | tall(X0) [cnf transformation 34]
80. rich(mary) | ~tall(X0) | creative(X0) [cnf transformation 35]
95. curious(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 43]
96. ~quiet(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 43]
105. humble(X0) | rich(X0) [cnf transformation 47]
136. ~humble(X0) | ~funny(X0) [cnf transformation 65]
137. ~rich(X0) | ~creative(X0) [cnf transformation 66]
139. generous(paul) [cnf transformation 17]
149. quiet(mary) [cnf transformation 25]
151. 1 <=> ! [X0] : (~tall(X0) | creative(X0)) [avatar definition]
152. ~tall(X0) | creative(X0) <- (1) [avatar component clause 151]
163. 4 <=> rich(mary) [avatar definition]
166. 1 | 4 [avatar split clause 80,163,151]
199. ~quiet(X0) | ~rich(X0) [subsumption resolution 95,96]
365. tall(paul) [resolution 76,139]
383. ~rich(mary) [resolution 199,149]
386. ~4 [avatar split clause 383,163]
403. creative(paul) <- (1) [resolution 152,365]
473. 50 <=> humble(paul) [avatar definition]
474. ~humble(paul) <- (~50) [avatar component clause 473]
475. humble(paul) <- (50) [avatar component clause 473]
483. ~funny(paul) <- (50) [resolution 475,136]
502. ~generous(paul) | funny(paul) <- (1) [resolution 403,75]
504. funny(paul) <- (1) [subsumption resolution 502,139]
505. $false <- (1, 50) [subsumption resolution 504,483]
506. ~1 | ~50 [avatar contradiction clause 505]
508. rich(paul) <- (~50) [resolution 474,105]
649. ~creative(paul) <- (~50) [resolution 508,137]
650. $false <- (1, ~50) [subsumption resolution 649,403]
651. ~1 | 50 [avatar contradiction clause 650]
652. $false [avatar sat refutation 166,386,506,651]
% SZS output end Proof for 2307403126182111514123101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then mary is patient or happy.
Everyone who is not old or wise is quiet or not calm and vice versa.
If someone is both quiet and not strong then someone is rich or kind.
Everyone who is either not generous or not rich is happy and vice versa.
If susan is not calm then fred is humble and vice versa.
Everyone who is both not old and strong is both not calm and quiet and vice versa.
Everyone who is either not rich or strong is happy or rich.
Everyone who is curious or rich is not rich or not calm and vice versa.
Everyone who is both happy and not curious is wise or kind and vice versa.
If susan is not brave then fred is either curious or not humble.
Everyone who is either not kind or curious is either calm or not creative and vice versa.
If john is either not funny or not rich then lucy is not wise or patient and vice versa.
Everyone who is not happy or kind is old or not patient and vice versa.
If alice is calm then someone is either creative or not humble and vice versa.
If someone is strong or not brave then someone is both not calm and old and vice versa.
Everyone who is not strong is strong or curious and vice versa.
Lucy is either tall or not kind.
Mary is wise or quiet.
Paul is either tall or curious.
Fred is not funny.
Someone is either calm or funny.
Someone is both not tall and not quiet.
Someone is both not old and tall. | Mary is generous. | entailment | ((?[X]:(quiet(X)))=>((patient(mary)|happy(mary))))&
(![X]:((~old(X)|wise(X))<=>(quiet(X)|~calm(X))))&
((?[X]:((quiet(X)&~strong(X))))=>(?[X]:((rich(X)|kind(X)))))&
(![X]:((~generous(X)<~>~rich(X))<=>happy(X)))&
((~calm(susan))<=>(humble(fred)))&
(![X]:((~old(X)&strong(X))<=>(~calm(X)&quiet(X))))&
(![X]:((~rich(X)<~>strong(X))=>(happy(X)|rich(X))))&
(![X]:((curious(X)|rich(X))<=>(~rich(X)|~calm(X))))&
(![X]:((happy(X)&~curious(X))<=>(wise(X)|kind(X))))&
((~brave(susan))=>((curious(fred)<~>~humble(fred))))&
(![X]:((~kind(X)<~>curious(X))<=>(calm(X)<~>~creative(X))))&
(((~funny(john)<~>~rich(john)))<=>((~wise(lucy)|patient(lucy))))&
(![X]:((~happy(X)|kind(X))<=>(old(X)|~patient(X))))&
((calm(alice))<=>(?[X]:((creative(X)<~>~humble(X)))))&
((?[X]:((strong(X)|~brave(X))))<=>(?[X]:((~calm(X)&old(X)))))&
(![X]:(~strong(X)<=>(strong(X)|curious(X))))&
((tall(lucy)<~>~kind(lucy)))&
((wise(mary)|quiet(mary)))&
((tall(paul)<~>curious(paul)))&
(~funny(fred))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
(?[X]:((~old(X)&tall(X)))) | generous(mary) | [
"p0",
"p1",
"p3",
"p5",
"p7",
"p8",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1536749832689839407967108
% SZS output start Proof for 1536749832689839407967108
1. ? [X0] : quiet(X0) => (happy(mary) | patient(mary)) [input p0]
2. ! [X0] : ((wise(X0) | ~old(X0)) <=> (~calm(X0) | quiet(X0))) [input p1]
4. ! [X0] : ((~generous(X0) <~> ~rich(X0)) <=> happy(X0)) [input p3]
6. ! [X0] : ((strong(X0) & ~old(X0)) <=> (quiet(X0) & ~calm(X0))) [input p5]
8. ! [X0] : ((rich(X0) | curious(X0)) <=> (~calm(X0) | ~rich(X0))) [input p7]
9. ! [X0] : ((~curious(X0) & happy(X0)) <=> (kind(X0) | wise(X0))) [input p8]
13. ! [X0] : ((kind(X0) | ~happy(X0)) <=> (~patient(X0) | old(X0))) [input p12]
16. ! [X0] : (~strong(X0) <=> (curious(X0) | strong(X0))) [input p15]
18. quiet(mary) | wise(mary) [input p17]
24. ~generous(mary) [input hypothesis]
27. (happy(mary) | patient(mary)) | ! [X0] : ~quiet(X0) [ennf transformation 1]
28. happy(mary) | patient(mary) | ! [X0] : ~quiet(X0) [flattening 27]
33. ! [X0] : (((wise(X0) | ~old(X0)) | (calm(X0) & ~quiet(X0))) & ((~calm(X0) | quiet(X0)) | (~wise(X0) & old(X0)))) [nnf transformation 2]
34. ! [X0] : ((wise(X0) | ~old(X0) | (calm(X0) & ~quiet(X0))) & (~calm(X0) | quiet(X0) | (~wise(X0) & old(X0)))) [flattening 33]
38. ! [X0] : ((((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | ~happy(X0)) & (happy(X0) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))))) [nnf transformation 4]
40. ! [X0] : (((strong(X0) & ~old(X0)) | (~quiet(X0) | calm(X0))) & ((quiet(X0) & ~calm(X0)) | (~strong(X0) | old(X0)))) [nnf transformation 6]
41. ! [X0] : (((strong(X0) & ~old(X0)) | ~quiet(X0) | calm(X0)) & ((quiet(X0) & ~calm(X0)) | ~strong(X0) | old(X0))) [flattening 40]
43. ! [X0] : (((rich(X0) | curious(X0)) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | (~rich(X0) & ~curious(X0)))) [nnf transformation 8]
44. ! [X0] : ((rich(X0) | curious(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | (~rich(X0) & ~curious(X0)))) [flattening 43]
45. ! [X0] : (((~curious(X0) & happy(X0)) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | (curious(X0) | ~happy(X0)))) [nnf transformation 9]
46. ! [X0] : (((~curious(X0) & happy(X0)) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | curious(X0) | ~happy(X0))) [flattening 45]
51. ! [X0] : (((kind(X0) | ~happy(X0)) | (patient(X0) & ~old(X0))) & ((~patient(X0) | old(X0)) | (~kind(X0) & happy(X0)))) [nnf transformation 13]
52. ! [X0] : ((kind(X0) | ~happy(X0) | (patient(X0) & ~old(X0))) & (~patient(X0) | old(X0) | (~kind(X0) & happy(X0)))) [flattening 51]
62. ! [X0] : ((~strong(X0) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | strong(X0))) [nnf transformation 16]
63. ! [X0] : ((~strong(X0) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | strong(X0))) [flattening 62]
73. happy(mary) | patient(mary) | ~quiet(X0) [cnf transformation 28]
76. ~old(X0) | wise(X0) | ~quiet(X0) [cnf transformation 34]
82. ~happy(X0) | generous(X0) | rich(X0) [cnf transformation 38]
88. ~quiet(X0) | strong(X0) | calm(X0) [cnf transformation 41]
92. ~calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 44]
98. ~curious(X0) | ~wise(X0) [cnf transformation 46]
116. ~patient(X0) | old(X0) | happy(X0) [cnf transformation 52]
129. curious(X0) | strong(X0) | strong(X0) [cnf transformation 63]
130. ~strong(X0) | ~strong(X0) [cnf transformation 63]
134. quiet(mary) | wise(mary) [cnf transformation 18]
144. ~generous(mary) [cnf transformation 24]
145. curious(X0) | strong(X0) [duplicate literal removal 129]
146. ~strong(X0) [duplicate literal removal 130]
147. ~rich(X0) | ~calm(X0) [duplicate literal removal 92]
151. 1 <=> ! [X0] : ~quiet(X0) [avatar definition]
152. ~quiet(X0) <- (1) [avatar component clause 151]
154. 2 <=> patient(mary) [avatar definition]
156. patient(mary) <- (2) [avatar component clause 154]
158. 3 <=> happy(mary) [avatar definition]
160. happy(mary) <- (3) [avatar component clause 158]
161. 1 | 2 | 3 [avatar split clause 73,158,154,151]
263. 25 <=> ! [X3] : ~strong(X3) [avatar definition]
264. ~strong(X3) <- (25) [avatar component clause 263]
272. 25 [avatar split clause 146,263]
284. 29 <=> wise(mary) [avatar definition]
286. wise(mary) <- (29) [avatar component clause 284]
288. 30 <=> quiet(mary) [avatar definition]
290. quiet(mary) <- (30) [avatar component clause 288]
291. 29 | 30 [avatar split clause 134,288,284]
322. strong(X2) | ~wise(X2) [resolution 145,98]
328. ~wise(X2) <- (25) [subsumption resolution 322,264]
385. old(mary) | happy(mary) <- (2) [resolution 116,156]
387. 41 <=> old(mary) [avatar definition]
389. old(mary) <- (41) [avatar component clause 387]
390. 3 | 41 | ~2 [avatar split clause 385,154,387,158]
391. $false <- (1, 30) [resolution 152,290]
392. ~1 | ~30 [avatar contradiction clause 391]
393. $false <- (25, 29) [subsumption resolution 286,328]
394. ~25 | ~29 [avatar contradiction clause 393]
395. generous(mary) | rich(mary) <- (3) [resolution 160,82]
396. rich(mary) <- (3) [subsumption resolution 395,144]
397. strong(mary) | calm(mary) <- (30) [resolution 290,88]
398. calm(mary) <- (25, 30) [subsumption resolution 397,264]
400. ~calm(mary) <- (3) [resolution 396,147]
401. $false <- (3, 25, 30) [subsumption resolution 400,398]
402. ~3 | ~25 | ~30 [avatar contradiction clause 401]
406. wise(mary) | ~quiet(mary) <- (41) [resolution 389,76]
408. ~quiet(mary) <- (25, 41) [subsumption resolution 406,328]
409. $false <- (25, 30, 41) [subsumption resolution 408,290]
410. ~25 | ~30 | ~41 [avatar contradiction clause 409]
411. $false [avatar sat refutation 161,272,291,390,392,394,402,410]
% SZS output end Proof for 1536749832689839407967108
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not brave is either funny or curious and vice versa. If paul is both not strong and not rich then fred is either curious or tall. Everyone who is brave is both happy and not quiet and vice versa. If mary is not calm or not creative then someone is not tall and vice versa. If someone is not quiet then john is not wise. If someone is both not funny and not strong then someone is not humble. Everyone who is both not generous and not curious is either happy or kind and vice versa. Everyone who is creative or curious is funny or curious and vice versa. Everyone who is either not tall or patient is not humble. If someone is humble then someone is both not creative and rich. If someone is not kind then john is wise or quiet and vice versa. If someone is both not funny and brave then john is humble or not calm and vice versa. Everyone who is not calm is both humble and calm and vice versa. If fred is not curious then someone is not generous or patient and vice versa. If john is calm then alice is old or not wise and vice versa. If fred is kind then paul is not rich or not wise. Someone is not calm or funny. Fred is both generous and not tall. John is either wise or not quiet. Paul is either kind or tall. Fred is both not wise and not rich. Paul is kind or patient. Alice is either humble or not patient. Someone is both not happy and not curious. | Fred is not wise. | entailment | (![X]:((kind(X)|~brave(X))<=>(funny(X)<~>curious(X))))&
(((~strong(paul)&~rich(paul)))=>((curious(fred)<~>tall(fred))))&
(![X]:(brave(X)<=>(happy(X)&~quiet(X))))&
(((~calm(mary)|~creative(mary)))<=>(?[X]:(~tall(X))))&
((?[X]:(~quiet(X)))=>(~wise(john)))&
((?[X]:((~funny(X)&~strong(X))))=>(?[X]:(~humble(X))))&
(![X]:((~generous(X)&~curious(X))<=>(happy(X)<~>kind(X))))&
(![X]:((creative(X)|curious(X))<=>(funny(X)|curious(X))))&
(![X]:((~tall(X)<~>patient(X))=>~humble(X)))&
((?[X]:(humble(X)))=>(?[X]:((~creative(X)&rich(X)))))&
((?[X]:(~kind(X)))<=>((wise(john)|quiet(john))))&
((?[X]:((~funny(X)&brave(X))))<=>((humble(john)|~calm(john))))&
(![X]:(~calm(X)<=>(humble(X)&calm(X))))&
((~curious(fred))<=>(?[X]:((~generous(X)|patient(X)))))&
((calm(john))<=>((old(alice)|~wise(alice))))&
((kind(fred))=>((~rich(paul)|~wise(paul))))&
(?[X]:((~calm(X)|funny(X))))&
((generous(fred)&~tall(fred)))&
((wise(john)<~>~quiet(john)))&
((kind(paul)<~>tall(paul)))&
((~wise(fred)&~rich(fred)))&
((kind(paul)|patient(paul)))&
((humble(alice)<~>~patient(alice)))&
(?[X]:((~happy(X)&~curious(X)))) | ~wise(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2798254301553891824438440
% SZS output start Proof for 2798254301553891824438440
21. ~rich(fred) & ~wise(fred) [input p20]
25. wise(fred) [input hypothesis]
129. ~wise(fred) [cnf transformation 21]
136. wise(fred) [cnf transformation 25]
288. $false [subsumption resolution 136,129]
% SZS output end Proof for 2798254301553891824438440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not happy or not generous then someone is both not humble and brave and vice versa.
Everyone who is either rich or not happy is both not patient and generous and vice versa.
Everyone who is either patient or funny is either not generous or rich and vice versa.
Everyone who is both not strong and not happy is both not quiet and tall.
Everyone who is rich is calm.
If someone is both not kind and curious then someone is strong or not old and vice versa.
Everyone who is either kind or not happy is not strong or patient and vice versa.
If fred is either happy or not kind then someone is both not quiet and not creative and vice versa.
If someone is both humble and funny then fred is not kind or not rich.
Everyone who is not calm or happy is not curious and vice versa.
Everyone who is either not tall or not generous is both not quiet and brave.
Everyone who is not funny is kind or strong and vice versa.
Everyone who is either creative or not curious is both wise and not calm.
Everyone who is both not happy and tall is old or not rich.
Everyone who is tall or not generous is generous and vice versa.
If someone is both not rich and not curious then someone is not tall.
Someone is rich.
Someone is not happy.
Someone is not generous or kind.
Susan is both old and not creative.
Alice is not generous or old.
Someone is not wise or not funny. | Alice is funny. | contradiction | (((~happy(fred)|~generous(fred)))<=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((rich(X)<~>~happy(X))<=>(~patient(X)&generous(X))))&
(![X]:((patient(X)<~>funny(X))<=>(~generous(X)<~>rich(X))))&
(![X]:((~strong(X)&~happy(X))=>(~quiet(X)&tall(X))))&
(![X]:(rich(X)=>calm(X)))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((kind(X)<~>~happy(X))<=>(~strong(X)|patient(X))))&
(((happy(fred)<~>~kind(fred)))<=>(?[X]:((~quiet(X)&~creative(X)))))&
((?[X]:((humble(X)&funny(X))))=>((~kind(fred)|~rich(fred))))&
(![X]:((~calm(X)|happy(X))<=>~curious(X)))&
(![X]:((~tall(X)<~>~generous(X))=>(~quiet(X)&brave(X))))&
(![X]:(~funny(X)<=>(kind(X)|strong(X))))&
(![X]:((creative(X)<~>~curious(X))=>(wise(X)&~calm(X))))&
(![X]:((~happy(X)&tall(X))=>(old(X)|~rich(X))))&
(![X]:((tall(X)|~generous(X))<=>generous(X)))&
((?[X]:((~rich(X)&~curious(X))))=>(?[X]:(~tall(X))))&
(?[X]:(rich(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~generous(X)|kind(X))))&
((old(susan)&~creative(susan)))&
((~generous(alice)|old(alice)))&
(?[X]:((~wise(X)|~funny(X)))) | funny(alice) | [
"p1",
"p2",
"p6",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2155780628530514831936483
% SZS output start Proof for 2155780628530514831936483
2. ! [X0] : ((rich(X0) <~> ~happy(X0)) <=> (generous(X0) & ~patient(X0))) [input p1]
3. ! [X0] : ((patient(X0) <~> funny(X0)) <=> (~generous(X0) <~> rich(X0))) [input p2]
7. ! [X0] : ((kind(X0) <~> ~happy(X0)) <=> (patient(X0) | ~strong(X0))) [input p6]
12. ! [X0] : (~funny(X0) <=> (strong(X0) | kind(X0))) [input p11]
15. ! [X0] : ((~generous(X0) | tall(X0)) <=> generous(X0)) [input p14]
23. funny(alice) [input hypothesis]
41. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [nnf transformation 2]
42. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [flattening 41]
43. ! [X0] : ((((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0))))) [nnf transformation 3]
49. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [nnf transformation 7]
50. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [flattening 49]
58. ! [X0] : ((~funny(X0) | (~strong(X0) & ~kind(X0))) & ((strong(X0) | kind(X0)) | funny(X0))) [nnf transformation 12]
59. ! [X0] : ((~funny(X0) | (~strong(X0) & ~kind(X0))) & (strong(X0) | kind(X0) | funny(X0))) [flattening 58]
61. ! [X0] : (((~generous(X0) | tall(X0)) | ~generous(X0)) & (generous(X0) | (generous(X0) & ~tall(X0)))) [nnf transformation 15]
62. ! [X0] : ((~generous(X0) | tall(X0) | ~generous(X0)) & (generous(X0) | (generous(X0) & ~tall(X0)))) [flattening 61]
80. ~patient(X0) | rich(X0) | happy(X0) [cnf transformation 42]
84. ~rich(X0) | happy(X0) | ~generous(X0) | patient(X0) [cnf transformation 42]
86. ~funny(X0) | ~generous(X0) | patient(X0) | rich(X0) [cnf transformation 43]
92. ~funny(X0) | ~patient(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 43]
103. ~happy(X0) | kind(X0) | strong(X0) [cnf transformation 50]
122. ~kind(X0) | ~funny(X0) [cnf transformation 59]
123. ~strong(X0) | ~funny(X0) [cnf transformation 59]
130. generous(X0) | generous(X0) [cnf transformation 62]
140. funny(alice) [cnf transformation 23]
141. generous(X0) [duplicate literal removal 130]
359. ~generous(alice) | patient(alice) | rich(alice) [resolution 86,140]
362. patient(alice) | rich(alice) [subsumption resolution 359,141]
364. 32 <=> rich(alice) [avatar definition]
365. ~rich(alice) <- (~32) [avatar component clause 364]
366. rich(alice) <- (32) [avatar component clause 364]
368. 33 <=> patient(alice) [avatar definition]
370. patient(alice) <- (33) [avatar component clause 368]
371. 32 | 33 [avatar split clause 362,368,364]
388. happy(alice) | ~generous(alice) | patient(alice) <- (32) [resolution 366,84]
391. happy(alice) | patient(alice) <- (32) [subsumption resolution 388,141]
393. 36 <=> happy(alice) [avatar definition]
394. ~happy(alice) <- (~36) [avatar component clause 393]
395. happy(alice) <- (36) [avatar component clause 393]
396. 33 | 36 | ~32 [avatar split clause 391,364,393,368]
410. 37 <=> kind(alice) [avatar definition]
412. kind(alice) <- (37) [avatar component clause 410]
448. ~patient(alice) | ~generous(alice) | ~rich(alice) [resolution 92,140]
460. ~patient(alice) | ~rich(alice) [subsumption resolution 448,141]
660. kind(alice) | strong(alice) <- (36) [resolution 395,103]
663. 44 <=> strong(alice) [avatar definition]
665. strong(alice) <- (44) [avatar component clause 663]
666. 44 | 37 | ~36 [avatar split clause 660,393,410,663]
670. ~funny(alice) <- (37) [resolution 412,122]
674. $false <- (37) [subsumption resolution 670,140]
675. ~37 [avatar contradiction clause 674]
739. ~funny(alice) <- (44) [resolution 665,123]
740. $false <- (44) [subsumption resolution 739,140]
741. ~44 [avatar contradiction clause 740]
742. ~32 | ~33 [avatar split clause 460,368,364]
748. rich(alice) | happy(alice) <- (33) [resolution 370,80]
750. happy(alice) <- (~32, 33) [subsumption resolution 748,365]
751. $false <- (~32, 33, ~36) [subsumption resolution 750,394]
752. 32 | ~33 | 36 [avatar contradiction clause 751]
753. $false [avatar sat refutation 371,396,666,675,741,742,752]
% SZS output end Proof for 2155780628530514831936483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is brave then alice is both not quiet and not calm.
Everyone who is rich or not curious is both not kind and rich.
Everyone who is patient or curious is either patient or creative and vice versa.
Everyone who is either not creative or not calm is both kind and quiet.
If mary is both kind and not quiet then someone is either happy or not calm and vice versa.
If paul is creative then lucy is either generous or not wise.
Everyone who is not tall is either not brave or strong.
If mary is either not calm or not brave then someone is either generous or old.
Everyone who is both not wise and patient is both strong and not generous and vice versa.
Everyone who is either curious or kind is patient or brave and vice versa.
Everyone who is quiet or not wise is not strong and vice versa.
Everyone who is calm is patient.
Everyone who is calm or old is both not old and not rich.
If someone is brave or not strong then paul is wise.
Everyone who is both not old and curious is not curious.
Everyone who is not quiet is either not old or quiet and vice versa.
Someone is not patient or not old.
John is not patient or old.
John is both not creative and not curious.
Paul is kind or quiet.
Mary is kind or not tall.
John is wise.
John is funny. | Paul is not calm. | entailment | ((?[X]:(brave(X)))=>((~quiet(alice)&~calm(alice))))&
(![X]:((rich(X)|~curious(X))=>(~kind(X)&rich(X))))&
(![X]:((patient(X)|curious(X))<=>(patient(X)<~>creative(X))))&
(![X]:((~creative(X)<~>~calm(X))=>(kind(X)&quiet(X))))&
(((kind(mary)&~quiet(mary)))<=>(?[X]:((happy(X)<~>~calm(X)))))&
((creative(paul))=>((generous(lucy)<~>~wise(lucy))))&
(![X]:(~tall(X)=>(~brave(X)<~>strong(X))))&
(((~calm(mary)<~>~brave(mary)))=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((~wise(X)&patient(X))<=>(strong(X)&~generous(X))))&
(![X]:((curious(X)<~>kind(X))<=>(patient(X)|brave(X))))&
(![X]:((quiet(X)|~wise(X))<=>~strong(X)))&
(![X]:(calm(X)=>patient(X)))&
(![X]:((calm(X)|old(X))=>(~old(X)&~rich(X))))&
((?[X]:((brave(X)|~strong(X))))=>(wise(paul)))&
(![X]:((~old(X)&curious(X))=>~curious(X)))&
(![X]:(~quiet(X)<=>(~old(X)<~>quiet(X))))&
(?[X]:((~patient(X)|~old(X))))&
((~patient(john)|old(john)))&
((~creative(john)&~curious(john)))&
((kind(paul)|quiet(paul)))&
((kind(mary)|~tall(mary)))&
(wise(john))&
(funny(john)) | ~calm(paul) | [
"p1",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 294913725819282269876812
% SZS output start Proof for 294913725819282269876812
2. ! [X0] : ((~curious(X0) | rich(X0)) => (rich(X0) & ~kind(X0))) [input p1]
13. ! [X0] : ((old(X0) | calm(X0)) => (~rich(X0) & ~old(X0))) [input p12]
15. ! [X0] : ((curious(X0) & ~old(X0)) => ~curious(X0)) [input p14]
24. calm(paul) [input hypothesis]
27. ! [X0] : ((rich(X0) & ~kind(X0)) | (curious(X0) & ~rich(X0))) [ennf transformation 2]
33. ! [X0] : ((~rich(X0) & ~old(X0)) | (~old(X0) & ~calm(X0))) [ennf transformation 13]
35. ! [X0] : (~curious(X0) | (~curious(X0) | old(X0))) [ennf transformation 15]
36. ! [X0] : (~curious(X0) | ~curious(X0) | old(X0)) [flattening 35]
64. curious(X0) | rich(X0) [cnf transformation 27]
104. ~old(X0) | ~old(X0) [cnf transformation 33]
105. ~rich(X0) | ~calm(X0) [cnf transformation 33]
109. ~curious(X0) | ~curious(X0) | old(X0) [cnf transformation 36]
121. calm(paul) [cnf transformation 24]
124. ~curious(X0) | old(X0) [duplicate literal removal 109]
125. ~old(X0) [duplicate literal removal 104]
216. ~curious(X0) [subsumption resolution 124,125]
236. rich(X0) [resolution 64,216]
238. ~calm(X0) [resolution 105,236]
239. $false [resolution 238,121]
% SZS output end Proof for 294913725819282269876812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both kind and not humble then someone is both not funny and not creative and vice versa.
If someone is either happy or generous then alice is either brave or rich and vice versa.
If susan is either not tall or strong then someone is both not creative and humble and vice versa.
Everyone who is either tall or funny is either funny or not humble and vice versa.
If mary is either not calm or not generous then someone is kind.
Everyone who is not curious or brave is either not old or not happy and vice versa.
If someone is either brave or creative then someone is not brave and vice versa.
Everyone who is curious is funny.
If lucy is funny then fred is not quiet and vice versa.
Everyone who is calm is either funny or not rich and vice versa.
If john is not kind then someone is either quiet or old.
Everyone who is not strong is both generous and old and vice versa.
If someone is either patient or kind then fred is both curious and not rich and vice versa.
Everyone who is wise is rich.
Everyone who is both funny and not funny is both happy and tall.
If susan is both quiet and generous then someone is either not generous or not patient.
Someone is not creative or not patient.
Fred is both not generous and not brave.
Someone is both not wise and kind.
Someone is not kind.
Alice is rich.
Mary is either not calm or not brave.
Someone is either not generous or not happy.
Alice is not generous or not calm. | Alice is not rich. | contradiction | (((kind(alice)&~humble(alice)))<=>(?[X]:((~funny(X)&~creative(X)))))&
((?[X]:((happy(X)<~>generous(X))))<=>((brave(alice)<~>rich(alice))))&
(((~tall(susan)<~>strong(susan)))<=>(?[X]:((~creative(X)&humble(X)))))&
(![X]:((tall(X)<~>funny(X))<=>(funny(X)<~>~humble(X))))&
(((~calm(mary)<~>~generous(mary)))=>(?[X]:(kind(X))))&
(![X]:((~curious(X)|brave(X))<=>(~old(X)<~>~happy(X))))&
((?[X]:((brave(X)<~>creative(X))))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)=>funny(X)))&
((funny(lucy))<=>(~quiet(fred)))&
(![X]:(calm(X)<=>(funny(X)<~>~rich(X))))&
((~kind(john))=>(?[X]:((quiet(X)<~>old(X)))))&
(![X]:(~strong(X)<=>(generous(X)&old(X))))&
((?[X]:((patient(X)<~>kind(X))))<=>((curious(fred)&~rich(fred))))&
(![X]:(wise(X)=>rich(X)))&
(![X]:((funny(X)&~funny(X))=>(happy(X)&tall(X))))&
(((quiet(susan)&generous(susan)))=>(?[X]:((~generous(X)<~>~patient(X)))))&
(?[X]:((~creative(X)|~patient(X))))&
((~generous(fred)&~brave(fred)))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:(~kind(X)))&
(rich(alice))&
((~calm(mary)<~>~brave(mary)))&
(?[X]:((~generous(X)<~>~happy(X))))&
((~generous(alice)|~calm(alice))) | ~rich(alice) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6638268031181461185368028
% SZS output start Proof for 6638268031181461185368028
21. rich(alice) [input p20]
25. ~rich(alice) [input hypothesis]
150. rich(alice) [cnf transformation 21]
156. ~rich(alice) [cnf transformation 25]
185. 6 <=> rich(alice) [avatar definition]
359. 6 [avatar split clause 150,185]
385. ~6 [avatar split clause 156,185]
386. $false [avatar sat refutation 359,385]
% SZS output end Proof for 6638268031181461185368028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is tall or not patient then paul is not kind or happy and vice versa. Everyone who is quiet is kind. Everyone who is either rich or funny is either strong or generous and vice versa. Everyone who is either tall or creative is quiet or not strong. Everyone who is both not tall and wise is not curious and vice versa. Everyone who is generous is brave or old and vice versa. Everyone who is not rich or brave is either brave or not old and vice versa. Everyone who is not humble is kind. If alice is either not quiet or humble then someone is both tall and old and vice versa. Everyone who is creative is either not curious or not funny. Everyone who is both kind and generous is not brave or tall and vice versa. If fred is kind then susan is not curious. If someone is either strong or not quiet then someone is either brave or not rich. If someone is not creative or quiet then john is not generous and vice versa. Everyone who is both creative and not rich is both not wise and not curious and vice versa. If john is either funny or happy then someone is not humble and vice versa. Alice is either not patient or strong. Lucy is either not tall or not curious. Someone is not strong or generous. Alice is either not funny or funny. Someone is old. | Fred is rich. | entailment | (((tall(fred)|~patient(fred)))<=>((~kind(paul)|happy(paul))))&
(![X]:(quiet(X)=>kind(X)))&
(![X]:((rich(X)<~>funny(X))<=>(strong(X)<~>generous(X))))&
(![X]:((tall(X)<~>creative(X))=>(quiet(X)|~strong(X))))&
(![X]:((~tall(X)&wise(X))<=>~curious(X)))&
(![X]:(generous(X)<=>(brave(X)|old(X))))&
(![X]:((~rich(X)|brave(X))<=>(brave(X)<~>~old(X))))&
(![X]:(~humble(X)=>kind(X)))&
(((~quiet(alice)<~>humble(alice)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:(creative(X)=>(~curious(X)<~>~funny(X))))&
(![X]:((kind(X)&generous(X))<=>(~brave(X)|tall(X))))&
((kind(fred))=>(~curious(susan)))&
((?[X]:((strong(X)<~>~quiet(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
((?[X]:((~creative(X)|quiet(X))))<=>(~generous(john)))&
(![X]:((creative(X)&~rich(X))<=>(~wise(X)&~curious(X))))&
(((funny(john)<~>happy(john)))<=>(?[X]:(~humble(X))))&
((~patient(alice)<~>strong(alice)))&
((~tall(lucy)<~>~curious(lucy)))&
(?[X]:((~strong(X)|generous(X))))&
((~funny(alice)<~>funny(alice)))&
(?[X]:(old(X))) | rich(fred) | [
"p4",
"p5",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2393571622927216507578843
% SZS output start Proof for 2393571622927216507578843
5. ! [X0] : ((wise(X0) & ~tall(X0)) <=> ~curious(X0)) [input p4]
6. ! [X0] : (generous(X0) <=> (old(X0) | brave(X0))) [input p5]
11. ! [X0] : ((generous(X0) & kind(X0)) <=> (tall(X0) | ~brave(X0))) [input p10]
14. ? [X0] : (quiet(X0) | ~creative(X0)) <=> ~generous(john) [input p13]
15. ! [X0] : ((~rich(X0) & creative(X0)) <=> (~curious(X0) & ~wise(X0))) [input p14]
22. ~rich(fred) [input hypothesis]
35. ! [X0] : (((wise(X0) & ~tall(X0)) | curious(X0)) & (~curious(X0) | (~wise(X0) | tall(X0)))) [nnf transformation 5]
36. ! [X0] : (((wise(X0) & ~tall(X0)) | curious(X0)) & (~curious(X0) | ~wise(X0) | tall(X0))) [flattening 35]
37. ! [X0] : ((generous(X0) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | ~generous(X0))) [nnf transformation 6]
38. ! [X0] : ((generous(X0) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ~generous(X0))) [flattening 37]
46. ! [X0] : (((generous(X0) & kind(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (~generous(X0) | ~kind(X0)))) [nnf transformation 11]
47. ! [X0] : (((generous(X0) & kind(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | ~generous(X0) | ~kind(X0))) [flattening 46]
52. (? [X0] : (quiet(X0) | ~creative(X0)) | generous(john)) & (~generous(john) | ! [X0] : (~quiet(X0) & creative(X0))) [nnf transformation 14]
53. (? [X0] : (quiet(X0) | ~creative(X0)) | generous(john)) & (~generous(john) | ! [X1] : (~quiet(X1) & creative(X1))) [rectify 52]
54. ? [X0] : (quiet(X0) | ~creative(X0)) => (quiet(sK2) | ~creative(sK2)) [choice axiom]
55. ((quiet(sK2) | ~creative(sK2)) | generous(john)) & (~generous(john) | ! [X1] : (~quiet(X1) & creative(X1))) [skolemisation 53,54]
56. ! [X0] : (((~rich(X0) & creative(X0)) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | (rich(X0) | ~creative(X0)))) [nnf transformation 15]
57. ! [X0] : (((~rich(X0) & creative(X0)) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | rich(X0) | ~creative(X0))) [flattening 56]
86. curious(X0) | wise(X0) [cnf transformation 36]
88. ~brave(X0) | generous(X0) [cnf transformation 38]
108. generous(X0) | brave(X0) [cnf transformation 47]
115. ~generous(john) | creative(X1) [cnf transformation 55]
118. ~wise(X0) | rich(X0) | ~creative(X0) [cnf transformation 57]
119. ~curious(X0) | rich(X0) | ~creative(X0) [cnf transformation 57]
134. ~rich(fred) [cnf transformation 22]
182. generous(X0) [subsumption resolution 108,88]
212. creative(X1) [subsumption resolution 115,182]
213. ~curious(X0) | rich(X0) [subsumption resolution 119,212]
214. ~wise(X0) | rich(X0) [subsumption resolution 118,212]
259. rich(X0) | wise(X0) [resolution 213,86]
260. rich(X0) [subsumption resolution 259,214]
261. $false [resolution 260,134]
% SZS output end Proof for 2393571622927216507578843
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is both funny and patient and vice versa.
If someone is either not creative or not wise then someone is both brave and tall.
If susan is not old then someone is either not calm or not brave.
Everyone who is not rich is both quiet and not funny.
Everyone who is either calm or generous is not generous.
If susan is not humble or generous then someone is patient or not kind and vice versa.
If someone is not strong or calm then someone is humble or tall.
Everyone who is both not wise and quiet is either not tall or patient.
Everyone who is not wise or calm is either brave or not patient and vice versa.
If fred is not funny then someone is both not humble and not brave and vice versa.
Everyone who is old or rich is either happy or not generous.
Everyone who is either not humble or not curious is either quiet or not quiet and vice versa.
Everyone who is either not tall or tall is not strong.
Everyone who is strong is both happy and not old.
If someone is not strong then someone is either not rich or strong.
If someone is both curious and not creative then fred is both quiet and happy.
Someone is not generous or strong.
Paul is not quiet or not rich.
Susan is generous or strong.
Paul is either strong or patient.
Paul is not brave.
Someone is generous or not quiet.
Someone is either not calm or patient. | Paul is quiet. | contradiction | (![X]:(patient(X)<=>(funny(X)&patient(X))))&
((?[X]:((~creative(X)<~>~wise(X))))=>(?[X]:((brave(X)&tall(X)))))&
((~old(susan))=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:(~rich(X)=>(quiet(X)&~funny(X))))&
(![X]:((calm(X)<~>generous(X))=>~generous(X)))&
(((~humble(susan)|generous(susan)))<=>(?[X]:((patient(X)|~kind(X)))))&
((?[X]:((~strong(X)|calm(X))))=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((~wise(X)&quiet(X))=>(~tall(X)<~>patient(X))))&
(![X]:((~wise(X)|calm(X))<=>(brave(X)<~>~patient(X))))&
((~funny(fred))<=>(?[X]:((~humble(X)&~brave(X)))))&
(![X]:((old(X)|rich(X))=>(happy(X)<~>~generous(X))))&
(![X]:((~humble(X)<~>~curious(X))<=>(quiet(X)<~>~quiet(X))))&
(![X]:((~tall(X)<~>tall(X))=>~strong(X)))&
(![X]:(strong(X)=>(happy(X)&~old(X))))&
((?[X]:(~strong(X)))=>(?[X]:((~rich(X)<~>strong(X)))))&
((?[X]:((curious(X)&~creative(X))))=>((quiet(fred)&happy(fred))))&
(?[X]:((~generous(X)|strong(X))))&
((~quiet(paul)|~rich(paul)))&
((generous(susan)|strong(susan)))&
((strong(paul)<~>patient(paul)))&
(~brave(paul))&
(?[X]:((generous(X)|~quiet(X))))&
(?[X]:((~calm(X)<~>patient(X)))) | quiet(paul) | [
"p0",
"p3",
"p12",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1168658260562504659568042
% SZS output start Proof for 1168658260562504659568042
1. ! [X0] : (patient(X0) <=> (patient(X0) & funny(X0))) [input p0]
4. ! [X0] : (~rich(X0) => (~funny(X0) & quiet(X0))) [input p3]
13. ! [X0] : ((~tall(X0) <~> tall(X0)) => ~strong(X0)) [input p12]
18. ~rich(paul) | ~quiet(paul) [input p17]
20. strong(paul) <~> patient(paul) [input p19]
24. quiet(paul) [input hypothesis]
30. ! [X0] : ((~funny(X0) & quiet(X0)) | rich(X0)) [ennf transformation 4]
36. ! [X0] : (~strong(X0) | (~tall(X0) <=> tall(X0))) [ennf transformation 13]
40. ! [X0] : ((patient(X0) | (~patient(X0) | ~funny(X0))) & ((patient(X0) & funny(X0)) | ~patient(X0))) [nnf transformation 1]
41. ! [X0] : ((patient(X0) | ~patient(X0) | ~funny(X0)) & ((patient(X0) & funny(X0)) | ~patient(X0))) [flattening 40]
67. ! [X0] : (~strong(X0) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) [nnf transformation 36]
74. (~patient(paul) | ~strong(paul)) & (patient(paul) | strong(paul)) [nnf transformation 20]
80. ~patient(X0) | funny(X0) [cnf transformation 41]
90. ~funny(X0) | rich(X0) [cnf transformation 30]
122. ~strong(X0) | tall(X0) | tall(X0) [cnf transformation 67]
123. ~strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 67]
131. ~rich(paul) | ~quiet(paul) [cnf transformation 18]
133. patient(paul) | strong(paul) [cnf transformation 74]
139. quiet(paul) [cnf transformation 24]
140. ~strong(X0) | tall(X0) [duplicate literal removal 122]
141. ~strong(X0) | ~tall(X0) [duplicate literal removal 123]
241. ~strong(X0) [subsumption resolution 140,141]
259. 25 <=> quiet(paul) [avatar definition]
263. 26 <=> rich(paul) [avatar definition]
265. ~rich(paul) <- (~26) [avatar component clause 263]
266. ~25 | ~26 [avatar split clause 131,263,259]
269. patient(paul) [subsumption resolution 133,241]
289. 25 [avatar split clause 139,259]
290. funny(paul) [resolution 80,269]
292. rich(paul) [resolution 90,290]
293. $false <- (~26) [subsumption resolution 292,265]
294. 26 [avatar contradiction clause 293]
295. $false [avatar sat refutation 266,289,294]
% SZS output end Proof for 1168658260562504659568042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not rich then john is either not rich or curious. If someone is not rich or not generous then someone is wise and vice versa. Everyone who is either not old or humble is both patient and not old and vice versa. Everyone who is either patient or not generous is strong. If fred is not generous or curious then someone is either not old or generous and vice versa. If someone is rich or happy then someone is either curious or not tall and vice versa. If john is not curious then alice is happy. Everyone who is both not quiet and old is both kind and creative. Everyone who is both not rich and not funny is kind. Everyone who is quiet or old is either quiet or strong and vice versa. Everyone who is both tall and kind is not patient or not rich. If lucy is not humble then fred is both happy and not patient. Everyone who is not funny or not calm is either brave or not funny. Everyone who is both generous and not brave is either happy or not happy and vice versa. If susan is either not generous or quiet then john is humble and vice versa. If someone is both quiet and old then someone is not calm or wise and vice versa. Lucy is both not creative and humble. Paul is either wise or calm. Someone is both not patient and not humble. Mary is not funny or funny. | Lucy is not strong. | entailment | ((?[X]:((creative(X)&~rich(X))))=>((~rich(john)<~>curious(john))))&
((?[X]:((~rich(X)|~generous(X))))<=>(?[X]:(wise(X))))&
(![X]:((~old(X)<~>humble(X))<=>(patient(X)&~old(X))))&
(![X]:((patient(X)<~>~generous(X))=>strong(X)))&
(((~generous(fred)|curious(fred)))<=>(?[X]:((~old(X)<~>generous(X)))))&
((?[X]:((rich(X)|happy(X))))<=>(?[X]:((curious(X)<~>~tall(X)))))&
((~curious(john))=>(happy(alice)))&
(![X]:((~quiet(X)&old(X))=>(kind(X)&creative(X))))&
(![X]:((~rich(X)&~funny(X))=>kind(X)))&
(![X]:((quiet(X)|old(X))<=>(quiet(X)<~>strong(X))))&
(![X]:((tall(X)&kind(X))=>(~patient(X)|~rich(X))))&
((~humble(lucy))=>((happy(fred)&~patient(fred))))&
(![X]:((~funny(X)|~calm(X))=>(brave(X)<~>~funny(X))))&
(![X]:((generous(X)&~brave(X))<=>(happy(X)<~>~happy(X))))&
(((~generous(susan)<~>quiet(susan)))<=>(humble(john)))&
((?[X]:((quiet(X)&old(X))))<=>(?[X]:((~calm(X)|wise(X)))))&
((~creative(lucy)&humble(lucy)))&
((wise(paul)<~>calm(paul)))&
(?[X]:((~patient(X)&~humble(X))))&
((~funny(mary)|funny(mary))) | ~strong(lucy) | [
"p2",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6114535350371906004999832
% SZS output start Proof for 6114535350371906004999832
3. ! [X0] : ((~old(X0) <~> humble(X0)) <=> (~old(X0) & patient(X0))) [input p2]
10. ! [X0] : ((old(X0) | quiet(X0)) <=> (quiet(X0) <~> strong(X0))) [input p9]
17. humble(lucy) & ~creative(lucy) [input p16]
21. strong(lucy) [input hypothesis]
42. ! [X0] : ((((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | (old(X0) | ~patient(X0))) & ((~old(X0) & patient(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0))))) [nnf transformation 3]
43. ! [X0] : ((((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | old(X0) | ~patient(X0)) & ((~old(X0) & patient(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0))))) [flattening 42]
55. ! [X0] : (((old(X0) | quiet(X0)) | ((quiet(X0) | ~strong(X0)) & (strong(X0) | ~quiet(X0)))) & (((~strong(X0) | ~quiet(X0)) & (strong(X0) | quiet(X0))) | (~old(X0) & ~quiet(X0)))) [nnf transformation 10]
56. ! [X0] : ((old(X0) | quiet(X0) | ((quiet(X0) | ~strong(X0)) & (strong(X0) | ~quiet(X0)))) & (((~strong(X0) | ~quiet(X0)) & (strong(X0) | quiet(X0))) | (~old(X0) & ~quiet(X0)))) [flattening 55]
77. ~old(X0) | ~old(X0) | ~humble(X0) [cnf transformation 43]
100. ~strong(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 56]
103. old(X0) | quiet(X0) | quiet(X0) | ~strong(X0) [cnf transformation 56]
127. humble(lucy) [cnf transformation 17]
133. strong(lucy) [cnf transformation 21]
139. ~quiet(X0) | ~strong(X0) [duplicate literal removal 100]
140. ~strong(X0) | quiet(X0) | old(X0) [duplicate literal removal 103]
141. ~humble(X0) | ~old(X0) [duplicate literal removal 77]
248. 25 <=> humble(lucy) [avatar definition]
250. humble(lucy) <- (25) [avatar component clause 248]
307. 25 [avatar split clause 127,248]
334. ~old(lucy) <- (25) [resolution 141,250]
384. quiet(lucy) | old(lucy) [resolution 140,133]
386. quiet(lucy) <- (25) [subsumption resolution 384,334]
388. ~strong(lucy) <- (25) [resolution 386,139]
389. $false <- (25) [subsumption resolution 388,133]
390. ~25 [avatar contradiction clause 389]
391. $false [avatar sat refutation 307,390]
% SZS output end Proof for 6114535350371906004999832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not wise then lucy is both quiet and happy.
Everyone who is not brave or wise is either curious or not generous and vice versa.
Everyone who is brave is not patient.
Everyone who is patient is either not humble or not tall and vice versa.
If alice is not happy or not curious then someone is both not tall and strong and vice versa.
If someone is quiet or humble then paul is both not tall and not calm and vice versa.
Everyone who is both not funny and funny is not generous and vice versa.
If someone is both not strong and not happy then john is both tall and funny and vice versa.
If john is either patient or not humble then someone is not tall or not strong and vice versa.
If fred is both brave and not brave then someone is both wise and not patient.
If someone is either not brave or not patient then paul is either not funny or generous.
Everyone who is rich is both not rich and tall.
Everyone who is quiet or not kind is tall or not kind.
If someone is either not creative or calm then susan is funny and vice versa.
If someone is both wise and old then fred is both brave and creative.
Everyone who is not creative is either not rich or happy and vice versa.
Alice is kind.
Lucy is not wise or not quiet.
Someone is both wise and old.
Someone is either not curious or quiet.
Lucy is either wise or kind.
Paul is tall or not brave.
Someone is calm or strong.
Someone is old. | Fred is patient. | contradiction | ((?[X]:((~patient(X)|~wise(X))))=>((quiet(lucy)&happy(lucy))))&
(![X]:((~brave(X)|wise(X))<=>(curious(X)<~>~generous(X))))&
(![X]:(brave(X)=>~patient(X)))&
(![X]:(patient(X)<=>(~humble(X)<~>~tall(X))))&
(((~happy(alice)|~curious(alice)))<=>(?[X]:((~tall(X)&strong(X)))))&
((?[X]:((quiet(X)|humble(X))))<=>((~tall(paul)&~calm(paul))))&
(![X]:((~funny(X)&funny(X))<=>~generous(X)))&
((?[X]:((~strong(X)&~happy(X))))<=>((tall(john)&funny(john))))&
(((patient(john)<~>~humble(john)))<=>(?[X]:((~tall(X)|~strong(X)))))&
(((brave(fred)&~brave(fred)))=>(?[X]:((wise(X)&~patient(X)))))&
((?[X]:((~brave(X)<~>~patient(X))))=>((~funny(paul)<~>generous(paul))))&
(![X]:(rich(X)=>(~rich(X)&tall(X))))&
(![X]:((quiet(X)|~kind(X))=>(tall(X)|~kind(X))))&
((?[X]:((~creative(X)<~>calm(X))))<=>(funny(susan)))&
((?[X]:((wise(X)&old(X))))=>((brave(fred)&creative(fred))))&
(![X]:(~creative(X)<=>(~rich(X)<~>happy(X))))&
(kind(alice))&
((~wise(lucy)|~quiet(lucy)))&
(?[X]:((wise(X)&old(X))))&
(?[X]:((~curious(X)<~>quiet(X))))&
((wise(lucy)<~>kind(lucy)))&
((tall(paul)|~brave(paul)))&
(?[X]:((calm(X)|strong(X))))&
(?[X]:(old(X))) | patient(fred) | [
"p2",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5696821335568711239874154
% SZS output start Proof for 5696821335568711239874154
3. ! [X0] : (brave(X0) => ~patient(X0)) [input p2]
15. ? [X0] : (old(X0) & wise(X0)) => (creative(fred) & brave(fred)) [input p14]
19. ? [X0] : (old(X0) & wise(X0)) [input p18]
25. patient(fred) [input hypothesis]
27. ! [X0] : (~patient(X0) | ~brave(X0)) [ennf transformation 3]
34. (creative(fred) & brave(fred)) | ! [X0] : (~old(X0) | ~wise(X0)) [ennf transformation 15]
67. ? [X0] : (old(X0) & wise(X0)) => (old(sK6) & wise(sK6)) [choice axiom]
68. old(sK6) & wise(sK6) [skolemisation 19,67]
87. ~brave(X0) | ~patient(X0) [cnf transformation 27]
129. brave(fred) | ~old(X0) | ~wise(X0) [cnf transformation 34]
137. wise(sK6) [cnf transformation 68]
138. old(sK6) [cnf transformation 68]
146. patient(fred) [cnf transformation 25]
308. 35 <=> ! [X0] : (~old(X0) | ~wise(X0)) [avatar definition]
309. ~old(X0) | ~wise(X0) <- (35) [avatar component clause 308]
316. 37 <=> brave(fred) [avatar definition]
318. brave(fred) <- (37) [avatar component clause 316]
319. 35 | 37 [avatar split clause 129,316,308]
357. ~wise(sK6) <- (35) [resolution 309,138]
359. $false <- (35) [subsumption resolution 357,137]
360. ~35 [avatar contradiction clause 359]
361. ~patient(fred) <- (37) [resolution 318,87]
362. $false <- (37) [subsumption resolution 361,146]
363. ~37 [avatar contradiction clause 362]
364. $false [avatar sat refutation 319,360,363]
% SZS output end Proof for 5696821335568711239874154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or not curious then fred is both happy and not happy and vice versa. Everyone who is kind or calm is both not funny and tall. Everyone who is both not brave and old is either not rich or brave and vice versa. If john is either humble or not kind then fred is both tall and curious and vice versa. Everyone who is either tall or not kind is tall or not calm and vice versa. If someone is both creative and not old then someone is patient or not old and vice versa. Everyone who is both not happy and old is old and vice versa. Everyone who is patient is both not patient and old and vice versa. Everyone who is either creative or wise is either funny or not funny. Everyone who is not old is not tall. Everyone who is either not strong or happy is both quiet and not generous and vice versa. Everyone who is both old and kind is either not calm or not rich. If someone is not tall then fred is humble or quiet and vice versa. Everyone who is calm is both not kind and strong. Everyone who is either patient or not creative is both not wise and curious and vice versa. Someone is not humble. Someone is not tall or creative. Lucy is either quiet or creative. Someone is either kind or quiet. Someone is both not quiet and not calm. | Fred is not tall. | entailment | ((?[X]:((~creative(X)<~>~curious(X))))<=>((happy(fred)&~happy(fred))))&
(![X]:((kind(X)|calm(X))=>(~funny(X)&tall(X))))&
(![X]:((~brave(X)&old(X))<=>(~rich(X)<~>brave(X))))&
(((humble(john)<~>~kind(john)))<=>((tall(fred)&curious(fred))))&
(![X]:((tall(X)<~>~kind(X))<=>(tall(X)|~calm(X))))&
((?[X]:((creative(X)&~old(X))))<=>(?[X]:((patient(X)|~old(X)))))&
(![X]:((~happy(X)&old(X))<=>old(X)))&
(![X]:(patient(X)<=>(~patient(X)&old(X))))&
(![X]:((creative(X)<~>wise(X))=>(funny(X)<~>~funny(X))))&
(![X]:(~old(X)=>~tall(X)))&
(![X]:((~strong(X)<~>happy(X))<=>(quiet(X)&~generous(X))))&
(![X]:((old(X)&kind(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:(~tall(X)))<=>((humble(fred)|quiet(fred))))&
(![X]:(calm(X)=>(~kind(X)&strong(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~wise(X)&curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~tall(X)|creative(X))))&
((quiet(lucy)<~>creative(lucy)))&
(?[X]:((kind(X)<~>quiet(X))))&
(?[X]:((~quiet(X)&~calm(X)))) | ~tall(fred) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1102907205090492977301252
% SZS output start Proof for 1102907205090492977301252
8. ! [X0] : (patient(X0) <=> (old(X0) & ~patient(X0))) [input p7]
10. ! [X0] : (~old(X0) => ~tall(X0)) [input p9]
21. tall(fred) [input hypothesis]
25. ! [X0] : (~tall(X0) | old(X0)) [ennf transformation 10]
47. ! [X0] : ((patient(X0) | (~old(X0) | patient(X0))) & ((old(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 8]
48. ! [X0] : ((patient(X0) | ~old(X0) | patient(X0)) & ((old(X0) & ~patient(X0)) | ~patient(X0))) [flattening 47]
106. ~patient(X0) | ~patient(X0) [cnf transformation 48]
108. patient(X0) | ~old(X0) | patient(X0) [cnf transformation 48]
113. ~tall(X0) | old(X0) [cnf transformation 25]
141. tall(fred) [cnf transformation 21]
142. ~patient(X0) [duplicate literal removal 106]
143. ~old(X0) | patient(X0) [duplicate literal removal 108]
164. 4 <=> tall(fred) [avatar definition]
165. tall(fred) <- (4) [avatar component clause 164]
194. 10 <=> ! [X1] : ~patient(X1) [avatar definition]
195. ~patient(X1) <- (10) [avatar component clause 194]
215. 10 [avatar split clause 142,194]
264. 4 [avatar split clause 141,164]
270. old(fred) <- (4) [resolution 113,165]
278. patient(fred) <- (4) [resolution 270,143]
280. $false <- (4, 10) [subsumption resolution 278,195]
281. ~4 | ~10 [avatar contradiction clause 280]
283. $false [avatar sat refutation 215,264,281]
% SZS output end Proof for 1102907205090492977301252
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not humble then someone is either not wise or funny. If someone is quiet or not patient then paul is curious and vice versa. Everyone who is not creative is either not generous or funny and vice versa. If someone is both curious and rich then someone is both patient and not tall and vice versa. Everyone who is not curious is old and vice versa. Everyone who is either not old or not happy is strong. If someone is either not creative or not strong then fred is both generous and creative and vice versa. If paul is both curious and not humble then lucy is not funny. Everyone who is either humble or tall is not brave or not tall and vice versa. Everyone who is patient or calm is old or brave. Everyone who is not curious or not generous is either not generous or not happy. If someone is rich then someone is both not patient and not rich. Everyone who is either not humble or kind is both strong and old. Everyone who is not happy is either not patient or not calm and vice versa. If mary is either not tall or not wise then john is not humble or kind and vice versa. If paul is kind then someone is brave or calm and vice versa. Alice is both not creative and not brave. Someone is happy. Lucy is either not wise or brave. Someone is quiet or not tall. Paul is not kind or rich. Alice is either not humble or not rich. Susan is wise or kind. Someone is creative. | Paul is not patient. | entailment | ((?[X]:((~quiet(X)<~>~humble(X))))=>(?[X]:((~wise(X)<~>funny(X)))))&
((?[X]:((quiet(X)|~patient(X))))<=>(curious(paul)))&
(![X]:(~creative(X)<=>(~generous(X)<~>funny(X))))&
((?[X]:((curious(X)&rich(X))))<=>(?[X]:((patient(X)&~tall(X)))))&
(![X]:(~curious(X)<=>old(X)))&
(![X]:((~old(X)<~>~happy(X))=>strong(X)))&
((?[X]:((~creative(X)<~>~strong(X))))<=>((generous(fred)&creative(fred))))&
(((curious(paul)&~humble(paul)))=>(~funny(lucy)))&
(![X]:((humble(X)<~>tall(X))<=>(~brave(X)|~tall(X))))&
(![X]:((patient(X)|calm(X))=>(old(X)|brave(X))))&
(![X]:((~curious(X)|~generous(X))=>(~generous(X)<~>~happy(X))))&
((?[X]:(rich(X)))=>(?[X]:((~patient(X)&~rich(X)))))&
(![X]:((~humble(X)<~>kind(X))=>(strong(X)&old(X))))&
(![X]:(~happy(X)<=>(~patient(X)<~>~calm(X))))&
(((~tall(mary)<~>~wise(mary)))<=>((~humble(john)|kind(john))))&
((kind(paul))<=>(?[X]:((brave(X)|calm(X)))))&
((~creative(alice)&~brave(alice)))&
(?[X]:(happy(X)))&
((~wise(lucy)<~>brave(lucy)))&
(?[X]:((quiet(X)|~tall(X))))&
((~kind(paul)|rich(paul)))&
((~humble(alice)<~>~rich(alice)))&
((wise(susan)|kind(susan)))&
(?[X]:(creative(X))) | ~patient(paul) | [
"p1",
"p4",
"p8",
"p9",
"p11",
"p12",
"p13",
"p15",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6087626765616545550850339
% SZS output start Proof for 6087626765616545550850339
2. ? [X0] : (~patient(X0) | quiet(X0)) <=> curious(paul) [input p1]
5. ! [X0] : (~curious(X0) <=> old(X0)) [input p4]
9. ! [X0] : ((humble(X0) <~> tall(X0)) <=> (~tall(X0) | ~brave(X0))) [input p8]
10. ! [X0] : ((calm(X0) | patient(X0)) => (brave(X0) | old(X0))) [input p9]
12. ? [X0] : rich(X0) => ? [X0] : (~rich(X0) & ~patient(X0)) [input p11]
13. ! [X0] : ((~humble(X0) <~> kind(X0)) => (old(X0) & strong(X0))) [input p12]
14. ! [X0] : (~happy(X0) <=> (~patient(X0) <~> ~calm(X0))) [input p13]
16. kind(paul) <=> ? [X0] : (calm(X0) | brave(X0)) [input p15]
18. ? [X0] : happy(X0) [input p17]
21. rich(paul) | ~kind(paul) [input p20]
25. patient(paul) [input hypothesis]
28. ? [X0] : rich(X0) => ? [X1] : (~rich(X1) & ~patient(X1)) [rectify 12]
33. ! [X0] : ((brave(X0) | old(X0)) | (~calm(X0) & ~patient(X0))) [ennf transformation 10]
34. ! [X0] : (brave(X0) | old(X0) | (~calm(X0) & ~patient(X0))) [flattening 33]
36. ? [X1] : (~rich(X1) & ~patient(X1)) | ! [X0] : ~rich(X0) [ennf transformation 28]
37. ! [X0] : ((old(X0) & strong(X0)) | (~humble(X0) <=> kind(X0))) [ennf transformation 13]
42. (? [X0] : (~patient(X0) | quiet(X0)) | ~curious(paul)) & (curious(paul) | ! [X0] : (patient(X0) & ~quiet(X0))) [nnf transformation 2]
43. (? [X0] : (~patient(X0) | quiet(X0)) | ~curious(paul)) & (curious(paul) | ! [X1] : (patient(X1) & ~quiet(X1))) [rectify 42]
44. ? [X0] : (~patient(X0) | quiet(X0)) => (~patient(sK1) | quiet(sK1)) [choice axiom]
45. ((~patient(sK1) | quiet(sK1)) | ~curious(paul)) & (curious(paul) | ! [X1] : (patient(X1) & ~quiet(X1))) [skolemisation 43,44]
52. ! [X0] : ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0))) [nnf transformation 5]
59. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (tall(X0) & brave(X0))) & ((~tall(X0) | ~brave(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [nnf transformation 9]
60. ! [X0] : ((((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (tall(X0) & brave(X0))) & (~tall(X0) | ~brave(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0))))) [flattening 59]
62. ? [X0] : (~rich(X0) & ~patient(X0)) | ! [X1] : ~rich(X1) [rectify 36]
63. ? [X0] : (~rich(X0) & ~patient(X0)) => (~rich(sK5) & ~patient(sK5)) [choice axiom]
64. (~rich(sK5) & ~patient(sK5)) | ! [X1] : ~rich(X1) [skolemisation 62,63]
65. ! [X0] : ((old(X0) & strong(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0)))) [nnf transformation 37]
66. ! [X0] : ((~happy(X0) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | happy(X0))) [nnf transformation 14]
69. (kind(paul) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X0] : (calm(X0) | brave(X0)) | ~kind(paul)) [nnf transformation 16]
70. (kind(paul) | ! [X0] : (~calm(X0) & ~brave(X0))) & (? [X1] : (calm(X1) | brave(X1)) | ~kind(paul)) [rectify 69]
71. ? [X1] : (calm(X1) | brave(X1)) => (calm(sK6) | brave(sK6)) [choice axiom]
72. (kind(paul) | ! [X0] : (~calm(X0) & ~brave(X0))) & ((calm(sK6) | brave(sK6)) | ~kind(paul)) [skolemisation 70,71]
73. ? [X0] : happy(X0) => happy(sK7) [choice axiom]
74. happy(sK7) [skolemisation 18,73]
86. curious(paul) | patient(X1) [cnf transformation 45]
97. ~old(X0) | ~curious(X0) [cnf transformation 52]
108. ~tall(X0) | ~brave(X0) | humble(X0) | ~tall(X0) [cnf transformation 60]
110. tall(X0) | humble(X0) | tall(X0) [cnf transformation 60]
113. ~patient(X0) | old(X0) | brave(X0) [cnf transformation 34]
119. ~patient(sK5) | ~rich(X1) [cnf transformation 64]
124. ~kind(X0) | ~humble(X0) | old(X0) [cnf transformation 65]
128. ~happy(X0) | ~patient(X0) | calm(X0) [cnf transformation 66]
136. kind(paul) | ~brave(X0) [cnf transformation 72]
137. kind(paul) | ~calm(X0) [cnf transformation 72]
140. happy(sK7) [cnf transformation 74]
144. rich(paul) | ~kind(paul) [cnf transformation 21]
149. patient(paul) [cnf transformation 25]
151. ~tall(X0) | ~brave(X0) | humble(X0) [duplicate literal removal 108]
152. tall(X0) | humble(X0) [duplicate literal removal 110]
172. 5 <=> curious(paul) [avatar definition]
173. curious(paul) <- (5) [avatar component clause 172]
185. 8 <=> ! [X1] : patient(X1) [avatar definition]
186. patient(X1) <- (8) [avatar component clause 185]
187. 8 | 5 [avatar split clause 86,172,185]
247. 22 <=> humble(paul) [avatar definition]
255. ~brave(X0) | humble(X0) [subsumption resolution 151,152]
257. 24 <=> ! [X1] : ~rich(X1) [avatar definition]
258. ~rich(X1) <- (24) [avatar component clause 257]
265. 26 <=> patient(sK5) [avatar definition]
267. ~patient(sK5) <- (~26) [avatar component clause 265]
268. 24 | ~26 [avatar split clause 119,265,257]
292. 31 <=> ! [X0] : ~calm(X0) [avatar definition]
293. ~calm(X0) <- (31) [avatar component clause 292]
295. 32 <=> kind(paul) [avatar definition]
297. kind(paul) <- (32) [avatar component clause 295]
298. 31 | 32 [avatar split clause 137,295,292]
300. 33 <=> ! [X0] : ~brave(X0) [avatar definition]
301. ~brave(X0) <- (33) [avatar component clause 300]
302. 33 | 32 [avatar split clause 136,295,300]
332. 40 <=> rich(paul) [avatar definition]
334. rich(paul) <- (40) [avatar component clause 332]
335. ~32 | 40 [avatar split clause 144,332,295]
406. old(paul) | brave(paul) [resolution 113,149]
407. old(paul) <- (33) [subsumption resolution 406,301]
409. ~curious(paul) <- (33) [resolution 407,97]
419. $false <- (5, 33) [subsumption resolution 409,173]
420. ~5 | ~33 [avatar contradiction clause 419]
422. 53 <=> brave(paul) [avatar definition]
424. brave(paul) <- (53) [avatar component clause 422]
426. 54 <=> old(paul) [avatar definition]
428. old(paul) <- (54) [avatar component clause 426]
429. 53 | 54 [avatar split clause 406,426,422]
458. $false <- (8, ~26) [resolution 186,267]
461. ~8 | 26 [avatar contradiction clause 458]
474. $false <- (24, 40) [resolution 258,334]
475. ~24 | ~40 [avatar contradiction clause 474]
493. humble(paul) <- (53) [resolution 424,255]
496. 22 | ~53 [avatar split clause 493,422,247]
518. ~humble(paul) | old(paul) <- (32) [resolution 124,297]
523. ~curious(paul) <- (54) [resolution 428,97]
525. $false <- (5, 54) [subsumption resolution 523,173]
526. ~5 | ~54 [avatar contradiction clause 525]
527. 54 | ~22 | ~32 [avatar split clause 518,295,247,426]
554. ~patient(sK7) | calm(sK7) [resolution 128,140]
556. calm(sK7) <- (8) [subsumption resolution 554,186]
557. $false <- (8, 31) [subsumption resolution 556,293]
558. ~8 | ~31 [avatar contradiction clause 557]
561. $false [avatar sat refutation 187,268,298,302,335,420,429,461,475,496,526,527,558]
% SZS output end Proof for 6087626765616545550850339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not rich then someone is brave or not brave and vice versa.
Everyone who is not curious is either creative or not brave and vice versa.
Everyone who is not quiet or not funny is both brave and strong and vice versa.
Everyone who is funny is both not humble and not kind.
Everyone who is either not humble or not happy is not patient and vice versa.
If someone is tall then someone is calm.
If someone is both not curious and rich then paul is not rich.
Everyone who is both not quiet and quiet is either humble or brave.
If lucy is either not wise or curious then paul is either calm or not tall.
If someone is not generous then lucy is either kind or not quiet and vice versa.
Everyone who is both not strong and not patient is not funny or brave and vice versa.
Everyone who is not happy or quiet is rich or happy and vice versa.
If someone is either not rich or not old then someone is old and vice versa.
Everyone who is not patient or not kind is not humble and vice versa.
Everyone who is not brave or not tall is either not creative or not rich.
If someone is either not kind or not patient then mary is generous or not quiet and vice versa.
Fred is both rich and generous.
Fred is both not strong and not patient.
John is both wise and strong.
Someone is either happy or not strong.
Someone is not happy.
Someone is not rich or not happy.
Paul is both happy and not rich.
Susan is creative. | Lucy is humble. | contradiction | ((~rich(paul))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:(~curious(X)<=>(creative(X)<~>~brave(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(brave(X)&strong(X))))&
(![X]:(funny(X)=>(~humble(X)&~kind(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>~patient(X)))&
((?[X]:(tall(X)))=>(?[X]:(calm(X))))&
((?[X]:((~curious(X)&rich(X))))=>(~rich(paul)))&
(![X]:((~quiet(X)&quiet(X))=>(humble(X)<~>brave(X))))&
(((~wise(lucy)<~>curious(lucy)))=>((calm(paul)<~>~tall(paul))))&
((?[X]:(~generous(X)))<=>((kind(lucy)<~>~quiet(lucy))))&
(![X]:((~strong(X)&~patient(X))<=>(~funny(X)|brave(X))))&
(![X]:((~happy(X)|quiet(X))<=>(rich(X)|happy(X))))&
((?[X]:((~rich(X)<~>~old(X))))<=>(?[X]:(old(X))))&
(![X]:((~patient(X)|~kind(X))<=>~humble(X)))&
(![X]:((~brave(X)|~tall(X))=>(~creative(X)<~>~rich(X))))&
((?[X]:((~kind(X)<~>~patient(X))))<=>((generous(mary)|~quiet(mary))))&
((rich(fred)&generous(fred)))&
((~strong(fred)&~patient(fred)))&
((wise(john)&strong(john)))&
(?[X]:((happy(X)<~>~strong(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~rich(X)|~happy(X))))&
((happy(paul)&~rich(paul)))&
(creative(susan)) | humble(lucy) | [
"p2",
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5629974675613956378222830
% SZS output start Proof for 5629974675613956378222830
3. ! [X0] : ((~funny(X0) | ~quiet(X0)) <=> (strong(X0) & brave(X0))) [input p2]
4. ! [X0] : (funny(X0) => (~kind(X0) & ~humble(X0))) [input p3]
11. ! [X0] : ((~patient(X0) & ~strong(X0)) <=> (brave(X0) | ~funny(X0))) [input p10]
25. humble(lucy) [input hypothesis]
28. ! [X0] : ((~kind(X0) & ~humble(X0)) | ~funny(X0)) [ennf transformation 4]
40. ! [X0] : (((~funny(X0) | ~quiet(X0)) | (~strong(X0) | ~brave(X0))) & ((strong(X0) & brave(X0)) | (funny(X0) & quiet(X0)))) [nnf transformation 3]
41. ! [X0] : ((~funny(X0) | ~quiet(X0) | ~strong(X0) | ~brave(X0)) & ((strong(X0) & brave(X0)) | (funny(X0) & quiet(X0)))) [flattening 40]
52. ! [X0] : (((~patient(X0) & ~strong(X0)) | (~brave(X0) & funny(X0))) & ((brave(X0) | ~funny(X0)) | (patient(X0) | strong(X0)))) [nnf transformation 11]
53. ! [X0] : (((~patient(X0) & ~strong(X0)) | (~brave(X0) & funny(X0))) & (brave(X0) | ~funny(X0) | patient(X0) | strong(X0))) [flattening 52]
86. strong(X0) | funny(X0) [cnf transformation 41]
88. ~humble(X0) | ~funny(X0) [cnf transformation 28]
107. ~strong(X0) | funny(X0) [cnf transformation 53]
145. humble(lucy) [cnf transformation 25]
211. funny(X0) [subsumption resolution 107,86]
294. ~funny(lucy) [resolution 88,145]
295. $false [subsumption resolution 294,211]
% SZS output end Proof for 5629974675613956378222830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not strong then someone is both creative and tall. If fred is both funny and not curious then alice is generous or not curious. Everyone who is not tall or not happy is both creative and kind. If susan is creative then susan is humble or not curious. If someone is either rich or not old then john is either not brave or not rich. Everyone who is not generous is both happy and generous and vice versa. Everyone who is kind is either not humble or not patient. If lucy is both funny and not patient then someone is not patient or not humble. Everyone who is not old is either strong or not rich. If alice is both brave and not generous then lucy is generous. If someone is either not calm or not strong then someone is both creative and not humble. If someone is not wise then someone is not patient and vice versa. If someone is either rich or old then someone is both not kind and generous and vice versa. Everyone who is either not old or not curious is both curious and happy and vice versa. If someone is generous then mary is both funny and curious and vice versa. Everyone who is wise is happy or not old. Someone is not old or funny. Susan is both not brave and not funny. Someone is not curious. Someone is both strong and not patient. Someone is both not funny and not rich. Alice is both not funny and tall. Someone is either generous or curious. | Alice is tall. | entailment | ((?[X]:((brave(X)<~>~strong(X))))=>(?[X]:((creative(X)&tall(X)))))&
(((funny(fred)&~curious(fred)))=>((generous(alice)|~curious(alice))))&
(![X]:((~tall(X)|~happy(X))=>(creative(X)&kind(X))))&
((creative(susan))=>((humble(susan)|~curious(susan))))&
((?[X]:((rich(X)<~>~old(X))))=>((~brave(john)<~>~rich(john))))&
(![X]:(~generous(X)<=>(happy(X)&generous(X))))&
(![X]:(kind(X)=>(~humble(X)<~>~patient(X))))&
(((funny(lucy)&~patient(lucy)))=>(?[X]:((~patient(X)|~humble(X)))))&
(![X]:(~old(X)=>(strong(X)<~>~rich(X))))&
(((brave(alice)&~generous(alice)))=>(generous(lucy)))&
((?[X]:((~calm(X)<~>~strong(X))))=>(?[X]:((creative(X)&~humble(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:(~patient(X))))&
((?[X]:((rich(X)<~>old(X))))<=>(?[X]:((~kind(X)&generous(X)))))&
(![X]:((~old(X)<~>~curious(X))<=>(curious(X)&happy(X))))&
((?[X]:(generous(X)))<=>((funny(mary)&curious(mary))))&
(![X]:(wise(X)=>(happy(X)|~old(X))))&
(?[X]:((~old(X)|funny(X))))&
((~brave(susan)&~funny(susan)))&
(?[X]:(~curious(X)))&
(?[X]:((strong(X)&~patient(X))))&
(?[X]:((~funny(X)&~rich(X))))&
((~funny(alice)&tall(alice)))&
(?[X]:((generous(X)<~>curious(X)))) | tall(alice) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5866077012171855592155925
% SZS output start Proof for 5866077012171855592155925
22. tall(alice) & ~funny(alice) [input p21]
24. ~tall(alice) [input hypothesis]
142. tall(alice) [cnf transformation 22]
145. ~tall(alice) [cnf transformation 24]
306. $false [subsumption resolution 145,142]
% SZS output end Proof for 5866077012171855592155925
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not kind then paul is both patient and quiet.
If paul is both not wise and old then someone is not humble.
Everyone who is either not rich or kind is not strong or not happy and vice versa.
If someone is either not kind or old then someone is either not wise or not brave and vice versa.
Everyone who is both not creative and strong is both not rich and calm.
If someone is both happy and strong then john is either not old or not brave.
Everyone who is not patient or strong is not old or wise and vice versa.
Everyone who is either not generous or not rich is funny.
If lucy is both brave and not humble then someone is both tall and not creative and vice versa.
Everyone who is either patient or not curious is either not happy or quiet.
If someone is either funny or happy then lucy is both not curious and humble.
Everyone who is both not old and not kind is either wise or not brave.
Everyone who is not patient is either quiet or kind and vice versa.
Everyone who is both not quiet and not curious is brave.
If someone is generous or not tall then someone is not tall or creative and vice versa.
If someone is either not quiet or funny then john is both not old and not wise and vice versa.
John is not strong.
Mary is not curious.
Someone is either not rich or creative.
Someone is both not tall and not curious.
Someone is both not brave and happy.
Fred is both not rich and not funny.
Someone is either not rich or generous. | Lucy is not funny. | neutral | ((?[X]:(~kind(X)))=>((patient(paul)&quiet(paul))))&
(((~wise(paul)&old(paul)))=>(?[X]:(~humble(X))))&
(![X]:((~rich(X)<~>kind(X))<=>(~strong(X)|~happy(X))))&
((?[X]:((~kind(X)<~>old(X))))<=>(?[X]:((~wise(X)<~>~brave(X)))))&
(![X]:((~creative(X)&strong(X))=>(~rich(X)&calm(X))))&
((?[X]:((happy(X)&strong(X))))=>((~old(john)<~>~brave(john))))&
(![X]:((~patient(X)|strong(X))<=>(~old(X)|wise(X))))&
(![X]:((~generous(X)<~>~rich(X))=>funny(X)))&
(((brave(lucy)&~humble(lucy)))<=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((patient(X)<~>~curious(X))=>(~happy(X)<~>quiet(X))))&
((?[X]:((funny(X)<~>happy(X))))=>((~curious(lucy)&humble(lucy))))&
(![X]:((~old(X)&~kind(X))=>(wise(X)<~>~brave(X))))&
(![X]:(~patient(X)<=>(quiet(X)<~>kind(X))))&
(![X]:((~quiet(X)&~curious(X))=>brave(X)))&
((?[X]:((generous(X)|~tall(X))))<=>(?[X]:((~tall(X)|creative(X)))))&
((?[X]:((~quiet(X)<~>funny(X))))<=>((~old(john)&~wise(john))))&
(~strong(john))&
(~curious(mary))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((~tall(X)&~curious(X))))&
(?[X]:((~brave(X)&happy(X))))&
((~rich(fred)&~funny(fred)))&
(?[X]:((~rich(X)<~>generous(X)))) | ~funny(lucy) | [] | null | 0 |
If fred is kind or not happy then alice is brave and vice versa.
Everyone who is not generous or happy is brave.
If mary is generous then someone is wise or not calm.
Everyone who is not curious or quiet is both generous and not humble and vice versa.
Everyone who is both generous and not old is tall and vice versa.
Everyone who is happy is creative or old and vice versa.
Everyone who is quiet or not tall is not creative or brave.
If someone is curious or not rich then someone is funny.
Everyone who is not generous or happy is either strong or not patient and vice versa.
Everyone who is not brave is not old or not wise and vice versa.
Everyone who is kind is happy and vice versa.
If someone is kind or strong then someone is both calm and not strong and vice versa.
Everyone who is both calm and not generous is not generous and vice versa.
Everyone who is brave or not creative is wise.
Everyone who is old is either not kind or kind.
Everyone who is both happy and humble is both humble and not kind.
Alice is either tall or kind.
Someone is not rich or not kind.
Someone is either not brave or creative.
Susan is both kind and happy.
John is either patient or not patient.
Someone is both wise and curious.
Fred is old or wise. | Fred is not quiet. | neutral | (((kind(fred)|~happy(fred)))<=>(brave(alice)))&
(![X]:((~generous(X)|happy(X))=>brave(X)))&
((generous(mary))=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:((~curious(X)|quiet(X))<=>(generous(X)&~humble(X))))&
(![X]:((generous(X)&~old(X))<=>tall(X)))&
(![X]:(happy(X)<=>(creative(X)|old(X))))&
(![X]:((quiet(X)|~tall(X))=>(~creative(X)|brave(X))))&
((?[X]:((curious(X)|~rich(X))))=>(?[X]:(funny(X))))&
(![X]:((~generous(X)|happy(X))<=>(strong(X)<~>~patient(X))))&
(![X]:(~brave(X)<=>(~old(X)|~wise(X))))&
(![X]:(kind(X)<=>happy(X)))&
((?[X]:((kind(X)|strong(X))))<=>(?[X]:((calm(X)&~strong(X)))))&
(![X]:((calm(X)&~generous(X))<=>~generous(X)))&
(![X]:((brave(X)|~creative(X))=>wise(X)))&
(![X]:(old(X)=>(~kind(X)<~>kind(X))))&
(![X]:((happy(X)&humble(X))=>(humble(X)&~kind(X))))&
((tall(alice)<~>kind(alice)))&
(?[X]:((~rich(X)|~kind(X))))&
(?[X]:((~brave(X)<~>creative(X))))&
((kind(susan)&happy(susan)))&
((patient(john)<~>~patient(john)))&
(?[X]:((wise(X)&curious(X))))&
((old(fred)|wise(fred))) | ~quiet(fred) | [] | null | 0 |
If susan is both not wise and not tall then someone is either not wise or humble. Everyone who is not calm or tall is either curious or humble and vice versa. If susan is not generous or generous then mary is both not old and not kind and vice versa. If mary is curious then paul is either not curious or not patient. If someone is either not funny or not generous then mary is not brave and vice versa. Everyone who is either happy or rich is both creative and generous and vice versa. Everyone who is kind or not happy is creative or not calm and vice versa. If someone is not quiet then mary is rich and vice versa. Everyone who is not old is either strong or not brave. Everyone who is rich is calm and vice versa. Everyone who is both wise and not creative is brave and vice versa. Everyone who is both not patient and not funny is either old or patient. Everyone who is either not tall or happy is both creative and not happy and vice versa. Everyone who is both not funny and not generous is both not rich and curious. If someone is not generous or brave then someone is not calm or happy. Everyone who is not calm is not curious and vice versa. Mary is either kind or not generous. Someone is both not creative and not funny. Someone is both quiet and curious. Fred is not calm. Paul is both not generous and curious. John is not quiet. John is not rich. Someone is either humble or generous. | Mary is strong. | contradiction | (((~wise(susan)&~tall(susan)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((~calm(X)|tall(X))<=>(curious(X)<~>humble(X))))&
(((~generous(susan)|generous(susan)))<=>((~old(mary)&~kind(mary))))&
((curious(mary))=>((~curious(paul)<~>~patient(paul))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(~brave(mary)))&
(![X]:((happy(X)<~>rich(X))<=>(creative(X)&generous(X))))&
(![X]:((kind(X)|~happy(X))<=>(creative(X)|~calm(X))))&
((?[X]:(~quiet(X)))<=>(rich(mary)))&
(![X]:(~old(X)=>(strong(X)<~>~brave(X))))&
(![X]:(rich(X)<=>calm(X)))&
(![X]:((wise(X)&~creative(X))<=>brave(X)))&
(![X]:((~patient(X)&~funny(X))=>(old(X)<~>patient(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(creative(X)&~happy(X))))&
(![X]:((~funny(X)&~generous(X))=>(~rich(X)&curious(X))))&
((?[X]:((~generous(X)|brave(X))))=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:(~calm(X)<=>~curious(X)))&
((kind(mary)<~>~generous(mary)))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((quiet(X)&curious(X))))&
(~calm(fred))&
((~generous(paul)&curious(paul)))&
(~quiet(john))&
(~rich(john))&
(?[X]:((humble(X)<~>generous(X)))) | strong(mary) | [
"p2",
"p4",
"p7",
"p8",
"p13",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 170715761056998086622955
% SZS output start Proof for 170715761056998086622955
3. (generous(susan) | ~generous(susan)) <=> (~kind(mary) & ~old(mary)) [input p2]
5. ? [X0] : (~funny(X0) <~> ~generous(X0)) <=> ~brave(mary) [input p4]
8. ? [X0] : ~quiet(X0) <=> rich(mary) [input p7]
9. ! [X0] : (~old(X0) => (strong(X0) <~> ~brave(X0))) [input p8]
14. ! [X0] : ((~generous(X0) & ~funny(X0)) => (curious(X0) & ~rich(X0))) [input p13]
17. kind(mary) <~> ~generous(mary) [input p16]
22. ~quiet(john) [input p21]
25. strong(mary) [input hypothesis]
30. ! [X0] : ((strong(X0) <~> ~brave(X0)) | old(X0)) [ennf transformation 9]
33. ! [X0] : ((curious(X0) & ~rich(X0)) | (generous(X0) | funny(X0))) [ennf transformation 14]
34. ! [X0] : ((curious(X0) & ~rich(X0)) | generous(X0) | funny(X0)) [flattening 33]
41. ((generous(susan) | ~generous(susan)) | (kind(mary) | old(mary))) & ((~kind(mary) & ~old(mary)) | (~generous(susan) & generous(susan))) [nnf transformation 3]
42. (generous(susan) | ~generous(susan) | kind(mary) | old(mary)) & ((~kind(mary) & ~old(mary)) | (~generous(susan) & generous(susan))) [flattening 41]
44. (? [X0] : ((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | brave(mary)) & (~brave(mary) | ! [X0] : ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0)))) [nnf transformation 5]
45. (? [X0] : ((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | brave(mary)) & (~brave(mary) | ! [X1] : ((~funny(X1) | generous(X1)) & (~generous(X1) | funny(X1)))) [rectify 44]
46. ? [X0] : ((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) => ((generous(sK1) | funny(sK1)) & (~generous(sK1) | ~funny(sK1))) [choice axiom]
47. (((generous(sK1) | funny(sK1)) & (~generous(sK1) | ~funny(sK1))) | brave(mary)) & (~brave(mary) | ! [X1] : ((~funny(X1) | generous(X1)) & (~generous(X1) | funny(X1)))) [skolemisation 45,46]
52. (? [X0] : ~quiet(X0) | ~rich(mary)) & (rich(mary) | ! [X0] : quiet(X0)) [nnf transformation 8]
53. (? [X0] : ~quiet(X0) | ~rich(mary)) & (rich(mary) | ! [X1] : quiet(X1)) [rectify 52]
54. ? [X0] : ~quiet(X0) => ~quiet(sK2) [choice axiom]
55. (~quiet(sK2) | ~rich(mary)) & (rich(mary) | ! [X1] : quiet(X1)) [skolemisation 53,54]
56. ! [X0] : (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | old(X0)) [nnf transformation 30]
67. (generous(mary) | ~kind(mary)) & (~generous(mary) | kind(mary)) [nnf transformation 17]
83. ~old(mary) | generous(susan) [cnf transformation 42]
84. ~old(mary) | ~generous(susan) [cnf transformation 42]
85. ~kind(mary) | generous(susan) [cnf transformation 42]
86. ~kind(mary) | ~generous(susan) [cnf transformation 42]
91. ~brave(mary) | ~funny(X1) | generous(X1) [cnf transformation 47]
104. rich(mary) | quiet(X1) [cnf transformation 55]
107. ~strong(X0) | brave(X0) | old(X0) [cnf transformation 56]
121. ~rich(X0) | generous(X0) | funny(X0) [cnf transformation 34]
127. ~generous(mary) | kind(mary) [cnf transformation 67]
136. ~quiet(john) [cnf transformation 22]
140. strong(mary) [cnf transformation 25]
163. 5 <=> generous(susan) [avatar definition]
167. 6 <=> kind(mary) [avatar definition]
170. ~5 | ~6 [avatar split clause 86,167,163]
171. 5 | ~6 [avatar split clause 85,167,163]
173. 7 <=> old(mary) [avatar definition]
175. ~old(mary) <- (~7) [avatar component clause 173]
176. ~5 | ~7 [avatar split clause 84,173,163]
177. 5 | ~7 [avatar split clause 83,173,163]
193. 11 <=> brave(mary) [avatar definition]
207. 14 <=> ! [X1] : (~funny(X1) | generous(X1)) [avatar definition]
208. ~funny(X1) | generous(X1) <- (14) [avatar component clause 207]
209. 14 | ~11 [avatar split clause 91,193,207]
215. 16 <=> rich(mary) [avatar definition]
216. rich(mary) <- (16) [avatar component clause 215]
224. 18 <=> ! [X1] : quiet(X1) [avatar definition]
225. quiet(X1) <- (18) [avatar component clause 224]
226. 18 | 16 [avatar split clause 104,215,224]
244. 23 <=> generous(mary) [avatar definition]
245. ~generous(mary) <- (~23) [avatar component clause 244]
248. 6 | ~23 [avatar split clause 127,244,167]
348. $false <- (18) [resolution 225,136]
351. ~18 [avatar contradiction clause 348]
384. brave(mary) | old(mary) [resolution 107,140]
388. brave(mary) <- (~7) [subsumption resolution 384,175]
389. 11 | 7 [avatar split clause 388,173,193]
416. generous(mary) | funny(mary) <- (16) [resolution 121,216]
419. funny(mary) <- (16, ~23) [subsumption resolution 416,245]
434. generous(mary) <- (14, 16, ~23) [resolution 419,208]
435. $false <- (14, 16, ~23) [subsumption resolution 434,245]
436. ~14 | ~16 | 23 [avatar contradiction clause 435]
437. $false [avatar sat refutation 170,171,176,177,209,226,248,351,389,436]
% SZS output end Proof for 170715761056998086622955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not funny is not tall or not calm and vice versa. If someone is either brave or not creative then paul is wise and vice versa. If someone is curious then alice is both brave and not happy. If someone is not generous or not old then alice is calm or not calm. Everyone who is both not rich and rich is old and vice versa. Everyone who is both old and kind is either tall or not wise and vice versa. If john is either not wise or not curious then fred is either not happy or not old. Everyone who is funny or not wise is not tall. Everyone who is either not wise or not rich is both not kind and patient. If someone is tall or strong then mary is either not generous or calm and vice versa. If alice is not strong then someone is both not creative and not quiet and vice versa. If john is either not rich or not patient then someone is either not creative or not wise and vice versa. Everyone who is either not happy or curious is not creative or kind. If someone is old or generous then fred is either not rich or not happy and vice versa. Everyone who is either not generous or old is both not brave and not strong. Someone is either not old or not brave. Susan is either old or not old. Someone is tall or brave. Someone is both not old and happy. Susan is either happy or not quiet. Someone is not wise or not quiet. Someone is not strong. Paul is patient or creative. | Susan is not creative. | neutral | (![X]:((generous(X)&~funny(X))<=>(~tall(X)|~calm(X))))&
((?[X]:((brave(X)<~>~creative(X))))<=>(wise(paul)))&
((?[X]:(curious(X)))=>((brave(alice)&~happy(alice))))&
((?[X]:((~generous(X)|~old(X))))=>((calm(alice)|~calm(alice))))&
(![X]:((~rich(X)&rich(X))<=>old(X)))&
(![X]:((old(X)&kind(X))<=>(tall(X)<~>~wise(X))))&
(((~wise(john)<~>~curious(john)))=>((~happy(fred)<~>~old(fred))))&
(![X]:((funny(X)|~wise(X))=>~tall(X)))&
(![X]:((~wise(X)<~>~rich(X))=>(~kind(X)&patient(X))))&
((?[X]:((tall(X)|strong(X))))<=>((~generous(mary)<~>calm(mary))))&
((~strong(alice))<=>(?[X]:((~creative(X)&~quiet(X)))))&
(((~rich(john)<~>~patient(john)))<=>(?[X]:((~creative(X)<~>~wise(X)))))&
(![X]:((~happy(X)<~>curious(X))=>(~creative(X)|kind(X))))&
((?[X]:((old(X)|generous(X))))<=>((~rich(fred)<~>~happy(fred))))&
(![X]:((~generous(X)<~>old(X))=>(~brave(X)&~strong(X))))&
(?[X]:((~old(X)<~>~brave(X))))&
((old(susan)<~>~old(susan)))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((~old(X)&happy(X))))&
((happy(susan)<~>~quiet(susan)))&
(?[X]:((~wise(X)|~quiet(X))))&
(?[X]:(~strong(X)))&
((patient(paul)|creative(paul))) | ~creative(susan) | [] | null | 0 |
If someone is not old or not calm then someone is rich or not brave.
Everyone who is curious or patient is both humble and not humble.
Everyone who is both funny and not wise is creative or patient and vice versa.
Everyone who is not tall is funny or humble and vice versa.
Everyone who is happy or generous is both strong and generous.
If lucy is creative or strong then alice is not funny or curious and vice versa.
If someone is not rich or not quiet then someone is either not strong or happy and vice versa.
If someone is brave or not funny then lucy is both brave and wise.
If someone is either brave or old then someone is either not strong or humble.
If fred is either kind or funny then someone is either tall or happy and vice versa.
Everyone who is calm is both not generous and wise.
If john is either not old or not rich then paul is curious or not funny.
If someone is not brave then mary is not rich or not wise and vice versa.
If someone is rich or not rich then john is either brave or not curious.
If john is both calm and not quiet then someone is generous.
If john is either wise or generous then someone is both generous and brave and vice versa.
Someone is either not quiet or creative.
John is both not old and not humble.
Someone is not curious.
Alice is both happy and not quiet.
Susan is either old or brave.
Someone is both brave and old. | Susan is brave. | neutral | ((?[X]:((~old(X)|~calm(X))))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:((curious(X)|patient(X))=>(humble(X)&~humble(X))))&
(![X]:((funny(X)&~wise(X))<=>(creative(X)|patient(X))))&
(![X]:(~tall(X)<=>(funny(X)|humble(X))))&
(![X]:((happy(X)|generous(X))=>(strong(X)&generous(X))))&
(((creative(lucy)|strong(lucy)))<=>((~funny(alice)|curious(alice))))&
((?[X]:((~rich(X)|~quiet(X))))<=>(?[X]:((~strong(X)<~>happy(X)))))&
((?[X]:((brave(X)|~funny(X))))=>((brave(lucy)&wise(lucy))))&
((?[X]:((brave(X)<~>old(X))))=>(?[X]:((~strong(X)<~>humble(X)))))&
(((kind(fred)<~>funny(fred)))<=>(?[X]:((tall(X)<~>happy(X)))))&
(![X]:(calm(X)=>(~generous(X)&wise(X))))&
(((~old(john)<~>~rich(john)))=>((curious(paul)|~funny(paul))))&
((?[X]:(~brave(X)))<=>((~rich(mary)|~wise(mary))))&
((?[X]:((rich(X)|~rich(X))))=>((brave(john)<~>~curious(john))))&
(((calm(john)&~quiet(john)))=>(?[X]:(generous(X))))&
(((wise(john)<~>generous(john)))<=>(?[X]:((generous(X)&brave(X)))))&
(?[X]:((~quiet(X)<~>creative(X))))&
((~old(john)&~humble(john)))&
(?[X]:(~curious(X)))&
((happy(alice)&~quiet(alice)))&
((old(susan)<~>brave(susan)))&
(?[X]:((brave(X)&old(X)))) | brave(susan) | [] | null | 0 |
Everyone who is either not curious or generous is humble and vice versa. Everyone who is old is not humble or funny. Everyone who is generous is curious. If someone is happy or not brave then someone is either not quiet or curious. If someone is not humble or not wise then mary is both funny and not curious and vice versa. Everyone who is either not rich or funny is both happy and not brave. Everyone who is not kind is not humble or not quiet and vice versa. Everyone who is either rich or tall is happy or not strong and vice versa. Everyone who is both not kind and not happy is humble or not humble and vice versa. Everyone who is both humble and not rich is funny and vice versa. Everyone who is both strong and not generous is not tall. Everyone who is funny or not humble is not calm or generous and vice versa. If someone is generous then john is tall and vice versa. If alice is both not humble and not tall then fred is not rich or not humble. Everyone who is brave or not brave is not funny or not wise. Everyone who is wise is not humble. Mary is funny. Fred is both not tall and not humble. Someone is wise. Someone is not brave or patient. Susan is not generous. | Fred is quiet. | neutral | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(~humble(X)|funny(X))))&
(![X]:(generous(X)=>curious(X)))&
((?[X]:((happy(X)|~brave(X))))=>(?[X]:((~quiet(X)<~>curious(X)))))&
((?[X]:((~humble(X)|~wise(X))))<=>((funny(mary)&~curious(mary))))&
(![X]:((~rich(X)<~>funny(X))=>(happy(X)&~brave(X))))&
(![X]:(~kind(X)<=>(~humble(X)|~quiet(X))))&
(![X]:((rich(X)<~>tall(X))<=>(happy(X)|~strong(X))))&
(![X]:((~kind(X)&~happy(X))<=>(humble(X)|~humble(X))))&
(![X]:((humble(X)&~rich(X))<=>funny(X)))&
(![X]:((strong(X)&~generous(X))=>~tall(X)))&
(![X]:((funny(X)|~humble(X))<=>(~calm(X)|generous(X))))&
((?[X]:(generous(X)))<=>(tall(john)))&
(((~humble(alice)&~tall(alice)))=>((~rich(fred)|~humble(fred))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|~wise(X))))&
(![X]:(wise(X)=>~humble(X)))&
(funny(mary))&
((~tall(fred)&~humble(fred)))&
(?[X]:(wise(X)))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan)) | quiet(fred) | [] | null | 0 |
If someone is quiet or old then someone is either not kind or generous and vice versa.
Everyone who is not calm is not kind or not humble.
If someone is either not brave or creative then someone is either not quiet or not creative.
If someone is either brave or creative then john is not humble or not calm.
If mary is humble or not rich then someone is either humble or brave and vice versa.
Everyone who is humble is rich.
If someone is both not calm and funny then someone is both old and not strong and vice versa.
If alice is both kind and not patient then someone is happy or not wise.
If john is both not happy and not patient then someone is either strong or not creative and vice versa.
Everyone who is not happy or not patient is not funny or not wise and vice versa.
If alice is calm or not rich then someone is either not strong or not patient.
Everyone who is both humble and rich is both not generous and quiet and vice versa.
Everyone who is either curious or strong is both funny and kind.
Everyone who is not happy is either not brave or not funny and vice versa.
Everyone who is rich is both creative and not strong and vice versa.
Everyone who is old is either funny or not brave and vice versa.
Someone is wise.
Alice is funny.
Lucy is quiet or not funny.
Someone is both not curious and not tall.
Someone is strong.
Someone is both kind and brave.
Someone is rich.
Someone is kind or happy. | Lucy is not tall. | neutral | ((?[X]:((quiet(X)|old(X))))<=>(?[X]:((~kind(X)<~>generous(X)))))&
(![X]:(~calm(X)=>(~kind(X)|~humble(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:((~quiet(X)<~>~creative(X)))))&
((?[X]:((brave(X)<~>creative(X))))=>((~humble(john)|~calm(john))))&
(((humble(mary)|~rich(mary)))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(humble(X)=>rich(X)))&
((?[X]:((~calm(X)&funny(X))))<=>(?[X]:((old(X)&~strong(X)))))&
(((kind(alice)&~patient(alice)))=>(?[X]:((happy(X)|~wise(X)))))&
(((~happy(john)&~patient(john)))<=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((~happy(X)|~patient(X))<=>(~funny(X)|~wise(X))))&
(((calm(alice)|~rich(alice)))=>(?[X]:((~strong(X)<~>~patient(X)))))&
(![X]:((humble(X)&rich(X))<=>(~generous(X)&quiet(X))))&
(![X]:((curious(X)<~>strong(X))=>(funny(X)&kind(X))))&
(![X]:(~happy(X)<=>(~brave(X)<~>~funny(X))))&
(![X]:(rich(X)<=>(creative(X)&~strong(X))))&
(![X]:(old(X)<=>(funny(X)<~>~brave(X))))&
(?[X]:(wise(X)))&
(funny(alice))&
((quiet(lucy)|~funny(lucy)))&
(?[X]:((~curious(X)&~tall(X))))&
(?[X]:(strong(X)))&
(?[X]:((kind(X)&brave(X))))&
(?[X]:(rich(X)))&
(?[X]:((kind(X)|happy(X)))) | ~tall(lucy) | [] | null | 0 |
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