premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is generous or rich is both not wise and not calm.
If susan is either rich or not curious then paul is both rich and kind and vice versa.
If someone is either creative or calm then john is both patient and not funny and vice versa.
Everyone who is not calm or not humble is not happy or generous and vice versa.
Everyone who is both generous and not brave is not patient or not quiet and vice versa.
Everyone who is not quiet is not curious or patient and vice versa.
Everyone who is both not generous and brave is either not funny or not calm.
If john is either not calm or strong then john is tall and vice versa.
Everyone who is both wise and not rich is either not creative or rich.
Everyone who is not wise is funny and vice versa.
If someone is both not happy and not tall then someone is both not curious and wise.
Everyone who is funny is not wise and vice versa.
If someone is both not tall and quiet then someone is strong and vice versa.
If someone is not brave or not funny then fred is not tall and vice versa.
Everyone who is not quiet or not tall is either quiet or not strong and vice versa.
If john is either not tall or patient then paul is either not humble or curious and vice versa.
Someone is happy or not quiet.
Mary is rich.
Someone is both curious and not wise.
John is both tall and quiet.
Fred is either not rich or not tall.
Someone is both tall and rich.
Paul is both not rich and not quiet.
Someone is not humble. | Mary is funny. | entailment | (![X]:((generous(X)|rich(X))=>(~wise(X)&~calm(X))))&
(((rich(susan)<~>~curious(susan)))<=>((rich(paul)&kind(paul))))&
((?[X]:((creative(X)<~>calm(X))))<=>((patient(john)&~funny(john))))&
(![X]:((~calm(X)|~humble(X))<=>(~happy(X)|generous(X))))&
(![X]:((generous(X)&~brave(X))<=>(~patient(X)|~quiet(X))))&
(![X]:(~quiet(X)<=>(~curious(X)|patient(X))))&
(![X]:((~generous(X)&brave(X))=>(~funny(X)<~>~calm(X))))&
(((~calm(john)<~>strong(john)))<=>(tall(john)))&
(![X]:((wise(X)&~rich(X))=>(~creative(X)<~>rich(X))))&
(![X]:(~wise(X)<=>funny(X)))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)|~funny(X))))<=>(~tall(fred)))&
(![X]:((~quiet(X)|~tall(X))<=>(quiet(X)<~>~strong(X))))&
(((~tall(john)<~>patient(john)))<=>((~humble(paul)<~>curious(paul))))&
(?[X]:((happy(X)|~quiet(X))))&
(rich(mary))&
(?[X]:((curious(X)&~wise(X))))&
((tall(john)&quiet(john)))&
((~rich(fred)<~>~tall(fred)))&
(?[X]:((tall(X)&rich(X))))&
((~rich(paul)&~quiet(paul)))&
(?[X]:(~humble(X))) | funny(mary) | [
"p0",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 983274117568869970487606
% SZS output start Proof for 983274117568869970487606
1. ! [X0] : ((rich(X0) | generous(X0)) => (~calm(X0) & ~wise(X0))) [input p0]
10. ! [X0] : (~wise(X0) <=> funny(X0)) [input p9]
18. rich(mary) [input p17]
25. ~funny(mary) [input hypothesis]
28. ! [X0] : ((~calm(X0) & ~wise(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 1]
50. ! [X0] : ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))) [nnf transformation 10]
77. ~wise(X0) | ~rich(X0) [cnf transformation 28]
112. funny(X0) | wise(X0) [cnf transformation 50]
139. rich(mary) [cnf transformation 18]
151. ~funny(mary) [cnf transformation 25]
341. wise(mary) [resolution 112,151]
343. ~rich(mary) [resolution 341,77]
345. $false [subsumption resolution 343,139]
% SZS output end Proof for 983274117568869970487606
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either humble or not tall then someone is not kind or not wise.
Everyone who is either tall or quiet is strong and vice versa.
Everyone who is either rich or not quiet is rich.
Everyone who is brave is both rich and not curious and vice versa.
Everyone who is both not calm and not quiet is not brave and vice versa.
Everyone who is funny or creative is happy and vice versa.
If susan is both brave and not wise then someone is not kind and vice versa.
If someone is old then susan is rich or not quiet.
If mary is both tall and not kind then someone is old.
Everyone who is both not wise and not patient is not brave and vice versa.
Everyone who is both creative and funny is either quiet or humble.
Everyone who is quiet or generous is not old or not happy.
If lucy is both kind and not tall then someone is curious.
If someone is rich then someone is either not tall or not wise.
If someone is either not humble or wise then susan is old or kind.
Everyone who is not calm or not curious is brave and vice versa.
Paul is creative.
Someone is both not calm and funny.
John is not old.
Someone is both wise and not kind.
Someone is both not patient and brave.
Susan is not curious.
Someone is both not tall and not strong.
Paul is not kind or humble. | Fred is not brave. | contradiction | (((humble(fred)<~>~tall(fred)))=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:((tall(X)<~>quiet(X))<=>strong(X)))&
(![X]:((rich(X)<~>~quiet(X))=>rich(X)))&
(![X]:(brave(X)<=>(rich(X)&~curious(X))))&
(![X]:((~calm(X)&~quiet(X))<=>~brave(X)))&
(![X]:((funny(X)|creative(X))<=>happy(X)))&
(((brave(susan)&~wise(susan)))<=>(?[X]:(~kind(X))))&
((?[X]:(old(X)))=>((rich(susan)|~quiet(susan))))&
(((tall(mary)&~kind(mary)))=>(?[X]:(old(X))))&
(![X]:((~wise(X)&~patient(X))<=>~brave(X)))&
(![X]:((creative(X)&funny(X))=>(quiet(X)<~>humble(X))))&
(![X]:((quiet(X)|generous(X))=>(~old(X)|~happy(X))))&
(((kind(lucy)&~tall(lucy)))=>(?[X]:(curious(X))))&
((?[X]:(rich(X)))=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((~humble(X)<~>wise(X))))=>((old(susan)|kind(susan))))&
(![X]:((~calm(X)|~curious(X))<=>brave(X)))&
(creative(paul))&
(?[X]:((~calm(X)&funny(X))))&
(~old(john))&
(?[X]:((wise(X)&~kind(X))))&
(?[X]:((~patient(X)&brave(X))))&
(~curious(susan))&
(?[X]:((~tall(X)&~strong(X))))&
((~kind(paul)|humble(paul))) | ~brave(fred) | [
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5616640406883451214658312
% SZS output start Proof for 5616640406883451214658312
5. ! [X0] : ((~quiet(X0) & ~calm(X0)) <=> ~brave(X0)) [input p4]
16. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> brave(X0)) [input p15]
25. ~brave(fred) [input hypothesis]
54. ! [X0] : (((~quiet(X0) & ~calm(X0)) | brave(X0)) & (~brave(X0) | (quiet(X0) | calm(X0)))) [nnf transformation 5]
55. ! [X0] : (((~quiet(X0) & ~calm(X0)) | brave(X0)) & (~brave(X0) | quiet(X0) | calm(X0))) [flattening 54]
73. ! [X0] : (((~curious(X0) | ~calm(X0)) | ~brave(X0)) & (brave(X0) | (curious(X0) & calm(X0)))) [nnf transformation 16]
74. ! [X0] : ((~curious(X0) | ~calm(X0) | ~brave(X0)) & (brave(X0) | (curious(X0) & calm(X0)))) [flattening 73]
93. ~calm(X0) | brave(X0) [cnf transformation 55]
113. brave(X0) | calm(X0) [cnf transformation 74]
128. ~brave(fred) [cnf transformation 25]
230. brave(X0) [subsumption resolution 113,93]
240. $false [subsumption resolution 128,230]
% SZS output end Proof for 5616640406883451214658312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or curious is either humble or happy. If fred is either rich or not curious then someone is brave or quiet and vice versa. Everyone who is not strong or wise is brave and vice versa. If someone is not rich then fred is not calm. If someone is not tall then susan is not generous and vice versa. Everyone who is not rich is old and vice versa. Everyone who is both not quiet and not tall is strong and vice versa. If someone is either not humble or not funny then lucy is both creative and rich and vice versa. If someone is humble or quiet then someone is kind or not calm. Everyone who is calm or not humble is tall and vice versa. If someone is either not curious or not calm then mary is curious and vice versa. If someone is wise or not old then someone is both generous and brave and vice versa. Everyone who is not tall or not calm is both not curious and funny. If alice is either not wise or not calm then john is not strong and vice versa. Everyone who is both old and not kind is both happy and creative. If alice is not happy then someone is either not kind or not calm. Fred is rich or old. Someone is not humble or calm. Fred is either strong or old. Alice is both not humble and kind. Someone is creative or old. Paul is either happy or not tall. Someone is either not patient or quiet. Someone is both not generous and creative. | Alice is tall. | entailment | (![X]:((~rich(X)<~>curious(X))=>(humble(X)<~>happy(X))))&
(((rich(fred)<~>~curious(fred)))<=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:((~strong(X)|wise(X))<=>brave(X)))&
((?[X]:(~rich(X)))=>(~calm(fred)))&
((?[X]:(~tall(X)))<=>(~generous(susan)))&
(![X]:(~rich(X)<=>old(X)))&
(![X]:((~quiet(X)&~tall(X))<=>strong(X)))&
((?[X]:((~humble(X)<~>~funny(X))))<=>((creative(lucy)&rich(lucy))))&
((?[X]:((humble(X)|quiet(X))))=>(?[X]:((kind(X)|~calm(X)))))&
(![X]:((calm(X)|~humble(X))<=>tall(X)))&
((?[X]:((~curious(X)<~>~calm(X))))<=>(curious(mary)))&
((?[X]:((wise(X)|~old(X))))<=>(?[X]:((generous(X)&brave(X)))))&
(![X]:((~tall(X)|~calm(X))=>(~curious(X)&funny(X))))&
(((~wise(alice)<~>~calm(alice)))<=>(~strong(john)))&
(![X]:((old(X)&~kind(X))=>(happy(X)&creative(X))))&
((~happy(alice))=>(?[X]:((~kind(X)<~>~calm(X)))))&
((rich(fred)|old(fred)))&
(?[X]:((~humble(X)|calm(X))))&
((strong(fred)<~>old(fred)))&
((~humble(alice)&kind(alice)))&
(?[X]:((creative(X)|old(X))))&
((happy(paul)<~>~tall(paul)))&
(?[X]:((~patient(X)<~>quiet(X))))&
(?[X]:((~generous(X)&creative(X)))) | tall(alice) | [
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8122872564320425091130107
% SZS output start Proof for 8122872564320425091130107
10. ! [X0] : ((~humble(X0) | calm(X0)) <=> tall(X0)) [input p9]
20. kind(alice) & ~humble(alice) [input p19]
25. ~tall(alice) [input hypothesis]
57. ! [X0] : (((~humble(X0) | calm(X0)) | ~tall(X0)) & (tall(X0) | (humble(X0) & ~calm(X0)))) [nnf transformation 10]
58. ! [X0] : ((~humble(X0) | calm(X0) | ~tall(X0)) & (tall(X0) | (humble(X0) & ~calm(X0)))) [flattening 57]
113. tall(X0) | humble(X0) [cnf transformation 58]
140. ~humble(alice) [cnf transformation 20]
149. ~tall(alice) [cnf transformation 25]
385. humble(alice) [resolution 113,149]
388. $false [subsumption resolution 385,140]
% SZS output end Proof for 8122872564320425091130107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not creative is both quiet and calm and vice versa.
Everyone who is either quiet or humble is tall and vice versa.
If someone is not curious then someone is either not calm or rich.
Everyone who is not calm or not creative is wise and vice versa.
Everyone who is not happy or not rich is both wise and funny and vice versa.
If someone is strong or not strong then someone is kind or not brave and vice versa.
Everyone who is either generous or creative is wise.
Everyone who is kind is both not patient and not brave.
Everyone who is either not brave or quiet is either not funny or strong and vice versa.
Everyone who is not happy is not creative or curious and vice versa.
If someone is either wise or not humble then someone is strong.
If someone is patient then someone is either wise or happy and vice versa.
Everyone who is not rich or not creative is both creative and tall.
Everyone who is both patient and not quiet is calm or not creative and vice versa.
If paul is kind or rich then someone is not rich or not curious.
If someone is both quiet and calm then john is either curious or kind.
Someone is both generous and not strong.
John is either generous or not rich.
Someone is brave.
Someone is not brave.
Someone is either not happy or tall.
Someone is curious or not patient.
Susan is kind or not curious. | John is funny. | entailment | (![X]:((~curious(X)|~creative(X))<=>(quiet(X)&calm(X))))&
(![X]:((quiet(X)<~>humble(X))<=>tall(X)))&
((?[X]:(~curious(X)))=>(?[X]:((~calm(X)<~>rich(X)))))&
(![X]:((~calm(X)|~creative(X))<=>wise(X)))&
(![X]:((~happy(X)|~rich(X))<=>(wise(X)&funny(X))))&
((?[X]:((strong(X)|~strong(X))))<=>(?[X]:((kind(X)|~brave(X)))))&
(![X]:((generous(X)<~>creative(X))=>wise(X)))&
(![X]:(kind(X)=>(~patient(X)&~brave(X))))&
(![X]:((~brave(X)<~>quiet(X))<=>(~funny(X)<~>strong(X))))&
(![X]:(~happy(X)<=>(~creative(X)|curious(X))))&
((?[X]:((wise(X)<~>~humble(X))))=>(?[X]:(strong(X))))&
((?[X]:(patient(X)))<=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((~rich(X)|~creative(X))=>(creative(X)&tall(X))))&
(![X]:((patient(X)&~quiet(X))<=>(calm(X)|~creative(X))))&
(((kind(paul)|rich(paul)))=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:((quiet(X)&calm(X))))=>((curious(john)<~>kind(john))))&
(?[X]:((generous(X)&~strong(X))))&
((generous(john)<~>~rich(john)))&
(?[X]:(brave(X)))&
(?[X]:(~brave(X)))&
(?[X]:((~happy(X)<~>tall(X))))&
(?[X]:((curious(X)|~patient(X))))&
((kind(susan)|~curious(susan))) | funny(john) | [
"p0",
"p4",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8694393313785228509674602
% SZS output start Proof for 8694393313785228509674602
1. ! [X0] : ((~creative(X0) | ~curious(X0)) <=> (calm(X0) & quiet(X0))) [input p0]
5. ! [X0] : ((~rich(X0) | ~happy(X0)) <=> (funny(X0) & wise(X0))) [input p4]
10. ! [X0] : (~happy(X0) <=> (curious(X0) | ~creative(X0))) [input p9]
14. ! [X0] : ((~quiet(X0) & patient(X0)) <=> (~creative(X0) | calm(X0))) [input p13]
24. ~funny(john) [input hypothesis]
36. ! [X0] : (((~creative(X0) | ~curious(X0)) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | (creative(X0) & curious(X0)))) [nnf transformation 1]
37. ! [X0] : ((~creative(X0) | ~curious(X0) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | (creative(X0) & curious(X0)))) [flattening 36]
45. ! [X0] : (((~rich(X0) | ~happy(X0)) | (~funny(X0) | ~wise(X0))) & ((funny(X0) & wise(X0)) | (rich(X0) & happy(X0)))) [nnf transformation 5]
46. ! [X0] : ((~rich(X0) | ~happy(X0) | ~funny(X0) | ~wise(X0)) & ((funny(X0) & wise(X0)) | (rich(X0) & happy(X0)))) [flattening 45]
54. ! [X0] : ((~happy(X0) | (~curious(X0) & creative(X0))) & ((curious(X0) | ~creative(X0)) | happy(X0))) [nnf transformation 10]
55. ! [X0] : ((~happy(X0) | (~curious(X0) & creative(X0))) & (curious(X0) | ~creative(X0) | happy(X0))) [flattening 54]
65. ! [X0] : (((~quiet(X0) & patient(X0)) | (creative(X0) & ~calm(X0))) & ((~creative(X0) | calm(X0)) | (quiet(X0) | ~patient(X0)))) [nnf transformation 14]
66. ! [X0] : (((~quiet(X0) & patient(X0)) | (creative(X0) & ~calm(X0))) & (~creative(X0) | calm(X0) | quiet(X0) | ~patient(X0))) [flattening 65]
82. quiet(X0) | curious(X0) [cnf transformation 37]
84. calm(X0) | curious(X0) [cnf transformation 37]
98. funny(X0) | happy(X0) [cnf transformation 46]
119. ~happy(X0) | ~curious(X0) [cnf transformation 55]
133. ~calm(X0) | ~quiet(X0) [cnf transformation 66]
149. ~funny(john) [cnf transformation 24]
152. 1 <=> ! [X1] : curious(X1) [avatar definition]
153. curious(X1) <- (1) [avatar component clause 152]
281. happy(john) [resolution 98,149]
291. ~curious(john) [resolution 119,281]
298. ~quiet(X1) | curious(X1) [resolution 133,84]
299. curious(X1) [subsumption resolution 298,82]
300. 1 [avatar split clause 299,152]
302. $false <- (1) [resolution 153,291]
303. ~1 [avatar contradiction clause 302]
305. $false [avatar sat refutation 300,303]
% SZS output end Proof for 8694393313785228509674602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and kind is either calm or not creative. Everyone who is not happy is creative or not brave. Everyone who is either not calm or not strong is creative. Everyone who is both not old and funny is either strong or patient and vice versa. If someone is rich then fred is funny or not patient. Everyone who is happy is either wise or not tall and vice versa. If someone is either tall or not happy then paul is both not funny and not calm. If someone is either patient or happy then paul is both calm and generous. Everyone who is not tall or rich is both not old and not happy and vice versa. If alice is not curious or not generous then susan is curious or calm and vice versa. Everyone who is not humble is not old or humble. Everyone who is not kind is either not brave or tall. If someone is both happy and not tall then lucy is not generous or quiet and vice versa. If fred is both calm and old then someone is brave. If fred is either not calm or not curious then someone is both humble and rich and vice versa. Everyone who is either strong or kind is either not kind or curious. Mary is either tall or not rich. Someone is not curious or patient. Susan is both not humble and not tall. Someone is either creative or not kind. Fred is either not quiet or not strong. Someone is generous or kind. Someone is both funny and old. | Paul is not funny. | entailment | (![X]:((~generous(X)&kind(X))=>(calm(X)<~>~creative(X))))&
(![X]:(~happy(X)=>(creative(X)|~brave(X))))&
(![X]:((~calm(X)<~>~strong(X))=>creative(X)))&
(![X]:((~old(X)&funny(X))<=>(strong(X)<~>patient(X))))&
((?[X]:(rich(X)))=>((funny(fred)|~patient(fred))))&
(![X]:(happy(X)<=>(wise(X)<~>~tall(X))))&
((?[X]:((tall(X)<~>~happy(X))))=>((~funny(paul)&~calm(paul))))&
((?[X]:((patient(X)<~>happy(X))))=>((calm(paul)&generous(paul))))&
(![X]:((~tall(X)|rich(X))<=>(~old(X)&~happy(X))))&
(((~curious(alice)|~generous(alice)))<=>((curious(susan)|calm(susan))))&
(![X]:(~humble(X)=>(~old(X)|humble(X))))&
(![X]:(~kind(X)=>(~brave(X)<~>tall(X))))&
((?[X]:((happy(X)&~tall(X))))<=>((~generous(lucy)|quiet(lucy))))&
(((calm(fred)&old(fred)))=>(?[X]:(brave(X))))&
(((~calm(fred)<~>~curious(fred)))<=>(?[X]:((humble(X)&rich(X)))))&
(![X]:((strong(X)<~>kind(X))=>(~kind(X)<~>curious(X))))&
((tall(mary)<~>~rich(mary)))&
(?[X]:((~curious(X)|patient(X))))&
((~humble(susan)&~tall(susan)))&
(?[X]:((creative(X)<~>~kind(X))))&
((~quiet(fred)<~>~strong(fred)))&
(?[X]:((generous(X)|kind(X))))&
(?[X]:((funny(X)&old(X)))) | ~funny(paul) | [
"p6",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6050665751309990425281665
% SZS output start Proof for 6050665751309990425281665
7. ? [X0] : (tall(X0) <~> ~happy(X0)) => (~calm(paul) & ~funny(paul)) [input p6]
9. ! [X0] : ((rich(X0) | ~tall(X0)) <=> (~happy(X0) & ~old(X0))) [input p8]
19. ~tall(susan) & ~humble(susan) [input p18]
24. funny(paul) [input hypothesis]
32. (~calm(paul) & ~funny(paul)) | ! [X0] : (tall(X0) <=> ~happy(X0)) [ennf transformation 7]
45. (~calm(paul) & ~funny(paul)) | ! [X0] : ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))) [nnf transformation 32]
47. ! [X0] : (((rich(X0) | ~tall(X0)) | (happy(X0) | old(X0))) & ((~happy(X0) & ~old(X0)) | (~rich(X0) & tall(X0)))) [nnf transformation 9]
48. ! [X0] : ((rich(X0) | ~tall(X0) | happy(X0) | old(X0)) & ((~happy(X0) & ~old(X0)) | (~rich(X0) & tall(X0)))) [flattening 47]
91. ~funny(paul) | ~happy(X0) | ~tall(X0) [cnf transformation 45]
92. ~funny(paul) | tall(X0) | happy(X0) [cnf transformation 45]
101. ~happy(X0) | tall(X0) [cnf transformation 48]
131. ~tall(susan) [cnf transformation 19]
139. funny(paul) [cnf transformation 24]
156. 4 <=> ! [X0] : (tall(X0) | happy(X0)) [avatar definition]
157. tall(X0) | happy(X0) <- (4) [avatar component clause 156]
164. 6 <=> ! [X0] : (~happy(X0) | ~tall(X0)) [avatar definition]
165. ~happy(X0) | ~tall(X0) <- (6) [avatar component clause 164]
168. 7 <=> funny(paul) [avatar definition]
171. 4 | ~7 [avatar split clause 92,168,156]
172. 6 | ~7 [avatar split clause 91,168,164]
309. 7 [avatar split clause 139,168]
310. ~happy(X0) <- (6) [subsumption resolution 165,101]
311. tall(X0) <- (4, 6) [subsumption resolution 157,310]
312. $false <- (4, 6) [resolution 311,131]
315. ~4 | ~6 [avatar contradiction clause 312]
316. $false [avatar sat refutation 171,172,309,315]
% SZS output end Proof for 6050665751309990425281665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and wise is not funny.
If mary is not rich or patient then someone is not generous or happy and vice versa.
If someone is rich then alice is old.
Everyone who is not humble or calm is not patient or tall and vice versa.
If someone is either not humble or not tall then someone is kind and vice versa.
If someone is both not rich and not happy then someone is kind.
If mary is either not kind or generous then someone is wise or not curious.
Everyone who is both calm and not quiet is not happy or wise.
If someone is not strong or funny then someone is either not old or not quiet and vice versa.
Everyone who is both not brave and not rich is not strong and vice versa.
If paul is both quiet and rich then alice is either tall or humble.
If mary is both kind and not strong then paul is not funny or quiet.
Everyone who is either not calm or not funny is not kind or not wise.
Everyone who is both not generous and not tall is calm.
Everyone who is either generous or not old is either not kind or not tall.
If fred is kind or rich then mary is tall and vice versa.
Fred is patient or tall.
Paul is not old or not calm.
Susan is not brave.
Mary is humble.
Someone is not happy or not rich.
Susan is both not humble and quiet.
Lucy is kind.
Susan is both rich and not humble. | Fred is tall. | neutral | (![X]:((creative(X)&wise(X))=>~funny(X)))&
(((~rich(mary)|patient(mary)))<=>(?[X]:((~generous(X)|happy(X)))))&
((?[X]:(rich(X)))=>(old(alice)))&
(![X]:((~humble(X)|calm(X))<=>(~patient(X)|tall(X))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(?[X]:(kind(X))))&
((?[X]:((~rich(X)&~happy(X))))=>(?[X]:(kind(X))))&
(((~kind(mary)<~>generous(mary)))=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:((calm(X)&~quiet(X))=>(~happy(X)|wise(X))))&
((?[X]:((~strong(X)|funny(X))))<=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:((~brave(X)&~rich(X))<=>~strong(X)))&
(((quiet(paul)&rich(paul)))=>((tall(alice)<~>humble(alice))))&
(((kind(mary)&~strong(mary)))=>((~funny(paul)|quiet(paul))))&
(![X]:((~calm(X)<~>~funny(X))=>(~kind(X)|~wise(X))))&
(![X]:((~generous(X)&~tall(X))=>calm(X)))&
(![X]:((generous(X)<~>~old(X))=>(~kind(X)<~>~tall(X))))&
(((kind(fred)|rich(fred)))<=>(tall(mary)))&
((patient(fred)|tall(fred)))&
((~old(paul)|~calm(paul)))&
(~brave(susan))&
(humble(mary))&
(?[X]:((~happy(X)|~rich(X))))&
((~humble(susan)&quiet(susan)))&
(kind(lucy))&
((rich(susan)&~humble(susan))) | tall(fred) | [] | null | 0 |
Everyone who is either kind or not happy is both patient and quiet. Everyone who is not humble or funny is both not quiet and not humble. If someone is old or quiet then someone is generous or not wise. Everyone who is either creative or not happy is not calm and vice versa. Everyone who is both patient and not strong is either not wise or brave. If lucy is not happy then someone is not creative or not calm. Everyone who is either not humble or not strong is old and vice versa. Everyone who is either not tall or not creative is not curious or not funny and vice versa. Everyone who is patient or not tall is both old and tall. If someone is either strong or not happy then mary is either quiet or curious. Everyone who is funny or tall is not generous and vice versa. Everyone who is calm is not kind or quiet. Everyone who is not funny or old is generous or funny. Everyone who is either rich or not humble is kind. Everyone who is tall or not brave is both patient and not generous. Someone is generous or kind. John is rich. Susan is both funny and not generous. Alice is both wise and tall. | Alice is happy. | neutral | (![X]:((kind(X)<~>~happy(X))=>(patient(X)&quiet(X))))&
(![X]:((~humble(X)|funny(X))=>(~quiet(X)&~humble(X))))&
((?[X]:((old(X)|quiet(X))))=>(?[X]:((generous(X)|~wise(X)))))&
(![X]:((creative(X)<~>~happy(X))<=>~calm(X)))&
(![X]:((patient(X)&~strong(X))=>(~wise(X)<~>brave(X))))&
((~happy(lucy))=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:((~humble(X)<~>~strong(X))<=>old(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>(~curious(X)|~funny(X))))&
(![X]:((patient(X)|~tall(X))=>(old(X)&tall(X))))&
((?[X]:((strong(X)<~>~happy(X))))=>((quiet(mary)<~>curious(mary))))&
(![X]:((funny(X)|tall(X))<=>~generous(X)))&
(![X]:(calm(X)=>(~kind(X)|quiet(X))))&
(![X]:((~funny(X)|old(X))=>(generous(X)|funny(X))))&
(![X]:((rich(X)<~>~humble(X))=>kind(X)))&
(![X]:((tall(X)|~brave(X))=>(patient(X)&~generous(X))))&
(?[X]:((generous(X)|kind(X))))&
(rich(john))&
((funny(susan)&~generous(susan)))&
((wise(alice)&tall(alice))) | happy(alice) | [] | null | 0 |
Everyone who is not generous is either generous or not wise and vice versa.
Everyone who is creative or rich is tall or not funny and vice versa.
If someone is not calm or not tall then lucy is both not strong and not old.
If someone is both patient and not curious then someone is creative or not quiet and vice versa.
Everyone who is calm is either not calm or not patient and vice versa.
Everyone who is either not tall or tall is not creative or creative and vice versa.
Everyone who is either not humble or not quiet is both calm and not quiet and vice versa.
If john is either happy or not rich then susan is tall.
If someone is either old or generous then someone is either kind or not calm.
Everyone who is not funny or wise is rich or not humble and vice versa.
Everyone who is not happy is both not wise and not kind.
If fred is both patient and old then fred is both not curious and wise and vice versa.
Everyone who is either rich or strong is not wise.
If john is not calm then someone is both not strong and funny.
Everyone who is both not tall and not calm is both curious and old and vice versa.
Fred is either tall or not patient.
Someone is either generous or humble.
Fred is either strong or kind.
Mary is not patient or humble.
Someone is not curious or funny.
Lucy is both not tall and not old. | Fred is calm. | neutral | (![X]:(~generous(X)<=>(generous(X)<~>~wise(X))))&
(![X]:((creative(X)|rich(X))<=>(tall(X)|~funny(X))))&
((?[X]:((~calm(X)|~tall(X))))=>((~strong(lucy)&~old(lucy))))&
((?[X]:((patient(X)&~curious(X))))<=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:(calm(X)<=>(~calm(X)<~>~patient(X))))&
(![X]:((~tall(X)<~>tall(X))<=>(~creative(X)|creative(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(calm(X)&~quiet(X))))&
(((happy(john)<~>~rich(john)))=>(tall(susan)))&
((?[X]:((old(X)<~>generous(X))))=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:((~funny(X)|wise(X))<=>(rich(X)|~humble(X))))&
(![X]:(~happy(X)=>(~wise(X)&~kind(X))))&
(((patient(fred)&old(fred)))<=>((~curious(fred)&wise(fred))))&
(![X]:((rich(X)<~>strong(X))=>~wise(X)))&
((~calm(john))=>(?[X]:((~strong(X)&funny(X)))))&
(![X]:((~tall(X)&~calm(X))<=>(curious(X)&old(X))))&
((tall(fred)<~>~patient(fred)))&
(?[X]:((generous(X)<~>humble(X))))&
((strong(fred)<~>kind(fred)))&
((~patient(mary)|humble(mary)))&
(?[X]:((~curious(X)|funny(X))))&
((~tall(lucy)&~old(lucy))) | calm(fred) | [] | null | 0 |
If someone is either not curious or not old then someone is not wise or not humble. Everyone who is either not rich or funny is wise and vice versa. If john is either not patient or not rich then mary is strong. If alice is both patient and not patient then susan is either not humble or not brave and vice versa. If mary is not wise then someone is both old and calm and vice versa. Everyone who is both not wise and not curious is both not old and not rich and vice versa. Everyone who is not quiet is not calm and vice versa. If john is either strong or generous then someone is kind and vice versa. Everyone who is not tall or not brave is both brave and not tall and vice versa. If someone is either kind or not calm then susan is both curious and rich and vice versa. If lucy is either not wise or funny then fred is not calm and vice versa. Everyone who is calm is both not creative and not quiet. Everyone who is both not curious and not humble is both not humble and not strong and vice versa. If someone is either not rich or calm then alice is either not happy or not patient. If lucy is both not calm and not quiet then susan is both not curious and strong and vice versa. If someone is not kind then someone is not curious. Someone is both creative and humble. Alice is funny or not tall. Someone is both not happy and humble. Someone is either not patient or tall. Alice is both strong and rich. Someone is not rich or happy. Fred is not strong or strong. | Susan is not brave. | contradiction | ((?[X]:((~curious(X)<~>~old(X))))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((~rich(X)<~>funny(X))<=>wise(X)))&
(((~patient(john)<~>~rich(john)))=>(strong(mary)))&
(((patient(alice)&~patient(alice)))<=>((~humble(susan)<~>~brave(susan))))&
((~wise(mary))<=>(?[X]:((old(X)&calm(X)))))&
(![X]:((~wise(X)&~curious(X))<=>(~old(X)&~rich(X))))&
(![X]:(~quiet(X)<=>~calm(X)))&
(((strong(john)<~>generous(john)))<=>(?[X]:(kind(X))))&
(![X]:((~tall(X)|~brave(X))<=>(brave(X)&~tall(X))))&
((?[X]:((kind(X)<~>~calm(X))))<=>((curious(susan)&rich(susan))))&
(((~wise(lucy)<~>funny(lucy)))<=>(~calm(fred)))&
(![X]:(calm(X)=>(~creative(X)&~quiet(X))))&
(![X]:((~curious(X)&~humble(X))<=>(~humble(X)&~strong(X))))&
((?[X]:((~rich(X)<~>calm(X))))=>((~happy(alice)<~>~patient(alice))))&
(((~calm(lucy)&~quiet(lucy)))<=>((~curious(susan)&strong(susan))))&
((?[X]:(~kind(X)))=>(?[X]:(~curious(X))))&
(?[X]:((creative(X)&humble(X))))&
((funny(alice)|~tall(alice)))&
(?[X]:((~happy(X)&humble(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
((strong(alice)&rich(alice)))&
(?[X]:((~rich(X)|happy(X))))&
((~strong(fred)|strong(fred))) | ~brave(susan) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3746058431359513148760538
% SZS output start Proof for 3746058431359513148760538
9. ! [X0] : ((~brave(X0) | ~tall(X0)) <=> (~tall(X0) & brave(X0))) [input p8]
24. ~brave(susan) [input hypothesis]
51. ! [X0] : (((~brave(X0) | ~tall(X0)) | (tall(X0) | ~brave(X0))) & ((~tall(X0) & brave(X0)) | (brave(X0) & tall(X0)))) [nnf transformation 9]
52. ! [X0] : ((~brave(X0) | ~tall(X0) | tall(X0) | ~brave(X0)) & ((~tall(X0) & brave(X0)) | (brave(X0) & tall(X0)))) [flattening 51]
104. brave(X0) | brave(X0) [cnf transformation 52]
144. ~brave(susan) [cnf transformation 24]
145. brave(X0) [duplicate literal removal 104]
335. $false [subsumption resolution 144,145]
% SZS output end Proof for 3746058431359513148760538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and generous then someone is either not humble or wise and vice versa.
Everyone who is either not creative or not tall is creative and vice versa.
If someone is humble or not generous then someone is both strong and not wise and vice versa.
Everyone who is generous is calm or not old and vice versa.
Everyone who is both not wise and not curious is quiet and vice versa.
Everyone who is both rich and happy is wise or old.
Everyone who is either not tall or not old is either not wise or humble.
If someone is either not rich or rich then someone is not happy or not old and vice versa.
If someone is not humble or not funny then someone is brave or not strong.
If susan is either not funny or quiet then alice is either strong or rich and vice versa.
Everyone who is calm or not creative is both not generous and creative and vice versa.
If mary is not curious then someone is either old or brave.
If someone is both old and rich then alice is not brave or quiet.
Everyone who is not creative is not quiet and vice versa.
Everyone who is both not patient and generous is either not happy or not curious.
Everyone who is either not tall or curious is either patient or kind and vice versa.
John is either creative or happy.
Someone is not generous or not curious.
John is calm or not brave.
Lucy is wise or happy.
Someone is both creative and strong. | Lucy is wise. | contradiction | ((?[X]:((curious(X)&generous(X))))<=>(?[X]:((~humble(X)<~>wise(X)))))&
(![X]:((~creative(X)<~>~tall(X))<=>creative(X)))&
((?[X]:((humble(X)|~generous(X))))<=>(?[X]:((strong(X)&~wise(X)))))&
(![X]:(generous(X)<=>(calm(X)|~old(X))))&
(![X]:((~wise(X)&~curious(X))<=>quiet(X)))&
(![X]:((rich(X)&happy(X))=>(wise(X)|old(X))))&
(![X]:((~tall(X)<~>~old(X))=>(~wise(X)<~>humble(X))))&
((?[X]:((~rich(X)<~>rich(X))))<=>(?[X]:((~happy(X)|~old(X)))))&
((?[X]:((~humble(X)|~funny(X))))=>(?[X]:((brave(X)|~strong(X)))))&
(((~funny(susan)<~>quiet(susan)))<=>((strong(alice)<~>rich(alice))))&
(![X]:((calm(X)|~creative(X))<=>(~generous(X)&creative(X))))&
((~curious(mary))=>(?[X]:((old(X)<~>brave(X)))))&
((?[X]:((old(X)&rich(X))))=>((~brave(alice)|quiet(alice))))&
(![X]:(~creative(X)<=>~quiet(X)))&
(![X]:((~patient(X)&generous(X))=>(~happy(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>curious(X))<=>(patient(X)<~>kind(X))))&
((creative(john)<~>happy(john)))&
(?[X]:((~generous(X)|~curious(X))))&
((calm(john)|~brave(john)))&
((wise(lucy)|happy(lucy)))&
(?[X]:((creative(X)&strong(X)))) | wise(lucy) | [
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5142701539915261951834956
% SZS output start Proof for 5142701539915261951834956
5. ! [X0] : ((~curious(X0) & ~wise(X0)) <=> quiet(X0)) [input p4]
11. ! [X0] : ((~creative(X0) | calm(X0)) <=> (creative(X0) & ~generous(X0))) [input p10]
14. ! [X0] : (~creative(X0) <=> ~quiet(X0)) [input p13]
22. wise(lucy) [input hypothesis]
49. ! [X0] : (((~curious(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | (curious(X0) | wise(X0)))) [nnf transformation 5]
50. ! [X0] : (((~curious(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | curious(X0) | wise(X0))) [flattening 49]
61. ! [X0] : (((~creative(X0) | calm(X0)) | (~creative(X0) | generous(X0))) & ((creative(X0) & ~generous(X0)) | (creative(X0) & ~calm(X0)))) [nnf transformation 11]
62. ! [X0] : ((~creative(X0) | calm(X0) | ~creative(X0) | generous(X0)) & ((creative(X0) & ~generous(X0)) | (creative(X0) & ~calm(X0)))) [flattening 61]
66. ! [X0] : ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))) [nnf transformation 14]
93. ~quiet(X0) | ~wise(X0) [cnf transformation 50]
119. creative(X0) | creative(X0) [cnf transformation 62]
125. ~creative(X0) | quiet(X0) [cnf transformation 66]
143. wise(lucy) [cnf transformation 22]
144. creative(X0) [duplicate literal removal 119]
298. quiet(X0) [subsumption resolution 125,144]
315. 35 <=> wise(lucy) [avatar definition]
317. wise(lucy) <- (35) [avatar component clause 315]
323. 35 [avatar split clause 143,315]
330. ~wise(X0) [resolution 93,298]
332. $false <- (35) [resolution 330,317]
333. ~35 [avatar contradiction clause 332]
334. $false [avatar sat refutation 323,333]
% SZS output end Proof for 5142701539915261951834956
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and generous is both old and not tall and vice versa.
If fred is not patient then someone is either not happy or calm.
Everyone who is both funny and not happy is patient or old.
Everyone who is either rich or brave is not brave or not patient and vice versa.
Everyone who is both not calm and creative is not generous and vice versa.
Everyone who is both not strong and quiet is both not wise and patient.
Everyone who is not tall or curious is both not kind and not brave.
If fred is either not rich or strong then someone is quiet or not calm.
Everyone who is both not humble and not tall is not rich or old.
Everyone who is not generous or strong is wise or patient and vice versa.
If someone is brave then someone is either not brave or funny.
Everyone who is not funny is either patient or not tall.
Everyone who is not tall or humble is humble or not generous.
Everyone who is not quiet is tall or rich and vice versa.
Everyone who is not strong is not old or not calm.
If someone is old or not rich then someone is either kind or quiet.
Lucy is both funny and curious.
Paul is not brave or old.
Someone is curious.
Someone is not creative.
Fred is both funny and curious.
Someone is either creative or not tall.
Someone is brave or strong. | Paul is not tall. | neutral | (![X]:((tall(X)&generous(X))<=>(old(X)&~tall(X))))&
((~patient(fred))=>(?[X]:((~happy(X)<~>calm(X)))))&
(![X]:((funny(X)&~happy(X))=>(patient(X)|old(X))))&
(![X]:((rich(X)<~>brave(X))<=>(~brave(X)|~patient(X))))&
(![X]:((~calm(X)&creative(X))<=>~generous(X)))&
(![X]:((~strong(X)&quiet(X))=>(~wise(X)&patient(X))))&
(![X]:((~tall(X)|curious(X))=>(~kind(X)&~brave(X))))&
(((~rich(fred)<~>strong(fred)))=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:((~humble(X)&~tall(X))=>(~rich(X)|old(X))))&
(![X]:((~generous(X)|strong(X))<=>(wise(X)|patient(X))))&
((?[X]:(brave(X)))=>(?[X]:((~brave(X)<~>funny(X)))))&
(![X]:(~funny(X)=>(patient(X)<~>~tall(X))))&
(![X]:((~tall(X)|humble(X))=>(humble(X)|~generous(X))))&
(![X]:(~quiet(X)<=>(tall(X)|rich(X))))&
(![X]:(~strong(X)=>(~old(X)|~calm(X))))&
((?[X]:((old(X)|~rich(X))))=>(?[X]:((kind(X)<~>quiet(X)))))&
((funny(lucy)&curious(lucy)))&
((~brave(paul)|old(paul)))&
(?[X]:(curious(X)))&
(?[X]:(~creative(X)))&
((funny(fred)&curious(fred)))&
(?[X]:((creative(X)<~>~tall(X))))&
(?[X]:((brave(X)|strong(X)))) | ~tall(paul) | [] | null | 0 |
If someone is not funny or not quiet then mary is either happy or brave and vice versa. If someone is creative then paul is both not old and kind and vice versa. Everyone who is brave is either not creative or brave and vice versa. Everyone who is both not brave and not kind is not funny. Everyone who is either not tall or not brave is strong or not creative. If alice is quiet or funny then someone is either not quiet or quiet and vice versa. Everyone who is both creative and funny is calm. Everyone who is humble or quiet is both not creative and not rich. If someone is either old or not creative then someone is either strong or not tall and vice versa. Everyone who is either tall or not quiet is either humble or generous and vice versa. Everyone who is both not humble and old is both not quiet and curious and vice versa. Everyone who is not brave is not happy. If susan is both happy and not wise then someone is both not strong and not curious. Everyone who is either not quiet or rich is wise or patient and vice versa. Lucy is not creative or tall. Someone is either kind or not happy. Someone is either old or not brave. Paul is either happy or not humble. Someone is either not wise or happy. Someone is not tall or not generous. Paul is both not rich and not generous. | Lucy is not creative. | contradiction | ((?[X]:((~funny(X)|~quiet(X))))<=>((happy(mary)<~>brave(mary))))&
((?[X]:(creative(X)))<=>((~old(paul)&kind(paul))))&
(![X]:(brave(X)<=>(~creative(X)<~>brave(X))))&
(![X]:((~brave(X)&~kind(X))=>~funny(X)))&
(![X]:((~tall(X)<~>~brave(X))=>(strong(X)|~creative(X))))&
(((quiet(alice)|funny(alice)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((creative(X)&funny(X))=>calm(X)))&
(![X]:((humble(X)|quiet(X))=>(~creative(X)&~rich(X))))&
((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((tall(X)<~>~quiet(X))<=>(humble(X)<~>generous(X))))&
(![X]:((~humble(X)&old(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~brave(X)=>~happy(X)))&
(((happy(susan)&~wise(susan)))=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((~quiet(X)<~>rich(X))<=>(wise(X)|patient(X))))&
((~creative(lucy)|tall(lucy)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((old(X)<~>~brave(X))))&
((happy(paul)<~>~humble(paul)))&
(?[X]:((~wise(X)<~>happy(X))))&
(?[X]:((~tall(X)|~generous(X))))&
((~rich(paul)&~generous(paul))) | ~creative(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 2352900041532278605454048
% SZS output start Proof for 2352900041532278605454048
3. ! [X0] : (brave(X0) <=> (~creative(X0) <~> brave(X0))) [input p2]
22. ~creative(lucy) [input hypothesis]
42. ! [X0] : ((brave(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ~brave(X0))) [nnf transformation 3]
83. ~brave(X0) | creative(X0) | ~brave(X0) [cnf transformation 42]
84. brave(X0) | brave(X0) | creative(X0) [cnf transformation 42]
140. ~creative(lucy) [cnf transformation 22]
143. ~brave(X0) | creative(X0) [duplicate literal removal 83]
144. brave(X0) | creative(X0) [duplicate literal removal 84]
191. creative(X0) [subsumption resolution 143,144]
308. $false [subsumption resolution 140,191]
% SZS output end Proof for 2352900041532278605454048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If john is creative then paul is not brave or kind and vice versa.
If someone is either old or generous then susan is either calm or patient and vice versa.
Everyone who is not rich or not old is old or kind.
Everyone who is not generous is happy or generous and vice versa.
If someone is either not wise or not generous then someone is either not strong or not quiet.
Everyone who is humble or tall is tall or funny and vice versa.
Everyone who is either not brave or rich is not rich or patient and vice versa.
Everyone who is wise or not patient is both curious and humble.
Everyone who is generous or not quiet is both not patient and wise.
If lucy is funny or not creative then someone is either not curious or not brave and vice versa.
Everyone who is either creative or rich is not funny or old and vice versa.
Everyone who is either not tall or not kind is both not strong and not patient and vice versa.
If susan is both curious and generous then someone is curious and vice versa.
Everyone who is both generous and not humble is not strong and vice versa.
Everyone who is either creative or old is both tall and humble and vice versa.
Everyone who is either strong or creative is both generous and curious.
Someone is not curious or happy.
Fred is either not happy or not rich.
Someone is not happy or happy.
Someone is either brave or kind.
Mary is either brave or not generous.
Susan is either not quiet or not old. | John is happy. | entailment | ((creative(john))<=>((~brave(paul)|kind(paul))))&
((?[X]:((old(X)<~>generous(X))))<=>((calm(susan)<~>patient(susan))))&
(![X]:((~rich(X)|~old(X))=>(old(X)|kind(X))))&
(![X]:(~generous(X)<=>(happy(X)|generous(X))))&
((?[X]:((~wise(X)<~>~generous(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:((humble(X)|tall(X))<=>(tall(X)|funny(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(~rich(X)|patient(X))))&
(![X]:((wise(X)|~patient(X))=>(curious(X)&humble(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
(?[X]:((~curious(X)|happy(X))))&
((~happy(fred)<~>~rich(fred)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((brave(mary)<~>~generous(mary)))&
((~quiet(susan)<~>~old(susan))) | happy(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2601657321140103618538
% SZS output start Proof for 2601657321140103618538
4. ! [X0] : (~generous(X0) <=> (generous(X0) | happy(X0))) [input p3]
23. ~happy(john) [input hypothesis]
37. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | generous(X0))) [nnf transformation 4]
38. ! [X0] : ((~generous(X0) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | generous(X0))) [flattening 37]
89. generous(X0) | happy(X0) | generous(X0) [cnf transformation 38]
91. ~generous(X0) | ~generous(X0) [cnf transformation 38]
158. ~happy(john) [cnf transformation 23]
161. generous(X0) | happy(X0) [duplicate literal removal 89]
162. ~generous(X0) [duplicate literal removal 91]
209. happy(X0) [subsumption resolution 161,162]
280. $false [subsumption resolution 158,209]
% SZS output end Proof for 2601657321140103618538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then someone is both quiet and happy and vice versa.
If susan is both not tall and calm then alice is either brave or generous and vice versa.
Everyone who is either not curious or kind is creative or not patient and vice versa.
If susan is either generous or not kind then alice is not calm and vice versa.
Everyone who is both brave and not old is either not wise or wise and vice versa.
Everyone who is both kind and not rich is both not kind and funny.
Everyone who is either funny or not happy is tall or not kind.
If lucy is both calm and patient then lucy is both humble and not calm and vice versa.
If paul is either not humble or brave then someone is calm or not funny.
If someone is not kind or calm then alice is old.
Everyone who is curious is not patient and vice versa.
Everyone who is either not kind or old is both not tall and not kind and vice versa.
Everyone who is both not creative and not patient is rich or strong and vice versa.
Everyone who is old is funny or humble.
If john is either not patient or strong then someone is not quiet or calm and vice versa.
If mary is either not strong or not quiet then someone is strong.
Someone is either rich or generous.
Someone is not funny or humble.
Lucy is both happy and not generous.
Someone is both not funny and quiet.
Fred is not creative or not rich.
Mary is either not patient or not happy.
Alice is not old or not generous. | Lucy is not humble. | entailment | ((?[X]:(~old(X)))<=>(?[X]:((quiet(X)&happy(X)))))&
(((~tall(susan)&calm(susan)))<=>((brave(alice)<~>generous(alice))))&
(![X]:((~curious(X)<~>kind(X))<=>(creative(X)|~patient(X))))&
(((generous(susan)<~>~kind(susan)))<=>(~calm(alice)))&
(![X]:((brave(X)&~old(X))<=>(~wise(X)<~>wise(X))))&
(![X]:((kind(X)&~rich(X))=>(~kind(X)&funny(X))))&
(![X]:((funny(X)<~>~happy(X))=>(tall(X)|~kind(X))))&
(((calm(lucy)&patient(lucy)))<=>((humble(lucy)&~calm(lucy))))&
(((~humble(paul)<~>brave(paul)))=>(?[X]:((calm(X)|~funny(X)))))&
((?[X]:((~kind(X)|calm(X))))=>(old(alice)))&
(![X]:(curious(X)<=>~patient(X)))&
(![X]:((~kind(X)<~>old(X))<=>(~tall(X)&~kind(X))))&
(![X]:((~creative(X)&~patient(X))<=>(rich(X)|strong(X))))&
(![X]:(old(X)=>(funny(X)|humble(X))))&
(((~patient(john)<~>strong(john)))<=>(?[X]:((~quiet(X)|calm(X)))))&
(((~strong(mary)<~>~quiet(mary)))=>(?[X]:(strong(X))))&
(?[X]:((rich(X)<~>generous(X))))&
(?[X]:((~funny(X)|humble(X))))&
((happy(lucy)&~generous(lucy)))&
(?[X]:((~funny(X)&quiet(X))))&
((~creative(fred)|~rich(fred)))&
((~patient(mary)<~>~happy(mary)))&
((~old(alice)|~generous(alice))) | ~humble(lucy) | [
"p4",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 153407481265557550182117
% SZS output start Proof for 153407481265557550182117
5. ! [X0] : ((~old(X0) & brave(X0)) <=> (~wise(X0) <~> wise(X0))) [input p4]
8. (patient(lucy) & calm(lucy)) <=> (~calm(lucy) & humble(lucy)) [input p7]
10. ? [X0] : (calm(X0) | ~kind(X0)) => old(alice) [input p9]
24. humble(lucy) [input hypothesis]
31. old(alice) | ! [X0] : (~calm(X0) & kind(X0)) [ennf transformation 10]
45. ! [X0] : (((~old(X0) & brave(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (old(X0) | ~brave(X0)))) [nnf transformation 5]
46. ! [X0] : (((~old(X0) & brave(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | old(X0) | ~brave(X0))) [flattening 45]
48. ((patient(lucy) & calm(lucy)) | (calm(lucy) | ~humble(lucy))) & ((~calm(lucy) & humble(lucy)) | (~patient(lucy) | ~calm(lucy))) [nnf transformation 8]
49. ((patient(lucy) & calm(lucy)) | calm(lucy) | ~humble(lucy)) & ((~calm(lucy) & humble(lucy)) | ~patient(lucy) | ~calm(lucy)) [flattening 48]
96. ~old(X0) | wise(X0) | wise(X0) [cnf transformation 46]
97. ~old(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 46]
104. calm(lucy) | calm(lucy) | ~humble(lucy) [cnf transformation 49]
109. old(alice) | ~calm(X0) [cnf transformation 31]
143. humble(lucy) [cnf transformation 24]
147. calm(lucy) | ~humble(lucy) [duplicate literal removal 104]
151. ~old(X0) | wise(X0) [duplicate literal removal 96]
152. ~old(X0) | ~wise(X0) [duplicate literal removal 97]
212. ~old(X0) [subsumption resolution 151,152]
215. 13 <=> humble(lucy) [avatar definition]
219. 14 <=> calm(lucy) [avatar definition]
221. calm(lucy) <- (14) [avatar component clause 219]
227. ~13 | 14 [avatar split clause 147,219,215]
244. ~calm(X0) [subsumption resolution 109,212]
310. 13 [avatar split clause 143,215]
311. $false <- (14) [subsumption resolution 221,244]
312. ~14 [avatar contradiction clause 311]
319. $false [avatar sat refutation 227,310,312]
% SZS output end Proof for 153407481265557550182117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not creative is not wise and vice versa.
Everyone who is both not wise and not brave is either calm or not generous.
Everyone who is not brave is both humble and kind and vice versa.
Everyone who is funny or humble is either quiet or not generous.
If mary is both kind and strong then someone is both quiet and not quiet and vice versa.
Everyone who is both tall and calm is either not happy or not creative and vice versa.
If susan is either strong or old then someone is not curious or brave and vice versa.
Everyone who is not old is not wise and vice versa.
Everyone who is either not humble or patient is not kind or not curious.
Everyone who is both not old and not rich is not strong and vice versa.
If paul is creative or not funny then someone is not rich or rich and vice versa.
If someone is either not funny or not generous then mary is calm or not brave and vice versa.
Everyone who is brave is not calm or brave and vice versa.
Everyone who is both brave and patient is rich and vice versa.
Everyone who is not rich or rich is either patient or tall and vice versa.
Everyone who is either creative or not quiet is not creative.
Someone is either generous or curious.
Someone is either rich or happy.
John is not creative.
Someone is both old and not patient.
Someone is either curious or generous.
Paul is strong or not strong.
Someone is not patient or quiet.
Someone is not tall. | Susan is generous. | entailment | (![X]:((generous(X)&~creative(X))<=>~wise(X)))&
(![X]:((~wise(X)&~brave(X))=>(calm(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>(humble(X)&kind(X))))&
(![X]:((funny(X)|humble(X))=>(quiet(X)<~>~generous(X))))&
(((kind(mary)&strong(mary)))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((tall(X)&calm(X))<=>(~happy(X)<~>~creative(X))))&
(((strong(susan)<~>old(susan)))<=>(?[X]:((~curious(X)|brave(X)))))&
(![X]:(~old(X)<=>~wise(X)))&
(![X]:((~humble(X)<~>patient(X))=>(~kind(X)|~curious(X))))&
(![X]:((~old(X)&~rich(X))<=>~strong(X)))&
(((creative(paul)|~funny(paul)))<=>(?[X]:((~rich(X)|rich(X)))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>((calm(mary)|~brave(mary))))&
(![X]:(brave(X)<=>(~calm(X)|brave(X))))&
(![X]:((brave(X)&patient(X))<=>rich(X)))&
(![X]:((~rich(X)|rich(X))<=>(patient(X)<~>tall(X))))&
(![X]:((creative(X)<~>~quiet(X))=>~creative(X)))&
(?[X]:((generous(X)<~>curious(X))))&
(?[X]:((rich(X)<~>happy(X))))&
(~creative(john))&
(?[X]:((old(X)&~patient(X))))&
(?[X]:((curious(X)<~>generous(X))))&
((strong(paul)|~strong(paul)))&
(?[X]:((~patient(X)|quiet(X))))&
(?[X]:(~tall(X))) | generous(susan) | [
"p0",
"p2",
"p6",
"p7",
"p8",
"p9",
"p13",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 177543115800571247288049
% SZS output start Proof for 177543115800571247288049
1. ! [X0] : ((~creative(X0) & generous(X0)) <=> ~wise(X0)) [input p0]
3. ! [X0] : (~brave(X0) <=> (kind(X0) & humble(X0))) [input p2]
7. (strong(susan) <~> old(susan)) <=> ? [X0] : (brave(X0) | ~curious(X0)) [input p6]
8. ! [X0] : (~old(X0) <=> ~wise(X0)) [input p7]
9. ! [X0] : ((~humble(X0) <~> patient(X0)) => (~curious(X0) | ~kind(X0))) [input p8]
10. ! [X0] : ((~rich(X0) & ~old(X0)) <=> ~strong(X0)) [input p9]
14. ! [X0] : ((patient(X0) & brave(X0)) <=> rich(X0)) [input p13]
15. ! [X0] : ((rich(X0) | ~rich(X0)) <=> (patient(X0) <~> tall(X0))) [input p14]
24. ? [X0] : ~tall(X0) [input p23]
25. ~generous(susan) [input hypothesis]
29. ! [X0] : ((~curious(X0) | ~kind(X0)) | (~humble(X0) <=> patient(X0))) [ennf transformation 9]
30. ! [X0] : (~curious(X0) | ~kind(X0) | (~humble(X0) <=> patient(X0))) [flattening 29]
32. ! [X0] : (((~creative(X0) & generous(X0)) | wise(X0)) & (~wise(X0) | (creative(X0) | ~generous(X0)))) [nnf transformation 1]
33. ! [X0] : (((~creative(X0) & generous(X0)) | wise(X0)) & (~wise(X0) | creative(X0) | ~generous(X0))) [flattening 32]
35. ! [X0] : ((~brave(X0) | (~kind(X0) | ~humble(X0))) & ((kind(X0) & humble(X0)) | brave(X0))) [nnf transformation 3]
36. ! [X0] : ((~brave(X0) | ~kind(X0) | ~humble(X0)) & ((kind(X0) & humble(X0)) | brave(X0))) [flattening 35]
45. (((~old(susan) | ~strong(susan)) & (old(susan) | strong(susan))) | ! [X0] : (~brave(X0) & curious(X0))) & (? [X0] : (brave(X0) | ~curious(X0)) | ((strong(susan) | ~old(susan)) & (old(susan) | ~strong(susan)))) [nnf transformation 7]
46. (((~old(susan) | ~strong(susan)) & (old(susan) | strong(susan))) | ! [X0] : (~brave(X0) & curious(X0))) & (? [X1] : (brave(X1) | ~curious(X1)) | ((strong(susan) | ~old(susan)) & (old(susan) | ~strong(susan)))) [rectify 45]
47. ? [X1] : (brave(X1) | ~curious(X1)) => (brave(sK1) | ~curious(sK1)) [choice axiom]
48. (((~old(susan) | ~strong(susan)) & (old(susan) | strong(susan))) | ! [X0] : (~brave(X0) & curious(X0))) & ((brave(sK1) | ~curious(sK1)) | ((strong(susan) | ~old(susan)) & (old(susan) | ~strong(susan)))) [skolemisation 46,47]
49. ! [X0] : ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0))) [nnf transformation 8]
50. ! [X0] : (~curious(X0) | ~kind(X0) | ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0)))) [nnf transformation 30]
51. ! [X0] : (((~rich(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | (rich(X0) | old(X0)))) [nnf transformation 10]
52. ! [X0] : (((~rich(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | rich(X0) | old(X0))) [flattening 51]
65. ! [X0] : (((patient(X0) & brave(X0)) | ~rich(X0)) & (rich(X0) | (~patient(X0) | ~brave(X0)))) [nnf transformation 14]
66. ! [X0] : (((patient(X0) & brave(X0)) | ~rich(X0)) & (rich(X0) | ~patient(X0) | ~brave(X0))) [flattening 65]
67. ! [X0] : (((rich(X0) | ~rich(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (~rich(X0) & rich(X0)))) [nnf transformation 15]
68. ! [X0] : ((rich(X0) | ~rich(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (~rich(X0) & rich(X0)))) [flattening 67]
83. ? [X0] : ~tall(X0) => ~tall(sK9) [choice axiom]
84. ~tall(sK9) [skolemisation 24,83]
86. wise(X0) | generous(X0) [cnf transformation 33]
90. humble(X0) | brave(X0) [cnf transformation 36]
91. kind(X0) | brave(X0) [cnf transformation 36]
111. ~old(susan) | ~strong(susan) | curious(X0) [cnf transformation 48]
112. ~old(susan) | ~strong(susan) | ~brave(X0) [cnf transformation 48]
113. ~wise(X0) | old(X0) [cnf transformation 49]
116. ~patient(X0) | ~kind(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 50]
118. ~old(X0) | strong(X0) [cnf transformation 52]
135. ~rich(X0) | patient(X0) [cnf transformation 66]
136. tall(X0) | patient(X0) | rich(X0) [cnf transformation 68]
155. ~tall(sK9) [cnf transformation 84]
156. ~generous(susan) [cnf transformation 25]
174. 4 <=> ! [X0] : ~brave(X0) [avatar definition]
175. ~brave(X0) <- (4) [avatar component clause 174]
177. 5 <=> strong(susan) [avatar definition]
181. 6 <=> old(susan) [avatar definition]
182. old(susan) <- (6) [avatar component clause 181]
183. ~old(susan) <- (~6) [avatar component clause 181]
184. 4 | ~5 | ~6 [avatar split clause 112,181,177,174]
186. 7 <=> ! [X0] : curious(X0) [avatar definition]
187. curious(X0) <- (7) [avatar component clause 186]
188. 7 | ~5 | ~6 [avatar split clause 111,181,177,186]
247. patient(X0) | tall(X0) [subsumption resolution 136,135]
287. old(X0) | generous(X0) [resolution 113,86]
313. generous(susan) <- (~6) [resolution 287,183]
316. $false <- (~6) [subsumption resolution 313,156]
317. 6 [avatar contradiction clause 316]
318. strong(susan) <- (6) [resolution 182,118]
322. 5 | ~6 [avatar split clause 318,181,177]
411. ~kind(X0) | ~humble(X0) | ~curious(X0) | tall(X0) [resolution 116,247]
412. ~kind(X0) | ~humble(X0) | tall(X0) <- (7) [subsumption resolution 411,187]
421. ~humble(X0) | tall(X0) | brave(X0) <- (7) [resolution 412,91]
423. ~humble(X0) | tall(X0) <- (4, 7) [subsumption resolution 421,175]
473. tall(X0) | brave(X0) <- (4, 7) [resolution 423,90]
476. tall(X0) <- (4, 7) [subsumption resolution 473,175]
481. $false <- (4, 7) [resolution 476,155]
482. ~4 | ~7 [avatar contradiction clause 481]
484. $false [avatar sat refutation 184,188,317,322,482]
% SZS output end Proof for 177543115800571247288049
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is kind or funny is both not strong and not quiet and vice versa.
Everyone who is patient or not brave is wise or not kind and vice versa.
Everyone who is either calm or curious is both not kind and not happy.
Everyone who is generous or not generous is not tall.
Everyone who is not quiet is creative.
Everyone who is strong is either not kind or creative and vice versa.
If someone is both not quiet and strong then paul is not wise or calm and vice versa.
If susan is not funny or patient then susan is happy or rich and vice versa.
Everyone who is either not wise or old is not creative or creative and vice versa.
Everyone who is both patient and strong is patient and vice versa.
Everyone who is generous is not strong or rich and vice versa.
If someone is both not calm and not old then susan is not strong or not curious and vice versa.
Everyone who is both not kind and old is both creative and not calm.
If susan is either patient or curious then alice is either not humble or not strong and vice versa.
If paul is not rich then susan is both happy and not tall and vice versa.
If someone is both not calm and old then someone is either not humble or funny and vice versa.
Someone is not generous.
Someone is funny or not patient.
Mary is not creative.
Someone is rich or not quiet.
Someone is rich or not brave.
Alice is both quiet and not generous.
Someone is not happy or strong.
Lucy is not calm or old. | Paul is not old. | contradiction | (![X]:((kind(X)|funny(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((patient(X)|~brave(X))<=>(wise(X)|~kind(X))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)&~happy(X))))&
(![X]:((generous(X)|~generous(X))=>~tall(X)))&
(![X]:(~quiet(X)=>creative(X)))&
(![X]:(strong(X)<=>(~kind(X)<~>creative(X))))&
((?[X]:((~quiet(X)&strong(X))))<=>((~wise(paul)|calm(paul))))&
(((~funny(susan)|patient(susan)))<=>((happy(susan)|rich(susan))))&
(![X]:((~wise(X)<~>old(X))<=>(~creative(X)|creative(X))))&
(![X]:((patient(X)&strong(X))<=>patient(X)))&
(![X]:(generous(X)<=>(~strong(X)|rich(X))))&
((?[X]:((~calm(X)&~old(X))))<=>((~strong(susan)|~curious(susan))))&
(![X]:((~kind(X)&old(X))=>(creative(X)&~calm(X))))&
(((patient(susan)<~>curious(susan)))<=>((~humble(alice)<~>~strong(alice))))&
((~rich(paul))<=>((happy(susan)&~tall(susan))))&
((?[X]:((~calm(X)&old(X))))<=>(?[X]:((~humble(X)<~>funny(X)))))&
(?[X]:(~generous(X)))&
(?[X]:((funny(X)|~patient(X))))&
(~creative(mary))&
(?[X]:((rich(X)|~quiet(X))))&
(?[X]:((rich(X)|~brave(X))))&
((quiet(alice)&~generous(alice)))&
(?[X]:((~happy(X)|strong(X))))&
((~calm(lucy)|old(lucy))) | ~old(paul) | [
"p0",
"p4",
"p5",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8095897429335290855655823
% SZS output start Proof for 8095897429335290855655823
1. ! [X0] : ((funny(X0) | kind(X0)) <=> (~quiet(X0) & ~strong(X0))) [input p0]
5. ! [X0] : (~quiet(X0) => creative(X0)) [input p4]
6. ! [X0] : (strong(X0) <=> (~kind(X0) <~> creative(X0))) [input p5]
7. ? [X0] : (strong(X0) & ~quiet(X0)) <=> (calm(paul) | ~wise(paul)) [input p6]
9. ! [X0] : ((~wise(X0) <~> old(X0)) <=> (creative(X0) | ~creative(X0))) [input p8]
25. ~old(paul) [input hypothesis]
29. ! [X0] : (creative(X0) | quiet(X0)) [ennf transformation 5]
32. ! [X0] : (((funny(X0) | kind(X0)) | (quiet(X0) | strong(X0))) & ((~quiet(X0) & ~strong(X0)) | (~funny(X0) & ~kind(X0)))) [nnf transformation 1]
33. ! [X0] : ((funny(X0) | kind(X0) | quiet(X0) | strong(X0)) & ((~quiet(X0) & ~strong(X0)) | (~funny(X0) & ~kind(X0)))) [flattening 32]
37. ! [X0] : ((strong(X0) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) & (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ~strong(X0))) [nnf transformation 6]
38. (? [X0] : (strong(X0) & ~quiet(X0)) | (~calm(paul) & wise(paul))) & ((calm(paul) | ~wise(paul)) | ! [X0] : (~strong(X0) | quiet(X0))) [nnf transformation 7]
39. (? [X0] : (strong(X0) & ~quiet(X0)) | (~calm(paul) & wise(paul))) & (calm(paul) | ~wise(paul) | ! [X0] : (~strong(X0) | quiet(X0))) [flattening 38]
40. (? [X0] : (strong(X0) & ~quiet(X0)) | (~calm(paul) & wise(paul))) & (calm(paul) | ~wise(paul) | ! [X1] : (~strong(X1) | quiet(X1))) [rectify 39]
41. ? [X0] : (strong(X0) & ~quiet(X0)) => (strong(sK0) & ~quiet(sK0)) [choice axiom]
42. ((strong(sK0) & ~quiet(sK0)) | (~calm(paul) & wise(paul))) & (calm(paul) | ~wise(paul) | ! [X1] : (~strong(X1) | quiet(X1))) [skolemisation 40,41]
45. ! [X0] : ((((~old(X0) | wise(X0)) & (old(X0) | ~wise(X0))) | (~creative(X0) & creative(X0))) & ((creative(X0) | ~creative(X0)) | ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0))))) [nnf transformation 9]
46. ! [X0] : ((((~old(X0) | wise(X0)) & (old(X0) | ~wise(X0))) | (~creative(X0) & creative(X0))) & (creative(X0) | ~creative(X0) | ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0))))) [flattening 45]
74. ~strong(X0) | ~kind(X0) [cnf transformation 33]
89. creative(X0) | quiet(X0) [cnf transformation 29]
91. ~creative(X0) | kind(X0) | ~strong(X0) [cnf transformation 37]
93. strong(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 37]
95. ~quiet(sK0) | wise(paul) [cnf transformation 42]
97. strong(sK0) | wise(paul) [cnf transformation 42]
105. old(X0) | ~wise(X0) | creative(X0) [cnf transformation 46]
106. old(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 46]
148. ~old(paul) [cnf transformation 25]
150. ~creative(X0) | ~kind(X0) [subsumption resolution 93,74]
151. ~creative(X0) | ~strong(X0) [subsumption resolution 91,150]
157. 2 <=> strong(sK0) [avatar definition]
159. strong(sK0) <- (2) [avatar component clause 157]
162. 3 <=> wise(paul) [avatar definition]
164. wise(paul) <- (3) [avatar component clause 162]
165. 3 | 2 [avatar split clause 97,157,162]
167. 4 <=> quiet(sK0) [avatar definition]
171. 3 | ~4 [avatar split clause 95,167,162]
173. 5 <=> ! [X1] : (~strong(X1) | quiet(X1)) [avatar definition]
174. ~strong(X1) | quiet(X1) <- (5) [avatar component clause 173]
197. ~wise(X0) | old(X0) [subsumption resolution 105,106]
341. ~strong(X0) | quiet(X0) [resolution 151,89]
342. 5 [avatar split clause 341,173]
343. quiet(sK0) <- (2, 5) [resolution 174,159]
348. 4 | ~2 | ~5 [avatar split clause 343,173,157,167]
352. old(paul) <- (3) [resolution 197,164]
354. $false <- (3) [subsumption resolution 352,148]
355. ~3 [avatar contradiction clause 354]
356. $false [avatar sat refutation 165,171,342,348,355]
% SZS output end Proof for 8095897429335290855655823
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not humble or wise and vice versa.
Everyone who is creative or kind is both quiet and strong and vice versa.
Everyone who is both old and not humble is not wise and vice versa.
If someone is both creative and not kind then paul is old or brave and vice versa.
If fred is both not rich and old then paul is both old and funny.
Everyone who is both not patient and strong is both quiet and not wise.
If fred is curious or not strong then lucy is both rich and not creative and vice versa.
Everyone who is both not wise and curious is either not quiet or not creative and vice versa.
Everyone who is either not funny or not calm is both rich and not creative.
If john is both not creative and patient then john is not strong and vice versa.
Everyone who is not generous is wise and vice versa.
Everyone who is not generous is either generous or funny.
If paul is humble then mary is quiet or curious and vice versa.
If fred is not strong or not humble then someone is quiet or not generous and vice versa.
If paul is patient then someone is not humble or happy.
Everyone who is either not creative or not generous is quiet or curious.
Lucy is both not brave and funny.
Someone is both not brave and not creative.
Susan is not creative.
Someone is not old or funny.
John is both rich and patient.
Someone is both generous and quiet.
Susan is either humble or not wise.
John is not calm. | Susan is not quiet. | neutral | (![X]:(funny(X)<=>(~humble(X)|wise(X))))&
(![X]:((creative(X)|kind(X))<=>(quiet(X)&strong(X))))&
(![X]:((old(X)&~humble(X))<=>~wise(X)))&
((?[X]:((creative(X)&~kind(X))))<=>((old(paul)|brave(paul))))&
(((~rich(fred)&old(fred)))=>((old(paul)&funny(paul))))&
(![X]:((~patient(X)&strong(X))=>(quiet(X)&~wise(X))))&
(((curious(fred)|~strong(fred)))<=>((rich(lucy)&~creative(lucy))))&
(![X]:((~wise(X)&curious(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~funny(X)<~>~calm(X))=>(rich(X)&~creative(X))))&
(((~creative(john)&patient(john)))<=>(~strong(john)))&
(![X]:(~generous(X)<=>wise(X)))&
(![X]:(~generous(X)=>(generous(X)<~>funny(X))))&
((humble(paul))<=>((quiet(mary)|curious(mary))))&
(((~strong(fred)|~humble(fred)))<=>(?[X]:((quiet(X)|~generous(X)))))&
((patient(paul))=>(?[X]:((~humble(X)|happy(X)))))&
(![X]:((~creative(X)<~>~generous(X))=>(quiet(X)|curious(X))))&
((~brave(lucy)&funny(lucy)))&
(?[X]:((~brave(X)&~creative(X))))&
(~creative(susan))&
(?[X]:((~old(X)|funny(X))))&
((rich(john)&patient(john)))&
(?[X]:((generous(X)&quiet(X))))&
((humble(susan)<~>~wise(susan)))&
(~calm(john)) | ~quiet(susan) | [] | null | 0 |
If someone is both kind and calm then lucy is both not creative and not wise. If fred is both happy and not curious then alice is both generous and not creative and vice versa. If someone is rich or not brave then someone is not tall and vice versa. If someone is not funny or quiet then someone is not quiet. If someone is not old then mary is either generous or brave. Everyone who is not curious is not generous or not kind. If susan is not generous then alice is strong or rich and vice versa. Everyone who is patient is creative and vice versa. If susan is either not creative or creative then someone is not strong. Everyone who is either not strong or not creative is not brave and vice versa. Everyone who is wise or not calm is both not kind and patient and vice versa. If paul is not happy then susan is either not brave or old. Everyone who is creative or generous is both not old and not calm and vice versa. If john is both not quiet and creative then john is calm and vice versa. Everyone who is both not creative and not curious is both rich and patient and vice versa. If someone is not wise or tall then someone is both not wise and not patient. Mary is not brave. Someone is not funny. Someone is not strong. Someone is not kind. Someone is either not calm or not patient. Someone is not happy. | Mary is not kind. | entailment | ((?[X]:((kind(X)&calm(X))))=>((~creative(lucy)&~wise(lucy))))&
(((happy(fred)&~curious(fred)))<=>((generous(alice)&~creative(alice))))&
((?[X]:((rich(X)|~brave(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((~funny(X)|quiet(X))))=>(?[X]:(~quiet(X))))&
((?[X]:(~old(X)))=>((generous(mary)<~>brave(mary))))&
(![X]:(~curious(X)=>(~generous(X)|~kind(X))))&
((~generous(susan))<=>((strong(alice)|rich(alice))))&
(![X]:(patient(X)<=>creative(X)))&
(((~creative(susan)<~>creative(susan)))=>(?[X]:(~strong(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>~brave(X)))&
(![X]:((wise(X)|~calm(X))<=>(~kind(X)&patient(X))))&
((~happy(paul))=>((~brave(susan)<~>old(susan))))&
(![X]:((creative(X)|generous(X))<=>(~old(X)&~calm(X))))&
(((~quiet(john)&creative(john)))<=>(calm(john)))&
(![X]:((~creative(X)&~curious(X))<=>(rich(X)&patient(X))))&
((?[X]:((~wise(X)|tall(X))))=>(?[X]:((~wise(X)&~patient(X)))))&
(~brave(mary))&
(?[X]:(~funny(X)))&
(?[X]:(~strong(X)))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)<~>~patient(X))))&
(?[X]:(~happy(X))) | ~kind(mary) | [
"p4",
"p7",
"p10",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 869032734437023321442232
% SZS output start Proof for 869032734437023321442232
5. ? [X0] : ~old(X0) => (generous(mary) <~> brave(mary)) [input p4]
8. ! [X0] : (patient(X0) <=> creative(X0)) [input p7]
11. ! [X0] : ((~calm(X0) | wise(X0)) <=> (patient(X0) & ~kind(X0))) [input p10]
13. ! [X0] : ((generous(X0) | creative(X0)) <=> (~calm(X0) & ~old(X0))) [input p12]
14. (creative(john) & ~quiet(john)) <=> calm(john) [input p13]
17. ~brave(mary) [input p16]
23. kind(mary) [input hypothesis]
29. (generous(mary) <~> brave(mary)) | ! [X0] : old(X0) [ennf transformation 5]
45. ((~brave(mary) | ~generous(mary)) & (brave(mary) | generous(mary))) | ! [X0] : old(X0) [nnf transformation 29]
48. ! [X0] : ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))) [nnf transformation 8]
53. ! [X0] : (((~calm(X0) | wise(X0)) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | (calm(X0) & ~wise(X0)))) [nnf transformation 11]
54. ! [X0] : ((~calm(X0) | wise(X0) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | (calm(X0) & ~wise(X0)))) [flattening 53]
56. ! [X0] : (((generous(X0) | creative(X0)) | (calm(X0) | old(X0))) & ((~calm(X0) & ~old(X0)) | (~generous(X0) & ~creative(X0)))) [nnf transformation 13]
57. ! [X0] : ((generous(X0) | creative(X0) | calm(X0) | old(X0)) & ((~calm(X0) & ~old(X0)) | (~generous(X0) & ~creative(X0)))) [flattening 56]
58. ((creative(john) & ~quiet(john)) | ~calm(john)) & (calm(john) | (~creative(john) | quiet(john))) [nnf transformation 14]
59. ((creative(john) & ~quiet(john)) | ~calm(john)) & (calm(john) | ~creative(john) | quiet(john)) [flattening 58]
87. brave(mary) | generous(mary) | old(X0) [cnf transformation 45]
93. ~patient(X0) | creative(X0) [cnf transformation 48]
102. ~kind(X0) | calm(X0) [cnf transformation 54]
104. patient(X0) | calm(X0) [cnf transformation 54]
108. ~old(X0) | ~creative(X0) [cnf transformation 57]
110. ~creative(X0) | ~calm(X0) [cnf transformation 57]
111. ~generous(X0) | ~calm(X0) [cnf transformation 57]
115. creative(john) | ~calm(john) [cnf transformation 59]
124. ~brave(mary) [cnf transformation 17]
131. kind(mary) [cnf transformation 23]
204. 17 <=> ! [X0] : old(X0) [avatar definition]
205. old(X0) <- (17) [avatar component clause 204]
207. 18 <=> generous(mary) [avatar definition]
208. generous(mary) <- (18) [avatar component clause 207]
211. 19 <=> brave(mary) [avatar definition]
215. 17 | 18 | 19 [avatar split clause 87,211,207,204]
255. ~calm(john) [subsumption resolution 115,110]
262. 29 <=> creative(john) [avatar definition]
263. creative(john) <- (29) [avatar component clause 262]
264. ~creative(john) <- (~29) [avatar component clause 262]
286. ~19 [avatar split clause 124,211]
298. calm(mary) [resolution 102,131]
301. creative(X0) | calm(X0) [resolution 104,93]
303. ~calm(mary) <- (18) [resolution 111,208]
304. $false <- (18) [subsumption resolution 303,298]
305. ~18 [avatar contradiction clause 304]
307. ~creative(X1) <- (17) [resolution 205,108]
312. calm(john) <- (~29) [resolution 301,264]
316. $false <- (~29) [subsumption resolution 312,255]
317. 29 [avatar contradiction clause 316]
318. $false <- (17, 29) [subsumption resolution 263,307]
319. ~17 | ~29 [avatar contradiction clause 318]
320. $false [avatar sat refutation 215,286,305,317,319]
% SZS output end Proof for 869032734437023321442232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or humble is either not creative or not kind and vice versa. If someone is quiet then someone is not calm. If someone is both not humble and creative then lucy is quiet or not tall. Everyone who is either happy or generous is both not creative and quiet. Everyone who is both generous and not quiet is both happy and calm and vice versa. If someone is brave or creative then alice is both not old and not strong and vice versa. If lucy is either strong or not funny then fred is kind or patient and vice versa. If alice is both tall and not calm then someone is both happy and not quiet. Everyone who is not tall is both wise and tall. Everyone who is not generous is not wise or tall and vice versa. Everyone who is either not calm or not wise is happy or calm. Everyone who is old is not generous and vice versa. Everyone who is quiet or old is either rich or not brave and vice versa. Everyone who is not calm or patient is either not funny or not humble and vice versa. Everyone who is either not rich or not quiet is wise or patient and vice versa. Everyone who is curious is not wise and vice versa. John is not kind. Fred is not creative or calm. Someone is either wise or humble. Mary is wise or not tall. Fred is either calm or tall. Mary is either not quiet or old. Alice is either funny or not generous. | Lucy is generous. | contradiction | (![X]:((~tall(X)<~>humble(X))<=>(~creative(X)<~>~kind(X))))&
((?[X]:(quiet(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~humble(X)&creative(X))))=>((quiet(lucy)|~tall(lucy))))&
(![X]:((happy(X)<~>generous(X))=>(~creative(X)&quiet(X))))&
(![X]:((generous(X)&~quiet(X))<=>(happy(X)&calm(X))))&
((?[X]:((brave(X)|creative(X))))<=>((~old(alice)&~strong(alice))))&
(((strong(lucy)<~>~funny(lucy)))<=>((kind(fred)|patient(fred))))&
(((tall(alice)&~calm(alice)))=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:(~tall(X)=>(wise(X)&tall(X))))&
(![X]:(~generous(X)<=>(~wise(X)|tall(X))))&
(![X]:((~calm(X)<~>~wise(X))=>(happy(X)|calm(X))))&
(![X]:(old(X)<=>~generous(X)))&
(![X]:((quiet(X)|old(X))<=>(rich(X)<~>~brave(X))))&
(![X]:((~calm(X)|patient(X))<=>(~funny(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(wise(X)|patient(X))))&
(![X]:(curious(X)<=>~wise(X)))&
(~kind(john))&
((~creative(fred)|calm(fred)))&
(?[X]:((wise(X)<~>humble(X))))&
((wise(mary)|~tall(mary)))&
((calm(fred)<~>tall(fred)))&
((~quiet(mary)<~>old(mary)))&
((funny(alice)<~>~generous(alice))) | generous(lucy) | [
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2975142610593912632654801
% SZS output start Proof for 2975142610593912632654801
9. ! [X0] : (~tall(X0) => (tall(X0) & wise(X0))) [input p8]
10. ! [X0] : (~generous(X0) <=> (tall(X0) | ~wise(X0))) [input p9]
24. generous(lucy) [input hypothesis]
32. ! [X0] : ((tall(X0) & wise(X0)) | tall(X0)) [ennf transformation 9]
51. ! [X0] : ((~generous(X0) | (~tall(X0) & wise(X0))) & ((tall(X0) | ~wise(X0)) | generous(X0))) [nnf transformation 10]
52. ! [X0] : ((~generous(X0) | (~tall(X0) & wise(X0))) & (tall(X0) | ~wise(X0) | generous(X0))) [flattening 51]
99. tall(X0) | tall(X0) [cnf transformation 32]
102. ~generous(X0) | ~tall(X0) [cnf transformation 52]
136. generous(lucy) [cnf transformation 24]
138. tall(X0) [duplicate literal removal 99]
226. ~generous(X0) [subsumption resolution 102,138]
254. $false [subsumption resolution 136,226]
% SZS output end Proof for 2975142610593912632654801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is not tall or not happy.
Everyone who is both not brave and calm is both not wise and curious.
Everyone who is rich or not creative is both not calm and funny.
Everyone who is either not generous or humble is either calm or tall.
Everyone who is kind is not brave and vice versa.
If someone is not humble or creative then fred is both old and brave and vice versa.
If someone is either not brave or not kind then lucy is either not creative or not funny and vice versa.
If someone is both not patient and not brave then someone is happy.
If mary is kind or not strong then paul is old or not rich and vice versa.
Everyone who is either creative or not rich is not generous and vice versa.
If someone is both not brave and not curious then mary is both brave and funny.
If lucy is both patient and not brave then someone is funny.
If someone is not curious then fred is either old or tall and vice versa.
If someone is not rich then alice is wise or not tall and vice versa.
Everyone who is either creative or not quiet is not rich or brave and vice versa.
Everyone who is not humble or brave is not brave or patient and vice versa.
Someone is either funny or not patient.
Susan is either not brave or not patient.
Someone is both not generous and brave.
Someone is either old or humble.
Someone is creative or tall.
Someone is both generous and not brave. | Susan is not quiet. | neutral | (![X]:(quiet(X)=>(~tall(X)|~happy(X))))&
(![X]:((~brave(X)&calm(X))=>(~wise(X)&curious(X))))&
(![X]:((rich(X)|~creative(X))=>(~calm(X)&funny(X))))&
(![X]:((~generous(X)<~>humble(X))=>(calm(X)<~>tall(X))))&
(![X]:(kind(X)<=>~brave(X)))&
((?[X]:((~humble(X)|creative(X))))<=>((old(fred)&brave(fred))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>((~creative(lucy)<~>~funny(lucy))))&
((?[X]:((~patient(X)&~brave(X))))=>(?[X]:(happy(X))))&
(((kind(mary)|~strong(mary)))<=>((old(paul)|~rich(paul))))&
(![X]:((creative(X)<~>~rich(X))<=>~generous(X)))&
((?[X]:((~brave(X)&~curious(X))))=>((brave(mary)&funny(mary))))&
(((patient(lucy)&~brave(lucy)))=>(?[X]:(funny(X))))&
((?[X]:(~curious(X)))<=>((old(fred)<~>tall(fred))))&
((?[X]:(~rich(X)))<=>((wise(alice)|~tall(alice))))&
(![X]:((creative(X)<~>~quiet(X))<=>(~rich(X)|brave(X))))&
(![X]:((~humble(X)|brave(X))<=>(~brave(X)|patient(X))))&
(?[X]:((funny(X)<~>~patient(X))))&
((~brave(susan)<~>~patient(susan)))&
(?[X]:((~generous(X)&brave(X))))&
(?[X]:((old(X)<~>humble(X))))&
(?[X]:((creative(X)|tall(X))))&
(?[X]:((generous(X)&~brave(X)))) | ~quiet(susan) | [] | null | 0 |
If someone is not humble then john is not funny or kind and vice versa.
Everyone who is patient is curious and vice versa.
If someone is either not kind or strong then mary is both curious and strong and vice versa.
Everyone who is both not brave and not quiet is both not curious and not happy and vice versa.
If alice is old then someone is both tall and strong.
If alice is humble or patient then someone is not patient or creative and vice versa.
If someone is kind or not generous then someone is generous.
Everyone who is brave or wise is wise and vice versa.
Everyone who is both quiet and not humble is both tall and quiet.
Everyone who is both brave and not creative is calm.
If someone is either not kind or not patient then paul is either strong or not calm and vice versa.
Everyone who is both not creative and funny is not kind.
If lucy is both calm and funny then someone is both not tall and tall.
Everyone who is not brave or not calm is both not curious and calm and vice versa.
Everyone who is not humble is either not patient or not kind.
If someone is patient or not wise then someone is either not tall or old and vice versa.
Fred is old.
John is both not rich and old.
Someone is strong or calm.
Someone is both not patient and creative.
Alice is calm or not tall.
Lucy is both tall and happy.
Someone is either curious or not brave.
Someone is both not quiet and not old. | Lucy is patient. | neutral | ((?[X]:(~humble(X)))<=>((~funny(john)|kind(john))))&
(![X]:(patient(X)<=>curious(X)))&
((?[X]:((~kind(X)<~>strong(X))))<=>((curious(mary)&strong(mary))))&
(![X]:((~brave(X)&~quiet(X))<=>(~curious(X)&~happy(X))))&
((old(alice))=>(?[X]:((tall(X)&strong(X)))))&
(((humble(alice)|patient(alice)))<=>(?[X]:((~patient(X)|creative(X)))))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:(generous(X))))&
(![X]:((brave(X)|wise(X))<=>wise(X)))&
(![X]:((quiet(X)&~humble(X))=>(tall(X)&quiet(X))))&
(![X]:((brave(X)&~creative(X))=>calm(X)))&
((?[X]:((~kind(X)<~>~patient(X))))<=>((strong(paul)<~>~calm(paul))))&
(![X]:((~creative(X)&funny(X))=>~kind(X)))&
(((calm(lucy)&funny(lucy)))=>(?[X]:((~tall(X)&tall(X)))))&
(![X]:((~brave(X)|~calm(X))<=>(~curious(X)&calm(X))))&
(![X]:(~humble(X)=>(~patient(X)<~>~kind(X))))&
((?[X]:((patient(X)|~wise(X))))<=>(?[X]:((~tall(X)<~>old(X)))))&
(old(fred))&
((~rich(john)&old(john)))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((~patient(X)&creative(X))))&
((calm(alice)|~tall(alice)))&
((tall(lucy)&happy(lucy)))&
(?[X]:((curious(X)<~>~brave(X))))&
(?[X]:((~quiet(X)&~old(X)))) | patient(lucy) | [] | null | 0 |
If someone is kind or generous then someone is both not humble and wise and vice versa.
If alice is wise then someone is old.
Everyone who is not patient or patient is both not brave and quiet and vice versa.
Everyone who is either not quiet or not brave is not happy.
If alice is either strong or happy then alice is funny.
Everyone who is either not brave or tall is funny and vice versa.
Everyone who is old or humble is old or not funny and vice versa.
Everyone who is strong or not tall is both creative and wise.
If someone is not wise or old then someone is either quiet or calm.
Everyone who is happy is both not tall and funny and vice versa.
Everyone who is both not patient and not tall is either brave or strong.
Everyone who is humble or not quiet is brave.
Everyone who is happy is both wise and not calm and vice versa.
If someone is humble then lucy is not generous or not wise and vice versa.
If someone is either not patient or curious then someone is both curious and not generous and vice versa.
If someone is either humble or not happy then alice is either not rich or not happy and vice versa.
John is not funny.
Alice is not generous or happy.
Someone is either patient or strong.
Someone is not kind or curious.
Someone is quiet or wise. | Lucy is old. | entailment | ((?[X]:((kind(X)|generous(X))))<=>(?[X]:((~humble(X)&wise(X)))))&
((wise(alice))=>(?[X]:(old(X))))&
(![X]:((~patient(X)|patient(X))<=>(~brave(X)&quiet(X))))&
(![X]:((~quiet(X)<~>~brave(X))=>~happy(X)))&
(((strong(alice)<~>happy(alice)))=>(funny(alice)))&
(![X]:((~brave(X)<~>tall(X))<=>funny(X)))&
(![X]:((old(X)|humble(X))<=>(old(X)|~funny(X))))&
(![X]:((strong(X)|~tall(X))=>(creative(X)&wise(X))))&
((?[X]:((~wise(X)|old(X))))=>(?[X]:((quiet(X)<~>calm(X)))))&
(![X]:(happy(X)<=>(~tall(X)&funny(X))))&
(![X]:((~patient(X)&~tall(X))=>(brave(X)<~>strong(X))))&
(![X]:((humble(X)|~quiet(X))=>brave(X)))&
(![X]:(happy(X)<=>(wise(X)&~calm(X))))&
((?[X]:(humble(X)))<=>((~generous(lucy)|~wise(lucy))))&
((?[X]:((~patient(X)<~>curious(X))))<=>(?[X]:((curious(X)&~generous(X)))))&
((?[X]:((humble(X)<~>~happy(X))))<=>((~rich(alice)<~>~happy(alice))))&
(~funny(john))&
((~generous(alice)|happy(alice)))&
(?[X]:((patient(X)<~>strong(X))))&
(?[X]:((~kind(X)|curious(X))))&
(?[X]:((quiet(X)|wise(X)))) | old(lucy) | [
"p2",
"p3",
"p5",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4705043526391093593101854
% SZS output start Proof for 4705043526391093593101854
3. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (quiet(X0) & ~brave(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) <~> ~brave(X0)) => ~happy(X0)) [input p3]
6. ! [X0] : ((~brave(X0) <~> tall(X0)) <=> funny(X0)) [input p5]
7. ! [X0] : ((humble(X0) | old(X0)) <=> (~funny(X0) | old(X0))) [input p6]
10. ! [X0] : (happy(X0) <=> (funny(X0) & ~tall(X0))) [input p9]
12. ! [X0] : ((~quiet(X0) | humble(X0)) => brave(X0)) [input p11]
22. ~old(lucy) [input hypothesis]
28. ! [X0] : (~happy(X0) | (~quiet(X0) <=> ~brave(X0))) [ennf transformation 4]
34. ! [X0] : (brave(X0) | (quiet(X0) & ~humble(X0))) [ennf transformation 12]
42. ! [X0] : (((patient(X0) | ~patient(X0)) | (~quiet(X0) | brave(X0))) & ((quiet(X0) & ~brave(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 3]
43. ! [X0] : ((patient(X0) | ~patient(X0) | ~quiet(X0) | brave(X0)) & ((quiet(X0) & ~brave(X0)) | (~patient(X0) & patient(X0)))) [flattening 42]
44. ! [X0] : (~happy(X0) | ((~quiet(X0) | brave(X0)) & (~brave(X0) | quiet(X0)))) [nnf transformation 28]
46. ! [X0] : ((((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | ~funny(X0)) & (funny(X0) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0))))) [nnf transformation 6]
47. ! [X0] : (((humble(X0) | old(X0)) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | (~humble(X0) & ~old(X0)))) [nnf transformation 7]
48. ! [X0] : ((humble(X0) | old(X0) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | (~humble(X0) & ~old(X0)))) [flattening 47]
53. ! [X0] : ((happy(X0) | (~funny(X0) | tall(X0))) & ((funny(X0) & ~tall(X0)) | ~happy(X0))) [nnf transformation 10]
54. ! [X0] : ((happy(X0) | ~funny(X0) | tall(X0)) & ((funny(X0) & ~tall(X0)) | ~happy(X0))) [flattening 53]
85. ~brave(X0) | patient(X0) [cnf transformation 43]
86. ~brave(X0) | ~patient(X0) [cnf transformation 43]
87. quiet(X0) | patient(X0) [cnf transformation 43]
88. ~patient(X0) | quiet(X0) [cnf transformation 43]
91. ~happy(X0) | ~quiet(X0) | brave(X0) [cnf transformation 44]
94. funny(X0) | tall(X0) | brave(X0) [cnf transformation 46]
97. ~tall(X0) | brave(X0) | ~funny(X0) [cnf transformation 46]
101. funny(X0) | old(X0) | humble(X0) [cnf transformation 48]
110. happy(X0) | ~funny(X0) | tall(X0) [cnf transformation 54]
113. brave(X0) | ~humble(X0) [cnf transformation 34]
141. ~old(lucy) [cnf transformation 22]
181. quiet(X0) [subsumption resolution 87,88]
182. ~brave(X0) [subsumption resolution 85,86]
183. ~happy(X0) | brave(X0) [subsumption resolution 91,181]
184. ~happy(X0) [subsumption resolution 183,182]
195. ~tall(X0) | ~funny(X0) [subsumption resolution 97,182]
196. tall(X0) | funny(X0) [subsumption resolution 94,182]
211. ~funny(X0) | tall(X0) [subsumption resolution 110,184]
212. tall(X0) [subsumption resolution 211,196]
213. ~humble(X0) [subsumption resolution 113,182]
273. ~funny(X1) [resolution 195,212]
287. old(X2) | humble(X2) [resolution 101,273]
291. old(X2) [subsumption resolution 287,213]
293. $false [resolution 291,141]
% SZS output end Proof for 4705043526391093593101854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not humble is not curious and vice versa. Everyone who is both calm and not quiet is either not brave or rich. Everyone who is both not generous and not wise is quiet and vice versa. Everyone who is patient is either funny or tall. If someone is either quiet or not curious then someone is both not curious and not strong and vice versa. If mary is creative or quiet then fred is brave and vice versa. Everyone who is either not brave or happy is either generous or creative. Everyone who is calm or tall is patient and vice versa. Everyone who is calm is creative. If someone is either not wise or not happy then paul is not quiet. Everyone who is either not curious or brave is not wise or quiet and vice versa. Everyone who is not strong or generous is either calm or not brave and vice versa. If lucy is either not wise or not generous then mary is not quiet and vice versa. Everyone who is not funny is not rich and vice versa. If paul is either kind or not patient then someone is both not rich and not strong. Everyone who is both humble and not kind is not funny and vice versa. Someone is either not old or not quiet. Alice is both curious and brave. Susan is not strong or happy. Someone is either generous or not curious. Lucy is both not rich and not patient. Fred is patient. Lucy is not funny or not happy. Mary is both not old and quiet. | Lucy is kind. | contradiction | (![X]:((~old(X)|~humble(X))<=>~curious(X)))&
(![X]:((calm(X)&~quiet(X))=>(~brave(X)<~>rich(X))))&
(![X]:((~generous(X)&~wise(X))<=>quiet(X)))&
(![X]:(patient(X)=>(funny(X)<~>tall(X))))&
((?[X]:((quiet(X)<~>~curious(X))))<=>(?[X]:((~curious(X)&~strong(X)))))&
(((creative(mary)|quiet(mary)))<=>(brave(fred)))&
(![X]:((~brave(X)<~>happy(X))=>(generous(X)<~>creative(X))))&
(![X]:((calm(X)|tall(X))<=>patient(X)))&
(![X]:(calm(X)=>creative(X)))&
((?[X]:((~wise(X)<~>~happy(X))))=>(~quiet(paul)))&
(![X]:((~curious(X)<~>brave(X))<=>(~wise(X)|quiet(X))))&
(![X]:((~strong(X)|generous(X))<=>(calm(X)<~>~brave(X))))&
(((~wise(lucy)<~>~generous(lucy)))<=>(~quiet(mary)))&
(![X]:(~funny(X)<=>~rich(X)))&
(((kind(paul)<~>~patient(paul)))=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:((humble(X)&~kind(X))<=>~funny(X)))&
(?[X]:((~old(X)<~>~quiet(X))))&
((curious(alice)&brave(alice)))&
((~strong(susan)|happy(susan)))&
(?[X]:((generous(X)<~>~curious(X))))&
((~rich(lucy)&~patient(lucy)))&
(patient(fred))&
((~funny(lucy)|~happy(lucy)))&
((~old(mary)&quiet(mary))) | kind(lucy) | [
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8948498882581176917337629
% SZS output start Proof for 8948498882581176917337629
14. ! [X0] : (~funny(X0) <=> ~rich(X0)) [input p13]
16. ! [X0] : ((~kind(X0) & humble(X0)) <=> ~funny(X0)) [input p15]
21. ~patient(lucy) & ~rich(lucy) [input p20]
25. kind(lucy) [input hypothesis]
56. ! [X0] : ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))) [nnf transformation 14]
60. ! [X0] : (((~kind(X0) & humble(X0)) | funny(X0)) & (~funny(X0) | (kind(X0) | ~humble(X0)))) [nnf transformation 16]
61. ! [X0] : (((~kind(X0) & humble(X0)) | funny(X0)) & (~funny(X0) | kind(X0) | ~humble(X0))) [flattening 60]
114. ~funny(X0) | rich(X0) [cnf transformation 56]
121. ~kind(X0) | funny(X0) [cnf transformation 61]
129. ~rich(lucy) [cnf transformation 21]
135. kind(lucy) [cnf transformation 25]
258. 26 <=> funny(lucy) [avatar definition]
259. funny(lucy) <- (26) [avatar component clause 258]
270. funny(lucy) [resolution 121,135]
271. 26 [avatar split clause 270,258]
272. rich(lucy) <- (26) [resolution 259,114]
273. $false <- (26) [subsumption resolution 272,129]
274. ~26 [avatar contradiction clause 273]
275. $false [avatar sat refutation 271,274]
% SZS output end Proof for 8948498882581176917337629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is generous then someone is not wise or calm and vice versa.
If someone is humble then lucy is patient and vice versa.
If susan is both rich and not old then susan is happy or strong and vice versa.
If susan is generous then someone is not tall or not patient.
Everyone who is both generous and strong is both not happy and brave and vice versa.
If someone is both not tall and not old then someone is not patient and vice versa.
Everyone who is either not brave or old is both not tall and not wise.
Everyone who is either generous or not funny is not happy and vice versa.
Everyone who is either rich or not quiet is either strong or wise.
If alice is rich or humble then someone is either not wise or tall.
Everyone who is both not happy and strong is either not funny or tall.
Everyone who is either wise or curious is humble or not curious.
If mary is not quiet or generous then someone is not wise or happy.
If someone is patient then fred is either not strong or curious and vice versa.
Everyone who is either old or rich is tall and vice versa.
Everyone who is tall or not tall is both not quiet and curious and vice versa.
John is either curious or quiet.
Fred is not calm or calm.
Mary is generous or curious.
Mary is both not strong and wise.
Someone is not brave or generous.
Someone is either old or not quiet.
Someone is either calm or not wise.
Someone is either old or not rich. | Fred is curious. | entailment | ((generous(mary))<=>(?[X]:((~wise(X)|calm(X)))))&
((?[X]:(humble(X)))<=>(patient(lucy)))&
(((rich(susan)&~old(susan)))<=>((happy(susan)|strong(susan))))&
((generous(susan))=>(?[X]:((~tall(X)|~patient(X)))))&
(![X]:((generous(X)&strong(X))<=>(~happy(X)&brave(X))))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~brave(X)<~>old(X))=>(~tall(X)&~wise(X))))&
(![X]:((generous(X)<~>~funny(X))<=>~happy(X)))&
(![X]:((rich(X)<~>~quiet(X))=>(strong(X)<~>wise(X))))&
(((rich(alice)|humble(alice)))=>(?[X]:((~wise(X)<~>tall(X)))))&
(![X]:((~happy(X)&strong(X))=>(~funny(X)<~>tall(X))))&
(![X]:((wise(X)<~>curious(X))=>(humble(X)|~curious(X))))&
(((~quiet(mary)|generous(mary)))=>(?[X]:((~wise(X)|happy(X)))))&
((?[X]:(patient(X)))<=>((~strong(fred)<~>curious(fred))))&
(![X]:((old(X)<~>rich(X))<=>tall(X)))&
(![X]:((tall(X)|~tall(X))<=>(~quiet(X)&curious(X))))&
((curious(john)<~>quiet(john)))&
((~calm(fred)|calm(fred)))&
((generous(mary)|curious(mary)))&
((~strong(mary)&wise(mary)))&
(?[X]:((~brave(X)|generous(X))))&
(?[X]:((old(X)<~>~quiet(X))))&
(?[X]:((calm(X)<~>~wise(X))))&
(?[X]:((old(X)<~>~rich(X)))) | curious(fred) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6468892600197182314726927
% SZS output start Proof for 6468892600197182314726927
16. ! [X0] : ((~tall(X0) | tall(X0)) <=> (curious(X0) & ~quiet(X0))) [input p15]
25. ~curious(fred) [input hypothesis]
70. ! [X0] : (((~tall(X0) | tall(X0)) | (~curious(X0) | quiet(X0))) & ((curious(X0) & ~quiet(X0)) | (tall(X0) & ~tall(X0)))) [nnf transformation 16]
71. ! [X0] : ((~tall(X0) | tall(X0) | ~curious(X0) | quiet(X0)) & ((curious(X0) & ~quiet(X0)) | (tall(X0) & ~tall(X0)))) [flattening 70]
134. curious(X0) | ~tall(X0) [cnf transformation 71]
135. curious(X0) | tall(X0) [cnf transformation 71]
150. ~curious(fred) [cnf transformation 25]
294. curious(X0) [subsumption resolution 134,135]
326. $false [subsumption resolution 150,294]
% SZS output end Proof for 6468892600197182314726927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich or calm then someone is both not brave and humble. Everyone who is tall is brave. Everyone who is happy is both not brave and not patient and vice versa. If someone is humble or quiet then someone is not patient and vice versa. Everyone who is either not strong or quiet is strong or not generous and vice versa. If fred is both brave and creative then susan is not kind and vice versa. If alice is not generous or not rich then someone is not patient or quiet. Everyone who is both not humble and not funny is strong. Everyone who is both not rich and rich is funny or old and vice versa. Everyone who is either not patient or generous is both not brave and not curious and vice versa. If mary is either not happy or tall then mary is both not tall and not strong. If paul is not kind then mary is not tall or not curious and vice versa. If alice is not curious then john is both not kind and not rich and vice versa. Everyone who is either not humble or not old is happy or not patient and vice versa. Everyone who is happy or not generous is not calm or generous. Fred is brave or not patient. Mary is curious. Someone is calm or old. Susan is not generous or happy. Paul is curious or tall. Someone is both not funny and brave. Fred is not happy or not old. Fred is either not happy or calm. | Alice is creative. | neutral | ((?[X]:((~rich(X)|calm(X))))=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:(tall(X)=>brave(X)))&
(![X]:(happy(X)<=>(~brave(X)&~patient(X))))&
((?[X]:((humble(X)|quiet(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>(strong(X)|~generous(X))))&
(((brave(fred)&creative(fred)))<=>(~kind(susan)))&
(((~generous(alice)|~rich(alice)))=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((~humble(X)&~funny(X))=>strong(X)))&
(![X]:((~rich(X)&rich(X))<=>(funny(X)|old(X))))&
(![X]:((~patient(X)<~>generous(X))<=>(~brave(X)&~curious(X))))&
(((~happy(mary)<~>tall(mary)))=>((~tall(mary)&~strong(mary))))&
((~kind(paul))<=>((~tall(mary)|~curious(mary))))&
((~curious(alice))<=>((~kind(john)&~rich(john))))&
(![X]:((~humble(X)<~>~old(X))<=>(happy(X)|~patient(X))))&
(![X]:((happy(X)|~generous(X))=>(~calm(X)|generous(X))))&
((brave(fred)|~patient(fred)))&
(curious(mary))&
(?[X]:((calm(X)|old(X))))&
((~generous(susan)|happy(susan)))&
((curious(paul)|tall(paul)))&
(?[X]:((~funny(X)&brave(X))))&
((~happy(fred)|~old(fred)))&
((~happy(fred)<~>calm(fred))) | creative(alice) | [] | null | 0 |
Everyone who is either generous or humble is not generous. If someone is either patient or quiet then john is calm or not kind. If someone is rich or not generous then lucy is both not tall and calm. If someone is either not happy or not funny then someone is both not curious and not brave. If someone is both not happy and not rich then someone is not strong or not funny. Everyone who is either not wise or calm is both not wise and not old. Everyone who is kind is calm. Everyone who is either tall or old is old and vice versa. If susan is either not kind or funny then fred is not curious or funny. If someone is not brave then someone is either calm or not brave and vice versa. Everyone who is either old or not old is generous and vice versa. Everyone who is wise is not creative or not quiet. If someone is not old then someone is either not tall or happy. Everyone who is either calm or not humble is both generous and not generous and vice versa. If someone is either not kind or not rich then fred is curious or not patient and vice versa. Everyone who is wise or not brave is either rich or tall and vice versa. Someone is both quiet and not rich. Paul is not rich. Someone is wise or curious. Alice is either not quiet or generous. Paul is both not strong and brave. Lucy is either humble or not happy. Mary is either funny or not tall. | Susan is not generous. | contradiction | (![X]:((generous(X)<~>humble(X))=>~generous(X)))&
((?[X]:((patient(X)<~>quiet(X))))=>((calm(john)|~kind(john))))&
((?[X]:((rich(X)|~generous(X))))=>((~tall(lucy)&calm(lucy))))&
((?[X]:((~happy(X)<~>~funny(X))))=>(?[X]:((~curious(X)&~brave(X)))))&
((?[X]:((~happy(X)&~rich(X))))=>(?[X]:((~strong(X)|~funny(X)))))&
(![X]:((~wise(X)<~>calm(X))=>(~wise(X)&~old(X))))&
(![X]:(kind(X)=>calm(X)))&
(![X]:((tall(X)<~>old(X))<=>old(X)))&
(((~kind(susan)<~>funny(susan)))=>((~curious(fred)|funny(fred))))&
((?[X]:(~brave(X)))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:((old(X)<~>~old(X))<=>generous(X)))&
(![X]:(wise(X)=>(~creative(X)|~quiet(X))))&
((?[X]:(~old(X)))=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((calm(X)<~>~humble(X))<=>(generous(X)&~generous(X))))&
((?[X]:((~kind(X)<~>~rich(X))))<=>((curious(fred)|~patient(fred))))&
(![X]:((wise(X)|~brave(X))<=>(rich(X)<~>tall(X))))&
(?[X]:((quiet(X)&~rich(X))))&
(~rich(paul))&
(?[X]:((wise(X)|curious(X))))&
((~quiet(alice)<~>generous(alice)))&
((~strong(paul)&brave(paul)))&
((humble(lucy)<~>~happy(lucy)))&
((funny(mary)<~>~tall(mary))) | ~generous(susan) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3136103800976537421806054
% SZS output start Proof for 3136103800976537421806054
11. ! [X0] : ((old(X0) <~> ~old(X0)) <=> generous(X0)) [input p10]
24. ~generous(susan) [input hypothesis]
56. ! [X0] : ((((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | ~generous(X0)) & (generous(X0) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0))))) [nnf transformation 11]
104. generous(X0) | ~old(X0) | ~old(X0) [cnf transformation 56]
105. generous(X0) | old(X0) | old(X0) [cnf transformation 56]
139. ~generous(susan) [cnf transformation 24]
140. generous(X0) | ~old(X0) [duplicate literal removal 104]
141. generous(X0) | old(X0) [duplicate literal removal 105]
163. 5 <=> ! [X0] : generous(X0) [avatar definition]
164. generous(X0) <- (5) [avatar component clause 163]
242. generous(X0) [subsumption resolution 140,141]
243. 5 [avatar split clause 242,163]
313. $false <- (5) [resolution 164,139]
314. ~5 [avatar contradiction clause 313]
315. $false [avatar sat refutation 243,314]
% SZS output end Proof for 3136103800976537421806054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not happy is patient. Everyone who is kind or not strong is both old and not funny and vice versa. Everyone who is both not tall and not curious is both not strong and not funny and vice versa. Everyone who is old or wise is not creative. If someone is funny or brave then someone is not kind or not creative. If mary is not strong then someone is either old or not tall and vice versa. If susan is either patient or not humble then fred is either patient or calm. If lucy is either not kind or not curious then lucy is tall. Everyone who is both not brave and not creative is not quiet and vice versa. Everyone who is not strong is either quiet or brave and vice versa. Everyone who is both brave and kind is either generous or not wise. Everyone who is not patient or happy is both not calm and funny. If someone is both quiet and generous then mary is not curious or calm. If someone is old then someone is both not wise and not tall and vice versa. Everyone who is not curious is either not curious or not wise. Everyone who is either not old or not patient is not quiet or rich. Paul is both old and strong. Someone is both happy and not rich. Lucy is happy or not tall. Susan is strong. Alice is rich or patient. | Paul is happy. | neutral | (![X]:((~wise(X)<~>~happy(X))=>patient(X)))&
(![X]:((kind(X)|~strong(X))<=>(old(X)&~funny(X))))&
(![X]:((~tall(X)&~curious(X))<=>(~strong(X)&~funny(X))))&
(![X]:((old(X)|wise(X))=>~creative(X)))&
((?[X]:((funny(X)|brave(X))))=>(?[X]:((~kind(X)|~creative(X)))))&
((~strong(mary))<=>(?[X]:((old(X)<~>~tall(X)))))&
(((patient(susan)<~>~humble(susan)))=>((patient(fred)<~>calm(fred))))&
(((~kind(lucy)<~>~curious(lucy)))=>(tall(lucy)))&
(![X]:((~brave(X)&~creative(X))<=>~quiet(X)))&
(![X]:(~strong(X)<=>(quiet(X)<~>brave(X))))&
(![X]:((brave(X)&kind(X))=>(generous(X)<~>~wise(X))))&
(![X]:((~patient(X)|happy(X))=>(~calm(X)&funny(X))))&
((?[X]:((quiet(X)&generous(X))))=>((~curious(mary)|calm(mary))))&
((?[X]:(old(X)))<=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:(~curious(X)=>(~curious(X)<~>~wise(X))))&
(![X]:((~old(X)<~>~patient(X))=>(~quiet(X)|rich(X))))&
((old(paul)&strong(paul)))&
(?[X]:((happy(X)&~rich(X))))&
((happy(lucy)|~tall(lucy)))&
(strong(susan))&
((rich(alice)|patient(alice))) | happy(paul) | [] | null | 0 |
Everyone who is either not kind or not patient is either not rich or calm and vice versa.
Everyone who is not calm is brave.
If someone is not brave or not creative then mary is quiet.
Everyone who is kind or not wise is either not funny or old.
Everyone who is not kind or quiet is not humble or wise and vice versa.
Everyone who is either not humble or not kind is either not tall or wise and vice versa.
Everyone who is not happy or curious is calm or not quiet and vice versa.
Everyone who is not calm or not generous is either not humble or not kind and vice versa.
If john is not rich then susan is both funny and not strong and vice versa.
If susan is calm or curious then someone is both strong and old.
Everyone who is not generous or not patient is not creative or rich and vice versa.
If fred is either curious or calm then lucy is either not brave or not strong.
Everyone who is strong or calm is generous or tall.
Everyone who is both happy and not calm is generous or strong and vice versa.
If someone is either kind or not strong then lucy is not strong and vice versa.
Everyone who is humble or generous is not tall.
John is creative or not creative.
Lucy is either not strong or tall.
Fred is either curious or not generous.
Mary is both not patient and not humble.
Someone is either not creative or not funny.
Lucy is not wise.
Mary is not strong or strong. | John is not patient. | neutral | (![X]:((~kind(X)<~>~patient(X))<=>(~rich(X)<~>calm(X))))&
(![X]:(~calm(X)=>brave(X)))&
((?[X]:((~brave(X)|~creative(X))))=>(quiet(mary)))&
(![X]:((kind(X)|~wise(X))=>(~funny(X)<~>old(X))))&
(![X]:((~kind(X)|quiet(X))<=>(~humble(X)|wise(X))))&
(![X]:((~humble(X)<~>~kind(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~happy(X)|curious(X))<=>(calm(X)|~quiet(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~humble(X)<~>~kind(X))))&
((~rich(john))<=>((funny(susan)&~strong(susan))))&
(((calm(susan)|curious(susan)))=>(?[X]:((strong(X)&old(X)))))&
(![X]:((~generous(X)|~patient(X))<=>(~creative(X)|rich(X))))&
(((curious(fred)<~>calm(fred)))=>((~brave(lucy)<~>~strong(lucy))))&
(![X]:((strong(X)|calm(X))=>(generous(X)|tall(X))))&
(![X]:((happy(X)&~calm(X))<=>(generous(X)|strong(X))))&
((?[X]:((kind(X)<~>~strong(X))))<=>(~strong(lucy)))&
(![X]:((humble(X)|generous(X))=>~tall(X)))&
((creative(john)|~creative(john)))&
((~strong(lucy)<~>tall(lucy)))&
((curious(fred)<~>~generous(fred)))&
((~patient(mary)&~humble(mary)))&
(?[X]:((~creative(X)<~>~funny(X))))&
(~wise(lucy))&
((~strong(mary)|strong(mary))) | ~patient(john) | [] | null | 0 |
If paul is either tall or not quiet then someone is not old.
If someone is both humble and not creative then someone is wise.
If someone is calm or not brave then lucy is both calm and strong.
If john is kind or not generous then someone is both patient and not brave and vice versa.
If someone is not quiet then someone is both not wise and not kind.
Everyone who is either not happy or not calm is tall.
If someone is both not funny and not tall then someone is kind or rich and vice versa.
Everyone who is both not humble and quiet is old or not calm.
Everyone who is not humble or creative is not brave or creative and vice versa.
If someone is either not funny or brave then alice is either not calm or not rich.
If susan is kind then someone is either not generous or not humble and vice versa.
If fred is either not humble or strong then someone is both rich and curious and vice versa.
Everyone who is both quiet and not old is calm or generous and vice versa.
If someone is creative or generous then fred is kind.
If susan is both not quiet and not happy then someone is either patient or old and vice versa.
If john is either not generous or not quiet then someone is either not quiet or not brave.
Someone is both not patient and old.
Someone is happy or tall.
Susan is both not tall and not calm.
Paul is either humble or not humble.
Someone is both not funny and rich.
Someone is both not tall and humble.
Someone is patient or generous.
Lucy is not quiet or not strong. | Susan is kind. | neutral | (((tall(paul)<~>~quiet(paul)))=>(?[X]:(~old(X))))&
((?[X]:((humble(X)&~creative(X))))=>(?[X]:(wise(X))))&
((?[X]:((calm(X)|~brave(X))))=>((calm(lucy)&strong(lucy))))&
(((kind(john)|~generous(john)))<=>(?[X]:((patient(X)&~brave(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:((~happy(X)<~>~calm(X))=>tall(X)))&
((?[X]:((~funny(X)&~tall(X))))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((~humble(X)&quiet(X))=>(old(X)|~calm(X))))&
(![X]:((~humble(X)|creative(X))<=>(~brave(X)|creative(X))))&
((?[X]:((~funny(X)<~>brave(X))))=>((~calm(alice)<~>~rich(alice))))&
((kind(susan))<=>(?[X]:((~generous(X)<~>~humble(X)))))&
(((~humble(fred)<~>strong(fred)))<=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((quiet(X)&~old(X))<=>(calm(X)|generous(X))))&
((?[X]:((creative(X)|generous(X))))=>(kind(fred)))&
(((~quiet(susan)&~happy(susan)))<=>(?[X]:((patient(X)<~>old(X)))))&
(((~generous(john)<~>~quiet(john)))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
(?[X]:((~patient(X)&old(X))))&
(?[X]:((happy(X)|tall(X))))&
((~tall(susan)&~calm(susan)))&
((humble(paul)<~>~humble(paul)))&
(?[X]:((~funny(X)&rich(X))))&
(?[X]:((~tall(X)&humble(X))))&
(?[X]:((patient(X)|generous(X))))&
((~quiet(lucy)|~strong(lucy))) | kind(susan) | [] | null | 0 |
Everyone who is either not rich or quiet is not strong or wise and vice versa. If someone is either not quiet or kind then paul is both not quiet and not kind. Everyone who is not brave or not patient is not patient. Everyone who is not kind is both not patient and quiet and vice versa. If someone is not funny or not tall then alice is humble or creative and vice versa. Everyone who is either not quiet or not calm is either not calm or patient and vice versa. Everyone who is either happy or humble is both not brave and kind. If susan is not patient then susan is tall or not quiet and vice versa. If someone is both strong and not strong then alice is either not calm or not quiet. If alice is not calm or not rich then someone is either happy or not tall and vice versa. Everyone who is quiet or not tall is not patient or brave and vice versa. If alice is either not rich or not strong then mary is both not tall and not kind and vice versa. Everyone who is either not creative or not wise is both not patient and not creative. If lucy is both not rich and humble then fred is not old. Everyone who is brave or not funny is tall. Everyone who is kind is not rich and vice versa. Someone is not wise or wise. Susan is generous or strong. Someone is humble. Paul is either not tall or not kind. Someone is both brave and quiet. Someone is not old. Fred is either kind or not funny. | Mary is quiet. | entailment | (![X]:((~rich(X)<~>quiet(X))<=>(~strong(X)|wise(X))))&
((?[X]:((~quiet(X)<~>kind(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((~brave(X)|~patient(X))=>~patient(X)))&
(![X]:(~kind(X)<=>(~patient(X)&quiet(X))))&
((?[X]:((~funny(X)|~tall(X))))<=>((humble(alice)|creative(alice))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~calm(X)<~>patient(X))))&
(![X]:((happy(X)<~>humble(X))=>(~brave(X)&kind(X))))&
((~patient(susan))<=>((tall(susan)|~quiet(susan))))&
((?[X]:((strong(X)&~strong(X))))=>((~calm(alice)<~>~quiet(alice))))&
(((~calm(alice)|~rich(alice)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
(![X]:((quiet(X)|~tall(X))<=>(~patient(X)|brave(X))))&
(((~rich(alice)<~>~strong(alice)))<=>((~tall(mary)&~kind(mary))))&
(![X]:((~creative(X)<~>~wise(X))=>(~patient(X)&~creative(X))))&
(((~rich(lucy)&humble(lucy)))=>(~old(fred)))&
(![X]:((brave(X)|~funny(X))=>tall(X)))&
(![X]:(kind(X)<=>~rich(X)))&
(?[X]:((~wise(X)|wise(X))))&
((generous(susan)|strong(susan)))&
(?[X]:(humble(X)))&
((~tall(paul)<~>~kind(paul)))&
(?[X]:((brave(X)&quiet(X))))&
(?[X]:(~old(X)))&
((kind(fred)<~>~funny(fred))) | quiet(mary) | [
"p2",
"p5",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5837332930266466133387002
% SZS output start Proof for 5837332930266466133387002
3. ! [X0] : ((~patient(X0) | ~brave(X0)) => ~patient(X0)) [input p2]
6. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~calm(X0) <~> patient(X0))) [input p5]
11. ! [X0] : ((~tall(X0) | quiet(X0)) <=> (brave(X0) | ~patient(X0))) [input p10]
15. ! [X0] : ((~funny(X0) | brave(X0)) => tall(X0)) [input p14]
24. ~quiet(mary) [input hypothesis]
29. ! [X0] : (~patient(X0) | (patient(X0) & brave(X0))) [ennf transformation 3]
33. ! [X0] : (tall(X0) | (funny(X0) & ~brave(X0))) [ennf transformation 15]
44. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0)))) & (((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 6]
54. ! [X0] : (((~tall(X0) | quiet(X0)) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | (tall(X0) & ~quiet(X0)))) [nnf transformation 11]
55. ! [X0] : ((~tall(X0) | quiet(X0) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | (tall(X0) & ~quiet(X0)))) [flattening 54]
78. ~patient(X0) | brave(X0) [cnf transformation 29]
87. patient(X0) | ~calm(X0) | ~calm(X0) | quiet(X0) [cnf transformation 44]
93. calm(X0) | quiet(X0) | patient(X0) | calm(X0) [cnf transformation 44]
113. ~tall(X0) | quiet(X0) | ~brave(X0) [cnf transformation 55]
124. ~brave(X0) | tall(X0) [cnf transformation 33]
136. ~quiet(mary) [cnf transformation 24]
138. patient(X0) | ~calm(X0) | quiet(X0) [duplicate literal removal 87]
141. calm(X0) | quiet(X0) | patient(X0) [duplicate literal removal 93]
188. patient(X0) | quiet(X0) [subsumption resolution 138,141]
288. brave(X2) | quiet(X2) [resolution 188,78]
351. tall(X0) | quiet(X0) [resolution 288,124]
374. quiet(X0) | quiet(X0) | ~brave(X0) [resolution 351,113]
378. quiet(X0) | ~brave(X0) [duplicate literal removal 374]
379. quiet(X0) [subsumption resolution 378,288]
380. $false [resolution 379,136]
% SZS output end Proof for 5837332930266466133387002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich or not patient then paul is both patient and not quiet.
Everyone who is both not kind and patient is not creative and vice versa.
Everyone who is not old is both calm and not brave and vice versa.
Everyone who is old or not rich is patient.
If someone is not funny then paul is either funny or not creative and vice versa.
If susan is either not calm or brave then someone is rich or humble and vice versa.
If paul is either not curious or not brave then someone is either curious or not rich and vice versa.
Everyone who is not rich or curious is both not old and not generous.
If someone is either not calm or not wise then alice is tall or rich and vice versa.
Everyone who is both patient and not patient is not wise.
Everyone who is either calm or happy is either generous or brave and vice versa.
Everyone who is humble is either not funny or calm and vice versa.
Everyone who is both wise and not funny is not calm.
Everyone who is not funny is both not humble and not patient and vice versa.
If someone is both not humble and creative then alice is not brave or not patient and vice versa.
Everyone who is both strong and not rich is not calm and vice versa.
Alice is not brave.
Susan is generous or not brave.
Someone is both not happy and not old.
John is either wise or old.
Susan is not creative.
Someone is both wise and not patient. | Susan is creative. | contradiction | ((?[X]:((~rich(X)|~patient(X))))=>((patient(paul)&~quiet(paul))))&
(![X]:((~kind(X)&patient(X))<=>~creative(X)))&
(![X]:(~old(X)<=>(calm(X)&~brave(X))))&
(![X]:((old(X)|~rich(X))=>patient(X)))&
((?[X]:(~funny(X)))<=>((funny(paul)<~>~creative(paul))))&
(((~calm(susan)<~>brave(susan)))<=>(?[X]:((rich(X)|humble(X)))))&
(((~curious(paul)<~>~brave(paul)))<=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:((~rich(X)|curious(X))=>(~old(X)&~generous(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>((tall(alice)|rich(alice))))&
(![X]:((patient(X)&~patient(X))=>~wise(X)))&
(![X]:((calm(X)<~>happy(X))<=>(generous(X)<~>brave(X))))&
(![X]:(humble(X)<=>(~funny(X)<~>calm(X))))&
(![X]:((wise(X)&~funny(X))=>~calm(X)))&
(![X]:(~funny(X)<=>(~humble(X)&~patient(X))))&
((?[X]:((~humble(X)&creative(X))))<=>((~brave(alice)|~patient(alice))))&
(![X]:((strong(X)&~rich(X))<=>~calm(X)))&
(~brave(alice))&
((generous(susan)|~brave(susan)))&
(?[X]:((~happy(X)&~old(X))))&
((wise(john)<~>old(john)))&
(~creative(susan))&
(?[X]:((wise(X)&~patient(X)))) | creative(susan) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4546570206534201864892371
% SZS output start Proof for 4546570206534201864892371
21. ~creative(susan) [input p20]
23. creative(susan) [input hypothesis]
138. ~creative(susan) [cnf transformation 21]
141. creative(susan) [cnf transformation 23]
299. $false [subsumption resolution 141,138]
% SZS output end Proof for 4546570206534201864892371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then mary is kind.
If susan is either not brave or humble then fred is either not wise or not rich and vice versa.
Everyone who is either not funny or wise is both old and not happy.
Everyone who is calm or not humble is humble and vice versa.
If mary is either not happy or curious then someone is both not creative and funny and vice versa.
If alice is brave then someone is either not tall or not happy and vice versa.
Everyone who is both not tall and kind is funny.
Everyone who is generous or not happy is not humble or not old and vice versa.
If mary is either calm or not wise then someone is either not creative or happy.
If susan is both curious and brave then someone is brave.
If someone is either not calm or humble then someone is both not quiet and curious.
If john is either calm or quiet then someone is both old and not calm and vice versa.
Everyone who is both tall and not wise is not generous or brave.
Everyone who is either wise or creative is not patient or happy and vice versa.
Everyone who is either not old or not funny is patient.
Everyone who is kind is both not quiet and quiet and vice versa.
Someone is both not old and brave.
Mary is both tall and curious.
Lucy is both rich and funny.
Someone is curious or tall.
Lucy is old.
John is patient. | Fred is not kind. | entailment | ((generous(susan))=>(kind(mary)))&
(((~brave(susan)<~>humble(susan)))<=>((~wise(fred)<~>~rich(fred))))&
(![X]:((~funny(X)<~>wise(X))=>(old(X)&~happy(X))))&
(![X]:((calm(X)|~humble(X))<=>humble(X)))&
(((~happy(mary)<~>curious(mary)))<=>(?[X]:((~creative(X)&funny(X)))))&
((brave(alice))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~tall(X)&kind(X))=>funny(X)))&
(![X]:((generous(X)|~happy(X))<=>(~humble(X)|~old(X))))&
(((calm(mary)<~>~wise(mary)))=>(?[X]:((~creative(X)<~>happy(X)))))&
(((curious(susan)&brave(susan)))=>(?[X]:(brave(X))))&
((?[X]:((~calm(X)<~>humble(X))))=>(?[X]:((~quiet(X)&curious(X)))))&
(((calm(john)<~>quiet(john)))<=>(?[X]:((old(X)&~calm(X)))))&
(![X]:((tall(X)&~wise(X))=>(~generous(X)|brave(X))))&
(![X]:((wise(X)<~>creative(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))=>patient(X)))&
(![X]:(kind(X)<=>(~quiet(X)&quiet(X))))&
(?[X]:((~old(X)&brave(X))))&
((tall(mary)&curious(mary)))&
((rich(lucy)&funny(lucy)))&
(?[X]:((curious(X)|tall(X))))&
(old(lucy))&
(patient(john)) | ~kind(fred) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3855073556543118355744762
% SZS output start Proof for 3855073556543118355744762
16. ! [X0] : (kind(X0) <=> (quiet(X0) & ~quiet(X0))) [input p15]
23. kind(fred) [input hypothesis]
66. ! [X0] : ((kind(X0) | (~quiet(X0) | quiet(X0))) & ((quiet(X0) & ~quiet(X0)) | ~kind(X0))) [nnf transformation 16]
67. ! [X0] : ((kind(X0) | ~quiet(X0) | quiet(X0)) & ((quiet(X0) & ~quiet(X0)) | ~kind(X0))) [flattening 66]
127. ~quiet(X0) | ~kind(X0) [cnf transformation 67]
128. quiet(X0) | ~kind(X0) [cnf transformation 67]
139. kind(fred) [cnf transformation 23]
293. ~kind(X0) [subsumption resolution 127,128]
304. $false [subsumption resolution 139,293]
% SZS output end Proof for 3855073556543118355744762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not tall and patient then someone is either not creative or curious and vice versa. Everyone who is not humble is either not creative or old and vice versa. Everyone who is both calm and not patient is patient or funny and vice versa. Everyone who is wise is either not kind or not humble and vice versa. Everyone who is both patient and creative is not tall or wise and vice versa. If fred is both quiet and calm then someone is patient. If someone is generous or tall then susan is not humble or old and vice versa. If someone is not happy then lucy is both tall and creative and vice versa. Everyone who is either not old or not creative is funny and vice versa. If fred is strong then mary is not wise or kind and vice versa. Everyone who is both not strong and old is funny. Everyone who is tall or not humble is either not curious or not old. Everyone who is either not funny or creative is both not generous and not strong and vice versa. Everyone who is not happy or not old is either not quiet or not funny. If alice is not generous or patient then mary is generous and vice versa. Someone is not brave or patient. Someone is not rich or wise. Someone is not curious. Alice is both not funny and not brave. John is either not kind or happy. Someone is either tall or patient. Mary is tall. | Fred is creative. | entailment | (((~tall(paul)&patient(paul)))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(![X]:(~humble(X)<=>(~creative(X)<~>old(X))))&
(![X]:((calm(X)&~patient(X))<=>(patient(X)|funny(X))))&
(![X]:(wise(X)<=>(~kind(X)<~>~humble(X))))&
(![X]:((patient(X)&creative(X))<=>(~tall(X)|wise(X))))&
(((quiet(fred)&calm(fred)))=>(?[X]:(patient(X))))&
((?[X]:((generous(X)|tall(X))))<=>((~humble(susan)|old(susan))))&
((?[X]:(~happy(X)))<=>((tall(lucy)&creative(lucy))))&
(![X]:((~old(X)<~>~creative(X))<=>funny(X)))&
((strong(fred))<=>((~wise(mary)|kind(mary))))&
(![X]:((~strong(X)&old(X))=>funny(X)))&
(![X]:((tall(X)|~humble(X))=>(~curious(X)<~>~old(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(~generous(X)&~strong(X))))&
(![X]:((~happy(X)|~old(X))=>(~quiet(X)<~>~funny(X))))&
(((~generous(alice)|patient(alice)))<=>(generous(mary)))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((~rich(X)|wise(X))))&
(?[X]:(~curious(X)))&
((~funny(alice)&~brave(alice)))&
((~kind(john)<~>happy(john)))&
(?[X]:((tall(X)<~>patient(X))))&
(tall(mary)) | creative(fred) | [
"p0",
"p1",
"p2",
"p4",
"p8",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3159230779148911893793841
% SZS output start Proof for 3159230779148911893793841
1. (patient(paul) & ~tall(paul)) <=> ? [X0] : (~creative(X0) <~> curious(X0)) [input p0]
2. ! [X0] : (~humble(X0) <=> (~creative(X0) <~> old(X0))) [input p1]
3. ! [X0] : ((~patient(X0) & calm(X0)) <=> (funny(X0) | patient(X0))) [input p2]
5. ! [X0] : ((creative(X0) & patient(X0)) <=> (wise(X0) | ~tall(X0))) [input p4]
9. ! [X0] : ((~old(X0) <~> ~creative(X0)) <=> funny(X0)) [input p8]
10. strong(fred) <=> (kind(mary) | ~wise(mary)) [input p9]
12. ! [X0] : ((~humble(X0) | tall(X0)) => (~curious(X0) <~> ~old(X0))) [input p11]
13. ! [X0] : ((~funny(X0) <~> creative(X0)) <=> (~strong(X0) & ~generous(X0))) [input p12]
23. ~creative(fred) [input hypothesis]
31. ! [X0] : ((~curious(X0) <~> ~old(X0)) | (humble(X0) & ~tall(X0))) [ennf transformation 12]
33. ((patient(paul) & ~tall(paul)) | ! [X0] : ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (? [X0] : ((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | (~patient(paul) | tall(paul))) [nnf transformation 1]
34. ((patient(paul) & ~tall(paul)) | ! [X0] : ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (? [X0] : ((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | ~patient(paul) | tall(paul)) [flattening 33]
35. ((patient(paul) & ~tall(paul)) | ! [X0] : ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (? [X1] : ((~curious(X1) | creative(X1)) & (curious(X1) | ~creative(X1))) | ~patient(paul) | tall(paul)) [rectify 34]
36. ? [X1] : ((~curious(X1) | creative(X1)) & (curious(X1) | ~creative(X1))) => ((~curious(sK0) | creative(sK0)) & (curious(sK0) | ~creative(sK0))) [choice axiom]
37. ((patient(paul) & ~tall(paul)) | ! [X0] : ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (((~curious(sK0) | creative(sK0)) & (curious(sK0) | ~creative(sK0))) | ~patient(paul) | tall(paul)) [skolemisation 35,36]
38. ! [X0] : ((~humble(X0) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) & (((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | humble(X0))) [nnf transformation 2]
39. ! [X0] : (((~patient(X0) & calm(X0)) | (~funny(X0) & ~patient(X0))) & ((funny(X0) | patient(X0)) | (patient(X0) | ~calm(X0)))) [nnf transformation 3]
40. ! [X0] : (((~patient(X0) & calm(X0)) | (~funny(X0) & ~patient(X0))) & (funny(X0) | patient(X0) | patient(X0) | ~calm(X0))) [flattening 39]
42. ! [X0] : (((creative(X0) & patient(X0)) | (~wise(X0) & tall(X0))) & ((wise(X0) | ~tall(X0)) | (~creative(X0) | ~patient(X0)))) [nnf transformation 5]
43. ! [X0] : (((creative(X0) & patient(X0)) | (~wise(X0) & tall(X0))) & (wise(X0) | ~tall(X0) | ~creative(X0) | ~patient(X0))) [flattening 42]
56. ! [X0] : ((((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | ~funny(X0)) & (funny(X0) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))))) [nnf transformation 9]
57. (strong(fred) | (~kind(mary) & wise(mary))) & ((kind(mary) | ~wise(mary)) | ~strong(fred)) [nnf transformation 10]
58. (strong(fred) | (~kind(mary) & wise(mary))) & (kind(mary) | ~wise(mary) | ~strong(fred)) [flattening 57]
59. ! [X0] : (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (humble(X0) & ~tall(X0))) [nnf transformation 31]
60. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | (strong(X0) | generous(X0))) & ((~strong(X0) & ~generous(X0)) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | strong(X0) | generous(X0)) & ((~strong(X0) & ~generous(X0)) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [flattening 60]
73. ~tall(paul) | curious(X0) | creative(X0) [cnf transformation 37]
78. ~old(X0) | creative(X0) | humble(X0) [cnf transformation 38]
80. ~old(X0) | ~creative(X0) | ~humble(X0) [cnf transformation 38]
84. ~patient(X0) | ~patient(X0) [cnf transformation 40]
91. patient(X0) | tall(X0) [cnf transformation 43]
92. patient(X0) | ~wise(X0) [cnf transformation 43]
106. ~funny(X0) | old(X0) | creative(X0) [cnf transformation 56]
108. strong(fred) | wise(mary) [cnf transformation 58]
111. ~old(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 59]
113. old(X0) | curious(X0) | ~tall(X0) [cnf transformation 59]
117. ~strong(X0) | creative(X0) | funny(X0) [cnf transformation 61]
135. ~creative(fred) [cnf transformation 23]
137. ~patient(X0) [duplicate literal removal 84]
147. 3 <=> ! [X0] : (curious(X0) | creative(X0)) [avatar definition]
148. curious(X0) | creative(X0) <- (3) [avatar component clause 147]
151. 4 <=> tall(paul) [avatar definition]
153. ~tall(paul) <- (~4) [avatar component clause 151]
155. 3 | ~4 [avatar split clause 73,151,147]
167. ~wise(X0) [subsumption resolution 92,137]
168. tall(X0) [subsumption resolution 91,137]
212. 16 <=> strong(fred) [avatar definition]
214. strong(fred) <- (16) [avatar component clause 212]
216. strong(fred) [subsumption resolution 108,167]
217. 16 [avatar split clause 216,212]
218. old(X0) | curious(X0) [subsumption resolution 113,168]
219. ~old(X0) | ~curious(X0) [subsumption resolution 111,168]
241. $false <- (~4) [subsumption resolution 153,168]
242. 4 [avatar contradiction clause 241]
282. ~creative(X0) | ~humble(X0) | curious(X0) [resolution 80,218]
283. ~humble(X0) | curious(X0) <- (3) [subsumption resolution 282,148]
398. creative(fred) | funny(fred) <- (16) [resolution 117,214]
399. funny(fred) <- (16) [subsumption resolution 398,135]
400. old(fred) | creative(fred) <- (16) [resolution 399,106]
404. old(fred) <- (16) [subsumption resolution 400,135]
506. creative(fred) | humble(fred) <- (16) [resolution 404,78]
507. ~curious(fred) <- (16) [resolution 404,219]
509. 43 <=> humble(fred) [avatar definition]
511. humble(fred) <- (43) [avatar component clause 509]
513. 44 <=> curious(fred) [avatar definition]
515. ~curious(fred) <- (~44) [avatar component clause 513]
517. humble(fred) <- (16) [subsumption resolution 506,135]
518. 43 | ~16 [avatar split clause 517,212,509]
519. ~44 | ~16 [avatar split clause 507,212,513]
539. curious(fred) <- (3, 43) [resolution 511,283]
542. $false <- (3, 43, ~44) [subsumption resolution 539,515]
543. ~3 | ~43 | 44 [avatar contradiction clause 542]
544. $false [avatar sat refutation 155,217,242,518,519,543]
% SZS output end Proof for 3159230779148911893793841
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both calm and not strong then alice is patient and vice versa. Everyone who is brave or not humble is both not humble and not curious and vice versa. Everyone who is both not generous and not wise is not brave. Everyone who is either not quiet or not kind is both creative and rich and vice versa. Everyone who is either not humble or not creative is funny or quiet and vice versa. If john is both not creative and not curious then someone is not generous or old and vice versa. Everyone who is either not humble or wise is kind or not generous and vice versa. Everyone who is not creative is not creative or curious. If lucy is both not funny and not generous then someone is not wise or not curious. If john is not quiet then someone is both not rich and not calm. If someone is both rich and not humble then someone is not curious or not calm and vice versa. Everyone who is not brave is both happy and not old and vice versa. Everyone who is not humble is both not kind and old. If someone is brave or not tall then fred is either not old or happy and vice versa. Everyone who is both not funny and not happy is either not funny or not creative. Everyone who is either kind or funny is both not kind and kind and vice versa. Fred is not strong. Someone is creative or not quiet. Fred is either not calm or old. Someone is both brave and generous. Someone is either generous or calm. Mary is not creative. Alice is both not brave and tall. Paul is either generous or not curious. | John is curious. | contradiction | ((?[X]:((calm(X)&~strong(X))))<=>(patient(alice)))&
(![X]:((brave(X)|~humble(X))<=>(~humble(X)&~curious(X))))&
(![X]:((~generous(X)&~wise(X))=>~brave(X)))&
(![X]:((~quiet(X)<~>~kind(X))<=>(creative(X)&rich(X))))&
(![X]:((~humble(X)<~>~creative(X))<=>(funny(X)|quiet(X))))&
(((~creative(john)&~curious(john)))<=>(?[X]:((~generous(X)|old(X)))))&
(![X]:((~humble(X)<~>wise(X))<=>(kind(X)|~generous(X))))&
(![X]:(~creative(X)=>(~creative(X)|curious(X))))&
(((~funny(lucy)&~generous(lucy)))=>(?[X]:((~wise(X)|~curious(X)))))&
((~quiet(john))=>(?[X]:((~rich(X)&~calm(X)))))&
((?[X]:((rich(X)&~humble(X))))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:(~brave(X)<=>(happy(X)&~old(X))))&
(![X]:(~humble(X)=>(~kind(X)&old(X))))&
((?[X]:((brave(X)|~tall(X))))<=>((~old(fred)<~>happy(fred))))&
(![X]:((~funny(X)&~happy(X))=>(~funny(X)<~>~creative(X))))&
(![X]:((kind(X)<~>funny(X))<=>(~kind(X)&kind(X))))&
(~strong(fred))&
(?[X]:((creative(X)|~quiet(X))))&
((~calm(fred)<~>old(fred)))&
(?[X]:((brave(X)&generous(X))))&
(?[X]:((generous(X)<~>calm(X))))&
(~creative(mary))&
((~brave(alice)&tall(alice)))&
((generous(paul)<~>~curious(paul))) | curious(john) | [
"p5",
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 196804372901251726352627
% SZS output start Proof for 196804372901251726352627
6. (~curious(john) & ~creative(john)) <=> ? [X0] : (old(X0) | ~generous(X0)) [input p5]
11. ? [X0] : (~humble(X0) & rich(X0)) <=> ? [X0] : (~calm(X0) | ~curious(X0)) [input p10]
13. ! [X0] : (~humble(X0) => (old(X0) & ~kind(X0))) [input p12]
21. ? [X0] : (generous(X0) <~> calm(X0)) [input p20]
25. curious(john) [input hypothesis]
26. ? [X0] : (~humble(X0) & rich(X0)) <=> ? [X1] : (~calm(X1) | ~curious(X1)) [rectify 11]
34. ! [X0] : ((old(X0) & ~kind(X0)) | humble(X0)) [ennf transformation 13]
47. ((~curious(john) & ~creative(john)) | ! [X0] : (~old(X0) & generous(X0))) & (? [X0] : (old(X0) | ~generous(X0)) | (curious(john) | creative(john))) [nnf transformation 6]
48. ((~curious(john) & ~creative(john)) | ! [X0] : (~old(X0) & generous(X0))) & (? [X0] : (old(X0) | ~generous(X0)) | curious(john) | creative(john)) [flattening 47]
49. ((~curious(john) & ~creative(john)) | ! [X0] : (~old(X0) & generous(X0))) & (? [X1] : (old(X1) | ~generous(X1)) | curious(john) | creative(john)) [rectify 48]
50. ? [X1] : (old(X1) | ~generous(X1)) => (old(sK1) | ~generous(sK1)) [choice axiom]
51. ((~curious(john) & ~creative(john)) | ! [X0] : (~old(X0) & generous(X0))) & ((old(sK1) | ~generous(sK1)) | curious(john) | creative(john)) [skolemisation 49,50]
58. (? [X0] : (~humble(X0) & rich(X0)) | ! [X1] : (calm(X1) & curious(X1))) & (? [X1] : (~calm(X1) | ~curious(X1)) | ! [X0] : (humble(X0) | ~rich(X0))) [nnf transformation 26]
59. (? [X0] : (~humble(X0) & rich(X0)) | ! [X1] : (calm(X1) & curious(X1))) & (? [X2] : (~calm(X2) | ~curious(X2)) | ! [X3] : (humble(X3) | ~rich(X3))) [rectify 58]
60. ? [X0] : (~humble(X0) & rich(X0)) => (~humble(sK4) & rich(sK4)) [choice axiom]
61. ? [X2] : (~calm(X2) | ~curious(X2)) => (~calm(sK5) | ~curious(sK5)) [choice axiom]
62. ((~humble(sK4) & rich(sK4)) | ! [X1] : (calm(X1) & curious(X1))) & ((~calm(sK5) | ~curious(sK5)) | ! [X3] : (humble(X3) | ~rich(X3))) [skolemisation 59,61,60]
77. ? [X0] : ((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) [nnf transformation 21]
78. ? [X0] : ((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) => ((~calm(sK9) | ~generous(sK9)) & (calm(sK9) | generous(sK9))) [choice axiom]
79. (~calm(sK9) | ~generous(sK9)) & (calm(sK9) | generous(sK9)) [skolemisation 77,78]
105. ~curious(john) | generous(X0) [cnf transformation 51]
106. ~curious(john) | ~old(X0) [cnf transformation 51]
121. ~humble(sK4) | calm(X1) [cnf transformation 62]
126. old(X0) | humble(X0) [cnf transformation 34]
148. ~calm(sK9) | ~generous(sK9) [cnf transformation 79]
154. curious(john) [cnf transformation 25]
179. 5 <=> ! [X0] : ~old(X0) [avatar definition]
180. ~old(X0) <- (5) [avatar component clause 179]
182. 6 <=> curious(john) [avatar definition]
185. 5 | ~6 [avatar split clause 106,182,179]
187. 7 <=> ! [X0] : generous(X0) [avatar definition]
188. generous(X0) <- (7) [avatar component clause 187]
189. 7 | ~6 [avatar split clause 105,182,187]
237. 18 <=> ! [X1] : calm(X1) [avatar definition]
238. calm(X1) <- (18) [avatar component clause 237]
240. 19 <=> humble(sK4) [avatar definition]
242. ~humble(sK4) <- (~19) [avatar component clause 240]
243. 18 | ~19 [avatar split clause 121,240,237]
310. 34 <=> generous(sK9) [avatar definition]
312. ~generous(sK9) <- (~34) [avatar component clause 310]
314. 35 <=> calm(sK9) [avatar definition]
316. ~calm(sK9) <- (~35) [avatar component clause 314]
317. ~34 | ~35 [avatar split clause 148,314,310]
329. 6 [avatar split clause 154,182]
347. humble(X1) <- (5) [resolution 126,180]
349. $false <- (5, ~19) [resolution 347,242]
351. ~5 | 19 [avatar contradiction clause 349]
353. $false <- (18, ~35) [resolution 238,316]
356. ~18 | 35 [avatar contradiction clause 353]
357. $false <- (7, ~34) [subsumption resolution 312,188]
358. ~7 | 34 [avatar contradiction clause 357]
361. $false [avatar sat refutation 185,189,243,317,329,351,356,358]
% SZS output end Proof for 196804372901251726352627
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is not patient or tall and vice versa.
Everyone who is either not humble or not funny is creative or not humble and vice versa.
Everyone who is either not strong or not rich is not creative or not calm and vice versa.
If paul is not old or old then someone is both not rich and old.
If mary is funny then someone is both not generous and calm.
If someone is either not rich or not calm then someone is tall or brave.
If alice is patient then susan is not wise and vice versa.
Everyone who is either not generous or tall is not curious or not kind and vice versa.
Everyone who is funny or wise is quiet.
If someone is either not happy or not rich then someone is either not calm or creative.
Everyone who is not wise or strong is not generous or not strong.
Everyone who is both not happy and calm is not strong.
If lucy is either not strong or not old then someone is brave or not humble and vice versa.
Everyone who is quiet or not humble is not creative or not generous.
Everyone who is not creative or not patient is strong.
If alice is calm or generous then alice is either curious or not curious and vice versa.
Someone is either tall or wise.
Someone is patient or old.
Fred is either rich or not happy.
Someone is not happy or quiet.
Someone is either not calm or not old.
Someone is either not humble or rich.
Someone is not strong or funny.
Alice is both brave and funny. | Alice is not generous. | entailment | (![X]:(~brave(X)<=>(~patient(X)|tall(X))))&
(![X]:((~humble(X)<~>~funny(X))<=>(creative(X)|~humble(X))))&
(![X]:((~strong(X)<~>~rich(X))<=>(~creative(X)|~calm(X))))&
(((~old(paul)|old(paul)))=>(?[X]:((~rich(X)&old(X)))))&
((funny(mary))=>(?[X]:((~generous(X)&calm(X)))))&
((?[X]:((~rich(X)<~>~calm(X))))=>(?[X]:((tall(X)|brave(X)))))&
((patient(alice))<=>(~wise(susan)))&
(![X]:((~generous(X)<~>tall(X))<=>(~curious(X)|~kind(X))))&
(![X]:((funny(X)|wise(X))=>quiet(X)))&
((?[X]:((~happy(X)<~>~rich(X))))=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~wise(X)|strong(X))=>(~generous(X)|~strong(X))))&
(![X]:((~happy(X)&calm(X))=>~strong(X)))&
(((~strong(lucy)<~>~old(lucy)))<=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((quiet(X)|~humble(X))=>(~creative(X)|~generous(X))))&
(![X]:((~creative(X)|~patient(X))=>strong(X)))&
(((calm(alice)|generous(alice)))<=>((curious(alice)<~>~curious(alice))))&
(?[X]:((tall(X)<~>wise(X))))&
(?[X]:((patient(X)|old(X))))&
((rich(fred)<~>~happy(fred)))&
(?[X]:((~happy(X)|quiet(X))))&
(?[X]:((~calm(X)<~>~old(X))))&
(?[X]:((~humble(X)<~>rich(X))))&
(?[X]:((~strong(X)|funny(X))))&
((brave(alice)&funny(alice))) | ~generous(alice) | [
"p8",
"p10",
"p13",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5471719057552688443915346
% SZS output start Proof for 5471719057552688443915346
9. ! [X0] : ((wise(X0) | funny(X0)) => quiet(X0)) [input p8]
11. ! [X0] : ((strong(X0) | ~wise(X0)) => (~strong(X0) | ~generous(X0))) [input p10]
14. ! [X0] : ((~humble(X0) | quiet(X0)) => (~generous(X0) | ~creative(X0))) [input p13]
15. ! [X0] : ((~patient(X0) | ~creative(X0)) => strong(X0)) [input p14]
24. funny(alice) & brave(alice) [input p23]
25. generous(alice) [input hypothesis]
31. ! [X0] : (quiet(X0) | (~wise(X0) & ~funny(X0))) [ennf transformation 9]
33. ! [X0] : ((~strong(X0) | ~generous(X0)) | (~strong(X0) & wise(X0))) [ennf transformation 11]
34. ! [X0] : (~strong(X0) | ~generous(X0) | (~strong(X0) & wise(X0))) [flattening 33]
37. ! [X0] : ((~generous(X0) | ~creative(X0)) | (humble(X0) & ~quiet(X0))) [ennf transformation 14]
38. ! [X0] : (~generous(X0) | ~creative(X0) | (humble(X0) & ~quiet(X0))) [flattening 37]
39. ! [X0] : (strong(X0) | (patient(X0) & creative(X0))) [ennf transformation 15]
114. ~funny(X0) | quiet(X0) [cnf transformation 31]
121. ~strong(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 34]
129. ~quiet(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 38]
131. strong(X0) | creative(X0) [cnf transformation 39]
151. funny(alice) [cnf transformation 24]
152. generous(alice) [cnf transformation 25]
155. ~generous(X0) | ~strong(X0) [duplicate literal removal 121]
270. 25 <=> generous(alice) [avatar definition]
272. generous(alice) <- (25) [avatar component clause 270]
342. 25 [avatar split clause 152,270]
350. quiet(alice) [resolution 114,151]
353. ~strong(alice) <- (25) [resolution 155,272]
355. creative(alice) <- (25) [resolution 353,131]
473. ~creative(alice) | ~generous(alice) [resolution 129,350]
475. ~generous(alice) <- (25) [subsumption resolution 473,355]
476. $false <- (25) [subsumption resolution 475,272]
477. ~25 [avatar contradiction clause 476]
487. $false [avatar sat refutation 342,477]
% SZS output end Proof for 5471719057552688443915346
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both generous and not brave is either not rich or not quiet and vice versa.
Everyone who is either quiet or kind is not strong or not creative and vice versa.
If lucy is not patient or not funny then someone is both tall and not quiet.
Everyone who is not calm or not patient is not kind or wise.
Everyone who is not wise or humble is not wise or tall and vice versa.
Everyone who is not kind is happy or old and vice versa.
If mary is not calm or rich then someone is either not kind or not calm.
If alice is either curious or not old then someone is either not rich or not strong.
Everyone who is curious or wise is either calm or humble.
If someone is both not quiet and not rich then alice is both patient and old and vice versa.
Everyone who is not old or creative is both not calm and not tall and vice versa.
Everyone who is either not rich or brave is both not brave and not happy and vice versa.
If john is not creative or humble then mary is not calm.
Everyone who is both rich and humble is both not kind and funny and vice versa.
If someone is either strong or tall then john is tall or kind.
Everyone who is both not creative and not calm is both happy and not quiet and vice versa.
Susan is not old.
Someone is quiet.
Someone is both not strong and not patient.
Someone is both not generous and tall.
Someone is both strong and happy.
Paul is both tall and not kind.
Someone is both not brave and not funny. | Alice is not kind. | entailment | (![X]:((generous(X)&~brave(X))<=>(~rich(X)<~>~quiet(X))))&
(![X]:((quiet(X)<~>kind(X))<=>(~strong(X)|~creative(X))))&
(((~patient(lucy)|~funny(lucy)))=>(?[X]:((tall(X)&~quiet(X)))))&
(![X]:((~calm(X)|~patient(X))=>(~kind(X)|wise(X))))&
(![X]:((~wise(X)|humble(X))<=>(~wise(X)|tall(X))))&
(![X]:(~kind(X)<=>(happy(X)|old(X))))&
(((~calm(mary)|rich(mary)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((curious(alice)<~>~old(alice)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)<~>humble(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>((patient(alice)&old(alice))))&
(![X]:((~old(X)|creative(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(~brave(X)&~happy(X))))&
(((~creative(john)|humble(john)))=>(~calm(mary)))&
(![X]:((rich(X)&humble(X))<=>(~kind(X)&funny(X))))&
((?[X]:((strong(X)<~>tall(X))))=>((tall(john)|kind(john))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)&~quiet(X))))&
(~old(susan))&
(?[X]:(quiet(X)))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((strong(X)&happy(X))))&
((tall(paul)&~kind(paul)))&
(?[X]:((~brave(X)&~funny(X)))) | ~kind(alice) | [
"p3",
"p4",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8381435436446495169225826
% SZS output start Proof for 8381435436446495169225826
4. ! [X0] : ((~patient(X0) | ~calm(X0)) => (wise(X0) | ~kind(X0))) [input p3]
5. ! [X0] : ((humble(X0) | ~wise(X0)) <=> (tall(X0) | ~wise(X0))) [input p4]
6. ! [X0] : (~kind(X0) <=> (old(X0) | happy(X0))) [input p5]
9. ! [X0] : ((wise(X0) | curious(X0)) => (calm(X0) <~> humble(X0))) [input p8]
11. ! [X0] : ((creative(X0) | ~old(X0)) <=> (~tall(X0) & ~calm(X0))) [input p10]
24. kind(alice) [input hypothesis]
26. ! [X0] : ((wise(X0) | ~kind(X0)) | (patient(X0) & calm(X0))) [ennf transformation 4]
27. ! [X0] : (wise(X0) | ~kind(X0) | (patient(X0) & calm(X0))) [flattening 26]
30. ! [X0] : ((calm(X0) <~> humble(X0)) | (~wise(X0) & ~curious(X0))) [ennf transformation 9]
40. ! [X0] : (((humble(X0) | ~wise(X0)) | (~tall(X0) & wise(X0))) & ((tall(X0) | ~wise(X0)) | (~humble(X0) & wise(X0)))) [nnf transformation 5]
41. ! [X0] : ((humble(X0) | ~wise(X0) | (~tall(X0) & wise(X0))) & (tall(X0) | ~wise(X0) | (~humble(X0) & wise(X0)))) [flattening 40]
42. ! [X0] : ((~kind(X0) | (~old(X0) & ~happy(X0))) & ((old(X0) | happy(X0)) | kind(X0))) [nnf transformation 6]
43. ! [X0] : ((~kind(X0) | (~old(X0) & ~happy(X0))) & (old(X0) | happy(X0) | kind(X0))) [flattening 42]
50. ! [X0] : (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (~wise(X0) & ~curious(X0))) [nnf transformation 30]
56. ! [X0] : (((creative(X0) | ~old(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~creative(X0) & old(X0)))) [nnf transformation 11]
57. ! [X0] : ((creative(X0) | ~old(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | (~creative(X0) & old(X0)))) [flattening 56]
91. ~kind(X0) | wise(X0) | calm(X0) [cnf transformation 27]
94. ~humble(X0) | ~wise(X0) | tall(X0) [cnf transformation 41]
99. ~old(X0) | ~kind(X0) [cnf transformation 43]
109. ~wise(X0) | calm(X0) | humble(X0) [cnf transformation 50]
116. ~calm(X0) | old(X0) [cnf transformation 57]
118. ~tall(X0) | old(X0) [cnf transformation 57]
151. kind(alice) [cnf transformation 24]
195. 9 <=> old(alice) [avatar definition]
196. ~old(alice) <- (~9) [avatar component clause 195]
197. old(alice) <- (9) [avatar component clause 195]
260. ~kind(alice) <- (9) [resolution 99,197]
261. $false <- (9) [subsumption resolution 260,151]
262. ~9 [avatar contradiction clause 261]
351. wise(alice) | calm(alice) [resolution 91,151]
354. 31 <=> calm(alice) [avatar definition]
355. ~calm(alice) <- (~31) [avatar component clause 354]
356. calm(alice) <- (31) [avatar component clause 354]
358. 32 <=> wise(alice) [avatar definition]
360. wise(alice) <- (32) [avatar component clause 358]
361. 31 | 32 [avatar split clause 351,358,354]
394. 36 <=> humble(alice) [avatar definition]
396. humble(alice) <- (36) [avatar component clause 394]
403. calm(alice) | humble(alice) <- (32) [resolution 360,109]
426. 37 <=> tall(alice) [avatar definition]
427. tall(alice) <- (37) [avatar component clause 426]
430. humble(alice) <- (~31, 32) [subsumption resolution 403,355]
431. 36 | 31 | ~32 [avatar split clause 430,358,354,394]
476. ~wise(alice) | tall(alice) <- (36) [resolution 396,94]
781. old(alice) <- (37) [resolution 427,118]
784. $false <- (~9, 37) [subsumption resolution 781,196]
785. 9 | ~37 [avatar contradiction clause 784]
787. 37 | ~32 | ~36 [avatar split clause 476,394,358,426]
789. old(alice) <- (31) [resolution 356,116]
792. $false <- (~9, 31) [subsumption resolution 789,196]
793. 9 | ~31 [avatar contradiction clause 792]
794. $false [avatar sat refutation 262,361,431,785,787,793]
% SZS output end Proof for 8381435436446495169225826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is calm and vice versa.
Everyone who is both patient and not kind is tall and vice versa.
If lucy is humble then someone is brave or not humble and vice versa.
Everyone who is both not funny and not kind is either not rich or brave and vice versa.
If someone is either rich or quiet then mary is not rich or curious.
If susan is both not quiet and generous then susan is not calm and vice versa.
If lucy is both tall and not patient then someone is rich or creative and vice versa.
Everyone who is happy or brave is both old and not generous.
If susan is either kind or not calm then someone is either not brave or not old.
Everyone who is either happy or calm is quiet.
Everyone who is either generous or not old is both rich and not brave and vice versa.
If mary is both wise and humble then susan is not patient and vice versa.
If paul is both not creative and creative then susan is either not curious or funny and vice versa.
If someone is not generous then someone is wise or creative and vice versa.
Someone is not creative or brave.
Someone is not happy or not curious.
Someone is both old and not humble.
John is either not quiet or not curious.
Someone is not kind or kind.
Someone is rich or not curious. | Susan is not creative. | entailment | ((?[X]:(~brave(X)))<=>(?[X]:(calm(X))))&
(![X]:((patient(X)&~kind(X))<=>tall(X)))&
((humble(lucy))<=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(~rich(X)<~>brave(X))))&
((?[X]:((rich(X)<~>quiet(X))))=>((~rich(mary)|curious(mary))))&
(((~quiet(susan)&generous(susan)))<=>(~calm(susan)))&
(((tall(lucy)&~patient(lucy)))<=>(?[X]:((rich(X)|creative(X)))))&
(![X]:((happy(X)|brave(X))=>(old(X)&~generous(X))))&
(((kind(susan)<~>~calm(susan)))=>(?[X]:((~brave(X)<~>~old(X)))))&
(![X]:((happy(X)<~>calm(X))=>quiet(X)))&
(![X]:((generous(X)<~>~old(X))<=>(rich(X)&~brave(X))))&
(((wise(mary)&humble(mary)))<=>(~patient(susan)))&
(((~creative(paul)&creative(paul)))<=>((~curious(susan)<~>funny(susan))))&
((?[X]:(~generous(X)))<=>(?[X]:((wise(X)|creative(X)))))&
(?[X]:((~creative(X)|brave(X))))&
(?[X]:((~happy(X)|~curious(X))))&
(?[X]:((old(X)&~humble(X))))&
((~quiet(john)<~>~curious(john)))&
(?[X]:((~kind(X)|kind(X))))&
(?[X]:((rich(X)|~curious(X)))) | ~creative(susan) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7495904712589312273894552
% SZS output start Proof for 7495904712589312273894552
2. ! [X0] : ((~kind(X0) & patient(X0)) <=> tall(X0)) [input p1]
7. (~patient(lucy) & tall(lucy)) <=> ? [X0] : (creative(X0) | rich(X0)) [input p6]
21. creative(susan) [input hypothesis]
34. ! [X0] : (((~kind(X0) & patient(X0)) | ~tall(X0)) & (tall(X0) | (kind(X0) | ~patient(X0)))) [nnf transformation 2]
35. ! [X0] : (((~kind(X0) & patient(X0)) | ~tall(X0)) & (tall(X0) | kind(X0) | ~patient(X0))) [flattening 34]
45. ((~patient(lucy) & tall(lucy)) | ! [X0] : (~creative(X0) & ~rich(X0))) & (? [X0] : (creative(X0) | rich(X0)) | (patient(lucy) | ~tall(lucy))) [nnf transformation 7]
46. ((~patient(lucy) & tall(lucy)) | ! [X0] : (~creative(X0) & ~rich(X0))) & (? [X0] : (creative(X0) | rich(X0)) | patient(lucy) | ~tall(lucy)) [flattening 45]
47. ((~patient(lucy) & tall(lucy)) | ! [X0] : (~creative(X0) & ~rich(X0))) & (? [X1] : (creative(X1) | rich(X1)) | patient(lucy) | ~tall(lucy)) [rectify 46]
48. ? [X1] : (creative(X1) | rich(X1)) => (creative(sK3) | rich(sK3)) [choice axiom]
49. ((~patient(lucy) & tall(lucy)) | ! [X0] : (~creative(X0) & ~rich(X0))) & ((creative(sK3) | rich(sK3)) | patient(lucy) | ~tall(lucy)) [skolemisation 47,48]
79. ~tall(X0) | patient(X0) [cnf transformation 35]
97. tall(lucy) | ~creative(X0) [cnf transformation 49]
99. ~patient(lucy) | ~creative(X0) [cnf transformation 49]
136. creative(susan) [cnf transformation 21]
206. 17 <=> ! [X0] : ~creative(X0) [avatar definition]
207. ~creative(X0) <- (17) [avatar component clause 206]
209. 18 <=> patient(lucy) [avatar definition]
211. ~patient(lucy) <- (~18) [avatar component clause 209]
212. 17 | ~18 [avatar split clause 99,209,206]
218. 20 <=> tall(lucy) [avatar definition]
220. tall(lucy) <- (20) [avatar component clause 218]
221. 17 | 20 [avatar split clause 97,218,206]
341. $false <- (17) [resolution 207,136]
342. ~17 [avatar contradiction clause 341]
345. patient(lucy) <- (20) [resolution 79,220]
346. $false <- (~18, 20) [subsumption resolution 345,211]
347. 18 | ~20 [avatar contradiction clause 346]
348. $false [avatar sat refutation 212,221,342,347]
% SZS output end Proof for 7495904712589312273894552
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not calm is both not tall and not curious. Everyone who is either strong or wise is not wise or not kind and vice versa. If someone is calm then susan is both rich and wise. If someone is not calm then john is kind or quiet. Everyone who is either not humble or not strong is both tall and funny and vice versa. If lucy is old or generous then mary is both not humble and strong and vice versa. Everyone who is not calm or tall is not calm or curious and vice versa. Everyone who is both not tall and strong is quiet or strong and vice versa. If alice is tall or not patient then fred is not rich and vice versa. If fred is both wise and not creative then someone is not creative or not strong and vice versa. If someone is either old or not generous then fred is not wise. If someone is rich then paul is humble. If lucy is both not strong and curious then mary is either not strong or not wise. Everyone who is kind is both tall and brave and vice versa. If lucy is wise then someone is quiet. Everyone who is either not quiet or kind is not old. Someone is both creative and not brave. Susan is either generous or tall. Paul is either not kind or not brave. Lucy is either generous or humble. Someone is both not kind and not old. Susan is either patient or rich. | Paul is not curious. | entailment | (![X]:((patient(X)|~calm(X))=>(~tall(X)&~curious(X))))&
(![X]:((strong(X)<~>wise(X))<=>(~wise(X)|~kind(X))))&
((?[X]:(calm(X)))=>((rich(susan)&wise(susan))))&
((?[X]:(~calm(X)))=>((kind(john)|quiet(john))))&
(![X]:((~humble(X)<~>~strong(X))<=>(tall(X)&funny(X))))&
(((old(lucy)|generous(lucy)))<=>((~humble(mary)&strong(mary))))&
(![X]:((~calm(X)|tall(X))<=>(~calm(X)|curious(X))))&
(![X]:((~tall(X)&strong(X))<=>(quiet(X)|strong(X))))&
(((tall(alice)|~patient(alice)))<=>(~rich(fred)))&
(((wise(fred)&~creative(fred)))<=>(?[X]:((~creative(X)|~strong(X)))))&
((?[X]:((old(X)<~>~generous(X))))=>(~wise(fred)))&
((?[X]:(rich(X)))=>(humble(paul)))&
(((~strong(lucy)&curious(lucy)))=>((~strong(mary)<~>~wise(mary))))&
(![X]:(kind(X)<=>(tall(X)&brave(X))))&
((wise(lucy))=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)<~>kind(X))=>~old(X)))&
(?[X]:((creative(X)&~brave(X))))&
((generous(susan)<~>tall(susan)))&
((~kind(paul)<~>~brave(paul)))&
((generous(lucy)<~>humble(lucy)))&
(?[X]:((~kind(X)&~old(X))))&
((patient(susan)<~>rich(susan))) | ~curious(paul) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1861785460443250019471943
% SZS output start Proof for 1861785460443250019471943
1. ! [X0] : ((~calm(X0) | patient(X0)) => (~curious(X0) & ~tall(X0))) [input p0]
5. ! [X0] : ((~humble(X0) <~> ~strong(X0)) <=> (funny(X0) & tall(X0))) [input p4]
6. (generous(lucy) | old(lucy)) <=> (strong(mary) & ~humble(mary)) [input p5]
7. ! [X0] : ((tall(X0) | ~calm(X0)) <=> (curious(X0) | ~calm(X0))) [input p6]
8. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (strong(X0) | quiet(X0))) [input p7]
10. (~creative(fred) & wise(fred)) <=> ? [X0] : (~strong(X0) | ~creative(X0)) [input p9]
11. ? [X0] : (old(X0) <~> ~generous(X0)) => ~wise(fred) [input p10]
23. curious(paul) [input hypothesis]
24. ! [X0] : ((~curious(X0) & ~tall(X0)) | (calm(X0) & ~patient(X0))) [ennf transformation 1]
28. ~wise(fred) | ! [X0] : (old(X0) <=> ~generous(X0)) [ennf transformation 11]
36. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | (~funny(X0) | ~tall(X0))) & ((funny(X0) & tall(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [nnf transformation 5]
37. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | ~funny(X0) | ~tall(X0)) & ((funny(X0) & tall(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [flattening 36]
38. ((generous(lucy) | old(lucy)) | (~strong(mary) | humble(mary))) & ((strong(mary) & ~humble(mary)) | (~generous(lucy) & ~old(lucy))) [nnf transformation 6]
39. (generous(lucy) | old(lucy) | ~strong(mary) | humble(mary)) & ((strong(mary) & ~humble(mary)) | (~generous(lucy) & ~old(lucy))) [flattening 38]
40. ! [X0] : (((tall(X0) | ~calm(X0)) | (~curious(X0) & calm(X0))) & ((curious(X0) | ~calm(X0)) | (~tall(X0) & calm(X0)))) [nnf transformation 7]
41. ! [X0] : ((tall(X0) | ~calm(X0) | (~curious(X0) & calm(X0))) & (curious(X0) | ~calm(X0) | (~tall(X0) & calm(X0)))) [flattening 40]
42. ! [X0] : (((strong(X0) & ~tall(X0)) | (~strong(X0) & ~quiet(X0))) & ((strong(X0) | quiet(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 8]
43. ! [X0] : (((strong(X0) & ~tall(X0)) | (~strong(X0) & ~quiet(X0))) & (strong(X0) | quiet(X0) | ~strong(X0) | tall(X0))) [flattening 42]
46. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X0] : (~strong(X0) | ~creative(X0)) | (creative(fred) | ~wise(fred))) [nnf transformation 10]
47. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X0] : (~strong(X0) | ~creative(X0)) | creative(fred) | ~wise(fred)) [flattening 46]
48. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X1] : (~strong(X1) | ~creative(X1)) | creative(fred) | ~wise(fred)) [rectify 47]
49. ? [X1] : (~strong(X1) | ~creative(X1)) => (~strong(sK0) | ~creative(sK0)) [choice axiom]
50. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & ((~strong(sK0) | ~creative(sK0)) | creative(fred) | ~wise(fred)) [skolemisation 48,49]
51. ~wise(fred) | ! [X0] : ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0))) [nnf transformation 28]
69. ~curious(X0) | calm(X0) [cnf transformation 24]
79. ~strong(X0) | tall(X0) | humble(X0) [cnf transformation 37]
85. ~humble(mary) | ~old(lucy) [cnf transformation 39]
86. ~humble(mary) | ~generous(lucy) [cnf transformation 39]
87. strong(mary) | ~old(lucy) [cnf transformation 39]
88. strong(mary) | ~generous(lucy) [cnf transformation 39]
93. tall(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 41]
96. ~strong(X0) | ~tall(X0) [cnf transformation 43]
104. wise(fred) | strong(X0) [cnf transformation 50]
108. ~wise(fred) | old(X0) | generous(X0) [cnf transformation 51]
130. curious(paul) [cnf transformation 23]
160. 7 <=> humble(mary) [avatar definition]
164. 8 <=> strong(mary) [avatar definition]
165. strong(mary) <- (8) [avatar component clause 164]
168. 9 <=> old(lucy) [avatar definition]
169. ~old(lucy) <- (~9) [avatar component clause 168]
172. 10 <=> generous(lucy) [avatar definition]
173. ~generous(lucy) <- (~10) [avatar component clause 172]
176. ~10 | 8 [avatar split clause 88,164,172]
177. ~9 | 8 [avatar split clause 87,164,168]
178. ~10 | ~7 [avatar split clause 86,160,172]
179. ~9 | ~7 [avatar split clause 85,160,168]
180. ~curious(X0) | tall(X0) [subsumption resolution 93,69]
199. 14 <=> ! [X0] : strong(X0) [avatar definition]
200. strong(X0) <- (14) [avatar component clause 199]
211. 17 <=> wise(fred) [avatar definition]
214. 14 | 17 [avatar split clause 104,211,199]
226. 20 <=> ! [X0] : (old(X0) | generous(X0)) [avatar definition]
227. generous(X0) | old(X0) <- (20) [avatar component clause 226]
228. 20 | ~17 [avatar split clause 108,211,226]
291. ~tall(X0) <- (14) [resolution 96,200]
294. tall(paul) [resolution 180,130]
295. $false <- (14) [subsumption resolution 294,291]
296. ~14 [avatar contradiction clause 295]
302. ~tall(mary) <- (8) [resolution 165,96]
338. tall(mary) | humble(mary) <- (8) [resolution 79,165]
340. humble(mary) <- (8) [subsumption resolution 338,302]
346. 7 | ~8 [avatar split clause 340,164,160]
348. old(lucy) <- (~10, 20) [resolution 173,227]
349. $false <- (~9, ~10, 20) [subsumption resolution 348,169]
350. 9 | 10 | ~20 [avatar contradiction clause 349]
351. $false [avatar sat refutation 176,177,178,179,214,228,296,346,350]
% SZS output end Proof for 1861785460443250019471943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or not brave then susan is both calm and not rich.
If someone is either not funny or funny then paul is either not calm or not tall and vice versa.
If someone is both generous and not generous then someone is kind and vice versa.
Everyone who is not funny is not calm or not generous and vice versa.
If alice is both patient and not generous then someone is wise.
If susan is tall then someone is not brave or not happy and vice versa.
If someone is either not calm or not brave then someone is both generous and not curious.
Everyone who is both rich and funny is not happy and vice versa.
Everyone who is both kind and creative is quiet and vice versa.
Everyone who is happy or old is both not funny and humble.
If lucy is either not generous or generous then someone is not funny or generous and vice versa.
Everyone who is tall or creative is either kind or not humble and vice versa.
Everyone who is not quiet is either not strong or funny and vice versa.
If someone is not brave or humble then someone is either not brave or not generous.
Everyone who is not strong or wise is either old or not rich.
If someone is both not old and not wise then someone is both not strong and curious.
Someone is not strong.
Someone is either patient or brave.
Someone is both not generous and humble.
John is both not quiet and not funny. | Paul is not brave. | contradiction | ((?[X]:((~happy(X)|~brave(X))))=>((calm(susan)&~rich(susan))))&
((?[X]:((~funny(X)<~>funny(X))))<=>((~calm(paul)<~>~tall(paul))))&
((?[X]:((generous(X)&~generous(X))))<=>(?[X]:(kind(X))))&
(![X]:(~funny(X)<=>(~calm(X)|~generous(X))))&
(((patient(alice)&~generous(alice)))=>(?[X]:(wise(X))))&
((tall(susan))<=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:((~calm(X)<~>~brave(X))))=>(?[X]:((generous(X)&~curious(X)))))&
(![X]:((rich(X)&funny(X))<=>~happy(X)))&
(![X]:((kind(X)&creative(X))<=>quiet(X)))&
(![X]:((happy(X)|old(X))=>(~funny(X)&humble(X))))&
(((~generous(lucy)<~>generous(lucy)))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((tall(X)|creative(X))<=>(kind(X)<~>~humble(X))))&
(![X]:(~quiet(X)<=>(~strong(X)<~>funny(X))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:((~brave(X)<~>~generous(X)))))&
(![X]:((~strong(X)|wise(X))=>(old(X)<~>~rich(X))))&
((?[X]:((~old(X)&~wise(X))))=>(?[X]:((~strong(X)&curious(X)))))&
(?[X]:(~strong(X)))&
(?[X]:((patient(X)<~>brave(X))))&
(?[X]:((~generous(X)&humble(X))))&
((~quiet(john)&~funny(john))) | ~brave(paul) | [
"p0",
"p2",
"p5",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7748700967134637375234144
% SZS output start Proof for 7748700967134637375234144
1. ? [X0] : (~brave(X0) | ~happy(X0)) => (~rich(susan) & calm(susan)) [input p0]
3. ? [X0] : (~generous(X0) & generous(X0)) <=> ? [X0] : kind(X0) [input p2]
6. tall(susan) <=> ? [X0] : (~happy(X0) | ~brave(X0)) [input p5]
8. ! [X0] : ((funny(X0) & rich(X0)) <=> ~happy(X0)) [input p7]
10. ! [X0] : ((old(X0) | happy(X0)) => (humble(X0) & ~funny(X0))) [input p9]
12. ! [X0] : ((creative(X0) | tall(X0)) <=> (kind(X0) <~> ~humble(X0))) [input p11]
21. ~brave(paul) [input hypothesis]
22. ? [X0] : (~generous(X0) & generous(X0)) <=> ? [X1] : kind(X1) [rectify 3]
26. (~rich(susan) & calm(susan)) | ! [X0] : (brave(X0) & happy(X0)) [ennf transformation 1]
30. ! [X0] : ((humble(X0) & ~funny(X0)) | (~old(X0) & ~happy(X0))) [ennf transformation 10]
38. (? [X0] : (~generous(X0) & generous(X0)) | ! [X1] : ~kind(X1)) & (? [X1] : kind(X1) | ! [X0] : (generous(X0) | ~generous(X0))) [nnf transformation 22]
39. (? [X0] : (~generous(X0) & generous(X0)) | ! [X1] : ~kind(X1)) & (? [X2] : kind(X2) | ! [X3] : (generous(X3) | ~generous(X3))) [rectify 38]
40. ? [X0] : (~generous(X0) & generous(X0)) => (~generous(sK1) & generous(sK1)) [choice axiom]
41. ? [X2] : kind(X2) => kind(sK2) [choice axiom]
42. ((~generous(sK1) & generous(sK1)) | ! [X1] : ~kind(X1)) & (kind(sK2) | ! [X3] : (generous(X3) | ~generous(X3))) [skolemisation 39,41,40]
47. (tall(susan) | ! [X0] : (happy(X0) & brave(X0))) & (? [X0] : (~happy(X0) | ~brave(X0)) | ~tall(susan)) [nnf transformation 6]
48. (tall(susan) | ! [X0] : (happy(X0) & brave(X0))) & (? [X1] : (~happy(X1) | ~brave(X1)) | ~tall(susan)) [rectify 47]
49. ? [X1] : (~happy(X1) | ~brave(X1)) => (~happy(sK4) | ~brave(sK4)) [choice axiom]
50. (tall(susan) | ! [X0] : (happy(X0) & brave(X0))) & ((~happy(sK4) | ~brave(sK4)) | ~tall(susan)) [skolemisation 48,49]
55. ! [X0] : (((funny(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | (~funny(X0) | ~rich(X0)))) [nnf transformation 8]
56. ! [X0] : (((funny(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | ~funny(X0) | ~rich(X0))) [flattening 55]
63. ! [X0] : (((creative(X0) | tall(X0)) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0)))) & (((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | (~creative(X0) & ~tall(X0)))) [nnf transformation 12]
64. ! [X0] : ((creative(X0) | tall(X0) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0)))) & (((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | (~creative(X0) & ~tall(X0)))) [flattening 63]
84. ~rich(susan) | brave(X0) [cnf transformation 26]
94. generous(sK1) | ~kind(X1) [cnf transformation 42]
95. ~generous(sK1) | ~kind(X1) [cnf transformation 42]
101. tall(susan) | brave(X0) [cnf transformation 50]
108. rich(X0) | happy(X0) [cnf transformation 56]
115. ~happy(X0) | humble(X0) [cnf transformation 30]
123. ~humble(X0) | kind(X0) | ~tall(X0) [cnf transformation 64]
150. ~brave(paul) [cnf transformation 21]
158. 1 <=> ! [X0] : brave(X0) [avatar definition]
159. brave(X0) <- (1) [avatar component clause 158]
161. 2 <=> rich(susan) [avatar definition]
163. ~rich(susan) <- (~2) [avatar component clause 161]
164. 1 | ~2 [avatar split clause 84,161,158]
194. 9 <=> ! [X1] : ~kind(X1) [avatar definition]
195. ~kind(X1) <- (9) [avatar component clause 194]
197. 10 <=> generous(sK1) [avatar definition]
200. 9 | ~10 [avatar split clause 95,197,194]
201. 9 | 10 [avatar split clause 94,197,194]
216. 14 <=> tall(susan) [avatar definition]
218. tall(susan) <- (14) [avatar component clause 216]
220. 1 | 14 [avatar split clause 101,216,158]
286. happy(susan) <- (~2) [resolution 108,163]
291. humble(susan) <- (~2) [resolution 115,286]
309. kind(susan) | ~tall(susan) <- (~2) [resolution 123,291]
312. ~tall(susan) <- (~2, 9) [subsumption resolution 309,195]
313. $false <- (~2, 9, 14) [subsumption resolution 312,218]
314. 2 | ~9 | ~14 [avatar contradiction clause 313]
317. $false <- (1) [resolution 159,150]
322. ~1 [avatar contradiction clause 317]
323. $false [avatar sat refutation 164,200,201,220,314,322]
% SZS output end Proof for 7748700967134637375234144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either generous or not curious.
If someone is both not funny and quiet then someone is either creative or not wise.
Everyone who is both not humble and not curious is either not patient or not humble and vice versa.
If lucy is not happy then someone is either not kind or not happy and vice versa.
Everyone who is patient is either rich or brave.
If lucy is not kind then paul is both creative and patient and vice versa.
If someone is not wise then someone is not kind or not funny and vice versa.
Everyone who is both not brave and curious is both not kind and kind and vice versa.
Everyone who is either funny or strong is not humble.
Everyone who is creative is both humble and wise.
Everyone who is wise or not old is either tall or old.
Everyone who is not kind is either happy or not curious.
Everyone who is patient is strong.
Everyone who is not brave is both happy and strong.
If someone is either curious or not curious then lucy is both not wise and tall and vice versa.
If susan is both not patient and humble then someone is either not tall or funny and vice versa.
Fred is either happy or not brave.
Fred is strong or not tall.
Susan is both wise and not brave.
Someone is humble.
Someone is both rich and generous.
Paul is happy or not happy.
Someone is strong.
John is both not humble and strong. | Fred is happy. | entailment | (![X]:(~patient(X)=>(generous(X)<~>~curious(X))))&
((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((creative(X)<~>~wise(X)))))&
(![X]:((~humble(X)&~curious(X))<=>(~patient(X)<~>~humble(X))))&
((~happy(lucy))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
(![X]:(patient(X)=>(rich(X)<~>brave(X))))&
((~kind(lucy))<=>((creative(paul)&patient(paul))))&
((?[X]:(~wise(X)))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:((~brave(X)&curious(X))<=>(~kind(X)&kind(X))))&
(![X]:((funny(X)<~>strong(X))=>~humble(X)))&
(![X]:(creative(X)=>(humble(X)&wise(X))))&
(![X]:((wise(X)|~old(X))=>(tall(X)<~>old(X))))&
(![X]:(~kind(X)=>(happy(X)<~>~curious(X))))&
(![X]:(patient(X)=>strong(X)))&
(![X]:(~brave(X)=>(happy(X)&strong(X))))&
((?[X]:((curious(X)<~>~curious(X))))<=>((~wise(lucy)&tall(lucy))))&
(((~patient(susan)&humble(susan)))<=>(?[X]:((~tall(X)<~>funny(X)))))&
((happy(fred)<~>~brave(fred)))&
((strong(fred)|~tall(fred)))&
((wise(susan)&~brave(susan)))&
(?[X]:(humble(X)))&
(?[X]:((rich(X)&generous(X))))&
((happy(paul)|~happy(paul)))&
(?[X]:(strong(X)))&
((~humble(john)&strong(john))) | happy(fred) | [
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7482349220951327217801818
% SZS output start Proof for 7482349220951327217801818
14. ! [X0] : (~brave(X0) => (strong(X0) & happy(X0))) [input p13]
17. happy(fred) <~> ~brave(fred) [input p16]
25. ~happy(fred) [input hypothesis]
36. ! [X0] : ((strong(X0) & happy(X0)) | brave(X0)) [ennf transformation 14]
67. (brave(fred) | ~happy(fred)) & (~brave(fred) | happy(fred)) [nnf transformation 17]
109. happy(X0) | brave(X0) [cnf transformation 36]
123. ~brave(fred) | happy(fred) [cnf transformation 67]
124. brave(fred) | ~happy(fred) [cnf transformation 67]
135. ~happy(fred) [cnf transformation 25]
242. brave(fred) [subsumption resolution 124,109]
243. happy(fred) [subsumption resolution 123,242]
253. $false [subsumption resolution 135,243]
% SZS output end Proof for 7482349220951327217801818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not calm or creative then someone is not curious. Everyone who is not quiet is either quiet or patient. Everyone who is both patient and quiet is wise or not happy and vice versa. Everyone who is kind is both brave and not funny. Everyone who is not tall or strong is either tall or not creative and vice versa. If someone is either not wise or not rich then paul is strong. If fred is not generous then someone is both kind and rich. If paul is both not brave and funny then someone is not old or happy. If alice is generous then paul is strong and vice versa. If john is not curious or not tall then susan is both rich and not rich. If susan is both not rich and old then alice is both not patient and wise and vice versa. If someone is either wise or not wise then fred is either funny or not brave. Everyone who is both not funny and strong is not old. Everyone who is either strong or not brave is both calm and not funny. Everyone who is both funny and kind is either not old or not wise and vice versa. Everyone who is happy or tall is either not quiet or not old. John is both creative and curious. John is either not rich or not creative. Fred is wise. Someone is rich. Someone is not old or happy. Someone is not generous. Fred is not tall or not happy. Lucy is either not brave or not humble. | Fred is not happy. | entailment | (((~calm(lucy)|creative(lucy)))=>(?[X]:(~curious(X))))&
(![X]:(~quiet(X)=>(quiet(X)<~>patient(X))))&
(![X]:((patient(X)&quiet(X))<=>(wise(X)|~happy(X))))&
(![X]:(kind(X)=>(brave(X)&~funny(X))))&
(![X]:((~tall(X)|strong(X))<=>(tall(X)<~>~creative(X))))&
((?[X]:((~wise(X)<~>~rich(X))))=>(strong(paul)))&
((~generous(fred))=>(?[X]:((kind(X)&rich(X)))))&
(((~brave(paul)&funny(paul)))=>(?[X]:((~old(X)|happy(X)))))&
((generous(alice))<=>(strong(paul)))&
(((~curious(john)|~tall(john)))=>((rich(susan)&~rich(susan))))&
(((~rich(susan)&old(susan)))<=>((~patient(alice)&wise(alice))))&
((?[X]:((wise(X)<~>~wise(X))))=>((funny(fred)<~>~brave(fred))))&
(![X]:((~funny(X)&strong(X))=>~old(X)))&
(![X]:((strong(X)<~>~brave(X))=>(calm(X)&~funny(X))))&
(![X]:((funny(X)&kind(X))<=>(~old(X)<~>~wise(X))))&
(![X]:((happy(X)|tall(X))=>(~quiet(X)<~>~old(X))))&
((creative(john)&curious(john)))&
((~rich(john)<~>~creative(john)))&
(wise(fred))&
(?[X]:(rich(X)))&
(?[X]:((~old(X)|happy(X))))&
(?[X]:(~generous(X)))&
((~tall(fred)|~happy(fred)))&
((~brave(lucy)<~>~humble(lucy))) | ~happy(fred) | [
"p2",
"p3",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4335336643161832338403933
% SZS output start Proof for 4335336643161832338403933
3. ! [X0] : ((quiet(X0) & patient(X0)) <=> (~happy(X0) | wise(X0))) [input p2]
4. ! [X0] : (kind(X0) => (~funny(X0) & brave(X0))) [input p3]
15. ! [X0] : ((kind(X0) & funny(X0)) <=> (~old(X0) <~> ~wise(X0))) [input p14]
16. ! [X0] : ((tall(X0) | happy(X0)) => (~quiet(X0) <~> ~old(X0))) [input p15]
19. wise(fred) [input p18]
25. happy(fred) [input hypothesis]
30. ! [X0] : ((~funny(X0) & brave(X0)) | ~kind(X0)) [ennf transformation 4]
40. ! [X0] : ((~quiet(X0) <~> ~old(X0)) | (~tall(X0) & ~happy(X0))) [ennf transformation 16]
44. ! [X0] : (((quiet(X0) & patient(X0)) | (happy(X0) & ~wise(X0))) & ((~happy(X0) | wise(X0)) | (~quiet(X0) | ~patient(X0)))) [nnf transformation 3]
45. ! [X0] : (((quiet(X0) & patient(X0)) | (happy(X0) & ~wise(X0))) & (~happy(X0) | wise(X0) | ~quiet(X0) | ~patient(X0))) [flattening 44]
58. ! [X0] : (((kind(X0) & funny(X0)) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0)))) & (((wise(X0) | old(X0)) & (~wise(X0) | ~old(X0))) | (~kind(X0) | ~funny(X0)))) [nnf transformation 15]
59. ! [X0] : (((kind(X0) & funny(X0)) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0)))) & (((wise(X0) | old(X0)) & (~wise(X0) | ~old(X0))) | ~kind(X0) | ~funny(X0))) [flattening 58]
60. ! [X0] : (((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | (~tall(X0) & ~happy(X0))) [nnf transformation 40]
75. ~wise(X0) | quiet(X0) [cnf transformation 45]
78. ~funny(X0) | ~kind(X0) [cnf transformation 30]
109. ~wise(X0) | funny(X0) | old(X0) [cnf transformation 59]
111. ~wise(X0) | kind(X0) | old(X0) [cnf transformation 59]
113. ~old(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 60]
121. wise(fred) [cnf transformation 19]
128. happy(fred) [cnf transformation 25]
228. 21 <=> funny(fred) [avatar definition]
229. funny(fred) <- (21) [avatar component clause 228]
230. ~funny(fred) <- (~21) [avatar component clause 228]
259. 27 <=> happy(fred) [avatar definition]
260. happy(fred) <- (27) [avatar component clause 259]
273. 27 [avatar split clause 128,259]
275. quiet(fred) [resolution 75,121]
286. funny(fred) | old(fred) [resolution 109,121]
288. old(fred) <- (~21) [subsumption resolution 286,230]
315. kind(fred) | old(fred) [resolution 111,121]
320. ~quiet(fred) | ~happy(fred) <- (~21) [resolution 113,288]
321. ~happy(fred) <- (~21) [subsumption resolution 320,275]
322. $false <- (~21, 27) [subsumption resolution 321,260]
323. 21 | ~27 [avatar contradiction clause 322]
325. 34 <=> old(fred) [avatar definition]
327. old(fred) <- (34) [avatar component clause 325]
329. 35 <=> kind(fred) [avatar definition]
332. 34 | 35 [avatar split clause 315,329,325]
335. ~kind(fred) <- (21) [resolution 229,78]
336. ~35 | ~21 [avatar split clause 335,228,329]
337. ~quiet(fred) | ~happy(fred) <- (34) [resolution 327,113]
341. ~happy(fred) <- (34) [subsumption resolution 337,275]
342. $false <- (27, 34) [subsumption resolution 341,260]
343. ~27 | ~34 [avatar contradiction clause 342]
344. $false [avatar sat refutation 273,323,332,336,343]
% SZS output end Proof for 4335336643161832338403933
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is quiet or not rich then fred is strong and vice versa.
If lucy is either creative or brave then susan is humble.
If john is not curious or patient then someone is rich and vice versa.
Everyone who is not kind or not old is both not wise and happy.
If paul is funny or not creative then fred is either not brave or generous and vice versa.
Everyone who is brave is rich or not calm and vice versa.
Everyone who is wise is both happy and not rich and vice versa.
If alice is kind then someone is not calm or rich.
If paul is curious or not generous then someone is both tall and not tall.
If lucy is either not kind or creative then paul is brave or wise.
Everyone who is not generous or happy is calm or curious and vice versa.
Everyone who is either not wise or not humble is both curious and humble and vice versa.
If mary is both not happy and not old then john is not brave.
If fred is not calm then mary is either calm or not rich and vice versa.
If paul is not generous then fred is either not quiet or wise.
Everyone who is not calm is happy.
Someone is either wise or not quiet.
Mary is not generous.
Someone is not happy.
Fred is both quiet and not creative.
John is both calm and not funny.
Paul is both not old and generous.
Fred is either humble or curious.
Fred is both quiet and patient. | Paul is not generous. | contradiction | (((quiet(lucy)|~rich(lucy)))<=>(strong(fred)))&
(((creative(lucy)<~>brave(lucy)))=>(humble(susan)))&
(((~curious(john)|patient(john)))<=>(?[X]:(rich(X))))&
(![X]:((~kind(X)|~old(X))=>(~wise(X)&happy(X))))&
(((funny(paul)|~creative(paul)))<=>((~brave(fred)<~>generous(fred))))&
(![X]:(brave(X)<=>(rich(X)|~calm(X))))&
(![X]:(wise(X)<=>(happy(X)&~rich(X))))&
((kind(alice))=>(?[X]:((~calm(X)|rich(X)))))&
(((curious(paul)|~generous(paul)))=>(?[X]:((tall(X)&~tall(X)))))&
(((~kind(lucy)<~>creative(lucy)))=>((brave(paul)|wise(paul))))&
(![X]:((~generous(X)|happy(X))<=>(calm(X)|curious(X))))&
(![X]:((~wise(X)<~>~humble(X))<=>(curious(X)&humble(X))))&
(((~happy(mary)&~old(mary)))=>(~brave(john)))&
((~calm(fred))<=>((calm(mary)<~>~rich(mary))))&
((~generous(paul))=>((~quiet(fred)<~>wise(fred))))&
(![X]:(~calm(X)=>happy(X)))&
(?[X]:((wise(X)<~>~quiet(X))))&
(~generous(mary))&
(?[X]:(~happy(X)))&
((quiet(fred)&~creative(fred)))&
((calm(john)&~funny(john)))&
((~old(paul)&generous(paul)))&
((humble(fred)<~>curious(fred)))&
((quiet(fred)&patient(fred))) | ~generous(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7254084944845139703562167
% SZS output start Proof for 7254084944845139703562167
22. generous(paul) & ~old(paul) [input p21]
25. ~generous(paul) [input hypothesis]
125. generous(paul) [cnf transformation 22]
130. ~generous(paul) [cnf transformation 25]
216. 18 <=> generous(paul) [avatar definition]
282. 18 [avatar split clause 125,216]
294. ~18 [avatar split clause 130,216]
295. $false [avatar sat refutation 282,294]
% SZS output end Proof for 7254084944845139703562167
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or not old then someone is not old or generous and vice versa.
If susan is either not kind or strong then someone is either not wise or not old and vice versa.
Everyone who is not quiet or not patient is either calm or happy and vice versa.
If someone is either not funny or not rich then alice is both not rich and tall.
Everyone who is not generous or not funny is not brave or not strong and vice versa.
If someone is old or creative then fred is not patient.
If someone is tall or strong then susan is either wise or not tall.
If lucy is either not rich or not old then someone is both not strong and wise and vice versa.
If mary is old then fred is rich or kind and vice versa.
If someone is patient or old then someone is wise and vice versa.
If someone is not old or not wise then someone is either not old or not brave.
If someone is patient or creative then mary is not curious or quiet.
Everyone who is not generous is not happy and vice versa.
If someone is both not brave and not strong then lucy is either not tall or rich and vice versa.
Everyone who is old or not calm is tall or quiet.
Everyone who is both not wise and old is either not rich or funny and vice versa.
Susan is not tall or not funny.
Fred is either not old or not quiet.
Someone is strong or not wise.
Mary is strong.
Mary is both quiet and kind.
Lucy is both not quiet and not patient.
Someone is either generous or not wise.
Alice is both funny and quiet. | Alice is not tall. | contradiction | ((?[X]:((strong(X)|~old(X))))<=>(?[X]:((~old(X)|generous(X)))))&
(((~kind(susan)<~>strong(susan)))<=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((~quiet(X)|~patient(X))<=>(calm(X)<~>happy(X))))&
((?[X]:((~funny(X)<~>~rich(X))))=>((~rich(alice)&tall(alice))))&
(![X]:((~generous(X)|~funny(X))<=>(~brave(X)|~strong(X))))&
((?[X]:((old(X)|creative(X))))=>(~patient(fred)))&
((?[X]:((tall(X)|strong(X))))=>((wise(susan)<~>~tall(susan))))&
(((~rich(lucy)<~>~old(lucy)))<=>(?[X]:((~strong(X)&wise(X)))))&
((old(mary))<=>((rich(fred)|kind(fred))))&
((?[X]:((patient(X)|old(X))))<=>(?[X]:(wise(X))))&
((?[X]:((~old(X)|~wise(X))))=>(?[X]:((~old(X)<~>~brave(X)))))&
((?[X]:((patient(X)|creative(X))))=>((~curious(mary)|quiet(mary))))&
(![X]:(~generous(X)<=>~happy(X)))&
((?[X]:((~brave(X)&~strong(X))))<=>((~tall(lucy)<~>rich(lucy))))&
(![X]:((old(X)|~calm(X))=>(tall(X)|quiet(X))))&
(![X]:((~wise(X)&old(X))<=>(~rich(X)<~>funny(X))))&
((~tall(susan)|~funny(susan)))&
((~old(fred)<~>~quiet(fred)))&
(?[X]:((strong(X)|~wise(X))))&
(strong(mary))&
((quiet(mary)&kind(mary)))&
((~quiet(lucy)&~patient(lucy)))&
(?[X]:((generous(X)<~>~wise(X))))&
((funny(alice)&quiet(alice))) | ~tall(alice) | [
"p3",
"p9",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4388473947957109057525720
% SZS output start Proof for 4388473947957109057525720
4. ? [X0] : (~funny(X0) <~> ~rich(X0)) => (tall(alice) & ~rich(alice)) [input p3]
10. ? [X0] : (old(X0) | patient(X0)) <=> ? [X0] : wise(X0) [input p9]
16. ! [X0] : ((old(X0) & ~wise(X0)) <=> (~rich(X0) <~> funny(X0))) [input p15]
24. quiet(alice) & funny(alice) [input p23]
25. ~tall(alice) [input hypothesis]
27. ? [X0] : (old(X0) | patient(X0)) <=> ? [X1] : wise(X1) [rectify 10]
31. (tall(alice) & ~rich(alice)) | ! [X0] : (~funny(X0) <=> ~rich(X0)) [ennf transformation 4]
48. (tall(alice) & ~rich(alice)) | ! [X0] : ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))) [nnf transformation 31]
58. (? [X0] : (old(X0) | patient(X0)) | ! [X1] : ~wise(X1)) & (? [X1] : wise(X1) | ! [X0] : (~old(X0) & ~patient(X0))) [nnf transformation 27]
59. (? [X0] : (old(X0) | patient(X0)) | ! [X1] : ~wise(X1)) & (? [X2] : wise(X2) | ! [X3] : (~old(X3) & ~patient(X3))) [rectify 58]
60. ? [X0] : (old(X0) | patient(X0)) => (old(sK4) | patient(sK4)) [choice axiom]
61. ? [X2] : wise(X2) => wise(sK5) [choice axiom]
62. ((old(sK4) | patient(sK4)) | ! [X1] : ~wise(X1)) & (wise(sK5) | ! [X3] : (~old(X3) & ~patient(X3))) [skolemisation 59,61,60]
72. ! [X0] : (((old(X0) & ~wise(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (~old(X0) | wise(X0)))) [nnf transformation 16]
73. ! [X0] : (((old(X0) & ~wise(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | ~old(X0) | wise(X0))) [flattening 72]
100. tall(alice) | ~rich(X0) | funny(X0) [cnf transformation 48]
101. tall(alice) | ~funny(X0) | rich(X0) [cnf transformation 48]
121. wise(sK5) | ~old(X3) [cnf transformation 62]
139. ~wise(X0) | funny(X0) | rich(X0) [cnf transformation 73]
140. ~rich(X0) | ~wise(X0) | ~funny(X0) [cnf transformation 73]
142. ~rich(X0) | old(X0) | ~funny(X0) [cnf transformation 73]
154. funny(alice) [cnf transformation 24]
156. ~tall(alice) [cnf transformation 25]
217. 14 <=> ! [X0] : (~funny(X0) | rich(X0)) [avatar definition]
218. ~funny(X0) | rich(X0) <- (14) [avatar component clause 217]
220. 15 <=> tall(alice) [avatar definition]
223. 14 | 15 [avatar split clause 101,220,217]
225. 16 <=> ! [X0] : (~rich(X0) | funny(X0)) [avatar definition]
226. ~rich(X0) | funny(X0) <- (16) [avatar component clause 225]
227. 16 | 15 [avatar split clause 100,220,225]
229. 17 <=> rich(alice) [avatar definition]
230. rich(alice) <- (17) [avatar component clause 229]
235. 18 <=> ! [X0] : ~old(X0) [avatar definition]
236. ~old(X0) <- (18) [avatar component clause 235]
310. 34 <=> wise(sK5) [avatar definition]
312. wise(sK5) <- (34) [avatar component clause 310]
313. 18 | 34 [avatar split clause 121,310,235]
388. ~15 [avatar split clause 156,220]
419. rich(alice) <- (14) [resolution 218,154]
420. 17 | ~14 [avatar split clause 419,217,229]
532. funny(sK5) | rich(sK5) <- (34) [resolution 139,312]
535. rich(sK5) <- (14, 34) [subsumption resolution 532,218]
545. ~wise(sK5) | ~funny(sK5) <- (14, 34) [resolution 535,140]
546. funny(sK5) <- (14, 16, 34) [resolution 535,226]
547. ~funny(sK5) <- (14, 34) [subsumption resolution 545,312]
548. $false <- (14, 16, 34) [subsumption resolution 546,547]
549. ~14 | ~16 | ~34 [avatar contradiction clause 548]
574. old(alice) | ~funny(alice) <- (17) [resolution 142,230]
577. ~funny(alice) <- (17, 18) [subsumption resolution 574,236]
578. $false <- (17, 18) [subsumption resolution 577,154]
579. ~17 | ~18 [avatar contradiction clause 578]
580. $false [avatar sat refutation 223,227,313,388,420,549,579]
% SZS output end Proof for 4388473947957109057525720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not strong or not wise is both funny and patient. Everyone who is both funny and not creative is not wise or not old and vice versa. If mary is creative then someone is not brave and vice versa. Everyone who is tall is both not happy and happy and vice versa. Everyone who is quiet is either not creative or patient. Everyone who is not old is either not strong or not happy. Everyone who is not old is either happy or humble. Everyone who is not generous or not rich is quiet and vice versa. Everyone who is quiet or not creative is either not creative or happy and vice versa. If someone is not patient or not creative then someone is not rich or not kind. Everyone who is quiet or not brave is either brave or patient and vice versa. If lucy is either kind or not kind then someone is either quiet or funny. Everyone who is either not happy or not strong is patient and vice versa. Everyone who is happy or old is either calm or not curious and vice versa. Everyone who is kind is not old or rich and vice versa. Lucy is either creative or calm. Paul is funny. Mary is both funny and patient. Susan is strong. Someone is both kind and not brave. Someone is either strong or not kind. Lucy is curious. | Susan is generous. | entailment | (![X]:((~strong(X)|~wise(X))=>(funny(X)&patient(X))))&
(![X]:((funny(X)&~creative(X))<=>(~wise(X)|~old(X))))&
((creative(mary))<=>(?[X]:(~brave(X))))&
(![X]:(tall(X)<=>(~happy(X)&happy(X))))&
(![X]:(quiet(X)=>(~creative(X)<~>patient(X))))&
(![X]:(~old(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~old(X)=>(happy(X)<~>humble(X))))&
(![X]:((~generous(X)|~rich(X))<=>quiet(X)))&
(![X]:((quiet(X)|~creative(X))<=>(~creative(X)<~>happy(X))))&
((?[X]:((~patient(X)|~creative(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((quiet(X)|~brave(X))<=>(brave(X)<~>patient(X))))&
(((kind(lucy)<~>~kind(lucy)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~happy(X)<~>~strong(X))<=>patient(X)))&
(![X]:((happy(X)|old(X))<=>(calm(X)<~>~curious(X))))&
(![X]:(kind(X)<=>(~old(X)|rich(X))))&
((creative(lucy)<~>calm(lucy)))&
(funny(paul))&
((funny(mary)&patient(mary)))&
(strong(susan))&
(?[X]:((kind(X)&~brave(X))))&
(?[X]:((strong(X)<~>~kind(X))))&
(curious(lucy)) | generous(susan) | [
"p0",
"p4",
"p7",
"p8",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3631142941880965049649826
% SZS output start Proof for 3631142941880965049649826
1. ! [X0] : ((~wise(X0) | ~strong(X0)) => (patient(X0) & funny(X0))) [input p0]
5. ! [X0] : (quiet(X0) => (~creative(X0) <~> patient(X0))) [input p4]
8. ! [X0] : ((~rich(X0) | ~generous(X0)) <=> quiet(X0)) [input p7]
9. ! [X0] : ((~creative(X0) | quiet(X0)) <=> (~creative(X0) <~> happy(X0))) [input p8]
13. ! [X0] : ((~happy(X0) <~> ~strong(X0)) <=> patient(X0)) [input p12]
19. strong(susan) [input p18]
23. ~generous(susan) [input hypothesis]
25. ! [X0] : ((patient(X0) & funny(X0)) | (wise(X0) & strong(X0))) [ennf transformation 1]
26. ! [X0] : ((~creative(X0) <~> patient(X0)) | ~quiet(X0)) [ennf transformation 5]
37. ! [X0] : (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | ~quiet(X0)) [nnf transformation 26]
40. ! [X0] : (((~rich(X0) | ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [nnf transformation 8]
41. ! [X0] : ((~rich(X0) | ~generous(X0) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [flattening 40]
42. ! [X0] : (((~creative(X0) | quiet(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [nnf transformation 9]
43. ! [X0] : ((~creative(X0) | quiet(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [flattening 42]
52. ! [X0] : ((((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | ~patient(X0)) & (patient(X0) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))))) [nnf transformation 13]
65. patient(X0) | strong(X0) [cnf transformation 25]
74. ~quiet(X0) | ~creative(X0) | patient(X0) [cnf transformation 37]
75. ~quiet(X0) | creative(X0) | ~patient(X0) [cnf transformation 37]
80. generous(X0) | quiet(X0) [cnf transformation 41]
83. ~quiet(X0) | ~creative(X0) | happy(X0) [cnf transformation 43]
86. ~happy(X0) | creative(X0) | creative(X0) [cnf transformation 43]
101. patient(X0) | ~strong(X0) | happy(X0) [cnf transformation 52]
103. ~happy(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 52]
104. strong(X0) | happy(X0) | ~patient(X0) [cnf transformation 52]
119. strong(susan) [cnf transformation 19]
125. ~generous(susan) [cnf transformation 23]
132. ~happy(X0) | creative(X0) [duplicate literal removal 86]
179. happy(X0) | strong(X0) [subsumption resolution 104,65]
180. happy(X0) | patient(X0) [subsumption resolution 101,179]
207. quiet(susan) [resolution 80,125]
214. patient(X0) | creative(X0) [resolution 180,132]
218. ~creative(susan) | patient(susan) [resolution 74,207]
220. patient(susan) [subsumption resolution 218,214]
222. creative(susan) | ~patient(susan) [resolution 75,207]
224. creative(susan) [subsumption resolution 222,220]
246. ~creative(susan) | happy(susan) [resolution 83,207]
250. happy(susan) [subsumption resolution 246,224]
272. ~strong(susan) | ~patient(susan) [resolution 250,103]
275. ~patient(susan) [subsumption resolution 272,119]
276. $false [subsumption resolution 275,220]
% SZS output end Proof for 3631142941880965049649826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or strong is calm or funny and vice versa.
If someone is either not rich or not strong then alice is both not funny and not rich.
If someone is either patient or not tall then fred is strong or funny.
Everyone who is not wise is happy and vice versa.
Everyone who is both not old and tall is either calm or not old and vice versa.
Everyone who is both not curious and calm is not strong and vice versa.
Everyone who is old is both not wise and calm.
Everyone who is either not quiet or happy is either not humble or funny.
If mary is either not kind or strong then someone is humble.
Everyone who is either tall or not brave is both strong and generous.
If fred is kind then someone is both humble and not generous and vice versa.
If someone is not wise or not funny then someone is either quiet or not old.
Everyone who is both not humble and strong is either not quiet or not strong.
Everyone who is not kind is wise.
Everyone who is both kind and wise is both not old and happy and vice versa.
Everyone who is both not old and not rich is either not tall or brave and vice versa.
Lucy is either not creative or wise.
John is not tall or not happy.
Someone is rich.
Susan is either funny or not humble.
Someone is curious or quiet. | Fred is generous. | entailment | (![X]:((calm(X)<~>strong(X))<=>(calm(X)|funny(X))))&
((?[X]:((~rich(X)<~>~strong(X))))=>((~funny(alice)&~rich(alice))))&
((?[X]:((patient(X)<~>~tall(X))))=>((strong(fred)|funny(fred))))&
(![X]:(~wise(X)<=>happy(X)))&
(![X]:((~old(X)&tall(X))<=>(calm(X)<~>~old(X))))&
(![X]:((~curious(X)&calm(X))<=>~strong(X)))&
(![X]:(old(X)=>(~wise(X)&calm(X))))&
(![X]:((~quiet(X)<~>happy(X))=>(~humble(X)<~>funny(X))))&
(((~kind(mary)<~>strong(mary)))=>(?[X]:(humble(X))))&
(![X]:((tall(X)<~>~brave(X))=>(strong(X)&generous(X))))&
((kind(fred))<=>(?[X]:((humble(X)&~generous(X)))))&
((?[X]:((~wise(X)|~funny(X))))=>(?[X]:((quiet(X)<~>~old(X)))))&
(![X]:((~humble(X)&strong(X))=>(~quiet(X)<~>~strong(X))))&
(![X]:(~kind(X)=>wise(X)))&
(![X]:((kind(X)&wise(X))<=>(~old(X)&happy(X))))&
(![X]:((~old(X)&~rich(X))<=>(~tall(X)<~>brave(X))))&
((~creative(lucy)<~>wise(lucy)))&
((~tall(john)|~happy(john)))&
(?[X]:(rich(X)))&
((funny(susan)<~>~humble(susan)))&
(?[X]:((curious(X)|quiet(X)))) | generous(fred) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p10",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3988745151974675853237164
% SZS output start Proof for 3988745151974675853237164
1. ! [X0] : ((calm(X0) <~> strong(X0)) <=> (funny(X0) | calm(X0))) [input p0]
2. ? [X0] : (~rich(X0) <~> ~strong(X0)) => (~rich(alice) & ~funny(alice)) [input p1]
4. ! [X0] : (~wise(X0) <=> happy(X0)) [input p3]
5. ! [X0] : ((tall(X0) & ~old(X0)) <=> (calm(X0) <~> ~old(X0))) [input p4]
6. ! [X0] : ((calm(X0) & ~curious(X0)) <=> ~strong(X0)) [input p5]
7. ! [X0] : (old(X0) => (calm(X0) & ~wise(X0))) [input p6]
8. ! [X0] : ((~quiet(X0) <~> happy(X0)) => (~humble(X0) <~> funny(X0))) [input p7]
10. ! [X0] : ((tall(X0) <~> ~brave(X0)) => (generous(X0) & strong(X0))) [input p9]
11. kind(fred) <=> ? [X0] : (~generous(X0) & humble(X0)) [input p10]
13. ! [X0] : ((strong(X0) & ~humble(X0)) => (~quiet(X0) <~> ~strong(X0))) [input p12]
15. ! [X0] : ((wise(X0) & kind(X0)) <=> (happy(X0) & ~old(X0))) [input p14]
16. ! [X0] : ((~rich(X0) & ~old(X0)) <=> (~tall(X0) <~> brave(X0))) [input p15]
22. ~generous(fred) [input hypothesis]
24. (~rich(alice) & ~funny(alice)) | ! [X0] : (~rich(X0) <=> ~strong(X0)) [ennf transformation 2]
27. ! [X0] : ((calm(X0) & ~wise(X0)) | ~old(X0)) [ennf transformation 7]
28. ! [X0] : ((~humble(X0) <~> funny(X0)) | (~quiet(X0) <=> happy(X0))) [ennf transformation 8]
30. ! [X0] : ((generous(X0) & strong(X0)) | (tall(X0) <=> ~brave(X0))) [ennf transformation 10]
32. ! [X0] : ((~quiet(X0) <~> ~strong(X0)) | (~strong(X0) | humble(X0))) [ennf transformation 13]
33. ! [X0] : ((~quiet(X0) <~> ~strong(X0)) | ~strong(X0) | humble(X0)) [flattening 32]
35. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [flattening 35]
37. (~rich(alice) & ~funny(alice)) | ! [X0] : ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0))) [nnf transformation 24]
39. ! [X0] : ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0))) [nnf transformation 4]
40. ! [X0] : (((tall(X0) & ~old(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | (~tall(X0) | old(X0)))) [nnf transformation 5]
41. ! [X0] : (((tall(X0) & ~old(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | ~tall(X0) | old(X0))) [flattening 40]
42. ! [X0] : (((calm(X0) & ~curious(X0)) | strong(X0)) & (~strong(X0) | (~calm(X0) | curious(X0)))) [nnf transformation 6]
43. ! [X0] : (((calm(X0) & ~curious(X0)) | strong(X0)) & (~strong(X0) | ~calm(X0) | curious(X0))) [flattening 42]
44. ! [X0] : (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) [nnf transformation 28]
48. ! [X0] : ((generous(X0) & strong(X0)) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) [nnf transformation 30]
49. (kind(fred) | ! [X0] : (generous(X0) | ~humble(X0))) & (? [X0] : (~generous(X0) & humble(X0)) | ~kind(fred)) [nnf transformation 11]
50. (kind(fred) | ! [X0] : (generous(X0) | ~humble(X0))) & (? [X1] : (~generous(X1) & humble(X1)) | ~kind(fred)) [rectify 49]
51. ? [X1] : (~generous(X1) & humble(X1)) => (~generous(sK1) & humble(sK1)) [choice axiom]
52. (kind(fred) | ! [X0] : (generous(X0) | ~humble(X0))) & ((~generous(sK1) & humble(sK1)) | ~kind(fred)) [skolemisation 50,51]
57. ! [X0] : (((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | ~strong(X0) | humble(X0)) [nnf transformation 33]
58. ! [X0] : (((wise(X0) & kind(X0)) | (~happy(X0) | old(X0))) & ((happy(X0) & ~old(X0)) | (~wise(X0) | ~kind(X0)))) [nnf transformation 15]
59. ! [X0] : (((wise(X0) & kind(X0)) | ~happy(X0) | old(X0)) & ((happy(X0) & ~old(X0)) | ~wise(X0) | ~kind(X0))) [flattening 58]
60. ! [X0] : (((~rich(X0) & ~old(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (rich(X0) | old(X0)))) [nnf transformation 16]
61. ! [X0] : (((~rich(X0) & ~old(X0)) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | rich(X0) | old(X0))) [flattening 60]
69. funny(X0) | calm(X0) | calm(X0) | ~strong(X0) [cnf transformation 36]
72. ~strong(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 36]
74. ~funny(alice) | ~strong(X0) | rich(X0) [cnf transformation 37]
76. ~rich(alice) | ~strong(X0) | rich(X0) [cnf transformation 37]
77. ~rich(alice) | ~rich(X0) | strong(X0) [cnf transformation 37]
80. happy(X0) | wise(X0) [cnf transformation 39]
81. ~happy(X0) | ~wise(X0) [cnf transformation 39]
83. old(X0) | ~calm(X0) | ~tall(X0) | old(X0) [cnf transformation 41]
84. ~old(X0) | ~old(X0) | ~calm(X0) [cnf transformation 41]
90. strong(X0) | calm(X0) [cnf transformation 43]
92. calm(X0) | ~old(X0) [cnf transformation 27]
95. ~funny(X0) | humble(X0) | happy(X0) | quiet(X0) [cnf transformation 44]
100. brave(X0) | tall(X0) | strong(X0) [cnf transformation 48]
105. kind(fred) | generous(X0) | ~humble(X0) [cnf transformation 52]
110. ~strong(X0) | ~quiet(X0) | ~strong(X0) | humble(X0) [cnf transformation 57]
114. happy(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 59]
116. wise(X0) | ~happy(X0) | old(X0) [cnf transformation 59]
118. ~brave(X0) | tall(X0) | rich(X0) | old(X0) [cnf transformation 61]
130. ~generous(fred) [cnf transformation 22]
131. ~quiet(X0) | ~strong(X0) | humble(X0) [duplicate literal removal 110]
132. old(X0) | ~calm(X0) | ~tall(X0) [duplicate literal removal 83]
133. ~old(X0) | ~calm(X0) [duplicate literal removal 84]
134. funny(X0) | calm(X0) | ~strong(X0) [duplicate literal removal 69]
135. ~strong(X0) | ~calm(X0) [duplicate literal removal 72]
136. ~strong(X0) | funny(X0) [subsumption resolution 134,135]
138. 1 <=> ! [X0] : (~rich(X0) | strong(X0)) [avatar definition]
139. ~rich(X0) | strong(X0) <- (1) [avatar component clause 138]
141. 2 <=> rich(alice) [avatar definition]
143. ~rich(alice) <- (~2) [avatar component clause 141]
144. 1 | ~2 [avatar split clause 77,141,138]
146. 3 <=> ! [X0] : (~strong(X0) | rich(X0)) [avatar definition]
147. ~strong(X0) | rich(X0) <- (3) [avatar component clause 146]
148. 3 | ~2 [avatar split clause 76,141,146]
150. 4 <=> funny(alice) [avatar definition]
152. ~funny(alice) <- (~4) [avatar component clause 150]
154. 3 | ~4 [avatar split clause 74,150,146]
160. 6 <=> funny(fred) [avatar definition]
161. ~funny(fred) <- (~6) [avatar component clause 160]
162. funny(fred) <- (6) [avatar component clause 160]
169. ~tall(X0) | ~calm(X0) [subsumption resolution 132,133]
170. ~old(X0) [subsumption resolution 92,133]
186. 11 <=> ! [X0] : (generous(X0) | ~humble(X0)) [avatar definition]
187. ~humble(X0) | generous(X0) <- (11) [avatar component clause 186]
189. 12 <=> kind(fred) [avatar definition]
191. kind(fred) <- (12) [avatar component clause 189]
192. 11 | 12 [avatar split clause 105,189,186]
205. 15 <=> ! [X1] : funny(X1) [avatar definition]
206. funny(X1) <- (15) [avatar component clause 205]
214. 17 <=> ! [X1] : wise(X1) [avatar definition]
215. wise(X1) <- (17) [avatar component clause 214]
217. wise(X0) | ~happy(X0) [subsumption resolution 116,170]
218. ~happy(X0) [subsumption resolution 217,81]
219. ~kind(X0) | ~wise(X0) [subsumption resolution 114,218]
220. ~brave(X0) | tall(X0) | rich(X0) [subsumption resolution 118,170]
251. wise(X0) [resolution 80,218]
252. 17 [avatar split clause 251,214]
263. funny(X0) | calm(X0) [resolution 136,90]
266. calm(alice) <- (~4) [resolution 263,152]
318. tall(X0) | rich(X0) | tall(X0) | strong(X0) [resolution 220,100]
320. tall(X0) | rich(X0) | strong(X0) [duplicate literal removal 318]
326. rich(X1) | strong(X1) | ~calm(X1) [resolution 320,169]
329. ~calm(X1) | rich(X1) [subsumption resolution 326,135]
330. rich(alice) <- (~4) [resolution 329,266]
333. $false <- (~2, ~4) [subsumption resolution 330,143]
334. 2 | 4 [avatar contradiction clause 333]
353. rich(X0) | calm(X0) <- (3) [resolution 147,90]
355. rich(X0) <- (3) [subsumption resolution 353,329]
360. humble(fred) | happy(fred) | quiet(fred) <- (6) [resolution 95,162]
374. humble(fred) | quiet(fred) <- (6) [subsumption resolution 360,218]
376. 33 <=> quiet(fred) [avatar definition]
378. quiet(fred) <- (33) [avatar component clause 376]
380. 34 <=> humble(fred) [avatar definition]
382. humble(fred) <- (34) [avatar component clause 380]
383. 33 | 34 | ~6 [avatar split clause 374,160,380,376]
418. $false <- (~2, 3) [resolution 355,143]
419. strong(X0) <- (1, 3) [resolution 355,139]
421. 2 | ~3 [avatar contradiction clause 418]
430. ~strong(fred) | humble(fred) <- (33) [resolution 378,131]
431. humble(fred) <- (1, 3, 33) [subsumption resolution 430,419]
432. 34 | ~1 | ~3 | ~33 [avatar split clause 431,376,146,138,380]
435. generous(fred) <- (11, 34) [resolution 382,187]
436. $false <- (11, 34) [subsumption resolution 435,130]
437. ~11 | ~34 [avatar contradiction clause 436]
438. ~wise(fred) <- (12) [resolution 191,219]
439. $false <- (12, 17) [subsumption resolution 438,215]
440. ~12 | ~17 [avatar contradiction clause 439]
493. funny(X1) <- (1, 3) [resolution 419,136]
495. 15 | ~1 | ~3 [avatar split clause 493,146,138,205]
500. $false <- (~6, 15) [resolution 206,161]
501. 6 | ~15 [avatar contradiction clause 500]
504. $false [avatar sat refutation 144,148,154,192,252,334,383,421,432,437,440,495,501]
% SZS output end Proof for 3988745151974675853237164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not wise is either creative or not old and vice versa. Everyone who is either not wise or not funny is both kind and creative. Everyone who is either funny or not wise is strong or humble and vice versa. Everyone who is quiet or funny is both humble and brave and vice versa. Everyone who is not patient is rich or not tall and vice versa. If someone is both funny and generous then lucy is both strong and not brave. If someone is creative or not patient then someone is not humble or quiet and vice versa. Everyone who is not old or brave is both generous and brave and vice versa. If john is not kind then someone is both not rich and not patient and vice versa. Everyone who is both humble and not strong is not tall and vice versa. Everyone who is brave is both not kind and not rich and vice versa. If someone is generous then john is funny or old and vice versa. Everyone who is either funny or strong is both not generous and not creative. If susan is both rich and not happy then alice is either not rich or not calm. Paul is either calm or not rich. John is not curious or not calm. Lucy is curious or brave. Someone is not patient or not wise. John is humble or tall. Lucy is old. | Alice is funny. | contradiction | (![X]:((brave(X)|~wise(X))<=>(creative(X)<~>~old(X))))&
(![X]:((~wise(X)<~>~funny(X))=>(kind(X)&creative(X))))&
(![X]:((funny(X)<~>~wise(X))<=>(strong(X)|humble(X))))&
(![X]:((quiet(X)|funny(X))<=>(humble(X)&brave(X))))&
(![X]:(~patient(X)<=>(rich(X)|~tall(X))))&
((?[X]:((funny(X)&generous(X))))=>((strong(lucy)&~brave(lucy))))&
((?[X]:((creative(X)|~patient(X))))<=>(?[X]:((~humble(X)|quiet(X)))))&
(![X]:((~old(X)|brave(X))<=>(generous(X)&brave(X))))&
((~kind(john))<=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:((humble(X)&~strong(X))<=>~tall(X)))&
(![X]:(brave(X)<=>(~kind(X)&~rich(X))))&
((?[X]:(generous(X)))<=>((funny(john)|old(john))))&
(![X]:((funny(X)<~>strong(X))=>(~generous(X)&~creative(X))))&
(((rich(susan)&~happy(susan)))=>((~rich(alice)<~>~calm(alice))))&
((calm(paul)<~>~rich(paul)))&
((~curious(john)|~calm(john)))&
((curious(lucy)|brave(lucy)))&
(?[X]:((~patient(X)|~wise(X))))&
((humble(john)|tall(john)))&
(old(lucy)) | funny(alice) | [
"p0",
"p2",
"p3",
"p5",
"p7",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6070679037937213232524269
% SZS output start Proof for 6070679037937213232524269
1. ! [X0] : ((~wise(X0) | brave(X0)) <=> (creative(X0) <~> ~old(X0))) [input p0]
3. ! [X0] : ((funny(X0) <~> ~wise(X0)) <=> (humble(X0) | strong(X0))) [input p2]
4. ! [X0] : ((funny(X0) | quiet(X0)) <=> (brave(X0) & humble(X0))) [input p3]
6. ? [X0] : (generous(X0) & funny(X0)) => (~brave(lucy) & strong(lucy)) [input p5]
8. ! [X0] : ((brave(X0) | ~old(X0)) <=> (brave(X0) & generous(X0))) [input p7]
13. ! [X0] : ((funny(X0) <~> strong(X0)) => (~creative(X0) & ~generous(X0))) [input p12]
20. old(lucy) [input p19]
21. funny(alice) [input hypothesis]
25. (~brave(lucy) & strong(lucy)) | ! [X0] : (~generous(X0) | ~funny(X0)) [ennf transformation 6]
26. ! [X0] : ((~creative(X0) & ~generous(X0)) | (funny(X0) <=> strong(X0))) [ennf transformation 13]
27. ! [X0] : (((~wise(X0) | brave(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | (wise(X0) & ~brave(X0)))) [nnf transformation 1]
28. ! [X0] : ((~wise(X0) | brave(X0) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | (wise(X0) & ~brave(X0)))) [flattening 27]
30. ! [X0] : ((((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))))) [nnf transformation 3]
31. ! [X0] : ((((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))))) [flattening 30]
32. ! [X0] : (((funny(X0) | quiet(X0)) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | (~funny(X0) & ~quiet(X0)))) [nnf transformation 4]
33. ! [X0] : ((funny(X0) | quiet(X0) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | (~funny(X0) & ~quiet(X0)))) [flattening 32]
41. ! [X0] : (((brave(X0) | ~old(X0)) | (~brave(X0) | ~generous(X0))) & ((brave(X0) & generous(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 8]
42. ! [X0] : ((brave(X0) | ~old(X0) | ~brave(X0) | ~generous(X0)) & ((brave(X0) & generous(X0)) | (~brave(X0) & old(X0)))) [flattening 41]
56. ! [X0] : ((~creative(X0) & ~generous(X0)) | ((funny(X0) | ~strong(X0)) & (strong(X0) | ~funny(X0)))) [nnf transformation 26]
61. ~old(X0) | creative(X0) | wise(X0) [cnf transformation 28]
72. ~strong(X0) | funny(X0) | ~wise(X0) [cnf transformation 31]
79. ~funny(X0) | brave(X0) [cnf transformation 33]
84. strong(lucy) | ~generous(X0) | ~funny(X0) [cnf transformation 25]
85. ~brave(lucy) | ~generous(X0) | ~funny(X0) [cnf transformation 25]
91. ~brave(X0) | generous(X0) [cnf transformation 42]
110. ~strong(X0) | funny(X0) | ~creative(X0) [cnf transformation 56]
117. old(lucy) [cnf transformation 20]
118. funny(alice) [cnf transformation 21]
120. 1 <=> ! [X0] : (~generous(X0) | ~funny(X0)) [avatar definition]
121. ~generous(X0) | ~funny(X0) <- (1) [avatar component clause 120]
123. 2 <=> brave(lucy) [avatar definition]
126. 1 | ~2 [avatar split clause 85,123,120]
128. 3 <=> strong(lucy) [avatar definition]
130. strong(lucy) <- (3) [avatar component clause 128]
131. 1 | 3 [avatar split clause 84,128,120]
234. brave(alice) [resolution 79,118]
235. generous(alice) [resolution 91,234]
249. creative(lucy) | wise(lucy) [resolution 61,117]
253. 29 <=> wise(lucy) [avatar definition]
257. 30 <=> creative(lucy) [avatar definition]
259. creative(lucy) <- (30) [avatar component clause 257]
260. 29 | 30 [avatar split clause 249,257,253]
307. 34 <=> funny(lucy) [avatar definition]
308. ~funny(lucy) <- (~34) [avatar component clause 307]
309. funny(lucy) <- (34) [avatar component clause 307]
322. brave(lucy) <- (34) [resolution 309,79]
326. 2 | ~34 [avatar split clause 322,307,123]
330. ~funny(alice) <- (1) [resolution 121,235]
332. $false <- (1) [subsumption resolution 330,118]
333. ~1 [avatar contradiction clause 332]
334. funny(lucy) | ~wise(lucy) <- (3) [resolution 72,130]
335. ~wise(lucy) <- (3, ~34) [subsumption resolution 334,308]
338. ~29 | ~3 | 34 [avatar split clause 335,307,128,253]
406. funny(lucy) | ~creative(lucy) <- (3) [resolution 110,130]
407. ~creative(lucy) <- (3, ~34) [subsumption resolution 406,308]
408. $false <- (3, 30, ~34) [subsumption resolution 407,259]
409. ~3 | ~30 | 34 [avatar contradiction clause 408]
410. $false [avatar sat refutation 126,131,260,326,333,338,409]
% SZS output end Proof for 6070679037937213232524269
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not curious is rich or not creative and vice versa.
If john is patient or not quiet then someone is both not creative and creative and vice versa.
If paul is both funny and generous then john is not old or not generous.
Everyone who is not humble is quiet or brave and vice versa.
Everyone who is both curious and quiet is both not old and not tall and vice versa.
If someone is happy or strong then mary is not generous.
Everyone who is not generous is not patient or not humble and vice versa.
Everyone who is both not patient and not happy is old or not rich.
Everyone who is not creative is not old or not brave.
If susan is not creative or curious then paul is both curious and rich and vice versa.
Everyone who is wise is either quiet or old.
Everyone who is not brave is not brave or brave and vice versa.
If alice is both not generous and quiet then susan is either curious or patient and vice versa.
If someone is either not calm or creative then someone is old or not quiet and vice versa.
Everyone who is both rich and quiet is not funny or wise and vice versa.
Everyone who is either patient or not wise is either not patient or funny.
Alice is both humble and not brave.
John is either tall or not kind.
Someone is either not tall or not happy.
Someone is not brave.
Someone is curious. | John is not happy. | neutral | (![X]:((quiet(X)|~curious(X))<=>(rich(X)|~creative(X))))&
(((patient(john)|~quiet(john)))<=>(?[X]:((~creative(X)&creative(X)))))&
(((funny(paul)&generous(paul)))=>((~old(john)|~generous(john))))&
(![X]:(~humble(X)<=>(quiet(X)|brave(X))))&
(![X]:((curious(X)&quiet(X))<=>(~old(X)&~tall(X))))&
((?[X]:((happy(X)|strong(X))))=>(~generous(mary)))&
(![X]:(~generous(X)<=>(~patient(X)|~humble(X))))&
(![X]:((~patient(X)&~happy(X))=>(old(X)|~rich(X))))&
(![X]:(~creative(X)=>(~old(X)|~brave(X))))&
(((~creative(susan)|curious(susan)))<=>((curious(paul)&rich(paul))))&
(![X]:(wise(X)=>(quiet(X)<~>old(X))))&
(![X]:(~brave(X)<=>(~brave(X)|brave(X))))&
(((~generous(alice)&quiet(alice)))<=>((curious(susan)<~>patient(susan))))&
((?[X]:((~calm(X)<~>creative(X))))<=>(?[X]:((old(X)|~quiet(X)))))&
(![X]:((rich(X)&quiet(X))<=>(~funny(X)|wise(X))))&
(![X]:((patient(X)<~>~wise(X))=>(~patient(X)<~>funny(X))))&
((humble(alice)&~brave(alice)))&
((tall(john)<~>~kind(john)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(?[X]:(~brave(X)))&
(?[X]:(curious(X))) | ~happy(john) | [] | null | 0 |
If alice is either not tall or not strong then someone is not old and vice versa.
Everyone who is both not tall and rich is both strong and not curious and vice versa.
Everyone who is both patient and not wise is kind.
Everyone who is either not strong or generous is either not creative or not happy and vice versa.
If someone is strong or not tall then fred is not quiet or tall and vice versa.
If someone is both not funny and generous then fred is both funny and humble and vice versa.
If someone is both tall and not strong then susan is either not wise or not curious.
If someone is either not calm or not curious then susan is both not calm and not old and vice versa.
Everyone who is old or tall is not humble.
Everyone who is both kind and not patient is not humble and vice versa.
If susan is not calm then paul is strong or calm.
Everyone who is strong or quiet is not humble or old.
If mary is both not strong and generous then someone is either not calm or not generous.
If alice is both not happy and not tall then someone is not strong and vice versa.
Everyone who is creative or not tall is not creative or creative and vice versa.
Everyone who is either not curious or not patient is not patient or curious and vice versa.
Someone is either patient or old.
Someone is not generous or curious.
Someone is either not strong or not creative.
Fred is not humble.
Alice is both not quiet and not humble.
Someone is either humble or not happy.
Someone is happy or curious. | Susan is humble. | neutral | (((~tall(alice)<~>~strong(alice)))<=>(?[X]:(~old(X))))&
(![X]:((~tall(X)&rich(X))<=>(strong(X)&~curious(X))))&
(![X]:((patient(X)&~wise(X))=>kind(X)))&
(![X]:((~strong(X)<~>generous(X))<=>(~creative(X)<~>~happy(X))))&
((?[X]:((strong(X)|~tall(X))))<=>((~quiet(fred)|tall(fred))))&
((?[X]:((~funny(X)&generous(X))))<=>((funny(fred)&humble(fred))))&
((?[X]:((tall(X)&~strong(X))))=>((~wise(susan)<~>~curious(susan))))&
((?[X]:((~calm(X)<~>~curious(X))))<=>((~calm(susan)&~old(susan))))&
(![X]:((old(X)|tall(X))=>~humble(X)))&
(![X]:((kind(X)&~patient(X))<=>~humble(X)))&
((~calm(susan))=>((strong(paul)|calm(paul))))&
(![X]:((strong(X)|quiet(X))=>(~humble(X)|old(X))))&
(((~strong(mary)&generous(mary)))=>(?[X]:((~calm(X)<~>~generous(X)))))&
(((~happy(alice)&~tall(alice)))<=>(?[X]:(~strong(X))))&
(![X]:((creative(X)|~tall(X))<=>(~creative(X)|creative(X))))&
(![X]:((~curious(X)<~>~patient(X))<=>(~patient(X)|curious(X))))&
(?[X]:((patient(X)<~>old(X))))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((~strong(X)<~>~creative(X))))&
(~humble(fred))&
((~quiet(alice)&~humble(alice)))&
(?[X]:((humble(X)<~>~happy(X))))&
(?[X]:((happy(X)|curious(X)))) | humble(susan) | [] | null | 0 |
If john is either not curious or not humble then someone is either happy or not creative and vice versa.
Everyone who is either not funny or old is happy or not kind.
If john is both rich and brave then someone is either not strong or happy.
If someone is not old then fred is either calm or not kind and vice versa.
Everyone who is not kind is not wise.
Everyone who is both patient and strong is both not happy and generous and vice versa.
Everyone who is either not funny or generous is either not calm or humble and vice versa.
Everyone who is both not rich and not brave is both calm and brave and vice versa.
Everyone who is brave or creative is not patient and vice versa.
Everyone who is funny is both old and wise.
Everyone who is either not calm or not old is both old and patient and vice versa.
If susan is either not humble or not rich then susan is not patient.
If susan is both not calm and not creative then someone is not creative or not generous and vice versa.
Everyone who is humble or not humble is not calm and vice versa.
Everyone who is not quiet or rich is not creative or not calm and vice versa.
Everyone who is both not wise and humble is not wise or creative and vice versa.
Someone is not creative.
Lucy is both not old and not generous.
Someone is either not wise or humble.
Someone is humble or not patient.
Paul is strong or patient.
Someone is rich.
Fred is either not tall or not rich.
Someone is not old or humble. | Fred is not funny. | entailment | (((~curious(john)<~>~humble(john)))<=>(?[X]:((happy(X)<~>~creative(X)))))&
(![X]:((~funny(X)<~>old(X))=>(happy(X)|~kind(X))))&
(((rich(john)&brave(john)))=>(?[X]:((~strong(X)<~>happy(X)))))&
((?[X]:(~old(X)))<=>((calm(fred)<~>~kind(fred))))&
(![X]:(~kind(X)=>~wise(X)))&
(![X]:((patient(X)&strong(X))<=>(~happy(X)&generous(X))))&
(![X]:((~funny(X)<~>generous(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((~rich(X)&~brave(X))<=>(calm(X)&brave(X))))&
(![X]:((brave(X)|creative(X))<=>~patient(X)))&
(![X]:(funny(X)=>(old(X)&wise(X))))&
(![X]:((~calm(X)<~>~old(X))<=>(old(X)&patient(X))))&
(((~humble(susan)<~>~rich(susan)))=>(~patient(susan)))&
(((~calm(susan)&~creative(susan)))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((humble(X)|~humble(X))<=>~calm(X)))&
(![X]:((~quiet(X)|rich(X))<=>(~creative(X)|~calm(X))))&
(![X]:((~wise(X)&humble(X))<=>(~wise(X)|creative(X))))&
(?[X]:(~creative(X)))&
((~old(lucy)&~generous(lucy)))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:((humble(X)|~patient(X))))&
((strong(paul)|patient(paul)))&
(?[X]:(rich(X)))&
((~tall(fred)<~>~rich(fred)))&
(?[X]:((~old(X)|humble(X)))) | ~funny(fred) | [
"p3",
"p4",
"p9",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2737206431779572789153857
% SZS output start Proof for 2737206431779572789153857
4. ? [X0] : ~old(X0) <=> (calm(fred) <~> ~kind(fred)) [input p3]
5. ! [X0] : (~kind(X0) => ~wise(X0)) [input p4]
10. ! [X0] : (funny(X0) => (wise(X0) & old(X0))) [input p9]
14. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~calm(X0)) [input p13]
18. ~generous(lucy) & ~old(lucy) [input p17]
25. funny(fred) [input hypothesis]
30. ! [X0] : (~wise(X0) | kind(X0)) [ennf transformation 5]
31. ! [X0] : ((wise(X0) & old(X0)) | ~funny(X0)) [ennf transformation 10]
41. (? [X0] : ~old(X0) | ((calm(fred) | kind(fred)) & (~kind(fred) | ~calm(fred)))) & (((kind(fred) | ~calm(fred)) & (~kind(fred) | calm(fred))) | ! [X0] : old(X0)) [nnf transformation 4]
42. (? [X0] : ~old(X0) | ((calm(fred) | kind(fred)) & (~kind(fred) | ~calm(fred)))) & (((kind(fred) | ~calm(fred)) & (~kind(fred) | calm(fred))) | ! [X1] : old(X1)) [rectify 41]
43. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
44. (~old(sK2) | ((calm(fred) | kind(fred)) & (~kind(fred) | ~calm(fred)))) & (((kind(fred) | ~calm(fred)) & (~kind(fred) | calm(fred))) | ! [X1] : old(X1)) [skolemisation 42,43]
60. ! [X0] : (((~humble(X0) | humble(X0)) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 14]
61. ! [X0] : ((~humble(X0) | humble(X0) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [flattening 60]
90. ~kind(fred) | calm(fred) | old(X1) [cnf transformation 44]
94. ~wise(X0) | kind(X0) [cnf transformation 30]
115. ~funny(X0) | wise(X0) [cnf transformation 31]
129. ~calm(X0) | ~humble(X0) [cnf transformation 61]
130. ~calm(X0) | humble(X0) [cnf transformation 61]
142. ~old(lucy) [cnf transformation 18]
152. funny(fred) [cnf transformation 25]
206. 11 <=> kind(fred) [avatar definition]
210. 12 <=> calm(fred) [avatar definition]
212. calm(fred) <- (12) [avatar component clause 210]
220. 14 <=> ! [X1] : old(X1) [avatar definition]
221. old(X1) <- (14) [avatar component clause 220]
223. 14 | 12 | ~11 [avatar split clause 90,206,210,220]
265. ~calm(X0) [subsumption resolution 129,130]
308. wise(fred) [resolution 115,152]
309. kind(fred) [resolution 308,94]
312. 11 [avatar split clause 309,206]
313. $false <- (12) [subsumption resolution 212,265]
314. ~12 [avatar contradiction clause 313]
315. $false <- (14) [resolution 221,142]
320. ~14 [avatar contradiction clause 315]
321. $false [avatar sat refutation 223,312,314,320]
% SZS output end Proof for 2737206431779572789153857
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not kind is not strong and vice versa. If susan is not curious or not tall then fred is brave or not generous and vice versa. Everyone who is both not happy and curious is curious or not creative and vice versa. If someone is both old and funny then someone is both rich and curious. Everyone who is not patient or not humble is either curious or not rich and vice versa. Everyone who is not wise or not patient is both wise and quiet and vice versa. If someone is both generous and not patient then susan is either humble or not wise and vice versa. Everyone who is generous or not tall is creative. If mary is both wise and not patient then mary is both not patient and creative and vice versa. Everyone who is patient is either kind or not old. Everyone who is both patient and not funny is both curious and wise. If someone is not wise then someone is both not calm and strong and vice versa. Everyone who is both not wise and not creative is calm or not quiet and vice versa. Everyone who is not calm or kind is either not calm or not rich. If someone is either not creative or old then someone is either rich or calm and vice versa. Everyone who is not old is both not strong and curious. Someone is either generous or not happy. Someone is either creative or not old. Fred is not calm. Someone is either patient or curious. Lucy is brave. Mary is not brave. | Susan is curious. | entailment | (![X]:((quiet(X)|~kind(X))<=>~strong(X)))&
(((~curious(susan)|~tall(susan)))<=>((brave(fred)|~generous(fred))))&
(![X]:((~happy(X)&curious(X))<=>(curious(X)|~creative(X))))&
((?[X]:((old(X)&funny(X))))=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((~patient(X)|~humble(X))<=>(curious(X)<~>~rich(X))))&
(![X]:((~wise(X)|~patient(X))<=>(wise(X)&quiet(X))))&
((?[X]:((generous(X)&~patient(X))))<=>((humble(susan)<~>~wise(susan))))&
(![X]:((generous(X)|~tall(X))=>creative(X)))&
(((wise(mary)&~patient(mary)))<=>((~patient(mary)&creative(mary))))&
(![X]:(patient(X)=>(kind(X)<~>~old(X))))&
(![X]:((patient(X)&~funny(X))=>(curious(X)&wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)&strong(X)))))&
(![X]:((~wise(X)&~creative(X))<=>(calm(X)|~quiet(X))))&
(![X]:((~calm(X)|kind(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((rich(X)<~>calm(X)))))&
(![X]:(~old(X)=>(~strong(X)&curious(X))))&
(?[X]:((generous(X)<~>~happy(X))))&
(?[X]:((creative(X)<~>~old(X))))&
(~calm(fred))&
(?[X]:((patient(X)<~>curious(X))))&
(brave(lucy))&
(~brave(mary)) | curious(susan) | [
"p4",
"p5",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4326592882313967243510413
% SZS output start Proof for 4326592882313967243510413
5. ! [X0] : ((~humble(X0) | ~patient(X0)) <=> (curious(X0) <~> ~rich(X0))) [input p4]
6. ! [X0] : ((~patient(X0) | ~wise(X0)) <=> (quiet(X0) & wise(X0))) [input p5]
13. ! [X0] : ((~creative(X0) & ~wise(X0)) <=> (~quiet(X0) | calm(X0))) [input p12]
14. ! [X0] : ((kind(X0) | ~calm(X0)) => (~calm(X0) <~> ~rich(X0))) [input p13]
23. ~curious(susan) [input hypothesis]
32. ! [X0] : ((~calm(X0) <~> ~rich(X0)) | (~kind(X0) & calm(X0))) [ennf transformation 14]
43. ! [X0] : (((~humble(X0) | ~patient(X0)) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) & (((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | (humble(X0) & patient(X0)))) [nnf transformation 5]
44. ! [X0] : ((~humble(X0) | ~patient(X0) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) & (((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | (humble(X0) & patient(X0)))) [flattening 43]
45. ! [X0] : (((~patient(X0) | ~wise(X0)) | (~quiet(X0) | ~wise(X0))) & ((quiet(X0) & wise(X0)) | (patient(X0) & wise(X0)))) [nnf transformation 6]
46. ! [X0] : ((~patient(X0) | ~wise(X0) | ~quiet(X0) | ~wise(X0)) & ((quiet(X0) & wise(X0)) | (patient(X0) & wise(X0)))) [flattening 45]
59. ! [X0] : (((~creative(X0) & ~wise(X0)) | (quiet(X0) & ~calm(X0))) & ((~quiet(X0) | calm(X0)) | (creative(X0) | wise(X0)))) [nnf transformation 13]
60. ! [X0] : (((~creative(X0) & ~wise(X0)) | (quiet(X0) & ~calm(X0))) & (~quiet(X0) | calm(X0) | creative(X0) | wise(X0))) [flattening 59]
61. ! [X0] : (((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | (~kind(X0) & calm(X0))) [nnf transformation 32]
90. ~rich(X0) | curious(X0) | patient(X0) [cnf transformation 44]
96. wise(X0) | wise(X0) [cnf transformation 46]
100. ~patient(X0) | ~wise(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 46]
121. ~wise(X0) | ~calm(X0) [cnf transformation 60]
122. ~wise(X0) | quiet(X0) [cnf transformation 60]
127. rich(X0) | calm(X0) | calm(X0) [cnf transformation 61]
148. ~curious(susan) [cnf transformation 23]
149. rich(X0) | calm(X0) [duplicate literal removal 127]
150. wise(X0) [duplicate literal removal 96]
151. ~wise(X0) | ~patient(X0) | ~quiet(X0) [duplicate literal removal 100]
157. 2 <=> curious(susan) [avatar definition]
159. ~curious(susan) <- (~2) [avatar component clause 157]
217. quiet(X0) [subsumption resolution 122,150]
218. ~calm(X0) [subsumption resolution 121,150]
220. rich(X0) [subsumption resolution 149,218]
265. ~2 [avatar split clause 148,157]
277. patient(X0) | curious(X0) [resolution 90,220]
326. ~patient(X2) | ~quiet(X2) [resolution 151,150]
327. ~patient(X2) [subsumption resolution 326,217]
337. curious(X0) [resolution 327,277]
346. $false <- (~2) [resolution 337,159]
349. 2 [avatar contradiction clause 346]
350. $false [avatar sat refutation 265,349]
% SZS output end Proof for 4326592882313967243510413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not strong is both funny and generous. Everyone who is not curious is not old and vice versa. If john is humble then someone is both not kind and rich. Everyone who is both kind and not humble is both not happy and not curious and vice versa. Everyone who is both calm and curious is both not kind and humble and vice versa. Everyone who is rich or not creative is creative. If alice is both old and creative then someone is rich or wise. If susan is brave or tall then john is generous or not patient. Everyone who is either curious or not brave is calm. If someone is not calm or humble then john is either not brave or quiet and vice versa. Everyone who is brave is not calm or happy and vice versa. If someone is old or funny then susan is not patient and vice versa. Everyone who is tall is either tall or funny. Everyone who is both curious and not quiet is both not wise and kind and vice versa. If someone is both not wise and quiet then paul is either not curious or funny. Everyone who is funny or happy is either not happy or tall. Mary is funny. Someone is not quiet. John is not rich or humble. Alice is either wise or funny. Fred is patient. Mary is either funny or quiet. | John is not humble. | entailment | (![X]:((creative(X)|~strong(X))=>(funny(X)&generous(X))))&
(![X]:(~curious(X)<=>~old(X)))&
((humble(john))=>(?[X]:((~kind(X)&rich(X)))))&
(![X]:((kind(X)&~humble(X))<=>(~happy(X)&~curious(X))))&
(![X]:((calm(X)&curious(X))<=>(~kind(X)&humble(X))))&
(![X]:((rich(X)|~creative(X))=>creative(X)))&
(((old(alice)&creative(alice)))=>(?[X]:((rich(X)|wise(X)))))&
(((brave(susan)|tall(susan)))=>((generous(john)|~patient(john))))&
(![X]:((curious(X)<~>~brave(X))=>calm(X)))&
((?[X]:((~calm(X)|humble(X))))<=>((~brave(john)<~>quiet(john))))&
(![X]:(brave(X)<=>(~calm(X)|happy(X))))&
((?[X]:((old(X)|funny(X))))<=>(~patient(susan)))&
(![X]:(tall(X)=>(tall(X)<~>funny(X))))&
(![X]:((curious(X)&~quiet(X))<=>(~wise(X)&kind(X))))&
((?[X]:((~wise(X)&quiet(X))))=>((~curious(paul)<~>funny(paul))))&
(![X]:((funny(X)|happy(X))=>(~happy(X)<~>tall(X))))&
(funny(mary))&
(?[X]:(~quiet(X)))&
((~rich(john)|humble(john)))&
((wise(alice)<~>funny(alice)))&
(patient(fred))&
((funny(mary)<~>quiet(mary))) | ~humble(john) | [
"p0",
"p3",
"p4",
"p5",
"p8",
"p9",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1177369625046242699790073
% SZS output start Proof for 1177369625046242699790073
1. ! [X0] : ((~strong(X0) | creative(X0)) => (generous(X0) & funny(X0))) [input p0]
4. ! [X0] : ((~humble(X0) & kind(X0)) <=> (~curious(X0) & ~happy(X0))) [input p3]
5. ! [X0] : ((curious(X0) & calm(X0)) <=> (humble(X0) & ~kind(X0))) [input p4]
6. ! [X0] : ((~creative(X0) | rich(X0)) => creative(X0)) [input p5]
9. ! [X0] : ((curious(X0) <~> ~brave(X0)) => calm(X0)) [input p8]
10. ? [X0] : (humble(X0) | ~calm(X0)) <=> (~brave(john) <~> quiet(john)) [input p9]
11. ! [X0] : (brave(X0) <=> (happy(X0) | ~calm(X0))) [input p10]
13. ! [X0] : (tall(X0) => (tall(X0) <~> funny(X0))) [input p12]
14. ! [X0] : ((~quiet(X0) & curious(X0)) <=> (kind(X0) & ~wise(X0))) [input p13]
16. ! [X0] : ((happy(X0) | funny(X0)) => (~happy(X0) <~> tall(X0))) [input p15]
23. humble(john) [input hypothesis]
24. ! [X0] : ((~strong(X0) | creative(X0)) => funny(X0)) [pure predicate removal 1]
26. ! [X0] : (creative(X0) => funny(X0)) [pure predicate removal 24]
27. ! [X0] : (funny(X0) | ~creative(X0)) [ennf transformation 26]
29. ! [X0] : (creative(X0) | (creative(X0) & ~rich(X0))) [ennf transformation 6]
32. ! [X0] : (calm(X0) | (curious(X0) <=> ~brave(X0))) [ennf transformation 9]
33. ! [X0] : ((tall(X0) <~> funny(X0)) | ~tall(X0)) [ennf transformation 13]
35. ! [X0] : ((~happy(X0) <~> tall(X0)) | (~happy(X0) & ~funny(X0))) [ennf transformation 16]
39. ! [X0] : (((~humble(X0) & kind(X0)) | (curious(X0) | happy(X0))) & ((~curious(X0) & ~happy(X0)) | (humble(X0) | ~kind(X0)))) [nnf transformation 4]
40. ! [X0] : (((~humble(X0) & kind(X0)) | curious(X0) | happy(X0)) & ((~curious(X0) & ~happy(X0)) | humble(X0) | ~kind(X0))) [flattening 39]
41. ! [X0] : (((curious(X0) & calm(X0)) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | (~curious(X0) | ~calm(X0)))) [nnf transformation 5]
42. ! [X0] : (((curious(X0) & calm(X0)) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | ~curious(X0) | ~calm(X0))) [flattening 41]
45. ! [X0] : (calm(X0) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) [nnf transformation 32]
46. (? [X0] : (humble(X0) | ~calm(X0)) | ((~brave(john) | ~quiet(john)) & (quiet(john) | brave(john)))) & (((~quiet(john) | brave(john)) & (quiet(john) | ~brave(john))) | ! [X0] : (~humble(X0) & calm(X0))) [nnf transformation 10]
47. (? [X0] : (humble(X0) | ~calm(X0)) | ((~brave(john) | ~quiet(john)) & (quiet(john) | brave(john)))) & (((~quiet(john) | brave(john)) & (quiet(john) | ~brave(john))) | ! [X1] : (~humble(X1) & calm(X1))) [rectify 46]
48. ? [X0] : (humble(X0) | ~calm(X0)) => (humble(sK2) | ~calm(sK2)) [choice axiom]
49. ((humble(sK2) | ~calm(sK2)) | ((~brave(john) | ~quiet(john)) & (quiet(john) | brave(john)))) & (((~quiet(john) | brave(john)) & (quiet(john) | ~brave(john))) | ! [X1] : (~humble(X1) & calm(X1))) [skolemisation 47,48]
50. ! [X0] : ((brave(X0) | (~happy(X0) & calm(X0))) & ((happy(X0) | ~calm(X0)) | ~brave(X0))) [nnf transformation 11]
51. ! [X0] : ((brave(X0) | (~happy(X0) & calm(X0))) & (happy(X0) | ~calm(X0) | ~brave(X0))) [flattening 50]
56. ! [X0] : (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | ~tall(X0)) [nnf transformation 33]
57. ! [X0] : (((~quiet(X0) & curious(X0)) | (~kind(X0) | wise(X0))) & ((kind(X0) & ~wise(X0)) | (quiet(X0) | ~curious(X0)))) [nnf transformation 14]
58. ! [X0] : (((~quiet(X0) & curious(X0)) | ~kind(X0) | wise(X0)) & ((kind(X0) & ~wise(X0)) | quiet(X0) | ~curious(X0))) [flattening 57]
60. ! [X0] : (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~happy(X0) & ~funny(X0))) [nnf transformation 35]
65. ~creative(X0) | funny(X0) [cnf transformation 27]
73. ~humble(X0) | curious(X0) | happy(X0) [cnf transformation 40]
74. ~calm(X0) | ~curious(X0) | ~kind(X0) [cnf transformation 42]
79. creative(X0) | creative(X0) [cnf transformation 29]
81. ~brave(X0) | calm(X0) | ~curious(X0) [cnf transformation 45]
86. ~quiet(john) | brave(john) | ~humble(X1) [cnf transformation 49]
89. ~brave(X0) | ~calm(X0) | happy(X0) [cnf transformation 51]
90. brave(X0) | calm(X0) [cnf transformation 51]
96. ~funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 56]
98. ~curious(X0) | quiet(X0) | kind(X0) [cnf transformation 58]
104. tall(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 60]
115. humble(john) [cnf transformation 23]
116. ~happy(X0) | tall(X0) [duplicate literal removal 104]
117. ~tall(X0) | ~funny(X0) [duplicate literal removal 96]
118. creative(X0) [duplicate literal removal 79]
120. 1 <=> humble(john) [avatar definition]
121. humble(john) <- (1) [avatar component clause 120]
148. 7 <=> quiet(john) [avatar definition]
152. 8 <=> brave(john) [avatar definition]
153. brave(john) <- (8) [avatar component clause 152]
166. 11 <=> ! [X1] : ~humble(X1) [avatar definition]
167. ~humble(X1) <- (11) [avatar component clause 166]
168. 11 | 8 | ~7 [avatar split clause 86,148,152,166]
225. 1 [avatar split clause 115,120]
226. funny(X0) [resolution 65,118]
237. curious(john) | happy(john) <- (1) [resolution 73,121]
239. 24 <=> happy(john) [avatar definition]
240. ~happy(john) <- (~24) [avatar component clause 239]
241. happy(john) <- (24) [avatar component clause 239]
243. 25 <=> curious(john) [avatar definition]
245. curious(john) <- (25) [avatar component clause 243]
246. 24 | 25 | ~1 [avatar split clause 237,120,243,239]
248. tall(john) <- (24) [resolution 241,116]
254. ~funny(john) <- (24) [resolution 248,117]
255. $false <- (24) [subsumption resolution 254,226]
256. ~24 [avatar contradiction clause 255]
259. 26 <=> kind(john) [avatar definition]
260. ~kind(john) <- (~26) [avatar component clause 259]
263. 27 <=> calm(john) [avatar definition]
265. calm(john) <- (27) [avatar component clause 263]
270. calm(X0) | ~curious(X0) | calm(X0) [resolution 81,90]
272. ~curious(X0) | calm(X0) [duplicate literal removal 270]
279. ~calm(john) | happy(john) <- (8) [resolution 89,153]
280. ~calm(john) <- (8, ~24) [subsumption resolution 279,240]
281. ~27 | ~8 | 24 [avatar split clause 280,239,152,263]
284. calm(john) <- (25) [resolution 272,245]
287. 27 | ~25 [avatar split clause 284,243,263]
291. quiet(john) | kind(john) <- (25) [resolution 98,245]
303. ~curious(john) | ~kind(john) <- (27) [resolution 265,74]
304. ~kind(john) <- (25, 27) [subsumption resolution 303,245]
307. ~26 | ~25 | ~27 [avatar split clause 304,263,243,259]
310. quiet(john) <- (25, ~26) [subsumption resolution 291,260]
311. 7 | ~25 | 26 [avatar split clause 310,259,243,148]
313. $false <- (1, 11) [resolution 167,121]
314. ~1 | ~11 [avatar contradiction clause 313]
315. $false [avatar sat refutation 168,225,246,256,281,287,307,311,314]
% SZS output end Proof for 1177369625046242699790073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not curious is generous and vice versa. Everyone who is both not patient and not happy is not brave or not rich and vice versa. If someone is both strong and not old then susan is both rich and not patient and vice versa. Everyone who is either not generous or not kind is not old. Everyone who is not brave is both not tall and not old. If someone is brave then someone is not patient or happy and vice versa. Everyone who is both generous and not funny is either kind or not quiet and vice versa. If someone is both wise and not brave then paul is either brave or not funny and vice versa. If lucy is kind then someone is humble or not generous and vice versa. If someone is both tall and happy then someone is not funny and vice versa. If lucy is not creative then lucy is not patient or funny. Everyone who is either calm or patient is not creative or not tall. If fred is either not old or kind then someone is funny or not wise. If fred is both not strong and rich then john is kind or not strong and vice versa. Everyone who is both not patient and brave is old or creative and vice versa. If someone is quiet then mary is not tall or funny. Mary is either rich or not kind. Paul is not calm. Someone is both not old and not quiet. Lucy is both not brave and not wise. Lucy is not rich or patient. Someone is both quiet and not creative. Fred is both not wise and tall. Mary is not generous. | Fred is strong. | neutral | (![X]:((~creative(X)<~>~curious(X))<=>generous(X)))&
(![X]:((~patient(X)&~happy(X))<=>(~brave(X)|~rich(X))))&
((?[X]:((strong(X)&~old(X))))<=>((rich(susan)&~patient(susan))))&
(![X]:((~generous(X)<~>~kind(X))=>~old(X)))&
(![X]:(~brave(X)=>(~tall(X)&~old(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~patient(X)|happy(X)))))&
(![X]:((generous(X)&~funny(X))<=>(kind(X)<~>~quiet(X))))&
((?[X]:((wise(X)&~brave(X))))<=>((brave(paul)<~>~funny(paul))))&
((kind(lucy))<=>(?[X]:((humble(X)|~generous(X)))))&
((?[X]:((tall(X)&happy(X))))<=>(?[X]:(~funny(X))))&
((~creative(lucy))=>((~patient(lucy)|funny(lucy))))&
(![X]:((calm(X)<~>patient(X))=>(~creative(X)|~tall(X))))&
(((~old(fred)<~>kind(fred)))=>(?[X]:((funny(X)|~wise(X)))))&
(((~strong(fred)&rich(fred)))<=>((kind(john)|~strong(john))))&
(![X]:((~patient(X)&brave(X))<=>(old(X)|creative(X))))&
((?[X]:(quiet(X)))=>((~tall(mary)|funny(mary))))&
((rich(mary)<~>~kind(mary)))&
(~calm(paul))&
(?[X]:((~old(X)&~quiet(X))))&
((~brave(lucy)&~wise(lucy)))&
((~rich(lucy)|patient(lucy)))&
(?[X]:((quiet(X)&~creative(X))))&
((~wise(fred)&tall(fred)))&
(~generous(mary)) | strong(fred) | [] | null | 0 |
Everyone who is not calm or not curious is tall or not tall.
Everyone who is either not old or humble is either humble or calm.
If someone is both not tall and not curious then susan is both not strong and happy.
If fred is not brave or not kind then someone is either tall or quiet.
Everyone who is not generous or not curious is creative or not kind and vice versa.
Everyone who is funny or not quiet is strong or happy and vice versa.
If someone is wise or not strong then someone is both calm and patient and vice versa.
If john is not calm then someone is both tall and not old and vice versa.
If someone is either strong or not rich then someone is either not creative or kind.
If lucy is both not kind and quiet then john is rich or not humble and vice versa.
Everyone who is both kind and not generous is funny or not calm.
If someone is not creative then someone is both funny and not patient and vice versa.
Everyone who is not humble is old or not old and vice versa.
Everyone who is both not humble and brave is not calm or not tall and vice versa.
If susan is not tall or tall then someone is both funny and not kind and vice versa.
Everyone who is curious is not humble or brave.
Someone is not rich or not old.
Someone is not happy.
Mary is both curious and not brave.
Fred is either patient or not wise.
John is not quiet or funny.
Someone is either not wise or not humble.
Fred is not rich. | Fred is kind. | neutral | (![X]:((~calm(X)|~curious(X))=>(tall(X)|~tall(X))))&
(![X]:((~old(X)<~>humble(X))=>(humble(X)<~>calm(X))))&
((?[X]:((~tall(X)&~curious(X))))=>((~strong(susan)&happy(susan))))&
(((~brave(fred)|~kind(fred)))=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:((~generous(X)|~curious(X))<=>(creative(X)|~kind(X))))&
(![X]:((funny(X)|~quiet(X))<=>(strong(X)|happy(X))))&
((?[X]:((wise(X)|~strong(X))))<=>(?[X]:((calm(X)&patient(X)))))&
((~calm(john))<=>(?[X]:((tall(X)&~old(X)))))&
((?[X]:((strong(X)<~>~rich(X))))=>(?[X]:((~creative(X)<~>kind(X)))))&
(((~kind(lucy)&quiet(lucy)))<=>((rich(john)|~humble(john))))&
(![X]:((kind(X)&~generous(X))=>(funny(X)|~calm(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:(~humble(X)<=>(old(X)|~old(X))))&
(![X]:((~humble(X)&brave(X))<=>(~calm(X)|~tall(X))))&
(((~tall(susan)|tall(susan)))<=>(?[X]:((funny(X)&~kind(X)))))&
(![X]:(curious(X)=>(~humble(X)|brave(X))))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:(~happy(X)))&
((curious(mary)&~brave(mary)))&
((patient(fred)<~>~wise(fred)))&
((~quiet(john)|funny(john)))&
(?[X]:((~wise(X)<~>~humble(X))))&
(~rich(fred)) | kind(fred) | [] | null | 0 |
If someone is both generous and kind then someone is both kind and not quiet. If someone is both not strong and curious then paul is wise and vice versa. Everyone who is not tall or not calm is generous or not curious and vice versa. Everyone who is either not curious or generous is either not happy or not funny. If lucy is rich then alice is funny. Everyone who is generous is not strong or rich and vice versa. If someone is not rich or not funny then mary is kind. Everyone who is quiet or not generous is not creative or happy and vice versa. Everyone who is not generous or not brave is happy and vice versa. If fred is both tall and not happy then mary is either not tall or not patient. If someone is not patient or not happy then mary is both not happy and not funny. Everyone who is either quiet or not tall is either not calm or funny. If fred is not rich then someone is funny. Everyone who is both quiet and wise is not brave. Everyone who is either not creative or kind is either rich or tall. Everyone who is humble or not quiet is not kind. Someone is either strong or not wise. Someone is not tall. Paul is curious. Fred is both not wise and patient. Susan is happy or calm. Someone is either generous or humble. Someone is either not calm or not strong. | Fred is not wise. | entailment | ((?[X]:((generous(X)&kind(X))))=>(?[X]:((kind(X)&~quiet(X)))))&
((?[X]:((~strong(X)&curious(X))))<=>(wise(paul)))&
(![X]:((~tall(X)|~calm(X))<=>(generous(X)|~curious(X))))&
(![X]:((~curious(X)<~>generous(X))=>(~happy(X)<~>~funny(X))))&
((rich(lucy))=>(funny(alice)))&
(![X]:(generous(X)<=>(~strong(X)|rich(X))))&
((?[X]:((~rich(X)|~funny(X))))=>(kind(mary)))&
(![X]:((quiet(X)|~generous(X))<=>(~creative(X)|happy(X))))&
(![X]:((~generous(X)|~brave(X))<=>happy(X)))&
(((tall(fred)&~happy(fred)))=>((~tall(mary)<~>~patient(mary))))&
((?[X]:((~patient(X)|~happy(X))))=>((~happy(mary)&~funny(mary))))&
(![X]:((quiet(X)<~>~tall(X))=>(~calm(X)<~>funny(X))))&
((~rich(fred))=>(?[X]:(funny(X))))&
(![X]:((quiet(X)&wise(X))=>~brave(X)))&
(![X]:((~creative(X)<~>kind(X))=>(rich(X)<~>tall(X))))&
(![X]:((humble(X)|~quiet(X))=>~kind(X)))&
(?[X]:((strong(X)<~>~wise(X))))&
(?[X]:(~tall(X)))&
(curious(paul))&
((~wise(fred)&patient(fred)))&
((happy(susan)|calm(susan)))&
(?[X]:((generous(X)<~>humble(X))))&
(?[X]:((~calm(X)<~>~strong(X)))) | ~wise(fred) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7826004358968871560344657
% SZS output start Proof for 7826004358968871560344657
20. patient(fred) & ~wise(fred) [input p19]
24. wise(fred) [input hypothesis]
119. ~wise(fred) [cnf transformation 20]
126. wise(fred) [cnf transformation 24]
263. $false [subsumption resolution 126,119]
% SZS output end Proof for 7826004358968871560344657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not kind then someone is either not curious or quiet.
Everyone who is calm is either curious or calm and vice versa.
Everyone who is either not creative or not kind is both patient and humble and vice versa.
Everyone who is both not calm and not kind is both old and happy and vice versa.
If susan is strong then someone is brave.
Everyone who is not funny or strong is both not tall and brave and vice versa.
If someone is not brave or not kind then fred is either happy or tall and vice versa.
If susan is not brave then someone is funny and vice versa.
Everyone who is either wise or happy is not quiet or creative and vice versa.
Everyone who is creative or curious is curious.
If susan is both creative and not quiet then alice is either not kind or not generous and vice versa.
If susan is not generous then paul is not funny.
If alice is not humble or not quiet then someone is tall or not calm and vice versa.
If someone is creative then lucy is either not strong or happy and vice versa.
If paul is not old or not calm then someone is wise.
Everyone who is both not rich and humble is not calm or kind.
Fred is either not tall or creative.
John is both not calm and not funny.
Paul is either rich or patient.
Lucy is both happy and not curious.
Someone is both not rich and not creative.
Alice is not generous. | Fred is strong. | neutral | ((?[X]:((creative(X)<~>~kind(X))))=>(?[X]:((~curious(X)<~>quiet(X)))))&
(![X]:(calm(X)<=>(curious(X)<~>calm(X))))&
(![X]:((~creative(X)<~>~kind(X))<=>(patient(X)&humble(X))))&
(![X]:((~calm(X)&~kind(X))<=>(old(X)&happy(X))))&
((strong(susan))=>(?[X]:(brave(X))))&
(![X]:((~funny(X)|strong(X))<=>(~tall(X)&brave(X))))&
((?[X]:((~brave(X)|~kind(X))))<=>((happy(fred)<~>tall(fred))))&
((~brave(susan))<=>(?[X]:(funny(X))))&
(![X]:((wise(X)<~>happy(X))<=>(~quiet(X)|creative(X))))&
(![X]:((creative(X)|curious(X))=>curious(X)))&
(((creative(susan)&~quiet(susan)))<=>((~kind(alice)<~>~generous(alice))))&
((~generous(susan))=>(~funny(paul)))&
(((~humble(alice)|~quiet(alice)))<=>(?[X]:((tall(X)|~calm(X)))))&
((?[X]:(creative(X)))<=>((~strong(lucy)<~>happy(lucy))))&
(((~old(paul)|~calm(paul)))=>(?[X]:(wise(X))))&
(![X]:((~rich(X)&humble(X))=>(~calm(X)|kind(X))))&
((~tall(fred)<~>creative(fred)))&
((~calm(john)&~funny(john)))&
((rich(paul)<~>patient(paul)))&
((happy(lucy)&~curious(lucy)))&
(?[X]:((~rich(X)&~creative(X))))&
(~generous(alice)) | strong(fred) | [] | null | 0 |
Everyone who is not old is both creative and wise and vice versa. Everyone who is not patient is not calm and vice versa. If someone is either creative or brave then someone is kind or old and vice versa. Everyone who is not old is not creative and vice versa. If someone is both not quiet and not humble then someone is humble and vice versa. If someone is not calm then someone is both not tall and wise and vice versa. Everyone who is funny or rich is not tall or not creative and vice versa. If someone is curious or not funny then paul is not humble or kind. If someone is both not old and not creative then lucy is tall and vice versa. If john is not quiet then someone is kind or not happy and vice versa. If paul is either not humble or not patient then someone is either not generous or strong. If fred is both not humble and not funny then susan is not humble. If someone is not wise then someone is not curious or wise and vice versa. If someone is either not curious or curious then alice is curious and vice versa. If someone is calm or humble then john is quiet or not creative. Someone is not generous or generous. Someone is old or not patient. Mary is strong. Someone is curious or not calm. Alice is creative. Someone is either rich or strong. | Lucy is old. | entailment | (![X]:(~old(X)<=>(creative(X)&wise(X))))&
(![X]:(~patient(X)<=>~calm(X)))&
((?[X]:((creative(X)<~>brave(X))))<=>(?[X]:((kind(X)|old(X)))))&
(![X]:(~old(X)<=>~creative(X)))&
((?[X]:((~quiet(X)&~humble(X))))<=>(?[X]:(humble(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((funny(X)|rich(X))<=>(~tall(X)|~creative(X))))&
((?[X]:((curious(X)|~funny(X))))=>((~humble(paul)|kind(paul))))&
((?[X]:((~old(X)&~creative(X))))<=>(tall(lucy)))&
((~quiet(john))<=>(?[X]:((kind(X)|~happy(X)))))&
(((~humble(paul)<~>~patient(paul)))=>(?[X]:((~generous(X)<~>strong(X)))))&
(((~humble(fred)&~funny(fred)))=>(~humble(susan)))&
((?[X]:(~wise(X)))<=>(?[X]:((~curious(X)|wise(X)))))&
((?[X]:((~curious(X)<~>curious(X))))<=>(curious(alice)))&
((?[X]:((calm(X)|humble(X))))=>((quiet(john)|~creative(john))))&
(?[X]:((~generous(X)|generous(X))))&
(?[X]:((old(X)|~patient(X))))&
(strong(mary))&
(?[X]:((curious(X)|~calm(X))))&
(creative(alice))&
(?[X]:((rich(X)<~>strong(X)))) | old(lucy) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3706110669480227081688324
% SZS output start Proof for 3706110669480227081688324
1. ! [X0] : (~old(X0) <=> (wise(X0) & creative(X0))) [input p0]
4. ! [X0] : (~old(X0) <=> ~creative(X0)) [input p3]
22. ~old(lucy) [input hypothesis]
34. ! [X0] : ((~old(X0) | (~wise(X0) | ~creative(X0))) & ((wise(X0) & creative(X0)) | old(X0))) [nnf transformation 1]
35. ! [X0] : ((~old(X0) | ~wise(X0) | ~creative(X0)) & ((wise(X0) & creative(X0)) | old(X0))) [flattening 34]
42. ! [X0] : ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))) [nnf transformation 4]
84. creative(X0) | old(X0) [cnf transformation 35]
95. ~creative(X0) | old(X0) [cnf transformation 42]
96. ~old(X0) | creative(X0) [cnf transformation 42]
136. ~old(lucy) [cnf transformation 22]
173. creative(X0) [subsumption resolution 96,84]
174. old(X0) [subsumption resolution 95,173]
339. $false [subsumption resolution 136,174]
% SZS output end Proof for 3706110669480227081688324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or humble then someone is not curious or brave.
Everyone who is both happy and funny is kind or not patient and vice versa.
Everyone who is either curious or rich is old or funny.
If someone is not strong then mary is both not funny and not happy.
If alice is not funny or funny then paul is not generous.
Everyone who is not happy is either tall or not creative and vice versa.
Everyone who is both not funny and not old is generous.
If someone is brave or humble then someone is not calm and vice versa.
If susan is not strong then fred is rich.
If paul is not kind then someone is tall and vice versa.
If someone is strong or humble then someone is quiet and vice versa.
Everyone who is both not quiet and not generous is old or generous.
Everyone who is tall or calm is both not patient and not kind and vice versa.
If john is both not quiet and not rich then susan is not curious or not strong.
Everyone who is not strong or wise is not tall.
Everyone who is either not old or rich is not quiet or funny and vice versa.
Someone is not curious or tall.
Someone is old or not strong.
Fred is not tall.
Someone is either not old or not happy.
Someone is both happy and not humble.
Someone is not wise.
Paul is either not creative or not generous.
Mary is not quiet. | Paul is not tall. | entailment | (((wise(susan)<~>humble(susan)))=>(?[X]:((~curious(X)|brave(X)))))&
(![X]:((happy(X)&funny(X))<=>(kind(X)|~patient(X))))&
(![X]:((curious(X)<~>rich(X))=>(old(X)|funny(X))))&
((?[X]:(~strong(X)))=>((~funny(mary)&~happy(mary))))&
(((~funny(alice)|funny(alice)))=>(~generous(paul)))&
(![X]:(~happy(X)<=>(tall(X)<~>~creative(X))))&
(![X]:((~funny(X)&~old(X))=>generous(X)))&
((?[X]:((brave(X)|humble(X))))<=>(?[X]:(~calm(X))))&
((~strong(susan))=>(rich(fred)))&
((~kind(paul))<=>(?[X]:(tall(X))))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&~generous(X))=>(old(X)|generous(X))))&
(![X]:((tall(X)|calm(X))<=>(~patient(X)&~kind(X))))&
(((~quiet(john)&~rich(john)))=>((~curious(susan)|~strong(susan))))&
(![X]:((~strong(X)|wise(X))=>~tall(X)))&
(![X]:((~old(X)<~>rich(X))<=>(~quiet(X)|funny(X))))&
(?[X]:((~curious(X)|tall(X))))&
(?[X]:((old(X)|~strong(X))))&
(~tall(fred))&
(?[X]:((~old(X)<~>~happy(X))))&
(?[X]:((happy(X)&~humble(X))))&
(?[X]:(~wise(X)))&
((~creative(paul)<~>~generous(paul)))&
(~quiet(mary)) | ~tall(paul) | [
"p1",
"p4",
"p5",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8710026537904499461452138
% SZS output start Proof for 8710026537904499461452138
2. ! [X0] : ((funny(X0) & happy(X0)) <=> (~patient(X0) | kind(X0))) [input p1]
5. (funny(alice) | ~funny(alice)) => ~generous(paul) [input p4]
6. ! [X0] : (~happy(X0) <=> (tall(X0) <~> ~creative(X0))) [input p5]
13. ! [X0] : ((calm(X0) | tall(X0)) <=> (~kind(X0) & ~patient(X0))) [input p12]
23. ~creative(paul) <~> ~generous(paul) [input p22]
25. tall(paul) [input hypothesis]
32. ~generous(paul) | (~funny(alice) & funny(alice)) [ennf transformation 5]
44. ! [X0] : (((funny(X0) & happy(X0)) | (patient(X0) & ~kind(X0))) & ((~patient(X0) | kind(X0)) | (~funny(X0) | ~happy(X0)))) [nnf transformation 2]
45. ! [X0] : (((funny(X0) & happy(X0)) | (patient(X0) & ~kind(X0))) & (~patient(X0) | kind(X0) | ~funny(X0) | ~happy(X0))) [flattening 44]
47. ! [X0] : ((~happy(X0) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | happy(X0))) [nnf transformation 6]
62. ! [X0] : (((calm(X0) | tall(X0)) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | (~calm(X0) & ~tall(X0)))) [nnf transformation 13]
63. ! [X0] : ((calm(X0) | tall(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | (~calm(X0) & ~tall(X0)))) [flattening 62]
77. (generous(paul) | creative(paul)) & (~generous(paul) | ~creative(paul)) [nnf transformation 23]
82. patient(X0) | happy(X0) [cnf transformation 45]
89. ~generous(paul) | funny(alice) [cnf transformation 32]
90. ~generous(paul) | ~funny(alice) [cnf transformation 32]
93. ~creative(X0) | ~happy(X0) | ~tall(X0) [cnf transformation 47]
106. ~tall(X0) | ~patient(X0) [cnf transformation 63]
129. generous(paul) | creative(paul) [cnf transformation 77]
131. tall(paul) [cnf transformation 25]
165. 8 <=> funny(alice) [avatar definition]
169. 9 <=> generous(paul) [avatar definition]
172. ~8 | ~9 [avatar split clause 90,169,165]
173. 8 | ~9 [avatar split clause 89,169,165]
283. 35 <=> creative(paul) [avatar definition]
285. creative(paul) <- (35) [avatar component clause 283]
286. 35 | 9 [avatar split clause 129,169,283]
294. ~patient(paul) [resolution 106,131]
297. happy(paul) [resolution 294,82]
313. ~happy(paul) | ~tall(paul) <- (35) [resolution 93,285]
314. ~tall(paul) <- (35) [subsumption resolution 313,297]
315. $false <- (35) [subsumption resolution 314,131]
316. ~35 [avatar contradiction clause 315]
317. $false [avatar sat refutation 172,173,286,316]
% SZS output end Proof for 8710026537904499461452138
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and generous is both funny and creative and vice versa.
Everyone who is either not curious or old is not old.
Everyone who is brave is both calm and generous.
Everyone who is both kind and not creative is both not quiet and not rich and vice versa.
Everyone who is not strong is both generous and not strong.
If someone is old or not kind then lucy is not calm or not wise and vice versa.
If paul is either strong or not patient then someone is either not tall or not happy.
If someone is old or calm then someone is old or curious and vice versa.
Everyone who is brave or creative is either not kind or creative and vice versa.
Everyone who is tall or funny is happy.
Everyone who is both not happy and generous is either not patient or kind and vice versa.
Everyone who is either kind or strong is both not patient and happy and vice versa.
Everyone who is both not strong and not rich is not creative.
If someone is not kind or not generous then someone is funny or generous and vice versa.
Everyone who is both not wise and kind is either not funny or not rich and vice versa.
If susan is not funny then someone is not tall and vice versa.
Lucy is either humble or not old.
Someone is either not creative or creative.
Someone is either brave or not old.
Someone is not generous.
Someone is both not strong and not kind.
Someone is not wise.
Someone is calm or not strong.
John is not tall or kind. | Paul is funny. | neutral | (![X]:((creative(X)&generous(X))<=>(funny(X)&creative(X))))&
(![X]:((~curious(X)<~>old(X))=>~old(X)))&
(![X]:(brave(X)=>(calm(X)&generous(X))))&
(![X]:((kind(X)&~creative(X))<=>(~quiet(X)&~rich(X))))&
(![X]:(~strong(X)=>(generous(X)&~strong(X))))&
((?[X]:((old(X)|~kind(X))))<=>((~calm(lucy)|~wise(lucy))))&
(((strong(paul)<~>~patient(paul)))=>(?[X]:((~tall(X)<~>~happy(X)))))&
((?[X]:((old(X)|calm(X))))<=>(?[X]:((old(X)|curious(X)))))&
(![X]:((brave(X)|creative(X))<=>(~kind(X)<~>creative(X))))&
(![X]:((tall(X)|funny(X))=>happy(X)))&
(![X]:((~happy(X)&generous(X))<=>(~patient(X)<~>kind(X))))&
(![X]:((kind(X)<~>strong(X))<=>(~patient(X)&happy(X))))&
(![X]:((~strong(X)&~rich(X))=>~creative(X)))&
((?[X]:((~kind(X)|~generous(X))))<=>(?[X]:((funny(X)|generous(X)))))&
(![X]:((~wise(X)&kind(X))<=>(~funny(X)<~>~rich(X))))&
((~funny(susan))<=>(?[X]:(~tall(X))))&
((humble(lucy)<~>~old(lucy)))&
(?[X]:((~creative(X)<~>creative(X))))&
(?[X]:((brave(X)<~>~old(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~strong(X)&~kind(X))))&
(?[X]:(~wise(X)))&
(?[X]:((calm(X)|~strong(X))))&
((~tall(john)|kind(john))) | funny(paul) | [] | null | 0 |
Everyone who is either not wise or kind is both creative and calm and vice versa.
If someone is both wise and calm then someone is both kind and not brave.
Everyone who is not kind or kind is either calm or tall.
Everyone who is both creative and strong is quiet or patient and vice versa.
Everyone who is either quiet or humble is not rich or patient and vice versa.
Everyone who is both not tall and funny is not old or curious and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
Alice is both calm and not tall.
Susan is not funny or funny.
Someone is both not tall and not wise.
Susan is either not generous or rich.
Fred is either rich or curious. | Susan is creative. | neutral | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((wise(X)&calm(X))))=>(?[X]:((kind(X)&~brave(X)))))&
(![X]:((~kind(X)|kind(X))=>(calm(X)<~>tall(X))))&
(![X]:((creative(X)&strong(X))<=>(quiet(X)|patient(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~rich(X)|patient(X))))&
(![X]:((~tall(X)&funny(X))<=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X))))&
((~generous(susan)<~>rich(susan)))&
((rich(fred)<~>curious(fred))) | creative(susan) | [] | null | 0 |
Everyone who is not calm is not generous or patient and vice versa.
Everyone who is funny or not strong is both not generous and brave and vice versa.
Everyone who is either brave or not wise is both not patient and humble.
Everyone who is not wise or not old is not strong.
If susan is either not old or not generous then alice is either calm or wise and vice versa.
Everyone who is generous or not rich is either not kind or happy and vice versa.
If someone is both curious and not generous then susan is both wise and not humble.
If someone is kind or curious then mary is brave or creative.
Everyone who is both creative and not strong is either not brave or rich and vice versa.
If alice is either not kind or rich then someone is either tall or not happy.
If alice is either not rich or not quiet then lucy is not rich.
If someone is strong or not kind then someone is wise or not funny and vice versa.
Everyone who is not brave or creative is either not funny or not wise and vice versa.
If someone is either brave or old then someone is either not rich or calm and vice versa.
Everyone who is either not old or curious is not rich.
If someone is wise then mary is both patient and wise.
Someone is both not kind and strong.
Fred is creative.
Fred is wise or generous.
John is humble or brave.
Someone is not strong or not patient.
Susan is both not kind and rich.
Someone is either strong or not patient.
Fred is either curious or kind. | Susan is curious. | contradiction | (![X]:(~calm(X)<=>(~generous(X)|patient(X))))&
(![X]:((funny(X)|~strong(X))<=>(~generous(X)&brave(X))))&
(![X]:((brave(X)<~>~wise(X))=>(~patient(X)&humble(X))))&
(![X]:((~wise(X)|~old(X))=>~strong(X)))&
(((~old(susan)<~>~generous(susan)))<=>((calm(alice)<~>wise(alice))))&
(![X]:((generous(X)|~rich(X))<=>(~kind(X)<~>happy(X))))&
((?[X]:((curious(X)&~generous(X))))=>((wise(susan)&~humble(susan))))&
((?[X]:((kind(X)|curious(X))))=>((brave(mary)|creative(mary))))&
(![X]:((creative(X)&~strong(X))<=>(~brave(X)<~>rich(X))))&
(((~kind(alice)<~>rich(alice)))=>(?[X]:((tall(X)<~>~happy(X)))))&
(((~rich(alice)<~>~quiet(alice)))=>(~rich(lucy)))&
((?[X]:((strong(X)|~kind(X))))<=>(?[X]:((wise(X)|~funny(X)))))&
(![X]:((~brave(X)|creative(X))<=>(~funny(X)<~>~wise(X))))&
((?[X]:((brave(X)<~>old(X))))<=>(?[X]:((~rich(X)<~>calm(X)))))&
(![X]:((~old(X)<~>curious(X))=>~rich(X)))&
((?[X]:(wise(X)))=>((patient(mary)&wise(mary))))&
(?[X]:((~kind(X)&strong(X))))&
(creative(fred))&
((wise(fred)|generous(fred)))&
((humble(john)|brave(john)))&
(?[X]:((~strong(X)|~patient(X))))&
((~kind(susan)&rich(susan)))&
(?[X]:((strong(X)<~>~patient(X))))&
((curious(fred)<~>kind(fred))) | curious(susan) | [
"p1",
"p2",
"p3",
"p6",
"p8",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2606328986145491138469005
% SZS output start Proof for 2606328986145491138469005
2. ! [X0] : ((~strong(X0) | funny(X0)) <=> (brave(X0) & ~generous(X0))) [input p1]
3. ! [X0] : ((brave(X0) <~> ~wise(X0)) => (humble(X0) & ~patient(X0))) [input p2]
4. ! [X0] : ((~old(X0) | ~wise(X0)) => ~strong(X0)) [input p3]
7. ? [X0] : (~generous(X0) & curious(X0)) => (~humble(susan) & wise(susan)) [input p6]
9. ! [X0] : ((~strong(X0) & creative(X0)) <=> (~brave(X0) <~> rich(X0))) [input p8]
15. ! [X0] : ((~old(X0) <~> curious(X0)) => ~rich(X0)) [input p14]
22. rich(susan) & ~kind(susan) [input p21]
25. curious(susan) [input hypothesis]
28. ! [X0] : ((humble(X0) & ~patient(X0)) | (brave(X0) <=> ~wise(X0))) [ennf transformation 3]
29. ! [X0] : (~strong(X0) | (old(X0) & wise(X0))) [ennf transformation 4]
30. (~humble(susan) & wise(susan)) | ! [X0] : (generous(X0) | ~curious(X0)) [ennf transformation 7]
35. ! [X0] : (~rich(X0) | (~old(X0) <=> curious(X0))) [ennf transformation 15]
39. ! [X0] : (((~strong(X0) | funny(X0)) | (~brave(X0) | generous(X0))) & ((brave(X0) & ~generous(X0)) | (strong(X0) & ~funny(X0)))) [nnf transformation 2]
40. ! [X0] : ((~strong(X0) | funny(X0) | ~brave(X0) | generous(X0)) & ((brave(X0) & ~generous(X0)) | (strong(X0) & ~funny(X0)))) [flattening 39]
41. ! [X0] : ((humble(X0) & ~patient(X0)) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0)))) [nnf transformation 28]
45. ! [X0] : (((~strong(X0) & creative(X0)) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) & (((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | (strong(X0) | ~creative(X0)))) [nnf transformation 9]
46. ! [X0] : (((~strong(X0) & creative(X0)) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) & (((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | strong(X0) | ~creative(X0))) [flattening 45]
63. ! [X0] : (~rich(X0) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) [nnf transformation 35]
76. ~generous(X0) | strong(X0) [cnf transformation 40]
78. brave(X0) | strong(X0) [cnf transformation 40]
82. ~wise(X0) | humble(X0) | ~brave(X0) [cnf transformation 41]
85. ~strong(X0) | old(X0) [cnf transformation 29]
100. wise(susan) | generous(X0) | ~curious(X0) [cnf transformation 30]
101. ~humble(susan) | generous(X0) | ~curious(X0) [cnf transformation 30]
109. ~rich(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 46]
135. ~curious(X0) | ~old(X0) | ~rich(X0) [cnf transformation 63]
145. rich(susan) [cnf transformation 22]
150. curious(susan) [cnf transformation 25]
160. 3 <=> old(susan) [avatar definition]
164. 4 <=> generous(susan) [avatar definition]
165. ~generous(susan) <- (~4) [avatar component clause 164]
166. generous(susan) <- (4) [avatar component clause 164]
176. 5 <=> ! [X0] : (generous(X0) | ~curious(X0)) [avatar definition]
177. ~curious(X0) | generous(X0) <- (5) [avatar component clause 176]
179. 6 <=> humble(susan) [avatar definition]
182. 5 | ~6 [avatar split clause 101,179,176]
184. 7 <=> wise(susan) [avatar definition]
186. wise(susan) <- (7) [avatar component clause 184]
187. 5 | 7 [avatar split clause 100,184,176]
368. generous(susan) <- (5) [resolution 177,150]
370. $false <- (~4, 5) [subsumption resolution 368,165]
371. 4 | ~5 [avatar contradiction clause 370]
383. 46 <=> brave(susan) [avatar definition]
385. ~brave(susan) <- (~46) [avatar component clause 383]
416. humble(susan) | ~brave(susan) <- (7) [resolution 82,186]
432. strong(susan) <- (~46) [resolution 385,78]
438. old(susan) <- (~46) [resolution 432,85]
442. 3 | 46 [avatar split clause 438,383,160]
444. strong(susan) <- (4) [resolution 166,76]
449. ~brave(susan) | ~strong(susan) [resolution 109,145]
461. ~old(susan) | ~rich(susan) [resolution 135,150]
467. ~old(susan) [subsumption resolution 461,145]
468. ~3 [avatar split clause 467,160]
469. ~46 | 6 | ~7 [avatar split clause 416,184,179,383]
471. 54 <=> strong(susan) [avatar definition]
474. ~54 | ~46 [avatar split clause 449,383,471]
480. 54 | ~4 [avatar split clause 444,164,471]
481. $false [avatar sat refutation 182,187,371,442,468,469,474,480]
% SZS output end Proof for 2606328986145491138469005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.046 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not rich and vice versa.
If mary is patient or not happy then someone is both not patient and patient and vice versa.
Everyone who is generous is rich.
If someone is happy then someone is both humble and not rich.
If someone is not patient or calm then alice is either not rich or not calm.
If someone is both generous and not wise then someone is not strong or strong and vice versa.
If someone is both calm and curious then someone is wise and vice versa.
If mary is either brave or creative then susan is both not wise and not funny and vice versa.
If lucy is both not calm and not humble then alice is not kind and vice versa.
Everyone who is either brave or not old is quiet and vice versa.
If john is both happy and rich then someone is not humble or funny and vice versa.
If paul is not funny or creative then alice is both not curious and not strong and vice versa.
Everyone who is quiet or wise is not quiet or not funny.
If john is kind then susan is calm or not humble and vice versa.
Everyone who is either funny or strong is tall.
Someone is either not patient or humble.
John is both creative and not generous.
Mary is not funny.
John is both creative and not happy.
Paul is either not tall or generous.
Paul is either creative or rich.
Lucy is both brave and not patient.
Paul is either quiet or not funny. | Alice is not strong. | entailment | (![X]:(~patient(X)<=>~rich(X)))&
(((patient(mary)|~happy(mary)))<=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:(generous(X)=>rich(X)))&
((?[X]:(happy(X)))=>(?[X]:((humble(X)&~rich(X)))))&
((?[X]:((~patient(X)|calm(X))))=>((~rich(alice)<~>~calm(alice))))&
((?[X]:((generous(X)&~wise(X))))<=>(?[X]:((~strong(X)|strong(X)))))&
((?[X]:((calm(X)&curious(X))))<=>(?[X]:(wise(X))))&
(((brave(mary)<~>creative(mary)))<=>((~wise(susan)&~funny(susan))))&
(((~calm(lucy)&~humble(lucy)))<=>(~kind(alice)))&
(![X]:((brave(X)<~>~old(X))<=>quiet(X)))&
(((happy(john)&rich(john)))<=>(?[X]:((~humble(X)|funny(X)))))&
(((~funny(paul)|creative(paul)))<=>((~curious(alice)&~strong(alice))))&
(![X]:((quiet(X)|wise(X))=>(~quiet(X)|~funny(X))))&
((kind(john))<=>((calm(susan)|~humble(susan))))&
(![X]:((funny(X)<~>strong(X))=>tall(X)))&
(?[X]:((~patient(X)<~>humble(X))))&
((creative(john)&~generous(john)))&
(~funny(mary))&
((creative(john)&~happy(john)))&
((~tall(paul)<~>generous(paul)))&
((creative(paul)<~>rich(paul)))&
((brave(lucy)&~patient(lucy)))&
((quiet(paul)<~>~funny(paul))) | ~strong(alice) | [
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 946534684011364549609183
% SZS output start Proof for 946534684011364549609183
12. (creative(paul) | ~funny(paul)) <=> (~strong(alice) & ~curious(alice)) [input p11]
13. ! [X0] : ((wise(X0) | quiet(X0)) => (~funny(X0) | ~quiet(X0))) [input p12]
23. quiet(paul) <~> ~funny(paul) [input p22]
24. strong(alice) [input hypothesis]
31. ! [X0] : ((~funny(X0) | ~quiet(X0)) | (~wise(X0) & ~quiet(X0))) [ennf transformation 13]
32. ! [X0] : (~funny(X0) | ~quiet(X0) | (~wise(X0) & ~quiet(X0))) [flattening 31]
64. ((creative(paul) | ~funny(paul)) | (strong(alice) | curious(alice))) & ((~strong(alice) & ~curious(alice)) | (~creative(paul) & funny(paul))) [nnf transformation 12]
65. (creative(paul) | ~funny(paul) | strong(alice) | curious(alice)) & ((~strong(alice) & ~curious(alice)) | (~creative(paul) & funny(paul))) [flattening 64]
74. (funny(paul) | ~quiet(paul)) & (~funny(paul) | quiet(paul)) [nnf transformation 23]
117. ~strong(alice) | funny(paul) [cnf transformation 65]
120. ~funny(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 32]
140. ~funny(paul) | quiet(paul) [cnf transformation 74]
141. funny(paul) | ~quiet(paul) [cnf transformation 74]
142. strong(alice) [cnf transformation 24]
143. ~funny(X0) | ~quiet(X0) [duplicate literal removal 120]
299. 34 <=> strong(alice) [avatar definition]
303. 35 <=> funny(paul) [avatar definition]
312. 35 | ~34 [avatar split clause 117,299,303]
357. ~quiet(paul) [subsumption resolution 141,143]
358. ~funny(paul) [subsumption resolution 140,357]
359. ~35 [avatar split clause 358,303]
360. 34 [avatar split clause 142,299]
361. $false [avatar sat refutation 312,359,360]
% SZS output end Proof for 946534684011364549609183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and not funny then alice is either humble or not calm and vice versa.
Everyone who is not tall or patient is not brave or humble and vice versa.
If lucy is either not kind or not rich then susan is tall and vice versa.
If someone is not patient or quiet then someone is not happy or not brave and vice versa.
Everyone who is not happy is both not brave and not rich and vice versa.
Everyone who is not old or not kind is not strong.
If lucy is not patient or not humble then paul is both humble and happy.
If someone is either brave or not rich then someone is not rich or not old.
If someone is either not creative or not tall then someone is not old and vice versa.
If mary is both kind and not creative then someone is both tall and wise and vice versa.
If someone is not generous or patient then john is patient or not wise and vice versa.
Everyone who is both funny and not rich is humble.
If fred is either humble or brave then someone is not tall or old and vice versa.
Everyone who is both wise and happy is both strong and calm.
Everyone who is both kind and not brave is both kind and not patient and vice versa.
Everyone who is both not funny and not rich is either brave or happy and vice versa.
Someone is either happy or calm.
Paul is calm.
Someone is both kind and quiet.
Paul is wise.
Mary is tall or strong.
Paul is both not generous and funny.
Alice is both generous and not curious.
Someone is patient. | Susan is not happy. | neutral | ((?[X]:((rich(X)&~funny(X))))<=>((humble(alice)<~>~calm(alice))))&
(![X]:((~tall(X)|patient(X))<=>(~brave(X)|humble(X))))&
(((~kind(lucy)<~>~rich(lucy)))<=>(tall(susan)))&
((?[X]:((~patient(X)|quiet(X))))<=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:(~happy(X)<=>(~brave(X)&~rich(X))))&
(![X]:((~old(X)|~kind(X))=>~strong(X)))&
(((~patient(lucy)|~humble(lucy)))=>((humble(paul)&happy(paul))))&
((?[X]:((brave(X)<~>~rich(X))))=>(?[X]:((~rich(X)|~old(X)))))&
((?[X]:((~creative(X)<~>~tall(X))))<=>(?[X]:(~old(X))))&
(((kind(mary)&~creative(mary)))<=>(?[X]:((tall(X)&wise(X)))))&
((?[X]:((~generous(X)|patient(X))))<=>((patient(john)|~wise(john))))&
(![X]:((funny(X)&~rich(X))=>humble(X)))&
(((humble(fred)<~>brave(fred)))<=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((wise(X)&happy(X))=>(strong(X)&calm(X))))&
(![X]:((kind(X)&~brave(X))<=>(kind(X)&~patient(X))))&
(![X]:((~funny(X)&~rich(X))<=>(brave(X)<~>happy(X))))&
(?[X]:((happy(X)<~>calm(X))))&
(calm(paul))&
(?[X]:((kind(X)&quiet(X))))&
(wise(paul))&
((tall(mary)|strong(mary)))&
((~generous(paul)&funny(paul)))&
((generous(alice)&~curious(alice)))&
(?[X]:(patient(X))) | ~happy(susan) | [] | null | 0 |
Everyone who is not funny is not brave.
Everyone who is both not tall and happy is either not funny or generous and vice versa.
Everyone who is either not old or not strong is either curious or not rich and vice versa.
Everyone who is either not humble or patient is funny.
If fred is not humble or not kind then fred is not rich or wise and vice versa.
If someone is both not old and not tall then alice is not old and vice versa.
If paul is either happy or funny then someone is tall or generous.
Everyone who is both generous and not rich is either not generous or not curious and vice versa.
If paul is either not generous or not curious then someone is humble or not happy and vice versa.
If fred is not quiet or old then someone is not old or funny and vice versa.
Everyone who is either patient or funny is both not curious and not quiet.
If fred is either not kind or old then someone is both tall and not rich and vice versa.
Everyone who is both funny and rich is either rich or not happy.
Everyone who is happy or not curious is strong.
Everyone who is humble is brave or tall.
Everyone who is both strong and not old is not happy or not brave and vice versa.
Susan is both brave and not quiet.
Someone is either not tall or humble.
Someone is both patient and creative.
Someone is tall.
Alice is both not funny and quiet.
Someone is happy or brave.
Someone is not brave. | Paul is not curious. | entailment | (![X]:(~funny(X)=>~brave(X)))&
(![X]:((~tall(X)&happy(X))<=>(~funny(X)<~>generous(X))))&
(![X]:((~old(X)<~>~strong(X))<=>(curious(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>patient(X))=>funny(X)))&
(((~humble(fred)|~kind(fred)))<=>((~rich(fred)|wise(fred))))&
((?[X]:((~old(X)&~tall(X))))<=>(~old(alice)))&
(((happy(paul)<~>funny(paul)))=>(?[X]:((tall(X)|generous(X)))))&
(![X]:((generous(X)&~rich(X))<=>(~generous(X)<~>~curious(X))))&
(((~generous(paul)<~>~curious(paul)))<=>(?[X]:((humble(X)|~happy(X)))))&
(((~quiet(fred)|old(fred)))<=>(?[X]:((~old(X)|funny(X)))))&
(![X]:((patient(X)<~>funny(X))=>(~curious(X)&~quiet(X))))&
(((~kind(fred)<~>old(fred)))<=>(?[X]:((tall(X)&~rich(X)))))&
(![X]:((funny(X)&rich(X))=>(rich(X)<~>~happy(X))))&
(![X]:((happy(X)|~curious(X))=>strong(X)))&
(![X]:(humble(X)=>(brave(X)|tall(X))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~brave(X))))&
((brave(susan)&~quiet(susan)))&
(?[X]:((~tall(X)<~>humble(X))))&
(?[X]:((patient(X)&creative(X))))&
(?[X]:(tall(X)))&
((~funny(alice)&quiet(alice)))&
(?[X]:((happy(X)|brave(X))))&
(?[X]:(~brave(X))) | ~curious(paul) | [
"p3",
"p7",
"p8",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4191862969487806737271986
% SZS output start Proof for 4191862969487806737271986
4. ! [X0] : ((~humble(X0) <~> patient(X0)) => funny(X0)) [input p3]
8. ! [X0] : ((~rich(X0) & generous(X0)) <=> (~generous(X0) <~> ~curious(X0))) [input p7]
9. (~generous(paul) <~> ~curious(paul)) <=> ? [X0] : (~happy(X0) | humble(X0)) [input p8]
11. ! [X0] : ((patient(X0) <~> funny(X0)) => (~quiet(X0) & ~curious(X0))) [input p10]
21. quiet(alice) & ~funny(alice) [input p20]
24. curious(paul) [input hypothesis]
27. ! [X0] : (funny(X0) | (~humble(X0) <=> patient(X0))) [ennf transformation 4]
29. ! [X0] : ((~quiet(X0) & ~curious(X0)) | (patient(X0) <=> funny(X0))) [ennf transformation 11]
38. ! [X0] : (funny(X0) | ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0)))) [nnf transformation 27]
48. ! [X0] : (((~rich(X0) & generous(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (rich(X0) | ~generous(X0)))) [nnf transformation 8]
49. ! [X0] : (((~rich(X0) & generous(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | rich(X0) | ~generous(X0))) [flattening 48]
50. (((curious(paul) | generous(paul)) & (~curious(paul) | ~generous(paul))) | ! [X0] : (happy(X0) & ~humble(X0))) & (? [X0] : (~happy(X0) | humble(X0)) | ((~generous(paul) | curious(paul)) & (~curious(paul) | generous(paul)))) [nnf transformation 9]
51. (((curious(paul) | generous(paul)) & (~curious(paul) | ~generous(paul))) | ! [X0] : (happy(X0) & ~humble(X0))) & (? [X1] : (~happy(X1) | humble(X1)) | ((~generous(paul) | curious(paul)) & (~curious(paul) | generous(paul)))) [rectify 50]
52. ? [X1] : (~happy(X1) | humble(X1)) => (~happy(sK2) | humble(sK2)) [choice axiom]
53. (((curious(paul) | generous(paul)) & (~curious(paul) | ~generous(paul))) | ! [X0] : (happy(X0) & ~humble(X0))) & ((~happy(sK2) | humble(sK2)) | ((~generous(paul) | curious(paul)) & (~curious(paul) | generous(paul)))) [skolemisation 51,52]
59. ! [X0] : ((~quiet(X0) & ~curious(X0)) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0)))) [nnf transformation 29]
93. patient(X0) | funny(X0) | humble(X0) [cnf transformation 38]
106. generous(X0) | ~curious(X0) | generous(X0) [cnf transformation 49]
112. ~curious(paul) | ~generous(paul) | ~humble(X0) [cnf transformation 53]
122. ~quiet(X0) | funny(X0) | ~patient(X0) [cnf transformation 59]
146. ~funny(alice) [cnf transformation 21]
147. quiet(alice) [cnf transformation 21]
150. curious(paul) [cnf transformation 24]
153. ~curious(X0) | generous(X0) [duplicate literal removal 106]
222. 15 <=> ! [X0] : ~humble(X0) [avatar definition]
223. ~humble(X0) <- (15) [avatar component clause 222]
227. 16 <=> curious(paul) [avatar definition]
231. ~curious(paul) | ~humble(X0) [subsumption resolution 112,153]
232. 15 | ~16 [avatar split clause 231,227,222]
306. 16 [avatar split clause 150,227]
377. funny(alice) | ~patient(alice) [resolution 122,147]
378. ~patient(alice) [subsumption resolution 377,146]
379. funny(alice) | humble(alice) [resolution 378,93]
380. humble(alice) [subsumption resolution 379,146]
381. $false <- (15) [subsumption resolution 380,223]
382. ~15 [avatar contradiction clause 381]
383. $false [avatar sat refutation 232,306,382]
% SZS output end Proof for 4191862969487806737271986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or old is both patient and generous and vice versa.
Everyone who is either strong or not rich is generous or brave.
Everyone who is patient is either not strong or quiet and vice versa.
If john is strong or wise then someone is old or not patient and vice versa.
If mary is not wise then mary is not humble and vice versa.
Everyone who is not wise is either not tall or not humble.
Everyone who is both not old and not brave is creative or not tall and vice versa.
Everyone who is strong or creative is both not quiet and funny.
Everyone who is both not patient and not creative is not wise.
If someone is humble or not generous then susan is wise or not calm.
Everyone who is creative is both generous and not patient.
Everyone who is either funny or curious is not creative or not kind and vice versa.
If someone is rich or not strong then john is both strong and not funny and vice versa.
If lucy is old or rich then fred is both tall and brave and vice versa.
If lucy is calm or tall then someone is both strong and brave and vice versa.
Everyone who is not kind or not curious is both kind and not happy and vice versa.
Lucy is not old.
Someone is either happy or not funny.
Someone is either quiet or not old.
Someone is not strong or not tall.
Someone is not quiet or not kind. | Mary is not strong. | contradiction | (![X]:((~strong(X)<~>old(X))<=>(patient(X)&generous(X))))&
(![X]:((strong(X)<~>~rich(X))=>(generous(X)|brave(X))))&
(![X]:(patient(X)<=>(~strong(X)<~>quiet(X))))&
(((strong(john)|wise(john)))<=>(?[X]:((old(X)|~patient(X)))))&
((~wise(mary))<=>(~humble(mary)))&
(![X]:(~wise(X)=>(~tall(X)<~>~humble(X))))&
(![X]:((~old(X)&~brave(X))<=>(creative(X)|~tall(X))))&
(![X]:((strong(X)|creative(X))=>(~quiet(X)&funny(X))))&
(![X]:((~patient(X)&~creative(X))=>~wise(X)))&
((?[X]:((humble(X)|~generous(X))))=>((wise(susan)|~calm(susan))))&
(![X]:(creative(X)=>(generous(X)&~patient(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((rich(X)|~strong(X))))<=>((strong(john)&~funny(john))))&
(((old(lucy)|rich(lucy)))<=>((tall(fred)&brave(fred))))&
(((calm(lucy)|tall(lucy)))<=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(kind(X)&~happy(X))))&
(~old(lucy))&
(?[X]:((happy(X)<~>~funny(X))))&
(?[X]:((quiet(X)<~>~old(X))))&
(?[X]:((~strong(X)|~tall(X))))&
(?[X]:((~quiet(X)|~kind(X)))) | ~strong(mary) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 339187144628370973636212
% SZS output start Proof for 339187144628370973636212
8. ! [X0] : ((creative(X0) | strong(X0)) => (funny(X0) & ~quiet(X0))) [input p7]
13. ? [X0] : (~strong(X0) | rich(X0)) <=> (~funny(john) & strong(john)) [input p12]
22. ~strong(mary) [input hypothesis]
26. ! [X0] : ((funny(X0) & ~quiet(X0)) | (~creative(X0) & ~strong(X0))) [ennf transformation 8]
47. (? [X0] : (~strong(X0) | rich(X0)) | (funny(john) | ~strong(john))) & ((~funny(john) & strong(john)) | ! [X0] : (strong(X0) & ~rich(X0))) [nnf transformation 13]
48. (? [X0] : (~strong(X0) | rich(X0)) | funny(john) | ~strong(john)) & ((~funny(john) & strong(john)) | ! [X0] : (strong(X0) & ~rich(X0))) [flattening 47]
49. (? [X0] : (~strong(X0) | rich(X0)) | funny(john) | ~strong(john)) & ((~funny(john) & strong(john)) | ! [X1] : (strong(X1) & ~rich(X1))) [rectify 48]
50. ? [X0] : (~strong(X0) | rich(X0)) => (~strong(sK1) | rich(sK1)) [choice axiom]
51. ((~strong(sK1) | rich(sK1)) | funny(john) | ~strong(john)) & ((~funny(john) & strong(john)) | ! [X1] : (strong(X1) & ~rich(X1))) [skolemisation 49,50]
98. ~strong(X0) | funny(X0) [cnf transformation 26]
112. strong(john) | strong(X1) [cnf transformation 51]
114. ~funny(john) | strong(X1) [cnf transformation 51]
138. ~strong(mary) [cnf transformation 22]
145. 2 <=> strong(john) [avatar definition]
147. strong(john) <- (2) [avatar component clause 145]
196. 13 <=> ! [X1] : strong(X1) [avatar definition]
197. strong(X1) <- (13) [avatar component clause 196]
199. 14 <=> funny(john) [avatar definition]
202. 13 | ~14 [avatar split clause 114,199,196]
207. 13 | 2 [avatar split clause 112,145,196]
286. funny(john) <- (2) [resolution 98,147]
289. 14 | ~2 [avatar split clause 286,145,199]
290. $false <- (13) [resolution 197,138]
294. ~13 [avatar contradiction clause 290]
295. $false [avatar sat refutation 202,207,289,294]
% SZS output end Proof for 339187144628370973636212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or generous is both not quiet and curious and vice versa.
Everyone who is not wise is wise or not strong and vice versa.
Everyone who is not creative or strong is either strong or rich and vice versa.
Everyone who is happy or not kind is both not happy and quiet and vice versa.
Everyone who is either not old or happy is both not funny and not tall.
Everyone who is both not kind and funny is both creative and not tall and vice versa.
If someone is old then someone is both not creative and generous and vice versa.
Everyone who is old is creative or tall.
Everyone who is both not old and not calm is curious or tall and vice versa.
Everyone who is funny is kind or funny and vice versa.
If mary is either calm or generous then someone is both generous and creative and vice versa.
If alice is not wise then alice is not curious or kind.
If someone is both not brave and not old then paul is calm or not quiet and vice versa.
If susan is not strong or not rich then fred is not brave.
If susan is not curious or not humble then someone is both not generous and not curious and vice versa.
Mary is brave or not strong.
Fred is both not patient and curious.
Alice is not creative.
Someone is either generous or not humble. | Alice is strong. | contradiction | (![X]:((funny(X)|generous(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~wise(X)<=>(wise(X)|~strong(X))))&
(![X]:((~creative(X)|strong(X))<=>(strong(X)<~>rich(X))))&
(![X]:((happy(X)|~kind(X))<=>(~happy(X)&quiet(X))))&
(![X]:((~old(X)<~>happy(X))=>(~funny(X)&~tall(X))))&
(![X]:((~kind(X)&funny(X))<=>(creative(X)&~tall(X))))&
((?[X]:(old(X)))<=>(?[X]:((~creative(X)&generous(X)))))&
(![X]:(old(X)=>(creative(X)|tall(X))))&
(![X]:((~old(X)&~calm(X))<=>(curious(X)|tall(X))))&
(![X]:(funny(X)<=>(kind(X)|funny(X))))&
(((calm(mary)<~>generous(mary)))<=>(?[X]:((generous(X)&creative(X)))))&
((~wise(alice))=>((~curious(alice)|kind(alice))))&
((?[X]:((~brave(X)&~old(X))))<=>((calm(paul)|~quiet(paul))))&
(((~strong(susan)|~rich(susan)))=>(~brave(fred)))&
(((~curious(susan)|~humble(susan)))<=>(?[X]:((~generous(X)&~curious(X)))))&
((brave(mary)|~strong(mary)))&
((~patient(fred)&curious(fred)))&
(~creative(alice))&
(?[X]:((generous(X)<~>~humble(X)))) | strong(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 4607096616837779496299740
% SZS output start Proof for 4607096616837779496299740
2. ! [X0] : (~wise(X0) <=> (~strong(X0) | wise(X0))) [input p1]
20. strong(alice) [input hypothesis]
31. ! [X0] : ((~wise(X0) | (strong(X0) & ~wise(X0))) & ((~strong(X0) | wise(X0)) | wise(X0))) [nnf transformation 2]
32. ! [X0] : ((~wise(X0) | (strong(X0) & ~wise(X0))) & (~strong(X0) | wise(X0) | wise(X0))) [flattening 31]
71. ~strong(X0) | wise(X0) | wise(X0) [cnf transformation 32]
72. ~wise(X0) | ~wise(X0) [cnf transformation 32]
129. strong(alice) [cnf transformation 20]
134. ~strong(X0) | wise(X0) [duplicate literal removal 71]
135. ~wise(X0) [duplicate literal removal 72]
136. ~strong(X0) [subsumption resolution 134,135]
269. $false [subsumption resolution 129,136]
% SZS output end Proof for 4607096616837779496299740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is not happy. If paul is not curious then someone is creative or not generous. If someone is either not wise or not curious then susan is quiet or kind. Everyone who is happy is not curious. If susan is humble then someone is not generous and vice versa. Everyone who is not wise is either not kind or generous. Everyone who is both calm and not kind is both rich and kind and vice versa. If someone is either creative or funny then paul is either not brave or not kind. Everyone who is not calm or kind is either not generous or humble. Everyone who is either not brave or not curious is either happy or humble. Everyone who is not wise is rich and vice versa. Everyone who is either calm or brave is not wise or not old. Everyone who is patient is old. Everyone who is rich or not funny is funny. If someone is both creative and not tall then paul is either patient or not patient and vice versa. Everyone who is both funny and not humble is not quiet or not funny. John is kind or not kind. John is strong or not brave. Someone is either calm or rich. Someone is either humble or quiet. Susan is not rich or kind. Paul is calm or not strong. Alice is both generous and calm. Susan is strong or calm. | John is brave. | neutral | (![X]:(~quiet(X)=>~happy(X)))&
((~curious(paul))=>(?[X]:((creative(X)|~generous(X)))))&
((?[X]:((~wise(X)<~>~curious(X))))=>((quiet(susan)|kind(susan))))&
(![X]:(happy(X)=>~curious(X)))&
((humble(susan))<=>(?[X]:(~generous(X))))&
(![X]:(~wise(X)=>(~kind(X)<~>generous(X))))&
(![X]:((calm(X)&~kind(X))<=>(rich(X)&kind(X))))&
((?[X]:((creative(X)<~>funny(X))))=>((~brave(paul)<~>~kind(paul))))&
(![X]:((~calm(X)|kind(X))=>(~generous(X)<~>humble(X))))&
(![X]:((~brave(X)<~>~curious(X))=>(happy(X)<~>humble(X))))&
(![X]:(~wise(X)<=>rich(X)))&
(![X]:((calm(X)<~>brave(X))=>(~wise(X)|~old(X))))&
(![X]:(patient(X)=>old(X)))&
(![X]:((rich(X)|~funny(X))=>funny(X)))&
((?[X]:((creative(X)&~tall(X))))<=>((patient(paul)<~>~patient(paul))))&
(![X]:((funny(X)&~humble(X))=>(~quiet(X)|~funny(X))))&
((kind(john)|~kind(john)))&
((strong(john)|~brave(john)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((humble(X)<~>quiet(X))))&
((~rich(susan)|kind(susan)))&
((calm(paul)|~strong(paul)))&
((generous(alice)&calm(alice)))&
((strong(susan)|calm(susan))) | brave(john) | [] | null | 0 |
Everyone who is humble or not funny is not brave or curious. If someone is quiet then fred is not rich and vice versa. If someone is not happy then someone is rich or funny. Everyone who is patient or not brave is both curious and not wise and vice versa. Everyone who is either not funny or rich is rich or not patient. Everyone who is both not happy and not tall is kind or not patient and vice versa. Everyone who is either not old or not wise is brave and vice versa. Everyone who is not humble is not rich. Everyone who is quiet or not funny is both not kind and kind and vice versa. If someone is not old then fred is happy. If someone is calm then someone is either wise or not quiet and vice versa. Everyone who is not brave or funny is either happy or not generous and vice versa. Everyone who is both happy and generous is not tall or not humble and vice versa. If mary is either not wise or quiet then someone is not old or not humble and vice versa. Everyone who is rich is not generous and vice versa. Someone is either not rich or curious. Someone is patient. Someone is wise or not calm. Someone is either old or kind. Alice is tall or not kind. Lucy is not creative or not happy. Paul is not calm. | Mary is not wise. | entailment | (![X]:((humble(X)|~funny(X))=>(~brave(X)|curious(X))))&
((?[X]:(quiet(X)))<=>(~rich(fred)))&
((?[X]:(~happy(X)))=>(?[X]:((rich(X)|funny(X)))))&
(![X]:((patient(X)|~brave(X))<=>(curious(X)&~wise(X))))&
(![X]:((~funny(X)<~>rich(X))=>(rich(X)|~patient(X))))&
(![X]:((~happy(X)&~tall(X))<=>(kind(X)|~patient(X))))&
(![X]:((~old(X)<~>~wise(X))<=>brave(X)))&
(![X]:(~humble(X)=>~rich(X)))&
(![X]:((quiet(X)|~funny(X))<=>(~kind(X)&kind(X))))&
((?[X]:(~old(X)))=>(happy(fred)))&
((?[X]:(calm(X)))<=>(?[X]:((wise(X)<~>~quiet(X)))))&
(![X]:((~brave(X)|funny(X))<=>(happy(X)<~>~generous(X))))&
(![X]:((happy(X)&generous(X))<=>(~tall(X)|~humble(X))))&
(((~wise(mary)<~>quiet(mary)))<=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:(rich(X)<=>~generous(X)))&
(?[X]:((~rich(X)<~>curious(X))))&
(?[X]:(patient(X)))&
(?[X]:((wise(X)|~calm(X))))&
(?[X]:((old(X)<~>kind(X))))&
((tall(alice)|~kind(alice)))&
((~creative(lucy)|~happy(lucy)))&
(~calm(paul)) | ~wise(mary) | [
"p3",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7299847041557984564374670
% SZS output start Proof for 7299847041557984564374670
4. ! [X0] : ((~brave(X0) | patient(X0)) <=> (~wise(X0) & curious(X0))) [input p3]
6. ! [X0] : ((~tall(X0) & ~happy(X0)) <=> (~patient(X0) | kind(X0))) [input p5]
13. ! [X0] : ((generous(X0) & happy(X0)) <=> (~humble(X0) | ~tall(X0))) [input p12]
23. wise(mary) [input hypothesis]
41. ! [X0] : (((~brave(X0) | patient(X0)) | (wise(X0) | ~curious(X0))) & ((~wise(X0) & curious(X0)) | (brave(X0) & ~patient(X0)))) [nnf transformation 4]
42. ! [X0] : ((~brave(X0) | patient(X0) | wise(X0) | ~curious(X0)) & ((~wise(X0) & curious(X0)) | (brave(X0) & ~patient(X0)))) [flattening 41]
44. ! [X0] : (((~tall(X0) & ~happy(X0)) | (patient(X0) & ~kind(X0))) & ((~patient(X0) | kind(X0)) | (tall(X0) | happy(X0)))) [nnf transformation 6]
45. ! [X0] : (((~tall(X0) & ~happy(X0)) | (patient(X0) & ~kind(X0))) & (~patient(X0) | kind(X0) | tall(X0) | happy(X0))) [flattening 44]
56. ! [X0] : (((generous(X0) & happy(X0)) | (humble(X0) & tall(X0))) & ((~humble(X0) | ~tall(X0)) | (~generous(X0) | ~happy(X0)))) [nnf transformation 13]
57. ! [X0] : (((generous(X0) & happy(X0)) | (humble(X0) & tall(X0))) & (~humble(X0) | ~tall(X0) | ~generous(X0) | ~happy(X0))) [flattening 56]
80. ~wise(X0) | ~patient(X0) [cnf transformation 42]
87. ~happy(X0) | patient(X0) [cnf transformation 45]
89. ~tall(X0) | patient(X0) [cnf transformation 45]
112. tall(X0) | happy(X0) [cnf transformation 57]
132. wise(mary) [cnf transformation 23]
204. 16 <=> wise(mary) [avatar definition]
206. wise(mary) <- (16) [avatar component clause 204]
255. 16 [avatar split clause 132,204]
264. ~patient(mary) <- (16) [resolution 80,206]
275. happy(X0) | patient(X0) [resolution 112,89]
276. patient(X0) [subsumption resolution 275,87]
278. $false <- (16) [resolution 276,264]
279. ~16 [avatar contradiction clause 278]
280. $false [avatar sat refutation 255,279]
% SZS output end Proof for 7299847041557984564374670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is not funny.
If someone is either not quiet or generous then mary is both not brave and not creative and vice versa.
Everyone who is not kind is either not tall or not brave.
Everyone who is not wise is either funny or not happy.
Everyone who is both not humble and not kind is both not curious and tall.
Everyone who is not old or rich is not quiet and vice versa.
If fred is either kind or not old then lucy is either quiet or not humble.
Everyone who is old or not patient is both rich and not creative and vice versa.
Everyone who is both humble and not kind is not wise or not rich.
Everyone who is not tall is not happy.
If john is both not quiet and not wise then someone is both not strong and not brave and vice versa.
Everyone who is either patient or creative is either humble or tall and vice versa.
Everyone who is tall or not generous is generous.
If someone is old then lucy is curious.
If someone is quiet then susan is both not rich and not creative and vice versa.
Everyone who is either happy or not generous is either not kind or wise and vice versa.
Fred is either funny or not rich.
Mary is both strong and calm.
John is either not humble or not brave.
Someone is either not patient or creative.
Susan is brave.
Someone is either wise or kind.
Paul is generous.
Fred is both not kind and not brave. | John is not humble. | neutral | (![X]:(quiet(X)=>~funny(X)))&
((?[X]:((~quiet(X)<~>generous(X))))<=>((~brave(mary)&~creative(mary))))&
(![X]:(~kind(X)=>(~tall(X)<~>~brave(X))))&
(![X]:(~wise(X)=>(funny(X)<~>~happy(X))))&
(![X]:((~humble(X)&~kind(X))=>(~curious(X)&tall(X))))&
(![X]:((~old(X)|rich(X))<=>~quiet(X)))&
(((kind(fred)<~>~old(fred)))=>((quiet(lucy)<~>~humble(lucy))))&
(![X]:((old(X)|~patient(X))<=>(rich(X)&~creative(X))))&
(![X]:((humble(X)&~kind(X))=>(~wise(X)|~rich(X))))&
(![X]:(~tall(X)=>~happy(X)))&
(((~quiet(john)&~wise(john)))<=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((patient(X)<~>creative(X))<=>(humble(X)<~>tall(X))))&
(![X]:((tall(X)|~generous(X))=>generous(X)))&
((?[X]:(old(X)))=>(curious(lucy)))&
((?[X]:(quiet(X)))<=>((~rich(susan)&~creative(susan))))&
(![X]:((happy(X)<~>~generous(X))<=>(~kind(X)<~>wise(X))))&
((funny(fred)<~>~rich(fred)))&
((strong(mary)&calm(mary)))&
((~humble(john)<~>~brave(john)))&
(?[X]:((~patient(X)<~>creative(X))))&
(brave(susan))&
(?[X]:((wise(X)<~>kind(X))))&
(generous(paul))&
((~kind(fred)&~brave(fred))) | ~humble(john) | [] | null | 0 |
If fred is old or quiet then someone is either not creative or not old and vice versa.
If paul is either rich or not curious then someone is both creative and not wise.
If john is not old or not creative then mary is not funny or happy and vice versa.
Everyone who is rich or curious is either not wise or creative and vice versa.
Everyone who is not brave or tall is both happy and not happy.
Everyone who is strong or not calm is strong or not generous.
Everyone who is both not kind and rich is not patient or not rich and vice versa.
Everyone who is not quiet is not funny and vice versa.
Everyone who is not curious or brave is not curious or rich.
If someone is both not tall and calm then john is both creative and not happy and vice versa.
Everyone who is funny or not old is not patient or brave and vice versa.
If someone is not humble or curious then lucy is not creative.
Everyone who is both not humble and patient is not funny or not curious and vice versa.
If someone is either not creative or old then someone is wise or not patient and vice versa.
Everyone who is either quiet or not tall is wise and vice versa.
Someone is not funny.
Someone is not quiet.
Someone is not happy or funny.
Someone is curious or not old.
Mary is both old and calm.
Lucy is either not funny or quiet.
Someone is not calm. | Lucy is creative. | contradiction | (((old(fred)|quiet(fred)))<=>(?[X]:((~creative(X)<~>~old(X)))))&
(((rich(paul)<~>~curious(paul)))=>(?[X]:((creative(X)&~wise(X)))))&
(((~old(john)|~creative(john)))<=>((~funny(mary)|happy(mary))))&
(![X]:((rich(X)|curious(X))<=>(~wise(X)<~>creative(X))))&
(![X]:((~brave(X)|tall(X))=>(happy(X)&~happy(X))))&
(![X]:((strong(X)|~calm(X))=>(strong(X)|~generous(X))))&
(![X]:((~kind(X)&rich(X))<=>(~patient(X)|~rich(X))))&
(![X]:(~quiet(X)<=>~funny(X)))&
(![X]:((~curious(X)|brave(X))=>(~curious(X)|rich(X))))&
((?[X]:((~tall(X)&calm(X))))<=>((creative(john)&~happy(john))))&
(![X]:((funny(X)|~old(X))<=>(~patient(X)|brave(X))))&
((?[X]:((~humble(X)|curious(X))))=>(~creative(lucy)))&
(![X]:((~humble(X)&patient(X))<=>(~funny(X)|~curious(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((quiet(X)<~>~tall(X))<=>wise(X)))&
(?[X]:(~funny(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((~happy(X)|funny(X))))&
(?[X]:((curious(X)|~old(X))))&
((old(mary)&calm(mary)))&
((~funny(lucy)<~>quiet(lucy)))&
(?[X]:(~calm(X))) | creative(lucy) | [
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3643544346730368048565145
% SZS output start Proof for 3643544346730368048565145
12. ? [X0] : (curious(X0) | ~humble(X0)) => ~creative(lucy) [input p11]
13. ! [X0] : ((patient(X0) & ~humble(X0)) <=> (~curious(X0) | ~funny(X0))) [input p12]
16. ? [X0] : ~funny(X0) [input p15]
23. creative(lucy) [input hypothesis]
30. ~creative(lucy) | ! [X0] : (~curious(X0) & humble(X0)) [ennf transformation 12]
53. ! [X0] : (((patient(X0) & ~humble(X0)) | (curious(X0) & funny(X0))) & ((~curious(X0) | ~funny(X0)) | (~patient(X0) | humble(X0)))) [nnf transformation 13]
54. ! [X0] : (((patient(X0) & ~humble(X0)) | (curious(X0) & funny(X0))) & (~curious(X0) | ~funny(X0) | ~patient(X0) | humble(X0))) [flattening 53]
61. ? [X0] : ~funny(X0) => ~funny(sK5) [choice axiom]
62. ~funny(sK5) [skolemisation 16,61]
113. ~creative(lucy) | humble(X0) [cnf transformation 30]
116. ~humble(X0) | funny(X0) [cnf transformation 54]
130. ~funny(sK5) [cnf transformation 62]
139. creative(lucy) [cnf transformation 23]
234. 19 <=> creative(lucy) [avatar definition]
239. 20 <=> ! [X0] : humble(X0) [avatar definition]
240. humble(X0) <- (20) [avatar component clause 239]
241. 20 | ~19 [avatar split clause 113,234,239]
296. 19 [avatar split clause 139,234]
303. funny(X0) <- (20) [resolution 116,240]
304. $false <- (20) [resolution 303,130]
308. ~20 [avatar contradiction clause 304]
309. $false [avatar sat refutation 241,296,308]
% SZS output end Proof for 3643544346730368048565145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not happy is not old or old and vice versa. Everyone who is either calm or rich is tall or quiet. If paul is both not quiet and brave then mary is quiet. If susan is both not creative and rich then someone is both not rich and old and vice versa. If lucy is either not patient or not strong then someone is both generous and not happy. If someone is either not quiet or not happy then someone is not wise or strong. If susan is both not strong and not happy then john is either not quiet or not calm and vice versa. Everyone who is not rich is calm. If paul is both tall and not funny then paul is both kind and not funny and vice versa. If someone is both not humble and funny then someone is not strong and vice versa. Everyone who is curious is either not calm or not quiet and vice versa. Everyone who is rich or not old is either not old or rich and vice versa. Everyone who is either curious or wise is not funny or not creative and vice versa. If alice is either humble or not tall then someone is either calm or not funny and vice versa. Everyone who is brave is both not patient and not quiet. If someone is not kind then someone is not wise or not strong and vice versa. Someone is not brave. Paul is either not generous or not old. Alice is either not funny or tall. Someone is both not kind and brave. Lucy is not strong or not rich. Someone is both tall and patient. | John is not humble. | contradiction | (![X]:((humble(X)&~happy(X))<=>(~old(X)|old(X))))&
(![X]:((calm(X)<~>rich(X))=>(tall(X)|quiet(X))))&
(((~quiet(paul)&brave(paul)))=>(quiet(mary)))&
(((~creative(susan)&rich(susan)))<=>(?[X]:((~rich(X)&old(X)))))&
(((~patient(lucy)<~>~strong(lucy)))=>(?[X]:((generous(X)&~happy(X)))))&
((?[X]:((~quiet(X)<~>~happy(X))))=>(?[X]:((~wise(X)|strong(X)))))&
(((~strong(susan)&~happy(susan)))<=>((~quiet(john)<~>~calm(john))))&
(![X]:(~rich(X)=>calm(X)))&
(((tall(paul)&~funny(paul)))<=>((kind(paul)&~funny(paul))))&
((?[X]:((~humble(X)&funny(X))))<=>(?[X]:(~strong(X))))&
(![X]:(curious(X)<=>(~calm(X)<~>~quiet(X))))&
(![X]:((rich(X)|~old(X))<=>(~old(X)<~>rich(X))))&
(![X]:((curious(X)<~>wise(X))<=>(~funny(X)|~creative(X))))&
(((humble(alice)<~>~tall(alice)))<=>(?[X]:((calm(X)<~>~funny(X)))))&
(![X]:(brave(X)=>(~patient(X)&~quiet(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~wise(X)|~strong(X)))))&
(?[X]:(~brave(X)))&
((~generous(paul)<~>~old(paul)))&
((~funny(alice)<~>tall(alice)))&
(?[X]:((~kind(X)&brave(X))))&
((~strong(lucy)|~rich(lucy)))&
(?[X]:((tall(X)&patient(X)))) | ~humble(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 5739149897551827557451252
% SZS output start Proof for 5739149897551827557451252
1. ! [X0] : ((~happy(X0) & humble(X0)) <=> (old(X0) | ~old(X0))) [input p0]
23. ~humble(john) [input hypothesis]
35. ! [X0] : (((~happy(X0) & humble(X0)) | (~old(X0) & old(X0))) & ((old(X0) | ~old(X0)) | (happy(X0) | ~humble(X0)))) [nnf transformation 1]
36. ! [X0] : (((~happy(X0) & humble(X0)) | (~old(X0) & old(X0))) & (old(X0) | ~old(X0) | happy(X0) | ~humble(X0))) [flattening 35]
82. humble(X0) | old(X0) [cnf transformation 36]
83. humble(X0) | ~old(X0) [cnf transformation 36]
152. ~humble(john) [cnf transformation 23]
158. humble(X0) [subsumption resolution 82,83]
332. $false [subsumption resolution 152,158]
% SZS output end Proof for 5739149897551827557451252
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both calm and curious then someone is either not curious or patient.
Everyone who is both not old and patient is both humble and not calm and vice versa.
If lucy is either not patient or calm then someone is funny and vice versa.
Everyone who is creative or quiet is either old or tall and vice versa.
Everyone who is both not tall and not calm is generous and vice versa.
Everyone who is not calm is tall or wise and vice versa.
Everyone who is both not kind and quiet is not generous or kind and vice versa.
Everyone who is not funny or humble is either not tall or not quiet.
If someone is both not strong and not rich then john is both not funny and not curious and vice versa.
Everyone who is either tall or humble is not tall and vice versa.
If john is quiet or happy then fred is strong and vice versa.
If mary is not patient or curious then someone is either tall or calm.
Everyone who is both old and not strong is either not kind or creative.
If someone is not calm or not brave then john is either not wise or brave and vice versa.
Everyone who is either calm or tall is both not rich and not curious.
John is funny or not funny.
Someone is either not strong or wise.
Lucy is both not strong and humble. | Lucy is not happy. | neutral | (((calm(mary)&curious(mary)))=>(?[X]:((~curious(X)<~>patient(X)))))&
(![X]:((~old(X)&patient(X))<=>(humble(X)&~calm(X))))&
(((~patient(lucy)<~>calm(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((creative(X)|quiet(X))<=>(old(X)<~>tall(X))))&
(![X]:((~tall(X)&~calm(X))<=>generous(X)))&
(![X]:(~calm(X)<=>(tall(X)|wise(X))))&
(![X]:((~kind(X)&quiet(X))<=>(~generous(X)|kind(X))))&
(![X]:((~funny(X)|humble(X))=>(~tall(X)<~>~quiet(X))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~funny(john)&~curious(john))))&
(![X]:((tall(X)<~>humble(X))<=>~tall(X)))&
(((quiet(john)|happy(john)))<=>(strong(fred)))&
(((~patient(mary)|curious(mary)))=>(?[X]:((tall(X)<~>calm(X)))))&
(![X]:((old(X)&~strong(X))=>(~kind(X)<~>creative(X))))&
((?[X]:((~calm(X)|~brave(X))))<=>((~wise(john)<~>brave(john))))&
(![X]:((calm(X)<~>tall(X))=>(~rich(X)&~curious(X))))&
((funny(john)|~funny(john)))&
(?[X]:((~strong(X)<~>wise(X))))&
((~strong(lucy)&humble(lucy))) | ~happy(lucy) | [] | null | 0 |
Everyone who is both quiet and not kind is not humble or not brave.
Everyone who is not tall or not happy is either calm or tall and vice versa.
If someone is not generous then someone is not kind or patient.
Everyone who is both brave and not wise is creative and vice versa.
Everyone who is not generous is either not humble or tall and vice versa.
Everyone who is creative or patient is quiet.
Everyone who is patient is both not funny and old.
If susan is not old then john is both not brave and generous.
Everyone who is both not happy and curious is not curious and vice versa.
If someone is creative or not generous then alice is not tall.
If someone is not kind or humble then fred is not kind and vice versa.
Everyone who is both old and not calm is not funny.
Everyone who is either not humble or not calm is creative and vice versa.
If alice is both kind and not tall then someone is wise or not quiet.
Everyone who is both not old and not calm is brave and vice versa.
Lucy is humble or rich.
Susan is either not patient or not quiet.
John is tall or kind.
Someone is both curious and not patient.
John is not kind.
John is either kind or not strong.
Fred is either strong or not kind. | Fred is tall. | neutral | (![X]:((quiet(X)&~kind(X))=>(~humble(X)|~brave(X))))&
(![X]:((~tall(X)|~happy(X))<=>(calm(X)<~>tall(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:((brave(X)&~wise(X))<=>creative(X)))&
(![X]:(~generous(X)<=>(~humble(X)<~>tall(X))))&
(![X]:((creative(X)|patient(X))=>quiet(X)))&
(![X]:(patient(X)=>(~funny(X)&old(X))))&
((~old(susan))=>((~brave(john)&generous(john))))&
(![X]:((~happy(X)&curious(X))<=>~curious(X)))&
((?[X]:((creative(X)|~generous(X))))=>(~tall(alice)))&
((?[X]:((~kind(X)|humble(X))))<=>(~kind(fred)))&
(![X]:((old(X)&~calm(X))=>~funny(X)))&
(![X]:((~humble(X)<~>~calm(X))<=>creative(X)))&
(((kind(alice)&~tall(alice)))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((~old(X)&~calm(X))<=>brave(X)))&
((humble(lucy)|rich(lucy)))&
((~patient(susan)<~>~quiet(susan)))&
((tall(john)|kind(john)))&
(?[X]:((curious(X)&~patient(X))))&
(~kind(john))&
((kind(john)<~>~strong(john)))&
((strong(fred)<~>~kind(fred))) | tall(fred) | [] | null | 0 |
If someone is either not kind or not humble then someone is both not funny and funny and vice versa.
If someone is either happy or wise then lucy is tall or not happy.
Everyone who is both curious and calm is both not tall and strong.
Everyone who is not wise or wise is both humble and brave and vice versa.
If someone is not wise then lucy is either not generous or not happy and vice versa.
Everyone who is old or not old is either curious or not quiet.
Everyone who is either strong or patient is both not wise and not old and vice versa.
If alice is both not kind and not funny then lucy is either not calm or funny.
If susan is kind then fred is both not old and tall.
Everyone who is not wise is not brave and vice versa.
If someone is either not old or curious then mary is both curious and not generous.
Everyone who is either curious or not rich is brave and vice versa.
Everyone who is tall is both patient and creative and vice versa.
If lucy is both not kind and not creative then john is both strong and rich and vice versa.
Everyone who is not strong is not rich or creative.
If alice is not rich then someone is not calm or kind and vice versa.
Someone is not humble or funny.
John is tall or not patient.
Someone is both not rich and tall.
Paul is not curious or humble.
John is not old or curious.
Susan is not curious or generous.
Someone is both patient and not generous. | Paul is not creative. | neutral | ((?[X]:((~kind(X)<~>~humble(X))))<=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((happy(X)<~>wise(X))))=>((tall(lucy)|~happy(lucy))))&
(![X]:((curious(X)&calm(X))=>(~tall(X)&strong(X))))&
(![X]:((~wise(X)|wise(X))<=>(humble(X)&brave(X))))&
((?[X]:(~wise(X)))<=>((~generous(lucy)<~>~happy(lucy))))&
(![X]:((old(X)|~old(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((strong(X)<~>patient(X))<=>(~wise(X)&~old(X))))&
(((~kind(alice)&~funny(alice)))=>((~calm(lucy)<~>funny(lucy))))&
((kind(susan))=>((~old(fred)&tall(fred))))&
(![X]:(~wise(X)<=>~brave(X)))&
((?[X]:((~old(X)<~>curious(X))))=>((curious(mary)&~generous(mary))))&
(![X]:((curious(X)<~>~rich(X))<=>brave(X)))&
(![X]:(tall(X)<=>(patient(X)&creative(X))))&
(((~kind(lucy)&~creative(lucy)))<=>((strong(john)&rich(john))))&
(![X]:(~strong(X)=>(~rich(X)|creative(X))))&
((~rich(alice))<=>(?[X]:((~calm(X)|kind(X)))))&
(?[X]:((~humble(X)|funny(X))))&
((tall(john)|~patient(john)))&
(?[X]:((~rich(X)&tall(X))))&
((~curious(paul)|humble(paul)))&
((~old(john)|curious(john)))&
((~curious(susan)|generous(susan)))&
(?[X]:((patient(X)&~generous(X)))) | ~creative(paul) | [] | null | 0 |
Everyone who is either curious or not tall is not tall. If someone is either old or not quiet then mary is either funny or not strong. Everyone who is both wise and creative is either not generous or not happy and vice versa. If someone is not strong then someone is creative or tall. Everyone who is either old or not brave is both not happy and kind. If someone is either wise or curious then someone is either not kind or not brave. Everyone who is either not patient or not wise is both curious and tall and vice versa. Everyone who is funny is not rich or not quiet and vice versa. Everyone who is both not funny and patient is not generous or generous and vice versa. If someone is both not happy and not quiet then alice is not funny. If someone is not humble then someone is both not curious and tall. If someone is either not brave or not tall then someone is either not happy or not tall and vice versa. Everyone who is either not generous or creative is either not strong or not old. If fred is tall or not creative then lucy is either old or brave. If susan is either curious or generous then john is both not kind and tall and vice versa. Everyone who is either patient or curious is not brave and vice versa. Paul is humble. Lucy is old or not curious. Fred is either happy or not patient. Paul is either rich or not kind. Someone is not old. | Susan is not quiet. | contradiction | (![X]:((curious(X)<~>~tall(X))=>~tall(X)))&
((?[X]:((old(X)<~>~quiet(X))))=>((funny(mary)<~>~strong(mary))))&
(![X]:((wise(X)&creative(X))<=>(~generous(X)<~>~happy(X))))&
((?[X]:(~strong(X)))=>(?[X]:((creative(X)|tall(X)))))&
(![X]:((old(X)<~>~brave(X))=>(~happy(X)&kind(X))))&
((?[X]:((wise(X)<~>curious(X))))=>(?[X]:((~kind(X)<~>~brave(X)))))&
(![X]:((~patient(X)<~>~wise(X))<=>(curious(X)&tall(X))))&
(![X]:(funny(X)<=>(~rich(X)|~quiet(X))))&
(![X]:((~funny(X)&patient(X))<=>(~generous(X)|generous(X))))&
((?[X]:((~happy(X)&~quiet(X))))=>(~funny(alice)))&
((?[X]:(~humble(X)))=>(?[X]:((~curious(X)&tall(X)))))&
((?[X]:((~brave(X)<~>~tall(X))))<=>(?[X]:((~happy(X)<~>~tall(X)))))&
(![X]:((~generous(X)<~>creative(X))=>(~strong(X)<~>~old(X))))&
(((tall(fred)|~creative(fred)))=>((old(lucy)<~>brave(lucy))))&
(((curious(susan)<~>generous(susan)))<=>((~kind(john)&tall(john))))&
(![X]:((patient(X)<~>curious(X))<=>~brave(X)))&
(humble(paul))&
((old(lucy)|~curious(lucy)))&
((happy(fred)<~>~patient(fred)))&
((rich(paul)<~>~kind(paul)))&
(?[X]:(~old(X))) | ~quiet(susan) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 200095900104670024286250
% SZS output start Proof for 200095900104670024286250
8. ! [X0] : (funny(X0) <=> (~quiet(X0) | ~rich(X0))) [input p7]
9. ! [X0] : ((patient(X0) & ~funny(X0)) <=> (generous(X0) | ~generous(X0))) [input p8]
22. ~quiet(susan) [input hypothesis]
51. ! [X0] : ((funny(X0) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | ~funny(X0))) [nnf transformation 8]
52. ! [X0] : ((funny(X0) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | ~funny(X0))) [flattening 51]
53. ! [X0] : (((patient(X0) & ~funny(X0)) | (~generous(X0) & generous(X0))) & ((generous(X0) | ~generous(X0)) | (~patient(X0) | funny(X0)))) [nnf transformation 9]
54. ! [X0] : (((patient(X0) & ~funny(X0)) | (~generous(X0) & generous(X0))) & (generous(X0) | ~generous(X0) | ~patient(X0) | funny(X0))) [flattening 53]
98. funny(X0) | quiet(X0) [cnf transformation 52]
100. ~funny(X0) | generous(X0) [cnf transformation 54]
101. ~generous(X0) | ~funny(X0) [cnf transformation 54]
137. ~quiet(susan) [cnf transformation 22]
188. ~funny(X0) [subsumption resolution 100,101]
290. quiet(X0) [resolution 98,188]
291. $false [resolution 290,137]
% SZS output end Proof for 200095900104670024286250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and tall then alice is happy or generous and vice versa. If someone is both not curious and patient then someone is both old and not generous and vice versa. If john is both creative and kind then someone is not wise. If someone is strong or wise then john is either not humble or funny. Everyone who is either humble or kind is either not curious or not humble and vice versa. Everyone who is both not curious and not brave is rich. Everyone who is calm or not quiet is creative or not old and vice versa. If paul is wise then someone is generous. Everyone who is quiet is both rich and wise. Everyone who is both curious and old is brave and vice versa. Everyone who is brave or not strong is not curious. Everyone who is either not funny or not quiet is not generous. Everyone who is both not patient and calm is either strong or calm and vice versa. Everyone who is wise is not strong. If someone is either tall or not humble then someone is both not funny and not happy and vice versa. Everyone who is rich is kind or not patient and vice versa. Susan is funny. Fred is curious. Fred is not old. Someone is both not kind and not tall. Someone is not quiet or not old. Someone is either not quiet or not humble. Someone is generous or quiet. Alice is not wise. | Alice is old. | contradiction | ((?[X]:((~tall(X)&tall(X))))<=>((happy(alice)|generous(alice))))&
((?[X]:((~curious(X)&patient(X))))<=>(?[X]:((old(X)&~generous(X)))))&
(((creative(john)&kind(john)))=>(?[X]:(~wise(X))))&
((?[X]:((strong(X)|wise(X))))=>((~humble(john)<~>funny(john))))&
(![X]:((humble(X)<~>kind(X))<=>(~curious(X)<~>~humble(X))))&
(![X]:((~curious(X)&~brave(X))=>rich(X)))&
(![X]:((calm(X)|~quiet(X))<=>(creative(X)|~old(X))))&
((wise(paul))=>(?[X]:(generous(X))))&
(![X]:(quiet(X)=>(rich(X)&wise(X))))&
(![X]:((curious(X)&old(X))<=>brave(X)))&
(![X]:((brave(X)|~strong(X))=>~curious(X)))&
(![X]:((~funny(X)<~>~quiet(X))=>~generous(X)))&
(![X]:((~patient(X)&calm(X))<=>(strong(X)<~>calm(X))))&
(![X]:(wise(X)=>~strong(X)))&
((?[X]:((tall(X)<~>~humble(X))))<=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:(rich(X)<=>(kind(X)|~patient(X))))&
(funny(susan))&
(curious(fred))&
(~old(fred))&
(?[X]:((~kind(X)&~tall(X))))&
(?[X]:((~quiet(X)|~old(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:((generous(X)|quiet(X))))&
(~wise(alice)) | old(alice) | [
"p0",
"p1",
"p4",
"p5",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4261800669534763646139883
% SZS output start Proof for 4261800669534763646139883
1. ? [X0] : (tall(X0) & ~tall(X0)) <=> (generous(alice) | happy(alice)) [input p0]
2. ? [X0] : (patient(X0) & ~curious(X0)) <=> ? [X0] : (~generous(X0) & old(X0)) [input p1]
5. ! [X0] : ((humble(X0) <~> kind(X0)) <=> (~curious(X0) <~> ~humble(X0))) [input p4]
6. ! [X0] : ((~brave(X0) & ~curious(X0)) => rich(X0)) [input p5]
10. ! [X0] : ((old(X0) & curious(X0)) <=> brave(X0)) [input p9]
11. ! [X0] : ((~strong(X0) | brave(X0)) => ~curious(X0)) [input p10]
16. ! [X0] : (rich(X0) <=> (~patient(X0) | kind(X0))) [input p15]
25. old(alice) [input hypothesis]
26. ? [X0] : (patient(X0) & ~curious(X0)) <=> ? [X1] : (~generous(X1) & old(X1)) [rectify 2]
28. ! [X0] : (rich(X0) => (~patient(X0) | kind(X0))) [unused predicate definition removal 16]
32. ! [X0] : (rich(X0) | (brave(X0) | curious(X0))) [ennf transformation 6]
33. ! [X0] : (rich(X0) | brave(X0) | curious(X0)) [flattening 32]
36. ! [X0] : (~curious(X0) | (strong(X0) & ~brave(X0))) [ennf transformation 11]
39. ! [X0] : ((~patient(X0) | kind(X0)) | ~rich(X0)) [ennf transformation 28]
40. ! [X0] : (~patient(X0) | kind(X0) | ~rich(X0)) [flattening 39]
41. (? [X0] : (tall(X0) & ~tall(X0)) | (~generous(alice) & ~happy(alice))) & ((generous(alice) | happy(alice)) | ! [X0] : (~tall(X0) | tall(X0))) [nnf transformation 1]
42. (? [X0] : (tall(X0) & ~tall(X0)) | (~generous(alice) & ~happy(alice))) & (generous(alice) | happy(alice) | ! [X0] : (~tall(X0) | tall(X0))) [flattening 41]
43. (? [X0] : (tall(X0) & ~tall(X0)) | (~generous(alice) & ~happy(alice))) & (generous(alice) | happy(alice) | ! [X1] : (~tall(X1) | tall(X1))) [rectify 42]
44. ? [X0] : (tall(X0) & ~tall(X0)) => (tall(sK0) & ~tall(sK0)) [choice axiom]
45. ((tall(sK0) & ~tall(sK0)) | (~generous(alice) & ~happy(alice))) & (generous(alice) | happy(alice) | ! [X1] : (~tall(X1) | tall(X1))) [skolemisation 43,44]
46. (? [X0] : (patient(X0) & ~curious(X0)) | ! [X1] : (generous(X1) | ~old(X1))) & (? [X1] : (~generous(X1) & old(X1)) | ! [X0] : (~patient(X0) | curious(X0))) [nnf transformation 26]
47. (? [X0] : (patient(X0) & ~curious(X0)) | ! [X1] : (generous(X1) | ~old(X1))) & (? [X2] : (~generous(X2) & old(X2)) | ! [X3] : (~patient(X3) | curious(X3))) [rectify 46]
48. ? [X0] : (patient(X0) & ~curious(X0)) => (patient(sK1) & ~curious(sK1)) [choice axiom]
49. ? [X2] : (~generous(X2) & old(X2)) => (~generous(sK2) & old(sK2)) [choice axiom]
50. ((patient(sK1) & ~curious(sK1)) | ! [X1] : (generous(X1) | ~old(X1))) & ((~generous(sK2) & old(sK2)) | ! [X3] : (~patient(X3) | curious(X3))) [skolemisation 47,49,48]
54. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) & (((humble(X0) | curious(X0)) & (~humble(X0) | ~curious(X0))) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [nnf transformation 5]
59. ! [X0] : (((old(X0) & curious(X0)) | ~brave(X0)) & (brave(X0) | (~old(X0) | ~curious(X0)))) [nnf transformation 10]
60. ! [X0] : (((old(X0) & curious(X0)) | ~brave(X0)) & (brave(X0) | ~old(X0) | ~curious(X0))) [flattening 59]
80. ~tall(sK0) | ~generous(alice) [cnf transformation 45]
82. tall(sK0) | ~generous(alice) [cnf transformation 45]
85. ~curious(sK1) | generous(X1) | ~old(X1) [cnf transformation 50]
86. patient(sK1) | generous(X1) | ~old(X1) [cnf transformation 50]
92. ~humble(X0) | ~curious(X0) | kind(X0) | ~humble(X0) [cnf transformation 54]
95. humble(X0) | curious(X0) | humble(X0) | ~kind(X0) [cnf transformation 54]
97. kind(X0) | humble(X0) | ~curious(X0) | humble(X0) [cnf transformation 54]
98. ~kind(X0) | ~humble(X0) | ~humble(X0) | curious(X0) [cnf transformation 54]
100. rich(X0) | brave(X0) | curious(X0) [cnf transformation 33]
109. ~brave(X0) | curious(X0) [cnf transformation 60]
111. ~curious(X0) | ~brave(X0) [cnf transformation 36]
128. ~rich(X0) | kind(X0) | ~patient(X0) [cnf transformation 40]
139. old(alice) [cnf transformation 25]
142. ~humble(X0) | ~curious(X0) | kind(X0) [duplicate literal removal 92]
143. humble(X0) | curious(X0) | ~kind(X0) [duplicate literal removal 95]
144. ~curious(X0) | humble(X0) | kind(X0) [duplicate literal removal 97]
145. ~humble(X0) | ~kind(X0) | curious(X0) [duplicate literal removal 98]
147. 1 <=> generous(alice) [avatar definition]
149. ~generous(alice) <- (~1) [avatar component clause 147]
151. 2 <=> tall(sK0) [avatar definition]
154. ~1 | 2 [avatar split clause 82,151,147]
160. ~1 | ~2 [avatar split clause 80,151,147]
163. 4 <=> ! [X1] : (generous(X1) | ~old(X1)) [avatar definition]
164. ~old(X1) | generous(X1) <- (4) [avatar component clause 163]
166. 5 <=> patient(sK1) [avatar definition]
168. patient(sK1) <- (5) [avatar component clause 166]
169. 4 | 5 [avatar split clause 86,166,163]
171. 6 <=> curious(sK1) [avatar definition]
173. ~curious(sK1) <- (~6) [avatar component clause 171]
174. 4 | ~6 [avatar split clause 85,171,163]
219. ~kind(X0) | curious(X0) [subsumption resolution 143,145]
220. ~curious(X0) | kind(X0) [subsumption resolution 142,144]
230. ~brave(X0) [subsumption resolution 111,109]
296. generous(alice) <- (4) [resolution 164,139]
297. $false <- (~1, 4) [subsumption resolution 296,149]
298. 1 | ~4 [avatar contradiction clause 297]
371. kind(X0) | ~patient(X0) | brave(X0) | curious(X0) [resolution 128,100]
372. kind(X0) | ~patient(X0) | curious(X0) [subsumption resolution 371,230]
373. ~patient(X0) | kind(X0) [subsumption resolution 372,220]
376. kind(sK1) <- (5) [resolution 373,168]
379. curious(sK1) <- (5) [resolution 376,219]
380. $false <- (5, ~6) [subsumption resolution 379,173]
381. ~5 | 6 [avatar contradiction clause 380]
382. $false [avatar sat refutation 154,160,169,174,298,381]
% SZS output end Proof for 4261800669534763646139883
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious then alice is not kind or patient and vice versa.
If mary is both not humble and not patient then mary is either not wise or brave and vice versa.
Everyone who is both humble and old is not tall or not humble.
If someone is not creative then someone is either tall or rich and vice versa.
If susan is not old then someone is both not brave and generous.
If someone is both rich and quiet then someone is both not strong and generous and vice versa.
If someone is humble or old then susan is both not tall and not wise and vice versa.
If someone is rich or funny then john is tall and vice versa.
Everyone who is either not quiet or old is rich or brave and vice versa.
Everyone who is humble or not kind is either humble or not old and vice versa.
If lucy is wise then fred is both rich and not rich and vice versa.
Everyone who is patient or old is either not kind or creative.
Everyone who is wise or generous is not wise or tall and vice versa.
Everyone who is calm is not funny and vice versa.
If fred is old then fred is both calm and old and vice versa.
Everyone who is not quiet is both not humble and not happy.
Alice is both not old and patient.
Mary is not generous.
Someone is both wise and curious.
Fred is both not curious and not kind.
Someone is both quiet and strong.
Someone is tall.
Someone is rich or not creative.
Someone is both rich and not curious. | John is not humble. | entailment | ((?[X]:(curious(X)))<=>((~kind(alice)|patient(alice))))&
(((~humble(mary)&~patient(mary)))<=>((~wise(mary)<~>brave(mary))))&
(![X]:((humble(X)&old(X))=>(~tall(X)|~humble(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((tall(X)<~>rich(X)))))&
((~old(susan))=>(?[X]:((~brave(X)&generous(X)))))&
((?[X]:((rich(X)&quiet(X))))<=>(?[X]:((~strong(X)&generous(X)))))&
((?[X]:((humble(X)|old(X))))<=>((~tall(susan)&~wise(susan))))&
((?[X]:((rich(X)|funny(X))))<=>(tall(john)))&
(![X]:((~quiet(X)<~>old(X))<=>(rich(X)|brave(X))))&
(![X]:((humble(X)|~kind(X))<=>(humble(X)<~>~old(X))))&
((wise(lucy))<=>((rich(fred)&~rich(fred))))&
(![X]:((patient(X)|old(X))=>(~kind(X)<~>creative(X))))&
(![X]:((wise(X)|generous(X))<=>(~wise(X)|tall(X))))&
(![X]:(calm(X)<=>~funny(X)))&
((old(fred))<=>((calm(fred)&old(fred))))&
(![X]:(~quiet(X)=>(~humble(X)&~happy(X))))&
((~old(alice)&patient(alice)))&
(~generous(mary))&
(?[X]:((wise(X)&curious(X))))&
((~curious(fred)&~kind(fred)))&
(?[X]:((quiet(X)&strong(X))))&
(?[X]:(tall(X)))&
(?[X]:((rich(X)|~creative(X))))&
(?[X]:((rich(X)&~curious(X)))) | ~humble(john) | [
"p2",
"p7",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2071349426747174532258745
% SZS output start Proof for 2071349426747174532258745
3. ! [X0] : ((old(X0) & humble(X0)) => (~humble(X0) | ~tall(X0))) [input p2]
8. ? [X0] : (funny(X0) | rich(X0)) <=> tall(john) [input p7]
10. ! [X0] : ((~kind(X0) | humble(X0)) <=> (humble(X0) <~> ~old(X0))) [input p9]
24. ? [X0] : (~curious(X0) & rich(X0)) [input p23]
25. humble(john) [input hypothesis]
29. ! [X0] : ((~humble(X0) | ~tall(X0)) | (~old(X0) | ~humble(X0))) [ennf transformation 3]
30. ! [X0] : (~humble(X0) | ~tall(X0) | ~old(X0) | ~humble(X0)) [flattening 29]
58. (? [X0] : (funny(X0) | rich(X0)) | ~tall(john)) & (tall(john) | ! [X0] : (~funny(X0) & ~rich(X0))) [nnf transformation 8]
59. (? [X0] : (funny(X0) | rich(X0)) | ~tall(john)) & (tall(john) | ! [X1] : (~funny(X1) & ~rich(X1))) [rectify 58]
60. ? [X0] : (funny(X0) | rich(X0)) => (funny(sK7) | rich(sK7)) [choice axiom]
61. ((funny(sK7) | rich(sK7)) | ~tall(john)) & (tall(john) | ! [X1] : (~funny(X1) & ~rich(X1))) [skolemisation 59,60]
64. ! [X0] : (((~kind(X0) | humble(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0)))) & (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | (kind(X0) & ~humble(X0)))) [nnf transformation 10]
65. ! [X0] : ((~kind(X0) | humble(X0) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0)))) & (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | (kind(X0) & ~humble(X0)))) [flattening 64]
82. ? [X0] : (~curious(X0) & rich(X0)) => (~curious(sK12) & rich(sK12)) [choice axiom]
83. ~curious(sK12) & rich(sK12) [skolemisation 24,82]
93. ~humble(X0) | ~tall(X0) | ~old(X0) | ~humble(X0) [cnf transformation 30]
109. tall(john) | ~rich(X1) [cnf transformation 61]
120. old(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 65]
152. rich(sK12) [cnf transformation 83]
154. humble(john) [cnf transformation 25]
157. ~humble(X0) | old(X0) [duplicate literal removal 120]
159. ~tall(X0) | ~humble(X0) | ~old(X0) [duplicate literal removal 93]
293. 30 <=> tall(john) [avatar definition]
294. tall(john) <- (30) [avatar component clause 293]
310. 34 <=> ! [X1] : ~rich(X1) [avatar definition]
311. ~rich(X1) <- (34) [avatar component clause 310]
312. 34 | 30 [avatar split clause 109,293,310]
355. old(john) [resolution 157,154]
472. ~humble(john) | ~old(john) <- (30) [resolution 159,294]
478. ~old(john) <- (30) [subsumption resolution 472,154]
479. $false <- (30) [subsumption resolution 478,355]
480. ~30 [avatar contradiction clause 479]
484. $false <- (34) [resolution 311,152]
487. ~34 [avatar contradiction clause 484]
488. $false [avatar sat refutation 312,480,487]
% SZS output end Proof for 2071349426747174532258745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or happy is either curious or not patient.
If someone is brave then someone is not funny.
If someone is curious or happy then lucy is both not curious and rich and vice versa.
Everyone who is not strong or quiet is calm or strong.
Everyone who is not humble or calm is brave.
Everyone who is brave or generous is both kind and not brave and vice versa.
If someone is not old or not creative then someone is both not strong and patient and vice versa.
Everyone who is not tall or not patient is not kind.
Everyone who is either quiet or patient is not calm.
If someone is both calm and rich then lucy is kind or not rich.
Everyone who is either creative or kind is either humble or not rich.
Everyone who is patient is not humble and vice versa.
If someone is either not patient or generous then someone is both not wise and funny.
Everyone who is not humble is not tall.
If fred is creative or happy then fred is either not wise or not creative and vice versa.
Everyone who is not rich is either tall or not generous.
Someone is not kind.
Someone is funny or not strong.
Someone is not wise or wise.
Lucy is strong.
Susan is kind or funny.
Susan is not brave.
Someone is either old or not curious. | Fred is rich. | entailment | (![X]:((generous(X)|happy(X))=>(curious(X)<~>~patient(X))))&
((?[X]:(brave(X)))=>(?[X]:(~funny(X))))&
((?[X]:((curious(X)|happy(X))))<=>((~curious(lucy)&rich(lucy))))&
(![X]:((~strong(X)|quiet(X))=>(calm(X)|strong(X))))&
(![X]:((~humble(X)|calm(X))=>brave(X)))&
(![X]:((brave(X)|generous(X))<=>(kind(X)&~brave(X))))&
((?[X]:((~old(X)|~creative(X))))<=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~tall(X)|~patient(X))=>~kind(X)))&
(![X]:((quiet(X)<~>patient(X))=>~calm(X)))&
((?[X]:((calm(X)&rich(X))))=>((kind(lucy)|~rich(lucy))))&
(![X]:((creative(X)<~>kind(X))=>(humble(X)<~>~rich(X))))&
(![X]:(patient(X)<=>~humble(X)))&
((?[X]:((~patient(X)<~>generous(X))))=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:(~humble(X)=>~tall(X)))&
(((creative(fred)|happy(fred)))<=>((~wise(fred)<~>~creative(fred))))&
(![X]:(~rich(X)=>(tall(X)<~>~generous(X))))&
(?[X]:(~kind(X)))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((~wise(X)|wise(X))))&
(strong(lucy))&
((kind(susan)|funny(susan)))&
(~brave(susan))&
(?[X]:((old(X)<~>~curious(X)))) | rich(fred) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5312793088149160939263730
% SZS output start Proof for 5312793088149160939263730
4. ! [X0] : ((quiet(X0) | ~strong(X0)) => (strong(X0) | calm(X0))) [input p3]
5. ! [X0] : ((calm(X0) | ~humble(X0)) => brave(X0)) [input p4]
6. ! [X0] : ((generous(X0) | brave(X0)) <=> (~brave(X0) & kind(X0))) [input p5]
7. ? [X0] : (~creative(X0) | ~old(X0)) <=> ? [X0] : (patient(X0) & ~strong(X0)) [input p6]
8. ! [X0] : ((~patient(X0) | ~tall(X0)) => ~kind(X0)) [input p7]
11. ! [X0] : ((creative(X0) <~> kind(X0)) => (humble(X0) <~> ~rich(X0))) [input p10]
12. ! [X0] : (patient(X0) <=> ~humble(X0)) [input p11]
24. ~rich(fred) [input hypothesis]
26. ? [X0] : (~creative(X0) | ~old(X0)) <=> ? [X1] : (patient(X1) & ~strong(X1)) [rectify 7]
30. ! [X0] : ((strong(X0) | calm(X0)) | (~quiet(X0) & strong(X0))) [ennf transformation 4]
31. ! [X0] : (strong(X0) | calm(X0) | (~quiet(X0) & strong(X0))) [flattening 30]
32. ! [X0] : (brave(X0) | (~calm(X0) & humble(X0))) [ennf transformation 5]
33. ! [X0] : (~kind(X0) | (patient(X0) & tall(X0))) [ennf transformation 8]
37. ! [X0] : ((humble(X0) <~> ~rich(X0)) | (creative(X0) <=> kind(X0))) [ennf transformation 11]
50. ! [X0] : (((generous(X0) | brave(X0)) | (brave(X0) | ~kind(X0))) & ((~brave(X0) & kind(X0)) | (~generous(X0) & ~brave(X0)))) [nnf transformation 6]
51. ! [X0] : ((generous(X0) | brave(X0) | brave(X0) | ~kind(X0)) & ((~brave(X0) & kind(X0)) | (~generous(X0) & ~brave(X0)))) [flattening 50]
52. (? [X0] : (~creative(X0) | ~old(X0)) | ! [X1] : (~patient(X1) | strong(X1))) & (? [X1] : (patient(X1) & ~strong(X1)) | ! [X0] : (creative(X0) & old(X0))) [nnf transformation 26]
53. (? [X0] : (~creative(X0) | ~old(X0)) | ! [X1] : (~patient(X1) | strong(X1))) & (? [X2] : (patient(X2) & ~strong(X2)) | ! [X3] : (creative(X3) & old(X3))) [rectify 52]
54. ? [X0] : (~creative(X0) | ~old(X0)) => (~creative(sK2) | ~old(sK2)) [choice axiom]
55. ? [X2] : (patient(X2) & ~strong(X2)) => (patient(sK3) & ~strong(sK3)) [choice axiom]
56. ((~creative(sK2) | ~old(sK2)) | ! [X1] : (~patient(X1) | strong(X1))) & ((patient(sK3) & ~strong(sK3)) | ! [X3] : (creative(X3) & old(X3))) [skolemisation 53,55,54]
58. ! [X0] : (((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0)))) [nnf transformation 37]
59. ! [X0] : ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))) [nnf transformation 12]
86. strong(X0) | calm(X0) | strong(X0) [cnf transformation 31]
88. humble(X0) | brave(X0) [cnf transformation 32]
89. ~calm(X0) | brave(X0) [cnf transformation 32]
92. ~brave(X0) | ~brave(X0) [cnf transformation 51]
96. ~strong(sK3) | creative(X3) [cnf transformation 56]
101. ~kind(X0) | patient(X0) [cnf transformation 33]
107. ~creative(X0) | ~humble(X0) | kind(X0) | rich(X0) [cnf transformation 58]
109. ~humble(X0) | ~patient(X0) [cnf transformation 59]
110. humble(X0) | patient(X0) [cnf transformation 59]
132. ~rich(fred) [cnf transformation 24]
135. ~brave(X0) [duplicate literal removal 92]
137. calm(X0) | strong(X0) [duplicate literal removal 86]
139. 1 <=> ! [X1] : ~brave(X1) [avatar definition]
140. ~brave(X1) <- (1) [avatar component clause 139]
173. 1 [avatar split clause 135,139]
187. 12 <=> ! [X3] : creative(X3) [avatar definition]
188. creative(X3) <- (12) [avatar component clause 187]
199. 15 <=> strong(sK3) [avatar definition]
201. ~strong(sK3) <- (~15) [avatar component clause 199]
202. 12 | ~15 [avatar split clause 96,199,187]
276. ~patient(X0) | brave(X0) [resolution 109,88]
277. ~patient(X0) <- (1) [subsumption resolution 276,140]
291. strong(X0) | brave(X0) [resolution 137,89]
292. strong(X0) <- (1) [subsumption resolution 291,140]
294. $false <- (1, ~15) [resolution 292,201]
297. ~1 | 15 [avatar contradiction clause 294]
320. ~humble(X0) | kind(X0) | rich(X0) <- (12) [resolution 107,188]
322. kind(X0) | rich(X0) | patient(X0) <- (12) [resolution 320,110]
325. kind(X0) | rich(X0) <- (1, 12) [subsumption resolution 322,277]
329. rich(X3) | patient(X3) <- (1, 12) [resolution 325,101]
336. rich(X3) <- (1, 12) [subsumption resolution 329,277]
337. $false <- (1, 12) [resolution 336,132]
339. ~1 | ~12 [avatar contradiction clause 337]
340. $false [avatar sat refutation 173,202,297,339]
% SZS output end Proof for 5312793088149160939263730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not happy is not brave or not funny and vice versa. Everyone who is creative is both tall and not generous. If john is brave then lucy is humble. If someone is funny then john is either not rich or happy. Everyone who is strong or old is old or creative. Everyone who is not quiet or happy is both not happy and generous. Everyone who is old is either generous or quiet and vice versa. Everyone who is calm or not happy is not wise. Everyone who is either not old or humble is both not creative and calm and vice versa. If alice is rich or wise then someone is both rich and creative and vice versa. Everyone who is not calm is either tall or rich and vice versa. If fred is both brave and not calm then mary is tall. If mary is either curious or happy then someone is both not patient and not creative and vice versa. Everyone who is tall or not quiet is both quiet and not funny and vice versa. If lucy is happy then someone is not old and vice versa. Everyone who is both not brave and not rich is both not generous and not tall. Fred is either strong or tall. Someone is not curious or not wise. Someone is old or quiet. Someone is either humble or old. Someone is either old or not curious. Someone is either not strong or tall. | Fred is not generous. | entailment | (![X]:((~kind(X)|~happy(X))<=>(~brave(X)|~funny(X))))&
(![X]:(creative(X)=>(tall(X)&~generous(X))))&
((brave(john))=>(humble(lucy)))&
((?[X]:(funny(X)))=>((~rich(john)<~>happy(john))))&
(![X]:((strong(X)|old(X))=>(old(X)|creative(X))))&
(![X]:((~quiet(X)|happy(X))=>(~happy(X)&generous(X))))&
(![X]:(old(X)<=>(generous(X)<~>quiet(X))))&
(![X]:((calm(X)|~happy(X))=>~wise(X)))&
(![X]:((~old(X)<~>humble(X))<=>(~creative(X)&calm(X))))&
(((rich(alice)|wise(alice)))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(~calm(X)<=>(tall(X)<~>rich(X))))&
(((brave(fred)&~calm(fred)))=>(tall(mary)))&
(((curious(mary)<~>happy(mary)))<=>(?[X]:((~patient(X)&~creative(X)))))&
(![X]:((tall(X)|~quiet(X))<=>(quiet(X)&~funny(X))))&
((happy(lucy))<=>(?[X]:(~old(X))))&
(![X]:((~brave(X)&~rich(X))=>(~generous(X)&~tall(X))))&
((strong(fred)<~>tall(fred)))&
(?[X]:((~curious(X)|~wise(X))))&
(?[X]:((old(X)|quiet(X))))&
(?[X]:((humble(X)<~>old(X))))&
(?[X]:((old(X)<~>~curious(X))))&
(?[X]:((~strong(X)<~>tall(X)))) | ~generous(fred) | [
"p5",
"p6",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6917073108771834594213824
% SZS output start Proof for 6917073108771834594213824
6. ! [X0] : ((happy(X0) | ~quiet(X0)) => (generous(X0) & ~happy(X0))) [input p5]
7. ! [X0] : (old(X0) <=> (generous(X0) <~> quiet(X0))) [input p6]
14. ! [X0] : ((~quiet(X0) | tall(X0)) <=> (~funny(X0) & quiet(X0))) [input p13]
15. happy(lucy) <=> ? [X0] : ~old(X0) [input p14]
23. generous(fred) [input hypothesis]
29. ! [X0] : ((generous(X0) & ~happy(X0)) | (~happy(X0) & quiet(X0))) [ennf transformation 6]
38. ! [X0] : ((old(X0) | ((generous(X0) | ~quiet(X0)) & (quiet(X0) | ~generous(X0)))) & (((~quiet(X0) | ~generous(X0)) & (quiet(X0) | generous(X0))) | ~old(X0))) [nnf transformation 7]
51. ! [X0] : (((~quiet(X0) | tall(X0)) | (funny(X0) | ~quiet(X0))) & ((~funny(X0) & quiet(X0)) | (quiet(X0) & ~tall(X0)))) [nnf transformation 14]
52. ! [X0] : ((~quiet(X0) | tall(X0) | funny(X0) | ~quiet(X0)) & ((~funny(X0) & quiet(X0)) | (quiet(X0) & ~tall(X0)))) [flattening 51]
53. (happy(lucy) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~happy(lucy)) [nnf transformation 15]
54. (happy(lucy) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~happy(lucy)) [rectify 53]
55. ? [X1] : ~old(X1) => ~old(sK2) [choice axiom]
56. (happy(lucy) | ! [X0] : old(X0)) & (~old(sK2) | ~happy(lucy)) [skolemisation 54,55]
83. ~happy(X0) | ~happy(X0) [cnf transformation 29]
87. ~quiet(X0) | ~generous(X0) | ~old(X0) [cnf transformation 38]
115. quiet(X0) | quiet(X0) [cnf transformation 52]
120. happy(lucy) | old(X0) [cnf transformation 56]
133. generous(fred) [cnf transformation 23]
134. quiet(X0) [duplicate literal removal 115]
136. ~happy(X0) [duplicate literal removal 83]
215. old(X0) [subsumption resolution 120,136]
242. ~generous(X2) | ~old(X2) [resolution 87,134]
243. ~generous(X2) [subsumption resolution 242,215]
244. $false [resolution 243,133]
% SZS output end Proof for 6917073108771834594213824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or not patient is creative.
If john is not patient then someone is both wise and not kind and vice versa.
If fred is not humble then someone is curious.
If alice is not patient then fred is either not strong or not quiet and vice versa.
Everyone who is strong or not rich is both creative and not patient.
Everyone who is both not happy and quiet is either not old or not happy and vice versa.
Everyone who is both funny and not creative is not quiet or not wise and vice versa.
If someone is quiet or not wise then someone is both not old and not rich and vice versa.
Everyone who is either strong or old is not kind or humble.
Everyone who is quiet is old or not funny and vice versa.
If someone is either not curious or kind then paul is both not calm and not creative and vice versa.
Everyone who is both not funny and not humble is both not old and brave.
Everyone who is old or not tall is patient.
If john is old then someone is not happy.
Fred is patient.
Mary is either patient or not rich.
Paul is not curious.
John is both kind and not curious.
Lucy is rich or not rich.
Someone is not strong.
Someone is not tall or not patient. | John is not creative. | entailment | (![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fred))=>(?[X]:(curious(X))))&
((~patient(alice))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:((strong(X)|~rich(X))=>(creative(X)&~patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~old(X)<~>~happy(X))))&
(![X]:((funny(X)&~creative(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|humble(X))))&
(![X]:(quiet(X)<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>kind(X))))<=>((~calm(paul)&~creative(paul))))&
(![X]:((~funny(X)&~humble(X))=>(~old(X)&brave(X))))&
(![X]:((old(X)|~tall(X))=>patient(X)))&
((old(john))=>(?[X]:(~happy(X))))&
(patient(fred))&
((patient(mary)<~>~rich(mary)))&
(~curious(paul))&
((kind(john)&~curious(john)))&
((rich(lucy)|~rich(lucy)))&
(?[X]:(~strong(X)))&
(?[X]:((~tall(X)|~patient(X)))) | ~creative(john) | [
"p4",
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 9047279716345359593774009
% SZS output start Proof for 9047279716345359593774009
5. ! [X0] : ((~rich(X0) | strong(X0)) => (~patient(X0) & creative(X0))) [input p4]
6. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p5]
7. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p6]
8. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X0] : (~rich(X0) & ~old(X0)) [input p7]
22. creative(john) [input hypothesis]
23. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X1] : (~rich(X1) & ~old(X1)) [rectify 8]
29. ! [X0] : ((~patient(X0) & creative(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 5]
37. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 6]
38. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ~quiet(X0) | happy(X0))) [flattening 37]
39. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 7]
40. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | creative(X0) | ~funny(X0))) [flattening 39]
41. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X1] : (~rich(X1) & ~old(X1)) | ! [X0] : (wise(X0) & ~quiet(X0))) [nnf transformation 23]
42. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X2] : (~rich(X2) & ~old(X2)) | ! [X3] : (wise(X3) & ~quiet(X3))) [rectify 41]
43. ? [X0] : (~wise(X0) | quiet(X0)) => (~wise(sK1) | quiet(sK1)) [choice axiom]
44. ? [X2] : (~rich(X2) & ~old(X2)) => (~rich(sK2) & ~old(sK2)) [choice axiom]
45. ((~wise(sK1) | quiet(sK1)) | ! [X1] : (rich(X1) | old(X1))) & ((~rich(sK2) & ~old(sK2)) | ! [X3] : (wise(X3) & ~quiet(X3))) [skolemisation 42,44,43]
70. rich(X0) | creative(X0) [cnf transformation 29]
74. happy(X0) | old(X0) | ~quiet(X0) | happy(X0) [cnf transformation 38]
75. ~happy(X0) | ~happy(X0) | old(X0) [cnf transformation 38]
82. ~creative(X0) | quiet(X0) [cnf transformation 40]
84. ~old(sK2) | ~quiet(X3) [cnf transformation 45]
86. ~rich(sK2) | ~quiet(X3) [cnf transformation 45]
110. creative(john) [cnf transformation 22]
111. happy(X0) | old(X0) | ~quiet(X0) [duplicate literal removal 74]
112. ~happy(X0) | old(X0) [duplicate literal removal 75]
147. ~quiet(X0) | old(X0) [subsumption resolution 111,112]
164. 12 <=> rich(sK2) [avatar definition]
166. ~rich(sK2) <- (~12) [avatar component clause 164]
169. 13 <=> ! [X3] : ~quiet(X3) [avatar definition]
170. ~quiet(X3) <- (13) [avatar component clause 169]
171. 13 | ~12 [avatar split clause 86,164,169]
173. 14 <=> old(sK2) [avatar definition]
175. ~old(sK2) <- (~14) [avatar component clause 173]
177. 13 | ~14 [avatar split clause 84,173,169]
235. creative(sK2) <- (~12) [resolution 70,166]
240. quiet(john) [resolution 82,110]
243. quiet(sK2) <- (~12) [resolution 82,235]
257. old(sK2) <- (~12) [resolution 147,243]
260. $false <- (~12, ~14) [subsumption resolution 257,175]
261. 12 | 14 [avatar contradiction clause 260]
265. $false <- (13) [resolution 170,240]
270. ~13 [avatar contradiction clause 265]
271. $false [avatar sat refutation 171,177,261,270]
% SZS output end Proof for 9047279716345359593774009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or not generous is rich and vice versa.
Everyone who is not brave or not strong is both not old and not wise and vice versa.
If someone is creative or patient then paul is brave and vice versa.
Everyone who is humble is both funny and not quiet.
Everyone who is funny is both happy and not tall and vice versa.
Everyone who is either not calm or not generous is either not wise or not rich and vice versa.
Everyone who is either not brave or curious is happy.
Everyone who is both not creative and quiet is not creative.
Everyone who is funny is not funny or curious and vice versa.
Everyone who is both curious and happy is both brave and kind and vice versa.
Everyone who is either not patient or not rich is either not brave or strong.
If mary is both not brave and calm then someone is either quiet or wise.
If someone is both not brave and humble then alice is both not strong and wise.
If paul is not strong then someone is not generous or rich.
If someone is not wise or patient then someone is either rich or creative and vice versa.
If someone is either rich or old then alice is both not rich and creative.
Someone is not calm or brave.
Alice is patient.
Someone is not patient.
Alice is not creative.
Someone is both not wise and funny. | Mary is generous. | neutral | (![X]:((~creative(X)<~>~generous(X))<=>rich(X)))&
(![X]:((~brave(X)|~strong(X))<=>(~old(X)&~wise(X))))&
((?[X]:((creative(X)|patient(X))))<=>(brave(paul)))&
(![X]:(humble(X)=>(funny(X)&~quiet(X))))&
(![X]:(funny(X)<=>(happy(X)&~tall(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:((~brave(X)<~>curious(X))=>happy(X)))&
(![X]:((~creative(X)&quiet(X))=>~creative(X)))&
(![X]:(funny(X)<=>(~funny(X)|curious(X))))&
(![X]:((curious(X)&happy(X))<=>(brave(X)&kind(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(~brave(X)<~>strong(X))))&
(((~brave(mary)&calm(mary)))=>(?[X]:((quiet(X)<~>wise(X)))))&
((?[X]:((~brave(X)&humble(X))))=>((~strong(alice)&wise(alice))))&
((~strong(paul))=>(?[X]:((~generous(X)|rich(X)))))&
((?[X]:((~wise(X)|patient(X))))<=>(?[X]:((rich(X)<~>creative(X)))))&
((?[X]:((rich(X)<~>old(X))))=>((~rich(alice)&creative(alice))))&
(?[X]:((~calm(X)|brave(X))))&
(patient(alice))&
(?[X]:(~patient(X)))&
(~creative(alice))&
(?[X]:((~wise(X)&funny(X)))) | generous(mary) | [] | null | 0 |
Everyone who is not generous or not funny is either not calm or rich and vice versa.
If mary is either patient or quiet then someone is both not generous and tall and vice versa.
Everyone who is not curious or not funny is either not old or not quiet.
If someone is either calm or not brave then someone is both not calm and not brave and vice versa.
Everyone who is both quiet and not kind is both not creative and kind.
If someone is not tall then someone is both not strong and kind.
If lucy is calm or not quiet then alice is both calm and curious and vice versa.
Everyone who is not kind or strong is either not humble or patient and vice versa.
If someone is not rich then alice is calm.
Everyone who is either quiet or not calm is not humble or wise.
If someone is either not curious or not tall then someone is quiet or creative.
Everyone who is either not humble or not wise is either not patient or rich and vice versa.
If someone is kind then someone is strong.
Everyone who is either old or not curious is not kind or old.
Everyone who is old is either kind or funny.
If lucy is strong then susan is not funny or not rich and vice versa.
Susan is either generous or not kind.
Someone is not wise or not rich.
Someone is both rich and kind.
Alice is not kind or calm.
Lucy is both not wise and funny.
Someone is either strong or not calm.
Someone is not happy.
Mary is either not tall or generous. | Susan is kind. | neutral | (![X]:((~generous(X)|~funny(X))<=>(~calm(X)<~>rich(X))))&
(((patient(mary)<~>quiet(mary)))<=>(?[X]:((~generous(X)&tall(X)))))&
(![X]:((~curious(X)|~funny(X))=>(~old(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((quiet(X)&~kind(X))=>(~creative(X)&kind(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~strong(X)&kind(X)))))&
(((calm(lucy)|~quiet(lucy)))<=>((calm(alice)&curious(alice))))&
(![X]:((~kind(X)|strong(X))<=>(~humble(X)<~>patient(X))))&
((?[X]:(~rich(X)))=>(calm(alice)))&
(![X]:((quiet(X)<~>~calm(X))=>(~humble(X)|wise(X))))&
((?[X]:((~curious(X)<~>~tall(X))))=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:((~humble(X)<~>~wise(X))<=>(~patient(X)<~>rich(X))))&
((?[X]:(kind(X)))=>(?[X]:(strong(X))))&
(![X]:((old(X)<~>~curious(X))=>(~kind(X)|old(X))))&
(![X]:(old(X)=>(kind(X)<~>funny(X))))&
((strong(lucy))<=>((~funny(susan)|~rich(susan))))&
((generous(susan)<~>~kind(susan)))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((rich(X)&kind(X))))&
((~kind(alice)|calm(alice)))&
((~wise(lucy)&funny(lucy)))&
(?[X]:((strong(X)<~>~calm(X))))&
(?[X]:(~happy(X)))&
((~tall(mary)<~>generous(mary))) | kind(susan) | [] | null | 0 |
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.
Everyone who is not funny is either funny or not wise and vice versa.
If lucy is either not happy or quiet then john is generous.
Everyone who is both brave and rich is old or not wise and vice versa.
If someone is either curious or not creative then alice is tall.
Someone is either not wise or patient.
Fred is either tall or not humble.
Lucy is not humble.
Someone is quiet or not calm.
Someone is both not kind and old. | Susan is calm. | contradiction | (![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]:(~funny(X)<=>(funny(X)<~>~wise(X))))&
(((~happy(lucy)<~>quiet(lucy)))=>(generous(john)))&
(![X]:((brave(X)&rich(X))<=>(old(X)|~wise(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>(tall(alice)))&
(?[X]:((~wise(X)<~>patient(X))))&
((tall(fred)<~>~humble(fred)))&
(~humble(lucy))&
(?[X]:((quiet(X)|~calm(X))))&
(?[X]:((~kind(X)&old(X)))) | calm(susan) | [
"p1",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2692753529526955988518113
% SZS output start Proof for 2692753529526955988518113
2. ! [X0] : ((~calm(X0) <~> ~curious(X0)) <=> (~strong(X0) | generous(X0))) [input p1]
5. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> strong(X0)) [input p4]
8. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X0] : curious(X0) [input p7]
22. calm(susan) [input hypothesis]
23. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X1] : curious(X1) [rectify 8]
35. ! [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 2]
36. ! [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 35]
39. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [nnf transformation 5]
40. ! [X0] : ((~generous(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [flattening 39]
45. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (funny(X0) | ~generous(X0))) [nnf transformation 23]
46. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (funny(X3) | ~generous(X3))) [rectify 45]
47. ? [X0] : (~funny(X0) & generous(X0)) => (~funny(sK1) & generous(sK1)) [choice axiom]
48. ? [X2] : curious(X2) => curious(sK2) [choice axiom]
49. ((~funny(sK1) & generous(sK1)) | ! [X1] : ~curious(X1)) & (curious(sK2) | ! [X3] : (funny(X3) | ~generous(X3))) [skolemisation 46,48,47]
70. ~strong(X0) | generous(X0) | ~calm(X0) | curious(X0) [cnf transformation 36]
83. strong(X0) | strong(X0) [cnf transformation 40]
84. strong(X0) | generous(X0) [cnf transformation 40]
85. ~generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 40]
94. generous(sK1) | ~curious(X1) [cnf transformation 49]
130. calm(susan) [cnf transformation 22]
133. strong(X0) [duplicate literal removal 83]
134. ~strong(X0) | ~generous(X0) [duplicate literal removal 85]
163. 6 <=> ! [X1] : ~curious(X1) [avatar definition]
164. ~curious(X1) <- (6) [avatar component clause 163]
171. 8 <=> generous(sK1) [avatar definition]
173. generous(sK1) <- (8) [avatar component clause 171]
174. 6 | 8 [avatar split clause 94,171,163]
260. ~generous(X1) [resolution 134,133]
264. $false <- (8) [subsumption resolution 173,260]
265. ~8 [avatar contradiction clause 264]
288. generous(X1) | ~calm(X1) | curious(X1) | generous(X1) [resolution 70,84]
290. generous(X1) | ~calm(X1) | curious(X1) [duplicate literal removal 288]
292. ~calm(X1) | curious(X1) [subsumption resolution 290,260]
293. ~calm(X1) <- (6) [subsumption resolution 292,164]
295. $false <- (6) [resolution 293,130]
296. ~6 [avatar contradiction clause 295]
297. $false [avatar sat refutation 174,265,296]
% SZS output end Proof for 2692753529526955988518113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or not quiet is not creative or kind and vice versa. Everyone who is both happy and not creative is not calm and vice versa. If john is both not patient and not strong then someone is either not happy or tall. If someone is both rich and old then susan is either funny or not tall. Everyone who is either generous or rich is not creative. Everyone who is not calm is both tall and not tall and vice versa. If someone is both not patient and funny then someone is both happy and not wise. Everyone who is both not calm and humble is calm or patient. Everyone who is either humble or not strong is not wise and vice versa. If susan is both not brave and not calm then fred is both generous and not patient and vice versa. If someone is not brave or quiet then susan is not patient or wise and vice versa. Everyone who is both curious and not funny is not patient or not kind. Everyone who is not wise or not old is wise or not strong. If someone is not patient or not curious then paul is either patient or not happy. Everyone who is kind or humble is both wise and not creative. Everyone who is both brave and happy is not humble or brave. Someone is either not calm or rich. Alice is funny. Someone is either happy or not patient. Someone is both quiet and patient. Lucy is both not patient and not creative. Mary is not brave or not wise. Someone is not generous. | Paul is not calm. | contradiction | (![X]:((quiet(X)|~quiet(X))<=>(~creative(X)|kind(X))))&
(![X]:((happy(X)&~creative(X))<=>~calm(X)))&
(((~patient(john)&~strong(john)))=>(?[X]:((~happy(X)<~>tall(X)))))&
((?[X]:((rich(X)&old(X))))=>((funny(susan)<~>~tall(susan))))&
(![X]:((generous(X)<~>rich(X))=>~creative(X)))&
(![X]:(~calm(X)<=>(tall(X)&~tall(X))))&
((?[X]:((~patient(X)&funny(X))))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~calm(X)&humble(X))=>(calm(X)|patient(X))))&
(![X]:((humble(X)<~>~strong(X))<=>~wise(X)))&
(((~brave(susan)&~calm(susan)))<=>((generous(fred)&~patient(fred))))&
((?[X]:((~brave(X)|quiet(X))))<=>((~patient(susan)|wise(susan))))&
(![X]:((curious(X)&~funny(X))=>(~patient(X)|~kind(X))))&
(![X]:((~wise(X)|~old(X))=>(wise(X)|~strong(X))))&
((?[X]:((~patient(X)|~curious(X))))=>((patient(paul)<~>~happy(paul))))&
(![X]:((kind(X)|humble(X))=>(wise(X)&~creative(X))))&
(![X]:((brave(X)&happy(X))=>(~humble(X)|brave(X))))&
(?[X]:((~calm(X)<~>rich(X))))&
(funny(alice))&
(?[X]:((happy(X)<~>~patient(X))))&
(?[X]:((quiet(X)&patient(X))))&
((~patient(lucy)&~creative(lucy)))&
((~brave(mary)|~wise(mary)))&
(?[X]:(~generous(X))) | ~calm(paul) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5048997651351075755954977
% SZS output start Proof for 5048997651351075755954977
6. ! [X0] : (~calm(X0) <=> (~tall(X0) & tall(X0))) [input p5]
24. ~calm(paul) [input hypothesis]
50. ! [X0] : ((~calm(X0) | (tall(X0) | ~tall(X0))) & ((~tall(X0) & tall(X0)) | calm(X0))) [nnf transformation 6]
51. ! [X0] : ((~calm(X0) | tall(X0) | ~tall(X0)) & ((~tall(X0) & tall(X0)) | calm(X0))) [flattening 50]
87. tall(X0) | calm(X0) [cnf transformation 51]
88. ~tall(X0) | calm(X0) [cnf transformation 51]
128. ~calm(paul) [cnf transformation 24]
163. calm(X0) [subsumption resolution 87,88]
257. $false [subsumption resolution 128,163]
% SZS output end Proof for 5048997651351075755954977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or kind is either not funny or generous and vice versa. If someone is not strong or not kind then fred is not generous or wise and vice versa. Everyone who is either calm or old is rich and vice versa. If someone is either calm or happy then someone is not tall and vice versa. If someone is humble or calm then mary is either patient or not tall. If alice is funny then john is both not old and not wise. Everyone who is both not generous and not brave is both curious and brave and vice versa. Everyone who is not brave is kind or not tall and vice versa. If fred is not funny or not humble then lucy is either not creative or wise and vice versa. Everyone who is both brave and not tall is creative or not wise. If paul is not brave then lucy is either brave or creative. Everyone who is both funny and not happy is either curious or wise. Everyone who is either old or curious is not calm and vice versa. Everyone who is either not wise or not brave is both not strong and not creative and vice versa. If john is humble then lucy is both not quiet and not happy. Everyone who is either not humble or not kind is not tall or old and vice versa. Susan is either brave or rich. Someone is kind. Fred is not happy. Susan is both not creative and not patient. Someone is tall or brave. Alice is both curious and funny. | Susan is calm. | neutral | (![X]:((brave(X)<~>kind(X))<=>(~funny(X)<~>generous(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>((~generous(fred)|wise(fred))))&
(![X]:((calm(X)<~>old(X))<=>rich(X)))&
((?[X]:((calm(X)<~>happy(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((humble(X)|calm(X))))=>((patient(mary)<~>~tall(mary))))&
((funny(alice))=>((~old(john)&~wise(john))))&
(![X]:((~generous(X)&~brave(X))<=>(curious(X)&brave(X))))&
(![X]:(~brave(X)<=>(kind(X)|~tall(X))))&
(((~funny(fred)|~humble(fred)))<=>((~creative(lucy)<~>wise(lucy))))&
(![X]:((brave(X)&~tall(X))=>(creative(X)|~wise(X))))&
((~brave(paul))=>((brave(lucy)<~>creative(lucy))))&
(![X]:((funny(X)&~happy(X))=>(curious(X)<~>wise(X))))&
(![X]:((old(X)<~>curious(X))<=>~calm(X)))&
(![X]:((~wise(X)<~>~brave(X))<=>(~strong(X)&~creative(X))))&
((humble(john))=>((~quiet(lucy)&~happy(lucy))))&
(![X]:((~humble(X)<~>~kind(X))<=>(~tall(X)|old(X))))&
((brave(susan)<~>rich(susan)))&
(?[X]:(kind(X)))&
(~happy(fred))&
((~creative(susan)&~patient(susan)))&
(?[X]:((tall(X)|brave(X))))&
((curious(alice)&funny(alice))) | calm(susan) | [] | null | 0 |
Everyone who is not quiet is both not patient and not curious. Everyone who is either humble or generous is not funny and vice versa. Everyone who is not patient is both kind and rich and vice versa. Everyone who is either old or not happy is generous. If someone is both not quiet and not old then fred is wise or not patient and vice versa. Everyone who is both not old and not curious is not humble and vice versa. If someone is either wise or not rich then susan is happy or calm and vice versa. Everyone who is strong is rich and vice versa. Everyone who is both humble and not calm is not curious and vice versa. Everyone who is both tall and old is humble. Everyone who is not kind is either strong or not rich and vice versa. Everyone who is either rich or strong is both patient and not funny and vice versa. If alice is generous then someone is either generous or not wise. If mary is calm or not happy then someone is creative or not generous and vice versa. If lucy is both quiet and kind then john is not old. Everyone who is generous or not humble is strong or not humble. Paul is not calm. Someone is not wise or curious. Someone is not humble or not brave. Someone is creative or not quiet. Susan is either not quiet or not kind. Lucy is not tall. | Alice is not humble. | contradiction | (![X]:(~quiet(X)=>(~patient(X)&~curious(X))))&
(![X]:((humble(X)<~>generous(X))<=>~funny(X)))&
(![X]:(~patient(X)<=>(kind(X)&rich(X))))&
(![X]:((old(X)<~>~happy(X))=>generous(X)))&
((?[X]:((~quiet(X)&~old(X))))<=>((wise(fred)|~patient(fred))))&
(![X]:((~old(X)&~curious(X))<=>~humble(X)))&
((?[X]:((wise(X)<~>~rich(X))))<=>((happy(susan)|calm(susan))))&
(![X]:(strong(X)<=>rich(X)))&
(![X]:((humble(X)&~calm(X))<=>~curious(X)))&
(![X]:((tall(X)&old(X))=>humble(X)))&
(![X]:(~kind(X)<=>(strong(X)<~>~rich(X))))&
(![X]:((rich(X)<~>strong(X))<=>(patient(X)&~funny(X))))&
((generous(alice))=>(?[X]:((generous(X)<~>~wise(X)))))&
(((calm(mary)|~happy(mary)))<=>(?[X]:((creative(X)|~generous(X)))))&
(((quiet(lucy)&kind(lucy)))=>(~old(john)))&
(![X]:((generous(X)|~humble(X))=>(strong(X)|~humble(X))))&
(~calm(paul))&
(?[X]:((~wise(X)|curious(X))))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:((creative(X)|~quiet(X))))&
((~quiet(susan)<~>~kind(susan)))&
(~tall(lucy)) | ~humble(alice) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1679185341687531603201691
% SZS output start Proof for 1679185341687531603201691
6. ! [X0] : ((~curious(X0) & ~old(X0)) <=> ~humble(X0)) [input p5]
9. ! [X0] : ((~calm(X0) & humble(X0)) <=> ~curious(X0)) [input p8]
23. ~humble(alice) [input hypothesis]
43. ! [X0] : (((~curious(X0) & ~old(X0)) | humble(X0)) & (~humble(X0) | (curious(X0) | old(X0)))) [nnf transformation 6]
44. ! [X0] : (((~curious(X0) & ~old(X0)) | humble(X0)) & (~humble(X0) | curious(X0) | old(X0))) [flattening 43]
51. ! [X0] : (((~calm(X0) & humble(X0)) | curious(X0)) & (~curious(X0) | (calm(X0) | ~humble(X0)))) [nnf transformation 9]
52. ! [X0] : (((~calm(X0) & humble(X0)) | curious(X0)) & (~curious(X0) | calm(X0) | ~humble(X0))) [flattening 51]
87. ~curious(X0) | humble(X0) [cnf transformation 44]
97. humble(X0) | curious(X0) [cnf transformation 52]
123. ~humble(alice) [cnf transformation 23]
176. humble(X0) [subsumption resolution 97,87]
244. $false [subsumption resolution 123,176]
% SZS output end Proof for 1679185341687531603201691
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or brave is either not curious or generous. If someone is not old or not wise then fred is not humble and vice versa. Everyone who is not humble or creative is not wise or calm and vice versa. Everyone who is not rich or rich is creative or wise. If someone is wise then someone is happy. Everyone who is not strong is both patient and not creative and vice versa. Everyone who is either wise or calm is either not patient or not creative and vice versa. Everyone who is either calm or not patient is rich or not creative. Everyone who is not creative or patient is either not wise or not brave. If someone is not calm then someone is kind. If john is either kind or not humble then susan is both not happy and brave and vice versa. Everyone who is wise is happy or not wise and vice versa. Everyone who is either happy or not humble is not curious and vice versa. If john is not tall then someone is not calm or happy. Everyone who is either not brave or wise is both not funny and not brave and vice versa. Everyone who is not creative or not happy is both curious and not creative. Someone is curious or not wise. Mary is both not kind and wise. Paul is either rich or humble. Someone is both curious and tall. Someone is kind. Someone is not curious or funny. Fred is not curious. | Mary is not strong. | contradiction | (![X]:((~quiet(X)<~>brave(X))=>(~curious(X)<~>generous(X))))&
((?[X]:((~old(X)|~wise(X))))<=>(~humble(fred)))&
(![X]:((~humble(X)|creative(X))<=>(~wise(X)|calm(X))))&
(![X]:((~rich(X)|rich(X))=>(creative(X)|wise(X))))&
((?[X]:(wise(X)))=>(?[X]:(happy(X))))&
(![X]:(~strong(X)<=>(patient(X)&~creative(X))))&
(![X]:((wise(X)<~>calm(X))<=>(~patient(X)<~>~creative(X))))&
(![X]:((calm(X)<~>~patient(X))=>(rich(X)|~creative(X))))&
(![X]:((~creative(X)|patient(X))=>(~wise(X)<~>~brave(X))))&
((?[X]:(~calm(X)))=>(?[X]:(kind(X))))&
(((kind(john)<~>~humble(john)))<=>((~happy(susan)&brave(susan))))&
(![X]:(wise(X)<=>(happy(X)|~wise(X))))&
(![X]:((happy(X)<~>~humble(X))<=>~curious(X)))&
((~tall(john))=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:((~brave(X)<~>wise(X))<=>(~funny(X)&~brave(X))))&
(![X]:((~creative(X)|~happy(X))=>(curious(X)&~creative(X))))&
(?[X]:((curious(X)|~wise(X))))&
((~kind(mary)&wise(mary)))&
((rich(paul)<~>humble(paul)))&
(?[X]:((curious(X)&tall(X))))&
(?[X]:(kind(X)))&
(?[X]:((~curious(X)|funny(X))))&
(~curious(fred)) | ~strong(mary) | [
"p2",
"p3",
"p5",
"p6",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5844999314248302696236996
% SZS output start Proof for 5844999314248302696236996
3. ! [X0] : ((creative(X0) | ~humble(X0)) <=> (calm(X0) | ~wise(X0))) [input p2]
4. ! [X0] : ((rich(X0) | ~rich(X0)) => (wise(X0) | creative(X0))) [input p3]
6. ! [X0] : (~strong(X0) <=> (~creative(X0) & patient(X0))) [input p5]
7. ! [X0] : ((wise(X0) <~> calm(X0)) <=> (~patient(X0) <~> ~creative(X0))) [input p6]
12. ! [X0] : (wise(X0) <=> (~wise(X0) | happy(X0))) [input p11]
13. ! [X0] : ((happy(X0) <~> ~humble(X0)) <=> ~curious(X0)) [input p12]
16. ! [X0] : ((~happy(X0) | ~creative(X0)) => (~creative(X0) & curious(X0))) [input p15]
24. ~strong(mary) [input hypothesis]
27. ! [X0] : (~strong(X0) => (~creative(X0) & patient(X0))) [unused predicate definition removal 6]
31. ! [X0] : ((wise(X0) | creative(X0)) | (~rich(X0) & rich(X0))) [ennf transformation 4]
32. ! [X0] : (wise(X0) | creative(X0) | (~rich(X0) & rich(X0))) [flattening 31]
34. ! [X0] : ((~creative(X0) & patient(X0)) | strong(X0)) [ennf transformation 27]
39. ! [X0] : ((~creative(X0) & curious(X0)) | (happy(X0) & creative(X0))) [ennf transformation 16]
45. ! [X0] : (((creative(X0) | ~humble(X0)) | (~calm(X0) & wise(X0))) & ((calm(X0) | ~wise(X0)) | (~creative(X0) & humble(X0)))) [nnf transformation 3]
46. ! [X0] : ((creative(X0) | ~humble(X0) | (~calm(X0) & wise(X0))) & (calm(X0) | ~wise(X0) | (~creative(X0) & humble(X0)))) [flattening 45]
50. ! [X0] : ((((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) | ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0)))) & (((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) | ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0))))) [nnf transformation 7]
58. ! [X0] : ((wise(X0) | (wise(X0) & ~happy(X0))) & ((~wise(X0) | happy(X0)) | ~wise(X0))) [nnf transformation 12]
59. ! [X0] : ((wise(X0) | (wise(X0) & ~happy(X0))) & (~wise(X0) | happy(X0) | ~wise(X0))) [flattening 58]
60. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | curious(X0)) & (~curious(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [nnf transformation 13]
79. ~wise(X0) | calm(X0) | humble(X0) [cnf transformation 46]
83. wise(X0) | creative(X0) | rich(X0) [cnf transformation 32]
84. ~rich(X0) | creative(X0) | wise(X0) [cnf transformation 32]
86. patient(X0) | strong(X0) [cnf transformation 34]
87. ~creative(X0) | strong(X0) [cnf transformation 34]
95. ~calm(X0) | ~wise(X0) | ~patient(X0) | creative(X0) [cnf transformation 50]
109. ~wise(X0) | happy(X0) | ~wise(X0) [cnf transformation 59]
111. wise(X0) | wise(X0) [cnf transformation 59]
112. ~happy(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 60]
122. creative(X0) | curious(X0) [cnf transformation 39]
135. ~strong(mary) [cnf transformation 24]
138. ~wise(X0) | happy(X0) [duplicate literal removal 109]
139. wise(X0) [duplicate literal removal 111]
154. 4 <=> ! [X1] : wise(X1) [avatar definition]
155. wise(X1) <- (4) [avatar component clause 154]
161. creative(X0) | wise(X0) [subsumption resolution 83,84]
170. ~patient(X0) | ~calm(X0) | creative(X0) [subsumption resolution 95,161]
208. 4 [avatar split clause 139,154]
242. strong(X0) | curious(X0) [resolution 122,87]
249. happy(X0) <- (4) [resolution 138,155]
259. calm(X0) | humble(X0) <- (4) [resolution 79,155]
260. curious(mary) [resolution 242,135]
270. ~humble(X0) | ~curious(X0) <- (4) [resolution 112,249]
298. ~calm(X1) | creative(X1) | strong(X1) [resolution 170,86]
310. ~calm(X1) | strong(X1) [subsumption resolution 298,87]
323. strong(X0) | humble(X0) <- (4) [resolution 310,259]
420. humble(mary) <- (4) [resolution 323,135]
422. ~curious(mary) <- (4) [resolution 420,270]
424. $false <- (4) [subsumption resolution 422,260]
425. ~4 [avatar contradiction clause 424]
426. $false [avatar sat refutation 208,425]
% SZS output end Proof for 5844999314248302696236996
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old or tall then someone is both not kind and quiet.
If someone is creative then someone is either rich or not strong.
If alice is either not kind or not humble then someone is either tall or not old and vice versa.
Everyone who is both not old and not brave is rich or curious.
Everyone who is humble is not rich.
Everyone who is not kind or not old is either calm or not quiet and vice versa.
Everyone who is not tall is either not humble or funny and vice versa.
If someone is rich then someone is not wise or kind and vice versa.
If mary is either not rich or not quiet then someone is wise.
If someone is both not rich and patient then alice is either not generous or not wise and vice versa.
Everyone who is both not generous and not patient is happy.
Everyone who is not quiet or not funny is not quiet or rich.
If someone is either patient or generous then john is not kind.
Everyone who is both not humble and curious is not funny or not strong and vice versa.
Everyone who is not old is either not tall or not calm and vice versa.
Everyone who is not old or not funny is both old and not old.
Someone is both not tall and curious.
Someone is not strong or not wise.
Someone is wise.
Someone is either not tall or brave.
Fred is not calm.
Someone is both happy and not humble.
Someone is both wise and strong. | Mary is funny. | entailment | ((?[X]:((~old(X)|tall(X))))=>(?[X]:((~kind(X)&quiet(X)))))&
((?[X]:(creative(X)))=>(?[X]:((rich(X)<~>~strong(X)))))&
(((~kind(alice)<~>~humble(alice)))<=>(?[X]:((tall(X)<~>~old(X)))))&
(![X]:((~old(X)&~brave(X))=>(rich(X)|curious(X))))&
(![X]:(humble(X)=>~rich(X)))&
(![X]:((~kind(X)|~old(X))<=>(calm(X)<~>~quiet(X))))&
(![X]:(~tall(X)<=>(~humble(X)<~>funny(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~wise(X)|kind(X)))))&
(((~rich(mary)<~>~quiet(mary)))=>(?[X]:(wise(X))))&
((?[X]:((~rich(X)&patient(X))))<=>((~generous(alice)<~>~wise(alice))))&
(![X]:((~generous(X)&~patient(X))=>happy(X)))&
(![X]:((~quiet(X)|~funny(X))=>(~quiet(X)|rich(X))))&
((?[X]:((patient(X)<~>generous(X))))=>(~kind(john)))&
(![X]:((~humble(X)&curious(X))<=>(~funny(X)|~strong(X))))&
(![X]:(~old(X)<=>(~tall(X)<~>~calm(X))))&
(![X]:((~old(X)|~funny(X))=>(old(X)&~old(X))))&
(?[X]:((~tall(X)&curious(X))))&
(?[X]:((~strong(X)|~wise(X))))&
(?[X]:(wise(X)))&
(?[X]:((~tall(X)<~>brave(X))))&
(~calm(fred))&
(?[X]:((happy(X)&~humble(X))))&
(?[X]:((wise(X)&strong(X)))) | funny(mary) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9183290086059651303587027
% SZS output start Proof for 9183290086059651303587027
16. ! [X0] : ((~funny(X0) | ~old(X0)) => (~old(X0) & old(X0))) [input p15]
24. ~funny(mary) [input hypothesis]
39. ! [X0] : ((~old(X0) & old(X0)) | (funny(X0) & old(X0))) [ennf transformation 16]
128. old(X0) | funny(X0) [cnf transformation 39]
130. ~old(X0) | funny(X0) [cnf transformation 39]
141. ~funny(mary) [cnf transformation 24]
266. funny(X0) [subsumption resolution 128,130]
287. $false [subsumption resolution 141,266]
% SZS output end Proof for 9183290086059651303587027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is patient or not curious then mary is either not curious or not tall and vice versa.
If someone is not kind then susan is not happy.
If susan is not brave then someone is not funny or not kind.
If fred is either not funny or happy then someone is either curious or humble and vice versa.
If someone is not old or strong then alice is both not creative and not calm.
If alice is quiet then someone is not wise and vice versa.
If someone is strong or not funny then someone is not creative and vice versa.
If alice is not creative or patient then fred is either not kind or not quiet and vice versa.
If someone is not brave then someone is either not curious or strong and vice versa.
Everyone who is either not tall or not curious is not brave or not funny.
Everyone who is not curious is either not creative or not happy.
Everyone who is not quiet or not patient is either not quiet or not old.
Everyone who is both not rich and brave is brave and vice versa.
Everyone who is creative is not calm and vice versa.
Everyone who is either not brave or not tall is either not happy or not calm and vice versa.
Everyone who is both not quiet and not humble is quiet or not old.
John is both not humble and not wise.
Someone is both not calm and creative.
Someone is either brave or not happy.
Lucy is patient or not rich.
Someone is tall.
Mary is generous.
Someone is either creative or not quiet.
Lucy is either not generous or not patient. | John is quiet. | entailment | (((patient(john)|~curious(john)))<=>((~curious(mary)<~>~tall(mary))))&
((?[X]:(~kind(X)))=>(~happy(susan)))&
((~brave(susan))=>(?[X]:((~funny(X)|~kind(X)))))&
(((~funny(fred)<~>happy(fred)))<=>(?[X]:((curious(X)<~>humble(X)))))&
((?[X]:((~old(X)|strong(X))))=>((~creative(alice)&~calm(alice))))&
((quiet(alice))<=>(?[X]:(~wise(X))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:(~creative(X))))&
(((~creative(alice)|patient(alice)))<=>((~kind(fred)<~>~quiet(fred))))&
((?[X]:(~brave(X)))<=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:((~tall(X)<~>~curious(X))=>(~brave(X)|~funny(X))))&
(![X]:(~curious(X)=>(~creative(X)<~>~happy(X))))&
(![X]:((~quiet(X)|~patient(X))=>(~quiet(X)<~>~old(X))))&
(![X]:((~rich(X)&brave(X))<=>brave(X)))&
(![X]:(creative(X)<=>~calm(X)))&
(![X]:((~brave(X)<~>~tall(X))<=>(~happy(X)<~>~calm(X))))&
(![X]:((~quiet(X)&~humble(X))=>(quiet(X)|~old(X))))&
((~humble(john)&~wise(john)))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((brave(X)<~>~happy(X))))&
((patient(lucy)|~rich(lucy)))&
(?[X]:(tall(X)))&
(generous(mary))&
(?[X]:((creative(X)<~>~quiet(X))))&
((~generous(lucy)<~>~patient(lucy))) | quiet(john) | [
"p11",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1083411086844935249257369
% SZS output start Proof for 1083411086844935249257369
12. ! [X0] : ((~patient(X0) | ~quiet(X0)) => (~quiet(X0) <~> ~old(X0))) [input p11]
16. ! [X0] : ((~humble(X0) & ~quiet(X0)) => (~old(X0) | quiet(X0))) [input p15]
17. ~wise(john) & ~humble(john) [input p16]
25. ~quiet(john) [input hypothesis]
34. ! [X0] : ((~quiet(X0) <~> ~old(X0)) | (patient(X0) & quiet(X0))) [ennf transformation 12]
35. ! [X0] : ((~old(X0) | quiet(X0)) | (humble(X0) | quiet(X0))) [ennf transformation 16]
36. ! [X0] : (~old(X0) | quiet(X0) | humble(X0) | quiet(X0)) [flattening 35]
63. ! [X0] : (((old(X0) | quiet(X0)) & (~old(X0) | ~quiet(X0))) | (patient(X0) & quiet(X0))) [nnf transformation 34]
120. old(X0) | quiet(X0) | quiet(X0) [cnf transformation 63]
135. ~old(X0) | quiet(X0) | humble(X0) | quiet(X0) [cnf transformation 36]
136. ~humble(john) [cnf transformation 17]
149. ~quiet(john) [cnf transformation 25]
150. ~old(X0) | quiet(X0) | humble(X0) [duplicate literal removal 135]
151. quiet(X0) | old(X0) [duplicate literal removal 120]
320. quiet(X0) | humble(X0) [subsumption resolution 150,151]
367. humble(john) [resolution 320,149]
370. $false [subsumption resolution 367,136]
% SZS output end Proof for 1083411086844935249257369
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and curious then someone is not brave or not patient and vice versa.
If someone is both not patient and rich then fred is not rich.
If someone is either generous or not wise then lucy is kind.
Everyone who is old or curious is humble or funny and vice versa.
If someone is not patient or quiet then someone is both calm and not humble and vice versa.
If someone is not generous or patient then susan is not tall and vice versa.
If someone is both tall and kind then someone is either curious or not curious and vice versa.
If someone is both strong and not creative then someone is not happy or not funny.
Everyone who is either not rich or not patient is wise or not strong and vice versa.
Everyone who is both calm and not humble is quiet or not old and vice versa.
Everyone who is both not old and curious is rich.
Everyone who is tall is generous or strong.
Everyone who is either not brave or not humble is happy or not wise.
Everyone who is funny is either old or not kind.
Susan is generous or not rich.
Someone is either not quiet or not tall.
Someone is funny.
Someone is either creative or not strong.
Paul is not creative.
Someone is both not humble and not creative.
Someone is either strong or creative. | Paul is not generous. | neutral | ((?[X]:((rich(X)&curious(X))))<=>(?[X]:((~brave(X)|~patient(X)))))&
((?[X]:((~patient(X)&rich(X))))=>(~rich(fred)))&
((?[X]:((generous(X)<~>~wise(X))))=>(kind(lucy)))&
(![X]:((old(X)|curious(X))<=>(humble(X)|funny(X))))&
((?[X]:((~patient(X)|quiet(X))))<=>(?[X]:((calm(X)&~humble(X)))))&
((?[X]:((~generous(X)|patient(X))))<=>(~tall(susan)))&
((?[X]:((tall(X)&kind(X))))<=>(?[X]:((curious(X)<~>~curious(X)))))&
((?[X]:((strong(X)&~creative(X))))=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~rich(X)<~>~patient(X))<=>(wise(X)|~strong(X))))&
(![X]:((calm(X)&~humble(X))<=>(quiet(X)|~old(X))))&
(![X]:((~old(X)&curious(X))=>rich(X)))&
(![X]:(tall(X)=>(generous(X)|strong(X))))&
(![X]:((~brave(X)<~>~humble(X))=>(happy(X)|~wise(X))))&
(![X]:(funny(X)=>(old(X)<~>~kind(X))))&
((generous(susan)|~rich(susan)))&
(?[X]:((~quiet(X)<~>~tall(X))))&
(?[X]:(funny(X)))&
(?[X]:((creative(X)<~>~strong(X))))&
(~creative(paul))&
(?[X]:((~humble(X)&~creative(X))))&
(?[X]:((strong(X)<~>creative(X)))) | ~generous(paul) | [] | null | 0 |
Everyone who is generous or humble is either kind or wise and vice versa.
If someone is both quiet and tall then susan is either not rich or generous and vice versa.
Everyone who is not brave is old and vice versa.
If mary is both humble and not humble then john is old and vice versa.
Everyone who is not quiet is either not funny or not kind and vice versa.
If someone is both not patient and funny then paul is either not humble or brave and vice versa.
Everyone who is not strong or not patient is either not funny or not strong.
If someone is either not generous or happy then john is both not old and not calm and vice versa.
Everyone who is either calm or not creative is either not patient or not rich and vice versa.
Everyone who is both humble and not funny is tall.
Everyone who is either creative or not strong is either funny or strong and vice versa.
If someone is both not curious and not funny then alice is both not kind and tall.
If lucy is both wise and not kind then paul is not tall and vice versa.
Everyone who is wise or not creative is humble or not calm.
If susan is either not quiet or brave then alice is either not quiet or not kind.
John is not brave or not quiet.
Someone is quiet.
Alice is not calm.
Someone is both humble and quiet.
Paul is either tall or not quiet.
Susan is both not old and patient.
Mary is not rich or calm.
Susan is both curious and not humble. | Mary is not humble. | neutral | (![X]:((generous(X)|humble(X))<=>(kind(X)<~>wise(X))))&
((?[X]:((quiet(X)&tall(X))))<=>((~rich(susan)<~>generous(susan))))&
(![X]:(~brave(X)<=>old(X)))&
(((humble(mary)&~humble(mary)))<=>(old(john)))&
(![X]:(~quiet(X)<=>(~funny(X)<~>~kind(X))))&
((?[X]:((~patient(X)&funny(X))))<=>((~humble(paul)<~>brave(paul))))&
(![X]:((~strong(X)|~patient(X))=>(~funny(X)<~>~strong(X))))&
((?[X]:((~generous(X)<~>happy(X))))<=>((~old(john)&~calm(john))))&
(![X]:((calm(X)<~>~creative(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:((humble(X)&~funny(X))=>tall(X)))&
(![X]:((creative(X)<~>~strong(X))<=>(funny(X)<~>strong(X))))&
((?[X]:((~curious(X)&~funny(X))))=>((~kind(alice)&tall(alice))))&
(((wise(lucy)&~kind(lucy)))<=>(~tall(paul)))&
(![X]:((wise(X)|~creative(X))=>(humble(X)|~calm(X))))&
(((~quiet(susan)<~>brave(susan)))=>((~quiet(alice)<~>~kind(alice))))&
((~brave(john)|~quiet(john)))&
(?[X]:(quiet(X)))&
(~calm(alice))&
(?[X]:((humble(X)&quiet(X))))&
((tall(paul)<~>~quiet(paul)))&
((~old(susan)&patient(susan)))&
((~rich(mary)|calm(mary)))&
((curious(susan)&~humble(susan))) | ~humble(mary) | [] | null | 0 |
Everyone who is both not happy and not curious is not tall and vice versa.
Everyone who is old is either humble or not wise.
If someone is not kind then john is both rich and not curious and vice versa.
If someone is calm or not calm then lucy is both creative and not generous and vice versa.
If someone is not generous or not curious then fred is not wise and vice versa.
Everyone who is either not calm or not happy is not calm and vice versa.
If someone is not curious then someone is kind or not happy.
Everyone who is either not kind or not rich is tall and vice versa.
Everyone who is not generous or not rich is curious.
If john is either humble or kind then john is either not kind or not brave.
Everyone who is not patient is old or calm.
Everyone who is not generous or not brave is both old and kind.
Everyone who is not brave is not curious and vice versa.
If lucy is not creative or happy then someone is not calm.
If someone is not funny then someone is not quiet or calm and vice versa.
If mary is rich then paul is calm and vice versa.
Susan is curious.
Someone is either old or not tall.
Mary is both creative and patient.
Someone is either not rich or funny.
Someone is not old.
Paul is curious. | Susan is not kind. | contradiction | (![X]:((~happy(X)&~curious(X))<=>~tall(X)))&
(![X]:(old(X)=>(humble(X)<~>~wise(X))))&
((?[X]:(~kind(X)))<=>((rich(john)&~curious(john))))&
((?[X]:((calm(X)|~calm(X))))<=>((creative(lucy)&~generous(lucy))))&
((?[X]:((~generous(X)|~curious(X))))<=>(~wise(fred)))&
(![X]:((~calm(X)<~>~happy(X))<=>~calm(X)))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((~kind(X)<~>~rich(X))<=>tall(X)))&
(![X]:((~generous(X)|~rich(X))=>curious(X)))&
(((humble(john)<~>kind(john)))=>((~kind(john)<~>~brave(john))))&
(![X]:(~patient(X)=>(old(X)|calm(X))))&
(![X]:((~generous(X)|~brave(X))=>(old(X)&kind(X))))&
(![X]:(~brave(X)<=>~curious(X)))&
(((~creative(lucy)|happy(lucy)))=>(?[X]:(~calm(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~quiet(X)|calm(X)))))&
((rich(mary))<=>(calm(paul)))&
(curious(susan))&
(?[X]:((old(X)<~>~tall(X))))&
((creative(mary)&patient(mary)))&
(?[X]:((~rich(X)<~>funny(X))))&
(?[X]:(~old(X)))&
(curious(paul)) | ~kind(susan) | [
"p0",
"p2",
"p5",
"p7",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4714256007729459950947059
% SZS output start Proof for 4714256007729459950947059
1. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> ~tall(X0)) [input p0]
3. ? [X0] : ~kind(X0) <=> (~curious(john) & rich(john)) [input p2]
6. ! [X0] : ((~calm(X0) <~> ~happy(X0)) <=> ~calm(X0)) [input p5]
8. ! [X0] : ((~kind(X0) <~> ~rich(X0)) <=> tall(X0)) [input p7]
9. ! [X0] : ((~rich(X0) | ~generous(X0)) => curious(X0)) [input p8]
12. ! [X0] : ((~brave(X0) | ~generous(X0)) => (kind(X0) & old(X0))) [input p11]
13. ! [X0] : (~brave(X0) <=> ~curious(X0)) [input p12]
23. ~kind(susan) [input hypothesis]
30. ! [X0] : (curious(X0) | (rich(X0) & generous(X0))) [ennf transformation 9]
32. ! [X0] : ((kind(X0) & old(X0)) | (brave(X0) & generous(X0))) [ennf transformation 12]
34. ! [X0] : (((~curious(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) | happy(X0)))) [nnf transformation 1]
35. ! [X0] : (((~curious(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | curious(X0) | happy(X0))) [flattening 34]
37. (? [X0] : ~kind(X0) | (curious(john) | ~rich(john))) & ((~curious(john) & rich(john)) | ! [X0] : kind(X0)) [nnf transformation 3]
38. (? [X0] : ~kind(X0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X0] : kind(X0)) [flattening 37]
39. (? [X0] : ~kind(X0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X1] : kind(X1)) [rectify 38]
40. ? [X0] : ~kind(X0) => ~kind(sK0) [choice axiom]
41. (~kind(sK0) | curious(john) | ~rich(john)) & ((~curious(john) & rich(john)) | ! [X1] : kind(X1)) [skolemisation 39,40]
51. ! [X0] : ((((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | calm(X0)) & (~calm(X0) | ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0))))) [nnf transformation 6]
55. ! [X0] : ((((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | ~tall(X0)) & (tall(X0) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0))))) [nnf transformation 8]
57. ! [X0] : ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0))) [nnf transformation 13]
75. ~happy(X0) | tall(X0) [cnf transformation 35]
80. ~curious(john) | kind(X1) [cnf transformation 41]
91. ~calm(X0) | ~calm(X0) | happy(X0) [cnf transformation 51]
93. happy(X0) | calm(X0) | calm(X0) [cnf transformation 51]
97. ~rich(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 55]
100. rich(X0) | curious(X0) [cnf transformation 30]
108. brave(X0) | kind(X0) [cnf transformation 32]
110. ~brave(X0) | curious(X0) [cnf transformation 57]
126. ~kind(susan) [cnf transformation 23]
129. ~calm(X0) | happy(X0) [duplicate literal removal 91]
130. calm(X0) | happy(X0) [duplicate literal removal 93]
136. 2 <=> curious(john) [avatar definition]
137. ~curious(john) <- (~2) [avatar component clause 136]
145. 4 <=> ! [X1] : kind(X1) [avatar definition]
146. kind(X1) <- (4) [avatar component clause 145]
147. 4 | ~2 [avatar split clause 80,136,145]
181. 12 <=> ! [X1] : curious(X1) [avatar definition]
182. curious(X1) <- (12) [avatar component clause 181]
188. happy(X0) [subsumption resolution 129,130]
267. $false <- (4) [resolution 146,126]
268. ~4 [avatar contradiction clause 267]
269. $false <- (~2, 12) [subsumption resolution 137,182]
270. 2 | ~12 [avatar contradiction clause 269]
273. tall(X0) [resolution 75,188]
296. kind(X0) | curious(X0) [resolution 110,108]
322. ~kind(X0) | ~tall(X0) | curious(X0) [resolution 97,100]
326. ~kind(X0) | curious(X0) [subsumption resolution 322,273]
327. curious(X0) [subsumption resolution 326,296]
328. 12 [avatar split clause 327,181]
329. $false [avatar sat refutation 147,268,270,328]
% SZS output end Proof for 4714256007729459950947059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or calm is either creative or not rich and vice versa. Everyone who is both old and not humble is not old and vice versa. If paul is either not rich or calm then someone is both patient and not calm and vice versa. Everyone who is both not humble and not quiet is both tall and humble and vice versa. Everyone who is humble or generous is not strong or not rich and vice versa. If someone is not quiet or not generous then mary is either not calm or not kind. If mary is happy or not strong then someone is generous. If mary is either humble or not kind then mary is not tall or patient. Everyone who is rich or calm is either kind or not patient and vice versa. Everyone who is not quiet or not rich is old or not kind and vice versa. Everyone who is curious or not strong is not quiet or not generous. If someone is either not creative or generous then someone is happy or not strong and vice versa. Everyone who is either not curious or not humble is both not brave and not humble. Everyone who is not brave or not humble is not humble or not happy. If fred is brave then someone is either curious or not humble. Susan is rich. Paul is either not rich or strong. Someone is both rich and brave. Someone is wise. Fred is not funny or not kind. Someone is patient. Mary is not curious or not happy. Paul is either not happy or wise. | Mary is strong. | neutral | (![X]:((~generous(X)<~>calm(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((old(X)&~humble(X))<=>~old(X)))&
(((~rich(paul)<~>calm(paul)))<=>(?[X]:((patient(X)&~calm(X)))))&
(![X]:((~humble(X)&~quiet(X))<=>(tall(X)&humble(X))))&
(![X]:((humble(X)|generous(X))<=>(~strong(X)|~rich(X))))&
((?[X]:((~quiet(X)|~generous(X))))=>((~calm(mary)<~>~kind(mary))))&
(((happy(mary)|~strong(mary)))=>(?[X]:(generous(X))))&
(((humble(mary)<~>~kind(mary)))=>((~tall(mary)|patient(mary))))&
(![X]:((rich(X)|calm(X))<=>(kind(X)<~>~patient(X))))&
(![X]:((~quiet(X)|~rich(X))<=>(old(X)|~kind(X))))&
(![X]:((curious(X)|~strong(X))=>(~quiet(X)|~generous(X))))&
((?[X]:((~creative(X)<~>generous(X))))<=>(?[X]:((happy(X)|~strong(X)))))&
(![X]:((~curious(X)<~>~humble(X))=>(~brave(X)&~humble(X))))&
(![X]:((~brave(X)|~humble(X))=>(~humble(X)|~happy(X))))&
((brave(fred))=>(?[X]:((curious(X)<~>~humble(X)))))&
(rich(susan))&
((~rich(paul)<~>strong(paul)))&
(?[X]:((rich(X)&brave(X))))&
(?[X]:(wise(X)))&
((~funny(fred)|~kind(fred)))&
(?[X]:(patient(X)))&
((~curious(mary)|~happy(mary)))&
((~happy(paul)<~>wise(paul))) | strong(mary) | [] | null | 0 |
Everyone who is either wise or not creative is not happy or curious.
Everyone who is both old and not quiet is not kind or generous.
Everyone who is either kind or old is old.
Everyone who is either not strong or patient is tall or not quiet.
Everyone who is both not quiet and not kind is happy.
If john is either not calm or tall then fred is both not humble and not patient and vice versa.
If lucy is not rich then someone is not humble.
Everyone who is not brave or strong is not patient or not strong and vice versa.
Everyone who is both not humble and generous is rich and vice versa.
If someone is curious then someone is not creative or not curious and vice versa.
Everyone who is curious or not curious is both not patient and not strong.
If someone is either not happy or tall then someone is not patient or not curious and vice versa.
Everyone who is either not calm or calm is curious or creative and vice versa.
Everyone who is both not rich and not calm is creative or calm.
Everyone who is both not humble and not strong is either not wise or not calm.
Everyone who is either creative or quiet is either not rich or humble and vice versa.
Someone is curious or not funny.
Susan is either not quiet or not calm.
Paul is both not brave and not calm.
Paul is not tall.
Fred is not wise.
Someone is either not happy or patient.
Someone is both kind and tall. | Lucy is brave. | contradiction | (![X]:((wise(X)<~>~creative(X))=>(~happy(X)|curious(X))))&
(![X]:((old(X)&~quiet(X))=>(~kind(X)|generous(X))))&
(![X]:((kind(X)<~>old(X))=>old(X)))&
(![X]:((~strong(X)<~>patient(X))=>(tall(X)|~quiet(X))))&
(![X]:((~quiet(X)&~kind(X))=>happy(X)))&
(((~calm(john)<~>tall(john)))<=>((~humble(fred)&~patient(fred))))&
((~rich(lucy))=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)|strong(X))<=>(~patient(X)|~strong(X))))&
(![X]:((~humble(X)&generous(X))<=>rich(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~creative(X)|~curious(X)))))&
(![X]:((curious(X)|~curious(X))=>(~patient(X)&~strong(X))))&
((?[X]:((~happy(X)<~>tall(X))))<=>(?[X]:((~patient(X)|~curious(X)))))&
(![X]:((~calm(X)<~>calm(X))<=>(curious(X)|creative(X))))&
(![X]:((~rich(X)&~calm(X))=>(creative(X)|calm(X))))&
(![X]:((~humble(X)&~strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(~rich(X)<~>humble(X))))&
(?[X]:((curious(X)|~funny(X))))&
((~quiet(susan)<~>~calm(susan)))&
((~brave(paul)&~calm(paul)))&
(~tall(paul))&
(~wise(fred))&
(?[X]:((~happy(X)<~>patient(X))))&
(?[X]:((kind(X)&tall(X)))) | brave(lucy) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3870253222068288393454216
% SZS output start Proof for 3870253222068288393454216
8. ! [X0] : ((strong(X0) | ~brave(X0)) <=> (~strong(X0) | ~patient(X0))) [input p7]
11. ! [X0] : ((~curious(X0) | curious(X0)) => (~strong(X0) & ~patient(X0))) [input p10]
24. brave(lucy) [input hypothesis]
38. ! [X0] : ((~strong(X0) & ~patient(X0)) | (curious(X0) & ~curious(X0))) [ennf transformation 11]
50. ! [X0] : (((strong(X0) | ~brave(X0)) | (strong(X0) & patient(X0))) & ((~strong(X0) | ~patient(X0)) | (~strong(X0) & brave(X0)))) [nnf transformation 8]
51. ! [X0] : ((strong(X0) | ~brave(X0) | (strong(X0) & patient(X0))) & (~strong(X0) | ~patient(X0) | (~strong(X0) & brave(X0)))) [flattening 50]
92. strong(X0) | ~brave(X0) | strong(X0) [cnf transformation 51]
101. ~strong(X0) | ~curious(X0) [cnf transformation 38]
102. ~strong(X0) | curious(X0) [cnf transformation 38]
136. brave(lucy) [cnf transformation 24]
141. ~brave(X0) | strong(X0) [duplicate literal removal 92]
198. ~strong(X0) [subsumption resolution 101,102]
232. strong(lucy) [resolution 141,136]
233. $false [subsumption resolution 232,198]
% SZS output end Proof for 3870253222068288393454216
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not curious and kind then someone is both quiet and not tall and vice versa.
Everyone who is both not tall and not curious is both not brave and curious and vice versa.
Everyone who is either brave or generous is both brave and curious and vice versa.
Everyone who is either not rich or strong is either strong or brave and vice versa.
If someone is not old or generous then someone is both not kind and calm and vice versa.
If someone is both not creative and patient then someone is creative.
If someone is not patient then someone is both brave and wise.
If someone is both tall and not wise then susan is tall or funny and vice versa.
Everyone who is both not kind and funny is both not calm and curious.
Everyone who is either not quiet or rich is both funny and not happy.
If fred is both humble and generous then lucy is both creative and not wise.
Everyone who is quiet or not quiet is tall.
If alice is generous then someone is happy.
Everyone who is both not creative and wise is old.
Everyone who is either not generous or not tall is wise or not humble.
If someone is either not patient or tall then someone is either creative or funny.
Someone is not creative or funny.
Susan is happy or generous.
Mary is wise.
Someone is not funny.
Someone is not quiet.
Someone is wise or creative.
Susan is generous or not humble. | Mary is rich. | neutral | (((~curious(mary)&kind(mary)))<=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((~tall(X)&~curious(X))<=>(~brave(X)&curious(X))))&
(![X]:((brave(X)<~>generous(X))<=>(brave(X)&curious(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(strong(X)<~>brave(X))))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((~kind(X)&calm(X)))))&
((?[X]:((~creative(X)&patient(X))))=>(?[X]:(creative(X))))&
((?[X]:(~patient(X)))=>(?[X]:((brave(X)&wise(X)))))&
((?[X]:((tall(X)&~wise(X))))<=>((tall(susan)|funny(susan))))&
(![X]:((~kind(X)&funny(X))=>(~calm(X)&curious(X))))&
(![X]:((~quiet(X)<~>rich(X))=>(funny(X)&~happy(X))))&
(((humble(fred)&generous(fred)))=>((creative(lucy)&~wise(lucy))))&
(![X]:((quiet(X)|~quiet(X))=>tall(X)))&
((generous(alice))=>(?[X]:(happy(X))))&
(![X]:((~creative(X)&wise(X))=>old(X)))&
(![X]:((~generous(X)<~>~tall(X))=>(wise(X)|~humble(X))))&
((?[X]:((~patient(X)<~>tall(X))))=>(?[X]:((creative(X)<~>funny(X)))))&
(?[X]:((~creative(X)|funny(X))))&
((happy(susan)|generous(susan)))&
(wise(mary))&
(?[X]:(~funny(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((wise(X)|creative(X))))&
((generous(susan)|~humble(susan))) | rich(mary) | [] | null | 0 |
Everyone who is not generous or humble is either not brave or not generous. Everyone who is not old or not rich is either not funny or generous. If someone is generous or not funny then someone is not old or not tall and vice versa. If someone is either not humble or not strong then someone is either not happy or calm. If lucy is both not rich and rich then someone is not old or not tall and vice versa. Everyone who is happy or calm is both quiet and happy and vice versa. Everyone who is both not creative and not old is calm and vice versa. Everyone who is both not happy and brave is brave or not quiet. Everyone who is both not generous and old is either not strong or not brave. Everyone who is either curious or not wise is both not generous and not wise and vice versa. If someone is curious or patient then paul is both quiet and not happy. Everyone who is patient is both funny and not wise and vice versa. Everyone who is both brave and not funny is kind. Everyone who is curious or old is either kind or tall. Someone is both humble and not kind. Lucy is patient or quiet. Someone is patient or generous. Lucy is either generous or not kind. Someone is funny. Mary is not wise. | Paul is quiet. | entailment | (![X]:((~generous(X)|humble(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~old(X)|~rich(X))=>(~funny(X)<~>generous(X))))&
((?[X]:((generous(X)|~funny(X))))<=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:((~humble(X)<~>~strong(X))))=>(?[X]:((~happy(X)<~>calm(X)))))&
(((~rich(lucy)&rich(lucy)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((happy(X)|calm(X))<=>(quiet(X)&happy(X))))&
(![X]:((~creative(X)&~old(X))<=>calm(X)))&
(![X]:((~happy(X)&brave(X))=>(brave(X)|~quiet(X))))&
(![X]:((~generous(X)&old(X))=>(~strong(X)<~>~brave(X))))&
(![X]:((curious(X)<~>~wise(X))<=>(~generous(X)&~wise(X))))&
((?[X]:((curious(X)|patient(X))))=>((quiet(paul)&~happy(paul))))&
(![X]:(patient(X)<=>(funny(X)&~wise(X))))&
(![X]:((brave(X)&~funny(X))=>kind(X)))&
(![X]:((curious(X)|old(X))=>(kind(X)<~>tall(X))))&
(?[X]:((humble(X)&~kind(X))))&
((patient(lucy)|quiet(lucy)))&
(?[X]:((patient(X)|generous(X))))&
((generous(lucy)<~>~kind(lucy)))&
(?[X]:(funny(X)))&
(~wise(mary)) | quiet(paul) | [
"p2",
"p4",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1189208677857373653889175
% SZS output start Proof for 1189208677857373653889175
3. ? [X0] : (~funny(X0) | generous(X0)) <=> ? [X0] : (~tall(X0) | ~old(X0)) [input p2]
5. (rich(lucy) & ~rich(lucy)) <=> ? [X0] : (~tall(X0) | ~old(X0)) [input p4]
11. ? [X0] : (patient(X0) | curious(X0)) => (~happy(paul) & quiet(paul)) [input p10]
17. ? [X0] : (generous(X0) | patient(X0)) [input p16]
21. ~quiet(paul) [input hypothesis]
22. ? [X0] : (~funny(X0) | generous(X0)) <=> ? [X1] : (~tall(X1) | ~old(X1)) [rectify 3]
31. (~happy(paul) & quiet(paul)) | ! [X0] : (~patient(X0) & ~curious(X0)) [ennf transformation 11]
37. (? [X0] : (~funny(X0) | generous(X0)) | ! [X1] : (tall(X1) & old(X1))) & (? [X1] : (~tall(X1) | ~old(X1)) | ! [X0] : (funny(X0) & ~generous(X0))) [nnf transformation 22]
38. (? [X0] : (~funny(X0) | generous(X0)) | ! [X1] : (tall(X1) & old(X1))) & (? [X2] : (~tall(X2) | ~old(X2)) | ! [X3] : (funny(X3) & ~generous(X3))) [rectify 37]
39. ? [X0] : (~funny(X0) | generous(X0)) => (~funny(sK0) | generous(sK0)) [choice axiom]
40. ? [X2] : (~tall(X2) | ~old(X2)) => (~tall(sK1) | ~old(sK1)) [choice axiom]
41. ((~funny(sK0) | generous(sK0)) | ! [X1] : (tall(X1) & old(X1))) & ((~tall(sK1) | ~old(sK1)) | ! [X3] : (funny(X3) & ~generous(X3))) [skolemisation 38,40,39]
46. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & (? [X0] : (~tall(X0) | ~old(X0)) | (~rich(lucy) | rich(lucy))) [nnf transformation 5]
47. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & (? [X0] : (~tall(X0) | ~old(X0)) | ~rich(lucy) | rich(lucy)) [flattening 46]
48. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & (? [X1] : (~tall(X1) | ~old(X1)) | ~rich(lucy) | rich(lucy)) [rectify 47]
49. ? [X1] : (~tall(X1) | ~old(X1)) => (~tall(sK3) | ~old(sK3)) [choice axiom]
50. ((rich(lucy) & ~rich(lucy)) | ! [X0] : (tall(X0) & old(X0))) & ((~tall(sK3) | ~old(sK3)) | ~rich(lucy) | rich(lucy)) [skolemisation 48,49]
63. ? [X0] : (generous(X0) | patient(X0)) => (generous(sK5) | patient(sK5)) [choice axiom]
64. generous(sK5) | patient(sK5) [skolemisation 17,63]
76. ~tall(sK1) | ~old(sK1) | ~generous(X3) [cnf transformation 41]
85. ~rich(lucy) | old(X0) [cnf transformation 50]
86. ~rich(lucy) | tall(X0) [cnf transformation 50]
87. rich(lucy) | old(X0) [cnf transformation 50]
88. rich(lucy) | tall(X0) [cnf transformation 50]
107. quiet(paul) | ~patient(X0) [cnf transformation 31]
121. generous(sK5) | patient(sK5) [cnf transformation 64]
126. ~quiet(paul) [cnf transformation 21]
131. 1 <=> ! [X1] : tall(X1) [avatar definition]
132. tall(X1) <- (1) [avatar component clause 131]
143. 4 <=> ! [X1] : old(X1) [avatar definition]
144. old(X1) <- (4) [avatar component clause 143]
150. 6 <=> old(sK1) [avatar definition]
152. ~old(sK1) <- (~6) [avatar component clause 150]
154. 7 <=> tall(sK1) [avatar definition]
156. ~tall(sK1) <- (~7) [avatar component clause 154]
159. 8 <=> ! [X3] : ~generous(X3) [avatar definition]
160. ~generous(X3) <- (8) [avatar component clause 159]
161. 8 | ~6 | ~7 [avatar split clause 76,154,150,159]
181. 13 <=> rich(lucy) [avatar definition]
184. 1 | 13 [avatar split clause 88,181,131]
185. 4 | 13 [avatar split clause 87,181,143]
186. 1 | ~13 [avatar split clause 86,181,131]
187. 4 | ~13 [avatar split clause 85,181,143]
190. 14 <=> ! [X0] : ~patient(X0) [avatar definition]
191. ~patient(X0) <- (14) [avatar component clause 190]
202. 17 <=> quiet(paul) [avatar definition]
205. 14 | 17 [avatar split clause 107,202,190]
217. 20 <=> patient(sK5) [avatar definition]
219. patient(sK5) <- (20) [avatar component clause 217]
221. 21 <=> generous(sK5) [avatar definition]
223. generous(sK5) <- (21) [avatar component clause 221]
224. 20 | 21 [avatar split clause 121,221,217]
235. ~17 [avatar split clause 126,202]
236. $false <- (1, ~7) [resolution 156,132]
237. ~1 | 7 [avatar contradiction clause 236]
238. $false <- (4, ~6) [subsumption resolution 152,144]
239. ~4 | 6 [avatar contradiction clause 238]
242. $false <- (14, 20) [resolution 219,191]
243. ~14 | ~20 [avatar contradiction clause 242]
244. $false <- (8, 21) [subsumption resolution 223,160]
245. ~8 | ~21 [avatar contradiction clause 244]
246. $false [avatar sat refutation 161,184,185,186,187,205,224,235,237,239,243,245]
% SZS output end Proof for 1189208677857373653889175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not calm or old then someone is not happy or curious. If susan is not generous or quiet then someone is either happy or creative. Everyone who is funny or creative is not generous or not happy. Everyone who is generous is both patient and funny. If mary is not rich or strong then paul is both patient and not old and vice versa. If lucy is either not humble or not happy then fred is not brave or not funny. If fred is quiet then john is either rich or not generous. If john is generous then someone is old or not rich. Everyone who is both quiet and curious is not patient and vice versa. Everyone who is not funny or happy is not generous. If someone is quiet or not humble then someone is funny and vice versa. Everyone who is happy or not curious is not brave or creative and vice versa. Everyone who is both wise and creative is both not rich and curious and vice versa. Everyone who is either brave or not quiet is generous and vice versa. Everyone who is not wise or not curious is both tall and not quiet and vice versa. Everyone who is both not humble and kind is patient or not old and vice versa. Someone is calm. Someone is patient or not curious. Someone is either rich or not kind. Someone is old or not wise. Lucy is not rich or not humble. Someone is patient. Fred is not calm. | Mary is not funny. | neutral | (((~calm(paul)|old(paul)))=>(?[X]:((~happy(X)|curious(X)))))&
(((~generous(susan)|quiet(susan)))=>(?[X]:((happy(X)<~>creative(X)))))&
(![X]:((funny(X)|creative(X))=>(~generous(X)|~happy(X))))&
(![X]:(generous(X)=>(patient(X)&funny(X))))&
(((~rich(mary)|strong(mary)))<=>((patient(paul)&~old(paul))))&
(((~humble(lucy)<~>~happy(lucy)))=>((~brave(fred)|~funny(fred))))&
((quiet(fred))=>((rich(john)<~>~generous(john))))&
((generous(john))=>(?[X]:((old(X)|~rich(X)))))&
(![X]:((quiet(X)&curious(X))<=>~patient(X)))&
(![X]:((~funny(X)|happy(X))=>~generous(X)))&
((?[X]:((quiet(X)|~humble(X))))<=>(?[X]:(funny(X))))&
(![X]:((happy(X)|~curious(X))<=>(~brave(X)|creative(X))))&
(![X]:((wise(X)&creative(X))<=>(~rich(X)&curious(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>generous(X)))&
(![X]:((~wise(X)|~curious(X))<=>(tall(X)&~quiet(X))))&
(![X]:((~humble(X)&kind(X))<=>(patient(X)|~old(X))))&
(?[X]:(calm(X)))&
(?[X]:((patient(X)|~curious(X))))&
(?[X]:((rich(X)<~>~kind(X))))&
(?[X]:((old(X)|~wise(X))))&
((~rich(lucy)|~humble(lucy)))&
(?[X]:(patient(X)))&
(~calm(fred)) | ~funny(mary) | [] | null | 0 |
If someone is curious or generous then mary is not wise and vice versa.
If paul is old or calm then alice is both wise and funny.
Everyone who is happy or patient is not old or creative.
If someone is happy or strong then lucy is either strong or rich and vice versa.
Everyone who is both not tall and rich is both not brave and tall.
Everyone who is not patient is both brave and humble.
Everyone who is either not tall or not patient is either funny or happy.
If someone is either not tall or not happy then lucy is not curious and vice versa.
If someone is not calm then mary is humble or patient and vice versa.
Everyone who is creative or not happy is both patient and not brave.
If someone is funny then someone is not happy or not old and vice versa.
Everyone who is not tall or generous is curious or quiet and vice versa.
If someone is humble or creative then lucy is both patient and happy and vice versa.
Everyone who is wise or not patient is wise or not strong.
If someone is not curious or patient then someone is either happy or not happy and vice versa.
Everyone who is curious or not generous is not humble or creative.
Someone is both not generous and strong.
Someone is creative.
Alice is brave.
Someone is either not brave or not tall.
Someone is both not funny and happy.
Mary is not wise.
Someone is generous.
Mary is either not creative or wise. | Lucy is strong. | neutral | ((?[X]:((curious(X)|generous(X))))<=>(~wise(mary)))&
(((old(paul)|calm(paul)))=>((wise(alice)&funny(alice))))&
(![X]:((happy(X)|patient(X))=>(~old(X)|creative(X))))&
((?[X]:((happy(X)|strong(X))))<=>((strong(lucy)<~>rich(lucy))))&
(![X]:((~tall(X)&rich(X))=>(~brave(X)&tall(X))))&
(![X]:(~patient(X)=>(brave(X)&humble(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(funny(X)<~>happy(X))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(~curious(lucy)))&
((?[X]:(~calm(X)))<=>((humble(mary)|patient(mary))))&
(![X]:((creative(X)|~happy(X))=>(patient(X)&~brave(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:((~tall(X)|generous(X))<=>(curious(X)|quiet(X))))&
((?[X]:((humble(X)|creative(X))))<=>((patient(lucy)&happy(lucy))))&
(![X]:((wise(X)|~patient(X))=>(wise(X)|~strong(X))))&
((?[X]:((~curious(X)|patient(X))))<=>(?[X]:((happy(X)<~>~happy(X)))))&
(![X]:((curious(X)|~generous(X))=>(~humble(X)|creative(X))))&
(?[X]:((~generous(X)&strong(X))))&
(?[X]:(creative(X)))&
(brave(alice))&
(?[X]:((~brave(X)<~>~tall(X))))&
(?[X]:((~funny(X)&happy(X))))&
(~wise(mary))&
(?[X]:(generous(X)))&
((~creative(mary)<~>wise(mary))) | strong(lucy) | [] | null | 0 |
Everyone who is kind is old. If someone is humble then lucy is not quiet or not old and vice versa. If someone is not tall then lucy is both wise and not tall. If lucy is either not old or not strong then paul is not happy. If susan is wise then someone is happy or wise. Everyone who is both not old and old is kind or wise and vice versa. Everyone who is either not curious or strong is either patient or not generous and vice versa. Everyone who is either calm or generous is not calm or kind and vice versa. If someone is happy or not tall then someone is wise or not generous. Everyone who is not tall or not strong is not rich or not calm and vice versa. Everyone who is either not quiet or not tall is either funny or not brave. If lucy is patient or rich then paul is not patient. If someone is not patient or patient then john is both not funny and not wise. Everyone who is either not generous or not funny is not rich and vice versa. If someone is strong then someone is both not tall and happy and vice versa. Fred is calm or not generous. Someone is funny. Alice is humble or quiet. Someone is either funny or not quiet. Someone is either brave or funny. John is curious. Someone is either quiet or creative. | Fred is funny. | contradiction | (![X]:(kind(X)=>old(X)))&
((?[X]:(humble(X)))<=>((~quiet(lucy)|~old(lucy))))&
((?[X]:(~tall(X)))=>((wise(lucy)&~tall(lucy))))&
(((~old(lucy)<~>~strong(lucy)))=>(~happy(paul)))&
((wise(susan))=>(?[X]:((happy(X)|wise(X)))))&
(![X]:((~old(X)&old(X))<=>(kind(X)|wise(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~calm(X)|kind(X))))&
((?[X]:((happy(X)|~tall(X))))=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:((~tall(X)|~strong(X))<=>(~rich(X)|~calm(X))))&
(![X]:((~quiet(X)<~>~tall(X))=>(funny(X)<~>~brave(X))))&
(((patient(lucy)|rich(lucy)))=>(~patient(paul)))&
((?[X]:((~patient(X)|patient(X))))=>((~funny(john)&~wise(john))))&
(![X]:((~generous(X)<~>~funny(X))<=>~rich(X)))&
((?[X]:(strong(X)))<=>(?[X]:((~tall(X)&happy(X)))))&
((calm(fred)|~generous(fred)))&
(?[X]:(funny(X)))&
((humble(alice)|quiet(alice)))&
(?[X]:((funny(X)<~>~quiet(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(curious(john))&
(?[X]:((quiet(X)<~>creative(X)))) | funny(fred) | [
"p0",
"p5",
"p7",
"p8",
"p9",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 115871609493200847188549
% SZS output start Proof for 115871609493200847188549
1. ! [X0] : (kind(X0) => old(X0)) [input p0]
6. ! [X0] : ((old(X0) & ~old(X0)) <=> (wise(X0) | kind(X0))) [input p5]
8. ! [X0] : ((calm(X0) <~> generous(X0)) <=> (kind(X0) | ~calm(X0))) [input p7]
9. ? [X0] : (~tall(X0) | happy(X0)) => ? [X0] : (~generous(X0) | wise(X0)) [input p8]
10. ! [X0] : ((~strong(X0) | ~tall(X0)) <=> (~calm(X0) | ~rich(X0))) [input p9]
14. ! [X0] : ((~generous(X0) <~> ~funny(X0)) <=> ~rich(X0)) [input p13]
15. ? [X0] : strong(X0) <=> ? [X0] : (happy(X0) & ~tall(X0)) [input p14]
16. ~generous(fred) | calm(fred) [input p15]
23. funny(fred) [input hypothesis]
24. ? [X0] : (~tall(X0) | happy(X0)) => ? [X1] : (~generous(X1) | wise(X1)) [rectify 9]
25. ? [X0] : strong(X0) <=> ? [X1] : (happy(X1) & ~tall(X1)) [rectify 15]
26. ! [X0] : (old(X0) | ~kind(X0)) [ennf transformation 1]
30. ? [X1] : (~generous(X1) | wise(X1)) | ! [X0] : (tall(X0) & ~happy(X0)) [ennf transformation 24]
42. ! [X0] : (((old(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & ((wise(X0) | kind(X0)) | (~old(X0) | old(X0)))) [nnf transformation 6]
43. ! [X0] : (((old(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & (wise(X0) | kind(X0) | ~old(X0) | old(X0))) [flattening 42]
45. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (~kind(X0) & calm(X0))) & ((kind(X0) | ~calm(X0)) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | (~kind(X0) & calm(X0))) & (kind(X0) | ~calm(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [flattening 45]
47. ? [X0] : (~generous(X0) | wise(X0)) | ! [X1] : (tall(X1) & ~happy(X1)) [rectify 30]
48. ? [X0] : (~generous(X0) | wise(X0)) => (~generous(sK2) | wise(sK2)) [choice axiom]
49. (~generous(sK2) | wise(sK2)) | ! [X1] : (tall(X1) & ~happy(X1)) [skolemisation 47,48]
50. ! [X0] : (((~strong(X0) | ~tall(X0)) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | (strong(X0) & tall(X0)))) [nnf transformation 10]
51. ! [X0] : ((~strong(X0) | ~tall(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | (strong(X0) & tall(X0)))) [flattening 50]
53. ! [X0] : ((((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | rich(X0)) & (~rich(X0) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))))) [nnf transformation 14]
54. (? [X0] : strong(X0) | ! [X1] : (~happy(X1) | tall(X1))) & (? [X1] : (happy(X1) & ~tall(X1)) | ! [X0] : ~strong(X0)) [nnf transformation 25]
55. (? [X0] : strong(X0) | ! [X1] : (~happy(X1) | tall(X1))) & (? [X2] : (happy(X2) & ~tall(X2)) | ! [X3] : ~strong(X3)) [rectify 54]
56. ? [X0] : strong(X0) => strong(sK3) [choice axiom]
57. ? [X2] : (happy(X2) & ~tall(X2)) => (happy(sK4) & ~tall(sK4)) [choice axiom]
58. (strong(sK3) | ! [X1] : (~happy(X1) | tall(X1))) & ((happy(sK4) & ~tall(sK4)) | ! [X3] : ~strong(X3)) [skolemisation 55,57,56]
70. ~kind(X0) | old(X0) [cnf transformation 26]
80. ~old(X0) | ~kind(X0) [cnf transformation 43]
81. ~old(X0) | ~wise(X0) [cnf transformation 43]
83. ~wise(X0) | old(X0) [cnf transformation 43]
92. kind(X0) | ~calm(X0) | generous(X0) | ~calm(X0) [cnf transformation 46]
94. generous(X0) | calm(X0) | calm(X0) [cnf transformation 46]
98. ~generous(sK2) | wise(sK2) | ~happy(X1) [cnf transformation 49]
101. ~rich(X0) | ~calm(X0) | strong(X0) [cnf transformation 51]
116. ~funny(X0) | ~generous(X0) | rich(X0) [cnf transformation 53]
119. happy(sK4) | ~strong(X3) [cnf transformation 58]
121. ~generous(fred) | calm(fred) [cnf transformation 16]
131. funny(fred) [cnf transformation 23]
132. kind(X0) | ~calm(X0) | generous(X0) [duplicate literal removal 92]
133. calm(X0) | generous(X0) [duplicate literal removal 94]
188. ~wise(X0) [subsumption resolution 81,83]
189. ~kind(X0) [subsumption resolution 80,70]
190. ~calm(X0) | generous(X0) [subsumption resolution 132,189]
191. generous(X0) [subsumption resolution 190,133]
195. wise(sK2) | ~happy(X1) [subsumption resolution 98,191]
196. ~happy(X1) [subsumption resolution 195,188]
223. ~funny(X0) | rich(X0) [subsumption resolution 116,191]
225. ~strong(X3) [subsumption resolution 119,196]
226. calm(fred) [subsumption resolution 121,191]
267. rich(fred) [resolution 223,131]
273. ~calm(fred) | strong(fred) [resolution 101,267]
275. strong(fred) [subsumption resolution 273,226]
276. $false [subsumption resolution 275,225]
% SZS output end Proof for 115871609493200847188549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or generous is rich. Everyone who is generous or calm is either quiet or wise and vice versa. Everyone who is both not patient and brave is either creative or kind. Everyone who is not patient or rich is curious or quiet. If someone is either not patient or not quiet then susan is curious or funny. Everyone who is either rich or quiet is either rich or not generous. If alice is not brave then someone is both tall and patient and vice versa. If paul is not humble then someone is both not curious and not generous. Everyone who is either calm or not calm is not humble. If someone is patient then someone is not generous or patient and vice versa. Everyone who is either humble or not rich is not creative or not patient and vice versa. Everyone who is either patient or brave is not curious. If someone is either tall or not creative then paul is either not humble or calm and vice versa. If someone is old or curious then someone is humble or funny. If susan is creative then someone is not patient or not happy and vice versa. If someone is both not calm and funny then someone is both not old and calm and vice versa. Fred is not calm. Susan is rich or not tall. Someone is either not quiet or calm. Someone is old. Someone is not old or not calm. Fred is kind or quiet. Susan is not creative or patient. | Fred is calm. | contradiction | (![X]:((wise(X)<~>generous(X))=>rich(X)))&
(![X]:((generous(X)|calm(X))<=>(quiet(X)<~>wise(X))))&
(![X]:((~patient(X)&brave(X))=>(creative(X)<~>kind(X))))&
(![X]:((~patient(X)|rich(X))=>(curious(X)|quiet(X))))&
((?[X]:((~patient(X)<~>~quiet(X))))=>((curious(susan)|funny(susan))))&
(![X]:((rich(X)<~>quiet(X))=>(rich(X)<~>~generous(X))))&
((~brave(alice))<=>(?[X]:((tall(X)&patient(X)))))&
((~humble(paul))=>(?[X]:((~curious(X)&~generous(X)))))&
(![X]:((calm(X)<~>~calm(X))=>~humble(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~generous(X)|patient(X)))))&
(![X]:((humble(X)<~>~rich(X))<=>(~creative(X)|~patient(X))))&
(![X]:((patient(X)<~>brave(X))=>~curious(X)))&
((?[X]:((tall(X)<~>~creative(X))))<=>((~humble(paul)<~>calm(paul))))&
((?[X]:((old(X)|curious(X))))=>(?[X]:((humble(X)|funny(X)))))&
((creative(susan))<=>(?[X]:((~patient(X)|~happy(X)))))&
((?[X]:((~calm(X)&funny(X))))<=>(?[X]:((~old(X)&calm(X)))))&
(~calm(fred))&
((rich(susan)|~tall(susan)))&
(?[X]:((~quiet(X)<~>calm(X))))&
(?[X]:(old(X)))&
(?[X]:((~old(X)|~calm(X))))&
((kind(fred)|quiet(fred)))&
((~creative(susan)|patient(susan))) | calm(fred) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2774157517060689331251084
% SZS output start Proof for 2774157517060689331251084
17. ~calm(fred) [input p16]
24. calm(fred) [input hypothesis]
137. ~calm(fred) [cnf transformation 17]
145. calm(fred) [cnf transformation 24]
352. $false [subsumption resolution 145,137]
% SZS output end Proof for 2774157517060689331251084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or calm.
If someone is not curious or not humble then someone is both not old and not happy.
Everyone who is either curious or not happy is both not kind and creative and vice versa.
If john is not tall or not quiet then someone is curious and vice versa.
Everyone who is not quiet or tall is both happy and not rich and vice versa.
Everyone who is happy or patient is not generous.
Everyone who is not strong or not old is both generous and not patient.
Everyone who is either not brave or generous is either not rich or not generous and vice versa.
Everyone who is both kind and not tall is strong.
If someone is both not calm and not generous then someone is either strong or not wise and vice versa.
If someone is not humble then paul is either rich or not creative and vice versa.
Everyone who is not calm or strong is not curious.
If someone is either kind or curious then john is not generous and vice versa.
Everyone who is both generous and not old is not kind or not happy.
If alice is either not generous or tall then lucy is humble or not calm.
If mary is both patient and humble then fred is not strong.
Someone is both generous and rich.
Paul is humble or curious.
Susan is both not patient and not funny.
Someone is not curious or not tall.
Alice is not quiet.
Lucy is either not humble or not brave.
Someone is both creative and not humble.
Someone is either strong or tall. | John is curious. | contradiction | (![X]:(happy(X)=>(rich(X)|calm(X))))&
((?[X]:((~curious(X)|~humble(X))))=>(?[X]:((~old(X)&~happy(X)))))&
(![X]:((curious(X)<~>~happy(X))<=>(~kind(X)&creative(X))))&
(((~tall(john)|~quiet(john)))<=>(?[X]:(curious(X))))&
(![X]:((~quiet(X)|tall(X))<=>(happy(X)&~rich(X))))&
(![X]:((happy(X)|patient(X))=>~generous(X)))&
(![X]:((~strong(X)|~old(X))=>(generous(X)&~patient(X))))&
(![X]:((~brave(X)<~>generous(X))<=>(~rich(X)<~>~generous(X))))&
(![X]:((kind(X)&~tall(X))=>strong(X)))&
((?[X]:((~calm(X)&~generous(X))))<=>(?[X]:((strong(X)<~>~wise(X)))))&
((?[X]:(~humble(X)))<=>((rich(paul)<~>~creative(paul))))&
(![X]:((~calm(X)|strong(X))=>~curious(X)))&
((?[X]:((kind(X)<~>curious(X))))<=>(~generous(john)))&
(![X]:((generous(X)&~old(X))=>(~kind(X)|~happy(X))))&
(((~generous(alice)<~>tall(alice)))=>((humble(lucy)|~calm(lucy))))&
(((patient(mary)&humble(mary)))=>(~strong(fred)))&
(?[X]:((generous(X)&rich(X))))&
((humble(paul)|curious(paul)))&
((~patient(susan)&~funny(susan)))&
(?[X]:((~curious(X)|~tall(X))))&
(~quiet(alice))&
((~humble(lucy)<~>~brave(lucy)))&
(?[X]:((creative(X)&~humble(X))))&
(?[X]:((strong(X)<~>tall(X)))) | curious(john) | [
"p3",
"p4",
"p5",
"p6",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2427330696752842140237777
% SZS output start Proof for 2427330696752842140237777
4. (~quiet(john) | ~tall(john)) <=> ? [X0] : curious(X0) [input p3]
5. ! [X0] : ((tall(X0) | ~quiet(X0)) <=> (~rich(X0) & happy(X0))) [input p4]
6. ! [X0] : ((patient(X0) | happy(X0)) => ~generous(X0)) [input p5]
7. ! [X0] : ((~old(X0) | ~strong(X0)) => (~patient(X0) & generous(X0))) [input p6]
9. ! [X0] : ((~tall(X0) & kind(X0)) => strong(X0)) [input p8]
12. ! [X0] : ((strong(X0) | ~calm(X0)) => ~curious(X0)) [input p11]
13. ? [X0] : (kind(X0) <~> curious(X0)) <=> ~generous(john) [input p12]
25. curious(john) [input hypothesis]
30. ! [X0] : (happy(X0) => ~generous(X0)) [pure predicate removal 6]
31. ! [X0] : ((~old(X0) | ~strong(X0)) => generous(X0)) [pure predicate removal 7]
36. ! [X0] : (~generous(X0) | ~happy(X0)) [ennf transformation 30]
37. ! [X0] : (generous(X0) | (old(X0) & strong(X0))) [ennf transformation 31]
38. ! [X0] : (strong(X0) | (tall(X0) | ~kind(X0))) [ennf transformation 9]
39. ! [X0] : (strong(X0) | tall(X0) | ~kind(X0)) [flattening 38]
40. ! [X0] : (~curious(X0) | (~strong(X0) & calm(X0))) [ennf transformation 12]
50. ((~quiet(john) | ~tall(john)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (quiet(john) & tall(john))) [nnf transformation 4]
51. (~quiet(john) | ~tall(john) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (quiet(john) & tall(john))) [flattening 50]
52. (~quiet(john) | ~tall(john) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | (quiet(john) & tall(john))) [rectify 51]
53. ? [X1] : curious(X1) => curious(sK1) [choice axiom]
54. (~quiet(john) | ~tall(john) | ! [X0] : ~curious(X0)) & (curious(sK1) | (quiet(john) & tall(john))) [skolemisation 52,53]
55. ! [X0] : (((tall(X0) | ~quiet(X0)) | (rich(X0) | ~happy(X0))) & ((~rich(X0) & happy(X0)) | (~tall(X0) & quiet(X0)))) [nnf transformation 5]
56. ! [X0] : ((tall(X0) | ~quiet(X0) | rich(X0) | ~happy(X0)) & ((~rich(X0) & happy(X0)) | (~tall(X0) & quiet(X0)))) [flattening 55]
67. (? [X0] : ((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | generous(john)) & (~generous(john) | ! [X0] : ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0)))) [nnf transformation 13]
68. (? [X0] : ((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | generous(john)) & (~generous(john) | ! [X1] : ((kind(X1) | ~curious(X1)) & (curious(X1) | ~kind(X1)))) [rectify 67]
69. ? [X0] : ((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) => ((~curious(sK5) | ~kind(sK5)) & (curious(sK5) | kind(sK5))) [choice axiom]
70. (((~curious(sK5) | ~kind(sK5)) & (curious(sK5) | kind(sK5))) | generous(john)) & (~generous(john) | ! [X1] : ((kind(X1) | ~curious(X1)) & (curious(X1) | ~kind(X1)))) [skolemisation 68,69]
95. ~quiet(john) | ~tall(john) | ~curious(X0) [cnf transformation 54]
96. quiet(X0) | happy(X0) [cnf transformation 56]
101. ~generous(X0) | ~happy(X0) [cnf transformation 36]
102. strong(X0) | generous(X0) [cnf transformation 37]
112. ~kind(X0) | tall(X0) | strong(X0) [cnf transformation 39]
124. ~strong(X0) | ~curious(X0) [cnf transformation 40]
126. ~generous(john) | kind(X1) | ~curious(X1) [cnf transformation 70]
143. curious(john) [cnf transformation 25]
167. 5 <=> ! [X0] : ~curious(X0) [avatar definition]
168. ~curious(X0) <- (5) [avatar component clause 167]
170. 6 <=> tall(john) [avatar definition]
172. ~tall(john) <- (~6) [avatar component clause 170]
174. 7 <=> quiet(john) [avatar definition]
176. ~quiet(john) <- (~7) [avatar component clause 174]
177. 5 | ~6 | ~7 [avatar split clause 95,174,170,167]
234. 19 <=> generous(john) [avatar definition]
236. generous(john) <- (19) [avatar component clause 234]
248. 22 <=> ! [X1] : (kind(X1) | ~curious(X1)) [avatar definition]
249. ~curious(X1) | kind(X1) <- (22) [avatar component clause 248]
250. 22 | ~19 [avatar split clause 126,234,248]
307. $false <- (5) [resolution 168,143]
308. ~5 [avatar contradiction clause 307]
310. happy(john) <- (~7) [resolution 96,176]
323. ~curious(X0) | generous(X0) [resolution 124,102]
432. generous(john) [resolution 323,143]
436. 19 [avatar split clause 432,234]
438. ~happy(john) <- (19) [resolution 236,101]
439. $false <- (~7, 19) [subsumption resolution 438,310]
440. 7 | ~19 [avatar contradiction clause 439]
442. kind(john) <- (22) [resolution 249,143]
468. tall(john) | strong(john) <- (22) [resolution 442,112]
471. strong(john) <- (~6, 22) [subsumption resolution 468,172]
492. ~curious(john) <- (~6, 22) [resolution 471,124]
493. $false <- (~6, 22) [subsumption resolution 492,143]
494. 6 | ~22 [avatar contradiction clause 493]
495. $false [avatar sat refutation 177,250,308,436,440,494]
% SZS output end Proof for 2427330696752842140237777
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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