premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not humble or kind is both happy and not curious.
If lucy is not happy then susan is humble or not rich and vice versa.
Everyone who is not humble or rich is either old or wise.
Everyone who is either curious or quiet is not happy or patient and vice versa.
If paul is either tall or not humble then someone is either not strong or not brave and vice versa.
Everyone who is both not generous and not kind is happy or wise and vice versa.
If alice is not tall or not humble then lucy is not calm or brave.
If john is calm then someone is either calm or not old and vice versa.
Everyone who is funny is creative or not tall.
Everyone who is either not strong or quiet is tall and vice versa.
Everyone who is not quiet is curious.
Everyone who is both not funny and tall is both patient and quiet.
Everyone who is either not funny or not patient is both calm and wise.
If mary is wise or tall then someone is old or not curious and vice versa.
If susan is either rich or not brave then someone is both not wise and humble.
Everyone who is both rich and not curious is either not kind or funny and vice versa.
Someone is both happy and not brave.
Fred is tall or funny.
Mary is old.
Someone is not strong.
Mary is humble or curious.
Someone is brave or not tall.
Alice is quiet. | Lucy is not kind. | entailment | (![X]:((~humble(X)|kind(X))=>(happy(X)&~curious(X))))&
((~happy(lucy))<=>((humble(susan)|~rich(susan))))&
(![X]:((~humble(X)|rich(X))=>(old(X)<~>wise(X))))&
(![X]:((curious(X)<~>quiet(X))<=>(~happy(X)|patient(X))))&
(((tall(paul)<~>~humble(paul)))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:((~generous(X)&~kind(X))<=>(happy(X)|wise(X))))&
(((~tall(alice)|~humble(alice)))=>((~calm(lucy)|brave(lucy))))&
((calm(john))<=>(?[X]:((calm(X)<~>~old(X)))))&
(![X]:(funny(X)=>(creative(X)|~tall(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>tall(X)))&
(![X]:(~quiet(X)=>curious(X)))&
(![X]:((~funny(X)&tall(X))=>(patient(X)&quiet(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(calm(X)&wise(X))))&
(((wise(mary)|tall(mary)))<=>(?[X]:((old(X)|~curious(X)))))&
(((rich(susan)<~>~brave(susan)))=>(?[X]:((~wise(X)&humble(X)))))&
(![X]:((rich(X)&~curious(X))<=>(~kind(X)<~>funny(X))))&
(?[X]:((happy(X)&~brave(X))))&
((tall(fred)|funny(fred)))&
(old(mary))&
(?[X]:(~strong(X)))&
((humble(mary)|curious(mary)))&
(?[X]:((brave(X)|~tall(X))))&
(quiet(alice)) | ~kind(lucy) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1084463971452534599882883
% SZS output start Proof for 1084463971452534599882883
1. ! [X0] : ((kind(X0) | ~humble(X0)) => (~curious(X0) & happy(X0))) [input p0]
6. ! [X0] : ((~kind(X0) & ~generous(X0)) <=> (wise(X0) | happy(X0))) [input p5]
24. kind(lucy) [input hypothesis]
26. ! [X0] : ((~curious(X0) & happy(X0)) | (~kind(X0) & humble(X0))) [ennf transformation 1]
44. ! [X0] : (((~kind(X0) & ~generous(X0)) | (~wise(X0) & ~happy(X0))) & ((wise(X0) | happy(X0)) | (kind(X0) | generous(X0)))) [nnf transformation 6]
45. ! [X0] : (((~kind(X0) & ~generous(X0)) | (~wise(X0) & ~happy(X0))) & (wise(X0) | happy(X0) | kind(X0) | generous(X0))) [flattening 44]
69. happy(X0) | ~kind(X0) [cnf transformation 26]
96. ~kind(X0) | ~happy(X0) [cnf transformation 45]
137. kind(lucy) [cnf transformation 24]
183. ~kind(X0) [subsumption resolution 96,69]
289. $false [subsumption resolution 137,183]
% SZS output end Proof for 1084463971452534599882883
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not brave is either creative or patient.
Everyone who is either brave or patient is either not humble or curious and vice versa.
Everyone who is both not humble and humble is not wise or not rich and vice versa.
Everyone who is either happy or not generous is old.
Everyone who is calm is both not brave and not tall and vice versa.
If fred is not funny then someone is both not patient and not quiet and vice versa.
If john is not creative then alice is both not quiet and not brave.
Everyone who is happy is not humble or not creative.
Everyone who is both not strong and kind is not calm and vice versa.
If john is both not tall and old then fred is rich or wise and vice versa.
If someone is not generous then someone is creative or patient.
Everyone who is both not rich and happy is calm and vice versa.
If someone is not patient or rich then someone is both not brave and not happy.
Everyone who is both not patient and curious is funny and vice versa.
Someone is not generous.
Someone is either old or not curious.
Someone is not patient or creative.
Someone is both not patient and not old.
John is both humble and happy.
Someone is either not rich or not strong.
Paul is creative. | Alice is not tall. | contradiction | (![X]:((~happy(X)&~brave(X))=>(creative(X)<~>patient(X))))&
(![X]:((brave(X)<~>patient(X))<=>(~humble(X)<~>curious(X))))&
(![X]:((~humble(X)&humble(X))<=>(~wise(X)|~rich(X))))&
(![X]:((happy(X)<~>~generous(X))=>old(X)))&
(![X]:(calm(X)<=>(~brave(X)&~tall(X))))&
((~funny(fred))<=>(?[X]:((~patient(X)&~quiet(X)))))&
((~creative(john))=>((~quiet(alice)&~brave(alice))))&
(![X]:(happy(X)=>(~humble(X)|~creative(X))))&
(![X]:((~strong(X)&kind(X))<=>~calm(X)))&
(((~tall(john)&old(john)))<=>((rich(fred)|wise(fred))))&
((?[X]:(~generous(X)))=>(?[X]:((creative(X)|patient(X)))))&
(![X]:((~rich(X)&happy(X))<=>calm(X)))&
((?[X]:((~patient(X)|rich(X))))=>(?[X]:((~brave(X)&~happy(X)))))&
(![X]:((~patient(X)&curious(X))<=>funny(X)))&
(?[X]:(~generous(X)))&
(?[X]:((old(X)<~>~curious(X))))&
(?[X]:((~patient(X)|creative(X))))&
(?[X]:((~patient(X)&~old(X))))&
((humble(john)&happy(john)))&
(?[X]:((~rich(X)<~>~strong(X))))&
(creative(paul)) | ~tall(alice) | [
"p2",
"p4",
"p6",
"p7",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2130083793555499937580564
% SZS output start Proof for 2130083793555499937580564
3. ! [X0] : ((humble(X0) & ~humble(X0)) <=> (~rich(X0) | ~wise(X0))) [input p2]
5. ! [X0] : (calm(X0) <=> (~tall(X0) & ~brave(X0))) [input p4]
7. ~creative(john) => (~brave(alice) & ~quiet(alice)) [input p6]
8. ! [X0] : (happy(X0) => (~creative(X0) | ~humble(X0))) [input p7]
12. ! [X0] : ((happy(X0) & ~rich(X0)) <=> calm(X0)) [input p11]
19. happy(john) & humble(john) [input p18]
22. ~tall(alice) [input hypothesis]
28. (~brave(alice) & ~quiet(alice)) | creative(john) [ennf transformation 7]
29. ! [X0] : ((~creative(X0) | ~humble(X0)) | ~happy(X0)) [ennf transformation 8]
30. ! [X0] : (~creative(X0) | ~humble(X0) | ~happy(X0)) [flattening 29]
35. ! [X0] : (((humble(X0) & ~humble(X0)) | (rich(X0) & wise(X0))) & ((~rich(X0) | ~wise(X0)) | (~humble(X0) | humble(X0)))) [nnf transformation 3]
36. ! [X0] : (((humble(X0) & ~humble(X0)) | (rich(X0) & wise(X0))) & (~rich(X0) | ~wise(X0) | ~humble(X0) | humble(X0))) [flattening 35]
38. ! [X0] : ((calm(X0) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | ~calm(X0))) [nnf transformation 5]
39. ! [X0] : ((calm(X0) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | ~calm(X0))) [flattening 38]
51. ! [X0] : (((happy(X0) & ~rich(X0)) | ~calm(X0)) & (calm(X0) | (~happy(X0) | rich(X0)))) [nnf transformation 12]
52. ! [X0] : (((happy(X0) & ~rich(X0)) | ~calm(X0)) & (calm(X0) | ~happy(X0) | rich(X0))) [flattening 51]
82. ~humble(X0) | rich(X0) [cnf transformation 36]
84. rich(X0) | humble(X0) [cnf transformation 36]
89. tall(X0) | calm(X0) | brave(X0) [cnf transformation 39]
94. ~brave(alice) | creative(john) [cnf transformation 28]
95. ~humble(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 30]
106. ~rich(X0) | ~calm(X0) [cnf transformation 52]
121. humble(john) [cnf transformation 19]
122. happy(john) [cnf transformation 19]
126. ~tall(alice) [cnf transformation 22]
127. rich(X0) [subsumption resolution 82,84]
148. 5 <=> creative(john) [avatar definition]
150. creative(john) <- (5) [avatar component clause 148]
152. 6 <=> brave(alice) [avatar definition]
155. 5 | ~6 [avatar split clause 94,152,148]
175. ~calm(X0) [subsumption resolution 106,127]
223. calm(alice) | brave(alice) [resolution 89,126]
226. brave(alice) [subsumption resolution 223,175]
230. 6 [avatar split clause 226,152]
231. ~creative(john) | ~happy(john) [resolution 95,121]
232. ~happy(john) <- (5) [subsumption resolution 231,150]
233. $false <- (5) [subsumption resolution 232,122]
234. ~5 [avatar contradiction clause 233]
235. $false [avatar sat refutation 155,230,234]
% SZS output end Proof for 2130083793555499937580564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or generous is either not happy or brave. If someone is creative then someone is not kind. Everyone who is both not strong and calm is both not creative and generous and vice versa. Everyone who is not patient is wise and vice versa. If someone is humble or not humble then someone is either rich or not brave and vice versa. Everyone who is funny or not wise is not old. If fred is strong or curious then john is quiet or not rich and vice versa. If fred is rich then alice is not wise or not creative. Everyone who is either not tall or humble is not quiet or curious and vice versa. If susan is either strong or happy then someone is both patient and creative and vice versa. If someone is patient or not tall then alice is either not brave or strong. If someone is not generous or not old then mary is not old. If lucy is not rich then alice is funny or rich and vice versa. If someone is not brave then someone is both not wise and curious and vice versa. If someone is tall then someone is both rich and not wise and vice versa. If someone is either brave or strong then someone is either funny or creative. Someone is brave or not generous. Paul is tall. Mary is kind or not quiet. John is not patient. Someone is creative. John is either not happy or not wise. Paul is either not patient or not generous. Fred is either not brave or not quiet. | Mary is old. | contradiction | (![X]:((calm(X)|generous(X))=>(~happy(X)<~>brave(X))))&
((?[X]:(creative(X)))=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)&calm(X))<=>(~creative(X)&generous(X))))&
(![X]:(~patient(X)<=>wise(X)))&
((?[X]:((humble(X)|~humble(X))))<=>(?[X]:((rich(X)<~>~brave(X)))))&
(![X]:((funny(X)|~wise(X))=>~old(X)))&
(((strong(fred)|curious(fred)))<=>((quiet(john)|~rich(john))))&
((rich(fred))=>((~wise(alice)|~creative(alice))))&
(![X]:((~tall(X)<~>humble(X))<=>(~quiet(X)|curious(X))))&
(((strong(susan)<~>happy(susan)))<=>(?[X]:((patient(X)&creative(X)))))&
((?[X]:((patient(X)|~tall(X))))=>((~brave(alice)<~>strong(alice))))&
((?[X]:((~generous(X)|~old(X))))=>(~old(mary)))&
((~rich(lucy))<=>((funny(alice)|rich(alice))))&
((?[X]:(~brave(X)))<=>(?[X]:((~wise(X)&curious(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((rich(X)&~wise(X)))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((funny(X)<~>creative(X)))))&
(?[X]:((brave(X)|~generous(X))))&
(tall(paul))&
((kind(mary)|~quiet(mary)))&
(~patient(john))&
(?[X]:(creative(X)))&
((~happy(john)<~>~wise(john)))&
((~patient(paul)<~>~generous(paul)))&
((~brave(fred)<~>~quiet(fred))) | old(mary) | [
"p5",
"p11",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 859268165248058116542710
% SZS output start Proof for 859268165248058116542710
6. ! [X0] : ((~wise(X0) | funny(X0)) => ~old(X0)) [input p5]
12. ? [X0] : (~old(X0) | ~generous(X0)) => ~old(mary) [input p11]
15. ? [X0] : tall(X0) <=> ? [X0] : (~wise(X0) & rich(X0)) [input p14]
18. tall(paul) [input p17]
25. old(mary) [input hypothesis]
29. ? [X0] : tall(X0) <=> ? [X1] : (~wise(X1) & rich(X1)) [rectify 15]
33. ! [X0] : (~old(X0) | (wise(X0) & ~funny(X0))) [ennf transformation 6]
37. ~old(mary) | ! [X0] : (old(X0) & generous(X0)) [ennf transformation 12]
67. (? [X0] : tall(X0) | ! [X1] : (wise(X1) | ~rich(X1))) & (? [X1] : (~wise(X1) & rich(X1)) | ! [X0] : ~tall(X0)) [nnf transformation 29]
68. (? [X0] : tall(X0) | ! [X1] : (wise(X1) | ~rich(X1))) & (? [X2] : (~wise(X2) & rich(X2)) | ! [X3] : ~tall(X3)) [rectify 67]
69. ? [X0] : tall(X0) => tall(sK6) [choice axiom]
70. ? [X2] : (~wise(X2) & rich(X2)) => (~wise(sK7) & rich(sK7)) [choice axiom]
71. (tall(sK6) | ! [X1] : (wise(X1) | ~rich(X1))) & ((~wise(sK7) & rich(sK7)) | ! [X3] : ~tall(X3)) [skolemisation 68,70,69]
101. ~old(X0) | wise(X0) [cnf transformation 33]
124. ~old(mary) | old(X0) [cnf transformation 37]
132. ~wise(sK7) | ~tall(X3) [cnf transformation 71]
139. tall(paul) [cnf transformation 18]
149. old(mary) [cnf transformation 25]
253. 23 <=> ! [X0] : old(X0) [avatar definition]
254. old(X0) <- (23) [avatar component clause 253]
256. 24 <=> old(mary) [avatar definition]
259. 23 | ~24 [avatar split clause 124,256,253]
309. 36 <=> ! [X3] : ~tall(X3) [avatar definition]
310. ~tall(X3) <- (36) [avatar component clause 309]
312. 37 <=> wise(sK7) [avatar definition]
314. ~wise(sK7) <- (~37) [avatar component clause 312]
315. 36 | ~37 [avatar split clause 132,312,309]
387. 24 [avatar split clause 149,256]
394. $false <- (36) [resolution 310,139]
395. ~36 [avatar contradiction clause 394]
408. wise(X0) <- (23) [resolution 101,254]
412. $false <- (23, ~37) [resolution 408,314]
414. ~23 | 37 [avatar contradiction clause 412]
416. $false [avatar sat refutation 259,315,387,395,414]
% SZS output end Proof for 859268165248058116542710
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either quiet or not funny then paul is quiet and vice versa.
If mary is not creative or not rich then someone is brave or not calm.
If someone is either brave or generous then mary is both tall and not funny and vice versa.
Everyone who is not tall is curious.
Everyone who is both humble and wise is both tall and not rich and vice versa.
If john is either strong or not happy then alice is both not kind and funny and vice versa.
Everyone who is either not tall or not kind is both quiet and not kind.
If alice is either not funny or not rich then susan is either humble or not humble and vice versa.
Everyone who is not wise is both happy and not quiet and vice versa.
Everyone who is tall is not calm and vice versa.
Everyone who is both not creative and not curious is not rich or not generous.
Everyone who is not happy is calm or creative and vice versa.
If mary is not brave then john is strong or brave and vice versa.
Everyone who is either humble or happy is humble or kind and vice versa.
Everyone who is not patient is not kind or tall and vice versa.
Everyone who is curious or not creative is not creative or happy and vice versa.
John is both happy and curious.
Alice is both creative and not quiet.
Someone is calm or not curious.
Someone is both not curious and not calm.
Someone is not old.
Someone is not old or patient.
Someone is wise or creative.
Someone is either not creative or wise. | John is kind. | entailment | ((?[X]:((quiet(X)<~>~funny(X))))<=>(quiet(paul)))&
(((~creative(mary)|~rich(mary)))=>(?[X]:((brave(X)|~calm(X)))))&
((?[X]:((brave(X)<~>generous(X))))<=>((tall(mary)&~funny(mary))))&
(![X]:(~tall(X)=>curious(X)))&
(![X]:((humble(X)&wise(X))<=>(tall(X)&~rich(X))))&
(((strong(john)<~>~happy(john)))<=>((~kind(alice)&funny(alice))))&
(![X]:((~tall(X)<~>~kind(X))=>(quiet(X)&~kind(X))))&
(((~funny(alice)<~>~rich(alice)))<=>((humble(susan)<~>~humble(susan))))&
(![X]:(~wise(X)<=>(happy(X)&~quiet(X))))&
(![X]:(tall(X)<=>~calm(X)))&
(![X]:((~creative(X)&~curious(X))=>(~rich(X)|~generous(X))))&
(![X]:(~happy(X)<=>(calm(X)|creative(X))))&
((~brave(mary))<=>((strong(john)|brave(john))))&
(![X]:((humble(X)<~>happy(X))<=>(humble(X)|kind(X))))&
(![X]:(~patient(X)<=>(~kind(X)|tall(X))))&
(![X]:((curious(X)|~creative(X))<=>(~creative(X)|happy(X))))&
((happy(john)&curious(john)))&
((creative(alice)&~quiet(alice)))&
(?[X]:((calm(X)|~curious(X))))&
(?[X]:((~curious(X)&~calm(X))))&
(?[X]:(~old(X)))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((wise(X)|creative(X))))&
(?[X]:((~creative(X)<~>wise(X)))) | kind(john) | [
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6484434240151057017432896
% SZS output start Proof for 6484434240151057017432896
14. ! [X0] : ((humble(X0) <~> happy(X0)) <=> (kind(X0) | humble(X0))) [input p13]
17. curious(john) & happy(john) [input p16]
25. ~kind(john) [input hypothesis]
59. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (~kind(X0) & ~humble(X0))) & ((kind(X0) | humble(X0)) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [nnf transformation 14]
60. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (~kind(X0) & ~humble(X0))) & (kind(X0) | humble(X0) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [flattening 59]
120. kind(X0) | humble(X0) | humble(X0) | ~happy(X0) [cnf transformation 60]
123. ~happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 60]
129. happy(john) [cnf transformation 17]
139. ~kind(john) [cnf transformation 25]
140. kind(X0) | humble(X0) | ~happy(X0) [duplicate literal removal 120]
141. ~happy(X0) | ~humble(X0) [duplicate literal removal 123]
228. 19 <=> happy(john) [avatar definition]
230. happy(john) <- (19) [avatar component clause 228]
260. ~happy(X0) | kind(X0) [subsumption resolution 140,141]
262. 19 [avatar split clause 129,228]
308. kind(john) <- (19) [resolution 260,230]
310. $false <- (19) [subsumption resolution 308,139]
311. ~19 [avatar contradiction clause 310]
312. $false [avatar sat refutation 262,311]
% SZS output end Proof for 6484434240151057017432896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or not curious then someone is both curious and strong and vice versa.
Everyone who is either curious or not strong is wise or not strong.
Everyone who is creative or not old is not funny or not rich and vice versa.
If john is old or generous then someone is both not wise and not happy and vice versa.
Everyone who is tall is either not kind or brave and vice versa.
If someone is either not strong or brave then someone is both funny and not rich and vice versa.
Everyone who is either calm or not quiet is both patient and quiet.
If mary is not generous then someone is wise or happy.
Everyone who is not calm or not curious is not funny.
If someone is not wise then mary is not quiet.
If fred is brave or not creative then mary is either tall or not strong.
If fred is not creative or rich then someone is either not generous or not creative and vice versa.
If someone is not brave then susan is either not patient or not generous and vice versa.
Everyone who is not creative or strong is not rich or curious and vice versa.
If someone is creative or quiet then fred is not wise and vice versa.
If someone is both wise and quiet then john is not creative.
Someone is quiet or not calm.
Someone is not wise.
Someone is either not strong or not creative.
Someone is calm.
Someone is both generous and not patient.
Paul is either not quiet or not creative.
Someone is either not tall or old.
Mary is calm or not curious. | Fred is wise. | contradiction | ((?[X]:((~brave(X)<~>~curious(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(![X]:((curious(X)<~>~strong(X))=>(wise(X)|~strong(X))))&
(![X]:((creative(X)|~old(X))<=>(~funny(X)|~rich(X))))&
(((old(john)|generous(john)))<=>(?[X]:((~wise(X)&~happy(X)))))&
(![X]:(tall(X)<=>(~kind(X)<~>brave(X))))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((funny(X)&~rich(X)))))&
(![X]:((calm(X)<~>~quiet(X))=>(patient(X)&quiet(X))))&
((~generous(mary))=>(?[X]:((wise(X)|happy(X)))))&
(![X]:((~calm(X)|~curious(X))=>~funny(X)))&
((?[X]:(~wise(X)))=>(~quiet(mary)))&
(((brave(fred)|~creative(fred)))=>((tall(mary)<~>~strong(mary))))&
(((~creative(fred)|rich(fred)))<=>(?[X]:((~generous(X)<~>~creative(X)))))&
((?[X]:(~brave(X)))<=>((~patient(susan)<~>~generous(susan))))&
(![X]:((~creative(X)|strong(X))<=>(~rich(X)|curious(X))))&
((?[X]:((creative(X)|quiet(X))))<=>(~wise(fred)))&
((?[X]:((wise(X)&quiet(X))))=>(~creative(john)))&
(?[X]:((quiet(X)|~calm(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~strong(X)<~>~creative(X))))&
(?[X]:(calm(X)))&
(?[X]:((generous(X)&~patient(X))))&
((~quiet(paul)<~>~creative(paul)))&
(?[X]:((~tall(X)<~>old(X))))&
((calm(mary)|~curious(mary))) | wise(fred) | [
"p6",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6266976292003313103777031
% SZS output start Proof for 6266976292003313103777031
7. ! [X0] : ((calm(X0) <~> ~quiet(X0)) => (quiet(X0) & patient(X0))) [input p6]
15. ? [X0] : (quiet(X0) | creative(X0)) <=> ~wise(fred) [input p14]
17. ? [X0] : (~calm(X0) | quiet(X0)) [input p16]
25. wise(fred) [input hypothesis]
30. ! [X0] : ((quiet(X0) & patient(X0)) | (calm(X0) <=> ~quiet(X0))) [ennf transformation 7]
55. ! [X0] : ((quiet(X0) & patient(X0)) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0)))) [nnf transformation 30]
70. (? [X0] : (quiet(X0) | creative(X0)) | wise(fred)) & (~wise(fred) | ! [X0] : (~quiet(X0) & ~creative(X0))) [nnf transformation 15]
71. (? [X0] : (quiet(X0) | creative(X0)) | wise(fred)) & (~wise(fred) | ! [X1] : (~quiet(X1) & ~creative(X1))) [rectify 70]
72. ? [X0] : (quiet(X0) | creative(X0)) => (quiet(sK8) | creative(sK8)) [choice axiom]
73. ((quiet(sK8) | creative(sK8)) | wise(fred)) & (~wise(fred) | ! [X1] : (~quiet(X1) & ~creative(X1))) [skolemisation 71,72]
74. ? [X0] : (~calm(X0) | quiet(X0)) => (~calm(sK9) | quiet(sK9)) [choice axiom]
75. ~calm(sK9) | quiet(sK9) [skolemisation 17,74]
119. quiet(X0) | calm(X0) | quiet(X0) [cnf transformation 55]
143. ~wise(fred) | ~quiet(X1) [cnf transformation 73]
146. ~calm(sK9) | quiet(sK9) [cnf transformation 75]
158. wise(fred) [cnf transformation 25]
159. quiet(X0) | calm(X0) [duplicate literal removal 119]
332. 38 <=> wise(fred) [avatar definition]
345. 41 <=> ! [X1] : ~quiet(X1) [avatar definition]
346. ~quiet(X1) <- (41) [avatar component clause 345]
347. 41 | ~38 [avatar split clause 143,332,345]
360. quiet(sK9) [subsumption resolution 146,159]
400. 38 [avatar split clause 158,332]
408. $false <- (41) [resolution 360,346]
409. ~41 [avatar contradiction clause 408]
410. $false [avatar sat refutation 347,400,409]
% SZS output end Proof for 6266976292003313103777031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or not old then paul is old or not tall.
If someone is funny then someone is either not tall or calm.
If alice is tall then someone is not calm or tall and vice versa.
Everyone who is either quiet or not rich is both not rich and brave and vice versa.
If mary is not kind or not funny then susan is old or strong.
If alice is either not patient or not humble then john is either not strong or tall.
Everyone who is not curious is not old or creative.
Everyone who is both not old and creative is creative or patient and vice versa.
If someone is not generous or not curious then fred is either quiet or strong and vice versa.
If paul is either not wise or not patient then fred is not funny.
If fred is both not quiet and not old then someone is either not quiet or not happy and vice versa.
Everyone who is not tall is not funny or funny and vice versa.
Everyone who is either not patient or not kind is rich.
If someone is not patient or creative then john is either creative or not generous and vice versa.
Everyone who is both not rich and not creative is kind and vice versa.
Everyone who is either not wise or not humble is not brave.
Someone is either not strong or not funny.
Someone is not curious.
Someone is both not quiet and not happy.
Mary is not happy.
Someone is not kind or not brave.
Someone is either humble or not wise. | Susan is not creative. | neutral | ((?[X]:((~strong(X)<~>~old(X))))=>((old(paul)|~tall(paul))))&
((?[X]:(funny(X)))=>(?[X]:((~tall(X)<~>calm(X)))))&
((tall(alice))<=>(?[X]:((~calm(X)|tall(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>(~rich(X)&brave(X))))&
(((~kind(mary)|~funny(mary)))=>((old(susan)|strong(susan))))&
(((~patient(alice)<~>~humble(alice)))=>((~strong(john)<~>tall(john))))&
(![X]:(~curious(X)=>(~old(X)|creative(X))))&
(![X]:((~old(X)&creative(X))<=>(creative(X)|patient(X))))&
((?[X]:((~generous(X)|~curious(X))))<=>((quiet(fred)<~>strong(fred))))&
(((~wise(paul)<~>~patient(paul)))=>(~funny(fred)))&
(((~quiet(fred)&~old(fred)))<=>(?[X]:((~quiet(X)<~>~happy(X)))))&
(![X]:(~tall(X)<=>(~funny(X)|funny(X))))&
(![X]:((~patient(X)<~>~kind(X))=>rich(X)))&
((?[X]:((~patient(X)|creative(X))))<=>((creative(john)<~>~generous(john))))&
(![X]:((~rich(X)&~creative(X))<=>kind(X)))&
(![X]:((~wise(X)<~>~humble(X))=>~brave(X)))&
(?[X]:((~strong(X)<~>~funny(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~quiet(X)&~happy(X))))&
(~happy(mary))&
(?[X]:((~kind(X)|~brave(X))))&
(?[X]:((humble(X)<~>~wise(X)))) | ~creative(susan) | [] | null | 0 |
Everyone who is either not calm or not creative is not brave or not creative and vice versa. If alice is not kind then someone is either not kind or old. If someone is not patient then lucy is both wise and not quiet. Everyone who is not strong is not old and vice versa. If susan is funny then someone is not calm. If mary is not funny then mary is either quiet or humble and vice versa. Everyone who is patient is both not happy and not tall. Everyone who is not old is not calm or wise. Everyone who is not curious or tall is either happy or tall. Everyone who is not humble is either happy or creative and vice versa. Everyone who is either brave or not funny is both wise and not creative and vice versa. If john is either tall or not quiet then paul is both not patient and calm. Everyone who is both tall and not generous is not brave or generous and vice versa. If lucy is both not kind and not calm then paul is not creative. If someone is wise or not strong then someone is both not quiet and creative. If someone is either not brave or calm then someone is not patient. Someone is both brave and not rich. Someone is not kind. Someone is curious or not humble. Someone is both not strong and quiet. Someone is either happy or not humble. Someone is patient or not patient. John is not creative. Someone is not old. | Lucy is quiet. | contradiction | (![X]:((~calm(X)<~>~creative(X))<=>(~brave(X)|~creative(X))))&
((~kind(alice))=>(?[X]:((~kind(X)<~>old(X)))))&
((?[X]:(~patient(X)))=>((wise(lucy)&~quiet(lucy))))&
(![X]:(~strong(X)<=>~old(X)))&
((funny(susan))=>(?[X]:(~calm(X))))&
((~funny(mary))<=>((quiet(mary)<~>humble(mary))))&
(![X]:(patient(X)=>(~happy(X)&~tall(X))))&
(![X]:(~old(X)=>(~calm(X)|wise(X))))&
(![X]:((~curious(X)|tall(X))=>(happy(X)<~>tall(X))))&
(![X]:(~humble(X)<=>(happy(X)<~>creative(X))))&
(![X]:((brave(X)<~>~funny(X))<=>(wise(X)&~creative(X))))&
(((tall(john)<~>~quiet(john)))=>((~patient(paul)&calm(paul))))&
(![X]:((tall(X)&~generous(X))<=>(~brave(X)|generous(X))))&
(((~kind(lucy)&~calm(lucy)))=>(~creative(paul)))&
((?[X]:((wise(X)|~strong(X))))=>(?[X]:((~quiet(X)&creative(X)))))&
((?[X]:((~brave(X)<~>calm(X))))=>(?[X]:(~patient(X))))&
(?[X]:((brave(X)&~rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((~strong(X)&quiet(X))))&
(?[X]:((happy(X)<~>~humble(X))))&
(?[X]:((patient(X)|~patient(X))))&
(~creative(john))&
(?[X]:(~old(X))) | quiet(lucy) | [
"p0",
"p2",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6974967904398608434743173
% SZS output start Proof for 6974967904398608434743173
1. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> (~creative(X0) | ~brave(X0))) [input p0]
3. ? [X0] : ~patient(X0) => (~quiet(lucy) & wise(lucy)) [input p2]
16. ? [X0] : (~brave(X0) <~> calm(X0)) => ? [X0] : ~patient(X0) [input p15]
17. ? [X0] : (~rich(X0) & brave(X0)) [input p16]
25. quiet(lucy) [input hypothesis]
27. ? [X0] : (~brave(X0) <~> calm(X0)) => ? [X1] : ~patient(X1) [rectify 16]
28. ? [X0] : brave(X0) [pure predicate removal 17]
32. (~quiet(lucy) & wise(lucy)) | ! [X0] : patient(X0) [ennf transformation 3]
42. ? [X1] : ~patient(X1) | ! [X0] : (~brave(X0) <=> calm(X0)) [ennf transformation 27]
43. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (creative(X0) & brave(X0))) & ((~creative(X0) | ~brave(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 1]
44. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (creative(X0) & brave(X0))) & (~creative(X0) | ~brave(X0) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [flattening 43]
62. ? [X1] : ~patient(X1) | ! [X0] : ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0))) [nnf transformation 42]
63. ? [X0] : ~patient(X0) | ! [X1] : ((~brave(X1) | ~calm(X1)) & (calm(X1) | brave(X1))) [rectify 62]
64. ? [X0] : ~patient(X0) => ~patient(sK3) [choice axiom]
65. ~patient(sK3) | ! [X1] : ((~brave(X1) | ~calm(X1)) & (calm(X1) | brave(X1))) [skolemisation 63,64]
66. ? [X0] : brave(X0) => brave(sK4) [choice axiom]
67. brave(sK4) [skolemisation 28,66]
79. ~creative(X0) | ~brave(X0) | ~creative(X0) | calm(X0) [cnf transformation 44]
84. creative(X0) | calm(X0) | creative(X0) [cnf transformation 44]
88. ~quiet(lucy) | patient(X0) [cnf transformation 32]
126. ~patient(sK3) | ~brave(X1) | ~calm(X1) [cnf transformation 65]
127. brave(sK4) [cnf transformation 67]
136. quiet(lucy) [cnf transformation 25]
140. ~creative(X0) | ~brave(X0) | calm(X0) [duplicate literal removal 79]
141. creative(X0) | calm(X0) [duplicate literal removal 84]
142. ~brave(X0) | calm(X0) [subsumption resolution 140,141]
158. 4 <=> ! [X0] : patient(X0) [avatar definition]
159. patient(X0) <- (4) [avatar component clause 158]
161. 5 <=> quiet(lucy) [avatar definition]
164. 4 | ~5 [avatar split clause 88,161,158]
247. ~patient(sK3) | ~brave(X1) [subsumption resolution 126,142]
249. 23 <=> ! [X1] : ~brave(X1) [avatar definition]
250. ~brave(X1) <- (23) [avatar component clause 249]
252. 24 <=> patient(sK3) [avatar definition]
254. ~patient(sK3) <- (~24) [avatar component clause 252]
255. 23 | ~24 [avatar split clause 247,252,249]
271. 5 [avatar split clause 136,161]
272. $false <- (4, ~24) [resolution 254,159]
273. ~4 | 24 [avatar contradiction clause 272]
274. $false <- (23) [resolution 250,127]
275. ~23 [avatar contradiction clause 274]
276. $false [avatar sat refutation 164,255,271,273,275]
% SZS output end Proof for 6974967904398608434743173
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not old is either tall or not creative and vice versa. Everyone who is curious or brave is both humble and quiet and vice versa. Everyone who is both not brave and not rich is not brave. Everyone who is not brave or wise is either tall or funny. Everyone who is either funny or not curious is generous. If someone is patient or quiet then susan is both funny and not quiet. Everyone who is kind is either not generous or not kind and vice versa. Everyone who is not strong is both humble and not brave and vice versa. Everyone who is rich or calm is not funny. Everyone who is either wise or quiet is either quiet or funny and vice versa. If someone is generous then lucy is either calm or not creative. If mary is happy then fred is brave and vice versa. If someone is not tall or wise then susan is strong. If someone is strong then someone is both wise and not calm and vice versa. If paul is rich then someone is funny. If john is not patient or generous then someone is strong or curious. Alice is both kind and not funny. Someone is not funny. Someone is either creative or quiet. Someone is either not strong or not kind. Someone is either not kind or calm. Alice is either rich or tall. Mary is not old or not strong. Mary is either not brave or curious. | Susan is not wise. | contradiction | (![X]:((~patient(X)|~old(X))<=>(tall(X)<~>~creative(X))))&
(![X]:((curious(X)|brave(X))<=>(humble(X)&quiet(X))))&
(![X]:((~brave(X)&~rich(X))=>~brave(X)))&
(![X]:((~brave(X)|wise(X))=>(tall(X)<~>funny(X))))&
(![X]:((funny(X)<~>~curious(X))=>generous(X)))&
((?[X]:((patient(X)|quiet(X))))=>((funny(susan)&~quiet(susan))))&
(![X]:(kind(X)<=>(~generous(X)<~>~kind(X))))&
(![X]:(~strong(X)<=>(humble(X)&~brave(X))))&
(![X]:((rich(X)|calm(X))=>~funny(X)))&
(![X]:((wise(X)<~>quiet(X))<=>(quiet(X)<~>funny(X))))&
((?[X]:(generous(X)))=>((calm(lucy)<~>~creative(lucy))))&
((happy(mary))<=>(brave(fred)))&
((?[X]:((~tall(X)|wise(X))))=>(strong(susan)))&
((?[X]:(strong(X)))<=>(?[X]:((wise(X)&~calm(X)))))&
((rich(paul))=>(?[X]:(funny(X))))&
(((~patient(john)|generous(john)))=>(?[X]:((strong(X)|curious(X)))))&
((kind(alice)&~funny(alice)))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)<~>quiet(X))))&
(?[X]:((~strong(X)<~>~kind(X))))&
(?[X]:((~kind(X)<~>calm(X))))&
((rich(alice)<~>tall(alice)))&
((~old(mary)|~strong(mary)))&
((~brave(mary)<~>curious(mary))) | ~wise(susan) | [
"p1",
"p4",
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6107918529561561575766059
% SZS output start Proof for 6107918529561561575766059
2. ! [X0] : ((brave(X0) | curious(X0)) <=> (quiet(X0) & humble(X0))) [input p1]
5. ! [X0] : ((funny(X0) <~> ~curious(X0)) => generous(X0)) [input p4]
6. ? [X0] : (quiet(X0) | patient(X0)) => (~quiet(susan) & funny(susan)) [input p5]
7. ! [X0] : (kind(X0) <=> (~generous(X0) <~> ~kind(X0))) [input p6]
10. ! [X0] : ((wise(X0) <~> quiet(X0)) <=> (quiet(X0) <~> funny(X0))) [input p9]
25. ~wise(susan) [input hypothesis]
30. ! [X0] : (generous(X0) | (funny(X0) <=> ~curious(X0))) [ennf transformation 5]
31. (~quiet(susan) & funny(susan)) | ! [X0] : (~quiet(X0) & ~patient(X0)) [ennf transformation 6]
39. ! [X0] : (((brave(X0) | curious(X0)) | (~quiet(X0) | ~humble(X0))) & ((quiet(X0) & humble(X0)) | (~brave(X0) & ~curious(X0)))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | curious(X0) | ~quiet(X0) | ~humble(X0)) & ((quiet(X0) & humble(X0)) | (~brave(X0) & ~curious(X0)))) [flattening 39]
42. ! [X0] : (generous(X0) | ((funny(X0) | curious(X0)) & (~curious(X0) | ~funny(X0)))) [nnf transformation 30]
43. ! [X0] : ((kind(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) & (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | ~kind(X0))) [nnf transformation 7]
46. ! [X0] : ((((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0)))) & (((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0))))) [nnf transformation 10]
79. ~curious(X0) | quiet(X0) [cnf transformation 40]
88. generous(X0) | funny(X0) | curious(X0) [cnf transformation 42]
90. funny(susan) | ~quiet(X0) [cnf transformation 31]
93. ~kind(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 43]
96. kind(X0) | ~generous(X0) | kind(X0) [cnf transformation 43]
105. ~funny(X0) | ~quiet(X0) | wise(X0) | ~quiet(X0) [cnf transformation 46]
107. quiet(X0) | wise(X0) | quiet(X0) | ~funny(X0) [cnf transformation 46]
136. ~wise(susan) [cnf transformation 25]
138. ~funny(X0) | ~quiet(X0) | wise(X0) [duplicate literal removal 105]
139. ~funny(X0) | wise(X0) | quiet(X0) [duplicate literal removal 107]
141. ~kind(X0) | ~generous(X0) [duplicate literal removal 93]
142. ~generous(X0) | kind(X0) [duplicate literal removal 96]
144. 1 <=> ! [X0] : ~quiet(X0) [avatar definition]
145. ~quiet(X0) <- (1) [avatar component clause 144]
156. 4 <=> funny(susan) [avatar definition]
157. ~funny(susan) <- (~4) [avatar component clause 156]
158. funny(susan) <- (4) [avatar component clause 156]
159. 1 | 4 [avatar split clause 90,156,144]
161. ~generous(X0) [subsumption resolution 141,142]
162. ~funny(X0) | wise(X0) [subsumption resolution 138,139]
297. wise(susan) <- (4) [resolution 162,158]
298. $false <- (4) [subsumption resolution 297,136]
299. ~4 [avatar contradiction clause 298]
407. funny(X1) | curious(X1) [resolution 88,161]
467. curious(susan) <- (~4) [resolution 407,157]
486. quiet(susan) <- (~4) [resolution 467,79]
488. $false <- (1, ~4) [subsumption resolution 486,145]
489. ~1 | 4 [avatar contradiction clause 488]
492. $false [avatar sat refutation 159,299,489]
% SZS output end Proof for 6107918529561561575766059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not humble is quiet. If someone is humble or not happy then someone is either not quiet or wise. If someone is creative then mary is strong or quiet. Everyone who is funny or not wise is happy or not kind. If someone is both not happy and wise then paul is rich or funny and vice versa. Everyone who is both tall and funny is both not generous and patient and vice versa. If fred is not quiet or humble then someone is both brave and kind and vice versa. Everyone who is humble or not brave is both quiet and wise. Everyone who is not wise or calm is not patient or humble and vice versa. Everyone who is old is either not humble or not old and vice versa. Everyone who is both kind and old is strong or happy. Everyone who is either creative or not quiet is both not happy and creative. If someone is brave or not quiet then someone is either not rich or not humble. If someone is both not curious and quiet then someone is strong and vice versa. If someone is not strong then someone is kind. Everyone who is both rich and humble is brave or not wise and vice versa. Paul is either not wise or not calm. Someone is not funny. Someone is either not curious or not brave. Someone is both not calm and curious. | Fred is creative. | neutral | (![X]:((~calm(X)&~humble(X))=>quiet(X)))&
((?[X]:((humble(X)|~happy(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:(creative(X)))=>((strong(mary)|quiet(mary))))&
(![X]:((funny(X)|~wise(X))=>(happy(X)|~kind(X))))&
((?[X]:((~happy(X)&wise(X))))<=>((rich(paul)|funny(paul))))&
(![X]:((tall(X)&funny(X))<=>(~generous(X)&patient(X))))&
(((~quiet(fred)|humble(fred)))<=>(?[X]:((brave(X)&kind(X)))))&
(![X]:((humble(X)|~brave(X))=>(quiet(X)&wise(X))))&
(![X]:((~wise(X)|calm(X))<=>(~patient(X)|humble(X))))&
(![X]:(old(X)<=>(~humble(X)<~>~old(X))))&
(![X]:((kind(X)&old(X))=>(strong(X)|happy(X))))&
(![X]:((creative(X)<~>~quiet(X))=>(~happy(X)&creative(X))))&
((?[X]:((brave(X)|~quiet(X))))=>(?[X]:((~rich(X)<~>~humble(X)))))&
((?[X]:((~curious(X)&quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:(~strong(X)))=>(?[X]:(kind(X))))&
(![X]:((rich(X)&humble(X))<=>(brave(X)|~wise(X))))&
((~wise(paul)<~>~calm(paul)))&
(?[X]:(~funny(X)))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((~calm(X)&curious(X)))) | creative(fred) | [] | null | 0 |
Everyone who is kind is either not kind or not happy and vice versa.
Everyone who is both not curious and generous is kind or tall and vice versa.
If someone is both calm and not patient then john is either strong or kind.
Everyone who is either curious or not old is kind or not calm and vice versa.
If paul is not rich then alice is humble.
Everyone who is both not quiet and not kind is either brave or not wise.
Everyone who is not happy or strong is old or happy and vice versa.
Everyone who is not quiet or not humble is both humble and not strong.
If someone is either curious or not wise then susan is generous or patient and vice versa.
Everyone who is either not strong or tall is both patient and not happy and vice versa.
If lucy is both not kind and curious then mary is either old or rich.
Everyone who is brave or not strong is not humble.
Everyone who is not curious is not tall and vice versa.
If lucy is either wise or not calm then someone is either not old or not brave.
If someone is not generous then fred is both old and strong.
John is either not creative or not old.
Paul is either not generous or funny.
Lucy is not rich or not patient.
Susan is either not quiet or humble.
Someone is not curious or not creative. | Mary is quiet. | entailment | (![X]:(kind(X)<=>(~kind(X)<~>~happy(X))))&
(![X]:((~curious(X)&generous(X))<=>(kind(X)|tall(X))))&
((?[X]:((calm(X)&~patient(X))))=>((strong(john)<~>kind(john))))&
(![X]:((curious(X)<~>~old(X))<=>(kind(X)|~calm(X))))&
((~rich(paul))=>(humble(alice)))&
(![X]:((~quiet(X)&~kind(X))=>(brave(X)<~>~wise(X))))&
(![X]:((~happy(X)|strong(X))<=>(old(X)|happy(X))))&
(![X]:((~quiet(X)|~humble(X))=>(humble(X)&~strong(X))))&
((?[X]:((curious(X)<~>~wise(X))))<=>((generous(susan)|patient(susan))))&
(![X]:((~strong(X)<~>tall(X))<=>(patient(X)&~happy(X))))&
(((~kind(lucy)&curious(lucy)))=>((old(mary)<~>rich(mary))))&
(![X]:((brave(X)|~strong(X))=>~humble(X)))&
(![X]:(~curious(X)<=>~tall(X)))&
(((wise(lucy)<~>~calm(lucy)))=>(?[X]:((~old(X)<~>~brave(X)))))&
((?[X]:(~generous(X)))=>((old(fred)&strong(fred))))&
((~creative(john)<~>~old(john)))&
((~generous(paul)<~>funny(paul)))&
((~rich(lucy)|~patient(lucy)))&
((~quiet(susan)<~>humble(susan)))&
(?[X]:((~curious(X)|~creative(X)))) | quiet(mary) | [
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5748304892875233229561344
% SZS output start Proof for 5748304892875233229561344
8. ! [X0] : ((~humble(X0) | ~quiet(X0)) => (~strong(X0) & humble(X0))) [input p7]
12. ! [X0] : ((~strong(X0) | brave(X0)) => ~humble(X0)) [input p11]
21. ~quiet(mary) [input hypothesis]
26. ! [X0] : ((~strong(X0) & humble(X0)) | (humble(X0) & quiet(X0))) [ennf transformation 8]
29. ! [X0] : (~humble(X0) | (strong(X0) & ~brave(X0))) [ennf transformation 12]
83. humble(X0) | humble(X0) [cnf transformation 26]
84. ~strong(X0) | quiet(X0) [cnf transformation 26]
101. ~humble(X0) | strong(X0) [cnf transformation 29]
118. ~quiet(mary) [cnf transformation 21]
119. humble(X0) [duplicate literal removal 83]
192. strong(X0) [subsumption resolution 101,119]
217. quiet(X0) [resolution 84,192]
219. $false [resolution 217,118]
% SZS output end Proof for 5748304892875233229561344
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not funny or not rich then someone is not curious.
If mary is wise then john is not wise or not tall.
Everyone who is either not curious or patient is old or not kind.
Everyone who is not happy is both not strong and not patient.
Everyone who is both brave and happy is not creative and vice versa.
If john is both not strong and kind then someone is either calm or rich and vice versa.
Everyone who is both not happy and creative is both not calm and not generous and vice versa.
Everyone who is either kind or not tall is not old or not tall and vice versa.
Everyone who is both funny and wise is not calm and vice versa.
Everyone who is both funny and not wise is calm or old and vice versa.
Everyone who is not patient is not humble and vice versa.
Everyone who is happy or generous is not curious or not old and vice versa.
Everyone who is not quiet or patient is patient and vice versa.
If someone is both not brave and kind then paul is not kind or not quiet and vice versa.
Everyone who is kind or not calm is curious or not wise.
If alice is not patient or wise then fred is either not happy or not generous and vice versa.
Lucy is either patient or not quiet.
Lucy is not calm.
Alice is funny or kind.
Someone is not brave or tall.
Someone is not calm or not funny.
Lucy is not rich or not happy.
Alice is old or humble.
Susan is not creative. | John is wise. | neutral | (((~funny(paul)<~>~rich(paul)))=>(?[X]:(~curious(X))))&
((wise(mary))=>((~wise(john)|~tall(john))))&
(![X]:((~curious(X)<~>patient(X))=>(old(X)|~kind(X))))&
(![X]:(~happy(X)=>(~strong(X)&~patient(X))))&
(![X]:((brave(X)&happy(X))<=>~creative(X)))&
(((~strong(john)&kind(john)))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~happy(X)&creative(X))<=>(~calm(X)&~generous(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(~old(X)|~tall(X))))&
(![X]:((funny(X)&wise(X))<=>~calm(X)))&
(![X]:((funny(X)&~wise(X))<=>(calm(X)|old(X))))&
(![X]:(~patient(X)<=>~humble(X)))&
(![X]:((happy(X)|generous(X))<=>(~curious(X)|~old(X))))&
(![X]:((~quiet(X)|patient(X))<=>patient(X)))&
((?[X]:((~brave(X)&kind(X))))<=>((~kind(paul)|~quiet(paul))))&
(![X]:((kind(X)|~calm(X))=>(curious(X)|~wise(X))))&
(((~patient(alice)|wise(alice)))<=>((~happy(fred)<~>~generous(fred))))&
((patient(lucy)<~>~quiet(lucy)))&
(~calm(lucy))&
((funny(alice)|kind(alice)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~calm(X)|~funny(X))))&
((~rich(lucy)|~happy(lucy)))&
((old(alice)|humble(alice)))&
(~creative(susan)) | wise(john) | [] | null | 0 |
Everyone who is not patient or quiet is both not generous and funny.
Everyone who is not quiet is not patient or not humble and vice versa.
Everyone who is both old and not wise is either not patient or rich and vice versa.
If fred is not tall then someone is both kind and happy and vice versa.
If susan is not generous or tall then someone is strong and vice versa.
If someone is humble then someone is strong or wise.
Everyone who is both not patient and wise is both not humble and not creative and vice versa.
Everyone who is either strong or not quiet is both strong and quiet.
Everyone who is either not brave or not kind is patient or tall.
If someone is either not old or quiet then someone is both quiet and funny.
If someone is generous or brave then someone is either not happy or strong and vice versa.
Everyone who is both not funny and creative is tall or not patient.
Everyone who is brave is either generous or kind and vice versa.
If paul is both happy and not tall then someone is both kind and creative.
Everyone who is kind or generous is either wise or old and vice versa.
If someone is both not calm and calm then someone is both not brave and not kind.
Someone is not happy.
John is both not quiet and brave.
Susan is both rich and not brave.
John is both not generous and not creative.
Paul is either not rich or not old.
Someone is either not happy or generous.
Someone is both funny and not wise. | John is patient. | contradiction | (![X]:((~patient(X)|quiet(X))=>(~generous(X)&funny(X))))&
(![X]:(~quiet(X)<=>(~patient(X)|~humble(X))))&
(![X]:((old(X)&~wise(X))<=>(~patient(X)<~>rich(X))))&
((~tall(fred))<=>(?[X]:((kind(X)&happy(X)))))&
(((~generous(susan)|tall(susan)))<=>(?[X]:(strong(X))))&
((?[X]:(humble(X)))=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((~patient(X)&wise(X))<=>(~humble(X)&~creative(X))))&
(![X]:((strong(X)<~>~quiet(X))=>(strong(X)&quiet(X))))&
(![X]:((~brave(X)<~>~kind(X))=>(patient(X)|tall(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((quiet(X)&funny(X)))))&
((?[X]:((generous(X)|brave(X))))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:((~funny(X)&creative(X))=>(tall(X)|~patient(X))))&
(![X]:(brave(X)<=>(generous(X)<~>kind(X))))&
(((happy(paul)&~tall(paul)))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:((kind(X)|generous(X))<=>(wise(X)<~>old(X))))&
((?[X]:((~calm(X)&calm(X))))=>(?[X]:((~brave(X)&~kind(X)))))&
(?[X]:(~happy(X)))&
((~quiet(john)&brave(john)))&
((rich(susan)&~brave(susan)))&
((~generous(john)&~creative(john)))&
((~rich(paul)<~>~old(paul)))&
(?[X]:((~happy(X)<~>generous(X))))&
(?[X]:((funny(X)&~wise(X)))) | patient(john) | [
"p1",
"p6",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 897715253033472179591095
% SZS output start Proof for 897715253033472179591095
2. ! [X0] : (~quiet(X0) <=> (~humble(X0) | ~patient(X0))) [input p1]
7. ! [X0] : ((wise(X0) & ~patient(X0)) <=> (~creative(X0) & ~humble(X0))) [input p6]
18. brave(john) & ~quiet(john) [input p17]
20. ~creative(john) & ~generous(john) [input p19]
24. patient(john) [input hypothesis]
42. ! [X0] : ((~quiet(X0) | (humble(X0) & patient(X0))) & ((~humble(X0) | ~patient(X0)) | quiet(X0))) [nnf transformation 2]
43. ! [X0] : ((~quiet(X0) | (humble(X0) & patient(X0))) & (~humble(X0) | ~patient(X0) | quiet(X0))) [flattening 42]
58. ! [X0] : (((wise(X0) & ~patient(X0)) | (creative(X0) | humble(X0))) & ((~creative(X0) & ~humble(X0)) | (~wise(X0) | patient(X0)))) [nnf transformation 7]
59. ! [X0] : (((wise(X0) & ~patient(X0)) | creative(X0) | humble(X0)) & ((~creative(X0) & ~humble(X0)) | ~wise(X0) | patient(X0))) [flattening 58]
89. ~humble(X0) | ~patient(X0) | quiet(X0) [cnf transformation 43]
107. ~patient(X0) | creative(X0) | humble(X0) [cnf transformation 59]
138. ~quiet(john) [cnf transformation 18]
143. ~creative(john) [cnf transformation 20]
149. patient(john) [cnf transformation 24]
349. creative(john) | humble(john) [resolution 107,149]
361. humble(john) [subsumption resolution 349,143]
375. ~patient(john) | quiet(john) [resolution 361,89]
376. quiet(john) [subsumption resolution 375,149]
377. $false [subsumption resolution 376,138]
% SZS output end Proof for 897715253033472179591095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or creative is not humble.
If someone is either funny or strong then paul is not strong or not funny and vice versa.
Everyone who is tall or not tall is brave.
Everyone who is not happy is not kind.
Everyone who is both not calm and curious is both wise and tall.
If someone is both generous and not happy then someone is not strong.
If john is both not happy and happy then someone is kind or tall.
If fred is both not patient and brave then someone is both not quiet and wise.
Everyone who is not wise or not curious is not humble or quiet.
If fred is either not strong or not tall then fred is both funny and not brave and vice versa.
If someone is both generous and funny then someone is both not brave and curious.
If someone is either not funny or funny then someone is not patient and vice versa.
Everyone who is calm or not patient is not calm.
Everyone who is either curious or calm is both not funny and not tall.
If someone is calm or not humble then someone is both creative and curious and vice versa.
Everyone who is not humble is strong or rich and vice versa.
Lucy is either happy or not happy.
John is tall or not calm.
Alice is not quiet or not funny.
Alice is either old or not happy.
Lucy is either happy or not kind.
Lucy is funny or not old. | Alice is not kind. | entailment | (![X]:((old(X)|creative(X))=>~humble(X)))&
((?[X]:((funny(X)<~>strong(X))))<=>((~strong(paul)|~funny(paul))))&
(![X]:((tall(X)|~tall(X))=>brave(X)))&
(![X]:(~happy(X)=>~kind(X)))&
(![X]:((~calm(X)&curious(X))=>(wise(X)&tall(X))))&
((?[X]:((generous(X)&~happy(X))))=>(?[X]:(~strong(X))))&
(((~happy(john)&happy(john)))=>(?[X]:((kind(X)|tall(X)))))&
(((~patient(fred)&brave(fred)))=>(?[X]:((~quiet(X)&wise(X)))))&
(![X]:((~wise(X)|~curious(X))=>(~humble(X)|quiet(X))))&
(((~strong(fred)<~>~tall(fred)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((generous(X)&funny(X))))=>(?[X]:((~brave(X)&curious(X)))))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:(~patient(X))))&
(![X]:((calm(X)|~patient(X))=>~calm(X)))&
(![X]:((curious(X)<~>calm(X))=>(~funny(X)&~tall(X))))&
((?[X]:((calm(X)|~humble(X))))<=>(?[X]:((creative(X)&curious(X)))))&
(![X]:(~humble(X)<=>(strong(X)|rich(X))))&
((happy(lucy)<~>~happy(lucy)))&
((tall(john)|~calm(john)))&
((~quiet(alice)|~funny(alice)))&
((old(alice)<~>~happy(alice)))&
((happy(lucy)<~>~kind(lucy)))&
((funny(lucy)|~old(lucy))) | ~kind(alice) | [
"p0",
"p3",
"p4",
"p12",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5876770956906930451632086
% SZS output start Proof for 5876770956906930451632086
1. ! [X0] : ((creative(X0) | old(X0)) => ~humble(X0)) [input p0]
4. ! [X0] : (~happy(X0) => ~kind(X0)) [input p3]
5. ! [X0] : ((curious(X0) & ~calm(X0)) => (tall(X0) & wise(X0))) [input p4]
13. ! [X0] : ((~patient(X0) | calm(X0)) => ~calm(X0)) [input p12]
14. ! [X0] : ((curious(X0) <~> calm(X0)) => (~tall(X0) & ~funny(X0))) [input p13]
15. ? [X0] : (~humble(X0) | calm(X0)) <=> ? [X0] : (curious(X0) & creative(X0)) [input p14]
20. old(alice) <~> ~happy(alice) [input p19]
23. kind(alice) [input hypothesis]
27. ? [X0] : (~humble(X0) | calm(X0)) <=> ? [X1] : (curious(X1) & creative(X1)) [rectify 15]
32. ! [X0] : ((curious(X0) & ~calm(X0)) => tall(X0)) [pure predicate removal 5]
33. ! [X0] : (~humble(X0) | (~creative(X0) & ~old(X0))) [ennf transformation 1]
35. ! [X0] : (~kind(X0) | happy(X0)) [ennf transformation 4]
36. ! [X0] : (tall(X0) | (~curious(X0) | calm(X0))) [ennf transformation 32]
37. ! [X0] : (tall(X0) | ~curious(X0) | calm(X0)) [flattening 36]
44. ! [X0] : (~calm(X0) | (patient(X0) & ~calm(X0))) [ennf transformation 13]
45. ! [X0] : ((~tall(X0) & ~funny(X0)) | (curious(X0) <=> calm(X0))) [ennf transformation 14]
62. ! [X0] : ((~tall(X0) & ~funny(X0)) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) [nnf transformation 45]
63. (? [X0] : (~humble(X0) | calm(X0)) | ! [X1] : (~curious(X1) | ~creative(X1))) & (? [X1] : (curious(X1) & creative(X1)) | ! [X0] : (humble(X0) & ~calm(X0))) [nnf transformation 27]
64. (? [X0] : (~humble(X0) | calm(X0)) | ! [X1] : (~curious(X1) | ~creative(X1))) & (? [X2] : (curious(X2) & creative(X2)) | ! [X3] : (humble(X3) & ~calm(X3))) [rectify 63]
65. ? [X0] : (~humble(X0) | calm(X0)) => (~humble(sK5) | calm(sK5)) [choice axiom]
66. ? [X2] : (curious(X2) & creative(X2)) => (curious(sK6) & creative(sK6)) [choice axiom]
67. ((~humble(sK5) | calm(sK5)) | ! [X1] : (~curious(X1) | ~creative(X1))) & ((curious(sK6) & creative(sK6)) | ! [X3] : (humble(X3) & ~calm(X3))) [skolemisation 64,66,65]
71. (happy(alice) | ~old(alice)) & (~happy(alice) | old(alice)) [nnf transformation 20]
73. ~humble(X0) | ~old(X0) [cnf transformation 33]
83. ~kind(X0) | happy(X0) [cnf transformation 35]
84. ~curious(X0) | tall(X0) | calm(X0) [cnf transformation 37]
98. ~calm(X0) | ~calm(X0) [cnf transformation 44]
102. ~tall(X0) | calm(X0) | ~curious(X0) [cnf transformation 62]
107. curious(sK6) | humble(X3) [cnf transformation 67]
116. ~happy(alice) | old(alice) [cnf transformation 71]
121. kind(alice) [cnf transformation 23]
122. ~calm(X0) [duplicate literal removal 98]
194. ~curious(X0) | ~tall(X0) [subsumption resolution 102,122]
206. 17 <=> ! [X3] : humble(X3) [avatar definition]
207. humble(X3) <- (17) [avatar component clause 206]
209. 18 <=> curious(sK6) [avatar definition]
211. curious(sK6) <- (18) [avatar component clause 209]
212. 17 | 18 [avatar split clause 107,209,206]
228. 22 <=> old(alice) [avatar definition]
229. old(alice) <- (22) [avatar component clause 228]
232. 23 <=> happy(alice) [avatar definition]
236. 22 | ~23 [avatar split clause 116,232,228]
257. ~old(X0) <- (17) [resolution 73,207]
259. happy(alice) [resolution 83,121]
262. 23 [avatar split clause 259,232]
263. $false <- (17, 22) [subsumption resolution 229,257]
264. ~17 | ~22 [avatar contradiction clause 263]
267. ~tall(sK6) <- (18) [resolution 194,211]
272. tall(sK6) | calm(sK6) <- (18) [resolution 84,211]
273. calm(sK6) <- (18) [subsumption resolution 272,267]
274. $false <- (18) [subsumption resolution 273,122]
275. ~18 [avatar contradiction clause 274]
276. $false [avatar sat refutation 212,236,262,264,275]
% SZS output end Proof for 5876770956906930451632086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not quiet then lucy is curious or strong.
If someone is either not old or not strong then someone is old or wise and vice versa.
If mary is wise then someone is either not funny or not old.
Everyone who is either not curious or not calm is not creative.
Everyone who is not funny is not old or not kind.
Everyone who is not tall or rich is either not tall or not old and vice versa.
If someone is either tall or not kind then someone is funny or brave and vice versa.
If someone is generous then someone is creative or old.
Everyone who is not generous is quiet and vice versa.
If someone is either brave or rich then paul is both kind and not funny and vice versa.
Everyone who is not happy or wise is tall or old and vice versa.
Everyone who is not calm or not strong is both kind and not brave.
Everyone who is calm or not tall is funny or strong and vice versa.
Everyone who is either strong or happy is both not happy and not patient and vice versa.
If alice is both not creative and happy then mary is happy or tall and vice versa.
If lucy is either humble or tall then john is both brave and calm and vice versa.
Someone is either not curious or not old.
Someone is generous or old.
Someone is quiet.
Mary is both not creative and funny.
Lucy is both not happy and rich.
Someone is either tall or not humble.
Susan is patient or not kind. | Susan is not happy. | neutral | ((?[X]:((~patient(X)|~quiet(X))))=>((curious(lucy)|strong(lucy))))&
((?[X]:((~old(X)<~>~strong(X))))<=>(?[X]:((old(X)|wise(X)))))&
((wise(mary))=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((~curious(X)<~>~calm(X))=>~creative(X)))&
(![X]:(~funny(X)=>(~old(X)|~kind(X))))&
(![X]:((~tall(X)|rich(X))<=>(~tall(X)<~>~old(X))))&
((?[X]:((tall(X)<~>~kind(X))))<=>(?[X]:((funny(X)|brave(X)))))&
((?[X]:(generous(X)))=>(?[X]:((creative(X)|old(X)))))&
(![X]:(~generous(X)<=>quiet(X)))&
((?[X]:((brave(X)<~>rich(X))))<=>((kind(paul)&~funny(paul))))&
(![X]:((~happy(X)|wise(X))<=>(tall(X)|old(X))))&
(![X]:((~calm(X)|~strong(X))=>(kind(X)&~brave(X))))&
(![X]:((calm(X)|~tall(X))<=>(funny(X)|strong(X))))&
(![X]:((strong(X)<~>happy(X))<=>(~happy(X)&~patient(X))))&
(((~creative(alice)&happy(alice)))<=>((happy(mary)|tall(mary))))&
(((humble(lucy)<~>tall(lucy)))<=>((brave(john)&calm(john))))&
(?[X]:((~curious(X)<~>~old(X))))&
(?[X]:((generous(X)|old(X))))&
(?[X]:(quiet(X)))&
((~creative(mary)&funny(mary)))&
((~happy(lucy)&rich(lucy)))&
(?[X]:((tall(X)<~>~humble(X))))&
((patient(susan)|~kind(susan))) | ~happy(susan) | [] | null | 0 |
Everyone who is not patient is both not quiet and not calm and vice versa.
If alice is both calm and strong then someone is calm or happy and vice versa.
Everyone who is either not calm or quiet is calm and vice versa.
If someone is not creative or not brave then fred is either not humble or brave.
If susan is either not calm or not funny then alice is both not strong and funny and vice versa.
If someone is kind or not kind then someone is funny or not calm.
If fred is creative or old then fred is both not funny and not strong and vice versa.
Everyone who is curious or not tall is not tall or not kind.
If mary is not wise then someone is generous and vice versa.
If someone is both happy and not tall then fred is rich.
Everyone who is either not calm or happy is funny or kind and vice versa.
Everyone who is not brave is either curious or not funny.
If john is kind or not brave then susan is either not calm or tall and vice versa.
If fred is quiet then mary is either curious or not tall and vice versa.
Everyone who is not strong or not humble is patient or brave and vice versa.
Everyone who is wise is not strong or generous and vice versa.
Someone is either not calm or not quiet.
Someone is wise.
Paul is not generous.
Alice is happy.
Someone is funny or rich.
John is calm.
Fred is not kind or not curious. | Alice is quiet. | entailment | (![X]:(~patient(X)<=>(~quiet(X)&~calm(X))))&
(((calm(alice)&strong(alice)))<=>(?[X]:((calm(X)|happy(X)))))&
(![X]:((~calm(X)<~>quiet(X))<=>calm(X)))&
((?[X]:((~creative(X)|~brave(X))))=>((~humble(fred)<~>brave(fred))))&
(((~calm(susan)<~>~funny(susan)))<=>((~strong(alice)&funny(alice))))&
((?[X]:((kind(X)|~kind(X))))=>(?[X]:((funny(X)|~calm(X)))))&
(((creative(fred)|old(fred)))<=>((~funny(fred)&~strong(fred))))&
(![X]:((curious(X)|~tall(X))=>(~tall(X)|~kind(X))))&
((~wise(mary))<=>(?[X]:(generous(X))))&
((?[X]:((happy(X)&~tall(X))))=>(rich(fred)))&
(![X]:((~calm(X)<~>happy(X))<=>(funny(X)|kind(X))))&
(![X]:(~brave(X)=>(curious(X)<~>~funny(X))))&
(((kind(john)|~brave(john)))<=>((~calm(susan)<~>tall(susan))))&
((quiet(fred))<=>((curious(mary)<~>~tall(mary))))&
(![X]:((~strong(X)|~humble(X))<=>(patient(X)|brave(X))))&
(![X]:(wise(X)<=>(~strong(X)|generous(X))))&
(?[X]:((~calm(X)<~>~quiet(X))))&
(?[X]:(wise(X)))&
(~generous(paul))&
(happy(alice))&
(?[X]:((funny(X)|rich(X))))&
(calm(john))&
((~kind(fred)|~curious(fred))) | quiet(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 374314486726809975681873
% SZS output start Proof for 374314486726809975681873
3. ! [X0] : ((~calm(X0) <~> quiet(X0)) <=> calm(X0)) [input p2]
24. ~quiet(alice) [input hypothesis]
40. ! [X0] : ((((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | ~calm(X0)) & (calm(X0) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0))))) [nnf transformation 3]
76. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 40]
78. quiet(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 40]
133. ~quiet(alice) [cnf transformation 24]
134. calm(X0) | quiet(X0) [duplicate literal removal 76]
135. quiet(X0) | ~calm(X0) [duplicate literal removal 78]
163. quiet(X0) [subsumption resolution 134,135]
290. $false [subsumption resolution 133,163]
% SZS output end Proof for 374314486726809975681873
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall or brave is either creative or not quiet and vice versa.
Everyone who is generous or not humble is either not brave or brave.
If susan is both not curious and not creative then lucy is either tall or quiet and vice versa.
If someone is creative or wise then someone is not quiet and vice versa.
If alice is not tall or curious then someone is humble and vice versa.
Everyone who is not rich is both strong and creative.
Everyone who is tall is calm and vice versa.
If susan is both generous and patient then alice is both not patient and not funny and vice versa.
If someone is funny then someone is funny or not strong.
If someone is wise then someone is not calm or curious.
If alice is either not old or not patient then fred is old or not generous and vice versa.
If john is not calm or kind then paul is old or calm.
Everyone who is happy is both funny and not old.
Everyone who is humble is either strong or not patient.
Everyone who is either not happy or brave is not old or funny and vice versa.
Everyone who is either brave or not old is wise or kind and vice versa.
John is either not tall or brave.
Someone is not calm or calm.
Someone is either not patient or not rich.
Someone is wise.
Susan is both happy and humble.
Alice is both tall and not old.
Someone is not old or not generous. | Susan is not creative. | neutral | (![X]:((~tall(X)|brave(X))<=>(creative(X)<~>~quiet(X))))&
(![X]:((generous(X)|~humble(X))=>(~brave(X)<~>brave(X))))&
(((~curious(susan)&~creative(susan)))<=>((tall(lucy)<~>quiet(lucy))))&
((?[X]:((creative(X)|wise(X))))<=>(?[X]:(~quiet(X))))&
(((~tall(alice)|curious(alice)))<=>(?[X]:(humble(X))))&
(![X]:(~rich(X)=>(strong(X)&creative(X))))&
(![X]:(tall(X)<=>calm(X)))&
(((generous(susan)&patient(susan)))<=>((~patient(alice)&~funny(alice))))&
((?[X]:(funny(X)))=>(?[X]:((funny(X)|~strong(X)))))&
((?[X]:(wise(X)))=>(?[X]:((~calm(X)|curious(X)))))&
(((~old(alice)<~>~patient(alice)))<=>((old(fred)|~generous(fred))))&
(((~calm(john)|kind(john)))=>((old(paul)|calm(paul))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
((~tall(john)<~>brave(john)))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((~patient(X)<~>~rich(X))))&
(?[X]:(wise(X)))&
((happy(susan)&humble(susan)))&
((tall(alice)&~old(alice)))&
(?[X]:((~old(X)|~generous(X)))) | ~creative(susan) | [] | null | 0 |
Everyone who is either funny or happy is patient or not patient. Everyone who is not kind is both not brave and old. If alice is kind or not wise then someone is not creative or not generous. Everyone who is funny or curious is not curious or funny. Everyone who is calm or creative is not generous. Everyone who is either not brave or not generous is either quiet or not creative. If fred is calm or not generous then someone is creative. If someone is tall or not patient then paul is not happy and vice versa. Everyone who is both not happy and creative is either strong or not kind and vice versa. Everyone who is not tall is both not humble and not strong and vice versa. Everyone who is both tall and not curious is not tall and vice versa. Everyone who is calm or not creative is both rich and kind and vice versa. Everyone who is not creative or not tall is not strong or not old. Everyone who is not patient is calm or funny. If alice is not happy then paul is not creative or not funny. Everyone who is tall or not strong is both kind and curious. Susan is not creative or not strong. Paul is not old. Someone is either not creative or calm. John is patient or not patient. Someone is both not old and quiet. Alice is wise or not calm. | Susan is not tall. | contradiction | (![X]:((funny(X)<~>happy(X))=>(patient(X)|~patient(X))))&
(![X]:(~kind(X)=>(~brave(X)&old(X))))&
(((kind(alice)|~wise(alice)))=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((funny(X)|curious(X))=>(~curious(X)|funny(X))))&
(![X]:((calm(X)|creative(X))=>~generous(X)))&
(![X]:((~brave(X)<~>~generous(X))=>(quiet(X)<~>~creative(X))))&
(((calm(fred)|~generous(fred)))=>(?[X]:(creative(X))))&
((?[X]:((tall(X)|~patient(X))))<=>(~happy(paul)))&
(![X]:((~happy(X)&creative(X))<=>(strong(X)<~>~kind(X))))&
(![X]:(~tall(X)<=>(~humble(X)&~strong(X))))&
(![X]:((tall(X)&~curious(X))<=>~tall(X)))&
(![X]:((calm(X)|~creative(X))<=>(rich(X)&kind(X))))&
(![X]:((~creative(X)|~tall(X))=>(~strong(X)|~old(X))))&
(![X]:(~patient(X)=>(calm(X)|funny(X))))&
((~happy(alice))=>((~creative(paul)|~funny(paul))))&
(![X]:((tall(X)|~strong(X))=>(kind(X)&curious(X))))&
((~creative(susan)|~strong(susan)))&
(~old(paul))&
(?[X]:((~creative(X)<~>calm(X))))&
((patient(john)|~patient(john)))&
(?[X]:((~old(X)&quiet(X))))&
((wise(alice)|~calm(alice))) | ~tall(susan) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1237372492129956480759774
% SZS output start Proof for 1237372492129956480759774
11. ! [X0] : ((~curious(X0) & tall(X0)) <=> ~tall(X0)) [input p10]
23. ~tall(susan) [input hypothesis]
56. ! [X0] : (((~curious(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) | ~tall(X0)))) [nnf transformation 11]
57. ! [X0] : (((~curious(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | curious(X0) | ~tall(X0))) [flattening 56]
93. tall(X0) | tall(X0) [cnf transformation 57]
115. ~tall(susan) [cnf transformation 23]
117. tall(X0) [duplicate literal removal 93]
203. $false [subsumption resolution 115,117]
% SZS output end Proof for 1237372492129956480759774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or curious is generous or not creative and vice versa.
Everyone who is both not creative and not brave is not creative or curious and vice versa.
Everyone who is curious is not old and vice versa.
If alice is either not tall or kind then someone is not kind and vice versa.
Everyone who is both generous and quiet is either curious or not quiet and vice versa.
Everyone who is either not kind or tall is not funny or not curious.
If mary is either creative or quiet then susan is wise.
If paul is both creative and wise then mary is funny and vice versa.
Everyone who is either not calm or humble is kind or funny and vice versa.
Everyone who is not rich is either not generous or not humble.
Everyone who is not generous or curious is either funny or not creative.
If someone is either curious or generous then someone is either calm or not rich.
Everyone who is curious is wise and vice versa.
If fred is either not curious or kind then mary is both patient and not quiet and vice versa.
If someone is creative or rich then someone is both calm and old and vice versa.
Everyone who is both brave and not wise is patient.
Someone is not rich or not patient.
Someone is not generous or not tall.
Susan is tall.
Someone is both not strong and quiet.
John is creative.
Someone is either happy or not rich. | Mary is not calm. | neutral | (![X]:((generous(X)<~>curious(X))<=>(generous(X)|~creative(X))))&
(![X]:((~creative(X)&~brave(X))<=>(~creative(X)|curious(X))))&
(![X]:(curious(X)<=>~old(X)))&
(((~tall(alice)<~>kind(alice)))<=>(?[X]:(~kind(X))))&
(![X]:((generous(X)&quiet(X))<=>(curious(X)<~>~quiet(X))))&
(![X]:((~kind(X)<~>tall(X))=>(~funny(X)|~curious(X))))&
(((creative(mary)<~>quiet(mary)))=>(wise(susan)))&
(((creative(paul)&wise(paul)))<=>(funny(mary)))&
(![X]:((~calm(X)<~>humble(X))<=>(kind(X)|funny(X))))&
(![X]:(~rich(X)=>(~generous(X)<~>~humble(X))))&
(![X]:((~generous(X)|curious(X))=>(funny(X)<~>~creative(X))))&
((?[X]:((curious(X)<~>generous(X))))=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:(curious(X)<=>wise(X)))&
(((~curious(fred)<~>kind(fred)))<=>((patient(mary)&~quiet(mary))))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:((calm(X)&old(X)))))&
(![X]:((brave(X)&~wise(X))=>patient(X)))&
(?[X]:((~rich(X)|~patient(X))))&
(?[X]:((~generous(X)|~tall(X))))&
(tall(susan))&
(?[X]:((~strong(X)&quiet(X))))&
(creative(john))&
(?[X]:((happy(X)<~>~rich(X)))) | ~calm(mary) | [] | null | 0 |
Everyone who is quiet or not kind is both not tall and not generous and vice versa. Everyone who is wise is tall. If paul is not rich then susan is both not humble and creative and vice versa. Everyone who is not strong or not humble is both not patient and humble and vice versa. If paul is both calm and not patient then someone is both strong and tall. Everyone who is quiet or not strong is both tall and calm. If john is both not rich and calm then someone is both not patient and happy and vice versa. If paul is either not calm or curious then susan is both not rich and curious and vice versa. Everyone who is both not strong and happy is either brave or not calm. If mary is not curious or brave then fred is not strong or happy. If mary is not generous then someone is both not brave and calm. If someone is curious or quiet then someone is curious and vice versa. If lucy is either brave or quiet then someone is both funny and rich and vice versa. Everyone who is either not wise or curious is not wise or not strong and vice versa. Everyone who is calm or rich is not creative or not rich and vice versa. Everyone who is happy or creative is curious or not creative. Susan is both not old and calm. Susan is either brave or not generous. Fred is either generous or not quiet. Susan is either not wise or happy. Someone is both brave and tall. Someone is not quiet or not generous. | Fred is old. | neutral | (![X]:((quiet(X)|~kind(X))<=>(~tall(X)&~generous(X))))&
(![X]:(wise(X)=>tall(X)))&
((~rich(paul))<=>((~humble(susan)&creative(susan))))&
(![X]:((~strong(X)|~humble(X))<=>(~patient(X)&humble(X))))&
(((calm(paul)&~patient(paul)))=>(?[X]:((strong(X)&tall(X)))))&
(![X]:((quiet(X)|~strong(X))=>(tall(X)&calm(X))))&
(((~rich(john)&calm(john)))<=>(?[X]:((~patient(X)&happy(X)))))&
(((~calm(paul)<~>curious(paul)))<=>((~rich(susan)&curious(susan))))&
(![X]:((~strong(X)&happy(X))=>(brave(X)<~>~calm(X))))&
(((~curious(mary)|brave(mary)))=>((~strong(fred)|happy(fred))))&
((~generous(mary))=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((curious(X)|quiet(X))))<=>(?[X]:(curious(X))))&
(((brave(lucy)<~>quiet(lucy)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~wise(X)|~strong(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)|~rich(X))))&
(![X]:((happy(X)|creative(X))=>(curious(X)|~creative(X))))&
((~old(susan)&calm(susan)))&
((brave(susan)<~>~generous(susan)))&
((generous(fred)<~>~quiet(fred)))&
((~wise(susan)<~>happy(susan)))&
(?[X]:((brave(X)&tall(X))))&
(?[X]:((~quiet(X)|~generous(X)))) | old(fred) | [] | null | 0 |
If paul is brave or happy then someone is not happy or curious and vice versa. Everyone who is both patient and not humble is both tall and kind. If someone is not creative then john is not quiet or not happy. If lucy is either humble or kind then john is either brave or not happy. If alice is either creative or generous then john is either tall or strong. Everyone who is tall or not wise is either curious or patient. If john is not generous then someone is both not strong and brave and vice versa. Everyone who is both not curious and humble is both not rich and not creative and vice versa. Everyone who is both not kind and old is either creative or not generous and vice versa. Everyone who is either not creative or happy is tall or rich and vice versa. Everyone who is both not creative and not strong is not tall or generous and vice versa. Everyone who is both creative and not quiet is not old or not happy and vice versa. Everyone who is either not brave or not calm is kind. If lucy is both not strong and tall then someone is both not happy and curious and vice versa. Everyone who is not quiet or not old is funny. Everyone who is both not brave and brave is both not quiet and funny and vice versa. Someone is quiet. Someone is patient or not funny. Someone is either creative or not happy. Mary is calm. Someone is calm or not humble. Mary is both kind and tall. Susan is strong. | Susan is kind. | entailment | (((brave(paul)|happy(paul)))<=>(?[X]:((~happy(X)|curious(X)))))&
(![X]:((patient(X)&~humble(X))=>(tall(X)&kind(X))))&
((?[X]:(~creative(X)))=>((~quiet(john)|~happy(john))))&
(((humble(lucy)<~>kind(lucy)))=>((brave(john)<~>~happy(john))))&
(((creative(alice)<~>generous(alice)))=>((tall(john)<~>strong(john))))&
(![X]:((tall(X)|~wise(X))=>(curious(X)<~>patient(X))))&
((~generous(john))<=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:((~curious(X)&humble(X))<=>(~rich(X)&~creative(X))))&
(![X]:((~kind(X)&old(X))<=>(creative(X)<~>~generous(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(tall(X)|rich(X))))&
(![X]:((~creative(X)&~strong(X))<=>(~tall(X)|generous(X))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)|~happy(X))))&
(![X]:((~brave(X)<~>~calm(X))=>kind(X)))&
(((~strong(lucy)&tall(lucy)))<=>(?[X]:((~happy(X)&curious(X)))))&
(![X]:((~quiet(X)|~old(X))=>funny(X)))&
(![X]:((~brave(X)&brave(X))<=>(~quiet(X)&funny(X))))&
(?[X]:(quiet(X)))&
(?[X]:((patient(X)|~funny(X))))&
(?[X]:((creative(X)<~>~happy(X))))&
(calm(mary))&
(?[X]:((calm(X)|~humble(X))))&
((kind(mary)&tall(mary)))&
(strong(susan)) | kind(susan) | [
"p2",
"p8",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6611756378478550554963555
% SZS output start Proof for 6611756378478550554963555
3. ? [X0] : ~creative(X0) => (~happy(john) | ~quiet(john)) [input p2]
9. ! [X0] : ((old(X0) & ~kind(X0)) <=> (creative(X0) <~> ~generous(X0))) [input p8]
11. ! [X0] : ((~strong(X0) & ~creative(X0)) <=> (generous(X0) | ~tall(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) & creative(X0)) <=> (~happy(X0) | ~old(X0))) [input p11]
15. ! [X0] : ((~old(X0) | ~quiet(X0)) => funny(X0)) [input p14]
16. ! [X0] : ((brave(X0) & ~brave(X0)) <=> (funny(X0) & ~quiet(X0))) [input p15]
24. ~kind(susan) [input hypothesis]
28. (~happy(john) | ~quiet(john)) | ! [X0] : creative(X0) [ennf transformation 3]
29. ~happy(john) | ~quiet(john) | ! [X0] : creative(X0) [flattening 28]
34. ! [X0] : (funny(X0) | (old(X0) & quiet(X0))) [ennf transformation 15]
49. ! [X0] : (((old(X0) & ~kind(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | (~old(X0) | kind(X0)))) [nnf transformation 9]
50. ! [X0] : (((old(X0) & ~kind(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | ~old(X0) | kind(X0))) [flattening 49]
53. ! [X0] : (((~strong(X0) & ~creative(X0)) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | (strong(X0) | creative(X0)))) [nnf transformation 11]
54. ! [X0] : (((~strong(X0) & ~creative(X0)) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | strong(X0) | creative(X0))) [flattening 53]
55. ! [X0] : (((~quiet(X0) & creative(X0)) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | (quiet(X0) | ~creative(X0)))) [nnf transformation 12]
56. ! [X0] : (((~quiet(X0) & creative(X0)) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | quiet(X0) | ~creative(X0))) [flattening 55]
63. ! [X0] : (((brave(X0) & ~brave(X0)) | (~funny(X0) | quiet(X0))) & ((funny(X0) & ~quiet(X0)) | (~brave(X0) | brave(X0)))) [nnf transformation 16]
64. ! [X0] : (((brave(X0) & ~brave(X0)) | ~funny(X0) | quiet(X0)) & ((funny(X0) & ~quiet(X0)) | ~brave(X0) | brave(X0))) [flattening 63]
80. ~happy(john) | ~quiet(john) | creative(X0) [cnf transformation 29]
99. ~old(X0) | ~creative(X0) | generous(X0) | kind(X0) [cnf transformation 50]
112. ~generous(X0) | ~creative(X0) [cnf transformation 54]
118. ~quiet(X0) | old(X0) [cnf transformation 56]
119. ~quiet(X0) | happy(X0) [cnf transformation 56]
126. funny(X0) | quiet(X0) [cnf transformation 34]
130. ~brave(X0) | ~funny(X0) | quiet(X0) [cnf transformation 64]
131. brave(X0) | ~funny(X0) | quiet(X0) [cnf transformation 64]
141. ~kind(susan) [cnf transformation 24]
155. 4 <=> ! [X0] : happy(X0) [avatar definition]
156. happy(X0) <- (4) [avatar component clause 155]
169. 7 <=> ! [X0] : creative(X0) [avatar definition]
170. creative(X0) <- (7) [avatar component clause 169]
172. 8 <=> quiet(john) [avatar definition]
174. ~quiet(john) <- (~8) [avatar component clause 172]
176. 9 <=> happy(john) [avatar definition]
178. ~happy(john) <- (~9) [avatar component clause 176]
179. 7 | ~8 | ~9 [avatar split clause 80,176,172,169]
257. quiet(X0) | brave(X0) [subsumption resolution 131,126]
258. ~funny(X0) | quiet(X0) [subsumption resolution 130,257]
259. quiet(X0) [subsumption resolution 258,126]
290. $false <- (~8) [subsumption resolution 174,259]
291. 8 [avatar contradiction clause 290]
297. old(X0) [resolution 118,259]
298. happy(X0) [resolution 119,259]
299. 4 [avatar split clause 298,155]
301. $false <- (4, ~9) [resolution 156,178]
302. ~4 | 9 [avatar contradiction clause 301]
390. ~creative(X1) | generous(X1) | kind(X1) [resolution 99,297]
393. generous(X1) | kind(X1) <- (7) [subsumption resolution 390,170]
409. kind(X2) | ~creative(X2) <- (7) [resolution 393,112]
414. kind(X2) <- (7) [subsumption resolution 409,170]
420. $false <- (7) [resolution 414,141]
424. ~7 [avatar contradiction clause 420]
425. $false [avatar sat refutation 179,291,299,302,424]
% SZS output end Proof for 6611756378478550554963555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is not patient.
Everyone who is either wise or calm is kind.
Everyone who is funny is not humble or kind.
If mary is not patient or calm then paul is both not tall and tall.
Everyone who is either not old or rich is humble or not quiet and vice versa.
If someone is not quiet then someone is generous or creative and vice versa.
If someone is both not creative and not old then susan is not funny.
If lucy is either not generous or not quiet then someone is not wise and vice versa.
If someone is both old and not old then paul is not wise and vice versa.
If someone is either not rich or not kind then someone is not tall and vice versa.
If fred is either curious or not funny then someone is either generous or strong.
If someone is kind then someone is generous and vice versa.
If mary is either not kind or not tall then someone is not creative or kind and vice versa.
Everyone who is either curious or not patient is either not old or not kind.
Everyone who is humble is both quiet and not humble and vice versa.
Everyone who is both quiet and humble is both calm and not curious.
John is either not rich or not calm.
Mary is rich or not rich.
Paul is either not happy or not tall.
Someone is either kind or not old.
Someone is both not strong and not humble.
Someone is both funny and not calm.
Someone is curious or not generous. | Mary is rich. | neutral | (![X]:(quiet(X)=>~patient(X)))&
(![X]:((wise(X)<~>calm(X))=>kind(X)))&
(![X]:(funny(X)=>(~humble(X)|kind(X))))&
(((~patient(mary)|calm(mary)))=>((~tall(paul)&tall(paul))))&
(![X]:((~old(X)<~>rich(X))<=>(humble(X)|~quiet(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((generous(X)|creative(X)))))&
((?[X]:((~creative(X)&~old(X))))=>(~funny(susan)))&
(((~generous(lucy)<~>~quiet(lucy)))<=>(?[X]:(~wise(X))))&
((?[X]:((old(X)&~old(X))))<=>(~wise(paul)))&
((?[X]:((~rich(X)<~>~kind(X))))<=>(?[X]:(~tall(X))))&
(((curious(fred)<~>~funny(fred)))=>(?[X]:((generous(X)<~>strong(X)))))&
((?[X]:(kind(X)))<=>(?[X]:(generous(X))))&
(((~kind(mary)<~>~tall(mary)))<=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((curious(X)<~>~patient(X))=>(~old(X)<~>~kind(X))))&
(![X]:(humble(X)<=>(quiet(X)&~humble(X))))&
(![X]:((quiet(X)&humble(X))=>(calm(X)&~curious(X))))&
((~rich(john)<~>~calm(john)))&
((rich(mary)|~rich(mary)))&
((~happy(paul)<~>~tall(paul)))&
(?[X]:((kind(X)<~>~old(X))))&
(?[X]:((~strong(X)&~humble(X))))&
(?[X]:((funny(X)&~calm(X))))&
(?[X]:((curious(X)|~generous(X)))) | rich(mary) | [] | null | 0 |
Everyone who is either rich or humble is funny or patient and vice versa.
Everyone who is both patient and not generous is either funny or brave.
If fred is either not rich or not generous then someone is patient or not quiet and vice versa.
If someone is either not calm or patient then someone is not tall and vice versa.
If susan is both wise and not strong then susan is generous or not rich and vice versa.
Everyone who is both humble and not patient is not brave or wise and vice versa.
Everyone who is both quiet and tall is either not creative or not brave.
Everyone who is wise is either not happy or not patient.
Everyone who is either quiet or rich is either kind or not old.
If someone is both creative and rich then lucy is rich.
If lucy is either calm or kind then susan is not calm or not happy.
If paul is both old and strong then someone is not calm or not patient and vice versa.
Everyone who is not strong or not tall is either patient or wise and vice versa.
Everyone who is generous or not creative is both not rich and generous.
If someone is creative or kind then someone is not humble.
Everyone who is patient is not strong or kind and vice versa.
Alice is not kind or not generous.
Susan is rich.
Someone is either humble or quiet.
Lucy is either happy or funny.
Fred is tall.
Susan is old or wise.
Someone is patient.
Fred is both not creative and curious. | Fred is wise. | contradiction | (![X]:((rich(X)<~>humble(X))<=>(funny(X)|patient(X))))&
(![X]:((patient(X)&~generous(X))=>(funny(X)<~>brave(X))))&
(((~rich(fred)<~>~generous(fred)))<=>(?[X]:((patient(X)|~quiet(X)))))&
((?[X]:((~calm(X)<~>patient(X))))<=>(?[X]:(~tall(X))))&
(((wise(susan)&~strong(susan)))<=>((generous(susan)|~rich(susan))))&
(![X]:((humble(X)&~patient(X))<=>(~brave(X)|wise(X))))&
(![X]:((quiet(X)&tall(X))=>(~creative(X)<~>~brave(X))))&
(![X]:(wise(X)=>(~happy(X)<~>~patient(X))))&
(![X]:((quiet(X)<~>rich(X))=>(kind(X)<~>~old(X))))&
((?[X]:((creative(X)&rich(X))))=>(rich(lucy)))&
(((calm(lucy)<~>kind(lucy)))=>((~calm(susan)|~happy(susan))))&
(((old(paul)&strong(paul)))<=>(?[X]:((~calm(X)|~patient(X)))))&
(![X]:((~strong(X)|~tall(X))<=>(patient(X)<~>wise(X))))&
(![X]:((generous(X)|~creative(X))=>(~rich(X)&generous(X))))&
((?[X]:((creative(X)|kind(X))))=>(?[X]:(~humble(X))))&
(![X]:(patient(X)<=>(~strong(X)|kind(X))))&
((~kind(alice)|~generous(alice)))&
(rich(susan))&
(?[X]:((humble(X)<~>quiet(X))))&
((happy(lucy)<~>funny(lucy)))&
(tall(fred))&
((old(susan)|wise(susan)))&
(?[X]:(patient(X)))&
((~creative(fred)&curious(fred))) | wise(fred) | [
"p5",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4670656304302681855792546
% SZS output start Proof for 4670656304302681855792546
6. ! [X0] : ((~patient(X0) & humble(X0)) <=> (wise(X0) | ~brave(X0))) [input p5]
13. ! [X0] : ((~tall(X0) | ~strong(X0)) <=> (patient(X0) <~> wise(X0))) [input p12]
16. ! [X0] : (patient(X0) <=> (kind(X0) | ~strong(X0))) [input p15]
21. tall(fred) [input p20]
25. wise(fred) [input hypothesis]
54. ! [X0] : (((~patient(X0) & humble(X0)) | (~wise(X0) & brave(X0))) & ((wise(X0) | ~brave(X0)) | (patient(X0) | ~humble(X0)))) [nnf transformation 6]
55. ! [X0] : (((~patient(X0) & humble(X0)) | (~wise(X0) & brave(X0))) & (wise(X0) | ~brave(X0) | patient(X0) | ~humble(X0))) [flattening 54]
65. ! [X0] : (((~tall(X0) | ~strong(X0)) | ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) & (((~wise(X0) | ~patient(X0)) & (wise(X0) | patient(X0))) | (tall(X0) & strong(X0)))) [nnf transformation 13]
66. ! [X0] : ((~tall(X0) | ~strong(X0) | ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) & (((~wise(X0) | ~patient(X0)) & (wise(X0) | patient(X0))) | (tall(X0) & strong(X0)))) [flattening 65]
70. ! [X0] : ((patient(X0) | (~kind(X0) & strong(X0))) & ((kind(X0) | ~strong(X0)) | ~patient(X0))) [nnf transformation 16]
71. ! [X0] : ((patient(X0) | (~kind(X0) & strong(X0))) & (kind(X0) | ~strong(X0) | ~patient(X0))) [flattening 70]
105. ~wise(X0) | ~patient(X0) [cnf transformation 55]
127. ~tall(X0) | ~strong(X0) | patient(X0) | ~wise(X0) [cnf transformation 66]
135. strong(X0) | patient(X0) [cnf transformation 71]
143. tall(fred) [cnf transformation 21]
147. wise(fred) [cnf transformation 25]
276. ~strong(X0) | ~tall(X0) | ~wise(X0) [subsumption resolution 127,105]
405. ~tall(X1) | ~wise(X1) | patient(X1) [resolution 276,135]
416. ~wise(X1) | ~tall(X1) [subsumption resolution 405,105]
589. ~tall(fred) [resolution 416,147]
591. $false [subsumption resolution 589,143]
% SZS output end Proof for 4670656304302681855792546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or brave is not old.
If fred is not strong then john is not brave and vice versa.
Everyone who is not patient is both tall and not happy and vice versa.
If mary is wise or not quiet then paul is either not calm or brave and vice versa.
Everyone who is generous or not strong is both not quiet and kind and vice versa.
Everyone who is either tall or not funny is both not patient and not funny and vice versa.
Everyone who is either calm or curious is both not kind and not happy.
If someone is not kind or calm then mary is not wise or not funny and vice versa.
Everyone who is either not curious or wise is both not kind and not tall.
Everyone who is both not rich and happy is either not rich or not brave and vice versa.
Everyone who is either patient or not funny is not calm and vice versa.
Everyone who is not calm is both creative and not happy.
Everyone who is both happy and calm is both not quiet and strong.
Everyone who is both quiet and not creative is not kind or funny and vice versa.
If someone is either funny or creative then someone is both not kind and patient and vice versa.
Everyone who is both generous and humble is brave.
Someone is both not rich and not wise.
Lucy is either not generous or generous.
Alice is either generous or not old.
Paul is either not rich or old. | John is not kind. | contradiction | (![X]:((~creative(X)<~>brave(X))=>~old(X)))&
((~strong(fred))<=>(~brave(john)))&
(![X]:(~patient(X)<=>(tall(X)&~happy(X))))&
(((wise(mary)|~quiet(mary)))<=>((~calm(paul)<~>brave(paul))))&
(![X]:((generous(X)|~strong(X))<=>(~quiet(X)&kind(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(~patient(X)&~funny(X))))&
(![X]:((calm(X)<~>curious(X))=>(~kind(X)&~happy(X))))&
((?[X]:((~kind(X)|calm(X))))<=>((~wise(mary)|~funny(mary))))&
(![X]:((~curious(X)<~>wise(X))=>(~kind(X)&~tall(X))))&
(![X]:((~rich(X)&happy(X))<=>(~rich(X)<~>~brave(X))))&
(![X]:((patient(X)<~>~funny(X))<=>~calm(X)))&
(![X]:(~calm(X)=>(creative(X)&~happy(X))))&
(![X]:((happy(X)&calm(X))=>(~quiet(X)&strong(X))))&
(![X]:((quiet(X)&~creative(X))<=>(~kind(X)|funny(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((generous(X)&humble(X))=>brave(X)))&
(?[X]:((~rich(X)&~wise(X))))&
((~generous(lucy)<~>generous(lucy)))&
((generous(alice)<~>~old(alice)))&
((~rich(paul)<~>old(paul))) | ~kind(john) | [
"p2",
"p5",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8030127142189275699396588
% SZS output start Proof for 8030127142189275699396588
3. ! [X0] : (~patient(X0) <=> (~happy(X0) & tall(X0))) [input p2]
6. ! [X0] : ((tall(X0) <~> ~funny(X0)) <=> (~funny(X0) & ~patient(X0))) [input p5]
11. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> ~calm(X0)) [input p10]
12. ! [X0] : (~calm(X0) => (~happy(X0) & creative(X0))) [input p11]
13. ! [X0] : ((calm(X0) & happy(X0)) => (strong(X0) & ~quiet(X0))) [input p12]
14. ! [X0] : ((~creative(X0) & quiet(X0)) <=> (funny(X0) | ~kind(X0))) [input p13]
21. ~kind(john) [input hypothesis]
27. ! [X0] : ((~happy(X0) & creative(X0)) | calm(X0)) [ennf transformation 12]
28. ! [X0] : ((strong(X0) & ~quiet(X0)) | (~calm(X0) | ~happy(X0))) [ennf transformation 13]
29. ! [X0] : ((strong(X0) & ~quiet(X0)) | ~calm(X0) | ~happy(X0)) [flattening 28]
32. ! [X0] : ((~patient(X0) | (happy(X0) | ~tall(X0))) & ((~happy(X0) & tall(X0)) | patient(X0))) [nnf transformation 3]
33. ! [X0] : ((~patient(X0) | happy(X0) | ~tall(X0)) & ((~happy(X0) & tall(X0)) | patient(X0))) [flattening 32]
38. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | (funny(X0) | patient(X0))) & ((~funny(X0) & ~patient(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [nnf transformation 6]
39. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | funny(X0) | patient(X0)) & ((~funny(X0) & ~patient(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [flattening 38]
49. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | calm(X0)) & (~calm(X0) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 11]
50. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | (creative(X0) | ~quiet(X0)))) [nnf transformation 14]
51. ! [X0] : (((~creative(X0) & quiet(X0)) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | creative(X0) | ~quiet(X0))) [flattening 50]
66. tall(X0) | patient(X0) [cnf transformation 33]
68. ~tall(X0) | happy(X0) | ~patient(X0) [cnf transformation 33]
81. ~patient(X0) | tall(X0) | funny(X0) [cnf transformation 39]
82. ~funny(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 39]
85. funny(X0) | ~tall(X0) | funny(X0) | patient(X0) [cnf transformation 39]
104. ~funny(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 49]
107. funny(X0) | ~patient(X0) | calm(X0) [cnf transformation 49]
108. calm(X0) | creative(X0) [cnf transformation 27]
109. ~happy(X0) | calm(X0) [cnf transformation 27]
110. ~quiet(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 29]
113. kind(X0) | quiet(X0) [cnf transformation 51]
116. ~funny(X0) | ~creative(X0) [cnf transformation 51]
131. ~kind(john) [cnf transformation 21]
134. ~funny(X0) | ~tall(X0) [duplicate literal removal 82]
135. funny(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 85]
168. funny(X0) | patient(X0) [subsumption resolution 135,66]
169. funny(X0) | tall(X0) [subsumption resolution 81,168]
193. funny(X0) | calm(X0) [subsumption resolution 107,168]
196. ~quiet(X0) | ~happy(X0) [subsumption resolution 110,109]
255. quiet(john) [resolution 113,131]
262. patient(X0) | ~tall(X0) [resolution 168,134]
265. patient(X0) [subsumption resolution 262,66]
270. calm(X1) | ~creative(X1) [resolution 193,116]
272. calm(X1) [subsumption resolution 270,108]
277. ~happy(john) [resolution 196,255]
318. ~calm(X1) | ~patient(X1) | tall(X1) [resolution 104,169]
321. ~patient(X1) | tall(X1) [subsumption resolution 318,272]
322. tall(X1) [subsumption resolution 321,265]
333. happy(X2) | ~patient(X2) [resolution 322,68]
334. happy(X2) [subsumption resolution 333,265]
350. $false [resolution 334,277]
% SZS output end Proof for 8030127142189275699396588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not kind is either quiet or not kind and vice versa.
Everyone who is old or not tall is generous or not curious and vice versa.
If someone is both not tall and not creative then susan is not creative or generous.
If someone is either curious or happy then someone is not old.
If someone is either not happy or curious then someone is both quiet and wise.
Everyone who is not wise or humble is not kind and vice versa.
If someone is either not happy or humble then john is either not curious or not brave and vice versa.
If john is either not tall or rich then someone is both strong and not strong.
If someone is either not old or not happy then someone is either not happy or kind.
Everyone who is happy or not generous is quiet and vice versa.
If mary is either wise or not tall then mary is either kind or not brave.
Everyone who is not curious or humble is patient or not generous and vice versa.
Everyone who is not strong is not old or not generous and vice versa.
Everyone who is either wise or not creative is not funny.
Everyone who is not rich is not funny or not calm.
Everyone who is either happy or not wise is not patient or humble and vice versa.
Lucy is both not strong and tall.
Fred is brave or not kind.
Fred is tall.
Someone is patient or not calm.
Someone is happy or curious.
Someone is happy or not strong.
Susan is not quiet.
Someone is old. | Lucy is not generous. | entailment | (![X]:((happy(X)|~kind(X))<=>(quiet(X)<~>~kind(X))))&
(![X]:((old(X)|~tall(X))<=>(generous(X)|~curious(X))))&
((?[X]:((~tall(X)&~creative(X))))=>((~creative(susan)|generous(susan))))&
((?[X]:((curious(X)<~>happy(X))))=>(?[X]:(~old(X))))&
((?[X]:((~happy(X)<~>curious(X))))=>(?[X]:((quiet(X)&wise(X)))))&
(![X]:((~wise(X)|humble(X))<=>~kind(X)))&
((?[X]:((~happy(X)<~>humble(X))))<=>((~curious(john)<~>~brave(john))))&
(((~tall(john)<~>rich(john)))=>(?[X]:((strong(X)&~strong(X)))))&
((?[X]:((~old(X)<~>~happy(X))))=>(?[X]:((~happy(X)<~>kind(X)))))&
(![X]:((happy(X)|~generous(X))<=>quiet(X)))&
(((wise(mary)<~>~tall(mary)))=>((kind(mary)<~>~brave(mary))))&
(![X]:((~curious(X)|humble(X))<=>(patient(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~old(X)|~generous(X))))&
(![X]:((wise(X)<~>~creative(X))=>~funny(X)))&
(![X]:(~rich(X)=>(~funny(X)|~calm(X))))&
(![X]:((happy(X)<~>~wise(X))<=>(~patient(X)|humble(X))))&
((~strong(lucy)&tall(lucy)))&
((brave(fred)|~kind(fred)))&
(tall(fred))&
(?[X]:((patient(X)|~calm(X))))&
(?[X]:((happy(X)|curious(X))))&
(?[X]:((happy(X)|~strong(X))))&
(~quiet(susan))&
(?[X]:(old(X))) | ~generous(lucy) | [
"p1",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5113078653603386283114379
% SZS output start Proof for 5113078653603386283114379
2. ! [X0] : ((~tall(X0) | old(X0)) <=> (~curious(X0) | generous(X0))) [input p1]
13. ! [X0] : (~strong(X0) <=> (~generous(X0) | ~old(X0))) [input p12]
17. tall(lucy) & ~strong(lucy) [input p16]
25. generous(lucy) [input hypothesis]
41. ! [X0] : (((~tall(X0) | old(X0)) | (curious(X0) & ~generous(X0))) & ((~curious(X0) | generous(X0)) | (tall(X0) & ~old(X0)))) [nnf transformation 2]
42. ! [X0] : ((~tall(X0) | old(X0) | (curious(X0) & ~generous(X0))) & (~curious(X0) | generous(X0) | (tall(X0) & ~old(X0)))) [flattening 41]
69. ! [X0] : ((~strong(X0) | (generous(X0) & old(X0))) & ((~generous(X0) | ~old(X0)) | strong(X0))) [nnf transformation 13]
70. ! [X0] : ((~strong(X0) | (generous(X0) & old(X0))) & (~generous(X0) | ~old(X0) | strong(X0))) [flattening 69]
87. ~generous(X0) | old(X0) | ~tall(X0) [cnf transformation 42]
126. ~generous(X0) | ~old(X0) | strong(X0) [cnf transformation 70]
135. ~strong(lucy) [cnf transformation 17]
136. tall(lucy) [cnf transformation 17]
143. generous(lucy) [cnf transformation 25]
312. old(lucy) | ~tall(lucy) [resolution 87,143]
314. old(lucy) [subsumption resolution 312,136]
370. ~old(lucy) | strong(lucy) [resolution 126,143]
372. strong(lucy) [subsumption resolution 370,314]
373. $false [subsumption resolution 372,135]
% SZS output end Proof for 5113078653603386283114379
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall then alice is both not funny and not strong and vice versa. Everyone who is not rich or calm is both not calm and not creative. If susan is not happy then someone is either patient or not creative. If alice is both not creative and not kind then paul is happy. Everyone who is not patient is both wise and not brave. If mary is not quiet then john is both not quiet and not kind and vice versa. Everyone who is kind is brave and vice versa. If someone is both not humble and not kind then john is both brave and not happy. Everyone who is tall or not creative is either tall or not kind and vice versa. If someone is not curious or wise then lucy is both not creative and not kind. Everyone who is brave or not patient is brave or not happy. Everyone who is not quiet is not tall or not wise. Everyone who is generous or brave is both kind and not old and vice versa. Everyone who is either not humble or happy is strong. If susan is humble then fred is not generous. Everyone who is kind or not humble is both not calm and not patient. Fred is both not generous and not creative. Paul is not rich or strong. Someone is humble. John is humble or patient. Someone is not happy or kind. Mary is either happy or not generous. | Fred is not kind. | entailment | ((?[X]:(tall(X)))<=>((~funny(alice)&~strong(alice))))&
(![X]:((~rich(X)|calm(X))=>(~calm(X)&~creative(X))))&
((~happy(susan))=>(?[X]:((patient(X)<~>~creative(X)))))&
(((~creative(alice)&~kind(alice)))=>(happy(paul)))&
(![X]:(~patient(X)=>(wise(X)&~brave(X))))&
((~quiet(mary))<=>((~quiet(john)&~kind(john))))&
(![X]:(kind(X)<=>brave(X)))&
((?[X]:((~humble(X)&~kind(X))))=>((brave(john)&~happy(john))))&
(![X]:((tall(X)|~creative(X))<=>(tall(X)<~>~kind(X))))&
((?[X]:((~curious(X)|wise(X))))=>((~creative(lucy)&~kind(lucy))))&
(![X]:((brave(X)|~patient(X))=>(brave(X)|~happy(X))))&
(![X]:(~quiet(X)=>(~tall(X)|~wise(X))))&
(![X]:((generous(X)|brave(X))<=>(kind(X)&~old(X))))&
(![X]:((~humble(X)<~>happy(X))=>strong(X)))&
((humble(susan))=>(~generous(fred)))&
(![X]:((kind(X)|~humble(X))=>(~calm(X)&~patient(X))))&
((~generous(fred)&~creative(fred)))&
((~rich(paul)|strong(paul)))&
(?[X]:(humble(X)))&
((humble(john)|patient(john)))&
(?[X]:((~happy(X)|kind(X))))&
((happy(mary)<~>~generous(mary))) | ~kind(fred) | [
"p4",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 102909014927404495220466
% SZS output start Proof for 102909014927404495220466
5. ! [X0] : (~patient(X0) => (~brave(X0) & wise(X0))) [input p4]
7. ! [X0] : (kind(X0) <=> brave(X0)) [input p6]
16. ! [X0] : ((~humble(X0) | kind(X0)) => (~patient(X0) & ~calm(X0))) [input p15]
23. kind(fred) [input hypothesis]
26. ! [X0] : ((~humble(X0) | kind(X0)) => ~patient(X0)) [pure predicate removal 16]
31. ! [X0] : ((~brave(X0) & wise(X0)) | patient(X0)) [ennf transformation 5]
40. ! [X0] : (~patient(X0) | (humble(X0) & ~kind(X0))) [ennf transformation 26]
51. ! [X0] : ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0))) [nnf transformation 7]
70. ~brave(X0) | patient(X0) [cnf transformation 31]
74. ~kind(X0) | brave(X0) [cnf transformation 51]
97. ~kind(X0) | ~patient(X0) [cnf transformation 40]
107. kind(fred) [cnf transformation 23]
237. brave(fred) [resolution 74,107]
239. patient(fred) [resolution 237,70]
240. ~patient(fred) [resolution 97,107]
241. $false [subsumption resolution 240,239]
% SZS output end Proof for 102909014927404495220466
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not happy is not old or calm and vice versa.
Everyone who is humble is both happy and brave and vice versa.
If john is either not wise or not quiet then john is rich and vice versa.
If mary is not patient or not calm then someone is either quiet or humble and vice versa.
Everyone who is funny or tall is not old or funny and vice versa.
If someone is not generous or not rich then someone is either creative or old.
If john is not creative then paul is both not creative and patient and vice versa.
Everyone who is happy is either not creative or not old and vice versa.
Everyone who is not strong or curious is either not curious or not quiet.
If paul is both not kind and kind then someone is both curious and not generous and vice versa.
Everyone who is calm or not happy is both not tall and funny.
Everyone who is not rich or not old is both not brave and not curious.
If someone is either not kind or patient then lucy is not wise or not rich.
If fred is either creative or rich then someone is not rich.
If someone is both not quiet and creative then susan is either humble or not old.
If someone is curious then someone is not brave.
Someone is not rich.
Someone is kind or calm.
John is not strong.
Someone is calm or not strong.
Susan is either not humble or calm.
Someone is both curious and generous.
Susan is funny.
Lucy is not brave or not curious. | Paul is kind. | neutral | (![X]:((~tall(X)<~>~happy(X))<=>(~old(X)|calm(X))))&
(![X]:(humble(X)<=>(happy(X)&brave(X))))&
(((~wise(john)<~>~quiet(john)))<=>(rich(john)))&
(((~patient(mary)|~calm(mary)))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:((funny(X)|tall(X))<=>(~old(X)|funny(X))))&
((?[X]:((~generous(X)|~rich(X))))=>(?[X]:((creative(X)<~>old(X)))))&
((~creative(john))<=>((~creative(paul)&patient(paul))))&
(![X]:(happy(X)<=>(~creative(X)<~>~old(X))))&
(![X]:((~strong(X)|curious(X))=>(~curious(X)<~>~quiet(X))))&
(((~kind(paul)&kind(paul)))<=>(?[X]:((curious(X)&~generous(X)))))&
(![X]:((calm(X)|~happy(X))=>(~tall(X)&funny(X))))&
(![X]:((~rich(X)|~old(X))=>(~brave(X)&~curious(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>((~wise(lucy)|~rich(lucy))))&
(((creative(fred)<~>rich(fred)))=>(?[X]:(~rich(X))))&
((?[X]:((~quiet(X)&creative(X))))=>((humble(susan)<~>~old(susan))))&
((?[X]:(curious(X)))=>(?[X]:(~brave(X))))&
(?[X]:(~rich(X)))&
(?[X]:((kind(X)|calm(X))))&
(~strong(john))&
(?[X]:((calm(X)|~strong(X))))&
((~humble(susan)<~>calm(susan)))&
(?[X]:((curious(X)&generous(X))))&
(funny(susan))&
((~brave(lucy)|~curious(lucy))) | kind(paul) | [] | null | 0 |
If susan is not calm then someone is either generous or not calm.
Everyone who is either wise or not old is either not wise or strong and vice versa.
If paul is humble then mary is not wise or not old.
Everyone who is not brave is curious or wise.
Everyone who is not brave or kind is quiet and vice versa.
If fred is funny or not humble then someone is both not rich and humble.
Everyone who is not calm or happy is not calm and vice versa.
If fred is both not quiet and not rich then someone is either not happy or strong.
If paul is not funny or brave then lucy is both strong and not quiet and vice versa.
If someone is either not old or tall then alice is both wise and calm and vice versa.
If someone is either brave or old then someone is not tall and vice versa.
If mary is either humble or brave then someone is either not quiet or wise.
Everyone who is humble is either humble or not wise and vice versa.
Everyone who is either not happy or not quiet is either creative or not curious and vice versa.
If someone is not calm or brave then fred is either strong or not kind and vice versa.
Everyone who is not patient or kind is either wise or old.
Someone is either wise or not calm.
Mary is funny.
Fred is patient.
Someone is generous.
Paul is curious or wise.
Someone is both tall and quiet.
Someone is generous or not generous. | Mary is brave. | neutral | ((~calm(susan))=>(?[X]:((generous(X)<~>~calm(X)))))&
(![X]:((wise(X)<~>~old(X))<=>(~wise(X)<~>strong(X))))&
((humble(paul))=>((~wise(mary)|~old(mary))))&
(![X]:(~brave(X)=>(curious(X)|wise(X))))&
(![X]:((~brave(X)|kind(X))<=>quiet(X)))&
(((funny(fred)|~humble(fred)))=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((~calm(X)|happy(X))<=>~calm(X)))&
(((~quiet(fred)&~rich(fred)))=>(?[X]:((~happy(X)<~>strong(X)))))&
(((~funny(paul)|brave(paul)))<=>((strong(lucy)&~quiet(lucy))))&
((?[X]:((~old(X)<~>tall(X))))<=>((wise(alice)&calm(alice))))&
((?[X]:((brave(X)<~>old(X))))<=>(?[X]:(~tall(X))))&
(((humble(mary)<~>brave(mary)))=>(?[X]:((~quiet(X)<~>wise(X)))))&
(![X]:(humble(X)<=>(humble(X)<~>~wise(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(creative(X)<~>~curious(X))))&
((?[X]:((~calm(X)|brave(X))))<=>((strong(fred)<~>~kind(fred))))&
(![X]:((~patient(X)|kind(X))=>(wise(X)<~>old(X))))&
(?[X]:((wise(X)<~>~calm(X))))&
(funny(mary))&
(patient(fred))&
(?[X]:(generous(X)))&
((curious(paul)|wise(paul)))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:((generous(X)|~generous(X)))) | brave(mary) | [] | null | 0 |
Everyone who is either patient or not happy is kind or not humble.
If someone is not wise then fred is either tall or generous.
If fred is either not generous or creative then someone is not quiet and vice versa.
Everyone who is quiet or not strong is both not creative and not rich and vice versa.
If someone is happy or not strong then susan is strong or not generous.
If someone is humble then someone is not old or wise and vice versa.
Everyone who is both quiet and not patient is either brave or not wise and vice versa.
Everyone who is either not curious or wise is either not rich or not wise and vice versa.
If paul is both rich and patient then someone is either brave or old and vice versa.
Everyone who is patient or funny is not old or funny.
If fred is wise or not generous then someone is both not old and not wise and vice versa.
If someone is not generous then someone is both not happy and quiet.
Everyone who is patient or not curious is both brave and not curious.
If mary is either not old or not quiet then someone is either patient or not quiet and vice versa.
Everyone who is not strong or humble is either happy or not patient and vice versa.
Everyone who is not strong is funny.
Mary is either patient or quiet.
Someone is humble or not curious.
Someone is either not quiet or patient.
Someone is not brave or rich.
Someone is rich.
Lucy is not calm or happy.
Mary is not patient.
Someone is either brave or not wise. | Mary is not old. | entailment | (![X]:((patient(X)<~>~happy(X))=>(kind(X)|~humble(X))))&
((?[X]:(~wise(X)))=>((tall(fred)<~>generous(fred))))&
(((~generous(fred)<~>creative(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)|~strong(X))<=>(~creative(X)&~rich(X))))&
((?[X]:((happy(X)|~strong(X))))=>((strong(susan)|~generous(susan))))&
((?[X]:(humble(X)))<=>(?[X]:((~old(X)|wise(X)))))&
(![X]:((quiet(X)&~patient(X))<=>(brave(X)<~>~wise(X))))&
(![X]:((~curious(X)<~>wise(X))<=>(~rich(X)<~>~wise(X))))&
(((rich(paul)&patient(paul)))<=>(?[X]:((brave(X)<~>old(X)))))&
(![X]:((patient(X)|funny(X))=>(~old(X)|funny(X))))&
(((wise(fred)|~generous(fred)))<=>(?[X]:((~old(X)&~wise(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((~happy(X)&quiet(X)))))&
(![X]:((patient(X)|~curious(X))=>(brave(X)&~curious(X))))&
(((~old(mary)<~>~quiet(mary)))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
(![X]:((~strong(X)|humble(X))<=>(happy(X)<~>~patient(X))))&
(![X]:(~strong(X)=>funny(X)))&
((patient(mary)<~>quiet(mary)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:(rich(X)))&
((~calm(lucy)|happy(lucy)))&
(~patient(mary))&
(?[X]:((brave(X)<~>~wise(X)))) | ~old(mary) | [
"p13",
"p16",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3137233303107408856479869
% SZS output start Proof for 3137233303107408856479869
14. (~old(mary) <~> ~quiet(mary)) <=> ? [X0] : (patient(X0) <~> ~quiet(X0)) [input p13]
17. patient(mary) <~> quiet(mary) [input p16]
19. ? [X0] : (~quiet(X0) <~> patient(X0)) [input p18]
23. ~patient(mary) [input p22]
25. old(mary) [input hypothesis]
66. (((quiet(mary) | old(mary)) & (~quiet(mary) | ~old(mary))) | ! [X0] : ((patient(X0) | quiet(X0)) & (~quiet(X0) | ~patient(X0)))) & (? [X0] : ((quiet(X0) | ~patient(X0)) & (~quiet(X0) | patient(X0))) | ((~old(mary) | quiet(mary)) & (~quiet(mary) | old(mary)))) [nnf transformation 14]
67. (((quiet(mary) | old(mary)) & (~quiet(mary) | ~old(mary))) | ! [X0] : ((patient(X0) | quiet(X0)) & (~quiet(X0) | ~patient(X0)))) & (? [X1] : ((quiet(X1) | ~patient(X1)) & (~quiet(X1) | patient(X1))) | ((~old(mary) | quiet(mary)) & (~quiet(mary) | old(mary)))) [rectify 66]
68. ? [X1] : ((quiet(X1) | ~patient(X1)) & (~quiet(X1) | patient(X1))) => ((quiet(sK6) | ~patient(sK6)) & (~quiet(sK6) | patient(sK6))) [choice axiom]
69. (((quiet(mary) | old(mary)) & (~quiet(mary) | ~old(mary))) | ! [X0] : ((patient(X0) | quiet(X0)) & (~quiet(X0) | ~patient(X0)))) & (((quiet(sK6) | ~patient(sK6)) & (~quiet(sK6) | patient(sK6))) | ((~old(mary) | quiet(mary)) & (~quiet(mary) | old(mary)))) [skolemisation 67,68]
72. (~quiet(mary) | ~patient(mary)) & (quiet(mary) | patient(mary)) [nnf transformation 17]
75. ? [X0] : ((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) [nnf transformation 19]
76. ? [X0] : ((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) => ((~patient(sK8) | quiet(sK8)) & (patient(sK8) | ~quiet(sK8))) [choice axiom]
77. (~patient(sK8) | quiet(sK8)) & (patient(sK8) | ~quiet(sK8)) [skolemisation 75,76]
138. ~quiet(mary) | ~old(mary) | ~quiet(X0) | ~patient(X0) [cnf transformation 69]
139. ~quiet(mary) | ~old(mary) | patient(X0) | quiet(X0) [cnf transformation 69]
149. quiet(mary) | patient(mary) [cnf transformation 72]
152. patient(sK8) | ~quiet(sK8) [cnf transformation 77]
153. ~patient(sK8) | quiet(sK8) [cnf transformation 77]
156. ~patient(mary) [cnf transformation 23]
159. old(mary) [cnf transformation 25]
296. 30 <=> ! [X0] : (patient(X0) | quiet(X0)) [avatar definition]
297. quiet(X0) | patient(X0) <- (30) [avatar component clause 296]
299. 31 <=> old(mary) [avatar definition]
303. 32 <=> quiet(mary) [avatar definition]
308. 33 <=> ! [X0] : (~quiet(X0) | ~patient(X0)) [avatar definition]
309. ~quiet(X0) | ~patient(X0) <- (33) [avatar component clause 308]
311. 30 | ~31 | ~32 [avatar split clause 139,303,299,296]
312. 33 | ~31 | ~32 [avatar split clause 138,303,299,308]
326. 36 <=> patient(mary) [avatar definition]
330. 36 | 32 [avatar split clause 149,303,326]
341. 39 <=> quiet(sK8) [avatar definition]
342. ~quiet(sK8) <- (~39) [avatar component clause 341]
343. quiet(sK8) <- (39) [avatar component clause 341]
345. 40 <=> patient(sK8) [avatar definition]
346. patient(sK8) <- (40) [avatar component clause 345]
347. ~patient(sK8) <- (~40) [avatar component clause 345]
348. 39 | ~40 [avatar split clause 153,345,341]
349. ~39 | 40 [avatar split clause 152,345,341]
359. ~36 [avatar split clause 156,326]
370. 31 [avatar split clause 159,299]
399. patient(sK8) <- (30, ~39) [resolution 297,342]
401. $false <- (30, ~39, ~40) [subsumption resolution 399,347]
402. ~30 | 39 | 40 [avatar contradiction clause 401]
408. ~patient(sK8) <- (33, 39) [resolution 309,343]
409. $false <- (33, 39, 40) [subsumption resolution 408,346]
410. ~33 | ~39 | ~40 [avatar contradiction clause 409]
411. $false [avatar sat refutation 311,312,330,348,349,359,370,402,410]
% SZS output end Proof for 3137233303107408856479869
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both old and not happy then someone is not tall. Everyone who is not creative or not brave is both tall and curious and vice versa. Everyone who is both funny and not patient is either rich or not calm and vice versa. If someone is not generous or funny then someone is funny and vice versa. Everyone who is either not old or not calm is not strong or strong and vice versa. Everyone who is both curious and tall is both not patient and creative. Everyone who is either not quiet or generous is rich or creative and vice versa. Everyone who is either not patient or not rich is both quiet and calm. Everyone who is either not brave or not wise is either not funny or curious. Everyone who is funny is either not brave or wise and vice versa. Everyone who is both patient and strong is strong and vice versa. If someone is either not patient or not humble then someone is both creative and not creative. Everyone who is both patient and not funny is both not funny and funny and vice versa. If someone is either not quiet or not strong then lucy is either kind or funny. If lucy is strong or funny then someone is both funny and not quiet and vice versa. If john is either not tall or happy then someone is either not humble or not strong. Alice is either brave or not happy. Someone is either not funny or not wise. Paul is both not quiet and strong. Susan is both old and brave. Someone is not funny or not rich. Alice is not quiet or not generous. Fred is not brave. | Paul is calm. | contradiction | (((old(lucy)&~happy(lucy)))=>(?[X]:(~tall(X))))&
(![X]:((~creative(X)|~brave(X))<=>(tall(X)&curious(X))))&
(![X]:((funny(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(~strong(X)|strong(X))))&
(![X]:((curious(X)&tall(X))=>(~patient(X)&creative(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(quiet(X)&calm(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~funny(X)<~>curious(X))))&
(![X]:(funny(X)<=>(~brave(X)<~>wise(X))))&
(![X]:((patient(X)&strong(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>~humble(X))))=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((patient(X)&~funny(X))<=>(~funny(X)&funny(X))))&
((?[X]:((~quiet(X)<~>~strong(X))))=>((kind(lucy)<~>funny(lucy))))&
(((strong(lucy)|funny(lucy)))<=>(?[X]:((funny(X)&~quiet(X)))))&
(((~tall(john)<~>happy(john)))=>(?[X]:((~humble(X)<~>~strong(X)))))&
((brave(alice)<~>~happy(alice)))&
(?[X]:((~funny(X)<~>~wise(X))))&
((~quiet(paul)&strong(paul)))&
((old(susan)&brave(susan)))&
(?[X]:((~funny(X)|~rich(X))))&
((~quiet(alice)|~generous(alice)))&
(~brave(fred)) | calm(paul) | [
"p2",
"p7",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2811554631902548067951568
% SZS output start Proof for 2811554631902548067951568
3. ! [X0] : ((~patient(X0) & funny(X0)) <=> (rich(X0) <~> ~calm(X0))) [input p2]
8. ! [X0] : ((~patient(X0) <~> ~rich(X0)) => (calm(X0) & quiet(X0))) [input p7]
11. ! [X0] : ((strong(X0) & patient(X0)) <=> strong(X0)) [input p10]
19. strong(paul) & ~quiet(paul) [input p18]
24. calm(paul) [input hypothesis]
31. ! [X0] : ((calm(X0) & quiet(X0)) | (~patient(X0) <=> ~rich(X0))) [ennf transformation 8]
40. ! [X0] : (((~patient(X0) & funny(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (patient(X0) | ~funny(X0)))) [nnf transformation 3]
41. ! [X0] : (((~patient(X0) & funny(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | patient(X0) | ~funny(X0))) [flattening 40]
51. ! [X0] : ((calm(X0) & quiet(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) [nnf transformation 31]
54. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | (~strong(X0) | ~patient(X0)))) [nnf transformation 11]
55. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | ~strong(X0) | ~patient(X0))) [flattening 54]
87. ~calm(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 41]
107. ~patient(X0) | quiet(X0) | rich(X0) [cnf transformation 51]
119. ~strong(X0) | patient(X0) [cnf transformation 55]
146. ~quiet(paul) [cnf transformation 19]
147. strong(paul) [cnf transformation 19]
153. calm(paul) [cnf transformation 24]
285. patient(paul) [resolution 119,147]
304. ~patient(paul) | ~rich(paul) [resolution 87,153]
307. ~rich(paul) [subsumption resolution 304,285]
323. quiet(paul) | rich(paul) [resolution 107,285]
324. rich(paul) [subsumption resolution 323,146]
325. $false [subsumption resolution 324,307]
% SZS output end Proof for 2811554631902548067951568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not creative is not kind.
Everyone who is either not quiet or not curious is both not funny and humble.
If someone is wise or not generous then lucy is both not curious and humble.
Everyone who is not tall is not generous or not calm.
Everyone who is both kind and not strong is not strong and vice versa.
Everyone who is both not calm and wise is not happy and vice versa.
Everyone who is either not happy or patient is both creative and not quiet.
Everyone who is creative or not happy is not creative and vice versa.
If fred is both not rich and rich then someone is either curious or brave and vice versa.
If someone is brave then someone is not calm.
Everyone who is both not curious and not funny is not rich and vice versa.
Everyone who is either calm or humble is either not quiet or not brave.
Everyone who is old or rich is not generous or not curious and vice versa.
Someone is happy or funny.
Someone is humble.
Someone is both not funny and not creative.
Mary is kind or not old.
Alice is wise or not calm.
Mary is both wise and not humble. | Fred is funny. | neutral | (![X]:((~kind(X)<~>~creative(X))=>~kind(X)))&
(![X]:((~quiet(X)<~>~curious(X))=>(~funny(X)&humble(X))))&
((?[X]:((wise(X)|~generous(X))))=>((~curious(lucy)&humble(lucy))))&
(![X]:(~tall(X)=>(~generous(X)|~calm(X))))&
(![X]:((kind(X)&~strong(X))<=>~strong(X)))&
(![X]:((~calm(X)&wise(X))<=>~happy(X)))&
(![X]:((~happy(X)<~>patient(X))=>(creative(X)&~quiet(X))))&
(![X]:((creative(X)|~happy(X))<=>~creative(X)))&
(((~rich(fred)&rich(fred)))<=>(?[X]:((curious(X)<~>brave(X)))))&
((?[X]:(brave(X)))=>(?[X]:(~calm(X))))&
(![X]:((~curious(X)&~funny(X))<=>~rich(X)))&
(![X]:((calm(X)<~>humble(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((old(X)|rich(X))<=>(~generous(X)|~curious(X))))&
(?[X]:((happy(X)|funny(X))))&
(?[X]:(humble(X)))&
(?[X]:((~funny(X)&~creative(X))))&
((kind(mary)|~old(mary)))&
((wise(alice)|~calm(alice)))&
((wise(mary)&~humble(mary))) | funny(fred) | [] | null | 0 |
If mary is creative or not curious then someone is both not brave and creative.
If lucy is either humble or old then fred is not brave.
If someone is not kind then john is both wise and old.
Everyone who is not quiet or strong is quiet or not creative and vice versa.
Everyone who is not humble is strong and vice versa.
Everyone who is not strong or old is not kind and vice versa.
Everyone who is not patient or not brave is either funny or happy and vice versa.
Everyone who is both not humble and kind is both kind and rich and vice versa.
If john is strong or quiet then someone is not patient.
Everyone who is creative is both not rich and wise and vice versa.
Everyone who is funny or tall is tall and vice versa.
Everyone who is not old or not funny is both not humble and not quiet.
If lucy is humble then alice is either not generous or tall and vice versa.
If someone is both not calm and funny then someone is not funny or brave and vice versa.
If mary is tall or not humble then someone is either wise or funny.
If someone is both wise and funny then alice is old and vice versa.
Fred is either not curious or brave.
Someone is both patient and not old.
Alice is either not strong or strong.
Lucy is either generous or rich.
Mary is not curious.
Mary is not old.
Fred is both not kind and rich.
Paul is not old. | Paul is not quiet. | entailment | (((creative(mary)|~curious(mary)))=>(?[X]:((~brave(X)&creative(X)))))&
(((humble(lucy)<~>old(lucy)))=>(~brave(fred)))&
((?[X]:(~kind(X)))=>((wise(john)&old(john))))&
(![X]:((~quiet(X)|strong(X))<=>(quiet(X)|~creative(X))))&
(![X]:(~humble(X)<=>strong(X)))&
(![X]:((~strong(X)|old(X))<=>~kind(X)))&
(![X]:((~patient(X)|~brave(X))<=>(funny(X)<~>happy(X))))&
(![X]:((~humble(X)&kind(X))<=>(kind(X)&rich(X))))&
(((strong(john)|quiet(john)))=>(?[X]:(~patient(X))))&
(![X]:(creative(X)<=>(~rich(X)&wise(X))))&
(![X]:((funny(X)|tall(X))<=>tall(X)))&
(![X]:((~old(X)|~funny(X))=>(~humble(X)&~quiet(X))))&
((humble(lucy))<=>((~generous(alice)<~>tall(alice))))&
((?[X]:((~calm(X)&funny(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(((tall(mary)|~humble(mary)))=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((wise(X)&funny(X))))<=>(old(alice)))&
((~curious(fred)<~>brave(fred)))&
(?[X]:((patient(X)&~old(X))))&
((~strong(alice)<~>strong(alice)))&
((generous(lucy)<~>rich(lucy)))&
(~curious(mary))&
(~old(mary))&
((~kind(fred)&rich(fred)))&
(~old(paul)) | ~quiet(paul) | [
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1142182141776540115318737
% SZS output start Proof for 1142182141776540115318737
12. ! [X0] : ((~funny(X0) | ~old(X0)) => (~quiet(X0) & ~humble(X0))) [input p11]
24. ~old(paul) [input p23]
25. quiet(paul) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & ~humble(X0)) | (funny(X0) & old(X0))) [ennf transformation 12]
106. ~quiet(X0) | old(X0) [cnf transformation 31]
136. ~old(paul) [cnf transformation 24]
137. quiet(paul) [cnf transformation 25]
310. old(paul) [resolution 106,137]
311. $false [subsumption resolution 310,136]
% SZS output end Proof for 1142182141776540115318737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either curious or not tall then mary is either old or curious and vice versa.
Everyone who is either not patient or curious is not curious or humble and vice versa.
If someone is not old or not brave then someone is not creative or not rich.
If john is not rich or quiet then fred is both humble and not creative.
Everyone who is not creative or not funny is not generous.
If fred is either not brave or strong then someone is wise and vice versa.
Everyone who is not strong or not generous is either not old or strong and vice versa.
Everyone who is calm or rich is either kind or not quiet and vice versa.
Everyone who is both rich and wise is not generous or tall and vice versa.
Everyone who is not wise or not curious is not strong or not old and vice versa.
Everyone who is rich is both humble and calm and vice versa.
Everyone who is either not quiet or not patient is not rich or not brave.
If someone is not generous or not old then someone is both not funny and wise and vice versa.
Everyone who is not brave is funny or quiet.
If someone is patient then someone is not tall or not calm.
Someone is both not tall and happy.
John is not quiet.
Lucy is curious or not tall.
Paul is either not quiet or funny.
Fred is not brave.
Someone is both wise and calm.
Susan is both humble and not brave. | Fred is old. | contradiction | ((?[X]:((curious(X)<~>~tall(X))))<=>((old(mary)<~>curious(mary))))&
(![X]:((~patient(X)<~>curious(X))<=>(~curious(X)|humble(X))))&
((?[X]:((~old(X)|~brave(X))))=>(?[X]:((~creative(X)|~rich(X)))))&
(((~rich(john)|quiet(john)))=>((humble(fred)&~creative(fred))))&
(![X]:((~creative(X)|~funny(X))=>~generous(X)))&
(((~brave(fred)<~>strong(fred)))<=>(?[X]:(wise(X))))&
(![X]:((~strong(X)|~generous(X))<=>(~old(X)<~>strong(X))))&
(![X]:((calm(X)|rich(X))<=>(kind(X)<~>~quiet(X))))&
(![X]:((rich(X)&wise(X))<=>(~generous(X)|tall(X))))&
(![X]:((~wise(X)|~curious(X))<=>(~strong(X)|~old(X))))&
(![X]:(rich(X)<=>(humble(X)&calm(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(~rich(X)|~brave(X))))&
((?[X]:((~generous(X)|~old(X))))<=>(?[X]:((~funny(X)&wise(X)))))&
(![X]:(~brave(X)=>(funny(X)|quiet(X))))&
((?[X]:(patient(X)))=>(?[X]:((~tall(X)|~calm(X)))))&
(?[X]:((~tall(X)&happy(X))))&
(~quiet(john))&
((curious(lucy)|~tall(lucy)))&
((~quiet(paul)<~>funny(paul)))&
(~brave(fred))&
(?[X]:((wise(X)&calm(X))))&
((humble(susan)&~brave(susan))) | old(fred) | [
"p5",
"p6",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5856261991634232440841582
% SZS output start Proof for 5856261991634232440841582
6. (~brave(fred) <~> strong(fred)) <=> ? [X0] : wise(X0) [input p5]
7. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> (~old(X0) <~> strong(X0))) [input p6]
20. ~brave(fred) [input p19]
21. ? [X0] : (calm(X0) & wise(X0)) [input p20]
23. old(fred) [input hypothesis]
45. (((~strong(fred) | brave(fred)) & (strong(fred) | ~brave(fred))) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | ((~brave(fred) | ~strong(fred)) & (strong(fred) | brave(fred)))) [nnf transformation 6]
46. (((~strong(fred) | brave(fred)) & (strong(fred) | ~brave(fred))) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | ((~brave(fred) | ~strong(fred)) & (strong(fred) | brave(fred)))) [rectify 45]
47. ? [X1] : wise(X1) => wise(sK2) [choice axiom]
48. (((~strong(fred) | brave(fred)) & (strong(fred) | ~brave(fred))) | ! [X0] : ~wise(X0)) & (wise(sK2) | ((~brave(fred) | ~strong(fred)) & (strong(fred) | brave(fred)))) [skolemisation 46,47]
49. ! [X0] : (((~generous(X0) | ~strong(X0)) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0)))) & (((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | (generous(X0) & strong(X0)))) [nnf transformation 7]
50. ! [X0] : ((~generous(X0) | ~strong(X0) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0)))) & (((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | (generous(X0) & strong(X0)))) [flattening 49]
71. ? [X0] : (calm(X0) & wise(X0)) => (calm(sK7) & wise(sK7)) [choice axiom]
72. calm(sK7) & wise(sK7) [skolemisation 21,71]
98. ~strong(fred) | brave(fred) | ~wise(X0) [cnf transformation 48]
99. strong(X0) | ~old(X0) | strong(X0) [cnf transformation 50]
137. ~brave(fred) [cnf transformation 20]
138. wise(sK7) [cnf transformation 72]
142. old(fred) [cnf transformation 23]
143. ~old(X0) | strong(X0) [duplicate literal removal 99]
215. 15 <=> ! [X0] : ~wise(X0) [avatar definition]
216. ~wise(X0) <- (15) [avatar component clause 215]
218. 16 <=> brave(fred) [avatar definition]
222. 17 <=> strong(fred) [avatar definition]
224. ~strong(fred) <- (~17) [avatar component clause 222]
225. 15 | 16 | ~17 [avatar split clause 98,222,218,215]
294. ~16 [avatar split clause 137,218]
295. $false <- (15) [resolution 216,138]
296. ~15 [avatar contradiction clause 295]
304. strong(fred) [resolution 143,142]
306. $false <- (~17) [subsumption resolution 304,224]
307. 17 [avatar contradiction clause 306]
308. $false [avatar sat refutation 225,294,296,307]
% SZS output end Proof for 5856261991634232440841582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not kind then mary is either not curious or not patient and vice versa. Everyone who is either not brave or not patient is both wise and not strong and vice versa. If someone is brave then someone is both wise and not brave and vice versa. Everyone who is not patient is both not old and tall and vice versa. Everyone who is either tall or not funny is not old or not wise and vice versa. If john is both generous and strong then someone is not rich and vice versa. Everyone who is not humble is not calm or not creative. If lucy is tall then someone is not wise or not patient and vice versa. If someone is creative then someone is old or quiet and vice versa. Everyone who is brave is humble or not calm and vice versa. If susan is both not old and tall then john is not wise or generous and vice versa. Everyone who is tall or not patient is both patient and not strong. If someone is both not humble and calm then someone is quiet or rich and vice versa. If someone is not funny then someone is both not generous and strong and vice versa. If someone is curious then someone is either brave or tall. If someone is not rich then susan is either not humble or not happy. Someone is either not kind or not wise. Someone is not kind or brave. Someone is not patient or not creative. Alice is both not quiet and creative. Someone is both wise and brave. Someone is either not curious or not creative. | Mary is not wise. | neutral | ((?[X]:((generous(X)|~kind(X))))<=>((~curious(mary)<~>~patient(mary))))&
(![X]:((~brave(X)<~>~patient(X))<=>(wise(X)&~strong(X))))&
((?[X]:(brave(X)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~patient(X)<=>(~old(X)&tall(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(~old(X)|~wise(X))))&
(((generous(john)&strong(john)))<=>(?[X]:(~rich(X))))&
(![X]:(~humble(X)=>(~calm(X)|~creative(X))))&
((tall(lucy))<=>(?[X]:((~wise(X)|~patient(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((old(X)|quiet(X)))))&
(![X]:(brave(X)<=>(humble(X)|~calm(X))))&
(((~old(susan)&tall(susan)))<=>((~wise(john)|generous(john))))&
(![X]:((tall(X)|~patient(X))=>(patient(X)&~strong(X))))&
((?[X]:((~humble(X)&calm(X))))<=>(?[X]:((quiet(X)|rich(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((~generous(X)&strong(X)))))&
((?[X]:(curious(X)))=>(?[X]:((brave(X)<~>tall(X)))))&
((?[X]:(~rich(X)))=>((~humble(susan)<~>~happy(susan))))&
(?[X]:((~kind(X)<~>~wise(X))))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((~patient(X)|~creative(X))))&
((~quiet(alice)&creative(alice)))&
(?[X]:((wise(X)&brave(X))))&
(?[X]:((~curious(X)<~>~creative(X)))) | ~wise(mary) | [] | null | 0 |
If someone is not old or creative then someone is either not rich or not humble.
Everyone who is wise or humble is calm.
Everyone who is not curious or rich is not strong or not brave.
If john is both calm and not strong then someone is both not humble and quiet.
Everyone who is either not kind or funny is not quiet or not old.
Everyone who is patient or funny is not strong.
Everyone who is either old or patient is both not rich and not happy.
If lucy is not old then mary is patient and vice versa.
If lucy is funny then alice is either not generous or calm.
If john is wise or not old then someone is both not humble and not generous.
Everyone who is calm or generous is old and vice versa.
Everyone who is patient or not rich is not humble and vice versa.
If someone is happy or not patient then someone is kind or not kind and vice versa.
Everyone who is calm or funny is not curious or funny and vice versa.
If mary is strong or not curious then someone is not generous and vice versa.
If john is both not quiet and not patient then someone is either not creative or wise.
Lucy is old.
Alice is old.
Lucy is either kind or not humble.
Someone is both not funny and old.
Fred is either not rich or wise.
Alice is calm.
Someone is creative or not humble.
Someone is not kind. | Lucy is kind. | contradiction | ((?[X]:((~old(X)|creative(X))))=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((wise(X)|humble(X))=>calm(X)))&
(![X]:((~curious(X)|rich(X))=>(~strong(X)|~brave(X))))&
(((calm(john)&~strong(john)))=>(?[X]:((~humble(X)&quiet(X)))))&
(![X]:((~kind(X)<~>funny(X))=>(~quiet(X)|~old(X))))&
(![X]:((patient(X)|funny(X))=>~strong(X)))&
(![X]:((old(X)<~>patient(X))=>(~rich(X)&~happy(X))))&
((~old(lucy))<=>(patient(mary)))&
((funny(lucy))=>((~generous(alice)<~>calm(alice))))&
(((wise(john)|~old(john)))=>(?[X]:((~humble(X)&~generous(X)))))&
(![X]:((calm(X)|generous(X))<=>old(X)))&
(![X]:((patient(X)|~rich(X))<=>~humble(X)))&
((?[X]:((happy(X)|~patient(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((calm(X)|funny(X))<=>(~curious(X)|funny(X))))&
(((strong(mary)|~curious(mary)))<=>(?[X]:(~generous(X))))&
(((~quiet(john)&~patient(john)))=>(?[X]:((~creative(X)<~>wise(X)))))&
(old(lucy))&
(old(alice))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((~funny(X)&old(X))))&
((~rich(fred)<~>wise(fred)))&
(calm(alice))&
(?[X]:((creative(X)|~humble(X))))&
(?[X]:(~kind(X))) | kind(lucy) | [
"p6",
"p11",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8633095683531833201336792
% SZS output start Proof for 8633095683531833201336792
7. ! [X0] : ((old(X0) <~> patient(X0)) => (~happy(X0) & ~rich(X0))) [input p6]
12. ! [X0] : ((~rich(X0) | patient(X0)) <=> ~humble(X0)) [input p11]
17. old(lucy) [input p16]
19. kind(lucy) <~> ~humble(lucy) [input p18]
25. kind(lucy) [input hypothesis]
36. ! [X0] : ((~happy(X0) & ~rich(X0)) | (old(X0) <=> patient(X0))) [ennf transformation 7]
48. ! [X0] : ((~happy(X0) & ~rich(X0)) | ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0)))) [nnf transformation 36]
55. ! [X0] : (((~rich(X0) | patient(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) & ~patient(X0)))) [nnf transformation 12]
56. ! [X0] : ((~rich(X0) | patient(X0) | humble(X0)) & (~humble(X0) | (rich(X0) & ~patient(X0)))) [flattening 55]
72. (humble(lucy) | ~kind(lucy)) & (~humble(lucy) | kind(lucy)) [nnf transformation 19]
92. ~rich(X0) | patient(X0) | ~old(X0) [cnf transformation 48]
107. ~patient(X0) | ~humble(X0) [cnf transformation 56]
108. ~humble(X0) | rich(X0) [cnf transformation 56]
123. old(lucy) [cnf transformation 17]
126. humble(lucy) | ~kind(lucy) [cnf transformation 72]
134. kind(lucy) [cnf transformation 25]
176. 10 <=> old(lucy) [avatar definition]
177. old(lucy) <- (10) [avatar component clause 176]
267. 10 [avatar split clause 123,176]
269. 30 <=> kind(lucy) [avatar definition]
273. 31 <=> humble(lucy) [avatar definition]
275. humble(lucy) <- (31) [avatar component clause 273]
276. ~30 | 31 [avatar split clause 126,273,269]
298. 30 [avatar split clause 134,269]
302. rich(lucy) <- (31) [resolution 108,275]
304. patient(lucy) | ~old(lucy) <- (31) [resolution 92,302]
314. patient(lucy) <- (10, 31) [subsumption resolution 304,177]
316. ~humble(lucy) <- (10, 31) [resolution 314,107]
318. $false <- (10, 31) [subsumption resolution 316,275]
319. ~10 | ~31 [avatar contradiction clause 318]
320. $false [avatar sat refutation 267,276,298,319]
% SZS output end Proof for 8633095683531833201336792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not creative is not brave or not creative and vice versa. If alice is not kind then someone is either not kind or old. If someone is not patient then lucy is both wise and not quiet. Everyone who is not strong is not old and vice versa. If susan is funny then someone is not calm. If mary is not funny then mary is either quiet or humble and vice versa. Everyone who is patient is both not happy and not tall. Everyone who is not old is not calm or wise. Everyone who is not curious or tall is either happy or tall. Everyone who is not humble is either happy or creative and vice versa. Everyone who is either brave or not funny is both wise and not creative and vice versa. If john is either tall or not quiet then paul is both not patient and calm. Everyone who is both tall and not generous is not brave or generous and vice versa. If lucy is both not kind and not calm then paul is not creative. If someone is wise or not strong then someone is both not quiet and creative. If someone is either not brave or calm then someone is not patient. Someone is both brave and not rich. Someone is not kind. Someone is curious or not humble. Someone is both not strong and quiet. Someone is either happy or not humble. Someone is patient or not patient. John is not creative. Someone is not old. | Lucy is not quiet. | entailment | (![X]:((~calm(X)<~>~creative(X))<=>(~brave(X)|~creative(X))))&
((~kind(alice))=>(?[X]:((~kind(X)<~>old(X)))))&
((?[X]:(~patient(X)))=>((wise(lucy)&~quiet(lucy))))&
(![X]:(~strong(X)<=>~old(X)))&
((funny(susan))=>(?[X]:(~calm(X))))&
((~funny(mary))<=>((quiet(mary)<~>humble(mary))))&
(![X]:(patient(X)=>(~happy(X)&~tall(X))))&
(![X]:(~old(X)=>(~calm(X)|wise(X))))&
(![X]:((~curious(X)|tall(X))=>(happy(X)<~>tall(X))))&
(![X]:(~humble(X)<=>(happy(X)<~>creative(X))))&
(![X]:((brave(X)<~>~funny(X))<=>(wise(X)&~creative(X))))&
(((tall(john)<~>~quiet(john)))=>((~patient(paul)&calm(paul))))&
(![X]:((tall(X)&~generous(X))<=>(~brave(X)|generous(X))))&
(((~kind(lucy)&~calm(lucy)))=>(~creative(paul)))&
((?[X]:((wise(X)|~strong(X))))=>(?[X]:((~quiet(X)&creative(X)))))&
((?[X]:((~brave(X)<~>calm(X))))=>(?[X]:(~patient(X))))&
(?[X]:((brave(X)&~rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((~strong(X)&quiet(X))))&
(?[X]:((happy(X)<~>~humble(X))))&
(?[X]:((patient(X)|~patient(X))))&
(~creative(john))&
(?[X]:(~old(X))) | ~quiet(lucy) | [
"p0",
"p2",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8957832594969352718564830
% SZS output start Proof for 8957832594969352718564830
1. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> (~creative(X0) | ~brave(X0))) [input p0]
3. ? [X0] : ~patient(X0) => (~quiet(lucy) & wise(lucy)) [input p2]
16. ? [X0] : (~brave(X0) <~> calm(X0)) => ? [X0] : ~patient(X0) [input p15]
17. ? [X0] : (~rich(X0) & brave(X0)) [input p16]
25. quiet(lucy) [input hypothesis]
27. ? [X0] : (~brave(X0) <~> calm(X0)) => ? [X1] : ~patient(X1) [rectify 16]
28. ? [X0] : brave(X0) [pure predicate removal 17]
32. (~quiet(lucy) & wise(lucy)) | ! [X0] : patient(X0) [ennf transformation 3]
42. ? [X1] : ~patient(X1) | ! [X0] : (~brave(X0) <=> calm(X0)) [ennf transformation 27]
43. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (creative(X0) & brave(X0))) & ((~creative(X0) | ~brave(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 1]
44. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (creative(X0) & brave(X0))) & (~creative(X0) | ~brave(X0) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [flattening 43]
62. ? [X1] : ~patient(X1) | ! [X0] : ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0))) [nnf transformation 42]
63. ? [X0] : ~patient(X0) | ! [X1] : ((~brave(X1) | ~calm(X1)) & (calm(X1) | brave(X1))) [rectify 62]
64. ? [X0] : ~patient(X0) => ~patient(sK3) [choice axiom]
65. ~patient(sK3) | ! [X1] : ((~brave(X1) | ~calm(X1)) & (calm(X1) | brave(X1))) [skolemisation 63,64]
66. ? [X0] : brave(X0) => brave(sK4) [choice axiom]
67. brave(sK4) [skolemisation 28,66]
79. ~creative(X0) | ~brave(X0) | ~creative(X0) | calm(X0) [cnf transformation 44]
84. creative(X0) | calm(X0) | creative(X0) [cnf transformation 44]
88. ~quiet(lucy) | patient(X0) [cnf transformation 32]
126. ~patient(sK3) | ~brave(X1) | ~calm(X1) [cnf transformation 65]
127. brave(sK4) [cnf transformation 67]
136. quiet(lucy) [cnf transformation 25]
140. ~creative(X0) | ~brave(X0) | calm(X0) [duplicate literal removal 79]
141. creative(X0) | calm(X0) [duplicate literal removal 84]
142. ~brave(X0) | calm(X0) [subsumption resolution 140,141]
158. 4 <=> ! [X0] : patient(X0) [avatar definition]
159. patient(X0) <- (4) [avatar component clause 158]
161. 5 <=> quiet(lucy) [avatar definition]
164. 4 | ~5 [avatar split clause 88,161,158]
247. ~patient(sK3) | ~brave(X1) [subsumption resolution 126,142]
249. 23 <=> ! [X1] : ~brave(X1) [avatar definition]
250. ~brave(X1) <- (23) [avatar component clause 249]
252. 24 <=> patient(sK3) [avatar definition]
254. ~patient(sK3) <- (~24) [avatar component clause 252]
255. 23 | ~24 [avatar split clause 247,252,249]
271. 5 [avatar split clause 136,161]
272. $false <- (4, ~24) [resolution 254,159]
273. ~4 | 24 [avatar contradiction clause 272]
274. $false <- (23) [resolution 250,127]
275. ~23 [avatar contradiction clause 274]
276. $false [avatar sat refutation 164,255,271,273,275]
% SZS output end Proof for 8957832594969352718564830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or brave then someone is both generous and not rich.
Everyone who is not humble is both not funny and not strong.
If someone is either tall or not patient then someone is not wise or strong and vice versa.
Everyone who is not quiet is either not creative or not curious and vice versa.
Everyone who is funny is either not tall or patient.
If paul is either humble or not tall then paul is strong.
Everyone who is both patient and generous is both happy and calm and vice versa.
If someone is either curious or not old then alice is kind.
Everyone who is both not happy and not old is rich or not creative.
Everyone who is funny or happy is funny and vice versa.
If susan is either humble or curious then someone is both brave and not kind and vice versa.
If mary is either old or kind then john is not tall or not funny.
Everyone who is both wise and funny is not creative or not funny and vice versa.
Everyone who is not curious is not rich.
If someone is both not brave and not patient then lucy is kind and vice versa.
If someone is not humble or not funny then someone is both calm and not generous.
Someone is rich.
Susan is either wise or not patient.
Alice is generous.
John is either humble or not tall.
Lucy is both not calm and generous.
Someone is calm.
John is either wise or patient.
Paul is brave. | Susan is funny. | entailment | ((?[X]:((~curious(X)<~>brave(X))))=>(?[X]:((generous(X)&~rich(X)))))&
(![X]:(~humble(X)=>(~funny(X)&~strong(X))))&
((?[X]:((tall(X)<~>~patient(X))))<=>(?[X]:((~wise(X)|strong(X)))))&
(![X]:(~quiet(X)<=>(~creative(X)<~>~curious(X))))&
(![X]:(funny(X)=>(~tall(X)<~>patient(X))))&
(((humble(paul)<~>~tall(paul)))=>(strong(paul)))&
(![X]:((patient(X)&generous(X))<=>(happy(X)&calm(X))))&
((?[X]:((curious(X)<~>~old(X))))=>(kind(alice)))&
(![X]:((~happy(X)&~old(X))=>(rich(X)|~creative(X))))&
(![X]:((funny(X)|happy(X))<=>funny(X)))&
(((humble(susan)<~>curious(susan)))<=>(?[X]:((brave(X)&~kind(X)))))&
(((old(mary)<~>kind(mary)))=>((~tall(john)|~funny(john))))&
(![X]:((wise(X)&funny(X))<=>(~creative(X)|~funny(X))))&
(![X]:(~curious(X)=>~rich(X)))&
((?[X]:((~brave(X)&~patient(X))))<=>(kind(lucy)))&
((?[X]:((~humble(X)|~funny(X))))=>(?[X]:((calm(X)&~generous(X)))))&
(?[X]:(rich(X)))&
((wise(susan)<~>~patient(susan)))&
(generous(alice))&
((humble(john)<~>~tall(john)))&
((~calm(lucy)&generous(lucy)))&
(?[X]:(calm(X)))&
((wise(john)<~>patient(john)))&
(brave(paul)) | funny(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7508482389899316110656212
% SZS output start Proof for 7508482389899316110656212
13. ! [X0] : ((funny(X0) & wise(X0)) <=> (~funny(X0) | ~creative(X0))) [input p12]
25. ~funny(susan) [input hypothesis]
61. ! [X0] : (((funny(X0) & wise(X0)) | (funny(X0) & creative(X0))) & ((~funny(X0) | ~creative(X0)) | (~funny(X0) | ~wise(X0)))) [nnf transformation 13]
62. ! [X0] : (((funny(X0) & wise(X0)) | (funny(X0) & creative(X0))) & (~funny(X0) | ~creative(X0) | ~funny(X0) | ~wise(X0))) [flattening 61]
115. funny(X0) | funny(X0) [cnf transformation 62]
136. ~funny(susan) [cnf transformation 25]
138. funny(X0) [duplicate literal removal 115]
319. $false [subsumption resolution 136,138]
% SZS output end Proof for 7508482389899316110656212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If alice is both not funny and not old then someone is either humble or not quiet.
Everyone who is either rich or not generous is not rich or happy and vice versa.
If someone is both brave and not funny then alice is creative and vice versa.
Everyone who is either kind or wise is old.
Everyone who is wise is not wise or patient.
If someone is not generous then susan is either not generous or old and vice versa.
If someone is both not strong and not curious then mary is generous or not calm and vice versa.
Everyone who is not generous or humble is both quiet and not kind.
If someone is both strong and curious then alice is not humble or humble.
If someone is quiet then someone is funny and vice versa.
Everyone who is either creative or not kind is either happy or not humble.
Everyone who is not tall or old is either quiet or kind.
Everyone who is either not happy or tall is both old and creative and vice versa.
If susan is both wise and brave then lucy is old or happy and vice versa.
Everyone who is brave or quiet is not creative and vice versa.
If paul is kind or not wise then fred is brave and vice versa.
Alice is either happy or not quiet.
Susan is either not old or not rich.
Fred is both generous and rich.
Someone is either generous or not strong.
Fred is either wise or funny.
Someone is kind.
Someone is either curious or not happy. | Mary is not calm. | neutral | (((~funny(alice)&~old(alice)))=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:((rich(X)<~>~generous(X))<=>(~rich(X)|happy(X))))&
((?[X]:((brave(X)&~funny(X))))<=>(creative(alice)))&
(![X]:((kind(X)<~>wise(X))=>old(X)))&
(![X]:(wise(X)=>(~wise(X)|patient(X))))&
((?[X]:(~generous(X)))<=>((~generous(susan)<~>old(susan))))&
((?[X]:((~strong(X)&~curious(X))))<=>((generous(mary)|~calm(mary))))&
(![X]:((~generous(X)|humble(X))=>(quiet(X)&~kind(X))))&
((?[X]:((strong(X)&curious(X))))=>((~humble(alice)|humble(alice))))&
((?[X]:(quiet(X)))<=>(?[X]:(funny(X))))&
(![X]:((creative(X)<~>~kind(X))=>(happy(X)<~>~humble(X))))&
(![X]:((~tall(X)|old(X))=>(quiet(X)<~>kind(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(old(X)&creative(X))))&
(((wise(susan)&brave(susan)))<=>((old(lucy)|happy(lucy))))&
(![X]:((brave(X)|quiet(X))<=>~creative(X)))&
(((kind(paul)|~wise(paul)))<=>(brave(fred)))&
((happy(alice)<~>~quiet(alice)))&
((~old(susan)<~>~rich(susan)))&
((generous(fred)&rich(fred)))&
(?[X]:((generous(X)<~>~strong(X))))&
((wise(fred)<~>funny(fred)))&
(?[X]:(kind(X)))&
(?[X]:((curious(X)<~>~happy(X)))) | ~calm(mary) | [] | null | 0 |
Everyone who is both not old and not strong is either humble or happy and vice versa.
Everyone who is both not wise and not generous is not brave and vice versa.
If paul is both tall and not humble then fred is creative.
If someone is both not happy and not humble then lucy is either not wise or strong and vice versa.
If someone is not old or brave then someone is not wise or not strong and vice versa.
If mary is both tall and humble then someone is not creative and vice versa.
If someone is either not strong or calm then mary is happy.
If someone is either humble or curious then susan is not calm or not generous and vice versa.
Everyone who is strong or tall is calm and vice versa.
Everyone who is either funny or not creative is both old and not rich.
Everyone who is not generous or not happy is funny.
If someone is both not tall and not humble then someone is either not creative or creative.
Everyone who is not happy is either not kind or creative and vice versa.
Everyone who is either happy or curious is both not wise and not humble and vice versa.
Everyone who is not strong or generous is either curious or not funny.
If someone is both patient and not quiet then alice is both not patient and humble and vice versa.
Lucy is not happy or not calm.
Paul is calm.
Susan is either not happy or not old.
Someone is old or kind.
John is either curious or creative.
Susan is curious.
Alice is either not generous or kind. | Susan is not creative. | neutral | (![X]:((~old(X)&~strong(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~wise(X)&~generous(X))<=>~brave(X)))&
(((tall(paul)&~humble(paul)))=>(creative(fred)))&
((?[X]:((~happy(X)&~humble(X))))<=>((~wise(lucy)<~>strong(lucy))))&
((?[X]:((~old(X)|brave(X))))<=>(?[X]:((~wise(X)|~strong(X)))))&
(((tall(mary)&humble(mary)))<=>(?[X]:(~creative(X))))&
((?[X]:((~strong(X)<~>calm(X))))=>(happy(mary)))&
((?[X]:((humble(X)<~>curious(X))))<=>((~calm(susan)|~generous(susan))))&
(![X]:((strong(X)|tall(X))<=>calm(X)))&
(![X]:((funny(X)<~>~creative(X))=>(old(X)&~rich(X))))&
(![X]:((~generous(X)|~happy(X))=>funny(X)))&
((?[X]:((~tall(X)&~humble(X))))=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:(~happy(X)<=>(~kind(X)<~>creative(X))))&
(![X]:((happy(X)<~>curious(X))<=>(~wise(X)&~humble(X))))&
(![X]:((~strong(X)|generous(X))=>(curious(X)<~>~funny(X))))&
((?[X]:((patient(X)&~quiet(X))))<=>((~patient(alice)&humble(alice))))&
((~happy(lucy)|~calm(lucy)))&
(calm(paul))&
((~happy(susan)<~>~old(susan)))&
(?[X]:((old(X)|kind(X))))&
((curious(john)<~>creative(john)))&
(curious(susan))&
((~generous(alice)<~>kind(alice))) | ~creative(susan) | [] | null | 0 |
Everyone who is curious or wise is not wise or not strong. Everyone who is happy is either strong or patient. Everyone who is not brave is not humble and vice versa. Everyone who is wise is both patient and funny and vice versa. Everyone who is either funny or old is not generous and vice versa. Everyone who is both not creative and not wise is old and vice versa. Everyone who is not kind is both not patient and not quiet. Everyone who is not brave or not happy is either patient or not creative and vice versa. Everyone who is not patient or patient is either not old or not curious. If john is both calm and not patient then mary is both rich and brave. If someone is both not kind and patient then someone is curious and vice versa. Everyone who is patient is rich or not generous and vice versa. If paul is both brave and kind then susan is both not kind and humble and vice versa. Everyone who is either tall or not calm is wise and vice versa. Everyone who is either not tall or humble is either calm or not kind. Everyone who is both generous and humble is not rich or happy and vice versa. Someone is both not tall and calm. Someone is not rich or not quiet. Someone is both not strong and not wise. Someone is both kind and not quiet. Someone is quiet or not tall. | John is not humble. | contradiction | (![X]:((curious(X)|wise(X))=>(~wise(X)|~strong(X))))&
(![X]:(happy(X)=>(strong(X)<~>patient(X))))&
(![X]:(~brave(X)<=>~humble(X)))&
(![X]:(wise(X)<=>(patient(X)&funny(X))))&
(![X]:((funny(X)<~>old(X))<=>~generous(X)))&
(![X]:((~creative(X)&~wise(X))<=>old(X)))&
(![X]:(~kind(X)=>(~patient(X)&~quiet(X))))&
(![X]:((~brave(X)|~happy(X))<=>(patient(X)<~>~creative(X))))&
(![X]:((~patient(X)|patient(X))=>(~old(X)<~>~curious(X))))&
(((calm(john)&~patient(john)))=>((rich(mary)&brave(mary))))&
((?[X]:((~kind(X)&patient(X))))<=>(?[X]:(curious(X))))&
(![X]:(patient(X)<=>(rich(X)|~generous(X))))&
(((brave(paul)&kind(paul)))<=>((~kind(susan)&humble(susan))))&
(![X]:((tall(X)<~>~calm(X))<=>wise(X)))&
(![X]:((~tall(X)<~>humble(X))=>(calm(X)<~>~kind(X))))&
(![X]:((generous(X)&humble(X))<=>(~rich(X)|happy(X))))&
(?[X]:((~tall(X)&calm(X))))&
(?[X]:((~rich(X)|~quiet(X))))&
(?[X]:((~strong(X)&~wise(X))))&
(?[X]:((kind(X)&~quiet(X))))&
(?[X]:((quiet(X)|~tall(X)))) | ~humble(john) | [
"p2",
"p5",
"p6",
"p7",
"p8",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 510524609500469866712621
% SZS output start Proof for 510524609500469866712621
3. ! [X0] : (~brave(X0) <=> ~humble(X0)) [input p2]
6. ! [X0] : ((~wise(X0) & ~creative(X0)) <=> old(X0)) [input p5]
7. ! [X0] : (~kind(X0) => (~quiet(X0) & ~patient(X0))) [input p6]
8. ! [X0] : ((~happy(X0) | ~brave(X0)) <=> (patient(X0) <~> ~creative(X0))) [input p7]
9. ! [X0] : ((patient(X0) | ~patient(X0)) => (~old(X0) <~> ~curious(X0))) [input p8]
11. ? [X0] : (patient(X0) & ~kind(X0)) <=> ? [X0] : curious(X0) [input p10]
12. ! [X0] : (patient(X0) <=> (~generous(X0) | rich(X0))) [input p11]
16. ! [X0] : ((humble(X0) & generous(X0)) <=> (happy(X0) | ~rich(X0))) [input p15]
22. ~humble(john) [input hypothesis]
23. ? [X0] : (patient(X0) & ~kind(X0)) <=> ? [X1] : curious(X1) [rectify 11]
27. ! [X0] : ((~quiet(X0) & ~patient(X0)) | kind(X0)) [ennf transformation 7]
28. ! [X0] : ((~old(X0) <~> ~curious(X0)) | (~patient(X0) & patient(X0))) [ennf transformation 9]
33. ! [X0] : ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0))) [nnf transformation 3]
37. ! [X0] : (((~wise(X0) & ~creative(X0)) | ~old(X0)) & (old(X0) | (wise(X0) | creative(X0)))) [nnf transformation 6]
38. ! [X0] : (((~wise(X0) & ~creative(X0)) | ~old(X0)) & (old(X0) | wise(X0) | creative(X0))) [flattening 37]
39. ! [X0] : (((~happy(X0) | ~brave(X0)) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) & (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | (happy(X0) & brave(X0)))) [nnf transformation 8]
40. ! [X0] : ((~happy(X0) | ~brave(X0) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) & (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | (happy(X0) & brave(X0)))) [flattening 39]
41. ! [X0] : (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (~patient(X0) & patient(X0))) [nnf transformation 28]
42. (? [X0] : (patient(X0) & ~kind(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (~patient(X0) | kind(X0))) [nnf transformation 23]
43. (? [X0] : (patient(X0) & ~kind(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (~patient(X3) | kind(X3))) [rectify 42]
44. ? [X0] : (patient(X0) & ~kind(X0)) => (patient(sK0) & ~kind(sK0)) [choice axiom]
45. ? [X2] : curious(X2) => curious(sK1) [choice axiom]
46. ((patient(sK0) & ~kind(sK0)) | ! [X1] : ~curious(X1)) & (curious(sK1) | ! [X3] : (~patient(X3) | kind(X3))) [skolemisation 43,45,44]
47. ! [X0] : ((patient(X0) | (generous(X0) & ~rich(X0))) & ((~generous(X0) | rich(X0)) | ~patient(X0))) [nnf transformation 12]
48. ! [X0] : ((patient(X0) | (generous(X0) & ~rich(X0))) & (~generous(X0) | rich(X0) | ~patient(X0))) [flattening 47]
53. ! [X0] : (((humble(X0) & generous(X0)) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | (~humble(X0) | ~generous(X0)))) [nnf transformation 16]
54. ! [X0] : (((humble(X0) & generous(X0)) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | ~humble(X0) | ~generous(X0))) [flattening 53]
70. ~brave(X0) | humble(X0) [cnf transformation 33]
79. ~creative(X0) | ~old(X0) [cnf transformation 38]
81. ~patient(X0) | kind(X0) [cnf transformation 27]
85. ~patient(X0) | creative(X0) | brave(X0) [cnf transformation 40]
91. curious(X0) | old(X0) | patient(X0) [cnf transformation 41]
92. ~patient(X0) | old(X0) | curious(X0) [cnf transformation 41]
96. ~kind(sK0) | ~curious(X1) [cnf transformation 46]
97. patient(sK0) | ~curious(X1) [cnf transformation 46]
99. ~rich(X0) | patient(X0) [cnf transformation 48]
116. rich(X0) | humble(X0) [cnf transformation 54]
126. ~humble(john) [cnf transformation 22]
128. old(X0) | curious(X0) [subsumption resolution 91,92]
135. 2 <=> patient(john) [avatar definition]
137. patient(john) <- (2) [avatar component clause 135]
149. 5 <=> ! [X1] : ~curious(X1) [avatar definition]
150. ~curious(X1) <- (5) [avatar component clause 149]
152. 6 <=> patient(sK0) [avatar definition]
154. patient(sK0) <- (6) [avatar component clause 152]
155. 5 | 6 [avatar split clause 97,152,149]
157. 7 <=> kind(sK0) [avatar definition]
159. ~kind(sK0) <- (~7) [avatar component clause 157]
160. 5 | ~7 [avatar split clause 96,157,149]
200. humble(X0) | patient(X0) [resolution 116,99]
204. patient(john) [resolution 200,126]
207. 2 [avatar split clause 204,135]
244. creative(john) | brave(john) <- (2) [resolution 85,137]
247. 20 <=> brave(john) [avatar definition]
249. brave(john) <- (20) [avatar component clause 247]
251. 21 <=> creative(john) [avatar definition]
253. creative(john) <- (21) [avatar component clause 251]
254. 20 | 21 | ~2 [avatar split clause 244,135,251,247]
266. humble(john) <- (20) [resolution 249,70]
267. $false <- (20) [subsumption resolution 266,126]
268. ~20 [avatar contradiction clause 267]
274. ~old(john) <- (21) [resolution 253,79]
276. curious(john) <- (21) [resolution 274,128]
277. $false <- (5, 21) [subsumption resolution 276,150]
278. ~5 | ~21 [avatar contradiction clause 277]
284. kind(sK0) <- (6) [resolution 154,81]
304. $false <- (6, ~7) [subsumption resolution 284,159]
305. ~6 | 7 [avatar contradiction clause 304]
306. $false [avatar sat refutation 155,160,207,254,268,278,305]
% SZS output end Proof for 510524609500469866712621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or humble is not humble and vice versa.
If someone is strong then someone is both not old and not wise.
Everyone who is not wise is both kind and not funny and vice versa.
Everyone who is either tall or not strong is not humble and vice versa.
If someone is both patient and not strong then someone is quiet and vice versa.
If lucy is not strong then fred is both humble and not funny.
If lucy is either rich or not patient then someone is kind and vice versa.
Everyone who is either not quiet or not curious is either not tall or not creative.
If someone is not tall then alice is not rich.
If someone is not patient or tall then someone is both not wise and not brave and vice versa.
Everyone who is not brave or not rich is both not curious and rich.
If someone is not brave then someone is both happy and rich.
Everyone who is kind is not strong or rich.
Someone is both not quiet and not creative.
Someone is both not kind and not brave.
Fred is both old and strong.
Mary is rich or old.
Susan is not tall or not calm. | Mary is not tall. | contradiction | (![X]:((~quiet(X)|humble(X))<=>~humble(X)))&
((?[X]:(strong(X)))=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:(~wise(X)<=>(kind(X)&~funny(X))))&
(![X]:((tall(X)<~>~strong(X))<=>~humble(X)))&
((?[X]:((patient(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
((~strong(lucy))=>((humble(fred)&~funny(fred))))&
(((rich(lucy)<~>~patient(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))=>(~tall(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(~rich(alice)))&
((?[X]:((~patient(X)|tall(X))))<=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~brave(X)|~rich(X))=>(~curious(X)&rich(X))))&
((?[X]:(~brave(X)))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:(kind(X)=>(~strong(X)|rich(X))))&
(?[X]:((~quiet(X)&~creative(X))))&
(?[X]:((~kind(X)&~brave(X))))&
((old(fred)&strong(fred)))&
((rich(mary)|old(mary)))&
((~tall(susan)|~calm(susan))) | ~tall(mary) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7783493122594995968913438
% SZS output start Proof for 7783493122594995968913438
9. ? [X0] : ~tall(X0) => ~rich(alice) [input p8]
11. ! [X0] : ((~rich(X0) | ~brave(X0)) => (rich(X0) & ~curious(X0))) [input p10]
19. ~tall(mary) [input hypothesis]
29. ~rich(alice) | ! [X0] : tall(X0) [ennf transformation 9]
30. ! [X0] : ((rich(X0) & ~curious(X0)) | (rich(X0) & brave(X0))) [ennf transformation 11]
89. ~rich(alice) | tall(X0) [cnf transformation 29]
98. rich(X0) | rich(X0) [cnf transformation 30]
108. ~tall(mary) [cnf transformation 19]
109. rich(X0) [duplicate literal removal 98]
179. 15 <=> ! [X0] : tall(X0) [avatar definition]
180. tall(X0) <- (15) [avatar component clause 179]
182. 16 <=> rich(alice) [avatar definition]
184. ~rich(alice) <- (~16) [avatar component clause 182]
185. 15 | ~16 [avatar split clause 89,182,179]
216. $false <- (~16) [subsumption resolution 184,109]
217. 16 [avatar contradiction clause 216]
218. $false <- (15) [resolution 180,108]
219. ~15 [avatar contradiction clause 218]
220. $false [avatar sat refutation 185,217,219]
% SZS output end Proof for 7783493122594995968913438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not patient is both brave and not calm and vice versa. Everyone who is both not patient and funny is not rich. Everyone who is both not brave and quiet is either not happy or not wise. If mary is old then mary is not strong or creative. If lucy is either not quiet or quiet then paul is not strong. Everyone who is both patient and tall is not kind or tall. If paul is funny then fred is both curious and not patient. Everyone who is tall is either calm or humble and vice versa. Everyone who is tall is both not humble and patient and vice versa. If someone is either tall or strong then alice is not strong. Everyone who is not kind or not tall is not curious or generous and vice versa. If fred is generous or wise then fred is both rich and humble. Everyone who is humble is either not quiet or not brave. If alice is old then fred is not creative or happy and vice versa. If someone is not quiet then someone is either not humble or not happy and vice versa. Everyone who is both not happy and not old is both not humble and happy and vice versa. Someone is either not humble or wise. John is strong or not generous. Someone is patient or not tall. Fred is either not creative or old. Someone is either kind or not strong. Paul is either not tall or not happy. Susan is calm. Someone is either tall or curious. | Susan is patient. | entailment | (![X]:((~calm(X)<~>~patient(X))<=>(brave(X)&~calm(X))))&
(![X]:((~patient(X)&funny(X))=>~rich(X)))&
(![X]:((~brave(X)&quiet(X))=>(~happy(X)<~>~wise(X))))&
((old(mary))=>((~strong(mary)|creative(mary))))&
(((~quiet(lucy)<~>quiet(lucy)))=>(~strong(paul)))&
(![X]:((patient(X)&tall(X))=>(~kind(X)|tall(X))))&
((funny(paul))=>((curious(fred)&~patient(fred))))&
(![X]:(tall(X)<=>(calm(X)<~>humble(X))))&
(![X]:(tall(X)<=>(~humble(X)&patient(X))))&
((?[X]:((tall(X)<~>strong(X))))=>(~strong(alice)))&
(![X]:((~kind(X)|~tall(X))<=>(~curious(X)|generous(X))))&
(((generous(fred)|wise(fred)))=>((rich(fred)&humble(fred))))&
(![X]:(humble(X)=>(~quiet(X)<~>~brave(X))))&
((old(alice))<=>((~creative(fred)|happy(fred))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~humble(X)<~>~happy(X)))))&
(![X]:((~happy(X)&~old(X))<=>(~humble(X)&happy(X))))&
(?[X]:((~humble(X)<~>wise(X))))&
((strong(john)|~generous(john)))&
(?[X]:((patient(X)|~tall(X))))&
((~creative(fred)<~>old(fred)))&
(?[X]:((kind(X)<~>~strong(X))))&
((~tall(paul)<~>~happy(paul)))&
(calm(susan))&
(?[X]:((tall(X)<~>curious(X)))) | patient(susan) | [
"p0",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6683651748243164516487831
% SZS output start Proof for 6683651748243164516487831
1. ! [X0] : ((~calm(X0) <~> ~patient(X0)) <=> (~calm(X0) & brave(X0))) [input p0]
23. calm(susan) [input p22]
25. ~patient(susan) [input hypothesis]
40. ! [X0] : ((((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (calm(X0) | ~brave(X0))) & ((~calm(X0) & brave(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0))))) [nnf transformation 1]
41. ! [X0] : ((((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | calm(X0) | ~brave(X0)) & ((~calm(X0) & brave(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0))))) [flattening 40]
76. ~calm(X0) | ~calm(X0) | patient(X0) [cnf transformation 41]
123. calm(susan) [cnf transformation 23]
126. ~patient(susan) [cnf transformation 25]
131. ~calm(X0) | patient(X0) [duplicate literal removal 76]
285. patient(susan) [resolution 131,123]
286. $false [subsumption resolution 285,126]
% SZS output end Proof for 6683651748243164516487831
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and old is brave or not brave.
Everyone who is either not generous or not calm is either curious or humble and vice versa.
If someone is either not wise or humble then alice is not brave.
Everyone who is either not patient or not humble is patient and vice versa.
Everyone who is either humble or not tall is both curious and brave and vice versa.
If someone is both brave and patient then fred is both creative and tall and vice versa.
Everyone who is happy is rich or calm.
Everyone who is both not brave and not creative is both funny and not quiet.
Everyone who is either funny or humble is not brave or funny and vice versa.
If someone is kind then mary is tall.
Everyone who is both tall and not funny is both not curious and not generous and vice versa.
Everyone who is wise or not tall is humble or not kind and vice versa.
Everyone who is rich or old is both not funny and patient and vice versa.
Everyone who is wise or generous is not happy and vice versa.
Everyone who is both not funny and calm is calm or not kind and vice versa.
Everyone who is either not generous or funny is strong and vice versa.
Someone is either happy or old.
Susan is not calm or not quiet.
Susan is both not old and not creative.
Susan is either humble or strong.
Someone is not rich.
John is not old.
Someone is not kind. | Alice is brave. | contradiction | (![X]:((curious(X)&old(X))=>(brave(X)|~brave(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(curious(X)<~>humble(X))))&
((?[X]:((~wise(X)<~>humble(X))))=>(~brave(alice)))&
(![X]:((~patient(X)<~>~humble(X))<=>patient(X)))&
(![X]:((humble(X)<~>~tall(X))<=>(curious(X)&brave(X))))&
((?[X]:((brave(X)&patient(X))))<=>((creative(fred)&tall(fred))))&
(![X]:(happy(X)=>(rich(X)|calm(X))))&
(![X]:((~brave(X)&~creative(X))=>(funny(X)&~quiet(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~brave(X)|funny(X))))&
((?[X]:(kind(X)))=>(tall(mary)))&
(![X]:((tall(X)&~funny(X))<=>(~curious(X)&~generous(X))))&
(![X]:((wise(X)|~tall(X))<=>(humble(X)|~kind(X))))&
(![X]:((rich(X)|old(X))<=>(~funny(X)&patient(X))))&
(![X]:((wise(X)|generous(X))<=>~happy(X)))&
(![X]:((~funny(X)&calm(X))<=>(calm(X)|~kind(X))))&
(![X]:((~generous(X)<~>funny(X))<=>strong(X)))&
(?[X]:((happy(X)<~>old(X))))&
((~calm(susan)|~quiet(susan)))&
((~old(susan)&~creative(susan)))&
((humble(susan)<~>strong(susan)))&
(?[X]:(~rich(X)))&
(~old(john))&
(?[X]:(~kind(X))) | brave(alice) | [
"p1",
"p2",
"p3",
"p5",
"p8",
"p10",
"p11",
"p12",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5833731055850582180942265
% SZS output start Proof for 5833731055850582180942265
2. ! [X0] : ((~generous(X0) <~> ~calm(X0)) <=> (curious(X0) <~> humble(X0))) [input p1]
3. ? [X0] : (~wise(X0) <~> humble(X0)) => ~brave(alice) [input p2]
4. ! [X0] : ((~patient(X0) <~> ~humble(X0)) <=> patient(X0)) [input p3]
6. ? [X0] : (patient(X0) & brave(X0)) <=> (tall(fred) & creative(fred)) [input p5]
9. ! [X0] : ((funny(X0) <~> humble(X0)) <=> (funny(X0) | ~brave(X0))) [input p8]
11. ! [X0] : ((~funny(X0) & tall(X0)) <=> (~generous(X0) & ~curious(X0))) [input p10]
12. ! [X0] : ((~tall(X0) | wise(X0)) <=> (~kind(X0) | humble(X0))) [input p11]
13. ! [X0] : ((old(X0) | rich(X0)) <=> (patient(X0) & ~funny(X0))) [input p12]
14. ! [X0] : ((generous(X0) | wise(X0)) <=> ~happy(X0)) [input p13]
15. ! [X0] : ((calm(X0) & ~funny(X0)) <=> (~kind(X0) | calm(X0))) [input p14]
17. ? [X0] : (happy(X0) <~> old(X0)) [input p16]
24. brave(alice) [input hypothesis]
29. ~brave(alice) | ! [X0] : (~wise(X0) <=> humble(X0)) [ennf transformation 3]
35. ! [X0] : ((((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))))) [nnf transformation 2]
36. ~brave(alice) | ! [X0] : ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0))) [nnf transformation 29]
37. ! [X0] : ((((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0))))) [nnf transformation 4]
40. (? [X0] : (patient(X0) & brave(X0)) | (~tall(fred) | ~creative(fred))) & ((tall(fred) & creative(fred)) | ! [X0] : (~patient(X0) | ~brave(X0))) [nnf transformation 6]
41. (? [X0] : (patient(X0) & brave(X0)) | ~tall(fred) | ~creative(fred)) & ((tall(fred) & creative(fred)) | ! [X0] : (~patient(X0) | ~brave(X0))) [flattening 40]
42. (? [X0] : (patient(X0) & brave(X0)) | ~tall(fred) | ~creative(fred)) & ((tall(fred) & creative(fred)) | ! [X1] : (~patient(X1) | ~brave(X1))) [rectify 41]
43. ? [X0] : (patient(X0) & brave(X0)) => (patient(sK0) & brave(sK0)) [choice axiom]
44. ((patient(sK0) & brave(sK0)) | ~tall(fred) | ~creative(fred)) & ((tall(fred) & creative(fred)) | ! [X1] : (~patient(X1) | ~brave(X1))) [skolemisation 42,43]
45. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | (~funny(X0) & brave(X0))) & ((funny(X0) | ~brave(X0)) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [nnf transformation 9]
46. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | (~funny(X0) & brave(X0))) & (funny(X0) | ~brave(X0) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [flattening 45]
47. ! [X0] : (((~funny(X0) & tall(X0)) | (generous(X0) | curious(X0))) & ((~generous(X0) & ~curious(X0)) | (funny(X0) | ~tall(X0)))) [nnf transformation 11]
48. ! [X0] : (((~funny(X0) & tall(X0)) | generous(X0) | curious(X0)) & ((~generous(X0) & ~curious(X0)) | funny(X0) | ~tall(X0))) [flattening 47]
49. ! [X0] : (((~tall(X0) | wise(X0)) | (kind(X0) & ~humble(X0))) & ((~kind(X0) | humble(X0)) | (tall(X0) & ~wise(X0)))) [nnf transformation 12]
50. ! [X0] : ((~tall(X0) | wise(X0) | (kind(X0) & ~humble(X0))) & (~kind(X0) | humble(X0) | (tall(X0) & ~wise(X0)))) [flattening 49]
51. ! [X0] : (((old(X0) | rich(X0)) | (~patient(X0) | funny(X0))) & ((patient(X0) & ~funny(X0)) | (~old(X0) & ~rich(X0)))) [nnf transformation 13]
52. ! [X0] : ((old(X0) | rich(X0) | ~patient(X0) | funny(X0)) & ((patient(X0) & ~funny(X0)) | (~old(X0) & ~rich(X0)))) [flattening 51]
53. ! [X0] : (((generous(X0) | wise(X0)) | happy(X0)) & (~happy(X0) | (~generous(X0) & ~wise(X0)))) [nnf transformation 14]
54. ! [X0] : ((generous(X0) | wise(X0) | happy(X0)) & (~happy(X0) | (~generous(X0) & ~wise(X0)))) [flattening 53]
55. ! [X0] : (((calm(X0) & ~funny(X0)) | (kind(X0) & ~calm(X0))) & ((~kind(X0) | calm(X0)) | (~calm(X0) | funny(X0)))) [nnf transformation 15]
56. ! [X0] : (((calm(X0) & ~funny(X0)) | (kind(X0) & ~calm(X0))) & (~kind(X0) | calm(X0) | ~calm(X0) | funny(X0))) [flattening 55]
58. ? [X0] : ((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) [nnf transformation 17]
59. ? [X0] : ((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) => ((~old(sK1) | ~happy(sK1)) & (old(sK1) | happy(sK1))) [choice axiom]
60. (~old(sK1) | ~happy(sK1)) & (old(sK1) | happy(sK1)) [skolemisation 58,59]
67. ~calm(X0) | curious(X0) | humble(X0) | generous(X0) [cnf transformation 35]
75. ~brave(alice) | humble(X0) | wise(X0) [cnf transformation 36]
77. patient(X0) | ~humble(X0) | patient(X0) [cnf transformation 37]
79. ~humble(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 37]
88. tall(fred) | ~patient(X1) | ~brave(X1) [cnf transformation 44]
95. humble(X0) | funny(X0) | brave(X0) [cnf transformation 46]
100. ~tall(X0) | funny(X0) | ~curious(X0) [cnf transformation 48]
101. ~tall(X0) | funny(X0) | ~generous(X0) [cnf transformation 48]
104. ~kind(X0) | humble(X0) | ~wise(X0) [cnf transformation 50]
111. ~old(X0) | patient(X0) [cnf transformation 52]
113. ~happy(X0) | ~wise(X0) [cnf transformation 54]
117. ~funny(X0) | ~calm(X0) [cnf transformation 56]
118. ~funny(X0) | kind(X0) [cnf transformation 56]
120. kind(X0) | calm(X0) [cnf transformation 56]
125. old(sK1) | happy(sK1) [cnf transformation 60]
134. brave(alice) [cnf transformation 24]
137. patient(X0) | ~humble(X0) [duplicate literal removal 77]
138. ~patient(X0) | ~humble(X0) [duplicate literal removal 79]
143. 2 <=> brave(alice) [avatar definition]
148. 3 <=> ! [X0] : (humble(X0) | wise(X0)) [avatar definition]
149. humble(X0) | wise(X0) <- (3) [avatar component clause 148]
150. 3 | ~2 [avatar split clause 75,143,148]
151. ~humble(X0) [subsumption resolution 137,138]
160. 5 <=> tall(fred) [avatar definition]
161. tall(fred) <- (5) [avatar component clause 160]
174. 8 <=> ! [X1] : (~patient(X1) | ~brave(X1)) [avatar definition]
175. ~patient(X1) | ~brave(X1) <- (8) [avatar component clause 174]
176. 8 | 5 [avatar split clause 88,160,174]
178. funny(X0) | brave(X0) [subsumption resolution 95,151]
188. ~kind(X0) | ~wise(X0) [subsumption resolution 104,151]
190. 11 <=> happy(sK1) [avatar definition]
191. happy(sK1) <- (11) [avatar component clause 190]
194. 12 <=> old(sK1) [avatar definition]
195. old(sK1) <- (12) [avatar component clause 194]
198. 11 | 12 [avatar split clause 125,194,190]
200. 2 [avatar split clause 134,143]
201. wise(X0) <- (3) [subsumption resolution 149,151]
202. ~wise(sK1) <- (11) [resolution 113,191]
203. $false <- (3, 11) [subsumption resolution 202,201]
204. ~3 | ~11 [avatar contradiction clause 203]
205. patient(sK1) <- (12) [resolution 195,111]
209. ~brave(sK1) <- (8, 12) [resolution 175,205]
210. kind(X0) | brave(X0) [resolution 178,118]
218. ~wise(X0) | calm(X0) [resolution 188,120]
219. calm(X0) <- (3) [subsumption resolution 218,201]
225. brave(X0) | ~wise(X0) [resolution 210,188]
227. brave(X0) <- (3) [subsumption resolution 225,201]
253. $false <- (3, 8, 12) [resolution 227,209]
254. ~3 | ~8 | ~12 [avatar contradiction clause 253]
256. funny(fred) | ~generous(fred) <- (5) [resolution 161,101]
257. funny(fred) | ~curious(fred) <- (5) [resolution 161,100]
259. 16 <=> generous(fred) [avatar definition]
261. ~generous(fred) <- (~16) [avatar component clause 259]
263. 17 <=> funny(fred) [avatar definition]
265. funny(fred) <- (17) [avatar component clause 263]
266. ~16 | 17 | ~5 [avatar split clause 256,160,263,259]
268. 18 <=> curious(fred) [avatar definition]
270. ~curious(fred) <- (~18) [avatar component clause 268]
271. ~18 | 17 | ~5 [avatar split clause 257,160,263,268]
306. curious(X0) | humble(X0) | generous(X0) <- (3) [resolution 67,219]
317. generous(X0) | curious(X0) <- (3) [subsumption resolution 306,151]
324. curious(fred) <- (3, ~16) [resolution 317,261]
328. $false <- (3, ~16, ~18) [subsumption resolution 324,270]
329. ~3 | 16 | 18 [avatar contradiction clause 328]
377. ~calm(fred) <- (17) [resolution 265,117]
383. $false <- (3, 17) [subsumption resolution 377,219]
384. ~3 | ~17 [avatar contradiction clause 383]
385. $false [avatar sat refutation 150,176,198,200,204,254,266,271,329,384]
% SZS output end Proof for 5833731055850582180942265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both not happy and not calm and vice versa. If alice is either not happy or patient then john is old. If susan is either tall or creative then someone is curious. Everyone who is rich is calm and vice versa. If someone is not wise then fred is either creative or not brave. Everyone who is either funny or not wise is calm or funny. If someone is not strong then someone is either not wise or creative and vice versa. If lucy is not rich or humble then someone is both not patient and calm. If someone is not humble or not calm then someone is not rich or kind. Everyone who is both creative and not happy is not quiet and vice versa. If someone is not old then paul is not wise. If someone is either not brave or creative then alice is either not humble or rich and vice versa. Everyone who is wise or not humble is happy and vice versa. Everyone who is not curious is either rich or humble and vice versa. If fred is either patient or curious then someone is humble and vice versa. If alice is curious or generous then someone is either not rich or humble and vice versa. Someone is both brave and funny. Someone is either not creative or not rich. Someone is either not quiet or not generous. Someone is not quiet or not patient. Someone is not brave. Fred is both generous and brave. | Lucy is kind. | neutral | (![X]:(happy(X)<=>(~happy(X)&~calm(X))))&
(((~happy(alice)<~>patient(alice)))=>(old(john)))&
(((tall(susan)<~>creative(susan)))=>(?[X]:(curious(X))))&
(![X]:(rich(X)<=>calm(X)))&
((?[X]:(~wise(X)))=>((creative(fred)<~>~brave(fred))))&
(![X]:((funny(X)<~>~wise(X))=>(calm(X)|funny(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~wise(X)<~>creative(X)))))&
(((~rich(lucy)|humble(lucy)))=>(?[X]:((~patient(X)&calm(X)))))&
((?[X]:((~humble(X)|~calm(X))))=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((creative(X)&~happy(X))<=>~quiet(X)))&
((?[X]:(~old(X)))=>(~wise(paul)))&
((?[X]:((~brave(X)<~>creative(X))))<=>((~humble(alice)<~>rich(alice))))&
(![X]:((wise(X)|~humble(X))<=>happy(X)))&
(![X]:(~curious(X)<=>(rich(X)<~>humble(X))))&
(((patient(fred)<~>curious(fred)))<=>(?[X]:(humble(X))))&
(((curious(alice)|generous(alice)))<=>(?[X]:((~rich(X)<~>humble(X)))))&
(?[X]:((brave(X)&funny(X))))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((~quiet(X)<~>~generous(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:(~brave(X)))&
((generous(fred)&brave(fred))) | kind(lucy) | [] | null | 0 |
If alice is not wise then someone is both curious and not happy and vice versa.
Everyone who is not curious or happy is quiet or not funny and vice versa.
If paul is funny then susan is either not humble or funny and vice versa.
If someone is rich then someone is not tall and vice versa.
Everyone who is tall is both calm and not humble and vice versa.
If someone is both not brave and curious then paul is tall.
Everyone who is not quiet is both not brave and not humble and vice versa.
Everyone who is both generous and rich is both rich and not funny and vice versa.
Everyone who is kind or brave is not old or old.
If someone is either not old or not quiet then paul is generous and vice versa.
If john is not wise or not happy then someone is rich or brave and vice versa.
Everyone who is not wise or curious is curious and vice versa.
Everyone who is not creative is either strong or rich and vice versa.
Everyone who is both not creative and old is either curious or not curious and vice versa.
If someone is both calm and patient then susan is both patient and not wise and vice versa.
Someone is both not creative and not curious.
Fred is not kind or not humble.
Lucy is not rich or strong.
Fred is both not patient and not rich.
Alice is either happy or not creative.
Alice is either not brave or happy.
Paul is not strong or not old.
Lucy is either old or not quiet. | Paul is old. | entailment | ((~wise(alice))<=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((~curious(X)|happy(X))<=>(quiet(X)|~funny(X))))&
((funny(paul))<=>((~humble(susan)<~>funny(susan))))&
((?[X]:(rich(X)))<=>(?[X]:(~tall(X))))&
(![X]:(tall(X)<=>(calm(X)&~humble(X))))&
((?[X]:((~brave(X)&curious(X))))=>(tall(paul)))&
(![X]:(~quiet(X)<=>(~brave(X)&~humble(X))))&
(![X]:((generous(X)&rich(X))<=>(rich(X)&~funny(X))))&
(![X]:((kind(X)|brave(X))=>(~old(X)|old(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(generous(paul)))&
(((~wise(john)|~happy(john)))<=>(?[X]:((rich(X)|brave(X)))))&
(![X]:((~wise(X)|curious(X))<=>curious(X)))&
(![X]:(~creative(X)<=>(strong(X)<~>rich(X))))&
(![X]:((~creative(X)&old(X))<=>(curious(X)<~>~curious(X))))&
((?[X]:((calm(X)&patient(X))))<=>((patient(susan)&~wise(susan))))&
(?[X]:((~creative(X)&~curious(X))))&
((~kind(fred)|~humble(fred)))&
((~rich(lucy)|strong(lucy)))&
((~patient(fred)&~rich(fred)))&
((happy(alice)<~>~creative(alice)))&
((~brave(alice)<~>happy(alice)))&
((~strong(paul)|~old(paul)))&
((old(lucy)<~>~quiet(lucy))) | old(paul) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 173909248415647162697197
% SZS output start Proof for 173909248415647162697197
14. ! [X0] : ((old(X0) & ~creative(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p13]
24. ~old(paul) [input hypothesis]
61. ! [X0] : (((old(X0) & ~creative(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (~old(X0) | creative(X0)))) [nnf transformation 14]
62. ! [X0] : (((old(X0) & ~creative(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ~old(X0) | creative(X0))) [flattening 61]
117. old(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 62]
118. old(X0) | curious(X0) | curious(X0) [cnf transformation 62]
135. ~old(paul) [cnf transformation 24]
138. old(X0) | ~curious(X0) [duplicate literal removal 117]
139. old(X0) | curious(X0) [duplicate literal removal 118]
243. old(X0) [subsumption resolution 138,139]
281. $false [subsumption resolution 135,243]
% SZS output end Proof for 173909248415647162697197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is both not generous and wise.
Everyone who is not quiet is not old and vice versa.
Everyone who is calm or quiet is not patient and vice versa.
Everyone who is not calm or not strong is either strong or not humble.
If lucy is either not quiet or curious then someone is either creative or not rich.
Everyone who is either old or funny is both tall and funny.
If someone is either not calm or old then someone is not strong.
If someone is either humble or not happy then alice is curious or not happy and vice versa.
Everyone who is both not strong and not happy is curious or creative.
Everyone who is not humble or not old is not happy or calm.
If lucy is not quiet then someone is both not patient and tall and vice versa.
If lucy is both rich and humble then someone is both not old and not generous and vice versa.
If susan is either tall or not strong then someone is not tall or not calm.
If fred is either not creative or rich then lucy is tall and vice versa.
Everyone who is either brave or not strong is not creative.
Everyone who is both curious and strong is not strong and vice versa.
Someone is either not funny or creative.
Someone is happy or rich.
Someone is not kind.
Susan is either not funny or curious. | Susan is generous. | neutral | (![X]:(~happy(X)=>(~generous(X)&wise(X))))&
(![X]:(~quiet(X)<=>~old(X)))&
(![X]:((calm(X)|quiet(X))<=>~patient(X)))&
(![X]:((~calm(X)|~strong(X))=>(strong(X)<~>~humble(X))))&
(((~quiet(lucy)<~>curious(lucy)))=>(?[X]:((creative(X)<~>~rich(X)))))&
(![X]:((old(X)<~>funny(X))=>(tall(X)&funny(X))))&
((?[X]:((~calm(X)<~>old(X))))=>(?[X]:(~strong(X))))&
((?[X]:((humble(X)<~>~happy(X))))<=>((curious(alice)|~happy(alice))))&
(![X]:((~strong(X)&~happy(X))=>(curious(X)|creative(X))))&
(![X]:((~humble(X)|~old(X))=>(~happy(X)|calm(X))))&
((~quiet(lucy))<=>(?[X]:((~patient(X)&tall(X)))))&
(((rich(lucy)&humble(lucy)))<=>(?[X]:((~old(X)&~generous(X)))))&
(((tall(susan)<~>~strong(susan)))=>(?[X]:((~tall(X)|~calm(X)))))&
(((~creative(fred)<~>rich(fred)))<=>(tall(lucy)))&
(![X]:((brave(X)<~>~strong(X))=>~creative(X)))&
(![X]:((curious(X)&strong(X))<=>~strong(X)))&
(?[X]:((~funny(X)<~>creative(X))))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(~kind(X)))&
((~funny(susan)<~>curious(susan))) | generous(susan) | [] | null | 0 |
Everyone who is both wise and not funny is either not creative or not old. If someone is not rich or happy then alice is both kind and not patient and vice versa. If someone is either not funny or wise then john is happy or not rich and vice versa. If someone is old then someone is both not rich and not old. Everyone who is generous or not humble is either not kind or patient. If someone is both rich and not happy then mary is not creative or not rich. Everyone who is not rich or generous is both not creative and not generous. Everyone who is curious is not tall or not strong. If someone is both not creative and generous then someone is both not calm and tall and vice versa. Everyone who is quiet or humble is patient. Everyone who is quiet is old. Everyone who is not generous is rich or patient. If someone is not patient then mary is not patient or creative and vice versa. Everyone who is strong is old or tall and vice versa. Everyone who is not generous is not kind or quiet and vice versa. If fred is not curious or not quiet then john is not patient. Someone is both not kind and creative. John is either creative or patient. Someone is both tall and funny. Alice is calm. Susan is either not humble or not wise. | John is quiet. | contradiction | (![X]:((wise(X)&~funny(X))=>(~creative(X)<~>~old(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((kind(alice)&~patient(alice))))&
((?[X]:((~funny(X)<~>wise(X))))<=>((happy(john)|~rich(john))))&
((?[X]:(old(X)))=>(?[X]:((~rich(X)&~old(X)))))&
(![X]:((generous(X)|~humble(X))=>(~kind(X)<~>patient(X))))&
((?[X]:((rich(X)&~happy(X))))=>((~creative(mary)|~rich(mary))))&
(![X]:((~rich(X)|generous(X))=>(~creative(X)&~generous(X))))&
(![X]:(curious(X)=>(~tall(X)|~strong(X))))&
((?[X]:((~creative(X)&generous(X))))<=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((quiet(X)|humble(X))=>patient(X)))&
(![X]:(quiet(X)=>old(X)))&
(![X]:(~generous(X)=>(rich(X)|patient(X))))&
((?[X]:(~patient(X)))<=>((~patient(mary)|creative(mary))))&
(![X]:(strong(X)<=>(old(X)|tall(X))))&
(![X]:(~generous(X)<=>(~kind(X)|quiet(X))))&
(((~curious(fred)|~quiet(fred)))=>(~patient(john)))&
(?[X]:((~kind(X)&creative(X))))&
((creative(john)<~>patient(john)))&
(?[X]:((tall(X)&funny(X))))&
(calm(alice))&
((~humble(susan)<~>~wise(susan))) | quiet(john) | [
"p1",
"p3",
"p6",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5889618530534228548929883
% SZS output start Proof for 5889618530534228548929883
2. ? [X0] : (happy(X0) | ~rich(X0)) <=> (~patient(alice) & kind(alice)) [input p1]
4. ? [X0] : old(X0) => ? [X0] : (~old(X0) & ~rich(X0)) [input p3]
7. ! [X0] : ((generous(X0) | ~rich(X0)) => (~generous(X0) & ~creative(X0))) [input p6]
10. ! [X0] : ((humble(X0) | quiet(X0)) => patient(X0)) [input p9]
11. ! [X0] : (quiet(X0) => old(X0)) [input p10]
15. ! [X0] : (~generous(X0) <=> (quiet(X0) | ~kind(X0))) [input p14]
22. quiet(john) [input hypothesis]
23. ? [X0] : old(X0) => ? [X1] : (~old(X1) & ~rich(X1)) [rectify 4]
28. ? [X1] : (~old(X1) & ~rich(X1)) | ! [X0] : ~old(X0) [ennf transformation 23]
32. ! [X0] : ((~generous(X0) & ~creative(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 7]
35. ! [X0] : (patient(X0) | (~humble(X0) & ~quiet(X0))) [ennf transformation 10]
36. ! [X0] : (old(X0) | ~quiet(X0)) [ennf transformation 11]
42. (? [X0] : (happy(X0) | ~rich(X0)) | (patient(alice) | ~kind(alice))) & ((~patient(alice) & kind(alice)) | ! [X0] : (~happy(X0) & rich(X0))) [nnf transformation 2]
43. (? [X0] : (happy(X0) | ~rich(X0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X0] : (~happy(X0) & rich(X0))) [flattening 42]
44. (? [X0] : (happy(X0) | ~rich(X0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X1] : (~happy(X1) & rich(X1))) [rectify 43]
45. ? [X0] : (happy(X0) | ~rich(X0)) => (happy(sK0) | ~rich(sK0)) [choice axiom]
46. ((happy(sK0) | ~rich(sK0)) | patient(alice) | ~kind(alice)) & ((~patient(alice) & kind(alice)) | ! [X1] : (~happy(X1) & rich(X1))) [skolemisation 44,45]
52. ? [X0] : (~old(X0) & ~rich(X0)) | ! [X1] : ~old(X1) [rectify 28]
53. ? [X0] : (~old(X0) & ~rich(X0)) => (~old(sK2) & ~rich(sK2)) [choice axiom]
54. (~old(sK2) & ~rich(sK2)) | ! [X1] : ~old(X1) [skolemisation 52,53]
66. ! [X0] : ((~generous(X0) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | generous(X0))) [nnf transformation 15]
67. ! [X0] : ((~generous(X0) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | generous(X0))) [flattening 66]
76. kind(alice) | rich(X1) [cnf transformation 46]
78. ~patient(alice) | rich(X1) [cnf transformation 46]
87. ~rich(sK2) | ~old(X1) [cnf transformation 54]
97. ~generous(X0) | ~generous(X0) [cnf transformation 32]
103. ~quiet(X0) | patient(X0) [cnf transformation 35]
105. ~quiet(X0) | old(X0) [cnf transformation 36]
112. quiet(X0) | ~kind(X0) | generous(X0) [cnf transformation 67]
126. quiet(john) [cnf transformation 22]
127. ~generous(X0) [duplicate literal removal 97]
129. 1 <=> kind(alice) [avatar definition]
130. kind(alice) <- (1) [avatar component clause 129]
133. 2 <=> patient(alice) [avatar definition]
134. ~patient(alice) <- (~2) [avatar component clause 133]
150. 6 <=> ! [X1] : rich(X1) [avatar definition]
151. rich(X1) <- (6) [avatar component clause 150]
152. 6 | ~2 [avatar split clause 78,133,150]
154. 6 | 1 [avatar split clause 76,129,150]
184. 13 <=> ! [X1] : ~old(X1) [avatar definition]
185. ~old(X1) <- (13) [avatar component clause 184]
192. 15 <=> rich(sK2) [avatar definition]
194. ~rich(sK2) <- (~15) [avatar component clause 192]
195. 13 | ~15 [avatar split clause 87,192,184]
224. ~kind(X0) | quiet(X0) [subsumption resolution 112,127]
259. $false <- (6, ~15) [resolution 194,151]
260. ~6 | 15 [avatar contradiction clause 259]
265. old(john) [resolution 105,126]
267. $false <- (13) [subsumption resolution 265,185]
268. ~13 [avatar contradiction clause 267]
285. quiet(alice) <- (1) [resolution 224,130]
289. patient(alice) <- (1) [resolution 285,103]
290. $false <- (1, ~2) [subsumption resolution 289,134]
291. ~1 | 2 [avatar contradiction clause 290]
292. $false [avatar sat refutation 152,154,195,260,268,291]
% SZS output end Proof for 5889618530534228548929883
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not old then john is humble or not brave.
Everyone who is either not tall or generous is happy.
If alice is either not old or tall then alice is either not creative or not calm.
Everyone who is wise or strong is not quiet or quiet.
If someone is wise or brave then alice is either not curious or funny.
Everyone who is both not brave and not curious is either not curious or strong and vice versa.
If mary is either curious or happy then alice is curious or not happy.
Everyone who is either not humble or generous is not humble or creative.
Everyone who is both not tall and not strong is not happy or calm and vice versa.
If someone is either funny or not strong then someone is curious or not patient.
If someone is both not humble and curious then someone is both happy and not curious.
Everyone who is either creative or generous is either not creative or not happy and vice versa.
If someone is generous or curious then someone is either calm or generous.
Everyone who is happy is either not strong or strong.
If someone is both quiet and not patient then someone is both not generous and strong and vice versa.
Everyone who is tall or calm is both brave and not kind.
Alice is strong.
Someone is tall or not tall.
Someone is both not curious and generous.
Someone is both generous and not patient.
Lucy is calm.
Someone is not kind or wise.
Someone is both happy and kind. | Alice is happy. | entailment | ((~old(alice))=>((humble(john)|~brave(john))))&
(![X]:((~tall(X)<~>generous(X))=>happy(X)))&
(((~old(alice)<~>tall(alice)))=>((~creative(alice)<~>~calm(alice))))&
(![X]:((wise(X)|strong(X))=>(~quiet(X)|quiet(X))))&
((?[X]:((wise(X)|brave(X))))=>((~curious(alice)<~>funny(alice))))&
(![X]:((~brave(X)&~curious(X))<=>(~curious(X)<~>strong(X))))&
(((curious(mary)<~>happy(mary)))=>((curious(alice)|~happy(alice))))&
(![X]:((~humble(X)<~>generous(X))=>(~humble(X)|creative(X))))&
(![X]:((~tall(X)&~strong(X))<=>(~happy(X)|calm(X))))&
((?[X]:((funny(X)<~>~strong(X))))=>(?[X]:((curious(X)|~patient(X)))))&
((?[X]:((~humble(X)&curious(X))))=>(?[X]:((happy(X)&~curious(X)))))&
(![X]:((creative(X)<~>generous(X))<=>(~creative(X)<~>~happy(X))))&
((?[X]:((generous(X)|curious(X))))=>(?[X]:((calm(X)<~>generous(X)))))&
(![X]:(happy(X)=>(~strong(X)<~>strong(X))))&
((?[X]:((quiet(X)&~patient(X))))<=>(?[X]:((~generous(X)&strong(X)))))&
(![X]:((tall(X)|calm(X))=>(brave(X)&~kind(X))))&
(strong(alice))&
(?[X]:((tall(X)|~tall(X))))&
(?[X]:((~curious(X)&generous(X))))&
(?[X]:((generous(X)&~patient(X))))&
(calm(lucy))&
(?[X]:((~kind(X)|wise(X))))&
(?[X]:((happy(X)&kind(X)))) | happy(alice) | [
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8011164176499943311459509
% SZS output start Proof for 8011164176499943311459509
9. ! [X0] : ((~strong(X0) & ~tall(X0)) <=> (calm(X0) | ~happy(X0))) [input p8]
17. strong(alice) [input p16]
24. ~happy(alice) [input hypothesis]
52. ! [X0] : (((~strong(X0) & ~tall(X0)) | (~calm(X0) & happy(X0))) & ((calm(X0) | ~happy(X0)) | (strong(X0) | tall(X0)))) [nnf transformation 9]
53. ! [X0] : (((~strong(X0) & ~tall(X0)) | (~calm(X0) & happy(X0))) & (calm(X0) | ~happy(X0) | strong(X0) | tall(X0))) [flattening 52]
108. ~strong(X0) | happy(X0) [cnf transformation 53]
136. strong(alice) [cnf transformation 17]
146. ~happy(alice) [cnf transformation 24]
211. 13 <=> happy(alice) [avatar definition]
213. ~happy(alice) <- (~13) [avatar component clause 211]
300. ~13 [avatar split clause 146,211]
306. happy(alice) [resolution 108,136]
307. $false <- (~13) [subsumption resolution 306,213]
308. 13 [avatar contradiction clause 307]
309. $false [avatar sat refutation 300,308]
% SZS output end Proof for 8011164176499943311459509
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or curious is kind.
Everyone who is not humble or curious is generous.
Everyone who is not quiet is not strong and vice versa.
Everyone who is not happy is both not kind and not calm and vice versa.
If john is not curious or not humble then someone is both calm and not quiet.
Everyone who is not calm or funny is not funny and vice versa.
If paul is not creative or funny then someone is not calm or not happy.
Everyone who is not calm or old is either not patient or tall.
Everyone who is patient or not tall is patient or funny.
If someone is either curious or not funny then susan is either not quiet or not old and vice versa.
If someone is strong then someone is not funny and vice versa.
If someone is either not happy or creative then susan is not wise or generous and vice versa.
If someone is both tall and not curious then someone is not tall and vice versa.
Everyone who is either creative or not tall is humble or not creative.
If paul is not generous then someone is not old.
Everyone who is both creative and not quiet is either not old or creative and vice versa.
Paul is strong.
Mary is either strong or not quiet.
Susan is calm or not brave.
Mary is either calm or not quiet.
Lucy is either wise or creative. | Susan is generous. | entailment | (![X]:((~wise(X)|curious(X))=>kind(X)))&
(![X]:((~humble(X)|curious(X))=>generous(X)))&
(![X]:(~quiet(X)<=>~strong(X)))&
(![X]:(~happy(X)<=>(~kind(X)&~calm(X))))&
(((~curious(john)|~humble(john)))=>(?[X]:((calm(X)&~quiet(X)))))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(((~creative(paul)|funny(paul)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~calm(X)|old(X))=>(~patient(X)<~>tall(X))))&
(![X]:((patient(X)|~tall(X))=>(patient(X)|funny(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>((~quiet(susan)<~>~old(susan))))&
((?[X]:(strong(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~happy(X)<~>creative(X))))<=>((~wise(susan)|generous(susan))))&
((?[X]:((tall(X)&~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>~tall(X))=>(humble(X)|~creative(X))))&
((~generous(paul))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)<~>creative(X))))&
(strong(paul))&
((strong(mary)<~>~quiet(mary)))&
((calm(susan)|~brave(susan)))&
((calm(mary)<~>~quiet(mary)))&
((wise(lucy)<~>creative(lucy))) | generous(susan) | [
"p1",
"p5",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4291675761470321854561945
% SZS output start Proof for 4291675761470321854561945
2. ! [X0] : ((curious(X0) | ~humble(X0)) => generous(X0)) [input p1]
6. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p5]
8. ! [X0] : ((old(X0) | ~calm(X0)) => (~patient(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((~tall(X0) | patient(X0)) => (funny(X0) | patient(X0))) [input p8]
13. ? [X0] : (~curious(X0) & tall(X0)) <=> ? [X0] : ~tall(X0) [input p12]
22. ~generous(susan) [input hypothesis]
24. ? [X0] : (~curious(X0) & tall(X0)) <=> ? [X1] : ~tall(X1) [rectify 13]
26. ! [X0] : (curious(X0) => generous(X0)) [pure predicate removal 2]
30. ! [X0] : (generous(X0) | ~curious(X0)) [ennf transformation 26]
33. ! [X0] : ((~patient(X0) <~> tall(X0)) | (~old(X0) & calm(X0))) [ennf transformation 8]
34. ! [X0] : ((funny(X0) | patient(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 9]
35. ! [X0] : (funny(X0) | patient(X0) | (tall(X0) & ~patient(X0))) [flattening 34]
42. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 6]
43. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 42]
46. ! [X0] : (((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | (~old(X0) & calm(X0))) [nnf transformation 33]
61. (? [X0] : (~curious(X0) & tall(X0)) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : (curious(X0) | ~tall(X0))) [nnf transformation 24]
62. (? [X0] : (~curious(X0) & tall(X0)) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : (curious(X3) | ~tall(X3))) [rectify 61]
63. ? [X0] : (~curious(X0) & tall(X0)) => (~curious(sK6) & tall(sK6)) [choice axiom]
64. ? [X2] : ~tall(X2) => ~tall(sK7) [choice axiom]
65. ((~curious(sK6) & tall(sK6)) | ! [X1] : tall(X1)) & (~tall(sK7) | ! [X3] : (curious(X3) | ~tall(X3))) [skolemisation 62,64,63]
75. ~curious(X0) | generous(X0) [cnf transformation 30]
84. ~funny(X0) | ~funny(X0) [cnf transformation 43]
85. funny(X0) | ~calm(X0) | funny(X0) [cnf transformation 43]
88. ~patient(X0) | tall(X0) | calm(X0) [cnf transformation 46]
93. funny(X0) | patient(X0) | tall(X0) [cnf transformation 35]
110. ~tall(sK7) | curious(X3) | ~tall(X3) [cnf transformation 65]
111. tall(sK6) | tall(X1) [cnf transformation 65]
112. ~curious(sK6) | tall(X1) [cnf transformation 65]
127. ~generous(susan) [cnf transformation 22]
130. ~funny(X0) [duplicate literal removal 84]
131. ~calm(X0) | funny(X0) [duplicate literal removal 85]
156. tall(X0) | patient(X0) [subsumption resolution 93,130]
175. 9 <=> ! [X1] : curious(X1) [avatar definition]
176. curious(X1) <- (9) [avatar component clause 175]
182. 10 <=> generous(susan) [avatar definition]
184. ~generous(susan) <- (~10) [avatar component clause 182]
210. 16 <=> ! [X1] : tall(X1) [avatar definition]
211. tall(X1) <- (16) [avatar component clause 210]
213. 17 <=> curious(sK6) [avatar definition]
216. 16 | ~17 [avatar split clause 112,213,210]
218. 18 <=> tall(sK6) [avatar definition]
220. tall(sK6) <- (18) [avatar component clause 218]
221. 16 | 18 [avatar split clause 111,218,210]
223. 19 <=> ! [X3] : (curious(X3) | ~tall(X3)) [avatar definition]
224. ~tall(X3) | curious(X3) <- (19) [avatar component clause 223]
226. 20 <=> tall(sK7) [avatar definition]
228. ~tall(sK7) <- (~20) [avatar component clause 226]
229. 19 | ~20 [avatar split clause 110,226,223]
260. ~10 [avatar split clause 127,182]
302. curious(X0) <- (16, 19) [resolution 224,211]
305. 9 | ~16 | ~19 [avatar split clause 302,223,210,175]
313. patient(sK7) <- (~20) [resolution 228,156]
330. tall(sK7) | calm(sK7) <- (~20) [resolution 313,88]
332. calm(sK7) <- (~20) [subsumption resolution 330,228]
341. funny(sK7) <- (~20) [resolution 332,131]
343. $false <- (~20) [subsumption resolution 341,130]
344. 20 [avatar contradiction clause 343]
348. curious(sK6) <- (18, 19) [resolution 224,220]
352. 17 | ~18 | ~19 [avatar split clause 348,223,218,213]
361. generous(X0) <- (9) [resolution 176,75]
371. $false <- (9, ~10) [resolution 361,184]
372. ~9 | 10 [avatar contradiction clause 371]
373. $false [avatar sat refutation 216,221,229,260,305,344,352,372]
% SZS output end Proof for 4291675761470321854561945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is creative.
If someone is either not rich or quiet then paul is patient.
If mary is either not generous or not creative then john is both rich and funny.
If alice is not funny or not rich then someone is both not happy and not tall.
If someone is either not strong or not curious then someone is both not quiet and not old and vice versa.
If lucy is either calm or humble then someone is calm or not strong.
Everyone who is either strong or curious is either not generous or not calm.
Everyone who is both curious and not patient is either rich or curious and vice versa.
Everyone who is either happy or not calm is either not rich or quiet.
If someone is either wise or creative then someone is both not strong and not quiet.
Everyone who is either patient or not calm is either not tall or not strong and vice versa.
Everyone who is both not humble and quiet is not old or not rich.
Everyone who is both patient and curious is either kind or brave and vice versa.
Everyone who is both not strong and not rich is not brave or strong and vice versa.
If susan is either funny or generous then mary is tall or not calm.
If someone is not tall then fred is not patient or calm and vice versa.
John is not happy.
Someone is both not wise and calm.
Someone is tall or not patient.
Susan is not generous.
Mary is patient.
Someone is not kind.
Alice is either kind or funny.
Paul is calm. | Mary is strong. | contradiction | (![X]:(rich(X)=>creative(X)))&
((?[X]:((~rich(X)<~>quiet(X))))=>(patient(paul)))&
(((~generous(mary)<~>~creative(mary)))=>((rich(john)&funny(john))))&
(((~funny(alice)|~rich(alice)))=>(?[X]:((~happy(X)&~tall(X)))))&
((?[X]:((~strong(X)<~>~curious(X))))<=>(?[X]:((~quiet(X)&~old(X)))))&
(((calm(lucy)<~>humble(lucy)))=>(?[X]:((calm(X)|~strong(X)))))&
(![X]:((strong(X)<~>curious(X))=>(~generous(X)<~>~calm(X))))&
(![X]:((curious(X)&~patient(X))<=>(rich(X)<~>curious(X))))&
(![X]:((happy(X)<~>~calm(X))=>(~rich(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>creative(X))))=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:((patient(X)<~>~calm(X))<=>(~tall(X)<~>~strong(X))))&
(![X]:((~humble(X)&quiet(X))=>(~old(X)|~rich(X))))&
(![X]:((patient(X)&curious(X))<=>(kind(X)<~>brave(X))))&
(![X]:((~strong(X)&~rich(X))<=>(~brave(X)|strong(X))))&
(((funny(susan)<~>generous(susan)))=>((tall(mary)|~calm(mary))))&
((?[X]:(~tall(X)))<=>((~patient(fred)|calm(fred))))&
(~happy(john))&
(?[X]:((~wise(X)&calm(X))))&
(?[X]:((tall(X)|~patient(X))))&
(~generous(susan))&
(patient(mary))&
(?[X]:(~kind(X)))&
((kind(alice)<~>funny(alice)))&
(calm(paul)) | strong(mary) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6262376717585822044902363
% SZS output start Proof for 6262376717585822044902363
14. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> (strong(X0) | ~brave(X0))) [input p13]
25. strong(mary) [input hypothesis]
63. ! [X0] : (((~rich(X0) & ~strong(X0)) | (~strong(X0) & brave(X0))) & ((strong(X0) | ~brave(X0)) | (rich(X0) | strong(X0)))) [nnf transformation 14]
64. ! [X0] : (((~rich(X0) & ~strong(X0)) | (~strong(X0) & brave(X0))) & (strong(X0) | ~brave(X0) | rich(X0) | strong(X0))) [flattening 63]
132. ~strong(X0) | ~strong(X0) [cnf transformation 64]
150. strong(mary) [cnf transformation 25]
152. ~strong(X0) [duplicate literal removal 132]
328. $false [subsumption resolution 150,152]
% SZS output end Proof for 6262376717585822044902363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either old or calm then someone is not patient or not kind and vice versa.
If someone is both old and not generous then someone is generous or tall.
If lucy is humble then someone is generous or not curious and vice versa.
Everyone who is rich or humble is strong and vice versa.
Everyone who is not happy is both funny and not quiet.
If mary is either not creative or brave then someone is rich or old and vice versa.
Everyone who is both old and brave is not creative or generous.
Everyone who is both not rich and curious is both curious and not humble and vice versa.
If someone is both patient and brave then susan is not funny.
If john is both kind and not kind then someone is old and vice versa.
Everyone who is either not quiet or curious is both patient and not funny and vice versa.
Everyone who is either rich or not strong is wise or patient and vice versa.
Everyone who is curious is not wise or not strong.
Everyone who is not tall or not generous is both tall and not old and vice versa.
Everyone who is tall or generous is both not generous and rich.
Alice is either happy or not strong.
Someone is funny or not kind.
John is old or not happy.
John is not old.
Lucy is both creative and calm. | Alice is not strong. | contradiction | (((old(paul)<~>calm(paul)))<=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((old(X)&~generous(X))))=>(?[X]:((generous(X)|tall(X)))))&
((humble(lucy))<=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((rich(X)|humble(X))<=>strong(X)))&
(![X]:(~happy(X)=>(funny(X)&~quiet(X))))&
(((~creative(mary)<~>brave(mary)))<=>(?[X]:((rich(X)|old(X)))))&
(![X]:((old(X)&brave(X))=>(~creative(X)|generous(X))))&
(![X]:((~rich(X)&curious(X))<=>(curious(X)&~humble(X))))&
((?[X]:((patient(X)&brave(X))))=>(~funny(susan)))&
(((kind(john)&~kind(john)))<=>(?[X]:(old(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>(patient(X)&~funny(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(wise(X)|patient(X))))&
(![X]:(curious(X)=>(~wise(X)|~strong(X))))&
(![X]:((~tall(X)|~generous(X))<=>(tall(X)&~old(X))))&
(![X]:((tall(X)|generous(X))=>(~generous(X)&rich(X))))&
((happy(alice)<~>~strong(alice)))&
(?[X]:((funny(X)|~kind(X))))&
((old(john)|~happy(john)))&
(~old(john))&
((creative(lucy)&calm(lucy))) | ~strong(alice) | [
"p3",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1894348297691863740459127
% SZS output start Proof for 1894348297691863740459127
4. ! [X0] : ((humble(X0) | rich(X0)) <=> strong(X0)) [input p3]
14. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~old(X0) & tall(X0))) [input p13]
15. ! [X0] : ((generous(X0) | tall(X0)) => (rich(X0) & ~generous(X0))) [input p14]
21. ~strong(alice) [input hypothesis]
30. ! [X0] : ((rich(X0) & ~generous(X0)) | (~generous(X0) & ~tall(X0))) [ennf transformation 15]
42. ! [X0] : (((humble(X0) | rich(X0)) | ~strong(X0)) & (strong(X0) | (~humble(X0) & ~rich(X0)))) [nnf transformation 4]
43. ! [X0] : ((humble(X0) | rich(X0) | ~strong(X0)) & (strong(X0) | (~humble(X0) & ~rich(X0)))) [flattening 42]
59. ! [X0] : (((~generous(X0) | ~tall(X0)) | (old(X0) | ~tall(X0))) & ((~old(X0) & tall(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 14]
60. ! [X0] : ((~generous(X0) | ~tall(X0) | old(X0) | ~tall(X0)) & ((~old(X0) & tall(X0)) | (generous(X0) & tall(X0)))) [flattening 59]
74. ~rich(X0) | strong(X0) [cnf transformation 43]
107. tall(X0) | tall(X0) [cnf transformation 60]
114. rich(X0) | ~tall(X0) [cnf transformation 30]
123. ~strong(alice) [cnf transformation 21]
125. tall(X0) [duplicate literal removal 107]
233. rich(X0) [subsumption resolution 114,125]
242. 25 <=> strong(alice) [avatar definition]
243. ~strong(alice) <- (~25) [avatar component clause 242]
266. ~25 [avatar split clause 123,242]
277. strong(X0) [resolution 74,233]
279. $false <- (~25) [resolution 277,243]
280. 25 [avatar contradiction clause 279]
281. $false [avatar sat refutation 266,280]
% SZS output end Proof for 1894348297691863740459127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either tall or quiet is both not tall and not funny and vice versa.
If someone is both not wise and not strong then paul is not humble or old.
If susan is either humble or not brave then paul is kind or tall and vice versa.
Everyone who is either not brave or tall is not happy or not tall.
Everyone who is patient or rich is either not brave or not rich.
Everyone who is not rich or generous is both not rich and not tall.
Everyone who is both calm and not tall is either patient or brave and vice versa.
If fred is wise or not funny then someone is either not quiet or not tall.
Everyone who is either not kind or not wise is both not tall and generous and vice versa.
If someone is either not wise or wise then alice is rich or not happy.
Everyone who is both not kind and curious is either curious or quiet.
If someone is rich or not old then john is both patient and not curious.
If paul is both not strong and calm then someone is strong or rich.
Everyone who is not rich or old is not old or not rich and vice versa.
Everyone who is happy or funny is both happy and wise and vice versa.
If fred is curious or tall then someone is not tall and vice versa.
Someone is generous or not tall.
Mary is both not happy and wise.
John is creative.
John is both kind and curious.
Someone is not curious.
John is either tall or humble.
Fred is both not humble and old. | John is curious. | entailment | (![X]:((tall(X)<~>quiet(X))<=>(~tall(X)&~funny(X))))&
((?[X]:((~wise(X)&~strong(X))))=>((~humble(paul)|old(paul))))&
(((humble(susan)<~>~brave(susan)))<=>((kind(paul)|tall(paul))))&
(![X]:((~brave(X)<~>tall(X))=>(~happy(X)|~tall(X))))&
(![X]:((patient(X)|rich(X))=>(~brave(X)<~>~rich(X))))&
(![X]:((~rich(X)|generous(X))=>(~rich(X)&~tall(X))))&
(![X]:((calm(X)&~tall(X))<=>(patient(X)<~>brave(X))))&
(((wise(fred)|~funny(fred)))=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~tall(X)&generous(X))))&
((?[X]:((~wise(X)<~>wise(X))))=>((rich(alice)|~happy(alice))))&
(![X]:((~kind(X)&curious(X))=>(curious(X)<~>quiet(X))))&
((?[X]:((rich(X)|~old(X))))=>((patient(john)&~curious(john))))&
(((~strong(paul)&calm(paul)))=>(?[X]:((strong(X)|rich(X)))))&
(![X]:((~rich(X)|old(X))<=>(~old(X)|~rich(X))))&
(![X]:((happy(X)|funny(X))<=>(happy(X)&wise(X))))&
(((curious(fred)|tall(fred)))<=>(?[X]:(~tall(X))))&
(?[X]:((generous(X)|~tall(X))))&
((~happy(mary)&wise(mary)))&
(creative(john))&
((kind(john)&curious(john)))&
(?[X]:(~curious(X)))&
((tall(john)<~>humble(john)))&
((~humble(fred)&old(fred))) | curious(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7560475720444179569442476
% SZS output start Proof for 7560475720444179569442476
20. curious(john) & kind(john) [input p19]
24. ~curious(john) [input hypothesis]
129. curious(john) [cnf transformation 20]
135. ~curious(john) [cnf transformation 24]
213. 14 <=> curious(john) [avatar definition]
248. 14 [avatar split clause 129,213]
259. ~14 [avatar split clause 135,213]
260. $false [avatar sat refutation 248,259]
% SZS output end Proof for 7560475720444179569442476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not generous or kind then fred is either not quiet or creative. If mary is both not generous and wise then someone is either not kind or not calm. Everyone who is not patient or not generous is not brave or creative and vice versa. Everyone who is brave or calm is both quiet and old and vice versa. Everyone who is both kind and rich is either tall or not creative. Everyone who is both strong and curious is both not kind and generous. Everyone who is not quiet is both generous and brave. If lucy is not quiet or not rich then someone is both humble and kind. Everyone who is generous is both brave and not happy and vice versa. Everyone who is calm or not old is creative. If john is generous then someone is not strong. If alice is both calm and not kind then someone is not calm and vice versa. Everyone who is both not tall and not curious is funny or not kind. If alice is not funny or generous then fred is not funny or not kind. If lucy is funny then someone is not old. If someone is curious then someone is both calm and not wise. Paul is not curious or creative. John is not happy or not funny. Fred is creative. Lucy is either not brave or old. Paul is either brave or humble. Someone is humble or not wise. Paul is both not funny and patient. John is curious. | John is not curious. | contradiction | (((~generous(alice)|kind(alice)))=>((~quiet(fred)<~>creative(fred))))&
(((~generous(mary)&wise(mary)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:((~patient(X)|~generous(X))<=>(~brave(X)|creative(X))))&
(![X]:((brave(X)|calm(X))<=>(quiet(X)&old(X))))&
(![X]:((kind(X)&rich(X))=>(tall(X)<~>~creative(X))))&
(![X]:((strong(X)&curious(X))=>(~kind(X)&generous(X))))&
(![X]:(~quiet(X)=>(generous(X)&brave(X))))&
(((~quiet(lucy)|~rich(lucy)))=>(?[X]:((humble(X)&kind(X)))))&
(![X]:(generous(X)<=>(brave(X)&~happy(X))))&
(![X]:((calm(X)|~old(X))=>creative(X)))&
((generous(john))=>(?[X]:(~strong(X))))&
(((calm(alice)&~kind(alice)))<=>(?[X]:(~calm(X))))&
(![X]:((~tall(X)&~curious(X))=>(funny(X)|~kind(X))))&
(((~funny(alice)|generous(alice)))=>((~funny(fred)|~kind(fred))))&
((funny(lucy))=>(?[X]:(~old(X))))&
((?[X]:(curious(X)))=>(?[X]:((calm(X)&~wise(X)))))&
((~curious(paul)|creative(paul)))&
((~happy(john)|~funny(john)))&
(creative(fred))&
((~brave(lucy)<~>old(lucy)))&
((brave(paul)<~>humble(paul)))&
(?[X]:((humble(X)|~wise(X))))&
((~funny(paul)&patient(paul)))&
(curious(john)) | ~curious(john) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7273709313443614752629116
% SZS output start Proof for 7273709313443614752629116
24. curious(john) [input p23]
25. ~curious(john) [input hypothesis]
109. curious(john) [cnf transformation 24]
110. ~curious(john) [cnf transformation 25]
229. $false [subsumption resolution 110,109]
% SZS output end Proof for 7273709313443614752629116
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not generous is not happy or not old.
If paul is both brave and not kind then paul is not kind.
Everyone who is both not generous and funny is generous or not brave and vice versa.
If someone is not old or tall then someone is both not kind and not humble.
Everyone who is both calm and not calm is not funny or not old and vice versa.
If john is either not rich or not quiet then someone is both calm and not strong and vice versa.
If someone is humble or not patient then someone is both happy and not old.
Everyone who is either wise or generous is not curious.
Everyone who is either humble or quiet is not tall.
Everyone who is calm or humble is humble or not strong.
If fred is both strong and brave then mary is rich and vice versa.
If mary is not funny or not generous then susan is either humble or not generous.
Everyone who is either not kind or not humble is either not rich or not funny and vice versa.
Everyone who is both not tall and not brave is happy.
Lucy is either not quiet or not creative.
Someone is both funny and old.
Someone is kind.
Paul is funny or not calm.
Mary is calm or not patient. | Paul is happy. | contradiction | (![X]:((~rich(X)|~generous(X))=>(~happy(X)|~old(X))))&
(((brave(paul)&~kind(paul)))=>(~kind(paul)))&
(![X]:((~generous(X)&funny(X))<=>(generous(X)|~brave(X))))&
((?[X]:((~old(X)|tall(X))))=>(?[X]:((~kind(X)&~humble(X)))))&
(![X]:((calm(X)&~calm(X))<=>(~funny(X)|~old(X))))&
(((~rich(john)<~>~quiet(john)))<=>(?[X]:((calm(X)&~strong(X)))))&
((?[X]:((humble(X)|~patient(X))))=>(?[X]:((happy(X)&~old(X)))))&
(![X]:((wise(X)<~>generous(X))=>~curious(X)))&
(![X]:((humble(X)<~>quiet(X))=>~tall(X)))&
(![X]:((calm(X)|humble(X))=>(humble(X)|~strong(X))))&
(((strong(fred)&brave(fred)))<=>(rich(mary)))&
(((~funny(mary)|~generous(mary)))=>((humble(susan)<~>~generous(susan))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:((~tall(X)&~brave(X))=>happy(X)))&
((~quiet(lucy)<~>~creative(lucy)))&
(?[X]:((funny(X)&old(X))))&
(?[X]:(kind(X)))&
((funny(paul)|~calm(paul)))&
((calm(mary)|~patient(mary))) | happy(paul) | [
"p0",
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 65854088426220735508050
% SZS output start Proof for 65854088426220735508050
1. ! [X0] : ((~generous(X0) | ~rich(X0)) => (~old(X0) | ~happy(X0))) [input p0]
3. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (~brave(X0) | generous(X0))) [input p2]
5. ! [X0] : ((~calm(X0) & calm(X0)) <=> (~old(X0) | ~funny(X0))) [input p4]
20. happy(paul) [input hypothesis]
24. ! [X0] : ((~old(X0) | ~happy(X0)) | (generous(X0) & rich(X0))) [ennf transformation 1]
25. ! [X0] : (~old(X0) | ~happy(X0) | (generous(X0) & rich(X0))) [flattening 24]
36. ! [X0] : (((funny(X0) & ~generous(X0)) | (brave(X0) & ~generous(X0))) & ((~brave(X0) | generous(X0)) | (~funny(X0) | generous(X0)))) [nnf transformation 3]
37. ! [X0] : (((funny(X0) & ~generous(X0)) | (brave(X0) & ~generous(X0))) & (~brave(X0) | generous(X0) | ~funny(X0) | generous(X0))) [flattening 36]
41. ! [X0] : (((~calm(X0) & calm(X0)) | (old(X0) & funny(X0))) & ((~old(X0) | ~funny(X0)) | (calm(X0) | ~calm(X0)))) [nnf transformation 5]
42. ! [X0] : (((~calm(X0) & calm(X0)) | (old(X0) & funny(X0))) & (~old(X0) | ~funny(X0) | calm(X0) | ~calm(X0))) [flattening 41]
61. ~old(X0) | ~happy(X0) | generous(X0) [cnf transformation 25]
64. ~generous(X0) | ~generous(X0) [cnf transformation 37]
74. calm(X0) | old(X0) [cnf transformation 42]
76. ~calm(X0) | old(X0) [cnf transformation 42]
114. happy(paul) [cnf transformation 20]
116. ~generous(X0) [duplicate literal removal 64]
127. 3 <=> ! [X1] : old(X1) [avatar definition]
128. old(X1) <- (3) [avatar component clause 127]
136. old(X0) [subsumption resolution 74,76]
137. 3 [avatar split clause 136,127]
243. ~happy(X0) | generous(X0) <- (3) [resolution 61,128]
244. ~happy(X0) <- (3) [subsumption resolution 243,116]
245. $false <- (3) [resolution 244,114]
246. ~3 [avatar contradiction clause 245]
247. $false [avatar sat refutation 137,246]
% SZS output end Proof for 65854088426220735508050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or quiet is either wise or not creative and vice versa.
Everyone who is either old or strong is strong and vice versa.
Everyone who is not curious or not creative is patient or not generous and vice versa.
Everyone who is rich or patient is not funny.
Everyone who is both not wise and not generous is funny and vice versa.
Everyone who is either not rich or humble is both not tall and quiet.
If someone is creative or not old then lucy is both not kind and wise and vice versa.
Everyone who is both creative and happy is both not kind and patient and vice versa.
If mary is either not rich or not creative then susan is not kind and vice versa.
If john is not funny then lucy is both tall and calm.
Everyone who is both generous and not brave is funny or calm and vice versa.
If someone is quiet then susan is not patient.
If lucy is both not patient and not brave then someone is humble or happy.
If susan is creative or not wise then john is rich or not rich.
If mary is either not kind or curious then someone is either old or creative.
Everyone who is brave or kind is either rich or not humble.
Susan is both happy and not kind.
Someone is either not curious or not creative.
Lucy is either not curious or wise.
Someone is not wise.
John is not strong.
Someone is curious or not happy.
Susan is not strong. | Mary is not quiet. | neutral | (![X]:((tall(X)<~>quiet(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((old(X)<~>strong(X))<=>strong(X)))&
(![X]:((~curious(X)|~creative(X))<=>(patient(X)|~generous(X))))&
(![X]:((rich(X)|patient(X))=>~funny(X)))&
(![X]:((~wise(X)&~generous(X))<=>funny(X)))&
(![X]:((~rich(X)<~>humble(X))=>(~tall(X)&quiet(X))))&
((?[X]:((creative(X)|~old(X))))<=>((~kind(lucy)&wise(lucy))))&
(![X]:((creative(X)&happy(X))<=>(~kind(X)&patient(X))))&
(((~rich(mary)<~>~creative(mary)))<=>(~kind(susan)))&
((~funny(john))=>((tall(lucy)&calm(lucy))))&
(![X]:((generous(X)&~brave(X))<=>(funny(X)|calm(X))))&
((?[X]:(quiet(X)))=>(~patient(susan)))&
(((~patient(lucy)&~brave(lucy)))=>(?[X]:((humble(X)|happy(X)))))&
(((creative(susan)|~wise(susan)))=>((rich(john)|~rich(john))))&
(((~kind(mary)<~>curious(mary)))=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:((brave(X)|kind(X))=>(rich(X)<~>~humble(X))))&
((happy(susan)&~kind(susan)))&
(?[X]:((~curious(X)<~>~creative(X))))&
((~curious(lucy)<~>wise(lucy)))&
(?[X]:(~wise(X)))&
(~strong(john))&
(?[X]:((curious(X)|~happy(X))))&
(~strong(susan)) | ~quiet(mary) | [] | null | 0 |
Everyone who is wise is both funny and not quiet and vice versa.
Everyone who is old or kind is humble or generous and vice versa.
Everyone who is either not wise or not patient is both not happy and wise and vice versa.
Everyone who is both rich and creative is either not humble or brave and vice versa.
Everyone who is not creative or quiet is not humble or not wise.
Everyone who is both quiet and old is rich or curious.
Everyone who is either strong or not quiet is either not generous or quiet and vice versa.
Everyone who is either not kind or curious is not calm or generous.
Everyone who is wise or calm is brave or not old.
Everyone who is either humble or curious is either kind or not wise and vice versa.
If john is both humble and not humble then someone is brave and vice versa.
Everyone who is not humble or not old is either calm or tall.
Everyone who is either not strong or not tall is funny or not rich and vice versa.
Everyone who is either generous or patient is patient and vice versa.
Everyone who is either tall or not generous is both old and wise.
Everyone who is brave or not calm is either funny or quiet and vice versa.
Someone is happy or rich.
Someone is curious or not wise.
Someone is curious or happy.
Fred is either happy or not strong. | John is tall. | entailment | (![X]:(wise(X)<=>(funny(X)&~quiet(X))))&
(![X]:((old(X)|kind(X))<=>(humble(X)|generous(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~happy(X)&wise(X))))&
(![X]:((rich(X)&creative(X))<=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)|quiet(X))=>(~humble(X)|~wise(X))))&
(![X]:((quiet(X)&old(X))=>(rich(X)|curious(X))))&
(![X]:((strong(X)<~>~quiet(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:((~kind(X)<~>curious(X))=>(~calm(X)|generous(X))))&
(![X]:((wise(X)|calm(X))=>(brave(X)|~old(X))))&
(![X]:((humble(X)<~>curious(X))<=>(kind(X)<~>~wise(X))))&
(((humble(john)&~humble(john)))<=>(?[X]:(brave(X))))&
(![X]:((~humble(X)|~old(X))=>(calm(X)<~>tall(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>(funny(X)|~rich(X))))&
(![X]:((generous(X)<~>patient(X))<=>patient(X)))&
(![X]:((tall(X)<~>~generous(X))=>(old(X)&wise(X))))&
(![X]:((brave(X)|~calm(X))<=>(funny(X)<~>quiet(X))))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:((curious(X)|~wise(X))))&
(?[X]:((curious(X)|happy(X))))&
((happy(fred)<~>~strong(fred))) | tall(john) | [
"p1",
"p8",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6743408512454199196946326
% SZS output start Proof for 6743408512454199196946326
2. ! [X0] : ((kind(X0) | old(X0)) <=> (generous(X0) | humble(X0))) [input p1]
9. ! [X0] : ((calm(X0) | wise(X0)) => (~old(X0) | brave(X0))) [input p8]
11. (~humble(john) & humble(john)) <=> ? [X0] : brave(X0) [input p10]
14. ! [X0] : ((generous(X0) <~> patient(X0)) <=> patient(X0)) [input p13]
15. ! [X0] : ((tall(X0) <~> ~generous(X0)) => (wise(X0) & old(X0))) [input p14]
21. ~tall(john) [input hypothesis]
28. ! [X0] : ((~old(X0) | brave(X0)) | (~calm(X0) & ~wise(X0))) [ennf transformation 9]
29. ! [X0] : (~old(X0) | brave(X0) | (~calm(X0) & ~wise(X0))) [flattening 28]
31. ! [X0] : ((wise(X0) & old(X0)) | (tall(X0) <=> ~generous(X0))) [ennf transformation 15]
34. ! [X0] : (((kind(X0) | old(X0)) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | (~kind(X0) & ~old(X0)))) [nnf transformation 2]
35. ! [X0] : ((kind(X0) | old(X0) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | (~kind(X0) & ~old(X0)))) [flattening 34]
43. ((~humble(john) & humble(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (humble(john) | ~humble(john))) [nnf transformation 11]
44. ((~humble(john) & humble(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | humble(john) | ~humble(john)) [flattening 43]
45. ((~humble(john) & humble(john)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | humble(john) | ~humble(john)) [rectify 44]
46. ? [X1] : brave(X1) => brave(sK0) [choice axiom]
47. ((~humble(john) & humble(john)) | ! [X0] : ~brave(X0)) & (brave(sK0) | humble(john) | ~humble(john)) [skolemisation 45,46]
51. ! [X0] : ((((~patient(X0) | ~generous(X0)) & (patient(X0) | generous(X0))) | ~patient(X0)) & (patient(X0) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0))))) [nnf transformation 14]
52. ! [X0] : ((wise(X0) & old(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) [nnf transformation 31]
65. ~old(X0) | humble(X0) | generous(X0) [cnf transformation 35]
94. ~old(X0) | brave(X0) | ~wise(X0) [cnf transformation 29]
106. ~humble(john) | ~brave(X0) [cnf transformation 47]
117. patient(X0) | patient(X0) | ~generous(X0) [cnf transformation 51]
120. ~patient(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 51]
122. old(X0) | tall(X0) | generous(X0) [cnf transformation 52]
124. wise(X0) | tall(X0) | generous(X0) [cnf transformation 52]
136. ~tall(john) [cnf transformation 21]
137. patient(X0) | ~generous(X0) [duplicate literal removal 117]
138. ~patient(X0) | ~generous(X0) [duplicate literal removal 120]
148. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
149. ~brave(X0) <- (1) [avatar component clause 148]
151. 2 <=> humble(john) [avatar definition]
154. 1 | ~2 [avatar split clause 106,151,148]
156. ~generous(X0) [subsumption resolution 137,138]
157. tall(X0) | wise(X0) [subsumption resolution 124,156]
158. tall(X0) | old(X0) [subsumption resolution 122,156]
196. wise(john) [resolution 157,136]
197. old(john) [resolution 158,136]
199. humble(john) | generous(john) [resolution 65,197]
200. humble(john) [subsumption resolution 199,156]
201. 2 [avatar split clause 200,151]
224. brave(john) | ~wise(john) [resolution 94,197]
225. ~wise(john) <- (1) [subsumption resolution 224,149]
226. $false <- (1) [subsumption resolution 225,196]
227. ~1 [avatar contradiction clause 226]
228. $false [avatar sat refutation 154,201,227]
% SZS output end Proof for 6743408512454199196946326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or tall is both calm and not calm and vice versa.
Everyone who is either not humble or rich is wise or not tall.
Everyone who is not quiet is either quiet or strong.
Everyone who is either not wise or funny is generous and vice versa.
Everyone who is either not generous or brave is either tall or not kind.
If someone is not old or not wise then lucy is both not patient and not funny.
If someone is not happy or curious then someone is both not brave and not creative.
Everyone who is either not generous or not humble is either not brave or not generous and vice versa.
Everyone who is either not wise or funny is both not brave and not curious and vice versa.
If lucy is either funny or not happy then alice is both patient and strong and vice versa.
If someone is both not patient and not kind then mary is not happy or strong and vice versa.
If someone is not curious then susan is brave and vice versa.
Everyone who is either generous or brave is either curious or rich.
Everyone who is wise is both not humble and not tall and vice versa.
If someone is creative or not quiet then alice is both tall and not calm.
Everyone who is both not old and calm is not wise.
Alice is not curious.
Someone is either tall or humble.
Mary is not tall.
Someone is not wise.
Mary is rich or creative.
Alice is both wise and not strong.
Someone is generous or happy.
John is not funny. | Lucy is not quiet. | contradiction | (![X]:((~funny(X)<~>tall(X))<=>(calm(X)&~calm(X))))&
(![X]:((~humble(X)<~>rich(X))=>(wise(X)|~tall(X))))&
(![X]:(~quiet(X)=>(quiet(X)<~>strong(X))))&
(![X]:((~wise(X)<~>funny(X))<=>generous(X)))&
(![X]:((~generous(X)<~>brave(X))=>(tall(X)<~>~kind(X))))&
((?[X]:((~old(X)|~wise(X))))=>((~patient(lucy)&~funny(lucy))))&
((?[X]:((~happy(X)|curious(X))))=>(?[X]:((~brave(X)&~creative(X)))))&
(![X]:((~generous(X)<~>~humble(X))<=>(~brave(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>funny(X))<=>(~brave(X)&~curious(X))))&
(((funny(lucy)<~>~happy(lucy)))<=>((patient(alice)&strong(alice))))&
((?[X]:((~patient(X)&~kind(X))))<=>((~happy(mary)|strong(mary))))&
((?[X]:(~curious(X)))<=>(brave(susan)))&
(![X]:((generous(X)<~>brave(X))=>(curious(X)<~>rich(X))))&
(![X]:(wise(X)<=>(~humble(X)&~tall(X))))&
((?[X]:((creative(X)|~quiet(X))))=>((tall(alice)&~calm(alice))))&
(![X]:((~old(X)&calm(X))=>~wise(X)))&
(~curious(alice))&
(?[X]:((tall(X)<~>humble(X))))&
(~tall(mary))&
(?[X]:(~wise(X)))&
((rich(mary)|creative(mary)))&
((wise(alice)&~strong(alice)))&
(?[X]:((generous(X)|happy(X))))&
(~funny(john)) | ~quiet(lucy) | [
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 799108001346392964998512
% SZS output start Proof for 799108001346392964998512
14. ! [X0] : (wise(X0) <=> (~tall(X0) & ~humble(X0))) [input p13]
15. ? [X0] : (~quiet(X0) | creative(X0)) => (~calm(alice) & tall(alice)) [input p14]
22. ~strong(alice) & wise(alice) [input p21]
25. ~quiet(lucy) [input hypothesis]
36. (~calm(alice) & tall(alice)) | ! [X0] : (quiet(X0) & ~creative(X0)) [ennf transformation 15]
61. ! [X0] : ((wise(X0) | (tall(X0) | humble(X0))) & ((~tall(X0) & ~humble(X0)) | ~wise(X0))) [nnf transformation 14]
62. ! [X0] : ((wise(X0) | tall(X0) | humble(X0)) & ((~tall(X0) & ~humble(X0)) | ~wise(X0))) [flattening 61]
126. ~wise(X0) | ~tall(X0) [cnf transformation 62]
129. tall(alice) | quiet(X0) [cnf transformation 36]
138. wise(alice) [cnf transformation 22]
142. ~quiet(lucy) [cnf transformation 25]
239. 19 <=> ! [X0] : quiet(X0) [avatar definition]
240. quiet(X0) <- (19) [avatar component clause 239]
251. 22 <=> tall(alice) [avatar definition]
253. tall(alice) <- (22) [avatar component clause 251]
254. 19 | 22 [avatar split clause 129,251,239]
285. $false <- (19) [resolution 240,142]
286. ~19 [avatar contradiction clause 285]
288. ~tall(alice) [resolution 126,138]
289. $false <- (22) [subsumption resolution 288,253]
290. ~22 [avatar contradiction clause 289]
291. $false [avatar sat refutation 254,286,290]
% SZS output end Proof for 799108001346392964998512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or wise is both quiet and wise and vice versa. If alice is either not creative or quiet then someone is both tall and not humble. If fred is not generous or generous then someone is not curious or calm. If someone is both not happy and not brave then mary is funny. If someone is not rich or not tall then susan is not patient and vice versa. Everyone who is not humble is old or kind. If someone is rich or not strong then someone is not creative. If someone is both not happy and calm then someone is kind or not happy and vice versa. Everyone who is brave or not tall is both not quiet and curious and vice versa. If someone is wise or not wise then someone is not kind or strong. Everyone who is kind or curious is either old or not brave and vice versa. Everyone who is brave is not old. Everyone who is not tall or old is both not generous and calm and vice versa. Everyone who is both happy and not kind is both happy and wise. Everyone who is not humble is creative or not kind and vice versa. If someone is not kind or not happy then someone is either funny or not old. Someone is creative or kind. Mary is either not calm or tall. Paul is both not calm and wise. Someone is not brave. Susan is not calm. Someone is either generous or not curious. | Paul is not tall. | contradiction | (![X]:((~old(X)|wise(X))<=>(quiet(X)&wise(X))))&
(((~creative(alice)<~>quiet(alice)))=>(?[X]:((tall(X)&~humble(X)))))&
(((~generous(fred)|generous(fred)))=>(?[X]:((~curious(X)|calm(X)))))&
((?[X]:((~happy(X)&~brave(X))))=>(funny(mary)))&
((?[X]:((~rich(X)|~tall(X))))<=>(~patient(susan)))&
(![X]:(~humble(X)=>(old(X)|kind(X))))&
((?[X]:((rich(X)|~strong(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~happy(X)&calm(X))))<=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((brave(X)|~tall(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:((~kind(X)|strong(X)))))&
(![X]:((kind(X)|curious(X))<=>(old(X)<~>~brave(X))))&
(![X]:(brave(X)=>~old(X)))&
(![X]:((~tall(X)|old(X))<=>(~generous(X)&calm(X))))&
(![X]:((happy(X)&~kind(X))=>(happy(X)&wise(X))))&
(![X]:(~humble(X)<=>(creative(X)|~kind(X))))&
((?[X]:((~kind(X)|~happy(X))))=>(?[X]:((funny(X)<~>~old(X)))))&
(?[X]:((creative(X)|kind(X))))&
((~calm(mary)<~>tall(mary)))&
((~calm(paul)&wise(paul)))&
(?[X]:(~brave(X)))&
(~calm(susan))&
(?[X]:((generous(X)<~>~curious(X)))) | ~tall(paul) | [
"p0",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8726318282922150152911426
% SZS output start Proof for 8726318282922150152911426
1. ! [X0] : ((wise(X0) | ~old(X0)) <=> (wise(X0) & quiet(X0))) [input p0]
9. ! [X0] : ((~tall(X0) | brave(X0)) <=> (curious(X0) & ~quiet(X0))) [input p8]
19. wise(paul) & ~calm(paul) [input p18]
23. ~tall(paul) [input hypothesis]
40. ! [X0] : (((wise(X0) | ~old(X0)) | (~wise(X0) | ~quiet(X0))) & ((wise(X0) & quiet(X0)) | (~wise(X0) & old(X0)))) [nnf transformation 1]
41. ! [X0] : ((wise(X0) | ~old(X0) | ~wise(X0) | ~quiet(X0)) & ((wise(X0) & quiet(X0)) | (~wise(X0) & old(X0)))) [flattening 40]
59. ! [X0] : (((~tall(X0) | brave(X0)) | (~curious(X0) | quiet(X0))) & ((curious(X0) & ~quiet(X0)) | (tall(X0) & ~brave(X0)))) [nnf transformation 9]
60. ! [X0] : ((~tall(X0) | brave(X0) | ~curious(X0) | quiet(X0)) & ((curious(X0) & ~quiet(X0)) | (tall(X0) & ~brave(X0)))) [flattening 59]
80. ~wise(X0) | quiet(X0) [cnf transformation 41]
102. ~quiet(X0) | tall(X0) [cnf transformation 60]
131. wise(paul) [cnf transformation 19]
136. ~tall(paul) [cnf transformation 23]
280. quiet(paul) [resolution 80,131]
283. tall(paul) [resolution 102,280]
284. $false [subsumption resolution 283,136]
% SZS output end Proof for 8726318282922150152911426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and happy is either generous or not rich.
Everyone who is both not patient and not curious is either not strong or generous.
If susan is not humble or calm then fred is either calm or not calm.
Everyone who is either quiet or funny is not brave or humble.
If someone is creative or brave then someone is both not rich and kind.
If john is either not brave or happy then someone is not wise and vice versa.
Everyone who is not strong or patient is both not tall and not happy and vice versa.
Everyone who is both wise and not tall is creative and vice versa.
If someone is either calm or curious then john is either not old or tall.
Everyone who is not tall or not calm is not generous or happy and vice versa.
Everyone who is either quiet or not generous is both not creative and not happy.
Everyone who is either creative or not calm is both not happy and happy.
Everyone who is both quiet and calm is funny or not calm and vice versa.
If someone is wise then someone is either creative or kind.
If someone is not humble then someone is happy or funny.
If mary is both kind and quiet then someone is either not patient or strong.
Susan is either not creative or strong.
Someone is either not strong or old.
Someone is not strong or tall.
Someone is both funny and not creative.
Someone is either not funny or wise.
Someone is not generous.
Alice is wise. | Alice is not tall. | contradiction | (![X]:((kind(X)&happy(X))=>(generous(X)<~>~rich(X))))&
(![X]:((~patient(X)&~curious(X))=>(~strong(X)<~>generous(X))))&
(((~humble(susan)|calm(susan)))=>((calm(fred)<~>~calm(fred))))&
(![X]:((quiet(X)<~>funny(X))=>(~brave(X)|humble(X))))&
((?[X]:((creative(X)|brave(X))))=>(?[X]:((~rich(X)&kind(X)))))&
(((~brave(john)<~>happy(john)))<=>(?[X]:(~wise(X))))&
(![X]:((~strong(X)|patient(X))<=>(~tall(X)&~happy(X))))&
(![X]:((wise(X)&~tall(X))<=>creative(X)))&
((?[X]:((calm(X)<~>curious(X))))=>((~old(john)<~>tall(john))))&
(![X]:((~tall(X)|~calm(X))<=>(~generous(X)|happy(X))))&
(![X]:((quiet(X)<~>~generous(X))=>(~creative(X)&~happy(X))))&
(![X]:((creative(X)<~>~calm(X))=>(~happy(X)&happy(X))))&
(![X]:((quiet(X)&calm(X))<=>(funny(X)|~calm(X))))&
((?[X]:(wise(X)))=>(?[X]:((creative(X)<~>kind(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((happy(X)|funny(X)))))&
(((kind(mary)&quiet(mary)))=>(?[X]:((~patient(X)<~>strong(X)))))&
((~creative(susan)<~>strong(susan)))&
(?[X]:((~strong(X)<~>old(X))))&
(?[X]:((~strong(X)|tall(X))))&
(?[X]:((funny(X)&~creative(X))))&
(?[X]:((~funny(X)<~>wise(X))))&
(?[X]:(~generous(X)))&
(wise(alice)) | ~tall(alice) | [
"p7",
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 731091362865482513140400
% SZS output start Proof for 731091362865482513140400
8. ! [X0] : ((~tall(X0) & wise(X0)) <=> creative(X0)) [input p7]
12. ! [X0] : ((creative(X0) <~> ~calm(X0)) => (happy(X0) & ~happy(X0))) [input p11]
13. ! [X0] : ((calm(X0) & quiet(X0)) <=> (~calm(X0) | funny(X0))) [input p12]
23. wise(alice) [input p22]
24. ~tall(alice) [input hypothesis]
39. ! [X0] : ((happy(X0) & ~happy(X0)) | (creative(X0) <=> ~calm(X0))) [ennf transformation 12]
55. ! [X0] : (((~tall(X0) & wise(X0)) | ~creative(X0)) & (creative(X0) | (tall(X0) | ~wise(X0)))) [nnf transformation 8]
56. ! [X0] : (((~tall(X0) & wise(X0)) | ~creative(X0)) & (creative(X0) | tall(X0) | ~wise(X0))) [flattening 55]
61. ! [X0] : ((happy(X0) & ~happy(X0)) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0)))) [nnf transformation 39]
62. ! [X0] : (((calm(X0) & quiet(X0)) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | (~calm(X0) | ~quiet(X0)))) [nnf transformation 13]
63. ! [X0] : (((calm(X0) & quiet(X0)) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | ~calm(X0) | ~quiet(X0))) [flattening 62]
103. ~wise(X0) | tall(X0) | creative(X0) [cnf transformation 56]
118. ~happy(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 61]
120. happy(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 61]
126. calm(X0) | calm(X0) [cnf transformation 63]
141. wise(alice) [cnf transformation 23]
142. ~tall(alice) [cnf transformation 24]
144. calm(X0) [duplicate literal removal 126]
201. ~creative(X0) | ~calm(X0) [subsumption resolution 118,120]
286. tall(alice) | creative(alice) [resolution 103,141]
287. creative(alice) [subsumption resolution 286,142]
288. ~calm(alice) [resolution 287,201]
290. $false [subsumption resolution 288,144]
% SZS output end Proof for 731091362865482513140400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either calm or not strong.
Everyone who is not calm is either not strong or not brave.
Everyone who is both happy and funny is generous or creative and vice versa.
Everyone who is both happy and not strong is old or not calm and vice versa.
Everyone who is generous is not rich or not happy and vice versa.
Everyone who is both curious and old is both humble and wise.
Everyone who is not quiet or strong is both generous and not generous.
If someone is funny or not kind then lucy is not brave or quiet.
If someone is either funny or brave then alice is kind or rich.
If someone is wise or not curious then alice is kind or generous.
If someone is rich or not calm then susan is either not creative or patient.
Everyone who is not curious is tall or kind.
If paul is not brave then someone is patient or wise and vice versa.
If john is both old and not happy then someone is old and vice versa.
Everyone who is not rich or calm is generous or not humble and vice versa.
Everyone who is both not funny and happy is both not generous and humble and vice versa.
Someone is not calm.
Fred is kind.
Lucy is rich.
Someone is not old or not curious.
Someone is not patient. | Alice is happy. | entailment | (![X]:(patient(X)=>(calm(X)<~>~strong(X))))&
(![X]:(~calm(X)=>(~strong(X)<~>~brave(X))))&
(![X]:((happy(X)&funny(X))<=>(generous(X)|creative(X))))&
(![X]:((happy(X)&~strong(X))<=>(old(X)|~calm(X))))&
(![X]:(generous(X)<=>(~rich(X)|~happy(X))))&
(![X]:((curious(X)&old(X))=>(humble(X)&wise(X))))&
(![X]:((~quiet(X)|strong(X))=>(generous(X)&~generous(X))))&
((?[X]:((funny(X)|~kind(X))))=>((~brave(lucy)|quiet(lucy))))&
((?[X]:((funny(X)<~>brave(X))))=>((kind(alice)|rich(alice))))&
((?[X]:((wise(X)|~curious(X))))=>((kind(alice)|generous(alice))))&
((?[X]:((rich(X)|~calm(X))))=>((~creative(susan)<~>patient(susan))))&
(![X]:(~curious(X)=>(tall(X)|kind(X))))&
((~brave(paul))<=>(?[X]:((patient(X)|wise(X)))))&
(((old(john)&~happy(john)))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)|calm(X))<=>(generous(X)|~humble(X))))&
(![X]:((~funny(X)&happy(X))<=>(~generous(X)&humble(X))))&
(?[X]:(~calm(X)))&
(kind(fred))&
(rich(lucy))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:(~patient(X))) | happy(alice) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 2497738093285575348859890
% SZS output start Proof for 2497738093285575348859890
3. ! [X0] : ((funny(X0) & happy(X0)) <=> (creative(X0) | generous(X0))) [input p2]
5. ! [X0] : (generous(X0) <=> (~happy(X0) | ~rich(X0))) [input p4]
22. ~happy(alice) [input hypothesis]
38. ! [X0] : (((funny(X0) & happy(X0)) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | (~funny(X0) | ~happy(X0)))) [nnf transformation 3]
39. ! [X0] : (((funny(X0) & happy(X0)) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | ~funny(X0) | ~happy(X0))) [flattening 38]
42. ! [X0] : ((generous(X0) | (happy(X0) & rich(X0))) & ((~happy(X0) | ~rich(X0)) | ~generous(X0))) [nnf transformation 5]
43. ! [X0] : ((generous(X0) | (happy(X0) & rich(X0))) & (~happy(X0) | ~rich(X0) | ~generous(X0))) [flattening 42]
67. happy(X0) | ~generous(X0) [cnf transformation 39]
78. generous(X0) | happy(X0) [cnf transformation 43]
102. ~happy(alice) [cnf transformation 22]
103. happy(X0) [subsumption resolution 78,67]
147. $false [subsumption resolution 102,103]
% SZS output end Proof for 2497738093285575348859890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is either not patient or not wise.
Everyone who is both not curious and humble is either not humble or not generous and vice versa.
Everyone who is both humble and creative is not calm and vice versa.
Everyone who is patient is both not wise and not patient.
Everyone who is both wise and kind is generous or not patient and vice versa.
If someone is both not wise and not calm then someone is both not old and not happy.
Everyone who is either not curious or humble is not humble.
If paul is not kind then lucy is both not strong and old.
Everyone who is either not calm or not old is creative or not brave.
Everyone who is both not old and not strong is both humble and brave.
If someone is either rich or quiet then alice is kind or not creative.
If someone is rich then mary is patient.
If someone is either not generous or not rich then paul is kind.
Everyone who is calm or strong is both not creative and humble and vice versa.
Everyone who is generous or not strong is both not calm and not rich.
If mary is not kind or curious then lucy is both not kind and wise and vice versa.
Fred is not generous or funny.
Mary is not patient.
Fred is both not generous and wise.
Mary is either not generous or calm.
Mary is either wise or not creative.
Someone is generous or not happy. | Fred is patient. | contradiction | (![X]:(~kind(X)=>(~patient(X)<~>~wise(X))))&
(![X]:((~curious(X)&humble(X))<=>(~humble(X)<~>~generous(X))))&
(![X]:((humble(X)&creative(X))<=>~calm(X)))&
(![X]:(patient(X)=>(~wise(X)&~patient(X))))&
(![X]:((wise(X)&kind(X))<=>(generous(X)|~patient(X))))&
((?[X]:((~wise(X)&~calm(X))))=>(?[X]:((~old(X)&~happy(X)))))&
(![X]:((~curious(X)<~>humble(X))=>~humble(X)))&
((~kind(paul))=>((~strong(lucy)&old(lucy))))&
(![X]:((~calm(X)<~>~old(X))=>(creative(X)|~brave(X))))&
(![X]:((~old(X)&~strong(X))=>(humble(X)&brave(X))))&
((?[X]:((rich(X)<~>quiet(X))))=>((kind(alice)|~creative(alice))))&
((?[X]:(rich(X)))=>(patient(mary)))&
((?[X]:((~generous(X)<~>~rich(X))))=>(kind(paul)))&
(![X]:((calm(X)|strong(X))<=>(~creative(X)&humble(X))))&
(![X]:((generous(X)|~strong(X))=>(~calm(X)&~rich(X))))&
(((~kind(mary)|curious(mary)))<=>((~kind(lucy)&wise(lucy))))&
((~generous(fred)|funny(fred)))&
(~patient(mary))&
((~generous(fred)&wise(fred)))&
((~generous(mary)<~>calm(mary)))&
((wise(mary)<~>~creative(mary)))&
(?[X]:((generous(X)|~happy(X)))) | patient(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 9002900531588607905864569
% SZS output start Proof for 9002900531588607905864569
4. ! [X0] : (patient(X0) => (~patient(X0) & ~wise(X0))) [input p3]
23. patient(fred) [input hypothesis]
29. ! [X0] : ((~patient(X0) & ~wise(X0)) | ~patient(X0)) [ennf transformation 4]
74. ~patient(X0) | ~patient(X0) [cnf transformation 29]
115. patient(fred) [cnf transformation 23]
117. ~patient(X0) [duplicate literal removal 74]
130. $false [subsumption resolution 115,117]
% SZS output end Proof for 9002900531588607905864569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and generous then someone is either wise or brave.
Everyone who is not funny or not calm is humble or not funny and vice versa.
If someone is both tall and not rich then alice is not creative and vice versa.
If someone is both rich and creative then someone is either generous or not creative.
Everyone who is not old is either wise or not quiet and vice versa.
Everyone who is not old or not happy is not rich.
Everyone who is kind is old and vice versa.
Everyone who is not patient or not rich is both not old and not quiet and vice versa.
If someone is both not quiet and not generous then someone is both kind and humble.
If fred is not humble then someone is not quiet or not kind and vice versa.
Everyone who is both rich and not creative is not kind and vice versa.
Everyone who is quiet or humble is not calm or not curious.
Everyone who is both not patient and wise is funny and vice versa.
If mary is not brave then someone is either not quiet or not brave.
Everyone who is not curious or old is not calm or wise.
Someone is both generous and not tall.
Someone is either strong or not brave.
Someone is either not patient or not brave.
Mary is not tall.
Paul is strong or not patient.
Someone is not humble. | Fred is kind. | entailment | ((?[X]:((brave(X)&generous(X))))=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((~funny(X)|~calm(X))<=>(humble(X)|~funny(X))))&
((?[X]:((tall(X)&~rich(X))))<=>(~creative(alice)))&
((?[X]:((rich(X)&creative(X))))=>(?[X]:((generous(X)<~>~creative(X)))))&
(![X]:(~old(X)<=>(wise(X)<~>~quiet(X))))&
(![X]:((~old(X)|~happy(X))=>~rich(X)))&
(![X]:(kind(X)<=>old(X)))&
(![X]:((~patient(X)|~rich(X))<=>(~old(X)&~quiet(X))))&
((?[X]:((~quiet(X)&~generous(X))))=>(?[X]:((kind(X)&humble(X)))))&
((~humble(fred))<=>(?[X]:((~quiet(X)|~kind(X)))))&
(![X]:((rich(X)&~creative(X))<=>~kind(X)))&
(![X]:((quiet(X)|humble(X))=>(~calm(X)|~curious(X))))&
(![X]:((~patient(X)&wise(X))<=>funny(X)))&
((~brave(mary))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
(![X]:((~curious(X)|old(X))=>(~calm(X)|wise(X))))&
(?[X]:((generous(X)&~tall(X))))&
(?[X]:((strong(X)<~>~brave(X))))&
(?[X]:((~patient(X)<~>~brave(X))))&
(~tall(mary))&
((strong(paul)|~patient(paul)))&
(?[X]:(~humble(X))) | kind(fred) | [
"p5",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2971979832835151156971829
% SZS output start Proof for 2971979832835151156971829
6. ! [X0] : ((~happy(X0) | ~old(X0)) => ~rich(X0)) [input p5]
7. ! [X0] : (kind(X0) <=> old(X0)) [input p6]
11. ! [X0] : ((~creative(X0) & rich(X0)) <=> ~kind(X0)) [input p10]
22. ~kind(fred) [input hypothesis]
26. ! [X0] : (~old(X0) => ~rich(X0)) [pure predicate removal 6]
29. ! [X0] : (~rich(X0) | old(X0)) [ennf transformation 26]
51. ! [X0] : ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))) [nnf transformation 7]
61. ! [X0] : (((~creative(X0) & rich(X0)) | kind(X0)) & (~kind(X0) | (creative(X0) | ~rich(X0)))) [nnf transformation 11]
62. ! [X0] : (((~creative(X0) & rich(X0)) | kind(X0)) & (~kind(X0) | creative(X0) | ~rich(X0))) [flattening 61]
93. ~rich(X0) | old(X0) [cnf transformation 29]
94. ~kind(X0) | old(X0) [cnf transformation 51]
95. ~old(X0) | kind(X0) [cnf transformation 51]
107. kind(X0) | rich(X0) [cnf transformation 62]
127. ~kind(fred) [cnf transformation 22]
186. 14 <=> ! [X0] : kind(X0) [avatar definition]
187. kind(X0) <- (14) [avatar component clause 186]
251. rich(X0) | old(X0) [resolution 107,94]
252. old(X0) [subsumption resolution 251,93]
258. kind(X2) [resolution 252,95]
259. 14 [avatar split clause 258,186]
260. $false <- (14) [resolution 187,127]
264. ~14 [avatar contradiction clause 260]
265. $false [avatar sat refutation 259,264]
% SZS output end Proof for 2971979832835151156971829
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not brave then mary is funny or not humble and vice versa.
Everyone who is both happy and curious is not old or not creative.
Everyone who is not quiet or not kind is both not quiet and not kind and vice versa.
Everyone who is not tall is calm or quiet.
Everyone who is kind is either not patient or not tall and vice versa.
Everyone who is not creative is both not funny and funny and vice versa.
If paul is not calm or not rich then alice is either not kind or not generous and vice versa.
Everyone who is either not patient or not calm is funny.
If susan is either strong or not calm then someone is both not old and not calm.
If susan is old then mary is either not quiet or creative and vice versa.
Everyone who is curious or humble is either old or happy.
Everyone who is funny or not calm is both not tall and generous and vice versa.
Everyone who is not generous is not brave and vice versa.
Everyone who is kind is both calm and generous.
Everyone who is both not funny and funny is either not funny or not kind and vice versa.
If john is either calm or not old then someone is not happy.
Someone is either tall or not curious.
John is either humble or rich.
Lucy is both funny and patient.
Lucy is both creative and funny.
Someone is both patient and funny.
Lucy is not happy or brave.
Mary is either not happy or not wise. | Susan is not calm. | contradiction | ((~brave(john))<=>((funny(mary)|~humble(mary))))&
(![X]:((happy(X)&curious(X))=>(~old(X)|~creative(X))))&
(![X]:((~quiet(X)|~kind(X))<=>(~quiet(X)&~kind(X))))&
(![X]:(~tall(X)=>(calm(X)|quiet(X))))&
(![X]:(kind(X)<=>(~patient(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(~funny(X)&funny(X))))&
(((~calm(paul)|~rich(paul)))<=>((~kind(alice)<~>~generous(alice))))&
(![X]:((~patient(X)<~>~calm(X))=>funny(X)))&
(((strong(susan)<~>~calm(susan)))=>(?[X]:((~old(X)&~calm(X)))))&
((old(susan))<=>((~quiet(mary)<~>creative(mary))))&
(![X]:((curious(X)|humble(X))=>(old(X)<~>happy(X))))&
(![X]:((funny(X)|~calm(X))<=>(~tall(X)&generous(X))))&
(![X]:(~generous(X)<=>~brave(X)))&
(![X]:(kind(X)=>(calm(X)&generous(X))))&
(![X]:((~funny(X)&funny(X))<=>(~funny(X)<~>~kind(X))))&
(((calm(john)<~>~old(john)))=>(?[X]:(~happy(X))))&
(?[X]:((tall(X)<~>~curious(X))))&
((humble(john)<~>rich(john)))&
((funny(lucy)&patient(lucy)))&
((creative(lucy)&funny(lucy)))&
(?[X]:((patient(X)&funny(X))))&
((~happy(lucy)|brave(lucy)))&
((~happy(mary)<~>~wise(mary))) | ~calm(susan) | [
"p2",
"p3",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5325858936248182528223910
% SZS output start Proof for 5325858936248182528223910
3. ! [X0] : ((~kind(X0) | ~quiet(X0)) <=> (~kind(X0) & ~quiet(X0))) [input p2]
4. ! [X0] : (~tall(X0) => (quiet(X0) | calm(X0))) [input p3]
12. ! [X0] : ((~calm(X0) | funny(X0)) <=> (generous(X0) & ~tall(X0))) [input p11]
14. ! [X0] : (kind(X0) => (generous(X0) & calm(X0))) [input p13]
24. ~calm(susan) [input hypothesis]
27. ! [X0] : ((quiet(X0) | calm(X0)) | tall(X0)) [ennf transformation 4]
28. ! [X0] : (quiet(X0) | calm(X0) | tall(X0)) [flattening 27]
32. ! [X0] : ((generous(X0) & calm(X0)) | ~kind(X0)) [ennf transformation 14]
36. ! [X0] : (((~kind(X0) | ~quiet(X0)) | (kind(X0) | quiet(X0))) & ((~kind(X0) & ~quiet(X0)) | (kind(X0) & quiet(X0)))) [nnf transformation 3]
37. ! [X0] : ((~kind(X0) | ~quiet(X0) | kind(X0) | quiet(X0)) & ((~kind(X0) & ~quiet(X0)) | (kind(X0) & quiet(X0)))) [flattening 36]
49. ! [X0] : (((~calm(X0) | funny(X0)) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | (calm(X0) & ~funny(X0)))) [nnf transformation 12]
50. ! [X0] : ((~calm(X0) | funny(X0) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | (calm(X0) & ~funny(X0)))) [flattening 49]
69. ~quiet(X0) | kind(X0) [cnf transformation 37]
73. calm(X0) | quiet(X0) | tall(X0) [cnf transformation 28]
102. ~tall(X0) | calm(X0) [cnf transformation 50]
108. ~kind(X0) | calm(X0) [cnf transformation 32]
131. ~calm(susan) [cnf transformation 24]
175. 8 <=> calm(susan) [avatar definition]
176. ~calm(susan) <- (~8) [avatar component clause 175]
259. ~8 [avatar split clause 131,175]
280. quiet(susan) | tall(susan) <- (~8) [resolution 73,176]
283. 25 <=> tall(susan) [avatar definition]
285. tall(susan) <- (25) [avatar component clause 283]
287. 26 <=> quiet(susan) [avatar definition]
289. quiet(susan) <- (26) [avatar component clause 287]
290. 25 | 26 | 8 [avatar split clause 280,175,287,283]
300. calm(susan) <- (25) [resolution 285,102]
302. $false <- (~8, 25) [subsumption resolution 300,176]
303. 8 | ~25 [avatar contradiction clause 302]
310. kind(susan) <- (26) [resolution 289,69]
407. calm(susan) <- (26) [resolution 310,108]
410. $false <- (~8, 26) [subsumption resolution 407,176]
411. 8 | ~26 [avatar contradiction clause 410]
412. $false [avatar sat refutation 259,290,303,411]
% SZS output end Proof for 5325858936248182528223910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or old is creative or not funny and vice versa.
Everyone who is both not humble and not wise is not curious or not brave.
Everyone who is happy or calm is not quiet.
Everyone who is not kind or not quiet is quiet and vice versa.
Everyone who is both not rich and strong is either not calm or not patient and vice versa.
If mary is patient or not old then susan is not curious or rich.
Everyone who is either not calm or quiet is either old or brave.
If mary is both kind and tall then paul is both patient and not happy.
Everyone who is either not patient or rich is not kind or not generous and vice versa.
Everyone who is both funny and not patient is both not brave and old and vice versa.
If john is either not generous or not wise then lucy is humble or not wise and vice versa.
If someone is kind then susan is either rich or not generous and vice versa.
Everyone who is not brave is either not strong or not rich and vice versa.
Everyone who is either kind or not curious is both not curious and brave and vice versa.
If someone is both not kind and not creative then someone is not kind and vice versa.
Someone is not curious or not strong.
Lucy is old.
John is both quiet and old.
Susan is both wise and curious. | Lucy is rich. | contradiction | (![X]:((~funny(X)|old(X))<=>(creative(X)|~funny(X))))&
(![X]:((~humble(X)&~wise(X))=>(~curious(X)|~brave(X))))&
(![X]:((happy(X)|calm(X))=>~quiet(X)))&
(![X]:((~kind(X)|~quiet(X))<=>quiet(X)))&
(![X]:((~rich(X)&strong(X))<=>(~calm(X)<~>~patient(X))))&
(((patient(mary)|~old(mary)))=>((~curious(susan)|rich(susan))))&
(![X]:((~calm(X)<~>quiet(X))=>(old(X)<~>brave(X))))&
(((kind(mary)&tall(mary)))=>((patient(paul)&~happy(paul))))&
(![X]:((~patient(X)<~>rich(X))<=>(~kind(X)|~generous(X))))&
(![X]:((funny(X)&~patient(X))<=>(~brave(X)&old(X))))&
(((~generous(john)<~>~wise(john)))<=>((humble(lucy)|~wise(lucy))))&
((?[X]:(kind(X)))<=>((rich(susan)<~>~generous(susan))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~rich(X))))&
(![X]:((kind(X)<~>~curious(X))<=>(~curious(X)&brave(X))))&
((?[X]:((~kind(X)&~creative(X))))<=>(?[X]:(~kind(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(old(lucy))&
((quiet(john)&old(john)))&
((wise(susan)&curious(susan))) | rich(lucy) | [
"p2",
"p3",
"p4",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7929827460639741885297186
% SZS output start Proof for 7929827460639741885297186
3. ! [X0] : ((calm(X0) | happy(X0)) => ~quiet(X0)) [input p2]
4. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> quiet(X0)) [input p3]
5. ! [X0] : ((strong(X0) & ~rich(X0)) <=> (~calm(X0) <~> ~patient(X0))) [input p4]
9. ! [X0] : ((~patient(X0) <~> rich(X0)) <=> (~generous(X0) | ~kind(X0))) [input p8]
12. ? [X0] : kind(X0) <=> (rich(susan) <~> ~generous(susan)) [input p11]
20. rich(lucy) [input hypothesis]
23. ! [X0] : (calm(X0) => ~quiet(X0)) [pure predicate removal 3]
26. ! [X0] : (~quiet(X0) | ~calm(X0)) [ennf transformation 23]
32. ! [X0] : (((~quiet(X0) | ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & kind(X0)))) [nnf transformation 4]
33. ! [X0] : ((~quiet(X0) | ~kind(X0) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) & kind(X0)))) [flattening 32]
34. ! [X0] : (((strong(X0) & ~rich(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (~strong(X0) | rich(X0)))) [nnf transformation 5]
35. ! [X0] : (((strong(X0) & ~rich(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | ~strong(X0) | rich(X0))) [flattening 34]
37. ! [X0] : ((((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (generous(X0) & kind(X0))) & ((~generous(X0) | ~kind(X0)) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0))))) [nnf transformation 9]
38. ! [X0] : ((((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (generous(X0) & kind(X0))) & (~generous(X0) | ~kind(X0) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0))))) [flattening 37]
43. (? [X0] : kind(X0) | ((rich(susan) | generous(susan)) & (~generous(susan) | ~rich(susan)))) & (((generous(susan) | ~rich(susan)) & (~generous(susan) | rich(susan))) | ! [X0] : ~kind(X0)) [nnf transformation 12]
44. (? [X0] : kind(X0) | ((rich(susan) | generous(susan)) & (~generous(susan) | ~rich(susan)))) & (((generous(susan) | ~rich(susan)) & (~generous(susan) | rich(susan))) | ! [X1] : ~kind(X1)) [rectify 43]
45. ? [X0] : kind(X0) => kind(sK0) [choice axiom]
46. (kind(sK0) | ((rich(susan) | generous(susan)) & (~generous(susan) | ~rich(susan)))) & (((generous(susan) | ~rich(susan)) & (~generous(susan) | rich(susan))) | ! [X1] : ~kind(X1)) [skolemisation 44,45]
62. ~quiet(X0) | ~calm(X0) [cnf transformation 26]
64. quiet(X0) | quiet(X0) [cnf transformation 33]
65. ~quiet(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 33]
68. ~patient(X0) | ~rich(X0) | calm(X0) [cnf transformation 35]
82. ~rich(X0) | patient(X0) | kind(X0) [cnf transformation 38]
94. ~generous(susan) | rich(susan) | ~kind(X1) [cnf transformation 46]
95. generous(susan) | ~rich(susan) | ~kind(X1) [cnf transformation 46]
96. kind(sK0) | ~generous(susan) | ~rich(susan) [cnf transformation 46]
97. kind(sK0) | rich(susan) | generous(susan) [cnf transformation 46]
117. rich(lucy) [cnf transformation 20]
120. quiet(X0) [duplicate literal removal 64]
121. ~kind(X0) | ~quiet(X0) [duplicate literal removal 65]
131. 3 <=> rich(susan) [avatar definition]
163. 9 <=> generous(susan) [avatar definition]
167. 10 <=> kind(sK0) [avatar definition]
169. kind(sK0) <- (10) [avatar component clause 167]
170. 9 | 3 | 10 [avatar split clause 97,167,131,163]
171. ~3 | ~9 | 10 [avatar split clause 96,167,163,131]
173. 11 <=> ! [X1] : ~kind(X1) [avatar definition]
174. ~kind(X1) <- (11) [avatar component clause 173]
175. 11 | ~3 | 9 [avatar split clause 95,163,131,173]
176. 11 | 3 | ~9 [avatar split clause 94,163,131,173]
208. ~calm(X0) [resolution 62,120]
210. ~quiet(sK0) <- (10) [resolution 121,169]
211. $false <- (10) [subsumption resolution 210,120]
212. ~10 [avatar contradiction clause 211]
235. patient(lucy) | kind(lucy) [resolution 82,117]
237. patient(lucy) <- (11) [subsumption resolution 235,174]
244. ~rich(lucy) | calm(lucy) <- (11) [resolution 237,68]
246. calm(lucy) <- (11) [subsumption resolution 244,117]
247. $false <- (11) [subsumption resolution 246,208]
248. ~11 [avatar contradiction clause 247]
249. $false [avatar sat refutation 170,171,175,176,212,248]
% SZS output end Proof for 7929827460639741885297186
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not humble is either not patient or not generous and vice versa.
Everyone who is both strong and not patient is rich or calm.
If lucy is either not generous or old then paul is both generous and strong and vice versa.
Everyone who is either not curious or not quiet is either tall or brave and vice versa.
If mary is either not brave or not kind then mary is either not quiet or strong.
If someone is either not funny or happy then someone is either not creative or brave.
If someone is not kind or humble then paul is creative.
If someone is either kind or not funny then john is both kind and not calm and vice versa.
If someone is either not brave or not creative then mary is not humble.
Everyone who is not quiet or patient is creative.
If fred is quiet then fred is not humble or wise.
If someone is not kind or not curious then someone is either not kind or not tall and vice versa.
Everyone who is either not happy or not curious is both tall and happy and vice versa.
If someone is either not happy or patient then someone is generous or old and vice versa.
Everyone who is either not calm or old is not wise.
If someone is not brave or humble then someone is either not curious or not brave.
Alice is either not patient or rich.
Lucy is both calm and not happy.
Someone is rich or not humble.
John is not quiet.
Someone is not curious or calm.
Alice is humble.
Mary is not rich or generous. | Lucy is creative. | neutral | (![X]:((kind(X)<~>~humble(X))<=>(~patient(X)<~>~generous(X))))&
(![X]:((strong(X)&~patient(X))=>(rich(X)|calm(X))))&
(((~generous(lucy)<~>old(lucy)))<=>((generous(paul)&strong(paul))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(tall(X)<~>brave(X))))&
(((~brave(mary)<~>~kind(mary)))=>((~quiet(mary)<~>strong(mary))))&
((?[X]:((~funny(X)<~>happy(X))))=>(?[X]:((~creative(X)<~>brave(X)))))&
((?[X]:((~kind(X)|humble(X))))=>(creative(paul)))&
((?[X]:((kind(X)<~>~funny(X))))<=>((kind(john)&~calm(john))))&
((?[X]:((~brave(X)<~>~creative(X))))=>(~humble(mary)))&
(![X]:((~quiet(X)|patient(X))=>creative(X)))&
((quiet(fred))=>((~humble(fred)|wise(fred))))&
((?[X]:((~kind(X)|~curious(X))))<=>(?[X]:((~kind(X)<~>~tall(X)))))&
(![X]:((~happy(X)<~>~curious(X))<=>(tall(X)&happy(X))))&
((?[X]:((~happy(X)<~>patient(X))))<=>(?[X]:((generous(X)|old(X)))))&
(![X]:((~calm(X)<~>old(X))=>~wise(X)))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:((~curious(X)<~>~brave(X)))))&
((~patient(alice)<~>rich(alice)))&
((calm(lucy)&~happy(lucy)))&
(?[X]:((rich(X)|~humble(X))))&
(~quiet(john))&
(?[X]:((~curious(X)|calm(X))))&
(humble(alice))&
((~rich(mary)|generous(mary))) | creative(lucy) | [] | null | 0 |
Everyone who is either not brave or quiet is not creative.
Everyone who is either not creative or kind is not happy or not patient and vice versa.
If mary is not quiet then someone is both not creative and creative and vice versa.
Everyone who is creative or not funny is both strong and wise.
If susan is tall or generous then someone is quiet.
Everyone who is both funny and not brave is patient.
If paul is either humble or not calm then someone is patient or not happy and vice versa.
Everyone who is strong or patient is both rich and funny and vice versa.
Everyone who is either not patient or tall is kind or not funny.
Everyone who is patient is both tall and not tall.
Everyone who is either not quiet or creative is both not happy and not quiet.
Everyone who is either not strong or not brave is not curious or tall.
Everyone who is not brave is either happy or not generous and vice versa.
Everyone who is not quiet is both not creative and not curious.
If someone is either not creative or humble then lucy is both not generous and not quiet.
If someone is rich then someone is both calm and not happy.
Someone is either quiet or strong.
Someone is curious.
Paul is rich or not wise.
Someone is creative or not kind.
Lucy is patient or not curious.
Someone is both not calm and rich.
Someone is rich or not creative.
Someone is either not curious or creative. | Lucy is curious. | contradiction | (![X]:((~brave(X)<~>quiet(X))=>~creative(X)))&
(![X]:((~creative(X)<~>kind(X))<=>(~happy(X)|~patient(X))))&
((~quiet(mary))<=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:((creative(X)|~funny(X))=>(strong(X)&wise(X))))&
(((tall(susan)|generous(susan)))=>(?[X]:(quiet(X))))&
(![X]:((funny(X)&~brave(X))=>patient(X)))&
(((humble(paul)<~>~calm(paul)))<=>(?[X]:((patient(X)|~happy(X)))))&
(![X]:((strong(X)|patient(X))<=>(rich(X)&funny(X))))&
(![X]:((~patient(X)<~>tall(X))=>(kind(X)|~funny(X))))&
(![X]:(patient(X)=>(tall(X)&~tall(X))))&
(![X]:((~quiet(X)<~>creative(X))=>(~happy(X)&~quiet(X))))&
(![X]:((~strong(X)<~>~brave(X))=>(~curious(X)|tall(X))))&
(![X]:(~brave(X)<=>(happy(X)<~>~generous(X))))&
(![X]:(~quiet(X)=>(~creative(X)&~curious(X))))&
((?[X]:((~creative(X)<~>humble(X))))=>((~generous(lucy)&~quiet(lucy))))&
((?[X]:(rich(X)))=>(?[X]:((calm(X)&~happy(X)))))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:(curious(X)))&
((rich(paul)|~wise(paul)))&
(?[X]:((creative(X)|~kind(X))))&
((patient(lucy)|~curious(lucy)))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((rich(X)|~creative(X))))&
(?[X]:((~curious(X)<~>creative(X)))) | curious(lucy) | [
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8506648820772428257480295
% SZS output start Proof for 8506648820772428257480295
10. ! [X0] : (patient(X0) => (~tall(X0) & tall(X0))) [input p9]
21. ~curious(lucy) | patient(lucy) [input p20]
25. curious(lucy) [input hypothesis]
34. ! [X0] : ((~tall(X0) & tall(X0)) | ~patient(X0)) [ennf transformation 10]
109. tall(X0) | ~patient(X0) [cnf transformation 34]
110. ~tall(X0) | ~patient(X0) [cnf transformation 34]
134. ~curious(lucy) | patient(lucy) [cnf transformation 21]
140. curious(lucy) [cnf transformation 25]
179. 9 <=> ! [X0] : ~patient(X0) [avatar definition]
180. ~patient(X0) <- (9) [avatar component clause 179]
198. ~patient(X0) [subsumption resolution 109,110]
199. 9 [avatar split clause 198,179]
250. 22 <=> patient(lucy) [avatar definition]
252. patient(lucy) <- (22) [avatar component clause 250]
254. 23 <=> curious(lucy) [avatar definition]
257. 22 | ~23 [avatar split clause 134,254,250]
259. 23 [avatar split clause 140,254]
262. $false <- (9, 22) [resolution 252,180]
263. ~9 | ~22 [avatar contradiction clause 262]
264. $false [avatar sat refutation 199,257,259,263]
% SZS output end Proof for 8506648820772428257480295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not quiet is both not strong and kind.
Everyone who is either tall or not patient is not creative.
If paul is not creative then alice is not wise or wise and vice versa.
If someone is either not kind or curious then lucy is quiet and vice versa.
Everyone who is creative or not calm is either tall or not funny and vice versa.
Everyone who is either not patient or happy is either not curious or not tall and vice versa.
If someone is not kind then someone is rich or humble and vice versa.
If someone is both not kind and not quiet then someone is both not funny and old.
If someone is both not creative and wise then lucy is rich.
If susan is wise or rich then someone is rich or not brave and vice versa.
Everyone who is either not curious or not brave is both not humble and calm and vice versa.
If someone is tall or wise then someone is not generous or not rich.
Everyone who is old is not happy or happy and vice versa.
If alice is not old or not kind then someone is both not wise and happy and vice versa.
Everyone who is brave or old is wise and vice versa.
Someone is either happy or calm.
Someone is not kind or tall.
Someone is both creative and not strong.
Someone is humble or not kind.
Mary is either happy or generous.
Mary is either rich or happy.
Paul is curious or generous.
Alice is not creative. | Alice is old. | entailment | (![X]:((tall(X)<~>~quiet(X))=>(~strong(X)&kind(X))))&
(![X]:((tall(X)<~>~patient(X))=>~creative(X)))&
((~creative(paul))<=>((~wise(alice)|wise(alice))))&
((?[X]:((~kind(X)<~>curious(X))))<=>(quiet(lucy)))&
(![X]:((creative(X)|~calm(X))<=>(tall(X)<~>~funny(X))))&
(![X]:((~patient(X)<~>happy(X))<=>(~curious(X)<~>~tall(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((rich(X)|humble(X)))))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:((~funny(X)&old(X)))))&
((?[X]:((~creative(X)&wise(X))))=>(rich(lucy)))&
(((wise(susan)|rich(susan)))<=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:((~curious(X)<~>~brave(X))<=>(~humble(X)&calm(X))))&
((?[X]:((tall(X)|wise(X))))=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:(old(X)<=>(~happy(X)|happy(X))))&
(((~old(alice)|~kind(alice)))<=>(?[X]:((~wise(X)&happy(X)))))&
(![X]:((brave(X)|old(X))<=>wise(X)))&
(?[X]:((happy(X)<~>calm(X))))&
(?[X]:((~kind(X)|tall(X))))&
(?[X]:((creative(X)&~strong(X))))&
(?[X]:((humble(X)|~kind(X))))&
((happy(mary)<~>generous(mary)))&
((rich(mary)<~>happy(mary)))&
((curious(paul)|generous(paul)))&
(~creative(alice)) | old(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 944564735277956914275083
% SZS output start Proof for 944564735277956914275083
13. ! [X0] : (old(X0) <=> (happy(X0) | ~happy(X0))) [input p12]
24. ~old(alice) [input hypothesis]
64. ! [X0] : ((old(X0) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | ~old(X0))) [nnf transformation 13]
65. ! [X0] : ((old(X0) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | ~old(X0))) [flattening 64]
128. old(X0) | happy(X0) [cnf transformation 65]
129. old(X0) | ~happy(X0) [cnf transformation 65]
149. ~old(alice) [cnf transformation 24]
266. old(X0) [subsumption resolution 128,129]
340. $false [subsumption resolution 149,266]
% SZS output end Proof for 944564735277956914275083
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or patient is both not creative and quiet. If someone is either creative or funny then someone is not calm. Everyone who is either strong or rich is both not calm and creative and vice versa. If lucy is not funny then someone is both not strong and generous and vice versa. Everyone who is both not rich and not curious is either calm or quiet and vice versa. If lucy is both not brave and tall then someone is either tall or not humble. If alice is generous or not quiet then someone is both not tall and not rich and vice versa. If fred is not wise then someone is not humble. If someone is either patient or old then someone is not happy or not wise and vice versa. Everyone who is either not happy or not rich is not quiet and vice versa. Everyone who is strong is not funny and vice versa. If mary is both quiet and not kind then someone is both not kind and not rich. If alice is not old then lucy is funny and vice versa. If john is either curious or creative then paul is not happy or brave and vice versa. If someone is not curious then lucy is either not happy or quiet. If fred is both curious and quiet then lucy is happy. Susan is old or not strong. Someone is both old and not kind. Someone is patient or not rich. Someone is wise. Alice is not old. Paul is not humble. Someone is not strong. Paul is not rich. | Lucy is generous. | contradiction | (![X]:((rich(X)<~>patient(X))=>(~creative(X)&quiet(X))))&
((?[X]:((creative(X)<~>funny(X))))=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>rich(X))<=>(~calm(X)&creative(X))))&
((~funny(lucy))<=>(?[X]:((~strong(X)&generous(X)))))&
(![X]:((~rich(X)&~curious(X))<=>(calm(X)<~>quiet(X))))&
(((~brave(lucy)&tall(lucy)))=>(?[X]:((tall(X)<~>~humble(X)))))&
(((generous(alice)|~quiet(alice)))<=>(?[X]:((~tall(X)&~rich(X)))))&
((~wise(fred))=>(?[X]:(~humble(X))))&
((?[X]:((patient(X)<~>old(X))))<=>(?[X]:((~happy(X)|~wise(X)))))&
(![X]:((~happy(X)<~>~rich(X))<=>~quiet(X)))&
(![X]:(strong(X)<=>~funny(X)))&
(((quiet(mary)&~kind(mary)))=>(?[X]:((~kind(X)&~rich(X)))))&
((~old(alice))<=>(funny(lucy)))&
(((curious(john)<~>creative(john)))<=>((~happy(paul)|brave(paul))))&
((?[X]:(~curious(X)))=>((~happy(lucy)<~>quiet(lucy))))&
(((curious(fred)&quiet(fred)))=>(happy(lucy)))&
((old(susan)|~strong(susan)))&
(?[X]:((old(X)&~kind(X))))&
(?[X]:((patient(X)|~rich(X))))&
(?[X]:(wise(X)))&
(~old(alice))&
(~humble(paul))&
(?[X]:(~strong(X)))&
(~rich(paul)) | generous(lucy) | [
"p3",
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7352605542000644157672986
% SZS output start Proof for 7352605542000644157672986
4. ~funny(lucy) <=> ? [X0] : (generous(X0) & ~strong(X0)) [input p3]
11. ! [X0] : (strong(X0) <=> ~funny(X0)) [input p10]
13. ~old(alice) <=> funny(lucy) [input p12]
21. ~old(alice) [input p20]
25. generous(lucy) [input hypothesis]
45. (~funny(lucy) | ! [X0] : (~generous(X0) | strong(X0))) & (? [X0] : (generous(X0) & ~strong(X0)) | funny(lucy)) [nnf transformation 4]
46. (~funny(lucy) | ! [X0] : (~generous(X0) | strong(X0))) & (? [X1] : (generous(X1) & ~strong(X1)) | funny(lucy)) [rectify 45]
47. ? [X1] : (generous(X1) & ~strong(X1)) => (generous(sK1) & ~strong(sK1)) [choice axiom]
48. (~funny(lucy) | ! [X0] : (~generous(X0) | strong(X0))) & ((generous(sK1) & ~strong(sK1)) | funny(lucy)) [skolemisation 46,47]
67. ! [X0] : ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0))) [nnf transformation 11]
70. (~old(alice) | ~funny(lucy)) & (funny(lucy) | old(alice)) [nnf transformation 13]
96. ~funny(lucy) | ~generous(X0) | strong(X0) [cnf transformation 48]
121. ~strong(X0) | ~funny(X0) [cnf transformation 67]
125. funny(lucy) | old(alice) [cnf transformation 70]
141. ~old(alice) [cnf transformation 21]
145. generous(lucy) [cnf transformation 25]
159. 4 <=> ! [X0] : (~generous(X0) | strong(X0)) [avatar definition]
160. ~generous(X0) | strong(X0) <- (4) [avatar component clause 159]
162. 5 <=> funny(lucy) [avatar definition]
163. funny(lucy) <- (5) [avatar component clause 162]
165. 4 | ~5 [avatar split clause 96,162,159]
280. 31 <=> old(alice) [avatar definition]
284. 31 | 5 [avatar split clause 125,162,280]
347. ~31 [avatar split clause 141,280]
351. strong(lucy) <- (4) [resolution 160,145]
352. ~funny(lucy) <- (4) [resolution 351,121]
353. $false <- (4, 5) [subsumption resolution 352,163]
354. ~4 | ~5 [avatar contradiction clause 353]
355. $false [avatar sat refutation 165,284,347,354]
% SZS output end Proof for 7352605542000644157672986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then lucy is patient. If john is either not strong or not rich then someone is both calm and not calm and vice versa. Everyone who is both creative and wise is both calm and not creative and vice versa. Everyone who is not tall or not rich is not quiet or not rich and vice versa. If paul is either tall or generous then someone is both strong and not kind and vice versa. Everyone who is both not rich and not humble is not humble or not creative and vice versa. If someone is not kind then alice is either patient or not calm. If susan is not creative or not tall then someone is not calm and vice versa. If susan is kind then mary is either generous or not old and vice versa. If someone is kind then paul is both not generous and humble. Everyone who is both brave and patient is not brave or not quiet and vice versa. If alice is either strong or rich then lucy is not happy or not quiet. If mary is wise or curious then someone is happy or quiet and vice versa. If mary is both tall and strong then someone is kind or not old. If someone is both brave and rich then someone is not kind and vice versa. Everyone who is either not happy or patient is not creative or not funny. Mary is rich or not old. Someone is both creative and not rich. Mary is either happy or not curious. Someone is strong. Someone is not funny. Lucy is tall or not brave. Someone is not rich. Someone is not generous or creative. | John is not rich. | neutral | ((?[X]:(~funny(X)))=>(patient(lucy)))&
(((~strong(john)<~>~rich(john)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:((creative(X)&wise(X))<=>(calm(X)&~creative(X))))&
(![X]:((~tall(X)|~rich(X))<=>(~quiet(X)|~rich(X))))&
(((tall(paul)<~>generous(paul)))<=>(?[X]:((strong(X)&~kind(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(~humble(X)|~creative(X))))&
((?[X]:(~kind(X)))=>((patient(alice)<~>~calm(alice))))&
(((~creative(susan)|~tall(susan)))<=>(?[X]:(~calm(X))))&
((kind(susan))<=>((generous(mary)<~>~old(mary))))&
((?[X]:(kind(X)))=>((~generous(paul)&humble(paul))))&
(![X]:((brave(X)&patient(X))<=>(~brave(X)|~quiet(X))))&
(((strong(alice)<~>rich(alice)))=>((~happy(lucy)|~quiet(lucy))))&
(((wise(mary)|curious(mary)))<=>(?[X]:((happy(X)|quiet(X)))))&
(((tall(mary)&strong(mary)))=>(?[X]:((kind(X)|~old(X)))))&
((?[X]:((brave(X)&rich(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~happy(X)<~>patient(X))=>(~creative(X)|~funny(X))))&
((rich(mary)|~old(mary)))&
(?[X]:((creative(X)&~rich(X))))&
((happy(mary)<~>~curious(mary)))&
(?[X]:(strong(X)))&
(?[X]:(~funny(X)))&
((tall(lucy)|~brave(lucy)))&
(?[X]:(~rich(X)))&
(?[X]:((~generous(X)|creative(X)))) | ~rich(john) | [] | null | 0 |
If someone is both humble and happy then someone is either generous or not tall and vice versa.
If someone is both not happy and not curious then susan is either funny or not humble and vice versa.
If alice is either calm or not humble then paul is both not funny and not kind.
If mary is not wise then fred is happy or funny and vice versa.
If someone is either funny or creative then john is both creative and quiet.
If someone is either patient or not kind then someone is not rich and vice versa.
Everyone who is both calm and tall is both not old and wise.
Everyone who is old is not patient or not old and vice versa.
Everyone who is both humble and not strong is either creative or not funny.
If someone is both not rich and not generous then someone is kind or not wise.
Everyone who is both not patient and humble is either calm or humble and vice versa.
Everyone who is either strong or not kind is either calm or not kind.
Everyone who is either patient or brave is not rich or humble and vice versa.
If john is both tall and rich then someone is not humble or calm.
If susan is both not curious and creative then fred is curious.
If someone is strong then lucy is either rich or wise and vice versa.
Someone is either not strong or tall.
Fred is humble.
Lucy is humble or not quiet.
Someone is kind.
Someone is not happy or not quiet.
John is not creative or not funny.
Someone is not rich or not tall. | Alice is not old. | contradiction | ((?[X]:((humble(X)&happy(X))))<=>(?[X]:((generous(X)<~>~tall(X)))))&
((?[X]:((~happy(X)&~curious(X))))<=>((funny(susan)<~>~humble(susan))))&
(((calm(alice)<~>~humble(alice)))=>((~funny(paul)&~kind(paul))))&
((~wise(mary))<=>((happy(fred)|funny(fred))))&
((?[X]:((funny(X)<~>creative(X))))=>((creative(john)&quiet(john))))&
((?[X]:((patient(X)<~>~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((calm(X)&tall(X))=>(~old(X)&wise(X))))&
(![X]:(old(X)<=>(~patient(X)|~old(X))))&
(![X]:((humble(X)&~strong(X))=>(creative(X)<~>~funny(X))))&
((?[X]:((~rich(X)&~generous(X))))=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((~patient(X)&humble(X))<=>(calm(X)<~>humble(X))))&
(![X]:((strong(X)<~>~kind(X))=>(calm(X)<~>~kind(X))))&
(![X]:((patient(X)<~>brave(X))<=>(~rich(X)|humble(X))))&
(((tall(john)&rich(john)))=>(?[X]:((~humble(X)|calm(X)))))&
(((~curious(susan)&creative(susan)))=>(curious(fred)))&
((?[X]:(strong(X)))<=>((rich(lucy)<~>wise(lucy))))&
(?[X]:((~strong(X)<~>tall(X))))&
(humble(fred))&
((humble(lucy)|~quiet(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((~happy(X)|~quiet(X))))&
((~creative(john)|~funny(john)))&
(?[X]:((~rich(X)|~tall(X)))) | ~old(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2886412948139028311226232
% SZS output start Proof for 2886412948139028311226232
8. ! [X0] : (old(X0) <=> (~old(X0) | ~patient(X0))) [input p7]
24. ~old(alice) [input hypothesis]
58. ! [X0] : ((old(X0) | (old(X0) & patient(X0))) & ((~old(X0) | ~patient(X0)) | ~old(X0))) [nnf transformation 8]
59. ! [X0] : ((old(X0) | (old(X0) & patient(X0))) & (~old(X0) | ~patient(X0) | ~old(X0))) [flattening 58]
115. old(X0) | old(X0) [cnf transformation 59]
149. ~old(alice) [cnf transformation 24]
155. old(X0) [duplicate literal removal 115]
397. $false [subsumption resolution 149,155]
% SZS output end Proof for 2886412948139028311226232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is brave then someone is both tall and not brave and vice versa. Everyone who is patient or calm is creative or kind and vice versa. If someone is not old or strong then someone is rich or quiet. If someone is both not strong and not brave then john is happy. If someone is not generous then lucy is either not generous or patient and vice versa. Everyone who is either not tall or not generous is both humble and not humble. If someone is not wise then someone is not old and vice versa. Everyone who is not creative is both quiet and strong and vice versa. If someone is not patient or not humble then lucy is not brave. Everyone who is not strong or rich is both not rich and curious. If someone is wise then mary is both brave and not happy and vice versa. Everyone who is both quiet and generous is not wise or calm and vice versa. Everyone who is not calm is both curious and happy and vice versa. Everyone who is quiet or not tall is not generous or not strong and vice versa. If someone is humble or not curious then someone is either not kind or not calm and vice versa. If mary is both not wise and strong then lucy is both creative and kind and vice versa. Someone is patient or happy. Someone is either tall or not old. Someone is not happy. Someone is both humble and calm. Someone is both tall and happy. Someone is generous or not kind. Susan is either not old or patient. Someone is either generous or old. | Lucy is not kind. | entailment | ((brave(fred))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)|kind(X))))&
((?[X]:((~old(X)|strong(X))))=>(?[X]:((rich(X)|quiet(X)))))&
((?[X]:((~strong(X)&~brave(X))))=>(happy(john)))&
((?[X]:(~generous(X)))<=>((~generous(lucy)<~>patient(lucy))))&
(![X]:((~tall(X)<~>~generous(X))=>(humble(X)&~humble(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(~old(X))))&
(![X]:(~creative(X)<=>(quiet(X)&strong(X))))&
((?[X]:((~patient(X)|~humble(X))))=>(~brave(lucy)))&
(![X]:((~strong(X)|rich(X))=>(~rich(X)&curious(X))))&
((?[X]:(wise(X)))<=>((brave(mary)&~happy(mary))))&
(![X]:((quiet(X)&generous(X))<=>(~wise(X)|calm(X))))&
(![X]:(~calm(X)<=>(curious(X)&happy(X))))&
(![X]:((quiet(X)|~tall(X))<=>(~generous(X)|~strong(X))))&
((?[X]:((humble(X)|~curious(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((~wise(mary)&strong(mary)))<=>((creative(lucy)&kind(lucy))))&
(?[X]:((patient(X)|happy(X))))&
(?[X]:((tall(X)<~>~old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)&calm(X))))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:((generous(X)|~kind(X))))&
((~old(susan)<~>patient(susan)))&
(?[X]:((generous(X)<~>old(X)))) | ~kind(lucy) | [
"p1",
"p4",
"p7",
"p10",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6880222751943882622375677
% SZS output start Proof for 6880222751943882622375677
2. ! [X0] : ((calm(X0) | patient(X0)) <=> (kind(X0) | creative(X0))) [input p1]
5. ? [X0] : ~generous(X0) <=> (~generous(lucy) <~> patient(lucy)) [input p4]
8. ! [X0] : (~creative(X0) <=> (strong(X0) & quiet(X0))) [input p7]
11. ? [X0] : wise(X0) <=> (~happy(mary) & brave(mary)) [input p10]
12. ! [X0] : ((generous(X0) & quiet(X0)) <=> (calm(X0) | ~wise(X0))) [input p11]
13. ! [X0] : (~calm(X0) <=> (happy(X0) & curious(X0))) [input p12]
14. ! [X0] : ((~tall(X0) | quiet(X0)) <=> (~strong(X0) | ~generous(X0))) [input p13]
16. (strong(mary) & ~wise(mary)) <=> (kind(lucy) & creative(lucy)) [input p15]
25. kind(lucy) [input hypothesis]
38. ! [X0] : (((calm(X0) | patient(X0)) | (~kind(X0) & ~creative(X0))) & ((kind(X0) | creative(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 2]
39. ! [X0] : ((calm(X0) | patient(X0) | (~kind(X0) & ~creative(X0))) & (kind(X0) | creative(X0) | (~calm(X0) & ~patient(X0)))) [flattening 38]
43. (? [X0] : ~generous(X0) | ((~generous(lucy) | ~patient(lucy)) & (patient(lucy) | generous(lucy)))) & (((~patient(lucy) | generous(lucy)) & (patient(lucy) | ~generous(lucy))) | ! [X0] : generous(X0)) [nnf transformation 5]
44. (? [X0] : ~generous(X0) | ((~generous(lucy) | ~patient(lucy)) & (patient(lucy) | generous(lucy)))) & (((~patient(lucy) | generous(lucy)) & (patient(lucy) | ~generous(lucy))) | ! [X1] : generous(X1)) [rectify 43]
45. ? [X0] : ~generous(X0) => ~generous(sK2) [choice axiom]
46. (~generous(sK2) | ((~generous(lucy) | ~patient(lucy)) & (patient(lucy) | generous(lucy)))) & (((~patient(lucy) | generous(lucy)) & (patient(lucy) | ~generous(lucy))) | ! [X1] : generous(X1)) [skolemisation 44,45]
53. ! [X0] : ((~creative(X0) | (~strong(X0) | ~quiet(X0))) & ((strong(X0) & quiet(X0)) | creative(X0))) [nnf transformation 8]
54. ! [X0] : ((~creative(X0) | ~strong(X0) | ~quiet(X0)) & ((strong(X0) & quiet(X0)) | creative(X0))) [flattening 53]
55. (? [X0] : wise(X0) | (happy(mary) | ~brave(mary))) & ((~happy(mary) & brave(mary)) | ! [X0] : ~wise(X0)) [nnf transformation 11]
56. (? [X0] : wise(X0) | happy(mary) | ~brave(mary)) & ((~happy(mary) & brave(mary)) | ! [X0] : ~wise(X0)) [flattening 55]
57. (? [X0] : wise(X0) | happy(mary) | ~brave(mary)) & ((~happy(mary) & brave(mary)) | ! [X1] : ~wise(X1)) [rectify 56]
58. ? [X0] : wise(X0) => wise(sK5) [choice axiom]
59. (wise(sK5) | happy(mary) | ~brave(mary)) & ((~happy(mary) & brave(mary)) | ! [X1] : ~wise(X1)) [skolemisation 57,58]
60. ! [X0] : (((generous(X0) & quiet(X0)) | (~calm(X0) & wise(X0))) & ((calm(X0) | ~wise(X0)) | (~generous(X0) | ~quiet(X0)))) [nnf transformation 12]
61. ! [X0] : (((generous(X0) & quiet(X0)) | (~calm(X0) & wise(X0))) & (calm(X0) | ~wise(X0) | ~generous(X0) | ~quiet(X0))) [flattening 60]
62. ! [X0] : ((~calm(X0) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | calm(X0))) [nnf transformation 13]
63. ! [X0] : ((~calm(X0) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | calm(X0))) [flattening 62]
64. ! [X0] : (((~tall(X0) | quiet(X0)) | (strong(X0) & generous(X0))) & ((~strong(X0) | ~generous(X0)) | (tall(X0) & ~quiet(X0)))) [nnf transformation 14]
65. ! [X0] : ((~tall(X0) | quiet(X0) | (strong(X0) & generous(X0))) & (~strong(X0) | ~generous(X0) | (tall(X0) & ~quiet(X0)))) [flattening 64]
71. ((strong(mary) & ~wise(mary)) | (~kind(lucy) | ~creative(lucy))) & ((kind(lucy) & creative(lucy)) | (~strong(mary) | wise(mary))) [nnf transformation 16]
72. ((strong(mary) & ~wise(mary)) | ~kind(lucy) | ~creative(lucy)) & ((kind(lucy) & creative(lucy)) | ~strong(mary) | wise(mary)) [flattening 71]
96. ~kind(X0) | patient(X0) | calm(X0) [cnf transformation 39]
101. ~patient(lucy) | generous(lucy) | generous(X1) [cnf transformation 46]
110. quiet(X0) | creative(X0) [cnf transformation 54]
111. strong(X0) | creative(X0) [cnf transformation 54]
120. ~happy(mary) | ~wise(X1) [cnf transformation 59]
123. wise(X0) | quiet(X0) [cnf transformation 61]
124. ~calm(X0) | quiet(X0) [cnf transformation 61]
125. wise(X0) | generous(X0) [cnf transformation 61]
126. ~calm(X0) | generous(X0) [cnf transformation 61]
128. happy(X0) | calm(X0) [cnf transformation 63]
130. ~generous(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 65]
142. ~wise(mary) | ~kind(lucy) | ~creative(lucy) [cnf transformation 72]
143. strong(mary) | ~kind(lucy) | ~creative(lucy) [cnf transformation 72]
157. kind(lucy) [cnf transformation 25]
202. 11 <=> patient(lucy) [avatar definition]
204. ~patient(lucy) <- (~11) [avatar component clause 202]
206. 12 <=> generous(lucy) [avatar definition]
207. generous(lucy) <- (12) [avatar component clause 206]
208. ~generous(lucy) <- (~12) [avatar component clause 206]
216. 14 <=> ! [X1] : generous(X1) [avatar definition]
217. generous(X1) <- (14) [avatar component clause 216]
218. 14 | 12 | ~11 [avatar split clause 101,202,206,216]
252. 22 <=> happy(mary) [avatar definition]
253. ~happy(mary) <- (~22) [avatar component clause 252]
261. 24 <=> ! [X1] : ~wise(X1) [avatar definition]
262. ~wise(X1) <- (24) [avatar component clause 261]
263. 24 | ~22 [avatar split clause 120,252,261]
300. 33 <=> creative(lucy) [avatar definition]
302. ~creative(lucy) <- (~33) [avatar component clause 300]
304. 34 <=> kind(lucy) [avatar definition]
305. kind(lucy) <- (34) [avatar component clause 304]
308. 35 <=> strong(mary) [avatar definition]
310. strong(mary) <- (35) [avatar component clause 308]
311. ~33 | ~34 | 35 [avatar split clause 143,308,304,300]
313. 36 <=> wise(mary) [avatar definition]
315. ~wise(mary) <- (~36) [avatar component clause 313]
316. ~33 | ~34 | ~36 [avatar split clause 142,313,304,300]
367. 34 [avatar split clause 157,304]
380. calm(mary) <- (~22) [resolution 128,253]
384. generous(mary) <- (~22) [resolution 380,126]
385. quiet(mary) <- (~22) [resolution 380,124]
438. patient(lucy) | calm(lucy) <- (34) [resolution 96,305]
441. calm(lucy) <- (~11, 34) [subsumption resolution 438,204]
446. generous(lucy) <- (~11, 34) [resolution 441,126]
448. $false <- (~11, ~12, 34) [subsumption resolution 446,208]
449. 11 | 12 | ~34 [avatar contradiction clause 448]
499. ~strong(lucy) | ~quiet(lucy) <- (12) [resolution 130,207]
507. 63 <=> quiet(lucy) [avatar definition]
509. ~quiet(lucy) <- (~63) [avatar component clause 507]
511. 64 <=> strong(lucy) [avatar definition]
513. ~strong(lucy) <- (~64) [avatar component clause 511]
514. ~63 | ~64 | ~12 [avatar split clause 499,206,511,507]
576. creative(lucy) <- (~64) [resolution 513,111]
581. 33 | 64 [avatar split clause 576,511,300]
593. quiet(mary) <- (~36) [resolution 315,123]
638. ~strong(mary) | ~quiet(mary) <- (~22) [resolution 384,130]
640. ~quiet(mary) <- (~22, 35) [subsumption resolution 638,310]
641. $false <- (~22, 35) [subsumption resolution 640,385]
642. 22 | ~35 [avatar contradiction clause 641]
645. generous(X0) <- (24) [resolution 262,125]
648. 14 | ~24 [avatar split clause 645,261,216]
652. creative(lucy) <- (~63) [resolution 509,110]
653. $false <- (~33, ~63) [subsumption resolution 652,302]
654. 33 | 63 [avatar contradiction clause 653]
655. ~quiet(X0) | ~strong(X0) <- (14) [resolution 217,130]
688. ~strong(X1) | creative(X1) <- (14) [resolution 655,110]
690. ~strong(mary) <- (14, ~36) [resolution 655,593]
696. creative(X1) <- (14) [subsumption resolution 688,111]
697. $false <- (14, 35, ~36) [subsumption resolution 690,310]
698. ~14 | ~35 | 36 [avatar contradiction clause 697]
703. $false <- (14, ~33) [subsumption resolution 302,696]
704. ~14 | 33 [avatar contradiction clause 703]
707. $false [avatar sat refutation 218,263,311,316,367,449,514,581,642,648,654,698,704]
% SZS output end Proof for 6880222751943882622375677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or patient is either not strong or funny and vice versa. Everyone who is either not kind or old is either humble or kind. Everyone who is both not quiet and not curious is not calm. If someone is not happy or wise then someone is old and vice versa. If susan is wise or strong then paul is either generous or happy. Everyone who is both happy and not creative is both not patient and humble. Everyone who is wise or not rich is not rich or not funny and vice versa. Everyone who is happy is kind or rich. Everyone who is either kind or not funny is both curious and not tall and vice versa. If mary is not generous or not patient then john is both tall and happy. Everyone who is not calm is not calm or old and vice versa. If someone is both funny and humble then someone is both not quiet and quiet and vice versa. Everyone who is both curious and not tall is patient or not rich and vice versa. If mary is either not tall or strong then lucy is both not tall and generous. If alice is rich then alice is happy. Everyone who is both not brave and not generous is not strong or generous. Fred is not strong. Someone is both not curious and rich. Someone is both not funny and rich. John is either funny or not kind. Mary is both old and generous. Someone is funny. Someone is not kind or rich. Paul is not calm. | Mary is not calm. | entailment | (![X]:((~patient(X)|patient(X))<=>(~strong(X)<~>funny(X))))&
(![X]:((~kind(X)<~>old(X))=>(humble(X)<~>kind(X))))&
(![X]:((~quiet(X)&~curious(X))=>~calm(X)))&
((?[X]:((~happy(X)|wise(X))))<=>(?[X]:(old(X))))&
(((wise(susan)|strong(susan)))=>((generous(paul)<~>happy(paul))))&
(![X]:((happy(X)&~creative(X))=>(~patient(X)&humble(X))))&
(![X]:((wise(X)|~rich(X))<=>(~rich(X)|~funny(X))))&
(![X]:(happy(X)=>(kind(X)|rich(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(curious(X)&~tall(X))))&
(((~generous(mary)|~patient(mary)))=>((tall(john)&happy(john))))&
(![X]:(~calm(X)<=>(~calm(X)|old(X))))&
((?[X]:((funny(X)&humble(X))))<=>(?[X]:((~quiet(X)&quiet(X)))))&
(![X]:((curious(X)&~tall(X))<=>(patient(X)|~rich(X))))&
(((~tall(mary)<~>strong(mary)))=>((~tall(lucy)&generous(lucy))))&
((rich(alice))=>(happy(alice)))&
(![X]:((~brave(X)&~generous(X))=>(~strong(X)|generous(X))))&
(~strong(fred))&
(?[X]:((~curious(X)&rich(X))))&
(?[X]:((~funny(X)&rich(X))))&
((funny(john)<~>~kind(john)))&
((old(mary)&generous(mary)))&
(?[X]:(funny(X)))&
(?[X]:((~kind(X)|rich(X))))&
(~calm(paul)) | ~calm(mary) | [
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3823225693948540161605903
% SZS output start Proof for 3823225693948540161605903
11. ! [X0] : (~calm(X0) <=> (old(X0) | ~calm(X0))) [input p10]
21. generous(mary) & old(mary) [input p20]
25. calm(mary) [input hypothesis]
52. ! [X0] : ((~calm(X0) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | calm(X0))) [nnf transformation 11]
53. ! [X0] : ((~calm(X0) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | calm(X0))) [flattening 52]
106. ~calm(X0) | ~old(X0) [cnf transformation 53]
128. old(mary) [cnf transformation 21]
133. calm(mary) [cnf transformation 25]
260. ~old(mary) [resolution 106,133]
261. $false [subsumption resolution 260,128]
% SZS output end Proof for 3823225693948540161605903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.015 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 not old then fred is either not humble or not happy. If lucy is either generous or not funny then someone is quiet. If lucy is rich then someone is both wise and not brave. Everyone who is happy or not strong is either quiet or curious and vice versa. If someone is creative then john is strong or generous and vice versa. If fred is both curious and generous then someone is not quiet and vice versa. Everyone who is both not wise and happy is either not kind or tall. Everyone who is not wise or not happy is not curious or not rich and vice versa. Everyone who is quiet or brave is either curious or kind. Everyone who is not happy is not curious or not funny. If fred is either not generous or humble then susan is patient or not old and vice versa. Everyone who is quiet or strong is either not humble or not brave and vice versa. Everyone who is tall is either rich or not old and vice versa. Everyone who is kind is either not old or not rich. Fred is calm. Alice is not old. Paul is not curious. Mary is not creative. Lucy is rich or not brave. Fred is not curious. Someone is either not wise or quiet. Someone is not humble. | Fred is rich. | entailment | (![X]:((creative(X)|~strong(X))=>(funny(X)&generous(X))))&
(![X]:(~curious(X)<=>~old(X)))&
((~old(john))=>((~humble(fred)<~>~happy(fred))))&
(((generous(lucy)<~>~funny(lucy)))=>(?[X]:(quiet(X))))&
((rich(lucy))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>(quiet(X)<~>curious(X))))&
((?[X]:(creative(X)))<=>((strong(john)|generous(john))))&
(((curious(fred)&generous(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((~wise(X)&happy(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~curious(X)|~rich(X))))&
(![X]:((quiet(X)|brave(X))=>(curious(X)<~>kind(X))))&
(![X]:(~happy(X)=>(~curious(X)|~funny(X))))&
(((~generous(fred)<~>humble(fred)))<=>((patient(susan)|~old(susan))))&
(![X]:((quiet(X)|strong(X))<=>(~humble(X)<~>~brave(X))))&
(![X]:(tall(X)<=>(rich(X)<~>~old(X))))&
(![X]:(kind(X)=>(~old(X)<~>~rich(X))))&
(calm(fred))&
(~old(alice))&
(~curious(paul))&
(~creative(mary))&
((rich(lucy)|~brave(lucy)))&
(~curious(fred))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:(~humble(X))) | rich(fred) | [
"p1",
"p7",
"p10",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8549736688218376880942479
% SZS output start Proof for 8549736688218376880942479
2. ! [X0] : (~curious(X0) <=> ~old(X0)) [input p1]
8. (generous(fred) & curious(fred)) <=> ? [X0] : ~quiet(X0) [input p7]
11. ! [X0] : ((brave(X0) | quiet(X0)) => (curious(X0) <~> kind(X0))) [input p10]
16. ! [X0] : (kind(X0) => (~old(X0) <~> ~rich(X0))) [input p15]
22. ~curious(fred) [input p21]
25. ~rich(fred) [input hypothesis]
33. ! [X0] : ((curious(X0) <~> kind(X0)) | (~brave(X0) & ~quiet(X0))) [ennf transformation 11]
36. ! [X0] : ((~old(X0) <~> ~rich(X0)) | ~kind(X0)) [ennf transformation 16]
37. ! [X0] : ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))) [nnf transformation 2]
51. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (~generous(fred) | ~curious(fred))) [nnf transformation 8]
52. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | ~generous(fred) | ~curious(fred)) [flattening 51]
53. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | ~generous(fred) | ~curious(fred)) [rectify 52]
54. ? [X1] : ~quiet(X1) => ~quiet(sK3) [choice axiom]
55. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (~quiet(sK3) | ~generous(fred) | ~curious(fred)) [skolemisation 53,54]
59. ! [X0] : (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (~brave(X0) & ~quiet(X0))) [nnf transformation 33]
65. ! [X0] : (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ~kind(X0)) [nnf transformation 36]
75. ~old(X0) | curious(X0) [cnf transformation 37]
76. ~curious(X0) | old(X0) [cnf transformation 37]
93. curious(fred) | quiet(X0) [cnf transformation 55]
101. ~quiet(X0) | curious(X0) | kind(X0) [cnf transformation 59]
123. ~kind(X0) | old(X0) | rich(X0) [cnf transformation 65]
128. ~curious(fred) [cnf transformation 22]
132. ~rich(fred) [cnf transformation 25]
190. 13 <=> ! [X0] : quiet(X0) [avatar definition]
191. quiet(X0) <- (13) [avatar component clause 190]
198. 15 <=> curious(fred) [avatar definition]
199. ~curious(fred) <- (~15) [avatar component clause 198]
201. 13 | 15 [avatar split clause 93,198,190]
226. ~15 [avatar split clause 128,198]
257. kind(X1) | curious(X1) <- (13) [resolution 101,191]
281. old(X1) | rich(X1) | curious(X1) <- (13) [resolution 123,257]
282. rich(X1) | old(X1) <- (13) [subsumption resolution 281,76]
283. old(fred) <- (13) [resolution 282,132]
291. curious(fred) <- (13) [resolution 283,75]
292. $false <- (13, ~15) [subsumption resolution 291,199]
293. ~13 | 15 [avatar contradiction clause 292]
294. $false [avatar sat refutation 201,226,293]
% SZS output end Proof for 8549736688218376880942479
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then fred is either rich or not tall.
Everyone who is not kind or tall is both not old and not kind.
If someone is either old or not old then lucy is not generous.
Everyone who is both calm and not rich is funny or strong.
Everyone who is not creative is both calm and generous.
Everyone who is kind is not strong or rich.
If someone is either not strong or not curious then paul is not old or not generous.
Everyone who is not strong is brave or calm.
If alice is either not tall or funny then paul is either not strong or not brave and vice versa.
If someone is both not calm and wise then fred is patient and vice versa.
If someone is brave then alice is not quiet or not happy and vice versa.
Everyone who is not quiet is either quiet or tall and vice versa.
If john is either kind or humble then paul is both brave and tall and vice versa.
If someone is both not calm and not quiet then lucy is either funny or wise and vice versa.
If someone is patient then john is not calm or not strong.
Everyone who is not happy or not brave is happy and vice versa.
John is rich.
Someone is both calm and strong.
Someone is tall.
Susan is both tall and patient.
Alice is both not brave and not wise.
Someone is curious.
Someone is creative.
Mary is either not kind or strong. | Fred is rich. | entailment | ((?[X]:(~humble(X)))=>((rich(fred)<~>~tall(fred))))&
(![X]:((~kind(X)|tall(X))=>(~old(X)&~kind(X))))&
((?[X]:((old(X)<~>~old(X))))=>(~generous(lucy)))&
(![X]:((calm(X)&~rich(X))=>(funny(X)|strong(X))))&
(![X]:(~creative(X)=>(calm(X)&generous(X))))&
(![X]:(kind(X)=>(~strong(X)|rich(X))))&
((?[X]:((~strong(X)<~>~curious(X))))=>((~old(paul)|~generous(paul))))&
(![X]:(~strong(X)=>(brave(X)|calm(X))))&
(((~tall(alice)<~>funny(alice)))<=>((~strong(paul)<~>~brave(paul))))&
((?[X]:((~calm(X)&wise(X))))<=>(patient(fred)))&
((?[X]:(brave(X)))<=>((~quiet(alice)|~happy(alice))))&
(![X]:(~quiet(X)<=>(quiet(X)<~>tall(X))))&
(((kind(john)<~>humble(john)))<=>((brave(paul)&tall(paul))))&
((?[X]:((~calm(X)&~quiet(X))))<=>((funny(lucy)<~>wise(lucy))))&
((?[X]:(patient(X)))=>((~calm(john)|~strong(john))))&
(![X]:((~happy(X)|~brave(X))<=>happy(X)))&
(rich(john))&
(?[X]:((calm(X)&strong(X))))&
(?[X]:(tall(X)))&
((tall(susan)&patient(susan)))&
((~brave(alice)&~wise(alice)))&
(?[X]:(curious(X)))&
(?[X]:(creative(X)))&
((~kind(mary)<~>strong(mary))) | rich(fred) | [
"p0",
"p1",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1218005073076213311811168
% SZS output start Proof for 1218005073076213311811168
1. ? [X0] : ~humble(X0) => (rich(fred) <~> ~tall(fred)) [input p0]
2. ! [X0] : ((tall(X0) | ~kind(X0)) => (~kind(X0) & ~old(X0))) [input p1]
12. ! [X0] : (~quiet(X0) <=> (quiet(X0) <~> tall(X0))) [input p11]
13. (kind(john) <~> humble(john)) <=> (tall(paul) & brave(paul)) [input p12]
16. ! [X0] : ((~brave(X0) | ~happy(X0)) <=> happy(X0)) [input p15]
25. ~rich(fred) [input hypothesis]
31. ! [X0] : ((tall(X0) | ~kind(X0)) => ~kind(X0)) [pure predicate removal 2]
32. (rich(fred) <~> ~tall(fred)) | ! [X0] : humble(X0) [ennf transformation 1]
33. ! [X0] : (~kind(X0) | (~tall(X0) & kind(X0))) [ennf transformation 31]
42. ((tall(fred) | ~rich(fred)) & (~tall(fred) | rich(fred))) | ! [X0] : humble(X0) [nnf transformation 32]
53. ! [X0] : ((~quiet(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | quiet(X0))) [nnf transformation 12]
54. (((~humble(john) | ~kind(john)) & (humble(john) | kind(john))) | (~tall(paul) | ~brave(paul))) & ((tall(paul) & brave(paul)) | ((kind(john) | ~humble(john)) & (humble(john) | ~kind(john)))) [nnf transformation 13]
55. (((~humble(john) | ~kind(john)) & (humble(john) | kind(john))) | ~tall(paul) | ~brave(paul)) & ((tall(paul) & brave(paul)) | ((kind(john) | ~humble(john)) & (humble(john) | ~kind(john)))) [flattening 54]
60. ! [X0] : (((~brave(X0) | ~happy(X0)) | ~happy(X0)) & (happy(X0) | (brave(X0) & happy(X0)))) [nnf transformation 16]
61. ! [X0] : ((~brave(X0) | ~happy(X0) | ~happy(X0)) & (happy(X0) | (brave(X0) & happy(X0)))) [flattening 60]
67. ~tall(fred) | rich(fred) | humble(X0) [cnf transformation 42]
70. ~kind(X0) | ~tall(X0) [cnf transformation 33]
88. tall(X0) | quiet(X0) | quiet(X0) [cnf transformation 53]
90. ~quiet(X0) | tall(X0) | ~quiet(X0) [cnf transformation 53]
93. brave(paul) | kind(john) | ~humble(john) [cnf transformation 55]
105. happy(X0) | happy(X0) [cnf transformation 61]
107. ~brave(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 61]
118. ~rich(fred) [cnf transformation 25]
119. happy(X0) [duplicate literal removal 105]
120. ~happy(X0) | ~brave(X0) [duplicate literal removal 107]
121. tall(X0) | quiet(X0) [duplicate literal removal 88]
122. ~quiet(X0) | tall(X0) [duplicate literal removal 90]
124. 1 <=> ! [X0] : humble(X0) [avatar definition]
125. humble(X0) <- (1) [avatar component clause 124]
127. 2 <=> rich(fred) [avatar definition]
131. 3 <=> tall(fred) [avatar definition]
132. ~tall(fred) <- (~3) [avatar component clause 131]
135. 1 | 2 | ~3 [avatar split clause 67,131,127,124]
137. 4 <=> brave(paul) [avatar definition]
139. brave(paul) <- (4) [avatar component clause 137]
193. 15 <=> ! [X1] : ~brave(X1) [avatar definition]
194. ~brave(X1) <- (15) [avatar component clause 193]
196. tall(X0) [subsumption resolution 121,122]
199. 16 <=> kind(john) [avatar definition]
200. kind(john) <- (16) [avatar component clause 199]
203. 17 <=> humble(john) [avatar definition]
205. ~humble(john) <- (~17) [avatar component clause 203]
209. ~17 | 16 | 4 [avatar split clause 93,137,199,203]
258. ~2 [avatar split clause 118,127]
261. $false <- (~3) [subsumption resolution 132,196]
262. 3 [avatar contradiction clause 261]
263. $false <- (1, ~17) [resolution 205,125]
264. ~1 | 17 [avatar contradiction clause 263]
266. ~brave(X1) [resolution 120,119]
267. 15 [avatar split clause 266,193]
269. $false <- (4, 15) [resolution 194,139]
270. ~4 | ~15 [avatar contradiction clause 269]
272. ~tall(john) <- (16) [resolution 200,70]
273. $false <- (16) [subsumption resolution 272,196]
274. ~16 [avatar contradiction clause 273]
275. $false [avatar sat refutation 135,209,258,262,264,267,270,274]
% SZS output end Proof for 1218005073076213311811168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or tall is funny or brave and vice versa.
Everyone who is tall is both calm and not creative and vice versa.
If someone is not old then alice is not humble.
If paul is either not curious or generous then mary is either not generous or funny.
Everyone who is patient or happy is either tall or wise and vice versa.
If someone is either not funny or not strong then someone is not old.
Everyone who is not old or patient is tall.
If someone is curious or creative then someone is both curious and not kind and vice versa.
If paul is not quiet or not funny then someone is calm and vice versa.
Everyone who is both tall and not brave is not tall or old and vice versa.
If someone is not humble then fred is both not funny and patient.
Everyone who is strong or not kind is humble.
If john is either happy or funny then john is wise and vice versa.
Everyone who is either calm or not patient is both not old and not kind.
Everyone who is both wise and not humble is either not kind or not creative and vice versa.
Everyone who is happy or old is not brave or old and vice versa.
Someone is not generous.
Someone is either calm or not kind.
Someone is both funny and not rich.
Lucy is curious or old.
Fred is not strong or not happy.
Someone is either not calm or not strong. | Alice is not funny. | neutral | (![X]:((~funny(X)|tall(X))<=>(funny(X)|brave(X))))&
(![X]:(tall(X)<=>(calm(X)&~creative(X))))&
((?[X]:(~old(X)))=>(~humble(alice)))&
(((~curious(paul)<~>generous(paul)))=>((~generous(mary)<~>funny(mary))))&
(![X]:((patient(X)|happy(X))<=>(tall(X)<~>wise(X))))&
((?[X]:((~funny(X)<~>~strong(X))))=>(?[X]:(~old(X))))&
(![X]:((~old(X)|patient(X))=>tall(X)))&
((?[X]:((curious(X)|creative(X))))<=>(?[X]:((curious(X)&~kind(X)))))&
(((~quiet(paul)|~funny(paul)))<=>(?[X]:(calm(X))))&
(![X]:((tall(X)&~brave(X))<=>(~tall(X)|old(X))))&
((?[X]:(~humble(X)))=>((~funny(fred)&patient(fred))))&
(![X]:((strong(X)|~kind(X))=>humble(X)))&
(((happy(john)<~>funny(john)))<=>(wise(john)))&
(![X]:((calm(X)<~>~patient(X))=>(~old(X)&~kind(X))))&
(![X]:((wise(X)&~humble(X))<=>(~kind(X)<~>~creative(X))))&
(![X]:((happy(X)|old(X))<=>(~brave(X)|old(X))))&
(?[X]:(~generous(X)))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((funny(X)&~rich(X))))&
((curious(lucy)|old(lucy)))&
((~strong(fred)|~happy(fred)))&
(?[X]:((~calm(X)<~>~strong(X)))) | ~funny(alice) | [] | null | 0 |
Everyone who is not wise is not tall and vice versa. If alice is both not strong and not generous then someone is not tall or patient and vice versa. If someone is either happy or humble then paul is not strong. Everyone who is either not humble or quiet is brave or tall and vice versa. If someone is both creative and not humble then someone is either not creative or tall and vice versa. If paul is either not generous or not patient then someone is old or not strong and vice versa. If someone is either not calm or not happy then mary is both not generous and not rich. If someone is both not tall and not humble then someone is both calm and not happy and vice versa. Everyone who is either brave or not creative is either brave or happy. Everyone who is not humble is both strong and not funny and vice versa. If someone is either old or not kind then someone is creative. Everyone who is creative or not creative is not generous or humble and vice versa. If someone is either wise or rich then someone is either not humble or strong and vice versa. Everyone who is both not kind and not tall is both not generous and wise. Everyone who is both not curious and curious is not quiet or creative and vice versa. If lucy is both not strong and not brave then someone is strong or brave. Paul is not generous. Lucy is either not quiet or not creative. Someone is curious or not humble. Someone is not kind or not curious. Someone is both not brave and not patient. Someone is tall or not brave. Someone is quiet or not curious. Someone is either funny or humble. | Lucy is humble. | entailment | (![X]:(~wise(X)<=>~tall(X)))&
(((~strong(alice)&~generous(alice)))<=>(?[X]:((~tall(X)|patient(X)))))&
((?[X]:((happy(X)<~>humble(X))))=>(~strong(paul)))&
(![X]:((~humble(X)<~>quiet(X))<=>(brave(X)|tall(X))))&
((?[X]:((creative(X)&~humble(X))))<=>(?[X]:((~creative(X)<~>tall(X)))))&
(((~generous(paul)<~>~patient(paul)))<=>(?[X]:((old(X)|~strong(X)))))&
((?[X]:((~calm(X)<~>~happy(X))))=>((~generous(mary)&~rich(mary))))&
((?[X]:((~tall(X)&~humble(X))))<=>(?[X]:((calm(X)&~happy(X)))))&
(![X]:((brave(X)<~>~creative(X))=>(brave(X)<~>happy(X))))&
(![X]:(~humble(X)<=>(strong(X)&~funny(X))))&
((?[X]:((old(X)<~>~kind(X))))=>(?[X]:(creative(X))))&
(![X]:((creative(X)|~creative(X))<=>(~generous(X)|humble(X))))&
((?[X]:((wise(X)<~>rich(X))))<=>(?[X]:((~humble(X)<~>strong(X)))))&
(![X]:((~kind(X)&~tall(X))=>(~generous(X)&wise(X))))&
(![X]:((~curious(X)&curious(X))<=>(~quiet(X)|creative(X))))&
(((~strong(lucy)&~brave(lucy)))=>(?[X]:((strong(X)|brave(X)))))&
(~generous(paul))&
((~quiet(lucy)<~>~creative(lucy)))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((~kind(X)|~curious(X))))&
(?[X]:((~brave(X)&~patient(X))))&
(?[X]:((tall(X)|~brave(X))))&
(?[X]:((quiet(X)|~curious(X))))&
(?[X]:((funny(X)<~>humble(X)))) | humble(lucy) | [
"p3",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 628653419615854868346778
% SZS output start Proof for 628653419615854868346778
4. ! [X0] : ((~humble(X0) <~> quiet(X0)) <=> (tall(X0) | brave(X0))) [input p3]
5. ? [X0] : (~humble(X0) & creative(X0)) <=> ? [X0] : (~creative(X0) <~> tall(X0)) [input p4]
15. ! [X0] : ((curious(X0) & ~curious(X0)) <=> (creative(X0) | ~quiet(X0))) [input p14]
25. ~humble(lucy) [input hypothesis]
26. ? [X0] : (~humble(X0) & creative(X0)) <=> ? [X1] : (~creative(X1) <~> tall(X1)) [rectify 5]
45. ! [X0] : ((((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (~tall(X0) & ~brave(X0))) & ((tall(X0) | brave(X0)) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))))) [nnf transformation 4]
46. ! [X0] : ((((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (~tall(X0) & ~brave(X0))) & (tall(X0) | brave(X0) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))))) [flattening 45]
47. (? [X0] : (~humble(X0) & creative(X0)) | ! [X1] : ((~creative(X1) | ~tall(X1)) & (tall(X1) | creative(X1)))) & (? [X1] : ((~tall(X1) | creative(X1)) & (tall(X1) | ~creative(X1))) | ! [X0] : (humble(X0) | ~creative(X0))) [nnf transformation 26]
48. (? [X0] : (~humble(X0) & creative(X0)) | ! [X1] : ((~creative(X1) | ~tall(X1)) & (tall(X1) | creative(X1)))) & (? [X2] : ((~tall(X2) | creative(X2)) & (tall(X2) | ~creative(X2))) | ! [X3] : (humble(X3) | ~creative(X3))) [rectify 47]
49. ? [X0] : (~humble(X0) & creative(X0)) => (~humble(sK1) & creative(sK1)) [choice axiom]
50. ? [X2] : ((~tall(X2) | creative(X2)) & (tall(X2) | ~creative(X2))) => ((~tall(sK2) | creative(sK2)) & (tall(sK2) | ~creative(sK2))) [choice axiom]
51. ((~humble(sK1) & creative(sK1)) | ! [X1] : ((~creative(X1) | ~tall(X1)) & (tall(X1) | creative(X1)))) & (((~tall(sK2) | creative(sK2)) & (tall(sK2) | ~creative(sK2))) | ! [X3] : (humble(X3) | ~creative(X3))) [skolemisation 48,50,49]
76. ! [X0] : (((curious(X0) & ~curious(X0)) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | (~curious(X0) | curious(X0)))) [nnf transformation 15]
77. ! [X0] : (((curious(X0) & ~curious(X0)) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ~curious(X0) | curious(X0))) [flattening 76]
108. ~quiet(X0) | humble(X0) | ~tall(X0) [cnf transformation 46]
111. creative(sK1) | tall(X1) | creative(X1) [cnf transformation 51]
153. ~curious(X0) | quiet(X0) [cnf transformation 77]
154. ~curious(X0) | ~creative(X0) [cnf transformation 77]
155. curious(X0) | quiet(X0) [cnf transformation 77]
156. ~creative(X0) | curious(X0) [cnf transformation 77]
169. ~humble(lucy) [cnf transformation 25]
181. 3 <=> ! [X0] : tall(X0) [avatar definition]
182. tall(X0) <- (3) [avatar component clause 181]
220. 12 <=> ! [X1] : (tall(X1) | creative(X1)) [avatar definition]
221. tall(X1) | creative(X1) <- (12) [avatar component clause 220]
224. 13 <=> creative(sK1) [avatar definition]
226. creative(sK1) <- (13) [avatar component clause 224]
228. 12 | 13 [avatar split clause 111,224,220]
360. ~creative(X0) [subsumption resolution 154,156]
361. quiet(X0) [subsumption resolution 153,155]
413. $false <- (13) [subsumption resolution 226,360]
414. ~13 [avatar contradiction clause 413]
415. tall(X1) <- (12) [subsumption resolution 221,360]
416. 3 | ~12 [avatar split clause 415,220,181]
447. humble(X0) | ~tall(X0) [resolution 108,361]
448. humble(X0) <- (3) [subsumption resolution 447,182]
455. $false <- (3) [resolution 448,169]
462. ~3 [avatar contradiction clause 455]
463. $false [avatar sat refutation 228,414,416,462]
% SZS output end Proof for 628653419615854868346778
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not curious and not old is not generous.
If paul is rich or old then alice is either not brave or not kind and vice versa.
If someone is generous or not tall then fred is either calm or not strong and vice versa.
Everyone who is not wise or calm is wise and vice versa.
If someone is both brave and not strong then someone is either not happy or tall and vice versa.
Everyone who is either not brave or not patient is quiet.
Everyone who is wise is either not curious or tall and vice versa.
Everyone who is not wise is happy and vice versa.
Everyone who is happy is not quiet and vice versa.
If someone is brave or old then lucy is not old or wise and vice versa.
If john is funny or brave then mary is not happy or old and vice versa.
If someone is both not wise and not calm then alice is both not humble and not old.
If someone is either kind or patient then someone is not kind or tall.
If john is brave then paul is patient or quiet and vice versa.
If paul is either humble or brave then someone is either quiet or not happy and vice versa.
If someone is both not tall and tall then lucy is happy and vice versa.
Someone is either not tall or not strong.
Someone is wise or not generous.
Fred is either not wise or rich.
Someone is either not funny or not creative.
Paul is both creative and not tall.
John is either not quiet or rich.
Paul is humble or funny. | Paul is not quiet. | contradiction | (![X]:((~curious(X)&~old(X))=>~generous(X)))&
(((rich(paul)|old(paul)))<=>((~brave(alice)<~>~kind(alice))))&
((?[X]:((generous(X)|~tall(X))))<=>((calm(fred)<~>~strong(fred))))&
(![X]:((~wise(X)|calm(X))<=>wise(X)))&
((?[X]:((brave(X)&~strong(X))))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(![X]:((~brave(X)<~>~patient(X))=>quiet(X)))&
(![X]:(wise(X)<=>(~curious(X)<~>tall(X))))&
(![X]:(~wise(X)<=>happy(X)))&
(![X]:(happy(X)<=>~quiet(X)))&
((?[X]:((brave(X)|old(X))))<=>((~old(lucy)|wise(lucy))))&
(((funny(john)|brave(john)))<=>((~happy(mary)|old(mary))))&
((?[X]:((~wise(X)&~calm(X))))=>((~humble(alice)&~old(alice))))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:((~kind(X)|tall(X)))))&
((brave(john))<=>((patient(paul)|quiet(paul))))&
(((humble(paul)<~>brave(paul)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
((?[X]:((~tall(X)&tall(X))))<=>(happy(lucy)))&
(?[X]:((~tall(X)<~>~strong(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~wise(fred)<~>rich(fred)))&
(?[X]:((~funny(X)<~>~creative(X))))&
((creative(paul)&~tall(paul)))&
((~quiet(john)<~>rich(john)))&
((humble(paul)|funny(paul))) | ~quiet(paul) | [
"p3",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7029864980088751371980057
% SZS output start Proof for 7029864980088751371980057
4. ! [X0] : ((calm(X0) | ~wise(X0)) <=> wise(X0)) [input p3]
8. ! [X0] : (~wise(X0) <=> happy(X0)) [input p7]
9. ! [X0] : (happy(X0) <=> ~quiet(X0)) [input p8]
24. ~quiet(paul) [input hypothesis]
38. ! [X0] : (((calm(X0) | ~wise(X0)) | ~wise(X0)) & (wise(X0) | (~calm(X0) & wise(X0)))) [nnf transformation 4]
39. ! [X0] : ((calm(X0) | ~wise(X0) | ~wise(X0)) & (wise(X0) | (~calm(X0) & wise(X0)))) [flattening 38]
47. ! [X0] : ((~wise(X0) | ~happy(X0)) & (happy(X0) | wise(X0))) [nnf transformation 8]
48. ! [X0] : ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))) [nnf transformation 9]
93. wise(X0) | wise(X0) [cnf transformation 39]
109. ~wise(X0) | ~happy(X0) [cnf transformation 47]
111. happy(X0) | quiet(X0) [cnf transformation 48]
150. ~quiet(paul) [cnf transformation 24]
151. wise(X0) [duplicate literal removal 93]
236. ~happy(X0) [subsumption resolution 109,151]
237. quiet(X0) [subsumption resolution 111,236]
332. $false [subsumption resolution 150,237]
% SZS output end Proof for 7029864980088751371980057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or old then mary is not rich or not humble. Everyone who is both not kind and funny is strong or happy and vice versa. If someone is both not tall and not patient then someone is not strong and vice versa. Everyone who is either kind or not brave is not old and vice versa. Everyone who is generous or not generous is not rich. If susan is both patient and happy then susan is not rich and vice versa. Everyone who is both not generous and rich is either not calm or rich. Everyone who is not quiet or not humble is strong. Everyone who is not funny or not rich is both not old and happy and vice versa. Everyone who is either strong or not tall is both strong and not curious. Everyone who is either not generous or old is not patient. If susan is either not curious or not kind then fred is strong and vice versa. Everyone who is either not brave or creative is both generous and not curious. If lucy is not patient then lucy is both strong and not patient and vice versa. Everyone who is either quiet or not curious is funny and vice versa. Lucy is not generous. John is either not humble or kind. Someone is both wise and calm. Someone is not quiet or strong. Someone is not humble or curious. Someone is either quiet or wise. | Susan is not old. | entailment | ((?[X]:((quiet(X)|old(X))))=>((~rich(mary)|~humble(mary))))&
(![X]:((~kind(X)&funny(X))<=>(strong(X)|happy(X))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:(~strong(X))))&
(![X]:((kind(X)<~>~brave(X))<=>~old(X)))&
(![X]:((generous(X)|~generous(X))=>~rich(X)))&
(((patient(susan)&happy(susan)))<=>(~rich(susan)))&
(![X]:((~generous(X)&rich(X))=>(~calm(X)<~>rich(X))))&
(![X]:((~quiet(X)|~humble(X))=>strong(X)))&
(![X]:((~funny(X)|~rich(X))<=>(~old(X)&happy(X))))&
(![X]:((strong(X)<~>~tall(X))=>(strong(X)&~curious(X))))&
(![X]:((~generous(X)<~>old(X))=>~patient(X)))&
(((~curious(susan)<~>~kind(susan)))<=>(strong(fred)))&
(![X]:((~brave(X)<~>creative(X))=>(generous(X)&~curious(X))))&
((~patient(lucy))<=>((strong(lucy)&~patient(lucy))))&
(![X]:((quiet(X)<~>~curious(X))<=>funny(X)))&
(~generous(lucy))&
((~humble(john)<~>kind(john)))&
(?[X]:((wise(X)&calm(X))))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((~humble(X)|curious(X))))&
(?[X]:((quiet(X)<~>wise(X)))) | ~old(susan) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 608562245356995833250355
% SZS output start Proof for 608562245356995833250355
5. ! [X0] : ((~generous(X0) | generous(X0)) => ~rich(X0)) [input p4]
9. ! [X0] : ((~rich(X0) | ~funny(X0)) <=> (happy(X0) & ~old(X0))) [input p8]
22. old(susan) [input hypothesis]
26. ! [X0] : (~rich(X0) | (generous(X0) & ~generous(X0))) [ennf transformation 5]
44. ! [X0] : (((~rich(X0) | ~funny(X0)) | (~happy(X0) | old(X0))) & ((happy(X0) & ~old(X0)) | (rich(X0) & funny(X0)))) [nnf transformation 9]
45. ! [X0] : ((~rich(X0) | ~funny(X0) | ~happy(X0) | old(X0)) & ((happy(X0) & ~old(X0)) | (rich(X0) & funny(X0)))) [flattening 44]
77. ~rich(X0) | ~generous(X0) [cnf transformation 26]
78. ~rich(X0) | generous(X0) [cnf transformation 26]
87. ~old(X0) | rich(X0) [cnf transformation 45]
121. old(susan) [cnf transformation 22]
125. 1 <=> ! [X0] : ~old(X0) [avatar definition]
126. ~old(X0) <- (1) [avatar component clause 125]
161. ~rich(X0) [subsumption resolution 77,78]
165. ~old(X0) [subsumption resolution 87,161]
166. 1 [avatar split clause 165,125]
222. $false <- (1) [resolution 126,121]
223. ~1 [avatar contradiction clause 222]
224. $false [avatar sat refutation 166,223]
% SZS output end Proof for 608562245356995833250355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is either rich or creative.
If someone is generous then someone is patient.
Everyone who is either tall or not rich is both patient and not wise.
If john is not humble then someone is either wise or brave and vice versa.
Everyone who is not rich or not curious is both not generous and not happy.
Everyone who is kind or not tall is happy and vice versa.
If alice is not brave or generous then paul is both quiet and humble and vice versa.
Everyone who is both funny and not quiet is both not funny and not happy and vice versa.
If someone is not old then fred is both quiet and not old and vice versa.
Everyone who is happy is either not wise or not old.
Everyone who is not kind is both generous and wise.
If someone is either not quiet or kind then fred is either not tall or not humble.
If someone is patient then lucy is both wise and not rich and vice versa.
If mary is both quiet and not funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
Mary is quiet.
Someone is strong.
Someone is kind.
Someone is both humble and rich.
John is not strong.
Someone is either creative or old.
Lucy is either rich or not happy. | Lucy is curious. | entailment | (![X]:(old(X)=>(rich(X)<~>creative(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
(![X]:((tall(X)<~>~rich(X))=>(patient(X)&~wise(X))))&
((~humble(john))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((~rich(X)|~curious(X))=>(~generous(X)&~happy(X))))&
(![X]:((kind(X)|~tall(X))<=>happy(X)))&
(((~brave(alice)|generous(alice)))<=>((quiet(paul)&humble(paul))))&
(![X]:((funny(X)&~quiet(X))<=>(~funny(X)&~happy(X))))&
((?[X]:(~old(X)))<=>((quiet(fred)&~old(fred))))&
(![X]:(happy(X)=>(~wise(X)<~>~old(X))))&
(![X]:(~kind(X)=>(generous(X)&wise(X))))&
((?[X]:((~quiet(X)<~>kind(X))))=>((~tall(fred)<~>~humble(fred))))&
((?[X]:(patient(X)))<=>((wise(lucy)&~rich(lucy))))&
(((quiet(mary)&~funny(mary)))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(quiet(mary))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&rich(X))))&
(~strong(john))&
(?[X]:((creative(X)<~>old(X))))&
((rich(lucy)<~>~happy(lucy))) | curious(lucy) | [
"p4",
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 609713338046140736879935
% SZS output start Proof for 609713338046140736879935
5. ! [X0] : ((~curious(X0) | ~rich(X0)) => (~happy(X0) & ~generous(X0))) [input p4]
6. ! [X0] : ((~tall(X0) | kind(X0)) <=> happy(X0)) [input p5]
11. ! [X0] : (~kind(X0) => (wise(X0) & generous(X0))) [input p10]
24. ~curious(lucy) [input hypothesis]
29. ! [X0] : ((~happy(X0) & ~generous(X0)) | (curious(X0) & rich(X0))) [ennf transformation 5]
31. ! [X0] : ((wise(X0) & generous(X0)) | kind(X0)) [ennf transformation 11]
44. ! [X0] : (((~tall(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [nnf transformation 6]
45. ! [X0] : ((~tall(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [flattening 44]
90. ~generous(X0) | curious(X0) [cnf transformation 29]
92. ~happy(X0) | curious(X0) [cnf transformation 29]
93. ~kind(X0) | happy(X0) [cnf transformation 45]
110. kind(X0) | generous(X0) [cnf transformation 31]
138. ~curious(lucy) [cnf transformation 24]
296. happy(X0) | generous(X0) [resolution 110,93]
338. generous(X1) | curious(X1) [resolution 296,92]
340. curious(X1) [subsumption resolution 338,90]
345. $false [resolution 340,138]
% SZS output end Proof for 609713338046140736879935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not kind and creative then someone is either quiet or generous.
If lucy is kind then someone is quiet or not old.
Everyone who is both kind and old is strong.
Everyone who is creative is both tall and patient and vice versa.
Everyone who is both kind and quiet is brave.
Everyone who is kind or not curious is not quiet or not happy.
Everyone who is curious or not funny is either humble or not generous.
If someone is either not funny or not curious then someone is humble or not funny and vice versa.
Everyone who is not quiet is happy.
Everyone who is not patient is not rich or not happy.
Everyone who is not brave is not rich and vice versa.
If someone is patient or humble then fred is creative and vice versa.
If someone is generous or not strong then someone is old.
Everyone who is not happy is either wise or not rich and vice versa.
If paul is either not tall or strong then someone is not creative or generous.
Everyone who is either calm or not brave is not quiet.
Someone is either not patient or not quiet.
Someone is either not old or not creative.
Paul is not creative or not happy.
Someone is either happy or not quiet.
Lucy is not kind or generous.
Mary is both not creative and humble.
Someone is brave or wise.
Lucy is both tall and humble. | Fred is creative. | entailment | (((~kind(fred)&creative(fred)))=>(?[X]:((quiet(X)<~>generous(X)))))&
((kind(lucy))=>(?[X]:((quiet(X)|~old(X)))))&
(![X]:((kind(X)&old(X))=>strong(X)))&
(![X]:(creative(X)<=>(tall(X)&patient(X))))&
(![X]:((kind(X)&quiet(X))=>brave(X)))&
(![X]:((kind(X)|~curious(X))=>(~quiet(X)|~happy(X))))&
(![X]:((curious(X)|~funny(X))=>(humble(X)<~>~generous(X))))&
((?[X]:((~funny(X)<~>~curious(X))))<=>(?[X]:((humble(X)|~funny(X)))))&
(![X]:(~quiet(X)=>happy(X)))&
(![X]:(~patient(X)=>(~rich(X)|~happy(X))))&
(![X]:(~brave(X)<=>~rich(X)))&
((?[X]:((patient(X)|humble(X))))<=>(creative(fred)))&
((?[X]:((generous(X)|~strong(X))))=>(?[X]:(old(X))))&
(![X]:(~happy(X)<=>(wise(X)<~>~rich(X))))&
(((~tall(paul)<~>strong(paul)))=>(?[X]:((~creative(X)|generous(X)))))&
(![X]:((calm(X)<~>~brave(X))=>~quiet(X)))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((~old(X)<~>~creative(X))))&
((~creative(paul)|~happy(paul)))&
(?[X]:((happy(X)<~>~quiet(X))))&
((~kind(lucy)|generous(lucy)))&
((~creative(mary)&humble(mary)))&
(?[X]:((brave(X)|wise(X))))&
((tall(lucy)&humble(lucy))) | creative(fred) | [
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8579986864660293739603636
% SZS output start Proof for 8579986864660293739603636
12. ? [X0] : (humble(X0) | patient(X0)) <=> creative(fred) [input p11]
22. humble(mary) & ~creative(mary) [input p21]
25. ~creative(fred) [input hypothesis]
58. (? [X0] : (humble(X0) | patient(X0)) | ~creative(fred)) & (creative(fred) | ! [X0] : (~humble(X0) & ~patient(X0))) [nnf transformation 12]
59. (? [X0] : (humble(X0) | patient(X0)) | ~creative(fred)) & (creative(fred) | ! [X1] : (~humble(X1) & ~patient(X1))) [rectify 58]
60. ? [X0] : (humble(X0) | patient(X0)) => (humble(sK4) | patient(sK4)) [choice axiom]
61. ((humble(sK4) | patient(sK4)) | ~creative(fred)) & (creative(fred) | ! [X1] : (~humble(X1) & ~patient(X1))) [skolemisation 59,60]
106. creative(fred) | ~humble(X1) [cnf transformation 61]
127. humble(mary) [cnf transformation 22]
131. ~creative(fred) [cnf transformation 25]
137. 2 <=> creative(fred) [avatar definition]
176. 11 <=> ! [X1] : ~humble(X1) [avatar definition]
177. ~humble(X1) <- (11) [avatar component clause 176]
206. 11 | 2 [avatar split clause 106,137,176]
286. ~2 [avatar split clause 131,137]
287. $false <- (11) [resolution 177,127]
290. ~11 [avatar contradiction clause 287]
291. $false [avatar sat refutation 206,286,290]
% SZS output end Proof for 8579986864660293739603636
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not brave is either not creative or not old and vice versa.
Everyone who is either brave or kind is either happy or brave.
Everyone who is not kind is both not humble and generous.
If susan is both not generous and generous then lucy is not wise or not funny.
Everyone who is either old or not happy is happy.
Everyone who is both quiet and not brave is not curious or old.
Everyone who is humble is not quiet or strong.
If fred is not tall or humble then fred is not creative or humble and vice versa.
If fred is quiet or strong then someone is either funny or not creative and vice versa.
Everyone who is rich or quiet is both humble and calm.
Everyone who is both not patient and not kind is both generous and strong and vice versa.
Everyone who is not generous or not humble is not tall.
Everyone who is either kind or strong is both old and not calm.
Everyone who is old is either tall or wise and vice versa.
If alice is either not tall or not kind then someone is not brave or not calm and vice versa.
If alice is either humble or generous then fred is either wise or not wise and vice versa.
Someone is not funny or not humble.
Someone is humble or tall.
Someone is not happy or not strong.
Someone is both not humble and happy.
Susan is both not creative and not happy.
Someone is either not tall or calm.
Someone is both not curious and happy.
Someone is calm. | Alice is kind. | entailment | (![X]:((patient(X)&~brave(X))<=>(~creative(X)<~>~old(X))))&
(![X]:((brave(X)<~>kind(X))=>(happy(X)<~>brave(X))))&
(![X]:(~kind(X)=>(~humble(X)&generous(X))))&
(((~generous(susan)&generous(susan)))=>((~wise(lucy)|~funny(lucy))))&
(![X]:((old(X)<~>~happy(X))=>happy(X)))&
(![X]:((quiet(X)&~brave(X))=>(~curious(X)|old(X))))&
(![X]:(humble(X)=>(~quiet(X)|strong(X))))&
(((~tall(fred)|humble(fred)))<=>((~creative(fred)|humble(fred))))&
(((quiet(fred)|strong(fred)))<=>(?[X]:((funny(X)<~>~creative(X)))))&
(![X]:((rich(X)|quiet(X))=>(humble(X)&calm(X))))&
(![X]:((~patient(X)&~kind(X))<=>(generous(X)&strong(X))))&
(![X]:((~generous(X)|~humble(X))=>~tall(X)))&
(![X]:((kind(X)<~>strong(X))=>(old(X)&~calm(X))))&
(![X]:(old(X)<=>(tall(X)<~>wise(X))))&
(((~tall(alice)<~>~kind(alice)))<=>(?[X]:((~brave(X)|~calm(X)))))&
(((humble(alice)<~>generous(alice)))<=>((wise(fred)<~>~wise(fred))))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((humble(X)|tall(X))))&
(?[X]:((~happy(X)|~strong(X))))&
(?[X]:((~humble(X)&happy(X))))&
((~creative(susan)&~happy(susan)))&
(?[X]:((~tall(X)<~>calm(X))))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:(calm(X))) | kind(alice) | [
"p0",
"p2",
"p4",
"p11",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6109212400303253949483000
% SZS output start Proof for 6109212400303253949483000
1. ! [X0] : ((~brave(X0) & patient(X0)) <=> (~creative(X0) <~> ~old(X0))) [input p0]
3. ! [X0] : (~kind(X0) => (generous(X0) & ~humble(X0))) [input p2]
5. ! [X0] : ((old(X0) <~> ~happy(X0)) => happy(X0)) [input p4]
12. ! [X0] : ((~humble(X0) | ~generous(X0)) => ~tall(X0)) [input p11]
15. (~tall(alice) <~> ~kind(alice)) <=> ? [X0] : (~calm(X0) | ~brave(X0)) [input p14]
21. ~happy(susan) & ~creative(susan) [input p20]
25. ~kind(alice) [input hypothesis]
30. ! [X0] : ((generous(X0) & ~humble(X0)) | kind(X0)) [ennf transformation 3]
33. ! [X0] : (happy(X0) | (old(X0) <=> ~happy(X0))) [ennf transformation 5]
37. ! [X0] : (~tall(X0) | (humble(X0) & generous(X0))) [ennf transformation 12]
39. ! [X0] : (((~brave(X0) & patient(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) & (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (brave(X0) | ~patient(X0)))) [nnf transformation 1]
40. ! [X0] : (((~brave(X0) & patient(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) & (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | brave(X0) | ~patient(X0))) [flattening 39]
42. ! [X0] : (happy(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 33]
54. (((kind(alice) | tall(alice)) & (~kind(alice) | ~tall(alice))) | ! [X0] : (calm(X0) & brave(X0))) & (? [X0] : (~calm(X0) | ~brave(X0)) | ((~tall(alice) | kind(alice)) & (~kind(alice) | tall(alice)))) [nnf transformation 15]
55. (((kind(alice) | tall(alice)) & (~kind(alice) | ~tall(alice))) | ! [X0] : (calm(X0) & brave(X0))) & (? [X1] : (~calm(X1) | ~brave(X1)) | ((~tall(alice) | kind(alice)) & (~kind(alice) | tall(alice)))) [rectify 54]
56. ? [X1] : (~calm(X1) | ~brave(X1)) => (~calm(sK1) | ~brave(sK1)) [choice axiom]
57. (((kind(alice) | tall(alice)) & (~kind(alice) | ~tall(alice))) | ! [X0] : (calm(X0) & brave(X0))) & ((~calm(sK1) | ~brave(sK1)) | ((~tall(alice) | kind(alice)) & (~kind(alice) | tall(alice)))) [skolemisation 55,56]
78. ~old(X0) | ~brave(X0) | creative(X0) [cnf transformation 40]
84. ~humble(X0) | kind(X0) [cnf transformation 30]
88. happy(X0) | old(X0) | happy(X0) [cnf transformation 42]
107. ~tall(X0) | humble(X0) [cnf transformation 37]
120. kind(alice) | tall(alice) | brave(X0) [cnf transformation 57]
135. ~creative(susan) [cnf transformation 21]
136. ~happy(susan) [cnf transformation 21]
141. ~kind(alice) [cnf transformation 25]
146. happy(X0) | old(X0) [duplicate literal removal 88]
195. 11 <=> tall(alice) [avatar definition]
197. tall(alice) <- (11) [avatar component clause 195]
199. 12 <=> kind(alice) [avatar definition]
200. ~kind(alice) <- (~12) [avatar component clause 199]
204. 13 <=> ! [X0] : brave(X0) [avatar definition]
205. brave(X0) <- (13) [avatar component clause 204]
206. 13 | 11 | 12 [avatar split clause 120,199,195,204]
224. 17 <=> humble(alice) [avatar definition]
225. humble(alice) <- (17) [avatar component clause 224]
226. ~humble(alice) <- (~17) [avatar component clause 224]
264. ~12 [avatar split clause 141,199]
265. kind(alice) <- (17) [resolution 84,225]
267. $false <- (~12, 17) [subsumption resolution 265,200]
268. 12 | ~17 [avatar contradiction clause 267]
270. humble(alice) <- (11) [resolution 107,197]
271. $false <- (11, ~17) [subsumption resolution 270,226]
272. ~11 | 17 [avatar contradiction clause 271]
280. old(susan) [resolution 146,136]
295. ~brave(susan) | creative(susan) [resolution 78,280]
296. creative(susan) <- (13) [subsumption resolution 295,205]
297. $false <- (13) [subsumption resolution 296,135]
298. ~13 [avatar contradiction clause 297]
299. $false [avatar sat refutation 206,264,268,272,298]
% SZS output end Proof for 6109212400303253949483000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or brave is both not kind and generous and vice versa.
If someone is funny then fred is curious and vice versa.
If paul is both strong and not wise then someone is happy and vice versa.
If mary is both funny and not brave then paul is not happy or quiet and vice versa.
Everyone who is either quiet or brave is either tall or not calm.
Everyone who is tall or not funny is either not calm or not funny.
If someone is either not old or not strong then alice is both old and rich.
If paul is either tall or calm then someone is either calm or happy and vice versa.
Everyone who is creative is brave or strong.
Everyone who is not funny is not strong.
If someone is not humble then someone is both not quiet and happy.
Everyone who is not kind or calm is both not brave and happy and vice versa.
If alice is either not curious or strong then someone is both not funny and not generous and vice versa.
Everyone who is not old is either not tall or curious.
Everyone who is quiet is either not calm or not generous and vice versa.
If someone is calm then someone is not wise or happy.
Someone is patient.
Someone is both not patient and not curious.
Susan is both funny and not quiet.
Someone is quiet or not humble.
Someone is both not creative and calm.
Someone is either not happy or not humble.
Alice is not creative. | Paul is tall. | contradiction | (![X]:((strong(X)|brave(X))<=>(~kind(X)&generous(X))))&
((?[X]:(funny(X)))<=>(curious(fred)))&
(((strong(paul)&~wise(paul)))<=>(?[X]:(happy(X))))&
(((funny(mary)&~brave(mary)))<=>((~happy(paul)|quiet(paul))))&
(![X]:((quiet(X)<~>brave(X))=>(tall(X)<~>~calm(X))))&
(![X]:((tall(X)|~funny(X))=>(~calm(X)<~>~funny(X))))&
((?[X]:((~old(X)<~>~strong(X))))=>((old(alice)&rich(alice))))&
(((tall(paul)<~>calm(paul)))<=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:(creative(X)=>(brave(X)|strong(X))))&
(![X]:(~funny(X)=>~strong(X)))&
((?[X]:(~humble(X)))=>(?[X]:((~quiet(X)&happy(X)))))&
(![X]:((~kind(X)|calm(X))<=>(~brave(X)&happy(X))))&
(((~curious(alice)<~>strong(alice)))<=>(?[X]:((~funny(X)&~generous(X)))))&
(![X]:(~old(X)=>(~tall(X)<~>curious(X))))&
(![X]:(quiet(X)<=>(~calm(X)<~>~generous(X))))&
((?[X]:(calm(X)))=>(?[X]:((~wise(X)|happy(X)))))&
(?[X]:(patient(X)))&
(?[X]:((~patient(X)&~curious(X))))&
((funny(susan)&~quiet(susan)))&
(?[X]:((quiet(X)|~humble(X))))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((~happy(X)<~>~humble(X))))&
(~creative(alice)) | tall(paul) | [
"p0",
"p2",
"p4",
"p5",
"p9",
"p11",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 338137539273959225445238
% SZS output start Proof for 338137539273959225445238
1. ! [X0] : ((brave(X0) | strong(X0)) <=> (generous(X0) & ~kind(X0))) [input p0]
3. (~wise(paul) & strong(paul)) <=> ? [X0] : happy(X0) [input p2]
5. ! [X0] : ((quiet(X0) <~> brave(X0)) => (tall(X0) <~> ~calm(X0))) [input p4]
6. ! [X0] : ((~funny(X0) | tall(X0)) => (~calm(X0) <~> ~funny(X0))) [input p5]
10. ! [X0] : (~funny(X0) => ~strong(X0)) [input p9]
12. ! [X0] : ((calm(X0) | ~kind(X0)) <=> (happy(X0) & ~brave(X0))) [input p11]
15. ! [X0] : (quiet(X0) <=> (~calm(X0) <~> ~generous(X0))) [input p14]
21. ? [X0] : (calm(X0) & ~creative(X0)) [input p20]
24. tall(paul) [input hypothesis]
27. ? [X0] : calm(X0) [pure predicate removal 21]
31. ! [X0] : ((tall(X0) <~> ~calm(X0)) | (quiet(X0) <=> brave(X0))) [ennf transformation 5]
32. ! [X0] : ((~calm(X0) <~> ~funny(X0)) | (funny(X0) & ~tall(X0))) [ennf transformation 6]
34. ! [X0] : (~strong(X0) | funny(X0)) [ennf transformation 10]
38. ! [X0] : (((brave(X0) | strong(X0)) | (~generous(X0) | kind(X0))) & ((generous(X0) & ~kind(X0)) | (~brave(X0) & ~strong(X0)))) [nnf transformation 1]
39. ! [X0] : ((brave(X0) | strong(X0) | ~generous(X0) | kind(X0)) & ((generous(X0) & ~kind(X0)) | (~brave(X0) & ~strong(X0)))) [flattening 38]
44. ((~wise(paul) & strong(paul)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | (wise(paul) | ~strong(paul))) [nnf transformation 3]
45. ((~wise(paul) & strong(paul)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | wise(paul) | ~strong(paul)) [flattening 44]
46. ((~wise(paul) & strong(paul)) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | wise(paul) | ~strong(paul)) [rectify 45]
47. ? [X1] : happy(X1) => happy(sK1) [choice axiom]
48. ((~wise(paul) & strong(paul)) | ! [X0] : ~happy(X0)) & (happy(sK1) | wise(paul) | ~strong(paul)) [skolemisation 46,47]
51. ! [X0] : (((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) [nnf transformation 31]
52. ! [X0] : (((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | (funny(X0) & ~tall(X0))) [nnf transformation 32]
61. ! [X0] : (((calm(X0) | ~kind(X0)) | (~happy(X0) | brave(X0))) & ((happy(X0) & ~brave(X0)) | (~calm(X0) & kind(X0)))) [nnf transformation 12]
62. ! [X0] : ((calm(X0) | ~kind(X0) | ~happy(X0) | brave(X0)) & ((happy(X0) & ~brave(X0)) | (~calm(X0) & kind(X0)))) [flattening 61]
68. ! [X0] : ((quiet(X0) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0)))) & (((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | ~quiet(X0))) [nnf transformation 15]
78. ? [X0] : calm(X0) => calm(sK9) [choice axiom]
79. calm(sK9) [skolemisation 27,78]
84. ~kind(X0) | ~brave(X0) [cnf transformation 39]
85. ~strong(X0) | generous(X0) [cnf transformation 39]
91. strong(paul) | ~happy(X0) [cnf transformation 48]
100. ~tall(X0) | calm(X0) | brave(X0) | ~quiet(X0) [cnf transformation 51]
102. ~calm(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 52]
116. ~strong(X0) | funny(X0) [cnf transformation 34]
119. ~brave(X0) | kind(X0) [cnf transformation 62]
122. happy(X0) | ~calm(X0) [cnf transformation 62]
134. ~generous(X0) | quiet(X0) | calm(X0) [cnf transformation 68]
143. calm(sK9) [cnf transformation 79]
146. tall(paul) [cnf transformation 24]
162. 4 <=> ! [X0] : ~happy(X0) [avatar definition]
163. ~happy(X0) <- (4) [avatar component clause 162]
170. 6 <=> strong(paul) [avatar definition]
172. strong(paul) <- (6) [avatar component clause 170]
173. 4 | 6 [avatar split clause 91,170,162]
180. 8 <=> quiet(paul) [avatar definition]
181. quiet(paul) <- (8) [avatar component clause 180]
182. ~quiet(paul) <- (~8) [avatar component clause 180]
216. 16 <=> tall(paul) [avatar definition]
217. tall(paul) <- (16) [avatar component clause 216]
220. 17 <=> calm(paul) [avatar definition]
221. calm(paul) <- (17) [avatar component clause 220]
222. ~calm(paul) <- (~17) [avatar component clause 220]
225. 18 <=> ! [X0] : (happy(X0) | ~calm(X0)) [avatar definition]
226. ~calm(X0) | happy(X0) <- (18) [avatar component clause 225]
256. 18 [avatar split clause 122,225]
257. ~brave(X0) [subsumption resolution 119,84]
314. 16 [avatar split clause 146,216]
321. generous(paul) <- (6) [resolution 85,172]
322. funny(paul) <- (6) [resolution 116,172]
335. happy(sK9) <- (18) [resolution 226,143]
339. ~funny(paul) | ~tall(paul) <- (17) [resolution 102,221]
343. ~tall(paul) <- (6, 17) [subsumption resolution 339,322]
344. $false <- (6, 16, 17) [subsumption resolution 343,217]
345. ~6 | ~16 | ~17 [avatar contradiction clause 344]
422. quiet(paul) | calm(paul) <- (6) [resolution 134,321]
423. calm(paul) <- (6, ~8) [subsumption resolution 422,182]
424. $false <- (6, ~8, ~17) [subsumption resolution 423,222]
425. ~6 | 8 | 17 [avatar contradiction clause 424]
430. $false <- (4, 18) [resolution 163,335]
433. ~4 | ~18 [avatar contradiction clause 430]
500. calm(paul) | brave(paul) | ~quiet(paul) <- (16) [resolution 100,217]
501. brave(paul) | ~quiet(paul) <- (16, ~17) [subsumption resolution 500,222]
502. ~quiet(paul) <- (16, ~17) [subsumption resolution 501,257]
503. $false <- (8, 16, ~17) [subsumption resolution 502,181]
504. ~8 | ~16 | 17 [avatar contradiction clause 503]
505. $false [avatar sat refutation 173,256,314,345,425,433,504]
% SZS output end Proof for 338137539273959225445238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is not happy or creative.
If someone is either old or not wise then someone is tall and vice versa.
If mary is rich then someone is rich and vice versa.
If alice is creative then someone is either not funny or not happy.
Everyone who is not rich or not calm is either not creative or wise and vice versa.
If someone is happy then someone is not creative and vice versa.
If someone is either not funny or creative then fred is not quiet or not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
If john is kind or not patient then someone is not creative or not strong and vice versa.
If john is not strong or rich then someone is either not kind or old and vice versa.
Everyone who is both strong and not wise is both not happy and calm and vice versa.
Everyone who is not wise or not patient is either humble or not strong.
If john is both not kind and strong then john is both quiet and not brave.
Someone is both tall and calm.
John is tall.
Someone is either not tall or not happy.
Alice is both not tall and not happy.
Someone is either not kind or brave.
Lucy is both not calm and brave.
Someone is brave or patient.
John is funny or quiet. | Fred is brave. | neutral | (![X]:(tall(X)=>(~happy(X)|creative(X))))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:(tall(X))))&
((rich(mary))<=>(?[X]:(rich(X))))&
((creative(alice))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~quiet(fred)|~patient(fred))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
(((kind(john)|~patient(john)))<=>(?[X]:((~creative(X)|~strong(X)))))&
(((~strong(john)|rich(john)))<=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((strong(X)&~wise(X))<=>(~happy(X)&calm(X))))&
(![X]:((~wise(X)|~patient(X))=>(humble(X)<~>~strong(X))))&
(((~kind(john)&strong(john)))=>((quiet(john)&~brave(john))))&
(?[X]:((tall(X)&calm(X))))&
(tall(john))&
(?[X]:((~tall(X)<~>~happy(X))))&
((~tall(alice)&~happy(alice)))&
(?[X]:((~kind(X)<~>brave(X))))&
((~calm(lucy)&brave(lucy)))&
(?[X]:((brave(X)|patient(X))))&
((funny(john)|quiet(john))) | brave(fred) | [] | null | 0 |
Everyone who is both not patient and tall is not old or not humble and vice versa.
Everyone who is both funny and not generous is both not brave and not old.
If someone is both not tall and old then mary is not happy and vice versa.
Everyone who is not humble is not old or calm and vice versa.
If paul is humble or not kind then susan is not patient.
Everyone who is both not brave and strong is not humble and vice versa.
Everyone who is funny is either quiet or calm and vice versa.
Everyone who is not brave is generous or not quiet and vice versa.
If someone is not quiet or not old then fred is not creative.
If someone is both kind and not creative then someone is either patient or not curious.
Everyone who is happy is both not patient and not happy.
Everyone who is calm or not old is either wise or patient.
If alice is not happy or creative then someone is calm or not brave and vice versa.
If paul is either strong or not calm then someone is old or not humble.
Everyone who is kind is either not happy or not strong and vice versa.
Everyone who is wise is both not wise and rich.
Alice is not creative or not curious.
Paul is not kind.
John is not patient or not generous.
Lucy is either not patient or not funny.
Someone is brave or humble.
Mary is either quiet or humble.
Paul is not happy.
Someone is not calm. | Alice is humble. | entailment | (![X]:((~patient(X)&tall(X))<=>(~old(X)|~humble(X))))&
(![X]:((funny(X)&~generous(X))=>(~brave(X)&~old(X))))&
((?[X]:((~tall(X)&old(X))))<=>(~happy(mary)))&
(![X]:(~humble(X)<=>(~old(X)|calm(X))))&
(((humble(paul)|~kind(paul)))=>(~patient(susan)))&
(![X]:((~brave(X)&strong(X))<=>~humble(X)))&
(![X]:(funny(X)<=>(quiet(X)<~>calm(X))))&
(![X]:(~brave(X)<=>(generous(X)|~quiet(X))))&
((?[X]:((~quiet(X)|~old(X))))=>(~creative(fred)))&
((?[X]:((kind(X)&~creative(X))))=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:(happy(X)=>(~patient(X)&~happy(X))))&
(![X]:((calm(X)|~old(X))=>(wise(X)<~>patient(X))))&
(((~happy(alice)|creative(alice)))<=>(?[X]:((calm(X)|~brave(X)))))&
(((strong(paul)<~>~calm(paul)))=>(?[X]:((old(X)|~humble(X)))))&
(![X]:(kind(X)<=>(~happy(X)<~>~strong(X))))&
(![X]:(wise(X)=>(~wise(X)&rich(X))))&
((~creative(alice)|~curious(alice)))&
(~kind(paul))&
((~patient(john)|~generous(john)))&
((~patient(lucy)<~>~funny(lucy)))&
(?[X]:((brave(X)|humble(X))))&
((quiet(mary)<~>humble(mary)))&
(~happy(paul))&
(?[X]:(~calm(X))) | humble(alice) | [
"p0",
"p3",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3443630929045599744457945
% SZS output start Proof for 3443630929045599744457945
1. ! [X0] : ((tall(X0) & ~patient(X0)) <=> (~humble(X0) | ~old(X0))) [input p0]
4. ! [X0] : (~humble(X0) <=> (calm(X0) | ~old(X0))) [input p3]
12. ! [X0] : ((~old(X0) | calm(X0)) => (wise(X0) <~> patient(X0))) [input p11]
16. ! [X0] : (wise(X0) => (rich(X0) & ~wise(X0))) [input p15]
25. ~humble(alice) [input hypothesis]
27. ! [X0] : (wise(X0) => ~wise(X0)) [pure predicate removal 16]
34. ! [X0] : ((wise(X0) <~> patient(X0)) | (old(X0) & ~calm(X0))) [ennf transformation 12]
36. ! [X0] : (~wise(X0) | ~wise(X0)) [ennf transformation 27]
37. ! [X0] : (((tall(X0) & ~patient(X0)) | (humble(X0) & old(X0))) & ((~humble(X0) | ~old(X0)) | (~tall(X0) | patient(X0)))) [nnf transformation 1]
38. ! [X0] : (((tall(X0) & ~patient(X0)) | (humble(X0) & old(X0))) & (~humble(X0) | ~old(X0) | ~tall(X0) | patient(X0))) [flattening 37]
43. ! [X0] : ((~humble(X0) | (~calm(X0) & old(X0))) & ((calm(X0) | ~old(X0)) | humble(X0))) [nnf transformation 4]
44. ! [X0] : ((~humble(X0) | (~calm(X0) & old(X0))) & (calm(X0) | ~old(X0) | humble(X0))) [flattening 43]
54. ! [X0] : (((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | (old(X0) & ~calm(X0))) [nnf transformation 34]
71. ~patient(X0) | old(X0) [cnf transformation 38]
72. ~patient(X0) | humble(X0) [cnf transformation 38]
80. ~old(X0) | calm(X0) | humble(X0) [cnf transformation 44]
101. ~calm(X0) | wise(X0) | patient(X0) [cnf transformation 54]
102. patient(X0) | wise(X0) | old(X0) [cnf transformation 54]
115. ~wise(X0) | ~wise(X0) [cnf transformation 36]
126. ~humble(alice) [cnf transformation 25]
127. ~wise(X0) [duplicate literal removal 115]
163. 8 <=> ! [X0] : old(X0) [avatar definition]
164. old(X0) <- (8) [avatar component clause 163]
187. wise(X0) | old(X0) [subsumption resolution 102,71]
248. old(X0) [resolution 187,127]
249. 8 [avatar split clause 248,163]
255. calm(X0) | humble(X0) <- (8) [resolution 80,164]
279. wise(X0) | patient(X0) | humble(X0) <- (8) [resolution 101,255]
280. patient(X0) | humble(X0) <- (8) [subsumption resolution 279,127]
281. humble(X0) <- (8) [subsumption resolution 280,72]
283. $false <- (8) [resolution 281,126]
285. ~8 [avatar contradiction clause 283]
286. $false [avatar sat refutation 249,285]
% SZS output end Proof for 3443630929045599744457945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and curious then fred is either not generous or generous and vice versa.
If lucy is not kind then john is generous and vice versa.
If fred is brave then someone is both not calm and humble and vice versa.
If someone is either kind or not strong then lucy is funny or not generous and vice versa.
Everyone who is not happy is either not old or not creative.
Everyone who is humble or patient is both creative and not strong.
Everyone who is funny is both not happy and not strong.
If susan is creative or not quiet then someone is calm and vice versa.
If john is not old then someone is both brave and not tall and vice versa.
If someone is both not old and not quiet then paul is not kind.
Everyone who is not tall or not quiet is either not strong or not old.
Everyone who is both happy and not creative is not brave or brave and vice versa.
Everyone who is not quiet is not funny or creative and vice versa.
If someone is either curious or not kind then john is not generous.
Everyone who is both creative and kind is both wise and not generous.
If someone is either humble or wise then someone is either quiet or not calm.
Someone is either happy or not kind.
Someone is either not funny or tall.
Someone is not tall.
Susan is not creative.
John is old. | John is not creative. | entailment | (((wise(mary)&curious(mary)))<=>((~generous(fred)<~>generous(fred))))&
((~kind(lucy))<=>(generous(john)))&
((brave(fred))<=>(?[X]:((~calm(X)&humble(X)))))&
((?[X]:((kind(X)<~>~strong(X))))<=>((funny(lucy)|~generous(lucy))))&
(![X]:(~happy(X)=>(~old(X)<~>~creative(X))))&
(![X]:((humble(X)|patient(X))=>(creative(X)&~strong(X))))&
(![X]:(funny(X)=>(~happy(X)&~strong(X))))&
(((creative(susan)|~quiet(susan)))<=>(?[X]:(calm(X))))&
((~old(john))<=>(?[X]:((brave(X)&~tall(X)))))&
((?[X]:((~old(X)&~quiet(X))))=>(~kind(paul)))&
(![X]:((~tall(X)|~quiet(X))=>(~strong(X)<~>~old(X))))&
(![X]:((happy(X)&~creative(X))<=>(~brave(X)|brave(X))))&
(![X]:(~quiet(X)<=>(~funny(X)|creative(X))))&
((?[X]:((curious(X)<~>~kind(X))))=>(~generous(john)))&
(![X]:((creative(X)&kind(X))=>(wise(X)&~generous(X))))&
((?[X]:((humble(X)<~>wise(X))))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(?[X]:((happy(X)<~>~kind(X))))&
(?[X]:((~funny(X)<~>tall(X))))&
(?[X]:(~tall(X)))&
(~creative(susan))&
(old(john)) | ~creative(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8490845859751292448896820
% SZS output start Proof for 8490845859751292448896820
12. ! [X0] : ((~creative(X0) & happy(X0)) <=> (brave(X0) | ~brave(X0))) [input p11]
22. creative(john) [input hypothesis]
57. ! [X0] : (((~creative(X0) & happy(X0)) | (~brave(X0) & brave(X0))) & ((brave(X0) | ~brave(X0)) | (creative(X0) | ~happy(X0)))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) & happy(X0)) | (~brave(X0) & brave(X0))) & (brave(X0) | ~brave(X0) | creative(X0) | ~happy(X0))) [flattening 57]
111. ~creative(X0) | brave(X0) [cnf transformation 58]
112. ~creative(X0) | ~brave(X0) [cnf transformation 58]
131. creative(john) [cnf transformation 22]
252. ~creative(X0) [subsumption resolution 111,112]
293. $false [subsumption resolution 131,252]
% SZS output end Proof for 8490845859751292448896820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not funny then lucy is strong and vice versa. If john is not wise or humble then fred is both wise and creative and vice versa. If fred is generous then mary is not wise or not funny. If fred is both wise and not funny then paul is both not humble and old. Everyone who is either patient or not patient is both creative and funny and vice versa. If susan is both not kind and old then susan is not old. Everyone who is not kind is not wise or funny and vice versa. Everyone who is not kind or rich is either not quiet or calm. If lucy is humble then alice is curious and vice versa. Everyone who is not generous or patient is not creative and vice versa. Everyone who is both rich and strong is both generous and not curious. Everyone who is humble is not patient or not humble. Everyone who is not humble or tall is both funny and wise. If someone is patient or not quiet then paul is not patient or strong and vice versa. Everyone who is not happy or not patient is not strong and vice versa. Someone is both curious and not old. Fred is not strong. Alice is either not generous or calm. Fred is tall. Alice is generous. Someone is funny or not patient. Someone is not patient. | Mary is strong. | contradiction | ((~funny(alice))<=>(strong(lucy)))&
(((~wise(john)|humble(john)))<=>((wise(fred)&creative(fred))))&
((generous(fred))=>((~wise(mary)|~funny(mary))))&
(((wise(fred)&~funny(fred)))=>((~humble(paul)&old(paul))))&
(![X]:((patient(X)<~>~patient(X))<=>(creative(X)&funny(X))))&
(((~kind(susan)&old(susan)))=>(~old(susan)))&
(![X]:(~kind(X)<=>(~wise(X)|funny(X))))&
(![X]:((~kind(X)|rich(X))=>(~quiet(X)<~>calm(X))))&
((humble(lucy))<=>(curious(alice)))&
(![X]:((~generous(X)|patient(X))<=>~creative(X)))&
(![X]:((rich(X)&strong(X))=>(generous(X)&~curious(X))))&
(![X]:(humble(X)=>(~patient(X)|~humble(X))))&
(![X]:((~humble(X)|tall(X))=>(funny(X)&wise(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>((~patient(paul)|strong(paul))))&
(![X]:((~happy(X)|~patient(X))<=>~strong(X)))&
(?[X]:((curious(X)&~old(X))))&
(~strong(fred))&
((~generous(alice)<~>calm(alice)))&
(tall(fred))&
(generous(alice))&
(?[X]:((funny(X)|~patient(X))))&
(?[X]:(~patient(X))) | strong(mary) | [
"p4",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3251615534556055348853616
% SZS output start Proof for 3251615534556055348853616
5. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> (funny(X0) & creative(X0))) [input p4]
10. ! [X0] : ((patient(X0) | ~generous(X0)) <=> ~creative(X0)) [input p9]
15. ! [X0] : ((~patient(X0) | ~happy(X0)) <=> ~strong(X0)) [input p14]
23. strong(mary) [input hypothesis]
41. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 5]
42. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [flattening 41]
45. ! [X0] : (((patient(X0) | ~generous(X0)) | creative(X0)) & (~creative(X0) | (~patient(X0) & generous(X0)))) [nnf transformation 10]
46. ! [X0] : ((patient(X0) | ~generous(X0) | creative(X0)) & (~creative(X0) | (~patient(X0) & generous(X0)))) [flattening 45]
52. ! [X0] : (((~patient(X0) | ~happy(X0)) | strong(X0)) & (~strong(X0) | (patient(X0) & happy(X0)))) [nnf transformation 15]
53. ! [X0] : ((~patient(X0) | ~happy(X0) | strong(X0)) & (~strong(X0) | (patient(X0) & happy(X0)))) [flattening 52]
71. creative(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 42]
72. creative(X0) | patient(X0) | patient(X0) [cnf transformation 42]
85. ~creative(X0) | ~patient(X0) [cnf transformation 46]
97. ~strong(X0) | patient(X0) [cnf transformation 53]
108. strong(mary) [cnf transformation 23]
111. creative(X0) | ~patient(X0) [duplicate literal removal 71]
112. creative(X0) | patient(X0) [duplicate literal removal 72]
174. creative(X0) [subsumption resolution 111,112]
197. ~patient(X0) [subsumption resolution 85,174]
212. ~strong(X0) [subsumption resolution 97,197]
214. $false [subsumption resolution 108,212]
% SZS output end Proof for 3251615534556055348853616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not creative is not brave or generous.
If someone is not old then john is calm or strong.
Everyone who is not strong or curious is not generous or not kind and vice versa.
Everyone who is strong is calm.
Everyone who is either funny or generous is both not rich and not generous and vice versa.
If susan is both generous and happy then someone is either not old or patient and vice versa.
Everyone who is not calm or humble is either brave or creative.
Everyone who is both not old and not curious is either not patient or old.
Everyone who is calm is not rich.
If lucy is funny then john is either not curious or brave.
Everyone who is not rich or not humble is wise or not curious and vice versa.
Everyone who is either not generous or brave is strong and vice versa.
If someone is not calm or humble then someone is both strong and old.
If someone is wise then susan is curious and vice versa.
If someone is either tall or old then lucy is either not old or not rich and vice versa.
Everyone who is happy is both curious and creative and vice versa.
Alice is not funny.
Someone is generous or quiet.
Lucy is old.
Susan is not kind or tall.
Someone is either not tall or curious.
Paul is quiet or wise.
Susan is either not humble or rich.
Lucy is not happy. | Alice is not wise. | entailment | (![X]:((humble(X)<~>~creative(X))=>(~brave(X)|generous(X))))&
((?[X]:(~old(X)))=>((calm(john)|strong(john))))&
(![X]:((~strong(X)|curious(X))<=>(~generous(X)|~kind(X))))&
(![X]:(strong(X)=>calm(X)))&
(![X]:((funny(X)<~>generous(X))<=>(~rich(X)&~generous(X))))&
(((generous(susan)&happy(susan)))<=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~calm(X)|humble(X))=>(brave(X)<~>creative(X))))&
(![X]:((~old(X)&~curious(X))=>(~patient(X)<~>old(X))))&
(![X]:(calm(X)=>~rich(X)))&
((funny(lucy))=>((~curious(john)<~>brave(john))))&
(![X]:((~rich(X)|~humble(X))<=>(wise(X)|~curious(X))))&
(![X]:((~generous(X)<~>brave(X))<=>strong(X)))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:((strong(X)&old(X)))))&
((?[X]:(wise(X)))<=>(curious(susan)))&
((?[X]:((tall(X)<~>old(X))))<=>((~old(lucy)<~>~rich(lucy))))&
(![X]:(happy(X)<=>(curious(X)&creative(X))))&
(~funny(alice))&
(?[X]:((generous(X)|quiet(X))))&
(old(lucy))&
((~kind(susan)|tall(susan)))&
(?[X]:((~tall(X)<~>curious(X))))&
((quiet(paul)|wise(paul)))&
((~humble(susan)<~>rich(susan)))&
(~happy(lucy)) | ~wise(alice) | [
"p0",
"p3",
"p4",
"p6",
"p8",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8814618247839157652583639
% SZS output start Proof for 8814618247839157652583639
1. ! [X0] : ((humble(X0) <~> ~creative(X0)) => (generous(X0) | ~brave(X0))) [input p0]
4. ! [X0] : (strong(X0) => calm(X0)) [input p3]
5. ! [X0] : ((funny(X0) <~> generous(X0)) <=> (~generous(X0) & ~rich(X0))) [input p4]
7. ! [X0] : ((humble(X0) | ~calm(X0)) => (brave(X0) <~> creative(X0))) [input p6]
9. ! [X0] : (calm(X0) => ~rich(X0)) [input p8]
11. ! [X0] : ((~humble(X0) | ~rich(X0)) <=> (~curious(X0) | wise(X0))) [input p10]
12. ! [X0] : ((~generous(X0) <~> brave(X0)) <=> strong(X0)) [input p11]
17. ~funny(alice) [input p16]
25. wise(alice) [input hypothesis]
29. ! [X0] : ((generous(X0) | ~brave(X0)) | (humble(X0) <=> ~creative(X0))) [ennf transformation 1]
30. ! [X0] : (generous(X0) | ~brave(X0) | (humble(X0) <=> ~creative(X0))) [flattening 29]
33. ! [X0] : (calm(X0) | ~strong(X0)) [ennf transformation 4]
34. ! [X0] : ((brave(X0) <~> creative(X0)) | (~humble(X0) & calm(X0))) [ennf transformation 7]
37. ! [X0] : (~rich(X0) | ~calm(X0)) [ennf transformation 9]
40. ! [X0] : (generous(X0) | ~brave(X0) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) [nnf transformation 30]
43. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (generous(X0) | rich(X0))) & ((~generous(X0) & ~rich(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [nnf transformation 5]
44. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | generous(X0) | rich(X0)) & ((~generous(X0) & ~rich(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [flattening 43]
50. ! [X0] : (((~creative(X0) | ~brave(X0)) & (creative(X0) | brave(X0))) | (~humble(X0) & calm(X0))) [nnf transformation 34]
53. ! [X0] : (((~humble(X0) | ~rich(X0)) | (curious(X0) & ~wise(X0))) & ((~curious(X0) | wise(X0)) | (humble(X0) & rich(X0)))) [nnf transformation 11]
54. ! [X0] : ((~humble(X0) | ~rich(X0) | (curious(X0) & ~wise(X0))) & (~curious(X0) | wise(X0) | (humble(X0) & rich(X0)))) [flattening 53]
55. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | ~strong(X0)) & (strong(X0) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [nnf transformation 12]
74. ~brave(X0) | generous(X0) | humble(X0) | creative(X0) [cnf transformation 40]
80. ~strong(X0) | calm(X0) [cnf transformation 33]
84. ~generous(X0) | funny(X0) | ~generous(X0) [cnf transformation 44]
85. generous(X0) | funny(X0) | generous(X0) | rich(X0) [cnf transformation 44]
95. ~brave(X0) | ~creative(X0) | calm(X0) [cnf transformation 50]
99. ~rich(X0) | ~calm(X0) [cnf transformation 37]
104. ~wise(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 54]
106. strong(X0) | brave(X0) | generous(X0) [cnf transformation 55]
127. ~funny(alice) [cnf transformation 17]
135. wise(alice) [cnf transformation 25]
137. ~generous(X0) | funny(X0) [duplicate literal removal 84]
138. rich(X0) | funny(X0) | generous(X0) [duplicate literal removal 85]
288. ~rich(alice) | ~humble(alice) [resolution 104,135]
293. calm(X2) | generous(X2) | brave(X2) [resolution 106,80]
316. funny(X2) | generous(X2) | ~calm(X2) [resolution 138,99]
339. ~calm(X2) | funny(X2) [subsumption resolution 316,137]
382. generous(X0) | brave(X0) | funny(X0) [resolution 293,339]
383. funny(X0) | brave(X0) [subsumption resolution 382,137]
421. brave(alice) [resolution 383,127]
422. generous(alice) | humble(alice) | creative(alice) [resolution 421,74]
425. ~creative(alice) | calm(alice) [resolution 421,95]
428. 43 <=> creative(alice) [avatar definition]
432. 44 <=> generous(alice) [avatar definition]
434. generous(alice) <- (44) [avatar component clause 432]
437. 45 <=> calm(alice) [avatar definition]
439. calm(alice) <- (45) [avatar component clause 437]
440. 45 | ~43 [avatar split clause 425,428,437]
442. 46 <=> humble(alice) [avatar definition]
447. 43 | 46 | 44 [avatar split clause 422,432,442,428]
482. 54 <=> rich(alice) [avatar definition]
483. rich(alice) <- (54) [avatar component clause 482]
484. ~rich(alice) <- (~54) [avatar component clause 482]
485. ~46 | ~54 [avatar split clause 288,482,442]
490. funny(alice) | generous(alice) <- (~54) [resolution 484,138]
510. funny(alice) <- (44) [resolution 434,137]
512. $false <- (44) [subsumption resolution 510,127]
513. ~44 [avatar contradiction clause 512]
514. generous(alice) <- (~54) [subsumption resolution 490,127]
515. 44 | 54 [avatar split clause 514,482,432]
518. ~calm(alice) <- (54) [resolution 483,99]
519. $false <- (45, 54) [subsumption resolution 518,439]
520. ~45 | ~54 [avatar contradiction clause 519]
521. $false [avatar sat refutation 440,447,485,513,515,520]
% SZS output end Proof for 8814618247839157652583639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is generous or old and vice versa.
Everyone who is creative or old is both not kind and old.
Everyone who is either creative or not creative is not curious or not old.
Everyone who is not brave or old is both not happy and happy.
If susan is both not strong and not quiet then someone is either funny or not happy and vice versa.
If someone is funny or calm then alice is either creative or not brave and vice versa.
Everyone who is not old is kind.
Everyone who is not generous is tall or not strong and vice versa.
If someone is old or not brave then susan is not patient or not kind and vice versa.
If lucy is funny then alice is either calm or not strong.
Everyone who is not happy is both not funny and not creative.
If john is either not happy or not kind then someone is tall and vice versa.
If someone is not tall then someone is either not curious or not rich.
If paul is either humble or calm then someone is both old and not strong and vice versa.
If someone is either not generous or not creative then lucy is not rich or not kind.
John is either rich or not generous.
Lucy is not funny or humble.
Paul is not tall.
Someone is not generous or not brave.
Someone is not creative or not wise.
Someone is not curious or not tall.
Fred is patient or not quiet.
Someone is not happy. | Alice is not funny. | entailment | (![X]:(tall(X)<=>(generous(X)|old(X))))&
(![X]:((creative(X)|old(X))=>(~kind(X)&old(X))))&
(![X]:((creative(X)<~>~creative(X))=>(~curious(X)|~old(X))))&
(![X]:((~brave(X)|old(X))=>(~happy(X)&happy(X))))&
(((~strong(susan)&~quiet(susan)))<=>(?[X]:((funny(X)<~>~happy(X)))))&
((?[X]:((funny(X)|calm(X))))<=>((creative(alice)<~>~brave(alice))))&
(![X]:(~old(X)=>kind(X)))&
(![X]:(~generous(X)<=>(tall(X)|~strong(X))))&
((?[X]:((old(X)|~brave(X))))<=>((~patient(susan)|~kind(susan))))&
((funny(lucy))=>((calm(alice)<~>~strong(alice))))&
(![X]:(~happy(X)=>(~funny(X)&~creative(X))))&
(((~happy(john)<~>~kind(john)))<=>(?[X]:(tall(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~curious(X)<~>~rich(X)))))&
(((humble(paul)<~>calm(paul)))<=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:((~generous(X)<~>~creative(X))))=>((~rich(lucy)|~kind(lucy))))&
((rich(john)<~>~generous(john)))&
((~funny(lucy)|humble(lucy)))&
(~tall(paul))&
(?[X]:((~generous(X)|~brave(X))))&
(?[X]:((~creative(X)|~wise(X))))&
(?[X]:((~curious(X)|~tall(X))))&
((patient(fred)|~quiet(fred)))&
(?[X]:(~happy(X))) | ~funny(alice) | [
"p1",
"p3",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4204338385665870283961635
% SZS output start Proof for 4204338385665870283961635
2. ! [X0] : ((old(X0) | creative(X0)) => (old(X0) & ~kind(X0))) [input p1]
4. ! [X0] : ((old(X0) | ~brave(X0)) => (happy(X0) & ~happy(X0))) [input p3]
6. ? [X0] : (calm(X0) | funny(X0)) <=> (creative(alice) <~> ~brave(alice)) [input p5]
7. ! [X0] : (~old(X0) => kind(X0)) [input p6]
24. funny(alice) [input hypothesis]
27. ! [X0] : ((old(X0) & ~kind(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 2]
30. ! [X0] : ((happy(X0) & ~happy(X0)) | (~old(X0) & brave(X0))) [ennf transformation 4]
31. ! [X0] : (kind(X0) | old(X0)) [ennf transformation 7]
45. (? [X0] : (calm(X0) | funny(X0)) | ((creative(alice) | brave(alice)) & (~brave(alice) | ~creative(alice)))) & (((brave(alice) | ~creative(alice)) & (~brave(alice) | creative(alice))) | ! [X0] : (~calm(X0) & ~funny(X0))) [nnf transformation 6]
46. (? [X0] : (calm(X0) | funny(X0)) | ((creative(alice) | brave(alice)) & (~brave(alice) | ~creative(alice)))) & (((brave(alice) | ~creative(alice)) & (~brave(alice) | creative(alice))) | ! [X1] : (~calm(X1) & ~funny(X1))) [rectify 45]
47. ? [X0] : (calm(X0) | funny(X0)) => (calm(sK1) | funny(sK1)) [choice axiom]
48. ((calm(sK1) | funny(sK1)) | ((creative(alice) | brave(alice)) & (~brave(alice) | ~creative(alice)))) & (((brave(alice) | ~creative(alice)) & (~brave(alice) | creative(alice))) | ! [X1] : (~calm(X1) & ~funny(X1))) [skolemisation 46,47]
80. ~kind(X0) | ~creative(X0) [cnf transformation 27]
86. ~happy(X0) | brave(X0) [cnf transformation 30]
87. ~happy(X0) | ~old(X0) [cnf transformation 30]
88. happy(X0) | brave(X0) [cnf transformation 30]
89. happy(X0) | ~old(X0) [cnf transformation 30]
96. ~brave(alice) | creative(alice) | ~funny(X1) [cnf transformation 48]
102. kind(X0) | old(X0) [cnf transformation 31]
136. funny(alice) [cnf transformation 24]
140. ~old(X0) [subsumption resolution 87,89]
141. brave(X0) [subsumption resolution 86,88]
172. 7 <=> creative(alice) [avatar definition]
173. creative(alice) <- (7) [avatar component clause 172]
189. creative(alice) | ~funny(X1) [subsumption resolution 96,141]
191. 11 <=> ! [X1] : ~funny(X1) [avatar definition]
192. ~funny(X1) <- (11) [avatar component clause 191]
193. 11 | 7 [avatar split clause 189,172,191]
194. kind(X0) [subsumption resolution 102,140]
262. 24 <=> ! [X0] : ~creative(X0) [avatar definition]
263. ~creative(X0) <- (24) [avatar component clause 262]
297. ~creative(X0) [resolution 80,194]
298. 24 [avatar split clause 297,262]
299. $false <- (7, 24) [resolution 263,173]
300. ~7 | ~24 [avatar contradiction clause 299]
301. $false <- (11) [resolution 192,136]
304. ~11 [avatar contradiction clause 301]
305. $false [avatar sat refutation 193,298,300,304]
% SZS output end Proof for 4204338385665870283961635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is creative then john is either not quiet or wise.
If someone is kind or not old then paul is calm or strong.
Everyone who is not quiet or old is both kind and not patient.
Everyone who is either not happy or funny is brave.
If susan is either not wise or brave then alice is quiet or not humble and vice versa.
Everyone who is happy or generous is quiet or patient and vice versa.
Everyone who is generous is strong or humble and vice versa.
If mary is not wise or not funny then someone is either creative or not generous.
Everyone who is calm is not patient or not quiet.
Everyone who is either wise or funny is either happy or not rich and vice versa.
Everyone who is not generous is not wise or not happy and vice versa.
Everyone who is either not creative or not wise is not tall or not humble.
If someone is curious or wise then susan is tall or not humble.
If someone is either quiet or not generous then lucy is not humble or tall.
If someone is not humble then susan is not brave.
Everyone who is not wise is strong or not rich and vice versa.
Someone is not curious.
Mary is old.
Alice is both patient and generous.
Paul is either not creative or not curious.
Someone is brave or not creative.
Someone is wise.
Someone is humble.
Someone is not rich. | Paul is strong. | contradiction | ((creative(paul))=>((~quiet(john)<~>wise(john))))&
((?[X]:((kind(X)|~old(X))))=>((calm(paul)|strong(paul))))&
(![X]:((~quiet(X)|old(X))=>(kind(X)&~patient(X))))&
(![X]:((~happy(X)<~>funny(X))=>brave(X)))&
(((~wise(susan)<~>brave(susan)))<=>((quiet(alice)|~humble(alice))))&
(![X]:((happy(X)|generous(X))<=>(quiet(X)|patient(X))))&
(![X]:(generous(X)<=>(strong(X)|humble(X))))&
(((~wise(mary)|~funny(mary)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(calm(X)=>(~patient(X)|~quiet(X))))&
(![X]:((wise(X)<~>funny(X))<=>(happy(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(~wise(X)|~happy(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(~tall(X)|~humble(X))))&
((?[X]:((curious(X)|wise(X))))=>((tall(susan)|~humble(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>((~humble(lucy)|tall(lucy))))&
((?[X]:(~humble(X)))=>(~brave(susan)))&
(![X]:(~wise(X)<=>(strong(X)|~rich(X))))&
(?[X]:(~curious(X)))&
(old(mary))&
((patient(alice)&generous(alice)))&
((~creative(paul)<~>~curious(paul)))&
(?[X]:((brave(X)|~creative(X))))&
(?[X]:(wise(X)))&
(?[X]:(humble(X)))&
(?[X]:(~rich(X))) | strong(paul) | [
"p6",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5824824705180691081353885
% SZS output start Proof for 5824824705180691081353885
7. ! [X0] : (generous(X0) <=> (humble(X0) | strong(X0))) [input p6]
11. ! [X0] : (~generous(X0) <=> (~happy(X0) | ~wise(X0))) [input p10]
16. ! [X0] : (~wise(X0) <=> (~rich(X0) | strong(X0))) [input p15]
25. strong(paul) [input hypothesis]
47. ! [X0] : ((generous(X0) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | ~generous(X0))) [nnf transformation 7]
48. ! [X0] : ((generous(X0) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | ~generous(X0))) [flattening 47]
53. ! [X0] : ((~generous(X0) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | generous(X0))) [nnf transformation 11]
54. ! [X0] : ((~generous(X0) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | generous(X0))) [flattening 53]
57. ! [X0] : ((~wise(X0) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | wise(X0))) [nnf transformation 16]
58. ! [X0] : ((~wise(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | wise(X0))) [flattening 57]
91. ~strong(X0) | generous(X0) [cnf transformation 48]
107. ~generous(X0) | wise(X0) [cnf transformation 54]
117. ~strong(X0) | ~wise(X0) [cnf transformation 58]
129. strong(paul) [cnf transformation 25]
152. 6 <=> strong(paul) [avatar definition]
154. strong(paul) <- (6) [avatar component clause 152]
258. 6 [avatar split clause 129,152]
263. generous(paul) <- (6) [resolution 91,154]
266. wise(paul) <- (6) [resolution 107,263]
271. ~wise(paul) <- (6) [resolution 117,154]
272. $false <- (6) [subsumption resolution 271,266]
273. ~6 [avatar contradiction clause 272]
274. $false [avatar sat refutation 258,273]
% SZS output end Proof for 5824824705180691081353885
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not brave is either humble or funny. Everyone who is not rich or not wise is both kind and not generous. Everyone who is either not funny or funny is wise and vice versa. If someone is both not tall and happy then someone is both not kind and not funny and vice versa. If someone is not humble then someone is both creative and not rich. Everyone who is both generous and kind is not rich and vice versa. If mary is either not funny or patient then someone is old or not calm. Everyone who is both not kind and tall is either funny or not brave. Everyone who is wise or patient is kind. Everyone who is tall is either not brave or generous. If mary is creative then someone is either not tall or creative. If susan is not humble or happy then mary is both not rich and not old and vice versa. If someone is both not curious and wise then mary is not curious or old and vice versa. If someone is generous or not funny then someone is both not quiet and not curious and vice versa. Everyone who is either creative or brave is kind. Lucy is brave or tall. Someone is both calm and not creative. Someone is either not rich or not tall. Fred is tall. Someone is rich or patient. Susan is not humble or humble. | Susan is happy. | contradiction | (![X]:((old(X)&~brave(X))=>(humble(X)<~>funny(X))))&
(![X]:((~rich(X)|~wise(X))=>(kind(X)&~generous(X))))&
(![X]:((~funny(X)<~>funny(X))<=>wise(X)))&
((?[X]:((~tall(X)&happy(X))))<=>(?[X]:((~kind(X)&~funny(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((generous(X)&kind(X))<=>~rich(X)))&
(((~funny(mary)<~>patient(mary)))=>(?[X]:((old(X)|~calm(X)))))&
(![X]:((~kind(X)&tall(X))=>(funny(X)<~>~brave(X))))&
(![X]:((wise(X)|patient(X))=>kind(X)))&
(![X]:(tall(X)=>(~brave(X)<~>generous(X))))&
((creative(mary))=>(?[X]:((~tall(X)<~>creative(X)))))&
(((~humble(susan)|happy(susan)))<=>((~rich(mary)&~old(mary))))&
((?[X]:((~curious(X)&wise(X))))<=>((~curious(mary)|old(mary))))&
((?[X]:((generous(X)|~funny(X))))<=>(?[X]:((~quiet(X)&~curious(X)))))&
(![X]:((creative(X)<~>brave(X))=>kind(X)))&
((brave(lucy)|tall(lucy)))&
(?[X]:((calm(X)&~creative(X))))&
(?[X]:((~rich(X)<~>~tall(X))))&
(tall(fred))&
(?[X]:((rich(X)|patient(X))))&
((~humble(susan)|humble(susan))) | happy(susan) | [
"p1",
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2548027431819512445622665
% SZS output start Proof for 2548027431819512445622665
2. ! [X0] : ((~wise(X0) | ~rich(X0)) => (~generous(X0) & kind(X0))) [input p1]
6. ! [X0] : ((kind(X0) & generous(X0)) <=> ~rich(X0)) [input p5]
12. (happy(susan) | ~humble(susan)) <=> (~old(mary) & ~rich(mary)) [input p11]
22. happy(susan) [input hypothesis]
28. ! [X0] : ((~generous(X0) & kind(X0)) | (wise(X0) & rich(X0))) [ennf transformation 2]
47. ! [X0] : (((kind(X0) & generous(X0)) | rich(X0)) & (~rich(X0) | (~kind(X0) | ~generous(X0)))) [nnf transformation 6]
48. ! [X0] : (((kind(X0) & generous(X0)) | rich(X0)) & (~rich(X0) | ~kind(X0) | ~generous(X0))) [flattening 47]
57. ((happy(susan) | ~humble(susan)) | (old(mary) | rich(mary))) & ((~old(mary) & ~rich(mary)) | (~happy(susan) & humble(susan))) [nnf transformation 12]
58. (happy(susan) | ~humble(susan) | old(mary) | rich(mary)) & ((~old(mary) & ~rich(mary)) | (~happy(susan) & humble(susan))) [flattening 57]
81. ~generous(X0) | rich(X0) [cnf transformation 28]
94. generous(X0) | rich(X0) [cnf transformation 48]
107. ~rich(mary) | ~happy(susan) [cnf transformation 58]
131. happy(susan) [cnf transformation 22]
174. rich(X0) [subsumption resolution 94,81]
210. 17 <=> happy(susan) [avatar definition]
223. ~happy(susan) [subsumption resolution 107,174]
224. ~17 [avatar split clause 223,210]
282. 17 [avatar split clause 131,210]
283. $false [avatar sat refutation 224,282]
% SZS output end Proof for 2548027431819512445622665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either not quiet or not calm then someone is either not generous or humble and vice versa.
Everyone who is both not curious and not happy is either patient or not tall.
If someone is kind or patient then someone is either quiet or not humble.
Everyone who is not kind or brave is either not humble or quiet and vice versa.
If someone is not wise then someone is not humble.
Everyone who is not strong or not happy is not old.
Everyone who is either not tall or not kind is either wise or rich.
Everyone who is either not creative or creative is curious.
Everyone who is either not calm or not tall is both curious and old.
If someone is not calm or not tall then mary is either tall or not generous and vice versa.
Everyone who is not strong or not quiet is brave or not patient.
Everyone who is either not patient or not calm is either strong or patient and vice versa.
Everyone who is not curious or rich is either rich or not old.
If lucy is not calm or not humble then someone is old or happy.
If lucy is either not curious or strong then john is wise.
If someone is brave then someone is quiet or not creative and vice versa.
Paul is both not calm and kind.
Alice is both humble and not happy.
Fred is curious or not curious.
John is either kind or not happy.
Mary is both happy and calm.
Someone is both not brave and not generous.
Someone is not strong. | Alice is not happy. | entailment | (((~quiet(susan)<~>~calm(susan)))<=>(?[X]:((~generous(X)<~>humble(X)))))&
(![X]:((~curious(X)&~happy(X))=>(patient(X)<~>~tall(X))))&
((?[X]:((kind(X)|patient(X))))=>(?[X]:((quiet(X)<~>~humble(X)))))&
(![X]:((~kind(X)|brave(X))<=>(~humble(X)<~>quiet(X))))&
((?[X]:(~wise(X)))=>(?[X]:(~humble(X))))&
(![X]:((~strong(X)|~happy(X))=>~old(X)))&
(![X]:((~tall(X)<~>~kind(X))=>(wise(X)<~>rich(X))))&
(![X]:((~creative(X)<~>creative(X))=>curious(X)))&
(![X]:((~calm(X)<~>~tall(X))=>(curious(X)&old(X))))&
((?[X]:((~calm(X)|~tall(X))))<=>((tall(mary)<~>~generous(mary))))&
(![X]:((~strong(X)|~quiet(X))=>(brave(X)|~patient(X))))&
(![X]:((~patient(X)<~>~calm(X))<=>(strong(X)<~>patient(X))))&
(![X]:((~curious(X)|rich(X))=>(rich(X)<~>~old(X))))&
(((~calm(lucy)|~humble(lucy)))=>(?[X]:((old(X)|happy(X)))))&
(((~curious(lucy)<~>strong(lucy)))=>(wise(john)))&
((?[X]:(brave(X)))<=>(?[X]:((quiet(X)|~creative(X)))))&
((~calm(paul)&kind(paul)))&
((humble(alice)&~happy(alice)))&
((curious(fred)|~curious(fred)))&
((kind(john)<~>~happy(john)))&
((happy(mary)&calm(mary)))&
(?[X]:((~brave(X)&~generous(X))))&
(?[X]:(~strong(X))) | ~happy(alice) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5520324801124988326639400
% SZS output start Proof for 5520324801124988326639400
18. ~happy(alice) & humble(alice) [input p17]
24. happy(alice) [input hypothesis]
140. ~happy(alice) [cnf transformation 18]
149. happy(alice) [cnf transformation 24]
304. $false [subsumption resolution 149,140]
% SZS output end Proof for 5520324801124988326639400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not patient is both kind and not generous.
If someone is humble or rich then john is either old or patient and vice versa.
If someone is either not strong or happy then paul is both funny and not brave.
Everyone who is both not humble and not calm is either rich or humble.
If someone is either not calm or not wise then someone is strong or wise and vice versa.
Everyone who is not calm or happy is not humble and vice versa.
Everyone who is either not funny or calm is both funny and not rich.
Everyone who is both brave and not quiet is both generous and not calm and vice versa.
If susan is not tall then someone is either not happy or not old and vice versa.
Everyone who is not calm or not old is not happy.
If someone is humble or old then someone is both happy and not calm and vice versa.
Everyone who is either old or not funny is either quiet or calm.
Everyone who is both quiet and curious is wise or kind and vice versa.
If susan is either calm or brave then alice is both old and not kind.
If someone is either not wise or not humble then lucy is rich or not funny.
Everyone who is not funny is either calm or not rich.
Mary is not calm.
Someone is either kind or not calm.
Someone is both not strong and not patient.
Someone is tall.
Lucy is not rich or generous.
Someone is both funny and quiet.
Paul is not happy or not humble. | Susan is rich. | entailment | (![X]:((wise(X)<~>~patient(X))=>(kind(X)&~generous(X))))&
((?[X]:((humble(X)|rich(X))))<=>((old(john)<~>patient(john))))&
((?[X]:((~strong(X)<~>happy(X))))=>((funny(paul)&~brave(paul))))&
(![X]:((~humble(X)&~calm(X))=>(rich(X)<~>humble(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((~calm(X)|happy(X))<=>~humble(X)))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:((old(X)<~>~funny(X))=>(quiet(X)<~>calm(X))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|kind(X))))&
(((calm(susan)<~>brave(susan)))=>((old(alice)&~kind(alice))))&
((?[X]:((~wise(X)<~>~humble(X))))=>((rich(lucy)|~funny(lucy))))&
(![X]:(~funny(X)=>(calm(X)<~>~rich(X))))&
(~calm(mary))&
(?[X]:((kind(X)<~>~calm(X))))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:(tall(X)))&
((~rich(lucy)|generous(lucy)))&
(?[X]:((funny(X)&quiet(X))))&
((~happy(paul)|~humble(paul))) | rich(susan) | [
"p3",
"p5",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4495172252842782288451705
% SZS output start Proof for 4495172252842782288451705
4. ! [X0] : ((~calm(X0) & ~humble(X0)) => (rich(X0) <~> humble(X0))) [input p3]
6. ! [X0] : ((happy(X0) | ~calm(X0)) <=> ~humble(X0)) [input p5]
10. ! [X0] : ((~old(X0) | ~calm(X0)) => ~happy(X0)) [input p9]
11. ? [X0] : (old(X0) | humble(X0)) <=> ? [X0] : (~calm(X0) & happy(X0)) [input p10]
24. ~rich(susan) [input hypothesis]
26. ? [X0] : (old(X0) | humble(X0)) <=> ? [X1] : (~calm(X1) & happy(X1)) [rectify 11]
29. ! [X0] : ((rich(X0) <~> humble(X0)) | (calm(X0) | humble(X0))) [ennf transformation 4]
30. ! [X0] : ((rich(X0) <~> humble(X0)) | calm(X0) | humble(X0)) [flattening 29]
32. ! [X0] : (~happy(X0) | (old(X0) & calm(X0))) [ennf transformation 10]
44. ! [X0] : (((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | calm(X0) | humble(X0)) [nnf transformation 30]
50. ! [X0] : (((happy(X0) | ~calm(X0)) | humble(X0)) & (~humble(X0) | (~happy(X0) & calm(X0)))) [nnf transformation 6]
51. ! [X0] : ((happy(X0) | ~calm(X0) | humble(X0)) & (~humble(X0) | (~happy(X0) & calm(X0)))) [flattening 50]
59. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X1] : (~calm(X1) & happy(X1)) | ! [X0] : (~old(X0) & ~humble(X0))) [nnf transformation 26]
60. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X2] : (~calm(X2) & happy(X2)) | ! [X3] : (~old(X3) & ~humble(X3))) [rectify 59]
61. ? [X0] : (old(X0) | humble(X0)) => (old(sK4) | humble(sK4)) [choice axiom]
62. ? [X2] : (~calm(X2) & happy(X2)) => (~calm(sK5) & happy(sK5)) [choice axiom]
63. ((old(sK4) | humble(sK4)) | ! [X1] : (calm(X1) | ~happy(X1))) & ((~calm(sK5) & happy(sK5)) | ! [X3] : (~old(X3) & ~humble(X3))) [skolemisation 60,62,61]
93. humble(X0) | rich(X0) | calm(X0) | humble(X0) [cnf transformation 44]
103. ~calm(X0) | happy(X0) | humble(X0) [cnf transformation 51]
116. ~happy(X0) | calm(X0) [cnf transformation 32]
117. ~happy(X0) | old(X0) [cnf transformation 32]
118. happy(sK5) | ~humble(X3) [cnf transformation 63]
119. happy(sK5) | ~old(X3) [cnf transformation 63]
120. ~calm(sK5) | ~humble(X3) [cnf transformation 63]
121. ~calm(sK5) | ~old(X3) [cnf transformation 63]
150. ~rich(susan) [cnf transformation 24]
152. calm(X0) | rich(X0) | humble(X0) [duplicate literal removal 93]
176. 6 <=> ! [X1] : ~humble(X1) [avatar definition]
177. ~humble(X1) <- (6) [avatar component clause 176]
234. 19 <=> ! [X0] : (~happy(X0) | old(X0)) [avatar definition]
235. ~happy(X0) | old(X0) <- (19) [avatar component clause 234]
255. 19 [avatar split clause 117,234]
257. 24 <=> ! [X3] : ~old(X3) [avatar definition]
258. ~old(X3) <- (24) [avatar component clause 257]
260. 25 <=> calm(sK5) [avatar definition]
263. 24 | ~25 [avatar split clause 121,260,257]
264. 6 | ~25 [avatar split clause 120,260,176]
266. 26 <=> happy(sK5) [avatar definition]
268. happy(sK5) <- (26) [avatar component clause 266]
269. 24 | 26 [avatar split clause 119,266,257]
270. 6 | 26 [avatar split clause 118,266,176]
278. 28 <=> calm(susan) [avatar definition]
279. ~calm(susan) <- (~28) [avatar component clause 278]
280. calm(susan) <- (28) [avatar component clause 278]
333. calm(sK5) <- (26) [resolution 116,268]
336. 25 | ~26 [avatar split clause 333,266,260]
453. rich(susan) | humble(susan) <- (~28) [resolution 152,279]
461. humble(susan) <- (~28) [subsumption resolution 453,150]
462. $false <- (6, ~28) [subsumption resolution 461,177]
463. ~6 | 28 [avatar contradiction clause 462]
480. happy(susan) | humble(susan) <- (28) [resolution 280,103]
483. happy(susan) <- (6, 28) [subsumption resolution 480,177]
528. old(susan) <- (6, 19, 28) [resolution 483,235]
532. $false <- (6, 19, 24, 28) [subsumption resolution 528,258]
533. ~6 | ~19 | ~24 | ~28 [avatar contradiction clause 532]
534. $false [avatar sat refutation 255,263,264,269,270,336,463,533]
% SZS output end Proof for 4495172252842782288451705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and patient is not curious or creative and vice versa.
Everyone who is strong or not old is curious or not funny.
Everyone who is both tall and quiet is calm or not tall and vice versa.
If someone is humble or funny then lucy is not curious or not kind and vice versa.
If lucy is both patient and not wise then mary is either patient or old and vice versa.
Everyone who is both funny and not rich is not old.
If someone is kind or humble then someone is either strong or funny.
If someone is both not curious and strong then someone is both not old and patient.
If fred is either not brave or not happy then someone is both not brave and humble and vice versa.
Everyone who is either patient or not calm is calm or quiet and vice versa.
Everyone who is not funny or wise is not quiet or curious.
Everyone who is patient is either not generous or not patient and vice versa.
If mary is both not funny and not wise then someone is both happy and generous.
If someone is either humble or calm then someone is either not old or not generous and vice versa.
Everyone who is either not strong or not kind is not funny or curious and vice versa.
If someone is not happy then alice is not strong.
Someone is curious or not happy.
Someone is both rich and not generous.
Someone is not strong or not happy.
Susan is both patient and rich.
Someone is not creative or not humble.
Someone is creative.
Someone is not humble or not kind. | Lucy is not patient. | contradiction | (![X]:((~strong(X)&patient(X))<=>(~curious(X)|creative(X))))&
(![X]:((strong(X)|~old(X))=>(curious(X)|~funny(X))))&
(![X]:((tall(X)&quiet(X))<=>(calm(X)|~tall(X))))&
((?[X]:((humble(X)|funny(X))))<=>((~curious(lucy)|~kind(lucy))))&
(((patient(lucy)&~wise(lucy)))<=>((patient(mary)<~>old(mary))))&
(![X]:((funny(X)&~rich(X))=>~old(X)))&
((?[X]:((kind(X)|humble(X))))=>(?[X]:((strong(X)<~>funny(X)))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:((~old(X)&patient(X)))))&
(((~brave(fred)<~>~happy(fred)))<=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:((patient(X)<~>~calm(X))<=>(calm(X)|quiet(X))))&
(![X]:((~funny(X)|wise(X))=>(~quiet(X)|curious(X))))&
(![X]:(patient(X)<=>(~generous(X)<~>~patient(X))))&
(((~funny(mary)&~wise(mary)))=>(?[X]:((happy(X)&generous(X)))))&
((?[X]:((humble(X)<~>calm(X))))<=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((~strong(X)<~>~kind(X))<=>(~funny(X)|curious(X))))&
((?[X]:(~happy(X)))=>(~strong(alice)))&
(?[X]:((curious(X)|~happy(X))))&
(?[X]:((rich(X)&~generous(X))))&
(?[X]:((~strong(X)|~happy(X))))&
((patient(susan)&rich(susan)))&
(?[X]:((~creative(X)|~humble(X))))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|~kind(X)))) | ~patient(lucy) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3140492261688545136786188
% SZS output start Proof for 3140492261688545136786188
3. ! [X0] : ((quiet(X0) & tall(X0)) <=> (~tall(X0) | calm(X0))) [input p2]
10. ! [X0] : ((patient(X0) <~> ~calm(X0)) <=> (quiet(X0) | calm(X0))) [input p9]
24. ~patient(lucy) [input hypothesis]
42. ! [X0] : (((quiet(X0) & tall(X0)) | (tall(X0) & ~calm(X0))) & ((~tall(X0) | calm(X0)) | (~quiet(X0) | ~tall(X0)))) [nnf transformation 3]
43. ! [X0] : (((quiet(X0) & tall(X0)) | (tall(X0) & ~calm(X0))) & (~tall(X0) | calm(X0) | ~quiet(X0) | ~tall(X0))) [flattening 42]
62. ! [X0] : ((((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0))))) [nnf transformation 10]
63. ! [X0] : ((((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0))))) [flattening 62]
93. ~tall(X0) | calm(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 43]
95. tall(X0) | tall(X0) [cnf transformation 43]
121. quiet(X0) | calm(X0) | patient(X0) | calm(X0) [cnf transformation 63]
122. ~calm(X0) | patient(X0) | ~calm(X0) [cnf transformation 63]
123. ~calm(X0) | patient(X0) | ~quiet(X0) [cnf transformation 63]
156. ~patient(lucy) [cnf transformation 24]
159. quiet(X0) | calm(X0) | patient(X0) [duplicate literal removal 121]
160. ~calm(X0) | patient(X0) [duplicate literal removal 122]
161. ~tall(X0) | calm(X0) | ~quiet(X0) [duplicate literal removal 93]
162. tall(X0) [duplicate literal removal 95]
163. calm(X0) | ~quiet(X0) [subsumption resolution 161,162]
252. patient(X0) | ~quiet(X0) [subsumption resolution 123,163]
253. calm(X0) | patient(X0) [subsumption resolution 159,252]
254. patient(X0) [subsumption resolution 253,160]
346. $false [subsumption resolution 156,254]
% SZS output end Proof for 3140492261688545136786188
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either not strong or brave then someone is either not calm or not funny.
Everyone who is either strong or not tall is both strong and not kind and vice versa.
Everyone who is both not creative and not generous is calm and vice versa.
Everyone who is either not funny or not strong is either tall or not wise and vice versa.
Everyone who is not humble or not brave is quiet or not old.
If someone is both not calm and not wise then someone is either happy or brave.
Everyone who is both not creative and not kind is both not curious and not kind.
Everyone who is both not wise and not old is strong and vice versa.
Everyone who is either not creative or not brave is either not strong or strong and vice versa.
Everyone who is patient or calm is both creative and not tall and vice versa.
Everyone who is both not wise and not kind is rich or not creative.
Everyone who is not calm or not tall is happy and vice versa.
If alice is both not kind and not tall then alice is not brave.
If paul is not happy or not tall then someone is both not quiet and rich.
If paul is not happy or brave then alice is either creative or brave.
If paul is strong or not strong then john is old and vice versa.
Alice is strong or wise.
Someone is wise.
Someone is either creative or not humble.
Someone is either happy or not creative.
Someone is quiet or not patient.
Fred is not patient or rich. | Paul is kind. | neutral | (((~strong(fred)<~>brave(fred)))=>(?[X]:((~calm(X)<~>~funny(X)))))&
(![X]:((strong(X)<~>~tall(X))<=>(strong(X)&~kind(X))))&
(![X]:((~creative(X)&~generous(X))<=>calm(X)))&
(![X]:((~funny(X)<~>~strong(X))<=>(tall(X)<~>~wise(X))))&
(![X]:((~humble(X)|~brave(X))=>(quiet(X)|~old(X))))&
((?[X]:((~calm(X)&~wise(X))))=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((~creative(X)&~kind(X))=>(~curious(X)&~kind(X))))&
(![X]:((~wise(X)&~old(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))&
(![X]:((~calm(X)|~tall(X))<=>happy(X)))&
(((~kind(alice)&~tall(alice)))=>(~brave(alice)))&
(((~happy(paul)|~tall(paul)))=>(?[X]:((~quiet(X)&rich(X)))))&
(((~happy(paul)|brave(paul)))=>((creative(alice)<~>brave(alice))))&
(((strong(paul)|~strong(paul)))<=>(old(john)))&
((strong(alice)|wise(alice)))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)<~>~humble(X))))&
(?[X]:((happy(X)<~>~creative(X))))&
(?[X]:((quiet(X)|~patient(X))))&
((~patient(fred)|rich(fred))) | kind(paul) | [] | null | 0 |
Everyone who is quiet or strong is either humble or happy.
Everyone who is both funny and generous is not patient.
Everyone who is not strong or brave is not strong or quiet.
Everyone who is either not old or not rich is both strong and patient and vice versa.
Everyone who is not creative or not calm is both rich and tall.
If someone is either not curious or kind then someone is wise or strong.
Everyone who is rich is tall or not quiet.
Everyone who is tall or not calm is either calm or generous and vice versa.
Everyone who is both tall and creative is strong.
Everyone who is both not curious and happy is tall or wise.
Everyone who is strong or not generous is either tall or not curious and vice versa.
Everyone who is either not kind or not old is both not happy and not patient.
Everyone who is both brave and not funny is both rich and not happy and vice versa.
Everyone who is not strong or not calm is both curious and creative.
If fred is not quiet then susan is both calm and not funny and vice versa.
If someone is not strong or not brave then fred is both not curious and not wise and vice versa.
Someone is not patient.
Fred is both rich and not wise.
Someone is not wise.
Someone is both not wise and brave.
Someone is humble.
Alice is either not humble or patient.
Lucy is not generous. | Susan is not kind. | neutral | (![X]:((quiet(X)|strong(X))=>(humble(X)<~>happy(X))))&
(![X]:((funny(X)&generous(X))=>~patient(X)))&
(![X]:((~strong(X)|brave(X))=>(~strong(X)|quiet(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(strong(X)&patient(X))))&
(![X]:((~creative(X)|~calm(X))=>(rich(X)&tall(X))))&
((?[X]:((~curious(X)<~>kind(X))))=>(?[X]:((wise(X)|strong(X)))))&
(![X]:(rich(X)=>(tall(X)|~quiet(X))))&
(![X]:((tall(X)|~calm(X))<=>(calm(X)<~>generous(X))))&
(![X]:((tall(X)&creative(X))=>strong(X)))&
(![X]:((~curious(X)&happy(X))=>(tall(X)|wise(X))))&
(![X]:((strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~happy(X)&~patient(X))))&
(![X]:((brave(X)&~funny(X))<=>(rich(X)&~happy(X))))&
(![X]:((~strong(X)|~calm(X))=>(curious(X)&creative(X))))&
((~quiet(fred))<=>((calm(susan)&~funny(susan))))&
((?[X]:((~strong(X)|~brave(X))))<=>((~curious(fred)&~wise(fred))))&
(?[X]:(~patient(X)))&
((rich(fred)&~wise(fred)))&
(?[X]:(~wise(X)))&
(?[X]:((~wise(X)&brave(X))))&
(?[X]:(humble(X)))&
((~humble(alice)<~>patient(alice)))&
(~generous(lucy)) | ~kind(susan) | [] | null | 0 |
If someone is not calm or quiet then susan is both old and not brave.
Everyone who is patient or generous is not funny and vice versa.
If someone is not tall then alice is generous or not calm.
Everyone who is not generous is both old and not strong.
Everyone who is not rich or not humble is both kind and not tall and vice versa.
If fred is not old or not tall then someone is either tall or not rich.
Everyone who is either rich or quiet is both kind and quiet.
If someone is both not curious and calm then someone is curious or not generous.
Everyone who is both kind and not rich is both rich and calm.
Everyone who is either tall or not funny is brave or quiet and vice versa.
Everyone who is both not old and not curious is both wise and patient and vice versa.
If someone is either funny or not kind then mary is happy or not old and vice versa.
If someone is tall then mary is not funny and vice versa.
Everyone who is both generous and brave is either happy or not old and vice versa.
If someone is patient or kind then alice is not creative.
If someone is either not funny or not happy then alice is brave.
Mary is either generous or curious.
Susan is not kind.
Paul is either brave or not strong.
Lucy is not happy or not quiet.
Mary is not funny or not generous.
Alice is either not generous or not tall.
Someone is both rich and not curious.
Someone is not tall or brave. | Mary is quiet. | entailment | ((?[X]:((~calm(X)|quiet(X))))=>((old(susan)&~brave(susan))))&
(![X]:((patient(X)|generous(X))<=>~funny(X)))&
((?[X]:(~tall(X)))=>((generous(alice)|~calm(alice))))&
(![X]:(~generous(X)=>(old(X)&~strong(X))))&
(![X]:((~rich(X)|~humble(X))<=>(kind(X)&~tall(X))))&
(((~old(fred)|~tall(fred)))=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((rich(X)<~>quiet(X))=>(kind(X)&quiet(X))))&
((?[X]:((~curious(X)&calm(X))))=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:((kind(X)&~rich(X))=>(rich(X)&calm(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)|quiet(X))))&
(![X]:((~old(X)&~curious(X))<=>(wise(X)&patient(X))))&
((?[X]:((funny(X)<~>~kind(X))))<=>((happy(mary)|~old(mary))))&
((?[X]:(tall(X)))<=>(~funny(mary)))&
(![X]:((generous(X)&brave(X))<=>(happy(X)<~>~old(X))))&
((?[X]:((patient(X)|kind(X))))=>(~creative(alice)))&
((?[X]:((~funny(X)<~>~happy(X))))=>(brave(alice)))&
((generous(mary)<~>curious(mary)))&
(~kind(susan))&
((brave(paul)<~>~strong(paul)))&
((~happy(lucy)|~quiet(lucy)))&
((~funny(mary)|~generous(mary)))&
((~generous(alice)<~>~tall(alice)))&
(?[X]:((rich(X)&~curious(X))))&
(?[X]:((~tall(X)|brave(X)))) | quiet(mary) | [
"p4",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1854803689197645203699957
% SZS output start Proof for 1854803689197645203699957
5. ! [X0] : ((~humble(X0) | ~rich(X0)) <=> (~tall(X0) & kind(X0))) [input p4]
7. ! [X0] : ((rich(X0) <~> quiet(X0)) => (quiet(X0) & kind(X0))) [input p6]
9. ! [X0] : ((~rich(X0) & kind(X0)) => (calm(X0) & rich(X0))) [input p8]
25. ~quiet(mary) [input hypothesis]
33. ! [X0] : ((quiet(X0) & kind(X0)) | (rich(X0) <=> quiet(X0))) [ennf transformation 7]
35. ! [X0] : ((calm(X0) & rich(X0)) | (rich(X0) | ~kind(X0))) [ennf transformation 9]
36. ! [X0] : ((calm(X0) & rich(X0)) | rich(X0) | ~kind(X0)) [flattening 35]
40. ! [X0] : (((~humble(X0) | ~rich(X0)) | (tall(X0) | ~kind(X0))) & ((~tall(X0) & kind(X0)) | (humble(X0) & rich(X0)))) [nnf transformation 5]
41. ! [X0] : ((~humble(X0) | ~rich(X0) | tall(X0) | ~kind(X0)) & ((~tall(X0) & kind(X0)) | (humble(X0) & rich(X0)))) [flattening 40]
45. ! [X0] : ((quiet(X0) & kind(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) [nnf transformation 33]
82. kind(X0) | rich(X0) [cnf transformation 41]
93. quiet(X0) | quiet(X0) | ~rich(X0) [cnf transformation 45]
96. rich(X0) | rich(X0) | ~kind(X0) [cnf transformation 36]
136. ~quiet(mary) [cnf transformation 25]
137. rich(X0) | ~kind(X0) [duplicate literal removal 96]
138. ~rich(X0) | quiet(X0) [duplicate literal removal 93]
200. rich(X0) [subsumption resolution 137,82]
311. quiet(X0) [resolution 138,200]
313. $false [resolution 311,136]
% SZS output end Proof for 1854803689197645203699957
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not rich is either not patient or generous.
If someone is either humble or strong then someone is not creative.
Everyone who is not quiet or not wise is both wise and not brave and vice versa.
Everyone who is not happy or rich is both happy and not strong and vice versa.
Everyone who is either brave or humble is not calm or not creative and vice versa.
Everyone who is both calm and patient is not brave and vice versa.
Everyone who is either creative or quiet is not tall or strong.
If someone is humble then someone is not tall.
Everyone who is quiet or happy is brave or calm and vice versa.
Everyone who is either calm or patient is happy.
Everyone who is either not creative or old is not tall or not calm.
If someone is both wise and not old then someone is both not patient and creative and vice versa.
If someone is either patient or not brave then someone is either not patient or not strong.
If susan is either curious or wise then mary is strong or old.
If someone is both funny and not rich then mary is either not brave or strong and vice versa.
Everyone who is not strong is either not happy or kind.
Susan is brave or old.
Fred is both brave and tall.
Someone is either not wise or wise.
Someone is both not rich and not old.
Someone is both not rich and tall.
Someone is not kind. | Fred is calm. | neutral | (![X]:((~happy(X)<~>~rich(X))=>(~patient(X)<~>generous(X))))&
((?[X]:((humble(X)<~>strong(X))))=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(wise(X)&~brave(X))))&
(![X]:((~happy(X)|rich(X))<=>(happy(X)&~strong(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~calm(X)|~creative(X))))&
(![X]:((calm(X)&patient(X))<=>~brave(X)))&
(![X]:((creative(X)<~>quiet(X))=>(~tall(X)|strong(X))))&
((?[X]:(humble(X)))=>(?[X]:(~tall(X))))&
(![X]:((quiet(X)|happy(X))<=>(brave(X)|calm(X))))&
(![X]:((calm(X)<~>patient(X))=>happy(X)))&
(![X]:((~creative(X)<~>old(X))=>(~tall(X)|~calm(X))))&
((?[X]:((wise(X)&~old(X))))<=>(?[X]:((~patient(X)&creative(X)))))&
((?[X]:((patient(X)<~>~brave(X))))=>(?[X]:((~patient(X)<~>~strong(X)))))&
(((curious(susan)<~>wise(susan)))=>((strong(mary)|old(mary))))&
((?[X]:((funny(X)&~rich(X))))<=>((~brave(mary)<~>strong(mary))))&
(![X]:(~strong(X)=>(~happy(X)<~>kind(X))))&
((brave(susan)|old(susan)))&
((brave(fred)&tall(fred)))&
(?[X]:((~wise(X)<~>wise(X))))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:(~kind(X))) | calm(fred) | [] | null | 0 |
If paul is either happy or not quiet then lucy is rich or tall and vice versa.
Everyone who is either not humble or not strong is either calm or not old.
Everyone who is either not generous or rich is not old or not patient.
Everyone who is both funny and not funny is humble or not curious and vice versa.
If mary is strong or not creative then someone is either not patient or not generous and vice versa.
Everyone who is both not old and not calm is creative and vice versa.
Everyone who is both calm and wise is happy.
Everyone who is not tall is both funny and curious and vice versa.
Everyone who is either not humble or not patient is tall.
If susan is both not happy and brave then someone is old or not rich.
Everyone who is not tall or funny is either generous or not rich and vice versa.
Everyone who is calm is both generous and not old and vice versa.
Everyone who is either strong or not quiet is rich or kind and vice versa.
Everyone who is either kind or humble is creative or not patient and vice versa.
If john is kind then susan is not kind or calm.
Everyone who is tall is both quiet and tall and vice versa.
Lucy is strong.
Susan is both not funny and old.
Someone is strong.
Someone is both funny and not quiet.
Someone is not funny.
Someone is not wise or not brave.
Paul is both not kind and brave. | Paul is not rich. | entailment | (((happy(paul)<~>~quiet(paul)))<=>((rich(lucy)|tall(lucy))))&
(![X]:((~humble(X)<~>~strong(X))=>(calm(X)<~>~old(X))))&
(![X]:((~generous(X)<~>rich(X))=>(~old(X)|~patient(X))))&
(![X]:((funny(X)&~funny(X))<=>(humble(X)|~curious(X))))&
(((strong(mary)|~creative(mary)))<=>(?[X]:((~patient(X)<~>~generous(X)))))&
(![X]:((~old(X)&~calm(X))<=>creative(X)))&
(![X]:((calm(X)&wise(X))=>happy(X)))&
(![X]:(~tall(X)<=>(funny(X)&curious(X))))&
(![X]:((~humble(X)<~>~patient(X))=>tall(X)))&
(((~happy(susan)&brave(susan)))=>(?[X]:((old(X)|~rich(X)))))&
(![X]:((~tall(X)|funny(X))<=>(generous(X)<~>~rich(X))))&
(![X]:(calm(X)<=>(generous(X)&~old(X))))&
(![X]:((strong(X)<~>~quiet(X))<=>(rich(X)|kind(X))))&
(![X]:((kind(X)<~>humble(X))<=>(creative(X)|~patient(X))))&
((kind(john))=>((~kind(susan)|calm(susan))))&
(![X]:(tall(X)<=>(quiet(X)&tall(X))))&
(strong(lucy))&
((~funny(susan)&old(susan)))&
(?[X]:(strong(X)))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~wise(X)|~brave(X))))&
((~kind(paul)&brave(paul))) | ~rich(paul) | [
"p1",
"p3",
"p5",
"p8",
"p11",
"p12",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1923572677477357824887749
% SZS output start Proof for 1923572677477357824887749
2. ! [X0] : ((~humble(X0) <~> ~strong(X0)) => (calm(X0) <~> ~old(X0))) [input p1]
4. ! [X0] : ((~funny(X0) & funny(X0)) <=> (~curious(X0) | humble(X0))) [input p3]
6. ! [X0] : ((~calm(X0) & ~old(X0)) <=> creative(X0)) [input p5]
9. ! [X0] : ((~humble(X0) <~> ~patient(X0)) => tall(X0)) [input p8]
12. ! [X0] : (calm(X0) <=> (~old(X0) & generous(X0))) [input p11]
13. ! [X0] : ((strong(X0) <~> ~quiet(X0)) <=> (kind(X0) | rich(X0))) [input p12]
14. ! [X0] : ((kind(X0) <~> humble(X0)) <=> (~patient(X0) | creative(X0))) [input p13]
16. ! [X0] : (tall(X0) <=> (tall(X0) & quiet(X0))) [input p15]
23. brave(paul) & ~kind(paul) [input p22]
24. rich(paul) [input hypothesis]
27. ! [X0] : ((calm(X0) <~> ~old(X0)) | (~humble(X0) <=> ~strong(X0))) [ennf transformation 2]
30. ! [X0] : (tall(X0) | (~humble(X0) <=> ~patient(X0))) [ennf transformation 9]
37. ! [X0] : (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) [nnf transformation 27]
39. ! [X0] : (((~funny(X0) & funny(X0)) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | (funny(X0) | ~funny(X0)))) [nnf transformation 4]
40. ! [X0] : (((~funny(X0) & funny(X0)) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | funny(X0) | ~funny(X0))) [flattening 39]
46. ! [X0] : (((~calm(X0) & ~old(X0)) | ~creative(X0)) & (creative(X0) | (calm(X0) | old(X0)))) [nnf transformation 6]
47. ! [X0] : (((~calm(X0) & ~old(X0)) | ~creative(X0)) & (creative(X0) | calm(X0) | old(X0))) [flattening 46]
50. ! [X0] : (tall(X0) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) [nnf transformation 30]
55. ! [X0] : ((calm(X0) | (old(X0) | ~generous(X0))) & ((~old(X0) & generous(X0)) | ~calm(X0))) [nnf transformation 12]
56. ! [X0] : ((calm(X0) | old(X0) | ~generous(X0)) & ((~old(X0) & generous(X0)) | ~calm(X0))) [flattening 55]
57. ! [X0] : ((((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (~kind(X0) & ~rich(X0))) & ((kind(X0) | rich(X0)) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0))))) [nnf transformation 13]
58. ! [X0] : ((((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (~kind(X0) & ~rich(X0))) & (kind(X0) | rich(X0) | ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0))))) [flattening 57]
59. ! [X0] : ((((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0))))) [nnf transformation 14]
60. ! [X0] : ((((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0))))) [flattening 59]
61. ! [X0] : ((tall(X0) | (~tall(X0) | ~quiet(X0))) & ((tall(X0) & quiet(X0)) | ~tall(X0))) [nnf transformation 16]
62. ! [X0] : ((tall(X0) | ~tall(X0) | ~quiet(X0)) & ((tall(X0) & quiet(X0)) | ~tall(X0))) [flattening 61]
75. ~old(X0) | calm(X0) | ~strong(X0) | humble(X0) [cnf transformation 37]
77. ~calm(X0) | old(X0) | ~strong(X0) | humble(X0) [cnf transformation 37]
82. funny(X0) | ~humble(X0) [cnf transformation 40]
84. ~funny(X0) | ~humble(X0) [cnf transformation 40]
92. creative(X0) | calm(X0) | old(X0) [cnf transformation 47]
98. tall(X0) | ~patient(X0) | humble(X0) [cnf transformation 50]
108. ~old(X0) | ~calm(X0) [cnf transformation 56]
112. ~rich(X0) | strong(X0) | ~quiet(X0) [cnf transformation 58]
118. humble(X0) | kind(X0) | ~creative(X0) [cnf transformation 60]
119. humble(X0) | kind(X0) | patient(X0) [cnf transformation 60]
123. ~tall(X0) | quiet(X0) [cnf transformation 62]
133. ~kind(paul) [cnf transformation 23]
135. rich(paul) [cnf transformation 24]
145. 3 <=> quiet(paul) [avatar definition]
147. quiet(paul) <- (3) [avatar component clause 145]
159. ~humble(X0) [subsumption resolution 82,84]
189. ~patient(X0) | tall(X0) [subsumption resolution 98,159]
209. kind(X0) | patient(X0) [subsumption resolution 119,159]
210. ~creative(X0) | kind(X0) [subsumption resolution 118,159]
239. patient(paul) [resolution 209,133]
241. tall(paul) [resolution 239,189]
246. kind(X0) | old(X0) | calm(X0) [resolution 92,210]
250. quiet(paul) [resolution 241,123]
253. 3 [avatar split clause 250,145]
289. strong(paul) | ~quiet(paul) [resolution 112,135]
291. strong(paul) <- (3) [subsumption resolution 289,147]
313. 25 <=> calm(paul) [avatar definition]
315. calm(paul) <- (25) [avatar component clause 313]
317. 26 <=> old(paul) [avatar definition]
318. ~old(paul) <- (~26) [avatar component clause 317]
319. old(paul) <- (26) [avatar component clause 317]
433. old(paul) | calm(paul) [resolution 246,133]
502. calm(paul) | ~strong(paul) | humble(paul) <- (26) [resolution 319,75]
503. ~calm(paul) <- (26) [resolution 319,108]
504. calm(paul) | humble(paul) <- (3, 26) [subsumption resolution 502,291]
505. calm(paul) <- (3, 26) [subsumption resolution 504,159]
506. 25 | ~3 | ~26 [avatar split clause 505,317,145,313]
507. ~25 | ~26 [avatar split clause 503,317,313]
508. 25 | 26 [avatar split clause 433,317,313]
521. old(paul) | ~strong(paul) | humble(paul) <- (25) [resolution 315,77]
523. ~strong(paul) | humble(paul) <- (25, ~26) [subsumption resolution 521,318]
524. humble(paul) <- (3, 25, ~26) [subsumption resolution 523,291]
525. $false <- (3, 25, ~26) [subsumption resolution 524,159]
526. ~3 | ~25 | 26 [avatar contradiction clause 525]
528. $false [avatar sat refutation 253,506,507,508,526]
% SZS output end Proof for 1923572677477357824887749
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is quiet and vice versa. Everyone who is either quiet or brave is either not funny or not rich. Everyone who is not kind or not generous is either not happy or brave and vice versa. Everyone who is either not tall or quiet is both brave and not brave. Everyone who is both creative and happy is not humble or generous and vice versa. If someone is both quiet and not kind then someone is either wise or kind and vice versa. If someone is either rich or funny then fred is either not kind or not generous and vice versa. Everyone who is not generous or not wise is not patient. If john is both calm and brave then someone is both not tall and happy and vice versa. Everyone who is not strong is not rich or not kind and vice versa. If someone is both tall and quiet then mary is either not calm or not curious. Everyone who is both not brave and brave is tall or wise and vice versa. If susan is not curious or not old then someone is either not calm or not curious. If someone is not patient or creative then paul is not kind. Someone is not brave or not calm. Lucy is both humble and funny. Someone is not rich. Mary is not calm. Someone is both not funny and not humble. Someone is funny or not kind. | John is not happy. | contradiction | (![X]:(~rich(X)<=>quiet(X)))&
(![X]:((quiet(X)<~>brave(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((~kind(X)|~generous(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~tall(X)<~>quiet(X))=>(brave(X)&~brave(X))))&
(![X]:((creative(X)&happy(X))<=>(~humble(X)|generous(X))))&
((?[X]:((quiet(X)&~kind(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
((?[X]:((rich(X)<~>funny(X))))<=>((~kind(fred)<~>~generous(fred))))&
(![X]:((~generous(X)|~wise(X))=>~patient(X)))&
(((calm(john)&brave(john)))<=>(?[X]:((~tall(X)&happy(X)))))&
(![X]:(~strong(X)<=>(~rich(X)|~kind(X))))&
((?[X]:((tall(X)&quiet(X))))=>((~calm(mary)<~>~curious(mary))))&
(![X]:((~brave(X)&brave(X))<=>(tall(X)|wise(X))))&
(((~curious(susan)|~old(susan)))=>(?[X]:((~calm(X)<~>~curious(X)))))&
((?[X]:((~patient(X)|creative(X))))=>(~kind(paul)))&
(?[X]:((~brave(X)|~calm(X))))&
((humble(lucy)&funny(lucy)))&
(?[X]:(~rich(X)))&
(~calm(mary))&
(?[X]:((~funny(X)&~humble(X))))&
(?[X]:((funny(X)|~kind(X)))) | ~happy(john) | [
"p2",
"p4",
"p8",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6317316315948221352537624
% SZS output start Proof for 6317316315948221352537624
3. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (~happy(X0) <~> brave(X0))) [input p2]
5. ! [X0] : ((happy(X0) & creative(X0)) <=> (generous(X0) | ~humble(X0))) [input p4]
9. (brave(john) & calm(john)) <=> ? [X0] : (happy(X0) & ~tall(X0)) [input p8]
12. ! [X0] : ((brave(X0) & ~brave(X0)) <=> (wise(X0) | tall(X0))) [input p11]
19. ? [X0] : (~humble(X0) & ~funny(X0)) [input p18]
21. ~happy(john) [input hypothesis]
32. ! [X0] : (((~generous(X0) | ~kind(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (generous(X0) & kind(X0)))) [nnf transformation 3]
33. ! [X0] : ((~generous(X0) | ~kind(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (generous(X0) & kind(X0)))) [flattening 32]
35. ! [X0] : (((happy(X0) & creative(X0)) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 5]
36. ! [X0] : (((happy(X0) & creative(X0)) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | ~happy(X0) | ~creative(X0))) [flattening 35]
46. ((brave(john) & calm(john)) | ! [X0] : (~happy(X0) | tall(X0))) & (? [X0] : (happy(X0) & ~tall(X0)) | (~brave(john) | ~calm(john))) [nnf transformation 9]
47. ((brave(john) & calm(john)) | ! [X0] : (~happy(X0) | tall(X0))) & (? [X0] : (happy(X0) & ~tall(X0)) | ~brave(john) | ~calm(john)) [flattening 46]
48. ((brave(john) & calm(john)) | ! [X0] : (~happy(X0) | tall(X0))) & (? [X1] : (happy(X1) & ~tall(X1)) | ~brave(john) | ~calm(john)) [rectify 47]
49. ? [X1] : (happy(X1) & ~tall(X1)) => (happy(sK3) & ~tall(sK3)) [choice axiom]
50. ((brave(john) & calm(john)) | ! [X0] : (~happy(X0) | tall(X0))) & ((happy(sK3) & ~tall(sK3)) | ~brave(john) | ~calm(john)) [skolemisation 48,49]
52. ! [X0] : (((brave(X0) & ~brave(X0)) | (~wise(X0) & ~tall(X0))) & ((wise(X0) | tall(X0)) | (~brave(X0) | brave(X0)))) [nnf transformation 12]
53. ! [X0] : (((brave(X0) & ~brave(X0)) | (~wise(X0) & ~tall(X0))) & (wise(X0) | tall(X0) | ~brave(X0) | brave(X0))) [flattening 52]
61. ? [X0] : (~humble(X0) & ~funny(X0)) => (~humble(sK7) & ~funny(sK7)) [choice axiom]
62. ~humble(sK7) & ~funny(sK7) [skolemisation 19,61]
74. ~brave(X0) | happy(X0) | generous(X0) [cnf transformation 33]
84. humble(X0) | happy(X0) [cnf transformation 36]
85. ~generous(X0) | happy(X0) [cnf transformation 36]
105. brave(john) | ~happy(X0) | tall(X0) [cnf transformation 50]
109. ~brave(X0) | ~tall(X0) [cnf transformation 53]
111. ~tall(X0) | brave(X0) [cnf transformation 53]
123. ~humble(sK7) [cnf transformation 62]
125. ~happy(john) [cnf transformation 21]
192. 14 <=> ! [X0] : (~happy(X0) | tall(X0)) [avatar definition]
193. ~happy(X0) | tall(X0) <- (14) [avatar component clause 192]
195. 15 <=> brave(john) [avatar definition]
197. brave(john) <- (15) [avatar component clause 195]
198. 14 | 15 [avatar split clause 105,195,192]
215. ~tall(X0) [subsumption resolution 109,111]
260. ~happy(X0) <- (14) [subsumption resolution 193,215]
265. happy(sK7) [resolution 84,123]
266. $false <- (14) [subsumption resolution 265,260]
267. ~14 [avatar contradiction clause 266]
313. happy(john) | generous(john) <- (15) [resolution 74,197]
314. generous(john) <- (15) [subsumption resolution 313,125]
316. happy(john) <- (15) [resolution 314,85]
318. $false <- (15) [subsumption resolution 316,125]
319. ~15 [avatar contradiction clause 318]
320. $false [avatar sat refutation 198,267,319]
% SZS output end Proof for 6317316315948221352537624
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not rich and not patient then john is not tall.
If john is both wise and generous then someone is not rich and vice versa.
If someone is not brave or not strong then someone is either not happy or not funny and vice versa.
If susan is not patient then alice is strong or curious and vice versa.
Everyone who is not rich or not creative is rich or not calm.
Everyone who is happy is not brave and vice versa.
Everyone who is both not humble and rich is either not quiet or not creative and vice versa.
Everyone who is either not calm or happy is either curious or happy.
If susan is both creative and happy then someone is either not brave or humble.
If alice is either curious or generous then someone is old or happy and vice versa.
If susan is quiet or old then paul is both not old and curious and vice versa.
Everyone who is not creative is either wise or creative.
Everyone who is tall or not kind is both happy and wise.
Everyone who is creative is calm or not funny.
Everyone who is wise is not strong or not rich and vice versa.
If someone is patient or not funny then fred is both not generous and patient.
Paul is either not curious or not humble.
Someone is both patient and brave.
Someone is both generous and not happy.
Susan is either kind or brave.
Someone is not rich.
Someone is not quiet or rich.
Someone is both not humble and generous.
Alice is not wise. | Fred is generous. | contradiction | (((~rich(susan)&~patient(susan)))=>(~tall(john)))&
(((wise(john)&generous(john)))<=>(?[X]:(~rich(X))))&
((?[X]:((~brave(X)|~strong(X))))<=>(?[X]:((~happy(X)<~>~funny(X)))))&
((~patient(susan))<=>((strong(alice)|curious(alice))))&
(![X]:((~rich(X)|~creative(X))=>(rich(X)|~calm(X))))&
(![X]:(happy(X)<=>~brave(X)))&
(![X]:((~humble(X)&rich(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~calm(X)<~>happy(X))=>(curious(X)<~>happy(X))))&
(((creative(susan)&happy(susan)))=>(?[X]:((~brave(X)<~>humble(X)))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(((quiet(susan)|old(susan)))<=>((~old(paul)&curious(paul))))&
(![X]:(~creative(X)=>(wise(X)<~>creative(X))))&
(![X]:((tall(X)|~kind(X))=>(happy(X)&wise(X))))&
(![X]:(creative(X)=>(calm(X)|~funny(X))))&
(![X]:(wise(X)<=>(~strong(X)|~rich(X))))&
((?[X]:((patient(X)|~funny(X))))=>((~generous(fred)&patient(fred))))&
((~curious(paul)<~>~humble(paul)))&
(?[X]:((patient(X)&brave(X))))&
(?[X]:((generous(X)&~happy(X))))&
((kind(susan)<~>brave(susan)))&
(?[X]:(~rich(X)))&
(?[X]:((~quiet(X)|rich(X))))&
(?[X]:((~humble(X)&generous(X))))&
(~wise(alice)) | generous(fred) | [
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2529668647087071222769509
% SZS output start Proof for 2529668647087071222769509
16. ? [X0] : (~funny(X0) | patient(X0)) => (patient(fred) & ~generous(fred)) [input p15]
18. ? [X0] : (brave(X0) & patient(X0)) [input p17]
25. generous(fred) [input hypothesis]
38. (patient(fred) & ~generous(fred)) | ! [X0] : (funny(X0) & ~patient(X0)) [ennf transformation 16]
68. ? [X0] : (brave(X0) & patient(X0)) => (brave(sK5) & patient(sK5)) [choice axiom]
69. brave(sK5) & patient(sK5) [skolemisation 18,68]
126. ~generous(fred) | ~patient(X0) [cnf transformation 38]
132. patient(sK5) [cnf transformation 69]
143. generous(fred) [cnf transformation 25]
287. 31 <=> ! [X0] : ~patient(X0) [avatar definition]
288. ~patient(X0) <- (31) [avatar component clause 287]
291. 32 <=> generous(fred) [avatar definition]
295. 31 | ~32 [avatar split clause 126,291,287]
321. 32 [avatar split clause 143,291]
330. $false <- (31) [resolution 288,132]
331. ~31 [avatar contradiction clause 330]
332. $false [avatar sat refutation 295,321,331]
% SZS output end Proof for 2529668647087071222769509
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is not strong and vice versa.
If someone is not patient or not quiet then someone is humble.
Everyone who is not happy is either not patient or not quiet and vice versa.
If someone is old then fred is either not rich or happy.
Everyone who is both creative and patient is quiet or curious and vice versa.
Everyone who is not brave is either not brave or not curious and vice versa.
If someone is wise or quiet then alice is not tall and vice versa.
Everyone who is both not brave and quiet is old.
If lucy is both quiet and not tall then someone is either curious or patient.
Everyone who is generous or happy is happy and vice versa.
Everyone who is calm is not tall or not old and vice versa.
If john is not calm or not happy then someone is both not funny and strong and vice versa.
If mary is either not generous or not creative then john is not calm and vice versa.
Everyone who is not creative or brave is calm.
Everyone who is strong or funny is not brave or not creative and vice versa.
Someone is creative or generous.
Someone is not humble or quiet.
Alice is tall.
Lucy is humble.
Susan is both not generous and not rich. | Alice is not happy. | entailment | (![X]:(~patient(X)<=>~strong(X)))&
((?[X]:((~patient(X)|~quiet(X))))=>(?[X]:(humble(X))))&
(![X]:(~happy(X)<=>(~patient(X)<~>~quiet(X))))&
((?[X]:(old(X)))=>((~rich(fred)<~>happy(fred))))&
(![X]:((creative(X)&patient(X))<=>(quiet(X)|curious(X))))&
(![X]:(~brave(X)<=>(~brave(X)<~>~curious(X))))&
((?[X]:((wise(X)|quiet(X))))<=>(~tall(alice)))&
(![X]:((~brave(X)&quiet(X))=>old(X)))&
(((quiet(lucy)&~tall(lucy)))=>(?[X]:((curious(X)<~>patient(X)))))&
(![X]:((generous(X)|happy(X))<=>happy(X)))&
(![X]:(calm(X)<=>(~tall(X)|~old(X))))&
(((~calm(john)|~happy(john)))<=>(?[X]:((~funny(X)&strong(X)))))&
(((~generous(mary)<~>~creative(mary)))<=>(~calm(john)))&
(![X]:((~creative(X)|brave(X))=>calm(X)))&
(![X]:((strong(X)|funny(X))<=>(~brave(X)|~creative(X))))&
(?[X]:((creative(X)|generous(X))))&
(?[X]:((~humble(X)|quiet(X))))&
(tall(alice))&
(humble(lucy))&
((~generous(susan)&~rich(susan))) | ~happy(alice) | [
"p2",
"p4",
"p5",
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4853060151390378449357902
% SZS output start Proof for 4853060151390378449357902
3. ! [X0] : (~happy(X0) <=> (~patient(X0) <~> ~quiet(X0))) [input p2]
5. ! [X0] : ((patient(X0) & creative(X0)) <=> (curious(X0) | quiet(X0))) [input p4]
6. ! [X0] : (~brave(X0) <=> (~brave(X0) <~> ~curious(X0))) [input p5]
7. ? [X0] : (quiet(X0) | wise(X0)) <=> ~tall(alice) [input p6]
18. tall(alice) [input p17]
21. happy(alice) [input hypothesis]
34. ! [X0] : ((~happy(X0) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | happy(X0))) [nnf transformation 3]
36. ! [X0] : (((patient(X0) & creative(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (~patient(X0) | ~creative(X0)))) [nnf transformation 5]
37. ! [X0] : (((patient(X0) & creative(X0)) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | ~patient(X0) | ~creative(X0))) [flattening 36]
38. ! [X0] : ((~brave(X0) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) & (((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | brave(X0))) [nnf transformation 6]
39. (? [X0] : (quiet(X0) | wise(X0)) | tall(alice)) & (~tall(alice) | ! [X0] : (~quiet(X0) & ~wise(X0))) [nnf transformation 7]
40. (? [X0] : (quiet(X0) | wise(X0)) | tall(alice)) & (~tall(alice) | ! [X1] : (~quiet(X1) & ~wise(X1))) [rectify 39]
41. ? [X0] : (quiet(X0) | wise(X0)) => (quiet(sK1) | wise(sK1)) [choice axiom]
42. ((quiet(sK1) | wise(sK1)) | tall(alice)) & (~tall(alice) | ! [X1] : (~quiet(X1) & ~wise(X1))) [skolemisation 40,41]
69. ~happy(X0) | ~patient(X0) | quiet(X0) [cnf transformation 34]
76. ~curious(X0) | patient(X0) [cnf transformation 37]
78. curious(X0) | brave(X0) | brave(X0) [cnf transformation 38]
80. ~brave(X0) | ~brave(X0) | curious(X0) [cnf transformation 38]
82. ~tall(alice) | ~quiet(X1) [cnf transformation 42]
110. tall(alice) [cnf transformation 18]
114. happy(alice) [cnf transformation 21]
115. curious(X0) | brave(X0) [duplicate literal removal 78]
116. ~brave(X0) | curious(X0) [duplicate literal removal 80]
126. 3 <=> ! [X1] : patient(X1) [avatar definition]
127. patient(X1) <- (3) [avatar component clause 126]
142. curious(X0) [subsumption resolution 115,116]
144. 7 <=> tall(alice) [avatar definition]
157. 10 <=> ! [X1] : ~quiet(X1) [avatar definition]
158. ~quiet(X1) <- (10) [avatar component clause 157]
159. 10 | ~7 [avatar split clause 82,144,157]
232. 7 [avatar split clause 110,144]
238. patient(X0) [resolution 76,142]
239. 3 [avatar split clause 238,126]
256. ~patient(alice) | quiet(alice) [resolution 69,114]
260. quiet(alice) <- (3) [subsumption resolution 256,127]
261. $false <- (3, 10) [subsumption resolution 260,158]
262. ~3 | ~10 [avatar contradiction clause 261]
266. $false [avatar sat refutation 159,232,239,262]
% SZS output end Proof for 4853060151390378449357902
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.