premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
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sequencelengths 0
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stringlengths 684
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If someone is both not quiet and generous then someone is both strong and happy. Everyone who is not funny or not creative is not rich or not kind and vice versa. Everyone who is not calm or not happy is both not wise and not brave. Everyone who is patient is wise or strong and vice versa. Everyone who is either rich or curious is either not strong or humble and vice versa. Everyone who is not humble is either not calm or not funny. Everyone who is both brave and not old is both wise and not creative. Everyone who is generous is not strong or not funny and vice versa. Everyone who is brave is both kind and not tall and vice versa. Everyone who is either wise or not strong is either kind or not humble and vice versa. Everyone who is funny or not brave is funny and vice versa. If paul is both not calm and calm then someone is quiet or generous and vice versa. Everyone who is tall is either not happy or brave. Everyone who is quiet is either old or wise. If alice is not old or rich then someone is both not tall and not kind. Everyone who is not old is either tall or calm and vice versa. Lucy is wise. Paul is rich. Susan is either rich or not curious. Mary is either generous or not tall. Someone is not brave or not strong. | Alice is humble. | neutral | ((?[X]:((~quiet(X)&generous(X))))=>(?[X]:((strong(X)&happy(X)))))&
(![X]:((~funny(X)|~creative(X))<=>(~rich(X)|~kind(X))))&
(![X]:((~calm(X)|~happy(X))=>(~wise(X)&~brave(X))))&
(![X]:(patient(X)<=>(wise(X)|strong(X))))&
(![X]:((rich(X)<~>curious(X))<=>(~strong(X)<~>humble(X))))&
(![X]:(~humble(X)=>(~calm(X)<~>~funny(X))))&
(![X]:((brave(X)&~old(X))=>(wise(X)&~creative(X))))&
(![X]:(generous(X)<=>(~strong(X)|~funny(X))))&
(![X]:(brave(X)<=>(kind(X)&~tall(X))))&
(![X]:((wise(X)<~>~strong(X))<=>(kind(X)<~>~humble(X))))&
(![X]:((funny(X)|~brave(X))<=>funny(X)))&
(((~calm(paul)&calm(paul)))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:(tall(X)=>(~happy(X)<~>brave(X))))&
(![X]:(quiet(X)=>(old(X)<~>wise(X))))&
(((~old(alice)|rich(alice)))=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:(~old(X)<=>(tall(X)<~>calm(X))))&
(wise(lucy))&
(rich(paul))&
((rich(susan)<~>~curious(susan)))&
((generous(mary)<~>~tall(mary)))&
(?[X]:((~brave(X)|~strong(X)))) | humble(alice) | [] | null | 0 |
Everyone who is happy is both not brave and not kind and vice versa.
If alice is both rich and not patient then fred is both not patient and not tall.
If someone is either old or brave then lucy is funny or strong and vice versa.
If someone is not creative then paul is both not old and patient and vice versa.
If susan is not patient or not old then paul is not rich or not quiet and vice versa.
Everyone who is either not generous or not creative is both not creative and curious.
If fred is both brave and not humble then someone is both patient and brave and vice versa.
Everyone who is creative is both humble and not humble and vice versa.
Everyone who is either not old or happy is both not kind and patient and vice versa.
If paul is old then susan is both not humble and old and vice versa.
Everyone who is both not generous and brave is both happy and generous and vice versa.
If someone is both strong and creative then someone is either wise or kind and vice versa.
If someone is not tall then mary is both kind and brave and vice versa.
Everyone who is not patient is either curious or not patient.
Everyone who is calm or rich is both tall and kind and vice versa.
If john is not generous or tall then mary is generous or not patient.
Someone is humble or funny.
Someone is not rich or brave.
Alice is happy or kind.
Someone is both not kind and patient.
Someone is not kind.
Someone is not wise or creative.
John is either funny or wise.
Someone is kind or not kind. | Paul is not curious. | contradiction | (![X]:(happy(X)<=>(~brave(X)&~kind(X))))&
(((rich(alice)&~patient(alice)))=>((~patient(fred)&~tall(fred))))&
((?[X]:((old(X)<~>brave(X))))<=>((funny(lucy)|strong(lucy))))&
((?[X]:(~creative(X)))<=>((~old(paul)&patient(paul))))&
(((~patient(susan)|~old(susan)))<=>((~rich(paul)|~quiet(paul))))&
(![X]:((~generous(X)<~>~creative(X))=>(~creative(X)&curious(X))))&
(((brave(fred)&~humble(fred)))<=>(?[X]:((patient(X)&brave(X)))))&
(![X]:(creative(X)<=>(humble(X)&~humble(X))))&
(![X]:((~old(X)<~>happy(X))<=>(~kind(X)&patient(X))))&
((old(paul))<=>((~humble(susan)&old(susan))))&
(![X]:((~generous(X)&brave(X))<=>(happy(X)&generous(X))))&
((?[X]:((strong(X)&creative(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
((?[X]:(~tall(X)))<=>((kind(mary)&brave(mary))))&
(![X]:(~patient(X)=>(curious(X)<~>~patient(X))))&
(![X]:((calm(X)|rich(X))<=>(tall(X)&kind(X))))&
(((~generous(john)|tall(john)))=>((generous(mary)|~patient(mary))))&
(?[X]:((humble(X)|funny(X))))&
(?[X]:((~rich(X)|brave(X))))&
((happy(alice)|kind(alice)))&
(?[X]:((~kind(X)&patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)|creative(X))))&
((funny(john)<~>wise(john)))&
(?[X]:((kind(X)|~kind(X)))) | ~curious(paul) | [
"p0",
"p3",
"p5",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3291988799784691832733914
% SZS output start Proof for 3291988799784691832733914
1. ! [X0] : (happy(X0) <=> (~kind(X0) & ~brave(X0))) [input p0]
4. ? [X0] : ~creative(X0) <=> (patient(paul) & ~old(paul)) [input p3]
6. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => (curious(X0) & ~creative(X0))) [input p5]
8. ! [X0] : (creative(X0) <=> (~humble(X0) & humble(X0))) [input p7]
9. ! [X0] : ((~old(X0) <~> happy(X0)) <=> (patient(X0) & ~kind(X0))) [input p8]
11. ! [X0] : ((brave(X0) & ~generous(X0)) <=> (generous(X0) & happy(X0))) [input p10]
25. ~curious(paul) [input hypothesis]
29. ! [X0] : ((curious(X0) & ~creative(X0)) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 6]
33. ! [X0] : ((happy(X0) | (kind(X0) | brave(X0))) & ((~kind(X0) & ~brave(X0)) | ~happy(X0))) [nnf transformation 1]
34. ! [X0] : ((happy(X0) | kind(X0) | brave(X0)) & ((~kind(X0) & ~brave(X0)) | ~happy(X0))) [flattening 33]
40. (? [X0] : ~creative(X0) | (~patient(paul) | old(paul))) & ((patient(paul) & ~old(paul)) | ! [X0] : creative(X0)) [nnf transformation 4]
41. (? [X0] : ~creative(X0) | ~patient(paul) | old(paul)) & ((patient(paul) & ~old(paul)) | ! [X0] : creative(X0)) [flattening 40]
42. (? [X0] : ~creative(X0) | ~patient(paul) | old(paul)) & ((patient(paul) & ~old(paul)) | ! [X1] : creative(X1)) [rectify 41]
43. ? [X0] : ~creative(X0) => ~creative(sK1) [choice axiom]
44. (~creative(sK1) | ~patient(paul) | old(paul)) & ((patient(paul) & ~old(paul)) | ! [X1] : creative(X1)) [skolemisation 42,43]
47. ! [X0] : ((curious(X0) & ~creative(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 29]
53. ! [X0] : ((creative(X0) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | ~creative(X0))) [nnf transformation 8]
54. ! [X0] : ((creative(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | ~creative(X0))) [flattening 53]
55. ! [X0] : ((((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))))) [nnf transformation 9]
56. ! [X0] : ((((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))))) [flattening 55]
59. ! [X0] : (((brave(X0) & ~generous(X0)) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | (~brave(X0) | generous(X0)))) [nnf transformation 11]
60. ! [X0] : (((brave(X0) & ~generous(X0)) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | ~brave(X0) | generous(X0))) [flattening 59]
88. ~kind(X0) | ~happy(X0) [cnf transformation 34]
89. kind(X0) | happy(X0) | brave(X0) [cnf transformation 34]
98. ~old(paul) | creative(X1) [cnf transformation 44]
99. patient(paul) | creative(X1) [cnf transformation 44]
108. ~generous(X0) | curious(X0) | creative(X0) [cnf transformation 47]
113. humble(X0) | ~creative(X0) [cnf transformation 54]
114. ~humble(X0) | ~creative(X0) [cnf transformation 54]
116. ~kind(X0) | happy(X0) | old(X0) [cnf transformation 56]
121. ~happy(X0) | old(X0) | ~patient(X0) | kind(X0) [cnf transformation 56]
126. generous(X0) | ~brave(X0) | generous(X0) [cnf transformation 60]
157. ~curious(paul) [cnf transformation 25]
159. ~brave(X0) | generous(X0) [duplicate literal removal 126]
209. 11 <=> old(paul) [avatar definition]
210. ~old(paul) <- (~11) [avatar component clause 209]
213. 12 <=> patient(paul) [avatar definition]
214. patient(paul) <- (12) [avatar component clause 213]
222. 14 <=> ! [X1] : creative(X1) [avatar definition]
223. creative(X1) <- (14) [avatar component clause 222]
224. 14 | 12 [avatar split clause 99,213,222]
225. 14 | ~11 [avatar split clause 98,209,222]
269. ~creative(X0) [subsumption resolution 113,114]
270. ~patient(X0) | old(X0) | ~happy(X0) [subsumption resolution 121,88]
271. ~kind(X0) | old(X0) [subsumption resolution 116,88]
371. old(X1) | brave(X1) | happy(X1) [resolution 89,271]
408. old(paul) | ~happy(paul) <- (12) [resolution 270,214]
465. 51 <=> happy(paul) [avatar definition]
467. ~happy(paul) <- (~51) [avatar component clause 465]
468. ~51 | 11 | ~12 [avatar split clause 408,213,209,465]
469. $false <- (14) [subsumption resolution 223,269]
470. ~14 [avatar contradiction clause 469]
485. brave(paul) | happy(paul) <- (~11) [resolution 210,371]
487. brave(paul) <- (~11, ~51) [subsumption resolution 485,467]
541. generous(paul) <- (~11, ~51) [resolution 487,159]
550. curious(paul) | creative(paul) <- (~11, ~51) [resolution 541,108]
552. creative(paul) <- (~11, ~51) [subsumption resolution 550,157]
553. $false <- (~11, ~51) [subsumption resolution 552,269]
554. 11 | 51 [avatar contradiction clause 553]
555. $false [avatar sat refutation 224,225,468,470,554]
% SZS output end Proof for 3291988799784691832733914
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and patient is kind. Everyone who is humble is either not old or not kind. If someone is both not curious and strong then fred is tall or not humble and vice versa. Everyone who is either brave or not wise is either not funny or wise and vice versa. If someone is not calm or not generous then mary is funny and vice versa. If someone is wise then alice is either generous or not old and vice versa. If paul is not wise then someone is not creative and vice versa. Everyone who is both not curious and not generous is both not kind and happy and vice versa. If mary is generous then susan is not old or not kind and vice versa. Everyone who is both old and not wise is both not humble and not rich. Everyone who is both happy and not curious is not happy or calm and vice versa. Everyone who is not happy is patient and vice versa. Everyone who is strong is either not brave or not curious. If someone is either quiet or humble then lucy is happy and vice versa. If lucy is both not generous and not old then someone is both not creative and old and vice versa. Everyone who is not wise or not happy is rich or humble. Alice is not kind. Someone is not humble or kind. Someone is curious. Mary is both not creative and not kind. Paul is not funny. Fred is both not wise and creative. Alice is not quiet or not patient. | Mary is not strong. | neutral | (![X]:((quiet(X)&patient(X))=>kind(X)))&
(![X]:(humble(X)=>(~old(X)<~>~kind(X))))&
((?[X]:((~curious(X)&strong(X))))<=>((tall(fred)|~humble(fred))))&
(![X]:((brave(X)<~>~wise(X))<=>(~funny(X)<~>wise(X))))&
((?[X]:((~calm(X)|~generous(X))))<=>(funny(mary)))&
((?[X]:(wise(X)))<=>((generous(alice)<~>~old(alice))))&
((~wise(paul))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)&~generous(X))<=>(~kind(X)&happy(X))))&
((generous(mary))<=>((~old(susan)|~kind(susan))))&
(![X]:((old(X)&~wise(X))=>(~humble(X)&~rich(X))))&
(![X]:((happy(X)&~curious(X))<=>(~happy(X)|calm(X))))&
(![X]:(~happy(X)<=>patient(X)))&
(![X]:(strong(X)=>(~brave(X)<~>~curious(X))))&
((?[X]:((quiet(X)<~>humble(X))))<=>(happy(lucy)))&
(((~generous(lucy)&~old(lucy)))<=>(?[X]:((~creative(X)&old(X)))))&
(![X]:((~wise(X)|~happy(X))=>(rich(X)|humble(X))))&
(~kind(alice))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:(curious(X)))&
((~creative(mary)&~kind(mary)))&
(~funny(paul))&
((~wise(fred)&creative(fred)))&
((~quiet(alice)|~patient(alice))) | ~strong(mary) | [] | null | 0 |
Everyone who is not old or humble is either not tall or not quiet.
If someone is brave or not calm then paul is humble.
Everyone who is either old or funny is not brave.
If someone is happy then someone is either not rich or not quiet.
Everyone who is humble or tall is either brave or not curious.
Everyone who is not creative is rich.
Everyone who is either not tall or not wise is both not curious and not rich and vice versa.
Everyone who is both not old and not rich is not humble or not wise.
If susan is both strong and quiet then someone is both not strong and not generous and vice versa.
If someone is not happy or curious then someone is either not patient or not curious.
If someone is quiet then someone is happy and vice versa.
If mary is kind then someone is not wise or not old.
If someone is strong or curious then someone is happy or not generous.
Everyone who is not generous is not tall.
If lucy is not tall then paul is both generous and patient and vice versa.
Everyone who is both not creative and wise is not happy or not rich and vice versa.
Fred is not calm.
Someone is happy.
Alice is both kind and tall.
Someone is not creative or not happy.
Someone is both not wise and happy.
Fred is either not patient or rich. | Lucy is rich. | entailment | (![X]:((~old(X)|humble(X))=>(~tall(X)<~>~quiet(X))))&
((?[X]:((brave(X)|~calm(X))))=>(humble(paul)))&
(![X]:((old(X)<~>funny(X))=>~brave(X)))&
((?[X]:(happy(X)))=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(![X]:((humble(X)|tall(X))=>(brave(X)<~>~curious(X))))&
(![X]:(~creative(X)=>rich(X)))&
(![X]:((~tall(X)<~>~wise(X))<=>(~curious(X)&~rich(X))))&
(![X]:((~old(X)&~rich(X))=>(~humble(X)|~wise(X))))&
(((strong(susan)&quiet(susan)))<=>(?[X]:((~strong(X)&~generous(X)))))&
((?[X]:((~happy(X)|curious(X))))=>(?[X]:((~patient(X)<~>~curious(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:(happy(X))))&
((kind(mary))=>(?[X]:((~wise(X)|~old(X)))))&
((?[X]:((strong(X)|curious(X))))=>(?[X]:((happy(X)|~generous(X)))))&
(![X]:(~generous(X)=>~tall(X)))&
((~tall(lucy))<=>((generous(paul)&patient(paul))))&
(![X]:((~creative(X)&wise(X))<=>(~happy(X)|~rich(X))))&
(~calm(fred))&
(?[X]:(happy(X)))&
((kind(alice)&tall(alice)))&
(?[X]:((~creative(X)|~happy(X))))&
(?[X]:((~wise(X)&happy(X))))&
((~patient(fred)<~>rich(fred))) | rich(lucy) | [
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7600435490025086273593029
% SZS output start Proof for 7600435490025086273593029
6. ! [X0] : (~creative(X0) => rich(X0)) [input p5]
16. ! [X0] : ((wise(X0) & ~creative(X0)) <=> (~rich(X0) | ~happy(X0))) [input p15]
23. ~rich(lucy) [input hypothesis]
33. ! [X0] : (rich(X0) | creative(X0)) [ennf transformation 6]
70. ! [X0] : (((wise(X0) & ~creative(X0)) | (rich(X0) & happy(X0))) & ((~rich(X0) | ~happy(X0)) | (~wise(X0) | creative(X0)))) [nnf transformation 16]
71. ! [X0] : (((wise(X0) & ~creative(X0)) | (rich(X0) & happy(X0))) & (~rich(X0) | ~happy(X0) | ~wise(X0) | creative(X0))) [flattening 70]
93. rich(X0) | creative(X0) [cnf transformation 33]
120. ~creative(X0) | rich(X0) [cnf transformation 71]
132. ~rich(lucy) [cnf transformation 23]
253. rich(X0) [subsumption resolution 120,93]
257. $false [subsumption resolution 132,253]
% SZS output end Proof for 7600435490025086273593029
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or strong is both wise and rich and vice versa.
If alice is not creative then someone is generous and vice versa.
Everyone who is both curious and not strong is not wise.
If someone is either not patient or old then someone is not rich and vice versa.
Everyone who is either not brave or kind is either patient or generous and vice versa.
If someone is either brave or not brave then fred is either not patient or rich and vice versa.
If susan is either not brave or not wise then john is both not humble and humble.
Everyone who is both old and calm is either not rich or strong.
If someone is not tall or not creative then someone is both not patient and not old and vice versa.
If john is both strong and patient then someone is not calm or not wise.
Everyone who is both quiet and curious is not creative and vice versa.
If lucy is either not old or not generous then mary is both wise and calm and vice versa.
If fred is brave then someone is either tall or quiet and vice versa.
If someone is not calm then susan is both not brave and not patient and vice versa.
Everyone who is either humble or not happy is rich or not funny.
Everyone who is not tall or not quiet is not old or generous.
John is not funny.
John is not old.
Someone is patient.
Someone is either not strong or not wise. | Mary is old. | neutral | (![X]:((~strong(X)|strong(X))<=>(wise(X)&rich(X))))&
((~creative(alice))<=>(?[X]:(generous(X))))&
(![X]:((curious(X)&~strong(X))=>~wise(X)))&
((?[X]:((~patient(X)<~>old(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(patient(X)<~>generous(X))))&
((?[X]:((brave(X)<~>~brave(X))))<=>((~patient(fred)<~>rich(fred))))&
(((~brave(susan)<~>~wise(susan)))=>((~humble(john)&humble(john))))&
(![X]:((old(X)&calm(X))=>(~rich(X)<~>strong(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(((strong(john)&patient(john)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((quiet(X)&curious(X))<=>~creative(X)))&
(((~old(lucy)<~>~generous(lucy)))<=>((wise(mary)&calm(mary))))&
((brave(fred))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))<=>((~brave(susan)&~patient(susan))))&
(![X]:((humble(X)<~>~happy(X))=>(rich(X)|~funny(X))))&
(![X]:((~tall(X)|~quiet(X))=>(~old(X)|generous(X))))&
(~funny(john))&
(~old(john))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)<~>~wise(X)))) | old(mary) | [] | null | 0 |
Everyone who is wise or not tall is not kind or not happy and vice versa. Everyone who is either not patient or not kind is brave. If someone is either strong or not quiet then alice is both not strong and not wise and vice versa. Everyone who is brave or strong is humble or curious and vice versa. If fred is either not creative or not humble then paul is either not happy or old and vice versa. If susan is either not wise or not tall then someone is happy. Everyone who is not funny or not humble is either humble or brave. If someone is either not strong or strong then lucy is both rich and generous. Everyone who is either not patient or not quiet is not quiet or not tall and vice versa. Everyone who is either strong or not patient is either kind or not old and vice versa. If alice is either not humble or happy then someone is either not happy or brave. Everyone who is both curious and not strong is not kind or generous and vice versa. If someone is either not tall or curious then someone is either not tall or humble and vice versa. Everyone who is both old and humble is tall. Everyone who is not rich or not calm is either not wise or not creative. Everyone who is both not old and tall is tall or not calm and vice versa. Someone is either not humble or not rich. Susan is calm or not quiet. Susan is either patient or old. Susan is either not wise or not quiet. Lucy is either not quiet or not generous. Someone is both not rich and not strong. Mary is funny or not funny. | Alice is patient. | neutral | (![X]:((wise(X)|~tall(X))<=>(~kind(X)|~happy(X))))&
(![X]:((~patient(X)<~>~kind(X))=>brave(X)))&
((?[X]:((strong(X)<~>~quiet(X))))<=>((~strong(alice)&~wise(alice))))&
(![X]:((brave(X)|strong(X))<=>(humble(X)|curious(X))))&
(((~creative(fred)<~>~humble(fred)))<=>((~happy(paul)<~>old(paul))))&
(((~wise(susan)<~>~tall(susan)))=>(?[X]:(happy(X))))&
(![X]:((~funny(X)|~humble(X))=>(humble(X)<~>brave(X))))&
((?[X]:((~strong(X)<~>strong(X))))=>((rich(lucy)&generous(lucy))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~quiet(X)|~tall(X))))&
(![X]:((strong(X)<~>~patient(X))<=>(kind(X)<~>~old(X))))&
(((~humble(alice)<~>happy(alice)))=>(?[X]:((~happy(X)<~>brave(X)))))&
(![X]:((curious(X)&~strong(X))<=>(~kind(X)|generous(X))))&
((?[X]:((~tall(X)<~>curious(X))))<=>(?[X]:((~tall(X)<~>humble(X)))))&
(![X]:((old(X)&humble(X))=>tall(X)))&
(![X]:((~rich(X)|~calm(X))=>(~wise(X)<~>~creative(X))))&
(![X]:((~old(X)&tall(X))<=>(tall(X)|~calm(X))))&
(?[X]:((~humble(X)<~>~rich(X))))&
((calm(susan)|~quiet(susan)))&
((patient(susan)<~>old(susan)))&
((~wise(susan)<~>~quiet(susan)))&
((~quiet(lucy)<~>~generous(lucy)))&
(?[X]:((~rich(X)&~strong(X))))&
((funny(mary)|~funny(mary))) | patient(alice) | [] | null | 0 |
If fred is either not strong or calm then someone is brave.
If mary is either not wise or not humble then someone is either not rich or not strong and vice versa.
Everyone who is old or not rich is curious.
If mary is both kind and not humble then someone is wise.
Everyone who is happy is either not generous or not curious and vice versa.
If paul is not rich then someone is both not strong and wise.
Everyone who is both not patient and happy is strong or not tall and vice versa.
Everyone who is generous or creative is not creative or old and vice versa.
If paul is either not curious or calm then mary is both tall and not curious.
Everyone who is either creative or curious is both not strong and happy and vice versa.
Everyone who is either happy or not brave is either tall or curious and vice versa.
If paul is both not wise and old then someone is old or patient and vice versa.
Everyone who is humble is either strong or not humble and vice versa.
Everyone who is old is either not calm or not generous.
If someone is either old or not brave then someone is both not funny and funny and vice versa.
If mary is either not kind or curious then someone is tall or not happy and vice versa.
Someone is both creative and tall.
John is not quiet.
Alice is either not generous or not calm.
Someone is either brave or old.
Someone is either funny or quiet.
Fred is both curious and funny.
Someone is either not happy or not generous. | Alice is old. | neutral | (((~strong(fred)<~>calm(fred)))=>(?[X]:(brave(X))))&
(((~wise(mary)<~>~humble(mary)))<=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((old(X)|~rich(X))=>curious(X)))&
(((kind(mary)&~humble(mary)))=>(?[X]:(wise(X))))&
(![X]:(happy(X)<=>(~generous(X)<~>~curious(X))))&
((~rich(paul))=>(?[X]:((~strong(X)&wise(X)))))&
(![X]:((~patient(X)&happy(X))<=>(strong(X)|~tall(X))))&
(![X]:((generous(X)|creative(X))<=>(~creative(X)|old(X))))&
(((~curious(paul)<~>calm(paul)))=>((tall(mary)&~curious(mary))))&
(![X]:((creative(X)<~>curious(X))<=>(~strong(X)&happy(X))))&
(![X]:((happy(X)<~>~brave(X))<=>(tall(X)<~>curious(X))))&
(((~wise(paul)&old(paul)))<=>(?[X]:((old(X)|patient(X)))))&
(![X]:(humble(X)<=>(strong(X)<~>~humble(X))))&
(![X]:(old(X)=>(~calm(X)<~>~generous(X))))&
((?[X]:((old(X)<~>~brave(X))))<=>(?[X]:((~funny(X)&funny(X)))))&
(((~kind(mary)<~>curious(mary)))<=>(?[X]:((tall(X)|~happy(X)))))&
(?[X]:((creative(X)&tall(X))))&
(~quiet(john))&
((~generous(alice)<~>~calm(alice)))&
(?[X]:((brave(X)<~>old(X))))&
(?[X]:((funny(X)<~>quiet(X))))&
((curious(fred)&funny(fred)))&
(?[X]:((~happy(X)<~>~generous(X)))) | old(alice) | [] | null | 0 |
If someone is rich or not rich then someone is either not old or strong and vice versa.
Everyone who is tall is patient and vice versa.
If someone is either funny or humble then susan is not happy or not calm.
Everyone who is not quiet or calm is either not humble or calm and vice versa.
If john is both strong and quiet then mary is both not generous and not kind and vice versa.
Everyone who is happy is rich or not funny and vice versa.
If someone is either not patient or not kind then someone is kind or not brave and vice versa.
Everyone who is not happy is both not creative and not funny and vice versa.
Everyone who is either generous or rich is rich or not generous and vice versa.
Everyone who is either generous or happy is both rich and funny.
If fred is either not humble or not patient then susan is not curious or creative and vice versa.
If fred is either creative or calm then someone is not brave.
If john is either not humble or not happy then someone is both not happy and old and vice versa.
Everyone who is both not strong and not old is not tall.
If someone is both not patient and tall then susan is both happy and not brave and vice versa.
If lucy is both not creative and not humble then lucy is either not funny or not wise.
Someone is not generous or not creative.
Alice is calm.
Paul is both calm and not tall.
John is tall.
Mary is both not quiet and patient.
Someone is both not creative and not old. | John is not happy. | contradiction | ((?[X]:((rich(X)|~rich(X))))<=>(?[X]:((~old(X)<~>strong(X)))))&
(![X]:(tall(X)<=>patient(X)))&
((?[X]:((funny(X)<~>humble(X))))=>((~happy(susan)|~calm(susan))))&
(![X]:((~quiet(X)|calm(X))<=>(~humble(X)<~>calm(X))))&
(((strong(john)&quiet(john)))<=>((~generous(mary)&~kind(mary))))&
(![X]:(happy(X)<=>(rich(X)|~funny(X))))&
((?[X]:((~patient(X)<~>~kind(X))))<=>(?[X]:((kind(X)|~brave(X)))))&
(![X]:(~happy(X)<=>(~creative(X)&~funny(X))))&
(![X]:((generous(X)<~>rich(X))<=>(rich(X)|~generous(X))))&
(![X]:((generous(X)<~>happy(X))=>(rich(X)&funny(X))))&
(((~humble(fred)<~>~patient(fred)))<=>((~curious(susan)|creative(susan))))&
(((creative(fred)<~>calm(fred)))=>(?[X]:(~brave(X))))&
(((~humble(john)<~>~happy(john)))<=>(?[X]:((~happy(X)&old(X)))))&
(![X]:((~strong(X)&~old(X))=>~tall(X)))&
((?[X]:((~patient(X)&tall(X))))<=>((happy(susan)&~brave(susan))))&
(((~creative(lucy)&~humble(lucy)))=>((~funny(lucy)<~>~wise(lucy))))&
(?[X]:((~generous(X)|~creative(X))))&
(calm(alice))&
((calm(paul)&~tall(paul)))&
(tall(john))&
((~quiet(mary)&patient(mary)))&
(?[X]:((~creative(X)&~old(X)))) | ~happy(john) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3899293173191194178388379
% SZS output start Proof for 3899293173191194178388379
6. ! [X0] : (happy(X0) <=> (~funny(X0) | rich(X0))) [input p5]
8. ! [X0] : (~happy(X0) <=> (~funny(X0) & ~creative(X0))) [input p7]
23. ~happy(john) [input hypothesis]
45. ! [X0] : ((happy(X0) | (funny(X0) & ~rich(X0))) & ((~funny(X0) | rich(X0)) | ~happy(X0))) [nnf transformation 6]
46. ! [X0] : ((happy(X0) | (funny(X0) & ~rich(X0))) & (~funny(X0) | rich(X0) | ~happy(X0))) [flattening 45]
52. ! [X0] : ((~happy(X0) | (funny(X0) | creative(X0))) & ((~funny(X0) & ~creative(X0)) | happy(X0))) [nnf transformation 8]
53. ! [X0] : ((~happy(X0) | funny(X0) | creative(X0)) & ((~funny(X0) & ~creative(X0)) | happy(X0))) [flattening 52]
98. happy(X0) | funny(X0) [cnf transformation 46]
106. ~funny(X0) | happy(X0) [cnf transformation 53]
148. ~happy(john) [cnf transformation 23]
243. happy(X0) [subsumption resolution 106,98]
326. $false [subsumption resolution 148,243]
% SZS output end Proof for 3899293173191194178388379
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and patient then someone is either rich or calm and vice versa. Everyone who is both not old and funny is both old and not kind. If someone is not tall then john is either generous or wise and vice versa. Everyone who is both not brave and funny is not patient or funny and vice versa. Everyone who is either kind or not creative is not kind or not wise and vice versa. Everyone who is either not rich or wise is both quiet and strong and vice versa. Everyone who is both wise and patient is either rich or not tall and vice versa. If someone is either happy or not old then someone is not strong. Everyone who is not strong is not tall or rich. Everyone who is either generous or funny is either not creative or not patient. Everyone who is happy is funny and vice versa. If paul is not patient then mary is not creative or not brave and vice versa. Everyone who is calm is both brave and humble and vice versa. If paul is not calm then fred is both generous and creative and vice versa. If mary is either generous or not calm then someone is not curious or brave. If alice is both not tall and wise then john is both not calm and not brave. Someone is funny or wise. Someone is generous. John is not brave. Someone is not kind. Fred is either not generous or not old. Someone is humble or not curious. Someone is both curious and not calm. | Mary is happy. | contradiction | ((?[X]:((curious(X)&patient(X))))<=>(?[X]:((rich(X)<~>calm(X)))))&
(![X]:((~old(X)&funny(X))=>(old(X)&~kind(X))))&
((?[X]:(~tall(X)))<=>((generous(john)<~>wise(john))))&
(![X]:((~brave(X)&funny(X))<=>(~patient(X)|funny(X))))&
(![X]:((kind(X)<~>~creative(X))<=>(~kind(X)|~wise(X))))&
(![X]:((~rich(X)<~>wise(X))<=>(quiet(X)&strong(X))))&
(![X]:((wise(X)&patient(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((happy(X)<~>~old(X))))=>(?[X]:(~strong(X))))&
(![X]:(~strong(X)=>(~tall(X)|rich(X))))&
(![X]:((generous(X)<~>funny(X))=>(~creative(X)<~>~patient(X))))&
(![X]:(happy(X)<=>funny(X)))&
((~patient(paul))<=>((~creative(mary)|~brave(mary))))&
(![X]:(calm(X)<=>(brave(X)&humble(X))))&
((~calm(paul))<=>((generous(fred)&creative(fred))))&
(((generous(mary)<~>~calm(mary)))=>(?[X]:((~curious(X)|brave(X)))))&
(((~tall(alice)&wise(alice)))=>((~calm(john)&~brave(john))))&
(?[X]:((funny(X)|wise(X))))&
(?[X]:(generous(X)))&
(~brave(john))&
(?[X]:(~kind(X)))&
((~generous(fred)<~>~old(fred)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:((curious(X)&~calm(X)))) | happy(mary) | [
"p1",
"p3",
"p9",
"p10",
"p11",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3367705682526902206545296
% SZS output start Proof for 3367705682526902206545296
2. ! [X0] : ((funny(X0) & ~old(X0)) => (~kind(X0) & old(X0))) [input p1]
4. ! [X0] : ((funny(X0) & ~brave(X0)) <=> (funny(X0) | ~patient(X0))) [input p3]
10. ! [X0] : ((generous(X0) <~> funny(X0)) => (~creative(X0) <~> ~patient(X0))) [input p9]
11. ! [X0] : (happy(X0) <=> funny(X0)) [input p10]
12. ~patient(paul) <=> (~brave(mary) | ~creative(mary)) [input p11]
13. ! [X0] : (calm(X0) <=> (humble(X0) & brave(X0))) [input p12]
14. ~calm(paul) <=> (creative(fred) & generous(fred)) [input p13]
21. ~generous(fred) <~> ~old(fred) [input p20]
24. happy(mary) [input hypothesis]
27. ! [X0] : ((~kind(X0) & old(X0)) | (~funny(X0) | old(X0))) [ennf transformation 2]
28. ! [X0] : ((~kind(X0) & old(X0)) | ~funny(X0) | old(X0)) [flattening 27]
32. ! [X0] : ((~creative(X0) <~> ~patient(X0)) | (generous(X0) <=> funny(X0))) [ennf transformation 10]
45. ! [X0] : (((funny(X0) & ~brave(X0)) | (~funny(X0) & patient(X0))) & ((funny(X0) | ~patient(X0)) | (~funny(X0) | brave(X0)))) [nnf transformation 4]
46. ! [X0] : (((funny(X0) & ~brave(X0)) | (~funny(X0) & patient(X0))) & (funny(X0) | ~patient(X0) | ~funny(X0) | brave(X0))) [flattening 45]
57. ! [X0] : (((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0)))) [nnf transformation 32]
58. ! [X0] : ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0))) [nnf transformation 11]
59. (~patient(paul) | (brave(mary) & creative(mary))) & ((~brave(mary) | ~creative(mary)) | patient(paul)) [nnf transformation 12]
60. (~patient(paul) | (brave(mary) & creative(mary))) & (~brave(mary) | ~creative(mary) | patient(paul)) [flattening 59]
61. ! [X0] : ((calm(X0) | (~humble(X0) | ~brave(X0))) & ((humble(X0) & brave(X0)) | ~calm(X0))) [nnf transformation 13]
62. ! [X0] : ((calm(X0) | ~humble(X0) | ~brave(X0)) & ((humble(X0) & brave(X0)) | ~calm(X0))) [flattening 61]
63. (~calm(paul) | (~creative(fred) | ~generous(fred))) & ((creative(fred) & generous(fred)) | calm(paul)) [nnf transformation 14]
64. (~calm(paul) | ~creative(fred) | ~generous(fred)) & ((creative(fred) & generous(fred)) | calm(paul)) [flattening 63]
74. (old(fred) | generous(fred)) & (~old(fred) | ~generous(fred)) [nnf transformation 21]
85. old(X0) | ~funny(X0) | old(X0) [cnf transformation 28]
92. ~brave(X0) | patient(X0) [cnf transformation 46]
93. ~brave(X0) | ~funny(X0) [cnf transformation 46]
94. funny(X0) | patient(X0) [cnf transformation 46]
117. ~patient(X0) | ~creative(X0) | funny(X0) | ~generous(X0) [cnf transformation 57]
121. ~happy(X0) | funny(X0) [cnf transformation 58]
125. ~patient(paul) | brave(mary) [cnf transformation 60]
126. ~calm(X0) | brave(X0) [cnf transformation 62]
129. generous(fred) | calm(paul) [cnf transformation 64]
130. creative(fred) | calm(paul) [cnf transformation 64]
140. ~old(fred) | ~generous(fred) [cnf transformation 74]
145. happy(mary) [cnf transformation 24]
148. ~funny(X0) | old(X0) [duplicate literal removal 85]
213. ~creative(X0) | funny(X0) | ~generous(X0) [subsumption resolution 117,94]
215. 15 <=> brave(mary) [avatar definition]
217. brave(mary) <- (15) [avatar component clause 215]
219. 16 <=> patient(paul) [avatar definition]
222. 15 | ~16 [avatar split clause 125,219,215]
230. 18 <=> generous(fred) [avatar definition]
231. generous(fred) <- (18) [avatar component clause 230]
234. 19 <=> creative(fred) [avatar definition]
235. creative(fred) <- (19) [avatar component clause 234]
238. 20 <=> calm(paul) [avatar definition]
239. calm(paul) <- (20) [avatar component clause 238]
242. 20 | 19 [avatar split clause 130,234,238]
243. 20 | 18 [avatar split clause 129,230,238]
291. 31 <=> old(fred) [avatar definition]
292. ~old(fred) <- (~31) [avatar component clause 291]
295. ~18 | ~31 [avatar split clause 140,291,230]
305. funny(mary) [resolution 121,145]
377. brave(paul) <- (20) [resolution 239,126]
400. patient(paul) <- (20) [resolution 377,92]
403. 16 | ~20 [avatar split clause 400,238,219]
404. ~funny(mary) <- (15) [resolution 217,93]
406. $false <- (15) [subsumption resolution 404,305]
407. ~15 [avatar contradiction clause 406]
445. funny(fred) | ~generous(fred) <- (19) [resolution 213,235]
447. funny(fred) <- (18, 19) [subsumption resolution 445,231]
457. old(fred) <- (18, 19) [resolution 447,148]
459. $false <- (18, 19, ~31) [subsumption resolution 457,292]
460. ~18 | ~19 | 31 [avatar contradiction clause 459]
461. $false [avatar sat refutation 222,242,243,295,403,407,460]
% SZS output end Proof for 3367705682526902206545296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and strong is not rich or not quiet and vice versa.
If fred is both wise and funny then john is either brave or not wise and vice versa.
If lucy is not happy or patient then fred is humble and vice versa.
Everyone who is both tall and old is both generous and not funny.
If john is either strong or not generous then alice is either not curious or calm and vice versa.
Everyone who is wise is not humble and vice versa.
If lucy is either rich or not curious then someone is brave or not quiet and vice versa.
Everyone who is strong is both not curious and brave.
If paul is both quiet and not wise then someone is both not patient and brave and vice versa.
If paul is both wise and not old then someone is creative or curious and vice versa.
If someone is not funny then mary is either funny or wise and vice versa.
If lucy is both humble and not curious then someone is curious or not humble and vice versa.
Everyone who is not humble or not brave is either quiet or not rich.
Everyone who is wise or kind is both not patient and not brave.
If someone is either not old or calm then someone is quiet or not brave.
If susan is either not brave or not tall then someone is either funny or rich and vice versa.
Lucy is creative.
Paul is not generous or not funny.
Someone is rich or not generous.
Someone is wise.
Someone is brave or wise.
Someone is calm.
Someone is generous or calm. | Alice is not strong. | entailment | (![X]:((~creative(X)&strong(X))<=>(~rich(X)|~quiet(X))))&
(((wise(fred)&funny(fred)))<=>((brave(john)<~>~wise(john))))&
(((~happy(lucy)|patient(lucy)))<=>(humble(fred)))&
(![X]:((tall(X)&old(X))=>(generous(X)&~funny(X))))&
(((strong(john)<~>~generous(john)))<=>((~curious(alice)<~>calm(alice))))&
(![X]:(wise(X)<=>~humble(X)))&
(((rich(lucy)<~>~curious(lucy)))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:(strong(X)=>(~curious(X)&brave(X))))&
(((quiet(paul)&~wise(paul)))<=>(?[X]:((~patient(X)&brave(X)))))&
(((wise(paul)&~old(paul)))<=>(?[X]:((creative(X)|curious(X)))))&
((?[X]:(~funny(X)))<=>((funny(mary)<~>wise(mary))))&
(((humble(lucy)&~curious(lucy)))<=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((~humble(X)|~brave(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((wise(X)|kind(X))=>(~patient(X)&~brave(X))))&
((?[X]:((~old(X)<~>calm(X))))=>(?[X]:((quiet(X)|~brave(X)))))&
(((~brave(susan)<~>~tall(susan)))<=>(?[X]:((funny(X)<~>rich(X)))))&
(creative(lucy))&
((~generous(paul)|~funny(paul)))&
(?[X]:((rich(X)|~generous(X))))&
(?[X]:(wise(X)))&
(?[X]:((brave(X)|wise(X))))&
(?[X]:(calm(X)))&
(?[X]:((generous(X)|calm(X)))) | ~strong(alice) | [
"p0",
"p6",
"p7",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 718626960760028590990934
% SZS output start Proof for 718626960760028590990934
1. ! [X0] : ((strong(X0) & ~creative(X0)) <=> (~quiet(X0) | ~rich(X0))) [input p0]
7. (rich(lucy) <~> ~curious(lucy)) <=> ? [X0] : (~quiet(X0) | brave(X0)) [input p6]
8. ! [X0] : (strong(X0) => (brave(X0) & ~curious(X0))) [input p7]
12. (~curious(lucy) & humble(lucy)) <=> ? [X0] : (~humble(X0) | curious(X0)) [input p11]
17. creative(lucy) [input p16]
24. strong(alice) [input hypothesis]
29. ! [X0] : ((brave(X0) & ~curious(X0)) | ~strong(X0)) [ennf transformation 8]
33. ! [X0] : (((strong(X0) & ~creative(X0)) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | (~strong(X0) | creative(X0)))) [nnf transformation 1]
34. ! [X0] : (((strong(X0) & ~creative(X0)) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | ~strong(X0) | creative(X0))) [flattening 33]
41. (((curious(lucy) | ~rich(lucy)) & (~curious(lucy) | rich(lucy))) | ! [X0] : (quiet(X0) & ~brave(X0))) & (? [X0] : (~quiet(X0) | brave(X0)) | ((rich(lucy) | curious(lucy)) & (~curious(lucy) | ~rich(lucy)))) [nnf transformation 7]
42. (((curious(lucy) | ~rich(lucy)) & (~curious(lucy) | rich(lucy))) | ! [X0] : (quiet(X0) & ~brave(X0))) & (? [X1] : (~quiet(X1) | brave(X1)) | ((rich(lucy) | curious(lucy)) & (~curious(lucy) | ~rich(lucy)))) [rectify 41]
43. ? [X1] : (~quiet(X1) | brave(X1)) => (~quiet(sK0) | brave(sK0)) [choice axiom]
44. (((curious(lucy) | ~rich(lucy)) & (~curious(lucy) | rich(lucy))) | ! [X0] : (quiet(X0) & ~brave(X0))) & ((~quiet(sK0) | brave(sK0)) | ((rich(lucy) | curious(lucy)) & (~curious(lucy) | ~rich(lucy)))) [skolemisation 42,43]
59. ((~curious(lucy) & humble(lucy)) | ! [X0] : (humble(X0) & ~curious(X0))) & (? [X0] : (~humble(X0) | curious(X0)) | (curious(lucy) | ~humble(lucy))) [nnf transformation 12]
60. ((~curious(lucy) & humble(lucy)) | ! [X0] : (humble(X0) & ~curious(X0))) & (? [X0] : (~humble(X0) | curious(X0)) | curious(lucy) | ~humble(lucy)) [flattening 59]
61. ((~curious(lucy) & humble(lucy)) | ! [X0] : (humble(X0) & ~curious(X0))) & (? [X1] : (~humble(X1) | curious(X1)) | curious(lucy) | ~humble(lucy)) [rectify 60]
62. ? [X1] : (~humble(X1) | curious(X1)) => (~humble(sK4) | curious(sK4)) [choice axiom]
63. ((~curious(lucy) & humble(lucy)) | ! [X0] : (humble(X0) & ~curious(X0))) & ((~humble(sK4) | curious(sK4)) | curious(lucy) | ~humble(lucy)) [skolemisation 61,62]
84. ~creative(X0) | rich(X0) [cnf transformation 34]
113. curious(lucy) | ~rich(lucy) | ~brave(X0) [cnf transformation 44]
116. ~strong(X0) | brave(X0) [cnf transformation 29]
133. ~curious(lucy) | ~curious(X0) [cnf transformation 63]
151. creative(lucy) [cnf transformation 17]
158. strong(alice) [cnf transformation 24]
224. 13 <=> rich(lucy) [avatar definition]
228. 14 <=> curious(lucy) [avatar definition]
230. curious(lucy) <- (14) [avatar component clause 228]
233. 15 <=> ! [X0] : ~brave(X0) [avatar definition]
234. ~brave(X0) <- (15) [avatar component clause 233]
235. 15 | ~13 | 14 [avatar split clause 113,228,224,233]
272. 23 <=> ! [X0] : ~curious(X0) [avatar definition]
273. ~curious(X0) <- (23) [avatar component clause 272]
317. 23 | ~14 [avatar split clause 133,228,272]
423. rich(lucy) [resolution 84,151]
426. 13 [avatar split clause 423,224]
440. brave(alice) [resolution 116,158]
441. $false <- (15) [subsumption resolution 440,234]
442. ~15 [avatar contradiction clause 441]
443. $false <- (14, 23) [subsumption resolution 230,273]
444. ~14 | ~23 [avatar contradiction clause 443]
445. $false [avatar sat refutation 235,317,426,442,444]
% SZS output end Proof for 718626960760028590990934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is not wise.
If someone is both not patient and strong then john is either not happy or not creative and vice versa.
Everyone who is not patient or not generous is creative.
If paul is either not happy or happy then someone is both not funny and not patient.
Everyone who is patient is both not kind and happy.
Everyone who is not funny or not old is curious or not old and vice versa.
Everyone who is either not old or generous is both rich and brave and vice versa.
If lucy is old then john is not quiet or quiet.
If lucy is not funny or funny then someone is both funny and happy and vice versa.
Everyone who is either not brave or tall is old or not brave.
Everyone who is both quiet and not generous is not brave or curious and vice versa.
If someone is either not funny or curious then john is either not patient or not quiet.
Everyone who is either not patient or wise is patient and vice versa.
If someone is either not rich or not patient then susan is both tall and not brave.
Everyone who is brave or not generous is not tall and vice versa.
Everyone who is funny or not brave is either brave or strong.
Fred is either quiet or not strong.
Mary is generous.
Susan is kind.
Fred is not calm.
Paul is not kind or not happy. | Fred is tall. | contradiction | (![X]:(quiet(X)=>~wise(X)))&
((?[X]:((~patient(X)&strong(X))))<=>((~happy(john)<~>~creative(john))))&
(![X]:((~patient(X)|~generous(X))=>creative(X)))&
(((~happy(paul)<~>happy(paul)))=>(?[X]:((~funny(X)&~patient(X)))))&
(![X]:(patient(X)=>(~kind(X)&happy(X))))&
(![X]:((~funny(X)|~old(X))<=>(curious(X)|~old(X))))&
(![X]:((~old(X)<~>generous(X))<=>(rich(X)&brave(X))))&
((old(lucy))=>((~quiet(john)|quiet(john))))&
(((~funny(lucy)|funny(lucy)))<=>(?[X]:((funny(X)&happy(X)))))&
(![X]:((~brave(X)<~>tall(X))=>(old(X)|~brave(X))))&
(![X]:((quiet(X)&~generous(X))<=>(~brave(X)|curious(X))))&
((?[X]:((~funny(X)<~>curious(X))))=>((~patient(john)<~>~quiet(john))))&
(![X]:((~patient(X)<~>wise(X))<=>patient(X)))&
((?[X]:((~rich(X)<~>~patient(X))))=>((tall(susan)&~brave(susan))))&
(![X]:((brave(X)|~generous(X))<=>~tall(X)))&
(![X]:((funny(X)|~brave(X))=>(brave(X)<~>strong(X))))&
((quiet(fred)<~>~strong(fred)))&
(generous(mary))&
(kind(susan))&
(~calm(fred))&
((~kind(paul)|~happy(paul))) | tall(fred) | [
"p0",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3707998072974502653785040
% SZS output start Proof for 3707998072974502653785040
1. ! [X0] : (quiet(X0) => ~wise(X0)) [input p0]
11. ! [X0] : ((~generous(X0) & quiet(X0)) <=> (curious(X0) | ~brave(X0))) [input p10]
13. ! [X0] : ((~patient(X0) <~> wise(X0)) <=> patient(X0)) [input p12]
15. ! [X0] : ((~generous(X0) | brave(X0)) <=> ~tall(X0)) [input p14]
22. tall(fred) [input hypothesis]
24. ! [X0] : (~wise(X0) | ~quiet(X0)) [ennf transformation 1]
52. ! [X0] : (((~generous(X0) & quiet(X0)) | (~curious(X0) & brave(X0))) & ((curious(X0) | ~brave(X0)) | (generous(X0) | ~quiet(X0)))) [nnf transformation 11]
53. ! [X0] : (((~generous(X0) & quiet(X0)) | (~curious(X0) & brave(X0))) & (curious(X0) | ~brave(X0) | generous(X0) | ~quiet(X0))) [flattening 52]
55. ! [X0] : ((((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0))))) [nnf transformation 13]
57. ! [X0] : (((~generous(X0) | brave(X0)) | tall(X0)) & (~tall(X0) | (generous(X0) & ~brave(X0)))) [nnf transformation 15]
58. ! [X0] : ((~generous(X0) | brave(X0) | tall(X0)) & (~tall(X0) | (generous(X0) & ~brave(X0)))) [flattening 57]
61. ~wise(X0) | ~quiet(X0) [cnf transformation 24]
95. brave(X0) | quiet(X0) [cnf transformation 53]
103. patient(X0) | wise(X0) | patient(X0) [cnf transformation 55]
105. wise(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 55]
111. ~tall(X0) | ~brave(X0) [cnf transformation 58]
123. tall(fred) [cnf transformation 22]
125. patient(X0) | wise(X0) [duplicate literal removal 103]
126. wise(X0) | ~patient(X0) [duplicate literal removal 105]
207. wise(X0) [subsumption resolution 125,126]
241. ~quiet(X0) [resolution 61,207]
250. ~brave(fred) [resolution 111,123]
251. quiet(fred) [resolution 250,95]
254. $false [subsumption resolution 251,241]
% SZS output end Proof for 3707998072974502653785040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is humble or not strong and vice versa.
If someone is not wise then paul is not rich or not humble and vice versa.
Everyone who is either not curious or generous is both not brave and kind.
If paul is funny then paul is not tall or happy and vice versa.
Everyone who is not old or not happy is both calm and not old and vice versa.
Everyone who is wise or brave is not strong or happy and vice versa.
If someone is either not creative or not strong then fred is not calm.
If susan is not quiet or funny then susan is both wise and not tall.
If someone is either not humble or not tall then mary is rich and vice versa.
Everyone who is both strong and not generous is wise and vice versa.
If someone is funny then mary is happy or not rich and vice versa.
If mary is both strong and not kind then someone is wise.
If someone is either creative or humble then fred is not rich.
If alice is both not happy and kind then alice is either brave or not tall and vice versa.
Everyone who is patient is wise or not rich.
Everyone who is both not kind and not old is not kind or not happy.
Someone is quiet.
Mary is strong.
Paul is either curious or tall.
Lucy is not rich.
Fred is either rich or not tall.
Fred is not creative.
Fred is not patient. | Fred is calm. | contradiction | (![X]:(strong(X)<=>(humble(X)|~strong(X))))&
((?[X]:(~wise(X)))<=>((~rich(paul)|~humble(paul))))&
(![X]:((~curious(X)<~>generous(X))=>(~brave(X)&kind(X))))&
((funny(paul))<=>((~tall(paul)|happy(paul))))&
(![X]:((~old(X)|~happy(X))<=>(calm(X)&~old(X))))&
(![X]:((wise(X)|brave(X))<=>(~strong(X)|happy(X))))&
((?[X]:((~creative(X)<~>~strong(X))))=>(~calm(fred)))&
(((~quiet(susan)|funny(susan)))=>((wise(susan)&~tall(susan))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(rich(mary)))&
(![X]:((strong(X)&~generous(X))<=>wise(X)))&
((?[X]:(funny(X)))<=>((happy(mary)|~rich(mary))))&
(((strong(mary)&~kind(mary)))=>(?[X]:(wise(X))))&
((?[X]:((creative(X)<~>humble(X))))=>(~rich(fred)))&
(((~happy(alice)&kind(alice)))<=>((brave(alice)<~>~tall(alice))))&
(![X]:(patient(X)=>(wise(X)|~rich(X))))&
(![X]:((~kind(X)&~old(X))=>(~kind(X)|~happy(X))))&
(?[X]:(quiet(X)))&
(strong(mary))&
((curious(paul)<~>tall(paul)))&
(~rich(lucy))&
((rich(fred)<~>~tall(fred)))&
(~creative(fred))&
(~patient(fred)) | calm(fred) | [
"p0",
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3563778789870022702967969
% SZS output start Proof for 3563778789870022702967969
1. ! [X0] : (strong(X0) <=> (~strong(X0) | humble(X0))) [input p0]
7. ? [X0] : (~creative(X0) <~> ~strong(X0)) => ~calm(fred) [input p6]
22. ~creative(fred) [input p21]
24. calm(fred) [input hypothesis]
30. ~calm(fred) | ! [X0] : (~creative(X0) <=> ~strong(X0)) [ennf transformation 7]
37. ! [X0] : ((strong(X0) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | ~strong(X0))) [nnf transformation 1]
38. ! [X0] : ((strong(X0) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | ~strong(X0))) [flattening 37]
51. ~calm(fred) | ! [X0] : ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0))) [nnf transformation 30]
72. strong(X0) | strong(X0) [cnf transformation 38]
92. ~calm(fred) | ~strong(X0) | creative(X0) [cnf transformation 51]
122. ~creative(fred) [cnf transformation 22]
123. calm(fred) [cnf transformation 24]
125. strong(X0) [duplicate literal removal 72]
158. ~calm(fred) | creative(X0) [subsumption resolution 92,125]
160. 7 <=> ! [X0] : creative(X0) [avatar definition]
161. creative(X0) <- (7) [avatar component clause 160]
163. 8 <=> calm(fred) [avatar definition]
166. 7 | ~8 [avatar split clause 158,163,160]
262. 8 [avatar split clause 123,163]
263. $false <- (7) [resolution 161,122]
264. ~7 [avatar contradiction clause 263]
265. $false [avatar sat refutation 166,262,264]
% SZS output end Proof for 3563778789870022702967969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or generous is calm or generous and vice versa.
If someone is not patient or patient then paul is brave or old.
Everyone who is either not strong or not old is not calm and vice versa.
Everyone who is both not calm and not patient is patient.
If someone is both generous and not funny then someone is generous and vice versa.
If mary is either strong or not creative then someone is either not calm or generous.
If alice is not generous or not tall then someone is both not curious and calm and vice versa.
If someone is either patient or not strong then someone is either strong or not creative.
Everyone who is old or not quiet is not old and vice versa.
Everyone who is both not strong and calm is humble or old.
Everyone who is curious or generous is tall or not old and vice versa.
Everyone who is both quiet and not rich is both rich and patient and vice versa.
Everyone who is creative is wise and vice versa.
Everyone who is either not wise or not creative is not calm and vice versa.
If someone is either not generous or calm then susan is both not funny and not old.
If mary is calm then mary is humble and vice versa.
Someone is both not curious and not strong.
Someone is either humble or not rich.
Someone is either not old or curious.
Lucy is strong or not tall.
Susan is either quiet or calm.
Someone is not patient or not brave.
Alice is either not humble or not rich. | Alice is tall. | contradiction | (![X]:((~calm(X)|generous(X))<=>(calm(X)|generous(X))))&
((?[X]:((~patient(X)|patient(X))))=>((brave(paul)|old(paul))))&
(![X]:((~strong(X)<~>~old(X))<=>~calm(X)))&
(![X]:((~calm(X)&~patient(X))=>patient(X)))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(generous(X))))&
(((strong(mary)<~>~creative(mary)))=>(?[X]:((~calm(X)<~>generous(X)))))&
(((~generous(alice)|~tall(alice)))<=>(?[X]:((~curious(X)&calm(X)))))&
((?[X]:((patient(X)<~>~strong(X))))=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((old(X)|~quiet(X))<=>~old(X)))&
(![X]:((~strong(X)&calm(X))=>(humble(X)|old(X))))&
(![X]:((curious(X)|generous(X))<=>(tall(X)|~old(X))))&
(![X]:((quiet(X)&~rich(X))<=>(rich(X)&patient(X))))&
(![X]:(creative(X)<=>wise(X)))&
(![X]:((~wise(X)<~>~creative(X))<=>~calm(X)))&
((?[X]:((~generous(X)<~>calm(X))))=>((~funny(susan)&~old(susan))))&
((calm(mary))<=>(humble(mary)))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:((~old(X)<~>curious(X))))&
((strong(lucy)|~tall(lucy)))&
((quiet(susan)<~>calm(susan)))&
(?[X]:((~patient(X)|~brave(X))))&
((~humble(alice)<~>~rich(alice))) | tall(alice) | [
"p0",
"p6",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 873000780738231193569388
% SZS output start Proof for 873000780738231193569388
1. ! [X0] : ((generous(X0) | ~calm(X0)) <=> (generous(X0) | calm(X0))) [input p0]
7. (~tall(alice) | ~generous(alice)) <=> ? [X0] : (calm(X0) & ~curious(X0)) [input p6]
13. ! [X0] : (creative(X0) <=> wise(X0)) [input p12]
14. ! [X0] : ((~wise(X0) <~> ~creative(X0)) <=> ~calm(X0)) [input p13]
17. ? [X0] : (~strong(X0) & ~curious(X0)) [input p16]
24. tall(alice) [input hypothesis]
36. ! [X0] : (((generous(X0) | ~calm(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (~generous(X0) & calm(X0)))) [nnf transformation 1]
37. ! [X0] : ((generous(X0) | ~calm(X0) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | (~generous(X0) & calm(X0)))) [flattening 36]
47. ((~tall(alice) | ~generous(alice)) | ! [X0] : (~calm(X0) | curious(X0))) & (? [X0] : (calm(X0) & ~curious(X0)) | (tall(alice) & generous(alice))) [nnf transformation 7]
48. (~tall(alice) | ~generous(alice) | ! [X0] : (~calm(X0) | curious(X0))) & (? [X0] : (calm(X0) & ~curious(X0)) | (tall(alice) & generous(alice))) [flattening 47]
49. (~tall(alice) | ~generous(alice) | ! [X0] : (~calm(X0) | curious(X0))) & (? [X1] : (calm(X1) & ~curious(X1)) | (tall(alice) & generous(alice))) [rectify 48]
50. ? [X1] : (calm(X1) & ~curious(X1)) => (calm(sK3) & ~curious(sK3)) [choice axiom]
51. (~tall(alice) | ~generous(alice) | ! [X0] : (~calm(X0) | curious(X0))) & ((calm(sK3) & ~curious(sK3)) | (tall(alice) & generous(alice))) [skolemisation 49,50]
62. ! [X0] : ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))) [nnf transformation 13]
63. ! [X0] : ((((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | calm(X0)) & (~calm(X0) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0))))) [nnf transformation 14]
66. ? [X0] : (~strong(X0) & ~curious(X0)) => (~strong(sK5) & ~curious(sK5)) [choice axiom]
67. ~strong(sK5) & ~curious(sK5) [skolemisation 17,66]
78. generous(X0) | calm(X0) | calm(X0) [cnf transformation 37]
80. generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 37]
100. ~tall(alice) | ~generous(alice) | ~calm(X0) | curious(X0) [cnf transformation 51]
117. wise(X0) | ~creative(X0) [cnf transformation 62]
118. creative(X0) | ~wise(X0) [cnf transformation 62]
121. ~creative(X0) | ~wise(X0) | calm(X0) [cnf transformation 63]
122. creative(X0) | wise(X0) | calm(X0) [cnf transformation 63]
129. ~curious(sK5) [cnf transformation 67]
141. tall(alice) [cnf transformation 24]
147. generous(X0) | calm(X0) [duplicate literal removal 78]
148. generous(X0) | ~calm(X0) [duplicate literal removal 80]
149. generous(X0) [subsumption resolution 147,148]
183. ~tall(alice) | ~calm(X0) | curious(X0) [subsumption resolution 100,149]
185. 8 <=> ! [X0] : (~calm(X0) | curious(X0)) [avatar definition]
186. ~calm(X0) | curious(X0) <- (8) [avatar component clause 185]
188. 9 <=> tall(alice) [avatar definition]
191. 8 | ~9 [avatar split clause 183,188,185]
221. wise(X0) | calm(X0) [subsumption resolution 122,117]
222. ~wise(X0) | calm(X0) [subsumption resolution 121,118]
223. calm(X0) [subsumption resolution 222,221]
267. 9 [avatar split clause 141,188]
268. curious(X0) <- (8) [subsumption resolution 186,223]
269. $false <- (8) [resolution 268,129]
272. ~8 [avatar contradiction clause 269]
273. $false [avatar sat refutation 191,267,272]
% SZS output end Proof for 873000780738231193569388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both not quiet and not creative is tall or not strong and vice versa.
If fred is creative then susan is not generous.
If lucy is both rich and curious then john is strong and vice versa.
Everyone who is either creative or not patient is old or not brave.
Everyone who is calm or not humble is either creative or not happy.
Everyone who is both not rich and curious is both not patient and not quiet.
Everyone who is not quiet or old is humble.
Everyone who is both rich and brave is either strong or not strong and vice versa.
Everyone who is either quiet or strong is both not patient and happy.
If alice is either funny or rich then alice is not quiet and vice versa.
Everyone who is calm is generous and vice versa.
If mary is both strong and not funny then someone is tall and vice versa.
If someone is both kind and brave then mary is not rich or generous and vice versa.
If mary is either quiet or not quiet then mary is not calm and vice versa.
If someone is calm or not happy then john is both not generous and not patient and vice versa.
If someone is both old and not quiet then someone is funny.
John is creative.
Someone is either not brave or patient.
Alice is either happy or tall.
John is either not humble or kind.
Someone is not curious or humble.
Someone is calm.
Susan is either not funny or wise. | John is not humble. | entailment | (![X]:((~quiet(X)&~creative(X))<=>(tall(X)|~strong(X))))&
((creative(fred))=>(~generous(susan)))&
(((rich(lucy)&curious(lucy)))<=>(strong(john)))&
(![X]:((creative(X)<~>~patient(X))=>(old(X)|~brave(X))))&
(![X]:((calm(X)|~humble(X))=>(creative(X)<~>~happy(X))))&
(![X]:((~rich(X)&curious(X))=>(~patient(X)&~quiet(X))))&
(![X]:((~quiet(X)|old(X))=>humble(X)))&
(![X]:((rich(X)&brave(X))<=>(strong(X)<~>~strong(X))))&
(![X]:((quiet(X)<~>strong(X))=>(~patient(X)&happy(X))))&
(((funny(alice)<~>rich(alice)))<=>(~quiet(alice)))&
(![X]:(calm(X)<=>generous(X)))&
(((strong(mary)&~funny(mary)))<=>(?[X]:(tall(X))))&
((?[X]:((kind(X)&brave(X))))<=>((~rich(mary)|generous(mary))))&
(((quiet(mary)<~>~quiet(mary)))<=>(~calm(mary)))&
((?[X]:((calm(X)|~happy(X))))<=>((~generous(john)&~patient(john))))&
((?[X]:((old(X)&~quiet(X))))=>(?[X]:(funny(X))))&
(creative(john))&
(?[X]:((~brave(X)<~>patient(X))))&
((happy(alice)<~>tall(alice)))&
((~humble(john)<~>kind(john)))&
(?[X]:((~curious(X)|humble(X))))&
(?[X]:(calm(X)))&
((~funny(susan)<~>wise(susan))) | ~humble(john) | [
"p7",
"p10",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3409050605065310574535927
% SZS output start Proof for 3409050605065310574535927
8. ! [X0] : ((brave(X0) & rich(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p7]
11. ! [X0] : (calm(X0) <=> generous(X0)) [input p10]
13. ? [X0] : (brave(X0) & kind(X0)) <=> (generous(mary) | ~rich(mary)) [input p12]
14. (quiet(mary) <~> ~quiet(mary)) <=> ~calm(mary) [input p13]
20. ~humble(john) <~> kind(john) [input p19]
24. humble(john) [input hypothesis]
41. ! [X0] : (((brave(X0) & rich(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~brave(X0) | ~rich(X0)))) [nnf transformation 8]
42. ! [X0] : (((brave(X0) & rich(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~brave(X0) | ~rich(X0))) [flattening 41]
45. ! [X0] : ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))) [nnf transformation 11]
51. (? [X0] : (brave(X0) & kind(X0)) | (~generous(mary) & rich(mary))) & ((generous(mary) | ~rich(mary)) | ! [X0] : (~brave(X0) | ~kind(X0))) [nnf transformation 13]
52. (? [X0] : (brave(X0) & kind(X0)) | (~generous(mary) & rich(mary))) & (generous(mary) | ~rich(mary) | ! [X0] : (~brave(X0) | ~kind(X0))) [flattening 51]
53. (? [X0] : (brave(X0) & kind(X0)) | (~generous(mary) & rich(mary))) & (generous(mary) | ~rich(mary) | ! [X1] : (~brave(X1) | ~kind(X1))) [rectify 52]
54. ? [X0] : (brave(X0) & kind(X0)) => (brave(sK1) & kind(sK1)) [choice axiom]
55. ((brave(sK1) & kind(sK1)) | (~generous(mary) & rich(mary))) & (generous(mary) | ~rich(mary) | ! [X1] : (~brave(X1) | ~kind(X1))) [skolemisation 53,54]
56. (((quiet(mary) | ~quiet(mary)) & (~quiet(mary) | quiet(mary))) | calm(mary)) & (~calm(mary) | ((quiet(mary) | quiet(mary)) & (~quiet(mary) | ~quiet(mary)))) [nnf transformation 14]
69. (~kind(john) | humble(john)) & (kind(john) | ~humble(john)) [nnf transformation 20]
96. rich(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 42]
97. rich(X0) | strong(X0) | strong(X0) [cnf transformation 42]
98. brave(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 42]
99. brave(X0) | strong(X0) | strong(X0) [cnf transformation 42]
109. ~generous(X0) | calm(X0) [cnf transformation 45]
113. generous(mary) | ~rich(mary) | ~brave(X1) | ~kind(X1) [cnf transformation 55]
118. ~calm(mary) | ~quiet(mary) | ~quiet(mary) [cnf transformation 56]
119. ~calm(mary) | quiet(mary) | quiet(mary) [cnf transformation 56]
133. kind(john) | ~humble(john) [cnf transformation 69]
139. humble(john) [cnf transformation 24]
140. ~calm(mary) | ~quiet(mary) [duplicate literal removal 118]
141. ~calm(mary) | quiet(mary) [duplicate literal removal 119]
142. rich(X0) | ~strong(X0) [duplicate literal removal 96]
143. rich(X0) | strong(X0) [duplicate literal removal 97]
144. brave(X0) | ~strong(X0) [duplicate literal removal 98]
145. brave(X0) | strong(X0) [duplicate literal removal 99]
170. brave(X0) [subsumption resolution 144,145]
171. rich(X0) [subsumption resolution 142,143]
203. 12 <=> generous(mary) [avatar definition]
204. generous(mary) <- (12) [avatar component clause 203]
211. generous(mary) | ~brave(X1) | ~kind(X1) [subsumption resolution 113,171]
212. generous(mary) | ~kind(X1) [subsumption resolution 211,170]
214. 14 <=> ! [X1] : ~kind(X1) [avatar definition]
215. ~kind(X1) <- (14) [avatar component clause 214]
216. 14 | 12 [avatar split clause 212,203,214]
218. 15 <=> quiet(mary) [avatar definition]
222. 16 <=> calm(mary) [avatar definition]
224. ~calm(mary) <- (~16) [avatar component clause 222]
225. 15 | ~16 [avatar split clause 141,222,218]
226. ~15 | ~16 [avatar split clause 140,222,218]
274. 27 <=> humble(john) [avatar definition]
278. 28 <=> kind(john) [avatar definition]
279. kind(john) <- (28) [avatar component clause 278]
282. ~27 | 28 [avatar split clause 133,278,274]
302. 27 [avatar split clause 139,274]
308. calm(mary) <- (12) [resolution 109,204]
310. $false <- (12, ~16) [subsumption resolution 308,224]
311. ~12 | 16 [avatar contradiction clause 310]
313. $false <- (14, 28) [resolution 215,279]
314. ~14 | ~28 [avatar contradiction clause 313]
316. $false [avatar sat refutation 216,225,226,282,302,311,314]
% SZS output end Proof for 3409050605065310574535927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not curious and vice versa. If paul is patient then john is not quiet and vice versa. If someone is brave or not quiet then alice is not happy. Everyone who is both not kind and not rich is tall and vice versa. Everyone who is humble or kind is both not calm and patient. If someone is both patient and not curious then alice is patient and vice versa. Everyone who is both not old and not generous is not patient. If someone is either not humble or tall then susan is either old or not brave. Everyone who is either not kind or not rich is both not old and funny. Everyone who is either calm or strong is not strong and vice versa. Everyone who is strong is not creative or not funny and vice versa. If someone is not brave then someone is either not happy or not strong. Everyone who is not happy or not funny is both happy and kind and vice versa. If alice is not quiet then someone is either not tall or not brave. If fred is both not curious and patient then john is patient. Alice is either brave or creative. Someone is brave or tall. Alice is wise. Someone is rich or not wise. Someone is either not wise or rich. Fred is either not patient or rich. John is both rich and creative. | Alice is strong. | contradiction | (![X]:(funny(X)<=>~curious(X)))&
((patient(paul))<=>(~quiet(john)))&
((?[X]:((brave(X)|~quiet(X))))=>(~happy(alice)))&
(![X]:((~kind(X)&~rich(X))<=>tall(X)))&
(![X]:((humble(X)|kind(X))=>(~calm(X)&patient(X))))&
((?[X]:((patient(X)&~curious(X))))<=>(patient(alice)))&
(![X]:((~old(X)&~generous(X))=>~patient(X)))&
((?[X]:((~humble(X)<~>tall(X))))=>((old(susan)<~>~brave(susan))))&
(![X]:((~kind(X)<~>~rich(X))=>(~old(X)&funny(X))))&
(![X]:((calm(X)<~>strong(X))<=>~strong(X)))&
(![X]:(strong(X)<=>(~creative(X)|~funny(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((~happy(X)|~funny(X))<=>(happy(X)&kind(X))))&
((~quiet(alice))=>(?[X]:((~tall(X)<~>~brave(X)))))&
(((~curious(fred)&patient(fred)))=>(patient(john)))&
((brave(alice)<~>creative(alice)))&
(?[X]:((brave(X)|tall(X))))&
(wise(alice))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~wise(X)<~>rich(X))))&
((~patient(fred)<~>rich(fred)))&
((rich(john)&creative(john))) | strong(alice) | [
"p2",
"p4",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8352885552764934138557842
% SZS output start Proof for 8352885552764934138557842
3. ? [X0] : (~quiet(X0) | brave(X0)) => ~happy(alice) [input p2]
5. ! [X0] : ((kind(X0) | humble(X0)) => (patient(X0) & ~calm(X0))) [input p4]
10. ! [X0] : ((calm(X0) <~> strong(X0)) <=> ~strong(X0)) [input p9]
11. ! [X0] : (strong(X0) <=> (~funny(X0) | ~creative(X0))) [input p10]
13. ! [X0] : ((~funny(X0) | ~happy(X0)) <=> (kind(X0) & happy(X0))) [input p12]
16. brave(alice) <~> creative(alice) [input p15]
23. strong(alice) [input hypothesis]
26. ~happy(alice) | ! [X0] : (quiet(X0) & ~brave(X0)) [ennf transformation 3]
27. ! [X0] : ((patient(X0) & ~calm(X0)) | (~kind(X0) & ~humble(X0))) [ennf transformation 5]
44. ! [X0] : ((((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | strong(X0)) & (~strong(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0))))) [nnf transformation 10]
45. ! [X0] : ((strong(X0) | (funny(X0) & creative(X0))) & ((~funny(X0) | ~creative(X0)) | ~strong(X0))) [nnf transformation 11]
46. ! [X0] : ((strong(X0) | (funny(X0) & creative(X0))) & (~funny(X0) | ~creative(X0) | ~strong(X0))) [flattening 45]
51. ! [X0] : (((~funny(X0) | ~happy(X0)) | (~kind(X0) | ~happy(X0))) & ((kind(X0) & happy(X0)) | (funny(X0) & happy(X0)))) [nnf transformation 13]
52. ! [X0] : ((~funny(X0) | ~happy(X0) | ~kind(X0) | ~happy(X0)) & ((kind(X0) & happy(X0)) | (funny(X0) & happy(X0)))) [flattening 51]
56. (~creative(alice) | ~brave(alice)) & (creative(alice) | brave(alice)) [nnf transformation 16]
69. ~happy(alice) | ~brave(X0) [cnf transformation 26]
75. ~calm(X0) | ~kind(X0) [cnf transformation 27]
90. ~strong(X0) | calm(X0) | ~strong(X0) [cnf transformation 44]
91. strong(X0) | calm(X0) | strong(X0) [cnf transformation 44]
93. ~creative(X0) | ~funny(X0) | ~strong(X0) [cnf transformation 46]
98. happy(X0) | happy(X0) [cnf transformation 52]
101. kind(X0) | funny(X0) [cnf transformation 52]
106. creative(alice) | brave(alice) [cnf transformation 56]
117. strong(alice) [cnf transformation 23]
118. happy(X0) [duplicate literal removal 98]
120. ~strong(X0) | calm(X0) [duplicate literal removal 90]
121. strong(X0) | calm(X0) [duplicate literal removal 91]
136. 4 <=> happy(alice) [avatar definition]
138. ~happy(alice) <- (~4) [avatar component clause 136]
141. 5 <=> ! [X0] : ~brave(X0) [avatar definition]
142. ~brave(X0) <- (5) [avatar component clause 141]
143. 5 | ~4 [avatar split clause 69,136,141]
180. calm(X0) [subsumption resolution 120,121]
222. 23 <=> brave(alice) [avatar definition]
223. brave(alice) <- (23) [avatar component clause 222]
226. 24 <=> creative(alice) [avatar definition]
227. creative(alice) <- (24) [avatar component clause 226]
230. 23 | 24 [avatar split clause 106,226,222]
267. $false <- (~4) [subsumption resolution 138,118]
268. 4 [avatar contradiction clause 267]
275. $false <- (5, 23) [resolution 223,142]
276. ~5 | ~23 [avatar contradiction clause 275]
284. ~kind(X0) [resolution 75,180]
291. funny(X1) [resolution 101,284]
302. ~funny(alice) | ~strong(alice) <- (24) [resolution 93,227]
305. ~strong(alice) <- (24) [subsumption resolution 302,291]
306. $false <- (24) [subsumption resolution 305,117]
307. ~24 [avatar contradiction clause 306]
308. $false [avatar sat refutation 143,230,268,276,307]
% SZS output end Proof for 8352885552764934138557842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not creative is brave or not old and vice versa.
Everyone who is either not funny or not kind is not kind and vice versa.
If someone is not creative or calm then someone is not old or not brave and vice versa.
Everyone who is both quiet and not curious is either brave or not quiet and vice versa.
Everyone who is either brave or not patient is not brave and vice versa.
Everyone who is kind or not generous is not happy or patient.
If someone is either not wise or wise then fred is happy.
If someone is both not wise and not humble then john is rich and vice versa.
Everyone who is either not kind or not brave is not generous or strong and vice versa.
If mary is not quiet or not strong then john is not creative or humble and vice versa.
Everyone who is either patient or kind is not calm or not humble.
Everyone who is either not strong or funny is both strong and not brave.
If someone is both not patient and wise then someone is strong.
If john is either not wise or tall then someone is both patient and old.
Everyone who is not calm is either not rich or brave and vice versa.
If alice is either not brave or humble then alice is either not funny or tall.
Fred is not kind.
Someone is not curious.
Someone is either not quiet or not calm.
Someone is either not tall or not calm.
John is not curious.
Someone is not rich or generous.
Mary is not patient. | John is strong. | contradiction | (![X]:((~strong(X)|~creative(X))<=>(brave(X)|~old(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>~kind(X)))&
((?[X]:((~creative(X)|calm(X))))<=>(?[X]:((~old(X)|~brave(X)))))&
(![X]:((quiet(X)&~curious(X))<=>(brave(X)<~>~quiet(X))))&
(![X]:((brave(X)<~>~patient(X))<=>~brave(X)))&
(![X]:((kind(X)|~generous(X))=>(~happy(X)|patient(X))))&
((?[X]:((~wise(X)<~>wise(X))))=>(happy(fred)))&
((?[X]:((~wise(X)&~humble(X))))<=>(rich(john)))&
(![X]:((~kind(X)<~>~brave(X))<=>(~generous(X)|strong(X))))&
(((~quiet(mary)|~strong(mary)))<=>((~creative(john)|humble(john))))&
(![X]:((patient(X)<~>kind(X))=>(~calm(X)|~humble(X))))&
(![X]:((~strong(X)<~>funny(X))=>(strong(X)&~brave(X))))&
((?[X]:((~patient(X)&wise(X))))=>(?[X]:(strong(X))))&
(((~wise(john)<~>tall(john)))=>(?[X]:((patient(X)&old(X)))))&
(![X]:(~calm(X)<=>(~rich(X)<~>brave(X))))&
(((~brave(alice)<~>humble(alice)))=>((~funny(alice)<~>tall(alice))))&
(~kind(fred))&
(?[X]:(~curious(X)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
(?[X]:((~tall(X)<~>~calm(X))))&
(~curious(john))&
(?[X]:((~rich(X)|generous(X))))&
(~patient(mary)) | strong(john) | [
"p1",
"p3",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6181798233236307817213008
% SZS output start Proof for 6181798233236307817213008
2. ! [X0] : ((~funny(X0) <~> ~kind(X0)) <=> ~kind(X0)) [input p1]
4. ! [X0] : ((~curious(X0) & quiet(X0)) <=> (brave(X0) <~> ~quiet(X0))) [input p3]
12. ! [X0] : ((~strong(X0) <~> funny(X0)) => (~brave(X0) & strong(X0))) [input p11]
21. ~curious(john) [input p20]
24. strong(john) [input hypothesis]
32. ! [X0] : ((~brave(X0) & strong(X0)) | (~strong(X0) <=> funny(X0))) [ennf transformation 12]
38. ! [X0] : ((((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | kind(X0)) & (~kind(X0) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))))) [nnf transformation 2]
44. ! [X0] : (((~curious(X0) & quiet(X0)) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0)))) & (((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | (curious(X0) | ~quiet(X0)))) [nnf transformation 4]
45. ! [X0] : (((~curious(X0) & quiet(X0)) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0)))) & (((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | curious(X0) | ~quiet(X0))) [flattening 44]
57. ! [X0] : ((~brave(X0) & strong(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) [nnf transformation 32]
80. ~kind(X0) | ~kind(X0) | funny(X0) [cnf transformation 38]
83. kind(X0) | funny(X0) | kind(X0) [cnf transformation 38]
88. ~quiet(X0) | brave(X0) | curious(X0) | ~quiet(X0) [cnf transformation 45]
91. quiet(X0) | brave(X0) | quiet(X0) [cnf transformation 45]
120. ~brave(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 57]
140. ~curious(john) [cnf transformation 21]
143. strong(john) [cnf transformation 24]
149. ~quiet(X0) | brave(X0) | curious(X0) [duplicate literal removal 88]
150. quiet(X0) | brave(X0) [duplicate literal removal 91]
151. ~kind(X0) | funny(X0) [duplicate literal removal 80]
152. kind(X0) | funny(X0) [duplicate literal removal 83]
153. funny(X0) [subsumption resolution 151,152]
186. curious(X0) | brave(X0) [subsumption resolution 149,150]
241. ~brave(X0) | ~strong(X0) [subsumption resolution 120,153]
314. brave(john) [resolution 186,140]
319. ~strong(john) [resolution 241,314]
321. $false [subsumption resolution 319,143]
% SZS output end Proof for 6181798233236307817213008
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or creative then mary is both brave and old. If someone is not quiet then mary is both not quiet and kind. If someone is both not old and not humble then alice is not rich. If susan is patient or not old then someone is not funny or humble and vice versa. Everyone who is either humble or not patient is both not funny and happy and vice versa. If john is not brave or funny then someone is both not tall and strong and vice versa. Everyone who is both not humble and kind is curious or not quiet. If john is both not calm and brave then paul is patient and vice versa. Everyone who is wise is either not generous or happy and vice versa. Everyone who is wise is either wise or generous and vice versa. If john is not brave or not patient then someone is kind. If someone is both not strong and wise then paul is either not funny or not brave and vice versa. Everyone who is humble is both quiet and strong and vice versa. Everyone who is tall or quiet is either not kind or not rich. Everyone who is either humble or not wise is either calm or not quiet and vice versa. If someone is humble then fred is both calm and rich. John is rich or strong. Alice is either strong or creative. Someone is either not calm or generous. Alice is both not patient and not humble. Someone is both not kind and quiet. Someone is strong or happy. Fred is not generous. Someone is both patient and not generous. | Mary is quiet. | neutral | ((?[X]:((~humble(X)|creative(X))))=>((brave(mary)&old(mary))))&
((?[X]:(~quiet(X)))=>((~quiet(mary)&kind(mary))))&
((?[X]:((~old(X)&~humble(X))))=>(~rich(alice)))&
(((patient(susan)|~old(susan)))<=>(?[X]:((~funny(X)|humble(X)))))&
(![X]:((humble(X)<~>~patient(X))<=>(~funny(X)&happy(X))))&
(((~brave(john)|funny(john)))<=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((~humble(X)&kind(X))=>(curious(X)|~quiet(X))))&
(((~calm(john)&brave(john)))<=>(patient(paul)))&
(![X]:(wise(X)<=>(~generous(X)<~>happy(X))))&
(![X]:(wise(X)<=>(wise(X)<~>generous(X))))&
(((~brave(john)|~patient(john)))=>(?[X]:(kind(X))))&
((?[X]:((~strong(X)&wise(X))))<=>((~funny(paul)<~>~brave(paul))))&
(![X]:(humble(X)<=>(quiet(X)&strong(X))))&
(![X]:((tall(X)|quiet(X))=>(~kind(X)<~>~rich(X))))&
(![X]:((humble(X)<~>~wise(X))<=>(calm(X)<~>~quiet(X))))&
((?[X]:(humble(X)))=>((calm(fred)&rich(fred))))&
((rich(john)|strong(john)))&
((strong(alice)<~>creative(alice)))&
(?[X]:((~calm(X)<~>generous(X))))&
((~patient(alice)&~humble(alice)))&
(?[X]:((~kind(X)&quiet(X))))&
(?[X]:((strong(X)|happy(X))))&
(~generous(fred))&
(?[X]:((patient(X)&~generous(X)))) | quiet(mary) | [] | null | 0 |
If someone is either calm or not old then someone is either curious or happy.
Everyone who is both kind and not kind is brave and vice versa.
Everyone who is not funny or funny is wise or not tall and vice versa.
If fred is kind or not funny then john is brave and vice versa.
If someone is creative then john is either generous or happy and vice versa.
If someone is either generous or not brave then mary is either calm or not quiet.
Everyone who is either kind or wise is both not curious and calm and vice versa.
Everyone who is either not strong or quiet is both wise and not patient.
Everyone who is not happy or patient is not wise and vice versa.
Everyone who is not brave or calm is happy and vice versa.
Everyone who is either not creative or not patient is either not happy or not old and vice versa.
Everyone who is patient or not creative is both rich and not humble.
Everyone who is funny is either not rich or not wise and vice versa.
Everyone who is not funny or not calm is either not kind or not old and vice versa.
Everyone who is both not tall and happy is not strong or strong and vice versa.
If someone is both calm and curious then someone is wise and vice versa.
Someone is either not patient or not strong.
Someone is both not brave and not kind.
Lucy is either not kind or not generous.
Paul is either wise or calm.
Someone is either not happy or not wise. | John is tall. | contradiction | ((?[X]:((calm(X)<~>~old(X))))=>(?[X]:((curious(X)<~>happy(X)))))&
(![X]:((kind(X)&~kind(X))<=>brave(X)))&
(![X]:((~funny(X)|funny(X))<=>(wise(X)|~tall(X))))&
(((kind(fred)|~funny(fred)))<=>(brave(john)))&
((?[X]:(creative(X)))<=>((generous(john)<~>happy(john))))&
((?[X]:((generous(X)<~>~brave(X))))=>((calm(mary)<~>~quiet(mary))))&
(![X]:((kind(X)<~>wise(X))<=>(~curious(X)&calm(X))))&
(![X]:((~strong(X)<~>quiet(X))=>(wise(X)&~patient(X))))&
(![X]:((~happy(X)|patient(X))<=>~wise(X)))&
(![X]:((~brave(X)|calm(X))<=>happy(X)))&
(![X]:((~creative(X)<~>~patient(X))<=>(~happy(X)<~>~old(X))))&
(![X]:((patient(X)|~creative(X))=>(rich(X)&~humble(X))))&
(![X]:(funny(X)<=>(~rich(X)<~>~wise(X))))&
(![X]:((~funny(X)|~calm(X))<=>(~kind(X)<~>~old(X))))&
(![X]:((~tall(X)&happy(X))<=>(~strong(X)|strong(X))))&
((?[X]:((calm(X)&curious(X))))<=>(?[X]:(wise(X))))&
(?[X]:((~patient(X)<~>~strong(X))))&
(?[X]:((~brave(X)&~kind(X))))&
((~kind(lucy)<~>~generous(lucy)))&
((wise(paul)<~>calm(paul)))&
(?[X]:((~happy(X)<~>~wise(X)))) | tall(john) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5498004472837414135771999
% SZS output start Proof for 5498004472837414135771999
15. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (strong(X0) | ~strong(X0))) [input p14]
22. tall(john) [input hypothesis]
56. ! [X0] : (((happy(X0) & ~tall(X0)) | (~strong(X0) & strong(X0))) & ((strong(X0) | ~strong(X0)) | (~happy(X0) | tall(X0)))) [nnf transformation 15]
57. ! [X0] : (((happy(X0) & ~tall(X0)) | (~strong(X0) & strong(X0))) & (strong(X0) | ~strong(X0) | ~happy(X0) | tall(X0))) [flattening 56]
132. ~tall(X0) | strong(X0) [cnf transformation 57]
133. ~tall(X0) | ~strong(X0) [cnf transformation 57]
149. tall(john) [cnf transformation 22]
211. ~tall(X0) [subsumption resolution 132,133]
264. $false [subsumption resolution 149,211]
% SZS output end Proof for 5498004472837414135771999
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or kind then someone is quiet or curious and vice versa. If someone is not generous then fred is both not wise and funny and vice versa. Everyone who is not curious or not calm is either not curious or not patient and vice versa. Everyone who is not generous or wise is not tall or wise. Everyone who is both curious and old is strong and vice versa. Everyone who is not patient or funny is both quiet and not funny and vice versa. If fred is either patient or not humble then someone is curious or not wise. Everyone who is not brave or not kind is either happy or not funny and vice versa. If alice is both tall and calm then someone is either not patient or curious. If someone is wise or creative then alice is either not brave or humble and vice versa. If someone is either curious or kind then fred is either not kind or not old. Everyone who is both not brave and not humble is either generous or old. If someone is not wise then someone is both not funny and not happy. If susan is either old or not brave then susan is brave and vice versa. If john is not old or creative then mary is either rich or not patient. If someone is not humble or not old then fred is both not old and not calm and vice versa. Someone is either tall or not generous. Someone is both generous and curious. Someone is not curious. Someone is not happy or creative. Someone is both not wise and happy. Susan is brave. | Fred is strong. | neutral | ((?[X]:((~rich(X)|kind(X))))<=>(?[X]:((quiet(X)|curious(X)))))&
((?[X]:(~generous(X)))<=>((~wise(fred)&funny(fred))))&
(![X]:((~curious(X)|~calm(X))<=>(~curious(X)<~>~patient(X))))&
(![X]:((~generous(X)|wise(X))=>(~tall(X)|wise(X))))&
(![X]:((curious(X)&old(X))<=>strong(X)))&
(![X]:((~patient(X)|funny(X))<=>(quiet(X)&~funny(X))))&
(((patient(fred)<~>~humble(fred)))=>(?[X]:((curious(X)|~wise(X)))))&
(![X]:((~brave(X)|~kind(X))<=>(happy(X)<~>~funny(X))))&
(((tall(alice)&calm(alice)))=>(?[X]:((~patient(X)<~>curious(X)))))&
((?[X]:((wise(X)|creative(X))))<=>((~brave(alice)<~>humble(alice))))&
((?[X]:((curious(X)<~>kind(X))))=>((~kind(fred)<~>~old(fred))))&
(![X]:((~brave(X)&~humble(X))=>(generous(X)<~>old(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~funny(X)&~happy(X)))))&
(((old(susan)<~>~brave(susan)))<=>(brave(susan)))&
(((~old(john)|creative(john)))=>((rich(mary)<~>~patient(mary))))&
((?[X]:((~humble(X)|~old(X))))<=>((~old(fred)&~calm(fred))))&
(?[X]:((tall(X)<~>~generous(X))))&
(?[X]:((generous(X)&curious(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~happy(X)|creative(X))))&
(?[X]:((~wise(X)&happy(X))))&
(brave(susan)) | strong(fred) | [] | null | 0 |
Everyone who is not kind or calm is not wise or patient. If someone is not kind then fred is generous and vice versa. If paul is generous then fred is both not quiet and not wise. If susan is humble or strong then mary is either rich or old and vice versa. If someone is patient or generous then mary is either not creative or curious and vice versa. Everyone who is both calm and not brave is either quiet or not brave and vice versa. If alice is not old then someone is both tall and old. If paul is both funny and not creative then someone is not creative or curious and vice versa. If lucy is not wise then paul is both not funny and wise and vice versa. If someone is tall or generous then fred is not curious and vice versa. Everyone who is both generous and wise is either wise or kind. If someone is not wise then someone is not rich or wise. Everyone who is both not funny and happy is funny and vice versa. If someone is either rich or creative then john is not generous. Everyone who is either not patient or not happy is not brave. Lucy is not happy or quiet. Someone is either old or tall. Mary is either not quiet or not calm. | Mary is not tall. | neutral | (![X]:((~kind(X)|calm(X))=>(~wise(X)|patient(X))))&
((?[X]:(~kind(X)))<=>(generous(fred)))&
((generous(paul))=>((~quiet(fred)&~wise(fred))))&
(((humble(susan)|strong(susan)))<=>((rich(mary)<~>old(mary))))&
((?[X]:((patient(X)|generous(X))))<=>((~creative(mary)<~>curious(mary))))&
(![X]:((calm(X)&~brave(X))<=>(quiet(X)<~>~brave(X))))&
((~old(alice))=>(?[X]:((tall(X)&old(X)))))&
(((funny(paul)&~creative(paul)))<=>(?[X]:((~creative(X)|curious(X)))))&
((~wise(lucy))<=>((~funny(paul)&wise(paul))))&
((?[X]:((tall(X)|generous(X))))<=>(~curious(fred)))&
(![X]:((generous(X)&wise(X))=>(wise(X)<~>kind(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~rich(X)|wise(X)))))&
(![X]:((~funny(X)&happy(X))<=>funny(X)))&
((?[X]:((rich(X)<~>creative(X))))=>(~generous(john)))&
(![X]:((~patient(X)<~>~happy(X))=>~brave(X)))&
((~happy(lucy)|quiet(lucy)))&
(?[X]:((old(X)<~>tall(X))))&
((~quiet(mary)<~>~calm(mary))) | ~tall(mary) | [] | null | 0 |
Everyone who is both old and not strong is either not brave or old. If john is both tall and rich then someone is not rich and vice versa. Everyone who is either not brave or brave is rich or humble and vice versa. Everyone who is either not funny or not humble is not old or wise. If someone is both generous and not tall then lucy is not generous or patient. Everyone who is not happy or strong is not creative. Everyone who is not old is both strong and wise. Everyone who is either humble or generous is humble. Everyone who is strong is not kind and vice versa. Everyone who is curious is not kind and vice versa. If someone is both happy and not creative then alice is either not patient or not strong and vice versa. Everyone who is wise or curious is not tall or not brave. If susan is either not funny or not wise then paul is quiet and vice versa. Everyone who is both kind and not brave is wise and vice versa. Everyone who is either wise or not tall is curious or not generous and vice versa. If someone is both not patient and happy then someone is curious or funny. Someone is creative. Someone is not rich. Someone is not tall. Someone is not humble. Someone is funny or not rich. Someone is not generous. Susan is both creative and happy. John is creative or brave. | Alice is kind. | neutral | (![X]:((old(X)&~strong(X))=>(~brave(X)<~>old(X))))&
(((tall(john)&rich(john)))<=>(?[X]:(~rich(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(rich(X)|humble(X))))&
(![X]:((~funny(X)<~>~humble(X))=>(~old(X)|wise(X))))&
((?[X]:((generous(X)&~tall(X))))=>((~generous(lucy)|patient(lucy))))&
(![X]:((~happy(X)|strong(X))=>~creative(X)))&
(![X]:(~old(X)=>(strong(X)&wise(X))))&
(![X]:((humble(X)<~>generous(X))=>humble(X)))&
(![X]:(strong(X)<=>~kind(X)))&
(![X]:(curious(X)<=>~kind(X)))&
((?[X]:((happy(X)&~creative(X))))<=>((~patient(alice)<~>~strong(alice))))&
(![X]:((wise(X)|curious(X))=>(~tall(X)|~brave(X))))&
(((~funny(susan)<~>~wise(susan)))<=>(quiet(paul)))&
(![X]:((kind(X)&~brave(X))<=>wise(X)))&
(![X]:((wise(X)<~>~tall(X))<=>(curious(X)|~generous(X))))&
((?[X]:((~patient(X)&happy(X))))=>(?[X]:((curious(X)|funny(X)))))&
(?[X]:(creative(X)))&
(?[X]:(~rich(X)))&
(?[X]:(~tall(X)))&
(?[X]:(~humble(X)))&
(?[X]:((funny(X)|~rich(X))))&
(?[X]:(~generous(X)))&
((creative(susan)&happy(susan)))&
((creative(john)|brave(john))) | kind(alice) | [] | null | 0 |
Everyone who is not creative or not curious is patient and vice versa. If someone is calm or tall then susan is both old and creative and vice versa. Everyone who is not generous is either creative or not rich and vice versa. Everyone who is not generous is not wise. Everyone who is both not curious and not creative is not strong and vice versa. If someone is not tall then mary is not humble or wise. If alice is curious then someone is either not rich or generous and vice versa. Everyone who is not tall is both not quiet and not curious. If someone is either tall or happy then lucy is both humble and brave. Everyone who is not patient or quiet is both not curious and generous and vice versa. Everyone who is either rich or not tall is either generous or not happy and vice versa. If paul is not old then someone is either wise or not generous. If someone is brave then someone is either not calm or not happy. If someone is both not kind and not curious then someone is not brave or not creative and vice versa. Everyone who is quiet or generous is curious or happy and vice versa. If someone is not calm then someone is brave or generous and vice versa. Paul is both quiet and not kind. Someone is both not calm and happy. Susan is humble or calm. Someone is either kind or humble. Lucy is both not wise and not strong. Someone is either not creative or kind. | Paul is not tall. | contradiction | (![X]:((~creative(X)|~curious(X))<=>patient(X)))&
((?[X]:((calm(X)|tall(X))))<=>((old(susan)&creative(susan))))&
(![X]:(~generous(X)<=>(creative(X)<~>~rich(X))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~curious(X)&~creative(X))<=>~strong(X)))&
((?[X]:(~tall(X)))=>((~humble(mary)|wise(mary))))&
((curious(alice))<=>(?[X]:((~rich(X)<~>generous(X)))))&
(![X]:(~tall(X)=>(~quiet(X)&~curious(X))))&
((?[X]:((tall(X)<~>happy(X))))=>((humble(lucy)&brave(lucy))))&
(![X]:((~patient(X)|quiet(X))<=>(~curious(X)&generous(X))))&
(![X]:((rich(X)<~>~tall(X))<=>(generous(X)<~>~happy(X))))&
((~old(paul))=>(?[X]:((wise(X)<~>~generous(X)))))&
((?[X]:(brave(X)))=>(?[X]:((~calm(X)<~>~happy(X)))))&
((?[X]:((~kind(X)&~curious(X))))<=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:((quiet(X)|generous(X))<=>(curious(X)|happy(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((brave(X)|generous(X)))))&
((quiet(paul)&~kind(paul)))&
(?[X]:((~calm(X)&happy(X))))&
((humble(susan)|calm(susan)))&
(?[X]:((kind(X)<~>humble(X))))&
((~wise(lucy)&~strong(lucy)))&
(?[X]:((~creative(X)<~>kind(X)))) | ~tall(paul) | [
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7932354503587216278515651
% SZS output start Proof for 7932354503587216278515651
8. ! [X0] : (~tall(X0) => (~curious(X0) & ~quiet(X0))) [input p7]
17. ~kind(paul) & quiet(paul) [input p16]
23. ~tall(paul) [input hypothesis]
32. ! [X0] : ((~curious(X0) & ~quiet(X0)) | tall(X0)) [ennf transformation 8]
99. ~quiet(X0) | tall(X0) [cnf transformation 32]
134. quiet(paul) [cnf transformation 17]
145. ~tall(paul) [cnf transformation 23]
345. tall(paul) [resolution 99,134]
346. $false [subsumption resolution 345,145]
% SZS output end Proof for 7932354503587216278515651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind or humble is funny or not calm and vice versa.
If mary is either calm or not kind then someone is both not strong and not calm.
If paul is either curious or quiet then someone is not funny or not humble.
Everyone who is either funny or not wise is both not happy and not brave.
Everyone who is both strong and not brave is quiet or old.
Everyone who is either old or curious is rich or not wise and vice versa.
Everyone who is not curious is not quiet.
Everyone who is old is both wise and not wise.
If someone is not creative or brave then someone is both not curious and quiet.
If someone is not strong then john is not wise.
If john is quiet or happy then someone is both creative and not kind.
Everyone who is both not kind and not happy is not strong or not patient and vice versa.
Everyone who is either not creative or wise is funny or brave.
Everyone who is both not funny and not happy is either not brave or not old and vice versa.
Everyone who is both not happy and generous is not happy.
Everyone who is not rich or not kind is wise or humble and vice versa.
Lucy is either not humble or humble.
Fred is not patient or not wise.
Someone is not happy or not kind.
Lucy is not quiet.
Someone is quiet.
Someone is either not curious or wise.
Susan is either not wise or wise.
Susan is kind. | John is strong. | entailment | (![X]:((~kind(X)<~>humble(X))<=>(funny(X)|~calm(X))))&
(((calm(mary)<~>~kind(mary)))=>(?[X]:((~strong(X)&~calm(X)))))&
(((curious(paul)<~>quiet(paul)))=>(?[X]:((~funny(X)|~humble(X)))))&
(![X]:((funny(X)<~>~wise(X))=>(~happy(X)&~brave(X))))&
(![X]:((strong(X)&~brave(X))=>(quiet(X)|old(X))))&
(![X]:((old(X)<~>curious(X))<=>(rich(X)|~wise(X))))&
(![X]:(~curious(X)=>~quiet(X)))&
(![X]:(old(X)=>(wise(X)&~wise(X))))&
((?[X]:((~creative(X)|brave(X))))=>(?[X]:((~curious(X)&quiet(X)))))&
((?[X]:(~strong(X)))=>(~wise(john)))&
(((quiet(john)|happy(john)))=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:((~kind(X)&~happy(X))<=>(~strong(X)|~patient(X))))&
(![X]:((~creative(X)<~>wise(X))=>(funny(X)|brave(X))))&
(![X]:((~funny(X)&~happy(X))<=>(~brave(X)<~>~old(X))))&
(![X]:((~happy(X)&generous(X))=>~happy(X)))&
(![X]:((~rich(X)|~kind(X))<=>(wise(X)|humble(X))))&
((~humble(lucy)<~>humble(lucy)))&
((~patient(fred)|~wise(fred)))&
(?[X]:((~happy(X)|~kind(X))))&
(~quiet(lucy))&
(?[X]:(quiet(X)))&
(?[X]:((~curious(X)<~>wise(X))))&
((~wise(susan)<~>wise(susan)))&
(kind(susan)) | strong(john) | [
"p0",
"p6",
"p7",
"p8",
"p9",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7563734894769850591593581
% SZS output start Proof for 7563734894769850591593581
1. ! [X0] : ((~kind(X0) <~> humble(X0)) <=> (~calm(X0) | funny(X0))) [input p0]
7. ! [X0] : (~curious(X0) => ~quiet(X0)) [input p6]
8. ! [X0] : (old(X0) => (~wise(X0) & wise(X0))) [input p7]
9. ? [X0] : (brave(X0) | ~creative(X0)) => ? [X0] : (quiet(X0) & ~curious(X0)) [input p8]
10. ? [X0] : ~strong(X0) => ~wise(john) [input p9]
12. ! [X0] : ((~happy(X0) & ~kind(X0)) <=> (~patient(X0) | ~strong(X0))) [input p11]
14. ! [X0] : ((~happy(X0) & ~funny(X0)) <=> (~brave(X0) <~> ~old(X0))) [input p13]
16. ! [X0] : ((~kind(X0) | ~rich(X0)) <=> (humble(X0) | wise(X0))) [input p15]
25. ~strong(john) [input hypothesis]
26. ? [X0] : (brave(X0) | ~creative(X0)) => ? [X1] : (quiet(X1) & ~curious(X1)) [rectify 9]
33. ! [X0] : (~quiet(X0) | curious(X0)) [ennf transformation 7]
34. ! [X0] : ((~wise(X0) & wise(X0)) | ~old(X0)) [ennf transformation 8]
35. ? [X1] : (quiet(X1) & ~curious(X1)) | ! [X0] : (~brave(X0) & creative(X0)) [ennf transformation 26]
36. ~wise(john) | ! [X0] : strong(X0) [ennf transformation 10]
40. ! [X0] : ((((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0))))) [nnf transformation 1]
41. ! [X0] : ((((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0))))) [flattening 40]
51. ? [X0] : (quiet(X0) & ~curious(X0)) | ! [X1] : (~brave(X1) & creative(X1)) [rectify 35]
52. ? [X0] : (quiet(X0) & ~curious(X0)) => (quiet(sK2) & ~curious(sK2)) [choice axiom]
53. (quiet(sK2) & ~curious(sK2)) | ! [X1] : (~brave(X1) & creative(X1)) [skolemisation 51,52]
56. ! [X0] : (((~happy(X0) & ~kind(X0)) | (patient(X0) & strong(X0))) & ((~patient(X0) | ~strong(X0)) | (happy(X0) | kind(X0)))) [nnf transformation 12]
57. ! [X0] : (((~happy(X0) & ~kind(X0)) | (patient(X0) & strong(X0))) & (~patient(X0) | ~strong(X0) | happy(X0) | kind(X0))) [flattening 56]
59. ! [X0] : (((~happy(X0) & ~funny(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) & (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (happy(X0) | funny(X0)))) [nnf transformation 14]
60. ! [X0] : (((~happy(X0) & ~funny(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) & (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | happy(X0) | funny(X0))) [flattening 59]
61. ! [X0] : (((~kind(X0) | ~rich(X0)) | (~humble(X0) & ~wise(X0))) & ((humble(X0) | wise(X0)) | (kind(X0) & rich(X0)))) [nnf transformation 16]
62. ! [X0] : ((~kind(X0) | ~rich(X0) | (~humble(X0) & ~wise(X0))) & (humble(X0) | wise(X0) | (kind(X0) & rich(X0)))) [flattening 61]
76. ~funny(X0) | kind(X0) | ~humble(X0) [cnf transformation 41]
95. ~quiet(X0) | curious(X0) [cnf transformation 33]
96. wise(X0) | ~old(X0) [cnf transformation 34]
97. ~old(X0) | ~wise(X0) [cnf transformation 34]
99. ~curious(sK2) | ~brave(X1) [cnf transformation 53]
101. quiet(sK2) | ~brave(X1) [cnf transformation 53]
102. ~wise(john) | strong(X0) [cnf transformation 36]
108. ~kind(X0) | strong(X0) [cnf transformation 57]
110. ~happy(X0) | strong(X0) [cnf transformation 57]
115. old(X0) | brave(X0) | happy(X0) | funny(X0) [cnf transformation 60]
121. wise(X0) | humble(X0) | kind(X0) [cnf transformation 62]
135. ~strong(john) [cnf transformation 25]
174. ~old(X0) [subsumption resolution 96,97]
176. 9 <=> ! [X1] : ~brave(X1) [avatar definition]
177. ~brave(X1) <- (9) [avatar component clause 176]
179. 10 <=> quiet(sK2) [avatar definition]
181. quiet(sK2) <- (10) [avatar component clause 179]
182. 9 | 10 [avatar split clause 101,179,176]
188. 12 <=> curious(sK2) [avatar definition]
190. ~curious(sK2) <- (~12) [avatar component clause 188]
191. 9 | ~12 [avatar split clause 99,188,176]
194. 13 <=> ! [X0] : strong(X0) [avatar definition]
195. strong(X0) <- (13) [avatar component clause 194]
197. 14 <=> wise(john) [avatar definition]
199. ~wise(john) <- (~14) [avatar component clause 197]
200. 13 | ~14 [avatar split clause 102,197,194]
202. 15 <=> happy(john) [avatar definition]
203. happy(john) <- (15) [avatar component clause 202]
204. ~happy(john) <- (~15) [avatar component clause 202]
224. brave(X0) | happy(X0) | funny(X0) [subsumption resolution 115,174]
254. curious(sK2) <- (10) [resolution 95,181]
255. $false <- (10, ~12) [subsumption resolution 254,190]
256. ~10 | 12 [avatar contradiction clause 255]
283. 27 <=> kind(john) [avatar definition]
284. ~kind(john) <- (~27) [avatar component clause 283]
285. kind(john) <- (27) [avatar component clause 283]
287. 28 <=> humble(john) [avatar definition]
289. humble(john) <- (28) [avatar component clause 287]
300. $false <- (13) [resolution 195,135]
303. ~13 [avatar contradiction clause 300]
304. humble(john) | kind(john) <- (~14) [resolution 199,121]
308. strong(john) <- (27) [resolution 285,108]
314. $false <- (27) [subsumption resolution 308,135]
315. ~27 [avatar contradiction clause 314]
316. 27 | 28 | 14 [avatar split clause 304,197,287,283]
326. happy(X4) | funny(X4) <- (9) [resolution 224,177]
331. funny(john) <- (9, ~15) [resolution 326,204]
348. kind(john) | ~humble(john) <- (9, ~15) [resolution 331,76]
350. ~humble(john) <- (9, ~15, ~27) [subsumption resolution 348,284]
351. $false <- (9, ~15, ~27, 28) [subsumption resolution 350,289]
352. ~9 | 15 | 27 | ~28 [avatar contradiction clause 351]
356. strong(john) <- (15) [resolution 203,110]
357. $false <- (15) [subsumption resolution 356,135]
358. ~15 [avatar contradiction clause 357]
359. $false [avatar sat refutation 182,191,200,256,303,315,316,352,358]
% SZS output end Proof for 7563734894769850591593581
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or generous is patient. Everyone who is both wise and generous is either not quiet or not generous and vice versa. If paul is not old or not curious then fred is not kind or wise. Everyone who is not quiet or not kind is both creative and not old and vice versa. If someone is either not curious or not brave then someone is not happy or calm. Everyone who is both generous and curious is humble or not quiet and vice versa. If someone is not funny then someone is tall and vice versa. If someone is both generous and quiet then someone is not curious or calm and vice versa. Everyone who is both not generous and not funny is old or not happy and vice versa. Everyone who is curious or not patient is generous and vice versa. If someone is creative then someone is not funny and vice versa. If someone is not brave then fred is either wise or not calm. If someone is either happy or wise then paul is both not brave and humble and vice versa. If someone is both rich and wise then mary is brave. Everyone who is either not old or creative is either not wise or patient and vice versa. Everyone who is both not strong and not kind is either not happy or not quiet. Someone is both tall and curious. Someone is tall. Someone is happy. Fred is either not quiet or generous. Someone is not brave or not wise. | Mary is not kind. | entailment | (![X]:((~old(X)|generous(X))=>patient(X)))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)<~>~generous(X))))&
(((~old(paul)|~curious(paul)))=>((~kind(fred)|wise(fred))))&
(![X]:((~quiet(X)|~kind(X))<=>(creative(X)&~old(X))))&
((?[X]:((~curious(X)<~>~brave(X))))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((generous(X)&curious(X))<=>(humble(X)|~quiet(X))))&
((?[X]:(~funny(X)))<=>(?[X]:(tall(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:((~generous(X)&~funny(X))<=>(old(X)|~happy(X))))&
(![X]:((curious(X)|~patient(X))<=>generous(X)))&
((?[X]:(creative(X)))<=>(?[X]:(~funny(X))))&
((?[X]:(~brave(X)))=>((wise(fred)<~>~calm(fred))))&
((?[X]:((happy(X)<~>wise(X))))<=>((~brave(paul)&humble(paul))))&
((?[X]:((rich(X)&wise(X))))=>(brave(mary)))&
(![X]:((~old(X)<~>creative(X))<=>(~wise(X)<~>patient(X))))&
(![X]:((~strong(X)&~kind(X))=>(~happy(X)<~>~quiet(X))))&
(?[X]:((tall(X)&curious(X))))&
(?[X]:(tall(X)))&
(?[X]:(happy(X)))&
((~quiet(fred)<~>generous(fred)))&
(?[X]:((~brave(X)|~wise(X)))) | ~kind(mary) | [
"p0",
"p1",
"p3",
"p5",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 806736324359091296584947
% SZS output start Proof for 806736324359091296584947
1. ! [X0] : ((generous(X0) | ~old(X0)) => patient(X0)) [input p0]
2. ! [X0] : ((generous(X0) & wise(X0)) <=> (~quiet(X0) <~> ~generous(X0))) [input p1]
4. ! [X0] : ((~kind(X0) | ~quiet(X0)) <=> (~old(X0) & creative(X0))) [input p3]
6. ! [X0] : ((curious(X0) & generous(X0)) <=> (~quiet(X0) | humble(X0))) [input p5]
9. ! [X0] : ((~funny(X0) & ~generous(X0)) <=> (~happy(X0) | old(X0))) [input p8]
15. ! [X0] : ((~old(X0) <~> creative(X0)) <=> (~wise(X0) <~> patient(X0))) [input p14]
22. kind(mary) [input hypothesis]
29. ! [X0] : (patient(X0) | (~generous(X0) & old(X0))) [ennf transformation 1]
34. ! [X0] : (((generous(X0) & wise(X0)) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0)))) & (((generous(X0) | quiet(X0)) & (~generous(X0) | ~quiet(X0))) | (~generous(X0) | ~wise(X0)))) [nnf transformation 2]
35. ! [X0] : (((generous(X0) & wise(X0)) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0)))) & (((generous(X0) | quiet(X0)) & (~generous(X0) | ~quiet(X0))) | ~generous(X0) | ~wise(X0))) [flattening 34]
36. ! [X0] : (((~kind(X0) | ~quiet(X0)) | (old(X0) | ~creative(X0))) & ((~old(X0) & creative(X0)) | (kind(X0) & quiet(X0)))) [nnf transformation 4]
37. ! [X0] : ((~kind(X0) | ~quiet(X0) | old(X0) | ~creative(X0)) & ((~old(X0) & creative(X0)) | (kind(X0) & quiet(X0)))) [flattening 36]
42. ! [X0] : (((curious(X0) & generous(X0)) | (quiet(X0) & ~humble(X0))) & ((~quiet(X0) | humble(X0)) | (~curious(X0) | ~generous(X0)))) [nnf transformation 6]
43. ! [X0] : (((curious(X0) & generous(X0)) | (quiet(X0) & ~humble(X0))) & (~quiet(X0) | humble(X0) | ~curious(X0) | ~generous(X0))) [flattening 42]
54. ! [X0] : (((~funny(X0) & ~generous(X0)) | (happy(X0) & ~old(X0))) & ((~happy(X0) | old(X0)) | (funny(X0) | generous(X0)))) [nnf transformation 9]
55. ! [X0] : (((~funny(X0) & ~generous(X0)) | (happy(X0) & ~old(X0))) & (~happy(X0) | old(X0) | funny(X0) | generous(X0))) [flattening 54]
69. ! [X0] : ((((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | ((~wise(X0) | ~patient(X0)) & (patient(X0) | wise(X0)))) & (((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0))))) [nnf transformation 15]
80. ~generous(X0) | patient(X0) [cnf transformation 29]
81. ~generous(X0) | ~quiet(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 35]
83. ~generous(X0) | wise(X0) | quiet(X0) [cnf transformation 35]
86. generous(X0) | ~quiet(X0) | generous(X0) [cnf transformation 35]
89. creative(X0) | quiet(X0) [cnf transformation 37]
93. ~creative(X0) | ~quiet(X0) | old(X0) | ~kind(X0) [cnf transformation 37]
98. generous(X0) | quiet(X0) [cnf transformation 43]
109. ~generous(X0) | ~old(X0) [cnf transformation 55]
128. ~patient(X0) | wise(X0) | creative(X0) | old(X0) [cnf transformation 69]
133. ~creative(X0) | old(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 69]
141. kind(mary) [cnf transformation 22]
142. ~generous(X0) | ~quiet(X0) | ~wise(X0) [duplicate literal removal 81]
143. ~quiet(X0) | generous(X0) [duplicate literal removal 86]
144. ~quiet(X0) | ~wise(X0) [subsumption resolution 142,143]
179. generous(X0) [subsumption resolution 98,143]
223. ~old(X0) [subsumption resolution 109,179]
268. ~creative(X0) | ~wise(X0) | ~patient(X0) [subsumption resolution 133,223]
269. ~patient(X0) | wise(X0) | creative(X0) [subsumption resolution 128,223]
288. patient(X0) [resolution 80,179]
325. quiet(X0) | wise(X0) [resolution 83,179]
344. ~wise(X1) | ~patient(X1) | quiet(X1) [resolution 268,89]
347. ~wise(X1) | quiet(X1) [subsumption resolution 344,288]
348. quiet(X1) [subsumption resolution 347,325]
349. creative(X0) | wise(X0) [resolution 269,288]
351. ~wise(X0) [resolution 348,144]
368. wise(X0) | ~quiet(X0) | old(X0) | ~kind(X0) [resolution 349,93]
370. ~quiet(X0) | old(X0) | ~kind(X0) [subsumption resolution 368,351]
371. old(X0) | ~kind(X0) [subsumption resolution 370,348]
372. ~kind(X0) [subsumption resolution 371,223]
373. $false [resolution 372,141]
% SZS output end Proof for 806736324359091296584947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both rich and quiet then john is not generous.
Everyone who is not brave is old.
Everyone who is both happy and wise is both old and generous and vice versa.
If someone is rich then someone is not humble or not happy and vice versa.
If paul is strong then someone is not wise or brave and vice versa.
Everyone who is both not generous and not old is quiet and vice versa.
If someone is both not tall and calm then someone is not brave or not generous.
If someone is not wise or not calm then someone is tall or not wise.
Everyone who is strong or not funny is curious or not curious.
If someone is rich then lucy is either not happy or not rich.
If someone is both not patient and not curious then someone is humble or not kind and vice versa.
Everyone who is either calm or wise is not tall and vice versa.
Everyone who is not curious is not strong.
If someone is not creative then someone is both not old and happy and vice versa.
If paul is quiet then someone is both curious and not happy and vice versa.
Everyone who is rich or old is not calm.
Susan is not creative.
Mary is not curious or not happy.
Alice is either strong or not strong.
John is not patient.
Mary is both not happy and not funny.
Susan is not brave.
Mary is not happy or not funny.
Someone is either strong or not tall. | Susan is quiet. | contradiction | (((rich(lucy)&quiet(lucy)))=>(~generous(john)))&
(![X]:(~brave(X)=>old(X)))&
(![X]:((happy(X)&wise(X))<=>(old(X)&generous(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~humble(X)|~happy(X)))))&
((strong(paul))<=>(?[X]:((~wise(X)|brave(X)))))&
(![X]:((~generous(X)&~old(X))<=>quiet(X)))&
((?[X]:((~tall(X)&calm(X))))=>(?[X]:((~brave(X)|~generous(X)))))&
((?[X]:((~wise(X)|~calm(X))))=>(?[X]:((tall(X)|~wise(X)))))&
(![X]:((strong(X)|~funny(X))=>(curious(X)|~curious(X))))&
((?[X]:(rich(X)))=>((~happy(lucy)<~>~rich(lucy))))&
((?[X]:((~patient(X)&~curious(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((calm(X)<~>wise(X))<=>~tall(X)))&
(![X]:(~curious(X)=>~strong(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((~old(X)&happy(X)))))&
((quiet(paul))<=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((rich(X)|old(X))=>~calm(X)))&
(~creative(susan))&
((~curious(mary)|~happy(mary)))&
((strong(alice)<~>~strong(alice)))&
(~patient(john))&
((~happy(mary)&~funny(mary)))&
(~brave(susan))&
((~happy(mary)|~funny(mary)))&
(?[X]:((strong(X)<~>~tall(X)))) | quiet(susan) | [
"p1",
"p5",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5183985965305600551638677
% SZS output start Proof for 5183985965305600551638677
2. ! [X0] : (~brave(X0) => old(X0)) [input p1]
6. ! [X0] : ((~old(X0) & ~generous(X0)) <=> quiet(X0)) [input p5]
22. ~brave(susan) [input p21]
25. quiet(susan) [input hypothesis]
33. ! [X0] : (old(X0) | brave(X0)) [ennf transformation 2]
52. ! [X0] : (((~old(X0) & ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | (old(X0) | generous(X0)))) [nnf transformation 6]
53. ! [X0] : (((~old(X0) & ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | old(X0) | generous(X0))) [flattening 52]
81. old(X0) | brave(X0) [cnf transformation 33]
94. ~old(X0) | ~quiet(X0) [cnf transformation 53]
127. ~brave(susan) [cnf transformation 22]
131. quiet(susan) [cnf transformation 25]
321. ~quiet(X0) | brave(X0) [resolution 94,81]
328. brave(susan) [resolution 321,131]
329. $false [subsumption resolution 328,127]
% SZS output end Proof for 5183985965305600551638677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not curious then someone is both calm and not calm and vice versa.
If someone is either patient or strong then someone is tall.
Everyone who is both humble and not curious is either not rich or not quiet.
Everyone who is rich is not quiet and vice versa.
If lucy is both not strong and not old then paul is not old or not curious and vice versa.
Everyone who is both calm and not humble is humble and vice versa.
If someone is quiet then someone is not quiet and vice versa.
Everyone who is either not kind or not quiet is not kind.
Everyone who is not quiet is either not old or funny and vice versa.
Everyone who is either generous or rich is brave and vice versa.
If someone is both generous and calm then someone is both not rich and not creative and vice versa.
Everyone who is both happy and not patient is happy or not generous.
If someone is either not strong or generous then john is not tall.
If alice is not quiet or not generous then someone is both generous and strong.
If someone is either not wise or not quiet then alice is both not old and not brave and vice versa.
Someone is not curious or creative.
Susan is both not generous and old.
Fred is both strong and funny.
Paul is both not kind and not calm.
John is either kind or not humble.
Someone is curious or patient. | Alice is humble. | contradiction | ((~curious(susan))<=>(?[X]:((calm(X)&~calm(X)))))&
((?[X]:((patient(X)<~>strong(X))))=>(?[X]:(tall(X))))&
(![X]:((humble(X)&~curious(X))=>(~rich(X)<~>~quiet(X))))&
(![X]:(rich(X)<=>~quiet(X)))&
(((~strong(lucy)&~old(lucy)))<=>((~old(paul)|~curious(paul))))&
(![X]:((calm(X)&~humble(X))<=>humble(X)))&
((?[X]:(quiet(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((~kind(X)<~>~quiet(X))=>~kind(X)))&
(![X]:(~quiet(X)<=>(~old(X)<~>funny(X))))&
(![X]:((generous(X)<~>rich(X))<=>brave(X)))&
((?[X]:((generous(X)&calm(X))))<=>(?[X]:((~rich(X)&~creative(X)))))&
(![X]:((happy(X)&~patient(X))=>(happy(X)|~generous(X))))&
((?[X]:((~strong(X)<~>generous(X))))=>(~tall(john)))&
(((~quiet(alice)|~generous(alice)))=>(?[X]:((generous(X)&strong(X)))))&
((?[X]:((~wise(X)<~>~quiet(X))))<=>((~old(alice)&~brave(alice))))&
(?[X]:((~curious(X)|creative(X))))&
((~generous(susan)&old(susan)))&
((strong(fred)&funny(fred)))&
((~kind(paul)&~calm(paul)))&
((kind(john)<~>~humble(john)))&
(?[X]:((curious(X)|patient(X)))) | humble(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6326616859511221872132095
% SZS output start Proof for 6326616859511221872132095
6. ! [X0] : ((~humble(X0) & calm(X0)) <=> humble(X0)) [input p5]
22. humble(alice) [input hypothesis]
46. ! [X0] : (((~humble(X0) & calm(X0)) | ~humble(X0)) & (humble(X0) | (humble(X0) | ~calm(X0)))) [nnf transformation 6]
47. ! [X0] : (((~humble(X0) & calm(X0)) | ~humble(X0)) & (humble(X0) | humble(X0) | ~calm(X0))) [flattening 46]
90. ~humble(X0) | ~humble(X0) [cnf transformation 47]
130. humble(alice) [cnf transformation 22]
133. ~humble(X0) [duplicate literal removal 90]
274. $false [subsumption resolution 130,133]
% SZS output end Proof for 6326616859511221872132095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not patient is both not calm and curious.
If alice is calm then john is either creative or not funny.
If someone is quiet then paul is tall and vice versa.
If someone is both quiet and brave then someone is both patient and strong.
If someone is kind or not patient then mary is either strong or not humble.
Everyone who is both generous and not tall is both curious and kind and vice versa.
Everyone who is either not happy or happy is both not rich and not wise and vice versa.
If john is either tall or not kind then someone is both not happy and rich and vice versa.
If mary is either generous or creative then lucy is both wise and not funny and vice versa.
If someone is either funny or not tall then susan is not funny and vice versa.
If lucy is both not funny and rich then susan is both not old and happy.
If someone is both kind and patient then someone is both not strong and rich.
Everyone who is old or curious is both quiet and happy and vice versa.
Everyone who is both curious and humble is not old or not tall and vice versa.
Everyone who is either calm or rich is either wise or not quiet.
Lucy is brave or kind.
Someone is both creative and not patient.
Someone is not strong.
Someone is either not humble or brave. | Mary is not quiet. | contradiction | (![X]:((funny(X)&~patient(X))=>(~calm(X)&curious(X))))&
((calm(alice))=>((creative(john)<~>~funny(john))))&
((?[X]:(quiet(X)))<=>(tall(paul)))&
((?[X]:((quiet(X)&brave(X))))=>(?[X]:((patient(X)&strong(X)))))&
((?[X]:((kind(X)|~patient(X))))=>((strong(mary)<~>~humble(mary))))&
(![X]:((generous(X)&~tall(X))<=>(curious(X)&kind(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~rich(X)&~wise(X))))&
(((tall(john)<~>~kind(john)))<=>(?[X]:((~happy(X)&rich(X)))))&
(((generous(mary)<~>creative(mary)))<=>((wise(lucy)&~funny(lucy))))&
((?[X]:((funny(X)<~>~tall(X))))<=>(~funny(susan)))&
(((~funny(lucy)&rich(lucy)))=>((~old(susan)&happy(susan))))&
((?[X]:((kind(X)&patient(X))))=>(?[X]:((~strong(X)&rich(X)))))&
(![X]:((old(X)|curious(X))<=>(quiet(X)&happy(X))))&
(![X]:((curious(X)&humble(X))<=>(~old(X)|~tall(X))))&
(![X]:((calm(X)<~>rich(X))=>(wise(X)<~>~quiet(X))))&
((brave(lucy)|kind(lucy)))&
(?[X]:((creative(X)&~patient(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~humble(X)<~>brave(X)))) | ~quiet(mary) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4040506289327490364795755
% SZS output start Proof for 4040506289327490364795755
13. ! [X0] : ((curious(X0) | old(X0)) <=> (happy(X0) & quiet(X0))) [input p12]
14. ! [X0] : ((humble(X0) & curious(X0)) <=> (~tall(X0) | ~old(X0))) [input p13]
20. ~quiet(mary) [input hypothesis]
58. ! [X0] : (((curious(X0) | old(X0)) | (~happy(X0) | ~quiet(X0))) & ((happy(X0) & quiet(X0)) | (~curious(X0) & ~old(X0)))) [nnf transformation 13]
59. ! [X0] : ((curious(X0) | old(X0) | ~happy(X0) | ~quiet(X0)) & ((happy(X0) & quiet(X0)) | (~curious(X0) & ~old(X0)))) [flattening 58]
60. ! [X0] : (((humble(X0) & curious(X0)) | (tall(X0) & old(X0))) & ((~tall(X0) | ~old(X0)) | (~humble(X0) | ~curious(X0)))) [nnf transformation 14]
61. ! [X0] : (((humble(X0) & curious(X0)) | (tall(X0) & old(X0))) & (~tall(X0) | ~old(X0) | ~humble(X0) | ~curious(X0))) [flattening 60]
112. ~old(X0) | quiet(X0) [cnf transformation 59]
113. ~curious(X0) | quiet(X0) [cnf transformation 59]
118. old(X0) | curious(X0) [cnf transformation 61]
132. ~quiet(mary) [cnf transformation 20]
278. curious(X1) | quiet(X1) [resolution 118,112]
280. quiet(X1) [subsumption resolution 278,113]
283. $false [resolution 280,132]
% SZS output end Proof for 4040506289327490364795755
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not calm is both not patient and old and vice versa.
If fred is strong or old then someone is not kind.
Everyone who is both not brave and not humble is both not calm and strong.
Everyone who is either not curious or funny is both curious and creative and vice versa.
Everyone who is both not kind and not curious is both not strong and humble and vice versa.
Everyone who is patient is both brave and not quiet and vice versa.
If mary is brave or quiet then mary is either rich or not patient and vice versa.
Everyone who is both generous and not patient is both not kind and humble.
If someone is either strong or tall then alice is humble.
Everyone who is both not calm and not curious is old or rich and vice versa.
If someone is funny or not brave then someone is not curious or not kind and vice versa.
If someone is not wise or not old then lucy is curious or not calm and vice versa.
Everyone who is not calm is old.
If alice is both not humble and funny then someone is not curious and vice versa.
If susan is not strong then someone is not happy or curious and vice versa.
Everyone who is wise is not patient.
John is both calm and curious.
Someone is brave.
Someone is either happy or funny.
Someone is not quiet or strong.
Lucy is not calm or brave.
Mary is old.
Lucy is either not rich or quiet.
John is both funny and not kind. | Mary is not generous. | neutral | (![X]:((happy(X)|~calm(X))<=>(~patient(X)&old(X))))&
(((strong(fred)|old(fred)))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)&~humble(X))=>(~calm(X)&strong(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(curious(X)&creative(X))))&
(![X]:((~kind(X)&~curious(X))<=>(~strong(X)&humble(X))))&
(![X]:(patient(X)<=>(brave(X)&~quiet(X))))&
(((brave(mary)|quiet(mary)))<=>((rich(mary)<~>~patient(mary))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(![X]:(~calm(X)=>old(X)))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((~strong(susan))<=>(?[X]:((~happy(X)|curious(X)))))&
(![X]:(wise(X)=>~patient(X)))&
((calm(john)&curious(john)))&
(?[X]:(brave(X)))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy)))&
(old(mary))&
((~rich(lucy)<~>quiet(lucy)))&
((funny(john)&~kind(john))) | ~generous(mary) | [] | null | 0 |
Everyone who is quiet is not rich or not old and vice versa. Everyone who is funny or strong is generous. Everyone who is not calm is creative or not old. If someone is not happy then someone is either not brave or not humble and vice versa. If john is either not curious or not patient then susan is not calm. Everyone who is funny or not kind is either not generous or not wise. If susan is not humble or kind then mary is either tall or not generous. Everyone who is wise or rich is tall and vice versa. If fred is either generous or curious then susan is not strong. Everyone who is not funny or humble is both not curious and humble. If lucy is not quiet or creative then someone is either not funny or not brave. If susan is either creative or funny then john is both not tall and calm. Everyone who is creative is brave or not brave. Everyone who is quiet or funny is either generous or calm. Everyone who is both not humble and rich is not quiet and vice versa. If someone is brave then alice is wise or humble. Someone is not wise or not funny. John is not quiet or rich. Someone is not tall. Alice is not strong or tall. John is either not humble or quiet. Someone is both old and not kind. Lucy is not quiet. | Alice is not wise. | neutral | (![X]:(quiet(X)<=>(~rich(X)|~old(X))))&
(![X]:((funny(X)|strong(X))=>generous(X)))&
(![X]:(~calm(X)=>(creative(X)|~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(((~curious(john)<~>~patient(john)))=>(~calm(susan)))&
(![X]:((funny(X)|~kind(X))=>(~generous(X)<~>~wise(X))))&
(((~humble(susan)|kind(susan)))=>((tall(mary)<~>~generous(mary))))&
(![X]:((wise(X)|rich(X))<=>tall(X)))&
(((generous(fred)<~>curious(fred)))=>(~strong(susan)))&
(![X]:((~funny(X)|humble(X))=>(~curious(X)&humble(X))))&
(((~quiet(lucy)|creative(lucy)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(((creative(susan)<~>funny(susan)))=>((~tall(john)&calm(john))))&
(![X]:(creative(X)=>(brave(X)|~brave(X))))&
(![X]:((quiet(X)|funny(X))=>(generous(X)<~>calm(X))))&
(![X]:((~humble(X)&rich(X))<=>~quiet(X)))&
((?[X]:(brave(X)))=>((wise(alice)|humble(alice))))&
(?[X]:((~wise(X)|~funny(X))))&
((~quiet(john)|rich(john)))&
(?[X]:(~tall(X)))&
((~strong(alice)|tall(alice)))&
((~humble(john)<~>quiet(john)))&
(?[X]:((old(X)&~kind(X))))&
(~quiet(lucy)) | ~wise(alice) | [] | null | 0 |
Everyone who is kind or not creative is either not wise or rich.
If someone is both brave and funny then lucy is both not generous and humble.
If someone is either not humble or creative then john is both not brave and not strong.
Everyone who is tall or kind is quiet or not rich.
If someone is old then someone is not brave or not generous.
If susan is both not brave and happy then someone is either humble or not humble.
Everyone who is not calm or wise is wise.
If mary is both not creative and not happy then someone is not patient or kind and vice versa.
Everyone who is not kind or not wise is both rich and not curious and vice versa.
Everyone who is wise or not wise is both curious and not generous and vice versa.
Everyone who is creative or not patient is humble or tall and vice versa.
If someone is either not quiet or quiet then someone is not creative and vice versa.
Everyone who is not strong is either not rich or kind and vice versa.
If someone is not curious then lucy is both not patient and not brave and vice versa.
Everyone who is both patient and not calm is not patient.
If someone is both quiet and calm then someone is brave or old.
Susan is humble or not creative.
Lucy is either calm or not creative.
Someone is not brave.
John is either not old or tall.
Someone is both not brave and old.
Alice is either not patient or not wise.
Mary is both not funny and brave.
Paul is either not tall or quiet. | Mary is quiet. | entailment | (![X]:((kind(X)|~creative(X))=>(~wise(X)<~>rich(X))))&
((?[X]:((brave(X)&funny(X))))=>((~generous(lucy)&humble(lucy))))&
((?[X]:((~humble(X)<~>creative(X))))=>((~brave(john)&~strong(john))))&
(![X]:((tall(X)|kind(X))=>(quiet(X)|~rich(X))))&
((?[X]:(old(X)))=>(?[X]:((~brave(X)|~generous(X)))))&
(((~brave(susan)&happy(susan)))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~calm(X)|wise(X))=>wise(X)))&
(((~creative(mary)&~happy(mary)))<=>(?[X]:((~patient(X)|kind(X)))))&
(![X]:((~kind(X)|~wise(X))<=>(rich(X)&~curious(X))))&
(![X]:((wise(X)|~wise(X))<=>(curious(X)&~generous(X))))&
(![X]:((creative(X)|~patient(X))<=>(humble(X)|tall(X))))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)<=>(~rich(X)<~>kind(X))))&
((?[X]:(~curious(X)))<=>((~patient(lucy)&~brave(lucy))))&
(![X]:((patient(X)&~calm(X))=>~patient(X)))&
((?[X]:((quiet(X)&calm(X))))=>(?[X]:((brave(X)|old(X)))))&
((humble(susan)|~creative(susan)))&
((calm(lucy)<~>~creative(lucy)))&
(?[X]:(~brave(X)))&
((~old(john)<~>tall(john)))&
(?[X]:((~brave(X)&old(X))))&
((~patient(alice)<~>~wise(alice)))&
((~funny(mary)&brave(mary)))&
((~tall(paul)<~>quiet(paul))) | quiet(mary) | [
"p0",
"p3",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 163930091828257451288719
% SZS output start Proof for 163930091828257451288719
1. ! [X0] : ((~creative(X0) | kind(X0)) => (~wise(X0) <~> rich(X0))) [input p0]
4. ! [X0] : ((kind(X0) | tall(X0)) => (~rich(X0) | quiet(X0))) [input p3]
9. ! [X0] : ((~wise(X0) | ~kind(X0)) <=> (~curious(X0) & rich(X0))) [input p8]
10. ! [X0] : ((~wise(X0) | wise(X0)) <=> (~generous(X0) & curious(X0))) [input p9]
25. ~quiet(mary) [input hypothesis]
32. ! [X0] : ((~wise(X0) <~> rich(X0)) | (creative(X0) & ~kind(X0))) [ennf transformation 1]
34. ! [X0] : ((~rich(X0) | quiet(X0)) | (~kind(X0) & ~tall(X0))) [ennf transformation 4]
35. ! [X0] : (~rich(X0) | quiet(X0) | (~kind(X0) & ~tall(X0))) [flattening 34]
44. ! [X0] : (((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | (creative(X0) & ~kind(X0))) [nnf transformation 32]
57. ! [X0] : (((~wise(X0) | ~kind(X0)) | (curious(X0) | ~rich(X0))) & ((~curious(X0) & rich(X0)) | (wise(X0) & kind(X0)))) [nnf transformation 9]
58. ! [X0] : ((~wise(X0) | ~kind(X0) | curious(X0) | ~rich(X0)) & ((~curious(X0) & rich(X0)) | (wise(X0) & kind(X0)))) [flattening 57]
59. ! [X0] : (((~wise(X0) | wise(X0)) | (generous(X0) | ~curious(X0))) & ((~generous(X0) & curious(X0)) | (wise(X0) & ~wise(X0)))) [nnf transformation 10]
60. ! [X0] : ((~wise(X0) | wise(X0) | generous(X0) | ~curious(X0)) & ((~generous(X0) & curious(X0)) | (wise(X0) & ~wise(X0)))) [flattening 59]
85. ~wise(X0) | rich(X0) | ~kind(X0) [cnf transformation 44]
94. ~rich(X0) | quiet(X0) | ~kind(X0) [cnf transformation 35]
107. ~curious(X0) | kind(X0) [cnf transformation 58]
108. ~curious(X0) | wise(X0) [cnf transformation 58]
110. curious(X0) | ~wise(X0) [cnf transformation 60]
111. curious(X0) | wise(X0) [cnf transformation 60]
143. ~quiet(mary) [cnf transformation 25]
206. wise(X0) [subsumption resolution 111,108]
207. curious(X0) [subsumption resolution 110,206]
217. 16 <=> ! [X3] : quiet(X3) [avatar definition]
218. quiet(X3) <- (16) [avatar component clause 217]
285. kind(X0) [resolution 107,207]
293. rich(X0) | ~kind(X0) [resolution 85,206]
294. rich(X0) [subsumption resolution 293,285]
306. quiet(X0) | ~kind(X0) [resolution 94,294]
310. quiet(X0) [subsumption resolution 306,285]
311. 16 [avatar split clause 310,217]
313. $false <- (16) [resolution 218,143]
316. ~16 [avatar contradiction clause 313]
317. $false [avatar sat refutation 311,316]
% SZS output end Proof for 163930091828257451288719
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and kind is happy and vice versa. If lucy is both brave and humble then someone is creative or not calm. If someone is either curious or creative then susan is either calm or creative. If mary is generous then someone is not brave or not patient and vice versa. Everyone who is either not wise or not happy is kind or patient and vice versa. Everyone who is either not tall or not calm is not rich. Everyone who is both rich and not patient is tall or curious. Everyone who is not creative is both not quiet and happy. If someone is brave or strong then someone is either not tall or happy and vice versa. Everyone who is not wise or not kind is happy. If fred is either not calm or tall then lucy is not brave or kind. Everyone who is not curious or generous is curious and vice versa. Everyone who is either not happy or not calm is not tall and vice versa. Everyone who is either tall or not quiet is either wise or not funny and vice versa. Fred is both quiet and funny. Lucy is both not brave and creative. Fred is happy or brave. Someone is not kind or not tall. Mary is both not humble and brave. Someone is not patient. Lucy is either not humble or funny. | Lucy is rich. | contradiction | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((creative(X)|~calm(X)))))&
((?[X]:((curious(X)<~>creative(X))))=>((calm(susan)<~>creative(susan))))&
((generous(mary))<=>(?[X]:((~brave(X)|~patient(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(kind(X)|patient(X))))&
(![X]:((~tall(X)<~>~calm(X))=>~rich(X)))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
((quiet(fred)&funny(fred)))&
((~brave(lucy)&creative(lucy)))&
((happy(fred)|brave(fred)))&
(?[X]:((~kind(X)|~tall(X))))&
((~humble(mary)&brave(mary)))&
(?[X]:(~patient(X)))&
((~humble(lucy)<~>funny(lucy))) | rich(lucy) | [
"p0",
"p5",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7604811921727406788669822
% SZS output start Proof for 7604811921727406788669822
1. ! [X0] : ((kind(X0) & ~curious(X0)) <=> happy(X0)) [input p0]
6. ! [X0] : ((~tall(X0) <~> ~calm(X0)) => ~rich(X0)) [input p5]
12. ! [X0] : ((generous(X0) | ~curious(X0)) <=> curious(X0)) [input p11]
13. ! [X0] : ((~happy(X0) <~> ~calm(X0)) <=> ~tall(X0)) [input p12]
22. rich(lucy) [input hypothesis]
27. ! [X0] : (~rich(X0) | (~tall(X0) <=> ~calm(X0))) [ennf transformation 6]
34. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | (~kind(X0) | curious(X0)))) [nnf transformation 1]
35. ! [X0] : (((kind(X0) & ~curious(X0)) | ~happy(X0)) & (happy(X0) | ~kind(X0) | curious(X0))) [flattening 34]
45. ! [X0] : (~rich(X0) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0)))) [nnf transformation 27]
52. ! [X0] : (((generous(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [nnf transformation 12]
53. ! [X0] : ((generous(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [flattening 52]
54. ! [X0] : ((((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | tall(X0)) & (~tall(X0) | ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))))) [nnf transformation 13]
62. ~happy(X0) | ~curious(X0) [cnf transformation 35]
78. ~rich(X0) | ~calm(X0) | tall(X0) [cnf transformation 45]
79. ~rich(X0) | ~tall(X0) | calm(X0) [cnf transformation 45]
93. curious(X0) | curious(X0) [cnf transformation 53]
96. ~tall(X0) | ~calm(X0) | happy(X0) [cnf transformation 54]
99. tall(X0) | happy(X0) | calm(X0) [cnf transformation 54]
119. rich(lucy) [cnf transformation 22]
120. curious(X0) [duplicate literal removal 93]
248. ~calm(lucy) | tall(lucy) [resolution 78,119]
250. 25 <=> tall(lucy) [avatar definition]
251. ~tall(lucy) <- (~25) [avatar component clause 250]
252. tall(lucy) <- (25) [avatar component clause 250]
254. 26 <=> calm(lucy) [avatar definition]
255. calm(lucy) <- (26) [avatar component clause 254]
256. ~calm(lucy) <- (~26) [avatar component clause 254]
257. 25 | ~26 [avatar split clause 248,254,250]
258. ~tall(lucy) | calm(lucy) [resolution 79,119]
263. happy(lucy) | calm(lucy) <- (~25) [resolution 99,251]
268. happy(lucy) <- (~25, ~26) [subsumption resolution 263,256]
300. ~curious(lucy) <- (~25, ~26) [resolution 268,62]
301. $false <- (~25, ~26) [subsumption resolution 300,120]
302. 25 | 26 [avatar contradiction clause 301]
303. 26 | ~25 [avatar split clause 258,250,254]
306. ~calm(lucy) | happy(lucy) <- (25) [resolution 252,96]
307. happy(lucy) <- (25, 26) [subsumption resolution 306,255]
351. ~curious(lucy) <- (25, 26) [resolution 307,62]
352. $false <- (25, 26) [subsumption resolution 351,120]
353. ~25 | ~26 [avatar contradiction clause 352]
354. $false [avatar sat refutation 257,302,303,353]
% SZS output end Proof for 7604811921727406788669822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not kind is either quiet or happy and vice versa.
Everyone who is either patient or not calm is not kind or not curious and vice versa.
If alice is not calm or old then someone is either funny or not tall and vice versa.
If someone is calm or humble then someone is both funny and happy.
Everyone who is not generous is both brave and not kind and vice versa.
If lucy is rich or humble then someone is either happy or kind.
If someone is not brave or kind then lucy is either not funny or not strong and vice versa.
If john is not curious or not tall then mary is wise and vice versa.
If someone is generous then lucy is either generous or not strong.
If someone is not patient or not rich then lucy is both not generous and not humble.
Everyone who is either not patient or not kind is not quiet and vice versa.
Everyone who is both not strong and not generous is not happy or not kind and vice versa.
If someone is either not calm or not generous then someone is rich or wise and vice versa.
Everyone who is either kind or humble is either not patient or not old and vice versa.
Everyone who is old is either humble or not generous.
Everyone who is either not calm or kind is not happy and vice versa.
Someone is either tall or not rich.
John is quiet.
Someone is not creative.
Lucy is both happy and humble.
Someone is patient or not strong.
Someone is both not kind and not curious.
Lucy is wise or humble. | John is not brave. | neutral | (![X]:((~funny(X)&~kind(X))<=>(quiet(X)<~>happy(X))))&
(![X]:((patient(X)<~>~calm(X))<=>(~kind(X)|~curious(X))))&
(((~calm(alice)|old(alice)))<=>(?[X]:((funny(X)<~>~tall(X)))))&
((?[X]:((calm(X)|humble(X))))=>(?[X]:((funny(X)&happy(X)))))&
(![X]:(~generous(X)<=>(brave(X)&~kind(X))))&
(((rich(lucy)|humble(lucy)))=>(?[X]:((happy(X)<~>kind(X)))))&
((?[X]:((~brave(X)|kind(X))))<=>((~funny(lucy)<~>~strong(lucy))))&
(((~curious(john)|~tall(john)))<=>(wise(mary)))&
((?[X]:(generous(X)))=>((generous(lucy)<~>~strong(lucy))))&
((?[X]:((~patient(X)|~rich(X))))=>((~generous(lucy)&~humble(lucy))))&
(![X]:((~patient(X)<~>~kind(X))<=>~quiet(X)))&
(![X]:((~strong(X)&~generous(X))<=>(~happy(X)|~kind(X))))&
((?[X]:((~calm(X)<~>~generous(X))))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((kind(X)<~>humble(X))<=>(~patient(X)<~>~old(X))))&
(![X]:(old(X)=>(humble(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>kind(X))<=>~happy(X)))&
(?[X]:((tall(X)<~>~rich(X))))&
(quiet(john))&
(?[X]:(~creative(X)))&
((happy(lucy)&humble(lucy)))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:((~kind(X)&~curious(X))))&
((wise(lucy)|humble(lucy))) | ~brave(john) | [] | null | 0 |
If someone is not generous then someone is not brave or rich and vice versa.
If fred is generous or not funny then someone is strong or creative.
If paul is either funny or not creative then mary is not creative and vice versa.
Everyone who is quiet is strong.
If someone is either not humble or old then someone is both not old and not patient.
Everyone who is strong or old is quiet or not old and vice versa.
Everyone who is not patient is not rich or creative.
Everyone who is not patient is brave.
Everyone who is not humble or creative is not curious.
Everyone who is both happy and quiet is either not calm or not quiet and vice versa.
Everyone who is either not wise or funny is not generous.
If someone is either funny or not generous then mary is both strong and not humble and vice versa.
Everyone who is creative or not calm is either not old or not tall and vice versa.
Everyone who is either humble or not rich is both not generous and not curious.
If paul is either not wise or not tall then someone is creative or quiet and vice versa.
Everyone who is either not kind or not curious is not kind and vice versa.
Someone is not rich.
Someone is not brave.
Lucy is not funny.
Someone is not funny or calm.
Someone is not funny or not wise.
Alice is either kind or tall.
Someone is not happy or funny.
Alice is not old or happy. | Alice is not creative. | entailment | ((?[X]:(~generous(X)))<=>(?[X]:((~brave(X)|rich(X)))))&
(((generous(fred)|~funny(fred)))=>(?[X]:((strong(X)|creative(X)))))&
(((funny(paul)<~>~creative(paul)))<=>(~creative(mary)))&
(![X]:(quiet(X)=>strong(X)))&
((?[X]:((~humble(X)<~>old(X))))=>(?[X]:((~old(X)&~patient(X)))))&
(![X]:((strong(X)|old(X))<=>(quiet(X)|~old(X))))&
(![X]:(~patient(X)=>(~rich(X)|creative(X))))&
(![X]:(~patient(X)=>brave(X)))&
(![X]:((~humble(X)|creative(X))=>~curious(X)))&
(![X]:((happy(X)&quiet(X))<=>(~calm(X)<~>~quiet(X))))&
(![X]:((~wise(X)<~>funny(X))=>~generous(X)))&
((?[X]:((funny(X)<~>~generous(X))))<=>((strong(mary)&~humble(mary))))&
(![X]:((creative(X)|~calm(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((humble(X)<~>~rich(X))=>(~generous(X)&~curious(X))))&
(((~wise(paul)<~>~tall(paul)))<=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:((~kind(X)<~>~curious(X))<=>~kind(X)))&
(?[X]:(~rich(X)))&
(?[X]:(~brave(X)))&
(~funny(lucy))&
(?[X]:((~funny(X)|calm(X))))&
(?[X]:((~funny(X)|~wise(X))))&
((kind(alice)<~>tall(alice)))&
(?[X]:((~happy(X)|funny(X))))&
((~old(alice)|happy(alice))) | ~creative(alice) | [
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8805598145908180581829978
% SZS output start Proof for 8805598145908180581829978
9. ! [X0] : ((creative(X0) | ~humble(X0)) => ~curious(X0)) [input p8]
16. ! [X0] : ((~kind(X0) <~> ~curious(X0)) <=> ~kind(X0)) [input p15]
25. creative(alice) [input hypothesis]
34. ! [X0] : (~curious(X0) | (~creative(X0) & humble(X0))) [ennf transformation 9]
66. ! [X0] : ((((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | kind(X0)) & (~kind(X0) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0))))) [nnf transformation 16]
99. ~curious(X0) | ~creative(X0) [cnf transformation 34]
131. ~kind(X0) | ~kind(X0) | curious(X0) [cnf transformation 66]
133. curious(X0) | kind(X0) | kind(X0) [cnf transformation 66]
143. creative(alice) [cnf transformation 25]
144. ~kind(X0) | curious(X0) [duplicate literal removal 131]
145. curious(X0) | kind(X0) [duplicate literal removal 133]
269. 27 <=> ! [X0] : ~creative(X0) [avatar definition]
270. ~creative(X0) <- (27) [avatar component clause 269]
284. curious(X0) [subsumption resolution 144,145]
331. $false <- (27) [resolution 270,143]
332. ~27 [avatar contradiction clause 331]
338. ~creative(X0) [resolution 99,284]
339. 27 [avatar split clause 338,269]
340. $false [avatar sat refutation 332,339]
% SZS output end Proof for 8805598145908180581829978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or patient is both old and not brave and vice versa.
Everyone who is happy is not kind or tall.
Everyone who is not patient or not curious is not creative or not curious and vice versa.
If someone is rich then alice is both generous and funny and vice versa.
Everyone who is old is both not wise and not calm.
If susan is either creative or quiet then someone is either quiet or wise.
Everyone who is not rich or not quiet is either not creative or curious and vice versa.
If someone is not old then susan is brave and vice versa.
Everyone who is both rich and strong is not kind or old and vice versa.
Everyone who is patient or not kind is both not tall and not patient.
Everyone who is not curious is either not strong or wise.
If john is not patient or old then paul is either generous or happy and vice versa.
Everyone who is both not quiet and tall is either not patient or old.
If someone is either not happy or strong then someone is not happy and vice versa.
If fred is both not happy and not generous then someone is both tall and humble.
If someone is not funny or calm then susan is both not quiet and quiet and vice versa.
Someone is both not calm and not wise.
Susan is not strong.
Paul is humble or not old.
Someone is either creative or not wise.
Fred is not curious or curious.
Someone is not humble or strong.
John is either not calm or creative.
John is not tall or not quiet. | John is calm. | contradiction | (![X]:((rich(X)|patient(X))<=>(old(X)&~brave(X))))&
(![X]:(happy(X)=>(~kind(X)|tall(X))))&
(![X]:((~patient(X)|~curious(X))<=>(~creative(X)|~curious(X))))&
((?[X]:(rich(X)))<=>((generous(alice)&funny(alice))))&
(![X]:(old(X)=>(~wise(X)&~calm(X))))&
(((creative(susan)<~>quiet(susan)))=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:((~rich(X)|~quiet(X))<=>(~creative(X)<~>curious(X))))&
((?[X]:(~old(X)))<=>(brave(susan)))&
(![X]:((rich(X)&strong(X))<=>(~kind(X)|old(X))))&
(![X]:((patient(X)|~kind(X))=>(~tall(X)&~patient(X))))&
(![X]:(~curious(X)=>(~strong(X)<~>wise(X))))&
(((~patient(john)|old(john)))<=>((generous(paul)<~>happy(paul))))&
(![X]:((~quiet(X)&tall(X))=>(~patient(X)<~>old(X))))&
((?[X]:((~happy(X)<~>strong(X))))<=>(?[X]:(~happy(X))))&
(((~happy(fred)&~generous(fred)))=>(?[X]:((tall(X)&humble(X)))))&
((?[X]:((~funny(X)|calm(X))))<=>((~quiet(susan)&quiet(susan))))&
(?[X]:((~calm(X)&~wise(X))))&
(~strong(susan))&
((humble(paul)|~old(paul)))&
(?[X]:((creative(X)<~>~wise(X))))&
((~curious(fred)|curious(fred)))&
(?[X]:((~humble(X)|strong(X))))&
((~calm(john)<~>creative(john)))&
((~tall(john)|~quiet(john))) | calm(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3028779863397210603738696
% SZS output start Proof for 3028779863397210603738696
16. ? [X0] : (calm(X0) | ~funny(X0)) <=> (quiet(susan) & ~quiet(susan)) [input p15]
25. calm(john) [input hypothesis]
68. (? [X0] : (calm(X0) | ~funny(X0)) | (~quiet(susan) | quiet(susan))) & ((quiet(susan) & ~quiet(susan)) | ! [X0] : (~calm(X0) & funny(X0))) [nnf transformation 16]
69. (? [X0] : (calm(X0) | ~funny(X0)) | ~quiet(susan) | quiet(susan)) & ((quiet(susan) & ~quiet(susan)) | ! [X0] : (~calm(X0) & funny(X0))) [flattening 68]
70. (? [X0] : (calm(X0) | ~funny(X0)) | ~quiet(susan) | quiet(susan)) & ((quiet(susan) & ~quiet(susan)) | ! [X1] : (~calm(X1) & funny(X1))) [rectify 69]
71. ? [X0] : (calm(X0) | ~funny(X0)) => (calm(sK6) | ~funny(sK6)) [choice axiom]
72. ((calm(sK6) | ~funny(sK6)) | ~quiet(susan) | quiet(susan)) & ((quiet(susan) & ~quiet(susan)) | ! [X1] : (~calm(X1) & funny(X1))) [skolemisation 70,71]
134. ~quiet(susan) | ~calm(X1) [cnf transformation 72]
136. quiet(susan) | ~calm(X1) [cnf transformation 72]
149. calm(john) [cnf transformation 25]
170. 5 <=> quiet(susan) [avatar definition]
265. 25 <=> ! [X1] : ~calm(X1) [avatar definition]
266. ~calm(X1) <- (25) [avatar component clause 265]
267. 25 | 5 [avatar split clause 136,170,265]
272. 25 | ~5 [avatar split clause 134,170,265]
303. 33 <=> calm(john) [avatar definition]
305. calm(john) <- (33) [avatar component clause 303]
321. 33 [avatar split clause 149,303]
324. $false <- (25, 33) [resolution 305,266]
325. ~25 | ~33 [avatar contradiction clause 324]
326. $false [avatar sat refutation 267,272,321,325]
% SZS output end Proof for 3028779863397210603738696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is both not rich and funny and vice versa.
Everyone who is brave or happy is curious.
If someone is both rich and not curious then alice is either creative or kind.
Everyone who is not creative is both rich and tall and vice versa.
Everyone who is both quiet and funny is both calm and kind.
Everyone who is not funny is brave or old.
Everyone who is not kind is both not humble and old and vice versa.
Everyone who is not creative or strong is not strong or quiet.
Everyone who is either funny or not humble is not generous and vice versa.
Everyone who is both not happy and not funny is kind or funny.
Everyone who is either not brave or not funny is either not strong or wise and vice versa.
Everyone who is not humble or happy is either not humble or not patient and vice versa.
If someone is humble then lucy is either not humble or old.
Everyone who is either old or brave is both creative and not humble.
Everyone who is both not rich and not tall is either not rich or calm and vice versa.
Everyone who is either not calm or not old is either not patient or not strong and vice versa.
Someone is kind or calm.
Someone is either not strong or not rich.
Lucy is both creative and not old.
Paul is not happy.
Fred is either rich or not kind.
Mary is generous or calm.
Mary is funny.
Someone is generous. | Lucy is not rich. | entailment | (![X]:(brave(X)<=>(~rich(X)&funny(X))))&
(![X]:((brave(X)|happy(X))=>curious(X)))&
((?[X]:((rich(X)&~curious(X))))=>((creative(alice)<~>kind(alice))))&
(![X]:(~creative(X)<=>(rich(X)&tall(X))))&
(![X]:((quiet(X)&funny(X))=>(calm(X)&kind(X))))&
(![X]:(~funny(X)=>(brave(X)|old(X))))&
(![X]:(~kind(X)<=>(~humble(X)&old(X))))&
(![X]:((~creative(X)|strong(X))=>(~strong(X)|quiet(X))))&
(![X]:((funny(X)<~>~humble(X))<=>~generous(X)))&
(![X]:((~happy(X)&~funny(X))=>(kind(X)|funny(X))))&
(![X]:((~brave(X)<~>~funny(X))<=>(~strong(X)<~>wise(X))))&
(![X]:((~humble(X)|happy(X))<=>(~humble(X)<~>~patient(X))))&
((?[X]:(humble(X)))=>((~humble(lucy)<~>old(lucy))))&
(![X]:((old(X)<~>brave(X))=>(creative(X)&~humble(X))))&
(![X]:((~rich(X)&~tall(X))<=>(~rich(X)<~>calm(X))))&
(![X]:((~calm(X)<~>~old(X))<=>(~patient(X)<~>~strong(X))))&
(?[X]:((kind(X)|calm(X))))&
(?[X]:((~strong(X)<~>~rich(X))))&
((creative(lucy)&~old(lucy)))&
(~happy(paul))&
((rich(fred)<~>~kind(fred)))&
((generous(mary)|calm(mary)))&
(funny(mary))&
(?[X]:(generous(X))) | ~rich(lucy) | [
"p0",
"p4",
"p5",
"p7",
"p11",
"p12",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6229313858983776398274842
% SZS output start Proof for 6229313858983776398274842
1. ! [X0] : (brave(X0) <=> (funny(X0) & ~rich(X0))) [input p0]
5. ! [X0] : ((funny(X0) & quiet(X0)) => (kind(X0) & calm(X0))) [input p4]
6. ! [X0] : (~funny(X0) => (old(X0) | brave(X0))) [input p5]
8. ! [X0] : ((strong(X0) | ~creative(X0)) => (quiet(X0) | ~strong(X0))) [input p7]
12. ! [X0] : ((happy(X0) | ~humble(X0)) <=> (~humble(X0) <~> ~patient(X0))) [input p11]
13. ? [X0] : humble(X0) => (~humble(lucy) <~> old(lucy)) [input p12]
15. ! [X0] : ((~tall(X0) & ~rich(X0)) <=> (~rich(X0) <~> calm(X0))) [input p14]
16. ! [X0] : ((~calm(X0) <~> ~old(X0)) <=> (~patient(X0) <~> ~strong(X0))) [input p15]
19. ~old(lucy) & creative(lucy) [input p18]
25. rich(lucy) [input hypothesis]
32. ! [X0] : ((kind(X0) & calm(X0)) | (~funny(X0) | ~quiet(X0))) [ennf transformation 5]
33. ! [X0] : ((kind(X0) & calm(X0)) | ~funny(X0) | ~quiet(X0)) [flattening 32]
34. ! [X0] : ((old(X0) | brave(X0)) | funny(X0)) [ennf transformation 6]
35. ! [X0] : (old(X0) | brave(X0) | funny(X0)) [flattening 34]
36. ! [X0] : ((quiet(X0) | ~strong(X0)) | (~strong(X0) & creative(X0))) [ennf transformation 8]
37. ! [X0] : (quiet(X0) | ~strong(X0) | (~strong(X0) & creative(X0))) [flattening 36]
41. (~humble(lucy) <~> old(lucy)) | ! [X0] : ~humble(X0) [ennf transformation 13]
43. ! [X0] : ((brave(X0) | (~funny(X0) | rich(X0))) & ((funny(X0) & ~rich(X0)) | ~brave(X0))) [nnf transformation 1]
44. ! [X0] : ((brave(X0) | ~funny(X0) | rich(X0)) & ((funny(X0) & ~rich(X0)) | ~brave(X0))) [flattening 43]
49. ! [X0] : (((happy(X0) | ~humble(X0)) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) & (((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | (~happy(X0) & humble(X0)))) [nnf transformation 12]
50. ! [X0] : ((happy(X0) | ~humble(X0) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) & (((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | (~happy(X0) & humble(X0)))) [flattening 49]
51. ((~old(lucy) | humble(lucy)) & (old(lucy) | ~humble(lucy))) | ! [X0] : ~humble(X0) [nnf transformation 41]
53. ! [X0] : (((~tall(X0) & ~rich(X0)) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0)))) & (((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | (tall(X0) | rich(X0)))) [nnf transformation 15]
54. ! [X0] : (((~tall(X0) & ~rich(X0)) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0)))) & (((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | tall(X0) | rich(X0))) [flattening 53]
55. ! [X0] : ((((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))))) [nnf transformation 16]
65. ~brave(X0) | funny(X0) [cnf transformation 44]
68. ~quiet(X0) | ~funny(X0) | calm(X0) [cnf transformation 33]
70. old(X0) | brave(X0) | funny(X0) [cnf transformation 35]
75. quiet(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 37]
89. patient(X0) | humble(X0) | humble(X0) [cnf transformation 50]
93. old(lucy) | ~humble(lucy) | ~humble(X0) [cnf transformation 51]
102. ~rich(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 54]
112. ~patient(X0) | calm(X0) | old(X0) | strong(X0) [cnf transformation 55]
117. ~old(lucy) [cnf transformation 19]
124. rich(lucy) [cnf transformation 25]
126. ~calm(X0) | ~rich(X0) [duplicate literal removal 102]
127. patient(X0) | humble(X0) [duplicate literal removal 89]
130. ~strong(X0) | quiet(X0) [duplicate literal removal 75]
131. old(X0) | funny(X0) [subsumption resolution 70,65]
137. 1 <=> ! [X0] : ~humble(X0) [avatar definition]
138. ~humble(X0) <- (1) [avatar component clause 137]
140. 2 <=> humble(lucy) [avatar definition]
141. ~humble(lucy) <- (~2) [avatar component clause 140]
142. humble(lucy) <- (2) [avatar component clause 140]
144. 3 <=> old(lucy) [avatar definition]
146. ~old(lucy) <- (~3) [avatar component clause 144]
148. 1 | ~2 | 3 [avatar split clause 93,144,140,137]
169. ~3 [avatar split clause 117,144]
192. funny(lucy) <- (~3) [resolution 131,146]
379. strong(X0) | old(X0) | calm(X0) | humble(X0) [resolution 112,127]
508. humble(X5) | calm(X5) | old(X5) | quiet(X5) [resolution 379,130]
578. calm(lucy) | old(lucy) | quiet(lucy) <- (~2) [resolution 508,141]
584. calm(lucy) | quiet(lucy) <- (~2, ~3) [subsumption resolution 578,146]
586. 45 <=> quiet(lucy) [avatar definition]
588. quiet(lucy) <- (45) [avatar component clause 586]
590. 46 <=> calm(lucy) [avatar definition]
592. calm(lucy) <- (46) [avatar component clause 590]
593. 45 | 46 | 2 | 3 [avatar split clause 584,144,140,590,586]
614. ~funny(lucy) | calm(lucy) <- (45) [resolution 588,68]
615. calm(lucy) <- (~3, 45) [subsumption resolution 614,192]
616. 46 | 3 | ~45 [avatar split clause 615,586,144,590]
626. ~rich(lucy) <- (46) [resolution 592,126]
640. $false <- (46) [subsumption resolution 626,124]
641. ~46 [avatar contradiction clause 640]
644. $false <- (1, 2) [resolution 142,138]
650. ~1 | ~2 [avatar contradiction clause 644]
656. $false [avatar sat refutation 148,169,593,616,641,650]
% SZS output end Proof for 6229313858983776398274842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or calm is either quiet or not humble.
If john is both not kind and creative then someone is both not creative and not kind and vice versa.
Everyone who is brave or wise is old or curious and vice versa.
If someone is both not calm and not humble then alice is creative and vice versa.
Everyone who is curious is not rich and vice versa.
If fred is either not wise or not quiet then john is either quiet or not calm and vice versa.
Everyone who is either not tall or happy is either brave or generous.
Everyone who is not funny or not wise is kind.
Everyone who is both not creative and not tall is both rich and patient and vice versa.
Everyone who is not happy or generous is rich or happy and vice versa.
If someone is strong then lucy is funny.
Everyone who is either not quiet or not humble is humble.
If alice is either not tall or not humble then john is both not patient and old.
Everyone who is not quiet is both tall and not happy and vice versa.
If someone is both tall and not strong then john is either old or not tall and vice versa.
If someone is curious then susan is both creative and not quiet and vice versa.
Mary is either old or curious.
Someone is generous or calm.
Lucy is either not calm or not curious.
Susan is either not brave or tall.
Someone is either patient or not tall.
Fred is patient.
Someone is either patient or not kind. | John is not creative. | neutral | (![X]:((tall(X)<~>calm(X))=>(quiet(X)<~>~humble(X))))&
(((~kind(john)&creative(john)))<=>(?[X]:((~creative(X)&~kind(X)))))&
(![X]:((brave(X)|wise(X))<=>(old(X)|curious(X))))&
((?[X]:((~calm(X)&~humble(X))))<=>(creative(alice)))&
(![X]:(curious(X)<=>~rich(X)))&
(((~wise(fred)<~>~quiet(fred)))<=>((quiet(john)<~>~calm(john))))&
(![X]:((~tall(X)<~>happy(X))=>(brave(X)<~>generous(X))))&
(![X]:((~funny(X)|~wise(X))=>kind(X)))&
(![X]:((~creative(X)&~tall(X))<=>(rich(X)&patient(X))))&
(![X]:((~happy(X)|generous(X))<=>(rich(X)|happy(X))))&
((?[X]:(strong(X)))=>(funny(lucy)))&
(![X]:((~quiet(X)<~>~humble(X))=>humble(X)))&
(((~tall(alice)<~>~humble(alice)))=>((~patient(john)&old(john))))&
(![X]:(~quiet(X)<=>(tall(X)&~happy(X))))&
((?[X]:((tall(X)&~strong(X))))<=>((old(john)<~>~tall(john))))&
((?[X]:(curious(X)))<=>((creative(susan)&~quiet(susan))))&
((old(mary)<~>curious(mary)))&
(?[X]:((generous(X)|calm(X))))&
((~calm(lucy)<~>~curious(lucy)))&
((~brave(susan)<~>tall(susan)))&
(?[X]:((patient(X)<~>~tall(X))))&
(patient(fred))&
(?[X]:((patient(X)<~>~kind(X)))) | ~creative(john) | [] | null | 0 |
Everyone who is both brave and wise is both not kind and patient. If someone is quiet then someone is both creative and not funny. Everyone who is curious or funny is both curious and not creative and vice versa. If susan is tall then alice is both quiet and tall and vice versa. If someone is not patient or strong then someone is both not patient and not strong and vice versa. Everyone who is happy or not tall is quiet or not quiet. If someone is both quiet and not creative then someone is brave or not happy and vice versa. Everyone who is either brave or humble is both not calm and happy and vice versa. Everyone who is both not creative and curious is not old or happy and vice versa. Everyone who is either creative or funny is funny and vice versa. Everyone who is either not rich or creative is both not patient and not humble and vice versa. If john is not wise or generous then someone is both not funny and not kind. If someone is not old or not curious then fred is either strong or not rich. If alice is both not tall and not humble then susan is either humble or not quiet and vice versa. Everyone who is not humble is either funny or not creative. Everyone who is humble or not quiet is not strong or rich and vice versa. Someone is not patient or not kind. Someone is either strong or kind. Alice is both not creative and strong. Fred is either wise or not rich. Mary is either rich or not brave. | Susan is not wise. | neutral | (![X]:((brave(X)&wise(X))=>(~kind(X)&patient(X))))&
((?[X]:(quiet(X)))=>(?[X]:((creative(X)&~funny(X)))))&
(![X]:((curious(X)|funny(X))<=>(curious(X)&~creative(X))))&
((tall(susan))<=>((quiet(alice)&tall(alice))))&
((?[X]:((~patient(X)|strong(X))))<=>(?[X]:((~patient(X)&~strong(X)))))&
(![X]:((happy(X)|~tall(X))=>(quiet(X)|~quiet(X))))&
((?[X]:((quiet(X)&~creative(X))))<=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((brave(X)<~>humble(X))<=>(~calm(X)&happy(X))))&
(![X]:((~creative(X)&curious(X))<=>(~old(X)|happy(X))))&
(![X]:((creative(X)<~>funny(X))<=>funny(X)))&
(![X]:((~rich(X)<~>creative(X))<=>(~patient(X)&~humble(X))))&
(((~wise(john)|generous(john)))=>(?[X]:((~funny(X)&~kind(X)))))&
((?[X]:((~old(X)|~curious(X))))=>((strong(fred)<~>~rich(fred))))&
(((~tall(alice)&~humble(alice)))<=>((humble(susan)<~>~quiet(susan))))&
(![X]:(~humble(X)=>(funny(X)<~>~creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~strong(X)|rich(X))))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((strong(X)<~>kind(X))))&
((~creative(alice)&strong(alice)))&
((wise(fred)<~>~rich(fred)))&
((rich(mary)<~>~brave(mary))) | ~wise(susan) | [] | null | 0 |
Everyone who is either not strong or generous is both not wise and happy and vice versa. Everyone who is both kind and brave is patient. Everyone who is either not tall or tall is both happy and rich. Everyone who is happy is not curious or quiet. If someone is either generous or not curious then lucy is either tall or humble. If someone is not happy or not curious then someone is both happy and not funny and vice versa. If fred is either not patient or humble then mary is quiet or wise and vice versa. If someone is both not rich and not brave then alice is either funny or calm and vice versa. If fred is either not old or not creative then susan is rich and vice versa. If lucy is not generous then alice is funny or curious. Everyone who is old or not curious is both not funny and curious. Everyone who is either patient or brave is not strong. If john is both calm and not brave then someone is creative. If mary is both not patient and not creative then fred is both not rich and not kind. If someone is both rich and not tall then someone is both not strong and not curious and vice versa. Everyone who is both tall and quiet is either old or not kind. Lucy is not creative or generous. Someone is not patient or not kind. Someone is generous or not brave. Someone is happy or calm. Someone is old or not wise. Susan is either not rich or not patient. | Susan is kind. | contradiction | (![X]:((~strong(X)<~>generous(X))<=>(~wise(X)&happy(X))))&
(![X]:((kind(X)&brave(X))=>patient(X)))&
(![X]:((~tall(X)<~>tall(X))=>(happy(X)&rich(X))))&
(![X]:(happy(X)=>(~curious(X)|quiet(X))))&
((?[X]:((generous(X)<~>~curious(X))))=>((tall(lucy)<~>humble(lucy))))&
((?[X]:((~happy(X)|~curious(X))))<=>(?[X]:((happy(X)&~funny(X)))))&
(((~patient(fred)<~>humble(fred)))<=>((quiet(mary)|wise(mary))))&
((?[X]:((~rich(X)&~brave(X))))<=>((funny(alice)<~>calm(alice))))&
(((~old(fred)<~>~creative(fred)))<=>(rich(susan)))&
((~generous(lucy))=>((funny(alice)|curious(alice))))&
(![X]:((old(X)|~curious(X))=>(~funny(X)&curious(X))))&
(![X]:((patient(X)<~>brave(X))=>~strong(X)))&
(((calm(john)&~brave(john)))=>(?[X]:(creative(X))))&
(((~patient(mary)&~creative(mary)))=>((~rich(fred)&~kind(fred))))&
((?[X]:((rich(X)&~tall(X))))<=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((tall(X)&quiet(X))=>(old(X)<~>~kind(X))))&
((~creative(lucy)|generous(lucy)))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((generous(X)|~brave(X))))&
(?[X]:((happy(X)|calm(X))))&
(?[X]:((old(X)|~wise(X))))&
((~rich(susan)<~>~patient(susan))) | kind(susan) | [
"p2",
"p3",
"p5",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4473066378682183411513287
% SZS output start Proof for 4473066378682183411513287
3. ! [X0] : ((~tall(X0) <~> tall(X0)) => (rich(X0) & happy(X0))) [input p2]
4. ! [X0] : (happy(X0) => (quiet(X0) | ~curious(X0))) [input p3]
6. ? [X0] : (~curious(X0) | ~happy(X0)) <=> ? [X0] : (~funny(X0) & happy(X0)) [input p5]
11. ! [X0] : ((~curious(X0) | old(X0)) => (curious(X0) & ~funny(X0))) [input p10]
15. ? [X0] : (~tall(X0) & rich(X0)) <=> ? [X0] : (~curious(X0) & ~strong(X0)) [input p14]
16. ! [X0] : ((quiet(X0) & tall(X0)) => (old(X0) <~> ~kind(X0))) [input p15]
23. kind(susan) [input hypothesis]
24. ? [X0] : (~curious(X0) | ~happy(X0)) <=> ? [X1] : (~funny(X1) & happy(X1)) [rectify 6]
25. ? [X0] : (~tall(X0) & rich(X0)) <=> ? [X1] : (~curious(X1) & ~strong(X1)) [rectify 15]
28. ! [X0] : ((rich(X0) & happy(X0)) | (~tall(X0) <=> tall(X0))) [ennf transformation 3]
29. ! [X0] : ((quiet(X0) | ~curious(X0)) | ~happy(X0)) [ennf transformation 4]
30. ! [X0] : (quiet(X0) | ~curious(X0) | ~happy(X0)) [flattening 29]
34. ! [X0] : ((curious(X0) & ~funny(X0)) | (curious(X0) & ~old(X0))) [ennf transformation 11]
40. ! [X0] : ((old(X0) <~> ~kind(X0)) | (~quiet(X0) | ~tall(X0))) [ennf transformation 16]
41. ! [X0] : ((old(X0) <~> ~kind(X0)) | ~quiet(X0) | ~tall(X0)) [flattening 40]
44. ! [X0] : ((rich(X0) & happy(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) [nnf transformation 28]
46. (? [X0] : (~curious(X0) | ~happy(X0)) | ! [X1] : (funny(X1) | ~happy(X1))) & (? [X1] : (~funny(X1) & happy(X1)) | ! [X0] : (curious(X0) & happy(X0))) [nnf transformation 24]
47. (? [X0] : (~curious(X0) | ~happy(X0)) | ! [X1] : (funny(X1) | ~happy(X1))) & (? [X2] : (~funny(X2) & happy(X2)) | ! [X3] : (curious(X3) & happy(X3))) [rectify 46]
48. ? [X0] : (~curious(X0) | ~happy(X0)) => (~curious(sK0) | ~happy(sK0)) [choice axiom]
49. ? [X2] : (~funny(X2) & happy(X2)) => (~funny(sK1) & happy(sK1)) [choice axiom]
50. ((~curious(sK0) | ~happy(sK0)) | ! [X1] : (funny(X1) | ~happy(X1))) & ((~funny(sK1) & happy(sK1)) | ! [X3] : (curious(X3) & happy(X3))) [skolemisation 47,49,48]
61. (? [X0] : (~tall(X0) & rich(X0)) | ! [X1] : (curious(X1) | strong(X1))) & (? [X1] : (~curious(X1) & ~strong(X1)) | ! [X0] : (tall(X0) | ~rich(X0))) [nnf transformation 25]
62. (? [X0] : (~tall(X0) & rich(X0)) | ! [X1] : (curious(X1) | strong(X1))) & (? [X2] : (~curious(X2) & ~strong(X2)) | ! [X3] : (tall(X3) | ~rich(X3))) [rectify 61]
63. ? [X0] : (~tall(X0) & rich(X0)) => (~tall(sK4) & rich(sK4)) [choice axiom]
64. ? [X2] : (~curious(X2) & ~strong(X2)) => (~curious(sK5) & ~strong(sK5)) [choice axiom]
65. ((~tall(sK4) & rich(sK4)) | ! [X1] : (curious(X1) | strong(X1))) & ((~curious(sK5) & ~strong(sK5)) | ! [X3] : (tall(X3) | ~rich(X3))) [skolemisation 62,64,63]
66. ! [X0] : (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | ~quiet(X0) | ~tall(X0)) [nnf transformation 41]
83. happy(X0) | tall(X0) | tall(X0) [cnf transformation 44]
84. happy(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 44]
85. rich(X0) | tall(X0) | tall(X0) [cnf transformation 44]
86. rich(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 44]
87. quiet(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 30]
96. ~curious(sK0) | ~happy(sK0) | funny(X1) | ~happy(X1) [cnf transformation 50]
114. ~old(X0) | ~funny(X0) [cnf transformation 34]
117. curious(X0) | curious(X0) [cnf transformation 34]
124. ~curious(sK5) | tall(X3) | ~rich(X3) [cnf transformation 65]
127. ~quiet(X0) | old(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 66]
136. kind(susan) [cnf transformation 23]
137. curious(X0) [duplicate literal removal 117]
138. happy(X0) | tall(X0) [duplicate literal removal 83]
139. ~tall(X0) | happy(X0) [duplicate literal removal 84]
140. rich(X0) | tall(X0) [duplicate literal removal 85]
141. ~tall(X0) | rich(X0) [duplicate literal removal 86]
142. rich(X0) [subsumption resolution 140,141]
143. happy(X0) [subsumption resolution 138,139]
144. ~curious(X0) | quiet(X0) [subsumption resolution 87,143]
163. ~curious(sK0) | funny(X1) | ~happy(X1) [subsumption resolution 96,143]
164. ~curious(sK0) | funny(X1) [subsumption resolution 163,143]
166. 5 <=> ! [X1] : funny(X1) [avatar definition]
167. funny(X1) <- (5) [avatar component clause 166]
169. 6 <=> curious(sK0) [avatar definition]
171. ~curious(sK0) <- (~6) [avatar component clause 169]
172. 5 | ~6 [avatar split clause 164,169,166]
174. 7 <=> ! [X3] : curious(X3) [avatar definition]
175. curious(X3) <- (7) [avatar component clause 174]
242. 7 [avatar split clause 137,174]
279. ~curious(sK5) | tall(X3) [subsumption resolution 124,142]
281. 28 <=> ! [X3] : tall(X3) [avatar definition]
282. tall(X3) <- (28) [avatar component clause 281]
284. 29 <=> curious(sK5) [avatar definition]
286. ~curious(sK5) <- (~29) [avatar component clause 284]
287. 28 | ~29 [avatar split clause 279,284,281]
327. $false <- (~6, 7) [subsumption resolution 171,175]
328. 6 | ~7 [avatar contradiction clause 327]
329. $false <- (7, ~29) [resolution 286,175]
330. ~7 | 29 [avatar contradiction clause 329]
342. quiet(X0) <- (7) [resolution 144,175]
367. old(X0) | ~kind(X0) | ~tall(X0) <- (7) [resolution 127,342]
368. ~kind(X0) | old(X0) <- (7, 28) [subsumption resolution 367,282]
369. old(susan) <- (7, 28) [resolution 368,136]
372. ~funny(susan) <- (7, 28) [resolution 369,114]
373. $false <- (5, 7, 28) [subsumption resolution 372,167]
374. ~5 | ~7 | ~28 [avatar contradiction clause 373]
375. $false [avatar sat refutation 172,242,287,328,330,374]
% SZS output end Proof for 4473066378682183411513287
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient then fred is not happy.
Everyone who is old is happy or not kind and vice versa.
If someone is not calm or tall then someone is either not humble or not strong and vice versa.
Everyone who is not kind is both wise and not strong.
Everyone who is either old or not curious is either not strong or generous and vice versa.
If someone is either not funny or not creative then someone is either not brave or brave and vice versa.
If someone is either not rich or not wise then paul is either not curious or not brave and vice versa.
If someone is curious or not tall then someone is kind and vice versa.
Everyone who is either not patient or creative is either not patient or not curious and vice versa.
Everyone who is either not patient or quiet is wise or humble and vice versa.
Everyone who is not strong is not old.
Everyone who is either strong or tall is quiet or happy.
Everyone who is either not happy or not strong is both curious and not humble and vice versa.
Everyone who is generous or not brave is either not patient or funny and vice versa.
If fred is both not creative and old then fred is strong or quiet and vice versa.
Everyone who is generous is either not creative or patient.
Someone is not wise.
Someone is not kind or happy.
Someone is not rich.
Mary is either not strong or not humble.
Someone is not rich or not funny.
Someone is both old and not brave.
Mary is not tall or not kind.
Paul is not quiet. | Fred is not old. | entailment | ((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:(~kind(X)=>(wise(X)&~strong(X))))&
(![X]:((old(X)<~>~curious(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>(?[X]:((~brave(X)<~>brave(X)))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>((~curious(paul)<~>~brave(paul))))&
((?[X]:((curious(X)|~tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((~patient(X)<~>creative(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((~patient(X)<~>quiet(X))<=>(wise(X)|humble(X))))&
(![X]:(~strong(X)=>~old(X)))&
(![X]:((strong(X)<~>tall(X))=>(quiet(X)|happy(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>(curious(X)&~humble(X))))&
(![X]:((generous(X)|~brave(X))<=>(~patient(X)<~>funny(X))))&
(((~creative(fred)&old(fred)))<=>((strong(fred)|quiet(fred))))&
(![X]:(generous(X)=>(~creative(X)<~>patient(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~kind(X)|happy(X))))&
(?[X]:(~rich(X)))&
((~strong(mary)<~>~humble(mary)))&
(?[X]:((~rich(X)|~funny(X))))&
(?[X]:((old(X)&~brave(X))))&
((~tall(mary)|~kind(mary)))&
(~quiet(paul)) | ~old(fred) | [
"p0",
"p1",
"p3",
"p4",
"p8",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8557229986025677664251673
% SZS output start Proof for 8557229986025677664251673
1. ? [X0] : ~patient(X0) => ~happy(fred) [input p0]
2. ! [X0] : (old(X0) <=> (~kind(X0) | happy(X0))) [input p1]
4. ! [X0] : (~kind(X0) => (~strong(X0) & wise(X0))) [input p3]
5. ! [X0] : ((old(X0) <~> ~curious(X0)) <=> (~strong(X0) <~> generous(X0))) [input p4]
9. ! [X0] : ((~patient(X0) <~> creative(X0)) <=> (~patient(X0) <~> ~curious(X0))) [input p8]
11. ! [X0] : (~strong(X0) => ~old(X0)) [input p10]
15. (old(fred) & ~creative(fred)) <=> (quiet(fred) | strong(fred)) [input p14]
16. ! [X0] : (generous(X0) => (~creative(X0) <~> patient(X0))) [input p15]
25. old(fred) [input hypothesis]
29. ~happy(fred) | ! [X0] : patient(X0) [ennf transformation 1]
30. ! [X0] : ((~strong(X0) & wise(X0)) | kind(X0)) [ennf transformation 4]
31. ! [X0] : (~old(X0) | strong(X0)) [ennf transformation 11]
34. ! [X0] : ((~creative(X0) <~> patient(X0)) | ~generous(X0)) [ennf transformation 16]
35. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | ~old(X0))) [nnf transformation 2]
36. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | ~old(X0))) [flattening 35]
42. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [nnf transformation 5]
57. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) & (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [nnf transformation 9]
65. ((old(fred) & ~creative(fred)) | (~quiet(fred) & ~strong(fred))) & ((quiet(fred) | strong(fred)) | (~old(fred) | creative(fred))) [nnf transformation 15]
66. ((old(fred) & ~creative(fred)) | (~quiet(fred) & ~strong(fred))) & (quiet(fred) | strong(fred) | ~old(fred) | creative(fred)) [flattening 65]
67. ! [X0] : (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | ~generous(X0)) [nnf transformation 34]
79. ~happy(fred) | patient(X0) [cnf transformation 29]
80. ~kind(X0) | happy(X0) | ~old(X0) [cnf transformation 36]
90. ~strong(X0) | kind(X0) [cnf transformation 30]
91. ~curious(X0) | ~strong(X0) | generous(X0) | ~old(X0) [cnf transformation 42]
120. curious(X0) | patient(X0) | creative(X0) | patient(X0) [cnf transformation 57]
123. creative(X0) | ~patient(X0) | ~patient(X0) | curious(X0) [cnf transformation 57]
132. ~old(X0) | strong(X0) [cnf transformation 31]
148. ~creative(fred) | ~strong(fred) [cnf transformation 66]
153. ~generous(X0) | creative(X0) | ~patient(X0) [cnf transformation 67]
164. old(fred) [cnf transformation 25]
166. curious(X0) | patient(X0) | creative(X0) [duplicate literal removal 120]
167. ~patient(X0) | creative(X0) | curious(X0) [duplicate literal removal 123]
174. 1 <=> ! [X0] : patient(X0) [avatar definition]
175. patient(X0) <- (1) [avatar component clause 174]
177. 2 <=> happy(fred) [avatar definition]
180. 1 | ~2 [avatar split clause 79,177,174]
287. creative(X0) | curious(X0) [subsumption resolution 166,167]
294. 28 <=> old(fred) [avatar definition]
296. old(fred) <- (28) [avatar component clause 294]
299. 29 <=> strong(fred) [avatar definition]
300. strong(fred) <- (29) [avatar component clause 299]
304. 30 <=> creative(fred) [avatar definition]
306. ~creative(fred) <- (~30) [avatar component clause 304]
308. ~29 | ~30 [avatar split clause 148,304,299]
346. 28 [avatar split clause 164,294]
353. strong(fred) <- (28) [resolution 132,296]
355. 29 | ~28 [avatar split clause 353,294,299]
356. kind(fred) <- (29) [resolution 300,90]
358. curious(fred) <- (~30) [resolution 287,306]
402. happy(fred) | ~old(fred) <- (29) [resolution 356,80]
406. happy(fred) <- (28, 29) [subsumption resolution 402,296]
407. 2 | ~28 | ~29 [avatar split clause 406,299,294,177]
481. ~strong(fred) | generous(fred) | ~old(fred) <- (~30) [resolution 91,358]
485. generous(fred) | ~old(fred) <- (29, ~30) [subsumption resolution 481,300]
486. generous(fred) <- (28, 29, ~30) [subsumption resolution 485,296]
499. creative(fred) | ~patient(fred) <- (28, 29, ~30) [resolution 486,153]
501. ~patient(fred) <- (28, 29, ~30) [subsumption resolution 499,306]
502. $false <- (1, 28, 29, ~30) [subsumption resolution 501,175]
503. ~1 | ~28 | ~29 | 30 [avatar contradiction clause 502]
505. $false [avatar sat refutation 180,308,346,355,407,503]
% SZS output end Proof for 8557229986025677664251673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and strong then someone is humble or not humble.
Everyone who is either humble or funny is either not funny or not wise.
If someone is either not wise or not rich then alice is happy and vice versa.
Everyone who is both patient and not humble is either brave or not happy and vice versa.
Everyone who is not old or not funny is either not patient or not strong.
Everyone who is not happy is both not kind and brave.
Everyone who is both strong and tall is both not strong and not old.
Everyone who is not curious or not humble is both creative and not patient.
Everyone who is either funny or not humble is not quiet or not creative.
If someone is patient or not creative then someone is either old or generous.
Everyone who is not brave is strong or not tall and vice versa.
If john is not generous then fred is kind.
If lucy is not kind then someone is either not creative or not curious.
If susan is not kind then mary is both not funny and not quiet and vice versa.
Everyone who is both humble and not creative is either generous or not generous and vice versa.
Everyone who is not quiet or calm is either wise or quiet.
Someone is either not kind or funny.
Someone is both patient and not creative.
Fred is old or happy.
Mary is either patient or not kind.
Someone is strong.
Someone is both brave and quiet.
Someone is either not rich or not wise. | Fred is old. | neutral | ((?[X]:((tall(X)&strong(X))))=>(?[X]:((humble(X)|~humble(X)))))&
(![X]:((humble(X)<~>funny(X))=>(~funny(X)<~>~wise(X))))&
((?[X]:((~wise(X)<~>~rich(X))))<=>(happy(alice)))&
(![X]:((patient(X)&~humble(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((~old(X)|~funny(X))=>(~patient(X)<~>~strong(X))))&
(![X]:(~happy(X)=>(~kind(X)&brave(X))))&
(![X]:((strong(X)&tall(X))=>(~strong(X)&~old(X))))&
(![X]:((~curious(X)|~humble(X))=>(creative(X)&~patient(X))))&
(![X]:((funny(X)<~>~humble(X))=>(~quiet(X)|~creative(X))))&
((?[X]:((patient(X)|~creative(X))))=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:(~brave(X)<=>(strong(X)|~tall(X))))&
((~generous(john))=>(kind(fred)))&
((~kind(lucy))=>(?[X]:((~creative(X)<~>~curious(X)))))&
((~kind(susan))<=>((~funny(mary)&~quiet(mary))))&
(![X]:((humble(X)&~creative(X))<=>(generous(X)<~>~generous(X))))&
(![X]:((~quiet(X)|calm(X))=>(wise(X)<~>quiet(X))))&
(?[X]:((~kind(X)<~>funny(X))))&
(?[X]:((patient(X)&~creative(X))))&
((old(fred)|happy(fred)))&
((patient(mary)<~>~kind(mary)))&
(?[X]:(strong(X)))&
(?[X]:((brave(X)&quiet(X))))&
(?[X]:((~rich(X)<~>~wise(X)))) | old(fred) | [] | null | 0 |
Everyone who is both not rich and quiet is calm.
Everyone who is either not quiet or humble is either creative or not quiet and vice versa.
Everyone who is both wise and generous is either not generous or patient.
Everyone who is either rich or not wise is both brave and not tall.
Everyone who is both not rich and tall is both tall and kind and vice versa.
Everyone who is either tall or funny is either not tall or creative.
Everyone who is old is both not humble and not creative.
If fred is either humble or not creative then someone is both not rich and not calm.
If someone is not calm or not humble then mary is not tall.
Everyone who is not rich is both not humble and not funny and vice versa.
Everyone who is not strong or curious is both not strong and strong and vice versa.
Everyone who is creative is both happy and creative and vice versa.
Everyone who is both not rich and calm is either not funny or not tall.
If mary is not quiet then someone is not strong and vice versa.
If alice is both not funny and not creative then someone is tall and vice versa.
Everyone who is not wise or not strong is both not quiet and not brave and vice versa.
Someone is both not creative and not calm.
Someone is either not kind or not tall.
Paul is not rich.
Alice is patient.
Someone is both not humble and brave.
Alice is either funny or not tall.
Someone is both not kind and not calm.
Someone is both creative and funny. | Fred is kind. | neutral | (![X]:((~rich(X)&quiet(X))=>calm(X)))&
(![X]:((~quiet(X)<~>humble(X))<=>(creative(X)<~>~quiet(X))))&
(![X]:((wise(X)&generous(X))=>(~generous(X)<~>patient(X))))&
(![X]:((rich(X)<~>~wise(X))=>(brave(X)&~tall(X))))&
(![X]:((~rich(X)&tall(X))<=>(tall(X)&kind(X))))&
(![X]:((tall(X)<~>funny(X))=>(~tall(X)<~>creative(X))))&
(![X]:(old(X)=>(~humble(X)&~creative(X))))&
(((humble(fred)<~>~creative(fred)))=>(?[X]:((~rich(X)&~calm(X)))))&
((?[X]:((~calm(X)|~humble(X))))=>(~tall(mary)))&
(![X]:(~rich(X)<=>(~humble(X)&~funny(X))))&
(![X]:((~strong(X)|curious(X))<=>(~strong(X)&strong(X))))&
(![X]:(creative(X)<=>(happy(X)&creative(X))))&
(![X]:((~rich(X)&calm(X))=>(~funny(X)<~>~tall(X))))&
((~quiet(mary))<=>(?[X]:(~strong(X))))&
(((~funny(alice)&~creative(alice)))<=>(?[X]:(tall(X))))&
(![X]:((~wise(X)|~strong(X))<=>(~quiet(X)&~brave(X))))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:((~kind(X)<~>~tall(X))))&
(~rich(paul))&
(patient(alice))&
(?[X]:((~humble(X)&brave(X))))&
((funny(alice)<~>~tall(alice)))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((creative(X)&funny(X)))) | kind(fred) | [] | null | 0 |
Everyone who is either tall or not patient is either not curious or strong and vice versa. Everyone who is not calm is either not tall or not old. Everyone who is not kind is both quiet and brave and vice versa. If someone is not happy or generous then someone is funny or humble and vice versa. If someone is both curious and not humble then someone is not patient or brave. Everyone who is both funny and happy is humble. Everyone who is strong is either generous or not strong and vice versa. Everyone who is funny is both humble and kind. Everyone who is not funny or humble is not funny or calm and vice versa. If someone is not wise then lucy is rich or not old. If john is both creative and not patient then someone is not brave and vice versa. If john is brave then john is curious or not brave and vice versa. Everyone who is not patient or not curious is either strong or not humble. If someone is either not humble or brave then alice is calm. Everyone who is wise or old is not curious and vice versa. Someone is both not tall and curious. Someone is either not old or not rich. Someone is old. Someone is either not tall or not quiet. Paul is not kind. Susan is both rich and wise. Lucy is either not quiet or not brave. | Lucy is not old. | neutral | (![X]:((tall(X)<~>~patient(X))<=>(~curious(X)<~>strong(X))))&
(![X]:(~calm(X)=>(~tall(X)<~>~old(X))))&
(![X]:(~kind(X)<=>(quiet(X)&brave(X))))&
((?[X]:((~happy(X)|generous(X))))<=>(?[X]:((funny(X)|humble(X)))))&
((?[X]:((curious(X)&~humble(X))))=>(?[X]:((~patient(X)|brave(X)))))&
(![X]:((funny(X)&happy(X))=>humble(X)))&
(![X]:(strong(X)<=>(generous(X)<~>~strong(X))))&
(![X]:(funny(X)=>(humble(X)&kind(X))))&
(![X]:((~funny(X)|humble(X))<=>(~funny(X)|calm(X))))&
((?[X]:(~wise(X)))=>((rich(lucy)|~old(lucy))))&
(((creative(john)&~patient(john)))<=>(?[X]:(~brave(X))))&
((brave(john))<=>((curious(john)|~brave(john))))&
(![X]:((~patient(X)|~curious(X))=>(strong(X)<~>~humble(X))))&
((?[X]:((~humble(X)<~>brave(X))))=>(calm(alice)))&
(![X]:((wise(X)|old(X))<=>~curious(X)))&
(?[X]:((~tall(X)&curious(X))))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:(old(X)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(~kind(paul))&
((rich(susan)&wise(susan)))&
((~quiet(lucy)<~>~brave(lucy))) | ~old(lucy) | [] | null | 0 |
If alice is either rich or not calm then someone is both quiet and not patient and vice versa. Everyone who is either happy or not strong is both not brave and not happy. If someone is rich then susan is happy and vice versa. If someone is patient or not curious then someone is creative and vice versa. Everyone who is not wise or not humble is not creative or rich. Everyone who is not happy or patient is both not kind and funny. If lucy is either not funny or happy then fred is either not humble or not funny and vice versa. Everyone who is both not generous and not kind is either not generous or generous and vice versa. If paul is both kind and patient then someone is both not calm and happy and vice versa. If fred is not generous then fred is old. Everyone who is both patient and quiet is both not kind and not humble. If someone is either not quiet or rich then someone is not creative or not strong and vice versa. If someone is old or not curious then someone is creative and vice versa. Everyone who is both not rich and strong is both brave and not rich and vice versa. If someone is either rich or generous then someone is not quiet and vice versa. Everyone who is calm is not calm. Susan is rich or wise. Susan is not brave or not kind. Paul is either not creative or brave. Someone is not tall or curious. Someone is happy or curious. Someone is not kind or not quiet. Someone is not calm or patient. | Lucy is not strong. | contradiction | (((rich(alice)<~>~calm(alice)))<=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((happy(X)<~>~strong(X))=>(~brave(X)&~happy(X))))&
((?[X]:(rich(X)))<=>(happy(susan)))&
((?[X]:((patient(X)|~curious(X))))<=>(?[X]:(creative(X))))&
(![X]:((~wise(X)|~humble(X))=>(~creative(X)|rich(X))))&
(![X]:((~happy(X)|patient(X))=>(~kind(X)&funny(X))))&
(((~funny(lucy)<~>happy(lucy)))<=>((~humble(fred)<~>~funny(fred))))&
(![X]:((~generous(X)&~kind(X))<=>(~generous(X)<~>generous(X))))&
(((kind(paul)&patient(paul)))<=>(?[X]:((~calm(X)&happy(X)))))&
((~generous(fred))=>(old(fred)))&
(![X]:((patient(X)&quiet(X))=>(~kind(X)&~humble(X))))&
((?[X]:((~quiet(X)<~>rich(X))))<=>(?[X]:((~creative(X)|~strong(X)))))&
((?[X]:((old(X)|~curious(X))))<=>(?[X]:(creative(X))))&
(![X]:((~rich(X)&strong(X))<=>(brave(X)&~rich(X))))&
((?[X]:((rich(X)<~>generous(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(calm(X)=>~calm(X)))&
((rich(susan)|wise(susan)))&
((~brave(susan)|~kind(susan)))&
((~creative(paul)<~>brave(paul)))&
(?[X]:((~tall(X)|curious(X))))&
(?[X]:((happy(X)|curious(X))))&
(?[X]:((~kind(X)|~quiet(X))))&
(?[X]:((~calm(X)|patient(X)))) | ~strong(lucy) | [
"p2",
"p7",
"p8",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1122113596645118264504368
% SZS output start Proof for 1122113596645118264504368
3. ? [X0] : rich(X0) <=> happy(susan) [input p2]
8. ! [X0] : ((~kind(X0) & ~generous(X0)) <=> (~generous(X0) <~> generous(X0))) [input p7]
9. (patient(paul) & kind(paul)) <=> ? [X0] : (happy(X0) & ~calm(X0)) [input p8]
12. ? [X0] : (~quiet(X0) <~> rich(X0)) <=> ? [X0] : (~strong(X0) | ~creative(X0)) [input p11]
15. ? [X0] : (rich(X0) <~> generous(X0)) <=> ? [X0] : ~quiet(X0) [input p14]
16. ! [X0] : (calm(X0) => ~calm(X0)) [input p15]
24. ~strong(lucy) [input hypothesis]
26. ? [X0] : (~quiet(X0) <~> rich(X0)) <=> ? [X1] : (~strong(X1) | ~creative(X1)) [rectify 12]
28. ? [X0] : (rich(X0) <~> generous(X0)) <=> ? [X1] : ~quiet(X1) [rectify 15]
39. ! [X0] : (~calm(X0) | ~calm(X0)) [ennf transformation 16]
45. (? [X0] : rich(X0) | ~happy(susan)) & (happy(susan) | ! [X0] : ~rich(X0)) [nnf transformation 3]
46. (? [X0] : rich(X0) | ~happy(susan)) & (happy(susan) | ! [X1] : ~rich(X1)) [rectify 45]
47. ? [X0] : rich(X0) => rich(sK1) [choice axiom]
48. (rich(sK1) | ~happy(susan)) & (happy(susan) | ! [X1] : ~rich(X1)) [skolemisation 46,47]
55. ! [X0] : (((~kind(X0) & ~generous(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (kind(X0) | generous(X0)))) [nnf transformation 8]
56. ! [X0] : (((~kind(X0) & ~generous(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | kind(X0) | generous(X0))) [flattening 55]
57. ((patient(paul) & kind(paul)) | ! [X0] : (~happy(X0) | calm(X0))) & (? [X0] : (happy(X0) & ~calm(X0)) | (~patient(paul) | ~kind(paul))) [nnf transformation 9]
58. ((patient(paul) & kind(paul)) | ! [X0] : (~happy(X0) | calm(X0))) & (? [X0] : (happy(X0) & ~calm(X0)) | ~patient(paul) | ~kind(paul)) [flattening 57]
59. ((patient(paul) & kind(paul)) | ! [X0] : (~happy(X0) | calm(X0))) & (? [X1] : (happy(X1) & ~calm(X1)) | ~patient(paul) | ~kind(paul)) [rectify 58]
60. ? [X1] : (happy(X1) & ~calm(X1)) => (happy(sK4) & ~calm(sK4)) [choice axiom]
61. ((patient(paul) & kind(paul)) | ! [X0] : (~happy(X0) | calm(X0))) & ((happy(sK4) & ~calm(sK4)) | ~patient(paul) | ~kind(paul)) [skolemisation 59,60]
62. (? [X0] : ((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | ! [X1] : (strong(X1) & creative(X1))) & (? [X1] : (~strong(X1) | ~creative(X1)) | ! [X0] : ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) [nnf transformation 26]
63. (? [X0] : ((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | ! [X1] : (strong(X1) & creative(X1))) & (? [X2] : (~strong(X2) | ~creative(X2)) | ! [X3] : ((~quiet(X3) | ~rich(X3)) & (rich(X3) | quiet(X3)))) [rectify 62]
64. ? [X0] : ((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) => ((~rich(sK5) | quiet(sK5)) & (rich(sK5) | ~quiet(sK5))) [choice axiom]
65. ? [X2] : (~strong(X2) | ~creative(X2)) => (~strong(sK6) | ~creative(sK6)) [choice axiom]
66. (((~rich(sK5) | quiet(sK5)) & (rich(sK5) | ~quiet(sK5))) | ! [X1] : (strong(X1) & creative(X1))) & ((~strong(sK6) | ~creative(sK6)) | ! [X3] : ((~quiet(X3) | ~rich(X3)) & (rich(X3) | quiet(X3)))) [skolemisation 63,65,64]
74. (? [X0] : ((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) | ! [X1] : quiet(X1)) & (? [X1] : ~quiet(X1) | ! [X0] : ((rich(X0) | ~generous(X0)) & (generous(X0) | ~rich(X0)))) [nnf transformation 28]
75. (? [X0] : ((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) | ! [X1] : quiet(X1)) & (? [X2] : ~quiet(X2) | ! [X3] : ((rich(X3) | ~generous(X3)) & (generous(X3) | ~rich(X3)))) [rectify 74]
76. ? [X0] : ((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) => ((~generous(sK9) | ~rich(sK9)) & (generous(sK9) | rich(sK9))) [choice axiom]
77. ? [X2] : ~quiet(X2) => ~quiet(sK10) [choice axiom]
78. (((~generous(sK9) | ~rich(sK9)) & (generous(sK9) | rich(sK9))) | ! [X1] : quiet(X1)) & (~quiet(sK10) | ! [X3] : ((rich(X3) | ~generous(X3)) & (generous(X3) | ~rich(X3)))) [skolemisation 75,77,76]
96. happy(susan) | ~rich(X1) [cnf transformation 48]
117. ~generous(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 56]
118. ~kind(X0) | generous(X0) | generous(X0) [cnf transformation 56]
119. ~kind(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 56]
122. kind(paul) | ~happy(X0) | calm(X0) [cnf transformation 61]
130. rich(sK5) | ~quiet(sK5) | strong(X1) [cnf transformation 66]
142. generous(sK9) | rich(sK9) | quiet(X1) [cnf transformation 78]
144. ~calm(X0) | ~calm(X0) [cnf transformation 39]
151. ~strong(lucy) [cnf transformation 24]
152. ~calm(X0) [duplicate literal removal 144]
156. ~generous(X0) [duplicate literal removal 117]
157. ~kind(X0) | generous(X0) [duplicate literal removal 118]
158. ~kind(X0) | ~generous(X0) [duplicate literal removal 119]
186. 6 <=> happy(susan) [avatar definition]
187. happy(susan) <- (6) [avatar component clause 186]
195. 8 <=> ! [X1] : ~rich(X1) [avatar definition]
196. ~rich(X1) <- (8) [avatar component clause 195]
197. 8 | 6 [avatar split clause 96,186,195]
248. ~kind(X0) [subsumption resolution 157,158]
250. 19 <=> ! [X0] : (~happy(X0) | calm(X0)) [avatar definition]
251. ~happy(X0) | calm(X0) <- (19) [avatar component clause 250]
257. ~happy(X0) | calm(X0) [subsumption resolution 122,248]
258. 19 [avatar split clause 257,250]
261. 21 <=> ! [X1] : strong(X1) [avatar definition]
262. strong(X1) <- (21) [avatar component clause 261]
264. 22 <=> quiet(sK5) [avatar definition]
265. ~quiet(sK5) <- (~22) [avatar component clause 264]
268. 23 <=> rich(sK5) [avatar definition]
269. rich(sK5) <- (23) [avatar component clause 268]
276. 21 | ~22 | 23 [avatar split clause 130,268,264,261]
312. rich(sK9) | quiet(X1) [subsumption resolution 142,156]
314. 33 <=> ! [X1] : quiet(X1) [avatar definition]
315. quiet(X1) <- (33) [avatar component clause 314]
317. 34 <=> rich(sK9) [avatar definition]
319. rich(sK9) <- (34) [avatar component clause 317]
320. 33 | 34 [avatar split clause 312,317,314]
346. $false <- (~22, 33) [subsumption resolution 265,315]
347. 22 | ~33 [avatar contradiction clause 346]
348. ~happy(X0) <- (19) [subsumption resolution 251,152]
349. $false <- (6, 19) [subsumption resolution 187,348]
350. ~6 | ~19 [avatar contradiction clause 349]
353. $false <- (8, 23) [resolution 269,196]
354. ~8 | ~23 [avatar contradiction clause 353]
355. $false <- (8, 34) [subsumption resolution 319,196]
356. ~8 | ~34 [avatar contradiction clause 355]
357. $false <- (21) [resolution 262,151]
358. ~21 [avatar contradiction clause 357]
359. $false [avatar sat refutation 197,258,276,320,347,350,354,356,358]
% SZS output end Proof for 1122113596645118264504368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not creative and happy then fred is either quiet or not curious.
If someone is old or not creative then mary is both not humble and not happy.
Everyone who is either not curious or calm is either not quiet or calm.
If lucy is creative then susan is generous or not generous.
If fred is rich or not creative then lucy is both kind and happy.
If john is either brave or not humble then fred is quiet or creative and vice versa.
Everyone who is not wise is not brave or not quiet.
Everyone who is either tall or happy is tall.
Everyone who is both not brave and generous is either not patient or wise.
If someone is not quiet then susan is either not wise or strong and vice versa.
Everyone who is not humble or not patient is both strong and curious.
If someone is patient or generous then fred is wise and vice versa.
If lucy is either quiet or not generous then someone is funny or curious and vice versa.
Everyone who is both not brave and generous is not rich and vice versa.
Everyone who is wise is both old and tall.
Everyone who is both quiet and not happy is either not creative or rich.
Someone is not patient.
Paul is either not kind or strong.
Fred is patient or not funny.
Fred is both not calm and quiet.
Mary is either calm or not curious.
Someone is both brave and generous.
Someone is either not rich or not curious.
Paul is not tall or not creative. | Mary is calm. | entailment | (((~creative(john)&happy(john)))=>((quiet(fred)<~>~curious(fred))))&
((?[X]:((old(X)|~creative(X))))=>((~humble(mary)&~happy(mary))))&
(![X]:((~curious(X)<~>calm(X))=>(~quiet(X)<~>calm(X))))&
((creative(lucy))=>((generous(susan)|~generous(susan))))&
(((rich(fred)|~creative(fred)))=>((kind(lucy)&happy(lucy))))&
(((brave(john)<~>~humble(john)))<=>((quiet(fred)|creative(fred))))&
(![X]:(~wise(X)=>(~brave(X)|~quiet(X))))&
(![X]:((tall(X)<~>happy(X))=>tall(X)))&
(![X]:((~brave(X)&generous(X))=>(~patient(X)<~>wise(X))))&
((?[X]:(~quiet(X)))<=>((~wise(susan)<~>strong(susan))))&
(![X]:((~humble(X)|~patient(X))=>(strong(X)&curious(X))))&
((?[X]:((patient(X)|generous(X))))<=>(wise(fred)))&
(((quiet(lucy)<~>~generous(lucy)))<=>(?[X]:((funny(X)|curious(X)))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
(![X]:(wise(X)=>(old(X)&tall(X))))&
(![X]:((quiet(X)&~happy(X))=>(~creative(X)<~>rich(X))))&
(?[X]:(~patient(X)))&
((~kind(paul)<~>strong(paul)))&
((patient(fred)|~funny(fred)))&
((~calm(fred)&quiet(fred)))&
((calm(mary)<~>~curious(mary)))&
(?[X]:((brave(X)&generous(X))))&
(?[X]:((~rich(X)<~>~curious(X))))&
((~tall(paul)|~creative(paul))) | calm(mary) | [
"p1",
"p10",
"p11",
"p14",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6197245956337404301400063
% SZS output start Proof for 6197245956337404301400063
2. ? [X0] : (~creative(X0) | old(X0)) => (~happy(mary) & ~humble(mary)) [input p1]
11. ! [X0] : ((~patient(X0) | ~humble(X0)) => (curious(X0) & strong(X0))) [input p10]
12. ? [X0] : (generous(X0) | patient(X0)) <=> wise(fred) [input p11]
15. ! [X0] : (wise(X0) => (tall(X0) & old(X0))) [input p14]
21. calm(mary) <~> ~curious(mary) [input p20]
22. ? [X0] : (generous(X0) & brave(X0)) [input p21]
25. ~calm(mary) [input hypothesis]
28. (~happy(mary) & ~humble(mary)) | ! [X0] : (creative(X0) & ~old(X0)) [ennf transformation 2]
38. ! [X0] : ((curious(X0) & strong(X0)) | (patient(X0) & humble(X0))) [ennf transformation 11]
39. ! [X0] : ((tall(X0) & old(X0)) | ~wise(X0)) [ennf transformation 15]
52. (? [X0] : (generous(X0) | patient(X0)) | ~wise(fred)) & (wise(fred) | ! [X0] : (~generous(X0) & ~patient(X0))) [nnf transformation 12]
53. (? [X0] : (generous(X0) | patient(X0)) | ~wise(fred)) & (wise(fred) | ! [X1] : (~generous(X1) & ~patient(X1))) [rectify 52]
54. ? [X0] : (generous(X0) | patient(X0)) => (generous(sK1) | patient(sK1)) [choice axiom]
55. ((generous(sK1) | patient(sK1)) | ~wise(fred)) & (wise(fred) | ! [X1] : (~generous(X1) & ~patient(X1))) [skolemisation 53,54]
66. (curious(mary) | ~calm(mary)) & (~curious(mary) | calm(mary)) [nnf transformation 21]
67. ? [X0] : (generous(X0) & brave(X0)) => (generous(sK4) & brave(sK4)) [choice axiom]
68. generous(sK4) & brave(sK4) [skolemisation 22,67]
74. ~humble(mary) | ~old(X0) [cnf transformation 28]
104. humble(X0) | curious(X0) [cnf transformation 38]
107. wise(fred) | ~generous(X1) [cnf transformation 55]
118. ~wise(X0) | old(X0) [cnf transformation 39]
128. ~curious(mary) | calm(mary) [cnf transformation 66]
131. generous(sK4) [cnf transformation 68]
135. ~calm(mary) [cnf transformation 25]
166. 7 <=> ! [X0] : ~old(X0) [avatar definition]
167. ~old(X0) <- (7) [avatar component clause 166]
170. 8 <=> humble(mary) [avatar definition]
172. ~humble(mary) <- (~8) [avatar component clause 170]
174. 7 | ~8 [avatar split clause 74,170,166]
229. 19 <=> wise(fred) [avatar definition]
230. wise(fred) <- (19) [avatar component clause 229]
242. 22 <=> ! [X1] : ~generous(X1) [avatar definition]
243. ~generous(X1) <- (22) [avatar component clause 242]
244. 22 | 19 [avatar split clause 107,229,242]
298. 34 <=> calm(mary) [avatar definition]
302. 35 <=> curious(mary) [avatar definition]
303. ~curious(mary) <- (~35) [avatar component clause 302]
306. 34 | ~35 [avatar split clause 128,302,298]
326. ~34 [avatar split clause 135,298]
331. curious(mary) <- (~8) [resolution 104,172]
333. $false <- (~8, ~35) [subsumption resolution 331,303]
334. 8 | 35 [avatar contradiction clause 333]
345. old(fred) <- (19) [resolution 118,230]
346. $false <- (7, 19) [subsumption resolution 345,167]
347. ~7 | ~19 [avatar contradiction clause 346]
348. $false <- (22) [resolution 243,131]
351. ~22 [avatar contradiction clause 348]
352. $false [avatar sat refutation 174,244,306,326,334,347,351]
% SZS output end Proof for 6197245956337404301400063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or calm is not old or not funny and vice versa. Everyone who is not kind is both not brave and rich. If someone is either not happy or old then someone is both not strong and humble and vice versa. If someone is not tall then someone is both funny and old. Everyone who is strong or kind is strong or creative and vice versa. If someone is both not calm and not kind then someone is happy. If susan is generous or old then alice is not brave. Everyone who is not calm is both quiet and tall and vice versa. Everyone who is not tall or happy is both not quiet and kind and vice versa. If mary is both patient and generous then lucy is quiet or kind. Everyone who is not wise or not rich is not kind. If alice is either brave or not generous then someone is strong. Everyone who is either not humble or not curious is both curious and not kind. Everyone who is not kind is patient and vice versa. Everyone who is wise is brave. Everyone who is not rich or quiet is both quiet and calm and vice versa. John is not brave. Lucy is both not kind and creative. Someone is either generous or not patient. Someone is patient or not kind. Someone is calm. Mary is wise. John is both curious and not strong. | Susan is not tall. | contradiction | (![X]:((rich(X)|calm(X))<=>(~old(X)|~funny(X))))&
(![X]:(~kind(X)=>(~brave(X)&rich(X))))&
((?[X]:((~happy(X)<~>old(X))))<=>(?[X]:((~strong(X)&humble(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((funny(X)&old(X)))))&
(![X]:((strong(X)|kind(X))<=>(strong(X)|creative(X))))&
((?[X]:((~calm(X)&~kind(X))))=>(?[X]:(happy(X))))&
(((generous(susan)|old(susan)))=>(~brave(alice)))&
(![X]:(~calm(X)<=>(quiet(X)&tall(X))))&
(![X]:((~tall(X)|happy(X))<=>(~quiet(X)&kind(X))))&
(((patient(mary)&generous(mary)))=>((quiet(lucy)|kind(lucy))))&
(![X]:((~wise(X)|~rich(X))=>~kind(X)))&
(((brave(alice)<~>~generous(alice)))=>(?[X]:(strong(X))))&
(![X]:((~humble(X)<~>~curious(X))=>(curious(X)&~kind(X))))&
(![X]:(~kind(X)<=>patient(X)))&
(![X]:(wise(X)=>brave(X)))&
(![X]:((~rich(X)|quiet(X))<=>(quiet(X)&calm(X))))&
(~brave(john))&
((~kind(lucy)&creative(lucy)))&
(?[X]:((generous(X)<~>~patient(X))))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:(calm(X)))&
(wise(mary))&
((curious(john)&~strong(john))) | ~tall(susan) | [
"p0",
"p1",
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8375546671192274035297668
% SZS output start Proof for 8375546671192274035297668
1. ! [X0] : ((calm(X0) | rich(X0)) <=> (~funny(X0) | ~old(X0))) [input p0]
2. ! [X0] : (~kind(X0) => (rich(X0) & ~brave(X0))) [input p1]
4. ? [X0] : ~tall(X0) => ? [X0] : (old(X0) & funny(X0)) [input p3]
11. ! [X0] : ((~rich(X0) | ~wise(X0)) => ~kind(X0)) [input p10]
24. ~tall(susan) [input hypothesis]
26. ? [X0] : ~tall(X0) => ? [X1] : (old(X1) & funny(X1)) [rectify 4]
28. ! [X0] : ((rich(X0) & ~brave(X0)) | kind(X0)) [ennf transformation 2]
29. ? [X1] : (old(X1) & funny(X1)) | ! [X0] : tall(X0) [ennf transformation 26]
34. ! [X0] : (~kind(X0) | (rich(X0) & wise(X0))) [ennf transformation 11]
38. ! [X0] : (((calm(X0) | rich(X0)) | (funny(X0) & old(X0))) & ((~funny(X0) | ~old(X0)) | (~calm(X0) & ~rich(X0)))) [nnf transformation 1]
39. ! [X0] : ((calm(X0) | rich(X0) | (funny(X0) & old(X0))) & (~funny(X0) | ~old(X0) | (~calm(X0) & ~rich(X0)))) [flattening 38]
45. ? [X0] : (old(X0) & funny(X0)) | ! [X1] : tall(X1) [rectify 29]
46. ? [X0] : (old(X0) & funny(X0)) => (old(sK2) & funny(sK2)) [choice axiom]
47. (old(sK2) & funny(sK2)) | ! [X1] : tall(X1) [skolemisation 45,46]
71. ~funny(X0) | ~old(X0) | ~rich(X0) [cnf transformation 39]
76. kind(X0) | rich(X0) [cnf transformation 28]
83. funny(sK2) | tall(X1) [cnf transformation 47]
84. old(sK2) | tall(X1) [cnf transformation 47]
102. ~kind(X0) | rich(X0) [cnf transformation 34]
127. ~tall(susan) [cnf transformation 24]
161. 8 <=> ! [X1] : tall(X1) [avatar definition]
162. tall(X1) <- (8) [avatar component clause 161]
164. 9 <=> old(sK2) [avatar definition]
166. old(sK2) <- (9) [avatar component clause 164]
167. 8 | 9 [avatar split clause 84,164,161]
169. 10 <=> funny(sK2) [avatar definition]
171. funny(sK2) <- (10) [avatar component clause 169]
172. 8 | 10 [avatar split clause 83,169,161]
212. rich(X0) [subsumption resolution 102,76]
236. $false <- (8) [resolution 162,127]
237. ~8 [avatar contradiction clause 236]
255. ~old(sK2) | ~rich(sK2) <- (10) [resolution 71,171]
256. ~rich(sK2) <- (9, 10) [subsumption resolution 255,166]
257. $false <- (9, 10) [subsumption resolution 256,212]
258. ~9 | ~10 [avatar contradiction clause 257]
259. $false [avatar sat refutation 167,172,237,258]
% SZS output end Proof for 8375546671192274035297668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and patient then susan is either not brave or not humble.
Everyone who is both not curious and not humble is not old.
If someone is happy or not creative then mary is either humble or generous.
Everyone who is not patient is both calm and kind.
If someone is not kind then fred is generous.
Everyone who is either not humble or not funny is both not quiet and quiet.
Everyone who is either not strong or quiet is either creative or not old and vice versa.
Everyone who is both not rich and not strong is both not humble and not old.
If someone is tall then lucy is either not kind or not old and vice versa.
If someone is patient then mary is both patient and tall.
Everyone who is either not old or tall is either happy or wise and vice versa.
If alice is either not curious or not wise then someone is not creative.
Everyone who is not funny is both creative and happy.
Everyone who is creative is not creative or rich and vice versa.
If lucy is wise then alice is curious or humble.
If someone is not strong then someone is not strong or not wise and vice versa.
Mary is either rich or not tall.
Paul is patient.
John is not funny.
Someone is not calm or not rich.
Someone is either not kind or rich.
Someone is funny or not quiet.
Paul is not brave or not creative.
Mary is not funny or not calm. | John is creative. | entailment | ((?[X]:((generous(X)&patient(X))))=>((~brave(susan)<~>~humble(susan))))&
(![X]:((~curious(X)&~humble(X))=>~old(X)))&
((?[X]:((happy(X)|~creative(X))))=>((humble(mary)<~>generous(mary))))&
(![X]:(~patient(X)=>(calm(X)&kind(X))))&
((?[X]:(~kind(X)))=>(generous(fred)))&
(![X]:((~humble(X)<~>~funny(X))=>(~quiet(X)&quiet(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>(creative(X)<~>~old(X))))&
(![X]:((~rich(X)&~strong(X))=>(~humble(X)&~old(X))))&
((?[X]:(tall(X)))<=>((~kind(lucy)<~>~old(lucy))))&
((?[X]:(patient(X)))=>((patient(mary)&tall(mary))))&
(![X]:((~old(X)<~>tall(X))<=>(happy(X)<~>wise(X))))&
(((~curious(alice)<~>~wise(alice)))=>(?[X]:(~creative(X))))&
(![X]:(~funny(X)=>(creative(X)&happy(X))))&
(![X]:(creative(X)<=>(~creative(X)|rich(X))))&
((wise(lucy))=>((curious(alice)|humble(alice))))&
((?[X]:(~strong(X)))<=>(?[X]:((~strong(X)|~wise(X)))))&
((rich(mary)<~>~tall(mary)))&
(patient(paul))&
(~funny(john))&
(?[X]:((~calm(X)|~rich(X))))&
(?[X]:((~kind(X)<~>rich(X))))&
(?[X]:((funny(X)|~quiet(X))))&
((~brave(paul)|~creative(paul)))&
((~funny(mary)|~calm(mary))) | creative(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4404809593774124325531239
% SZS output start Proof for 4404809593774124325531239
14. ! [X0] : (creative(X0) <=> (rich(X0) | ~creative(X0))) [input p13]
25. ~creative(john) [input hypothesis]
53. ! [X0] : ((creative(X0) | (~rich(X0) & creative(X0))) & ((rich(X0) | ~creative(X0)) | ~creative(X0))) [nnf transformation 14]
54. ! [X0] : ((creative(X0) | (~rich(X0) & creative(X0))) & (rich(X0) | ~creative(X0) | ~creative(X0))) [flattening 53]
111. creative(X0) | creative(X0) [cnf transformation 54]
127. ~creative(john) [cnf transformation 25]
129. creative(X0) [duplicate literal removal 111]
144. 4 <=> ! [X0] : creative(X0) [avatar definition]
145. creative(X0) <- (4) [avatar component clause 144]
217. 4 [avatar split clause 129,144]
300. $false <- (4) [resolution 145,127]
301. ~4 [avatar contradiction clause 300]
302. $false [avatar sat refutation 217,301]
% SZS output end Proof for 4404809593774124325531239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not wise or curious then someone is both not tall and humble and vice versa. If lucy is generous then alice is both not creative and not wise and vice versa. If mary is both curious and not rich then someone is both happy and funny and vice versa. Everyone who is either brave or humble is either not patient or wise and vice versa. Everyone who is calm is happy or not kind. If someone is calm or not tall then someone is not old or curious. Everyone who is both creative and not generous is either patient or strong. Everyone who is both not humble and not strong is both creative and patient. Everyone who is not generous or not curious is either not kind or not brave and vice versa. Everyone who is both not happy and not generous is happy. Everyone who is both rich and wise is happy or not brave. If someone is not curious or quiet then someone is both quiet and not patient. If someone is not quiet or patient then someone is not funny. If lucy is not funny or not kind then someone is either not generous or generous. Everyone who is old is either strong or creative and vice versa. Lucy is both tall and not wise. John is calm or not calm. Fred is rich. Fred is both not tall and old. Paul is both funny and old. Someone is either not brave or not generous. Someone is either not kind or patient. Fred is either calm or not calm. | Alice is not creative. | neutral | (((~wise(fred)|curious(fred)))<=>(?[X]:((~tall(X)&humble(X)))))&
((generous(lucy))<=>((~creative(alice)&~wise(alice))))&
(((curious(mary)&~rich(mary)))<=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((brave(X)<~>humble(X))<=>(~patient(X)<~>wise(X))))&
(![X]:(calm(X)=>(happy(X)|~kind(X))))&
((?[X]:((calm(X)|~tall(X))))=>(?[X]:((~old(X)|curious(X)))))&
(![X]:((creative(X)&~generous(X))=>(patient(X)<~>strong(X))))&
(![X]:((~humble(X)&~strong(X))=>(creative(X)&patient(X))))&
(![X]:((~generous(X)|~curious(X))<=>(~kind(X)<~>~brave(X))))&
(![X]:((~happy(X)&~generous(X))=>happy(X)))&
(![X]:((rich(X)&wise(X))=>(happy(X)|~brave(X))))&
((?[X]:((~curious(X)|quiet(X))))=>(?[X]:((quiet(X)&~patient(X)))))&
((?[X]:((~quiet(X)|patient(X))))=>(?[X]:(~funny(X))))&
(((~funny(lucy)|~kind(lucy)))=>(?[X]:((~generous(X)<~>generous(X)))))&
(![X]:(old(X)<=>(strong(X)<~>creative(X))))&
((tall(lucy)&~wise(lucy)))&
((calm(john)|~calm(john)))&
(rich(fred))&
((~tall(fred)&old(fred)))&
((funny(paul)&old(paul)))&
(?[X]:((~brave(X)<~>~generous(X))))&
(?[X]:((~kind(X)<~>patient(X))))&
((calm(fred)<~>~calm(fred))) | ~creative(alice) | [] | null | 0 |
Everyone who is either humble or not strong is either not quiet or not rich.
Everyone who is not old is both old and calm.
Everyone who is patient is either not patient or not strong and vice versa.
Everyone who is both not generous and curious is not funny or old.
Everyone who is creative is both happy and not old.
If someone is both humble and creative then paul is both not funny and quiet and vice versa.
Everyone who is not generous is kind.
If someone is old or rich then john is not creative.
If someone is either not creative or not old then paul is either old or not quiet and vice versa.
If someone is not curious or not wise then someone is either not generous or not humble.
Everyone who is either calm or not quiet is both wise and not happy and vice versa.
If someone is either humble or not tall then someone is both not generous and not kind.
If someone is both not calm and wise then mary is not tall and vice versa.
Everyone who is not quiet or happy is either kind or wise.
Everyone who is either brave or not creative is not brave and vice versa.
Someone is either not tall or not quiet.
Someone is either humble or generous.
Someone is not rich.
John is both not wise and generous.
Lucy is not brave.
Someone is both quiet and humble.
Someone is rich or not wise. | Lucy is strong. | contradiction | (![X]:((humble(X)<~>~strong(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:(~old(X)=>(old(X)&calm(X))))&
(![X]:(patient(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:((~generous(X)&curious(X))=>(~funny(X)|old(X))))&
(![X]:(creative(X)=>(happy(X)&~old(X))))&
((?[X]:((humble(X)&creative(X))))<=>((~funny(paul)&quiet(paul))))&
(![X]:(~generous(X)=>kind(X)))&
((?[X]:((old(X)|rich(X))))=>(~creative(john)))&
((?[X]:((~creative(X)<~>~old(X))))<=>((old(paul)<~>~quiet(paul))))&
((?[X]:((~curious(X)|~wise(X))))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:((calm(X)<~>~quiet(X))<=>(wise(X)&~happy(X))))&
((?[X]:((humble(X)<~>~tall(X))))=>(?[X]:((~generous(X)&~kind(X)))))&
((?[X]:((~calm(X)&wise(X))))<=>(~tall(mary)))&
(![X]:((~quiet(X)|happy(X))=>(kind(X)<~>wise(X))))&
(![X]:((brave(X)<~>~creative(X))<=>~brave(X)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((humble(X)<~>generous(X))))&
(?[X]:(~rich(X)))&
((~wise(john)&generous(john)))&
(~brave(lucy))&
(?[X]:((quiet(X)&humble(X))))&
(?[X]:((rich(X)|~wise(X)))) | strong(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 626454107427292037346075
% SZS output start Proof for 626454107427292037346075
3. ! [X0] : (patient(X0) <=> (~patient(X0) <~> ~strong(X0))) [input p2]
23. strong(lucy) [input hypothesis]
37. ! [X0] : ((patient(X0) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ~patient(X0))) [nnf transformation 3]
81. ~strong(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 37]
83. patient(X0) | ~strong(X0) | patient(X0) [cnf transformation 37]
139. strong(lucy) [cnf transformation 23]
142. ~strong(X0) | ~patient(X0) [duplicate literal removal 81]
143. patient(X0) | ~strong(X0) [duplicate literal removal 83]
145. ~strong(X0) [subsumption resolution 142,143]
249. $false [subsumption resolution 139,145]
% SZS output end Proof for 626454107427292037346075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or wise is either humble or not generous.
If susan is not old or tall then lucy is not funny.
If someone is not old then mary is not happy or brave.
Everyone who is either humble or old is both not brave and not curious and vice versa.
Everyone who is not generous is not funny and vice versa.
If mary is either rich or kind then someone is not quiet.
If fred is not humble or not generous then alice is not curious and vice versa.
Everyone who is not creative is either not humble or not funny.
Everyone who is either wise or funny is not brave.
Everyone who is both not creative and strong is not tall.
Everyone who is both curious and not wise is both humble and not strong and vice versa.
Everyone who is either generous or not humble is not strong or generous and vice versa.
If someone is not funny or not humble then someone is either calm or not wise and vice versa.
Everyone who is not calm or not creative is either not brave or not old.
Everyone who is not wise or not curious is not curious and vice versa.
If lucy is both not patient and quiet then someone is humble.
Someone is either brave or creative.
Someone is not patient.
Someone is both tall and calm.
Lucy is calm.
Alice is either not curious or happy.
Someone is either not brave or old.
Lucy is either not curious or creative.
Someone is either not creative or strong. | Lucy is creative. | entailment | (![X]:((~creative(X)<~>wise(X))=>(humble(X)<~>~generous(X))))&
(((~old(susan)|tall(susan)))=>(~funny(lucy)))&
((?[X]:(~old(X)))=>((~happy(mary)|brave(mary))))&
(![X]:((humble(X)<~>old(X))<=>(~brave(X)&~curious(X))))&
(![X]:(~generous(X)<=>~funny(X)))&
(((rich(mary)<~>kind(mary)))=>(?[X]:(~quiet(X))))&
(((~humble(fred)|~generous(fred)))<=>(~curious(alice)))&
(![X]:(~creative(X)=>(~humble(X)<~>~funny(X))))&
(![X]:((wise(X)<~>funny(X))=>~brave(X)))&
(![X]:((~creative(X)&strong(X))=>~tall(X)))&
(![X]:((curious(X)&~wise(X))<=>(humble(X)&~strong(X))))&
(![X]:((generous(X)<~>~humble(X))<=>(~strong(X)|generous(X))))&
((?[X]:((~funny(X)|~humble(X))))<=>(?[X]:((calm(X)<~>~wise(X)))))&
(![X]:((~calm(X)|~creative(X))=>(~brave(X)<~>~old(X))))&
(![X]:((~wise(X)|~curious(X))<=>~curious(X)))&
(((~patient(lucy)&quiet(lucy)))=>(?[X]:(humble(X))))&
(?[X]:((brave(X)<~>creative(X))))&
(?[X]:(~patient(X)))&
(?[X]:((tall(X)&calm(X))))&
(calm(lucy))&
((~curious(alice)<~>happy(alice)))&
(?[X]:((~brave(X)<~>old(X))))&
((~curious(lucy)<~>creative(lucy)))&
(?[X]:((~creative(X)<~>strong(X)))) | creative(lucy) | [
"p3",
"p4",
"p7",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5705701657060128930140522
% SZS output start Proof for 5705701657060128930140522
4. ! [X0] : ((humble(X0) <~> old(X0)) <=> (~curious(X0) & ~brave(X0))) [input p3]
5. ! [X0] : (~generous(X0) <=> ~funny(X0)) [input p4]
8. ! [X0] : (~creative(X0) => (~humble(X0) <~> ~funny(X0))) [input p7]
12. ! [X0] : ((generous(X0) <~> ~humble(X0)) <=> (generous(X0) | ~strong(X0))) [input p11]
14. ! [X0] : ((~creative(X0) | ~calm(X0)) => (~brave(X0) <~> ~old(X0))) [input p13]
23. ~curious(lucy) <~> creative(lucy) [input p22]
25. ~creative(lucy) [input hypothesis]
34. ! [X0] : ((~humble(X0) <~> ~funny(X0)) | creative(X0)) [ennf transformation 8]
38. ! [X0] : ((~brave(X0) <~> ~old(X0)) | (creative(X0) & calm(X0))) [ennf transformation 14]
40. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (curious(X0) | brave(X0))) & ((~curious(X0) & ~brave(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 4]
41. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | curious(X0) | brave(X0)) & ((~curious(X0) & ~brave(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 40]
42. ! [X0] : ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))) [nnf transformation 5]
45. ! [X0] : (((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | creative(X0)) [nnf transformation 34]
49. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (~generous(X0) & strong(X0))) & ((generous(X0) | ~strong(X0)) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [nnf transformation 12]
50. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (~generous(X0) & strong(X0))) & (generous(X0) | ~strong(X0) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [flattening 49]
56. ! [X0] : (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (creative(X0) & calm(X0))) [nnf transformation 38]
68. (~creative(lucy) | curious(lucy)) & (creative(lucy) | ~curious(lucy)) [nnf transformation 23]
79. ~brave(X0) | old(X0) | ~humble(X0) [cnf transformation 41]
84. ~old(X0) | ~humble(X0) | curious(X0) | brave(X0) [cnf transformation 41]
85. ~funny(X0) | generous(X0) [cnf transformation 42]
91. funny(X0) | humble(X0) | creative(X0) [cnf transformation 45]
104. humble(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
112. ~brave(X0) | ~old(X0) | creative(X0) [cnf transformation 56]
114. brave(X0) | old(X0) | creative(X0) [cnf transformation 56]
127. creative(lucy) | ~curious(lucy) [cnf transformation 68]
131. ~creative(lucy) [cnf transformation 25]
133. ~generous(X0) | humble(X0) [duplicate literal removal 104]
237. 23 <=> curious(lucy) [avatar definition]
238. ~curious(lucy) <- (~23) [avatar component clause 237]
241. 24 <=> creative(lucy) [avatar definition]
243. ~creative(lucy) <- (~24) [avatar component clause 241]
245. ~23 | 24 [avatar split clause 127,241,237]
256. ~24 [avatar split clause 131,241]
272. humble(X1) | creative(X1) | generous(X1) [resolution 91,85]
275. humble(X1) | creative(X1) [subsumption resolution 272,133]
323. old(X5) | creative(X5) | old(X5) | ~humble(X5) [resolution 114,79]
325. old(X5) | creative(X5) | ~humble(X5) [duplicate literal removal 323]
328. old(X5) | creative(X5) [subsumption resolution 325,275]
403. 41 <=> brave(lucy) [avatar definition]
405. brave(lucy) <- (41) [avatar component clause 403]
407. 42 <=> old(lucy) [avatar definition]
408. ~old(lucy) <- (~42) [avatar component clause 407]
451. ~humble(X0) | curious(X0) | brave(X0) | creative(X0) [resolution 84,328]
453. curious(X0) | brave(X0) | creative(X0) [subsumption resolution 451,275]
468. ~old(lucy) | creative(lucy) <- (41) [resolution 405,112]
474. ~old(lucy) <- (~24, 41) [subsumption resolution 468,243]
475. ~42 | 24 | ~41 [avatar split clause 474,403,241,407]
591. brave(lucy) | creative(lucy) <- (~23) [resolution 453,238]
595. brave(lucy) <- (~23, ~24) [subsumption resolution 591,243]
596. 41 | 23 | 24 [avatar split clause 595,241,237,403]
614. creative(lucy) <- (~42) [resolution 408,328]
615. $false <- (~24, ~42) [subsumption resolution 614,243]
616. 24 | 42 [avatar contradiction clause 615]
617. $false [avatar sat refutation 245,256,475,596,616]
% SZS output end Proof for 5705701657060128930140522
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or generous is either not calm or not old and vice versa.
If someone is both not funny and not curious then someone is either generous or not humble and vice versa.
If someone is both kind and not strong then susan is both not kind and old.
Everyone who is both kind and not patient is either not quiet or not wise and vice versa.
Everyone who is not wise or kind is either humble or funny.
Everyone who is both not rich and humble is wise.
Everyone who is both funny and not creative is not generous or happy and vice versa.
Everyone who is calm or humble is both patient and strong.
Everyone who is not brave is both not calm and not humble and vice versa.
Everyone who is not wise is not calm or not curious.
Everyone who is either not patient or calm is either funny or not brave.
If someone is not funny then someone is not calm or strong.
Everyone who is not patient is creative.
Everyone who is either not curious or not happy is not humble or not creative and vice versa.
Everyone who is either not old or calm is either patient or strong and vice versa.
If lucy is strong then someone is kind and vice versa.
Someone is not strong.
Someone is not patient or not humble.
Lucy is either not patient or humble.
Someone is either funny or not creative.
Someone is not brave.
John is not quiet or not calm.
Lucy is both rich and brave.
Someone is either funny or not strong. | Susan is kind. | neutral | (![X]:((~brave(X)|generous(X))<=>(~calm(X)<~>~old(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:((generous(X)<~>~humble(X)))))&
((?[X]:((kind(X)&~strong(X))))=>((~kind(susan)&old(susan))))&
(![X]:((kind(X)&~patient(X))<=>(~quiet(X)<~>~wise(X))))&
(![X]:((~wise(X)|kind(X))=>(humble(X)<~>funny(X))))&
(![X]:((~rich(X)&humble(X))=>wise(X)))&
(![X]:((funny(X)&~creative(X))<=>(~generous(X)|happy(X))))&
(![X]:((calm(X)|humble(X))=>(patient(X)&strong(X))))&
(![X]:(~brave(X)<=>(~calm(X)&~humble(X))))&
(![X]:(~wise(X)=>(~calm(X)|~curious(X))))&
(![X]:((~patient(X)<~>calm(X))=>(funny(X)<~>~brave(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~calm(X)|strong(X)))))&
(![X]:(~patient(X)=>creative(X)))&
(![X]:((~curious(X)<~>~happy(X))<=>(~humble(X)|~creative(X))))&
(![X]:((~old(X)<~>calm(X))<=>(patient(X)<~>strong(X))))&
((strong(lucy))<=>(?[X]:(kind(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~patient(X)|~humble(X))))&
((~patient(lucy)<~>humble(lucy)))&
(?[X]:((funny(X)<~>~creative(X))))&
(?[X]:(~brave(X)))&
((~quiet(john)|~calm(john)))&
((rich(lucy)&brave(lucy)))&
(?[X]:((funny(X)<~>~strong(X)))) | kind(susan) | [] | null | 0 |
If lucy is not creative or kind then someone is kind or brave and vice versa. Everyone who is either generous or curious is creative. Everyone who is curious is funny or not brave. If mary is not strong then someone is not funny and vice versa. Everyone who is not happy or not brave is either calm or not curious. If someone is humble or patient then someone is not funny or not kind and vice versa. Everyone who is generous is either brave or creative. Everyone who is either old or not rich is either not brave or strong and vice versa. Everyone who is both quiet and not generous is not old or patient. Everyone who is either not funny or not calm is either wise or generous and vice versa. If john is either not strong or strong then someone is happy and vice versa. Everyone who is not strong or patient is either patient or not old. If lucy is either not creative or calm then paul is not strong or humble and vice versa. Everyone who is both patient and rich is either wise or not kind and vice versa. Everyone who is not creative or funny is both wise and not rich. Everyone who is not tall or calm is both humble and kind and vice versa. Fred is both happy and not creative. Alice is not calm. Mary is not happy or not brave. Alice is funny or quiet. Someone is not strong. Someone is either brave or funny. Someone is tall or not generous. | Lucy is not brave. | neutral | (((~creative(lucy)|kind(lucy)))<=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((generous(X)<~>curious(X))=>creative(X)))&
(![X]:(curious(X)=>(funny(X)|~brave(X))))&
((~strong(mary))<=>(?[X]:(~funny(X))))&
(![X]:((~happy(X)|~brave(X))=>(calm(X)<~>~curious(X))))&
((?[X]:((humble(X)|patient(X))))<=>(?[X]:((~funny(X)|~kind(X)))))&
(![X]:(generous(X)=>(brave(X)<~>creative(X))))&
(![X]:((old(X)<~>~rich(X))<=>(~brave(X)<~>strong(X))))&
(![X]:((quiet(X)&~generous(X))=>(~old(X)|patient(X))))&
(![X]:((~funny(X)<~>~calm(X))<=>(wise(X)<~>generous(X))))&
(((~strong(john)<~>strong(john)))<=>(?[X]:(happy(X))))&
(![X]:((~strong(X)|patient(X))=>(patient(X)<~>~old(X))))&
(((~creative(lucy)<~>calm(lucy)))<=>((~strong(paul)|humble(paul))))&
(![X]:((patient(X)&rich(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((~creative(X)|funny(X))=>(wise(X)&~rich(X))))&
(![X]:((~tall(X)|calm(X))<=>(humble(X)&kind(X))))&
((happy(fred)&~creative(fred)))&
(~calm(alice))&
((~happy(mary)|~brave(mary)))&
((funny(alice)|quiet(alice)))&
(?[X]:(~strong(X)))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((tall(X)|~generous(X)))) | ~brave(lucy) | [] | null | 0 |
Everyone who is not rich is not funny or not strong.
If someone is either not old or not tall then someone is not quiet or not patient and vice versa.
If someone is not curious then paul is either not tall or patient.
If someone is either happy or humble then someone is both not wise and tall and vice versa.
Everyone who is both not brave and not tall is both not kind and humble and vice versa.
If someone is either not tall or funny then someone is strong and vice versa.
If someone is both brave and quiet then someone is calm.
Everyone who is not strong is either humble or quiet and vice versa.
If someone is not calm or not funny then alice is not generous or creative and vice versa.
If someone is either not calm or happy then mary is funny and vice versa.
If john is humble or not curious then someone is either not humble or not generous and vice versa.
If susan is not wise or humble then alice is curious.
Everyone who is kind or happy is both not funny and not humble and vice versa.
If someone is generous or tall then someone is rich or patient.
If someone is rich then someone is not creative or not happy and vice versa.
Everyone who is calm or strong is either not brave or not patient.
Someone is not happy.
Someone is both brave and wise.
Someone is either not happy or brave.
Lucy is both not happy and funny.
Someone is not brave or not kind.
Someone is both happy and not kind.
Fred is tall.
Fred is humble or not patient. | Fred is patient. | contradiction | (![X]:(~rich(X)=>(~funny(X)|~strong(X))))&
((?[X]:((~old(X)<~>~tall(X))))<=>(?[X]:((~quiet(X)|~patient(X)))))&
((?[X]:(~curious(X)))=>((~tall(paul)<~>patient(paul))))&
((?[X]:((happy(X)<~>humble(X))))<=>(?[X]:((~wise(X)&tall(X)))))&
(![X]:((~brave(X)&~tall(X))<=>(~kind(X)&humble(X))))&
((?[X]:((~tall(X)<~>funny(X))))<=>(?[X]:(strong(X))))&
((?[X]:((brave(X)&quiet(X))))=>(?[X]:(calm(X))))&
(![X]:(~strong(X)<=>(humble(X)<~>quiet(X))))&
((?[X]:((~calm(X)|~funny(X))))<=>((~generous(alice)|creative(alice))))&
((?[X]:((~calm(X)<~>happy(X))))<=>(funny(mary)))&
(((humble(john)|~curious(john)))<=>(?[X]:((~humble(X)<~>~generous(X)))))&
(((~wise(susan)|humble(susan)))=>(curious(alice)))&
(![X]:((kind(X)|happy(X))<=>(~funny(X)&~humble(X))))&
((?[X]:((generous(X)|tall(X))))=>(?[X]:((rich(X)|patient(X)))))&
((?[X]:(rich(X)))<=>(?[X]:((~creative(X)|~happy(X)))))&
(![X]:((calm(X)|strong(X))=>(~brave(X)<~>~patient(X))))&
(?[X]:(~happy(X)))&
(?[X]:((brave(X)&wise(X))))&
(?[X]:((~happy(X)<~>brave(X))))&
((~happy(lucy)&funny(lucy)))&
(?[X]:((~brave(X)|~kind(X))))&
(?[X]:((happy(X)&~kind(X))))&
(tall(fred))&
((humble(fred)|~patient(fred))) | patient(fred) | [
"p4",
"p12",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4335215460119414843309142
% SZS output start Proof for 4335215460119414843309142
5. ! [X0] : ((~tall(X0) & ~brave(X0)) <=> (humble(X0) & ~kind(X0))) [input p4]
13. ! [X0] : ((happy(X0) | kind(X0)) <=> (~humble(X0) & ~funny(X0))) [input p12]
23. tall(fred) [input p22]
24. ~patient(fred) | humble(fred) [input p23]
25. patient(fred) [input hypothesis]
50. ! [X0] : (((~tall(X0) & ~brave(X0)) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | (tall(X0) | brave(X0)))) [nnf transformation 5]
51. ! [X0] : (((~tall(X0) & ~brave(X0)) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | tall(X0) | brave(X0))) [flattening 50]
75. ! [X0] : (((happy(X0) | kind(X0)) | (humble(X0) | funny(X0))) & ((~humble(X0) & ~funny(X0)) | (~happy(X0) & ~kind(X0)))) [nnf transformation 13]
76. ! [X0] : ((happy(X0) | kind(X0) | humble(X0) | funny(X0)) & ((~humble(X0) & ~funny(X0)) | (~happy(X0) & ~kind(X0)))) [flattening 75]
115. ~humble(X0) | ~tall(X0) | kind(X0) [cnf transformation 51]
143. ~kind(X0) | ~humble(X0) [cnf transformation 76]
165. tall(fred) [cnf transformation 23]
166. ~patient(fred) | humble(fred) [cnf transformation 24]
167. patient(fred) [cnf transformation 25]
429. 61 <=> humble(fred) [avatar definition]
431. humble(fred) <- (61) [avatar component clause 429]
433. 62 <=> patient(fred) [avatar definition]
436. 61 | ~62 [avatar split clause 166,433,429]
437. 62 [avatar split clause 167,433]
491. ~tall(fred) | kind(fred) <- (61) [resolution 115,431]
492. kind(fred) <- (61) [subsumption resolution 491,165]
608. ~humble(fred) <- (61) [resolution 492,143]
610. $false <- (61) [subsumption resolution 608,431]
611. ~61 [avatar contradiction clause 610]
612. $false [avatar sat refutation 436,437,611]
% SZS output end Proof for 4335215460119414843309142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or not tall is quiet or not patient and vice versa.
If alice is happy or strong then someone is both not rich and not humble.
If someone is either wise or tall then someone is either old or not happy.
Everyone who is either not happy or not quiet is both curious and calm and vice versa.
If someone is strong or not old then someone is not creative or not brave and vice versa.
If someone is generous then lucy is either curious or creative.
Everyone who is both not kind and not tall is not calm or old and vice versa.
If lucy is both generous and not rich then someone is both generous and happy and vice versa.
Everyone who is both not kind and not wise is not generous.
Everyone who is both not tall and calm is either not patient or not calm and vice versa.
Everyone who is either kind or not old is either curious or tall.
Everyone who is either rich or curious is not kind or not patient and vice versa.
Everyone who is not kind or not brave is not kind or funny and vice versa.
If alice is generous then someone is tall.
If susan is either not quiet or not brave then susan is both not kind and calm and vice versa.
Everyone who is kind is both patient and not rich.
Susan is either calm or not calm.
Paul is both not old and not tall.
John is both not funny and not generous.
Susan is funny.
Someone is both old and not tall.
Someone is either not strong or not tall.
Someone is both old and funny. | Susan is kind. | contradiction | (![X]:((~happy(X)<~>~tall(X))<=>(quiet(X)|~patient(X))))&
(((happy(alice)|strong(alice)))=>(?[X]:((~rich(X)&~humble(X)))))&
((?[X]:((wise(X)<~>tall(X))))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(curious(X)&calm(X))))&
((?[X]:((strong(X)|~old(X))))<=>(?[X]:((~creative(X)|~brave(X)))))&
((?[X]:(generous(X)))=>((curious(lucy)<~>creative(lucy))))&
(![X]:((~kind(X)&~tall(X))<=>(~calm(X)|old(X))))&
(((generous(lucy)&~rich(lucy)))<=>(?[X]:((generous(X)&happy(X)))))&
(![X]:((~kind(X)&~wise(X))=>~generous(X)))&
(![X]:((~tall(X)&calm(X))<=>(~patient(X)<~>~calm(X))))&
(![X]:((kind(X)<~>~old(X))=>(curious(X)<~>tall(X))))&
(![X]:((rich(X)<~>curious(X))<=>(~kind(X)|~patient(X))))&
(![X]:((~kind(X)|~brave(X))<=>(~kind(X)|funny(X))))&
((generous(alice))=>(?[X]:(tall(X))))&
(((~quiet(susan)<~>~brave(susan)))<=>((~kind(susan)&calm(susan))))&
(![X]:(kind(X)=>(patient(X)&~rich(X))))&
((calm(susan)<~>~calm(susan)))&
((~old(paul)&~tall(paul)))&
((~funny(john)&~generous(john)))&
(funny(susan))&
(?[X]:((old(X)&~tall(X))))&
(?[X]:((~strong(X)<~>~tall(X))))&
(?[X]:((old(X)&funny(X)))) | kind(susan) | [
"p0",
"p3",
"p9",
"p11",
"p12",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6281665138677922886633801
% SZS output start Proof for 6281665138677922886633801
1. ! [X0] : ((~happy(X0) <~> ~tall(X0)) <=> (~patient(X0) | quiet(X0))) [input p0]
4. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) <=> (calm(X0) & curious(X0))) [input p3]
10. ! [X0] : ((calm(X0) & ~tall(X0)) <=> (~patient(X0) <~> ~calm(X0))) [input p9]
12. ! [X0] : ((rich(X0) <~> curious(X0)) <=> (~patient(X0) | ~kind(X0))) [input p11]
13. ! [X0] : ((~brave(X0) | ~kind(X0)) <=> (funny(X0) | ~kind(X0))) [input p12]
15. (~quiet(susan) <~> ~brave(susan)) <=> (calm(susan) & ~kind(susan)) [input p14]
16. ! [X0] : (kind(X0) => (~rich(X0) & patient(X0))) [input p15]
20. funny(susan) [input p19]
24. kind(susan) [input hypothesis]
35. ! [X0] : ((~rich(X0) & patient(X0)) | ~kind(X0)) [ennf transformation 16]
36. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (patient(X0) & ~quiet(X0))) & ((~patient(X0) | quiet(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [nnf transformation 1]
37. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (patient(X0) & ~quiet(X0))) & (~patient(X0) | quiet(X0) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [flattening 36]
44. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (~calm(X0) | ~curious(X0))) & ((calm(X0) & curious(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [nnf transformation 4]
45. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | ~calm(X0) | ~curious(X0)) & ((calm(X0) & curious(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [flattening 44]
59. ! [X0] : (((calm(X0) & ~tall(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~calm(X0) | tall(X0)))) [nnf transformation 10]
60. ! [X0] : (((calm(X0) & ~tall(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ~calm(X0) | tall(X0))) [flattening 59]
62. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (patient(X0) & kind(X0))) & ((~patient(X0) | ~kind(X0)) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [nnf transformation 12]
63. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (patient(X0) & kind(X0))) & (~patient(X0) | ~kind(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [flattening 62]
64. ! [X0] : (((~brave(X0) | ~kind(X0)) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | (brave(X0) & kind(X0)))) [nnf transformation 13]
65. ! [X0] : ((~brave(X0) | ~kind(X0) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | (brave(X0) & kind(X0)))) [flattening 64]
68. (((brave(susan) | quiet(susan)) & (~brave(susan) | ~quiet(susan))) | (~calm(susan) | kind(susan))) & ((calm(susan) & ~kind(susan)) | ((~quiet(susan) | brave(susan)) & (~brave(susan) | quiet(susan)))) [nnf transformation 15]
69. (((brave(susan) | quiet(susan)) & (~brave(susan) | ~quiet(susan))) | ~calm(susan) | kind(susan)) & ((calm(susan) & ~kind(susan)) | ((~quiet(susan) | brave(susan)) & (~brave(susan) | quiet(susan)))) [flattening 68]
78. ~patient(X0) | quiet(X0) | ~tall(X0) | happy(X0) [cnf transformation 37]
91. ~happy(X0) | curious(X0) | quiet(X0) [cnf transformation 45]
112. ~calm(X0) | ~patient(X0) | ~calm(X0) | tall(X0) [cnf transformation 60]
117. calm(X0) | ~patient(X0) | calm(X0) [cnf transformation 60]
123. ~kind(X0) | ~patient(X0) | rich(X0) | ~curious(X0) [cnf transformation 63]
131. ~funny(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 65]
134. ~kind(susan) | ~quiet(susan) | brave(susan) [cnf transformation 69]
139. ~kind(X0) | patient(X0) [cnf transformation 35]
140. ~kind(X0) | ~rich(X0) [cnf transformation 35]
147. funny(susan) [cnf transformation 20]
154. kind(susan) [cnf transformation 24]
155. ~calm(X0) | ~patient(X0) | tall(X0) [duplicate literal removal 112]
156. ~patient(X0) | calm(X0) [duplicate literal removal 117]
258. ~patient(X0) | tall(X0) [subsumption resolution 155,156]
270. 26 <=> kind(susan) [avatar definition]
272. kind(susan) <- (26) [avatar component clause 270]
278. 28 <=> quiet(susan) [avatar definition]
279. ~quiet(susan) <- (~28) [avatar component clause 278]
282. 29 <=> brave(susan) [avatar definition]
289. 29 | ~28 | ~26 [avatar split clause 134,270,278,282]
301. 26 [avatar split clause 154,270]
307. patient(susan) <- (26) [resolution 139,272]
308. ~rich(susan) <- (26) [resolution 140,272]
310. tall(susan) <- (26) [resolution 258,307]
401. ~kind(susan) | ~brave(susan) [resolution 131,147]
413. quiet(susan) | ~tall(susan) | happy(susan) <- (26) [resolution 78,307]
419. ~tall(susan) | happy(susan) <- (26, ~28) [subsumption resolution 413,279]
420. happy(susan) <- (26, ~28) [subsumption resolution 419,310]
423. curious(susan) | quiet(susan) <- (26, ~28) [resolution 420,91]
424. curious(susan) <- (26, ~28) [subsumption resolution 423,279]
478. ~patient(susan) | rich(susan) | ~curious(susan) <- (26) [resolution 123,272]
482. rich(susan) | ~curious(susan) <- (26) [subsumption resolution 478,307]
483. ~curious(susan) <- (26) [subsumption resolution 482,308]
484. $false <- (26, ~28) [subsumption resolution 483,424]
485. ~26 | 28 [avatar contradiction clause 484]
486. ~brave(susan) <- (26) [subsumption resolution 401,272]
487. ~29 | ~26 [avatar split clause 486,270,282]
488. $false [avatar sat refutation 289,301,485,487]
% SZS output end Proof for 6281665138677922886633801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not calm or old then someone is creative and vice versa.
Everyone who is curious or not quiet is curious or not humble and vice versa.
If someone is not quiet then someone is kind or humble.
If fred is either wise or not old then someone is either not patient or patient.
Everyone who is not old is both curious and kind.
If someone is brave or not kind then paul is either humble or not strong.
Everyone who is both rich and patient is either not strong or not calm and vice versa.
Everyone who is both curious and not quiet is both funny and not old and vice versa.
Everyone who is not wise is either curious or rich.
Everyone who is patient or rich is not patient or generous.
Everyone who is not patient or humble is generous or patient.
Everyone who is both tall and not brave is not creative.
If paul is either not humble or rich then someone is either not humble or not patient and vice versa.
Everyone who is not brave or not calm is not funny and vice versa.
Everyone who is not old is humble and vice versa.
Everyone who is both not old and curious is either not funny or not old.
Alice is both humble and not old.
Fred is patient or not kind.
Someone is both not wise and not funny.
Someone is not wise or not kind.
Someone is wise or not patient.
Someone is tall or calm.
Someone is patient or not rich. | Paul is not curious. | neutral | (((~calm(mary)|old(mary)))<=>(?[X]:(creative(X))))&
(![X]:((curious(X)|~quiet(X))<=>(curious(X)|~humble(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((kind(X)|humble(X)))))&
(((wise(fred)<~>~old(fred)))=>(?[X]:((~patient(X)<~>patient(X)))))&
(![X]:(~old(X)=>(curious(X)&kind(X))))&
((?[X]:((brave(X)|~kind(X))))=>((humble(paul)<~>~strong(paul))))&
(![X]:((rich(X)&patient(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:((curious(X)&~quiet(X))<=>(funny(X)&~old(X))))&
(![X]:(~wise(X)=>(curious(X)<~>rich(X))))&
(![X]:((patient(X)|rich(X))=>(~patient(X)|generous(X))))&
(![X]:((~patient(X)|humble(X))=>(generous(X)|patient(X))))&
(![X]:((tall(X)&~brave(X))=>~creative(X)))&
(((~humble(paul)<~>rich(paul)))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((~brave(X)|~calm(X))<=>~funny(X)))&
(![X]:(~old(X)<=>humble(X)))&
(![X]:((~old(X)&curious(X))=>(~funny(X)<~>~old(X))))&
((humble(alice)&~old(alice)))&
((patient(fred)|~kind(fred)))&
(?[X]:((~wise(X)&~funny(X))))&
(?[X]:((~wise(X)|~kind(X))))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:((patient(X)|~rich(X)))) | ~curious(paul) | [] | null | 0 |
Everyone who is either not strong or not creative is humble and vice versa.
Everyone who is either calm or not brave is not patient and vice versa.
Everyone who is both not brave and not strong is both not quiet and not wise.
Everyone who is not generous or rich is both tall and not brave.
Everyone who is not happy or funny is not patient or kind.
Everyone who is not strong is both patient and not tall and vice versa.
Everyone who is not calm or humble is both not humble and not happy and vice versa.
Everyone who is both not funny and not strong is not happy or quiet and vice versa.
If someone is not happy then someone is both not old and not creative.
If susan is both curious and not funny then someone is both kind and not curious and vice versa.
Everyone who is both not kind and not calm is both not creative and humble and vice versa.
Everyone who is both patient and not creative is not rich and vice versa.
Everyone who is either funny or generous is not old or strong.
If fred is creative then lucy is both humble and not patient.
If someone is either tall or old then someone is curious or not wise and vice versa.
If alice is either patient or tall then mary is calm or not humble and vice versa.
Fred is either not strong or old.
Someone is either creative or curious.
Someone is creative or not tall.
Someone is either not calm or not tall.
Someone is not brave.
Susan is not tall.
Someone is either funny or old.
Fred is either generous or rich. | Alice is creative. | contradiction | (![X]:((~strong(X)<~>~creative(X))<=>humble(X)))&
(![X]:((calm(X)<~>~brave(X))<=>~patient(X)))&
(![X]:((~brave(X)&~strong(X))=>(~quiet(X)&~wise(X))))&
(![X]:((~generous(X)|rich(X))=>(tall(X)&~brave(X))))&
(![X]:((~happy(X)|funny(X))=>(~patient(X)|kind(X))))&
(![X]:(~strong(X)<=>(patient(X)&~tall(X))))&
(![X]:((~calm(X)|humble(X))<=>(~humble(X)&~happy(X))))&
(![X]:((~funny(X)&~strong(X))<=>(~happy(X)|quiet(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~old(X)&~creative(X)))))&
(((curious(susan)&~funny(susan)))<=>(?[X]:((kind(X)&~curious(X)))))&
(![X]:((~kind(X)&~calm(X))<=>(~creative(X)&humble(X))))&
(![X]:((patient(X)&~creative(X))<=>~rich(X)))&
(![X]:((funny(X)<~>generous(X))=>(~old(X)|strong(X))))&
((creative(fred))=>((humble(lucy)&~patient(lucy))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((curious(X)|~wise(X)))))&
(((patient(alice)<~>tall(alice)))<=>((calm(mary)|~humble(mary))))&
((~strong(fred)<~>old(fred)))&
(?[X]:((creative(X)<~>curious(X))))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:(~brave(X)))&
(~tall(susan))&
(?[X]:((funny(X)<~>old(X))))&
((generous(fred)<~>rich(fred))) | creative(alice) | [
"p1",
"p3",
"p5",
"p6",
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 94257408159262384265878
% SZS output start Proof for 94257408159262384265878
2. ! [X0] : ((calm(X0) <~> ~brave(X0)) <=> ~patient(X0)) [input p1]
4. ! [X0] : ((rich(X0) | ~generous(X0)) => (~brave(X0) & tall(X0))) [input p3]
6. ! [X0] : (~strong(X0) <=> (~tall(X0) & patient(X0))) [input p5]
7. ! [X0] : ((humble(X0) | ~calm(X0)) <=> (~happy(X0) & ~humble(X0))) [input p6]
8. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (quiet(X0) | ~happy(X0))) [input p7]
12. ! [X0] : ((~creative(X0) & patient(X0)) <=> ~rich(X0)) [input p11]
16. (patient(alice) <~> tall(alice)) <=> (~humble(mary) | calm(mary)) [input p15]
25. creative(alice) [input hypothesis]
30. ! [X0] : ((~brave(X0) & tall(X0)) | (~rich(X0) & generous(X0))) [ennf transformation 4]
38. ! [X0] : ((((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | patient(X0)) & (~patient(X0) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0))))) [nnf transformation 2]
39. ! [X0] : ((~strong(X0) | (tall(X0) | ~patient(X0))) & ((~tall(X0) & patient(X0)) | strong(X0))) [nnf transformation 6]
40. ! [X0] : ((~strong(X0) | tall(X0) | ~patient(X0)) & ((~tall(X0) & patient(X0)) | strong(X0))) [flattening 39]
41. ! [X0] : (((humble(X0) | ~calm(X0)) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | (~humble(X0) & calm(X0)))) [nnf transformation 7]
42. ! [X0] : ((humble(X0) | ~calm(X0) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | (~humble(X0) & calm(X0)))) [flattening 41]
43. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~quiet(X0) & happy(X0))) & ((quiet(X0) | ~happy(X0)) | (strong(X0) | funny(X0)))) [nnf transformation 8]
44. ! [X0] : (((~strong(X0) & ~funny(X0)) | (~quiet(X0) & happy(X0))) & (quiet(X0) | ~happy(X0) | strong(X0) | funny(X0))) [flattening 43]
55. ! [X0] : (((~creative(X0) & patient(X0)) | rich(X0)) & (~rich(X0) | (creative(X0) | ~patient(X0)))) [nnf transformation 12]
56. ! [X0] : (((~creative(X0) & patient(X0)) | rich(X0)) & (~rich(X0) | creative(X0) | ~patient(X0))) [flattening 55]
63. (((~tall(alice) | ~patient(alice)) & (tall(alice) | patient(alice))) | (humble(mary) & ~calm(mary))) & ((~humble(mary) | calm(mary)) | ((patient(alice) | ~tall(alice)) & (tall(alice) | ~patient(alice)))) [nnf transformation 16]
64. (((~tall(alice) | ~patient(alice)) & (tall(alice) | patient(alice))) | (humble(mary) & ~calm(mary))) & (~humble(mary) | calm(mary) | ((patient(alice) | ~tall(alice)) & (tall(alice) | ~patient(alice)))) [flattening 63]
87. ~calm(X0) | brave(X0) | patient(X0) [cnf transformation 38]
91. ~rich(X0) | tall(X0) [cnf transformation 30]
93. ~rich(X0) | ~brave(X0) [cnf transformation 30]
96. patient(X0) | strong(X0) [cnf transformation 40]
100. ~humble(X0) | ~humble(X0) [cnf transformation 42]
101. ~happy(X0) | calm(X0) [cnf transformation 42]
107. ~strong(X0) | happy(X0) [cnf transformation 44]
121. ~creative(X0) | rich(X0) [cnf transformation 56]
137. ~tall(alice) | ~patient(alice) | humble(mary) [cnf transformation 64]
151. creative(alice) [cnf transformation 25]
152. ~humble(X0) [duplicate literal removal 100]
236. ~tall(alice) | ~patient(alice) [subsumption resolution 137,152]
238. 19 <=> patient(alice) [avatar definition]
240. ~patient(alice) <- (~19) [avatar component clause 238]
242. 20 <=> tall(alice) [avatar definition]
245. ~19 | ~20 [avatar split clause 236,242,238]
329. rich(alice) [resolution 121,151]
331. ~brave(alice) [resolution 329,93]
332. tall(alice) [resolution 329,91]
335. 20 [avatar split clause 332,242]
336. strong(alice) <- (~19) [resolution 240,96]
341. happy(alice) <- (~19) [resolution 336,107]
363. calm(alice) <- (~19) [resolution 341,101]
546. brave(alice) | patient(alice) <- (~19) [resolution 363,87]
547. patient(alice) <- (~19) [subsumption resolution 546,331]
548. $false <- (~19) [subsumption resolution 547,240]
549. 19 [avatar contradiction clause 548]
550. $false [avatar sat refutation 245,335,549]
% SZS output end Proof for 94257408159262384265878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and old then someone is both patient and not brave.
If mary is both rich and wise then susan is both generous and not wise.
If someone is either not tall or kind then someone is strong and vice versa.
Everyone who is not kind is not rich.
Everyone who is tall or not calm is both not happy and kind.
Everyone who is not old is either not rich or not humble.
If susan is either tall or not old then susan is either generous or strong and vice versa.
If fred is quiet then someone is either not strong or patient and vice versa.
If someone is either quiet or not funny then susan is both not rich and rich and vice versa.
Everyone who is quiet is rich or strong.
Everyone who is not kind or not happy is not calm.
Everyone who is both not tall and patient is both creative and tall and vice versa.
If someone is quiet then susan is funny.
If john is both strong and not brave then someone is both tall and not calm and vice versa.
If john is both humble and not generous then someone is not curious or funny and vice versa.
If someone is not calm or brave then john is old.
Someone is both old and not patient.
Someone is brave or not strong.
Susan is patient or generous.
Someone is not strong or brave.
Susan is either wise or not curious.
Someone is not happy or not kind.
Susan is not kind or generous.
John is both tall and old. | Susan is old. | neutral | ((?[X]:((patient(X)&old(X))))=>(?[X]:((patient(X)&~brave(X)))))&
(((rich(mary)&wise(mary)))=>((generous(susan)&~wise(susan))))&
((?[X]:((~tall(X)<~>kind(X))))<=>(?[X]:(strong(X))))&
(![X]:(~kind(X)=>~rich(X)))&
(![X]:((tall(X)|~calm(X))=>(~happy(X)&kind(X))))&
(![X]:(~old(X)=>(~rich(X)<~>~humble(X))))&
(((tall(susan)<~>~old(susan)))<=>((generous(susan)<~>strong(susan))))&
((quiet(fred))<=>(?[X]:((~strong(X)<~>patient(X)))))&
((?[X]:((quiet(X)<~>~funny(X))))<=>((~rich(susan)&rich(susan))))&
(![X]:(quiet(X)=>(rich(X)|strong(X))))&
(![X]:((~kind(X)|~happy(X))=>~calm(X)))&
(![X]:((~tall(X)&patient(X))<=>(creative(X)&tall(X))))&
((?[X]:(quiet(X)))=>(funny(susan)))&
(((strong(john)&~brave(john)))<=>(?[X]:((tall(X)&~calm(X)))))&
(((humble(john)&~generous(john)))<=>(?[X]:((~curious(X)|funny(X)))))&
((?[X]:((~calm(X)|brave(X))))=>(old(john)))&
(?[X]:((old(X)&~patient(X))))&
(?[X]:((brave(X)|~strong(X))))&
((patient(susan)|generous(susan)))&
(?[X]:((~strong(X)|brave(X))))&
((wise(susan)<~>~curious(susan)))&
(?[X]:((~happy(X)|~kind(X))))&
((~kind(susan)|generous(susan)))&
((tall(john)&old(john))) | old(susan) | [] | null | 0 |
Everyone who is not strong is either curious or funny.
If someone is either quiet or generous then someone is not old or not quiet.
Everyone who is both quiet and not brave is either curious or funny and vice versa.
If someone is either not curious or quiet then someone is both funny and brave.
If someone is funny then someone is either patient or creative and vice versa.
Everyone who is either not wise or not funny is not quiet and vice versa.
If someone is not quiet or not wise then someone is creative and vice versa.
Everyone who is either not strong or not quiet is both not quiet and not brave and vice versa.
If someone is both curious and quiet then someone is either generous or not patient and vice versa.
If fred is both not quiet and humble then susan is either old or not quiet and vice versa.
If someone is funny then someone is not old and vice versa.
If john is both humble and kind then someone is either humble or not strong and vice versa.
If someone is not wise or tall then susan is not tall and vice versa.
Everyone who is old or not generous is both not curious and creative and vice versa.
Everyone who is wise is not brave and vice versa.
Everyone who is generous or not funny is both calm and not kind.
Susan is either patient or not calm.
Mary is wise or not rich.
Someone is both happy and not funny. | Fred is curious. | contradiction | (![X]:(~strong(X)=>(curious(X)<~>funny(X))))&
((?[X]:((quiet(X)<~>generous(X))))=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:((quiet(X)&~brave(X))<=>(curious(X)<~>funny(X))))&
((?[X]:((~curious(X)<~>quiet(X))))=>(?[X]:((funny(X)&brave(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((~wise(X)<~>~funny(X))<=>~quiet(X)))&
((?[X]:((~quiet(X)|~wise(X))))<=>(?[X]:(creative(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(~quiet(X)&~brave(X))))&
((?[X]:((curious(X)&quiet(X))))<=>(?[X]:((generous(X)<~>~patient(X)))))&
(((~quiet(fred)&humble(fred)))<=>((old(susan)<~>~quiet(susan))))&
((?[X]:(funny(X)))<=>(?[X]:(~old(X))))&
(((humble(john)&kind(john)))<=>(?[X]:((humble(X)<~>~strong(X)))))&
((?[X]:((~wise(X)|tall(X))))<=>(~tall(susan)))&
(![X]:((old(X)|~generous(X))<=>(~curious(X)&creative(X))))&
(![X]:(wise(X)<=>~brave(X)))&
(![X]:((generous(X)|~funny(X))=>(calm(X)&~kind(X))))&
((patient(susan)<~>~calm(susan)))&
((wise(mary)|~rich(mary)))&
(?[X]:((happy(X)&~funny(X)))) | curious(fred) | [
"p0",
"p2",
"p5",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5579856704230087272459461
% SZS output start Proof for 5579856704230087272459461
1. ! [X0] : (~strong(X0) => (curious(X0) <~> funny(X0))) [input p0]
3. ! [X0] : ((~brave(X0) & quiet(X0)) <=> (curious(X0) <~> funny(X0))) [input p2]
6. ! [X0] : ((~wise(X0) <~> ~funny(X0)) <=> ~quiet(X0)) [input p5]
8. ! [X0] : ((~strong(X0) <~> ~quiet(X0)) <=> (~brave(X0) & ~quiet(X0))) [input p7]
15. ! [X0] : (wise(X0) <=> ~brave(X0)) [input p14]
20. curious(fred) [input hypothesis]
29. ! [X0] : ((curious(X0) <~> funny(X0)) | strong(X0)) [ennf transformation 1]
33. ! [X0] : (((~funny(X0) | ~curious(X0)) & (funny(X0) | curious(X0))) | strong(X0)) [nnf transformation 29]
38. ! [X0] : (((~brave(X0) & quiet(X0)) | ((curious(X0) | ~funny(X0)) & (funny(X0) | ~curious(X0)))) & (((~funny(X0) | ~curious(X0)) & (funny(X0) | curious(X0))) | (brave(X0) | ~quiet(X0)))) [nnf transformation 3]
39. ! [X0] : (((~brave(X0) & quiet(X0)) | ((curious(X0) | ~funny(X0)) & (funny(X0) | ~curious(X0)))) & (((~funny(X0) | ~curious(X0)) & (funny(X0) | curious(X0))) | brave(X0) | ~quiet(X0))) [flattening 38]
49. ! [X0] : ((((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | quiet(X0)) & (~quiet(X0) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0))))) [nnf transformation 6]
55. ! [X0] : ((((quiet(X0) | strong(X0)) & (~quiet(X0) | ~strong(X0))) | (brave(X0) | quiet(X0))) & ((~brave(X0) & ~quiet(X0)) | ((~strong(X0) | quiet(X0)) & (~quiet(X0) | strong(X0))))) [nnf transformation 8]
56. ! [X0] : ((((quiet(X0) | strong(X0)) & (~quiet(X0) | ~strong(X0))) | brave(X0) | quiet(X0)) & ((~brave(X0) & ~quiet(X0)) | ((~strong(X0) | quiet(X0)) & (~quiet(X0) | strong(X0))))) [flattening 55]
80. ! [X0] : ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0))) [nnf transformation 15]
85. ~funny(X0) | ~curious(X0) | strong(X0) [cnf transformation 33]
89. ~quiet(X0) | ~curious(X0) | brave(X0) | ~funny(X0) [cnf transformation 39]
90. ~curious(X0) | funny(X0) | quiet(X0) [cnf transformation 39]
92. ~brave(X0) | funny(X0) | ~curious(X0) [cnf transformation 39]
102. ~quiet(X0) | ~funny(X0) | wise(X0) [cnf transformation 49]
103. ~wise(X0) | ~quiet(X0) | funny(X0) [cnf transformation 49]
104. ~wise(X0) | ~funny(X0) | quiet(X0) [cnf transformation 49]
112. ~brave(X0) | ~strong(X0) | quiet(X0) [cnf transformation 56]
143. ~wise(X0) | ~brave(X0) [cnf transformation 80]
144. wise(X0) | brave(X0) [cnf transformation 80]
152. curious(fred) [cnf transformation 20]
281. 30 <=> quiet(fred) [avatar definition]
282. quiet(fred) <- (30) [avatar component clause 281]
283. ~quiet(fred) <- (~30) [avatar component clause 281]
452. funny(fred) | quiet(fred) [resolution 90,152]
455. 54 <=> funny(fred) [avatar definition]
456. ~funny(fred) <- (~54) [avatar component clause 455]
457. funny(fred) <- (54) [avatar component clause 455]
458. 30 | 54 [avatar split clause 452,455,281]
501. ~curious(fred) | strong(fred) <- (54) [resolution 457,85]
502. strong(fred) <- (54) [subsumption resolution 501,152]
520. ~quiet(X0) | funny(X0) | brave(X0) [resolution 103,144]
526. ~funny(X0) | quiet(X0) | brave(X0) [resolution 104,144]
639. quiet(fred) | brave(fred) <- (54) [resolution 526,457]
644. brave(fred) <- (~30, 54) [subsumption resolution 639,283]
697. ~strong(fred) | quiet(fred) <- (~30, 54) [resolution 644,112]
701. quiet(fred) <- (~30, 54) [subsumption resolution 697,502]
702. $false <- (~30, 54) [subsumption resolution 701,283]
703. 30 | ~54 [avatar contradiction clause 702]
706. 66 <=> brave(fred) [avatar definition]
708. brave(fred) <- (66) [avatar component clause 706]
759. funny(fred) | brave(fred) <- (30) [resolution 282,520]
760. ~curious(fred) | brave(fred) | ~funny(fred) <- (30) [resolution 282,89]
762. ~funny(fred) | wise(fred) <- (30) [resolution 282,102]
764. brave(fred) | ~funny(fred) <- (30) [subsumption resolution 760,152]
765. brave(fred) <- (30, 54) [subsumption resolution 764,457]
766. 66 | ~30 | ~54 [avatar split clause 765,455,281,706]
767. wise(fred) <- (30, 54) [subsumption resolution 762,457]
784. ~brave(fred) <- (30, 54) [resolution 767,143]
785. $false <- (30, 54, 66) [subsumption resolution 784,708]
786. ~30 | ~54 | ~66 [avatar contradiction clause 785]
804. funny(fred) | ~curious(fred) <- (66) [resolution 708,92]
805. ~curious(fred) <- (~54, 66) [subsumption resolution 804,456]
806. $false <- (~54, 66) [subsumption resolution 805,152]
807. 54 | ~66 [avatar contradiction clause 806]
808. brave(fred) <- (30, ~54) [subsumption resolution 759,456]
809. 66 | ~30 | 54 [avatar split clause 808,455,281,706]
810. $false [avatar sat refutation 458,703,766,786,807,809]
% SZS output end Proof for 5579856704230087272459461
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either quiet or not tall then someone is both calm and funny and vice versa.
Everyone who is both not generous and rich is both brave and not old and vice versa.
Everyone who is not curious is not humble or not funny.
Everyone who is not brave or not curious is either not rich or creative and vice versa.
Everyone who is either not brave or not quiet is not calm or not patient.
Everyone who is not brave is either not generous or not patient.
If someone is either tall or creative then someone is not quiet and vice versa.
Everyone who is both old and kind is not wise.
If someone is not brave or not wise then lucy is either old or patient.
Everyone who is not tall or kind is not quiet.
Everyone who is happy is both not kind and not humble and vice versa.
Everyone who is rich or not brave is not generous.
Everyone who is either not funny or humble is both not brave and not generous and vice versa.
If john is not old or tall then paul is happy or brave and vice versa.
Everyone who is both old and curious is quiet and vice versa.
Everyone who is both not old and not kind is not curious or curious and vice versa.
Alice is not creative or humble.
Fred is happy.
Someone is not tall.
John is happy.
Someone is either not tall or curious.
Someone is not humble or not wise.
John is both wise and not old. | John is not generous. | entailment | (((quiet(susan)<~>~tall(susan)))<=>(?[X]:((calm(X)&funny(X)))))&
(![X]:((~generous(X)&rich(X))<=>(brave(X)&~old(X))))&
(![X]:(~curious(X)=>(~humble(X)|~funny(X))))&
(![X]:((~brave(X)|~curious(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((~brave(X)<~>~quiet(X))=>(~calm(X)|~patient(X))))&
(![X]:(~brave(X)=>(~generous(X)<~>~patient(X))))&
((?[X]:((tall(X)<~>creative(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((old(X)&kind(X))=>~wise(X)))&
((?[X]:((~brave(X)|~wise(X))))=>((old(lucy)<~>patient(lucy))))&
(![X]:((~tall(X)|kind(X))=>~quiet(X)))&
(![X]:(happy(X)<=>(~kind(X)&~humble(X))))&
(![X]:((rich(X)|~brave(X))=>~generous(X)))&
(![X]:((~funny(X)<~>humble(X))<=>(~brave(X)&~generous(X))))&
(((~old(john)|tall(john)))<=>((happy(paul)|brave(paul))))&
(![X]:((old(X)&curious(X))<=>quiet(X)))&
(![X]:((~old(X)&~kind(X))<=>(~curious(X)|curious(X))))&
((~creative(alice)|humble(alice)))&
(happy(fred))&
(?[X]:(~tall(X)))&
(happy(john))&
(?[X]:((~tall(X)<~>curious(X))))&
(?[X]:((~humble(X)|~wise(X))))&
((wise(john)&~old(john))) | ~generous(john) | [
"p1",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6687548889746431677543768
% SZS output start Proof for 6687548889746431677543768
2. ! [X0] : ((rich(X0) & ~generous(X0)) <=> (~old(X0) & brave(X0))) [input p1]
12. ! [X0] : ((~brave(X0) | rich(X0)) => ~generous(X0)) [input p11]
16. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (curious(X0) | ~curious(X0))) [input p15]
24. generous(john) [input hypothesis]
35. ! [X0] : (~generous(X0) | (brave(X0) & ~rich(X0))) [ennf transformation 12]
40. ! [X0] : (((rich(X0) & ~generous(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (~rich(X0) | generous(X0)))) [nnf transformation 2]
41. ! [X0] : (((rich(X0) & ~generous(X0)) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | ~rich(X0) | generous(X0))) [flattening 40]
60. ! [X0] : (((~kind(X0) & ~old(X0)) | (~curious(X0) & curious(X0))) & ((curious(X0) | ~curious(X0)) | (kind(X0) | old(X0)))) [nnf transformation 16]
61. ! [X0] : (((~kind(X0) & ~old(X0)) | (~curious(X0) & curious(X0))) & (curious(X0) | ~curious(X0) | kind(X0) | old(X0))) [flattening 60]
77. ~brave(X0) | old(X0) | ~generous(X0) [cnf transformation 41]
105. ~generous(X0) | brave(X0) [cnf transformation 35]
120. ~old(X0) | curious(X0) [cnf transformation 61]
121. ~curious(X0) | ~old(X0) [cnf transformation 61]
133. generous(john) [cnf transformation 24]
225. ~old(X0) [subsumption resolution 120,121]
262. brave(john) [resolution 105,133]
274. old(john) | ~generous(john) [resolution 262,77]
276. ~generous(john) [subsumption resolution 274,225]
277. $false [subsumption resolution 276,133]
% SZS output end Proof for 6687548889746431677543768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not wise is patient and vice versa.
Everyone who is not kind is not rich.
If john is both not rich and quiet then someone is both not funny and creative and vice versa.
Everyone who is both kind and happy is either not wise or old and vice versa.
Everyone who is not funny is both tall and not brave.
Everyone who is both calm and curious is not humble or not funny.
Everyone who is both kind and curious is not creative.
If john is both patient and not curious then someone is both not curious and not rich and vice versa.
If susan is not tall then someone is not happy or patient.
Everyone who is either tall or not kind is brave or not curious and vice versa.
If alice is generous or not creative then fred is both brave and not funny and vice versa.
If someone is both not humble and rich then someone is either patient or not patient.
Everyone who is strong is not old.
If someone is not brave or not patient then someone is either rich or creative and vice versa.
If someone is kind then paul is not quiet or not creative and vice versa.
If someone is kind or funny then lucy is both kind and not calm and vice versa.
Someone is not old or funny.
Paul is both not strong and not curious.
Alice is either quiet or old.
Someone is both calm and wise.
Mary is either not strong or happy.
John is quiet or not tall.
Susan is curious or not wise.
Someone is either quiet or brave. | Paul is calm. | neutral | (![X]:((wise(X)|~wise(X))<=>patient(X)))&
(![X]:(~kind(X)=>~rich(X)))&
(((~rich(john)&quiet(john)))<=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((kind(X)&happy(X))<=>(~wise(X)<~>old(X))))&
(![X]:(~funny(X)=>(tall(X)&~brave(X))))&
(![X]:((calm(X)&curious(X))=>(~humble(X)|~funny(X))))&
(![X]:((kind(X)&curious(X))=>~creative(X)))&
(((patient(john)&~curious(john)))<=>(?[X]:((~curious(X)&~rich(X)))))&
((~tall(susan))=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((tall(X)<~>~kind(X))<=>(brave(X)|~curious(X))))&
(((generous(alice)|~creative(alice)))<=>((brave(fred)&~funny(fred))))&
((?[X]:((~humble(X)&rich(X))))=>(?[X]:((patient(X)<~>~patient(X)))))&
(![X]:(strong(X)=>~old(X)))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((rich(X)<~>creative(X)))))&
((?[X]:(kind(X)))<=>((~quiet(paul)|~creative(paul))))&
((?[X]:((kind(X)|funny(X))))<=>((kind(lucy)&~calm(lucy))))&
(?[X]:((~old(X)|funny(X))))&
((~strong(paul)&~curious(paul)))&
((quiet(alice)<~>old(alice)))&
(?[X]:((calm(X)&wise(X))))&
((~strong(mary)<~>happy(mary)))&
((quiet(john)|~tall(john)))&
((curious(susan)|~wise(susan)))&
(?[X]:((quiet(X)<~>brave(X)))) | calm(paul) | [] | null | 0 |
Everyone who is both not rich and not kind is not humble and vice versa. If someone is not curious then someone is either funny or not generous. Everyone who is both not kind and not curious is not patient. Everyone who is both not humble and not creative is either not curious or not patient. Everyone who is old or rich is not rich or strong and vice versa. If alice is both old and not generous then someone is both old and not creative. Everyone who is not quiet or patient is not patient. Everyone who is funny is wise. If someone is either not patient or wise then someone is both not quiet and not old. If mary is both not curious and tall then someone is old or wise and vice versa. Everyone who is not curious is funny and vice versa. If someone is both not tall and wise then lucy is either patient or not curious and vice versa. If someone is both wise and not curious then someone is both not humble and patient. If someone is generous or wise then someone is either not quiet or wise and vice versa. If someone is either not creative or patient then mary is both strong and not strong and vice versa. Someone is calm. Someone is creative or curious. Alice is not funny. Susan is either brave or tall. | Susan is not old. | entailment | (![X]:((~rich(X)&~kind(X))<=>~humble(X)))&
((?[X]:(~curious(X)))=>(?[X]:((funny(X)<~>~generous(X)))))&
(![X]:((~kind(X)&~curious(X))=>~patient(X)))&
(![X]:((~humble(X)&~creative(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((old(X)|rich(X))<=>(~rich(X)|strong(X))))&
(((old(alice)&~generous(alice)))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((~quiet(X)|patient(X))=>~patient(X)))&
(![X]:(funny(X)=>wise(X)))&
((?[X]:((~patient(X)<~>wise(X))))=>(?[X]:((~quiet(X)&~old(X)))))&
(((~curious(mary)&tall(mary)))<=>(?[X]:((old(X)|wise(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
((?[X]:((~tall(X)&wise(X))))<=>((patient(lucy)<~>~curious(lucy))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:((~creative(X)<~>patient(X))))<=>((strong(mary)&~strong(mary))))&
(?[X]:(calm(X)))&
(?[X]:((creative(X)|curious(X))))&
(~funny(alice))&
((brave(susan)<~>tall(susan))) | ~old(susan) | [
"p6",
"p7",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4255006837143436570112971
% SZS output start Proof for 4255006837143436570112971
7. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~patient(X0)) [input p6]
8. ! [X0] : (funny(X0) => wise(X0)) [input p7]
10. (tall(mary) & ~curious(mary)) <=> ? [X0] : (wise(X0) | old(X0)) [input p9]
11. ! [X0] : (~curious(X0) <=> funny(X0)) [input p10]
13. ? [X0] : (~curious(X0) & wise(X0)) => ? [X0] : (patient(X0) & ~humble(X0)) [input p12]
20. old(susan) [input hypothesis]
23. ? [X0] : (~curious(X0) & wise(X0)) => ? [X1] : (patient(X1) & ~humble(X1)) [rectify 13]
33. ! [X0] : (~patient(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 7]
34. ! [X0] : (wise(X0) | ~funny(X0)) [ennf transformation 8]
36. ? [X1] : (patient(X1) & ~humble(X1)) | ! [X0] : (curious(X0) | ~wise(X0)) [ennf transformation 23]
52. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X0] : (wise(X0) | old(X0)) | (~tall(mary) | curious(mary))) [nnf transformation 10]
53. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X0] : (wise(X0) | old(X0)) | ~tall(mary) | curious(mary)) [flattening 52]
54. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X1] : (wise(X1) | old(X1)) | ~tall(mary) | curious(mary)) [rectify 53]
55. ? [X1] : (wise(X1) | old(X1)) => (wise(sK3) | old(sK3)) [choice axiom]
56. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & ((wise(sK3) | old(sK3)) | ~tall(mary) | curious(mary)) [skolemisation 54,55]
57. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 11]
62. ? [X0] : (patient(X0) & ~humble(X0)) | ! [X1] : (curious(X1) | ~wise(X1)) [rectify 36]
63. ? [X0] : (patient(X0) & ~humble(X0)) => (patient(sK5) & ~humble(sK5)) [choice axiom]
64. (patient(sK5) & ~humble(sK5)) | ! [X1] : (curious(X1) | ~wise(X1)) [skolemisation 62,63]
93. ~patient(X0) | ~patient(X0) [cnf transformation 33]
94. ~funny(X0) | wise(X0) [cnf transformation 34]
100. ~curious(mary) | ~old(X0) [cnf transformation 56]
104. funny(X0) | curious(X0) [cnf transformation 57]
113. patient(sK5) | curious(X1) | ~wise(X1) [cnf transformation 64]
130. old(susan) [cnf transformation 20]
131. ~patient(X0) [duplicate literal removal 93]
135. 1 <=> ! [X1] : curious(X1) [avatar definition]
136. curious(X1) <- (1) [avatar component clause 135]
189. 13 <=> ! [X0] : ~old(X0) [avatar definition]
190. ~old(X0) <- (13) [avatar component clause 189]
193. 14 <=> curious(mary) [avatar definition]
195. ~curious(mary) <- (~14) [avatar component clause 193]
197. 13 | ~14 [avatar split clause 100,193,189]
228. curious(X1) | ~wise(X1) [subsumption resolution 113,131]
290. $false <- (13) [resolution 190,130]
291. ~13 [avatar contradiction clause 290]
296. curious(X0) | wise(X0) [resolution 104,94]
297. curious(X0) [subsumption resolution 296,228]
298. 1 [avatar split clause 297,135]
299. $false <- (1, ~14) [resolution 136,195]
302. ~1 | 14 [avatar contradiction clause 299]
303. $false [avatar sat refutation 197,291,298,302]
% SZS output end Proof for 4255006837143436570112971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient then someone is both not rich and not kind.
Everyone who is not calm or generous is both tall and not patient.
If someone is kind then someone is either happy or kind.
If someone is curious then someone is not kind and vice versa.
Everyone who is not generous or kind is not calm.
If someone is not patient or brave then john is either not old or not generous and vice versa.
Everyone who is humble is both brave and not wise.
If someone is kind then someone is both wise and tall and vice versa.
If mary is calm or brave then someone is patient and vice versa.
If someone is both generous and not brave then someone is wise and vice versa.
Everyone who is either curious or not kind is not tall and vice versa.
Everyone who is kind is not humble.
If someone is both not curious and not rich then lucy is quiet and vice versa.
Everyone who is either not strong or brave is not happy.
Everyone who is both brave and calm is generous or not creative.
Someone is both not old and not strong.
Mary is both creative and not happy.
Someone is brave or not rich.
Mary is either not old or not tall.
Mary is patient or not kind.
Alice is not funny.
Someone is wise or happy. | Mary is not quiet. | neutral | ((?[X]:(~patient(X)))=>(?[X]:((~rich(X)&~kind(X)))))&
(![X]:((~calm(X)|generous(X))=>(tall(X)&~patient(X))))&
((?[X]:(kind(X)))=>(?[X]:((happy(X)<~>kind(X)))))&
((?[X]:(curious(X)))<=>(?[X]:(~kind(X))))&
(![X]:((~generous(X)|kind(X))=>~calm(X)))&
((?[X]:((~patient(X)|brave(X))))<=>((~old(john)<~>~generous(john))))&
(![X]:(humble(X)=>(brave(X)&~wise(X))))&
((?[X]:(kind(X)))<=>(?[X]:((wise(X)&tall(X)))))&
(((calm(mary)|brave(mary)))<=>(?[X]:(patient(X))))&
((?[X]:((generous(X)&~brave(X))))<=>(?[X]:(wise(X))))&
(![X]:((curious(X)<~>~kind(X))<=>~tall(X)))&
(![X]:(kind(X)=>~humble(X)))&
((?[X]:((~curious(X)&~rich(X))))<=>(quiet(lucy)))&
(![X]:((~strong(X)<~>brave(X))=>~happy(X)))&
(![X]:((brave(X)&calm(X))=>(generous(X)|~creative(X))))&
(?[X]:((~old(X)&~strong(X))))&
((creative(mary)&~happy(mary)))&
(?[X]:((brave(X)|~rich(X))))&
((~old(mary)<~>~tall(mary)))&
((patient(mary)|~kind(mary)))&
(~funny(alice))&
(?[X]:((wise(X)|happy(X)))) | ~quiet(mary) | [] | null | 0 |
Everyone who is not tall or not quiet is not kind or not quiet. If susan is kind then john is wise or not funny and vice versa. Everyone who is not funny is either creative or happy and vice versa. Everyone who is patient or not tall is both not patient and quiet and vice versa. Everyone who is not creative or old is quiet. If fred is either patient or not humble then someone is kind or not funny and vice versa. Everyone who is either not creative or not calm is quiet and vice versa. If susan is not generous or not creative then someone is both humble and not happy. Everyone who is calm or brave is both quiet and not creative and vice versa. Everyone who is both not strong and not tall is funny or rich. If lucy is both not funny and not tall then someone is not patient or generous. If john is either not funny or not humble then someone is both strong and not happy. Everyone who is calm or generous is both old and humble and vice versa. If someone is both not wise and kind then someone is old or not brave. If alice is either not wise or funny then someone is old or quiet. Everyone who is patient is either brave or not wise. Someone is not happy or not humble. Someone is not patient or calm. Mary is both not happy and not generous. John is not curious. Lucy is not generous or humble. Someone is quiet. Someone is strong. | John is quiet. | entailment | (![X]:((~tall(X)|~quiet(X))=>(~kind(X)|~quiet(X))))&
((kind(susan))<=>((wise(john)|~funny(john))))&
(![X]:(~funny(X)<=>(creative(X)<~>happy(X))))&
(![X]:((patient(X)|~tall(X))<=>(~patient(X)&quiet(X))))&
(![X]:((~creative(X)|old(X))=>quiet(X)))&
(((patient(fred)<~>~humble(fred)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((~creative(X)<~>~calm(X))<=>quiet(X)))&
(((~generous(susan)|~creative(susan)))=>(?[X]:((humble(X)&~happy(X)))))&
(![X]:((calm(X)|brave(X))<=>(quiet(X)&~creative(X))))&
(![X]:((~strong(X)&~tall(X))=>(funny(X)|rich(X))))&
(((~funny(lucy)&~tall(lucy)))=>(?[X]:((~patient(X)|generous(X)))))&
(((~funny(john)<~>~humble(john)))=>(?[X]:((strong(X)&~happy(X)))))&
(![X]:((calm(X)|generous(X))<=>(old(X)&humble(X))))&
((?[X]:((~wise(X)&kind(X))))=>(?[X]:((old(X)|~brave(X)))))&
(((~wise(alice)<~>funny(alice)))=>(?[X]:((old(X)|quiet(X)))))&
(![X]:(patient(X)=>(brave(X)<~>~wise(X))))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((~patient(X)|calm(X))))&
((~happy(mary)&~generous(mary)))&
(~curious(john))&
((~generous(lucy)|humble(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X))) | quiet(john) | [
"p4",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5047116462686419765945737
% SZS output start Proof for 5047116462686419765945737
5. ! [X0] : ((old(X0) | ~creative(X0)) => quiet(X0)) [input p4]
7. ! [X0] : ((~creative(X0) <~> ~calm(X0)) <=> quiet(X0)) [input p6]
9. ! [X0] : ((brave(X0) | calm(X0)) <=> (~creative(X0) & quiet(X0))) [input p8]
24. ~quiet(john) [input hypothesis]
32. ! [X0] : (quiet(X0) | (~old(X0) & creative(X0))) [ennf transformation 5]
49. ! [X0] : ((((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ~quiet(X0)) & (quiet(X0) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0))))) [nnf transformation 7]
52. ! [X0] : (((brave(X0) | calm(X0)) | (creative(X0) | ~quiet(X0))) & ((~creative(X0) & quiet(X0)) | (~brave(X0) & ~calm(X0)))) [nnf transformation 9]
53. ! [X0] : ((brave(X0) | calm(X0) | creative(X0) | ~quiet(X0)) & ((~creative(X0) & quiet(X0)) | (~brave(X0) & ~calm(X0)))) [flattening 52]
88. quiet(X0) | creative(X0) [cnf transformation 32]
97. quiet(X0) | ~creative(X0) | calm(X0) [cnf transformation 49]
99. calm(X0) | creative(X0) | ~quiet(X0) [cnf transformation 49]
104. quiet(X0) | ~calm(X0) [cnf transformation 53]
128. ~quiet(john) [cnf transformation 24]
170. calm(X0) | creative(X0) [subsumption resolution 99,88]
171. quiet(X0) | calm(X0) [subsumption resolution 97,170]
192. quiet(X0) [subsumption resolution 104,171]
224. $false [subsumption resolution 128,192]
% SZS output end Proof for 5047116462686419765945737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is wise then someone is both creative and not creative.
Everyone who is both brave and happy is not calm and vice versa.
If alice is either funny or patient then someone is both not strong and creative.
Everyone who is both not patient and patient is rich or funny.
Everyone who is not calm or old is not funny or not rich and vice versa.
Everyone who is either not humble or not tall is both funny and not humble.
Everyone who is not happy or not funny is both not calm and creative and vice versa.
Everyone who is either humble or brave is either happy or creative.
If someone is patient then someone is both humble and tall.
Everyone who is happy is both tall and not calm.
If someone is both not patient and not funny then mary is not patient.
Everyone who is old or happy is not funny.
Everyone who is both not happy and not curious is not curious or generous.
If mary is not creative or rich then alice is funny or not calm and vice versa.
Everyone who is not humble or humble is not calm or not funny and vice versa.
Someone is humble.
Someone is not patient.
Someone is patient.
Someone is either not kind or kind.
Alice is not old.
Mary is generous or old.
Someone is curious. | John is not generous. | neutral | ((wise(john))=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((brave(X)&happy(X))<=>~calm(X)))&
(((funny(alice)<~>patient(alice)))=>(?[X]:((~strong(X)&creative(X)))))&
(![X]:((~patient(X)&patient(X))=>(rich(X)|funny(X))))&
(![X]:((~calm(X)|old(X))<=>(~funny(X)|~rich(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(funny(X)&~humble(X))))&
(![X]:((~happy(X)|~funny(X))<=>(~calm(X)&creative(X))))&
(![X]:((humble(X)<~>brave(X))=>(happy(X)<~>creative(X))))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)&tall(X)))))&
(![X]:(happy(X)=>(tall(X)&~calm(X))))&
((?[X]:((~patient(X)&~funny(X))))=>(~patient(mary)))&
(![X]:((old(X)|happy(X))=>~funny(X)))&
(![X]:((~happy(X)&~curious(X))=>(~curious(X)|generous(X))))&
(((~creative(mary)|rich(mary)))<=>((funny(alice)|~calm(alice))))&
(![X]:((~humble(X)|humble(X))<=>(~calm(X)|~funny(X))))&
(?[X]:(humble(X)))&
(?[X]:(~patient(X)))&
(?[X]:(patient(X)))&
(?[X]:((~kind(X)<~>kind(X))))&
(~old(alice))&
((generous(mary)|old(mary)))&
(?[X]:(curious(X))) | ~generous(john) | [] | null | 0 |
If paul is both not quiet and not tall then someone is both humble and curious and vice versa.
If mary is happy or not happy then lucy is either not tall or not curious and vice versa.
Everyone who is either not calm or not old is not calm and vice versa.
If alice is not curious then john is both not kind and not rich and vice versa.
Everyone who is either not humble or not old is happy or not patient and vice versa.
Everyone who is happy or not generous is not calm or generous.
Everyone who is both humble and not patient is not curious.
Everyone who is not funny or old is both not curious and not kind and vice versa.
Everyone who is both not quiet and tall is either curious or rich and vice versa.
If someone is both not quiet and not old then fred is either not happy or calm and vice versa.
Everyone who is both curious and patient is either not creative or wise.
If someone is either happy or not calm then someone is both old and tall.
Everyone who is funny or kind is either patient or happy and vice versa.
Everyone who is either funny or curious is not calm or not brave.
If someone is either calm or not wise then someone is either tall or happy and vice versa.
Everyone who is both not wise and kind is patient or not funny and vice versa.
Someone is quiet.
John is not humble.
Alice is either not quiet or not patient.
Alice is both not brave and old. | Mary is calm. | neutral | (((~quiet(paul)&~tall(paul)))<=>(?[X]:((humble(X)&curious(X)))))&
(((happy(mary)|~happy(mary)))<=>((~tall(lucy)<~>~curious(lucy))))&
(![X]:((~calm(X)<~>~old(X))<=>~calm(X)))&
((~curious(alice))<=>((~kind(john)&~rich(john))))&
(![X]:((~humble(X)<~>~old(X))<=>(happy(X)|~patient(X))))&
(![X]:((happy(X)|~generous(X))=>(~calm(X)|generous(X))))&
(![X]:((humble(X)&~patient(X))=>~curious(X)))&
(![X]:((~funny(X)|old(X))<=>(~curious(X)&~kind(X))))&
(![X]:((~quiet(X)&tall(X))<=>(curious(X)<~>rich(X))))&
((?[X]:((~quiet(X)&~old(X))))<=>((~happy(fred)<~>calm(fred))))&
(![X]:((curious(X)&patient(X))=>(~creative(X)<~>wise(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((old(X)&tall(X)))))&
(![X]:((funny(X)|kind(X))<=>(patient(X)<~>happy(X))))&
(![X]:((funny(X)<~>curious(X))=>(~calm(X)|~brave(X))))&
((?[X]:((calm(X)<~>~wise(X))))<=>(?[X]:((tall(X)<~>happy(X)))))&
(![X]:((~wise(X)&kind(X))<=>(patient(X)|~funny(X))))&
(?[X]:(quiet(X)))&
(~humble(john))&
((~quiet(alice)<~>~patient(alice)))&
((~brave(alice)&old(alice))) | calm(mary) | [] | null | 0 |
If paul is either not old or creative then someone is not curious and vice versa.
Everyone who is not brave is both creative and brave.
Everyone who is tall is not brave.
Everyone who is either not strong or rich is both generous and quiet.
If paul is old then susan is both funny and curious.
Everyone who is brave or funny is either not old or not brave and vice versa.
If someone is not curious or quiet then someone is either not happy or funny and vice versa.
If someone is both not old and brave then mary is brave or funny and vice versa.
Everyone who is not old is both not wise and not funny and vice versa.
Everyone who is either not old or kind is either generous or tall and vice versa.
Everyone who is both tall and humble is either not strong or kind.
If someone is not generous then lucy is not curious.
Everyone who is quiet or not creative is strong.
If someone is either not curious or tall then susan is wise or calm and vice versa.
Everyone who is either not strong or not brave is not rich.
Everyone who is kind or funny is either not strong or not curious and vice versa.
Alice is both not kind and not patient.
Lucy is calm.
Someone is either tall or generous.
Someone is either not brave or brave.
John is funny or curious.
Someone is not funny or not happy.
Paul is calm. | Alice is not funny. | entailment | (((~old(paul)<~>creative(paul)))<=>(?[X]:(~curious(X))))&
(![X]:(~brave(X)=>(creative(X)&brave(X))))&
(![X]:(tall(X)=>~brave(X)))&
(![X]:((~strong(X)<~>rich(X))=>(generous(X)&quiet(X))))&
((old(paul))=>((funny(susan)&curious(susan))))&
(![X]:((brave(X)|funny(X))<=>(~old(X)<~>~brave(X))))&
((?[X]:((~curious(X)|quiet(X))))<=>(?[X]:((~happy(X)<~>funny(X)))))&
((?[X]:((~old(X)&brave(X))))<=>((brave(mary)|funny(mary))))&
(![X]:(~old(X)<=>(~wise(X)&~funny(X))))&
(![X]:((~old(X)<~>kind(X))<=>(generous(X)<~>tall(X))))&
(![X]:((tall(X)&humble(X))=>(~strong(X)<~>kind(X))))&
((?[X]:(~generous(X)))=>(~curious(lucy)))&
(![X]:((quiet(X)|~creative(X))=>strong(X)))&
((?[X]:((~curious(X)<~>tall(X))))<=>((wise(susan)|calm(susan))))&
(![X]:((~strong(X)<~>~brave(X))=>~rich(X)))&
(![X]:((kind(X)|funny(X))<=>(~strong(X)<~>~curious(X))))&
((~kind(alice)&~patient(alice)))&
(calm(lucy))&
(?[X]:((tall(X)<~>generous(X))))&
(?[X]:((~brave(X)<~>brave(X))))&
((funny(john)|curious(john)))&
(?[X]:((~funny(X)|~happy(X))))&
(calm(paul)) | ~funny(alice) | [
"p1",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 117629372654731640679923
% SZS output start Proof for 117629372654731640679923
2. ! [X0] : (~brave(X0) => (brave(X0) & creative(X0))) [input p1]
6. ! [X0] : ((funny(X0) | brave(X0)) <=> (~old(X0) <~> ~brave(X0))) [input p5]
9. ! [X0] : (~old(X0) <=> (~funny(X0) & ~wise(X0))) [input p8]
24. funny(alice) [input hypothesis]
28. ! [X0] : ((brave(X0) & creative(X0)) | brave(X0)) [ennf transformation 2]
40. ! [X0] : (((funny(X0) | brave(X0)) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | (~funny(X0) & ~brave(X0)))) [nnf transformation 6]
41. ! [X0] : ((funny(X0) | brave(X0) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0)))) & (((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | (~funny(X0) & ~brave(X0)))) [flattening 40]
52. ! [X0] : ((~old(X0) | (funny(X0) | wise(X0))) & ((~funny(X0) & ~wise(X0)) | old(X0))) [nnf transformation 9]
53. ! [X0] : ((~old(X0) | funny(X0) | wise(X0)) & ((~funny(X0) & ~wise(X0)) | old(X0))) [flattening 52]
76. brave(X0) | brave(X0) [cnf transformation 28]
84. ~brave(X0) | ~old(X0) | ~brave(X0) [cnf transformation 41]
102. ~funny(X0) | old(X0) [cnf transformation 53]
138. funny(alice) [cnf transformation 24]
139. ~brave(X0) | ~old(X0) [duplicate literal removal 84]
141. brave(X0) [duplicate literal removal 76]
173. ~old(X0) [subsumption resolution 139,141]
205. ~funny(X0) [subsumption resolution 102,173]
237. $false [subsumption resolution 138,205]
% SZS output end Proof for 117629372654731640679923
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or calm is not creative.
Everyone who is not patient or not brave is either humble or generous and vice versa.
If fred is both quiet and rich then mary is both strong and creative.
If susan is either not calm or not rich then john is both not old and not creative and vice versa.
If someone is either not wise or not tall then mary is funny or brave and vice versa.
Everyone who is strong or quiet is not tall and vice versa.
If mary is both not rich and not kind then susan is either not strong or not rich and vice versa.
Everyone who is either not tall or strong is not calm or tall and vice versa.
If someone is kind or not strong then mary is either calm or not old.
Everyone who is generous or strong is not humble or patient and vice versa.
If mary is either kind or old then fred is curious.
If someone is both not creative and not curious then john is both patient and quiet and vice versa.
Everyone who is not quiet or not rich is not brave and vice versa.
Everyone who is not brave is either not generous or calm.
Everyone who is not patient or not old is either happy or wise.
Everyone who is funny is not calm.
Someone is not strong.
Someone is both not brave and not old.
Mary is humble or not generous.
Mary is not tall.
Fred is either not old or humble.
Fred is not rich or not strong.
John is humble or patient.
Someone is both not calm and generous. | John is not happy. | neutral | (![X]:((curious(X)<~>calm(X))=>~creative(X)))&
(![X]:((~patient(X)|~brave(X))<=>(humble(X)<~>generous(X))))&
(((quiet(fred)&rich(fred)))=>((strong(mary)&creative(mary))))&
(((~calm(susan)<~>~rich(susan)))<=>((~old(john)&~creative(john))))&
((?[X]:((~wise(X)<~>~tall(X))))<=>((funny(mary)|brave(mary))))&
(![X]:((strong(X)|quiet(X))<=>~tall(X)))&
(((~rich(mary)&~kind(mary)))<=>((~strong(susan)<~>~rich(susan))))&
(![X]:((~tall(X)<~>strong(X))<=>(~calm(X)|tall(X))))&
((?[X]:((kind(X)|~strong(X))))=>((calm(mary)<~>~old(mary))))&
(![X]:((generous(X)|strong(X))<=>(~humble(X)|patient(X))))&
(((kind(mary)<~>old(mary)))=>(curious(fred)))&
((?[X]:((~creative(X)&~curious(X))))<=>((patient(john)&quiet(john))))&
(![X]:((~quiet(X)|~rich(X))<=>~brave(X)))&
(![X]:(~brave(X)=>(~generous(X)<~>calm(X))))&
(![X]:((~patient(X)|~old(X))=>(happy(X)<~>wise(X))))&
(![X]:(funny(X)=>~calm(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~brave(X)&~old(X))))&
((humble(mary)|~generous(mary)))&
(~tall(mary))&
((~old(fred)<~>humble(fred)))&
((~rich(fred)|~strong(fred)))&
((humble(john)|patient(john)))&
(?[X]:((~calm(X)&generous(X)))) | ~happy(john) | [] | null | 0 |
If mary is both curious and not wise then fred is both tall and curious.
If mary is not calm then mary is both not quiet and not kind and vice versa.
Everyone who is curious or wise is rich or calm.
If someone is not calm or tall then paul is curious and vice versa.
Everyone who is rich is either funny or strong.
If fred is both wise and humble then alice is either not strong or tall.
Everyone who is patient is either not wise or not strong.
Everyone who is not calm is both not tall and not quiet and vice versa.
If john is either kind or not curious then someone is either not humble or generous.
If someone is not happy then someone is happy or patient.
If someone is not kind or strong then mary is either humble or not tall.
Everyone who is not rich is not old or not calm.
Everyone who is wise or not wise is not calm and vice versa.
Everyone who is both not quiet and not brave is both funny and creative.
Everyone who is tall or calm is not strong or not old and vice versa.
Everyone who is either not curious or not brave is generous.
Fred is not patient.
Alice is both kind and not brave.
Someone is either not curious or wise.
Lucy is not generous.
Alice is not curious or not creative.
Mary is either creative or rich.
Paul is brave or quiet. | Fred is brave. | neutral | (((curious(mary)&~wise(mary)))=>((tall(fred)&curious(fred))))&
((~calm(mary))<=>((~quiet(mary)&~kind(mary))))&
(![X]:((curious(X)|wise(X))=>(rich(X)|calm(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(curious(paul)))&
(![X]:(rich(X)=>(funny(X)<~>strong(X))))&
(((wise(fred)&humble(fred)))=>((~strong(alice)<~>tall(alice))))&
(![X]:(patient(X)=>(~wise(X)<~>~strong(X))))&
(![X]:(~calm(X)<=>(~tall(X)&~quiet(X))))&
(((kind(john)<~>~curious(john)))=>(?[X]:((~humble(X)<~>generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((happy(X)|patient(X)))))&
((?[X]:((~kind(X)|strong(X))))=>((humble(mary)<~>~tall(mary))))&
(![X]:(~rich(X)=>(~old(X)|~calm(X))))&
(![X]:((wise(X)|~wise(X))<=>~calm(X)))&
(![X]:((~quiet(X)&~brave(X))=>(funny(X)&creative(X))))&
(![X]:((tall(X)|calm(X))<=>(~strong(X)|~old(X))))&
(![X]:((~curious(X)<~>~brave(X))=>generous(X)))&
(~patient(fred))&
((kind(alice)&~brave(alice)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~generous(lucy))&
((~curious(alice)|~creative(alice)))&
((creative(mary)<~>rich(mary)))&
((brave(paul)|quiet(paul))) | brave(fred) | [] | null | 0 |
If alice is either not happy or wise then someone is either not old or kind.
If mary is either not happy or quiet then mary is kind.
If someone is generous then someone is either not creative or wise.
If paul is both rich and not strong then mary is both tall and not calm.
If someone is both calm and generous then mary is either curious or creative.
Everyone who is kind or rich is not kind and vice versa.
Everyone who is old or quiet is either not curious or curious.
Everyone who is not patient or old is either not patient or not brave and vice versa.
Everyone who is both not rich and quiet is not wise and vice versa.
Everyone who is not brave is not brave or not happy.
If fred is calm then someone is patient or not quiet and vice versa.
Everyone who is both quiet and funny is not strong or calm and vice versa.
If alice is both not humble and not old then susan is either tall or not strong.
Everyone who is both not kind and old is not curious and vice versa.
If someone is either not wise or rich then alice is wise.
Everyone who is rich or funny is not strong and vice versa.
Someone is not brave or patient.
Someone is either happy or calm.
John is either calm or quiet.
Lucy is brave.
Someone is either not rich or funny.
Susan is either not rich or rich. | Paul is not humble. | neutral | (((~happy(alice)<~>wise(alice)))=>(?[X]:((~old(X)<~>kind(X)))))&
(((~happy(mary)<~>quiet(mary)))=>(kind(mary)))&
((?[X]:(generous(X)))=>(?[X]:((~creative(X)<~>wise(X)))))&
(((rich(paul)&~strong(paul)))=>((tall(mary)&~calm(mary))))&
((?[X]:((calm(X)&generous(X))))=>((curious(mary)<~>creative(mary))))&
(![X]:((kind(X)|rich(X))<=>~kind(X)))&
(![X]:((old(X)|quiet(X))=>(~curious(X)<~>curious(X))))&
(![X]:((~patient(X)|old(X))<=>(~patient(X)<~>~brave(X))))&
(![X]:((~rich(X)&quiet(X))<=>~wise(X)))&
(![X]:(~brave(X)=>(~brave(X)|~happy(X))))&
((calm(fred))<=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:((quiet(X)&funny(X))<=>(~strong(X)|calm(X))))&
(((~humble(alice)&~old(alice)))=>((tall(susan)<~>~strong(susan))))&
(![X]:((~kind(X)&old(X))<=>~curious(X)))&
((?[X]:((~wise(X)<~>rich(X))))=>(wise(alice)))&
(![X]:((rich(X)|funny(X))<=>~strong(X)))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((happy(X)<~>calm(X))))&
((calm(john)<~>quiet(john)))&
(brave(lucy))&
(?[X]:((~rich(X)<~>funny(X))))&
((~rich(susan)<~>rich(susan))) | ~humble(paul) | [] | null | 0 |
Everyone who is not wise or brave is not kind.
Everyone who is either happy or tall is both rich and curious.
Everyone who is not calm or not humble is both happy and wise.
Everyone who is either not tall or not happy is both generous and creative and vice versa.
If someone is both quiet and creative then alice is not patient.
Everyone who is rich or not strong is both happy and brave and vice versa.
Everyone who is rich is patient or not brave.
Everyone who is strong is not patient or happy and vice versa.
Everyone who is old or not wise is either generous or funny.
If someone is either brave or not calm then john is not old or not quiet.
If alice is both creative and patient then someone is either not wise or not quiet and vice versa.
Everyone who is not kind or not old is either not kind or generous.
Everyone who is either not rich or not creative is brave.
If someone is not strong then someone is kind or not wise and vice versa.
If lucy is not happy then mary is creative and vice versa.
Everyone who is either not patient or not strong is either strong or rich and vice versa.
Susan is quiet or not calm.
Someone is not curious or strong.
Fred is brave.
Someone is both not tall and brave. | Alice is curious. | neutral | (![X]:((~wise(X)|brave(X))=>~kind(X)))&
(![X]:((happy(X)<~>tall(X))=>(rich(X)&curious(X))))&
(![X]:((~calm(X)|~humble(X))=>(happy(X)&wise(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(generous(X)&creative(X))))&
((?[X]:((quiet(X)&creative(X))))=>(~patient(alice)))&
(![X]:((rich(X)|~strong(X))<=>(happy(X)&brave(X))))&
(![X]:(rich(X)=>(patient(X)|~brave(X))))&
(![X]:(strong(X)<=>(~patient(X)|happy(X))))&
(![X]:((old(X)|~wise(X))=>(generous(X)<~>funny(X))))&
((?[X]:((brave(X)<~>~calm(X))))=>((~old(john)|~quiet(john))))&
(((creative(alice)&patient(alice)))<=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:((~kind(X)|~old(X))=>(~kind(X)<~>generous(X))))&
(![X]:((~rich(X)<~>~creative(X))=>brave(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((kind(X)|~wise(X)))))&
((~happy(lucy))<=>(creative(mary)))&
(![X]:((~patient(X)<~>~strong(X))<=>(strong(X)<~>rich(X))))&
((quiet(susan)|~calm(susan)))&
(?[X]:((~curious(X)|strong(X))))&
(brave(fred))&
(?[X]:((~tall(X)&brave(X)))) | curious(alice) | [] | null | 0 |
Everyone who is either not rich or not calm is not brave or not rich and vice versa.
Everyone who is not old or wise is either wise or not patient and vice versa.
If someone is not happy then alice is both not tall and not happy.
Everyone who is calm is both patient and not patient and vice versa.
If someone is both curious and calm then someone is either calm or not patient.
If paul is curious then alice is either not kind or not humble and vice versa.
If someone is not old then susan is both quiet and not curious.
Everyone who is not tall is both rich and not happy.
If someone is either not happy or humble then alice is not calm or not funny and vice versa.
Everyone who is tall or kind is either not curious or tall.
Everyone who is not rich is happy or not rich.
Everyone who is not wise or curious is rich.
If someone is happy or not rich then mary is both funny and not generous and vice versa.
If someone is both not kind and wise then someone is not generous or calm and vice versa.
Everyone who is not tall or not wise is strong and vice versa.
Everyone who is both not calm and not brave is either not kind or not patient and vice versa.
Someone is either humble or not humble.
Someone is either not quiet or not humble.
John is both not quiet and not wise.
Someone is either not patient or brave.
Someone is not curious or generous.
Fred is not funny or not happy. | Paul is not brave. | entailment | (![X]:((~rich(X)<~>~calm(X))<=>(~brave(X)|~rich(X))))&
(![X]:((~old(X)|wise(X))<=>(wise(X)<~>~patient(X))))&
((?[X]:(~happy(X)))=>((~tall(alice)&~happy(alice))))&
(![X]:(calm(X)<=>(patient(X)&~patient(X))))&
((?[X]:((curious(X)&calm(X))))=>(?[X]:((calm(X)<~>~patient(X)))))&
((curious(paul))<=>((~kind(alice)<~>~humble(alice))))&
((?[X]:(~old(X)))=>((quiet(susan)&~curious(susan))))&
(![X]:(~tall(X)=>(rich(X)&~happy(X))))&
((?[X]:((~happy(X)<~>humble(X))))<=>((~calm(alice)|~funny(alice))))&
(![X]:((tall(X)|kind(X))=>(~curious(X)<~>tall(X))))&
(![X]:(~rich(X)=>(happy(X)|~rich(X))))&
(![X]:((~wise(X)|curious(X))=>rich(X)))&
((?[X]:((happy(X)|~rich(X))))<=>((funny(mary)&~generous(mary))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((~generous(X)|calm(X)))))&
(![X]:((~tall(X)|~wise(X))<=>strong(X)))&
(![X]:((~calm(X)&~brave(X))<=>(~kind(X)<~>~patient(X))))&
(?[X]:((humble(X)<~>~humble(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
((~quiet(john)&~wise(john)))&
(?[X]:((~patient(X)<~>brave(X))))&
(?[X]:((~curious(X)|generous(X))))&
((~funny(fred)|~happy(fred))) | ~brave(paul) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3843515931001467144804183
% SZS output start Proof for 3843515931001467144804183
1. ! [X0] : ((~rich(X0) <~> ~calm(X0)) <=> (~rich(X0) | ~brave(X0))) [input p0]
4. ! [X0] : (calm(X0) <=> (~patient(X0) & patient(X0))) [input p3]
23. brave(paul) [input hypothesis]
34. ! [X0] : ((((calm(X0) | rich(X0)) & (~calm(X0) | ~rich(X0))) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0))))) [nnf transformation 1]
35. ! [X0] : ((((calm(X0) | rich(X0)) & (~calm(X0) | ~rich(X0))) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0))))) [flattening 34]
38. ! [X0] : ((calm(X0) | (patient(X0) | ~patient(X0))) & ((~patient(X0) & patient(X0)) | ~calm(X0))) [nnf transformation 4]
39. ! [X0] : ((calm(X0) | patient(X0) | ~patient(X0)) & ((~patient(X0) & patient(X0)) | ~calm(X0))) [flattening 38]
75. ~rich(X0) | ~brave(X0) | ~rich(X0) | calm(X0) [cnf transformation 35]
79. calm(X0) | rich(X0) | rich(X0) [cnf transformation 35]
88. patient(X0) | ~calm(X0) [cnf transformation 39]
89. ~patient(X0) | ~calm(X0) [cnf transformation 39]
140. brave(paul) [cnf transformation 23]
144. ~rich(X0) | ~brave(X0) | calm(X0) [duplicate literal removal 75]
145. calm(X0) | rich(X0) [duplicate literal removal 79]
146. ~brave(X0) | calm(X0) [subsumption resolution 144,145]
160. ~calm(X0) [subsumption resolution 88,89]
310. calm(paul) [resolution 146,140]
311. $false [subsumption resolution 310,160]
% SZS output end Proof for 3843515931001467144804183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not old and not calm then susan is either not quiet or generous.
Everyone who is not quiet or not curious is not wise and vice versa.
Everyone who is curious or old is not creative or wise and vice versa.
If susan is either calm or not brave then someone is patient or not tall.
If someone is both old and not kind then mary is not generous.
Everyone who is both not brave and kind is creative or not happy and vice versa.
Everyone who is not patient is both not wise and not humble and vice versa.
Everyone who is both not kind and not wise is funny and vice versa.
Everyone who is old or quiet is funny or kind and vice versa.
Everyone who is not creative or humble is both brave and not patient and vice versa.
If someone is not calm then someone is not funny.
If someone is creative then john is creative and vice versa.
Everyone who is both not calm and kind is either not patient or quiet.
If someone is either old or wise then someone is both brave and not happy.
If paul is humble then lucy is both patient and quiet.
Alice is either not patient or not rich.
Someone is either not patient or not kind.
Someone is kind.
Mary is quiet or curious. | Paul is rich. | neutral | (((~old(john)&~calm(john)))=>((~quiet(susan)<~>generous(susan))))&
(![X]:((~quiet(X)|~curious(X))<=>~wise(X)))&
(![X]:((curious(X)|old(X))<=>(~creative(X)|wise(X))))&
(((calm(susan)<~>~brave(susan)))=>(?[X]:((patient(X)|~tall(X)))))&
((?[X]:((old(X)&~kind(X))))=>(~generous(mary)))&
(![X]:((~brave(X)&kind(X))<=>(creative(X)|~happy(X))))&
(![X]:(~patient(X)<=>(~wise(X)&~humble(X))))&
(![X]:((~kind(X)&~wise(X))<=>funny(X)))&
(![X]:((old(X)|quiet(X))<=>(funny(X)|kind(X))))&
(![X]:((~creative(X)|humble(X))<=>(brave(X)&~patient(X))))&
((?[X]:(~calm(X)))=>(?[X]:(~funny(X))))&
((?[X]:(creative(X)))<=>(creative(john)))&
(![X]:((~calm(X)&kind(X))=>(~patient(X)<~>quiet(X))))&
((?[X]:((old(X)<~>wise(X))))=>(?[X]:((brave(X)&~happy(X)))))&
((humble(paul))=>((patient(lucy)&quiet(lucy))))&
((~patient(alice)<~>~rich(alice)))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:(kind(X)))&
((quiet(mary)|curious(mary))) | rich(paul) | [] | null | 0 |
If fred is calm then fred is both humble and not tall.
Everyone who is either calm or not rich is not tall or not generous.
Everyone who is either not calm or quiet is either generous or not tall and vice versa.
If lucy is both not strong and not rich then fred is either quiet or funny.
If fred is both kind and not curious then someone is both brave and not old.
Everyone who is either not happy or not brave is both happy and not calm.
If someone is both tall and not creative then someone is not quiet or not tall.
Everyone who is kind is not kind or calm and vice versa.
Everyone who is not patient or curious is not humble or not quiet.
If lucy is either not happy or old then someone is funny.
If someone is curious then someone is creative or humble.
Everyone who is not calm or not strong is either not rich or not wise and vice versa.
Everyone who is old is not creative.
If someone is tall then lucy is tall.
If mary is either not humble or tall then lucy is not quiet or happy.
If someone is quiet or calm then susan is either quiet or not generous.
Fred is not creative.
Someone is both curious and creative.
Mary is both calm and funny.
Lucy is quiet or not patient.
Lucy is either not tall or not patient.
Someone is both not old and not tall.
Fred is either quiet or kind.
Someone is not humble or not rich. | Fred is generous. | entailment | ((calm(fred))=>((humble(fred)&~tall(fred))))&
(![X]:((calm(X)<~>~rich(X))=>(~tall(X)|~generous(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(generous(X)<~>~tall(X))))&
(((~strong(lucy)&~rich(lucy)))=>((quiet(fred)<~>funny(fred))))&
(((kind(fred)&~curious(fred)))=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((~happy(X)<~>~brave(X))=>(happy(X)&~calm(X))))&
((?[X]:((tall(X)&~creative(X))))=>(?[X]:((~quiet(X)|~tall(X)))))&
(![X]:(kind(X)<=>(~kind(X)|calm(X))))&
(![X]:((~patient(X)|curious(X))=>(~humble(X)|~quiet(X))))&
(((~happy(lucy)<~>old(lucy)))=>(?[X]:(funny(X))))&
((?[X]:(curious(X)))=>(?[X]:((creative(X)|humble(X)))))&
(![X]:((~calm(X)|~strong(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:(old(X)=>~creative(X)))&
((?[X]:(tall(X)))=>(tall(lucy)))&
(((~humble(mary)<~>tall(mary)))=>((~quiet(lucy)|happy(lucy))))&
((?[X]:((quiet(X)|calm(X))))=>((quiet(susan)<~>~generous(susan))))&
(~creative(fred))&
(?[X]:((curious(X)&creative(X))))&
((calm(mary)&funny(mary)))&
((quiet(lucy)|~patient(lucy)))&
((~tall(lucy)<~>~patient(lucy)))&
(?[X]:((~old(X)&~tall(X))))&
((quiet(fred)<~>kind(fred)))&
(?[X]:((~humble(X)|~rich(X)))) | generous(fred) | [
"p0",
"p2",
"p7",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 54944003279579615082921
% SZS output start Proof for 54944003279579615082921
1. calm(fred) => (~tall(fred) & humble(fred)) [input p0]
3. ! [X0] : ((~calm(X0) <~> quiet(X0)) <=> (generous(X0) <~> ~tall(X0))) [input p2]
8. ! [X0] : (kind(X0) <=> (calm(X0) | ~kind(X0))) [input p7]
23. quiet(fred) <~> kind(fred) [input p22]
25. ~generous(fred) [input hypothesis]
28. (~tall(fred) & humble(fred)) | ~calm(fred) [ennf transformation 1]
47. ! [X0] : ((((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0))))) [nnf transformation 3]
55. ! [X0] : ((kind(X0) | (~calm(X0) & kind(X0))) & ((calm(X0) | ~kind(X0)) | ~kind(X0))) [nnf transformation 8]
56. ! [X0] : ((kind(X0) | (~calm(X0) & kind(X0))) & (calm(X0) | ~kind(X0) | ~kind(X0))) [flattening 55]
72. (~kind(fred) | ~quiet(fred)) & (kind(fred) | quiet(fred)) [nnf transformation 23]
76. ~tall(fred) | ~calm(fred) [cnf transformation 28]
84. ~calm(X0) | quiet(X0) | generous(X0) | tall(X0) [cnf transformation 47]
96. calm(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 56]
97. kind(X0) | kind(X0) [cnf transformation 56]
129. ~kind(fred) | ~quiet(fred) [cnf transformation 72]
131. ~generous(fred) [cnf transformation 25]
132. calm(X0) | ~kind(X0) [duplicate literal removal 96]
133. kind(X0) [duplicate literal removal 97]
136. 1 <=> calm(fred) [avatar definition]
138. ~calm(fred) <- (~1) [avatar component clause 136]
140. 2 <=> tall(fred) [avatar definition]
142. ~tall(fred) <- (~2) [avatar component clause 140]
143. ~1 | ~2 [avatar split clause 76,140,136]
158. 6 <=> quiet(fred) [avatar definition]
160. ~quiet(fred) <- (~6) [avatar component clause 158]
197. calm(X0) [subsumption resolution 132,133]
272. ~quiet(fred) [subsumption resolution 129,133]
273. ~6 [avatar split clause 272,158]
285. $false <- (~1) [subsumption resolution 138,197]
286. 1 [avatar contradiction clause 285]
318. quiet(X0) | generous(X0) | tall(X0) [resolution 84,197]
323. generous(fred) | tall(fred) <- (~6) [resolution 318,160]
329. tall(fred) <- (~6) [subsumption resolution 323,131]
330. $false <- (~2, ~6) [subsumption resolution 329,142]
331. 2 | 6 [avatar contradiction clause 330]
342. $false [avatar sat refutation 143,273,286,331]
% SZS output end Proof for 54944003279579615082921
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not calm and vice versa.
Everyone who is kind is not tall or curious.
Everyone who is either kind or not patient is strong.
If someone is either humble or not humble then alice is both happy and old and vice versa.
Everyone who is not generous or not kind is both not quiet and calm and vice versa.
Everyone who is not calm or patient is not strong or calm and vice versa.
Everyone who is either not patient or calm is not kind.
If lucy is both old and patient then someone is tall.
If someone is either not brave or brave then someone is either calm or wise and vice versa.
If alice is old then someone is funny.
Everyone who is kind or creative is generous or brave and vice versa.
If someone is either not patient or not humble then fred is old or creative.
If someone is both not humble and not brave then mary is both not generous and quiet.
Everyone who is not quiet is not tall or quiet.
Someone is either not humble or funny.
Alice is either humble or strong.
Someone is either calm or not humble.
Someone is curious or brave.
Mary is either not curious or happy.
Someone is generous.
John is not kind. | Fred is humble. | entailment | (![X]:(brave(X)<=>~calm(X)))&
(![X]:(kind(X)=>(~tall(X)|curious(X))))&
(![X]:((kind(X)<~>~patient(X))=>strong(X)))&
((?[X]:((humble(X)<~>~humble(X))))<=>((happy(alice)&old(alice))))&
(![X]:((~generous(X)|~kind(X))<=>(~quiet(X)&calm(X))))&
(![X]:((~calm(X)|patient(X))<=>(~strong(X)|calm(X))))&
(![X]:((~patient(X)<~>calm(X))=>~kind(X)))&
(((old(lucy)&patient(lucy)))=>(?[X]:(tall(X))))&
((?[X]:((~brave(X)<~>brave(X))))<=>(?[X]:((calm(X)<~>wise(X)))))&
((old(alice))=>(?[X]:(funny(X))))&
(![X]:((kind(X)|creative(X))<=>(generous(X)|brave(X))))&
((?[X]:((~patient(X)<~>~humble(X))))=>((old(fred)|creative(fred))))&
((?[X]:((~humble(X)&~brave(X))))=>((~generous(mary)&quiet(mary))))&
(![X]:(~quiet(X)=>(~tall(X)|quiet(X))))&
(?[X]:((~humble(X)<~>funny(X))))&
((humble(alice)<~>strong(alice)))&
(?[X]:((calm(X)<~>~humble(X))))&
(?[X]:((curious(X)|brave(X))))&
((~curious(mary)<~>happy(mary)))&
(?[X]:(generous(X)))&
(~kind(john)) | humble(fred) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2525619420658105333130715
% SZS output start Proof for 2525619420658105333130715
1. ! [X0] : (brave(X0) <=> ~calm(X0)) [input p0]
3. ! [X0] : ((kind(X0) <~> ~patient(X0)) => strong(X0)) [input p2]
5. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (calm(X0) & ~quiet(X0))) [input p4]
6. ! [X0] : ((patient(X0) | ~calm(X0)) <=> (calm(X0) | ~strong(X0))) [input p5]
7. ! [X0] : ((~patient(X0) <~> calm(X0)) => ~kind(X0)) [input p6]
13. ? [X0] : (~brave(X0) & ~humble(X0)) => (quiet(mary) & ~generous(mary)) [input p12]
22. ~humble(fred) [input hypothesis]
26. ! [X0] : (strong(X0) | (kind(X0) <=> ~patient(X0))) [ennf transformation 3]
27. ! [X0] : (~kind(X0) | (~patient(X0) <=> calm(X0))) [ennf transformation 7]
33. (quiet(mary) & ~generous(mary)) | ! [X0] : (brave(X0) | humble(X0)) [ennf transformation 13]
36. ! [X0] : ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0))) [nnf transformation 1]
37. ! [X0] : (strong(X0) | ((kind(X0) | patient(X0)) & (~patient(X0) | ~kind(X0)))) [nnf transformation 26]
43. ! [X0] : (((~kind(X0) | ~generous(X0)) | (~calm(X0) | quiet(X0))) & ((calm(X0) & ~quiet(X0)) | (kind(X0) & generous(X0)))) [nnf transformation 5]
44. ! [X0] : ((~kind(X0) | ~generous(X0) | ~calm(X0) | quiet(X0)) & ((calm(X0) & ~quiet(X0)) | (kind(X0) & generous(X0)))) [flattening 43]
45. ! [X0] : (((patient(X0) | ~calm(X0)) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | (~patient(X0) & calm(X0)))) [nnf transformation 6]
46. ! [X0] : ((patient(X0) | ~calm(X0) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | (~patient(X0) & calm(X0)))) [flattening 45]
47. ! [X0] : (~kind(X0) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) [nnf transformation 27]
72. ~calm(X0) | ~brave(X0) [cnf transformation 36]
75. ~patient(X0) | strong(X0) | ~kind(X0) [cnf transformation 37]
83. ~quiet(X0) | generous(X0) [cnf transformation 44]
86. kind(X0) | calm(X0) [cnf transformation 44]
88. calm(X0) | ~strong(X0) | calm(X0) [cnf transformation 46]
91. patient(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 46]
92. ~kind(X0) | calm(X0) | patient(X0) [cnf transformation 47]
110. ~generous(mary) | brave(X0) | humble(X0) [cnf transformation 33]
111. quiet(mary) | brave(X0) | humble(X0) [cnf transformation 33]
124. ~humble(fred) [cnf transformation 22]
130. ~strong(X0) | calm(X0) [duplicate literal removal 88]
131. ~calm(X0) | patient(X0) [duplicate literal removal 91]
155. ~kind(X0) | patient(X0) [subsumption resolution 92,131]
170. 8 <=> ! [X3] : ~brave(X3) [avatar definition]
171. ~brave(X3) <- (8) [avatar component clause 170]
209. 17 <=> ! [X0] : (brave(X0) | humble(X0)) [avatar definition]
210. humble(X0) | brave(X0) <- (17) [avatar component clause 209]
212. 18 <=> quiet(mary) [avatar definition]
214. quiet(mary) <- (18) [avatar component clause 212]
215. 17 | 18 [avatar split clause 111,212,209]
217. 19 <=> generous(mary) [avatar definition]
219. ~generous(mary) <- (~19) [avatar component clause 217]
220. 17 | ~19 [avatar split clause 110,217,209]
279. patient(X0) | calm(X0) [resolution 155,86]
280. patient(X0) [subsumption resolution 279,131]
281. brave(fred) <- (17) [resolution 210,124]
286. ~kind(X0) | strong(X0) [resolution 75,280]
301. strong(X0) | calm(X0) [resolution 286,86]
302. calm(X0) [subsumption resolution 301,130]
306. ~brave(X1) [resolution 302,72]
308. 8 [avatar split clause 306,170]
310. $false <- (8, 17) [resolution 171,281]
311. ~8 | ~17 [avatar contradiction clause 310]
314. generous(mary) <- (18) [resolution 214,83]
315. $false <- (18, ~19) [subsumption resolution 314,219]
316. ~18 | 19 [avatar contradiction clause 315]
317. $false [avatar sat refutation 215,220,308,311,316]
% SZS output end Proof for 2525619420658105333130715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or patient then fred is happy or curious and vice versa.
Everyone who is brave is happy or strong.
If someone is curious or not tall then mary is kind or not patient.
If mary is creative or not quiet then lucy is humble or generous.
Everyone who is either strong or wise is wise or not calm.
Everyone who is not funny or brave is both brave and not calm.
If fred is both not old and tall then someone is creative or funny and vice versa.
Everyone who is either rich or not wise is either not tall or wise and vice versa.
Everyone who is not curious or not funny is kind or not curious.
Everyone who is both happy and not tall is humble or not wise and vice versa.
Everyone who is both curious and quiet is brave.
Everyone who is either calm or curious is generous or not rich and vice versa.
If someone is both not creative and curious then mary is not strong or creative.
If fred is wise or not calm then fred is both not rich and strong and vice versa.
If someone is generous or not old then alice is not rich or funny.
Everyone who is not brave is either not tall or strong and vice versa.
Someone is both generous and rich.
Someone is kind or creative.
Someone is curious.
Lucy is old or patient.
Someone is not calm or tall. | Fred is creative. | contradiction | ((?[X]:((~rich(X)<~>patient(X))))<=>((happy(fred)|curious(fred))))&
(![X]:(brave(X)=>(happy(X)|strong(X))))&
((?[X]:((curious(X)|~tall(X))))=>((kind(mary)|~patient(mary))))&
(((creative(mary)|~quiet(mary)))=>((humble(lucy)|generous(lucy))))&
(![X]:((strong(X)<~>wise(X))=>(wise(X)|~calm(X))))&
(![X]:((~funny(X)|brave(X))=>(brave(X)&~calm(X))))&
(((~old(fred)&tall(fred)))<=>(?[X]:((creative(X)|funny(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~curious(X)|~funny(X))=>(kind(X)|~curious(X))))&
(![X]:((happy(X)&~tall(X))<=>(humble(X)|~wise(X))))&
(![X]:((curious(X)&quiet(X))=>brave(X)))&
(![X]:((calm(X)<~>curious(X))<=>(generous(X)|~rich(X))))&
((?[X]:((~creative(X)&curious(X))))=>((~strong(mary)|creative(mary))))&
(((wise(fred)|~calm(fred)))<=>((~rich(fred)&strong(fred))))&
((?[X]:((generous(X)|~old(X))))=>((~rich(alice)|funny(alice))))&
(![X]:(~brave(X)<=>(~tall(X)<~>strong(X))))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:(curious(X)))&
((old(lucy)|patient(lucy)))&
(?[X]:((~calm(X)|tall(X)))) | creative(fred) | [
"p6",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7033065204927155991397229
% SZS output start Proof for 7033065204927155991397229
7. (tall(fred) & ~old(fred)) <=> ? [X0] : (funny(X0) | creative(X0)) [input p6]
8. ! [X0] : ((rich(X0) <~> ~wise(X0)) <=> (~tall(X0) <~> wise(X0))) [input p7]
10. ! [X0] : ((~tall(X0) & happy(X0)) <=> (~wise(X0) | humble(X0))) [input p9]
14. (~calm(fred) | wise(fred)) <=> (strong(fred) & ~rich(fred)) [input p13]
22. creative(fred) [input hypothesis]
45. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | (~tall(fred) | old(fred))) [nnf transformation 7]
46. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | ~tall(fred) | old(fred)) [flattening 45]
47. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X1] : (funny(X1) | creative(X1)) | ~tall(fred) | old(fred)) [rectify 46]
48. ? [X1] : (funny(X1) | creative(X1)) => (funny(sK1) | creative(sK1)) [choice axiom]
49. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & ((funny(sK1) | creative(sK1)) | ~tall(fred) | old(fred)) [skolemisation 47,48]
50. ! [X0] : ((((wise(X0) | ~rich(X0)) & (~wise(X0) | rich(X0))) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0)))) & (((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))))) [nnf transformation 8]
51. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | (tall(X0) | ~happy(X0)))) [nnf transformation 10]
52. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | tall(X0) | ~happy(X0))) [flattening 51]
55. ((~calm(fred) | wise(fred)) | (~strong(fred) | rich(fred))) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [nnf transformation 14]
56. (~calm(fred) | wise(fred) | ~strong(fred) | rich(fred)) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [flattening 55]
82. tall(fred) | ~creative(X0) [cnf transformation 49]
85. wise(X0) | ~tall(X0) | rich(X0) | wise(X0) [cnf transformation 50]
89. ~wise(X0) | rich(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 50]
96. ~tall(X0) | wise(X0) [cnf transformation 52]
105. ~rich(fred) | ~wise(fred) [cnf transformation 56]
121. creative(fred) [cnf transformation 22]
122. wise(X0) | ~tall(X0) | rich(X0) [duplicate literal removal 85]
124. ~wise(X0) | rich(X0) | ~tall(X0) [duplicate literal removal 89]
177. 12 <=> tall(fred) [avatar definition]
179. tall(fred) <- (12) [avatar component clause 177]
182. 13 <=> ! [X0] : ~creative(X0) [avatar definition]
183. ~creative(X0) <- (13) [avatar component clause 182]
184. 13 | 12 [avatar split clause 82,177,182]
201. ~tall(X0) | rich(X0) [subsumption resolution 122,124]
220. 21 <=> wise(fred) [avatar definition]
225. 22 <=> rich(fred) [avatar definition]
227. ~rich(fred) <- (~22) [avatar component clause 225]
229. ~21 | ~22 [avatar split clause 105,225,220]
264. $false <- (13) [resolution 183,121]
265. ~13 [avatar contradiction clause 264]
272. wise(fred) <- (12) [resolution 96,179]
275. 21 | ~12 [avatar split clause 272,177,220]
278. rich(fred) <- (12) [resolution 201,179]
280. $false <- (12, ~22) [subsumption resolution 278,227]
281. ~12 | 22 [avatar contradiction clause 280]
282. $false [avatar sat refutation 184,229,265,275,281]
% SZS output end Proof for 7033065204927155991397229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not happy is either patient or creative and vice versa.
If someone is both not funny and not tall then someone is not funny and vice versa.
Everyone who is not happy is both old and not kind and vice versa.
If someone is wise then someone is either not curious or not happy and vice versa.
If mary is generous or not wise then someone is either happy or not funny.
If paul is both wise and quiet then someone is rich or not kind.
Everyone who is curious or not tall is both not curious and not creative.
If someone is not quiet then alice is either not kind or happy and vice versa.
If lucy is both not funny and funny then paul is old.
Everyone who is not generous is either not wise or tall and vice versa.
Everyone who is both curious and old is both kind and generous and vice versa.
Everyone who is not creative or not brave is either brave or not generous.
Everyone who is brave is quiet or creative and vice versa.
If paul is either not generous or not humble then someone is not wise and vice versa.
Everyone who is not generous or not tall is generous or not kind and vice versa.
If john is not quiet then alice is both not generous and rich.
Susan is either not kind or not brave.
Someone is not curious or kind.
John is strong.
Someone is old or generous.
Someone is not happy or not quiet.
Mary is both not rich and not curious.
Someone is not wise.
Mary is humble. | Mary is happy. | neutral | (![X]:((creative(X)&~happy(X))<=>(patient(X)<~>creative(X))))&
((?[X]:((~funny(X)&~tall(X))))<=>(?[X]:(~funny(X))))&
(![X]:(~happy(X)<=>(old(X)&~kind(X))))&
((?[X]:(wise(X)))<=>(?[X]:((~curious(X)<~>~happy(X)))))&
(((generous(mary)|~wise(mary)))=>(?[X]:((happy(X)<~>~funny(X)))))&
(((wise(paul)&quiet(paul)))=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((curious(X)|~tall(X))=>(~curious(X)&~creative(X))))&
((?[X]:(~quiet(X)))<=>((~kind(alice)<~>happy(alice))))&
(((~funny(lucy)&funny(lucy)))=>(old(paul)))&
(![X]:(~generous(X)<=>(~wise(X)<~>tall(X))))&
(![X]:((curious(X)&old(X))<=>(kind(X)&generous(X))))&
(![X]:((~creative(X)|~brave(X))=>(brave(X)<~>~generous(X))))&
(![X]:(brave(X)<=>(quiet(X)|creative(X))))&
(((~generous(paul)<~>~humble(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((~generous(X)|~tall(X))<=>(generous(X)|~kind(X))))&
((~quiet(john))=>((~generous(alice)&rich(alice))))&
((~kind(susan)<~>~brave(susan)))&
(?[X]:((~curious(X)|kind(X))))&
(strong(john))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((~happy(X)|~quiet(X))))&
((~rich(mary)&~curious(mary)))&
(?[X]:(~wise(X)))&
(humble(mary)) | happy(mary) | [] | null | 0 |
Everyone who is either funny or calm is both tall and not happy. Everyone who is not kind or not brave is either brave or calm and vice versa. Everyone who is generous or happy is tall or quiet and vice versa. If susan is patient then someone is not funny. Everyone who is not tall or not old is not funny or funny and vice versa. If mary is both not calm and not humble then fred is wise and vice versa. Everyone who is either strong or tall is not rich and vice versa. If mary is either not kind or funny then someone is both not rich and not funny and vice versa. Everyone who is both not happy and not wise is not generous or curious. Everyone who is not old is either not strong or patient. Everyone who is not humble or not patient is either not funny or not tall and vice versa. If someone is not quiet then someone is calm and vice versa. Everyone who is brave or not tall is brave. Everyone who is humble or old is funny. Everyone who is either happy or old is old or calm. Everyone who is kind or funny is not humble or old and vice versa. Fred is patient. Someone is strong. Lucy is strong. Mary is both not patient and quiet. Someone is both not patient and wise. Someone is not wise or old. Someone is not generous or brave. | Mary is not calm. | contradiction | (![X]:((funny(X)<~>calm(X))=>(tall(X)&~happy(X))))&
(![X]:((~kind(X)|~brave(X))<=>(brave(X)<~>calm(X))))&
(![X]:((generous(X)|happy(X))<=>(tall(X)|quiet(X))))&
((patient(susan))=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)|~old(X))<=>(~funny(X)|funny(X))))&
(((~calm(mary)&~humble(mary)))<=>(wise(fred)))&
(![X]:((strong(X)<~>tall(X))<=>~rich(X)))&
(((~kind(mary)<~>funny(mary)))<=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((~happy(X)&~wise(X))=>(~generous(X)|curious(X))))&
(![X]:(~old(X)=>(~strong(X)<~>patient(X))))&
(![X]:((~humble(X)|~patient(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(calm(X))))&
(![X]:((brave(X)|~tall(X))=>brave(X)))&
(![X]:((humble(X)|old(X))=>funny(X)))&
(![X]:((happy(X)<~>old(X))=>(old(X)|calm(X))))&
(![X]:((kind(X)|funny(X))<=>(~humble(X)|old(X))))&
(patient(fred))&
(?[X]:(strong(X)))&
(strong(lucy))&
((~patient(mary)&quiet(mary)))&
(?[X]:((~patient(X)&wise(X))))&
(?[X]:((~wise(X)|old(X))))&
(?[X]:((~generous(X)|brave(X)))) | ~calm(mary) | [
"p0",
"p1",
"p10",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6440148129230885128175826
% SZS output start Proof for 6440148129230885128175826
1. ! [X0] : ((funny(X0) <~> calm(X0)) => (~happy(X0) & tall(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | ~kind(X0)) <=> (brave(X0) <~> calm(X0))) [input p1]
11. ! [X0] : ((~patient(X0) | ~humble(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p10]
14. ! [X0] : ((old(X0) | humble(X0)) => funny(X0)) [input p13]
16. ! [X0] : ((funny(X0) | kind(X0)) <=> (old(X0) | ~humble(X0))) [input p15]
20. quiet(mary) & ~patient(mary) [input p19]
24. ~calm(mary) [input hypothesis]
27. ! [X0] : ((~happy(X0) & tall(X0)) | (funny(X0) <=> calm(X0))) [ennf transformation 1]
31. ! [X0] : (funny(X0) | (~old(X0) & ~humble(X0))) [ennf transformation 14]
34. ! [X0] : ((~happy(X0) & tall(X0)) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0)))) [nnf transformation 27]
35. ! [X0] : (((~brave(X0) | ~kind(X0)) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (brave(X0) & kind(X0)))) [nnf transformation 2]
36. ! [X0] : ((~brave(X0) | ~kind(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (brave(X0) & kind(X0)))) [flattening 35]
51. ! [X0] : (((~patient(X0) | ~humble(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (patient(X0) & humble(X0)))) [nnf transformation 11]
52. ! [X0] : ((~patient(X0) | ~humble(X0) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (patient(X0) & humble(X0)))) [flattening 51]
59. ! [X0] : (((funny(X0) | kind(X0)) | (~old(X0) & humble(X0))) & ((old(X0) | ~humble(X0)) | (~funny(X0) & ~kind(X0)))) [nnf transformation 16]
60. ! [X0] : ((funny(X0) | kind(X0) | (~old(X0) & humble(X0))) & (old(X0) | ~humble(X0) | (~funny(X0) & ~kind(X0)))) [flattening 59]
69. ~funny(X0) | calm(X0) | tall(X0) [cnf transformation 34]
74. calm(X0) | brave(X0) | brave(X0) [cnf transformation 36]
77. ~brave(X0) | ~kind(X0) | calm(X0) | ~brave(X0) [cnf transformation 36]
104. ~tall(X0) | ~funny(X0) | patient(X0) [cnf transformation 52]
113. ~humble(X0) | funny(X0) [cnf transformation 31]
119. funny(X0) | kind(X0) | humble(X0) [cnf transformation 60]
124. ~patient(mary) [cnf transformation 20]
130. ~calm(mary) [cnf transformation 24]
132. brave(X0) | calm(X0) [duplicate literal removal 74]
133. ~brave(X0) | ~kind(X0) | calm(X0) [duplicate literal removal 77]
154. 5 <=> calm(mary) [avatar definition]
156. ~calm(mary) <- (~5) [avatar component clause 154]
163. 7 <=> kind(mary) [avatar definition]
164. ~kind(mary) <- (~7) [avatar component clause 163]
165. kind(mary) <- (7) [avatar component clause 163]
167. 8 <=> funny(mary) [avatar definition]
168. funny(mary) <- (8) [avatar component clause 167]
169. ~funny(mary) <- (~8) [avatar component clause 167]
200. kind(X0) | funny(X0) [subsumption resolution 119,113]
220. ~5 [avatar split clause 130,154]
223. funny(mary) <- (~7) [resolution 200,164]
224. $false <- (~7, ~8) [subsumption resolution 223,169]
225. 7 | 8 [avatar contradiction clause 224]
370. ~kind(X0) | calm(X0) | calm(X0) [resolution 133,132]
372. ~kind(X0) | calm(X0) [duplicate literal removal 370]
403. calm(mary) | tall(mary) <- (8) [resolution 168,69]
404. tall(mary) <- (~5, 8) [subsumption resolution 403,156]
424. ~funny(mary) | patient(mary) <- (~5, 8) [resolution 404,104]
427. patient(mary) <- (~5, 8) [subsumption resolution 424,168]
428. $false <- (~5, 8) [subsumption resolution 427,124]
429. 5 | ~8 [avatar contradiction clause 428]
437. calm(mary) <- (7) [resolution 372,165]
438. $false <- (~5, 7) [subsumption resolution 437,156]
439. 5 | ~7 [avatar contradiction clause 438]
440. $false [avatar sat refutation 220,225,429,439]
% SZS output end Proof for 6440148129230885128175826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is both kind and strong.
If susan is both rich and funny then someone is both patient and not kind and vice versa.
If someone is humble then john is funny.
If john is either wise or generous then someone is brave or old and vice versa.
If alice is not happy then someone is not patient.
Everyone who is funny is both not humble and happy.
Everyone who is either not brave or old is both curious and brave.
If fred is both not tall and creative then susan is both generous and not brave.
Everyone who is either not wise or rich is both not wise and not funny and vice versa.
If someone is both not old and not tall then someone is humble or not wise.
If fred is not funny or not humble then mary is either brave or not creative and vice versa.
If paul is humble then someone is either old or not wise.
If someone is not rich then fred is not rich.
If alice is not kind or not brave then paul is not kind or not rich and vice versa.
Everyone who is either not brave or not strong is not old and vice versa.
If someone is either not brave or funny then someone is either quiet or strong.
Mary is quiet.
Someone is either calm or not old.
Lucy is both kind and rich.
Someone is rich or humble.
Someone is not old or not rich.
Someone is not creative. | Susan is brave. | entailment | (![X]:(~strong(X)=>(kind(X)&strong(X))))&
(((rich(susan)&funny(susan)))<=>(?[X]:((patient(X)&~kind(X)))))&
((?[X]:(humble(X)))=>(funny(john)))&
(((wise(john)<~>generous(john)))<=>(?[X]:((brave(X)|old(X)))))&
((~happy(alice))=>(?[X]:(~patient(X))))&
(![X]:(funny(X)=>(~humble(X)&happy(X))))&
(![X]:((~brave(X)<~>old(X))=>(curious(X)&brave(X))))&
(((~tall(fred)&creative(fred)))=>((generous(susan)&~brave(susan))))&
(![X]:((~wise(X)<~>rich(X))<=>(~wise(X)&~funny(X))))&
((?[X]:((~old(X)&~tall(X))))=>(?[X]:((humble(X)|~wise(X)))))&
(((~funny(fred)|~humble(fred)))<=>((brave(mary)<~>~creative(mary))))&
((humble(paul))=>(?[X]:((old(X)<~>~wise(X)))))&
((?[X]:(~rich(X)))=>(~rich(fred)))&
(((~kind(alice)|~brave(alice)))<=>((~kind(paul)|~rich(paul))))&
(![X]:((~brave(X)<~>~strong(X))<=>~old(X)))&
((?[X]:((~brave(X)<~>funny(X))))=>(?[X]:((quiet(X)<~>strong(X)))))&
(quiet(mary))&
(?[X]:((calm(X)<~>~old(X))))&
((kind(lucy)&rich(lucy)))&
(?[X]:((rich(X)|humble(X))))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:(~creative(X))) | brave(susan) | [
"p0",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1122653292741394684994135
% SZS output start Proof for 1122653292741394684994135
1. ! [X0] : (~strong(X0) => (strong(X0) & kind(X0))) [input p0]
7. ! [X0] : ((~brave(X0) <~> old(X0)) => (brave(X0) & curious(X0))) [input p6]
15. ! [X0] : ((~brave(X0) <~> ~strong(X0)) <=> ~old(X0)) [input p14]
23. ~brave(susan) [input hypothesis]
28. ! [X0] : ((~brave(X0) <~> old(X0)) => brave(X0)) [pure predicate removal 7]
31. ! [X0] : ((strong(X0) & kind(X0)) | strong(X0)) [ennf transformation 1]
34. ! [X0] : (brave(X0) | (~brave(X0) <=> old(X0))) [ennf transformation 28]
47. ! [X0] : (brave(X0) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) [nnf transformation 34]
57. ! [X0] : ((((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | old(X0)) & (~old(X0) | ((~brave(X0) | strong(X0)) & (~strong(X0) | brave(X0))))) [nnf transformation 15]
72. strong(X0) | strong(X0) [cnf transformation 31]
85. brave(X0) | old(X0) | brave(X0) [cnf transformation 47]
106. ~old(X0) | ~strong(X0) | brave(X0) [cnf transformation 57]
108. ~strong(X0) | ~brave(X0) | old(X0) [cnf transformation 57]
122. ~brave(susan) [cnf transformation 23]
125. brave(X0) | old(X0) [duplicate literal removal 85]
126. strong(X0) [duplicate literal removal 72]
248. ~brave(X0) | old(X0) [subsumption resolution 108,126]
249. old(X0) [subsumption resolution 248,125]
250. ~strong(X0) | brave(X0) [subsumption resolution 106,249]
251. brave(X0) [subsumption resolution 250,126]
273. $false [subsumption resolution 122,251]
% SZS output end Proof for 1122653292741394684994135
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or generous is not tall or not generous and vice versa.
If lucy is both quiet and happy then lucy is patient and vice versa.
If someone is not strong or not funny then mary is calm.
Everyone who is kind is creative or funny and vice versa.
Everyone who is both curious and rich is both not rich and creative and vice versa.
If someone is both quiet and old then someone is either not tall or not humble and vice versa.
If mary is either not strong or not tall then fred is either not curious or curious.
If someone is not strong then someone is either not strong or funny and vice versa.
If alice is both not creative and old then lucy is both kind and rich and vice versa.
Everyone who is both not happy and tall is not brave or not wise.
If paul is either not old or not happy then mary is either not happy or not brave.
Everyone who is both brave and quiet is not patient and vice versa.
If someone is not strong or patient then someone is happy.
Everyone who is either old or not curious is both not strong and strong.
If someone is not rich then susan is both not brave and not humble.
If someone is brave or not creative then paul is either not strong or not patient and vice versa.
Paul is either humble or patient.
Susan is tall or creative.
Mary is either quiet or funny.
Someone is either humble or creative.
Fred is either not brave or patient.
John is calm.
Someone is not patient.
Someone is not brave. | John is not creative. | neutral | (![X]:((quiet(X)|generous(X))<=>(~tall(X)|~generous(X))))&
(((quiet(lucy)&happy(lucy)))<=>(patient(lucy)))&
((?[X]:((~strong(X)|~funny(X))))=>(calm(mary)))&
(![X]:(kind(X)<=>(creative(X)|funny(X))))&
(![X]:((curious(X)&rich(X))<=>(~rich(X)&creative(X))))&
((?[X]:((quiet(X)&old(X))))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(((~strong(mary)<~>~tall(mary)))=>((~curious(fred)<~>curious(fred))))&
((?[X]:(~strong(X)))<=>(?[X]:((~strong(X)<~>funny(X)))))&
(((~creative(alice)&old(alice)))<=>((kind(lucy)&rich(lucy))))&
(![X]:((~happy(X)&tall(X))=>(~brave(X)|~wise(X))))&
(((~old(paul)<~>~happy(paul)))=>((~happy(mary)<~>~brave(mary))))&
(![X]:((brave(X)&quiet(X))<=>~patient(X)))&
((?[X]:((~strong(X)|patient(X))))=>(?[X]:(happy(X))))&
(![X]:((old(X)<~>~curious(X))=>(~strong(X)&strong(X))))&
((?[X]:(~rich(X)))=>((~brave(susan)&~humble(susan))))&
((?[X]:((brave(X)|~creative(X))))<=>((~strong(paul)<~>~patient(paul))))&
((humble(paul)<~>patient(paul)))&
((tall(susan)|creative(susan)))&
((quiet(mary)<~>funny(mary)))&
(?[X]:((humble(X)<~>creative(X))))&
((~brave(fred)<~>patient(fred)))&
(calm(john))&
(?[X]:(~patient(X)))&
(?[X]:(~brave(X))) | ~creative(john) | [] | null | 0 |
If someone is creative then mary is not patient or not creative.
Everyone who is not tall is not creative.
Everyone who is not brave is not rich or not brave and vice versa.
Everyone who is not quiet or not creative is rich or not happy.
If someone is strong or not wise then someone is either not curious or not tall.
Everyone who is happy is either brave or kind and vice versa.
Everyone who is either patient or humble is either rich or not funny.
Everyone who is either happy or not creative is either calm or patient.
Everyone who is both strong and not rich is both generous and not funny.
If susan is strong then someone is both happy and calm and vice versa.
Everyone who is strong or old is not old or kind and vice versa.
Everyone who is both not curious and quiet is not calm.
Everyone who is either not funny or not humble is happy.
Everyone who is either calm or brave is calm or not funny.
Everyone who is funny or not creative is not kind.
If paul is strong or calm then someone is both not humble and quiet.
Someone is either wise or not creative.
Someone is generous or happy.
Someone is not curious.
Fred is not creative or curious.
Someone is not tall.
Someone is brave or not quiet.
Mary is humble. | Susan is not curious. | neutral | ((?[X]:(creative(X)))=>((~patient(mary)|~creative(mary))))&
(![X]:(~tall(X)=>~creative(X)))&
(![X]:(~brave(X)<=>(~rich(X)|~brave(X))))&
(![X]:((~quiet(X)|~creative(X))=>(rich(X)|~happy(X))))&
((?[X]:((strong(X)|~wise(X))))=>(?[X]:((~curious(X)<~>~tall(X)))))&
(![X]:(happy(X)<=>(brave(X)<~>kind(X))))&
(![X]:((patient(X)<~>humble(X))=>(rich(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~creative(X))=>(calm(X)<~>patient(X))))&
(![X]:((strong(X)&~rich(X))=>(generous(X)&~funny(X))))&
((strong(susan))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((strong(X)|old(X))<=>(~old(X)|kind(X))))&
(![X]:((~curious(X)&quiet(X))=>~calm(X)))&
(![X]:((~funny(X)<~>~humble(X))=>happy(X)))&
(![X]:((calm(X)<~>brave(X))=>(calm(X)|~funny(X))))&
(![X]:((funny(X)|~creative(X))=>~kind(X)))&
(((strong(paul)|calm(paul)))=>(?[X]:((~humble(X)&quiet(X)))))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:((generous(X)|happy(X))))&
(?[X]:(~curious(X)))&
((~creative(fred)|curious(fred)))&
(?[X]:(~tall(X)))&
(?[X]:((brave(X)|~quiet(X))))&
(humble(mary)) | ~curious(susan) | [] | null | 0 |
Everyone who is humble or not rich is both not brave and not generous and vice versa. Everyone who is both wise and patient is strong. If alice is curious or humble then john is tall and vice versa. If someone is either patient or rich then john is calm and vice versa. Everyone who is either not wise or not rich is not creative and vice versa. Everyone who is not funny or kind is both quiet and not creative. Everyone who is not kind is wise and vice versa. Everyone who is either funny or calm is not brave or quiet. If someone is not happy then alice is either not rich or not quiet. Everyone who is both not humble and not generous is either not rich or not old and vice versa. If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa. If someone is generous or tall then alice is strong and vice versa. Everyone who is not happy is brave or humble. Everyone who is not happy or not funny is both creative and quiet. If someone is not creative or quiet then someone is both wise and not wise. Everyone who is not patient is both not kind and happy and vice versa. Someone is brave or wise. Susan is both brave and not strong. Someone is kind or happy. Alice is not tall or not old. Someone is not calm or funny. Mary is not rich or curious. | Mary is not humble. | entailment | (![X]:((humble(X)|~rich(X))<=>(~brave(X)&~generous(X))))&
(![X]:((wise(X)&patient(X))=>strong(X)))&
(((curious(alice)|humble(alice)))<=>(tall(john)))&
((?[X]:((patient(X)<~>rich(X))))<=>(calm(john)))&
(![X]:((~wise(X)<~>~rich(X))<=>~creative(X)))&
(![X]:((~funny(X)|kind(X))=>(quiet(X)&~creative(X))))&
(![X]:(~kind(X)<=>wise(X)))&
(![X]:((funny(X)<~>calm(X))=>(~brave(X)|quiet(X))))&
((?[X]:(~happy(X)))=>((~rich(alice)<~>~quiet(alice))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
(?[X]:((brave(X)|wise(X))))&
((brave(susan)&~strong(susan)))&
(?[X]:((kind(X)|happy(X))))&
((~tall(alice)|~old(alice)))&
(?[X]:((~calm(X)|funny(X))))&
((~rich(mary)|curious(mary))) | ~humble(mary) | [
"p0",
"p5",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 587514121597361814779510
% SZS output start Proof for 587514121597361814779510
1. ! [X0] : ((~rich(X0) | humble(X0)) <=> (~generous(X0) & ~brave(X0))) [input p0]
6. ! [X0] : ((kind(X0) | ~funny(X0)) => (~creative(X0) & quiet(X0))) [input p5]
7. ! [X0] : (~kind(X0) <=> wise(X0)) [input p6]
11. ? [X0] : (~brave(X0) & ~quiet(X0)) <=> ? [X0] : (~quiet(X0) & ~wise(X0)) [input p10]
15. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X0] : (~wise(X0) & wise(X0)) [input p14]
23. humble(mary) [input hypothesis]
24. ? [X0] : (~brave(X0) & ~quiet(X0)) <=> ? [X1] : (~quiet(X1) & ~wise(X1)) [rectify 11]
25. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 15]
28. ! [X0] : ((~creative(X0) & quiet(X0)) | (~kind(X0) & funny(X0))) [ennf transformation 6]
35. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (~quiet(X0) & creative(X0)) [ennf transformation 25]
36. ! [X0] : (((~rich(X0) | humble(X0)) | (generous(X0) | brave(X0))) & ((~generous(X0) & ~brave(X0)) | (rich(X0) & ~humble(X0)))) [nnf transformation 1]
37. ! [X0] : ((~rich(X0) | humble(X0) | generous(X0) | brave(X0)) & ((~generous(X0) & ~brave(X0)) | (rich(X0) & ~humble(X0)))) [flattening 36]
45. ! [X0] : ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))) [nnf transformation 7]
50. (? [X0] : (~brave(X0) & ~quiet(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X1] : (~quiet(X1) & ~wise(X1)) | ! [X0] : (brave(X0) | quiet(X0))) [nnf transformation 24]
51. (? [X0] : (~brave(X0) & ~quiet(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X2] : (~quiet(X2) & ~wise(X2)) | ! [X3] : (brave(X3) | quiet(X3))) [rectify 50]
52. ? [X0] : (~brave(X0) & ~quiet(X0)) => (~brave(sK1) & ~quiet(sK1)) [choice axiom]
53. ? [X2] : (~quiet(X2) & ~wise(X2)) => (~quiet(sK2) & ~wise(sK2)) [choice axiom]
54. ((~brave(sK1) & ~quiet(sK1)) | ! [X1] : (quiet(X1) | wise(X1))) & ((~quiet(sK2) & ~wise(sK2)) | ! [X3] : (brave(X3) | quiet(X3))) [skolemisation 51,53,52]
59. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : (~quiet(X1) & creative(X1)) [rectify 35]
60. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK4) & wise(sK4)) [choice axiom]
61. (~wise(sK4) & wise(sK4)) | ! [X1] : (~quiet(X1) & creative(X1)) [skolemisation 59,60]
70. ~brave(X0) | ~humble(X0) [cnf transformation 37]
90. ~kind(X0) | ~creative(X0) [cnf transformation 28]
91. kind(X0) | wise(X0) [cnf transformation 45]
103. ~wise(sK2) | brave(X3) | quiet(X3) [cnf transformation 54]
115. wise(sK4) | creative(X1) [cnf transformation 61]
116. wise(sK4) | ~quiet(X1) [cnf transformation 61]
117. ~wise(sK4) | creative(X1) [cnf transformation 61]
118. ~wise(sK4) | ~quiet(X1) [cnf transformation 61]
129. humble(mary) [cnf transformation 23]
197. 15 <=> ! [X3] : (brave(X3) | quiet(X3)) [avatar definition]
198. brave(X3) | quiet(X3) <- (15) [avatar component clause 197]
205. 17 <=> wise(sK2) [avatar definition]
207. ~wise(sK2) <- (~17) [avatar component clause 205]
208. 15 | ~17 [avatar split clause 103,205,197]
232. 23 <=> ! [X1] : ~quiet(X1) [avatar definition]
233. ~quiet(X1) <- (23) [avatar component clause 232]
235. 24 <=> wise(sK4) [avatar definition]
238. 23 | ~24 [avatar split clause 118,235,232]
240. 25 <=> ! [X1] : creative(X1) [avatar definition]
241. creative(X1) <- (25) [avatar component clause 240]
242. 25 | ~24 [avatar split clause 117,235,240]
243. 23 | 24 [avatar split clause 116,235,232]
244. 25 | 24 [avatar split clause 115,235,240]
292. wise(X0) | ~creative(X0) [resolution 91,90]
295. wise(X0) <- (25) [subsumption resolution 292,241]
297. $false <- (~17, 25) [resolution 295,207]
298. 17 | ~25 [avatar contradiction clause 297]
299. brave(X3) <- (15, 23) [subsumption resolution 198,233]
302. ~humble(X1) <- (15, 23) [resolution 299,70]
308. $false <- (15, 23) [resolution 302,129]
309. ~15 | ~23 [avatar contradiction clause 308]
310. $false [avatar sat refutation 208,238,242,243,244,298,309]
% SZS output end Proof for 587514121597361814779510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not generous and vice versa.
Everyone who is not quiet or not happy is either not happy or not calm.
If john is old then mary is calm or brave.
If someone is brave or calm then someone is both not calm and not quiet.
Everyone who is generous is either not curious or not calm.
Everyone who is not old is creative.
Everyone who is both not curious and not calm is either not happy or brave and vice versa.
Everyone who is strong or tall is both humble and brave.
If lucy is either generous or not strong then someone is old or not calm and vice versa.
Everyone who is generous is rich or not happy and vice versa.
Everyone who is either not calm or curious is not quiet or humble.
Everyone who is not kind or funny is not brave.
Everyone who is either not creative or tall is either calm or not generous and vice versa.
Everyone who is not wise or not happy is either not generous or not wise and vice versa.
Everyone who is either not wise or quiet is either not generous or wise.
Everyone who is strong is tall or not wise and vice versa.
Fred is not tall or not old.
Someone is not curious or not patient.
Mary is either not creative or tall.
Susan is curious or strong.
Someone is not kind or generous. | Mary is old. | entailment | (![X]:((~patient(X)|tall(X))<=>~generous(X)))&
(![X]:((~quiet(X)|~happy(X))=>(~happy(X)<~>~calm(X))))&
((old(john))=>((calm(mary)|brave(mary))))&
((?[X]:((brave(X)|calm(X))))=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:(generous(X)=>(~curious(X)<~>~calm(X))))&
(![X]:(~old(X)=>creative(X)))&
(![X]:((~curious(X)&~calm(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((strong(X)|tall(X))=>(humble(X)&brave(X))))&
(((generous(lucy)<~>~strong(lucy)))<=>(?[X]:((old(X)|~calm(X)))))&
(![X]:(generous(X)<=>(rich(X)|~happy(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~quiet(X)|humble(X))))&
(![X]:((~kind(X)|funny(X))=>~brave(X)))&
(![X]:((~creative(X)<~>tall(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(~generous(X)<~>wise(X))))&
(![X]:(strong(X)<=>(tall(X)|~wise(X))))&
((~tall(fred)|~old(fred)))&
(?[X]:((~curious(X)|~patient(X))))&
((~creative(mary)<~>tall(mary)))&
((curious(susan)|strong(susan)))&
(?[X]:((~kind(X)|generous(X)))) | old(mary) | [
"p0",
"p5",
"p9",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8879357163435069621458770
% SZS output start Proof for 8879357163435069621458770
1. ! [X0] : ((tall(X0) | ~patient(X0)) <=> ~generous(X0)) [input p0]
6. ! [X0] : (~old(X0) => creative(X0)) [input p5]
10. ! [X0] : (generous(X0) <=> (~happy(X0) | rich(X0))) [input p9]
14. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (~generous(X0) <~> ~wise(X0))) [input p13]
19. ~creative(mary) <~> tall(mary) [input p18]
22. ~old(mary) [input hypothesis]
32. ! [X0] : (creative(X0) | old(X0)) [ennf transformation 6]
36. ! [X0] : (((tall(X0) | ~patient(X0)) | generous(X0)) & (~generous(X0) | (~tall(X0) & patient(X0)))) [nnf transformation 1]
37. ! [X0] : ((tall(X0) | ~patient(X0) | generous(X0)) & (~generous(X0) | (~tall(X0) & patient(X0)))) [flattening 36]
49. ! [X0] : ((generous(X0) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | ~generous(X0))) [nnf transformation 10]
50. ! [X0] : ((generous(X0) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | ~generous(X0))) [flattening 49]
52. ! [X0] : (((~happy(X0) | ~wise(X0)) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (happy(X0) & wise(X0)))) [nnf transformation 14]
53. ! [X0] : ((~happy(X0) | ~wise(X0) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (happy(X0) & wise(X0)))) [flattening 52]
59. (~tall(mary) | creative(mary)) & (tall(mary) | ~creative(mary)) [nnf transformation 19]
63. ~generous(X0) | ~tall(X0) [cnf transformation 37]
76. creative(X0) | old(X0) [cnf transformation 32]
93. generous(X0) | happy(X0) [cnf transformation 50]
105. wise(X0) | generous(X0) | wise(X0) [cnf transformation 53]
107. ~happy(X0) | ~wise(X0) | ~wise(X0) | generous(X0) [cnf transformation 53]
118. tall(mary) | ~creative(mary) [cnf transformation 59]
122. ~old(mary) [cnf transformation 22]
125. wise(X0) | generous(X0) [duplicate literal removal 105]
126. ~happy(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 107]
193. ~wise(X0) | generous(X0) [subsumption resolution 126,93]
194. generous(X0) [subsumption resolution 125,193]
216. 18 <=> creative(mary) [avatar definition]
217. ~creative(mary) <- (~18) [avatar component clause 216]
220. 19 <=> tall(mary) [avatar definition]
221. tall(mary) <- (19) [avatar component clause 220]
224. ~18 | 19 [avatar split clause 118,220,216]
237. ~tall(X0) [resolution 63,194]
240. old(mary) <- (~18) [resolution 76,217]
241. $false <- (~18) [subsumption resolution 240,122]
242. 18 [avatar contradiction clause 241]
243. $false <- (19) [subsumption resolution 221,237]
244. ~19 [avatar contradiction clause 243]
245. $false [avatar sat refutation 224,242,244]
% SZS output end Proof for 8879357163435069621458770
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not old is kind or strong and vice versa.
Everyone who is funny or not generous is patient or not humble.
If alice is brave then fred is not wise and vice versa.
Everyone who is not happy is not strong or not calm and vice versa.
If mary is either old or not quiet then john is both not old and not curious.
If paul is curious then susan is calm or not patient and vice versa.
Everyone who is either not calm or not old is not curious or brave and vice versa.
If paul is brave then fred is either not old or strong and vice versa.
Everyone who is creative or not wise is both happy and kind and vice versa.
If fred is creative or not calm then someone is both not funny and not rich and vice versa.
If alice is either not humble or not wise then someone is not happy or patient and vice versa.
Everyone who is not strong or brave is generous or curious.
If someone is both not generous and creative then mary is both not strong and not curious.
If paul is not funny then someone is calm and vice versa.
Everyone who is strong is not happy or humble and vice versa.
Everyone who is not quiet or not humble is tall or patient and vice versa.
Paul is either not wise or brave.
Fred is either not humble or not brave.
Someone is not humble.
Mary is either old or not calm.
Lucy is either not kind or calm.
Someone is not calm.
Someone is patient. | Susan is happy. | neutral | (![X]:((brave(X)|~old(X))<=>(kind(X)|strong(X))))&
(![X]:((funny(X)|~generous(X))=>(patient(X)|~humble(X))))&
((brave(alice))<=>(~wise(fred)))&
(![X]:(~happy(X)<=>(~strong(X)|~calm(X))))&
(((old(mary)<~>~quiet(mary)))=>((~old(john)&~curious(john))))&
((curious(paul))<=>((calm(susan)|~patient(susan))))&
(![X]:((~calm(X)<~>~old(X))<=>(~curious(X)|brave(X))))&
((brave(paul))<=>((~old(fred)<~>strong(fred))))&
(![X]:((creative(X)|~wise(X))<=>(happy(X)&kind(X))))&
(((creative(fred)|~calm(fred)))<=>(?[X]:((~funny(X)&~rich(X)))))&
(((~humble(alice)<~>~wise(alice)))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~strong(X)|brave(X))=>(generous(X)|curious(X))))&
((?[X]:((~generous(X)&creative(X))))=>((~strong(mary)&~curious(mary))))&
((~funny(paul))<=>(?[X]:(calm(X))))&
(![X]:(strong(X)<=>(~happy(X)|humble(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(tall(X)|patient(X))))&
((~wise(paul)<~>brave(paul)))&
((~humble(fred)<~>~brave(fred)))&
(?[X]:(~humble(X)))&
((old(mary)<~>~calm(mary)))&
((~kind(lucy)<~>calm(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:(patient(X))) | happy(susan) | [] | null | 0 |
Everyone who is either creative or not kind is both not creative and not humble. If mary is quiet then someone is quiet or not tall. Everyone who is either not happy or not kind is calm or not patient. Everyone who is either not funny or creative is not creative and vice versa. Everyone who is either not rich or not happy is rich. Everyone who is not strong or rich is both calm and quiet and vice versa. If someone is either not old or creative then someone is both calm and not brave. Everyone who is either not wise or kind is both not old and not tall and vice versa. Everyone who is creative is not generous or not creative and vice versa. If paul is either not happy or not generous then someone is wise or not rich. If susan is old or not humble then someone is either generous or not humble and vice versa. Everyone who is not wise is either rich or strong and vice versa. Everyone who is happy or creative is either not calm or not quiet and vice versa. If mary is wise then fred is either not rich or not humble and vice versa. If alice is not curious then alice is both old and curious. Everyone who is either not curious or humble is both calm and not tall and vice versa. Someone is creative or calm. Someone is either brave or not wise. Someone is strong. Susan is either old or not funny. Someone is not wise. | Susan is not creative. | contradiction | (![X]:((creative(X)<~>~kind(X))=>(~creative(X)&~humble(X))))&
((quiet(mary))=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((~happy(X)<~>~kind(X))=>(calm(X)|~patient(X))))&
(![X]:((~funny(X)<~>creative(X))<=>~creative(X)))&
(![X]:((~rich(X)<~>~happy(X))=>rich(X)))&
(![X]:((~strong(X)|rich(X))<=>(calm(X)&quiet(X))))&
((?[X]:((~old(X)<~>creative(X))))=>(?[X]:((calm(X)&~brave(X)))))&
(![X]:((~wise(X)<~>kind(X))<=>(~old(X)&~tall(X))))&
(![X]:(creative(X)<=>(~generous(X)|~creative(X))))&
(((~happy(paul)<~>~generous(paul)))=>(?[X]:((wise(X)|~rich(X)))))&
(((old(susan)|~humble(susan)))<=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:(~wise(X)<=>(rich(X)<~>strong(X))))&
(![X]:((happy(X)|creative(X))<=>(~calm(X)<~>~quiet(X))))&
((wise(mary))<=>((~rich(fred)<~>~humble(fred))))&
((~curious(alice))=>((old(alice)&curious(alice))))&
(![X]:((~curious(X)<~>humble(X))<=>(calm(X)&~tall(X))))&
(?[X]:((creative(X)|calm(X))))&
(?[X]:((brave(X)<~>~wise(X))))&
(?[X]:(strong(X)))&
((old(susan)<~>~funny(susan)))&
(?[X]:(~wise(X))) | ~creative(susan) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4635629288006533044529949
% SZS output start Proof for 4635629288006533044529949
9. ! [X0] : (creative(X0) <=> (~creative(X0) | ~generous(X0))) [input p8]
22. ~creative(susan) [input hypothesis]
44. ! [X0] : ((creative(X0) | (creative(X0) & generous(X0))) & ((~creative(X0) | ~generous(X0)) | ~creative(X0))) [nnf transformation 9]
45. ! [X0] : ((creative(X0) | (creative(X0) & generous(X0))) & (~creative(X0) | ~generous(X0) | ~creative(X0))) [flattening 44]
98. creative(X0) | creative(X0) [cnf transformation 45]
136. ~creative(susan) [cnf transformation 22]
139. creative(X0) [duplicate literal removal 98]
242. $false [subsumption resolution 136,139]
% SZS output end Proof for 4635629288006533044529949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not quiet is quiet or not curious and vice versa. Everyone who is either not old or not strong is not humble. If alice is rich or not calm then someone is not calm or wise. Everyone who is both not tall and happy is either curious or not generous and vice versa. If someone is not patient then mary is brave and vice versa. Everyone who is old is both not old and curious and vice versa. Everyone who is happy is either brave or strong and vice versa. If someone is not creative then susan is not rich or patient and vice versa. Everyone who is either humble or brave is either strong or not rich. If paul is not patient or brave then someone is kind. If paul is both quiet and not curious then alice is both calm and old. Everyone who is not tall or calm is both not strong and not calm and vice versa. Everyone who is both not old and not kind is either calm or not generous. Everyone who is generous or wise is not old or not generous. Everyone who is either rich or old is not funny. If someone is either calm or happy then someone is either not funny or not curious and vice versa. Lucy is humble. Susan is not brave. Susan is either curious or humble. Someone is either not wise or not curious. Someone is both happy and not rich. Fred is not curious. | Mary is curious. | contradiction | (![X]:((tall(X)<~>~quiet(X))<=>(quiet(X)|~curious(X))))&
(![X]:((~old(X)<~>~strong(X))=>~humble(X)))&
(((rich(alice)|~calm(alice)))=>(?[X]:((~calm(X)|wise(X)))))&
(![X]:((~tall(X)&happy(X))<=>(curious(X)<~>~generous(X))))&
((?[X]:(~patient(X)))<=>(brave(mary)))&
(![X]:(old(X)<=>(~old(X)&curious(X))))&
(![X]:(happy(X)<=>(brave(X)<~>strong(X))))&
((?[X]:(~creative(X)))<=>((~rich(susan)|patient(susan))))&
(![X]:((humble(X)<~>brave(X))=>(strong(X)<~>~rich(X))))&
(((~patient(paul)|brave(paul)))=>(?[X]:(kind(X))))&
(((quiet(paul)&~curious(paul)))=>((calm(alice)&old(alice))))&
(![X]:((~tall(X)|calm(X))<=>(~strong(X)&~calm(X))))&
(![X]:((~old(X)&~kind(X))=>(calm(X)<~>~generous(X))))&
(![X]:((generous(X)|wise(X))=>(~old(X)|~generous(X))))&
(![X]:((rich(X)<~>old(X))=>~funny(X)))&
((?[X]:((calm(X)<~>happy(X))))<=>(?[X]:((~funny(X)<~>~curious(X)))))&
(humble(lucy))&
(~brave(susan))&
((curious(susan)<~>humble(susan)))&
(?[X]:((~wise(X)<~>~curious(X))))&
(?[X]:((happy(X)&~rich(X))))&
(~curious(fred)) | curious(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 531287498519382709179280
% SZS output start Proof for 531287498519382709179280
6. ! [X0] : (old(X0) <=> (curious(X0) & ~old(X0))) [input p5]
23. curious(mary) [input hypothesis]
46. ! [X0] : ((old(X0) | (~curious(X0) | old(X0))) & ((curious(X0) & ~old(X0)) | ~old(X0))) [nnf transformation 6]
47. ! [X0] : ((old(X0) | ~curious(X0) | old(X0)) & ((curious(X0) & ~old(X0)) | ~old(X0))) [flattening 46]
87. ~old(X0) | ~old(X0) [cnf transformation 47]
89. old(X0) | ~curious(X0) | old(X0) [cnf transformation 47]
129. curious(mary) [cnf transformation 23]
133. ~old(X0) [duplicate literal removal 87]
134. ~curious(X0) | old(X0) [duplicate literal removal 89]
254. old(mary) [resolution 134,129]
256. $false [subsumption resolution 254,133]
% SZS output end Proof for 531287498519382709179280
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both generous and not creative then someone is happy and vice versa. Everyone who is both not calm and quiet is either quiet or rich. If fred is either not curious or strong then someone is old or not curious. If someone is curious then mary is both not old and generous and vice versa. Everyone who is not curious is both not generous and not old and vice versa. Everyone who is not kind or wise is funny. Everyone who is either brave or rich is tall. Everyone who is not old is both not generous and not calm. If susan is either old or not strong then fred is strong or funny. If paul is not generous then john is not kind and vice versa. If someone is either not brave or wise then mary is both not old and generous. If alice is humble or patient then paul is not generous and vice versa. If someone is either rich or tall then someone is not quiet or humble. Everyone who is both generous and happy is either brave or tall and vice versa. Someone is either humble or not wise. Paul is not kind or patient. Someone is quiet. Someone is generous or not happy. Fred is either generous or strong. | Fred is not generous. | entailment | (((generous(fred)&~creative(fred)))<=>(?[X]:(happy(X))))&
(![X]:((~calm(X)&quiet(X))=>(quiet(X)<~>rich(X))))&
(((~curious(fred)<~>strong(fred)))=>(?[X]:((old(X)|~curious(X)))))&
((?[X]:(curious(X)))<=>((~old(mary)&generous(mary))))&
(![X]:(~curious(X)<=>(~generous(X)&~old(X))))&
(![X]:((~kind(X)|wise(X))=>funny(X)))&
(![X]:((brave(X)<~>rich(X))=>tall(X)))&
(![X]:(~old(X)=>(~generous(X)&~calm(X))))&
(((old(susan)<~>~strong(susan)))=>((strong(fred)|funny(fred))))&
((~generous(paul))<=>(~kind(john)))&
((?[X]:((~brave(X)<~>wise(X))))=>((~old(mary)&generous(mary))))&
(((humble(alice)|patient(alice)))<=>(~generous(paul)))&
((?[X]:((rich(X)<~>tall(X))))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((generous(X)&happy(X))<=>(brave(X)<~>tall(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
((~kind(paul)|patient(paul)))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)|~happy(X))))&
((generous(fred)<~>strong(fred))) | ~generous(fred) | [
"p3",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 682097599237220267478839
% SZS output start Proof for 682097599237220267478839
4. ? [X0] : curious(X0) <=> (generous(mary) & ~old(mary)) [input p3]
5. ! [X0] : (~curious(X0) <=> (~old(X0) & ~generous(X0))) [input p4]
8. ! [X0] : (~old(X0) => (~calm(X0) & ~generous(X0))) [input p7]
20. generous(fred) [input hypothesis]
28. ! [X0] : ((~calm(X0) & ~generous(X0)) | old(X0)) [ennf transformation 8]
40. (? [X0] : curious(X0) | (~generous(mary) | old(mary))) & ((generous(mary) & ~old(mary)) | ! [X0] : ~curious(X0)) [nnf transformation 4]
41. (? [X0] : curious(X0) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X0] : ~curious(X0)) [flattening 40]
42. (? [X0] : curious(X0) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X1] : ~curious(X1)) [rectify 41]
43. ? [X0] : curious(X0) => curious(sK2) [choice axiom]
44. (curious(sK2) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X1] : ~curious(X1)) [skolemisation 42,43]
45. ! [X0] : ((~curious(X0) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | curious(X0))) [nnf transformation 5]
46. ! [X0] : ((~curious(X0) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | curious(X0))) [flattening 45]
73. ~old(mary) | ~curious(X1) [cnf transformation 44]
74. generous(mary) | ~curious(X1) [cnf transformation 44]
76. ~generous(X0) | curious(X0) [cnf transformation 46]
81. ~generous(X0) | old(X0) [cnf transformation 28]
107. generous(fred) [cnf transformation 20]
118. 3 <=> generous(fred) [avatar definition]
120. generous(fred) <- (3) [avatar component clause 118]
132. 6 <=> curious(fred) [avatar definition]
133. curious(fred) <- (6) [avatar component clause 132]
146. 9 <=> old(mary) [avatar definition]
147. ~old(mary) <- (~9) [avatar component clause 146]
150. 10 <=> generous(mary) [avatar definition]
151. generous(mary) <- (10) [avatar component clause 150]
159. 12 <=> ! [X1] : ~curious(X1) [avatar definition]
160. ~curious(X1) <- (12) [avatar component clause 159]
161. 12 | 10 [avatar split clause 74,150,159]
162. 12 | ~9 [avatar split clause 73,146,159]
240. 3 [avatar split clause 107,118]
241. curious(fred) <- (3) [resolution 76,120]
244. 6 | ~3 [avatar split clause 241,118,132]
246. old(mary) <- (10) [resolution 81,151]
248. $false <- (~9, 10) [subsumption resolution 246,147]
249. 9 | ~10 [avatar contradiction clause 248]
250. $false <- (6, 12) [resolution 160,133]
255. ~6 | ~12 [avatar contradiction clause 250]
256. $false [avatar sat refutation 161,162,240,244,249,255]
% SZS output end Proof for 682097599237220267478839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and calm then someone is generous. If susan is not brave then lucy is both not wise and not kind and vice versa. If susan is both not rich and not calm then someone is both not calm and quiet. If someone is kind or not patient then john is not curious or not tall and vice versa. Everyone who is both quiet and not creative is both not rich and not wise and vice versa. Everyone who is not generous is either not generous or curious and vice versa. If someone is tall then john is rich. Everyone who is both curious and rich is old. Everyone who is strong or kind is either generous or not creative. Everyone who is not humble or not old is both generous and not tall. Everyone who is both curious and funny is either not funny or curious and vice versa. Everyone who is both not funny and not tall is not kind or humble. Everyone who is both generous and funny is both not kind and creative. If paul is not humble then fred is both not curious and not tall. Everyone who is both brave and not quiet is funny or not tall. Everyone who is either not humble or humble is not generous and vice versa. John is both not wise and happy. Someone is either not strong or not patient. Paul is both not generous and patient. Someone is either wise or calm. Someone is not kind. Fred is either kind or humble. | Paul is funny. | entailment | ((?[X]:((~old(X)&calm(X))))=>(?[X]:(generous(X))))&
((~brave(susan))<=>((~wise(lucy)&~kind(lucy))))&
(((~rich(susan)&~calm(susan)))=>(?[X]:((~calm(X)&quiet(X)))))&
((?[X]:((kind(X)|~patient(X))))<=>((~curious(john)|~tall(john))))&
(![X]:((quiet(X)&~creative(X))<=>(~rich(X)&~wise(X))))&
(![X]:(~generous(X)<=>(~generous(X)<~>curious(X))))&
((?[X]:(tall(X)))=>(rich(john)))&
(![X]:((curious(X)&rich(X))=>old(X)))&
(![X]:((strong(X)|kind(X))=>(generous(X)<~>~creative(X))))&
(![X]:((~humble(X)|~old(X))=>(generous(X)&~tall(X))))&
(![X]:((curious(X)&funny(X))<=>(~funny(X)<~>curious(X))))&
(![X]:((~funny(X)&~tall(X))=>(~kind(X)|humble(X))))&
(![X]:((generous(X)&funny(X))=>(~kind(X)&creative(X))))&
((~humble(paul))=>((~curious(fred)&~tall(fred))))&
(![X]:((brave(X)&~quiet(X))=>(funny(X)|~tall(X))))&
(![X]:((~humble(X)<~>humble(X))<=>~generous(X)))&
((~wise(john)&happy(john)))&
(?[X]:((~strong(X)<~>~patient(X))))&
((~generous(paul)&patient(paul)))&
(?[X]:((wise(X)<~>calm(X))))&
(?[X]:(~kind(X)))&
((kind(fred)<~>humble(fred))) | funny(paul) | [
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8657284007856491805116084
% SZS output start Proof for 8657284007856491805116084
6. ! [X0] : (~generous(X0) <=> (~generous(X0) <~> curious(X0))) [input p5]
11. ! [X0] : ((funny(X0) & curious(X0)) <=> (~funny(X0) <~> curious(X0))) [input p10]
23. ~funny(paul) [input hypothesis]
52. ! [X0] : ((~generous(X0) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) & (((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | generous(X0))) [nnf transformation 6]
54. ! [X0] : (((funny(X0) & curious(X0)) | ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0)))) & (((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | (~funny(X0) | ~curious(X0)))) [nnf transformation 11]
55. ! [X0] : (((funny(X0) & curious(X0)) | ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0)))) & (((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | ~funny(X0) | ~curious(X0))) [flattening 54]
80. ~curious(X0) | generous(X0) | generous(X0) [cnf transformation 52]
82. ~generous(X0) | ~generous(X0) | ~curious(X0) [cnf transformation 52]
94. funny(X0) | curious(X0) | funny(X0) [cnf transformation 55]
116. ~funny(paul) [cnf transformation 23]
122. funny(X0) | curious(X0) [duplicate literal removal 94]
123. ~curious(X0) | generous(X0) [duplicate literal removal 80]
124. ~generous(X0) | ~curious(X0) [duplicate literal removal 82]
184. ~curious(X0) [subsumption resolution 123,124]
193. funny(X0) [subsumption resolution 122,184]
227. $false [subsumption resolution 116,193]
% SZS output end Proof for 8657284007856491805116084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy or not happy then fred is not wise or not strong and vice versa.
Everyone who is either patient or wise is not generous and vice versa.
If someone is generous then alice is not old or wise and vice versa.
Everyone who is not strong or rich is not happy or patient.
Everyone who is not old or patient is humble and vice versa.
Everyone who is not wise is either strong or not kind and vice versa.
Everyone who is both patient and not generous is not generous and vice versa.
Everyone who is both kind and calm is both not funny and not brave and vice versa.
If john is both curious and not happy then someone is both not old and happy.
Everyone who is both not kind and old is both not calm and strong and vice versa.
If someone is not humble then someone is humble or rich and vice versa.
Everyone who is either funny or not tall is happy or generous.
Everyone who is creative or funny is either not happy or not generous and vice versa.
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.
Someone is humble.
Alice is happy or not quiet.
Mary is either funny or rich.
Paul is tall or not humble.
Someone is old or not old.
Someone is either brave or old.
Someone is both not generous and calm. | Alice is not kind. | entailment | ((?[X]:((happy(X)|~happy(X))))<=>((~wise(fred)|~strong(fred))))&
(![X]:((patient(X)<~>wise(X))<=>~generous(X)))&
((?[X]:(generous(X)))<=>((~old(alice)|wise(alice))))&
(![X]:((~strong(X)|rich(X))=>(~happy(X)|patient(X))))&
(![X]:((~old(X)|patient(X))<=>humble(X)))&
(![X]:(~wise(X)<=>(strong(X)<~>~kind(X))))&
(![X]:((patient(X)&~generous(X))<=>~generous(X)))&
(![X]:((kind(X)&calm(X))<=>(~funny(X)&~brave(X))))&
(((curious(john)&~happy(john)))=>(?[X]:((~old(X)&happy(X)))))&
(![X]:((~kind(X)&old(X))<=>(~calm(X)&strong(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)|rich(X)))))&
(![X]:((funny(X)<~>~tall(X))=>(happy(X)|generous(X))))&
(![X]:((creative(X)|funny(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:(~wise(X)<=>~tall(X)))&
(((~strong(alice)&~generous(alice)))<=>(?[X]:((~tall(X)|patient(X)))))&
((?[X]:((happy(X)<~>humble(X))))=>(~strong(paul)))&
(?[X]:(humble(X)))&
((happy(alice)|~quiet(alice)))&
((funny(mary)<~>rich(mary)))&
((tall(paul)|~humble(paul)))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((brave(X)<~>old(X))))&
(?[X]:((~generous(X)&calm(X)))) | ~kind(alice) | [
"p1",
"p5",
"p6",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 79224395919723504104889
% SZS output start Proof for 79224395919723504104889
2. ! [X0] : ((patient(X0) <~> wise(X0)) <=> ~generous(X0)) [input p1]
6. ! [X0] : (~wise(X0) <=> (strong(X0) <~> ~kind(X0))) [input p5]
7. ! [X0] : ((~generous(X0) & patient(X0)) <=> ~generous(X0)) [input p6]
15. (~generous(alice) & ~strong(alice)) <=> ? [X0] : (patient(X0) | ~tall(X0)) [input p14]
23. ? [X0] : (calm(X0) & ~generous(X0)) [input p22]
24. kind(alice) [input hypothesis]
38. ! [X0] : ((((~wise(X0) | ~patient(X0)) & (wise(X0) | patient(X0))) | generous(X0)) & (~generous(X0) | ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0))))) [nnf transformation 2]
46. ! [X0] : ((~wise(X0) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | wise(X0))) [nnf transformation 6]
47. ! [X0] : (((~generous(X0) & patient(X0)) | generous(X0)) & (~generous(X0) | (generous(X0) | ~patient(X0)))) [nnf transformation 7]
48. ! [X0] : (((~generous(X0) & patient(X0)) | generous(X0)) & (~generous(X0) | generous(X0) | ~patient(X0))) [flattening 47]
62. ((~generous(alice) & ~strong(alice)) | ! [X0] : (~patient(X0) & tall(X0))) & (? [X0] : (patient(X0) | ~tall(X0)) | (generous(alice) | strong(alice))) [nnf transformation 15]
63. ((~generous(alice) & ~strong(alice)) | ! [X0] : (~patient(X0) & tall(X0))) & (? [X0] : (patient(X0) | ~tall(X0)) | generous(alice) | strong(alice)) [flattening 62]
64. ((~generous(alice) & ~strong(alice)) | ! [X0] : (~patient(X0) & tall(X0))) & (? [X1] : (patient(X1) | ~tall(X1)) | generous(alice) | strong(alice)) [rectify 63]
65. ? [X1] : (patient(X1) | ~tall(X1)) => (patient(sK4) | ~tall(sK4)) [choice axiom]
66. ((~generous(alice) & ~strong(alice)) | ! [X0] : (~patient(X0) & tall(X0))) & ((patient(sK4) | ~tall(sK4)) | generous(alice) | strong(alice)) [skolemisation 64,65]
76. ? [X0] : (calm(X0) & ~generous(X0)) => (calm(sK8) & ~generous(sK8)) [choice axiom]
77. calm(sK8) & ~generous(sK8) [skolemisation 23,76]
85. ~patient(X0) | ~wise(X0) | generous(X0) [cnf transformation 38]
94. ~kind(X0) | strong(X0) | wise(X0) [cnf transformation 46]
99. generous(X0) | patient(X0) [cnf transformation 48]
124. ~strong(alice) | ~patient(X0) [cnf transformation 66]
126. ~generous(alice) | ~patient(X0) [cnf transformation 66]
136. ~generous(sK8) [cnf transformation 77]
138. kind(alice) [cnf transformation 24]
156. 5 <=> wise(alice) [avatar definition]
158. ~wise(alice) <- (~5) [avatar component clause 156]
198. 15 <=> ! [X0] : ~patient(X0) [avatar definition]
199. ~patient(X0) <- (15) [avatar component clause 198]
201. 16 <=> generous(alice) [avatar definition]
203. ~generous(alice) <- (~16) [avatar component clause 201]
204. 15 | ~16 [avatar split clause 126,201,198]
210. 18 <=> strong(alice) [avatar definition]
213. 15 | ~18 [avatar split clause 124,210,198]
278. patient(sK8) [resolution 99,136]
279. patient(alice) <- (~16) [resolution 99,203]
305. ~wise(alice) | generous(alice) <- (~16) [resolution 85,279]
307. ~wise(alice) <- (~16) [subsumption resolution 305,203]
308. ~5 | 16 [avatar split clause 307,201,156]
331. strong(alice) | wise(alice) [resolution 94,138]
335. strong(alice) <- (~5) [subsumption resolution 331,158]
336. 18 | 5 [avatar split clause 335,156,210]
337. $false <- (15) [resolution 199,278]
340. ~15 [avatar contradiction clause 337]
341. $false [avatar sat refutation 204,213,308,336,340]
% SZS output end Proof for 79224395919723504104889
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is calm or creative then fred is both not curious and not calm and vice versa. Everyone who is not patient or not curious is not humble or not curious and vice versa. If fred is not calm or not old then someone is either not humble or strong. If fred is either curious or rich then someone is tall and vice versa. If john is either brave or wise then someone is not tall or not calm. If someone is not rich or old then mary is not old or not strong and vice versa. Everyone who is both not humble and tall is either calm or creative and vice versa. Everyone who is either not happy or not tall is happy or not generous. Everyone who is both patient and not humble is funny or wise and vice versa. Everyone who is not generous is either kind or not quiet. If susan is not creative or not rich then paul is not tall or not strong and vice versa. Everyone who is not generous or not brave is calm and vice versa. Everyone who is either not wise or not old is not old or not funny and vice versa. Everyone who is not old is quiet and vice versa. If someone is either old or not funny then someone is either not calm or happy and vice versa. Everyone who is brave is not rich or not curious and vice versa. Fred is creative. Someone is both not creative and patient. John is calm. Lucy is both not humble and patient. Paul is tall or kind. Someone is either not funny or not wise. Paul is not quiet or not wise. Someone is either not brave or quiet. | Lucy is not patient. | contradiction | (((calm(fred)|creative(fred)))<=>((~curious(fred)&~calm(fred))))&
(![X]:((~patient(X)|~curious(X))<=>(~humble(X)|~curious(X))))&
(((~calm(fred)|~old(fred)))=>(?[X]:((~humble(X)<~>strong(X)))))&
(((curious(fred)<~>rich(fred)))<=>(?[X]:(tall(X))))&
(((brave(john)<~>wise(john)))=>(?[X]:((~tall(X)|~calm(X)))))&
((?[X]:((~rich(X)|old(X))))<=>((~old(mary)|~strong(mary))))&
(![X]:((~humble(X)&tall(X))<=>(calm(X)<~>creative(X))))&
(![X]:((~happy(X)<~>~tall(X))=>(happy(X)|~generous(X))))&
(![X]:((patient(X)&~humble(X))<=>(funny(X)|wise(X))))&
(![X]:(~generous(X)=>(kind(X)<~>~quiet(X))))&
(((~creative(susan)|~rich(susan)))<=>((~tall(paul)|~strong(paul))))&
(![X]:((~generous(X)|~brave(X))<=>calm(X)))&
(![X]:((~wise(X)<~>~old(X))<=>(~old(X)|~funny(X))))&
(![X]:(~old(X)<=>quiet(X)))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~calm(X)<~>happy(X)))))&
(![X]:(brave(X)<=>(~rich(X)|~curious(X))))&
(creative(fred))&
(?[X]:((~creative(X)&patient(X))))&
(calm(john))&
((~humble(lucy)&patient(lucy)))&
((tall(paul)|kind(paul)))&
(?[X]:((~funny(X)<~>~wise(X))))&
((~quiet(paul)|~wise(paul)))&
(?[X]:((~brave(X)<~>quiet(X)))) | ~patient(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2791177026715931017965634
% SZS output start Proof for 2791177026715931017965634
20. patient(lucy) & ~humble(lucy) [input p19]
25. ~patient(lucy) [input hypothesis]
148. patient(lucy) [cnf transformation 20]
155. ~patient(lucy) [cnf transformation 25]
337. $false [subsumption resolution 155,148]
% SZS output end Proof for 2791177026715931017965634
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or not quiet then john is both not calm and strong.
Everyone who is both creative and quiet is happy and vice versa.
Everyone who is kind or creative is either not old or not curious.
Everyone who is patient or wise is creative or humble and vice versa.
If alice is creative or not funny then paul is calm or kind and vice versa.
Everyone who is strong is either not brave or calm and vice versa.
Everyone who is not old is both calm and not calm.
If someone is either humble or quiet then someone is not humble or not strong and vice versa.
If someone is either not patient or rich then mary is both not quiet and not strong.
Everyone who is both not curious and not old is not quiet and vice versa.
Everyone who is old is kind.
If mary is not patient or old then paul is not happy or strong.
Everyone who is not strong or happy is either not kind or not happy and vice versa.
Everyone who is both calm and not calm is either not happy or not kind.
Everyone who is not rich or creative is either not rich or not quiet.
If susan is not generous then someone is not old or creative and vice versa.
Paul is either not patient or not quiet.
Someone is either generous or not humble.
Susan is humble.
Paul is not calm.
Alice is either not humble or not strong. | Paul is brave. | entailment | ((?[X]:((~rich(X)<~>~quiet(X))))=>((~calm(john)&strong(john))))&
(![X]:((creative(X)&quiet(X))<=>happy(X)))&
(![X]:((kind(X)|creative(X))=>(~old(X)<~>~curious(X))))&
(![X]:((patient(X)|wise(X))<=>(creative(X)|humble(X))))&
(((creative(alice)|~funny(alice)))<=>((calm(paul)|kind(paul))))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:(~old(X)=>(calm(X)&~calm(X))))&
((?[X]:((humble(X)<~>quiet(X))))<=>(?[X]:((~humble(X)|~strong(X)))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~quiet(mary)&~strong(mary))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
(![X]:(old(X)=>kind(X)))&
(((~patient(mary)|old(mary)))=>((~happy(paul)|strong(paul))))&
(![X]:((~strong(X)|happy(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:((calm(X)&~calm(X))=>(~happy(X)<~>~kind(X))))&
(![X]:((~rich(X)|creative(X))=>(~rich(X)<~>~quiet(X))))&
((~generous(susan))<=>(?[X]:((~old(X)|creative(X)))))&
((~patient(paul)<~>~quiet(paul)))&
(?[X]:((generous(X)<~>~humble(X))))&
(humble(susan))&
(~calm(paul))&
((~humble(alice)<~>~strong(alice))) | brave(paul) | [
"p5",
"p6",
"p10",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6012489149342753929847278
% SZS output start Proof for 6012489149342753929847278
6. ! [X0] : (strong(X0) <=> (~brave(X0) <~> calm(X0))) [input p5]
7. ! [X0] : (~old(X0) => (~calm(X0) & calm(X0))) [input p6]
11. ! [X0] : (old(X0) => kind(X0)) [input p10]
13. ! [X0] : ((happy(X0) | ~strong(X0)) <=> (~kind(X0) <~> ~happy(X0))) [input p12]
20. ~calm(paul) [input p19]
22. ~brave(paul) [input hypothesis]
26. ! [X0] : ((~calm(X0) & calm(X0)) | old(X0)) [ennf transformation 7]
28. ! [X0] : (kind(X0) | ~old(X0)) [ennf transformation 11]
42. ! [X0] : ((strong(X0) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) & (((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | ~strong(X0))) [nnf transformation 6]
51. ! [X0] : (((happy(X0) | ~strong(X0)) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0)))) & (((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | (~happy(X0) & strong(X0)))) [nnf transformation 13]
52. ! [X0] : ((happy(X0) | ~strong(X0) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0)))) & (((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | (~happy(X0) & strong(X0)))) [flattening 51]
85. brave(X0) | calm(X0) | strong(X0) [cnf transformation 42]
87. calm(X0) | old(X0) [cnf transformation 26]
88. ~calm(X0) | old(X0) [cnf transformation 26]
102. kind(X0) | ~old(X0) [cnf transformation 28]
106. ~happy(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 52]
110. happy(X0) | ~strong(X0) | ~kind(X0) | happy(X0) [cnf transformation 52]
125. ~calm(paul) [cnf transformation 20]
128. ~brave(paul) [cnf transformation 22]
130. ~happy(X0) | ~kind(X0) [duplicate literal removal 106]
131. happy(X0) | ~strong(X0) | ~kind(X0) [duplicate literal removal 110]
164. 8 <=> calm(paul) [avatar definition]
166. ~calm(paul) <- (~8) [avatar component clause 164]
170. old(X0) [subsumption resolution 87,88]
224. kind(X0) [subsumption resolution 102,170]
231. 22 <=> strong(paul) [avatar definition]
233. strong(paul) <- (22) [avatar component clause 231]
240. ~strong(X0) | happy(X0) [subsumption resolution 131,224]
241. ~happy(X0) [subsumption resolution 130,224]
268. ~8 [avatar split clause 125,164]
317. calm(paul) | strong(paul) [resolution 85,128]
320. strong(paul) <- (~8) [subsumption resolution 317,166]
321. 22 | 8 [avatar split clause 320,164,231]
323. happy(paul) <- (22) [resolution 233,240]
324. $false <- (22) [subsumption resolution 323,241]
325. ~22 [avatar contradiction clause 324]
326. $false [avatar sat refutation 268,321,325]
% SZS output end Proof for 6012489149342753929847278
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or brave then someone is not strong or not funny.
If mary is both brave and patient then alice is both not generous and not quiet.
Everyone who is either generous or not curious is both not humble and creative and vice versa.
If susan is both not humble and calm then susan is funny or calm and vice versa.
Everyone who is not patient is not happy and vice versa.
If fred is not quiet then someone is both not humble and not happy and vice versa.
If someone is not patient or not quiet then mary is both not rich and curious and vice versa.
If someone is either not calm or brave then alice is not wise or not kind.
If someone is either not patient or not quiet then someone is both strong and old.
Everyone who is either not wise or rich is both happy and funny and vice versa.
Everyone who is kind is calm and vice versa.
If someone is either kind or generous then fred is not patient or creative and vice versa.
If alice is kind or not quiet then mary is either not creative or not quiet and vice versa.
Everyone who is either calm or funny is both strong and tall.
If susan is both not tall and generous then someone is either rich or not tall.
Everyone who is old is not rich.
Someone is either not wise or tall.
Fred is both rich and patient.
Fred is not calm.
Lucy is old.
Someone is not humble or happy.
Someone is both humble and not quiet.
Someone is funny.
Someone is both funny and strong. | Lucy is quiet. | neutral | ((?[X]:((kind(X)|brave(X))))=>(?[X]:((~strong(X)|~funny(X)))))&
(((brave(mary)&patient(mary)))=>((~generous(alice)&~quiet(alice))))&
(![X]:((generous(X)<~>~curious(X))<=>(~humble(X)&creative(X))))&
(((~humble(susan)&calm(susan)))<=>((funny(susan)|calm(susan))))&
(![X]:(~patient(X)<=>~happy(X)))&
((~quiet(fred))<=>(?[X]:((~humble(X)&~happy(X)))))&
((?[X]:((~patient(X)|~quiet(X))))<=>((~rich(mary)&curious(mary))))&
((?[X]:((~calm(X)<~>brave(X))))=>((~wise(alice)|~kind(alice))))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:((strong(X)&old(X)))))&
(![X]:((~wise(X)<~>rich(X))<=>(happy(X)&funny(X))))&
(![X]:(kind(X)<=>calm(X)))&
((?[X]:((kind(X)<~>generous(X))))<=>((~patient(fred)|creative(fred))))&
(((kind(alice)|~quiet(alice)))<=>((~creative(mary)<~>~quiet(mary))))&
(![X]:((calm(X)<~>funny(X))=>(strong(X)&tall(X))))&
(((~tall(susan)&generous(susan)))=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:(old(X)=>~rich(X)))&
(?[X]:((~wise(X)<~>tall(X))))&
((rich(fred)&patient(fred)))&
(~calm(fred))&
(old(lucy))&
(?[X]:((~humble(X)|happy(X))))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:(funny(X)))&
(?[X]:((funny(X)&strong(X)))) | quiet(lucy) | [] | null | 0 |
If susan is both not happy and curious then paul is either calm or happy.
Everyone who is patient is not tall and vice versa.
Everyone who is both not brave and not happy is not patient and vice versa.
Everyone who is tall is both not strong and not curious and vice versa.
If fred is tall or happy then someone is both not creative and not quiet and vice versa.
Everyone who is not happy or not calm is generous or not calm and vice versa.
If someone is both not rich and rich then someone is both patient and tall.
Everyone who is either not rich or old is either wise or not quiet.
Everyone who is not humble or not curious is wise.
Everyone who is either not brave or not patient is tall and vice versa.
If someone is not generous then paul is not brave and vice versa.
If someone is either patient or strong then alice is both not old and not quiet.
If someone is not patient or generous then someone is rich.
If lucy is curious or creative then someone is not quiet.
Everyone who is kind is not tall or tall and vice versa.
If someone is both not creative and generous then someone is both not funny and quiet.
Paul is strong.
Someone is either quiet or kind.
Lucy is either not rich or not generous.
Someone is either not humble or strong.
Someone is either old or not strong.
Someone is either calm or not patient. | Alice is not generous. | contradiction | (((~happy(susan)&curious(susan)))=>((calm(paul)<~>happy(paul))))&
(![X]:(patient(X)<=>~tall(X)))&
(![X]:((~brave(X)&~happy(X))<=>~patient(X)))&
(![X]:(tall(X)<=>(~strong(X)&~curious(X))))&
(((tall(fred)|happy(fred)))<=>(?[X]:((~creative(X)&~quiet(X)))))&
(![X]:((~happy(X)|~calm(X))<=>(generous(X)|~calm(X))))&
((?[X]:((~rich(X)&rich(X))))=>(?[X]:((patient(X)&tall(X)))))&
(![X]:((~rich(X)<~>old(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((~humble(X)|~curious(X))=>wise(X)))&
(![X]:((~brave(X)<~>~patient(X))<=>tall(X)))&
((?[X]:(~generous(X)))<=>(~brave(paul)))&
((?[X]:((patient(X)<~>strong(X))))=>((~old(alice)&~quiet(alice))))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:(rich(X))))&
(((curious(lucy)|creative(lucy)))=>(?[X]:(~quiet(X))))&
(![X]:(kind(X)<=>(~tall(X)|tall(X))))&
((?[X]:((~creative(X)&generous(X))))=>(?[X]:((~funny(X)&quiet(X)))))&
(strong(paul))&
(?[X]:((quiet(X)<~>kind(X))))&
((~rich(lucy)<~>~generous(lucy)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:((old(X)<~>~strong(X))))&
(?[X]:((calm(X)<~>~patient(X)))) | ~generous(alice) | [
"p1",
"p3",
"p9",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 940623525768443736397643
% SZS output start Proof for 940623525768443736397643
2. ! [X0] : (patient(X0) <=> ~tall(X0)) [input p1]
4. ! [X0] : (tall(X0) <=> (~curious(X0) & ~strong(X0))) [input p3]
10. ! [X0] : ((~brave(X0) <~> ~patient(X0)) <=> tall(X0)) [input p9]
11. ? [X0] : ~generous(X0) <=> ~brave(paul) [input p10]
17. strong(paul) [input p16]
23. ~generous(alice) [input hypothesis]
38. ! [X0] : ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))) [nnf transformation 2]
41. ! [X0] : ((tall(X0) | (curious(X0) | strong(X0))) & ((~curious(X0) & ~strong(X0)) | ~tall(X0))) [nnf transformation 4]
42. ! [X0] : ((tall(X0) | curious(X0) | strong(X0)) & ((~curious(X0) & ~strong(X0)) | ~tall(X0))) [flattening 41]
54. ! [X0] : ((((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | ~tall(X0)) & (tall(X0) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0))))) [nnf transformation 10]
55. (? [X0] : ~generous(X0) | brave(paul)) & (~brave(paul) | ! [X0] : generous(X0)) [nnf transformation 11]
56. (? [X0] : ~generous(X0) | brave(paul)) & (~brave(paul) | ! [X1] : generous(X1)) [rectify 55]
57. ? [X0] : ~generous(X0) => ~generous(sK2) [choice axiom]
58. (~generous(sK2) | brave(paul)) & (~brave(paul) | ! [X1] : generous(X1)) [skolemisation 56,57]
85. ~tall(X0) | ~patient(X0) [cnf transformation 38]
86. tall(X0) | patient(X0) [cnf transformation 38]
90. ~strong(X0) | ~tall(X0) [cnf transformation 42]
110. tall(X0) | ~patient(X0) | brave(X0) [cnf transformation 54]
113. patient(X0) | brave(X0) | ~tall(X0) [cnf transformation 54]
114. ~brave(paul) | generous(X1) [cnf transformation 58]
128. strong(paul) [cnf transformation 17]
139. ~generous(alice) [cnf transformation 23]
182. ~tall(X0) | brave(X0) [subsumption resolution 113,85]
183. ~patient(X0) | brave(X0) [subsumption resolution 110,182]
185. 10 <=> brave(paul) [avatar definition]
186. ~brave(paul) <- (~10) [avatar component clause 185]
194. 12 <=> ! [X1] : generous(X1) [avatar definition]
195. generous(X1) <- (12) [avatar component clause 194]
196. 12 | ~10 [avatar split clause 114,185,194]
292. ~tall(paul) [resolution 90,128]
293. patient(paul) [resolution 292,86]
312. brave(paul) [resolution 183,293]
314. $false <- (~10) [subsumption resolution 312,186]
315. 10 [avatar contradiction clause 314]
316. $false <- (12) [resolution 195,139]
321. ~12 [avatar contradiction clause 316]
322. $false [avatar sat refutation 196,315,321]
% SZS output end Proof for 940623525768443736397643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is curious.
If susan is not happy or old then someone is not humble and vice versa.
Everyone who is both tall and kind is both generous and rich and vice versa.
If john is rich then lucy is both not funny and not rich and vice versa.
Everyone who is calm or humble is both creative and tall and vice versa.
If alice is either creative or not calm then paul is not tall or generous.
Everyone who is strong is either not patient or not kind and vice versa.
Everyone who is both patient and brave is not strong or patient and vice versa.
Everyone who is not calm or old is brave.
Everyone who is either old or not rich is rich and vice versa.
Everyone who is both not quiet and not patient is both quiet and not kind.
Everyone who is both not kind and not generous is not brave.
If lucy is happy then someone is creative.
Everyone who is either curious or not humble is creative.
Everyone who is creative or brave is both not happy and generous.
If mary is brave or not rich then fred is calm or not generous and vice versa.
Susan is either not kind or kind.
Someone is wise or not patient.
Paul is either tall or not creative.
Alice is not quiet.
Someone is both not kind and calm.
Someone is either strong or old.
Someone is either not quiet or not old. | Fred is creative. | entailment | (![X]:(~generous(X)=>curious(X)))&
(((~happy(susan)|old(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((tall(X)&kind(X))<=>(generous(X)&rich(X))))&
((rich(john))<=>((~funny(lucy)&~rich(lucy))))&
(![X]:((calm(X)|humble(X))<=>(creative(X)&tall(X))))&
(((creative(alice)<~>~calm(alice)))=>((~tall(paul)|generous(paul))))&
(![X]:(strong(X)<=>(~patient(X)<~>~kind(X))))&
(![X]:((patient(X)&brave(X))<=>(~strong(X)|patient(X))))&
(![X]:((~calm(X)|old(X))=>brave(X)))&
(![X]:((old(X)<~>~rich(X))<=>rich(X)))&
(![X]:((~quiet(X)&~patient(X))=>(quiet(X)&~kind(X))))&
(![X]:((~kind(X)&~generous(X))=>~brave(X)))&
((happy(lucy))=>(?[X]:(creative(X))))&
(![X]:((curious(X)<~>~humble(X))=>creative(X)))&
(![X]:((creative(X)|brave(X))=>(~happy(X)&generous(X))))&
(((brave(mary)|~rich(mary)))<=>((calm(fred)|~generous(fred))))&
((~kind(susan)<~>kind(susan)))&
(?[X]:((wise(X)|~patient(X))))&
((tall(paul)<~>~creative(paul)))&
(~quiet(alice))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((~quiet(X)<~>~old(X)))) | creative(fred) | [
"p4",
"p8",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4057021043580426978164882
% SZS output start Proof for 4057021043580426978164882
5. ! [X0] : ((humble(X0) | calm(X0)) <=> (tall(X0) & creative(X0))) [input p4]
9. ! [X0] : ((old(X0) | ~calm(X0)) => brave(X0)) [input p8]
10. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> rich(X0)) [input p9]
15. ! [X0] : ((brave(X0) | creative(X0)) => (generous(X0) & ~happy(X0))) [input p14]
16. (~rich(mary) | brave(mary)) <=> (~generous(fred) | calm(fred)) [input p15]
24. ~creative(fred) [input hypothesis]
29. ! [X0] : (brave(X0) | (~old(X0) & calm(X0))) [ennf transformation 9]
36. ! [X0] : ((generous(X0) & ~happy(X0)) | (~brave(X0) & ~creative(X0))) [ennf transformation 15]
46. ! [X0] : (((humble(X0) | calm(X0)) | (~tall(X0) | ~creative(X0))) & ((tall(X0) & creative(X0)) | (~humble(X0) & ~calm(X0)))) [nnf transformation 5]
47. ! [X0] : ((humble(X0) | calm(X0) | ~tall(X0) | ~creative(X0)) & ((tall(X0) & creative(X0)) | (~humble(X0) & ~calm(X0)))) [flattening 46]
52. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~rich(X0)) & (rich(X0) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 10]
56. ((~rich(mary) | brave(mary)) | (generous(fred) & ~calm(fred))) & ((~generous(fred) | calm(fred)) | (rich(mary) & ~brave(mary))) [nnf transformation 16]
57. (~rich(mary) | brave(mary) | (generous(fred) & ~calm(fred))) & (~generous(fred) | calm(fred) | (rich(mary) & ~brave(mary))) [flattening 56]
79. ~calm(X0) | creative(X0) [cnf transformation 47]
96. ~old(X0) | brave(X0) [cnf transformation 29]
98. rich(X0) | old(X0) | rich(X0) [cnf transformation 52]
99. ~rich(X0) | old(X0) | ~rich(X0) [cnf transformation 52]
110. ~brave(X0) | generous(X0) [cnf transformation 36]
111. ~generous(fred) | calm(fred) | ~brave(mary) [cnf transformation 57]
126. ~creative(fred) [cnf transformation 24]
128. rich(X0) | old(X0) [duplicate literal removal 98]
129. ~rich(X0) | old(X0) [duplicate literal removal 99]
183. old(X0) [subsumption resolution 128,129]
195. 14 <=> generous(fred) [avatar definition]
196. ~generous(fred) <- (~14) [avatar component clause 195]
199. 15 <=> brave(mary) [avatar definition]
200. ~brave(mary) <- (~15) [avatar component clause 199]
208. 17 <=> calm(fred) [avatar definition]
209. calm(fred) <- (17) [avatar component clause 208]
213. ~15 | 17 | ~14 [avatar split clause 111,195,208,199]
225. brave(X0) [resolution 96,183]
231. generous(X0) [resolution 110,225]
234. $false <- (~14) [resolution 231,196]
235. 14 [avatar contradiction clause 234]
236. $false <- (~15) [subsumption resolution 200,225]
237. 15 [avatar contradiction clause 236]
239. creative(fred) <- (17) [resolution 209,79]
240. $false <- (17) [subsumption resolution 239,126]
241. ~17 [avatar contradiction clause 240]
242. $false [avatar sat refutation 213,235,237,241]
% SZS output end Proof for 4057021043580426978164882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not generous then someone is either not happy or not quiet.
Everyone who is either not generous or not humble is either not quiet or creative.
Everyone who is not calm or not old is both not calm and calm and vice versa.
Everyone who is both old and kind is not generous and vice versa.
If john is both strong and not happy then someone is both not calm and not wise.
Everyone who is curious or happy is both not quiet and not calm and vice versa.
Everyone who is either old or generous is either not brave or rich.
If lucy is not patient then someone is creative and vice versa.
If john is either not patient or not kind then someone is both not brave and not happy.
Everyone who is both not rich and old is both not brave and generous and vice versa.
Everyone who is both not creative and not funny is both not strong and patient.
Everyone who is not quiet is either not happy or funny and vice versa.
If someone is either not generous or calm then paul is both not patient and patient and vice versa.
Everyone who is both not calm and happy is both not quiet and patient and vice versa.
Everyone who is both not curious and old is either rich or generous and vice versa.
If someone is not creative then someone is not strong and vice versa.
Alice is old.
Someone is funny or not patient.
John is either not humble or not brave.
Lucy is either calm or wise.
Someone is either calm or not patient. | John is kind. | entailment | (((funny(alice)|~generous(alice)))=>(?[X]:((~happy(X)<~>~quiet(X)))))&
(![X]:((~generous(X)<~>~humble(X))=>(~quiet(X)<~>creative(X))))&
(![X]:((~calm(X)|~old(X))<=>(~calm(X)&calm(X))))&
(![X]:((old(X)&kind(X))<=>~generous(X)))&
(((strong(john)&~happy(john)))=>(?[X]:((~calm(X)&~wise(X)))))&
(![X]:((curious(X)|happy(X))<=>(~quiet(X)&~calm(X))))&
(![X]:((old(X)<~>generous(X))=>(~brave(X)<~>rich(X))))&
((~patient(lucy))<=>(?[X]:(creative(X))))&
(((~patient(john)<~>~kind(john)))=>(?[X]:((~brave(X)&~happy(X)))))&
(![X]:((~rich(X)&old(X))<=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~funny(X))=>(~strong(X)&patient(X))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>funny(X))))&
((?[X]:((~generous(X)<~>calm(X))))<=>((~patient(paul)&patient(paul))))&
(![X]:((~calm(X)&happy(X))<=>(~quiet(X)&patient(X))))&
(![X]:((~curious(X)&old(X))<=>(rich(X)<~>generous(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~strong(X))))&
(old(alice))&
(?[X]:((funny(X)|~patient(X))))&
((~humble(john)<~>~brave(john)))&
((calm(lucy)<~>wise(lucy)))&
(?[X]:((calm(X)<~>~patient(X)))) | kind(john) | [
"p2",
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6767779066482884970432397
% SZS output start Proof for 6767779066482884970432397
3. ! [X0] : ((~old(X0) | ~calm(X0)) <=> (calm(X0) & ~calm(X0))) [input p2]
4. ! [X0] : ((kind(X0) & old(X0)) <=> ~generous(X0)) [input p3]
13. ? [X0] : (~generous(X0) <~> calm(X0)) <=> (patient(paul) & ~patient(paul)) [input p12]
22. ~kind(john) [input hypothesis]
36. ! [X0] : (((~old(X0) | ~calm(X0)) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | (old(X0) & calm(X0)))) [nnf transformation 3]
37. ! [X0] : ((~old(X0) | ~calm(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | (old(X0) & calm(X0)))) [flattening 36]
38. ! [X0] : (((kind(X0) & old(X0)) | generous(X0)) & (~generous(X0) | (~kind(X0) | ~old(X0)))) [nnf transformation 4]
39. ! [X0] : (((kind(X0) & old(X0)) | generous(X0)) & (~generous(X0) | ~kind(X0) | ~old(X0))) [flattening 38]
55. (? [X0] : ((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | (~patient(paul) | patient(paul))) & ((patient(paul) & ~patient(paul)) | ! [X0] : ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0)))) [nnf transformation 13]
56. (? [X0] : ((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | ~patient(paul) | patient(paul)) & ((patient(paul) & ~patient(paul)) | ! [X0] : ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0)))) [flattening 55]
57. (? [X0] : ((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | ~patient(paul) | patient(paul)) & ((patient(paul) & ~patient(paul)) | ! [X1] : ((~generous(X1) | ~calm(X1)) & (calm(X1) | generous(X1)))) [rectify 56]
58. ? [X0] : ((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) => ((~calm(sK4) | generous(sK4)) & (calm(sK4) | ~generous(sK4))) [choice axiom]
59. (((~calm(sK4) | generous(sK4)) & (calm(sK4) | ~generous(sK4))) | ~patient(paul) | patient(paul)) & ((patient(paul) & ~patient(paul)) | ! [X1] : ((~generous(X1) | ~calm(X1)) & (calm(X1) | generous(X1)))) [skolemisation 57,58]
86. calm(X0) | calm(X0) [cnf transformation 37]
91. kind(X0) | generous(X0) [cnf transformation 39]
120. ~patient(paul) | ~generous(X1) | ~calm(X1) [cnf transformation 59]
122. patient(paul) | ~generous(X1) | ~calm(X1) [cnf transformation 59]
145. ~kind(john) [cnf transformation 22]
146. calm(X0) [duplicate literal removal 86]
203. 11 <=> kind(john) [avatar definition]
204. ~kind(john) <- (~11) [avatar component clause 203]
221. patient(paul) | ~generous(X1) [subsumption resolution 122,146]
223. 14 <=> ! [X1] : ~generous(X1) [avatar definition]
224. ~generous(X1) <- (14) [avatar component clause 223]
226. 15 <=> patient(paul) [avatar definition]
229. 14 | 15 [avatar split clause 221,226,223]
230. ~patient(paul) | ~generous(X1) [subsumption resolution 120,146]
231. 14 | ~15 [avatar split clause 230,226,223]
272. ~11 [avatar split clause 145,203]
275. generous(john) <- (~11) [resolution 91,204]
276. $false <- (~11, 14) [subsumption resolution 275,224]
277. 11 | ~14 [avatar contradiction clause 276]
278. $false [avatar sat refutation 229,231,272,277]
% SZS output end Proof for 6767779066482884970432397
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not patient or calm then susan is either humble or not quiet.
If someone is either not old or brave then alice is rich or not brave.
Everyone who is humble is both not rich and wise.
Everyone who is not old or not calm is not brave or not funny.
If susan is not patient then fred is calm and vice versa.
If someone is both not rich and patient then someone is either patient or not old.
If someone is both strong and not generous then lucy is not generous or not wise and vice versa.
If someone is both brave and not patient then paul is both not quiet and not kind and vice versa.
If lucy is either not brave or not kind then someone is not old or humble.
Everyone who is either not strong or not quiet is curious or not wise.
Everyone who is both patient and not old is both not rich and not happy.
Everyone who is either not strong or tall is either funny or not brave and vice versa.
Everyone who is either humble or strong is either not wise or wise and vice versa.
If lucy is strong then someone is tall.
If someone is quiet or not brave then alice is happy or calm.
If alice is not funny or creative then someone is not old.
Lucy is either not tall or not wise.
Someone is either not wise or brave.
Alice is either not wise or not patient.
Fred is either old or humble.
Someone is curious.
Someone is rich or not generous.
John is either not curious or not calm. | Lucy is not brave. | neutral | (((~patient(paul)|calm(paul)))=>((humble(susan)<~>~quiet(susan))))&
((?[X]:((~old(X)<~>brave(X))))=>((rich(alice)|~brave(alice))))&
(![X]:(humble(X)=>(~rich(X)&wise(X))))&
(![X]:((~old(X)|~calm(X))=>(~brave(X)|~funny(X))))&
((~patient(susan))<=>(calm(fred)))&
((?[X]:((~rich(X)&patient(X))))=>(?[X]:((patient(X)<~>~old(X)))))&
((?[X]:((strong(X)&~generous(X))))<=>((~generous(lucy)|~wise(lucy))))&
((?[X]:((brave(X)&~patient(X))))<=>((~quiet(paul)&~kind(paul))))&
(((~brave(lucy)<~>~kind(lucy)))=>(?[X]:((~old(X)|humble(X)))))&
(![X]:((~strong(X)<~>~quiet(X))=>(curious(X)|~wise(X))))&
(![X]:((patient(X)&~old(X))=>(~rich(X)&~happy(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(funny(X)<~>~brave(X))))&
(![X]:((humble(X)<~>strong(X))<=>(~wise(X)<~>wise(X))))&
((strong(lucy))=>(?[X]:(tall(X))))&
((?[X]:((quiet(X)|~brave(X))))=>((happy(alice)|calm(alice))))&
(((~funny(alice)|creative(alice)))=>(?[X]:(~old(X))))&
((~tall(lucy)<~>~wise(lucy)))&
(?[X]:((~wise(X)<~>brave(X))))&
((~wise(alice)<~>~patient(alice)))&
((old(fred)<~>humble(fred)))&
(?[X]:(curious(X)))&
(?[X]:((rich(X)|~generous(X))))&
((~curious(john)<~>~calm(john))) | ~brave(lucy) | [] | null | 0 |
Everyone who is wise or kind is either not strong or humble and vice versa. Everyone who is wise is both not generous and brave and vice versa. Everyone who is either generous or not curious is not humble or not generous and vice versa. Everyone who is strong or generous is not creative. Everyone who is either brave or not rich is tall. If someone is either strong or old then someone is patient. Everyone who is either not curious or not brave is creative or not curious and vice versa. If someone is generous then alice is not creative and vice versa. Everyone who is not calm or not wise is either not curious or humble. If john is both not happy and not wise then someone is not kind or old. Everyone who is either not humble or not calm is either not old or strong. Everyone who is either old or wise is not kind or brave. Everyone who is either curious or patient is brave or not curious. Everyone who is brave is either happy or kind and vice versa. If fred is not funny then someone is strong or not curious. Everyone who is tall or not humble is either kind or calm. Someone is rich. Lucy is generous or not kind. John is both not generous and tall. Someone is both quiet and brave. Someone is both not strong and not funny. Someone is not tall or not brave. Mary is either not old or not happy. Someone is both brave and happy. | John is wise. | entailment | (![X]:((wise(X)|kind(X))<=>(~strong(X)<~>humble(X))))&
(![X]:(wise(X)<=>(~generous(X)&brave(X))))&
(![X]:((generous(X)<~>~curious(X))<=>(~humble(X)|~generous(X))))&
(![X]:((strong(X)|generous(X))=>~creative(X)))&
(![X]:((brave(X)<~>~rich(X))=>tall(X)))&
((?[X]:((strong(X)<~>old(X))))=>(?[X]:(patient(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(creative(X)|~curious(X))))&
((?[X]:(generous(X)))<=>(~creative(alice)))&
(![X]:((~calm(X)|~wise(X))=>(~curious(X)<~>humble(X))))&
(((~happy(john)&~wise(john)))=>(?[X]:((~kind(X)|old(X)))))&
(![X]:((~humble(X)<~>~calm(X))=>(~old(X)<~>strong(X))))&
(![X]:((old(X)<~>wise(X))=>(~kind(X)|brave(X))))&
(![X]:((curious(X)<~>patient(X))=>(brave(X)|~curious(X))))&
(![X]:(brave(X)<=>(happy(X)<~>kind(X))))&
((~funny(fred))=>(?[X]:((strong(X)|~curious(X)))))&
(![X]:((tall(X)|~humble(X))=>(kind(X)<~>calm(X))))&
(?[X]:(rich(X)))&
((generous(lucy)|~kind(lucy)))&
((~generous(john)&tall(john)))&
(?[X]:((quiet(X)&brave(X))))&
(?[X]:((~strong(X)&~funny(X))))&
(?[X]:((~tall(X)|~brave(X))))&
((~old(mary)<~>~happy(mary)))&
(?[X]:((brave(X)&happy(X)))) | wise(john) | [
"p1",
"p2",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4291746728796815458864391
% SZS output start Proof for 4291746728796815458864391
2. ! [X0] : (wise(X0) <=> (brave(X0) & ~generous(X0))) [input p1]
3. ! [X0] : ((generous(X0) <~> ~curious(X0)) <=> (~generous(X0) | ~humble(X0))) [input p2]
7. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (~curious(X0) | creative(X0))) [input p6]
19. tall(john) & ~generous(john) [input p18]
25. ~wise(john) [input hypothesis]
43. ! [X0] : ((wise(X0) | (~brave(X0) | generous(X0))) & ((brave(X0) & ~generous(X0)) | ~wise(X0))) [nnf transformation 2]
44. ! [X0] : ((wise(X0) | ~brave(X0) | generous(X0)) & ((brave(X0) & ~generous(X0)) | ~wise(X0))) [flattening 43]
45. ! [X0] : ((((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | (generous(X0) & humble(X0))) & ((~generous(X0) | ~humble(X0)) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0))))) [nnf transformation 3]
46. ! [X0] : ((((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | (generous(X0) & humble(X0))) & (~generous(X0) | ~humble(X0) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0))))) [flattening 45]
52. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (curious(X0) & ~creative(X0))) & ((~curious(X0) | creative(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 7]
53. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (curious(X0) & ~creative(X0))) & (~curious(X0) | creative(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 52]
87. ~brave(X0) | wise(X0) | generous(X0) [cnf transformation 44]
91. ~curious(X0) | generous(X0) | generous(X0) [cnf transformation 46]
105. brave(X0) | curious(X0) | curious(X0) [cnf transformation 53]
132. ~generous(john) [cnf transformation 19]
142. ~wise(john) [cnf transformation 25]
145. curious(X0) | brave(X0) [duplicate literal removal 105]
147. ~curious(X0) | generous(X0) [duplicate literal removal 91]
184. 8 <=> wise(john) [avatar definition]
185. ~wise(john) <- (~8) [avatar component clause 184]
240. ~8 [avatar split clause 142,184]
243. brave(X0) | generous(X0) [resolution 147,145]
253. wise(X0) | generous(X0) | generous(X0) [resolution 87,243]
259. generous(X0) | wise(X0) [duplicate literal removal 253]
260. wise(john) [resolution 259,132]
262. $false <- (~8) [subsumption resolution 260,185]
263. 8 [avatar contradiction clause 262]
264. $false [avatar sat refutation 240,263]
% SZS output end Proof for 4291746728796815458864391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not happy and vice versa.
If someone is both not brave and not strong then lucy is either not tall or rich and vice versa.
Everyone who is old or not calm is tall or quiet.
Everyone who is both not wise and old is either not rich or funny and vice versa.
Everyone who is either calm or not generous is not old or calm and vice versa.
Everyone who is brave is both kind and wise.
Everyone who is tall or patient is both old and not quiet.
If someone is either not tall or not generous then someone is happy or funny and vice versa.
If alice is tall then someone is both old and creative.
If someone is not kind then john is both not creative and not curious and vice versa.
Everyone who is either not creative or generous is both not calm and not tall.
If mary is generous then someone is either not quiet or quiet and vice versa.
Everyone who is both generous and humble is not brave or not kind and vice versa.
Everyone who is not old or not happy is generous and vice versa.
If someone is either brave or not rich then susan is either not creative or not generous and vice versa.
Everyone who is not tall is either not generous or strong.
Someone is humble.
John is not creative.
Susan is both not creative and generous.
Susan is either generous or not happy.
Mary is either not wise or not curious.
Someone is generous or not calm. | Susan is calm. | entailment | (![X]:(~generous(X)<=>~happy(X)))&
((?[X]:((~brave(X)&~strong(X))))<=>((~tall(lucy)<~>rich(lucy))))&
(![X]:((old(X)|~calm(X))=>(tall(X)|quiet(X))))&
(![X]:((~wise(X)&old(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(~old(X)|calm(X))))&
(![X]:(brave(X)=>(kind(X)&wise(X))))&
(![X]:((tall(X)|patient(X))=>(old(X)&~quiet(X))))&
((?[X]:((~tall(X)<~>~generous(X))))<=>(?[X]:((happy(X)|funny(X)))))&
((tall(alice))=>(?[X]:((old(X)&creative(X)))))&
((?[X]:(~kind(X)))<=>((~creative(john)&~curious(john))))&
(![X]:((~creative(X)<~>generous(X))=>(~calm(X)&~tall(X))))&
((generous(mary))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((generous(X)&humble(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~old(X)|~happy(X))<=>generous(X)))&
((?[X]:((brave(X)<~>~rich(X))))<=>((~creative(susan)<~>~generous(susan))))&
(![X]:(~tall(X)=>(~generous(X)<~>strong(X))))&
(?[X]:(humble(X)))&
(~creative(john))&
((~creative(susan)&generous(susan)))&
((generous(susan)<~>~happy(susan)))&
((~wise(mary)<~>~curious(mary)))&
(?[X]:((generous(X)|~calm(X)))) | calm(susan) | [
"p0",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4602042995785504240791149
% SZS output start Proof for 4602042995785504240791149
1. ! [X0] : (~generous(X0) <=> ~happy(X0)) [input p0]
5. ! [X0] : ((calm(X0) <~> ~generous(X0)) <=> (calm(X0) | ~old(X0))) [input p4]
14. ! [X0] : ((~happy(X0) | ~old(X0)) <=> generous(X0)) [input p13]
23. ~calm(susan) [input hypothesis]
33. ! [X0] : ((~generous(X0) | happy(X0)) & (~happy(X0) | generous(X0))) [nnf transformation 1]
40. ! [X0] : ((((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | (~calm(X0) & old(X0))) & ((calm(X0) | ~old(X0)) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0))))) [nnf transformation 5]
41. ! [X0] : ((((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | (~calm(X0) & old(X0))) & (calm(X0) | ~old(X0) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0))))) [flattening 40]
61. ! [X0] : (((~happy(X0) | ~old(X0)) | ~generous(X0)) & (generous(X0) | (happy(X0) & old(X0)))) [nnf transformation 14]
62. ! [X0] : ((~happy(X0) | ~old(X0) | ~generous(X0)) & (generous(X0) | (happy(X0) & old(X0)))) [flattening 61]
75. ~generous(X0) | happy(X0) [cnf transformation 33]
91. calm(X0) | ~old(X0) | calm(X0) | generous(X0) [cnf transformation 41]
92. ~generous(X0) | calm(X0) | old(X0) [cnf transformation 41]
95. generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 41]
124. generous(X0) | old(X0) [cnf transformation 62]
125. generous(X0) | happy(X0) [cnf transformation 62]
126. ~happy(X0) | ~old(X0) | ~generous(X0) [cnf transformation 62]
146. ~calm(susan) [cnf transformation 23]
149. calm(X0) | ~old(X0) | generous(X0) [duplicate literal removal 91]
150. ~calm(X0) | generous(X0) [duplicate literal removal 95]
176. ~old(X0) | generous(X0) [subsumption resolution 149,150]
257. ~old(X0) | ~happy(X0) [subsumption resolution 126,176]
258. happy(X0) [subsumption resolution 125,75]
259. generous(X0) [subsumption resolution 124,176]
339. calm(X0) | old(X0) [resolution 92,259]
341. old(susan) [resolution 339,146]
344. ~happy(susan) [resolution 341,257]
355. $false [subsumption resolution 344,258]
% SZS output end Proof for 4602042995785504240791149
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then paul is not rich or not kind and vice versa.
If someone is tall then lucy is not brave.
Everyone who is either not creative or not brave is both not calm and not tall and vice versa.
If fred is either rich or not calm then someone is either quiet or tall and vice versa.
If mary is both quiet and brave then someone is creative or not quiet.
Everyone who is not strong is either not calm or not patient.
If lucy is both not generous and quiet then paul is not curious and vice versa.
Everyone who is not generous is both brave and strong.
If susan is not curious then someone is either generous or not tall and vice versa.
Everyone who is either not rich or calm is old and vice versa.
Everyone who is not brave or humble is both calm and not tall and vice versa.
Everyone who is either not tall or old is either not strong or calm.
Everyone who is both tall and generous is not curious or rich and vice versa.
If paul is not humble then john is either quiet or not kind and vice versa.
If someone is old then alice is both strong and not rich.
Everyone who is wise is humble or curious and vice versa.
John is tall or kind.
Someone is calm or not patient.
Lucy is not quiet or patient.
Lucy is humble.
Someone is either rich or funny.
Someone is either creative or not generous.
Paul is not rich.
Alice is not tall. | Lucy is not calm. | contradiction | ((?[X]:(brave(X)))<=>((~rich(paul)|~kind(paul))))&
((?[X]:(tall(X)))=>(~brave(lucy)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~calm(X)&~tall(X))))&
(((rich(fred)<~>~calm(fred)))<=>(?[X]:((quiet(X)<~>tall(X)))))&
(((quiet(mary)&brave(mary)))=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:(~strong(X)=>(~calm(X)<~>~patient(X))))&
(((~generous(lucy)&quiet(lucy)))<=>(~curious(paul)))&
(![X]:(~generous(X)=>(brave(X)&strong(X))))&
((~curious(susan))<=>(?[X]:((generous(X)<~>~tall(X)))))&
(![X]:((~rich(X)<~>calm(X))<=>old(X)))&
(![X]:((~brave(X)|humble(X))<=>(calm(X)&~tall(X))))&
(![X]:((~tall(X)<~>old(X))=>(~strong(X)<~>calm(X))))&
(![X]:((tall(X)&generous(X))<=>(~curious(X)|rich(X))))&
((~humble(paul))<=>((quiet(john)<~>~kind(john))))&
((?[X]:(old(X)))=>((strong(alice)&~rich(alice))))&
(![X]:(wise(X)<=>(humble(X)|curious(X))))&
((tall(john)|kind(john)))&
(?[X]:((calm(X)|~patient(X))))&
((~quiet(lucy)|patient(lucy)))&
(humble(lucy))&
(?[X]:((rich(X)<~>funny(X))))&
(?[X]:((creative(X)<~>~generous(X))))&
(~rich(paul))&
(~tall(alice)) | ~calm(lucy) | [
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8027436490539544505661319
% SZS output start Proof for 8027436490539544505661319
11. ! [X0] : ((humble(X0) | ~brave(X0)) <=> (~tall(X0) & calm(X0))) [input p10]
20. humble(lucy) [input p19]
25. ~calm(lucy) [input hypothesis]
54. ! [X0] : (((humble(X0) | ~brave(X0)) | (tall(X0) | ~calm(X0))) & ((~tall(X0) & calm(X0)) | (~humble(X0) & brave(X0)))) [nnf transformation 11]
55. ! [X0] : ((humble(X0) | ~brave(X0) | tall(X0) | ~calm(X0)) & ((~tall(X0) & calm(X0)) | (~humble(X0) & brave(X0)))) [flattening 54]
103. ~humble(X0) | calm(X0) [cnf transformation 55]
125. humble(lucy) [cnf transformation 20]
132. ~calm(lucy) [cnf transformation 25]
321. calm(lucy) [resolution 103,125]
322. $false [subsumption resolution 321,132]
% SZS output end Proof for 8027436490539544505661319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either not happy or happy.
If someone is creative or not tall then john is both old and tall.
If someone is creative then someone is either rich or not humble.
If someone is not humble then alice is both calm and not kind.
Everyone who is calm is tall or not old.
If someone is not creative or rich then someone is happy and vice versa.
If someone is rich then someone is both not strong and strong and vice versa.
Everyone who is rich or not happy is not creative.
If paul is kind or strong then lucy is not old.
Everyone who is not strong is both not quiet and not wise and vice versa.
If lucy is either not generous or not strong then someone is not creative or funny.
Everyone who is both strong and not generous is brave or happy.
If someone is kind or patient then paul is not patient.
Everyone who is either rich or curious is both not generous and funny and vice versa.
If someone is old or curious then susan is not generous and vice versa.
Everyone who is either not old or tall is both quiet and not strong and vice versa.
Someone is not happy.
Lucy is not funny or not strong.
Someone is either not quiet or not creative.
Mary is either brave or not strong.
Someone is either generous or not tall.
Someone is both not kind and funny.
Someone is not old or brave.
Someone is either not funny or not humble. | Paul is old. | contradiction | (![X]:(happy(X)=>(~happy(X)<~>happy(X))))&
((?[X]:((creative(X)|~tall(X))))=>((old(john)&tall(john))))&
((?[X]:(creative(X)))=>(?[X]:((rich(X)<~>~humble(X)))))&
((?[X]:(~humble(X)))=>((calm(alice)&~kind(alice))))&
(![X]:(calm(X)=>(tall(X)|~old(X))))&
((?[X]:((~creative(X)|rich(X))))<=>(?[X]:(happy(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:((rich(X)|~happy(X))=>~creative(X)))&
(((kind(paul)|strong(paul)))=>(~old(lucy)))&
(![X]:(~strong(X)<=>(~quiet(X)&~wise(X))))&
(((~generous(lucy)<~>~strong(lucy)))=>(?[X]:((~creative(X)|funny(X)))))&
(![X]:((strong(X)&~generous(X))=>(brave(X)|happy(X))))&
((?[X]:((kind(X)|patient(X))))=>(~patient(paul)))&
(![X]:((rich(X)<~>curious(X))<=>(~generous(X)&funny(X))))&
((?[X]:((old(X)|curious(X))))<=>(~generous(susan)))&
(![X]:((~old(X)<~>tall(X))<=>(quiet(X)&~strong(X))))&
(?[X]:(~happy(X)))&
((~funny(lucy)|~strong(lucy)))&
(?[X]:((~quiet(X)<~>~creative(X))))&
((brave(mary)<~>~strong(mary)))&
(?[X]:((generous(X)<~>~tall(X))))&
(?[X]:((~kind(X)&funny(X))))&
(?[X]:((~old(X)|brave(X))))&
(?[X]:((~funny(X)<~>~humble(X)))) | old(paul) | [
"p1",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4742236246073914643464679
% SZS output start Proof for 4742236246073914643464679
2. ? [X0] : (~tall(X0) | creative(X0)) => (tall(john) & old(john)) [input p1]
10. ! [X0] : (~strong(X0) <=> (~wise(X0) & ~quiet(X0))) [input p9]
16. ! [X0] : ((~old(X0) <~> tall(X0)) <=> (~strong(X0) & quiet(X0))) [input p15]
25. old(paul) [input hypothesis]
34. (tall(john) & old(john)) | ! [X0] : (tall(X0) & ~creative(X0)) [ennf transformation 2]
59. ! [X0] : ((~strong(X0) | (wise(X0) | quiet(X0))) & ((~wise(X0) & ~quiet(X0)) | strong(X0))) [nnf transformation 10]
60. ! [X0] : ((~strong(X0) | wise(X0) | quiet(X0)) & ((~wise(X0) & ~quiet(X0)) | strong(X0))) [flattening 59]
70. ! [X0] : ((((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | (strong(X0) | ~quiet(X0))) & ((~strong(X0) & quiet(X0)) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))))) [nnf transformation 16]
71. ! [X0] : ((((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | strong(X0) | ~quiet(X0)) & ((~strong(X0) & quiet(X0)) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))))) [flattening 70]
91. old(john) | tall(X0) [cnf transformation 34]
93. tall(john) | tall(X0) [cnf transformation 34]
107. ~quiet(X0) | strong(X0) [cnf transformation 60]
123. ~old(X0) | quiet(X0) | ~tall(X0) [cnf transformation 71]
125. ~strong(X0) | ~old(X0) | ~tall(X0) [cnf transformation 71]
140. old(paul) [cnf transformation 25]
144. 1 <=> ! [X0] : tall(X0) [avatar definition]
145. tall(X0) <- (1) [avatar component clause 144]
147. 2 <=> tall(john) [avatar definition]
149. tall(john) <- (2) [avatar component clause 147]
150. 1 | 2 [avatar split clause 93,147,144]
156. 4 <=> old(john) [avatar definition]
158. old(john) <- (4) [avatar component clause 156]
159. 1 | 4 [avatar split clause 91,156,144]
210. 16 <=> strong(paul) [avatar definition]
211. strong(paul) <- (16) [avatar component clause 210]
331. quiet(paul) | ~tall(paul) [resolution 123,140]
332. quiet(john) | ~tall(john) <- (4) [resolution 123,158]
335. 40 <=> tall(paul) [avatar definition]
337. ~tall(paul) <- (~40) [avatar component clause 335]
339. 41 <=> quiet(paul) [avatar definition]
341. quiet(paul) <- (41) [avatar component clause 339]
342. ~40 | 41 [avatar split clause 331,339,335]
343. quiet(john) <- (2, 4) [subsumption resolution 332,149]
354. strong(john) <- (2, 4) [resolution 343,107]
414. ~old(john) | ~tall(john) <- (2, 4) [resolution 354,125]
430. ~tall(john) <- (2, 4) [subsumption resolution 414,158]
431. $false <- (2, 4) [subsumption resolution 430,149]
432. ~2 | ~4 [avatar contradiction clause 431]
434. $false <- (1, ~40) [resolution 145,337]
437. ~1 | 40 [avatar contradiction clause 434]
440. strong(paul) <- (41) [resolution 341,107]
441. 16 | ~41 [avatar split clause 440,339,210]
443. ~old(paul) | ~tall(paul) <- (16) [resolution 211,125]
459. ~tall(paul) <- (16) [subsumption resolution 443,140]
460. $false <- (1, 16) [subsumption resolution 459,145]
461. ~1 | ~16 [avatar contradiction clause 460]
462. $false [avatar sat refutation 150,159,342,432,437,441,461]
% SZS output end Proof for 4742236246073914643464679
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not wise and quiet then someone is both not humble and creative.
Everyone who is either not humble or not wise is quiet or kind and vice versa.
If fred is not funny or curious then john is both not curious and quiet.
Everyone who is calm is brave or happy and vice versa.
Everyone who is not happy or creative is either funny or creative and vice versa.
Everyone who is not happy or not wise is either not quiet or not happy and vice versa.
Everyone who is generous or not happy is not curious or not brave and vice versa.
If lucy is rich then john is not curious or not quiet and vice versa.
If fred is both creative and not patient then john is both not brave and wise and vice versa.
If someone is either not happy or curious then someone is kind or brave and vice versa.
If someone is strong or brave then susan is either brave or not patient.
If someone is both humble and not creative then someone is either happy or strong and vice versa.
Everyone who is not generous is either not rich or not happy and vice versa.
Everyone who is humble is either humble or calm and vice versa.
Everyone who is either quiet or not curious is either creative or not curious and vice versa.
Everyone who is not patient or not strong is not strong or creative and vice versa.
Paul is either kind or not rich.
Someone is not creative or rich.
Someone is either brave or quiet.
John is either not curious or not humble.
Paul is either generous or old. | Lucy is strong. | contradiction | (((~wise(susan)&quiet(susan)))=>(?[X]:((~humble(X)&creative(X)))))&
(![X]:((~humble(X)<~>~wise(X))<=>(quiet(X)|kind(X))))&
(((~funny(fred)|curious(fred)))=>((~curious(john)&quiet(john))))&
(![X]:(calm(X)<=>(brave(X)|happy(X))))&
(![X]:((~happy(X)|creative(X))<=>(funny(X)<~>creative(X))))&
(![X]:((~happy(X)|~wise(X))<=>(~quiet(X)<~>~happy(X))))&
(![X]:((generous(X)|~happy(X))<=>(~curious(X)|~brave(X))))&
((rich(lucy))<=>((~curious(john)|~quiet(john))))&
(((creative(fred)&~patient(fred)))<=>((~brave(john)&wise(john))))&
((?[X]:((~happy(X)<~>curious(X))))<=>(?[X]:((kind(X)|brave(X)))))&
((?[X]:((strong(X)|brave(X))))=>((brave(susan)<~>~patient(susan))))&
((?[X]:((humble(X)&~creative(X))))<=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:(~generous(X)<=>(~rich(X)<~>~happy(X))))&
(![X]:(humble(X)<=>(humble(X)<~>calm(X))))&
(![X]:((quiet(X)<~>~curious(X))<=>(creative(X)<~>~curious(X))))&
(![X]:((~patient(X)|~strong(X))<=>(~strong(X)|creative(X))))&
((kind(paul)<~>~rich(paul)))&
(?[X]:((~creative(X)|rich(X))))&
(?[X]:((brave(X)<~>quiet(X))))&
((~curious(john)<~>~humble(john)))&
((generous(paul)<~>old(paul))) | strong(lucy) | [
"p3",
"p5",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5552684478061537746454281
% SZS output start Proof for 5552684478061537746454281
4. ! [X0] : (calm(X0) <=> (happy(X0) | brave(X0))) [input p3]
6. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> (~quiet(X0) <~> ~happy(X0))) [input p5]
12. ? [X0] : (~creative(X0) & humble(X0)) <=> ? [X0] : (happy(X0) <~> strong(X0)) [input p11]
14. ! [X0] : (humble(X0) <=> (humble(X0) <~> calm(X0))) [input p13]
15. ! [X0] : ((quiet(X0) <~> ~curious(X0)) <=> (creative(X0) <~> ~curious(X0))) [input p14]
22. strong(lucy) [input hypothesis]
24. ? [X0] : (~creative(X0) & humble(X0)) <=> ? [X1] : (happy(X1) <~> strong(X1)) [rectify 12]
33. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | ~calm(X0))) [nnf transformation 4]
34. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ~calm(X0))) [flattening 33]
37. ! [X0] : (((~wise(X0) | ~happy(X0)) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0)))) & (((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | (wise(X0) & happy(X0)))) [nnf transformation 6]
38. ! [X0] : ((~wise(X0) | ~happy(X0) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0)))) & (((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | (wise(X0) & happy(X0)))) [flattening 37]
51. (? [X0] : (~creative(X0) & humble(X0)) | ! [X1] : ((happy(X1) | ~strong(X1)) & (strong(X1) | ~happy(X1)))) & (? [X1] : ((~strong(X1) | ~happy(X1)) & (strong(X1) | happy(X1))) | ! [X0] : (creative(X0) | ~humble(X0))) [nnf transformation 24]
52. (? [X0] : (~creative(X0) & humble(X0)) | ! [X1] : ((happy(X1) | ~strong(X1)) & (strong(X1) | ~happy(X1)))) & (? [X2] : ((~strong(X2) | ~happy(X2)) & (strong(X2) | happy(X2))) | ! [X3] : (creative(X3) | ~humble(X3))) [rectify 51]
53. ? [X0] : (~creative(X0) & humble(X0)) => (~creative(sK3) & humble(sK3)) [choice axiom]
54. ? [X2] : ((~strong(X2) | ~happy(X2)) & (strong(X2) | happy(X2))) => ((~strong(sK4) | ~happy(sK4)) & (strong(sK4) | happy(sK4))) [choice axiom]
55. ((~creative(sK3) & humble(sK3)) | ! [X1] : ((happy(X1) | ~strong(X1)) & (strong(X1) | ~happy(X1)))) & (((~strong(sK4) | ~happy(sK4)) & (strong(sK4) | happy(sK4))) | ! [X3] : (creative(X3) | ~humble(X3))) [skolemisation 52,54,53]
57. ! [X0] : ((humble(X0) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) & (((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | ~humble(X0))) [nnf transformation 14]
58. ! [X0] : ((((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | ((creative(X0) | curious(X0)) & (~curious(X0) | ~creative(X0)))) & (((curious(X0) | ~creative(X0)) & (~curious(X0) | creative(X0))) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0))))) [nnf transformation 15]
83. ~happy(X0) | calm(X0) [cnf transformation 34]
92. happy(X0) | quiet(X0) | happy(X0) [cnf transformation 38]
122. ~creative(sK3) | happy(X1) | ~strong(X1) [cnf transformation 55]
128. ~calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 57]
130. humble(X0) | humble(X0) | ~calm(X0) [cnf transformation 57]
131. ~curious(X0) | creative(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 58]
138. curious(X0) | ~quiet(X0) | creative(X0) | curious(X0) [cnf transformation 58]
152. strong(lucy) [cnf transformation 22]
153. ~curious(X0) | creative(X0) | ~quiet(X0) [duplicate literal removal 131]
156. curious(X0) | ~quiet(X0) | creative(X0) [duplicate literal removal 138]
157. ~calm(X0) | ~humble(X0) [duplicate literal removal 128]
158. ~calm(X0) | humble(X0) [duplicate literal removal 130]
159. happy(X0) | quiet(X0) [duplicate literal removal 92]
278. 25 <=> ! [X1] : (happy(X1) | ~strong(X1)) [avatar definition]
279. ~strong(X1) | happy(X1) <- (25) [avatar component clause 278]
281. 26 <=> creative(sK3) [avatar definition]
283. ~creative(sK3) <- (~26) [avatar component clause 281]
284. 25 | ~26 [avatar split clause 122,281,278]
308. ~calm(X0) [subsumption resolution 157,158]
310. ~quiet(X0) | creative(X0) [subsumption resolution 153,156]
360. quiet(X0) | calm(X0) [resolution 159,83]
361. quiet(X0) [subsumption resolution 360,308]
363. happy(lucy) <- (25) [resolution 279,152]
366. calm(lucy) <- (25) [resolution 363,83]
367. $false <- (25) [subsumption resolution 366,308]
368. ~25 [avatar contradiction clause 367]
380. creative(X0) [resolution 310,361]
386. $false <- (~26) [resolution 380,283]
389. 26 [avatar contradiction clause 386]
391. $false [avatar sat refutation 284,368,389]
% SZS output end Proof for 5552684478061537746454281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not patient is either not funny or not curious and vice versa.
Everyone who is kind is not old or strong.
Everyone who is either not calm or rich is both quiet and not patient.
Everyone who is both not curious and funny is not humble and vice versa.
If someone is either not funny or not brave then paul is funny.
If someone is curious or not tall then someone is happy or not creative.
If paul is either not creative or quiet then paul is both not rich and quiet.
If someone is either creative or calm then fred is either not patient or not creative.
If someone is not wise then someone is both rich and generous.
Everyone who is humble or not wise is generous or not tall.
Everyone who is both not patient and brave is not curious or kind.
Everyone who is not creative or happy is not wise and vice versa.
Everyone who is humble or brave is not funny.
Everyone who is not curious or funny is old.
Everyone who is strong is either curious or not wise.
Everyone who is not brave is either tall or not funny and vice versa.
Someone is either not humble or not tall.
Someone is not creative or humble.
Alice is generous.
Someone is wise or creative.
Paul is not calm or not quiet.
Paul is not calm or humble.
Paul is rich or generous.
Susan is either not brave or patient. | Susan is curious. | entailment | (![X]:((humble(X)&~patient(X))<=>(~funny(X)<~>~curious(X))))&
(![X]:(kind(X)=>(~old(X)|strong(X))))&
(![X]:((~calm(X)<~>rich(X))=>(quiet(X)&~patient(X))))&
(![X]:((~curious(X)&funny(X))<=>~humble(X)))&
((?[X]:((~funny(X)<~>~brave(X))))=>(funny(paul)))&
((?[X]:((curious(X)|~tall(X))))=>(?[X]:((happy(X)|~creative(X)))))&
(((~creative(paul)<~>quiet(paul)))=>((~rich(paul)&quiet(paul))))&
((?[X]:((creative(X)<~>calm(X))))=>((~patient(fred)<~>~creative(fred))))&
((?[X]:(~wise(X)))=>(?[X]:((rich(X)&generous(X)))))&
(![X]:((humble(X)|~wise(X))=>(generous(X)|~tall(X))))&
(![X]:((~patient(X)&brave(X))=>(~curious(X)|kind(X))))&
(![X]:((~creative(X)|happy(X))<=>~wise(X)))&
(![X]:((humble(X)|brave(X))=>~funny(X)))&
(![X]:((~curious(X)|funny(X))=>old(X)))&
(![X]:(strong(X)=>(curious(X)<~>~wise(X))))&
(![X]:(~brave(X)<=>(tall(X)<~>~funny(X))))&
(?[X]:((~humble(X)<~>~tall(X))))&
(?[X]:((~creative(X)|humble(X))))&
(generous(alice))&
(?[X]:((wise(X)|creative(X))))&
((~calm(paul)|~quiet(paul)))&
((~calm(paul)|humble(paul)))&
((rich(paul)|generous(paul)))&
((~brave(susan)<~>patient(susan))) | curious(susan) | [
"p0",
"p3",
"p4",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5880920099591293369581677
% SZS output start Proof for 5880920099591293369581677
1. ! [X0] : ((~patient(X0) & humble(X0)) <=> (~funny(X0) <~> ~curious(X0))) [input p0]
4. ! [X0] : ((funny(X0) & ~curious(X0)) <=> ~humble(X0)) [input p3]
5. ? [X0] : (~funny(X0) <~> ~brave(X0)) => funny(paul) [input p4]
13. ! [X0] : ((brave(X0) | humble(X0)) => ~funny(X0)) [input p12]
24. ~brave(susan) <~> patient(susan) [input p23]
25. ~curious(susan) [input hypothesis]
35. funny(paul) | ! [X0] : (~funny(X0) <=> ~brave(X0)) [ennf transformation 5]
42. ! [X0] : (~funny(X0) | (~brave(X0) & ~humble(X0))) [ennf transformation 13]
45. ! [X0] : (((~patient(X0) & humble(X0)) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0)))) & (((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | (patient(X0) | ~humble(X0)))) [nnf transformation 1]
46. ! [X0] : (((~patient(X0) & humble(X0)) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0)))) & (((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | patient(X0) | ~humble(X0))) [flattening 45]
48. ! [X0] : (((funny(X0) & ~curious(X0)) | humble(X0)) & (~humble(X0) | (~funny(X0) | curious(X0)))) [nnf transformation 4]
49. ! [X0] : (((funny(X0) & ~curious(X0)) | humble(X0)) & (~humble(X0) | ~funny(X0) | curious(X0))) [flattening 48]
50. funny(paul) | ! [X0] : ((~funny(X0) | brave(X0)) & (~brave(X0) | funny(X0))) [nnf transformation 35]
70. (~patient(susan) | brave(susan)) & (patient(susan) | ~brave(susan)) [nnf transformation 24]
72. ~humble(X0) | funny(X0) | patient(X0) | curious(X0) [cnf transformation 46]
74. ~funny(X0) | humble(X0) | curious(X0) [cnf transformation 46]
82. ~humble(X0) | ~funny(X0) | curious(X0) [cnf transformation 49]
83. ~curious(X0) | humble(X0) [cnf transformation 49]
84. funny(X0) | humble(X0) [cnf transformation 49]
85. funny(paul) | ~brave(X0) | funny(X0) [cnf transformation 50]
86. funny(paul) | ~funny(X0) | brave(X0) [cnf transformation 50]
102. ~funny(X0) | ~humble(X0) [cnf transformation 42]
103. ~brave(X0) | ~funny(X0) [cnf transformation 42]
119. ~patient(susan) | brave(susan) [cnf transformation 70]
120. ~curious(susan) [cnf transformation 25]
122. ~funny(X0) | curious(X0) [subsumption resolution 82,74]
124. 1 <=> ! [X0] : (~funny(X0) | brave(X0)) [avatar definition]
125. ~funny(X0) | brave(X0) <- (1) [avatar component clause 124]
127. 2 <=> funny(paul) [avatar definition]
129. funny(paul) <- (2) [avatar component clause 127]
130. 1 | 2 [avatar split clause 86,127,124]
132. 3 <=> ! [X0] : (~brave(X0) | funny(X0)) [avatar definition]
133. ~brave(X0) | funny(X0) <- (3) [avatar component clause 132]
134. 3 | 2 [avatar split clause 85,127,132]
220. 22 <=> humble(paul) [avatar definition]
221. ~humble(paul) <- (~22) [avatar component clause 220]
225. 23 <=> brave(susan) [avatar definition]
227. brave(susan) <- (23) [avatar component clause 225]
229. 24 <=> patient(susan) [avatar definition]
232. 23 | ~24 [avatar split clause 119,229,225]
241. ~humble(paul) <- (2) [resolution 102,129]
243. ~22 | ~2 [avatar split clause 241,127,220]
247. curious(X0) | humble(X0) [resolution 122,84]
248. humble(X0) [subsumption resolution 247,83]
250. $false <- (~22) [resolution 248,221]
251. 22 [avatar contradiction clause 250]
252. ~brave(X0) <- (3) [subsumption resolution 133,103]
253. ~funny(X0) <- (1, 3) [subsumption resolution 125,252]
332. funny(X0) | patient(X0) | curious(X0) [resolution 72,248]
343. curious(X0) | patient(X0) <- (1, 3) [subsumption resolution 332,253]
352. patient(susan) <- (1, 3) [resolution 343,120]
360. 24 | ~1 | ~3 [avatar split clause 352,132,124,229]
361. $false <- (3, 23) [subsumption resolution 227,252]
362. ~3 | ~23 [avatar contradiction clause 361]
363. $false [avatar sat refutation 130,134,232,243,251,360,362]
% SZS output end Proof for 5880920099591293369581677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
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