premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is rich or humble is both not happy and wise.
Everyone who is happy or not rich is either not patient or not curious and vice versa.
Everyone who is both patient and quiet is both brave and old.
If someone is not humble then john is either not brave or not patient and vice versa.
Everyone who is not humble or brave is both not wise and not strong and vice versa.
If fred is both strong and not patient then someone is not old or not happy.
Everyone who is wise is not patient or generous and vice versa.
If someone is both not creative and old then paul is either not generous or not kind.
If lucy is both calm and brave then someone is creative.
If someone is either not brave or not kind then someone is both not kind and curious and vice versa.
Everyone who is brave is happy or creative and vice versa.
Everyone who is kind is either kind or not rich.
Everyone who is either brave or not old is both not wise and not calm.
If paul is patient or rich then someone is both not quiet and kind.
Everyone who is either humble or funny is wise and vice versa.
If someone is either not patient or creative then someone is rich or not creative.
John is both not wise and not rich.
Someone is both not brave and not rich.
Paul is not strong or patient.
Someone is creative or patient.
Alice is either not happy or creative.
Lucy is both curious and not funny.
Susan is old.
Alice is not wise. | Lucy is happy. | contradiction | (![X]:((rich(X)|humble(X))=>(~happy(X)&wise(X))))&
(![X]:((happy(X)|~rich(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((patient(X)&quiet(X))=>(brave(X)&old(X))))&
((?[X]:(~humble(X)))<=>((~brave(john)<~>~patient(john))))&
(![X]:((~humble(X)|brave(X))<=>(~wise(X)&~strong(X))))&
(((strong(fred)&~patient(fred)))=>(?[X]:((~old(X)|~happy(X)))))&
(![X]:(wise(X)<=>(~patient(X)|generous(X))))&
((?[X]:((~creative(X)&old(X))))=>((~generous(paul)<~>~kind(paul))))&
(((calm(lucy)&brave(lucy)))=>(?[X]:(creative(X))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:(brave(X)<=>(happy(X)|creative(X))))&
(![X]:(kind(X)=>(kind(X)<~>~rich(X))))&
(![X]:((brave(X)<~>~old(X))=>(~wise(X)&~calm(X))))&
(((patient(paul)|rich(paul)))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((humble(X)<~>funny(X))<=>wise(X)))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:((rich(X)|~creative(X)))))&
((~wise(john)&~rich(john)))&
(?[X]:((~brave(X)&~rich(X))))&
((~strong(paul)|patient(paul)))&
(?[X]:((creative(X)|patient(X))))&
((~happy(alice)<~>creative(alice)))&
((curious(lucy)&~funny(lucy)))&
(old(susan))&
(~wise(alice)) | happy(lucy) | [
"p1",
"p4",
"p6",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7061212239804958318745960
% SZS output start Proof for 7061212239804958318745960
2. ! [X0] : ((~rich(X0) | happy(X0)) <=> (~patient(X0) <~> ~curious(X0))) [input p1]
5. ! [X0] : ((brave(X0) | ~humble(X0)) <=> (~strong(X0) & ~wise(X0))) [input p4]
7. ! [X0] : (wise(X0) <=> (generous(X0) | ~patient(X0))) [input p6]
11. ! [X0] : (brave(X0) <=> (creative(X0) | happy(X0))) [input p10]
22. ~funny(lucy) & curious(lucy) [input p21]
25. happy(lucy) [input hypothesis]
40. ! [X0] : (((~rich(X0) | happy(X0)) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) & (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | (rich(X0) & ~happy(X0)))) [nnf transformation 2]
41. ! [X0] : ((~rich(X0) | happy(X0) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) & (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | (rich(X0) & ~happy(X0)))) [flattening 40]
46. ! [X0] : (((brave(X0) | ~humble(X0)) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | (~brave(X0) & humble(X0)))) [nnf transformation 5]
47. ! [X0] : ((brave(X0) | ~humble(X0) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | (~brave(X0) & humble(X0)))) [flattening 46]
50. ! [X0] : ((wise(X0) | (~generous(X0) & patient(X0))) & ((generous(X0) | ~patient(X0)) | ~wise(X0))) [nnf transformation 7]
51. ! [X0] : ((wise(X0) | (~generous(X0) & patient(X0))) & (generous(X0) | ~patient(X0) | ~wise(X0))) [flattening 50]
58. ! [X0] : ((brave(X0) | (~creative(X0) & ~happy(X0))) & ((creative(X0) | happy(X0)) | ~brave(X0))) [nnf transformation 11]
59. ! [X0] : ((brave(X0) | (~creative(X0) & ~happy(X0))) & (creative(X0) | happy(X0) | ~brave(X0))) [flattening 58]
78. ~curious(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 41]
89. ~brave(X0) | ~wise(X0) [cnf transformation 47]
95. patient(X0) | wise(X0) [cnf transformation 51]
106. ~happy(X0) | brave(X0) [cnf transformation 59]
128. curious(lucy) [cnf transformation 22]
132. happy(lucy) [cnf transformation 25]
281. brave(lucy) [resolution 106,132]
282. ~wise(lucy) [resolution 281,89]
295. ~patient(lucy) | ~happy(lucy) [resolution 78,128]
297. ~patient(lucy) [subsumption resolution 295,132]
307. wise(lucy) [resolution 297,95]
308. $false [subsumption resolution 307,282]
% SZS output end Proof for 7061212239804958318745960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is both kind and not creative. If someone is both not brave and not happy then alice is either not happy or strong and vice versa. Everyone who is not generous or brave is both patient and brave and vice versa. If someone is either not patient or not generous then john is either old or not humble and vice versa. Everyone who is either not tall or rich is both happy and patient and vice versa. If someone is both not strong and not brave then alice is tall or not funny and vice versa. If someone is either not tall or funny then someone is both happy and funny. Everyone who is rich is wise and vice versa. If mary is either generous or not wise then someone is patient. Everyone who is not creative or not humble is brave or not happy. Everyone who is either not brave or happy is humble and vice versa. Everyone who is both old and not tall is both old and strong and vice versa. If someone is either happy or not tall then someone is quiet or kind. If someone is either creative or calm then fred is not patient. Everyone who is both tall and not quiet is either rich or not creative. Everyone who is not calm or not generous is both not strong and not tall and vice versa. John is either not happy or not patient. John is not quiet. Mary is tall or calm. Mary is not old or strong. Alice is both tall and calm. Alice is either rich or tall. Someone is either quiet or strong. | Fred is not generous. | contradiction | (![X]:(creative(X)=>(kind(X)&~creative(X))))&
((?[X]:((~brave(X)&~happy(X))))<=>((~happy(alice)<~>strong(alice))))&
(![X]:((~generous(X)|brave(X))<=>(patient(X)&brave(X))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>((old(john)<~>~humble(john))))&
(![X]:((~tall(X)<~>rich(X))<=>(happy(X)&patient(X))))&
((?[X]:((~strong(X)&~brave(X))))<=>((tall(alice)|~funny(alice))))&
((?[X]:((~tall(X)<~>funny(X))))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:(rich(X)<=>wise(X)))&
(((generous(mary)<~>~wise(mary)))=>(?[X]:(patient(X))))&
(![X]:((~creative(X)|~humble(X))=>(brave(X)|~happy(X))))&
(![X]:((~brave(X)<~>happy(X))<=>humble(X)))&
(![X]:((old(X)&~tall(X))<=>(old(X)&strong(X))))&
((?[X]:((happy(X)<~>~tall(X))))=>(?[X]:((quiet(X)|kind(X)))))&
((?[X]:((creative(X)<~>calm(X))))=>(~patient(fred)))&
(![X]:((tall(X)&~quiet(X))=>(rich(X)<~>~creative(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~strong(X)&~tall(X))))&
((~happy(john)<~>~patient(john)))&
(~quiet(john))&
((tall(mary)|calm(mary)))&
((~old(mary)|strong(mary)))&
((tall(alice)&calm(alice)))&
((rich(alice)<~>tall(alice)))&
(?[X]:((quiet(X)<~>strong(X)))) | ~generous(fred) | [
"p0",
"p2",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7770138955954779189813088
% SZS output start Proof for 7770138955954779189813088
1. ! [X0] : (creative(X0) => (~creative(X0) & kind(X0))) [input p0]
3. ! [X0] : ((brave(X0) | ~generous(X0)) <=> (brave(X0) & patient(X0))) [input p2]
14. ? [X0] : (creative(X0) <~> calm(X0)) => ~patient(fred) [input p13]
21. calm(alice) & tall(alice) [input p20]
24. ~generous(fred) [input hypothesis]
27. ! [X0] : (creative(X0) => ~creative(X0)) [pure predicate removal 1]
29. ! [X0] : (~creative(X0) | ~creative(X0)) [ennf transformation 27]
34. ~patient(fred) | ! [X0] : (creative(X0) <=> calm(X0)) [ennf transformation 14]
41. ! [X0] : (((brave(X0) | ~generous(X0)) | (~brave(X0) | ~patient(X0))) & ((brave(X0) & patient(X0)) | (~brave(X0) & generous(X0)))) [nnf transformation 3]
42. ! [X0] : ((brave(X0) | ~generous(X0) | ~brave(X0) | ~patient(X0)) & ((brave(X0) & patient(X0)) | (~brave(X0) & generous(X0)))) [flattening 41]
65. ~patient(fred) | ! [X0] : ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))) [nnf transformation 34]
74. ~creative(X0) | ~creative(X0) [cnf transformation 29]
81. patient(X0) | generous(X0) [cnf transformation 42]
124. ~patient(fred) | creative(X0) | ~calm(X0) [cnf transformation 65]
138. calm(alice) [cnf transformation 21]
143. ~generous(fred) [cnf transformation 24]
144. ~creative(X0) [duplicate literal removal 74]
261. ~patient(fred) | ~calm(X0) [subsumption resolution 124,144]
263. 24 <=> ! [X0] : ~calm(X0) [avatar definition]
264. ~calm(X0) <- (24) [avatar component clause 263]
266. 25 <=> patient(fred) [avatar definition]
268. ~patient(fred) <- (~25) [avatar component clause 266]
269. 24 | ~25 [avatar split clause 261,266,263]
308. generous(fred) <- (~25) [resolution 81,268]
310. $false <- (~25) [subsumption resolution 308,143]
311. 25 [avatar contradiction clause 310]
312. $false <- (24) [resolution 264,138]
315. ~24 [avatar contradiction clause 312]
316. $false [avatar sat refutation 269,311,315]
% SZS output end Proof for 7770138955954779189813088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is either not old or happy and vice versa.
Everyone who is quiet or not rich is not generous and vice versa.
Everyone who is both quiet and calm is strong.
Everyone who is either brave or not tall is generous or not creative.
Everyone who is both not kind and not strong is calm.
If paul is both not quiet and quiet then someone is old and vice versa.
If john is curious or not old then someone is not tall and vice versa.
Everyone who is tall is not calm or not rich and vice versa.
If someone is both not rich and kind then someone is quiet.
If alice is brave then someone is both humble and curious and vice versa.
Everyone who is not calm or rich is either not generous or not old.
If someone is happy or not funny then lucy is both happy and not calm and vice versa.
If susan is humble then mary is kind.
If alice is both old and strong then someone is both not funny and generous.
Everyone who is brave is both not strong and curious and vice versa.
Everyone who is not funny is both curious and creative and vice versa.
Mary is kind or tall.
Someone is both not old and not creative.
Someone is old or curious.
Someone is either curious or not humble.
Someone is kind or brave.
Paul is either old or strong.
Mary is calm or creative.
Mary is both funny and not calm. | Lucy is quiet. | contradiction | (![X]:(~creative(X)<=>(~old(X)<~>happy(X))))&
(![X]:((quiet(X)|~rich(X))<=>~generous(X)))&
(![X]:((quiet(X)&calm(X))=>strong(X)))&
(![X]:((brave(X)<~>~tall(X))=>(generous(X)|~creative(X))))&
(![X]:((~kind(X)&~strong(X))=>calm(X)))&
(((~quiet(paul)&quiet(paul)))<=>(?[X]:(old(X))))&
(((curious(john)|~old(john)))<=>(?[X]:(~tall(X))))&
(![X]:(tall(X)<=>(~calm(X)|~rich(X))))&
((?[X]:((~rich(X)&kind(X))))=>(?[X]:(quiet(X))))&
((brave(alice))<=>(?[X]:((humble(X)&curious(X)))))&
(![X]:((~calm(X)|rich(X))=>(~generous(X)<~>~old(X))))&
((?[X]:((happy(X)|~funny(X))))<=>((happy(lucy)&~calm(lucy))))&
((humble(susan))=>(kind(mary)))&
(((old(alice)&strong(alice)))=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:(brave(X)<=>(~strong(X)&curious(X))))&
(![X]:(~funny(X)<=>(curious(X)&creative(X))))&
((kind(mary)|tall(mary)))&
(?[X]:((~old(X)&~creative(X))))&
(?[X]:((old(X)|curious(X))))&
(?[X]:((curious(X)<~>~humble(X))))&
(?[X]:((kind(X)|brave(X))))&
((old(paul)<~>strong(paul)))&
((calm(mary)|creative(mary)))&
((funny(mary)&~calm(mary))) | quiet(lucy) | [
"p0",
"p1",
"p5",
"p10",
"p11",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7859745228546747652338153
% SZS output start Proof for 7859745228546747652338153
1. ! [X0] : (~creative(X0) <=> (~old(X0) <~> happy(X0))) [input p0]
2. ! [X0] : ((~rich(X0) | quiet(X0)) <=> ~generous(X0)) [input p1]
6. (quiet(paul) & ~quiet(paul)) <=> ? [X0] : old(X0) [input p5]
11. ! [X0] : ((rich(X0) | ~calm(X0)) => (~generous(X0) <~> ~old(X0))) [input p10]
12. ? [X0] : (~funny(X0) | happy(X0)) <=> (~calm(lucy) & happy(lucy)) [input p11]
23. creative(mary) | calm(mary) [input p22]
24. ~calm(mary) & funny(mary) [input p23]
25. quiet(lucy) [input hypothesis]
34. ! [X0] : ((~generous(X0) <~> ~old(X0)) | (~rich(X0) & calm(X0))) [ennf transformation 11]
38. ! [X0] : ((~creative(X0) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0)))) & (((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | creative(X0))) [nnf transformation 1]
39. ! [X0] : (((~rich(X0) | quiet(X0)) | generous(X0)) & (~generous(X0) | (rich(X0) & ~quiet(X0)))) [nnf transformation 2]
40. ! [X0] : ((~rich(X0) | quiet(X0) | generous(X0)) & (~generous(X0) | (rich(X0) & ~quiet(X0)))) [flattening 39]
42. ((quiet(paul) & ~quiet(paul)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (~quiet(paul) | quiet(paul))) [nnf transformation 6]
43. ((quiet(paul) & ~quiet(paul)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | ~quiet(paul) | quiet(paul)) [flattening 42]
44. ((quiet(paul) & ~quiet(paul)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | ~quiet(paul) | quiet(paul)) [rectify 43]
45. ? [X1] : old(X1) => old(sK0) [choice axiom]
46. ((quiet(paul) & ~quiet(paul)) | ! [X0] : ~old(X0)) & (old(sK0) | ~quiet(paul) | quiet(paul)) [skolemisation 44,45]
61. ! [X0] : (((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | (~rich(X0) & calm(X0))) [nnf transformation 34]
62. (? [X0] : (~funny(X0) | happy(X0)) | (calm(lucy) | ~happy(lucy))) & ((~calm(lucy) & happy(lucy)) | ! [X0] : (funny(X0) & ~happy(X0))) [nnf transformation 12]
63. (? [X0] : (~funny(X0) | happy(X0)) | calm(lucy) | ~happy(lucy)) & ((~calm(lucy) & happy(lucy)) | ! [X0] : (funny(X0) & ~happy(X0))) [flattening 62]
64. (? [X0] : (~funny(X0) | happy(X0)) | calm(lucy) | ~happy(lucy)) & ((~calm(lucy) & happy(lucy)) | ! [X1] : (funny(X1) & ~happy(X1))) [rectify 63]
65. ? [X0] : (~funny(X0) | happy(X0)) => (~funny(sK4) | happy(sK4)) [choice axiom]
66. ((~funny(sK4) | happy(sK4)) | calm(lucy) | ~happy(lucy)) & ((~calm(lucy) & happy(lucy)) | ! [X1] : (funny(X1) & ~happy(X1))) [skolemisation 64,65]
85. ~creative(X0) | happy(X0) | old(X0) [cnf transformation 38]
87. ~generous(X0) | ~quiet(X0) [cnf transformation 40]
95. ~quiet(paul) | ~old(X0) [cnf transformation 46]
96. quiet(paul) | ~old(X0) [cnf transformation 46]
109. calm(X0) | generous(X0) | old(X0) [cnf transformation 61]
113. ~calm(lucy) | ~happy(X1) [cnf transformation 66]
134. creative(mary) | calm(mary) [cnf transformation 23]
136. ~calm(mary) [cnf transformation 24]
137. quiet(lucy) [cnf transformation 25]
139. 1 <=> ! [X0] : ~old(X0) [avatar definition]
140. ~old(X0) <- (1) [avatar component clause 139]
142. 2 <=> quiet(paul) [avatar definition]
145. 1 | 2 [avatar split clause 96,142,139]
146. 1 | ~2 [avatar split clause 95,142,139]
197. 14 <=> calm(lucy) [avatar definition]
198. ~calm(lucy) <- (~14) [avatar component clause 197]
214. 18 <=> ! [X1] : ~happy(X1) [avatar definition]
215. ~happy(X1) <- (18) [avatar component clause 214]
216. 18 | ~14 [avatar split clause 113,197,214]
290. 34 <=> calm(mary) [avatar definition]
294. 35 <=> creative(mary) [avatar definition]
296. creative(mary) <- (35) [avatar component clause 294]
297. 34 | 35 [avatar split clause 134,294,290]
298. ~34 [avatar split clause 136,290]
309. happy(mary) | old(mary) <- (35) [resolution 85,296]
311. happy(mary) <- (1, 35) [subsumption resolution 309,140]
365. generous(lucy) | old(lucy) <- (~14) [resolution 109,198]
368. generous(lucy) <- (1, ~14) [subsumption resolution 365,140]
375. ~quiet(lucy) <- (1, ~14) [resolution 368,87]
376. $false <- (1, ~14) [subsumption resolution 375,137]
377. ~1 | 14 [avatar contradiction clause 376]
384. $false <- (1, 18, 35) [resolution 215,311]
385. ~1 | ~18 | ~35 [avatar contradiction clause 384]
388. $false [avatar sat refutation 145,146,216,297,298,377,385]
% SZS output end Proof for 7859745228546747652338153
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either funny or patient then lucy is generous. Everyone who is both rich and not humble is rich and vice versa. Everyone who is both kind and wise is either not calm or not tall. Everyone who is not wise is either not patient or strong and vice versa. If paul is both kind and not tall then lucy is both not strong and rich and vice versa. Everyone who is either old or not wise is either patient or rich and vice versa. If someone is not funny or kind then john is both not quiet and calm and vice versa. If paul is both not quiet and old then someone is not creative. Everyone who is not wise or patient is both not brave and tall and vice versa. If someone is not generous or not strong then john is either strong or tall. If paul is not kind then someone is not happy or patient. If someone is both quiet and not brave then someone is either calm or not calm and vice versa. If someone is both not tall and not happy then someone is both strong and not brave. Everyone who is both not tall and humble is not generous or not kind and vice versa. If mary is not brave or tall then lucy is both not kind and not quiet and vice versa. Everyone who is either wise or not strong is not calm or calm and vice versa. Susan is not wise. Alice is strong or creative. Someone is not old. Susan is both not calm and creative. Someone is not curious. Someone is both not creative and not rich. Someone is strong. Someone is not calm. | Lucy is old. | neutral | (((funny(susan)<~>patient(susan)))=>(generous(lucy)))&
(![X]:((rich(X)&~humble(X))<=>rich(X)))&
(![X]:((kind(X)&wise(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(~wise(X)<=>(~patient(X)<~>strong(X))))&
(((kind(paul)&~tall(paul)))<=>((~strong(lucy)&rich(lucy))))&
(![X]:((old(X)<~>~wise(X))<=>(patient(X)<~>rich(X))))&
((?[X]:((~funny(X)|kind(X))))<=>((~quiet(john)&calm(john))))&
(((~quiet(paul)&old(paul)))=>(?[X]:(~creative(X))))&
(![X]:((~wise(X)|patient(X))<=>(~brave(X)&tall(X))))&
((?[X]:((~generous(X)|~strong(X))))=>((strong(john)<~>tall(john))))&
((~kind(paul))=>(?[X]:((~happy(X)|patient(X)))))&
((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((calm(X)<~>~calm(X)))))&
((?[X]:((~tall(X)&~happy(X))))=>(?[X]:((strong(X)&~brave(X)))))&
(![X]:((~tall(X)&humble(X))<=>(~generous(X)|~kind(X))))&
(((~brave(mary)|tall(mary)))<=>((~kind(lucy)&~quiet(lucy))))&
(![X]:((wise(X)<~>~strong(X))<=>(~calm(X)|calm(X))))&
(~wise(susan))&
((strong(alice)|creative(alice)))&
(?[X]:(~old(X)))&
((~calm(susan)&creative(susan)))&
(?[X]:(~curious(X)))&
(?[X]:((~creative(X)&~rich(X))))&
(?[X]:(strong(X)))&
(?[X]:(~calm(X))) | old(lucy) | [] | null | 0 |
Everyone who is strong is not tall or not curious.
Everyone who is not brave or kind is either generous or not patient.
If lucy is either creative or not wise then someone is humble or wise and vice versa.
If lucy is either patient or not funny then lucy is humble and vice versa.
Everyone who is not kind is either not funny or happy and vice versa.
Everyone who is not old is both not wise and not calm.
If fred is brave then susan is not quiet or not wise.
Everyone who is not strong or old is not patient or funny.
Everyone who is either happy or not patient is not patient and vice versa.
Everyone who is both not funny and generous is either creative or not wise and vice versa.
If john is not calm or not strong then mary is not kind.
Everyone who is either generous or patient is either quiet or not wise and vice versa.
Everyone who is either not happy or not tall is either humble or not tall and vice versa.
Everyone who is not old or not rich is both old and not happy and vice versa.
Everyone who is quiet or brave is not curious or kind and vice versa.
Everyone who is both calm and not tall is creative or patient and vice versa.
Someone is not rich or not wise.
Someone is old.
Someone is either not creative or generous.
Someone is generous.
Fred is either generous or tall.
Someone is funny or rich.
Fred is both old and quiet. | Fred is not generous. | contradiction | (![X]:(strong(X)=>(~tall(X)|~curious(X))))&
(![X]:((~brave(X)|kind(X))=>(generous(X)<~>~patient(X))))&
(((creative(lucy)<~>~wise(lucy)))<=>(?[X]:((humble(X)|wise(X)))))&
(((patient(lucy)<~>~funny(lucy)))<=>(humble(lucy)))&
(![X]:(~kind(X)<=>(~funny(X)<~>happy(X))))&
(![X]:(~old(X)=>(~wise(X)&~calm(X))))&
((brave(fred))=>((~quiet(susan)|~wise(susan))))&
(![X]:((~strong(X)|old(X))=>(~patient(X)|funny(X))))&
(![X]:((happy(X)<~>~patient(X))<=>~patient(X)))&
(![X]:((~funny(X)&generous(X))<=>(creative(X)<~>~wise(X))))&
(((~calm(john)|~strong(john)))=>(~kind(mary)))&
(![X]:((generous(X)<~>patient(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~happy(X)<~>~tall(X))<=>(humble(X)<~>~tall(X))))&
(![X]:((~old(X)|~rich(X))<=>(old(X)&~happy(X))))&
(![X]:((quiet(X)|brave(X))<=>(~curious(X)|kind(X))))&
(![X]:((calm(X)&~tall(X))<=>(creative(X)|patient(X))))&
(?[X]:((~rich(X)|~wise(X))))&
(?[X]:(old(X)))&
(?[X]:((~creative(X)<~>generous(X))))&
(?[X]:(generous(X)))&
((generous(fred)<~>tall(fred)))&
(?[X]:((funny(X)|rich(X))))&
((old(fred)&quiet(fred))) | ~generous(fred) | [
"p9",
"p11",
"p15",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5858607784790830570531894
% SZS output start Proof for 5858607784790830570531894
10. ! [X0] : ((generous(X0) & ~funny(X0)) <=> (creative(X0) <~> ~wise(X0))) [input p9]
12. ! [X0] : ((generous(X0) <~> patient(X0)) <=> (quiet(X0) <~> ~wise(X0))) [input p11]
16. ! [X0] : ((~tall(X0) & calm(X0)) <=> (patient(X0) | creative(X0))) [input p15]
21. generous(fred) <~> tall(fred) [input p20]
23. quiet(fred) & old(fred) [input p22]
24. ~generous(fred) [input hypothesis]
42. ! [X0] : (((generous(X0) & ~funny(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (~generous(X0) | funny(X0)))) [nnf transformation 10]
43. ! [X0] : (((generous(X0) & ~funny(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | ~generous(X0) | funny(X0))) [flattening 42]
44. ! [X0] : ((((~patient(X0) | ~generous(X0)) & (patient(X0) | generous(X0))) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0)))) & (((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0))))) [nnf transformation 12]
50. ! [X0] : (((~tall(X0) & calm(X0)) | (~patient(X0) & ~creative(X0))) & ((patient(X0) | creative(X0)) | (tall(X0) | ~calm(X0)))) [nnf transformation 16]
51. ! [X0] : (((~tall(X0) & calm(X0)) | (~patient(X0) & ~creative(X0))) & (patient(X0) | creative(X0) | tall(X0) | ~calm(X0))) [flattening 50]
61. (~tall(fred) | ~generous(fred)) & (tall(fred) | generous(fred)) [nnf transformation 21]
97. wise(X0) | creative(X0) | generous(X0) [cnf transformation 43]
104. ~quiet(X0) | generous(X0) | ~wise(X0) | patient(X0) [cnf transformation 44]
128. ~creative(X0) | ~tall(X0) [cnf transformation 51]
129. ~patient(X0) | ~tall(X0) [cnf transformation 51]
135. tall(fred) | generous(fred) [cnf transformation 61]
139. quiet(fred) [cnf transformation 23]
140. ~generous(fred) [cnf transformation 24]
245. 20 <=> generous(fred) [avatar definition]
247. ~generous(fred) <- (~20) [avatar component clause 245]
249. 21 <=> tall(fred) [avatar definition]
250. tall(fred) <- (21) [avatar component clause 249]
253. 20 | 21 [avatar split clause 135,249,245]
263. ~20 [avatar split clause 140,245]
405. 43 <=> patient(fred) [avatar definition]
406. patient(fred) <- (43) [avatar component clause 405]
409. 44 <=> wise(fred) [avatar definition]
410. ~wise(fred) <- (~44) [avatar component clause 409]
413. generous(fred) | ~wise(fred) | patient(fred) [resolution 104,139]
415. ~wise(fred) | patient(fred) <- (~20) [subsumption resolution 413,247]
419. creative(fred) | generous(fred) <- (~44) [resolution 410,97]
420. creative(fred) <- (~20, ~44) [subsumption resolution 419,247]
440. ~tall(fred) <- (~20, ~44) [resolution 420,128]
442. $false <- (~20, 21, ~44) [subsumption resolution 440,250]
443. 20 | ~21 | 44 [avatar contradiction clause 442]
444. 43 | ~44 | 20 [avatar split clause 415,245,409,405]
450. ~tall(fred) <- (43) [resolution 406,129]
466. $false <- (21, 43) [subsumption resolution 450,250]
467. ~21 | ~43 [avatar contradiction clause 466]
469. $false [avatar sat refutation 253,263,443,444,467]
% SZS output end Proof for 5858607784790830570531894
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious then paul is not patient or happy and vice versa.
If someone is either not strong or not wise then john is both not patient and funny.
Everyone who is both calm and creative is strong and vice versa.
Everyone who is not calm or patient is not kind and vice versa.
Everyone who is both not rich and not funny is not tall.
If john is either not funny or calm then paul is calm or creative and vice versa.
Everyone who is humble or not funny is both not calm and curious.
If alice is not happy then fred is both not generous and not happy.
If susan is not brave then someone is either rich or not strong and vice versa.
If someone is creative then paul is either not quiet or not funny.
Everyone who is not old is strong or not patient and vice versa.
If someone is generous then someone is either calm or rich.
If mary is both humble and funny then someone is both humble and quiet and vice versa.
Everyone who is either wise or not strong is humble or wise and vice versa.
If john is either not strong or creative then someone is both not strong and quiet and vice versa.
Everyone who is kind is not brave and vice versa.
Lucy is either not wise or creative.
Alice is either patient or rich.
Paul is kind or happy.
Alice is either patient or strong.
Alice is either not strong or not funny.
Someone is both not kind and not generous.
Someone is creative or quiet. | Susan is not kind. | contradiction | ((?[X]:(~curious(X)))<=>((~patient(paul)|happy(paul))))&
((?[X]:((~strong(X)<~>~wise(X))))=>((~patient(john)&funny(john))))&
(![X]:((calm(X)&creative(X))<=>strong(X)))&
(![X]:((~calm(X)|patient(X))<=>~kind(X)))&
(![X]:((~rich(X)&~funny(X))=>~tall(X)))&
(((~funny(john)<~>calm(john)))<=>((calm(paul)|creative(paul))))&
(![X]:((humble(X)|~funny(X))=>(~calm(X)&curious(X))))&
((~happy(alice))=>((~generous(fred)&~happy(fred))))&
((~brave(susan))<=>(?[X]:((rich(X)<~>~strong(X)))))&
((?[X]:(creative(X)))=>((~quiet(paul)<~>~funny(paul))))&
(![X]:(~old(X)<=>(strong(X)|~patient(X))))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)<~>rich(X)))))&
(((humble(mary)&funny(mary)))<=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:((wise(X)<~>~strong(X))<=>(humble(X)|wise(X))))&
(((~strong(john)<~>creative(john)))<=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:(kind(X)<=>~brave(X)))&
((~wise(lucy)<~>creative(lucy)))&
((patient(alice)<~>rich(alice)))&
((kind(paul)|happy(paul)))&
((patient(alice)<~>strong(alice)))&
((~strong(alice)<~>~funny(alice)))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((creative(X)|quiet(X)))) | ~kind(susan) | [
"p2",
"p6",
"p8",
"p15",
"p17",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 853953399408676571088418
% SZS output start Proof for 853953399408676571088418
3. ! [X0] : ((creative(X0) & calm(X0)) <=> strong(X0)) [input p2]
7. ! [X0] : ((~funny(X0) | humble(X0)) => (curious(X0) & ~calm(X0))) [input p6]
9. ~brave(susan) <=> ? [X0] : (rich(X0) <~> ~strong(X0)) [input p8]
16. ! [X0] : (kind(X0) <=> ~brave(X0)) [input p15]
18. patient(alice) <~> rich(alice) [input p17]
20. patient(alice) <~> strong(alice) [input p19]
21. ~strong(alice) <~> ~funny(alice) [input p20]
24. ~kind(susan) [input hypothesis]
31. ! [X0] : ((curious(X0) & ~calm(X0)) | (funny(X0) & ~humble(X0))) [ennf transformation 7]
40. ! [X0] : (((creative(X0) & calm(X0)) | ~strong(X0)) & (strong(X0) | (~creative(X0) | ~calm(X0)))) [nnf transformation 3]
41. ! [X0] : (((creative(X0) & calm(X0)) | ~strong(X0)) & (strong(X0) | ~creative(X0) | ~calm(X0))) [flattening 40]
46. (~brave(susan) | ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (? [X0] : ((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | brave(susan)) [nnf transformation 9]
47. (~brave(susan) | ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (? [X1] : ((strong(X1) | ~rich(X1)) & (~strong(X1) | rich(X1))) | brave(susan)) [rectify 46]
48. ? [X1] : ((strong(X1) | ~rich(X1)) & (~strong(X1) | rich(X1))) => ((strong(sK1) | ~rich(sK1)) & (~strong(sK1) | rich(sK1))) [choice axiom]
49. (~brave(susan) | ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(sK1) | ~rich(sK1)) & (~strong(sK1) | rich(sK1))) | brave(susan)) [skolemisation 47,48]
62. ! [X0] : ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0))) [nnf transformation 16]
64. (~rich(alice) | ~patient(alice)) & (rich(alice) | patient(alice)) [nnf transformation 18]
65. (~strong(alice) | ~patient(alice)) & (strong(alice) | patient(alice)) [nnf transformation 20]
66. (funny(alice) | strong(alice)) & (~funny(alice) | ~strong(alice)) [nnf transformation 21]
79. ~strong(X0) | calm(X0) [cnf transformation 41]
91. ~calm(X0) | funny(X0) [cnf transformation 31]
98. ~brave(susan) | rich(X0) | strong(X0) [cnf transformation 49]
118. brave(X0) | kind(X0) [cnf transformation 62]
122. ~rich(alice) | ~patient(alice) [cnf transformation 64]
124. strong(alice) | patient(alice) [cnf transformation 65]
126. ~funny(alice) | ~strong(alice) [cnf transformation 66]
127. funny(alice) | strong(alice) [cnf transformation 66]
130. ~kind(susan) [cnf transformation 24]
197. 14 <=> ! [X0] : (rich(X0) | strong(X0)) [avatar definition]
198. rich(X0) | strong(X0) <- (14) [avatar component clause 197]
200. 15 <=> brave(susan) [avatar definition]
202. ~brave(susan) <- (~15) [avatar component clause 200]
203. 14 | ~15 [avatar split clause 98,200,197]
294. 34 <=> patient(alice) [avatar definition]
298. 35 <=> rich(alice) [avatar definition]
300. ~rich(alice) <- (~35) [avatar component clause 298]
301. ~34 | ~35 [avatar split clause 122,298,294]
309. 37 <=> strong(alice) [avatar definition]
310. strong(alice) <- (37) [avatar component clause 309]
311. ~strong(alice) <- (~37) [avatar component clause 309]
313. 34 | 37 [avatar split clause 124,309,294]
315. 38 <=> funny(alice) [avatar definition]
316. ~funny(alice) <- (~38) [avatar component clause 315]
318. 37 | 38 [avatar split clause 127,315,309]
319. ~37 | ~38 [avatar split clause 126,315,309]
331. calm(alice) <- (37) [resolution 79,310]
338. funny(alice) <- (37) [resolution 91,331]
340. $false <- (37, ~38) [subsumption resolution 338,316]
341. ~37 | 38 [avatar contradiction clause 340]
347. kind(susan) <- (~15) [resolution 118,202]
349. $false <- (~15) [subsumption resolution 347,130]
350. 15 [avatar contradiction clause 349]
353. strong(alice) <- (14, ~35) [resolution 198,300]
356. $false <- (14, ~35, ~37) [subsumption resolution 353,311]
357. ~14 | 35 | 37 [avatar contradiction clause 356]
358. $false [avatar sat refutation 203,301,313,318,319,341,350,357]
% SZS output end Proof for 853953399408676571088418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either quiet or not patient then someone is both rich and not tall and vice versa.
Everyone who is both not patient and kind is both not quiet and curious and vice versa.
If someone is both tall and not rich then someone is both not quiet and generous.
Everyone who is either calm or not creative is not brave or generous.
If someone is both humble and not quiet then lucy is either old or not funny and vice versa.
Everyone who is not calm is not strong.
If someone is not rich or curious then alice is not patient or tall.
Everyone who is not humble is both humble and generous.
Everyone who is not tall is either not old or brave and vice versa.
Everyone who is not wise or not quiet is both not tall and quiet.
If alice is both rich and kind then someone is not rich and vice versa.
If someone is not wise or wise then fred is not generous and vice versa.
If alice is not kind then fred is not rich.
If someone is either wise or old then someone is either rich or not curious.
Everyone who is humble or funny is strong and vice versa.
If fred is wise or tall then someone is both not happy and not wise and vice versa.
Someone is both old and brave.
Someone is either strong or not kind.
Alice is either not generous or not brave.
Mary is quiet or not wise.
Alice is tall.
Susan is quiet.
Alice is both not brave and generous.
Susan is both funny and tall. | Lucy is not calm. | contradiction | (((quiet(fred)<~>~patient(fred)))<=>(?[X]:((rich(X)&~tall(X)))))&
(![X]:((~patient(X)&kind(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((tall(X)&~rich(X))))=>(?[X]:((~quiet(X)&generous(X)))))&
(![X]:((calm(X)<~>~creative(X))=>(~brave(X)|generous(X))))&
((?[X]:((humble(X)&~quiet(X))))<=>((old(lucy)<~>~funny(lucy))))&
(![X]:(~calm(X)=>~strong(X)))&
((?[X]:((~rich(X)|curious(X))))=>((~patient(alice)|tall(alice))))&
(![X]:(~humble(X)=>(humble(X)&generous(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>brave(X))))&
(![X]:((~wise(X)|~quiet(X))=>(~tall(X)&quiet(X))))&
(((rich(alice)&kind(alice)))<=>(?[X]:(~rich(X))))&
((?[X]:((~wise(X)|wise(X))))<=>(~generous(fred)))&
((~kind(alice))=>(~rich(fred)))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:((humble(X)|funny(X))<=>strong(X)))&
(((wise(fred)|tall(fred)))<=>(?[X]:((~happy(X)&~wise(X)))))&
(?[X]:((old(X)&brave(X))))&
(?[X]:((strong(X)<~>~kind(X))))&
((~generous(alice)<~>~brave(alice)))&
((quiet(mary)|~wise(mary)))&
(tall(alice))&
(quiet(susan))&
((~brave(alice)&generous(alice)))&
((funny(susan)&tall(susan))) | ~calm(lucy) | [
"p5",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3197137651534599741816785
% SZS output start Proof for 3197137651534599741816785
6. ! [X0] : (~calm(X0) => ~strong(X0)) [input p5]
8. ! [X0] : (~humble(X0) => (generous(X0) & humble(X0))) [input p7]
15. ! [X0] : ((funny(X0) | humble(X0)) <=> strong(X0)) [input p14]
25. ~calm(lucy) [input hypothesis]
31. ! [X0] : (~strong(X0) | calm(X0)) [ennf transformation 6]
34. ! [X0] : ((generous(X0) & humble(X0)) | humble(X0)) [ennf transformation 8]
66. ! [X0] : (((funny(X0) | humble(X0)) | ~strong(X0)) & (strong(X0) | (~funny(X0) & ~humble(X0)))) [nnf transformation 15]
67. ! [X0] : ((funny(X0) | humble(X0) | ~strong(X0)) & (strong(X0) | (~funny(X0) & ~humble(X0)))) [flattening 66]
99. ~strong(X0) | calm(X0) [cnf transformation 31]
102. humble(X0) | humble(X0) [cnf transformation 34]
123. strong(X0) | ~humble(X0) [cnf transformation 67]
144. ~calm(lucy) [cnf transformation 25]
146. humble(X0) [duplicate literal removal 102]
276. strong(X0) [subsumption resolution 123,146]
320. calm(X0) [resolution 99,276]
321. $false [resolution 320,144]
% SZS output end Proof for 3197137651534599741816785
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 strong and tall is strong and vice versa.
Everyone who is both tall and not strong is not calm and vice versa.
Everyone who is curious is either not humble or not tall.
Everyone who is not tall is either not kind or not curious.
Everyone who is either not wise or funny is both strong and curious and vice versa.
Everyone who is either humble or not happy is funny.
If someone is wise or not humble then john is both old and strong.
Everyone who is both creative and rich is not funny or kind.
If someone is not funny or kind then someone is brave or kind.
Everyone who is tall or not kind is either old or strong.
Everyone who is both not humble and curious is both quiet and not happy and vice versa.
If alice is both creative and not creative then alice is both not brave and brave.
Everyone who is not quiet or not happy is patient and vice versa.
If someone is strong or not generous then someone is either not patient or humble and vice versa.
If john is both funny and not brave then paul is rich and vice versa.
Everyone who is either happy or not happy is both old and not calm.
Fred is either not old or quiet.
Someone is quiet.
Someone is kind.
Alice is patient.
Someone is not generous.
Someone is either not curious or not tall.
Susan is quiet. | Alice is tall. | entailment | (![X]:((strong(X)&tall(X))<=>strong(X)))&
(![X]:((tall(X)&~strong(X))<=>~calm(X)))&
(![X]:(curious(X)=>(~humble(X)<~>~tall(X))))&
(![X]:(~tall(X)=>(~kind(X)<~>~curious(X))))&
(![X]:((~wise(X)<~>funny(X))<=>(strong(X)&curious(X))))&
(![X]:((humble(X)<~>~happy(X))=>funny(X)))&
((?[X]:((wise(X)|~humble(X))))=>((old(john)&strong(john))))&
(![X]:((creative(X)&rich(X))=>(~funny(X)|kind(X))))&
((?[X]:((~funny(X)|kind(X))))=>(?[X]:((brave(X)|kind(X)))))&
(![X]:((tall(X)|~kind(X))=>(old(X)<~>strong(X))))&
(![X]:((~humble(X)&curious(X))<=>(quiet(X)&~happy(X))))&
(((creative(alice)&~creative(alice)))=>((~brave(alice)&brave(alice))))&
(![X]:((~quiet(X)|~happy(X))<=>patient(X)))&
((?[X]:((strong(X)|~generous(X))))<=>(?[X]:((~patient(X)<~>humble(X)))))&
(((funny(john)&~brave(john)))<=>(rich(paul)))&
(![X]:((happy(X)<~>~happy(X))=>(old(X)&~calm(X))))&
((~old(fred)<~>quiet(fred)))&
(?[X]:(quiet(X)))&
(?[X]:(kind(X)))&
(patient(alice))&
(?[X]:(~generous(X)))&
(?[X]:((~curious(X)<~>~tall(X))))&
(quiet(susan)) | tall(alice) | [
"p1",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2184135723589055821893729
% SZS output start Proof for 2184135723589055821893729
2. ! [X0] : ((~strong(X0) & tall(X0)) <=> ~calm(X0)) [input p1]
16. ! [X0] : ((happy(X0) <~> ~happy(X0)) => (~calm(X0) & old(X0))) [input p15]
24. ~tall(alice) [input hypothesis]
27. ! [X0] : (~calm(X0) => (~strong(X0) & tall(X0))) [unused predicate definition removal 2]
28. ! [X0] : ((~strong(X0) & tall(X0)) | calm(X0)) [ennf transformation 27]
39. ! [X0] : ((~calm(X0) & old(X0)) | (happy(X0) <=> ~happy(X0))) [ennf transformation 16]
62. ! [X0] : ((~calm(X0) & old(X0)) | ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) [nnf transformation 39]
76. calm(X0) | tall(X0) [cnf transformation 28]
121. ~calm(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 62]
122. ~calm(X0) | happy(X0) | happy(X0) [cnf transformation 62]
132. ~tall(alice) [cnf transformation 24]
135. ~calm(X0) | ~happy(X0) [duplicate literal removal 121]
136. ~calm(X0) | happy(X0) [duplicate literal removal 122]
221. ~calm(X0) [subsumption resolution 135,136]
235. tall(X0) [resolution 76,221]
241. $false [resolution 235,132]
% SZS output end Proof for 2184135723589055821893729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 brave or not happy is not curious or not happy.
If paul is both not strong and not old then someone is both not creative and kind and vice versa.
Everyone who is happy or wise is not happy or rich and vice versa.
Everyone who is old or tall is not happy.
If someone is both not tall and not rich then someone is either patient or not quiet.
If someone is wise then susan is either not kind or old and vice versa.
Everyone who is either not calm or not rich is strong.
Everyone who is not humble or happy is either not curious or generous and vice versa.
If fred is either not strong or not generous then someone is not creative and vice versa.
Everyone who is either not generous or quiet is both not curious and strong.
If mary is wise or not happy then susan is not strong and vice versa.
If lucy is either not humble or not creative then someone is not wise or happy.
If someone is not happy or generous then john is either not funny or brave and vice versa.
If fred is not calm then someone is funny and vice versa.
Everyone who is not quiet is patient.
Everyone who is humble or not kind is not happy.
Mary is funny.
Fred is both not tall and not brave.
Mary is both kind and rich.
Someone is not rich or rich.
Someone is wise or not quiet.
Someone is either humble or not kind.
Lucy is not old or not tall. | Susan is happy. | contradiction | (![X]:((~brave(X)|~happy(X))=>(~curious(X)|~happy(X))))&
(((~strong(paul)&~old(paul)))<=>(?[X]:((~creative(X)&kind(X)))))&
(![X]:((happy(X)|wise(X))<=>(~happy(X)|rich(X))))&
(![X]:((old(X)|tall(X))=>~happy(X)))&
((?[X]:((~tall(X)&~rich(X))))=>(?[X]:((patient(X)<~>~quiet(X)))))&
((?[X]:(wise(X)))<=>((~kind(susan)<~>old(susan))))&
(![X]:((~calm(X)<~>~rich(X))=>strong(X)))&
(![X]:((~humble(X)|happy(X))<=>(~curious(X)<~>generous(X))))&
(((~strong(fred)<~>~generous(fred)))<=>(?[X]:(~creative(X))))&
(![X]:((~generous(X)<~>quiet(X))=>(~curious(X)&strong(X))))&
(((wise(mary)|~happy(mary)))<=>(~strong(susan)))&
(((~humble(lucy)<~>~creative(lucy)))=>(?[X]:((~wise(X)|happy(X)))))&
((?[X]:((~happy(X)|generous(X))))<=>((~funny(john)<~>brave(john))))&
((~calm(fred))<=>(?[X]:(funny(X))))&
(![X]:(~quiet(X)=>patient(X)))&
(![X]:((humble(X)|~kind(X))=>~happy(X)))&
(funny(mary))&
((~tall(fred)&~brave(fred)))&
((kind(mary)&rich(mary)))&
(?[X]:((~rich(X)|rich(X))))&
(?[X]:((wise(X)|~quiet(X))))&
(?[X]:((humble(X)<~>~kind(X))))&
((~old(lucy)|~tall(lucy))) | happy(susan) | [
"p2",
"p3",
"p5",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8668751919161902083750020
% SZS output start Proof for 8668751919161902083750020
3. ! [X0] : ((wise(X0) | happy(X0)) <=> (rich(X0) | ~happy(X0))) [input p2]
4. ! [X0] : ((tall(X0) | old(X0)) => ~happy(X0)) [input p3]
6. ? [X0] : wise(X0) <=> (~kind(susan) <~> old(susan)) [input p5]
16. ! [X0] : ((~kind(X0) | humble(X0)) => ~happy(X0)) [input p15]
22. ? [X0] : (humble(X0) <~> ~kind(X0)) [input p21]
24. happy(susan) [input hypothesis]
28. ! [X0] : (~happy(X0) | (~tall(X0) & ~old(X0))) [ennf transformation 4]
34. ! [X0] : (~happy(X0) | (kind(X0) & ~humble(X0))) [ennf transformation 16]
40. ! [X0] : (((wise(X0) | happy(X0)) | (~rich(X0) & happy(X0))) & ((rich(X0) | ~happy(X0)) | (~wise(X0) & ~happy(X0)))) [nnf transformation 3]
41. ! [X0] : ((wise(X0) | happy(X0) | (~rich(X0) & happy(X0))) & (rich(X0) | ~happy(X0) | (~wise(X0) & ~happy(X0)))) [flattening 40]
46. (? [X0] : wise(X0) | ((~kind(susan) | ~old(susan)) & (old(susan) | kind(susan)))) & (((~old(susan) | kind(susan)) & (old(susan) | ~kind(susan))) | ! [X0] : ~wise(X0)) [nnf transformation 6]
47. (? [X0] : wise(X0) | ((~kind(susan) | ~old(susan)) & (old(susan) | kind(susan)))) & (((~old(susan) | kind(susan)) & (old(susan) | ~kind(susan))) | ! [X1] : ~wise(X1)) [rectify 46]
48. ? [X0] : wise(X0) => wise(sK2) [choice axiom]
49. (wise(sK2) | ((~kind(susan) | ~old(susan)) & (old(susan) | kind(susan)))) & (((~old(susan) | kind(susan)) & (old(susan) | ~kind(susan))) | ! [X1] : ~wise(X1)) [skolemisation 47,48]
75. ? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) [nnf transformation 22]
76. ? [X0] : ((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) => ((kind(sK9) | ~humble(sK9)) & (~kind(sK9) | humble(sK9))) [choice axiom]
77. (kind(sK9) | ~humble(sK9)) & (~kind(sK9) | humble(sK9)) [skolemisation 75,76]
86. wise(X0) | happy(X0) | happy(X0) [cnf transformation 41]
88. ~old(X0) | ~happy(X0) [cnf transformation 28]
92. old(susan) | ~kind(susan) | ~wise(X1) [cnf transformation 49]
126. ~humble(X0) | ~happy(X0) [cnf transformation 34]
127. ~happy(X0) | kind(X0) [cnf transformation 34]
135. ~kind(sK9) | humble(sK9) [cnf transformation 77]
138. happy(susan) [cnf transformation 24]
140. wise(X0) | happy(X0) [duplicate literal removal 86]
178. 9 <=> old(susan) [avatar definition]
179. old(susan) <- (9) [avatar component clause 178]
182. 10 <=> kind(susan) [avatar definition]
192. 12 <=> ! [X1] : ~wise(X1) [avatar definition]
193. ~wise(X1) <- (12) [avatar component clause 192]
195. 12 | ~10 | 9 [avatar split clause 92,178,182,192]
270. 28 <=> ! [X1] : happy(X1) [avatar definition]
271. happy(X1) <- (28) [avatar component clause 270]
298. 34 <=> humble(sK9) [avatar definition]
299. humble(sK9) <- (34) [avatar component clause 298]
302. 35 <=> kind(sK9) [avatar definition]
303. ~kind(sK9) <- (~35) [avatar component clause 302]
306. 34 | ~35 [avatar split clause 135,302,298]
324. kind(susan) [resolution 127,138]
327. 10 [avatar split clause 324,182]
328. ~happy(susan) <- (9) [resolution 179,88]
329. $false <- (9) [subsumption resolution 328,138]
330. ~9 [avatar contradiction clause 329]
338. happy(X0) <- (12) [resolution 140,193]
339. 28 | ~12 [avatar split clause 338,192,270]
342. kind(X1) <- (28) [resolution 271,127]
345. $false <- (28, ~35) [resolution 342,303]
346. ~28 | 35 [avatar contradiction clause 345]
347. ~happy(sK9) <- (34) [resolution 299,126]
348. $false <- (28, 34) [subsumption resolution 347,271]
349. ~28 | ~34 [avatar contradiction clause 348]
350. $false [avatar sat refutation 195,306,327,330,339,346,349]
% SZS output end Proof for 8668751919161902083750020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is both quiet and not generous.
If fred is not humble or old then someone is happy.
Everyone who is calm is calm or not wise.
Everyone who is not creative or not calm is either happy or not patient.
If alice is both not wise and strong then someone is both not rich and not patient.
If mary is not happy then susan is not curious.
Everyone who is either brave or not brave is not funny.
Everyone who is not calm is both not generous and not wise and vice versa.
If someone is not brave then someone is either curious or strong and vice versa.
If someone is patient then alice is either not rich or humble.
If someone is either happy or not generous then someone is both not kind and generous and vice versa.
If someone is not humble or not kind then john is either not calm or kind.
Everyone who is not patient is either not curious or not wise and vice versa.
Everyone who is either tall or not brave is either old or strong and vice versa.
Everyone who is both not tall and not creative is quiet or wise and vice versa.
If someone is funny then paul is humble.
Someone is strong or humble.
Lucy is either not curious or calm.
Someone is not quiet.
Someone is tall or patient.
Someone is not patient or not kind.
Someone is not brave or old.
Susan is not calm. | John is patient. | entailment | (![X]:(calm(X)=>(quiet(X)&~generous(X))))&
(((~humble(fred)|old(fred)))=>(?[X]:(happy(X))))&
(![X]:(calm(X)=>(calm(X)|~wise(X))))&
(![X]:((~creative(X)|~calm(X))=>(happy(X)<~>~patient(X))))&
(((~wise(alice)&strong(alice)))=>(?[X]:((~rich(X)&~patient(X)))))&
((~happy(mary))=>(~curious(susan)))&
(![X]:((brave(X)<~>~brave(X))=>~funny(X)))&
(![X]:(~calm(X)<=>(~generous(X)&~wise(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((curious(X)<~>strong(X)))))&
((?[X]:(patient(X)))=>((~rich(alice)<~>humble(alice))))&
((?[X]:((happy(X)<~>~generous(X))))<=>(?[X]:((~kind(X)&generous(X)))))&
((?[X]:((~humble(X)|~kind(X))))=>((~calm(john)<~>kind(john))))&
(![X]:(~patient(X)<=>(~curious(X)<~>~wise(X))))&
(![X]:((tall(X)<~>~brave(X))<=>(old(X)<~>strong(X))))&
(![X]:((~tall(X)&~creative(X))<=>(quiet(X)|wise(X))))&
((?[X]:(funny(X)))=>(humble(paul)))&
(?[X]:((strong(X)|humble(X))))&
((~curious(lucy)<~>calm(lucy)))&
(?[X]:(~quiet(X)))&
(?[X]:((tall(X)|patient(X))))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((~brave(X)|old(X))))&
(~calm(susan)) | patient(john) | [
"p0",
"p3",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1239802486015567622725998
% SZS output start Proof for 1239802486015567622725998
1. ! [X0] : (calm(X0) => (~generous(X0) & quiet(X0))) [input p0]
4. ! [X0] : ((~calm(X0) | ~creative(X0)) => (happy(X0) <~> ~patient(X0))) [input p3]
8. ! [X0] : (~calm(X0) <=> (~wise(X0) & ~generous(X0))) [input p7]
11. ? [X0] : (happy(X0) <~> ~generous(X0)) <=> ? [X0] : (generous(X0) & ~kind(X0)) [input p10]
15. ! [X0] : ((~creative(X0) & ~tall(X0)) <=> (wise(X0) | quiet(X0))) [input p14]
24. ~patient(john) [input hypothesis]
26. ? [X0] : (happy(X0) <~> ~generous(X0)) <=> ? [X1] : (generous(X1) & ~kind(X1)) [rectify 11]
29. ! [X0] : ((~generous(X0) & quiet(X0)) | ~calm(X0)) [ennf transformation 1]
33. ! [X0] : ((happy(X0) <~> ~patient(X0)) | (calm(X0) & creative(X0))) [ennf transformation 4]
41. ! [X0] : (((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (calm(X0) & creative(X0))) [nnf transformation 33]
44. ! [X0] : ((~calm(X0) | (wise(X0) | generous(X0))) & ((~wise(X0) & ~generous(X0)) | calm(X0))) [nnf transformation 8]
45. ! [X0] : ((~calm(X0) | wise(X0) | generous(X0)) & ((~wise(X0) & ~generous(X0)) | calm(X0))) [flattening 44]
52. (? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ! [X1] : (~generous(X1) | kind(X1))) & (? [X1] : (generous(X1) & ~kind(X1)) | ! [X0] : ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) [nnf transformation 26]
53. (? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ! [X1] : (~generous(X1) | kind(X1))) & (? [X2] : (generous(X2) & ~kind(X2)) | ! [X3] : ((happy(X3) | generous(X3)) & (~generous(X3) | ~happy(X3)))) [rectify 52]
54. ? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) => ((generous(sK4) | ~happy(sK4)) & (~generous(sK4) | happy(sK4))) [choice axiom]
55. ? [X2] : (generous(X2) & ~kind(X2)) => (generous(sK5) & ~kind(sK5)) [choice axiom]
56. (((generous(sK4) | ~happy(sK4)) & (~generous(sK4) | happy(sK4))) | ! [X1] : (~generous(X1) | kind(X1))) & ((generous(sK5) & ~kind(sK5)) | ! [X3] : ((happy(X3) | generous(X3)) & (~generous(X3) | ~happy(X3)))) [skolemisation 53,55,54]
60. ! [X0] : (((~creative(X0) & ~tall(X0)) | (~wise(X0) & ~quiet(X0))) & ((wise(X0) | quiet(X0)) | (creative(X0) | tall(X0)))) [nnf transformation 15]
61. ! [X0] : (((~creative(X0) & ~tall(X0)) | (~wise(X0) & ~quiet(X0))) & (wise(X0) | quiet(X0) | creative(X0) | tall(X0))) [flattening 60]
73. ~calm(X0) | quiet(X0) [cnf transformation 29]
74. ~generous(X0) | ~calm(X0) [cnf transformation 29]
80. ~happy(X0) | patient(X0) | creative(X0) [cnf transformation 41]
81. ~happy(X0) | patient(X0) | calm(X0) [cnf transformation 41]
85. ~generous(X0) | calm(X0) [cnf transformation 45]
97. generous(sK5) | happy(X3) | generous(X3) [cnf transformation 56]
119. ~creative(X0) | ~quiet(X0) [cnf transformation 61]
129. ~patient(john) [cnf transformation 24]
172. ~generous(X0) [subsumption resolution 85,74]
211. happy(X3) | generous(X3) [subsumption resolution 97,172]
212. happy(X3) [subsumption resolution 211,172]
217. 20 <=> calm(john) [avatar definition]
219. calm(john) <- (20) [avatar component clause 217]
288. patient(X0) | creative(X0) [resolution 80,212]
289. creative(john) [resolution 288,129]
293. patient(X0) | calm(X0) [resolution 81,212]
295. ~quiet(john) [resolution 289,119]
421. calm(john) [resolution 293,129]
429. 20 [avatar split clause 421,217]
432. quiet(john) <- (20) [resolution 219,73]
435. $false <- (20) [subsumption resolution 432,295]
436. ~20 [avatar contradiction clause 435]
437. $false [avatar sat refutation 429,436]
% SZS output end Proof for 1239802486015567622725998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either creative or kind then someone is not patient or generous.
If susan is both curious and funny then someone is either quiet or calm.
Everyone who is rich is either not rich or not kind.
Everyone who is kind is either not calm or quiet.
If someone is both old and rich then lucy is both not wise and calm and vice versa.
Everyone who is both not generous and rich is either not brave or funny.
Everyone who is not funny is not calm or patient and vice versa.
If someone is not old or not happy then someone is wise.
Everyone who is old or strong is happy or brave and vice versa.
Everyone who is kind is old or patient.
Everyone who is not old or strong is not tall or wise.
If mary is either curious or rich then john is both strong and tall.
Everyone who is wise is not quiet or not curious and vice versa.
Everyone who is either not generous or strong is either not patient or not calm and vice versa.
If lucy is brave or not brave then someone is either not quiet or generous and vice versa.
Everyone who is strong or not creative is either not quiet or funny and vice versa.
Someone is both not rich and not brave.
Someone is either humble or quiet.
Someone is happy.
Alice is either tall or funny.
Fred is either not humble or old.
Susan is either happy or rich.
Lucy is patient. | Fred is not wise. | neutral | ((?[X]:((creative(X)<~>kind(X))))=>(?[X]:((~patient(X)|generous(X)))))&
(((curious(susan)&funny(susan)))=>(?[X]:((quiet(X)<~>calm(X)))))&
(![X]:(rich(X)=>(~rich(X)<~>~kind(X))))&
(![X]:(kind(X)=>(~calm(X)<~>quiet(X))))&
((?[X]:((old(X)&rich(X))))<=>((~wise(lucy)&calm(lucy))))&
(![X]:((~generous(X)&rich(X))=>(~brave(X)<~>funny(X))))&
(![X]:(~funny(X)<=>(~calm(X)|patient(X))))&
((?[X]:((~old(X)|~happy(X))))=>(?[X]:(wise(X))))&
(![X]:((old(X)|strong(X))<=>(happy(X)|brave(X))))&
(![X]:(kind(X)=>(old(X)|patient(X))))&
(![X]:((~old(X)|strong(X))=>(~tall(X)|wise(X))))&
(((curious(mary)<~>rich(mary)))=>((strong(john)&tall(john))))&
(![X]:(wise(X)<=>(~quiet(X)|~curious(X))))&
(![X]:((~generous(X)<~>strong(X))<=>(~patient(X)<~>~calm(X))))&
(((brave(lucy)|~brave(lucy)))<=>(?[X]:((~quiet(X)<~>generous(X)))))&
(![X]:((strong(X)|~creative(X))<=>(~quiet(X)<~>funny(X))))&
(?[X]:((~rich(X)&~brave(X))))&
(?[X]:((humble(X)<~>quiet(X))))&
(?[X]:(happy(X)))&
((tall(alice)<~>funny(alice)))&
((~humble(fred)<~>old(fred)))&
((happy(susan)<~>rich(susan)))&
(patient(lucy)) | ~wise(fred) | [] | null | 0 |
Everyone who is brave is both not rich and not generous.
Everyone who is both tall and not tall is humble or quiet and vice versa.
Everyone who is strong is not generous or humble and vice versa.
Everyone who is happy is both not tall and patient.
If someone is not rich then mary is not tall or not brave.
Everyone who is not curious is tall or not calm and vice versa.
If someone is curious or kind then someone is both brave and not tall and vice versa.
Everyone who is not calm or not kind is quiet or generous and vice versa.
If susan is not old then someone is either strong or not brave.
Everyone who is either curious or not tall is quiet and vice versa.
If mary is either old or not brave then fred is either not happy or calm and vice versa.
Everyone who is either not calm or patient is humble and vice versa.
Everyone who is generous is not rich and vice versa.
If someone is both not creative and curious then mary is not rich.
If someone is either not wise or funny then john is not old and vice versa.
Everyone who is both not strong and not wise is both generous and not brave and vice versa.
Someone is generous.
Someone is not strong.
Lucy is not patient. | Susan is not generous. | contradiction | (![X]:(brave(X)=>(~rich(X)&~generous(X))))&
(![X]:((tall(X)&~tall(X))<=>(humble(X)|quiet(X))))&
(![X]:(strong(X)<=>(~generous(X)|humble(X))))&
(![X]:(happy(X)=>(~tall(X)&patient(X))))&
((?[X]:(~rich(X)))=>((~tall(mary)|~brave(mary))))&
(![X]:(~curious(X)<=>(tall(X)|~calm(X))))&
((?[X]:((curious(X)|kind(X))))<=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((~calm(X)|~kind(X))<=>(quiet(X)|generous(X))))&
((~old(susan))=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((curious(X)<~>~tall(X))<=>quiet(X)))&
(((old(mary)<~>~brave(mary)))<=>((~happy(fred)<~>calm(fred))))&
(![X]:((~calm(X)<~>patient(X))<=>humble(X)))&
(![X]:(generous(X)<=>~rich(X)))&
((?[X]:((~creative(X)&curious(X))))=>(~rich(mary)))&
((?[X]:((~wise(X)<~>funny(X))))<=>(~old(john)))&
(![X]:((~strong(X)&~wise(X))<=>(generous(X)&~brave(X))))&
(?[X]:(generous(X)))&
(?[X]:(~strong(X)))&
(~patient(lucy)) | ~generous(susan) | [
"p0",
"p1",
"p6",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4308939220001191546439689
% SZS output start Proof for 4308939220001191546439689
1. ! [X0] : (brave(X0) => (~generous(X0) & ~rich(X0))) [input p0]
2. ! [X0] : ((~tall(X0) & tall(X0)) <=> (quiet(X0) | humble(X0))) [input p1]
7. ? [X0] : (kind(X0) | curious(X0)) <=> ? [X0] : (~tall(X0) & brave(X0)) [input p6]
8. ! [X0] : ((~kind(X0) | ~calm(X0)) <=> (generous(X0) | quiet(X0))) [input p7]
13. ! [X0] : (generous(X0) <=> ~rich(X0)) [input p12]
20. ~generous(susan) [input hypothesis]
21. ? [X0] : (kind(X0) | curious(X0)) <=> ? [X1] : (~tall(X1) & brave(X1)) [rectify 7]
23. ! [X0] : ((~generous(X0) & ~rich(X0)) | ~brave(X0)) [ennf transformation 1]
28. ! [X0] : (((~tall(X0) & tall(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (tall(X0) | ~tall(X0)))) [nnf transformation 2]
29. ! [X0] : (((~tall(X0) & tall(X0)) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | tall(X0) | ~tall(X0))) [flattening 28]
34. (? [X0] : (kind(X0) | curious(X0)) | ! [X1] : (tall(X1) | ~brave(X1))) & (? [X1] : (~tall(X1) & brave(X1)) | ! [X0] : (~kind(X0) & ~curious(X0))) [nnf transformation 21]
35. (? [X0] : (kind(X0) | curious(X0)) | ! [X1] : (tall(X1) | ~brave(X1))) & (? [X2] : (~tall(X2) & brave(X2)) | ! [X3] : (~kind(X3) & ~curious(X3))) [rectify 34]
36. ? [X0] : (kind(X0) | curious(X0)) => (kind(sK0) | curious(sK0)) [choice axiom]
37. ? [X2] : (~tall(X2) & brave(X2)) => (~tall(sK1) & brave(sK1)) [choice axiom]
38. ((kind(sK0) | curious(sK0)) | ! [X1] : (tall(X1) | ~brave(X1))) & ((~tall(sK1) & brave(sK1)) | ! [X3] : (~kind(X3) & ~curious(X3))) [skolemisation 35,37,36]
39. ! [X0] : (((~kind(X0) | ~calm(X0)) | (~generous(X0) & ~quiet(X0))) & ((generous(X0) | quiet(X0)) | (kind(X0) & calm(X0)))) [nnf transformation 8]
40. ! [X0] : ((~kind(X0) | ~calm(X0) | (~generous(X0) & ~quiet(X0))) & (generous(X0) | quiet(X0) | (kind(X0) & calm(X0)))) [flattening 39]
47. ! [X0] : ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))) [nnf transformation 13]
58. ~rich(X0) | ~brave(X0) [cnf transformation 23]
59. ~generous(X0) | ~brave(X0) [cnf transformation 23]
62. tall(X0) | ~quiet(X0) [cnf transformation 29]
64. ~quiet(X0) | ~tall(X0) [cnf transformation 29]
75. brave(sK1) | ~kind(X3) [cnf transformation 38]
80. generous(X0) | quiet(X0) | kind(X0) [cnf transformation 40]
102. generous(X0) | rich(X0) [cnf transformation 47]
114. ~generous(susan) [cnf transformation 20]
115. ~quiet(X0) [subsumption resolution 62,64]
143. 7 <=> ! [X3] : ~kind(X3) [avatar definition]
144. ~kind(X3) <- (7) [avatar component clause 143]
155. 10 <=> brave(sK1) [avatar definition]
157. brave(sK1) <- (10) [avatar component clause 155]
158. 7 | 10 [avatar split clause 75,155,143]
160. kind(X0) | generous(X0) [subsumption resolution 80,115]
232. rich(X1) | ~brave(X1) [resolution 102,59]
233. ~brave(X1) [subsumption resolution 232,58]
236. generous(X0) <- (7) [resolution 160,144]
237. $false <- (7) [resolution 236,114]
240. ~7 [avatar contradiction clause 237]
241. $false <- (10) [subsumption resolution 157,233]
242. ~10 [avatar contradiction clause 241]
243. $false [avatar sat refutation 158,240,242]
% SZS output end Proof for 4308939220001191546439689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or not old then someone is brave.
Everyone who is not funny is not creative and vice versa.
Everyone who is either rich or not tall is either not strong or quiet.
Everyone who is both creative and calm is either old or creative.
Everyone who is both rich and not funny is rich or not strong.
Everyone who is both brave and not brave is not tall.
Everyone who is rich is not rich or not generous and vice versa.
If lucy is both tall and not kind then lucy is not funny and vice versa.
Everyone who is not happy is either not quiet or not rich.
If mary is either old or not rich then someone is both not quiet and not patient.
If someone is not brave or strong then susan is either wise or not rich.
If someone is either old or rich then lucy is either not happy or curious and vice versa.
If someone is both not rich and not old then someone is either calm or tall and vice versa.
Everyone who is not rich or patient is both generous and patient and vice versa.
Everyone who is both not rich and funny is patient.
Everyone who is rich is patient or not wise and vice versa.
Susan is brave or creative.
Someone is strong or not creative.
John is not humble.
John is both rich and not kind.
Susan is both funny and calm.
Mary is not generous or wise.
Lucy is either not happy or not humble. | John is not strong. | entailment | ((?[X]:((~generous(X)<~>~old(X))))=>(?[X]:(brave(X))))&
(![X]:(~funny(X)<=>~creative(X)))&
(![X]:((rich(X)<~>~tall(X))=>(~strong(X)<~>quiet(X))))&
(![X]:((creative(X)&calm(X))=>(old(X)<~>creative(X))))&
(![X]:((rich(X)&~funny(X))=>(rich(X)|~strong(X))))&
(![X]:((brave(X)&~brave(X))=>~tall(X)))&
(![X]:(rich(X)<=>(~rich(X)|~generous(X))))&
(((tall(lucy)&~kind(lucy)))<=>(~funny(lucy)))&
(![X]:(~happy(X)=>(~quiet(X)<~>~rich(X))))&
(((old(mary)<~>~rich(mary)))=>(?[X]:((~quiet(X)&~patient(X)))))&
((?[X]:((~brave(X)|strong(X))))=>((wise(susan)<~>~rich(susan))))&
((?[X]:((old(X)<~>rich(X))))<=>((~happy(lucy)<~>curious(lucy))))&
((?[X]:((~rich(X)&~old(X))))<=>(?[X]:((calm(X)<~>tall(X)))))&
(![X]:((~rich(X)|patient(X))<=>(generous(X)&patient(X))))&
(![X]:((~rich(X)&funny(X))=>patient(X)))&
(![X]:(rich(X)<=>(patient(X)|~wise(X))))&
((brave(susan)|creative(susan)))&
(?[X]:((strong(X)|~creative(X))))&
(~humble(john))&
((rich(john)&~kind(john)))&
((funny(susan)&calm(susan)))&
((~generous(mary)|wise(mary)))&
((~happy(lucy)<~>~humble(lucy))) | ~strong(john) | [
"p6",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8662276010940405230901318
% SZS output start Proof for 8662276010940405230901318
7. ! [X0] : (rich(X0) <=> (~generous(X0) | ~rich(X0))) [input p6]
11. ? [X0] : (strong(X0) | ~brave(X0)) => (wise(susan) <~> ~rich(susan)) [input p10]
14. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (patient(X0) & generous(X0))) [input p13]
16. ! [X0] : (rich(X0) <=> (~wise(X0) | patient(X0))) [input p15]
24. strong(john) [input hypothesis]
37. (wise(susan) <~> ~rich(susan)) | ! [X0] : (~strong(X0) & brave(X0)) [ennf transformation 11]
47. ! [X0] : ((rich(X0) | (generous(X0) & rich(X0))) & ((~generous(X0) | ~rich(X0)) | ~rich(X0))) [nnf transformation 7]
48. ! [X0] : ((rich(X0) | (generous(X0) & rich(X0))) & (~generous(X0) | ~rich(X0) | ~rich(X0))) [flattening 47]
55. ((rich(susan) | ~wise(susan)) & (~rich(susan) | wise(susan))) | ! [X0] : (~strong(X0) & brave(X0)) [nnf transformation 37]
65. ! [X0] : (((patient(X0) | ~rich(X0)) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 14]
66. ! [X0] : ((patient(X0) | ~rich(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | (~patient(X0) & rich(X0)))) [flattening 65]
67. ! [X0] : ((rich(X0) | (wise(X0) & ~patient(X0))) & ((~wise(X0) | patient(X0)) | ~rich(X0))) [nnf transformation 16]
68. ! [X0] : ((rich(X0) | (wise(X0) & ~patient(X0))) & (~wise(X0) | patient(X0) | ~rich(X0))) [flattening 67]
84. ~generous(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 48]
85. rich(X0) | rich(X0) [cnf transformation 48]
97. ~rich(susan) | wise(susan) | ~strong(X0) [cnf transformation 55]
115. generous(X0) | ~patient(X0) [cnf transformation 66]
120. ~wise(X0) | patient(X0) | ~rich(X0) [cnf transformation 68]
133. strong(john) [cnf transformation 24]
134. ~generous(X0) | ~rich(X0) [duplicate literal removal 84]
135. rich(X0) [duplicate literal removal 85]
149. ~generous(X0) [subsumption resolution 134,135]
182. wise(susan) | ~strong(X0) [subsumption resolution 97,135]
184. 10 <=> ! [X0] : ~strong(X0) [avatar definition]
185. ~strong(X0) <- (10) [avatar component clause 184]
187. 11 <=> wise(susan) [avatar definition]
189. wise(susan) <- (11) [avatar component clause 187]
190. 10 | 11 [avatar split clause 182,187,184]
235. ~patient(X0) [subsumption resolution 115,149]
236. ~wise(X0) | ~rich(X0) [subsumption resolution 120,235]
237. ~wise(X0) [subsumption resolution 236,135]
262. $false <- (11) [subsumption resolution 189,237]
263. ~11 [avatar contradiction clause 262]
264. $false <- (10) [resolution 185,133]
265. ~10 [avatar contradiction clause 264]
266. $false [avatar sat refutation 190,263,265]
% SZS output end Proof for 8662276010940405230901318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either generous or patient then john is wise or not quiet and vice versa.
Everyone who is both funny and strong is generous.
If someone is both wise and not creative then someone is either funny or not patient and vice versa.
Everyone who is not creative or funny is creative or tall and vice versa.
Everyone who is either old or calm is both not wise and not calm.
Everyone who is either curious or patient is not strong or quiet and vice versa.
Everyone who is funny or not wise is not creative.
Everyone who is both not calm and tall is either brave or not wise.
Everyone who is not creative is either funny or not creative and vice versa.
Everyone who is both strong and not strong is generous or not curious and vice versa.
Everyone who is both calm and not generous is not funny or creative.
Everyone who is creative or wise is humble or tall and vice versa.
If susan is either rich or patient then someone is funny or not tall and vice versa.
Someone is either calm or not calm.
Fred is both humble and rich.
Someone is either old or not humble.
Lucy is not brave or funny.
Someone is both not calm and not happy. | Susan is wise. | entailment | ((?[X]:((generous(X)<~>patient(X))))<=>((wise(john)|~quiet(john))))&
(![X]:((funny(X)&strong(X))=>generous(X)))&
((?[X]:((wise(X)&~creative(X))))<=>(?[X]:((funny(X)<~>~patient(X)))))&
(![X]:((~creative(X)|funny(X))<=>(creative(X)|tall(X))))&
(![X]:((old(X)<~>calm(X))=>(~wise(X)&~calm(X))))&
(![X]:((curious(X)<~>patient(X))<=>(~strong(X)|quiet(X))))&
(![X]:((funny(X)|~wise(X))=>~creative(X)))&
(![X]:((~calm(X)&tall(X))=>(brave(X)<~>~wise(X))))&
(![X]:(~creative(X)<=>(funny(X)<~>~creative(X))))&
(![X]:((strong(X)&~strong(X))<=>(generous(X)|~curious(X))))&
(![X]:((calm(X)&~generous(X))=>(~funny(X)|creative(X))))&
(![X]:((creative(X)|wise(X))<=>(humble(X)|tall(X))))&
(((rich(susan)<~>patient(susan)))<=>(?[X]:((funny(X)|~tall(X)))))&
(?[X]:((calm(X)<~>~calm(X))))&
((humble(fred)&rich(fred)))&
(?[X]:((old(X)<~>~humble(X))))&
((~brave(lucy)|funny(lucy)))&
(?[X]:((~calm(X)&~happy(X)))) | wise(susan) | [
"p3",
"p6",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5985473949972816943997329
% SZS output start Proof for 5985473949972816943997329
4. ! [X0] : ((funny(X0) | ~creative(X0)) <=> (tall(X0) | creative(X0))) [input p3]
7. ! [X0] : ((~wise(X0) | funny(X0)) => ~creative(X0)) [input p6]
9. ! [X0] : (~creative(X0) <=> (funny(X0) <~> ~creative(X0))) [input p8]
12. ! [X0] : ((wise(X0) | creative(X0)) <=> (tall(X0) | humble(X0))) [input p11]
13. (rich(susan) <~> patient(susan)) <=> ? [X0] : (~tall(X0) | funny(X0)) [input p12]
19. ~wise(susan) [input hypothesis]
25. ! [X0] : (~creative(X0) | (wise(X0) & ~funny(X0))) [ennf transformation 7]
40. ! [X0] : (((funny(X0) | ~creative(X0)) | (~tall(X0) & ~creative(X0))) & ((tall(X0) | creative(X0)) | (~funny(X0) & creative(X0)))) [nnf transformation 4]
41. ! [X0] : ((funny(X0) | ~creative(X0) | (~tall(X0) & ~creative(X0))) & (tall(X0) | creative(X0) | (~funny(X0) & creative(X0)))) [flattening 40]
46. ! [X0] : ((~creative(X0) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) & (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | creative(X0))) [nnf transformation 9]
49. ! [X0] : (((wise(X0) | creative(X0)) | (~tall(X0) & ~humble(X0))) & ((tall(X0) | humble(X0)) | (~wise(X0) & ~creative(X0)))) [nnf transformation 12]
50. ! [X0] : ((wise(X0) | creative(X0) | (~tall(X0) & ~humble(X0))) & (tall(X0) | humble(X0) | (~wise(X0) & ~creative(X0)))) [flattening 49]
51. (((~patient(susan) | ~rich(susan)) & (patient(susan) | rich(susan))) | ! [X0] : (tall(X0) & ~funny(X0))) & (? [X0] : (~tall(X0) | funny(X0)) | ((rich(susan) | ~patient(susan)) & (patient(susan) | ~rich(susan)))) [nnf transformation 13]
52. (((~patient(susan) | ~rich(susan)) & (patient(susan) | rich(susan))) | ! [X0] : (tall(X0) & ~funny(X0))) & (? [X1] : (~tall(X1) | funny(X1)) | ((rich(susan) | ~patient(susan)) & (patient(susan) | ~rich(susan)))) [rectify 51]
53. ? [X1] : (~tall(X1) | funny(X1)) => (~tall(sK3) | funny(sK3)) [choice axiom]
54. (((~patient(susan) | ~rich(susan)) & (patient(susan) | rich(susan))) | ! [X0] : (tall(X0) & ~funny(X0))) & ((~tall(sK3) | funny(sK3)) | ((rich(susan) | ~patient(susan)) & (patient(susan) | ~rich(susan)))) [skolemisation 52,53]
76. tall(X0) | creative(X0) | creative(X0) [cnf transformation 41]
78. funny(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 41]
90. ~creative(X0) | ~funny(X0) [cnf transformation 25]
95. creative(X0) | ~funny(X0) | creative(X0) [cnf transformation 46]
107. wise(X0) | creative(X0) | ~tall(X0) [cnf transformation 50]
108. ~tall(sK3) | funny(sK3) | patient(susan) | ~rich(susan) [cnf transformation 54]
109. ~tall(sK3) | funny(sK3) | rich(susan) | ~patient(susan) [cnf transformation 54]
111. patient(susan) | rich(susan) | tall(X0) [cnf transformation 54]
113. ~patient(susan) | ~rich(susan) | tall(X0) [cnf transformation 54]
122. ~wise(susan) [cnf transformation 19]
123. creative(X0) | ~funny(X0) [duplicate literal removal 95]
126. tall(X0) | creative(X0) [duplicate literal removal 76]
127. ~creative(X0) | funny(X0) [duplicate literal removal 78]
187. ~creative(X0) [subsumption resolution 90,127]
188. ~funny(X0) [subsumption resolution 123,187]
191. ~tall(X0) | wise(X0) [subsumption resolution 107,187]
194. 14 <=> ! [X0] : tall(X0) [avatar definition]
195. tall(X0) <- (14) [avatar component clause 194]
197. 15 <=> rich(susan) [avatar definition]
201. 16 <=> patient(susan) [avatar definition]
204. 14 | ~15 | ~16 [avatar split clause 113,201,197,194]
205. 14 | 15 | 16 [avatar split clause 111,201,197,194]
206. ~tall(sK3) | rich(susan) | ~patient(susan) [subsumption resolution 109,188]
208. 17 <=> tall(sK3) [avatar definition]
210. ~tall(sK3) <- (~17) [avatar component clause 208]
211. ~16 | 15 | ~17 [avatar split clause 206,208,197,201]
212. ~tall(sK3) | patient(susan) | ~rich(susan) [subsumption resolution 108,188]
213. ~15 | 16 | ~17 [avatar split clause 212,208,201,197]
234. creative(sK3) <- (~17) [resolution 126,210]
235. $false <- (~17) [subsumption resolution 234,187]
236. 17 [avatar contradiction clause 235]
237. wise(X0) <- (14) [resolution 191,195]
241. $false <- (14) [resolution 237,122]
242. ~14 [avatar contradiction clause 241]
243. $false [avatar sat refutation 204,205,211,213,236,242]
% SZS output end Proof for 5985473949972816943997329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 strong or not curious is either humble or brave.
Everyone who is both patient and rich is not calm and vice versa.
Everyone who is either not calm or tall is both not rich and not curious.
If john is both curious and not quiet then paul is not funny.
Everyone who is either not calm or happy is not patient or patient.
Everyone who is both not curious and not patient is both calm and rich.
Everyone who is brave or kind is kind or calm and vice versa.
Everyone who is both not strong and calm is not brave.
Everyone who is both old and creative is either wise or not humble.
Everyone who is funny or not kind is both kind and not strong.
Everyone who is not happy is either kind or old and vice versa.
If alice is not funny or not wise then someone is not happy or not kind and vice versa.
Everyone who is both brave and quiet is either not generous or not strong and vice versa.
If someone is either not rich or not generous then someone is both calm and kind and vice versa.
If someone is either not rich or not brave then someone is not generous and vice versa.
If someone is curious then someone is both curious and not calm.
Someone is strong.
Someone is either creative or curious.
Someone is either not brave or quiet.
Someone is either old or funny.
Someone is both creative and not curious.
Fred is both not curious and brave. | Fred is not kind. | contradiction | (![X]:((~strong(X)<~>~curious(X))=>(humble(X)<~>brave(X))))&
(![X]:((patient(X)&rich(X))<=>~calm(X)))&
(![X]:((~calm(X)<~>tall(X))=>(~rich(X)&~curious(X))))&
(((curious(john)&~quiet(john)))=>(~funny(paul)))&
(![X]:((~calm(X)<~>happy(X))=>(~patient(X)|patient(X))))&
(![X]:((~curious(X)&~patient(X))=>(calm(X)&rich(X))))&
(![X]:((brave(X)|kind(X))<=>(kind(X)|calm(X))))&
(![X]:((~strong(X)&calm(X))=>~brave(X)))&
(![X]:((old(X)&creative(X))=>(wise(X)<~>~humble(X))))&
(![X]:((funny(X)|~kind(X))=>(kind(X)&~strong(X))))&
(![X]:(~happy(X)<=>(kind(X)<~>old(X))))&
(((~funny(alice)|~wise(alice)))<=>(?[X]:((~happy(X)|~kind(X)))))&
(![X]:((brave(X)&quiet(X))<=>(~generous(X)<~>~strong(X))))&
((?[X]:((~rich(X)<~>~generous(X))))<=>(?[X]:((calm(X)&kind(X)))))&
((?[X]:((~rich(X)<~>~brave(X))))<=>(?[X]:(~generous(X))))&
((?[X]:(curious(X)))=>(?[X]:((curious(X)&~calm(X)))))&
(?[X]:(strong(X)))&
(?[X]:((creative(X)<~>curious(X))))&
(?[X]:((~brave(X)<~>quiet(X))))&
(?[X]:((old(X)<~>funny(X))))&
(?[X]:((creative(X)&~curious(X))))&
((~curious(fred)&brave(fred))) | ~kind(fred) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1068544159103357295788918
% SZS output start Proof for 1068544159103357295788918
10. ! [X0] : ((~kind(X0) | funny(X0)) => (~strong(X0) & kind(X0))) [input p9]
23. ~kind(fred) [input hypothesis]
39. ! [X0] : ((~strong(X0) & kind(X0)) | (kind(X0) & ~funny(X0))) [ennf transformation 10]
107. kind(X0) | kind(X0) [cnf transformation 39]
147. ~kind(fred) [cnf transformation 23]
148. kind(X0) [duplicate literal removal 107]
280. $false [subsumption resolution 147,148]
% SZS output end Proof for 1068544159103357295788918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 lucy is not rich or strong then lucy is patient and vice versa.
Everyone who is not creative is not curious or not old and vice versa.
Everyone who is not brave or old is both not happy and happy.
If susan is both not strong and not quiet then someone is either funny or not happy and vice versa.
If someone is funny or calm then alice is either creative or not brave and vice versa.
Everyone who is not old is kind.
Everyone who is not generous is tall or not strong and vice versa.
If someone is old or not brave then susan is not patient or not kind and vice versa.
If lucy is funny then alice is either calm or not strong.
Everyone who is not happy is both not funny and not creative.
If john is either not happy or not kind then someone is tall and vice versa.
If someone is not tall then someone is either not curious or not rich.
If paul is either humble or calm then someone is both old and not strong and vice versa.
If someone is either not generous or not creative then lucy is not rich or not kind.
If susan is either rich or curious then lucy is kind or generous and vice versa.
Paul is not generous.
Alice is not old.
Lucy is rich or quiet.
Someone is wise or not tall.
Fred is patient or not quiet.
Someone is not happy.
Someone is either calm or tall.
Lucy is not tall or happy. | Paul is not creative. | entailment | (((~rich(lucy)|strong(lucy)))<=>(patient(lucy)))&
(![X]:(~creative(X)<=>(~curious(X)|~old(X))))&
(![X]:((~brave(X)|old(X))=>(~happy(X)&happy(X))))&
(((~strong(susan)&~quiet(susan)))<=>(?[X]:((funny(X)<~>~happy(X)))))&
((?[X]:((funny(X)|calm(X))))<=>((creative(alice)<~>~brave(alice))))&
(![X]:(~old(X)=>kind(X)))&
(![X]:(~generous(X)<=>(tall(X)|~strong(X))))&
((?[X]:((old(X)|~brave(X))))<=>((~patient(susan)|~kind(susan))))&
((funny(lucy))=>((calm(alice)<~>~strong(alice))))&
(![X]:(~happy(X)=>(~funny(X)&~creative(X))))&
(((~happy(john)<~>~kind(john)))<=>(?[X]:(tall(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~curious(X)<~>~rich(X)))))&
(((humble(paul)<~>calm(paul)))<=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:((~generous(X)<~>~creative(X))))=>((~rich(lucy)|~kind(lucy))))&
(((rich(susan)<~>curious(susan)))<=>((kind(lucy)|generous(lucy))))&
(~generous(paul))&
(~old(alice))&
((rich(lucy)|quiet(lucy)))&
(?[X]:((wise(X)|~tall(X))))&
((patient(fred)|~quiet(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)<~>tall(X))))&
((~tall(lucy)|happy(lucy))) | ~creative(paul) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1992890634461500736123088
% SZS output start Proof for 1992890634461500736123088
2. ! [X0] : (~creative(X0) <=> (~old(X0) | ~curious(X0))) [input p1]
3. ! [X0] : ((old(X0) | ~brave(X0)) => (happy(X0) & ~happy(X0))) [input p2]
24. creative(paul) [input hypothesis]
27. ! [X0] : ((happy(X0) & ~happy(X0)) | (~old(X0) & brave(X0))) [ennf transformation 3]
36. ! [X0] : ((~creative(X0) | (old(X0) & curious(X0))) & ((~old(X0) | ~curious(X0)) | creative(X0))) [nnf transformation 2]
37. ! [X0] : ((~creative(X0) | (old(X0) & curious(X0))) & (~old(X0) | ~curious(X0) | creative(X0))) [flattening 36]
80. ~creative(X0) | old(X0) [cnf transformation 37]
82. ~happy(X0) | ~old(X0) [cnf transformation 27]
84. happy(X0) | ~old(X0) [cnf transformation 27]
137. creative(paul) [cnf transformation 24]
153. ~old(X0) [subsumption resolution 82,84]
337. old(paul) [resolution 80,137]
339. $false [subsumption resolution 337,153]
% SZS output end Proof for 1992890634461500736123088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or brave is brave or calm. Everyone who is strong is calm. If someone is either not old or wise then mary is both not funny and not humble. If susan is both humble and rich then someone is not curious or generous. Everyone who is both not generous and not humble is brave or not patient. If john is both not humble and not wise then fred is either tall or not old. If fred is either not wise or not rich then someone is either old or not kind. If someone is creative or not humble then mary is rich. Everyone who is either humble or wise is both patient and wise and vice versa. Everyone who is not tall is both not generous and old. If alice is patient or not curious then someone is not kind and vice versa. If lucy is not generous or wise then mary is not curious. If someone is happy or not quiet then someone is not rich. Everyone who is not funny is both not strong and rich and vice versa. Everyone who is both not generous and rich is not funny or not rich and vice versa. Everyone who is not calm or not brave is creative and vice versa. Someone is quiet or wise. Someone is not kind or not curious. Mary is patient. Someone is not brave or not rich. John is either not wise or happy. Mary is both not curious and not old. | Fred is strong. | neutral | (![X]:((strong(X)<~>brave(X))=>(brave(X)|calm(X))))&
(![X]:(strong(X)=>calm(X)))&
((?[X]:((~old(X)<~>wise(X))))=>((~funny(mary)&~humble(mary))))&
(((humble(susan)&rich(susan)))=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:((~generous(X)&~humble(X))=>(brave(X)|~patient(X))))&
(((~humble(john)&~wise(john)))=>((tall(fred)<~>~old(fred))))&
(((~wise(fred)<~>~rich(fred)))=>(?[X]:((old(X)<~>~kind(X)))))&
((?[X]:((creative(X)|~humble(X))))=>(rich(mary)))&
(![X]:((humble(X)<~>wise(X))<=>(patient(X)&wise(X))))&
(![X]:(~tall(X)=>(~generous(X)&old(X))))&
(((patient(alice)|~curious(alice)))<=>(?[X]:(~kind(X))))&
(((~generous(lucy)|wise(lucy)))=>(~curious(mary)))&
((?[X]:((happy(X)|~quiet(X))))=>(?[X]:(~rich(X))))&
(![X]:(~funny(X)<=>(~strong(X)&rich(X))))&
(![X]:((~generous(X)&rich(X))<=>(~funny(X)|~rich(X))))&
(![X]:((~calm(X)|~brave(X))<=>creative(X)))&
(?[X]:((quiet(X)|wise(X))))&
(?[X]:((~kind(X)|~curious(X))))&
(patient(mary))&
(?[X]:((~brave(X)|~rich(X))))&
((~wise(john)<~>happy(john)))&
((~curious(mary)&~old(mary))) | strong(fred) | [] | null | 0 |
Everyone who is not wise or not old is not funny or not patient and vice versa.
Everyone who is either not tall or not patient is either calm or wise and vice versa.
Everyone who is both curious and tall is tall or happy and vice versa.
Everyone who is both tall and not brave is either not rich or not wise.
If someone is not quiet then someone is both wise and not brave.
If someone is either not curious or not rich then susan is not generous and vice versa.
Everyone who is either old or funny is either brave or kind and vice versa.
Everyone who is not creative is creative or not rich.
If john is either not humble or old then someone is funny or not wise and vice versa.
If lucy is not old then someone is not tall and vice versa.
Everyone who is happy is not creative and vice versa.
Everyone who is happy is not funny and vice versa.
If someone is either old or patient then john is either generous or wise.
Everyone who is calm is both not humble and quiet and vice versa.
Everyone who is either happy or not curious is old or not patient.
If someone is not generous then paul is not kind or not funny.
Someone is not funny or not strong.
Susan is both not curious and not generous.
Someone is both generous and tall.
Someone is both not humble and wise.
Susan is not calm or calm.
Alice is both strong and not curious.
Someone is either generous or not funny. | Alice is old. | neutral | (![X]:((~wise(X)|~old(X))<=>(~funny(X)|~patient(X))))&
(![X]:((~tall(X)<~>~patient(X))<=>(calm(X)<~>wise(X))))&
(![X]:((curious(X)&tall(X))<=>(tall(X)|happy(X))))&
(![X]:((tall(X)&~brave(X))=>(~rich(X)<~>~wise(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((wise(X)&~brave(X)))))&
((?[X]:((~curious(X)<~>~rich(X))))<=>(~generous(susan)))&
(![X]:((old(X)<~>funny(X))<=>(brave(X)<~>kind(X))))&
(![X]:(~creative(X)=>(creative(X)|~rich(X))))&
(((~humble(john)<~>old(john)))<=>(?[X]:((funny(X)|~wise(X)))))&
((~old(lucy))<=>(?[X]:(~tall(X))))&
(![X]:(happy(X)<=>~creative(X)))&
(![X]:(happy(X)<=>~funny(X)))&
((?[X]:((old(X)<~>patient(X))))=>((generous(john)<~>wise(john))))&
(![X]:(calm(X)<=>(~humble(X)&quiet(X))))&
(![X]:((happy(X)<~>~curious(X))=>(old(X)|~patient(X))))&
((?[X]:(~generous(X)))=>((~kind(paul)|~funny(paul))))&
(?[X]:((~funny(X)|~strong(X))))&
((~curious(susan)&~generous(susan)))&
(?[X]:((generous(X)&tall(X))))&
(?[X]:((~humble(X)&wise(X))))&
((~calm(susan)|calm(susan)))&
((strong(alice)&~curious(alice)))&
(?[X]:((generous(X)<~>~funny(X)))) | old(alice) | [] | null | 0 |
Everyone who is patient is both not rich and not patient.
If fred is either not humble or rich then someone is not quiet or not humble.
Everyone who is generous is curious or not brave and vice versa.
Everyone who is not humble is either quiet or not funny and vice versa.
Everyone who is both not happy and wise is either brave or not old.
Everyone who is patient is not strong or not calm and vice versa.
Everyone who is tall or creative is creative or old.
Everyone who is not patient or not funny is not creative or not quiet.
Everyone who is quiet or curious is both wise and not kind.
If someone is rich or creative then mary is creative.
Everyone who is brave is patient.
If someone is either not calm or not rich then someone is strong or curious and vice versa.
If someone is not generous or old then someone is either kind or not brave.
If someone is both not happy and not generous then someone is brave or not creative and vice versa.
Everyone who is both funny and happy is both not humble and calm and vice versa.
Paul is both not tall and rich.
Someone is curious.
Mary is not brave or creative.
John is not curious or not calm.
Fred is rich or happy.
Someone is kind.
Alice is either curious or not wise. | John is not funny. | contradiction | (![X]:(patient(X)=>(~rich(X)&~patient(X))))&
(((~humble(fred)<~>rich(fred)))=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:(generous(X)<=>(curious(X)|~brave(X))))&
(![X]:(~humble(X)<=>(quiet(X)<~>~funny(X))))&
(![X]:((~happy(X)&wise(X))=>(brave(X)<~>~old(X))))&
(![X]:(patient(X)<=>(~strong(X)|~calm(X))))&
(![X]:((tall(X)|creative(X))=>(creative(X)|old(X))))&
(![X]:((~patient(X)|~funny(X))=>(~creative(X)|~quiet(X))))&
(![X]:((quiet(X)|curious(X))=>(wise(X)&~kind(X))))&
((?[X]:((rich(X)|creative(X))))=>(creative(mary)))&
(![X]:(brave(X)=>patient(X)))&
((?[X]:((~calm(X)<~>~rich(X))))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((funny(X)&happy(X))<=>(~humble(X)&calm(X))))&
((~tall(paul)&rich(paul)))&
(?[X]:(curious(X)))&
((~brave(mary)|creative(mary)))&
((~curious(john)|~calm(john)))&
((rich(fred)|happy(fred)))&
(?[X]:(kind(X)))&
((curious(alice)<~>~wise(alice))) | ~funny(john) | [
"p0",
"p2",
"p3",
"p5",
"p7",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 687342568822713571221806
% SZS output start Proof for 687342568822713571221806
1. ! [X0] : (patient(X0) => (~patient(X0) & ~rich(X0))) [input p0]
3. ! [X0] : (generous(X0) <=> (~brave(X0) | curious(X0))) [input p2]
4. ! [X0] : (~humble(X0) <=> (quiet(X0) <~> ~funny(X0))) [input p3]
6. ! [X0] : (patient(X0) <=> (~calm(X0) | ~strong(X0))) [input p5]
8. ! [X0] : ((~funny(X0) | ~patient(X0)) => (~quiet(X0) | ~creative(X0))) [input p7]
11. ! [X0] : (brave(X0) => patient(X0)) [input p10]
14. ? [X0] : (~generous(X0) & ~happy(X0)) <=> ? [X0] : (~creative(X0) | brave(X0)) [input p13]
15. ! [X0] : ((happy(X0) & funny(X0)) <=> (calm(X0) & ~humble(X0))) [input p14]
23. ~funny(john) [input hypothesis]
26. ? [X0] : (~generous(X0) & ~happy(X0)) <=> ? [X1] : (~creative(X1) | brave(X1)) [rectify 14]
29. ! [X0] : ((~patient(X0) & ~rich(X0)) | ~patient(X0)) [ennf transformation 1]
35. ! [X0] : ((~quiet(X0) | ~creative(X0)) | (funny(X0) & patient(X0))) [ennf transformation 8]
36. ! [X0] : (~quiet(X0) | ~creative(X0) | (funny(X0) & patient(X0))) [flattening 35]
39. ! [X0] : (patient(X0) | ~brave(X0)) [ennf transformation 11]
44. ! [X0] : ((generous(X0) | (brave(X0) & ~curious(X0))) & ((~brave(X0) | curious(X0)) | ~generous(X0))) [nnf transformation 3]
45. ! [X0] : ((generous(X0) | (brave(X0) & ~curious(X0))) & (~brave(X0) | curious(X0) | ~generous(X0))) [flattening 44]
46. ! [X0] : ((~humble(X0) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0)))) & (((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | humble(X0))) [nnf transformation 4]
48. ! [X0] : ((patient(X0) | (calm(X0) & strong(X0))) & ((~calm(X0) | ~strong(X0)) | ~patient(X0))) [nnf transformation 6]
49. ! [X0] : ((patient(X0) | (calm(X0) & strong(X0))) & (~calm(X0) | ~strong(X0) | ~patient(X0))) [flattening 48]
59. (? [X0] : (~generous(X0) & ~happy(X0)) | ! [X1] : (creative(X1) & ~brave(X1))) & (? [X1] : (~creative(X1) | brave(X1)) | ! [X0] : (generous(X0) | happy(X0))) [nnf transformation 26]
60. (? [X0] : (~generous(X0) & ~happy(X0)) | ! [X1] : (creative(X1) & ~brave(X1))) & (? [X2] : (~creative(X2) | brave(X2)) | ! [X3] : (generous(X3) | happy(X3))) [rectify 59]
61. ? [X0] : (~generous(X0) & ~happy(X0)) => (~generous(sK4) & ~happy(sK4)) [choice axiom]
62. ? [X2] : (~creative(X2) | brave(X2)) => (~creative(sK5) | brave(sK5)) [choice axiom]
63. ((~generous(sK4) & ~happy(sK4)) | ! [X1] : (creative(X1) & ~brave(X1))) & ((~creative(sK5) | brave(sK5)) | ! [X3] : (generous(X3) | happy(X3))) [skolemisation 60,62,61]
64. ! [X0] : (((happy(X0) & funny(X0)) | (~calm(X0) | humble(X0))) & ((calm(X0) & ~humble(X0)) | (~happy(X0) | ~funny(X0)))) [nnf transformation 15]
65. ! [X0] : (((happy(X0) & funny(X0)) | ~calm(X0) | humble(X0)) & ((calm(X0) & ~humble(X0)) | ~happy(X0) | ~funny(X0))) [flattening 64]
72. ~patient(X0) | ~patient(X0) [cnf transformation 29]
77. brave(X0) | generous(X0) [cnf transformation 45]
81. ~humble(X0) | quiet(X0) | funny(X0) [cnf transformation 46]
86. patient(X0) | calm(X0) [cnf transformation 49]
88. ~quiet(X0) | ~creative(X0) | patient(X0) [cnf transformation 36]
96. patient(X0) | ~brave(X0) [cnf transformation 39]
111. ~generous(sK4) | creative(X1) [cnf transformation 63]
114. funny(X0) | ~calm(X0) | humble(X0) [cnf transformation 65]
124. ~funny(john) [cnf transformation 23]
125. ~patient(X0) [duplicate literal removal 72]
144. calm(X0) [subsumption resolution 86,125]
146. ~creative(X0) | ~quiet(X0) [subsumption resolution 88,125]
159. ~brave(X0) [subsumption resolution 96,125]
183. 12 <=> ! [X1] : generous(X1) [avatar definition]
184. generous(X1) <- (12) [avatar component clause 183]
187. 13 <=> ! [X1] : creative(X1) [avatar definition]
188. creative(X1) <- (13) [avatar component clause 187]
190. 14 <=> generous(sK4) [avatar definition]
192. ~generous(sK4) <- (~14) [avatar component clause 190]
193. 13 | ~14 [avatar split clause 111,190,187]
209. funny(X0) | humble(X0) [subsumption resolution 114,144]
226. generous(X0) [resolution 77,159]
227. 12 [avatar split clause 226,183]
228. $false <- (12, ~14) [resolution 184,192]
229. ~12 | 14 [avatar contradiction clause 228]
236. ~quiet(X0) <- (13) [resolution 146,188]
238. humble(john) [resolution 209,124]
247. quiet(john) | funny(john) [resolution 81,238]
250. funny(john) <- (13) [subsumption resolution 247,236]
251. $false <- (13) [subsumption resolution 250,124]
252. ~13 [avatar contradiction clause 251]
254. $false [avatar sat refutation 193,227,229,252]
% SZS output end Proof for 687342568822713571221806
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 humble is either not brave or not generous and vice versa.
Everyone who is not funny or not patient is calm or not generous.
Everyone who is not quiet is not happy or not quiet and vice versa.
Everyone who is both not curious and not old is both not patient and tall and vice versa.
Everyone who is both not curious and not old is not quiet or creative.
If someone is either tall or strong then paul is funny and vice versa.
If someone is not patient then paul is not kind or not brave.
If fred is either not old or not strong then someone is not funny or strong and vice versa.
If susan is strong then someone is not kind and vice versa.
Everyone who is either not funny or not creative is either not funny or calm.
If fred is curious then someone is not wise.
Everyone who is both rich and happy is either not wise or kind and vice versa.
Everyone who is either not curious or brave is both happy and quiet and vice versa.
Everyone who is not creative or funny is either not humble or not wise.
Everyone who is not creative or wise is both humble and not kind.
If someone is both not brave and wise then someone is both not funny and funny.
Someone is both not kind and not creative.
John is either patient or not funny.
Someone is patient.
Paul is either curious or old.
John is both not creative and not brave.
Someone is either not creative or humble. | Susan is not calm. | neutral | (![X]:((rich(X)|humble(X))<=>(~brave(X)<~>~generous(X))))&
(![X]:((~funny(X)|~patient(X))=>(calm(X)|~generous(X))))&
(![X]:(~quiet(X)<=>(~happy(X)|~quiet(X))))&
(![X]:((~curious(X)&~old(X))<=>(~patient(X)&tall(X))))&
(![X]:((~curious(X)&~old(X))=>(~quiet(X)|creative(X))))&
((?[X]:((tall(X)<~>strong(X))))<=>(funny(paul)))&
((?[X]:(~patient(X)))=>((~kind(paul)|~brave(paul))))&
(((~old(fred)<~>~strong(fred)))<=>(?[X]:((~funny(X)|strong(X)))))&
((strong(susan))<=>(?[X]:(~kind(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(~funny(X)<~>calm(X))))&
((curious(fred))=>(?[X]:(~wise(X))))&
(![X]:((rich(X)&happy(X))<=>(~wise(X)<~>kind(X))))&
(![X]:((~curious(X)<~>brave(X))<=>(happy(X)&quiet(X))))&
(![X]:((~creative(X)|funny(X))=>(~humble(X)<~>~wise(X))))&
(![X]:((~creative(X)|wise(X))=>(humble(X)&~kind(X))))&
((?[X]:((~brave(X)&wise(X))))=>(?[X]:((~funny(X)&funny(X)))))&
(?[X]:((~kind(X)&~creative(X))))&
((patient(john)<~>~funny(john)))&
(?[X]:(patient(X)))&
((curious(paul)<~>old(paul)))&
((~creative(john)&~brave(john)))&
(?[X]:((~creative(X)<~>humble(X)))) | ~calm(susan) | [] | null | 0 |
If alice is curious then susan is both not creative and creative.
Everyone who is either curious or not creative is both not tall and calm.
Everyone who is calm is funny or humble and vice versa.
Everyone who is kind is either humble or tall.
If someone is not kind then lucy is brave.
Everyone who is not patient is not strong or calm.
If alice is old then someone is not humble.
If fred is wise or not curious then someone is strong or not tall and vice versa.
If susan is quiet or tall then someone is not quiet or not generous.
If someone is either not strong or not generous then someone is both not wise and strong.
If someone is both not wise and calm then mary is both creative and kind.
Everyone who is old or curious is not strong or brave.
If susan is not old or not kind then fred is both happy and curious and vice versa.
If paul is both strong and not generous then susan is both brave and not strong.
If alice is either not patient or not quiet then fred is not happy.
If fred is not curious or old then lucy is both kind and not creative and vice versa.
Alice is either wise or creative.
Someone is patient or not strong.
Someone is brave or not kind.
Alice is both not funny and wise.
Someone is not generous.
Someone is either brave or generous.
Someone is both not rich and not humble. | Alice is wise. | entailment | ((curious(alice))=>((~creative(susan)&creative(susan))))&
(![X]:((curious(X)<~>~creative(X))=>(~tall(X)&calm(X))))&
(![X]:(calm(X)<=>(funny(X)|humble(X))))&
(![X]:(kind(X)=>(humble(X)<~>tall(X))))&
((?[X]:(~kind(X)))=>(brave(lucy)))&
(![X]:(~patient(X)=>(~strong(X)|calm(X))))&
((old(alice))=>(?[X]:(~humble(X))))&
(((wise(fred)|~curious(fred)))<=>(?[X]:((strong(X)|~tall(X)))))&
(((quiet(susan)|tall(susan)))=>(?[X]:((~quiet(X)|~generous(X)))))&
((?[X]:((~strong(X)<~>~generous(X))))=>(?[X]:((~wise(X)&strong(X)))))&
((?[X]:((~wise(X)&calm(X))))=>((creative(mary)&kind(mary))))&
(![X]:((old(X)|curious(X))=>(~strong(X)|brave(X))))&
(((~old(susan)|~kind(susan)))<=>((happy(fred)&curious(fred))))&
(((strong(paul)&~generous(paul)))=>((brave(susan)&~strong(susan))))&
(((~patient(alice)<~>~quiet(alice)))=>(~happy(fred)))&
(((~curious(fred)|old(fred)))<=>((kind(lucy)&~creative(lucy))))&
((wise(alice)<~>creative(alice)))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:((brave(X)|~kind(X))))&
((~funny(alice)&wise(alice)))&
(?[X]:(~generous(X)))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:((~rich(X)&~humble(X)))) | wise(alice) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1909038041467579212666756
% SZS output start Proof for 1909038041467579212666756
20. wise(alice) & ~funny(alice) [input p19]
24. ~wise(alice) [input hypothesis]
123. wise(alice) [cnf transformation 20]
128. ~wise(alice) [cnf transformation 24]
294. 36 <=> wise(alice) [avatar definition]
321. 36 [avatar split clause 123,294]
332. ~36 [avatar split clause 128,294]
333. $false [avatar sat refutation 321,332]
% SZS output end Proof for 1909038041467579212666756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both wise and generous then fred is both not funny and not curious.
If mary is quiet then someone is either not patient or not tall and vice versa.
Everyone who is both not happy and not brave is either not calm or old and vice versa.
If someone is both old and strong then someone is either not strong or rich and vice versa.
If alice is kind then susan is either not humble or humble and vice versa.
If someone is calm or not curious then someone is creative and vice versa.
If lucy is calm or not strong then someone is both rich and wise and vice versa.
If someone is not happy then someone is both not creative and tall and vice versa.
Everyone who is either not quiet or not calm is tall or not old.
Everyone who is not calm is both patient and not wise.
Everyone who is either not rich or happy is brave or strong and vice versa.
Everyone who is either not wise or kind is either not kind or creative and vice versa.
Everyone who is not calm is not generous.
Everyone who is either not funny or strong is both brave and old and vice versa.
If someone is not humble or old then alice is either kind or strong.
If paul is rich then alice is not calm.
Alice is either not strong or not wise.
Lucy is both not old and funny.
Someone is creative or not curious.
Someone is rich or not creative.
Alice is either not tall or not strong.
Alice is old.
Someone is either humble or curious.
Someone is rich or not generous. | Alice is not creative. | contradiction | (((wise(paul)&generous(paul)))=>((~funny(fred)&~curious(fred))))&
((quiet(mary))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:((~happy(X)&~brave(X))<=>(~calm(X)<~>old(X))))&
((?[X]:((old(X)&strong(X))))<=>(?[X]:((~strong(X)<~>rich(X)))))&
((kind(alice))<=>((~humble(susan)<~>humble(susan))))&
((?[X]:((calm(X)|~curious(X))))<=>(?[X]:(creative(X))))&
(((calm(lucy)|~strong(lucy)))<=>(?[X]:((rich(X)&wise(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:((~quiet(X)<~>~calm(X))=>(tall(X)|~old(X))))&
(![X]:(~calm(X)=>(patient(X)&~wise(X))))&
(![X]:((~rich(X)<~>happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~wise(X)<~>kind(X))<=>(~kind(X)<~>creative(X))))&
(![X]:(~calm(X)=>~generous(X)))&
(![X]:((~funny(X)<~>strong(X))<=>(brave(X)&old(X))))&
((?[X]:((~humble(X)|old(X))))=>((kind(alice)<~>strong(alice))))&
((rich(paul))=>(~calm(alice)))&
((~strong(alice)<~>~wise(alice)))&
((~old(lucy)&funny(lucy)))&
(?[X]:((creative(X)|~curious(X))))&
(?[X]:((rich(X)|~creative(X))))&
((~tall(alice)<~>~strong(alice)))&
(old(alice))&
(?[X]:((humble(X)<~>curious(X))))&
(?[X]:((rich(X)|~generous(X)))) | ~creative(alice) | [
"p4",
"p11",
"p14",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4582892524015140843494275
% SZS output start Proof for 4582892524015140843494275
5. kind(alice) <=> (~humble(susan) <~> humble(susan)) [input p4]
12. ! [X0] : ((~wise(X0) <~> kind(X0)) <=> (~kind(X0) <~> creative(X0))) [input p11]
15. ? [X0] : (old(X0) | ~humble(X0)) => (kind(alice) <~> strong(alice)) [input p14]
17. ~strong(alice) <~> ~wise(alice) [input p16]
22. old(alice) [input p21]
25. ~creative(alice) [input hypothesis]
35. (kind(alice) <~> strong(alice)) | ! [X0] : (~old(X0) & humble(X0)) [ennf transformation 15]
48. (kind(alice) | ((~humble(susan) | ~humble(susan)) & (humble(susan) | humble(susan)))) & (((~humble(susan) | humble(susan)) & (humble(susan) | ~humble(susan))) | ~kind(alice)) [nnf transformation 5]
67. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) & (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [nnf transformation 12]
70. ((~strong(alice) | ~kind(alice)) & (strong(alice) | kind(alice))) | ! [X0] : (~old(X0) & humble(X0)) [nnf transformation 35]
71. (wise(alice) | strong(alice)) & (~wise(alice) | ~strong(alice)) [nnf transformation 17]
98. kind(alice) | humble(susan) | humble(susan) [cnf transformation 48]
99. kind(alice) | ~humble(susan) | ~humble(susan) [cnf transformation 48]
122. creative(X0) | ~kind(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 67]
125. kind(X0) | ~wise(X0) | creative(X0) | kind(X0) [cnf transformation 67]
138. ~strong(alice) | ~kind(alice) | ~old(X0) [cnf transformation 70]
141. wise(alice) | strong(alice) [cnf transformation 71]
148. old(alice) [cnf transformation 22]
151. ~creative(alice) [cnf transformation 25]
152. creative(X0) | ~kind(X0) | ~wise(X0) [duplicate literal removal 122]
154. kind(X0) | ~wise(X0) | creative(X0) [duplicate literal removal 125]
156. kind(alice) | humble(susan) [duplicate literal removal 98]
157. kind(alice) | ~humble(susan) [duplicate literal removal 99]
212. 13 <=> humble(susan) [avatar definition]
216. 14 <=> kind(alice) [avatar definition]
219. ~13 | 14 [avatar split clause 157,216,212]
220. 13 | 14 [avatar split clause 156,216,212]
291. ~wise(X0) | creative(X0) [subsumption resolution 152,154]
293. 31 <=> ! [X0] : ~old(X0) [avatar definition]
294. ~old(X0) <- (31) [avatar component clause 293]
296. 32 <=> strong(alice) [avatar definition]
299. 31 | ~14 | ~32 [avatar split clause 138,296,216,293]
316. 36 <=> wise(alice) [avatar definition]
318. wise(alice) <- (36) [avatar component clause 316]
319. 32 | 36 [avatar split clause 141,316,296]
357. $false <- (31) [resolution 294,148]
358. ~31 [avatar contradiction clause 357]
371. creative(alice) <- (36) [resolution 291,318]
372. $false <- (36) [subsumption resolution 371,151]
373. ~36 [avatar contradiction clause 372]
374. $false [avatar sat refutation 219,220,299,319,358,373]
% SZS output end Proof for 4582892524015140843494275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or humble then someone is either not happy or creative. If someone is both not brave and not happy then mary is old and vice versa. If susan is not creative or funny then susan is not kind or not old. Everyone who is both not kind and not old is not curious or not patient. Everyone who is either not brave or not wise is happy and vice versa. If someone is either not old or patient then someone is both funny and curious and vice versa. Everyone who is not old is funny or calm and vice versa. Everyone who is funny is not happy or happy and vice versa. If fred is not brave or not patient then fred is both not old and brave. If someone is both not strong and not rich then mary is both not patient and not wise and vice versa. If someone is not rich then mary is generous or brave. Everyone who is not kind is calm and vice versa. Everyone who is not creative is not rich or calm. Everyone who is either not kind or quiet is both not creative and not happy and vice versa. Everyone who is both calm and kind is either old or not tall and vice versa. If someone is quiet or wise then susan is both wise and not old. Someone is both not strong and brave. Fred is either not humble or not curious. Susan is quiet. Someone is both creative and brave. Someone is both not humble and not strong. Mary is not strong or not kind. | Mary is quiet. | neutral | ((?[X]:((generous(X)|humble(X))))=>(?[X]:((~happy(X)<~>creative(X)))))&
((?[X]:((~brave(X)&~happy(X))))<=>(old(mary)))&
(((~creative(susan)|funny(susan)))=>((~kind(susan)|~old(susan))))&
(![X]:((~kind(X)&~old(X))=>(~curious(X)|~patient(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>happy(X)))&
((?[X]:((~old(X)<~>patient(X))))<=>(?[X]:((funny(X)&curious(X)))))&
(![X]:(~old(X)<=>(funny(X)|calm(X))))&
(![X]:(funny(X)<=>(~happy(X)|happy(X))))&
(((~brave(fred)|~patient(fred)))=>((~old(fred)&brave(fred))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~patient(mary)&~wise(mary))))&
((?[X]:(~rich(X)))=>((generous(mary)|brave(mary))))&
(![X]:(~kind(X)<=>calm(X)))&
(![X]:(~creative(X)=>(~rich(X)|calm(X))))&
(![X]:((~kind(X)<~>quiet(X))<=>(~creative(X)&~happy(X))))&
(![X]:((calm(X)&kind(X))<=>(old(X)<~>~tall(X))))&
((?[X]:((quiet(X)|wise(X))))=>((wise(susan)&~old(susan))))&
(?[X]:((~strong(X)&brave(X))))&
((~humble(fred)<~>~curious(fred)))&
(quiet(susan))&
(?[X]:((creative(X)&brave(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~strong(mary)|~kind(mary))) | quiet(mary) | [] | null | 0 |
Everyone who is either not curious or generous is not humble or funny and vice versa.
Everyone who is generous is curious.
If someone is happy or not brave then someone is either not quiet or curious.
If someone is not humble or not wise then mary is both funny and not curious and vice versa.
Everyone who is either not rich or funny is both happy and not brave.
Everyone who is not kind is not humble or not quiet and vice versa.
Everyone who is either rich or tall is happy or not strong and vice versa.
Everyone who is both not kind and not happy is humble or not humble and vice versa.
Everyone who is both humble and not rich is funny and vice versa.
Everyone who is both strong and not generous is not tall.
Everyone who is funny or not humble is not calm or generous and vice versa.
If someone is generous then john is tall and vice versa.
If alice is both not humble and not tall then fred is not rich or not humble.
Everyone who is brave or not brave is not funny or not wise.
Everyone who is wise is not humble.
Everyone who is both strong and not generous is not humble or wise and vice versa.
Someone is not brave or patient.
Susan is not generous.
Fred is both not rich and not generous.
Someone is calm. | Mary is not quiet. | entailment | (![X]:((~curious(X)<~>generous(X))<=>(~humble(X)|funny(X))))&
(![X]:(generous(X)=>curious(X)))&
((?[X]:((happy(X)|~brave(X))))=>(?[X]:((~quiet(X)<~>curious(X)))))&
((?[X]:((~humble(X)|~wise(X))))<=>((funny(mary)&~curious(mary))))&
(![X]:((~rich(X)<~>funny(X))=>(happy(X)&~brave(X))))&
(![X]:(~kind(X)<=>(~humble(X)|~quiet(X))))&
(![X]:((rich(X)<~>tall(X))<=>(happy(X)|~strong(X))))&
(![X]:((~kind(X)&~happy(X))<=>(humble(X)|~humble(X))))&
(![X]:((humble(X)&~rich(X))<=>funny(X)))&
(![X]:((strong(X)&~generous(X))=>~tall(X)))&
(![X]:((funny(X)|~humble(X))<=>(~calm(X)|generous(X))))&
((?[X]:(generous(X)))<=>(tall(john)))&
(((~humble(alice)&~tall(alice)))=>((~rich(fred)|~humble(fred))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|~wise(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((strong(X)&~generous(X))<=>(~humble(X)|wise(X))))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan))&
((~rich(fred)&~generous(fred)))&
(?[X]:(calm(X))) | ~quiet(mary) | [
"p3",
"p5",
"p7",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5307572487300493480927283
% SZS output start Proof for 5307572487300493480927283
4. ? [X0] : (~wise(X0) | ~humble(X0)) <=> (~curious(mary) & funny(mary)) [input p3]
6. ! [X0] : (~kind(X0) <=> (~quiet(X0) | ~humble(X0))) [input p5]
8. ! [X0] : ((~happy(X0) & ~kind(X0)) <=> (~humble(X0) | humble(X0))) [input p7]
9. ! [X0] : ((~rich(X0) & humble(X0)) <=> funny(X0)) [input p8]
15. ! [X0] : (wise(X0) => ~humble(X0)) [input p14]
21. quiet(mary) [input hypothesis]
33. ! [X0] : (~humble(X0) | ~wise(X0)) [ennf transformation 15]
40. (? [X0] : (~wise(X0) | ~humble(X0)) | (curious(mary) | ~funny(mary))) & ((~curious(mary) & funny(mary)) | ! [X0] : (wise(X0) & humble(X0))) [nnf transformation 4]
41. (? [X0] : (~wise(X0) | ~humble(X0)) | curious(mary) | ~funny(mary)) & ((~curious(mary) & funny(mary)) | ! [X0] : (wise(X0) & humble(X0))) [flattening 40]
42. (? [X0] : (~wise(X0) | ~humble(X0)) | curious(mary) | ~funny(mary)) & ((~curious(mary) & funny(mary)) | ! [X1] : (wise(X1) & humble(X1))) [rectify 41]
43. ? [X0] : (~wise(X0) | ~humble(X0)) => (~wise(sK1) | ~humble(sK1)) [choice axiom]
44. ((~wise(sK1) | ~humble(sK1)) | curious(mary) | ~funny(mary)) & ((~curious(mary) & funny(mary)) | ! [X1] : (wise(X1) & humble(X1))) [skolemisation 42,43]
46. ! [X0] : ((~kind(X0) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | kind(X0))) [nnf transformation 6]
47. ! [X0] : ((~kind(X0) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | kind(X0))) [flattening 46]
50. ! [X0] : (((~happy(X0) & ~kind(X0)) | (humble(X0) & ~humble(X0))) & ((~humble(X0) | humble(X0)) | (happy(X0) | kind(X0)))) [nnf transformation 8]
51. ! [X0] : (((~happy(X0) & ~kind(X0)) | (humble(X0) & ~humble(X0))) & (~humble(X0) | humble(X0) | happy(X0) | kind(X0))) [flattening 50]
52. ! [X0] : (((~rich(X0) & humble(X0)) | ~funny(X0)) & (funny(X0) | (rich(X0) | ~humble(X0)))) [nnf transformation 9]
53. ! [X0] : (((~rich(X0) & humble(X0)) | ~funny(X0)) & (funny(X0) | rich(X0) | ~humble(X0))) [flattening 52]
75. funny(mary) | humble(X1) [cnf transformation 44]
76. funny(mary) | wise(X1) [cnf transformation 44]
84. ~quiet(X0) | ~humble(X0) | kind(X0) [cnf transformation 47]
85. ~kind(X0) | humble(X0) [cnf transformation 47]
94. ~kind(X0) | ~humble(X0) [cnf transformation 51]
99. ~funny(X0) | humble(X0) [cnf transformation 53]
111. ~wise(X0) | ~humble(X0) [cnf transformation 33]
121. quiet(mary) [cnf transformation 21]
141. 5 <=> funny(mary) [avatar definition]
142. funny(mary) <- (5) [avatar component clause 141]
158. 9 <=> ! [X1] : wise(X1) [avatar definition]
159. wise(X1) <- (9) [avatar component clause 158]
162. 10 <=> ! [X1] : humble(X1) [avatar definition]
163. humble(X1) <- (10) [avatar component clause 162]
165. 9 | 5 [avatar split clause 76,141,158]
166. 10 | 5 [avatar split clause 75,141,162]
169. ~kind(X0) [subsumption resolution 94,85]
204. humble(mary) <- (5) [resolution 99,142]
221. ~humble(mary) | kind(mary) [resolution 84,121]
222. kind(mary) <- (5) [subsumption resolution 221,204]
223. $false <- (5) [subsumption resolution 222,169]
224. ~5 [avatar contradiction clause 223]
230. ~humble(X3) <- (9) [resolution 159,111]
233. $false <- (9, 10) [subsumption resolution 230,163]
234. ~9 | ~10 [avatar contradiction clause 233]
235. $false [avatar sat refutation 165,166,224,234]
% SZS output end Proof for 5307572487300493480927283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not old or not curious then john is not wise or not quiet. Everyone who is strong or calm is both calm and tall and vice versa. If lucy is not wise or not patient then someone is both quiet and brave and vice versa. Everyone who is not quiet or generous is both calm and not happy and vice versa. Everyone who is rich is strong or not humble and vice versa. Everyone who is not brave or funny is either not calm or not patient and vice versa. Everyone who is not humble is either not funny or not brave. If someone is not rich then fred is either wise or funny. Everyone who is not happy or old is not tall and vice versa. Everyone who is both not patient and not tall is either strong or not tall. Everyone who is patient or curious is wise and vice versa. Everyone who is both funny and not rich is not calm or patient and vice versa. If paul is not strong or not old then someone is both funny and brave. Everyone who is both rich and happy is not brave or strong and vice versa. Everyone who is both not generous and strong is either tall or funny. Everyone who is not creative is not funny or not creative and vice versa. Someone is both not funny and not curious. Someone is curious or not funny. John is not generous or creative. Someone is old. Someone is both strong and not brave. John is happy or not brave. Susan is kind. Mary is either rich or not creative. | Lucy is calm. | entailment | (((~old(susan)|~curious(susan)))=>((~wise(john)|~quiet(john))))&
(![X]:((strong(X)|calm(X))<=>(calm(X)&tall(X))))&
(((~wise(lucy)|~patient(lucy)))<=>(?[X]:((quiet(X)&brave(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(calm(X)&~happy(X))))&
(![X]:(rich(X)<=>(strong(X)|~humble(X))))&
(![X]:((~brave(X)|funny(X))<=>(~calm(X)<~>~patient(X))))&
(![X]:(~humble(X)=>(~funny(X)<~>~brave(X))))&
((?[X]:(~rich(X)))=>((wise(fred)<~>funny(fred))))&
(![X]:((~happy(X)|old(X))<=>~tall(X)))&
(![X]:((~patient(X)&~tall(X))=>(strong(X)<~>~tall(X))))&
(![X]:((patient(X)|curious(X))<=>wise(X)))&
(![X]:((funny(X)&~rich(X))<=>(~calm(X)|patient(X))))&
(((~strong(paul)|~old(paul)))=>(?[X]:((funny(X)&brave(X)))))&
(![X]:((rich(X)&happy(X))<=>(~brave(X)|strong(X))))&
(![X]:((~generous(X)&strong(X))=>(tall(X)<~>funny(X))))&
(![X]:(~creative(X)<=>(~funny(X)|~creative(X))))&
(?[X]:((~funny(X)&~curious(X))))&
(?[X]:((curious(X)|~funny(X))))&
((~generous(john)|creative(john)))&
(?[X]:(old(X)))&
(?[X]:((strong(X)&~brave(X))))&
((happy(john)|~brave(john)))&
(kind(susan))&
((rich(mary)<~>~creative(mary))) | calm(lucy) | [
"p2",
"p3",
"p5",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1716688728566377918466499
% SZS output start Proof for 1716688728566377918466499
3. (~patient(lucy) | ~wise(lucy)) <=> ? [X0] : (brave(X0) & quiet(X0)) [input p2]
4. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (~happy(X0) & calm(X0))) [input p3]
6. ! [X0] : ((funny(X0) | ~brave(X0)) <=> (~calm(X0) <~> ~patient(X0))) [input p5]
11. ! [X0] : ((curious(X0) | patient(X0)) <=> wise(X0)) [input p10]
12. ! [X0] : ((~rich(X0) & funny(X0)) <=> (patient(X0) | ~calm(X0))) [input p11]
14. ! [X0] : ((happy(X0) & rich(X0)) <=> (strong(X0) | ~brave(X0))) [input p13]
25. ~calm(lucy) [input hypothesis]
38. ((~patient(lucy) | ~wise(lucy)) | ! [X0] : (~brave(X0) | ~quiet(X0))) & (? [X0] : (brave(X0) & quiet(X0)) | (patient(lucy) & wise(lucy))) [nnf transformation 3]
39. (~patient(lucy) | ~wise(lucy) | ! [X0] : (~brave(X0) | ~quiet(X0))) & (? [X0] : (brave(X0) & quiet(X0)) | (patient(lucy) & wise(lucy))) [flattening 38]
40. (~patient(lucy) | ~wise(lucy) | ! [X0] : (~brave(X0) | ~quiet(X0))) & (? [X1] : (brave(X1) & quiet(X1)) | (patient(lucy) & wise(lucy))) [rectify 39]
41. ? [X1] : (brave(X1) & quiet(X1)) => (brave(sK0) & quiet(sK0)) [choice axiom]
42. (~patient(lucy) | ~wise(lucy) | ! [X0] : (~brave(X0) | ~quiet(X0))) & ((brave(sK0) & quiet(sK0)) | (patient(lucy) & wise(lucy))) [skolemisation 40,41]
43. ! [X0] : (((generous(X0) | ~quiet(X0)) | (happy(X0) | ~calm(X0))) & ((~happy(X0) & calm(X0)) | (~generous(X0) & quiet(X0)))) [nnf transformation 4]
44. ! [X0] : ((generous(X0) | ~quiet(X0) | happy(X0) | ~calm(X0)) & ((~happy(X0) & calm(X0)) | (~generous(X0) & quiet(X0)))) [flattening 43]
47. ! [X0] : (((funny(X0) | ~brave(X0)) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (~funny(X0) & brave(X0)))) [nnf transformation 6]
48. ! [X0] : ((funny(X0) | ~brave(X0) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0)))) & (((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | (~funny(X0) & brave(X0)))) [flattening 47]
54. ! [X0] : (((curious(X0) | patient(X0)) | ~wise(X0)) & (wise(X0) | (~curious(X0) & ~patient(X0)))) [nnf transformation 11]
55. ! [X0] : ((curious(X0) | patient(X0) | ~wise(X0)) & (wise(X0) | (~curious(X0) & ~patient(X0)))) [flattening 54]
56. ! [X0] : (((~rich(X0) & funny(X0)) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | (rich(X0) | ~funny(X0)))) [nnf transformation 12]
57. ! [X0] : (((~rich(X0) & funny(X0)) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | rich(X0) | ~funny(X0))) [flattening 56]
60. ! [X0] : (((happy(X0) & rich(X0)) | (~strong(X0) & brave(X0))) & ((strong(X0) | ~brave(X0)) | (~happy(X0) | ~rich(X0)))) [nnf transformation 14]
61. ! [X0] : (((happy(X0) & rich(X0)) | (~strong(X0) & brave(X0))) & (strong(X0) | ~brave(X0) | ~happy(X0) | ~rich(X0))) [flattening 60]
85. ~patient(lucy) | ~wise(lucy) | ~brave(X0) | ~quiet(X0) [cnf transformation 42]
86. calm(X0) | quiet(X0) [cnf transformation 44]
97. ~funny(X0) | calm(X0) | patient(X0) [cnf transformation 48]
109. ~patient(X0) | wise(X0) [cnf transformation 55]
112. patient(X0) | ~calm(X0) | rich(X0) | ~funny(X0) [cnf transformation 57]
113. funny(X0) | calm(X0) [cnf transformation 57]
115. ~rich(X0) | calm(X0) [cnf transformation 57]
122. rich(X0) | brave(X0) [cnf transformation 61]
141. ~calm(lucy) [cnf transformation 25]
162. 5 <=> ! [X0] : (~brave(X0) | ~quiet(X0)) [avatar definition]
163. ~brave(X0) | ~quiet(X0) <- (5) [avatar component clause 162]
165. 6 <=> wise(lucy) [avatar definition]
167. ~wise(lucy) <- (~6) [avatar component clause 165]
169. 7 <=> patient(lucy) [avatar definition]
170. patient(lucy) <- (7) [avatar component clause 169]
171. ~patient(lucy) <- (~7) [avatar component clause 169]
172. 5 | ~6 | ~7 [avatar split clause 85,169,165,162]
198. ~funny(X0) | rich(X0) | patient(X0) [subsumption resolution 112,97]
257. quiet(lucy) [resolution 86,141]
289. brave(X1) | calm(X1) [resolution 122,115]
333. 26 <=> brave(lucy) [avatar definition]
334. brave(lucy) <- (26) [avatar component clause 333]
335. ~brave(lucy) <- (~26) [avatar component clause 333]
421. rich(X1) | patient(X1) | calm(X1) [resolution 198,113]
536. ~quiet(lucy) <- (5, 26) [resolution 334,163]
537. $false <- (5, 26) [subsumption resolution 536,257]
538. ~5 | ~26 [avatar contradiction clause 537]
555. patient(X1) | calm(X1) [subsumption resolution 421,115]
587. calm(lucy) <- (~26) [resolution 335,289]
589. $false <- (~26) [subsumption resolution 587,141]
590. 26 [avatar contradiction clause 589]
606. calm(lucy) <- (~7) [resolution 555,171]
611. $false <- (~7) [subsumption resolution 606,141]
612. 7 [avatar contradiction clause 611]
617. wise(lucy) <- (7) [resolution 170,109]
618. $false <- (~6, 7) [subsumption resolution 617,167]
619. 6 | ~7 [avatar contradiction clause 618]
620. $false [avatar sat refutation 172,538,590,612,619]
% SZS output end Proof for 1716688728566377918466499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not humble or not curious then alice is either quiet or strong and vice versa.
If fred is calm then lucy is either not curious or calm and vice versa.
Everyone who is old or tall is both tall and quiet and vice versa.
If lucy is happy then susan is both not strong and curious.
Everyone who is brave is happy and vice versa.
If someone is either quiet or not creative then alice is rich or not old.
Everyone who is both not humble and generous is either not creative or calm.
Everyone who is not humble is either not quiet or wise and vice versa.
Everyone who is generous is both not generous and funny and vice versa.
Everyone who is humble or calm is wise or not humble.
If someone is curious or not strong then someone is both humble and strong.
If susan is not patient or humble then mary is not creative or creative.
Everyone who is both wise and not old is not tall or kind and vice versa.
Everyone who is old or not humble is rich or not creative and vice versa.
Everyone who is either not curious or funny is not patient or curious and vice versa.
Everyone who is either rich or funny is both not strong and tall.
Someone is not quiet or funny.
Someone is not curious.
Someone is creative.
John is either quiet or calm.
Someone is not curious or not old.
Alice is both not tall and not kind. | Mary is not humble. | neutral | (((~humble(lucy)<~>~curious(lucy)))<=>((quiet(alice)<~>strong(alice))))&
((calm(fred))<=>((~curious(lucy)<~>calm(lucy))))&
(![X]:((old(X)|tall(X))<=>(tall(X)&quiet(X))))&
((happy(lucy))=>((~strong(susan)&curious(susan))))&
(![X]:(brave(X)<=>happy(X)))&
((?[X]:((quiet(X)<~>~creative(X))))=>((rich(alice)|~old(alice))))&
(![X]:((~humble(X)&generous(X))=>(~creative(X)<~>calm(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>wise(X))))&
(![X]:(generous(X)<=>(~generous(X)&funny(X))))&
(![X]:((humble(X)|calm(X))=>(wise(X)|~humble(X))))&
((?[X]:((curious(X)|~strong(X))))=>(?[X]:((humble(X)&strong(X)))))&
(((~patient(susan)|humble(susan)))=>((~creative(mary)|creative(mary))))&
(![X]:((wise(X)&~old(X))<=>(~tall(X)|kind(X))))&
(![X]:((old(X)|~humble(X))<=>(rich(X)|~creative(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(~patient(X)|curious(X))))&
(![X]:((rich(X)<~>funny(X))=>(~strong(X)&tall(X))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:(~curious(X)))&
(?[X]:(creative(X)))&
((quiet(john)<~>calm(john)))&
(?[X]:((~curious(X)|~old(X))))&
((~tall(alice)&~kind(alice))) | ~humble(mary) | [] | null | 0 |
If susan is either not generous or happy then someone is either happy or patient.
If someone is either not tall or not strong then someone is both strong and not quiet and vice versa.
Everyone who is either not wise or not generous is kind or not generous.
If someone is either not happy or brave then someone is not generous.
Everyone who is either not patient or not old is happy and vice versa.
Everyone who is both curious and brave is both brave and not funny and vice versa.
If fred is both old and patient then mary is not curious.
Everyone who is quiet or brave is both happy and not strong.
Everyone who is either old or humble is either not quiet or patient and vice versa.
Everyone who is creative is either not kind or kind and vice versa.
If someone is either not humble or not kind then lucy is both patient and wise and vice versa.
If someone is both funny and rich then someone is not rich or not tall and vice versa.
Everyone who is kind or happy is both creative and calm.
Everyone who is both humble and patient is tall or kind.
If someone is humble or creative then someone is calm and vice versa.
If someone is quiet or brave then alice is both not old and kind and vice versa.
Someone is either kind or tall.
Mary is kind.
Someone is both quiet and generous.
John is kind or patient.
Someone is both generous and not rich.
Someone is either wise or not calm.
John is both curious and not strong.
Someone is not wise. | Mary is not calm. | contradiction | (((~generous(susan)<~>happy(susan)))=>(?[X]:((happy(X)<~>patient(X)))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(kind(X)|~generous(X))))&
((?[X]:((~happy(X)<~>brave(X))))=>(?[X]:(~generous(X))))&
(![X]:((~patient(X)<~>~old(X))<=>happy(X)))&
(![X]:((curious(X)&brave(X))<=>(brave(X)&~funny(X))))&
(((old(fred)&patient(fred)))=>(~curious(mary)))&
(![X]:((quiet(X)|brave(X))=>(happy(X)&~strong(X))))&
(![X]:((old(X)<~>humble(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:(creative(X)<=>(~kind(X)<~>kind(X))))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((patient(lucy)&wise(lucy))))&
((?[X]:((funny(X)&rich(X))))<=>(?[X]:((~rich(X)|~tall(X)))))&
(![X]:((kind(X)|happy(X))=>(creative(X)&calm(X))))&
(![X]:((humble(X)&patient(X))=>(tall(X)|kind(X))))&
((?[X]:((humble(X)|creative(X))))<=>(?[X]:(calm(X))))&
((?[X]:((quiet(X)|brave(X))))<=>((~old(alice)&kind(alice))))&
(?[X]:((kind(X)<~>tall(X))))&
(kind(mary))&
(?[X]:((quiet(X)&generous(X))))&
((kind(john)|patient(john)))&
(?[X]:((generous(X)&~rich(X))))&
(?[X]:((wise(X)<~>~calm(X))))&
((curious(john)&~strong(john)))&
(?[X]:(~wise(X))) | ~calm(mary) | [
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6985591156130250185822253
% SZS output start Proof for 6985591156130250185822253
13. ! [X0] : ((happy(X0) | kind(X0)) => (calm(X0) & creative(X0))) [input p12]
18. kind(mary) [input p17]
25. ~calm(mary) [input hypothesis]
37. ! [X0] : ((calm(X0) & creative(X0)) | (~happy(X0) & ~kind(X0))) [ennf transformation 13]
142. ~kind(X0) | calm(X0) [cnf transformation 37]
155. kind(mary) [cnf transformation 18]
166. ~calm(mary) [cnf transformation 25]
374. calm(mary) [resolution 142,155]
378. $false [subsumption resolution 374,166]
% SZS output end Proof for 6985591156130250185822253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both generous and not brave then someone is either generous or not happy.
Everyone who is not strong is both not happy and curious and vice versa.
If mary is happy then mary is not quiet or not creative.
If someone is not tall then someone is either patient or not generous and vice versa.
Everyone who is both not strong and calm is not wise and vice versa.
Everyone who is either creative or not wise is humble and vice versa.
Everyone who is both not old and funny is either not humble or patient and vice versa.
Everyone who is brave is old.
If someone is either funny or brave then someone is either generous or not calm and vice versa.
If susan is either generous or not quiet then someone is not brave or tall and vice versa.
Everyone who is quiet is either not funny or wise and vice versa.
Everyone who is not calm is not tall and vice versa.
Everyone who is either generous or not rich is both calm and not calm and vice versa.
Everyone who is both rich and not generous is either quiet or not kind and vice versa.
Everyone who is wise is either wise or not funny and vice versa.
If someone is either kind or quiet then paul is generous.
Mary is calm.
Someone is tall or quiet.
Fred is either happy or not kind.
Mary is not rich.
Someone is not calm or not creative.
Someone is either brave or happy.
Paul is either humble or brave. | Susan is creative. | neutral | (((generous(mary)&~brave(mary)))=>(?[X]:((generous(X)<~>~happy(X)))))&
(![X]:(~strong(X)<=>(~happy(X)&curious(X))))&
((happy(mary))=>((~quiet(mary)|~creative(mary))))&
((?[X]:(~tall(X)))<=>(?[X]:((patient(X)<~>~generous(X)))))&
(![X]:((~strong(X)&calm(X))<=>~wise(X)))&
(![X]:((creative(X)<~>~wise(X))<=>humble(X)))&
(![X]:((~old(X)&funny(X))<=>(~humble(X)<~>patient(X))))&
(![X]:(brave(X)=>old(X)))&
((?[X]:((funny(X)<~>brave(X))))<=>(?[X]:((generous(X)<~>~calm(X)))))&
(((generous(susan)<~>~quiet(susan)))<=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:(quiet(X)<=>(~funny(X)<~>wise(X))))&
(![X]:(~calm(X)<=>~tall(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(calm(X)&~calm(X))))&
(![X]:((rich(X)&~generous(X))<=>(quiet(X)<~>~kind(X))))&
(![X]:(wise(X)<=>(wise(X)<~>~funny(X))))&
((?[X]:((kind(X)<~>quiet(X))))=>(generous(paul)))&
(calm(mary))&
(?[X]:((tall(X)|quiet(X))))&
((happy(fred)<~>~kind(fred)))&
(~rich(mary))&
(?[X]:((~calm(X)|~creative(X))))&
(?[X]:((brave(X)<~>happy(X))))&
((humble(paul)<~>brave(paul))) | creative(susan) | [] | null | 0 |
Everyone who is wise or not humble is both not brave and quiet and vice versa.
If paul is curious or not brave then alice is not kind or not humble.
If someone is both not calm and rich then someone is either patient or wise.
If susan is not wise then fred is not humble or funny and vice versa.
If lucy is both curious and old then someone is not brave or not funny and vice versa.
If susan is not calm then susan is both not tall and not old and vice versa.
If paul is both not kind and not funny then lucy is either not generous or not creative and vice versa.
Everyone who is not tall is not calm.
If someone is curious or strong then john is curious or tall.
If someone is kind then someone is either not curious or rich and vice versa.
Everyone who is not wise or creative is both humble and patient.
If someone is humble then alice is either old or humble.
Everyone who is either not kind or not funny is not rich or strong and vice versa.
Everyone who is kind or not tall is not wise or brave and vice versa.
Everyone who is both not calm and patient is both calm and creative.
If lucy is generous then susan is not humble or not happy and vice versa.
Someone is not old or not humble.
Someone is not generous or generous.
Susan is not patient or not happy.
Susan is rich.
Someone is not rich or not creative.
Someone is strong.
Fred is both funny and not creative. | Lucy is old. | entailment | (![X]:((wise(X)|~humble(X))<=>(~brave(X)&quiet(X))))&
(((curious(paul)|~brave(paul)))=>((~kind(alice)|~humble(alice))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:((patient(X)<~>wise(X)))))&
((~wise(susan))<=>((~humble(fred)|funny(fred))))&
(((curious(lucy)&old(lucy)))<=>(?[X]:((~brave(X)|~funny(X)))))&
((~calm(susan))<=>((~tall(susan)&~old(susan))))&
(((~kind(paul)&~funny(paul)))<=>((~generous(lucy)<~>~creative(lucy))))&
(![X]:(~tall(X)=>~calm(X)))&
((?[X]:((curious(X)|strong(X))))=>((curious(john)|tall(john))))&
((?[X]:(kind(X)))<=>(?[X]:((~curious(X)<~>rich(X)))))&
(![X]:((~wise(X)|creative(X))=>(humble(X)&patient(X))))&
((?[X]:(humble(X)))=>((old(alice)<~>humble(alice))))&
(![X]:((~kind(X)<~>~funny(X))<=>(~rich(X)|strong(X))))&
(![X]:((kind(X)|~tall(X))<=>(~wise(X)|brave(X))))&
(![X]:((~calm(X)&patient(X))=>(calm(X)&creative(X))))&
((generous(lucy))<=>((~humble(susan)|~happy(susan))))&
(?[X]:((~old(X)|~humble(X))))&
(?[X]:((~generous(X)|generous(X))))&
((~patient(susan)|~happy(susan)))&
(rich(susan))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:(strong(X)))&
((funny(fred)&~creative(fred))) | old(lucy) | [
"p0",
"p4",
"p7",
"p10",
"p12",
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 816097376701809934930559
% SZS output start Proof for 816097376701809934930559
1. ! [X0] : ((~humble(X0) | wise(X0)) <=> (quiet(X0) & ~brave(X0))) [input p0]
5. (old(lucy) & curious(lucy)) <=> ? [X0] : (~funny(X0) | ~brave(X0)) [input p4]
8. ! [X0] : (~tall(X0) => ~calm(X0)) [input p7]
11. ! [X0] : ((creative(X0) | ~wise(X0)) => (patient(X0) & humble(X0))) [input p10]
13. ! [X0] : ((~kind(X0) <~> ~funny(X0)) <=> (strong(X0) | ~rich(X0))) [input p12]
14. ! [X0] : ((~tall(X0) | kind(X0)) <=> (brave(X0) | ~wise(X0))) [input p13]
15. ! [X0] : ((patient(X0) & ~calm(X0)) => (creative(X0) & calm(X0))) [input p14]
22. ? [X0] : strong(X0) [input p21]
24. ~old(lucy) [input hypothesis]
30. ! [X0] : (~calm(X0) | tall(X0)) [ennf transformation 8]
33. ! [X0] : ((patient(X0) & humble(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 11]
35. ! [X0] : ((creative(X0) & calm(X0)) | (~patient(X0) | calm(X0))) [ennf transformation 15]
36. ! [X0] : ((creative(X0) & calm(X0)) | ~patient(X0) | calm(X0)) [flattening 35]
37. ! [X0] : (((~humble(X0) | wise(X0)) | (~quiet(X0) | brave(X0))) & ((quiet(X0) & ~brave(X0)) | (humble(X0) & ~wise(X0)))) [nnf transformation 1]
38. ! [X0] : ((~humble(X0) | wise(X0) | ~quiet(X0) | brave(X0)) & ((quiet(X0) & ~brave(X0)) | (humble(X0) & ~wise(X0)))) [flattening 37]
45. ((old(lucy) & curious(lucy)) | ! [X0] : (funny(X0) & brave(X0))) & (? [X0] : (~funny(X0) | ~brave(X0)) | (~old(lucy) | ~curious(lucy))) [nnf transformation 5]
46. ((old(lucy) & curious(lucy)) | ! [X0] : (funny(X0) & brave(X0))) & (? [X0] : (~funny(X0) | ~brave(X0)) | ~old(lucy) | ~curious(lucy)) [flattening 45]
47. ((old(lucy) & curious(lucy)) | ! [X0] : (funny(X0) & brave(X0))) & (? [X1] : (~funny(X1) | ~brave(X1)) | ~old(lucy) | ~curious(lucy)) [rectify 46]
48. ? [X1] : (~funny(X1) | ~brave(X1)) => (~funny(sK1) | ~brave(sK1)) [choice axiom]
49. ((old(lucy) & curious(lucy)) | ! [X0] : (funny(X0) & brave(X0))) & ((~funny(sK1) | ~brave(sK1)) | ~old(lucy) | ~curious(lucy)) [skolemisation 47,48]
60. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~strong(X0) & rich(X0))) & ((strong(X0) | ~rich(X0)) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [nnf transformation 13]
61. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~strong(X0) & rich(X0))) & (strong(X0) | ~rich(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [flattening 60]
62. ! [X0] : (((~tall(X0) | kind(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (tall(X0) & ~kind(X0)))) [nnf transformation 14]
63. ! [X0] : ((~tall(X0) | kind(X0) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | (tall(X0) & ~kind(X0)))) [flattening 62]
72. ? [X0] : strong(X0) => strong(sK7) [choice axiom]
73. strong(sK7) [skolemisation 22,72]
74. ~brave(X0) | ~wise(X0) [cnf transformation 38]
89. old(lucy) | brave(X0) [cnf transformation 49]
90. old(lucy) | funny(X0) [cnf transformation 49]
100. ~calm(X0) | tall(X0) [cnf transformation 30]
109. patient(X0) | wise(X0) [cnf transformation 33]
116. ~strong(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 61]
121. ~tall(X0) | kind(X0) | wise(X0) [cnf transformation 63]
123. calm(X0) | ~patient(X0) | calm(X0) [cnf transformation 36]
133. strong(sK7) [cnf transformation 73]
136. ~old(lucy) [cnf transformation 24]
137. ~patient(X0) | calm(X0) [duplicate literal removal 123]
185. 11 <=> ! [X0] : funny(X0) [avatar definition]
186. funny(X0) <- (11) [avatar component clause 185]
188. 12 <=> old(lucy) [avatar definition]
191. 11 | 12 [avatar split clause 90,188,185]
193. 13 <=> ! [X0] : brave(X0) [avatar definition]
194. brave(X0) <- (13) [avatar component clause 193]
195. 13 | 12 [avatar split clause 89,188,193]
335. ~12 [avatar split clause 136,188]
338. ~wise(X0) <- (13) [resolution 74,194]
344. calm(X0) | wise(X0) [resolution 137,109]
345. calm(X0) <- (13) [subsumption resolution 344,338]
349. tall(X0) <- (13) [resolution 345,100]
353. ~kind(sK7) | ~funny(sK7) [resolution 116,133]
354. ~kind(sK7) <- (11) [subsumption resolution 353,186]
360. kind(X0) | wise(X0) <- (13) [resolution 121,349]
361. kind(X0) <- (13) [subsumption resolution 360,338]
366. $false <- (11, 13) [resolution 361,354]
367. ~11 | ~13 [avatar contradiction clause 366]
370. $false [avatar sat refutation 191,195,335,367]
% SZS output end Proof for 816097376701809934930559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or happy is brave or quiet.
If someone is not patient then john is both not rich and rich and vice versa.
If fred is not quiet or wise then john is not rich or funny and vice versa.
Everyone who is either rich or happy is strong or humble.
Everyone who is both curious and not quiet is not old or wise.
Everyone who is creative or not calm is brave or happy.
Everyone who is quiet or not wise is both funny and not humble and vice versa.
If someone is both not kind and wise then someone is not patient or not wise.
If someone is both tall and not creative then someone is either not strong or kind and vice versa.
Everyone who is brave or not strong is happy.
If someone is generous then susan is both kind and calm.
Everyone who is either old or not kind is generous.
If someone is both patient and not curious then alice is either not kind or not humble and vice versa.
Everyone who is either not strong or not patient is strong.
Everyone who is both strong and curious is brave or not old and vice versa.
Everyone who is both curious and not creative is tall or patient.
Susan is tall.
Someone is not funny or not strong.
Paul is strong.
Someone is brave.
Someone is both not humble and not happy.
Alice is both generous and rich. | Susan is calm. | entailment | (![X]:((~generous(X)<~>happy(X))=>(brave(X)|quiet(X))))&
((?[X]:(~patient(X)))<=>((~rich(john)&rich(john))))&
(((~quiet(fred)|wise(fred)))<=>((~rich(john)|funny(john))))&
(![X]:((rich(X)<~>happy(X))=>(strong(X)|humble(X))))&
(![X]:((curious(X)&~quiet(X))=>(~old(X)|wise(X))))&
(![X]:((creative(X)|~calm(X))=>(brave(X)|happy(X))))&
(![X]:((quiet(X)|~wise(X))<=>(funny(X)&~humble(X))))&
((?[X]:((~kind(X)&wise(X))))=>(?[X]:((~patient(X)|~wise(X)))))&
((?[X]:((tall(X)&~creative(X))))<=>(?[X]:((~strong(X)<~>kind(X)))))&
(![X]:((brave(X)|~strong(X))=>happy(X)))&
((?[X]:(generous(X)))=>((kind(susan)&calm(susan))))&
(![X]:((old(X)<~>~kind(X))=>generous(X)))&
((?[X]:((patient(X)&~curious(X))))<=>((~kind(alice)<~>~humble(alice))))&
(![X]:((~strong(X)<~>~patient(X))=>strong(X)))&
(![X]:((strong(X)&curious(X))<=>(brave(X)|~old(X))))&
(![X]:((curious(X)&~creative(X))=>(tall(X)|patient(X))))&
(tall(susan))&
(?[X]:((~funny(X)|~strong(X))))&
(strong(paul))&
(?[X]:(brave(X)))&
(?[X]:((~humble(X)&~happy(X))))&
((generous(alice)&rich(alice))) | calm(susan) | [
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 389908394798733923417775
% SZS output start Proof for 389908394798733923417775
11. ? [X0] : generous(X0) => (calm(susan) & kind(susan)) [input p10]
22. rich(alice) & generous(alice) [input p21]
23. ~calm(susan) [input hypothesis]
36. (calm(susan) & kind(susan)) | ! [X0] : ~generous(X0) [ennf transformation 11]
103. calm(susan) | ~generous(X0) [cnf transformation 36]
126. generous(alice) [cnf transformation 22]
128. ~calm(susan) [cnf transformation 23]
199. 16 <=> ! [X0] : ~generous(X0) [avatar definition]
200. ~generous(X0) <- (16) [avatar component clause 199]
202. 17 <=> calm(susan) [avatar definition]
205. 16 | 17 [avatar split clause 103,202,199]
245. ~17 [avatar split clause 128,202]
246. $false <- (16) [resolution 200,126]
247. ~16 [avatar contradiction clause 246]
248. $false [avatar sat refutation 205,245,247]
% SZS output end Proof for 389908394798733923417775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and not quiet then mary is both calm and funny and vice versa. Everyone who is either not quiet or not rich is either not patient or happy and vice versa. If john is both not funny and rich then someone is patient and vice versa. If john is both humble and funny then someone is either calm or tall and vice versa. If fred is both not humble and not patient then john is generous or not happy and vice versa. Everyone who is both not patient and strong is both not strong and not funny and vice versa. Everyone who is both not creative and funny is either patient or wise and vice versa. If mary is rich then someone is either quiet or patient and vice versa. Everyone who is kind is not happy or kind. Everyone who is both not humble and rich is both not quiet and tall. If susan is either curious or brave then lucy is both not curious and calm. Everyone who is patient is calm or not strong and vice versa. If paul is both not patient and rich then mary is either not patient or not generous. Everyone who is both not calm and not old is both calm and not old. Everyone who is not quiet or strong is either humble or funny and vice versa. Someone is either quiet or kind. Someone is either humble or not wise. Someone is calm or old. Someone is strong or not creative. Someone is either not tall or calm. Alice is both curious and calm. Someone is curious. | John is not wise. | contradiction | ((?[X]:((patient(X)&~quiet(X))))<=>((calm(mary)&funny(mary))))&
(![X]:((~quiet(X)<~>~rich(X))<=>(~patient(X)<~>happy(X))))&
(((~funny(john)&rich(john)))<=>(?[X]:(patient(X))))&
(((humble(john)&funny(john)))<=>(?[X]:((calm(X)<~>tall(X)))))&
(((~humble(fred)&~patient(fred)))<=>((generous(john)|~happy(john))))&
(![X]:((~patient(X)&strong(X))<=>(~strong(X)&~funny(X))))&
(![X]:((~creative(X)&funny(X))<=>(patient(X)<~>wise(X))))&
((rich(mary))<=>(?[X]:((quiet(X)<~>patient(X)))))&
(![X]:(kind(X)=>(~happy(X)|kind(X))))&
(![X]:((~humble(X)&rich(X))=>(~quiet(X)&tall(X))))&
(((curious(susan)<~>brave(susan)))=>((~curious(lucy)&calm(lucy))))&
(![X]:(patient(X)<=>(calm(X)|~strong(X))))&
(((~patient(paul)&rich(paul)))=>((~patient(mary)<~>~generous(mary))))&
(![X]:((~calm(X)&~old(X))=>(calm(X)&~old(X))))&
(![X]:((~quiet(X)|strong(X))<=>(humble(X)<~>funny(X))))&
(?[X]:((quiet(X)<~>kind(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:((calm(X)|old(X))))&
(?[X]:((strong(X)|~creative(X))))&
(?[X]:((~tall(X)<~>calm(X))))&
((curious(alice)&calm(alice)))&
(?[X]:(curious(X))) | ~wise(john) | [
"p2",
"p5",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 9210595555211764555768280
% SZS output start Proof for 9210595555211764555768280
3. (rich(john) & ~funny(john)) <=> ? [X0] : patient(X0) [input p2]
6. ! [X0] : ((strong(X0) & ~patient(X0)) <=> (~funny(X0) & ~strong(X0))) [input p5]
7. ! [X0] : ((funny(X0) & ~creative(X0)) <=> (patient(X0) <~> wise(X0))) [input p6]
12. ! [X0] : (patient(X0) <=> (~strong(X0) | calm(X0))) [input p11]
23. ~wise(john) [input hypothesis]
39. ((rich(john) & ~funny(john)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (~rich(john) | funny(john))) [nnf transformation 3]
40. ((rich(john) & ~funny(john)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | ~rich(john) | funny(john)) [flattening 39]
41. ((rich(john) & ~funny(john)) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | ~rich(john) | funny(john)) [rectify 40]
42. ? [X1] : patient(X1) => patient(sK1) [choice axiom]
43. ((rich(john) & ~funny(john)) | ! [X0] : ~patient(X0)) & (patient(sK1) | ~rich(john) | funny(john)) [skolemisation 41,42]
51. ! [X0] : (((strong(X0) & ~patient(X0)) | (funny(X0) | strong(X0))) & ((~funny(X0) & ~strong(X0)) | (~strong(X0) | patient(X0)))) [nnf transformation 6]
52. ! [X0] : (((strong(X0) & ~patient(X0)) | funny(X0) | strong(X0)) & ((~funny(X0) & ~strong(X0)) | ~strong(X0) | patient(X0))) [flattening 51]
53. ! [X0] : (((funny(X0) & ~creative(X0)) | ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) & (((~wise(X0) | ~patient(X0)) & (wise(X0) | patient(X0))) | (~funny(X0) | creative(X0)))) [nnf transformation 7]
54. ! [X0] : (((funny(X0) & ~creative(X0)) | ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) & (((~wise(X0) | ~patient(X0)) & (wise(X0) | patient(X0))) | ~funny(X0) | creative(X0))) [flattening 53]
60. ! [X0] : ((patient(X0) | (strong(X0) & ~calm(X0))) & ((~strong(X0) | calm(X0)) | ~patient(X0))) [nnf transformation 12]
61. ! [X0] : ((patient(X0) | (strong(X0) & ~calm(X0))) & (~strong(X0) | calm(X0) | ~patient(X0))) [flattening 60]
93. ~funny(john) | ~patient(X0) [cnf transformation 43]
106. ~strong(X0) | ~strong(X0) | patient(X0) [cnf transformation 52]
114. ~patient(X0) | wise(X0) | funny(X0) [cnf transformation 54]
129. patient(X0) | strong(X0) [cnf transformation 61]
151. ~wise(john) [cnf transformation 23]
153. ~strong(X0) | patient(X0) [duplicate literal removal 106]
179. 6 <=> ! [X0] : ~patient(X0) [avatar definition]
180. ~patient(X0) <- (6) [avatar component clause 179]
187. 8 <=> funny(john) [avatar definition]
189. ~funny(john) <- (~8) [avatar component clause 187]
190. 6 | ~8 [avatar split clause 93,187,179]
280. patient(X0) [subsumption resolution 129,153]
325. $false <- (6) [subsumption resolution 180,280]
326. ~6 [avatar contradiction clause 325]
337. wise(X0) | funny(X0) [resolution 114,280]
339. funny(john) [resolution 337,151]
344. $false <- (~8) [subsumption resolution 339,189]
345. 8 [avatar contradiction clause 344]
346. $false [avatar sat refutation 190,326,345]
% SZS output end Proof for 9210595555211764555768280
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 both not calm and not brave is either kind or not generous and vice versa.
Everyone who is both tall and not strong is either not calm or generous.
Everyone who is either strong or curious is either not curious or not old.
Everyone who is either rich or not wise is not tall and vice versa.
If fred is both not strong and funny then someone is either patient or quiet.
If susan is not happy or wise then alice is calm and vice versa.
If lucy is not wise then someone is both not tall and patient.
Everyone who is both not funny and not creative is not tall or not old and vice versa.
Everyone who is either not happy or not old is rich.
If someone is not creative or not wise then fred is not creative and vice versa.
Everyone who is both not strong and brave is tall or wise and vice versa.
Everyone who is not rich is both generous and not calm and vice versa.
If someone is either not brave or humble then susan is both calm and not generous.
Everyone who is not patient or generous is either not quiet or not rich.
Everyone who is wise or generous is not happy or old.
If someone is either not old or not kind then fred is calm and vice versa.
Someone is not wise.
Someone is both not humble and wise.
Susan is brave or not kind.
John is not rich or not brave.
Alice is not curious.
Alice is strong or not tall.
Someone is rich or kind.
Paul is both wise and not generous. | Paul is rich. | entailment | (![X]:((~calm(X)&~brave(X))<=>(kind(X)<~>~generous(X))))&
(![X]:((tall(X)&~strong(X))=>(~calm(X)<~>generous(X))))&
(![X]:((strong(X)<~>curious(X))=>(~curious(X)<~>~old(X))))&
(![X]:((rich(X)<~>~wise(X))<=>~tall(X)))&
(((~strong(fred)&funny(fred)))=>(?[X]:((patient(X)<~>quiet(X)))))&
(((~happy(susan)|wise(susan)))<=>(calm(alice)))&
((~wise(lucy))=>(?[X]:((~tall(X)&patient(X)))))&
(![X]:((~funny(X)&~creative(X))<=>(~tall(X)|~old(X))))&
(![X]:((~happy(X)<~>~old(X))=>rich(X)))&
((?[X]:((~creative(X)|~wise(X))))<=>(~creative(fred)))&
(![X]:((~strong(X)&brave(X))<=>(tall(X)|wise(X))))&
(![X]:(~rich(X)<=>(generous(X)&~calm(X))))&
((?[X]:((~brave(X)<~>humble(X))))=>((calm(susan)&~generous(susan))))&
(![X]:((~patient(X)|generous(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:((wise(X)|generous(X))=>(~happy(X)|old(X))))&
((?[X]:((~old(X)<~>~kind(X))))<=>(calm(fred)))&
(?[X]:(~wise(X)))&
(?[X]:((~humble(X)&wise(X))))&
((brave(susan)|~kind(susan)))&
((~rich(john)|~brave(john)))&
(~curious(alice))&
((strong(alice)|~tall(alice)))&
(?[X]:((rich(X)|kind(X))))&
((wise(paul)&~generous(paul))) | rich(paul) | [
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3914005157343580173232930
% SZS output start Proof for 3914005157343580173232930
12. ! [X0] : (~rich(X0) <=> (~calm(X0) & generous(X0))) [input p11]
24. ~generous(paul) & wise(paul) [input p23]
25. ~rich(paul) [input hypothesis]
58. ! [X0] : ((~rich(X0) | (calm(X0) | ~generous(X0))) & ((~calm(X0) & generous(X0)) | rich(X0))) [nnf transformation 12]
59. ! [X0] : ((~rich(X0) | calm(X0) | ~generous(X0)) & ((~calm(X0) & generous(X0)) | rich(X0))) [flattening 58]
110. rich(X0) | generous(X0) [cnf transformation 59]
136. ~generous(paul) [cnf transformation 24]
137. ~rich(paul) [cnf transformation 25]
283. generous(paul) [resolution 110,137]
284. $false [subsumption resolution 283,136]
% SZS output end Proof for 3914005157343580173232930
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If fred is brave then someone is both tall and not brave and vice versa. Everyone who is patient or calm is creative or kind and vice versa. If someone is not old or strong then someone is rich or quiet. If someone is both not strong and not brave then john is happy. If someone is not generous then lucy is either not generous or patient and vice versa. Everyone who is either not tall or not generous is both humble and not humble. If someone is not wise then someone is not old and vice versa. Everyone who is not creative is both quiet and strong and vice versa. If someone is not patient or not humble then lucy is not brave. Everyone who is not strong or rich is both not rich and curious. If someone is wise then mary is both brave and not happy and vice versa. Everyone who is both quiet and generous is not wise or calm and vice versa. Everyone who is not calm is both curious and happy and vice versa. Everyone who is quiet or not tall is not generous or not strong and vice versa. If someone is humble or not curious then someone is either not kind or not calm and vice versa. If mary is both not wise and strong then lucy is both creative and kind and vice versa. Someone is patient or happy. Someone is either tall or not old. Someone is not happy. Someone is both humble and calm. Someone is both tall and happy. Someone is generous or not kind. Susan is either not old or patient. Someone is either generous or old. | Mary is not curious. | contradiction | ((brave(fred))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)|kind(X))))&
((?[X]:((~old(X)|strong(X))))=>(?[X]:((rich(X)|quiet(X)))))&
((?[X]:((~strong(X)&~brave(X))))=>(happy(john)))&
((?[X]:(~generous(X)))<=>((~generous(lucy)<~>patient(lucy))))&
(![X]:((~tall(X)<~>~generous(X))=>(humble(X)&~humble(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(~old(X))))&
(![X]:(~creative(X)<=>(quiet(X)&strong(X))))&
((?[X]:((~patient(X)|~humble(X))))=>(~brave(lucy)))&
(![X]:((~strong(X)|rich(X))=>(~rich(X)&curious(X))))&
((?[X]:(wise(X)))<=>((brave(mary)&~happy(mary))))&
(![X]:((quiet(X)&generous(X))<=>(~wise(X)|calm(X))))&
(![X]:(~calm(X)<=>(curious(X)&happy(X))))&
(![X]:((quiet(X)|~tall(X))<=>(~generous(X)|~strong(X))))&
((?[X]:((humble(X)|~curious(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((~wise(mary)&strong(mary)))<=>((creative(lucy)&kind(lucy))))&
(?[X]:((patient(X)|happy(X))))&
(?[X]:((tall(X)<~>~old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)&calm(X))))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:((generous(X)|~kind(X))))&
((~old(susan)<~>patient(susan)))&
(?[X]:((generous(X)<~>old(X)))) | ~curious(mary) | [
"p9",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5636554350876458140357554
% SZS output start Proof for 5636554350876458140357554
10. ! [X0] : ((rich(X0) | ~strong(X0)) => (curious(X0) & ~rich(X0))) [input p9]
12. ! [X0] : ((generous(X0) & quiet(X0)) <=> (calm(X0) | ~wise(X0))) [input p11]
13. ! [X0] : (~calm(X0) <=> (happy(X0) & curious(X0))) [input p12]
14. ! [X0] : ((~tall(X0) | quiet(X0)) <=> (~strong(X0) | ~generous(X0))) [input p13]
25. ~curious(mary) [input hypothesis]
33. ! [X0] : ((curious(X0) & ~rich(X0)) | (~rich(X0) & strong(X0))) [ennf transformation 10]
60. ! [X0] : (((generous(X0) & quiet(X0)) | (~calm(X0) & wise(X0))) & ((calm(X0) | ~wise(X0)) | (~generous(X0) | ~quiet(X0)))) [nnf transformation 12]
61. ! [X0] : (((generous(X0) & quiet(X0)) | (~calm(X0) & wise(X0))) & (calm(X0) | ~wise(X0) | ~generous(X0) | ~quiet(X0))) [flattening 60]
62. ! [X0] : ((~calm(X0) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | calm(X0))) [nnf transformation 13]
63. ! [X0] : ((~calm(X0) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | calm(X0))) [flattening 62]
64. ! [X0] : (((~tall(X0) | quiet(X0)) | (strong(X0) & generous(X0))) & ((~strong(X0) | ~generous(X0)) | (tall(X0) & ~quiet(X0)))) [nnf transformation 14]
65. ! [X0] : ((~tall(X0) | quiet(X0) | (strong(X0) & generous(X0))) & (~strong(X0) | ~generous(X0) | (tall(X0) & ~quiet(X0)))) [flattening 64]
117. curious(X0) | strong(X0) [cnf transformation 33]
124. ~calm(X0) | quiet(X0) [cnf transformation 61]
126. ~calm(X0) | generous(X0) [cnf transformation 61]
127. curious(X0) | calm(X0) [cnf transformation 63]
130. ~generous(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 65]
157. ~curious(mary) [cnf transformation 25]
308. 35 <=> strong(mary) [avatar definition]
310. strong(mary) <- (35) [avatar component clause 308]
370. strong(mary) [resolution 117,157]
374. 35 [avatar split clause 370,308]
381. calm(mary) [resolution 127,157]
387. generous(mary) [resolution 381,126]
388. quiet(mary) [resolution 381,124]
654. ~strong(mary) | ~quiet(mary) [resolution 387,130]
656. ~quiet(mary) <- (35) [subsumption resolution 654,310]
657. $false <- (35) [subsumption resolution 656,388]
658. ~35 [avatar contradiction clause 657]
659. $false [avatar sat refutation 374,658]
% SZS output end Proof for 5636554350876458140357554
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If paul is tall then someone is both not calm and calm.
Everyone who is either not wise or patient is both brave and humble.
If john is both wise and happy then fred is not curious or creative and vice versa.
If mary is not humble then someone is patient or tall.
If alice is either wise or creative then paul is not patient or creative and vice versa.
If someone is both creative and calm then lucy is either tall or not humble and vice versa.
If fred is both calm and not wise then alice is not calm and vice versa.
Everyone who is either quiet or not generous is not calm and vice versa.
If someone is calm then fred is both not rich and not humble and vice versa.
Everyone who is both not kind and not calm is both brave and funny.
If susan is generous then fred is both not creative and tall and vice versa.
If fred is either not quiet or funny then someone is not rich or tall and vice versa.
Everyone who is either not old or creative is patient.
If susan is both not curious and funny then someone is either strong or funny and vice versa.
If someone is either not humble or patient then someone is both happy and not wise and vice versa.
Everyone who is both funny and rich is not generous or calm and vice versa.
Someone is generous.
Mary is tall.
Someone is not rich.
Fred is generous.
Someone is not kind.
Susan is not creative or not kind.
Alice is not curious or calm.
Paul is patient or wise. | Fred is rich. | contradiction | ((tall(paul))=>(?[X]:((~calm(X)&calm(X)))))&
(![X]:((~wise(X)<~>patient(X))=>(brave(X)&humble(X))))&
(((wise(john)&happy(john)))<=>((~curious(fred)|creative(fred))))&
((~humble(mary))=>(?[X]:((patient(X)|tall(X)))))&
(((wise(alice)<~>creative(alice)))<=>((~patient(paul)|creative(paul))))&
((?[X]:((creative(X)&calm(X))))<=>((tall(lucy)<~>~humble(lucy))))&
(((calm(fred)&~wise(fred)))<=>(~calm(alice)))&
(![X]:((quiet(X)<~>~generous(X))<=>~calm(X)))&
((?[X]:(calm(X)))<=>((~rich(fred)&~humble(fred))))&
(![X]:((~kind(X)&~calm(X))=>(brave(X)&funny(X))))&
((generous(susan))<=>((~creative(fred)&tall(fred))))&
(((~quiet(fred)<~>funny(fred)))<=>(?[X]:((~rich(X)|tall(X)))))&
(![X]:((~old(X)<~>creative(X))=>patient(X)))&
(((~curious(susan)&funny(susan)))<=>(?[X]:((strong(X)<~>funny(X)))))&
((?[X]:((~humble(X)<~>patient(X))))<=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((funny(X)&rich(X))<=>(~generous(X)|calm(X))))&
(?[X]:(generous(X)))&
(tall(mary))&
(?[X]:(~rich(X)))&
(generous(fred))&
(?[X]:(~kind(X)))&
((~creative(susan)|~kind(susan)))&
((~curious(alice)|calm(alice)))&
((patient(paul)|wise(paul))) | rich(fred) | [
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1877529587360573158278268
% SZS output start Proof for 1877529587360573158278268
7. (~wise(fred) & calm(fred)) <=> ~calm(alice) [input p6]
9. ? [X0] : calm(X0) <=> (~humble(fred) & ~rich(fred)) [input p8]
25. rich(fred) [input hypothesis]
48. ((~wise(fred) & calm(fred)) | calm(alice)) & (~calm(alice) | (wise(fred) | ~calm(fred))) [nnf transformation 7]
49. ((~wise(fred) & calm(fred)) | calm(alice)) & (~calm(alice) | wise(fred) | ~calm(fred)) [flattening 48]
51. (? [X0] : calm(X0) | (humble(fred) | rich(fred))) & ((~humble(fred) & ~rich(fred)) | ! [X0] : ~calm(X0)) [nnf transformation 9]
52. (? [X0] : calm(X0) | humble(fred) | rich(fred)) & ((~humble(fred) & ~rich(fred)) | ! [X0] : ~calm(X0)) [flattening 51]
53. (? [X0] : calm(X0) | humble(fred) | rich(fred)) & ((~humble(fred) & ~rich(fred)) | ! [X1] : ~calm(X1)) [rectify 52]
54. ? [X0] : calm(X0) => calm(sK3) [choice axiom]
55. (calm(sK3) | humble(fred) | rich(fred)) & ((~humble(fred) & ~rich(fred)) | ! [X1] : ~calm(X1)) [skolemisation 53,54]
104. calm(fred) | calm(alice) [cnf transformation 49]
110. ~rich(fred) | ~calm(X1) [cnf transformation 55]
150. rich(fred) [cnf transformation 25]
243. 19 <=> calm(alice) [avatar definition]
245. calm(alice) <- (19) [avatar component clause 243]
252. 21 <=> calm(fred) [avatar definition]
254. calm(fred) <- (21) [avatar component clause 252]
255. 19 | 21 [avatar split clause 104,252,243]
258. 22 <=> rich(fred) [avatar definition]
271. 25 <=> ! [X1] : ~calm(X1) [avatar definition]
272. ~calm(X1) <- (25) [avatar component clause 271]
274. 25 | ~22 [avatar split clause 110,258,271]
392. 22 [avatar split clause 150,258]
393. $false <- (19, 25) [subsumption resolution 245,272]
394. ~19 | ~25 [avatar contradiction clause 393]
397. $false <- (21, 25) [subsumption resolution 254,272]
398. ~21 | ~25 [avatar contradiction clause 397]
399. $false [avatar sat refutation 255,274,392,394,398]
% SZS output end Proof for 1877529587360573158278268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is 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 8557229986025677664908092
% SZS output start Proof for 8557229986025677664908092
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 8557229986025677664908092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not generous is not humble.
Everyone who is both not creative and not kind is either not rich or funny and vice versa.
Everyone who is both tall and not old is both not creative and tall.
Everyone who is either not creative or brave is both not humble and old and vice versa.
Everyone who is either not creative or not funny is either kind or patient.
Everyone who is not rich is either tall or not strong.
If someone is quiet or not happy then john is not kind or quiet.
If alice is tall then paul is wise or not calm.
Everyone who is not quiet is not brave.
Everyone who is not wise or not kind is not happy or not brave and vice versa.
If mary is both not rich and calm then someone is not patient and vice versa.
If someone is happy or calm then someone is both not generous and not curious.
If paul is not wise or funny then someone is old and vice versa.
Everyone who is both calm and tall is not generous or wise and vice versa.
If fred is not generous or creative then someone is not rich.
If someone is either quiet or not humble then john is both humble and curious.
Someone is either not old or not creative.
Mary is not creative.
Paul is both generous and not rich.
John is not old.
Alice is both old and not patient.
Paul is wise.
Susan is wise. | Paul is not strong. | contradiction | (![X]:((~funny(X)<~>~generous(X))=>~humble(X)))&
(![X]:((~creative(X)&~kind(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((tall(X)&~old(X))=>(~creative(X)&tall(X))))&
(![X]:((~creative(X)<~>brave(X))<=>(~humble(X)&old(X))))&
(![X]:((~creative(X)<~>~funny(X))=>(kind(X)<~>patient(X))))&
(![X]:(~rich(X)=>(tall(X)<~>~strong(X))))&
((?[X]:((quiet(X)|~happy(X))))=>((~kind(john)|quiet(john))))&
((tall(alice))=>((wise(paul)|~calm(paul))))&
(![X]:(~quiet(X)=>~brave(X)))&
(![X]:((~wise(X)|~kind(X))<=>(~happy(X)|~brave(X))))&
(((~rich(mary)&calm(mary)))<=>(?[X]:(~patient(X))))&
((?[X]:((happy(X)|calm(X))))=>(?[X]:((~generous(X)&~curious(X)))))&
(((~wise(paul)|funny(paul)))<=>(?[X]:(old(X))))&
(![X]:((calm(X)&tall(X))<=>(~generous(X)|wise(X))))&
(((~generous(fred)|creative(fred)))=>(?[X]:(~rich(X))))&
((?[X]:((quiet(X)<~>~humble(X))))=>((humble(john)&curious(john))))&
(?[X]:((~old(X)<~>~creative(X))))&
(~creative(mary))&
((generous(paul)&~rich(paul)))&
(~old(john))&
((old(alice)&~patient(alice)))&
(wise(paul))&
(wise(susan)) | ~strong(paul) | [
"p5",
"p13",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5721874667915239846514451
% SZS output start Proof for 5721874667915239846514451
6. ! [X0] : (~rich(X0) => (tall(X0) <~> ~strong(X0))) [input p5]
14. ! [X0] : ((tall(X0) & calm(X0)) <=> (wise(X0) | ~generous(X0))) [input p13]
19. ~rich(paul) & generous(paul) [input p18]
22. wise(paul) [input p21]
24. ~strong(paul) [input hypothesis]
30. ! [X0] : ((tall(X0) <~> ~strong(X0)) | rich(X0)) [ennf transformation 6]
45. ! [X0] : (((strong(X0) | ~tall(X0)) & (~strong(X0) | tall(X0))) | rich(X0)) [nnf transformation 30]
61. ! [X0] : (((tall(X0) & calm(X0)) | (~wise(X0) & generous(X0))) & ((wise(X0) | ~generous(X0)) | (~tall(X0) | ~calm(X0)))) [nnf transformation 14]
62. ! [X0] : (((tall(X0) & calm(X0)) | (~wise(X0) & generous(X0))) & (wise(X0) | ~generous(X0) | ~tall(X0) | ~calm(X0))) [flattening 61]
90. ~tall(X0) | strong(X0) | rich(X0) [cnf transformation 45]
113. ~wise(X0) | tall(X0) [cnf transformation 62]
124. ~rich(paul) [cnf transformation 19]
128. wise(paul) [cnf transformation 22]
130. ~strong(paul) [cnf transformation 24]
152. 6 <=> wise(paul) [avatar definition]
154. wise(paul) <- (6) [avatar component clause 152]
252. 6 [avatar split clause 128,152]
261. tall(paul) <- (6) [resolution 113,154]
290. strong(paul) | rich(paul) <- (6) [resolution 90,261]
300. rich(paul) <- (6) [subsumption resolution 290,130]
301. $false <- (6) [subsumption resolution 300,124]
302. ~6 [avatar contradiction clause 301]
303. $false [avatar sat refutation 252,302]
% SZS output end Proof for 5721874667915239846514451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 generous is not patient or calm. If someone is tall or not strong then fred is either creative or not strong and vice versa. If someone is either rich or calm then mary is either patient or not funny and vice versa. Everyone who is either rich or not tall is both kind and not funny. If someone is both old and not curious then someone is both not patient and curious. Everyone who is not generous or not kind is either not old or not tall. Everyone who is not brave is both not calm and creative. If mary is either not quiet or not wise then alice is tall. If someone is both not happy and not tall then john is either not wise or generous and vice versa. Everyone who is both old and not kind is both kind and happy. Everyone who is either wise or happy is both not brave and old and vice versa. If lucy is calm then alice is not rich. Everyone who is quiet or creative is happy and vice versa. Everyone who is either funny or wise is either quiet or rich and vice versa. Everyone who is both not wise and not happy is not calm and vice versa. Everyone who is either old or not kind is either not curious or wise and vice versa. Someone is either quiet or tall. Susan is not kind. Lucy is both not quiet and brave. Fred is either rich or creative. Someone is not old. Mary is either not humble or old. Someone is both curious and not happy. Someone is not curious or not kind. | Susan is old. | contradiction | (![X]:(generous(X)=>(~patient(X)|calm(X))))&
((?[X]:((tall(X)|~strong(X))))<=>((creative(fred)<~>~strong(fred))))&
((?[X]:((rich(X)<~>calm(X))))<=>((patient(mary)<~>~funny(mary))))&
(![X]:((rich(X)<~>~tall(X))=>(kind(X)&~funny(X))))&
((?[X]:((old(X)&~curious(X))))=>(?[X]:((~patient(X)&curious(X)))))&
(![X]:((~generous(X)|~kind(X))=>(~old(X)<~>~tall(X))))&
(![X]:(~brave(X)=>(~calm(X)&creative(X))))&
(((~quiet(mary)<~>~wise(mary)))=>(tall(alice)))&
((?[X]:((~happy(X)&~tall(X))))<=>((~wise(john)<~>generous(john))))&
(![X]:((old(X)&~kind(X))=>(kind(X)&happy(X))))&
(![X]:((wise(X)<~>happy(X))<=>(~brave(X)&old(X))))&
((calm(lucy))=>(~rich(alice)))&
(![X]:((quiet(X)|creative(X))<=>happy(X)))&
(![X]:((funny(X)<~>wise(X))<=>(quiet(X)<~>rich(X))))&
(![X]:((~wise(X)&~happy(X))<=>~calm(X)))&
(![X]:((old(X)<~>~kind(X))<=>(~curious(X)<~>wise(X))))&
(?[X]:((quiet(X)<~>tall(X))))&
(~kind(susan))&
((~quiet(lucy)&brave(lucy)))&
((rich(fred)<~>creative(fred)))&
(?[X]:(~old(X)))&
((~humble(mary)<~>old(mary)))&
(?[X]:((curious(X)&~happy(X))))&
(?[X]:((~curious(X)|~kind(X)))) | old(susan) | [
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1138721214360944864935511
% SZS output start Proof for 1138721214360944864935511
10. ! [X0] : ((~kind(X0) & old(X0)) => (happy(X0) & kind(X0))) [input p9]
18. ~kind(susan) [input p17]
25. old(susan) [input hypothesis]
34. ! [X0] : ((happy(X0) & kind(X0)) | (kind(X0) | ~old(X0))) [ennf transformation 10]
35. ! [X0] : ((happy(X0) & kind(X0)) | kind(X0) | ~old(X0)) [flattening 34]
109. kind(X0) | kind(X0) | ~old(X0) [cnf transformation 35]
142. ~kind(susan) [cnf transformation 18]
153. old(susan) [cnf transformation 25]
154. ~old(X0) | kind(X0) [duplicate literal removal 109]
323. kind(susan) [resolution 154,153]
324. $false [subsumption resolution 323,142]
% SZS output end Proof for 1138721214360944864935511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 either kind or strong then someone is generous and vice versa.
If paul is either patient or not creative then someone is both not rich and funny and vice versa.
If someone is patient then someone is either not funny or funny.
If someone is generous then mary is brave or not rich and vice versa.
If someone is both not brave and humble then someone is not strong or not humble.
Everyone who is either patient or creative is both old and quiet.
Everyone who is both not happy and generous is not calm and vice versa.
Everyone who is not strong is kind or old and vice versa.
Everyone who is kind or old is quiet and vice versa.
Everyone who is both not humble and funny is either not generous or creative and vice versa.
Everyone who is funny or generous is not quiet.
If someone is either tall or kind then fred is calm.
Everyone who is wise or not patient is not generous.
If fred is both quiet and not quiet then mary is happy and vice versa.
Everyone who is both rich and not wise is either not calm or not old and vice versa.
If lucy is brave or old then lucy is either rich or humble.
Someone is not humble or humble.
Fred is both generous and rich.
Alice is both not funny and not strong.
Mary is either humble or wise.
Lucy is both rich and old.
Someone is tall or quiet.
Someone is not old or funny.
Someone is not wise or strong. | Lucy is generous. | contradiction | ((?[X]:((kind(X)<~>strong(X))))<=>(?[X]:(generous(X))))&
(((patient(paul)<~>~creative(paul)))<=>(?[X]:((~rich(X)&funny(X)))))&
((?[X]:(patient(X)))=>(?[X]:((~funny(X)<~>funny(X)))))&
((?[X]:(generous(X)))<=>((brave(mary)|~rich(mary))))&
((?[X]:((~brave(X)&humble(X))))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((patient(X)<~>creative(X))=>(old(X)&quiet(X))))&
(![X]:((~happy(X)&generous(X))<=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(![X]:((rich(X)&~wise(X))<=>(~calm(X)<~>~old(X))))&
(((brave(lucy)|old(lucy)))=>((rich(lucy)<~>humble(lucy))))&
(?[X]:((~humble(X)|humble(X))))&
((generous(fred)&rich(fred)))&
((~funny(alice)&~strong(alice)))&
((humble(mary)<~>wise(mary)))&
((rich(lucy)&old(lucy)))&
(?[X]:((tall(X)|quiet(X))))&
(?[X]:((~old(X)|funny(X))))&
(?[X]:((~wise(X)|strong(X)))) | generous(lucy) | [
"p8",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2177589437003112973860161
% SZS output start Proof for 2177589437003112973860161
9. ! [X0] : ((old(X0) | kind(X0)) <=> quiet(X0)) [input p8]
11. ! [X0] : ((generous(X0) | funny(X0)) => ~quiet(X0)) [input p10]
21. old(lucy) & rich(lucy) [input p20]
25. generous(lucy) [input hypothesis]
32. ! [X0] : (~quiet(X0) | (~generous(X0) & ~funny(X0))) [ennf transformation 11]
62. ! [X0] : (((old(X0) | kind(X0)) | ~quiet(X0)) & (quiet(X0) | (~old(X0) & ~kind(X0)))) [nnf transformation 9]
63. ! [X0] : ((old(X0) | kind(X0) | ~quiet(X0)) & (quiet(X0) | (~old(X0) & ~kind(X0)))) [flattening 62]
108. ~old(X0) | quiet(X0) [cnf transformation 63]
117. ~quiet(X0) | ~generous(X0) [cnf transformation 32]
143. old(lucy) [cnf transformation 21]
147. generous(lucy) [cnf transformation 25]
248. 23 <=> old(lucy) [avatar definition]
249. old(lucy) <- (23) [avatar component clause 248]
277. 23 [avatar split clause 143,248]
308. quiet(lucy) <- (23) [resolution 108,249]
312. ~generous(lucy) <- (23) [resolution 117,308]
313. $false <- (23) [subsumption resolution 312,147]
314. ~23 [avatar contradiction clause 313]
315. $false [avatar sat refutation 277,314]
% SZS output end Proof for 2177589437003112973860161
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 funny is both not happy and not tall.
If lucy is either not generous or old then mary is not curious and vice versa.
If someone is both happy and not humble then fred is not tall or generous.
Everyone who is kind or humble is both tall and generous.
Everyone who is either funny or kind is not rich or not quiet and vice versa.
If alice is not curious or not rich then someone is both happy and generous and vice versa.
Everyone who is both not funny and not kind is not quiet or curious and vice versa.
Everyone who is happy or kind is both not wise and funny and vice versa.
If someone is either not calm or brave then someone is tall or not generous and vice versa.
Everyone who is wise or not brave is either not tall or wise and vice versa.
If someone is either not kind or rich then someone is not patient or calm and vice versa.
If someone is strong then mary is not funny or not creative.
If someone is calm then someone is not generous and vice versa.
Everyone who is both strong and not calm is curious.
Everyone who is not wise is kind and vice versa.
Everyone who is curious or not strong is either strong or patient.
Someone is quiet or generous.
Susan is funny or wise.
Someone is either not humble or not calm.
Someone is quiet or not wise.
John is both tall and patient.
Someone is either calm or not calm.
Alice is both not creative and patient.
Someone is not generous or patient. | Alice is not calm. | entailment | (![X]:((brave(X)|funny(X))=>(~happy(X)&~tall(X))))&
(((~generous(lucy)<~>old(lucy)))<=>(~curious(mary)))&
((?[X]:((happy(X)&~humble(X))))=>((~tall(fred)|generous(fred))))&
(![X]:((kind(X)|humble(X))=>(tall(X)&generous(X))))&
(![X]:((funny(X)<~>kind(X))<=>(~rich(X)|~quiet(X))))&
(((~curious(alice)|~rich(alice)))<=>(?[X]:((happy(X)&generous(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(~quiet(X)|curious(X))))&
(![X]:((happy(X)|kind(X))<=>(~wise(X)&funny(X))))&
((?[X]:((~calm(X)<~>brave(X))))<=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:((wise(X)|~brave(X))<=>(~tall(X)<~>wise(X))))&
((?[X]:((~kind(X)<~>rich(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
((?[X]:(strong(X)))=>((~funny(mary)|~creative(mary))))&
((?[X]:(calm(X)))<=>(?[X]:(~generous(X))))&
(![X]:((strong(X)&~calm(X))=>curious(X)))&
(![X]:(~wise(X)<=>kind(X)))&
(![X]:((curious(X)|~strong(X))=>(strong(X)<~>patient(X))))&
(?[X]:((quiet(X)|generous(X))))&
((funny(susan)|wise(susan)))&
(?[X]:((~humble(X)<~>~calm(X))))&
(?[X]:((quiet(X)|~wise(X))))&
((tall(john)&patient(john)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~creative(alice)&patient(alice)))&
(?[X]:((~generous(X)|patient(X)))) | ~calm(alice) | [
"p0",
"p3",
"p4",
"p7",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1573272257710660056964449
% SZS output start Proof for 1573272257710660056964449
1. ! [X0] : ((funny(X0) | brave(X0)) => (~tall(X0) & ~happy(X0))) [input p0]
4. ! [X0] : ((humble(X0) | kind(X0)) => (generous(X0) & tall(X0))) [input p3]
5. ! [X0] : ((funny(X0) <~> kind(X0)) <=> (~quiet(X0) | ~rich(X0))) [input p4]
8. ! [X0] : ((kind(X0) | happy(X0)) <=> (funny(X0) & ~wise(X0))) [input p7]
10. ! [X0] : ((~brave(X0) | wise(X0)) <=> (~tall(X0) <~> wise(X0))) [input p9]
11. ? [X0] : (~kind(X0) <~> rich(X0)) <=> ? [X0] : (calm(X0) | ~patient(X0)) [input p10]
15. ! [X0] : (~wise(X0) <=> kind(X0)) [input p14]
25. calm(alice) [input hypothesis]
27. ? [X0] : (~kind(X0) <~> rich(X0)) <=> ? [X1] : (calm(X1) | ~patient(X1)) [rectify 11]
31. ! [X0] : ((~tall(X0) & ~happy(X0)) | (~funny(X0) & ~brave(X0))) [ennf transformation 1]
34. ! [X0] : ((generous(X0) & tall(X0)) | (~humble(X0) & ~kind(X0))) [ennf transformation 4]
39. ! [X0] : ((((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))))) [nnf transformation 5]
40. ! [X0] : ((((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))))) [flattening 39]
48. ! [X0] : (((kind(X0) | happy(X0)) | (~funny(X0) | wise(X0))) & ((funny(X0) & ~wise(X0)) | (~kind(X0) & ~happy(X0)))) [nnf transformation 8]
49. ! [X0] : ((kind(X0) | happy(X0) | ~funny(X0) | wise(X0)) & ((funny(X0) & ~wise(X0)) | (~kind(X0) & ~happy(X0)))) [flattening 48]
55. ! [X0] : (((~brave(X0) | wise(X0)) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0)))) & (((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | (brave(X0) & ~wise(X0)))) [nnf transformation 10]
56. ! [X0] : ((~brave(X0) | wise(X0) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0)))) & (((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | (brave(X0) & ~wise(X0)))) [flattening 55]
57. (? [X0] : ((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | ! [X1] : (~calm(X1) & patient(X1))) & (? [X1] : (calm(X1) | ~patient(X1)) | ! [X0] : ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) [nnf transformation 27]
58. (? [X0] : ((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | ! [X1] : (~calm(X1) & patient(X1))) & (? [X2] : (calm(X2) | ~patient(X2)) | ! [X3] : ((~kind(X3) | ~rich(X3)) & (rich(X3) | kind(X3)))) [rectify 57]
59. ? [X0] : ((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) => ((~rich(sK3) | kind(sK3)) & (rich(sK3) | ~kind(sK3))) [choice axiom]
60. ? [X2] : (calm(X2) | ~patient(X2)) => (calm(sK4) | ~patient(sK4)) [choice axiom]
61. (((~rich(sK3) | kind(sK3)) & (rich(sK3) | ~kind(sK3))) | ! [X1] : (~calm(X1) & patient(X1))) & ((calm(sK4) | ~patient(sK4)) | ! [X3] : ((~kind(X3) | ~rich(X3)) & (rich(X3) | kind(X3)))) [skolemisation 58,60,59]
67. ! [X0] : ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))) [nnf transformation 15]
84. ~tall(X0) | ~funny(X0) [cnf transformation 31]
90. ~kind(X0) | tall(X0) [cnf transformation 34]
96. rich(X0) | funny(X0) | kind(X0) [cnf transformation 40]
113. ~kind(X0) | funny(X0) [cnf transformation 49]
123. ~wise(X0) | tall(X0) | ~wise(X0) [cnf transformation 56]
132. ~rich(sK3) | kind(sK3) | ~calm(X1) [cnf transformation 61]
136. wise(X0) | kind(X0) [cnf transformation 67]
153. calm(alice) [cnf transformation 25]
155. ~wise(X0) | tall(X0) [duplicate literal removal 123]
249. 20 <=> ! [X1] : ~calm(X1) [avatar definition]
250. ~calm(X1) <- (20) [avatar component clause 249]
252. 21 <=> kind(sK3) [avatar definition]
253. ~kind(sK3) <- (~21) [avatar component clause 252]
254. kind(sK3) <- (21) [avatar component clause 252]
256. 22 <=> rich(sK3) [avatar definition]
258. ~rich(sK3) <- (~22) [avatar component clause 256]
259. 20 | 21 | ~22 [avatar split clause 132,256,252,249]
357. tall(X0) | kind(X0) [resolution 155,136]
358. tall(X0) [subsumption resolution 357,90]
360. ~funny(X0) [resolution 358,84]
368. funny(sK3) | kind(sK3) <- (~22) [resolution 96,258]
369. kind(sK3) <- (~22) [subsumption resolution 368,360]
370. $false <- (~21, ~22) [subsumption resolution 369,253]
371. 21 | 22 [avatar contradiction clause 370]
372. funny(sK3) <- (21) [resolution 254,113]
377. $false <- (21) [subsumption resolution 372,360]
378. ~21 [avatar contradiction clause 377]
379. $false <- (20) [resolution 250,153]
382. ~20 [avatar contradiction clause 379]
383. $false [avatar sat refutation 259,371,378,382]
% SZS output end Proof for 1573272257710660056964449
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not funny then susan is both not wise and not happy.
Everyone who is either generous or happy is old.
If paul is either tall or not strong then susan is both rich and not humble.
Everyone who is either creative or not quiet is both old and curious and vice versa.
Everyone who is either brave or wise is both strong and not rich and vice versa.
Everyone who is both not creative and kind is both funny and calm and vice versa.
If someone is both strong and not curious then someone is both not happy and quiet.
If susan is kind or not rich then paul is not patient and vice versa.
Everyone who is not old is strong or not humble and vice versa.
Everyone who is tall is not kind and vice versa.
Everyone who is both not old and not generous is not patient and vice versa.
If mary is funny then fred is either funny or brave.
If someone is either not curious or brave then john is either not humble or calm.
Everyone who is wise is not creative or not strong and vice versa.
Everyone who is either wise or not patient is curious or not calm.
If someone is both wise and not curious then someone is either curious or humble.
Paul is either not humble or strong.
Someone is not rich or happy.
Someone is calm or not curious.
Paul is either funny or rich.
Lucy is not calm.
Paul is not brave. | Lucy is not happy. | neutral | ((~funny(mary))=>((~wise(susan)&~happy(susan))))&
(![X]:((generous(X)<~>happy(X))=>old(X)))&
(((tall(paul)<~>~strong(paul)))=>((rich(susan)&~humble(susan))))&
(![X]:((creative(X)<~>~quiet(X))<=>(old(X)&curious(X))))&
(![X]:((brave(X)<~>wise(X))<=>(strong(X)&~rich(X))))&
(![X]:((~creative(X)&kind(X))<=>(funny(X)&calm(X))))&
((?[X]:((strong(X)&~curious(X))))=>(?[X]:((~happy(X)&quiet(X)))))&
(((kind(susan)|~rich(susan)))<=>(~patient(paul)))&
(![X]:(~old(X)<=>(strong(X)|~humble(X))))&
(![X]:(tall(X)<=>~kind(X)))&
(![X]:((~old(X)&~generous(X))<=>~patient(X)))&
((funny(mary))=>((funny(fred)<~>brave(fred))))&
((?[X]:((~curious(X)<~>brave(X))))=>((~humble(john)<~>calm(john))))&
(![X]:(wise(X)<=>(~creative(X)|~strong(X))))&
(![X]:((wise(X)<~>~patient(X))=>(curious(X)|~calm(X))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((curious(X)<~>humble(X)))))&
((~humble(paul)<~>strong(paul)))&
(?[X]:((~rich(X)|happy(X))))&
(?[X]:((calm(X)|~curious(X))))&
((funny(paul)<~>rich(paul)))&
(~calm(lucy))&
(~brave(paul)) | ~happy(lucy) | [] | null | 0 |
Everyone who is either old or not happy is both curious and not funny and vice versa. If fred is quiet then someone is not strong or kind. Everyone who is both not curious and not humble is humble and vice versa. Everyone who is wise is not tall. If someone is either quiet or not strong then someone is either tall or quiet. Everyone who is not happy is both creative and not rich. If someone is calm then someone is both strong and funny and vice versa. If john is not rich then paul is either not happy or kind. If alice is not rich then susan is creative or generous. If john is both not happy and generous then someone is either not happy or brave. If lucy is both not calm and strong then someone is either humble or tall. If someone is either not strong or tall then lucy is both not old and not humble and vice versa. If fred is kind then someone is either not creative or not brave. Everyone who is kind or tall is both not curious and funny and vice versa. Everyone who is either humble or quiet is both humble and not kind and vice versa. If susan is both not humble and not generous then alice is either creative or wise and vice versa. Alice is either funny or wise. Someone is both calm and not funny. Paul is curious or not strong. Mary is either brave or wise. Alice is either brave or curious. Paul is both calm and funny. | John is not strong. | contradiction | (![X]:((old(X)<~>~happy(X))<=>(curious(X)&~funny(X))))&
((quiet(fred))=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:((~curious(X)&~humble(X))<=>humble(X)))&
(![X]:(wise(X)=>~tall(X)))&
((?[X]:((quiet(X)<~>~strong(X))))=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:(~happy(X)=>(creative(X)&~rich(X))))&
((?[X]:(calm(X)))<=>(?[X]:((strong(X)&funny(X)))))&
((~rich(john))=>((~happy(paul)<~>kind(paul))))&
((~rich(alice))=>((creative(susan)|generous(susan))))&
(((~happy(john)&generous(john)))=>(?[X]:((~happy(X)<~>brave(X)))))&
(((~calm(lucy)&strong(lucy)))=>(?[X]:((humble(X)<~>tall(X)))))&
((?[X]:((~strong(X)<~>tall(X))))<=>((~old(lucy)&~humble(lucy))))&
((kind(fred))=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((kind(X)|tall(X))<=>(~curious(X)&funny(X))))&
(![X]:((humble(X)<~>quiet(X))<=>(humble(X)&~kind(X))))&
(((~humble(susan)&~generous(susan)))<=>((creative(alice)<~>wise(alice))))&
((funny(alice)<~>wise(alice)))&
(?[X]:((calm(X)&~funny(X))))&
((curious(paul)|~strong(paul)))&
((brave(mary)<~>wise(mary)))&
((brave(alice)<~>curious(alice)))&
((calm(paul)&funny(paul))) | ~strong(john) | [
"p2",
"p4",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1003743686169057220121811
% SZS output start Proof for 1003743686169057220121811
3. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> humble(X0)) [input p2]
5. ? [X0] : (quiet(X0) <~> ~strong(X0)) => ? [X0] : (tall(X0) <~> quiet(X0)) [input p4]
14. ! [X0] : ((tall(X0) | kind(X0)) <=> (funny(X0) & ~curious(X0))) [input p13]
15. ! [X0] : ((humble(X0) <~> quiet(X0)) <=> (~kind(X0) & humble(X0))) [input p14]
23. ~strong(john) [input hypothesis]
24. ? [X0] : (quiet(X0) <~> ~strong(X0)) => ? [X1] : (tall(X1) <~> quiet(X1)) [rectify 5]
28. ? [X1] : (tall(X1) <~> quiet(X1)) | ! [X0] : (quiet(X0) <=> ~strong(X0)) [ennf transformation 24]
42. ! [X0] : (((~humble(X0) & ~curious(X0)) | ~humble(X0)) & (humble(X0) | (humble(X0) | curious(X0)))) [nnf transformation 3]
43. ! [X0] : (((~humble(X0) & ~curious(X0)) | ~humble(X0)) & (humble(X0) | humble(X0) | curious(X0))) [flattening 42]
44. ? [X1] : ((~quiet(X1) | ~tall(X1)) & (quiet(X1) | tall(X1))) | ! [X0] : ((quiet(X0) | strong(X0)) & (~strong(X0) | ~quiet(X0))) [nnf transformation 28]
45. ? [X0] : ((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | ! [X1] : ((quiet(X1) | strong(X1)) & (~strong(X1) | ~quiet(X1))) [rectify 44]
46. ? [X0] : ((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) => ((~quiet(sK1) | ~tall(sK1)) & (quiet(sK1) | tall(sK1))) [choice axiom]
47. ((~quiet(sK1) | ~tall(sK1)) & (quiet(sK1) | tall(sK1))) | ! [X1] : ((quiet(X1) | strong(X1)) & (~strong(X1) | ~quiet(X1))) [skolemisation 45,46]
68. ! [X0] : (((tall(X0) | kind(X0)) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | (~tall(X0) & ~kind(X0)))) [nnf transformation 14]
69. ! [X0] : ((tall(X0) | kind(X0) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | (~tall(X0) & ~kind(X0)))) [flattening 68]
70. ! [X0] : ((((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | (kind(X0) | ~humble(X0))) & ((~kind(X0) & humble(X0)) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0))))) [nnf transformation 15]
71. ! [X0] : ((((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | kind(X0) | ~humble(X0)) & ((~kind(X0) & humble(X0)) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0))))) [flattening 70]
86. humble(X0) | humble(X0) | curious(X0) [cnf transformation 43]
88. ~humble(X0) | ~humble(X0) [cnf transformation 43]
91. quiet(sK1) | tall(sK1) | quiet(X1) | strong(X1) [cnf transformation 47]
115. ~curious(X0) | ~tall(X0) [cnf transformation 69]
120. humble(X0) | humble(X0) | ~quiet(X0) [cnf transformation 71]
142. ~strong(john) [cnf transformation 23]
143. humble(X0) | ~quiet(X0) [duplicate literal removal 120]
145. humble(X0) | curious(X0) [duplicate literal removal 86]
146. ~humble(X0) [duplicate literal removal 88]
160. curious(X0) [subsumption resolution 145,146]
162. 4 <=> ! [X1] : (quiet(X1) | strong(X1)) [avatar definition]
163. quiet(X1) | strong(X1) <- (4) [avatar component clause 162]
165. 5 <=> tall(sK1) [avatar definition]
166. tall(sK1) <- (5) [avatar component clause 165]
169. 6 <=> quiet(sK1) [avatar definition]
170. quiet(sK1) <- (6) [avatar component clause 169]
177. 4 | 5 | 6 [avatar split clause 91,169,165,162]
297. ~tall(X0) [subsumption resolution 115,160]
299. ~quiet(X0) [subsumption resolution 143,146]
331. $false <- (5) [subsumption resolution 166,297]
332. ~5 [avatar contradiction clause 331]
333. $false <- (6) [subsumption resolution 170,299]
334. ~6 [avatar contradiction clause 333]
335. strong(X1) <- (4) [subsumption resolution 163,299]
340. $false <- (4) [resolution 335,142]
347. ~4 [avatar contradiction clause 340]
348. $false [avatar sat refutation 177,332,334,347]
% SZS output end Proof for 1003743686169057220121811
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 lucy is either not humble or not curious then alice is either quiet or strong and vice versa.
If fred is calm then lucy is either not curious or calm and vice versa.
Everyone who is old or tall is both tall and quiet and vice versa.
If lucy is happy then susan is both not strong and curious.
Everyone who is brave is happy and vice versa.
If someone is either quiet or not creative then alice is rich or not old.
Everyone who is both not humble and generous is either not creative or calm.
Everyone who is not humble is either not quiet or wise and vice versa.
Everyone who is generous is both not generous and funny and vice versa.
Everyone who is humble or calm is wise or not humble.
If someone is curious or not strong then someone is both humble and strong.
If susan is not patient or humble then mary is not creative or creative.
Everyone who is both wise and not old is not tall or kind and vice versa.
Everyone who is old or not humble is rich or not creative and vice versa.
Everyone who is either not curious or funny is not patient or curious and vice versa.
Everyone who is either rich or funny is both not strong and tall.
Someone is not quiet or funny.
Someone is not curious.
Someone is creative.
John is either quiet or calm.
Someone is not curious or not old.
Alice is both not tall and not kind. | Fred is rich. | neutral | (((~humble(lucy)<~>~curious(lucy)))<=>((quiet(alice)<~>strong(alice))))&
((calm(fred))<=>((~curious(lucy)<~>calm(lucy))))&
(![X]:((old(X)|tall(X))<=>(tall(X)&quiet(X))))&
((happy(lucy))=>((~strong(susan)&curious(susan))))&
(![X]:(brave(X)<=>happy(X)))&
((?[X]:((quiet(X)<~>~creative(X))))=>((rich(alice)|~old(alice))))&
(![X]:((~humble(X)&generous(X))=>(~creative(X)<~>calm(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>wise(X))))&
(![X]:(generous(X)<=>(~generous(X)&funny(X))))&
(![X]:((humble(X)|calm(X))=>(wise(X)|~humble(X))))&
((?[X]:((curious(X)|~strong(X))))=>(?[X]:((humble(X)&strong(X)))))&
(((~patient(susan)|humble(susan)))=>((~creative(mary)|creative(mary))))&
(![X]:((wise(X)&~old(X))<=>(~tall(X)|kind(X))))&
(![X]:((old(X)|~humble(X))<=>(rich(X)|~creative(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(~patient(X)|curious(X))))&
(![X]:((rich(X)<~>funny(X))=>(~strong(X)&tall(X))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:(~curious(X)))&
(?[X]:(creative(X)))&
((quiet(john)<~>calm(john)))&
(?[X]:((~curious(X)|~old(X))))&
((~tall(alice)&~kind(alice))) | rich(fred) | [] | null | 0 |
Everyone who is generous or not curious is both not quiet and creative and vice versa.
Everyone who is either not happy or wise is generous and vice versa.
If lucy is either not rich or not tall then someone is either generous or not funny and vice versa.
Everyone who is either not generous or not creative is both kind and not brave and vice versa.
Everyone who is both not rich and calm is both not wise and happy and vice versa.
If someone is both curious and creative then fred is not patient or not old.
If paul is both strong and not old then someone is patient and vice versa.
Everyone who is either not kind or not wise is either not curious or old and vice versa.
If someone is both not generous and not calm then someone is not rich or not patient.
Everyone who is both not calm and rich is either not rich or not wise and vice versa.
If someone is either not creative or old then someone is either humble or not wise and vice versa.
If mary is not kind then alice is generous.
If alice is not calm then lucy is both not humble and not old and vice versa.
If someone is both not generous and not old then someone is rich.
If alice is calm then paul is both creative and rich.
Everyone who is both not wise and wise is both kind and not rich.
Paul is both patient and not old.
Someone is either happy or calm.
Alice is happy.
Susan is strong.
Susan is humble.
Someone is either not humble or not strong.
Lucy is not patient.
Someone is either strong or not curious. | Paul is not rich. | contradiction | (![X]:((generous(X)|~curious(X))<=>(~quiet(X)&creative(X))))&
(![X]:((~happy(X)<~>wise(X))<=>generous(X)))&
(((~rich(lucy)<~>~tall(lucy)))<=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:((~generous(X)<~>~creative(X))<=>(kind(X)&~brave(X))))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)&happy(X))))&
((?[X]:((curious(X)&creative(X))))=>((~patient(fred)|~old(fred))))&
(((strong(paul)&~old(paul)))<=>(?[X]:(patient(X))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~curious(X)<~>old(X))))&
((?[X]:((~generous(X)&~calm(X))))=>(?[X]:((~rich(X)|~patient(X)))))&
(![X]:((~calm(X)&rich(X))<=>(~rich(X)<~>~wise(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((humble(X)<~>~wise(X)))))&
((~kind(mary))=>(generous(alice)))&
((~calm(alice))<=>((~humble(lucy)&~old(lucy))))&
((?[X]:((~generous(X)&~old(X))))=>(?[X]:(rich(X))))&
((calm(alice))=>((creative(paul)&rich(paul))))&
(![X]:((~wise(X)&wise(X))=>(kind(X)&~rich(X))))&
((patient(paul)&~old(paul)))&
(?[X]:((happy(X)<~>calm(X))))&
(happy(alice))&
(strong(susan))&
(humble(susan))&
(?[X]:((~humble(X)<~>~strong(X))))&
(~patient(lucy))&
(?[X]:((strong(X)<~>~curious(X)))) | ~rich(paul) | [
"p4",
"p9",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5764617926692753543347313
% SZS output start Proof for 5764617926692753543347313
5. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (happy(X0) & ~wise(X0))) [input p4]
10. ! [X0] : ((rich(X0) & ~calm(X0)) <=> (~rich(X0) <~> ~wise(X0))) [input p9]
15. calm(alice) => (rich(paul) & creative(paul)) [input p14]
19. happy(alice) [input p18]
25. ~rich(paul) [input hypothesis]
34. (rich(paul) & creative(paul)) | ~calm(alice) [ennf transformation 15]
46. ! [X0] : (((calm(X0) & ~rich(X0)) | (~happy(X0) | wise(X0))) & ((happy(X0) & ~wise(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 5]
47. ! [X0] : (((calm(X0) & ~rich(X0)) | ~happy(X0) | wise(X0)) & ((happy(X0) & ~wise(X0)) | ~calm(X0) | rich(X0))) [flattening 46]
57. ! [X0] : (((rich(X0) & ~calm(X0)) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | (~rich(X0) | calm(X0)))) [nnf transformation 10]
58. ! [X0] : (((rich(X0) & ~calm(X0)) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | ~rich(X0) | calm(X0))) [flattening 57]
104. ~happy(X0) | calm(X0) | wise(X0) [cnf transformation 47]
118. ~wise(X0) | ~rich(X0) | ~rich(X0) | calm(X0) [cnf transformation 58]
122. rich(X0) | ~wise(X0) | rich(X0) [cnf transformation 58]
138. rich(paul) | ~calm(alice) [cnf transformation 34]
145. happy(alice) [cnf transformation 19]
153. ~rich(paul) [cnf transformation 25]
154. ~wise(X0) | ~rich(X0) | calm(X0) [duplicate literal removal 118]
155. ~wise(X0) | rich(X0) [duplicate literal removal 122]
230. ~wise(X0) | calm(X0) [subsumption resolution 154,155]
285. 29 <=> calm(alice) [avatar definition]
287. ~calm(alice) <- (~29) [avatar component clause 285]
300. 32 <=> rich(paul) [avatar definition]
303. ~29 | 32 [avatar split clause 138,300,285]
340. ~32 [avatar split clause 153,300]
373. 42 <=> wise(alice) [avatar definition]
375. wise(alice) <- (42) [avatar component clause 373]
415. calm(alice) | wise(alice) [resolution 104,145]
417. wise(alice) <- (~29) [subsumption resolution 415,287]
418. 42 | 29 [avatar split clause 417,285,373]
426. calm(alice) <- (42) [resolution 375,230]
431. $false <- (~29, 42) [subsumption resolution 426,287]
432. 29 | ~42 [avatar contradiction clause 431]
433. $false [avatar sat refutation 303,340,418,432]
% SZS output end Proof for 5764617926692753543347313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and kind is creative and vice versa. Everyone who is not old is not brave and vice versa. Everyone who is both not old and wise is rich or not old. If someone is not brave or not patient then fred is old and vice versa. If lucy is not creative then fred is not wise and vice versa. Everyone who is brave or not tall is calm or not rich and vice versa. 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. If someone is either creative or wise then john is not tall or tall 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. Everyone who is both rich and strong is tall or not tall and vice versa. Fred is happy or brave. Someone is not kind or not tall. Mary is both not humble and brave. Someone is not patient. Someone is both humble and not wise. Lucy is either not humble or funny. | Fred is not brave. | contradiction | (![X]:((~curious(X)&kind(X))<=>creative(X)))&
(![X]:(~old(X)<=>~brave(X)))&
(![X]:((~old(X)&wise(X))=>(rich(X)|~old(X))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(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]:((creative(X)<~>wise(X))))<=>((~tall(john)|tall(john))))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((rich(X)&strong(X))<=>(tall(X)|~tall(X))))&
((happy(fred)|brave(fred)))&
(?[X]:((~kind(X)|~tall(X))))&
((~humble(mary)&brave(mary)))&
(?[X]:(~patient(X)))&
(?[X]:((humble(X)&~wise(X))))&
((~humble(lucy)<~>funny(lucy))) | ~brave(fred) | [
"p1",
"p3",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6515515567012032238866050
% SZS output start Proof for 6515515567012032238866050
2. ! [X0] : (~old(X0) <=> ~brave(X0)) [input p1]
4. ? [X0] : (~patient(X0) | ~brave(X0)) <=> old(fred) [input p3]
20. ? [X0] : ~patient(X0) [input p19]
23. ~brave(fred) [input hypothesis]
35. ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0))) [nnf transformation 2]
36. (? [X0] : (~patient(X0) | ~brave(X0)) | ~old(fred)) & (old(fred) | ! [X0] : (patient(X0) & brave(X0))) [nnf transformation 4]
37. (? [X0] : (~patient(X0) | ~brave(X0)) | ~old(fred)) & (old(fred) | ! [X1] : (patient(X1) & brave(X1))) [rectify 36]
38. ? [X0] : (~patient(X0) | ~brave(X0)) => (~patient(sK0) | ~brave(sK0)) [choice axiom]
39. ((~patient(sK0) | ~brave(sK0)) | ~old(fred)) & (old(fred) | ! [X1] : (patient(X1) & brave(X1))) [skolemisation 37,38]
62. ? [X0] : ~patient(X0) => ~patient(sK5) [choice axiom]
63. ~patient(sK5) [skolemisation 20,62]
71. ~old(X0) | brave(X0) [cnf transformation 35]
74. old(fred) | patient(X1) [cnf transformation 39]
125. ~patient(sK5) [cnf transformation 63]
130. ~brave(fred) [cnf transformation 23]
134. 1 <=> old(fred) [avatar definition]
135. old(fred) <- (1) [avatar component clause 134]
147. 4 <=> ! [X1] : patient(X1) [avatar definition]
148. patient(X1) <- (4) [avatar component clause 147]
149. 4 | 1 [avatar split clause 74,134,147]
239. 24 <=> brave(fred) [avatar definition]
240. ~brave(fred) <- (~24) [avatar component clause 239]
262. ~24 [avatar split clause 130,239]
265. $false <- (4) [resolution 148,125]
266. ~4 [avatar contradiction clause 265]
274. brave(fred) <- (1) [resolution 71,135]
275. $false <- (1, ~24) [subsumption resolution 274,240]
276. ~1 | 24 [avatar contradiction clause 275]
277. $false [avatar sat refutation 149,262,266,276]
% SZS output end Proof for 6515515567012032238866050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is not generous and vice versa.
Everyone who is not tall or not calm is both old and not strong and vice versa.
Everyone who is not creative is both humble and old.
If mary is not strong or not humble then john is either not strong or calm.
If alice is either calm or tall then paul is curious and vice versa.
Everyone who is either not quiet or not rich is both curious and not brave.
If someone is not old or not quiet then someone is not funny or generous and vice versa.
Everyone who is both not creative and patient is not humble or not funny.
If john is creative or old then fred is both kind and brave and vice versa.
Everyone who is both old and curious is both not wise and old and vice versa.
Everyone who is not strong or funny is either quiet or not humble and vice versa.
If someone is either wise or not strong then lucy is humble or brave.
If mary is either old or humble then someone is either not calm or creative and vice versa.
Everyone who is not wise is both strong and wise and vice versa.
If john is both brave and not creative then someone is creative and vice versa.
If someone is both happy and not tall then john is either kind or quiet and vice versa.
Susan is creative.
Someone is both quiet and not strong.
John is either not creative or creative.
Someone is both quiet and not patient.
Someone is both happy and creative.
Someone is both tall and rich.
Someone is creative. | Susan is brave. | neutral | (![X]:(~happy(X)<=>~generous(X)))&
(![X]:((~tall(X)|~calm(X))<=>(old(X)&~strong(X))))&
(![X]:(~creative(X)=>(humble(X)&old(X))))&
(((~strong(mary)|~humble(mary)))=>((~strong(john)<~>calm(john))))&
(((calm(alice)<~>tall(alice)))<=>(curious(paul)))&
(![X]:((~quiet(X)<~>~rich(X))=>(curious(X)&~brave(X))))&
((?[X]:((~old(X)|~quiet(X))))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((~creative(X)&patient(X))=>(~humble(X)|~funny(X))))&
(((creative(john)|old(john)))<=>((kind(fred)&brave(fred))))&
(![X]:((old(X)&curious(X))<=>(~wise(X)&old(X))))&
(![X]:((~strong(X)|funny(X))<=>(quiet(X)<~>~humble(X))))&
((?[X]:((wise(X)<~>~strong(X))))=>((humble(lucy)|brave(lucy))))&
(((old(mary)<~>humble(mary)))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:(~wise(X)<=>(strong(X)&wise(X))))&
(((brave(john)&~creative(john)))<=>(?[X]:(creative(X))))&
((?[X]:((happy(X)&~tall(X))))<=>((kind(john)<~>quiet(john))))&
(creative(susan))&
(?[X]:((quiet(X)&~strong(X))))&
((~creative(john)<~>creative(john)))&
(?[X]:((quiet(X)&~patient(X))))&
(?[X]:((happy(X)&creative(X))))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:(creative(X))) | brave(susan) | [] | null | 0 |
Everyone who is both not brave and not calm is patient. Everyone who is generous or calm is old and vice versa. If someone is either not rich or not generous then someone is both not happy and old and vice versa. Everyone who is curious or not rich is either not humble or not quiet and vice versa. If alice is curious then someone is either generous or curious and vice versa. Everyone who is both not generous and not quiet is not calm and vice versa. Everyone who is either not patient or tall is not creative. If lucy is not quiet or not calm then someone is rich or strong and vice versa. If fred is calm or not generous then susan is quiet or not creative and vice versa. If someone is not generous then someone is either not wise or not happy and vice versa. If someone is not curious or not kind then someone is both not happy and humble and vice versa. Everyone who is not funny or old is quiet. Everyone who is both not quiet and quiet is either patient or not old and vice versa. Everyone who is creative is either not brave or not old and vice versa. If mary is both happy and generous then someone is not curious or humble and vice versa. If someone is either kind or not old then someone is both not creative and tall. Lucy is not patient or not humble. Someone is not quiet or strong. Fred is both not funny and not wise. Someone is curious. Paul is patient. Mary is not old or not humble. Fred is either not strong or funny. Someone is not generous or not tall. | Fred is not calm. | contradiction | (![X]:((~brave(X)&~calm(X))=>patient(X)))&
(![X]:((generous(X)|calm(X))<=>old(X)))&
((?[X]:((~rich(X)<~>~generous(X))))<=>(?[X]:((~happy(X)&old(X)))))&
(![X]:((curious(X)|~rich(X))<=>(~humble(X)<~>~quiet(X))))&
((curious(alice))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((~generous(X)&~quiet(X))<=>~calm(X)))&
(![X]:((~patient(X)<~>tall(X))=>~creative(X)))&
(((~quiet(lucy)|~calm(lucy)))<=>(?[X]:((rich(X)|strong(X)))))&
(((calm(fred)|~generous(fred)))<=>((quiet(susan)|~creative(susan))))&
((?[X]:(~generous(X)))<=>(?[X]:((~wise(X)<~>~happy(X)))))&
((?[X]:((~curious(X)|~kind(X))))<=>(?[X]:((~happy(X)&humble(X)))))&
(![X]:((~funny(X)|old(X))=>quiet(X)))&
(![X]:((~quiet(X)&quiet(X))<=>(patient(X)<~>~old(X))))&
(![X]:(creative(X)<=>(~brave(X)<~>~old(X))))&
(((happy(mary)&generous(mary)))<=>(?[X]:((~curious(X)|humble(X)))))&
((?[X]:((kind(X)<~>~old(X))))=>(?[X]:((~creative(X)&tall(X)))))&
((~patient(lucy)|~humble(lucy)))&
(?[X]:((~quiet(X)|strong(X))))&
((~funny(fred)&~wise(fred)))&
(?[X]:(curious(X)))&
(patient(paul))&
((~old(mary)|~humble(mary)))&
((~strong(fred)<~>funny(fred)))&
(?[X]:((~generous(X)|~tall(X)))) | ~calm(fred) | [
"p5",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2840128968327701475463298
% SZS output start Proof for 2840128968327701475463298
6. ! [X0] : ((~quiet(X0) & ~generous(X0)) <=> ~calm(X0)) [input p5]
12. ! [X0] : ((old(X0) | ~funny(X0)) => quiet(X0)) [input p11]
19. ~wise(fred) & ~funny(fred) [input p18]
25. ~calm(fred) [input hypothesis]
33. ! [X0] : (quiet(X0) | (~old(X0) & funny(X0))) [ennf transformation 12]
48. ! [X0] : (((~quiet(X0) & ~generous(X0)) | calm(X0)) & (~calm(X0) | (quiet(X0) | generous(X0)))) [nnf transformation 6]
49. ! [X0] : (((~quiet(X0) & ~generous(X0)) | calm(X0)) & (~calm(X0) | quiet(X0) | generous(X0))) [flattening 48]
109. ~quiet(X0) | calm(X0) [cnf transformation 49]
129. funny(X0) | quiet(X0) [cnf transformation 33]
152. ~funny(fred) [cnf transformation 19]
160. ~calm(fred) [cnf transformation 25]
256. 22 <=> calm(fred) [avatar definition]
258. ~calm(fred) <- (~22) [avatar component clause 256]
397. ~22 [avatar split clause 160,256]
421. quiet(fred) [resolution 129,152]
422. calm(fred) [resolution 421,109]
423. $false <- (~22) [subsumption resolution 422,258]
424. 22 [avatar contradiction clause 423]
425. $false [avatar sat refutation 397,424]
% SZS output end Proof for 2840128968327701475463298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either not quiet or not funny then mary is funny.
Everyone who is not rich or humble is both brave and tall.
Everyone who is not strong is generous or not rich and vice versa.
If someone is both not tall and not calm then someone is calm.
Everyone who is calm or not brave is quiet.
If someone is both quiet and not brave then someone is either not funny or patient and vice versa.
Everyone who is both not rich and not curious is not funny or strong and vice versa.
If someone is quiet then john is either tall or not tall and vice versa.
If paul is both not creative and kind then susan is either kind or generous and vice versa.
Everyone who is both not rich and rich is humble.
If susan is either wise or old then john is not quiet and vice versa.
Everyone who is curious is either not strong or generous and vice versa.
Everyone who is not happy or not old is tall.
If mary is not rich or wise then someone is not kind and vice versa.
Everyone who is wise or not generous is either old or not strong and vice versa.
Everyone who is brave or patient is both funny and not kind and vice versa.
Mary is not kind or generous.
Someone is not rich.
Someone is curious or not kind.
Someone is both old and generous.
Someone is not wise or not strong.
Someone is not generous or calm. | Paul is not humble. | neutral | ((?[X]:((~quiet(X)<~>~funny(X))))=>(funny(mary)))&
(![X]:((~rich(X)|humble(X))=>(brave(X)&tall(X))))&
(![X]:(~strong(X)<=>(generous(X)|~rich(X))))&
((?[X]:((~tall(X)&~calm(X))))=>(?[X]:(calm(X))))&
(![X]:((calm(X)|~brave(X))=>quiet(X)))&
((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((~rich(X)&~curious(X))<=>(~funny(X)|strong(X))))&
((?[X]:(quiet(X)))<=>((tall(john)<~>~tall(john))))&
(((~creative(paul)&kind(paul)))<=>((kind(susan)<~>generous(susan))))&
(![X]:((~rich(X)&rich(X))=>humble(X)))&
(((wise(susan)<~>old(susan)))<=>(~quiet(john)))&
(![X]:(curious(X)<=>(~strong(X)<~>generous(X))))&
(![X]:((~happy(X)|~old(X))=>tall(X)))&
(((~rich(mary)|wise(mary)))<=>(?[X]:(~kind(X))))&
(![X]:((wise(X)|~generous(X))<=>(old(X)<~>~strong(X))))&
(![X]:((brave(X)|patient(X))<=>(funny(X)&~kind(X))))&
((~kind(mary)|generous(mary)))&
(?[X]:(~rich(X)))&
(?[X]:((curious(X)|~kind(X))))&
(?[X]:((old(X)&generous(X))))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((~generous(X)|calm(X)))) | ~humble(paul) | [] | null | 0 |
Everyone who is either not happy or strong is both happy and calm.
Everyone who is either not brave or not strong is quiet.
Everyone who is both calm and not humble is not happy and vice versa.
If paul is wise then someone is either generous or patient.
Everyone who is not creative or not funny is not brave or rich.
Everyone who is calm is not funny.
Everyone who is not tall is creative or funny and vice versa.
Everyone who is both not curious and funny is generous or not calm and vice versa.
If someone is not wise then paul is not generous.
Everyone who is both curious and humble is both brave and not patient.
Everyone who is either not humble or not brave is either not kind or strong and vice versa.
Everyone who is not funny or happy is not brave or quiet and vice versa.
If paul is not patient then someone is either creative or curious and vice versa.
If john is both not generous and not creative then someone is both quiet and not funny and vice versa.
If someone is not calm then alice is quiet or wise and vice versa.
John is either curious or not happy.
Susan is both strong and calm.
Lucy is both not old and curious. | Paul is not wise. | neutral | (![X]:((~happy(X)<~>strong(X))=>(happy(X)&calm(X))))&
(![X]:((~brave(X)<~>~strong(X))=>quiet(X)))&
(![X]:((calm(X)&~humble(X))<=>~happy(X)))&
((wise(paul))=>(?[X]:((generous(X)<~>patient(X)))))&
(![X]:((~creative(X)|~funny(X))=>(~brave(X)|rich(X))))&
(![X]:(calm(X)=>~funny(X)))&
(![X]:(~tall(X)<=>(creative(X)|funny(X))))&
(![X]:((~curious(X)&funny(X))<=>(generous(X)|~calm(X))))&
((?[X]:(~wise(X)))=>(~generous(paul)))&
(![X]:((curious(X)&humble(X))=>(brave(X)&~patient(X))))&
(![X]:((~humble(X)<~>~brave(X))<=>(~kind(X)<~>strong(X))))&
(![X]:((~funny(X)|happy(X))<=>(~brave(X)|quiet(X))))&
((~patient(paul))<=>(?[X]:((creative(X)<~>curious(X)))))&
(((~generous(john)&~creative(john)))<=>(?[X]:((quiet(X)&~funny(X)))))&
((?[X]:(~calm(X)))<=>((quiet(alice)|wise(alice))))&
((curious(john)<~>~happy(john)))&
((strong(susan)&calm(susan)))&
((~old(lucy)&curious(lucy))) | ~wise(paul) | [] | null | 0 |
Everyone who is old is either happy or humble and vice versa.
If lucy is strong or generous then mary is both generous and not wise.
Everyone who is not brave or strong is either strong or not calm and vice versa.
Everyone who is either not rich or not happy is either not brave or not old.
Everyone who is not creative or rich is not curious.
If someone is both not funny and rich then someone is kind or not creative and vice versa.
Everyone who is not brave or not old is both not kind and kind and vice versa.
If someone is both not calm and old then mary is both not kind and not creative and vice versa.
If someone is both not quiet and not funny then someone is not brave or not kind.
Everyone who is patient is both not generous and not tall.
Everyone who is both not strong and tall is both not funny and not rich.
Everyone who is either calm or not brave is calm and vice versa.
Everyone who is either not curious or happy is kind and vice versa.
If someone is brave or not tall then someone is either kind or creative.
Everyone who is either not quiet or tall is humble and vice versa.
Everyone who is both tall and not old is both happy and strong.
John is either not tall or tall.
Alice is both wise and curious.
Someone is either not curious or not wise.
Someone is either creative or not curious.
Someone is either patient or not creative.
Someone is kind.
Someone is funny or not creative.
Alice is either not rich or tall. | Mary is not old. | contradiction | (![X]:(old(X)<=>(happy(X)<~>humble(X))))&
(((strong(lucy)|generous(lucy)))=>((generous(mary)&~wise(mary))))&
(![X]:((~brave(X)|strong(X))<=>(strong(X)<~>~calm(X))))&
(![X]:((~rich(X)<~>~happy(X))=>(~brave(X)<~>~old(X))))&
(![X]:((~creative(X)|rich(X))=>~curious(X)))&
((?[X]:((~funny(X)&rich(X))))<=>(?[X]:((kind(X)|~creative(X)))))&
(![X]:((~brave(X)|~old(X))<=>(~kind(X)&kind(X))))&
((?[X]:((~calm(X)&old(X))))<=>((~kind(mary)&~creative(mary))))&
((?[X]:((~quiet(X)&~funny(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:(patient(X)=>(~generous(X)&~tall(X))))&
(![X]:((~strong(X)&tall(X))=>(~funny(X)&~rich(X))))&
(![X]:((calm(X)<~>~brave(X))<=>calm(X)))&
(![X]:((~curious(X)<~>happy(X))<=>kind(X)))&
((?[X]:((brave(X)|~tall(X))))=>(?[X]:((kind(X)<~>creative(X)))))&
(![X]:((~quiet(X)<~>tall(X))<=>humble(X)))&
(![X]:((tall(X)&~old(X))=>(happy(X)&strong(X))))&
((~tall(john)<~>tall(john)))&
((wise(alice)&curious(alice)))&
(?[X]:((~curious(X)<~>~wise(X))))&
(?[X]:((creative(X)<~>~curious(X))))&
(?[X]:((patient(X)<~>~creative(X))))&
(?[X]:(kind(X)))&
(?[X]:((funny(X)|~creative(X))))&
((~rich(alice)<~>tall(alice))) | ~old(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8814978763487486572529445
% SZS output start Proof for 8814978763487486572529445
7. ! [X0] : ((~old(X0) | ~brave(X0)) <=> (kind(X0) & ~kind(X0))) [input p6]
25. ~old(mary) [input hypothesis]
48. ! [X0] : (((~old(X0) | ~brave(X0)) | (~kind(X0) | kind(X0))) & ((kind(X0) & ~kind(X0)) | (old(X0) & brave(X0)))) [nnf transformation 7]
49. ! [X0] : ((~old(X0) | ~brave(X0) | ~kind(X0) | kind(X0)) & ((kind(X0) & ~kind(X0)) | (old(X0) & brave(X0)))) [flattening 48]
106. ~kind(X0) | old(X0) [cnf transformation 49]
108. kind(X0) | old(X0) [cnf transformation 49]
151. ~old(mary) [cnf transformation 25]
206. old(X0) [subsumption resolution 106,108]
302. $false [subsumption resolution 151,206]
% SZS output end Proof for 8814978763487486572529445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not patient is not brave.
If someone is generous or calm then someone is both curious and not calm and vice versa.
If someone is not calm or not generous then someone is either not quiet or happy and vice versa.
Everyone who is both patient and quiet is patient and vice versa.
Everyone who is both tall and not kind is either not tall or not generous and vice versa.
If someone is humble or not wise then someone is either calm or curious and vice versa.
Everyone who is not curious is not tall.
Everyone who is not kind or not strong is both happy and not happy.
If someone is either generous or old then someone is either not humble or funny.
Everyone who is both quiet and brave is wise or not quiet.
If someone is not happy then someone is either not rich or not patient and vice versa.
Everyone who is not creative or patient is patient.
If someone is either old or curious then someone is rich.
Everyone who is old or not brave is tall.
Everyone who is tall or not strong is both not kind and kind and vice versa.
If someone is wise or calm then someone is not calm and vice versa.
Someone is patient.
Someone is wise or not patient.
Susan is either not strong or not curious.
Someone is both brave and calm.
Fred is either not humble or not creative.
Alice is either tall or patient. | Alice is tall. | contradiction | (![X]:((~generous(X)&~patient(X))=>~brave(X)))&
((?[X]:((generous(X)|calm(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
((?[X]:((~calm(X)|~generous(X))))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((patient(X)&quiet(X))<=>patient(X)))&
(![X]:((tall(X)&~kind(X))<=>(~tall(X)<~>~generous(X))))&
((?[X]:((humble(X)|~wise(X))))<=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:(~curious(X)=>~tall(X)))&
(![X]:((~kind(X)|~strong(X))=>(happy(X)&~happy(X))))&
((?[X]:((generous(X)<~>old(X))))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((quiet(X)&brave(X))=>(wise(X)|~quiet(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
(![X]:((~creative(X)|patient(X))=>patient(X)))&
((?[X]:((old(X)<~>curious(X))))=>(?[X]:(rich(X))))&
(![X]:((old(X)|~brave(X))=>tall(X)))&
(![X]:((tall(X)|~strong(X))<=>(~kind(X)&kind(X))))&
((?[X]:((wise(X)|calm(X))))<=>(?[X]:(~calm(X))))&
(?[X]:(patient(X)))&
(?[X]:((wise(X)|~patient(X))))&
((~strong(susan)<~>~curious(susan)))&
(?[X]:((brave(X)&calm(X))))&
((~humble(fred)<~>~creative(fred)))&
((tall(alice)<~>patient(alice))) | tall(alice) | [
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5920794957477226065979425
% SZS output start Proof for 5920794957477226065979425
8. ! [X0] : ((~strong(X0) | ~kind(X0)) => (~happy(X0) & happy(X0))) [input p7]
15. ! [X0] : ((~strong(X0) | tall(X0)) <=> (kind(X0) & ~kind(X0))) [input p14]
23. tall(alice) [input hypothesis]
34. ! [X0] : ((~happy(X0) & happy(X0)) | (strong(X0) & kind(X0))) [ennf transformation 8]
73. ! [X0] : (((~strong(X0) | tall(X0)) | (~kind(X0) | kind(X0))) & ((kind(X0) & ~kind(X0)) | (strong(X0) & ~tall(X0)))) [nnf transformation 15]
74. ! [X0] : ((~strong(X0) | tall(X0) | ~kind(X0) | kind(X0)) & ((kind(X0) & ~kind(X0)) | (strong(X0) & ~tall(X0)))) [flattening 73]
117. happy(X0) | kind(X0) [cnf transformation 34]
119. ~happy(X0) | kind(X0) [cnf transformation 34]
136. ~kind(X0) | ~tall(X0) [cnf transformation 74]
154. tall(alice) [cnf transformation 23]
255. kind(X0) [subsumption resolution 117,119]
311. ~tall(X0) [subsumption resolution 136,255]
351. $false [subsumption resolution 154,311]
% SZS output end Proof for 5920794957477226065979425
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and quiet is not calm or not brave and vice versa.
If lucy is both quiet and kind then someone is both not curious and not wise and vice versa.
Everyone who is both brave and rich is not patient.
If someone is both kind and curious then alice is both not kind and creative.
If someone is both brave and rich then fred is not rich and vice versa.
Everyone who is both rich and funny is not creative or not quiet and vice versa.
Everyone who is not generous is creative and vice versa.
Everyone who is both not funny and not brave is both not patient and not generous.
Everyone who is calm or kind is both humble and not strong and vice versa.
Everyone who is not brave or not funny is either not kind or not creative and vice versa.
Everyone who is both happy and not strong is either not generous or generous and vice versa.
Everyone who is both curious and not generous is either not kind or patient and vice versa.
If someone is either curious or not brave then someone is not kind or patient and vice versa.
Everyone who is both not funny and generous is either wise or not curious.
If someone is calm then someone is not happy or tall.
Fred is not strong or curious.
Paul is either not funny or kind.
Fred is not strong.
Susan is happy or not funny. | Fred is patient. | neutral | (![X]:((~creative(X)&quiet(X))<=>(~calm(X)|~brave(X))))&
(((quiet(lucy)&kind(lucy)))<=>(?[X]:((~curious(X)&~wise(X)))))&
(![X]:((brave(X)&rich(X))=>~patient(X)))&
((?[X]:((kind(X)&curious(X))))=>((~kind(alice)&creative(alice))))&
((?[X]:((brave(X)&rich(X))))<=>(~rich(fred)))&
(![X]:((rich(X)&funny(X))<=>(~creative(X)|~quiet(X))))&
(![X]:(~generous(X)<=>creative(X)))&
(![X]:((~funny(X)&~brave(X))=>(~patient(X)&~generous(X))))&
(![X]:((calm(X)|kind(X))<=>(humble(X)&~strong(X))))&
(![X]:((~brave(X)|~funny(X))<=>(~kind(X)<~>~creative(X))))&
(![X]:((happy(X)&~strong(X))<=>(~generous(X)<~>generous(X))))&
(![X]:((curious(X)&~generous(X))<=>(~kind(X)<~>patient(X))))&
((?[X]:((curious(X)<~>~brave(X))))<=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:((~funny(X)&generous(X))=>(wise(X)<~>~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~happy(X)|tall(X)))))&
((~strong(fred)|curious(fred)))&
((~funny(paul)<~>kind(paul)))&
(~strong(fred))&
((happy(susan)|~funny(susan))) | patient(fred) | [] | null | 0 |
Everyone who is funny is quiet.
If lucy is not patient then someone is tall or happy and vice versa.
Everyone who is both not wise and wise is either kind or not calm.
Everyone who is either calm or not wise is both not patient and humble and vice versa.
If lucy is funny or not patient then someone is not funny or rich and vice versa.
If someone is calm then someone is funny or old and vice versa.
Everyone who is not rich is not humble and vice versa.
Everyone who is either patient or not patient is either not tall or not creative.
Everyone who is not brave or not calm is either calm or quiet and vice versa.
If someone is both patient and not tall then susan is both not quiet and happy and vice versa.
Everyone who is both not happy and not curious is not curious or tall and vice versa.
Everyone who is either humble or brave is both not humble and curious.
If someone is calm then someone is curious and vice versa.
If someone is both not patient and wise then someone is either funny or not tall.
If someone is either tall or not rich then lucy is both not calm and not quiet and vice versa.
If someone is not quiet or not curious then john is either not patient or funny.
Susan is both humble and not calm.
Lucy is either not curious or quiet.
Fred is both calm and not patient.
Paul is both not curious and not tall.
Alice is either kind or not curious.
Lucy is curious or quiet.
Someone is either tall or kind.
Paul is not tall. | Lucy is brave. | entailment | (![X]:(funny(X)=>quiet(X)))&
((~patient(lucy))<=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((~wise(X)&wise(X))=>(kind(X)<~>~calm(X))))&
(![X]:((calm(X)<~>~wise(X))<=>(~patient(X)&humble(X))))&
(((funny(lucy)|~patient(lucy)))<=>(?[X]:((~funny(X)|rich(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((funny(X)|old(X)))))&
(![X]:(~rich(X)<=>~humble(X)))&
(![X]:((patient(X)<~>~patient(X))=>(~tall(X)<~>~creative(X))))&
(![X]:((~brave(X)|~calm(X))<=>(calm(X)<~>quiet(X))))&
((?[X]:((patient(X)&~tall(X))))<=>((~quiet(susan)&happy(susan))))&
(![X]:((~happy(X)&~curious(X))<=>(~curious(X)|tall(X))))&
(![X]:((humble(X)<~>brave(X))=>(~humble(X)&curious(X))))&
((?[X]:(calm(X)))<=>(?[X]:(curious(X))))&
((?[X]:((~patient(X)&wise(X))))=>(?[X]:((funny(X)<~>~tall(X)))))&
((?[X]:((tall(X)<~>~rich(X))))<=>((~calm(lucy)&~quiet(lucy))))&
((?[X]:((~quiet(X)|~curious(X))))=>((~patient(john)<~>funny(john))))&
((humble(susan)&~calm(susan)))&
((~curious(lucy)<~>quiet(lucy)))&
((calm(fred)&~patient(fred)))&
((~curious(paul)&~tall(paul)))&
((kind(alice)<~>~curious(alice)))&
((curious(lucy)|quiet(lucy)))&
(?[X]:((tall(X)<~>kind(X))))&
(~tall(paul)) | brave(lucy) | [
"p6",
"p10",
"p11",
"p14",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 971748505588457021558227
% SZS output start Proof for 971748505588457021558227
7. ! [X0] : (~rich(X0) <=> ~humble(X0)) [input p6]
11. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> (tall(X0) | ~curious(X0))) [input p10]
12. ! [X0] : ((humble(X0) <~> brave(X0)) => (curious(X0) & ~humble(X0))) [input p11]
15. ? [X0] : (tall(X0) <~> ~rich(X0)) <=> (~quiet(lucy) & ~calm(lucy)) [input p14]
18. ~curious(lucy) <~> quiet(lucy) [input p17]
22. quiet(lucy) | curious(lucy) [input p21]
25. ~brave(lucy) [input hypothesis]
33. ! [X0] : ((curious(X0) & ~humble(X0)) | (humble(X0) <=> brave(X0))) [ennf transformation 12]
53. ! [X0] : ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))) [nnf transformation 7]
62. ! [X0] : (((~curious(X0) & ~happy(X0)) | (~tall(X0) & curious(X0))) & ((tall(X0) | ~curious(X0)) | (curious(X0) | happy(X0)))) [nnf transformation 11]
63. ! [X0] : (((~curious(X0) & ~happy(X0)) | (~tall(X0) & curious(X0))) & (tall(X0) | ~curious(X0) | curious(X0) | happy(X0))) [flattening 62]
64. ! [X0] : ((curious(X0) & ~humble(X0)) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) [nnf transformation 33]
74. (? [X0] : ((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | (quiet(lucy) | calm(lucy))) & ((~quiet(lucy) & ~calm(lucy)) | ! [X0] : ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) [nnf transformation 15]
75. (? [X0] : ((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | quiet(lucy) | calm(lucy)) & ((~quiet(lucy) & ~calm(lucy)) | ! [X0] : ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) [flattening 74]
76. (? [X0] : ((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | quiet(lucy) | calm(lucy)) & ((~quiet(lucy) & ~calm(lucy)) | ! [X1] : ((tall(X1) | rich(X1)) & (~rich(X1) | ~tall(X1)))) [rectify 75]
77. ? [X0] : ((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) => ((rich(sK8) | ~tall(sK8)) & (~rich(sK8) | tall(sK8))) [choice axiom]
78. (((rich(sK8) | ~tall(sK8)) & (~rich(sK8) | tall(sK8))) | quiet(lucy) | calm(lucy)) & ((~quiet(lucy) & ~calm(lucy)) | ! [X1] : ((tall(X1) | rich(X1)) & (~rich(X1) | ~tall(X1)))) [skolemisation 76,77]
80. (~quiet(lucy) | curious(lucy)) & (quiet(lucy) | ~curious(lucy)) [nnf transformation 18]
105. ~rich(X0) | humble(X0) [cnf transformation 53]
124. ~curious(X0) | ~tall(X0) [cnf transformation 63]
125. ~humble(X0) | brave(X0) | ~humble(X0) [cnf transformation 64]
136. ~quiet(lucy) | tall(X1) | rich(X1) [cnf transformation 78]
145. quiet(lucy) | ~curious(lucy) [cnf transformation 80]
146. ~quiet(lucy) | curious(lucy) [cnf transformation 80]
153. quiet(lucy) | curious(lucy) [cnf transformation 22]
157. ~brave(lucy) [cnf transformation 25]
158. ~humble(X0) | brave(X0) [duplicate literal removal 125]
284. 28 <=> ! [X1] : (tall(X1) | rich(X1)) [avatar definition]
285. rich(X1) | tall(X1) <- (28) [avatar component clause 284]
287. 29 <=> quiet(lucy) [avatar definition]
290. 28 | ~29 [avatar split clause 136,287,284]
320. 36 <=> curious(lucy) [avatar definition]
322. curious(lucy) <- (36) [avatar component clause 320]
323. 36 | ~29 [avatar split clause 146,287,320]
324. ~36 | 29 [avatar split clause 145,287,320]
335. 36 | 29 [avatar split clause 153,287,320]
357. ~tall(lucy) <- (36) [resolution 124,322]
370. humble(X0) | tall(X0) <- (28) [resolution 285,105]
462. brave(X1) | tall(X1) <- (28) [resolution 370,158]
467. tall(lucy) <- (28) [resolution 462,157]
470. $false <- (28, 36) [subsumption resolution 467,357]
471. ~28 | ~36 [avatar contradiction clause 470]
473. $false [avatar sat refutation 290,323,324,335,471]
% SZS output end Proof for 971748505588457021558227
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not happy and happy then alice is kind or not generous.
If someone is either creative or funny then susan is not happy.
Everyone who is either not brave or not humble is either strong or not tall and vice versa.
Everyone who is strong or rich is not creative and vice versa.
If john is both funny and brave then fred is not brave or not rich.
If someone is both not kind and not tall then someone is not curious and vice versa.
If mary is happy or not funny then lucy is not kind and vice versa.
If someone is not quiet or rich then someone is not patient or not old.
Everyone who is brave is both not kind and old.
If someone is either not funny or not rich then someone is both kind and not kind.
If someone is both not brave and brave then lucy is quiet or brave and vice versa.
If lucy is not funny then susan is both calm and kind.
If susan is not curious then someone is both not quiet and tall and vice versa.
Everyone who is either curious or calm is either calm or not curious.
Everyone who is both kind and patient is either not calm or strong and vice versa.
Everyone who is both not brave and calm is brave and vice versa.
Someone is either not kind or patient.
Someone is either not wise or old.
Someone is either not generous or not funny.
John is creative or not kind.
Someone is either old or calm.
Someone is either strong or old.
Someone is humble. | Lucy is not creative. | entailment | (((~happy(fred)&happy(fred)))=>((kind(alice)|~generous(alice))))&
((?[X]:((creative(X)<~>funny(X))))=>(~happy(susan)))&
(![X]:((~brave(X)<~>~humble(X))<=>(strong(X)<~>~tall(X))))&
(![X]:((strong(X)|rich(X))<=>~creative(X)))&
(((funny(john)&brave(john)))=>((~brave(fred)|~rich(fred))))&
((?[X]:((~kind(X)&~tall(X))))<=>(?[X]:(~curious(X))))&
(((happy(mary)|~funny(mary)))<=>(~kind(lucy)))&
((?[X]:((~quiet(X)|rich(X))))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:(brave(X)=>(~kind(X)&old(X))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(?[X]:((kind(X)&~kind(X)))))&
((?[X]:((~brave(X)&brave(X))))<=>((quiet(lucy)|brave(lucy))))&
((~funny(lucy))=>((calm(susan)&kind(susan))))&
((~curious(susan))<=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((curious(X)<~>calm(X))=>(calm(X)<~>~curious(X))))&
(![X]:((kind(X)&patient(X))<=>(~calm(X)<~>strong(X))))&
(![X]:((~brave(X)&calm(X))<=>brave(X)))&
(?[X]:((~kind(X)<~>patient(X))))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((~generous(X)<~>~funny(X))))&
((creative(john)|~kind(john)))&
(?[X]:((old(X)<~>calm(X))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:(humble(X))) | ~creative(lucy) | [
"p3",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2975831551973674084261696
% SZS output start Proof for 2975831551973674084261696
4. ! [X0] : ((rich(X0) | strong(X0)) <=> ~creative(X0)) [input p3]
10. ? [X0] : (~funny(X0) <~> ~rich(X0)) => ? [X0] : (~kind(X0) & kind(X0)) [input p9]
12. ~funny(lucy) => (kind(susan) & calm(susan)) [input p11]
16. ! [X0] : ((calm(X0) & ~brave(X0)) <=> brave(X0)) [input p15]
24. creative(lucy) [input hypothesis]
27. ? [X0] : (~funny(X0) <~> ~rich(X0)) => ? [X1] : (~kind(X1) & kind(X1)) [rectify 10]
35. ? [X1] : (~kind(X1) & kind(X1)) | ! [X0] : (~funny(X0) <=> ~rich(X0)) [ennf transformation 27]
36. (kind(susan) & calm(susan)) | funny(lucy) [ennf transformation 12]
40. ! [X0] : (((rich(X0) | strong(X0)) | creative(X0)) & (~creative(X0) | (~rich(X0) & ~strong(X0)))) [nnf transformation 4]
41. ! [X0] : ((rich(X0) | strong(X0) | creative(X0)) & (~creative(X0) | (~rich(X0) & ~strong(X0)))) [flattening 40]
52. ? [X1] : (~kind(X1) & kind(X1)) | ! [X0] : ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))) [nnf transformation 35]
53. ? [X0] : (~kind(X0) & kind(X0)) | ! [X1] : ((~funny(X1) | rich(X1)) & (~rich(X1) | funny(X1))) [rectify 52]
54. ? [X0] : (~kind(X0) & kind(X0)) => (~kind(sK3) & kind(sK3)) [choice axiom]
55. (~kind(sK3) & kind(sK3)) | ! [X1] : ((~funny(X1) | rich(X1)) & (~rich(X1) | funny(X1))) [skolemisation 53,54]
68. ! [X0] : (((calm(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~calm(X0) | brave(X0)))) [nnf transformation 16]
69. ! [X0] : (((calm(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | ~calm(X0) | brave(X0))) [flattening 68]
99. ~rich(X0) | ~creative(X0) [cnf transformation 41]
113. kind(sK3) | ~funny(X1) | rich(X1) [cnf transformation 55]
115. ~kind(sK3) | ~funny(X1) | rich(X1) [cnf transformation 55]
121. calm(susan) | funny(lucy) [cnf transformation 36]
136. brave(X0) | ~calm(X0) | brave(X0) [cnf transformation 69]
137. ~brave(X0) | ~brave(X0) [cnf transformation 69]
151. creative(lucy) [cnf transformation 24]
152. brave(X0) | ~calm(X0) [duplicate literal removal 136]
153. ~brave(X0) [duplicate literal removal 137]
238. 20 <=> ! [X1] : (~funny(X1) | rich(X1)) [avatar definition]
239. ~funny(X1) | rich(X1) <- (20) [avatar component clause 238]
241. 21 <=> kind(sK3) [avatar definition]
244. 20 | ~21 [avatar split clause 115,241,238]
249. 20 | 21 [avatar split clause 113,241,238]
268. 26 <=> funny(lucy) [avatar definition]
270. funny(lucy) <- (26) [avatar component clause 268]
277. 28 <=> calm(susan) [avatar definition]
279. calm(susan) <- (28) [avatar component clause 277]
280. 26 | 28 [avatar split clause 121,277,268]
299. ~calm(X0) [subsumption resolution 152,153]
354. rich(lucy) <- (20, 26) [resolution 239,270]
356. ~creative(lucy) <- (20, 26) [resolution 354,99]
357. $false <- (20, 26) [subsumption resolution 356,151]
358. ~20 | ~26 [avatar contradiction clause 357]
359. $false <- (28) [subsumption resolution 279,299]
360. ~28 [avatar contradiction clause 359]
361. $false [avatar sat refutation 244,249,280,358,360]
% SZS output end Proof for 2975831551973674084261696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 not humble or not kind is not humble. Everyone who is creative or not old is both not patient and strong. If someone is not happy or humble then lucy is not happy or not old. Everyone who is not generous is either humble or happy. If susan is tall then lucy is funny or brave and vice versa. Everyone who is both tall and generous is either brave or not curious and vice versa. Everyone who is either humble or not kind is creative. If susan is both brave and not brave then someone is either not tall or old. If someone is either not calm or humble then mary is either not happy or strong. If someone is not rich or not happy then someone is generous or rich. If mary is not humble or not generous then paul is humble or happy. Everyone who is happy is both not wise and not strong and vice versa. If someone is either not quiet or curious then someone is either not calm or not patient. Everyone who is not generous is both creative and not strong and vice versa. Everyone who is kind or not brave is not brave. If someone is patient then susan is creative and vice versa. Someone is both not funny and patient. Someone is both not calm and not strong. Alice is both not quiet and not strong. John is either old or not generous. John is not wise. Someone is both curious and tall. Fred is not quiet or not wise. Paul is either humble or not patient. | Paul is kind. | entailment | (![X]:((~humble(X)|~kind(X))=>~humble(X)))&
(![X]:((creative(X)|~old(X))=>(~patient(X)&strong(X))))&
((?[X]:((~happy(X)|humble(X))))=>((~happy(lucy)|~old(lucy))))&
(![X]:(~generous(X)=>(humble(X)<~>happy(X))))&
((tall(susan))<=>((funny(lucy)|brave(lucy))))&
(![X]:((tall(X)&generous(X))<=>(brave(X)<~>~curious(X))))&
(![X]:((humble(X)<~>~kind(X))=>creative(X)))&
(((brave(susan)&~brave(susan)))=>(?[X]:((~tall(X)<~>old(X)))))&
((?[X]:((~calm(X)<~>humble(X))))=>((~happy(mary)<~>strong(mary))))&
((?[X]:((~rich(X)|~happy(X))))=>(?[X]:((generous(X)|rich(X)))))&
(((~humble(mary)|~generous(mary)))=>((humble(paul)|happy(paul))))&
(![X]:(happy(X)<=>(~wise(X)&~strong(X))))&
((?[X]:((~quiet(X)<~>curious(X))))=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:(~generous(X)<=>(creative(X)&~strong(X))))&
(![X]:((kind(X)|~brave(X))=>~brave(X)))&
((?[X]:(patient(X)))<=>(creative(susan)))&
(?[X]:((~funny(X)&patient(X))))&
(?[X]:((~calm(X)&~strong(X))))&
((~quiet(alice)&~strong(alice)))&
((old(john)<~>~generous(john)))&
(~wise(john))&
(?[X]:((curious(X)&tall(X))))&
((~quiet(fred)|~wise(fred)))&
((humble(paul)<~>~patient(paul))) | kind(paul) | [
"p0",
"p1",
"p6",
"p8",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8028630194728177154187850
% SZS output start Proof for 8028630194728177154187850
1. ! [X0] : ((~kind(X0) | ~humble(X0)) => ~humble(X0)) [input p0]
2. ! [X0] : ((~old(X0) | creative(X0)) => (strong(X0) & ~patient(X0))) [input p1]
7. ! [X0] : ((humble(X0) <~> ~kind(X0)) => creative(X0)) [input p6]
9. ? [X0] : (~calm(X0) <~> humble(X0)) => (~happy(mary) <~> strong(mary)) [input p8]
11. (~generous(mary) | ~humble(mary)) => (happy(paul) | humble(paul)) [input p10]
12. ! [X0] : (happy(X0) <=> (~strong(X0) & ~wise(X0))) [input p11]
18. ? [X0] : (~strong(X0) & ~calm(X0)) [input p17]
25. ~kind(paul) [input hypothesis]
29. ! [X0] : (~humble(X0) | (kind(X0) & humble(X0))) [ennf transformation 1]
30. ! [X0] : ((strong(X0) & ~patient(X0)) | (old(X0) & ~creative(X0))) [ennf transformation 2]
34. ! [X0] : (creative(X0) | (humble(X0) <=> ~kind(X0))) [ennf transformation 7]
37. (~happy(mary) <~> strong(mary)) | ! [X0] : (~calm(X0) <=> humble(X0)) [ennf transformation 9]
38. (happy(paul) | humble(paul)) | (generous(mary) & humble(mary)) [ennf transformation 11]
39. happy(paul) | humble(paul) | (generous(mary) & humble(mary)) [flattening 38]
47. ! [X0] : (creative(X0) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) [nnf transformation 34]
51. ((~strong(mary) | happy(mary)) & (strong(mary) | ~happy(mary))) | ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0))) [nnf transformation 37]
52. ! [X0] : ((happy(X0) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | ~happy(X0))) [nnf transformation 12]
53. ! [X0] : ((happy(X0) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | ~happy(X0))) [flattening 52]
66. ? [X0] : (~strong(X0) & ~calm(X0)) => (~strong(sK4) & ~calm(sK4)) [choice axiom]
67. ~strong(sK4) & ~calm(sK4) [skolemisation 18,66]
73. ~humble(X0) | kind(X0) [cnf transformation 29]
76. ~creative(X0) | strong(X0) [cnf transformation 30]
91. creative(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 47]
92. creative(X0) | humble(X0) | kind(X0) [cnf transformation 47]
97. ~strong(mary) | happy(mary) | humble(X0) | calm(X0) [cnf transformation 51]
99. happy(paul) | humble(paul) | humble(mary) [cnf transformation 39]
102. ~happy(X0) | ~strong(X0) [cnf transformation 53]
117. ~calm(sK4) [cnf transformation 67]
118. ~strong(sK4) [cnf transformation 67]
129. ~kind(paul) [cnf transformation 25]
161. creative(X0) | kind(X0) [subsumption resolution 92,73]
162. ~humble(X0) | creative(X0) [subsumption resolution 91,161]
167. 9 <=> happy(mary) [avatar definition]
169. happy(mary) <- (9) [avatar component clause 167]
171. 10 <=> strong(mary) [avatar definition]
172. strong(mary) <- (10) [avatar component clause 171]
176. 11 <=> ! [X0] : (humble(X0) | calm(X0)) [avatar definition]
177. calm(X0) | humble(X0) <- (11) [avatar component clause 176]
178. 11 | 9 | ~10 [avatar split clause 97,171,167,176]
186. 13 <=> humble(paul) [avatar definition]
188. humble(paul) <- (13) [avatar component clause 186]
190. 14 <=> happy(paul) [avatar definition]
192. happy(paul) <- (14) [avatar component clause 190]
195. 15 <=> humble(mary) [avatar definition]
197. humble(mary) <- (15) [avatar component clause 195]
198. 15 | 13 | 14 [avatar split clause 99,190,186,195]
263. ~strong(paul) <- (14) [resolution 102,192]
270. strong(X0) | kind(X0) [resolution 161,76]
302. kind(paul) <- (14) [resolution 270,263]
305. $false <- (14) [subsumption resolution 302,129]
306. ~14 [avatar contradiction clause 305]
307. creative(mary) <- (15) [resolution 197,162]
309. strong(mary) <- (15) [resolution 307,76]
312. 10 | ~15 [avatar split clause 309,195,171]
314. ~strong(mary) <- (9) [resolution 169,102]
315. $false <- (9, 10) [subsumption resolution 314,172]
316. ~9 | ~10 [avatar contradiction clause 315]
319. humble(sK4) <- (11) [resolution 177,117]
321. creative(sK4) <- (11) [resolution 319,162]
359. strong(sK4) <- (11) [resolution 321,76]
360. $false <- (11) [subsumption resolution 359,118]
361. ~11 [avatar contradiction clause 360]
365. kind(paul) <- (13) [resolution 188,73]
366. $false <- (13) [subsumption resolution 365,129]
367. ~13 [avatar contradiction clause 366]
368. $false [avatar sat refutation 178,198,306,312,316,361,367]
% SZS output end Proof for 8028630194728177154187850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or generous is both not tall and kind.
If someone is both not happy and not strong then mary is curious or not rich and vice versa.
If someone is not kind then fred is either not curious or not creative and vice versa.
If someone is generous or tall then someone is both funny and not creative.
Everyone who is curious is both brave and creative and vice versa.
Everyone who is not wise or funny is both not calm and patient.
Everyone who is generous or wise is both not quiet and generous.
If susan is both kind and brave then someone is either rich or funny.
Everyone who is not curious or not brave is both patient and funny and vice versa.
If someone is both funny and humble then someone is not creative or creative and vice versa.
If john is either not brave or generous then someone is not curious or humble.
If mary is either not generous or not creative then fred is either humble or not rich and vice versa.
Everyone who is wise or not humble is both funny and not kind and vice versa.
If susan is patient then someone is either not calm or not old.
If john is both not rich and patient then someone is rich and vice versa.
If alice is generous or not calm then someone is not brave or funny.
Someone is kind or not tall.
Fred is either old or not kind.
Mary is wise.
Someone is funny.
Susan is not strong.
Mary is not rich.
Fred is patient or creative. | Mary is not patient. | contradiction | (![X]:((old(X)<~>generous(X))=>(~tall(X)&kind(X))))&
((?[X]:((~happy(X)&~strong(X))))<=>((curious(mary)|~rich(mary))))&
((?[X]:(~kind(X)))<=>((~curious(fred)<~>~creative(fred))))&
((?[X]:((generous(X)|tall(X))))=>(?[X]:((funny(X)&~creative(X)))))&
(![X]:(curious(X)<=>(brave(X)&creative(X))))&
(![X]:((~wise(X)|funny(X))=>(~calm(X)&patient(X))))&
(![X]:((generous(X)|wise(X))=>(~quiet(X)&generous(X))))&
(((kind(susan)&brave(susan)))=>(?[X]:((rich(X)<~>funny(X)))))&
(![X]:((~curious(X)|~brave(X))<=>(patient(X)&funny(X))))&
((?[X]:((funny(X)&humble(X))))<=>(?[X]:((~creative(X)|creative(X)))))&
(((~brave(john)<~>generous(john)))=>(?[X]:((~curious(X)|humble(X)))))&
(((~generous(mary)<~>~creative(mary)))<=>((humble(fred)<~>~rich(fred))))&
(![X]:((wise(X)|~humble(X))<=>(funny(X)&~kind(X))))&
((patient(susan))=>(?[X]:((~calm(X)<~>~old(X)))))&
(((~rich(john)&patient(john)))<=>(?[X]:(rich(X))))&
(((generous(alice)|~calm(alice)))=>(?[X]:((~brave(X)|funny(X)))))&
(?[X]:((kind(X)|~tall(X))))&
((old(fred)<~>~kind(fred)))&
(wise(mary))&
(?[X]:(funny(X)))&
(~strong(susan))&
(~rich(mary))&
((patient(fred)|creative(fred))) | ~patient(mary) | [
"p5",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4749800451660789418243988
% SZS output start Proof for 4749800451660789418243988
6. ! [X0] : ((funny(X0) | ~wise(X0)) => (patient(X0) & ~calm(X0))) [input p5]
13. ! [X0] : ((~humble(X0) | wise(X0)) <=> (~kind(X0) & funny(X0))) [input p12]
19. wise(mary) [input p18]
24. ~patient(mary) [input hypothesis]
33. ! [X0] : ((patient(X0) & ~calm(X0)) | (~funny(X0) & wise(X0))) [ennf transformation 6]
69. ! [X0] : (((~humble(X0) | wise(X0)) | (kind(X0) | ~funny(X0))) & ((~kind(X0) & funny(X0)) | (humble(X0) & ~wise(X0)))) [nnf transformation 13]
70. ! [X0] : ((~humble(X0) | wise(X0) | kind(X0) | ~funny(X0)) & ((~kind(X0) & funny(X0)) | (humble(X0) & ~wise(X0)))) [flattening 69]
103. ~funny(X0) | patient(X0) [cnf transformation 33]
128. ~wise(X0) | funny(X0) [cnf transformation 70]
142. wise(mary) [cnf transformation 19]
147. ~patient(mary) [cnf transformation 24]
395. funny(mary) [resolution 128,142]
431. patient(mary) [resolution 395,103]
434. $false [subsumption resolution 431,147]
% SZS output end Proof for 4749800451660789418243988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then lucy is either not strong or creative. If someone is either not strong or not brave then john is not wise or not creative and vice versa. If someone is generous or happy then someone is both not strong and curious. Everyone who is curious is not wise and vice versa. Everyone who is not wise is both not quiet and not curious. Everyone who is kind or not creative is humble or not calm and vice versa. Everyone who is quiet or rich is either not generous or not old. If someone is both not creative and humble then someone is not happy. If someone is not patient then someone is both not patient and not brave and vice versa. If someone is generous or not quiet then someone is both not kind and rich. Everyone who is not brave is strong. If paul is either humble or quiet then alice is old or wise and vice versa. Everyone who is both old and kind is quiet or not generous and vice versa. Everyone who is not curious is tall and vice versa. Everyone who is either not humble or strong is kind or not curious and vice versa. Someone is calm. Paul is either not generous or calm. Someone is either not funny or calm. Someone is patient. Lucy is brave. Someone is either patient or not happy. | John is not tall. | contradiction | ((?[X]:(kind(X)))=>((~strong(lucy)<~>creative(lucy))))&
((?[X]:((~strong(X)<~>~brave(X))))<=>((~wise(john)|~creative(john))))&
((?[X]:((generous(X)|happy(X))))=>(?[X]:((~strong(X)&curious(X)))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:(~wise(X)=>(~quiet(X)&~curious(X))))&
(![X]:((kind(X)|~creative(X))<=>(humble(X)|~calm(X))))&
(![X]:((quiet(X)|rich(X))=>(~generous(X)<~>~old(X))))&
((?[X]:((~creative(X)&humble(X))))=>(?[X]:(~happy(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~patient(X)&~brave(X)))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((~kind(X)&rich(X)))))&
(![X]:(~brave(X)=>strong(X)))&
(((humble(paul)<~>quiet(paul)))<=>((old(alice)|wise(alice))))&
(![X]:((old(X)&kind(X))<=>(quiet(X)|~generous(X))))&
(![X]:(~curious(X)<=>tall(X)))&
(![X]:((~humble(X)<~>strong(X))<=>(kind(X)|~curious(X))))&
(?[X]:(calm(X)))&
((~generous(paul)<~>calm(paul)))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:(patient(X)))&
(brave(lucy))&
(?[X]:((patient(X)<~>~happy(X)))) | ~tall(john) | [
"p3",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1856693756050847657910657
% SZS output start Proof for 1856693756050847657910657
4. ! [X0] : (curious(X0) <=> ~wise(X0)) [input p3]
5. ! [X0] : (~wise(X0) => (~curious(X0) & ~quiet(X0))) [input p4]
14. ! [X0] : (~curious(X0) <=> tall(X0)) [input p13]
22. ~tall(john) [input hypothesis]
29. ! [X0] : ((~curious(X0) & ~quiet(X0)) | wise(X0)) [ennf transformation 5]
43. ! [X0] : ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))) [nnf transformation 4]
62. ! [X0] : ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0))) [nnf transformation 14]
88. ~curious(X0) | ~wise(X0) [cnf transformation 43]
89. curious(X0) | wise(X0) [cnf transformation 43]
91. ~curious(X0) | wise(X0) [cnf transformation 29]
120. tall(X0) | curious(X0) [cnf transformation 62]
137. ~tall(john) [cnf transformation 22]
197. wise(X0) [subsumption resolution 91,89]
298. curious(john) [resolution 120,137]
313. ~wise(john) [resolution 298,88]
314. $false [subsumption resolution 313,197]
% SZS output end Proof for 1856693756050847657910657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 alice is not generous or not creative then someone is both not old and tall and vice versa.
If susan is either old or not curious then mary is both not humble and funny and vice versa.
Everyone who is either not wise or curious is both curious and not creative.
If lucy is not funny then someone is quiet.
Everyone who is not humble or not wise is either not calm or not humble and vice versa.
If someone is generous or not curious then lucy is patient and vice versa.
If someone is kind or strong then someone is either not quiet or not creative.
If john is not happy or not tall then someone is both not patient and not tall.
Everyone who is patient is either not humble or wise.
Everyone who is not kind is not tall or not strong.
Everyone who is either patient or not humble is funny or rich.
Everyone who is not wise is strong.
Everyone who is not humble is either not wise or wise.
Everyone who is both funny and old is both not strong and not generous.
If someone is both not generous and not funny then lucy is not creative.
Everyone who is either humble or not strong is both not quiet and rich and vice versa.
Lucy is both not generous and patient.
Alice is not humble or tall.
Susan is patient.
Someone is not generous.
Someone is rich or not wise.
Alice is not creative.
Someone is not funny.
Someone is both kind and not funny. | Lucy is not creative. | neutral | (((~generous(alice)|~creative(alice)))<=>(?[X]:((~old(X)&tall(X)))))&
(((old(susan)<~>~curious(susan)))<=>((~humble(mary)&funny(mary))))&
(![X]:((~wise(X)<~>curious(X))=>(curious(X)&~creative(X))))&
((~funny(lucy))=>(?[X]:(quiet(X))))&
(![X]:((~humble(X)|~wise(X))<=>(~calm(X)<~>~humble(X))))&
((?[X]:((generous(X)|~curious(X))))<=>(patient(lucy)))&
((?[X]:((kind(X)|strong(X))))=>(?[X]:((~quiet(X)<~>~creative(X)))))&
(((~happy(john)|~tall(john)))=>(?[X]:((~patient(X)&~tall(X)))))&
(![X]:(patient(X)=>(~humble(X)<~>wise(X))))&
(![X]:(~kind(X)=>(~tall(X)|~strong(X))))&
(![X]:((patient(X)<~>~humble(X))=>(funny(X)|rich(X))))&
(![X]:(~wise(X)=>strong(X)))&
(![X]:(~humble(X)=>(~wise(X)<~>wise(X))))&
(![X]:((funny(X)&old(X))=>(~strong(X)&~generous(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(~creative(lucy)))&
(![X]:((humble(X)<~>~strong(X))<=>(~quiet(X)&rich(X))))&
((~generous(lucy)&patient(lucy)))&
((~humble(alice)|tall(alice)))&
(patient(susan))&
(?[X]:(~generous(X)))&
(?[X]:((rich(X)|~wise(X))))&
(~creative(alice))&
(?[X]:(~funny(X)))&
(?[X]:((kind(X)&~funny(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is not creative or not wise is both curious and quiet and vice versa.
Everyone who is both not brave and not generous is not rich or wise.
Everyone who is both patient and brave is not creative or not quiet.
If someone is either not wise or humble then alice is not creative and vice versa.
If someone is curious then mary is both creative and not tall.
Everyone who is quiet is both happy and curious.
If someone is both not funny and curious then someone is both patient and creative and vice versa.
If susan is either not happy or tall then mary is brave.
Everyone who is quiet is happy or humble.
If someone is not happy or not curious then mary is not patient or strong.
If someone is both not humble and not brave then john is not wise and vice versa.
Everyone who is both quiet and tall is not humble or not brave and vice versa.
Everyone who is kind or not creative is not curious or not rich and vice versa.
Everyone who is not strong or not rich is not brave or tall and vice versa.
If someone is wise or kind then mary is not kind or kind and vice versa.
Everyone who is either not brave or generous is both not old and rich and vice versa.
Lucy is not wise.
Fred is either generous or kind.
Alice is not creative.
Fred is kind.
Someone is strong or curious.
Mary is either generous or curious.
Susan is not kind. | Susan is not curious. | contradiction | (![X]:((~creative(X)|~wise(X))<=>(curious(X)&quiet(X))))&
(![X]:((~brave(X)&~generous(X))=>(~rich(X)|wise(X))))&
(![X]:((patient(X)&brave(X))=>(~creative(X)|~quiet(X))))&
((?[X]:((~wise(X)<~>humble(X))))<=>(~creative(alice)))&
((?[X]:(curious(X)))=>((creative(mary)&~tall(mary))))&
(![X]:(quiet(X)=>(happy(X)&curious(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((patient(X)&creative(X)))))&
(((~happy(susan)<~>tall(susan)))=>(brave(mary)))&
(![X]:(quiet(X)=>(happy(X)|humble(X))))&
((?[X]:((~happy(X)|~curious(X))))=>((~patient(mary)|strong(mary))))&
((?[X]:((~humble(X)&~brave(X))))<=>(~wise(john)))&
(![X]:((quiet(X)&tall(X))<=>(~humble(X)|~brave(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|~rich(X))))&
(![X]:((~strong(X)|~rich(X))<=>(~brave(X)|tall(X))))&
((?[X]:((wise(X)|kind(X))))<=>((~kind(mary)|kind(mary))))&
(![X]:((~brave(X)<~>generous(X))<=>(~old(X)&rich(X))))&
(~wise(lucy))&
((generous(fred)<~>kind(fred)))&
(~creative(alice))&
(kind(fred))&
(?[X]:((strong(X)|curious(X))))&
((generous(mary)<~>curious(mary)))&
(~kind(susan)) | ~curious(susan) | [
"p0",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4481313527887217335219117
% SZS output start Proof for 4481313527887217335219117
1. ! [X0] : ((~wise(X0) | ~creative(X0)) <=> (quiet(X0) & curious(X0))) [input p0]
13. ! [X0] : ((~creative(X0) | kind(X0)) <=> (~rich(X0) | ~curious(X0))) [input p12]
23. ~kind(susan) [input p22]
24. ~curious(susan) [input hypothesis]
37. ! [X0] : (((~wise(X0) | ~creative(X0)) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | (wise(X0) & creative(X0)))) [nnf transformation 1]
38. ! [X0] : ((~wise(X0) | ~creative(X0) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | (wise(X0) & creative(X0)))) [flattening 37]
55. ! [X0] : (((~creative(X0) | kind(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (creative(X0) & ~kind(X0)))) [nnf transformation 13]
56. ! [X0] : ((~creative(X0) | kind(X0) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | (creative(X0) & ~kind(X0)))) [flattening 55]
70. curious(X0) | creative(X0) [cnf transformation 38]
104. ~creative(X0) | kind(X0) | curious(X0) [cnf transformation 56]
128. ~kind(susan) [cnf transformation 23]
129. ~curious(susan) [cnf transformation 24]
239. kind(X0) | curious(X0) [subsumption resolution 104,70]
314. curious(susan) [resolution 239,128]
315. $false [subsumption resolution 314,129]
% SZS output end Proof for 4481313527887217335219117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or not curious then fred is both quiet and old and vice versa. Everyone who is not generous or calm is either happy or brave and vice versa. Everyone who is both funny and not funny is kind and vice versa. Everyone who is not calm or calm is either kind or not calm and vice versa. If susan is both not quiet and curious then someone is either strong or tall and vice versa. If susan is not quiet then someone is both not strong and brave. If someone is humble then someone is both not patient and generous and vice versa. If susan is either happy or not old then someone is either not rich or not quiet. If fred is not old or kind then lucy is both old and curious. If someone is not patient or not wise then fred is both not funny and not quiet. Everyone who is generous is not happy. If someone is both not strong and calm then someone is either not brave or generous and vice versa. If someone is either not funny or not rich then fred is not rich. If someone is not quiet then fred is happy or kind. Mary is not happy or curious. Someone is generous or not funny. Someone is generous or not quiet. Someone is either brave or not humble. Lucy is either not kind or not rich. Someone is not quiet or not brave. | Mary is quiet. | entailment | ((?[X]:((strong(X)|~curious(X))))<=>((quiet(fred)&old(fred))))&
(![X]:((~generous(X)|calm(X))<=>(happy(X)<~>brave(X))))&
(![X]:((funny(X)&~funny(X))<=>kind(X)))&
(![X]:((~calm(X)|calm(X))<=>(kind(X)<~>~calm(X))))&
(((~quiet(susan)&curious(susan)))<=>(?[X]:((strong(X)<~>tall(X)))))&
((~quiet(susan))=>(?[X]:((~strong(X)&brave(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~patient(X)&generous(X)))))&
(((happy(susan)<~>~old(susan)))=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(((~old(fred)|kind(fred)))=>((old(lucy)&curious(lucy))))&
((?[X]:((~patient(X)|~wise(X))))=>((~funny(fred)&~quiet(fred))))&
(![X]:(generous(X)=>~happy(X)))&
((?[X]:((~strong(X)&calm(X))))<=>(?[X]:((~brave(X)<~>generous(X)))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(~rich(fred)))&
((?[X]:(~quiet(X)))=>((happy(fred)|kind(fred))))&
((~happy(mary)|curious(mary)))&
(?[X]:((generous(X)|~funny(X))))&
(?[X]:((generous(X)|~quiet(X))))&
(?[X]:((brave(X)<~>~humble(X))))&
((~kind(lucy)<~>~rich(lucy)))&
(?[X]:((~quiet(X)|~brave(X)))) | quiet(mary) | [
"p1",
"p2",
"p3",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7894159452680446546253654
% SZS output start Proof for 7894159452680446546253654
2. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (happy(X0) <~> brave(X0))) [input p1]
3. ! [X0] : ((~funny(X0) & funny(X0)) <=> kind(X0)) [input p2]
4. ! [X0] : ((calm(X0) | ~calm(X0)) <=> (kind(X0) <~> ~calm(X0))) [input p3]
11. ! [X0] : (generous(X0) => ~happy(X0)) [input p10]
12. ? [X0] : (calm(X0) & ~strong(X0)) <=> ? [X0] : (~brave(X0) <~> generous(X0)) [input p11]
14. ? [X0] : ~quiet(X0) => (kind(fred) | happy(fred)) [input p13]
21. ~quiet(mary) [input hypothesis]
23. ? [X0] : (calm(X0) & ~strong(X0)) <=> ? [X1] : (~brave(X1) <~> generous(X1)) [rectify 12]
29. ! [X0] : (~happy(X0) | ~generous(X0)) [ennf transformation 11]
31. (kind(fred) | happy(fred)) | ! [X0] : quiet(X0) [ennf transformation 14]
32. kind(fred) | happy(fred) | ! [X0] : quiet(X0) [flattening 31]
38. ! [X0] : (((calm(X0) | ~generous(X0)) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | (~calm(X0) & generous(X0)))) [nnf transformation 2]
39. ! [X0] : ((calm(X0) | ~generous(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | (~calm(X0) & generous(X0)))) [flattening 38]
40. ! [X0] : (((~funny(X0) & funny(X0)) | ~kind(X0)) & (kind(X0) | (funny(X0) | ~funny(X0)))) [nnf transformation 3]
41. ! [X0] : (((~funny(X0) & funny(X0)) | ~kind(X0)) & (kind(X0) | funny(X0) | ~funny(X0))) [flattening 40]
42. ! [X0] : (((calm(X0) | ~calm(X0)) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0)))) & (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~calm(X0) & calm(X0)))) [nnf transformation 4]
43. ! [X0] : ((calm(X0) | ~calm(X0) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0)))) & (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~calm(X0) & calm(X0)))) [flattening 42]
59. (? [X0] : (calm(X0) & ~strong(X0)) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) & (? [X1] : ((~generous(X1) | brave(X1)) & (generous(X1) | ~brave(X1))) | ! [X0] : (~calm(X0) | strong(X0))) [nnf transformation 23]
60. (? [X0] : (calm(X0) & ~strong(X0)) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) & (? [X2] : ((~generous(X2) | brave(X2)) & (generous(X2) | ~brave(X2))) | ! [X3] : (~calm(X3) | strong(X3))) [rectify 59]
61. ? [X0] : (calm(X0) & ~strong(X0)) => (calm(sK6) & ~strong(sK6)) [choice axiom]
62. ? [X2] : ((~generous(X2) | brave(X2)) & (generous(X2) | ~brave(X2))) => ((~generous(sK7) | brave(sK7)) & (generous(sK7) | ~brave(sK7))) [choice axiom]
63. ((calm(sK6) & ~strong(sK6)) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1)))) & (((~generous(sK7) | brave(sK7)) & (generous(sK7) | ~brave(sK7))) | ! [X3] : (~calm(X3) | strong(X3))) [skolemisation 60,62,61]
82. ~brave(X0) | ~happy(X0) | generous(X0) [cnf transformation 39]
87. funny(X0) | ~kind(X0) [cnf transformation 41]
88. ~kind(X0) | ~funny(X0) [cnf transformation 41]
90. ~calm(X0) | kind(X0) | ~calm(X0) [cnf transformation 43]
116. ~happy(X0) | ~generous(X0) [cnf transformation 29]
121. calm(sK6) | generous(X1) | brave(X1) [cnf transformation 63]
125. kind(fred) | happy(fred) | quiet(X0) [cnf transformation 32]
134. ~quiet(mary) [cnf transformation 21]
135. ~calm(X0) | kind(X0) [duplicate literal removal 90]
166. ~kind(X0) [subsumption resolution 87,88]
167. ~calm(X0) [subsumption resolution 135,166]
267. brave(X1) | generous(X1) [subsumption resolution 121,167]
280. happy(fred) | quiet(X0) [subsumption resolution 125,166]
282. 31 <=> ! [X0] : quiet(X0) [avatar definition]
283. quiet(X0) <- (31) [avatar component clause 282]
285. 32 <=> happy(fred) [avatar definition]
287. happy(fred) <- (32) [avatar component clause 285]
288. 31 | 32 [avatar split clause 280,285,282]
348. ~happy(X1) | generous(X1) | generous(X1) [resolution 82,267]
349. ~happy(X1) | generous(X1) [duplicate literal removal 348]
351. ~happy(X1) [subsumption resolution 349,116]
352. $false <- (32) [resolution 351,287]
353. ~32 [avatar contradiction clause 352]
356. $false <- (31) [resolution 283,134]
359. ~31 [avatar contradiction clause 356]
360. $false [avatar sat refutation 288,353,359]
% SZS output end Proof for 7894159452680446546253654
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.015 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is either curious or not funny. If someone is either not generous or tall then someone is both happy and calm. If alice is either not rich or tall then fred is both happy and rich and vice versa. Everyone who is both not brave and quiet is not generous or curious. Everyone who is not kind or not humble is both not happy and rich and vice versa. Everyone who is either not calm or not creative is not kind or tall and vice versa. Everyone who is either not happy or not patient is not brave. Everyone who is not patient or brave is humble or not calm and vice versa. Everyone who is not old or wise is curious. Everyone who is both not humble and not rich is rich. Everyone who is not funny is either not generous or curious. Everyone who is not rich or tall is patient or not old. Everyone who is strong or old is generous or not strong. If paul is tall or not creative then lucy is not calm. Everyone who is both not strong and not brave is either not happy or brave. If alice is either wise or old then susan is not tall or not generous and vice versa. Someone is rich. John is kind. Lucy is calm or not old. Paul is either not humble or happy. John is not patient or happy. Fred is not kind or not funny. Fred is not rich. Someone is humble or not strong. | Fred is not strong. | entailment | (![X]:(kind(X)=>(curious(X)<~>~funny(X))))&
((?[X]:((~generous(X)<~>tall(X))))=>(?[X]:((happy(X)&calm(X)))))&
(((~rich(alice)<~>tall(alice)))<=>((happy(fred)&rich(fred))))&
(![X]:((~brave(X)&quiet(X))=>(~generous(X)|curious(X))))&
(![X]:((~kind(X)|~humble(X))<=>(~happy(X)&rich(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(~kind(X)|tall(X))))&
(![X]:((~happy(X)<~>~patient(X))=>~brave(X)))&
(![X]:((~patient(X)|brave(X))<=>(humble(X)|~calm(X))))&
(![X]:((~old(X)|wise(X))=>curious(X)))&
(![X]:((~humble(X)&~rich(X))=>rich(X)))&
(![X]:(~funny(X)=>(~generous(X)<~>curious(X))))&
(![X]:((~rich(X)|tall(X))=>(patient(X)|~old(X))))&
(![X]:((strong(X)|old(X))=>(generous(X)|~strong(X))))&
(((tall(paul)|~creative(paul)))=>(~calm(lucy)))&
(![X]:((~strong(X)&~brave(X))=>(~happy(X)<~>brave(X))))&
(((wise(alice)<~>old(alice)))<=>((~tall(susan)|~generous(susan))))&
(?[X]:(rich(X)))&
(kind(john))&
((calm(lucy)|~old(lucy)))&
((~humble(paul)<~>happy(paul)))&
((~patient(john)|happy(john)))&
((~kind(fred)|~funny(fred)))&
(~rich(fred))&
(?[X]:((humble(X)|~strong(X)))) | ~strong(fred) | [
"p0",
"p4",
"p10",
"p12",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3602841387972749250107460
% SZS output start Proof for 3602841387972749250107460
1. ! [X0] : (kind(X0) => (curious(X0) <~> ~funny(X0))) [input p0]
5. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> (rich(X0) & ~happy(X0))) [input p4]
11. ! [X0] : (~funny(X0) => (~generous(X0) <~> curious(X0))) [input p10]
13. ! [X0] : ((old(X0) | strong(X0)) => (~strong(X0) | generous(X0))) [input p12]
22. ~funny(fred) | ~kind(fred) [input p21]
23. ~rich(fred) [input p22]
25. strong(fred) [input hypothesis]
28. ! [X0] : ((curious(X0) <~> ~funny(X0)) | ~kind(X0)) [ennf transformation 1]
34. ! [X0] : ((~generous(X0) <~> curious(X0)) | funny(X0)) [ennf transformation 11]
37. ! [X0] : ((~strong(X0) | generous(X0)) | (~old(X0) & ~strong(X0))) [ennf transformation 13]
38. ! [X0] : (~strong(X0) | generous(X0) | (~old(X0) & ~strong(X0))) [flattening 37]
42. ! [X0] : (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | ~kind(X0)) [nnf transformation 28]
49. ! [X0] : (((~humble(X0) | ~kind(X0)) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | (humble(X0) & kind(X0)))) [nnf transformation 5]
50. ! [X0] : ((~humble(X0) | ~kind(X0) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | (humble(X0) & kind(X0)))) [flattening 49]
56. ! [X0] : (((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | funny(X0)) [nnf transformation 34]
66. ~curious(X0) | funny(X0) | ~kind(X0) [cnf transformation 42]
79. rich(X0) | kind(X0) [cnf transformation 50]
97. ~generous(X0) | curious(X0) | funny(X0) [cnf transformation 56]
101. ~strong(X0) | generous(X0) | ~strong(X0) [cnf transformation 38]
119. ~funny(fred) | ~kind(fred) [cnf transformation 22]
120. ~rich(fred) [cnf transformation 23]
122. strong(fred) [cnf transformation 25]
124. ~strong(X0) | generous(X0) [duplicate literal removal 101]
149. 6 <=> rich(fred) [avatar definition]
151. ~rich(fred) <- (~6) [avatar component clause 149]
226. 21 <=> kind(fred) [avatar definition]
227. kind(fred) <- (21) [avatar component clause 226]
230. 22 <=> funny(fred) [avatar definition]
232. ~funny(fred) <- (~22) [avatar component clause 230]
233. ~21 | ~22 [avatar split clause 119,230,226]
234. ~6 [avatar split clause 120,149]
246. kind(fred) <- (~6) [resolution 79,151]
247. 21 | 6 [avatar split clause 246,149,226]
252. generous(fred) [resolution 124,122]
277. curious(fred) | funny(fred) [resolution 97,252]
278. curious(fred) <- (~22) [subsumption resolution 277,232]
279. funny(fred) | ~kind(fred) <- (~22) [resolution 278,66]
280. ~kind(fred) <- (~22) [subsumption resolution 279,232]
281. $false <- (21, ~22) [subsumption resolution 280,227]
282. ~21 | 22 [avatar contradiction clause 281]
283. $false [avatar sat refutation 233,234,247,282]
% SZS output end Proof for 3602841387972749250107460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or calm is tall or not brave. If someone is both not tall and rich then john is either not kind or not creative. Everyone who is not strong or quiet is not brave and vice versa. Everyone who is not quiet or not humble is kind or creative. Everyone who is both not humble and strong is curious and vice versa. Everyone who is brave is both creative and not strong and vice versa. Everyone who is happy or not patient is either quiet or not strong. Everyone who is either wise or kind is either not funny or not brave. Everyone who is not tall is not wise. If someone is both not funny and not patient then someone is either humble or calm and vice versa. If someone is either not strong or not patient then someone is both not old and old. If susan is either kind or brave then someone is not curious and vice versa. Everyone who is either quiet or generous is both generous and creative. If mary is not creative then alice is both wise and not wise. Everyone who is not humble is either not calm or not patient. If someone is not happy or not calm then alice is not brave. Someone is either not generous or rich. Someone is not generous or curious. Someone is happy or wise. Someone is either not happy or not old. Someone is creative or curious. Someone is both not patient and kind. Alice is either not happy or creative. Someone is either rich or not patient. | Alice is not happy. | neutral | (![X]:((~wise(X)|calm(X))=>(tall(X)|~brave(X))))&
((?[X]:((~tall(X)&rich(X))))=>((~kind(john)<~>~creative(john))))&
(![X]:((~strong(X)|quiet(X))<=>~brave(X)))&
(![X]:((~quiet(X)|~humble(X))=>(kind(X)|creative(X))))&
(![X]:((~humble(X)&strong(X))<=>curious(X)))&
(![X]:(brave(X)<=>(creative(X)&~strong(X))))&
(![X]:((happy(X)|~patient(X))=>(quiet(X)<~>~strong(X))))&
(![X]:((wise(X)<~>kind(X))=>(~funny(X)<~>~brave(X))))&
(![X]:(~tall(X)=>~wise(X)))&
((?[X]:((~funny(X)&~patient(X))))<=>(?[X]:((humble(X)<~>calm(X)))))&
((?[X]:((~strong(X)<~>~patient(X))))=>(?[X]:((~old(X)&old(X)))))&
(((kind(susan)<~>brave(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)<~>generous(X))=>(generous(X)&creative(X))))&
((~creative(mary))=>((wise(alice)&~wise(alice))))&
(![X]:(~humble(X)=>(~calm(X)<~>~patient(X))))&
((?[X]:((~happy(X)|~calm(X))))=>(~brave(alice)))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((~happy(X)<~>~old(X))))&
(?[X]:((creative(X)|curious(X))))&
(?[X]:((~patient(X)&kind(X))))&
((~happy(alice)<~>creative(alice)))&
(?[X]:((rich(X)<~>~patient(X)))) | ~happy(alice) | [] | null | 0 |
Everyone who is both not rich and not old is tall or not tall. If mary is humble then someone is curious. Everyone who is calm or curious is either kind or not rich and vice versa. If alice is not creative then susan is curious or not calm. If someone is both not kind and creative then john is calm and vice versa. If mary is not rich or creative then alice is not funny. If paul is patient or strong then someone is both happy and kind. Everyone who is funny or not strong is both not rich and not funny and vice versa. If someone is both not quiet and not patient then mary is either not humble or not strong and vice versa. Everyone who is brave or not patient is either creative or not humble. If fred is either kind or not strong then someone is not happy and vice versa. If alice is both generous and not funny then susan is curious or not creative. If someone is not tall or old then someone is either not strong or not kind. Everyone who is either not rich or not happy is not funny or rich. If fred is quiet then someone is not rich or not quiet. Everyone who is both happy and not happy is not rich or curious and vice versa. John is happy or not old. Someone is tall. Alice is either patient or not happy. Someone is either humble or not kind. Someone is both not quiet and calm. Someone is not wise or not old. | Fred is not curious. | entailment | (![X]:((~rich(X)&~old(X))=>(tall(X)|~tall(X))))&
((humble(mary))=>(?[X]:(curious(X))))&
(![X]:((calm(X)|curious(X))<=>(kind(X)<~>~rich(X))))&
((~creative(alice))=>((curious(susan)|~calm(susan))))&
((?[X]:((~kind(X)&creative(X))))<=>(calm(john)))&
(((~rich(mary)|creative(mary)))=>(~funny(alice)))&
(((patient(paul)|strong(paul)))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((funny(X)|~strong(X))<=>(~rich(X)&~funny(X))))&
((?[X]:((~quiet(X)&~patient(X))))<=>((~humble(mary)<~>~strong(mary))))&
(![X]:((brave(X)|~patient(X))=>(creative(X)<~>~humble(X))))&
(((kind(fred)<~>~strong(fred)))<=>(?[X]:(~happy(X))))&
(((generous(alice)&~funny(alice)))=>((curious(susan)|~creative(susan))))&
((?[X]:((~tall(X)|old(X))))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~rich(X)<~>~happy(X))=>(~funny(X)|rich(X))))&
((quiet(fred))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((happy(X)&~happy(X))<=>(~rich(X)|curious(X))))&
((happy(john)|~old(john)))&
(?[X]:(tall(X)))&
((patient(alice)<~>~happy(alice)))&
(?[X]:((humble(X)<~>~kind(X))))&
(?[X]:((~quiet(X)&calm(X))))&
(?[X]:((~wise(X)|~old(X)))) | ~curious(fred) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2664546218159019080430566
% SZS output start Proof for 2664546218159019080430566
16. ! [X0] : ((~happy(X0) & happy(X0)) <=> (curious(X0) | ~rich(X0))) [input p15]
23. curious(fred) [input hypothesis]
68. ! [X0] : (((~happy(X0) & happy(X0)) | (~curious(X0) & rich(X0))) & ((curious(X0) | ~rich(X0)) | (happy(X0) | ~happy(X0)))) [nnf transformation 16]
69. ! [X0] : (((~happy(X0) & happy(X0)) | (~curious(X0) & rich(X0))) & (curious(X0) | ~rich(X0) | happy(X0) | ~happy(X0))) [flattening 68]
122. happy(X0) | ~curious(X0) [cnf transformation 69]
124. ~happy(X0) | ~curious(X0) [cnf transformation 69]
133. curious(fred) [cnf transformation 23]
282. ~curious(X0) [subsumption resolution 122,124]
313. $false [subsumption resolution 133,282]
% SZS output end Proof for 2664546218159019080430566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 tall or old then someone is either calm or funny and vice versa.
Everyone who is not brave or quiet is both not brave and not funny.
If someone is rich or strong then lucy is not funny and vice versa.
Everyone who is not quiet is both not strong and creative and vice versa.
If lucy is both not curious and not creative then someone is both not creative and rich.
Everyone who is not kind or generous is quiet or not rich and vice versa.
If someone is both generous and not curious then someone is either not kind or not quiet and vice versa.
Everyone who is both not old and funny is patient or tall and vice versa.
Everyone who is both generous and not patient is creative and vice versa.
Everyone who is either not strong or not humble is not funny.
If someone is both not strong and not happy then john is both not wise and patient and vice versa.
Everyone who is not curious or calm is old.
If someone is strong or wise then mary is both funny and generous and vice versa.
Everyone who is not quiet is either old or curious and vice versa.
Everyone who is not creative or not curious is both not wise and not strong.
Everyone who is not creative or happy is either not old or happy and vice versa.
Lucy is both rich and old.
Alice is not patient or not happy.
Paul is either calm or not kind.
Someone is not curious or not kind.
Lucy is humble.
Someone is funny or quiet. | Lucy is not calm. | entailment | ((?[X]:((~tall(X)<~>old(X))))<=>(?[X]:((calm(X)<~>funny(X)))))&
(![X]:((~brave(X)|quiet(X))=>(~brave(X)&~funny(X))))&
((?[X]:((rich(X)|strong(X))))<=>(~funny(lucy)))&
(![X]:(~quiet(X)<=>(~strong(X)&creative(X))))&
(((~curious(lucy)&~creative(lucy)))=>(?[X]:((~creative(X)&rich(X)))))&
(![X]:((~kind(X)|generous(X))<=>(quiet(X)|~rich(X))))&
((?[X]:((generous(X)&~curious(X))))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
(![X]:((~old(X)&funny(X))<=>(patient(X)|tall(X))))&
(![X]:((generous(X)&~patient(X))<=>creative(X)))&
(![X]:((~strong(X)<~>~humble(X))=>~funny(X)))&
((?[X]:((~strong(X)&~happy(X))))<=>((~wise(john)&patient(john))))&
(![X]:((~curious(X)|calm(X))=>old(X)))&
((?[X]:((strong(X)|wise(X))))<=>((funny(mary)&generous(mary))))&
(![X]:(~quiet(X)<=>(old(X)<~>curious(X))))&
(![X]:((~creative(X)|~curious(X))=>(~wise(X)&~strong(X))))&
(![X]:((~creative(X)|happy(X))<=>(~old(X)<~>happy(X))))&
((rich(lucy)&old(lucy)))&
((~patient(alice)|~happy(alice)))&
((calm(paul)<~>~kind(paul)))&
(?[X]:((~curious(X)|~kind(X))))&
(humble(lucy))&
(?[X]:((funny(X)|quiet(X)))) | ~calm(lucy) | [
"p0",
"p2",
"p3",
"p7",
"p9",
"p11",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1874980764326651088445818
% SZS output start Proof for 1874980764326651088445818
1. ? [X0] : (~tall(X0) <~> old(X0)) <=> ? [X0] : (calm(X0) <~> funny(X0)) [input p0]
3. ? [X0] : (strong(X0) | rich(X0)) <=> ~funny(lucy) [input p2]
4. ! [X0] : (~quiet(X0) <=> (creative(X0) & ~strong(X0))) [input p3]
8. ! [X0] : ((funny(X0) & ~old(X0)) <=> (tall(X0) | patient(X0))) [input p7]
10. ! [X0] : ((~strong(X0) <~> ~humble(X0)) => ~funny(X0)) [input p9]
12. ! [X0] : ((calm(X0) | ~curious(X0)) => old(X0)) [input p11]
14. ! [X0] : (~quiet(X0) <=> (old(X0) <~> curious(X0))) [input p13]
16. ! [X0] : ((happy(X0) | ~creative(X0)) <=> (~old(X0) <~> happy(X0))) [input p15]
21. humble(lucy) [input p20]
23. calm(lucy) [input hypothesis]
24. ? [X0] : (~tall(X0) <~> old(X0)) <=> ? [X1] : (calm(X1) <~> funny(X1)) [rectify 1]
29. ! [X0] : (~funny(X0) | (~strong(X0) <=> ~humble(X0))) [ennf transformation 10]
30. ! [X0] : (old(X0) | (~calm(X0) & curious(X0))) [ennf transformation 12]
32. (? [X0] : ((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ! [X1] : ((calm(X1) | ~funny(X1)) & (funny(X1) | ~calm(X1)))) & (? [X1] : ((~funny(X1) | ~calm(X1)) & (funny(X1) | calm(X1))) | ! [X0] : ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0)))) [nnf transformation 24]
33. (? [X0] : ((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ! [X1] : ((calm(X1) | ~funny(X1)) & (funny(X1) | ~calm(X1)))) & (? [X2] : ((~funny(X2) | ~calm(X2)) & (funny(X2) | calm(X2))) | ! [X3] : ((~tall(X3) | ~old(X3)) & (old(X3) | tall(X3)))) [rectify 32]
34. ? [X0] : ((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) => ((~old(sK0) | tall(sK0)) & (old(sK0) | ~tall(sK0))) [choice axiom]
35. ? [X2] : ((~funny(X2) | ~calm(X2)) & (funny(X2) | calm(X2))) => ((~funny(sK1) | ~calm(sK1)) & (funny(sK1) | calm(sK1))) [choice axiom]
36. (((~old(sK0) | tall(sK0)) & (old(sK0) | ~tall(sK0))) | ! [X1] : ((calm(X1) | ~funny(X1)) & (funny(X1) | ~calm(X1)))) & (((~funny(sK1) | ~calm(sK1)) & (funny(sK1) | calm(sK1))) | ! [X3] : ((~tall(X3) | ~old(X3)) & (old(X3) | tall(X3)))) [skolemisation 33,35,34]
37. (? [X0] : (strong(X0) | rich(X0)) | funny(lucy)) & (~funny(lucy) | ! [X0] : (~strong(X0) & ~rich(X0))) [nnf transformation 3]
38. (? [X0] : (strong(X0) | rich(X0)) | funny(lucy)) & (~funny(lucy) | ! [X1] : (~strong(X1) & ~rich(X1))) [rectify 37]
39. ? [X0] : (strong(X0) | rich(X0)) => (strong(sK2) | rich(sK2)) [choice axiom]
40. ((strong(sK2) | rich(sK2)) | funny(lucy)) & (~funny(lucy) | ! [X1] : (~strong(X1) & ~rich(X1))) [skolemisation 38,39]
41. ! [X0] : ((~quiet(X0) | (~creative(X0) | strong(X0))) & ((creative(X0) & ~strong(X0)) | quiet(X0))) [nnf transformation 4]
42. ! [X0] : ((~quiet(X0) | ~creative(X0) | strong(X0)) & ((creative(X0) & ~strong(X0)) | quiet(X0))) [flattening 41]
52. ! [X0] : (((funny(X0) & ~old(X0)) | (~tall(X0) & ~patient(X0))) & ((tall(X0) | patient(X0)) | (~funny(X0) | old(X0)))) [nnf transformation 8]
53. ! [X0] : (((funny(X0) & ~old(X0)) | (~tall(X0) & ~patient(X0))) & (tall(X0) | patient(X0) | ~funny(X0) | old(X0))) [flattening 52]
56. ! [X0] : (~funny(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) [nnf transformation 29]
67. ! [X0] : ((~quiet(X0) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0)))) & (((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | quiet(X0))) [nnf transformation 14]
68. ! [X0] : (((happy(X0) | ~creative(X0)) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0)))) & (((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | (~happy(X0) & creative(X0)))) [nnf transformation 16]
69. ! [X0] : ((happy(X0) | ~creative(X0) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0)))) & (((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | (~happy(X0) & creative(X0)))) [flattening 68]
81. ~old(sK0) | tall(sK0) | funny(X1) | ~calm(X1) [cnf transformation 36]
88. ~funny(lucy) | ~strong(X1) [cnf transformation 40]
91. creative(X0) | quiet(X0) [cnf transformation 42]
107. ~old(X0) | ~tall(X0) [cnf transformation 53]
113. ~humble(X0) | ~funny(X0) | strong(X0) [cnf transformation 56]
119. curious(X0) | old(X0) [cnf transformation 30]
129. ~quiet(X0) | old(X0) | ~curious(X0) [cnf transformation 67]
137. ~happy(X0) | old(X0) | ~happy(X0) [cnf transformation 69]
138. happy(X0) | ~creative(X0) | happy(X0) | old(X0) [cnf transformation 69]
146. humble(lucy) [cnf transformation 21]
148. calm(lucy) [cnf transformation 23]
149. ~happy(X0) | old(X0) [duplicate literal removal 137]
150. ~creative(X0) | happy(X0) | old(X0) [duplicate literal removal 138]
155. 2 <=> tall(sK0) [avatar definition]
157. tall(sK0) <- (2) [avatar component clause 155]
159. 3 <=> old(sK0) [avatar definition]
160. old(sK0) <- (3) [avatar component clause 159]
161. ~old(sK0) <- (~3) [avatar component clause 159]
164. 4 <=> ! [X1] : (funny(X1) | ~calm(X1)) [avatar definition]
165. ~calm(X1) | funny(X1) <- (4) [avatar component clause 164]
166. 4 | 2 | ~3 [avatar split clause 81,159,155,164]
170. 5 <=> ! [X3] : (~tall(X3) | ~old(X3)) [avatar definition]
171. ~old(X3) | ~tall(X3) <- (5) [avatar component clause 170]
188. 9 <=> funny(lucy) [avatar definition]
189. ~funny(lucy) <- (~9) [avatar component clause 188]
201. 12 <=> ! [X1] : ~strong(X1) [avatar definition]
202. ~strong(X1) <- (12) [avatar component clause 201]
203. 12 | ~9 [avatar split clause 88,188,201]
257. 5 [avatar split clause 107,170]
305. ~quiet(X0) | old(X0) [subsumption resolution 129,119]
428. ~funny(lucy) | strong(lucy) [resolution 113,146]
530. funny(lucy) <- (4) [resolution 165,148]
531. $false <- (4, ~9) [subsumption resolution 530,189]
532. ~4 | 9 [avatar contradiction clause 531]
534. ~tall(sK0) <- (3, 5) [resolution 160,171]
544. $false <- (2, 3, 5) [subsumption resolution 534,157]
545. ~2 | ~3 | ~5 [avatar contradiction clause 544]
551. happy(X0) | old(X0) | quiet(X0) [resolution 150,91]
554. old(X0) | quiet(X0) [subsumption resolution 551,149]
555. old(X0) [subsumption resolution 554,305]
617. $false <- (~3) [resolution 555,161]
618. 3 [avatar contradiction clause 617]
620. 64 <=> strong(lucy) [avatar definition]
622. strong(lucy) <- (64) [avatar component clause 620]
623. 64 | ~9 [avatar split clause 428,188,620]
627. $false <- (12, 64) [subsumption resolution 622,202]
628. ~12 | ~64 [avatar contradiction clause 627]
629. $false [avatar sat refutation 166,203,257,532,545,618,623,628]
% SZS output end Proof for 1874980764326651088445818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not patient and brave is either creative or curious. If someone is not creative then susan is humble. Everyone who is quiet or not strong is either not tall or calm. Everyone who is tall or kind is generous and vice versa. Everyone who is both not tall and not quiet is brave. If john is not humble or patient then someone is rich or not generous. If someone is not humble then someone is not old and vice versa. If someone is both calm and not wise then alice is not wise or creative. Everyone who is both not patient and not humble is either not curious or calm. If mary is patient or wise then lucy is both not calm and quiet. Everyone who is kind or humble is both not creative and kind. Everyone who is either quiet or brave is either not tall or humble and vice versa. Everyone who is either humble or kind is brave and vice versa. Everyone who is wise or quiet is not rich or strong. If paul is brave then someone is happy and vice versa. Everyone who is calm is both kind and patient. Someone is not funny. Lucy is both generous and not kind. Someone is both not kind and old. Lucy is either curious or calm. Susan is either calm or quiet. Mary is not funny or not wise. Someone is either not wise or not happy. Susan is not humble. | Mary is calm. | contradiction | (![X]:((~patient(X)&brave(X))=>(creative(X)<~>curious(X))))&
((?[X]:(~creative(X)))=>(humble(susan)))&
(![X]:((quiet(X)|~strong(X))=>(~tall(X)<~>calm(X))))&
(![X]:((tall(X)|kind(X))<=>generous(X)))&
(![X]:((~tall(X)&~quiet(X))=>brave(X)))&
(((~humble(john)|patient(john)))=>(?[X]:((rich(X)|~generous(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(~old(X))))&
((?[X]:((calm(X)&~wise(X))))=>((~wise(alice)|creative(alice))))&
(![X]:((~patient(X)&~humble(X))=>(~curious(X)<~>calm(X))))&
(((patient(mary)|wise(mary)))=>((~calm(lucy)&quiet(lucy))))&
(![X]:((kind(X)|humble(X))=>(~creative(X)&kind(X))))&
(![X]:((quiet(X)<~>brave(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((humble(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|quiet(X))=>(~rich(X)|strong(X))))&
((brave(paul))<=>(?[X]:(happy(X))))&
(![X]:(calm(X)=>(kind(X)&patient(X))))&
(?[X]:(~funny(X)))&
((generous(lucy)&~kind(lucy)))&
(?[X]:((~kind(X)&old(X))))&
((curious(lucy)<~>calm(lucy)))&
((calm(susan)<~>quiet(susan)))&
((~funny(mary)|~wise(mary)))&
(?[X]:((~wise(X)<~>~happy(X))))&
(~humble(susan)) | calm(mary) | [
"p1",
"p10",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8050524912982801902868131
% SZS output start Proof for 8050524912982801902868131
2. ? [X0] : ~creative(X0) => humble(susan) [input p1]
11. ! [X0] : ((humble(X0) | kind(X0)) => (kind(X0) & ~creative(X0))) [input p10]
16. ! [X0] : (calm(X0) => (patient(X0) & kind(X0))) [input p15]
24. ~humble(susan) [input p23]
25. calm(mary) [input hypothesis]
35. humble(susan) | ! [X0] : creative(X0) [ennf transformation 2]
46. ! [X0] : ((kind(X0) & ~creative(X0)) | (~humble(X0) & ~kind(X0))) [ennf transformation 11]
47. ! [X0] : ((patient(X0) & kind(X0)) | ~calm(X0)) [ennf transformation 16]
71. humble(susan) | creative(X0) [cnf transformation 35]
85. ~kind(X0) | ~creative(X0) [cnf transformation 46]
103. ~calm(X0) | kind(X0) [cnf transformation 47]
115. ~humble(susan) [cnf transformation 24]
116. calm(mary) [cnf transformation 25]
118. 1 <=> ! [X0] : creative(X0) [avatar definition]
119. creative(X0) <- (1) [avatar component clause 118]
121. 2 <=> humble(susan) [avatar definition]
124. 1 | 2 [avatar split clause 71,121,118]
217. ~2 [avatar split clause 115,121]
218. kind(mary) [resolution 103,116]
223. ~creative(mary) [resolution 218,85]
224. $false <- (1) [subsumption resolution 223,119]
225. ~1 [avatar contradiction clause 224]
226. $false [avatar sat refutation 124,217,225]
% SZS output end Proof for 8050524912982801902868131
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 rich is both humble and not calm.
If someone is not old or not curious then lucy is rich and vice versa.
If someone is either not patient or brave then someone is both generous and not creative.
Everyone who is both funny and quiet is both patient and quiet and vice versa.
If fred is both not tall and not strong then fred is either funny or not funny and vice versa.
Everyone who is either not generous or not brave is calm or not creative and vice versa.
If someone is not strong then lucy is not patient and vice versa.
Everyone who is wise or not curious is not brave or wise and vice versa.
Everyone who is both not funny and not kind is both not creative and curious and vice versa.
Everyone who is rich is creative.
If someone is either wise or calm then lucy is not strong or not quiet and vice versa.
Everyone who is both tall and humble is wise or not creative and vice versa.
If someone is not calm or curious then alice is rich or not kind and vice versa.
If someone is not tall then john is both not humble and not happy.
If john is not curious or not calm then someone is both not wise and not old.
If mary is both not generous and not old then fred is either not tall or tall and vice versa.
Lucy is not happy or not curious.
Someone is old.
Someone is happy.
Someone is both tall and wise.
Alice is either not old or not humble.
Someone is both not rich and tall. | Fred is quiet. | neutral | (![X]:(rich(X)=>(humble(X)&~calm(X))))&
((?[X]:((~old(X)|~curious(X))))<=>(rich(lucy)))&
((?[X]:((~patient(X)<~>brave(X))))=>(?[X]:((generous(X)&~creative(X)))))&
(![X]:((funny(X)&quiet(X))<=>(patient(X)&quiet(X))))&
(((~tall(fred)&~strong(fred)))<=>((funny(fred)<~>~funny(fred))))&
(![X]:((~generous(X)<~>~brave(X))<=>(calm(X)|~creative(X))))&
((?[X]:(~strong(X)))<=>(~patient(lucy)))&
(![X]:((wise(X)|~curious(X))<=>(~brave(X)|wise(X))))&
(![X]:((~funny(X)&~kind(X))<=>(~creative(X)&curious(X))))&
(![X]:(rich(X)=>creative(X)))&
((?[X]:((wise(X)<~>calm(X))))<=>((~strong(lucy)|~quiet(lucy))))&
(![X]:((tall(X)&humble(X))<=>(wise(X)|~creative(X))))&
((?[X]:((~calm(X)|curious(X))))<=>((rich(alice)|~kind(alice))))&
((?[X]:(~tall(X)))=>((~humble(john)&~happy(john))))&
(((~curious(john)|~calm(john)))=>(?[X]:((~wise(X)&~old(X)))))&
(((~generous(mary)&~old(mary)))<=>((~tall(fred)<~>tall(fred))))&
((~happy(lucy)|~curious(lucy)))&
(?[X]:(old(X)))&
(?[X]:(happy(X)))&
(?[X]:((tall(X)&wise(X))))&
((~old(alice)<~>~humble(alice)))&
(?[X]:((~rich(X)&tall(X)))) | quiet(fred) | [] | null | 0 |
Everyone who is either not creative or not generous is not happy. Everyone who is not tall or not generous is both not old and not patient. Everyone who is rich or creative is old or not patient and vice versa. Everyone who is either not old or kind is not creative or not humble and vice versa. If someone is not strong then someone is not old or not creative and vice versa. If someone is either not rich or funny then someone is not wise or not brave and vice versa. Everyone who is not creative is either not rich or quiet. Everyone who is not curious or quiet is curious or not brave. Everyone who is either not strong or kind is humble or brave and vice versa. Everyone who is calm is brave and vice versa. If lucy is both kind and not funny then someone is either not wise or not strong. Everyone who is both calm and brave is either strong or not humble and vice versa. If paul is curious then someone is either not tall or not creative. If lucy is not tall then mary is both not funny and not curious and vice versa. Everyone who is both creative and curious is either not old or not quiet and vice versa. If someone is either not tall or not brave then someone is not old or funny. Paul is not funny. Mary is not humble. Someone is quiet or not curious. Someone is not old or brave. Someone is both old and not kind. John is not strong. John is calm or kind. Someone is either calm or not creative. | John is not old. | entailment | (![X]:((~creative(X)<~>~generous(X))=>~happy(X)))&
(![X]:((~tall(X)|~generous(X))=>(~old(X)&~patient(X))))&
(![X]:((rich(X)|creative(X))<=>(old(X)|~patient(X))))&
(![X]:((~old(X)<~>kind(X))<=>(~creative(X)|~humble(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~old(X)|~creative(X)))))&
((?[X]:((~rich(X)<~>funny(X))))<=>(?[X]:((~wise(X)|~brave(X)))))&
(![X]:(~creative(X)=>(~rich(X)<~>quiet(X))))&
(![X]:((~curious(X)|quiet(X))=>(curious(X)|~brave(X))))&
(![X]:((~strong(X)<~>kind(X))<=>(humble(X)|brave(X))))&
(![X]:(calm(X)<=>brave(X)))&
(((kind(lucy)&~funny(lucy)))=>(?[X]:((~wise(X)<~>~strong(X)))))&
(![X]:((calm(X)&brave(X))<=>(strong(X)<~>~humble(X))))&
((curious(paul))=>(?[X]:((~tall(X)<~>~creative(X)))))&
((~tall(lucy))<=>((~funny(mary)&~curious(mary))))&
(![X]:((creative(X)&curious(X))<=>(~old(X)<~>~quiet(X))))&
((?[X]:((~tall(X)<~>~brave(X))))=>(?[X]:((~old(X)|funny(X)))))&
(~funny(paul))&
(~humble(mary))&
(?[X]:((quiet(X)|~curious(X))))&
(?[X]:((~old(X)|brave(X))))&
(?[X]:((old(X)&~kind(X))))&
(~strong(john))&
((calm(john)|kind(john)))&
(?[X]:((calm(X)<~>~creative(X)))) | ~old(john) | [
"p3",
"p8",
"p9",
"p11",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1900440083253168431920032
% SZS output start Proof for 1900440083253168431920032
4. ! [X0] : ((~old(X0) <~> kind(X0)) <=> (~humble(X0) | ~creative(X0))) [input p3]
9. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (brave(X0) | humble(X0))) [input p8]
10. ! [X0] : (calm(X0) <=> brave(X0)) [input p9]
12. ! [X0] : ((brave(X0) & calm(X0)) <=> (strong(X0) <~> ~humble(X0))) [input p11]
22. ~strong(john) [input p21]
23. kind(john) | calm(john) [input p22]
25. old(john) [input hypothesis]
41. ! [X0] : ((((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (humble(X0) & creative(X0))) & ((~humble(X0) | ~creative(X0)) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (humble(X0) & creative(X0))) & (~humble(X0) | ~creative(X0) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))))) [flattening 41]
54. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [flattening 54]
56. ! [X0] : ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0))) [nnf transformation 10]
60. ! [X0] : (((brave(X0) & calm(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (~brave(X0) | ~calm(X0)))) [nnf transformation 12]
61. ! [X0] : (((brave(X0) & calm(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | ~brave(X0) | ~calm(X0))) [flattening 60]
91. ~old(X0) | kind(X0) | humble(X0) [cnf transformation 42]
111. ~humble(X0) | strong(X0) | ~kind(X0) [cnf transformation 55]
112. ~brave(X0) | strong(X0) | ~kind(X0) [cnf transformation 55]
113. ~calm(X0) | brave(X0) [cnf transformation 56]
117. ~humble(X0) | strong(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 61]
122. brave(X0) | strong(X0) | humble(X0) [cnf transformation 61]
142. ~strong(john) [cnf transformation 22]
143. kind(john) | calm(john) [cnf transformation 23]
146. old(john) [cnf transformation 25]
225. ~calm(X0) | strong(X0) | ~humble(X0) [subsumption resolution 117,113]
290. 33 <=> calm(john) [avatar definition]
292. calm(john) <- (33) [avatar component clause 290]
294. 34 <=> kind(john) [avatar definition]
296. kind(john) <- (34) [avatar component clause 294]
297. 33 | 34 [avatar split clause 143,294,290]
353. kind(john) | humble(john) [resolution 91,146]
356. 44 <=> humble(john) [avatar definition]
358. humble(john) <- (44) [avatar component clause 356]
359. 44 | 34 [avatar split clause 353,294,356]
397. strong(X0) | humble(X0) | strong(X0) | ~kind(X0) [resolution 122,112]
401. strong(X0) | humble(X0) | ~kind(X0) [duplicate literal removal 397]
402. ~kind(X0) | strong(X0) [subsumption resolution 401,111]
434. strong(john) | ~humble(john) <- (33) [resolution 225,292]
437. ~humble(john) <- (33) [subsumption resolution 434,142]
438. $false <- (33, 44) [subsumption resolution 437,358]
439. ~33 | ~44 [avatar contradiction clause 438]
478. strong(john) <- (34) [resolution 402,296]
479. $false <- (34) [subsumption resolution 478,142]
480. ~34 [avatar contradiction clause 479]
481. $false [avatar sat refutation 297,359,439,480]
% SZS output end Proof for 1900440083253168431920032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not strong is not generous or not strong. Everyone who is both not strong and not calm is either not humble or humble. Everyone who is curious or humble is not curious and vice versa. If lucy is both brave and tall then someone is not patient and vice versa. Everyone who is not tall or not rich is wise. If someone is either not funny or not curious then someone is not curious or curious and vice versa. If susan is either kind or not rich then someone is either creative or strong and vice versa. If someone is not funny or rich then someone is old and vice versa. Everyone who is humble or not strong is both not wise and not calm. Everyone who is either quiet or humble is both not calm and not curious. If fred is either not generous or wise then someone is old. Everyone who is not old is not rich and vice versa. Everyone who is not funny is not generous and vice versa. If someone is not rich then someone is wise or quiet and vice versa. If someone is both kind and creative then paul is wise or old. If alice is wise then someone is either old or not quiet and vice versa. Someone is not tall or strong. John is not generous. Someone is either tall or generous. Mary is both rich and kind. Someone is not generous. Someone is either not strong or not calm. Someone is either generous or not calm. | Mary is not quiet. | entailment | (![X]:((~rich(X)<~>~strong(X))=>(~generous(X)|~strong(X))))&
(![X]:((~strong(X)&~calm(X))=>(~humble(X)<~>humble(X))))&
(![X]:((curious(X)|humble(X))<=>~curious(X)))&
(((brave(lucy)&tall(lucy)))<=>(?[X]:(~patient(X))))&
(![X]:((~tall(X)|~rich(X))=>wise(X)))&
((?[X]:((~funny(X)<~>~curious(X))))<=>(?[X]:((~curious(X)|curious(X)))))&
(((kind(susan)<~>~rich(susan)))<=>(?[X]:((creative(X)<~>strong(X)))))&
((?[X]:((~funny(X)|rich(X))))<=>(?[X]:(old(X))))&
(![X]:((humble(X)|~strong(X))=>(~wise(X)&~calm(X))))&
(![X]:((quiet(X)<~>humble(X))=>(~calm(X)&~curious(X))))&
(((~generous(fred)<~>wise(fred)))=>(?[X]:(old(X))))&
(![X]:(~old(X)<=>~rich(X)))&
(![X]:(~funny(X)<=>~generous(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((wise(X)|quiet(X)))))&
((?[X]:((kind(X)&creative(X))))=>((wise(paul)|old(paul))))&
((wise(alice))<=>(?[X]:((old(X)<~>~quiet(X)))))&
(?[X]:((~tall(X)|strong(X))))&
(~generous(john))&
(?[X]:((tall(X)<~>generous(X))))&
((rich(mary)&kind(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((~strong(X)<~>~calm(X))))&
(?[X]:((generous(X)<~>~calm(X)))) | ~quiet(mary) | [
"p2",
"p8",
"p11",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 395552678612028863710319
% SZS output start Proof for 395552678612028863710319
3. ! [X0] : ((humble(X0) | curious(X0)) <=> ~curious(X0)) [input p2]
9. ! [X0] : ((~strong(X0) | humble(X0)) => (~calm(X0) & ~wise(X0))) [input p8]
12. ! [X0] : (~old(X0) <=> ~rich(X0)) [input p11]
16. wise(alice) <=> ? [X0] : (old(X0) <~> ~quiet(X0)) [input p15]
20. kind(mary) & rich(mary) [input p19]
24. quiet(mary) [input hypothesis]
33. ! [X0] : ((~calm(X0) & ~wise(X0)) | (strong(X0) & ~humble(X0))) [ennf transformation 9]
40. ! [X0] : (((humble(X0) | curious(X0)) | curious(X0)) & (~curious(X0) | (~humble(X0) & ~curious(X0)))) [nnf transformation 3]
41. ! [X0] : ((humble(X0) | curious(X0) | curious(X0)) & (~curious(X0) | (~humble(X0) & ~curious(X0)))) [flattening 40]
65. ! [X0] : ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))) [nnf transformation 12]
72. (wise(alice) | ! [X0] : ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (? [X0] : ((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | ~wise(alice)) [nnf transformation 16]
73. (wise(alice) | ! [X0] : ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (? [X1] : ((quiet(X1) | ~old(X1)) & (~quiet(X1) | old(X1))) | ~wise(alice)) [rectify 72]
74. ? [X1] : ((quiet(X1) | ~old(X1)) & (~quiet(X1) | old(X1))) => ((quiet(sK9) | ~old(sK9)) & (~quiet(sK9) | old(sK9))) [choice axiom]
75. (wise(alice) | ! [X0] : ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(sK9) | ~old(sK9)) & (~quiet(sK9) | old(sK9))) | ~wise(alice)) [skolemisation 73,74]
93. ~curious(X0) | ~curious(X0) [cnf transformation 41]
95. humble(X0) | curious(X0) | curious(X0) [cnf transformation 41]
118. ~wise(X0) | ~humble(X0) [cnf transformation 33]
128. ~rich(X0) | old(X0) [cnf transformation 65]
138. wise(alice) | ~quiet(X0) | ~old(X0) [cnf transformation 75]
144. rich(mary) [cnf transformation 20]
151. quiet(mary) [cnf transformation 24]
152. ~curious(X0) [duplicate literal removal 93]
153. curious(X0) | humble(X0) [duplicate literal removal 95]
284. 30 <=> wise(alice) [avatar definition]
286. wise(alice) <- (30) [avatar component clause 284]
289. 31 <=> ! [X0] : (~quiet(X0) | ~old(X0)) [avatar definition]
290. ~quiet(X0) | ~old(X0) <- (31) [avatar component clause 289]
291. 31 | 30 [avatar split clause 138,284,289]
340. ~humble(alice) <- (30) [resolution 118,286]
347. old(mary) [resolution 128,144]
353. humble(X1) [resolution 153,152]
361. $false <- (30) [resolution 353,340]
364. ~30 [avatar contradiction clause 361]
385. ~old(mary) <- (31) [resolution 290,151]
388. $false <- (31) [subsumption resolution 385,347]
389. ~31 [avatar contradiction clause 388]
390. $false [avatar sat refutation 291,364,389]
% SZS output end Proof for 395552678612028863710319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not funny or not generous then someone is quiet and vice versa.
If mary is curious then someone is wise or funny.
Everyone who is not humble is brave or not quiet and vice versa.
Everyone who is both wise and not generous is not strong or wise and vice versa.
Everyone who is wise is funny or wise and vice versa.
If alice is both kind and happy then someone is both not kind and quiet.
If susan is both not old and kind then fred is either old or calm and vice versa.
If john is kind then someone is both old and brave.
If lucy is curious or not old then lucy is either not humble or brave.
Everyone who is humble is both calm and not calm and vice versa.
Everyone who is not curious or creative is both not patient and not old and vice versa.
If john is brave or calm then john is patient or strong and vice versa.
Everyone who is either not humble or patient is either happy or not patient and vice versa.
Everyone who is either strong or creative is tall or patient.
Everyone who is not kind or not calm is both curious and creative and vice versa.
Everyone who is both old and not strong is not humble or strong and vice versa.
Someone is not quiet.
Someone is either not quiet or not creative.
Someone is either rich or humble.
Lucy is not tall or not wise.
Lucy is either wise or generous.
Alice is either humble or patient. | Lucy is calm. | entailment | (((~funny(mary)|~generous(mary)))<=>(?[X]:(quiet(X))))&
((curious(mary))=>(?[X]:((wise(X)|funny(X)))))&
(![X]:(~humble(X)<=>(brave(X)|~quiet(X))))&
(![X]:((wise(X)&~generous(X))<=>(~strong(X)|wise(X))))&
(![X]:(wise(X)<=>(funny(X)|wise(X))))&
(((kind(alice)&happy(alice)))=>(?[X]:((~kind(X)&quiet(X)))))&
(((~old(susan)&kind(susan)))<=>((old(fred)<~>calm(fred))))&
((kind(john))=>(?[X]:((old(X)&brave(X)))))&
(((curious(lucy)|~old(lucy)))=>((~humble(lucy)<~>brave(lucy))))&
(![X]:(humble(X)<=>(calm(X)&~calm(X))))&
(![X]:((~curious(X)|creative(X))<=>(~patient(X)&~old(X))))&
(((brave(john)|calm(john)))<=>((patient(john)|strong(john))))&
(![X]:((~humble(X)<~>patient(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((strong(X)<~>creative(X))=>(tall(X)|patient(X))))&
(![X]:((~kind(X)|~calm(X))<=>(curious(X)&creative(X))))&
(![X]:((old(X)&~strong(X))<=>(~humble(X)|strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(?[X]:((rich(X)<~>humble(X))))&
((~tall(lucy)|~wise(lucy)))&
((wise(lucy)<~>generous(lucy)))&
((humble(alice)<~>patient(alice))) | calm(lucy) | [
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4606894052878318270974380
% SZS output start Proof for 4606894052878318270974380
10. ! [X0] : (humble(X0) <=> (~calm(X0) & calm(X0))) [input p9]
11. ! [X0] : ((creative(X0) | ~curious(X0)) <=> (~old(X0) & ~patient(X0))) [input p10]
15. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> (creative(X0) & curious(X0))) [input p14]
16. ! [X0] : ((~strong(X0) & old(X0)) <=> (strong(X0) | ~humble(X0))) [input p15]
23. ~calm(lucy) [input hypothesis]
51. ! [X0] : ((humble(X0) | (calm(X0) | ~calm(X0))) & ((~calm(X0) & calm(X0)) | ~humble(X0))) [nnf transformation 10]
52. ! [X0] : ((humble(X0) | calm(X0) | ~calm(X0)) & ((~calm(X0) & calm(X0)) | ~humble(X0))) [flattening 51]
53. ! [X0] : (((creative(X0) | ~curious(X0)) | (old(X0) | patient(X0))) & ((~old(X0) & ~patient(X0)) | (~creative(X0) & curious(X0)))) [nnf transformation 11]
54. ! [X0] : ((creative(X0) | ~curious(X0) | old(X0) | patient(X0)) & ((~old(X0) & ~patient(X0)) | (~creative(X0) & curious(X0)))) [flattening 53]
59. ! [X0] : (((~calm(X0) | ~kind(X0)) | (~creative(X0) | ~curious(X0))) & ((creative(X0) & curious(X0)) | (calm(X0) & kind(X0)))) [nnf transformation 15]
60. ! [X0] : ((~calm(X0) | ~kind(X0) | ~creative(X0) | ~curious(X0)) & ((creative(X0) & curious(X0)) | (calm(X0) & kind(X0)))) [flattening 59]
61. ! [X0] : (((~strong(X0) & old(X0)) | (~strong(X0) & humble(X0))) & ((strong(X0) | ~humble(X0)) | (strong(X0) | ~old(X0)))) [nnf transformation 16]
62. ! [X0] : (((~strong(X0) & old(X0)) | (~strong(X0) & humble(X0))) & (strong(X0) | ~humble(X0) | strong(X0) | ~old(X0))) [flattening 61]
102. calm(X0) | ~humble(X0) [cnf transformation 52]
103. ~calm(X0) | ~humble(X0) [cnf transformation 52]
108. ~creative(X0) | ~old(X0) [cnf transformation 54]
127. creative(X0) | calm(X0) [cnf transformation 60]
130. old(X0) | humble(X0) [cnf transformation 62]
144. ~calm(lucy) [cnf transformation 23]
260. ~humble(X0) [subsumption resolution 102,103]
285. old(X0) [subsumption resolution 130,260]
338. calm(X0) | ~old(X0) [resolution 127,108]
339. calm(X0) [subsumption resolution 338,285]
351. $false [resolution 339,144]
% SZS output end Proof for 4606894052878318270974380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not patient is not kind and vice versa. If someone is both creative and not creative then alice is not creative. If lucy is either not curious or old then alice is rich or quiet and vice versa. Everyone who is either humble or old is either strong or kind and vice versa. If someone is either curious or humble then lucy is not curious. If someone is either not tall or kind then someone is not generous or not funny and vice versa. Everyone who is quiet is both not quiet and not funny and vice versa. Everyone who is wise is calm or brave. If john is generous then someone is both not creative and old and vice versa. Everyone who is either not old or curious is not patient and vice versa. If someone is both not funny and not strong then mary is tall or not tall. If someone is not calm or quiet then someone is both not tall and strong. If someone is either not strong or generous then mary is either strong or quiet. If someone is both not kind and not wise then someone is both funny and rich. If mary is either not wise or quiet then someone is either not creative or old. If paul is either patient or old then paul is either not brave or happy. Someone is not brave or not happy. Susan is both not creative and not calm. Alice is either calm or not calm. Someone is either not wise or strong. Mary is tall or brave. Fred is not curious. Someone is not strong or not funny. | Susan is quiet. | contradiction | (![X]:((~happy(X)&~patient(X))<=>~kind(X)))&
((?[X]:((creative(X)&~creative(X))))=>(~creative(alice)))&
(((~curious(lucy)<~>old(lucy)))<=>((rich(alice)|quiet(alice))))&
(![X]:((humble(X)<~>old(X))<=>(strong(X)<~>kind(X))))&
((?[X]:((curious(X)<~>humble(X))))=>(~curious(lucy)))&
((?[X]:((~tall(X)<~>kind(X))))<=>(?[X]:((~generous(X)|~funny(X)))))&
(![X]:(quiet(X)<=>(~quiet(X)&~funny(X))))&
(![X]:(wise(X)=>(calm(X)|brave(X))))&
((generous(john))<=>(?[X]:((~creative(X)&old(X)))))&
(![X]:((~old(X)<~>curious(X))<=>~patient(X)))&
((?[X]:((~funny(X)&~strong(X))))=>((tall(mary)|~tall(mary))))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((~tall(X)&strong(X)))))&
((?[X]:((~strong(X)<~>generous(X))))=>((strong(mary)<~>quiet(mary))))&
((?[X]:((~kind(X)&~wise(X))))=>(?[X]:((funny(X)&rich(X)))))&
(((~wise(mary)<~>quiet(mary)))=>(?[X]:((~creative(X)<~>old(X)))))&
(((patient(paul)<~>old(paul)))=>((~brave(paul)<~>happy(paul))))&
(?[X]:((~brave(X)|~happy(X))))&
((~creative(susan)&~calm(susan)))&
((calm(alice)<~>~calm(alice)))&
(?[X]:((~wise(X)<~>strong(X))))&
((tall(mary)|brave(mary)))&
(~curious(fred))&
(?[X]:((~strong(X)|~funny(X)))) | quiet(susan) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 9118687529133038849719686
% SZS output start Proof for 9118687529133038849719686
7. ! [X0] : (quiet(X0) <=> (~funny(X0) & ~quiet(X0))) [input p6]
24. quiet(susan) [input hypothesis]
50. ! [X0] : ((quiet(X0) | (funny(X0) | quiet(X0))) & ((~funny(X0) & ~quiet(X0)) | ~quiet(X0))) [nnf transformation 7]
51. ! [X0] : ((quiet(X0) | funny(X0) | quiet(X0)) & ((~funny(X0) & ~quiet(X0)) | ~quiet(X0))) [flattening 50]
102. ~quiet(X0) | ~quiet(X0) [cnf transformation 51]
142. quiet(susan) [cnf transformation 24]
143. ~quiet(X0) [duplicate literal removal 102]
340. $false [subsumption resolution 142,143]
% SZS output end Proof for 9118687529133038849719686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or quiet is patient and vice versa. Everyone who is strong or not old is not funny and vice versa. Everyone who is not calm or happy is curious or generous and vice versa. If alice is generous or not quiet then someone is not happy and vice versa. Everyone who is both humble and not strong is both not quiet and not funny and vice versa. If someone is either not wise or not creative then someone is either not strong or calm and vice versa. Everyone who is either generous or kind is patient. Everyone who is not kind or calm is curious or rich and vice versa. Everyone who is not curious is either not brave or old and vice versa. If someone is either old or not happy then someone is either not brave or humble. Everyone who is old is not patient or not tall. If alice is rich or strong then someone is either generous or not humble and vice versa. Everyone who is both not funny and strong is both not calm and calm. Everyone who is old or not wise is not quiet or wise and vice versa. Everyone who is happy is both not generous and brave. If mary is both quiet and not calm then lucy is not brave or happy and vice versa. Fred is strong or not kind. Alice is both old and not creative. Paul is either not old or not creative. Someone is not creative. Someone is kind. Someone is not happy or not humble. | Alice is not calm. | entailment | (![X]:((~patient(X)|quiet(X))<=>patient(X)))&
(![X]:((strong(X)|~old(X))<=>~funny(X)))&
(![X]:((~calm(X)|happy(X))<=>(curious(X)|generous(X))))&
(((generous(alice)|~quiet(alice)))<=>(?[X]:(~happy(X))))&
(![X]:((humble(X)&~strong(X))<=>(~quiet(X)&~funny(X))))&
((?[X]:((~wise(X)<~>~creative(X))))<=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:((generous(X)<~>kind(X))=>patient(X)))&
(![X]:((~kind(X)|calm(X))<=>(curious(X)|rich(X))))&
(![X]:(~curious(X)<=>(~brave(X)<~>old(X))))&
((?[X]:((old(X)<~>~happy(X))))=>(?[X]:((~brave(X)<~>humble(X)))))&
(![X]:(old(X)=>(~patient(X)|~tall(X))))&
(((rich(alice)|strong(alice)))<=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:((~funny(X)&strong(X))=>(~calm(X)&calm(X))))&
(![X]:((old(X)|~wise(X))<=>(~quiet(X)|wise(X))))&
(![X]:(happy(X)=>(~generous(X)&brave(X))))&
(((quiet(mary)&~calm(mary)))<=>((~brave(lucy)|happy(lucy))))&
((strong(fred)|~kind(fred)))&
((old(alice)&~creative(alice)))&
((~old(paul)<~>~creative(paul)))&
(?[X]:(~creative(X)))&
(?[X]:(kind(X)))&
(?[X]:((~happy(X)|~humble(X)))) | ~calm(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p9",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3139706467440620311751763
% SZS output start Proof for 3139706467440620311751763
1. ! [X0] : ((quiet(X0) | ~patient(X0)) <=> patient(X0)) [input p0]
2. ! [X0] : ((~old(X0) | strong(X0)) <=> ~funny(X0)) [input p1]
3. ! [X0] : ((happy(X0) | ~calm(X0)) <=> (generous(X0) | curious(X0))) [input p2]
4. (~quiet(alice) | generous(alice)) <=> ? [X0] : ~happy(X0) [input p3]
5. ! [X0] : ((~strong(X0) & humble(X0)) <=> (~funny(X0) & ~quiet(X0))) [input p4]
10. ? [X0] : (old(X0) <~> ~happy(X0)) => ? [X0] : (~brave(X0) <~> humble(X0)) [input p9]
13. ! [X0] : ((strong(X0) & ~funny(X0)) => (calm(X0) & ~calm(X0))) [input p12]
14. ! [X0] : ((~wise(X0) | old(X0)) <=> (wise(X0) | ~quiet(X0))) [input p13]
15. ! [X0] : (happy(X0) => (brave(X0) & ~generous(X0))) [input p14]
23. calm(alice) [input hypothesis]
25. ? [X0] : (old(X0) <~> ~happy(X0)) => ? [X1] : (~brave(X1) <~> humble(X1)) [rectify 10]
28. ? [X1] : (~brave(X1) <~> humble(X1)) | ! [X0] : (old(X0) <=> ~happy(X0)) [ennf transformation 25]
29. ! [X0] : ((calm(X0) & ~calm(X0)) | (~strong(X0) | funny(X0))) [ennf transformation 13]
30. ! [X0] : ((calm(X0) & ~calm(X0)) | ~strong(X0) | funny(X0)) [flattening 29]
31. ! [X0] : ((brave(X0) & ~generous(X0)) | ~happy(X0)) [ennf transformation 15]
32. ! [X0] : (((quiet(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & patient(X0)))) [nnf transformation 1]
33. ! [X0] : ((quiet(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (~quiet(X0) & patient(X0)))) [flattening 32]
34. ! [X0] : (((~old(X0) | strong(X0)) | funny(X0)) & (~funny(X0) | (old(X0) & ~strong(X0)))) [nnf transformation 2]
35. ! [X0] : ((~old(X0) | strong(X0) | funny(X0)) & (~funny(X0) | (old(X0) & ~strong(X0)))) [flattening 34]
36. ! [X0] : (((happy(X0) | ~calm(X0)) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | (~happy(X0) & calm(X0)))) [nnf transformation 3]
37. ! [X0] : ((happy(X0) | ~calm(X0) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | (~happy(X0) & calm(X0)))) [flattening 36]
38. ((~quiet(alice) | generous(alice)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (quiet(alice) & ~generous(alice))) [nnf transformation 4]
39. (~quiet(alice) | generous(alice) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (quiet(alice) & ~generous(alice))) [flattening 38]
40. (~quiet(alice) | generous(alice) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | (quiet(alice) & ~generous(alice))) [rectify 39]
41. ? [X1] : ~happy(X1) => ~happy(sK0) [choice axiom]
42. (~quiet(alice) | generous(alice) | ! [X0] : happy(X0)) & (~happy(sK0) | (quiet(alice) & ~generous(alice))) [skolemisation 40,41]
43. ! [X0] : (((~strong(X0) & humble(X0)) | (funny(X0) | quiet(X0))) & ((~funny(X0) & ~quiet(X0)) | (strong(X0) | ~humble(X0)))) [nnf transformation 5]
44. ! [X0] : (((~strong(X0) & humble(X0)) | funny(X0) | quiet(X0)) & ((~funny(X0) & ~quiet(X0)) | strong(X0) | ~humble(X0))) [flattening 43]
54. ? [X1] : ((~humble(X1) | brave(X1)) & (humble(X1) | ~brave(X1))) | ! [X0] : ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0))) [nnf transformation 28]
55. ? [X0] : ((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | ! [X1] : ((old(X1) | happy(X1)) & (~happy(X1) | ~old(X1))) [rectify 54]
56. ? [X0] : ((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) => ((~humble(sK3) | brave(sK3)) & (humble(sK3) | ~brave(sK3))) [choice axiom]
57. ((~humble(sK3) | brave(sK3)) & (humble(sK3) | ~brave(sK3))) | ! [X1] : ((old(X1) | happy(X1)) & (~happy(X1) | ~old(X1))) [skolemisation 55,56]
63. ! [X0] : (((~wise(X0) | old(X0)) | (~wise(X0) & quiet(X0))) & ((wise(X0) | ~quiet(X0)) | (wise(X0) & ~old(X0)))) [nnf transformation 14]
64. ! [X0] : ((~wise(X0) | old(X0) | (~wise(X0) & quiet(X0))) & (wise(X0) | ~quiet(X0) | (wise(X0) & ~old(X0)))) [flattening 63]
74. patient(X0) | patient(X0) [cnf transformation 33]
76. quiet(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 33]
77. ~funny(X0) | ~strong(X0) [cnf transformation 35]
79. ~old(X0) | strong(X0) | funny(X0) [cnf transformation 35]
83. ~generous(X0) | ~calm(X0) | happy(X0) [cnf transformation 37]
86. ~quiet(alice) | generous(alice) | happy(X0) [cnf transformation 42]
88. ~funny(X0) | strong(X0) | ~humble(X0) [cnf transformation 44]
109. humble(sK3) | ~brave(sK3) | ~happy(X1) | ~old(X1) [cnf transformation 57]
119. ~calm(X0) | ~strong(X0) | funny(X0) [cnf transformation 30]
120. calm(X0) | ~strong(X0) | funny(X0) [cnf transformation 30]
122. wise(X0) | ~quiet(X0) | wise(X0) [cnf transformation 64]
124. ~wise(X0) | old(X0) | ~wise(X0) [cnf transformation 64]
125. ~generous(X0) | ~happy(X0) [cnf transformation 31]
126. ~happy(X0) | brave(X0) [cnf transformation 31]
140. calm(alice) [cnf transformation 23]
141. ~quiet(X0) | wise(X0) [duplicate literal removal 122]
142. ~wise(X0) | old(X0) [duplicate literal removal 124]
143. patient(X0) [duplicate literal removal 74]
144. ~patient(X0) | quiet(X0) [duplicate literal removal 76]
146. 1 <=> ! [X0] : happy(X0) [avatar definition]
147. happy(X0) <- (1) [avatar component clause 146]
149. 2 <=> generous(alice) [avatar definition]
151. generous(alice) <- (2) [avatar component clause 149]
153. 3 <=> quiet(alice) [avatar definition]
155. ~quiet(alice) <- (~3) [avatar component clause 153]
156. 1 | 2 | ~3 [avatar split clause 86,153,149,146]
164. ~humble(X0) | ~funny(X0) [subsumption resolution 88,77]
205. 14 <=> brave(sK3) [avatar definition]
206. ~brave(sK3) <- (~14) [avatar component clause 205]
209. 15 <=> humble(sK3) [avatar definition]
210. humble(sK3) <- (15) [avatar component clause 209]
214. 16 <=> ! [X1] : (~happy(X1) | ~old(X1)) [avatar definition]
215. ~happy(X1) | ~old(X1) <- (16) [avatar component clause 214]
218. 16 | ~14 | 15 [avatar split clause 109,209,205,214]
247. ~strong(X0) | calm(X0) [subsumption resolution 120,77]
248. ~calm(X0) | ~strong(X0) [subsumption resolution 119,77]
249. ~strong(X0) [subsumption resolution 248,247]
292. quiet(X0) [resolution 144,143]
293. $false <- (~3) [resolution 292,155]
295. wise(X0) [resolution 292,141]
298. 3 [avatar contradiction clause 293]
304. ~happy(alice) <- (2) [resolution 151,125]
305. old(X0) [resolution 295,142]
306. strong(X0) | funny(X0) [resolution 79,305]
310. funny(X0) [subsumption resolution 306,249]
332. ~calm(alice) | happy(alice) <- (2) [resolution 83,151]
336. happy(alice) <- (2) [subsumption resolution 332,140]
337. $false <- (2) [subsumption resolution 336,304]
338. ~2 [avatar contradiction clause 337]
351. brave(X1) <- (1) [resolution 147,126]
357. $false <- (1, ~14) [resolution 351,206]
358. ~1 | 14 [avatar contradiction clause 357]
361. ~funny(sK3) <- (15) [resolution 210,164]
365. $false <- (15) [subsumption resolution 361,310]
366. ~15 [avatar contradiction clause 365]
367. ~old(X1) <- (1, 16) [subsumption resolution 215,147]
368. $false <- (1, 16) [subsumption resolution 367,305]
369. ~1 | ~16 [avatar contradiction clause 368]
370. $false [avatar sat refutation 156,218,298,338,358,366,369]
% SZS output end Proof for 3139706467440620311751763
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or not quiet is kind or rich and vice versa. Everyone who is either not funny or not creative is happy or brave. Everyone who is not rich is either not creative or not wise and vice versa. Everyone who is both tall and kind is both brave and not curious. Everyone who is either not brave or not old is both not rich and kind and vice versa. If someone is either patient or quiet then someone is not generous or not humble and vice versa. If someone is tall or not brave then someone is not happy and vice versa. Everyone who is not strong is wise or not strong. Everyone who is not wise or curious is patient. Everyone who is either not kind or humble is strong. If someone is creative or not rich then susan is not wise or not happy. Everyone who is not kind is both not calm and not brave and vice versa. If paul is both not creative and rich then someone is creative. Everyone who is kind or patient is both not quiet and old and vice versa. If someone is either not rich or humble then paul is either not creative or not curious and vice versa. If susan is rich then someone is both curious and humble and vice versa. Susan is not wise. Someone is either funny or not funny. Someone is both not calm and not curious. Fred is not strong or not creative. Lucy is both funny and old. Someone is generous or not kind. Someone is either humble or not humble. | Paul is curious. | neutral | (![X]:((calm(X)|~quiet(X))<=>(kind(X)|rich(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(happy(X)|brave(X))))&
(![X]:(~rich(X)<=>(~creative(X)<~>~wise(X))))&
(![X]:((tall(X)&kind(X))=>(brave(X)&~curious(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~rich(X)&kind(X))))&
((?[X]:((patient(X)<~>quiet(X))))<=>(?[X]:((~generous(X)|~humble(X)))))&
((?[X]:((tall(X)|~brave(X))))<=>(?[X]:(~happy(X))))&
(![X]:(~strong(X)=>(wise(X)|~strong(X))))&
(![X]:((~wise(X)|curious(X))=>patient(X)))&
(![X]:((~kind(X)<~>humble(X))=>strong(X)))&
((?[X]:((creative(X)|~rich(X))))=>((~wise(susan)|~happy(susan))))&
(![X]:(~kind(X)<=>(~calm(X)&~brave(X))))&
(((~creative(paul)&rich(paul)))=>(?[X]:(creative(X))))&
(![X]:((kind(X)|patient(X))<=>(~quiet(X)&old(X))))&
((?[X]:((~rich(X)<~>humble(X))))<=>((~creative(paul)<~>~curious(paul))))&
((rich(susan))<=>(?[X]:((curious(X)&humble(X)))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((~calm(X)&~curious(X))))&
((~strong(fred)|~creative(fred)))&
((funny(lucy)&old(lucy)))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:((humble(X)<~>~humble(X)))) | curious(paul) | [] | null | 0 |
Everyone who is both not old and tall is not old or not creative and vice versa.
If alice is both humble and not wise then someone is rich.
If someone is either not strong or kind then susan is either old or tall.
Everyone who is either not generous or brave is not patient or brave and vice versa.
If alice is generous then alice is rich or strong.
Everyone who is funny or not calm is both creative and not patient and vice versa.
If someone is both curious and not old then someone is both not quiet and wise and vice versa.
Everyone who is either not wise or not rich is either brave or rich and vice versa.
If someone is either calm or not old then fred is either creative or generous.
Everyone who is not humble is either funny or quiet.
If someone is wise then someone is both not generous and not brave.
Everyone who is both old and kind is strong or not rich and vice versa.
Everyone who is not curious is either funny or not kind and vice versa.
Everyone who is quiet or not tall is not patient and vice versa.
Everyone who is either not calm or not creative is not brave.
Everyone who is kind is either not generous or tall and vice versa.
John is either not tall or not wise.
Someone is either happy or curious.
John is wise or rich.
Someone is strong or not strong.
Someone is not tall or strong.
Someone is not generous.
Mary is not humble or funny.
Someone is not brave. | John is not rich. | contradiction | (![X]:((~old(X)&tall(X))<=>(~old(X)|~creative(X))))&
(((humble(alice)&~wise(alice)))=>(?[X]:(rich(X))))&
((?[X]:((~strong(X)<~>kind(X))))=>((old(susan)<~>tall(susan))))&
(![X]:((~generous(X)<~>brave(X))<=>(~patient(X)|brave(X))))&
((generous(alice))=>((rich(alice)|strong(alice))))&
(![X]:((funny(X)|~calm(X))<=>(creative(X)&~patient(X))))&
((?[X]:((curious(X)&~old(X))))<=>(?[X]:((~quiet(X)&wise(X)))))&
(![X]:((~wise(X)<~>~rich(X))<=>(brave(X)<~>rich(X))))&
((?[X]:((calm(X)<~>~old(X))))=>((creative(fred)<~>generous(fred))))&
(![X]:(~humble(X)=>(funny(X)<~>quiet(X))))&
((?[X]:(wise(X)))=>(?[X]:((~generous(X)&~brave(X)))))&
(![X]:((old(X)&kind(X))<=>(strong(X)|~rich(X))))&
(![X]:(~curious(X)<=>(funny(X)<~>~kind(X))))&
(![X]:((quiet(X)|~tall(X))<=>~patient(X)))&
(![X]:((~calm(X)<~>~creative(X))=>~brave(X)))&
(![X]:(kind(X)<=>(~generous(X)<~>tall(X))))&
((~tall(john)<~>~wise(john)))&
(?[X]:((happy(X)<~>curious(X))))&
((wise(john)|rich(john)))&
(?[X]:((strong(X)|~strong(X))))&
(?[X]:((~tall(X)|strong(X))))&
(?[X]:(~generous(X)))&
((~humble(mary)|funny(mary)))&
(?[X]:(~brave(X))) | ~rich(john) | [
"p3",
"p7",
"p11",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1282598920838865968227571
% SZS output start Proof for 1282598920838865968227571
4. ! [X0] : ((~generous(X0) <~> brave(X0)) <=> (brave(X0) | ~patient(X0))) [input p3]
8. ! [X0] : ((~wise(X0) <~> ~rich(X0)) <=> (brave(X0) <~> rich(X0))) [input p7]
12. ! [X0] : ((kind(X0) & old(X0)) <=> (~rich(X0) | strong(X0))) [input p11]
16. ! [X0] : (kind(X0) <=> (~generous(X0) <~> tall(X0))) [input p15]
17. ~tall(john) <~> ~wise(john) [input p16]
19. rich(john) | wise(john) [input p18]
25. ~rich(john) [input hypothesis]
42. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [nnf transformation 4]
43. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [flattening 42]
51. ! [X0] : ((((rich(X0) | wise(X0)) & (~rich(X0) | ~wise(X0))) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0)))) & (((~rich(X0) | ~brave(X0)) & (rich(X0) | brave(X0))) | ((~wise(X0) | rich(X0)) & (~rich(X0) | wise(X0))))) [nnf transformation 8]
57. ! [X0] : (((kind(X0) & old(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (~kind(X0) | ~old(X0)))) [nnf transformation 12]
58. ! [X0] : (((kind(X0) & old(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | ~kind(X0) | ~old(X0))) [flattening 57]
63. ! [X0] : ((kind(X0) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | ~kind(X0))) [nnf transformation 16]
64. (wise(john) | tall(john)) & (~wise(john) | ~tall(john)) [nnf transformation 17]
91. ~brave(X0) | generous(X0) | ~brave(X0) [cnf transformation 43]
103. rich(X0) | brave(X0) | ~wise(X0) | rich(X0) [cnf transformation 51]
107. ~rich(X0) | ~wise(X0) | brave(X0) | ~rich(X0) [cnf transformation 51]
122. kind(X0) | rich(X0) [cnf transformation 58]
132. ~generous(X0) | tall(X0) | ~kind(X0) [cnf transformation 63]
136. ~wise(john) | ~tall(john) [cnf transformation 64]
140. rich(john) | wise(john) [cnf transformation 19]
146. ~rich(john) [cnf transformation 25]
147. rich(X0) | brave(X0) | ~wise(X0) [duplicate literal removal 103]
149. ~rich(X0) | ~wise(X0) | brave(X0) [duplicate literal removal 107]
152. ~brave(X0) | generous(X0) [duplicate literal removal 91]
223. ~wise(X0) | brave(X0) [subsumption resolution 147,149]
258. 24 <=> tall(john) [avatar definition]
259. ~tall(john) <- (~24) [avatar component clause 258]
262. 25 <=> wise(john) [avatar definition]
264. wise(john) <- (25) [avatar component clause 262]
266. ~24 | ~25 [avatar split clause 136,262,258]
278. 28 <=> rich(john) [avatar definition]
279. ~rich(john) <- (~28) [avatar component clause 278]
281. 25 | 28 [avatar split clause 140,278,262]
300. ~28 [avatar split clause 146,278]
308. brave(john) <- (25) [resolution 223,264]
311. generous(john) <- (25) [resolution 308,152]
330. tall(john) | ~kind(john) <- (25) [resolution 132,311]
331. ~kind(john) <- (~24, 25) [subsumption resolution 330,259]
333. rich(john) <- (~24, 25) [resolution 331,122]
334. $false <- (~24, 25, ~28) [subsumption resolution 333,279]
335. 24 | ~25 | 28 [avatar contradiction clause 334]
336. $false [avatar sat refutation 266,281,300,335]
% SZS output end Proof for 1282598920838865968227571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or funny then alice is not kind or not generous and vice versa.
Everyone who is wise or tall is not happy and vice versa.
Everyone who is not patient is not quiet.
Everyone who is not kind is both generous and wise and vice versa.
If john is both not old and curious then someone is not patient or wise and vice versa.
Everyone who is both calm and not calm is not happy or funny and vice versa.
If someone is either not rich or not humble then someone is both tall and not strong and vice versa.
If someone is both not curious and strong then someone is both generous and not wise.
Everyone who is either not curious or funny is both happy and not rich.
If mary is either not funny or curious then someone is either funny or brave.
If paul is not wise then someone is rich or tall.
Everyone who is both not funny and funny is not creative.
Everyone who is not funny is both patient and rich.
Everyone who is not wise is not generous or not kind and vice versa.
Everyone who is either not quiet or quiet is both not brave and quiet and vice versa.
If paul is both old and not creative then someone is both brave and not generous.
Paul is calm.
Paul is both not generous and quiet.
Susan is generous or not creative.
Someone is patient or not humble.
Someone is both humble and not tall. | Susan is not calm. | neutral | ((?[X]:((~wise(X)<~>funny(X))))<=>((~kind(alice)|~generous(alice))))&
(![X]:((wise(X)|tall(X))<=>~happy(X)))&
(![X]:(~patient(X)=>~quiet(X)))&
(![X]:(~kind(X)<=>(generous(X)&wise(X))))&
(((~old(john)&curious(john)))<=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:((calm(X)&~calm(X))<=>(~happy(X)|funny(X))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>(?[X]:((tall(X)&~strong(X)))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~curious(X)<~>funny(X))=>(happy(X)&~rich(X))))&
(((~funny(mary)<~>curious(mary)))=>(?[X]:((funny(X)<~>brave(X)))))&
((~wise(paul))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~funny(X)&funny(X))=>~creative(X)))&
(![X]:(~funny(X)=>(patient(X)&rich(X))))&
(![X]:(~wise(X)<=>(~generous(X)|~kind(X))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(~brave(X)&quiet(X))))&
(((old(paul)&~creative(paul)))=>(?[X]:((brave(X)&~generous(X)))))&
(calm(paul))&
((~generous(paul)&quiet(paul)))&
((generous(susan)|~creative(susan)))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((humble(X)&~tall(X)))) | ~calm(susan) | [] | null | 0 |
If someone is not rich then someone is not wise or not funny and vice versa.
Everyone who is not quiet is not humble and vice versa.
If mary is both not funny and strong then someone is either calm or not strong and vice versa.
Everyone who is happy or curious is not funny or happy.
If someone is old then susan is both generous and not generous.
Everyone who is not quiet is both not rich and humble and vice versa.
If someone is old then mary is either not old or not kind.
Everyone who is either not curious or not creative is both not strong and old.
If paul is curious or funny then mary is not curious or not strong.
Everyone who is wise or brave is both strong and funny.
Everyone who is both not generous and not patient is not humble and vice versa.
Everyone who is not calm is happy.
Everyone who is tall or rich is humble.
If someone is both not kind and not funny then mary is either kind or not tall.
If paul is kind or tall then paul is either tall or not wise and vice versa.
If someone is either humble or not generous then someone is either calm or not quiet.
Someone is both not calm and not kind.
Paul is both patient and not kind.
Someone is not happy or not kind.
Paul is strong.
Someone is curious or not quiet.
Someone is both strong and happy. | Mary is not kind. | neutral | ((?[X]:(~rich(X)))<=>(?[X]:((~wise(X)|~funny(X)))))&
(![X]:(~quiet(X)<=>~humble(X)))&
(((~funny(mary)&strong(mary)))<=>(?[X]:((calm(X)<~>~strong(X)))))&
(![X]:((happy(X)|curious(X))=>(~funny(X)|happy(X))))&
((?[X]:(old(X)))=>((generous(susan)&~generous(susan))))&
(![X]:(~quiet(X)<=>(~rich(X)&humble(X))))&
((?[X]:(old(X)))=>((~old(mary)<~>~kind(mary))))&
(![X]:((~curious(X)<~>~creative(X))=>(~strong(X)&old(X))))&
(((curious(paul)|funny(paul)))=>((~curious(mary)|~strong(mary))))&
(![X]:((wise(X)|brave(X))=>(strong(X)&funny(X))))&
(![X]:((~generous(X)&~patient(X))<=>~humble(X)))&
(![X]:(~calm(X)=>happy(X)))&
(![X]:((tall(X)|rich(X))=>humble(X)))&
((?[X]:((~kind(X)&~funny(X))))=>((kind(mary)<~>~tall(mary))))&
(((kind(paul)|tall(paul)))<=>((tall(paul)<~>~wise(paul))))&
((?[X]:((humble(X)<~>~generous(X))))=>(?[X]:((calm(X)<~>~quiet(X)))))&
(?[X]:((~calm(X)&~kind(X))))&
((patient(paul)&~kind(paul)))&
(?[X]:((~happy(X)|~kind(X))))&
(strong(paul))&
(?[X]:((curious(X)|~quiet(X))))&
(?[X]:((strong(X)&happy(X)))) | ~kind(mary) | [] | null | 0 |
If paul is not brave then someone is either rich or not calm.
Everyone who is both strong and not creative is both not quiet and not patient.
Everyone who is either humble or not quiet is not patient.
If someone is not quiet or not curious then john is both strong and not creative.
Everyone who is both curious and rich is not strong or brave and vice versa.
Everyone who is both not brave and not humble is brave.
If someone is either curious or rich then someone is tall and vice versa.
Everyone who is tall is not kind.
Everyone who is both strong and patient is either not strong or not funny and vice versa.
If someone is either not old or not happy then alice is quiet and vice versa.
Everyone who is not quiet is not tall or not generous.
If someone is both not patient and old then fred is either not patient or not calm and vice versa.
If someone is either not rich or quiet then someone is strong or happy.
If someone is either not kind or not generous then someone is either humble or not brave and vice versa.
If someone is both patient and not funny then someone is generous and vice versa.
If mary is both not calm and not old then paul is either kind or humble and vice versa.
Someone is both not funny and not generous.
Someone is not humble.
Someone is not generous.
Paul is both calm and old.
Someone is creative.
Someone is both not kind and not curious.
John is both kind and not old.
Someone is either not generous or not kind. | Paul is brave. | neutral | ((~brave(paul))=>(?[X]:((rich(X)<~>~calm(X)))))&
(![X]:((strong(X)&~creative(X))=>(~quiet(X)&~patient(X))))&
(![X]:((humble(X)<~>~quiet(X))=>~patient(X)))&
((?[X]:((~quiet(X)|~curious(X))))=>((strong(john)&~creative(john))))&
(![X]:((curious(X)&rich(X))<=>(~strong(X)|brave(X))))&
(![X]:((~brave(X)&~humble(X))=>brave(X)))&
((?[X]:((curious(X)<~>rich(X))))<=>(?[X]:(tall(X))))&
(![X]:(tall(X)=>~kind(X)))&
(![X]:((strong(X)&patient(X))<=>(~strong(X)<~>~funny(X))))&
((?[X]:((~old(X)<~>~happy(X))))<=>(quiet(alice)))&
(![X]:(~quiet(X)=>(~tall(X)|~generous(X))))&
((?[X]:((~patient(X)&old(X))))<=>((~patient(fred)<~>~calm(fred))))&
((?[X]:((~rich(X)<~>quiet(X))))=>(?[X]:((strong(X)|happy(X)))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((humble(X)<~>~brave(X)))))&
((?[X]:((patient(X)&~funny(X))))<=>(?[X]:(generous(X))))&
(((~calm(mary)&~old(mary)))<=>((kind(paul)<~>humble(paul))))&
(?[X]:((~funny(X)&~generous(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~generous(X)))&
((calm(paul)&old(paul)))&
(?[X]:(creative(X)))&
(?[X]:((~kind(X)&~curious(X))))&
((kind(john)&~old(john)))&
(?[X]:((~generous(X)<~>~kind(X)))) | brave(paul) | [] | null | 0 |
Everyone who is not creative is tall.
If someone is either wise or not happy then paul is either tall or not funny and vice versa.
Everyone who is either not tall or creative is both funny and not rich and vice versa.
Everyone who is both creative and not old is curious or tall and vice versa.
If someone is either not brave or humble then lucy is not quiet or rich and vice versa.
If someone is not patient or wise then someone is not patient.
If someone is tall then someone is not kind or funny and vice versa.
Everyone who is patient or not old is quiet or not happy and vice versa.
Everyone who is not happy is both old and not old.
If fred is not humble then mary is either not quiet or not humble.
Everyone who is brave or humble is creative.
If mary is wise then fred is kind and vice versa.
Everyone who is humble or wise is either not brave or old and vice versa.
Everyone who is generous or funny is both not funny and not quiet.
If susan is kind or wise then someone is either generous or old and vice versa.
Everyone who is both quiet and calm is both not happy and patient and vice versa.
Paul is both not strong and not brave.
Fred is not generous.
John is curious.
Lucy is both wise and not strong.
Someone is either happy or not strong.
Susan is either tall or kind. | John is not quiet. | contradiction | (![X]:(~creative(X)=>tall(X)))&
((?[X]:((wise(X)<~>~happy(X))))<=>((tall(paul)<~>~funny(paul))))&
(![X]:((~tall(X)<~>creative(X))<=>(funny(X)&~rich(X))))&
(![X]:((creative(X)&~old(X))<=>(curious(X)|tall(X))))&
((?[X]:((~brave(X)<~>humble(X))))<=>((~quiet(lucy)|rich(lucy))))&
((?[X]:((~patient(X)|wise(X))))=>(?[X]:(~patient(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~kind(X)|funny(X)))))&
(![X]:((patient(X)|~old(X))<=>(quiet(X)|~happy(X))))&
(![X]:(~happy(X)=>(old(X)&~old(X))))&
((~humble(fred))=>((~quiet(mary)<~>~humble(mary))))&
(![X]:((brave(X)|humble(X))=>creative(X)))&
((wise(mary))<=>(kind(fred)))&
(![X]:((humble(X)|wise(X))<=>(~brave(X)<~>old(X))))&
(![X]:((generous(X)|funny(X))=>(~funny(X)&~quiet(X))))&
(((kind(susan)|wise(susan)))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((quiet(X)&calm(X))<=>(~happy(X)&patient(X))))&
((~strong(paul)&~brave(paul)))&
(~generous(fred))&
(curious(john))&
((wise(lucy)&~strong(lucy)))&
(?[X]:((happy(X)<~>~strong(X))))&
((tall(susan)<~>kind(susan))) | ~quiet(john) | [
"p3",
"p7",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6858475844602049710832198
% SZS output start Proof for 6858475844602049710832198
4. ! [X0] : ((~old(X0) & creative(X0)) <=> (tall(X0) | curious(X0))) [input p3]
8. ! [X0] : ((~old(X0) | patient(X0)) <=> (~happy(X0) | quiet(X0))) [input p7]
9. ! [X0] : (~happy(X0) => (~old(X0) & old(X0))) [input p8]
19. curious(john) [input p18]
23. ~quiet(john) [input hypothesis]
28. ! [X0] : ((~old(X0) & old(X0)) | happy(X0)) [ennf transformation 9]
38. ! [X0] : (((~old(X0) & creative(X0)) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | (old(X0) | ~creative(X0)))) [nnf transformation 4]
39. ! [X0] : (((~old(X0) & creative(X0)) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | old(X0) | ~creative(X0))) [flattening 38]
53. ! [X0] : (((~old(X0) | patient(X0)) | (happy(X0) & ~quiet(X0))) & ((~happy(X0) | quiet(X0)) | (old(X0) & ~patient(X0)))) [nnf transformation 8]
54. ! [X0] : ((~old(X0) | patient(X0) | (happy(X0) & ~quiet(X0))) & (~happy(X0) | quiet(X0) | (old(X0) & ~patient(X0)))) [flattening 53]
88. ~curious(X0) | ~old(X0) [cnf transformation 39]
102. ~happy(X0) | quiet(X0) | old(X0) [cnf transformation 54]
105. old(X0) | happy(X0) [cnf transformation 28]
106. ~old(X0) | happy(X0) [cnf transformation 28]
136. curious(john) [cnf transformation 19]
143. ~quiet(john) [cnf transformation 23]
243. happy(X0) [subsumption resolution 105,106]
313. ~old(john) [resolution 88,136]
327. quiet(X0) | old(X0) [resolution 102,243]
330. old(john) [resolution 327,143]
332. $false [subsumption resolution 330,313]
% SZS output end Proof for 6858475844602049710832198
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 wise is either not old or generous. If lucy is curious then someone is both not funny and not calm. If someone is rich or tall then someone is generous or not old. Everyone who is either patient or calm is either not old or not kind and vice versa. Everyone who is either wise or not happy is both not old and not patient and vice versa. Everyone who is kind or old is both funny and rich. If mary is generous then paul is both not funny and not generous. Everyone who is both rich and not curious is not rich or not generous. Everyone who is patient is either not patient or not quiet and vice versa. If susan is brave then paul is not humble or not wise. Everyone who is either not creative or generous is either brave or not rich and vice versa. Everyone who is not funny or not kind is either not generous or not patient and vice versa. If john is both not tall and rich then mary is either wise or not tall. Everyone who is either generous or not creative is not funny or not rich and vice versa. Everyone who is either not calm or patient is both not patient and wise and vice versa. If alice is not old or not creative then someone is strong or not old and vice versa. Paul is funny. Susan is not quiet. Someone is either not wise or not humble. Someone is not kind. Paul is either kind or not humble. Someone is either funny or wise. | Susan is not rich. | contradiction | (![X]:(wise(X)=>(~old(X)<~>generous(X))))&
((curious(lucy))=>(?[X]:((~funny(X)&~calm(X)))))&
((?[X]:((rich(X)|tall(X))))=>(?[X]:((generous(X)|~old(X)))))&
(![X]:((patient(X)<~>calm(X))<=>(~old(X)<~>~kind(X))))&
(![X]:((wise(X)<~>~happy(X))<=>(~old(X)&~patient(X))))&
(![X]:((kind(X)|old(X))=>(funny(X)&rich(X))))&
((generous(mary))=>((~funny(paul)&~generous(paul))))&
(![X]:((rich(X)&~curious(X))=>(~rich(X)|~generous(X))))&
(![X]:(patient(X)<=>(~patient(X)<~>~quiet(X))))&
((brave(susan))=>((~humble(paul)|~wise(paul))))&
(![X]:((~creative(X)<~>generous(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((~funny(X)|~kind(X))<=>(~generous(X)<~>~patient(X))))&
(((~tall(john)&rich(john)))=>((wise(mary)<~>~tall(mary))))&
(![X]:((generous(X)<~>~creative(X))<=>(~funny(X)|~rich(X))))&
(![X]:((~calm(X)<~>patient(X))<=>(~patient(X)&wise(X))))&
(((~old(alice)|~creative(alice)))<=>(?[X]:((strong(X)|~old(X)))))&
(funny(paul))&
(~quiet(susan))&
(?[X]:((~wise(X)<~>~humble(X))))&
(?[X]:(~kind(X)))&
((kind(paul)<~>~humble(paul)))&
(?[X]:((funny(X)<~>wise(X)))) | ~rich(susan) | [
"p0",
"p3",
"p5",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4815762834057336384423564
% SZS output start Proof for 4815762834057336384423564
1. ! [X0] : (wise(X0) => (~old(X0) <~> generous(X0))) [input p0]
4. ! [X0] : ((patient(X0) <~> calm(X0)) <=> (~old(X0) <~> ~kind(X0))) [input p3]
6. ! [X0] : ((old(X0) | kind(X0)) => (rich(X0) & funny(X0))) [input p5]
12. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (~generous(X0) <~> ~patient(X0))) [input p11]
15. ! [X0] : ((~calm(X0) <~> patient(X0)) <=> (wise(X0) & ~patient(X0))) [input p14]
23. ~rich(susan) [input hypothesis]
25. ! [X0] : ((~old(X0) <~> generous(X0)) | ~wise(X0)) [ennf transformation 1]
28. ! [X0] : ((rich(X0) & funny(X0)) | (~old(X0) & ~kind(X0))) [ennf transformation 6]
36. ! [X0] : (((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | ~wise(X0)) [nnf transformation 25]
42. ! [X0] : ((((~calm(X0) | ~patient(X0)) & (calm(X0) | patient(X0))) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) & (((kind(X0) | old(X0)) & (~kind(X0) | ~old(X0))) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0))))) [nnf transformation 4]
47. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) & (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 12]
48. ! [X0] : ((~kind(X0) | ~funny(X0) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) & (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | (kind(X0) & funny(X0)))) [flattening 47]
52. ! [X0] : ((((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | (~wise(X0) | patient(X0))) & ((wise(X0) & ~patient(X0)) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0))))) [nnf transformation 15]
53. ! [X0] : ((((~patient(X0) | calm(X0)) & (patient(X0) | ~calm(X0))) | ~wise(X0) | patient(X0)) & ((wise(X0) & ~patient(X0)) | ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0))))) [flattening 52]
69. ~generous(X0) | old(X0) | ~wise(X0) [cnf transformation 36]
76. ~patient(X0) | old(X0) | calm(X0) | kind(X0) [cnf transformation 42]
77. ~calm(X0) | old(X0) | patient(X0) | kind(X0) [cnf transformation 42]
90. ~kind(X0) | rich(X0) [cnf transformation 28]
91. ~old(X0) | rich(X0) [cnf transformation 28]
109. ~patient(X0) | ~generous(X0) | kind(X0) [cnf transformation 48]
111. kind(X0) | generous(X0) | patient(X0) [cnf transformation 48]
123. ~patient(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 53]
124. patient(X0) | wise(X0) | calm(X0) [cnf transformation 53]
141. ~rich(susan) [cnf transformation 23]
142. ~patient(X0) | ~calm(X0) [duplicate literal removal 123]
285. patient(X0) | generous(X0) | rich(X0) [resolution 111,90]
361. ~generous(X0) | calm(X0) | wise(X0) | kind(X0) [resolution 124,109]
498. generous(X0) | rich(X0) | old(X0) | calm(X0) | kind(X0) [resolution 285,76]
504. generous(X6) | rich(X6) | ~calm(X6) [resolution 285,142]
506. generous(X0) | rich(X0) | calm(X0) | kind(X0) [subsumption resolution 498,91]
507. rich(X0) | generous(X0) | calm(X0) [subsumption resolution 506,90]
509. rich(X6) | generous(X6) [subsumption resolution 504,507]
511. generous(susan) [resolution 509,141]
519. old(susan) | ~wise(susan) [resolution 511,69]
523. 47 <=> wise(susan) [avatar definition]
525. ~wise(susan) <- (~47) [avatar component clause 523]
527. 48 <=> old(susan) [avatar definition]
529. old(susan) <- (48) [avatar component clause 527]
530. ~47 | 48 [avatar split clause 519,527,523]
591. calm(susan) | wise(susan) | kind(susan) [resolution 361,511]
593. calm(susan) | kind(susan) <- (~47) [subsumption resolution 591,525]
595. 54 <=> kind(susan) [avatar definition]
596. ~kind(susan) <- (~54) [avatar component clause 595]
597. kind(susan) <- (54) [avatar component clause 595]
599. 55 <=> calm(susan) [avatar definition]
601. calm(susan) <- (55) [avatar component clause 599]
602. 54 | 55 | 47 [avatar split clause 593,523,599,595]
788. old(susan) | patient(susan) | kind(susan) <- (55) [resolution 601,77]
791. 61 <=> patient(susan) [avatar definition]
793. patient(susan) <- (61) [avatar component clause 791]
794. 54 | 61 | 48 | ~55 [avatar split clause 788,599,527,791,595]
803. rich(susan) <- (48) [resolution 529,91]
806. $false <- (48) [subsumption resolution 803,141]
807. ~48 [avatar contradiction clause 806]
828. rich(susan) <- (54) [resolution 597,90]
831. $false <- (54) [subsumption resolution 828,141]
832. ~54 [avatar contradiction clause 831]
976. ~generous(susan) | kind(susan) <- (61) [resolution 793,109]
983. kind(susan) <- (61) [subsumption resolution 976,511]
984. $false <- (~54, 61) [subsumption resolution 983,596]
985. 54 | ~61 [avatar contradiction clause 984]
991. $false [avatar sat refutation 530,602,794,807,832,985]
% SZS output end Proof for 4815762834057336384423564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or patient is creative or tall and vice versa.
Everyone who is either strong or not patient is not patient.
Everyone who is rich is either rich or kind and vice versa.
If fred is either creative or not patient then someone is either not kind or rich.
Everyone who is both not strong and not happy is not funny.
If lucy is quiet or not kind then someone is wise and vice versa.
If alice is not quiet then someone is either calm or not kind.
Everyone who is both brave and kind is not curious or patient.
Everyone who is either not patient or not calm is funny.
Everyone who is either funny or generous is either not generous or not brave.
If paul is not creative or tall then someone is tall.
If someone is not generous or not old then someone is both not calm and brave and vice versa.
If john is kind then someone is not tall and vice versa.
If lucy is either not patient or not kind then someone is both not quiet and not wise and vice versa.
If susan is either patient or not kind then someone is not funny.
Paul is not quiet.
Susan is either not patient or funny.
John is either generous or not curious.
Someone is either funny or kind.
Paul is either generous or brave.
Someone is both rich and not calm.
Someone is both not strong and not happy. | Paul is not kind. | entailment | (![X]:((kind(X)<~>patient(X))<=>(creative(X)|tall(X))))&
(![X]:((strong(X)<~>~patient(X))=>~patient(X)))&
(![X]:(rich(X)<=>(rich(X)<~>kind(X))))&
(((creative(fred)<~>~patient(fred)))=>(?[X]:((~kind(X)<~>rich(X)))))&
(![X]:((~strong(X)&~happy(X))=>~funny(X)))&
(((quiet(lucy)|~kind(lucy)))<=>(?[X]:(wise(X))))&
((~quiet(alice))=>(?[X]:((calm(X)<~>~kind(X)))))&
(![X]:((brave(X)&kind(X))=>(~curious(X)|patient(X))))&
(![X]:((~patient(X)<~>~calm(X))=>funny(X)))&
(![X]:((funny(X)<~>generous(X))=>(~generous(X)<~>~brave(X))))&
(((~creative(paul)|tall(paul)))=>(?[X]:(tall(X))))&
((?[X]:((~generous(X)|~old(X))))<=>(?[X]:((~calm(X)&brave(X)))))&
((kind(john))<=>(?[X]:(~tall(X))))&
(((~patient(lucy)<~>~kind(lucy)))<=>(?[X]:((~quiet(X)&~wise(X)))))&
(((patient(susan)<~>~kind(susan)))=>(?[X]:(~funny(X))))&
(~quiet(paul))&
((~patient(susan)<~>funny(susan)))&
((generous(john)<~>~curious(john)))&
(?[X]:((funny(X)<~>kind(X))))&
((generous(paul)<~>brave(paul)))&
(?[X]:((rich(X)&~calm(X))))&
(?[X]:((~strong(X)&~happy(X)))) | ~kind(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 6987030165689149776210989
% SZS output start Proof for 6987030165689149776210989
3. ! [X0] : (rich(X0) <=> (rich(X0) <~> kind(X0))) [input p2]
23. kind(paul) [input hypothesis]
39. ! [X0] : ((rich(X0) | ((rich(X0) | ~kind(X0)) & (kind(X0) | ~rich(X0)))) & (((~kind(X0) | ~rich(X0)) & (kind(X0) | rich(X0))) | ~rich(X0))) [nnf transformation 3]
90. ~kind(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 39]
92. rich(X0) | rich(X0) | ~kind(X0) [cnf transformation 39]
140. kind(paul) [cnf transformation 23]
143. ~kind(X0) | ~rich(X0) [duplicate literal removal 90]
144. rich(X0) | ~kind(X0) [duplicate literal removal 92]
146. ~kind(X0) [subsumption resolution 143,144]
277. $false [subsumption resolution 140,146]
% SZS output end Proof for 6987030165689149776210989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 patient and rich is not generous or not funny and vice versa. If someone is not curious then someone is not quiet. Everyone who is not quiet is not calm and vice versa. If john is either brave or not tall then someone is either not kind or not generous and vice versa. If someone is both not brave and quiet then someone is not funny. Everyone who is either calm or not creative is either not patient or not rich and vice versa. Everyone who is both humble and not funny is tall. Everyone who is either creative or not strong is either funny or strong and vice versa. If someone is both not curious and not funny then alice is both not kind and tall. If lucy is both wise and not kind then paul is not tall and vice versa. Everyone who is wise or not creative is humble or not calm. If susan is either not quiet or brave then alice is either not quiet or not kind. Everyone who is brave is either happy or quiet. If paul is funny then someone is either not old or quiet. If susan is not strong then alice is either not wise or calm and vice versa. Susan is either humble or funny. John is not patient or wise. Mary is either funny or not rich. Someone is not creative or not generous. John is not curious. Someone is not strong. John is either kind or creative. Paul is both kind and not generous. | Susan is not quiet. | entailment | (![X]:((patient(X)&rich(X))<=>(~generous(X)|~funny(X))))&
((?[X]:(~curious(X)))=>(?[X]:(~quiet(X))))&
(![X]:(~quiet(X)<=>~calm(X)))&
(((brave(john)<~>~tall(john)))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
((?[X]:((~brave(X)&quiet(X))))=>(?[X]:(~funny(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:((humble(X)&~funny(X))=>tall(X)))&
(![X]:((creative(X)<~>~strong(X))<=>(funny(X)<~>strong(X))))&
((?[X]:((~curious(X)&~funny(X))))=>((~kind(alice)&tall(alice))))&
(((wise(lucy)&~kind(lucy)))<=>(~tall(paul)))&
(![X]:((wise(X)|~creative(X))=>(humble(X)|~calm(X))))&
(((~quiet(susan)<~>brave(susan)))=>((~quiet(alice)<~>~kind(alice))))&
(![X]:(brave(X)=>(happy(X)<~>quiet(X))))&
((funny(paul))=>(?[X]:((~old(X)<~>quiet(X)))))&
((~strong(susan))<=>((~wise(alice)<~>calm(alice))))&
((humble(susan)<~>funny(susan)))&
((~patient(john)|wise(john)))&
((funny(mary)<~>~rich(mary)))&
(?[X]:((~creative(X)|~generous(X))))&
(~curious(john))&
(?[X]:(~strong(X)))&
((kind(john)<~>creative(john)))&
((kind(paul)&~generous(paul))) | ~quiet(susan) | [
"p0",
"p2",
"p5",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8318348768985720386459635
% SZS output start Proof for 8318348768985720386459635
1. ! [X0] : ((rich(X0) & patient(X0)) <=> (~funny(X0) | ~generous(X0))) [input p0]
3. ! [X0] : (~quiet(X0) <=> ~calm(X0)) [input p2]
6. ! [X0] : ((calm(X0) <~> ~creative(X0)) <=> (~patient(X0) <~> ~rich(X0))) [input p5]
8. ! [X0] : ((creative(X0) <~> ~strong(X0)) <=> (funny(X0) <~> strong(X0))) [input p7]
11. ! [X0] : ((~creative(X0) | wise(X0)) => (~calm(X0) | humble(X0))) [input p10]
16. humble(susan) <~> funny(susan) [input p15]
24. quiet(susan) [input hypothesis]
32. ! [X0] : ((~calm(X0) | humble(X0)) | (creative(X0) & ~wise(X0))) [ennf transformation 11]
33. ! [X0] : (~calm(X0) | humble(X0) | (creative(X0) & ~wise(X0))) [flattening 32]
37. ! [X0] : (((rich(X0) & patient(X0)) | (funny(X0) & generous(X0))) & ((~funny(X0) | ~generous(X0)) | (~rich(X0) | ~patient(X0)))) [nnf transformation 1]
38. ! [X0] : (((rich(X0) & patient(X0)) | (funny(X0) & generous(X0))) & (~funny(X0) | ~generous(X0) | ~rich(X0) | ~patient(X0))) [flattening 37]
42. ! [X0] : ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))) [nnf transformation 3]
50. ! [X0] : ((((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0))))) [nnf transformation 6]
51. ! [X0] : ((((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | ((funny(X0) | ~strong(X0)) & (strong(X0) | ~funny(X0)))) & (((~strong(X0) | ~funny(X0)) & (strong(X0) | funny(X0))) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0))))) [nnf transformation 8]
60. (~funny(susan) | ~humble(susan)) & (funny(susan) | humble(susan)) [nnf transformation 16]
69. funny(X0) | patient(X0) [cnf transformation 38]
71. funny(X0) | rich(X0) [cnf transformation 38]
74. ~quiet(X0) | calm(X0) [cnf transformation 42]
84. ~creative(X0) | ~patient(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 50]
94. strong(X0) | funny(X0) | creative(X0) | strong(X0) [cnf transformation 51]
95. ~strong(X0) | ~funny(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 51]
98. ~strong(X0) | creative(X0) | funny(X0) | ~strong(X0) [cnf transformation 51]
99. strong(X0) | ~creative(X0) | strong(X0) | ~funny(X0) [cnf transformation 51]
107. ~calm(X0) | humble(X0) | creative(X0) [cnf transformation 33]
121. ~funny(susan) | ~humble(susan) [cnf transformation 60]
132. quiet(susan) [cnf transformation 24]
133. strong(X0) | funny(X0) | creative(X0) [duplicate literal removal 94]
134. ~strong(X0) | ~funny(X0) | ~creative(X0) [duplicate literal removal 95]
135. ~strong(X0) | creative(X0) | funny(X0) [duplicate literal removal 98]
136. ~creative(X0) | strong(X0) | ~funny(X0) [duplicate literal removal 99]
183. ~creative(X0) | ~funny(X0) [subsumption resolution 134,136]
184. creative(X0) | funny(X0) [subsumption resolution 133,135]
218. 18 <=> quiet(susan) [avatar definition]
219. quiet(susan) <- (18) [avatar component clause 218]
260. 26 <=> humble(susan) [avatar definition]
264. 27 <=> funny(susan) [avatar definition]
265. funny(susan) <- (27) [avatar component clause 264]
267. ~26 | ~27 [avatar split clause 121,264,260]
299. 18 [avatar split clause 132,218]
308. calm(susan) <- (18) [resolution 74,219]
325. humble(susan) | creative(susan) <- (18) [resolution 107,308]
355. ~patient(X0) | ~rich(X0) | ~calm(X0) | funny(X0) [resolution 84,184]
356. ~patient(X0) | ~calm(X0) | funny(X0) [subsumption resolution 355,71]
357. ~calm(X0) | funny(X0) [subsumption resolution 356,69]
432. funny(susan) <- (18) [resolution 357,308]
436. 44 <=> creative(susan) [avatar definition]
438. creative(susan) <- (44) [avatar component clause 436]
439. 44 | 26 | ~18 [avatar split clause 325,218,260,436]
440. 27 | ~18 [avatar split clause 432,218,264]
462. ~funny(susan) <- (44) [resolution 438,183]
469. $false <- (27, 44) [subsumption resolution 462,265]
470. ~27 | ~44 [avatar contradiction clause 469]
471. $false [avatar sat refutation 267,299,439,440,470]
% SZS output end Proof for 8318348768985720386459635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not tall then someone is both patient and generous. Everyone who is both not old and not strong is both tall and funny and vice versa. Everyone who is either not creative or not wise is either not old or tall. If alice is either generous or wise then john is both wise and old. Everyone who is both not humble and humble is tall or not curious and vice versa. Everyone who is both brave and happy is both rich and not funny and vice versa. If someone is both not patient and not rich then someone is generous. Everyone who is not kind is funny and vice versa. Everyone who is humble is either old or not brave and vice versa. If someone is either not humble or not rich then someone is both not humble and humble. If john is brave then someone is both generous and creative and vice versa. If john is not patient then lucy is funny and vice versa. If fred is either tall or strong then someone is not curious and vice versa. Everyone who is both happy and not old is creative and vice versa. Everyone who is either old or not creative is not curious or not brave and vice versa. If someone is either not strong or strong then someone is either not quiet or wise. Someone is either not creative or wise. Someone is happy or not kind. Someone is humble. Someone is patient or generous. Lucy is not old. John is not strong or generous. Someone is not calm or not patient. | John is old. | contradiction | ((~tall(mary))=>(?[X]:((patient(X)&generous(X)))))&
(![X]:((~old(X)&~strong(X))<=>(tall(X)&funny(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(~old(X)<~>tall(X))))&
(((generous(alice)<~>wise(alice)))=>((wise(john)&old(john))))&
(![X]:((~humble(X)&humble(X))<=>(tall(X)|~curious(X))))&
(![X]:((brave(X)&happy(X))<=>(rich(X)&~funny(X))))&
((?[X]:((~patient(X)&~rich(X))))=>(?[X]:(generous(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:(humble(X)<=>(old(X)<~>~brave(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>(?[X]:((~humble(X)&humble(X)))))&
((brave(john))<=>(?[X]:((generous(X)&creative(X)))))&
((~patient(john))<=>(funny(lucy)))&
(((tall(fred)<~>strong(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((happy(X)&~old(X))<=>creative(X)))&
(![X]:((old(X)<~>~creative(X))<=>(~curious(X)|~brave(X))))&
((?[X]:((~strong(X)<~>strong(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
(?[X]:((~creative(X)<~>wise(X))))&
(?[X]:((happy(X)|~kind(X))))&
(?[X]:(humble(X)))&
(?[X]:((patient(X)|generous(X))))&
(~old(lucy))&
((~strong(john)|generous(john)))&
(?[X]:((~calm(X)|~patient(X)))) | old(john) | [
"p5",
"p8",
"p9",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5438486940280595657200429
% SZS output start Proof for 5438486940280595657200429
6. ! [X0] : ((happy(X0) & brave(X0)) <=> (~funny(X0) & rich(X0))) [input p5]
9. ! [X0] : (humble(X0) <=> (old(X0) <~> ~brave(X0))) [input p8]
10. ? [X0] : (~humble(X0) <~> ~rich(X0)) => ? [X0] : (humble(X0) & ~humble(X0)) [input p9]
11. brave(john) <=> ? [X0] : (creative(X0) & generous(X0)) [input p10]
14. ! [X0] : ((~old(X0) & happy(X0)) <=> creative(X0)) [input p13]
15. ! [X0] : ((old(X0) <~> ~creative(X0)) <=> (~brave(X0) | ~curious(X0))) [input p14]
24. old(john) [input hypothesis]
26. ? [X0] : (~humble(X0) <~> ~rich(X0)) => ? [X1] : (humble(X1) & ~humble(X1)) [rectify 10]
35. ? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : (~humble(X0) <=> ~rich(X0)) [ennf transformation 26]
45. ! [X0] : (((happy(X0) & brave(X0)) | (funny(X0) | ~rich(X0))) & ((~funny(X0) & rich(X0)) | (~happy(X0) | ~brave(X0)))) [nnf transformation 6]
46. ! [X0] : (((happy(X0) & brave(X0)) | funny(X0) | ~rich(X0)) & ((~funny(X0) & rich(X0)) | ~happy(X0) | ~brave(X0))) [flattening 45]
50. ! [X0] : ((humble(X0) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0)))) & (((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | ~humble(X0))) [nnf transformation 9]
51. ? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))) [nnf transformation 35]
52. ? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1))) [rectify 51]
53. ? [X0] : (humble(X0) & ~humble(X0)) => (humble(sK2) & ~humble(sK2)) [choice axiom]
54. (humble(sK2) & ~humble(sK2)) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1))) [skolemisation 52,53]
55. (brave(john) | ! [X0] : (~creative(X0) | ~generous(X0))) & (? [X0] : (creative(X0) & generous(X0)) | ~brave(john)) [nnf transformation 11]
56. (brave(john) | ! [X0] : (~creative(X0) | ~generous(X0))) & (? [X1] : (creative(X1) & generous(X1)) | ~brave(john)) [rectify 55]
57. ? [X1] : (creative(X1) & generous(X1)) => (creative(sK3) & generous(sK3)) [choice axiom]
58. (brave(john) | ! [X0] : (~creative(X0) | ~generous(X0))) & ((creative(sK3) & generous(sK3)) | ~brave(john)) [skolemisation 56,57]
64. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 14]
65. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | old(X0) | ~happy(X0))) [flattening 64]
66. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & ((~brave(X0) | ~curious(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [nnf transformation 15]
67. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & (~brave(X0) | ~curious(X0) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [flattening 66]
100. ~happy(X0) | rich(X0) | ~brave(X0) [cnf transformation 46]
106. ~brave(X0) | old(X0) | ~humble(X0) [cnf transformation 50]
110. ~humble(sK2) | ~rich(X1) | humble(X1) [cnf transformation 54]
112. humble(sK2) | ~rich(X1) | humble(X1) [cnf transformation 54]
115. creative(sK3) | ~brave(john) [cnf transformation 58]
124. ~creative(X0) | happy(X0) [cnf transformation 65]
125. ~creative(X0) | ~old(X0) [cnf transformation 65]
129. ~creative(X0) | old(X0) | brave(X0) [cnf transformation 67]
131. creative(X0) | ~old(X0) | brave(X0) [cnf transformation 67]
143. old(john) [cnf transformation 24]
171. 6 <=> old(john) [avatar definition]
173. old(john) <- (6) [avatar component clause 171]
196. 11 <=> humble(sK2) [avatar definition]
201. 12 <=> ! [X1] : (~rich(X1) | humble(X1)) [avatar definition]
202. ~rich(X1) | humble(X1) <- (12) [avatar component clause 201]
203. 12 | 11 [avatar split clause 112,196,201]
205. 12 | ~11 [avatar split clause 110,196,201]
210. 14 <=> brave(john) [avatar definition]
215. 15 <=> creative(sK3) [avatar definition]
217. creative(sK3) <- (15) [avatar component clause 215]
218. ~14 | 15 [avatar split clause 115,215,210]
236. ~old(X0) | brave(X0) [subsumption resolution 131,125]
237. ~creative(X0) | brave(X0) [subsumption resolution 129,236]
294. 6 [avatar split clause 143,171]
299. brave(john) <- (6) [resolution 236,173]
302. 14 | ~6 [avatar split clause 299,171,210]
304. ~old(sK3) <- (15) [resolution 217,125]
305. happy(sK3) <- (15) [resolution 217,124]
308. brave(sK3) <- (15) [resolution 237,217]
319. rich(sK3) | ~brave(sK3) <- (15) [resolution 100,305]
320. rich(sK3) <- (15) [subsumption resolution 319,308]
321. humble(sK3) <- (12, 15) [resolution 320,202]
350. old(sK3) | ~humble(sK3) <- (15) [resolution 106,308]
352. ~humble(sK3) <- (15) [subsumption resolution 350,304]
353. $false <- (12, 15) [subsumption resolution 352,321]
354. ~12 | ~15 [avatar contradiction clause 353]
356. $false [avatar sat refutation 203,205,218,294,302,354]
% SZS output end Proof for 5438486940280595657200429
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 alice is either rich or generous then paul is not old or calm.
If john is not wise then fred is both creative and calm and vice versa.
Everyone who is both not curious and not quiet is either not tall or not rich.
If mary is either generous or not creative then susan is either brave or not strong and vice versa.
Everyone who is both not funny and patient is both rich and tall.
Everyone who is brave is not creative or strong.
Everyone who is patient is either not happy or creative.
If someone is both not old and funny then alice is both not creative and not curious.
Everyone who is both generous and not generous is not curious or not generous and vice versa.
If fred is brave then someone is not generous and vice versa.
Everyone who is not quiet or not patient is not curious.
If lucy is both funny and not rich then mary is either kind or curious and vice versa.
If someone is both wise and not calm then someone is wise or curious and vice versa.
If lucy is either not happy or not rich then someone is both not wise and not generous.
If someone is both not kind and not patient then john is not strong or not brave and vice versa.
Everyone who is rich is not quiet or old and vice versa.
Someone is either curious or funny.
Lucy is not rich or not brave.
Someone is generous or not brave.
Fred is not humble or quiet.
Susan is both brave and strong.
Paul is not calm. | Fred is calm. | neutral | (((rich(alice)<~>generous(alice)))=>((~old(paul)|calm(paul))))&
((~wise(john))<=>((creative(fred)&calm(fred))))&
(![X]:((~curious(X)&~quiet(X))=>(~tall(X)<~>~rich(X))))&
(((generous(mary)<~>~creative(mary)))<=>((brave(susan)<~>~strong(susan))))&
(![X]:((~funny(X)&patient(X))=>(rich(X)&tall(X))))&
(![X]:(brave(X)=>(~creative(X)|strong(X))))&
(![X]:(patient(X)=>(~happy(X)<~>creative(X))))&
((?[X]:((~old(X)&funny(X))))=>((~creative(alice)&~curious(alice))))&
(![X]:((generous(X)&~generous(X))<=>(~curious(X)|~generous(X))))&
((brave(fred))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|~patient(X))=>~curious(X)))&
(((funny(lucy)&~rich(lucy)))<=>((kind(mary)<~>curious(mary))))&
((?[X]:((wise(X)&~calm(X))))<=>(?[X]:((wise(X)|curious(X)))))&
(((~happy(lucy)<~>~rich(lucy)))=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~kind(X)&~patient(X))))<=>((~strong(john)|~brave(john))))&
(![X]:(rich(X)<=>(~quiet(X)|old(X))))&
(?[X]:((curious(X)<~>funny(X))))&
((~rich(lucy)|~brave(lucy)))&
(?[X]:((generous(X)|~brave(X))))&
((~humble(fred)|quiet(fred)))&
((brave(susan)&strong(susan)))&
(~calm(paul)) | calm(fred) | [] | null | 0 |
Everyone who is not brave is humble.
Everyone who is either not humble or old is quiet.
If someone is either old or not kind then someone is humble or old and vice versa.
Everyone who is strong or not humble is not brave or wise and vice versa.
If someone is both kind and not generous then someone is both not funny and calm and vice versa.
Everyone who is both creative and tall is not calm or wise and vice versa.
If someone is either not quiet or generous then fred is strong and vice versa.
If lucy is both not old and patient then john is not tall or not calm and vice versa.
Everyone who is not happy is not calm.
Everyone who is not funny or kind is not funny or not generous.
Everyone who is both not tall and not wise is both not curious and not calm.
Everyone who is either creative or humble is quiet.
Everyone who is not funny or humble is old.
If someone is either not old or not happy then john is both not rich and calm.
If someone is funny then someone is either not strong or rich.
Everyone who is tall or kind is both not wise and generous and vice versa.
Lucy is not humble or kind.
Someone is both creative and funny.
Someone is kind or not strong.
Paul is both curious and not rich.
Lucy is tall or not tall.
Mary is not strong or strong. | John is kind. | contradiction | (![X]:(~brave(X)=>humble(X)))&
(![X]:((~humble(X)<~>old(X))=>quiet(X)))&
((?[X]:((old(X)<~>~kind(X))))<=>(?[X]:((humble(X)|old(X)))))&
(![X]:((strong(X)|~humble(X))<=>(~brave(X)|wise(X))))&
((?[X]:((kind(X)&~generous(X))))<=>(?[X]:((~funny(X)&calm(X)))))&
(![X]:((creative(X)&tall(X))<=>(~calm(X)|wise(X))))&
((?[X]:((~quiet(X)<~>generous(X))))<=>(strong(fred)))&
(((~old(lucy)&patient(lucy)))<=>((~tall(john)|~calm(john))))&
(![X]:(~happy(X)=>~calm(X)))&
(![X]:((~funny(X)|kind(X))=>(~funny(X)|~generous(X))))&
(![X]:((~tall(X)&~wise(X))=>(~curious(X)&~calm(X))))&
(![X]:((creative(X)<~>humble(X))=>quiet(X)))&
(![X]:((~funny(X)|humble(X))=>old(X)))&
((?[X]:((~old(X)<~>~happy(X))))=>((~rich(john)&calm(john))))&
((?[X]:(funny(X)))=>(?[X]:((~strong(X)<~>rich(X)))))&
(![X]:((tall(X)|kind(X))<=>(~wise(X)&generous(X))))&
((~humble(lucy)|kind(lucy)))&
(?[X]:((creative(X)&funny(X))))&
(?[X]:((kind(X)|~strong(X))))&
((curious(paul)&~rich(paul)))&
((tall(lucy)|~tall(lucy)))&
((~strong(mary)|strong(mary))) | kind(john) | [
"p0",
"p3",
"p4",
"p5",
"p7",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8023539052688002110984824
% SZS output start Proof for 8023539052688002110984824
1. ! [X0] : (~brave(X0) => humble(X0)) [input p0]
4. ! [X0] : ((~humble(X0) | strong(X0)) <=> (wise(X0) | ~brave(X0))) [input p3]
5. ? [X0] : (~generous(X0) & kind(X0)) <=> ? [X0] : (calm(X0) & ~funny(X0)) [input p4]
6. ! [X0] : ((tall(X0) & creative(X0)) <=> (wise(X0) | ~calm(X0))) [input p5]
8. (patient(lucy) & ~old(lucy)) <=> (~calm(john) | ~tall(john)) [input p7]
10. ! [X0] : ((kind(X0) | ~funny(X0)) => (~generous(X0) | ~funny(X0))) [input p9]
11. ! [X0] : ((~wise(X0) & ~tall(X0)) => (~calm(X0) & ~curious(X0))) [input p10]
13. ! [X0] : ((humble(X0) | ~funny(X0)) => old(X0)) [input p12]
16. ! [X0] : ((kind(X0) | tall(X0)) <=> (generous(X0) & ~wise(X0))) [input p15]
23. kind(john) [input hypothesis]
25. ? [X0] : (~generous(X0) & kind(X0)) <=> ? [X1] : (calm(X1) & ~funny(X1)) [rectify 5]
27. ! [X0] : (humble(X0) | brave(X0)) [ennf transformation 1]
30. ! [X0] : ((~generous(X0) | ~funny(X0)) | (~kind(X0) & funny(X0))) [ennf transformation 10]
31. ! [X0] : (~generous(X0) | ~funny(X0) | (~kind(X0) & funny(X0))) [flattening 30]
32. ! [X0] : ((~calm(X0) & ~curious(X0)) | (wise(X0) | tall(X0))) [ennf transformation 11]
33. ! [X0] : ((~calm(X0) & ~curious(X0)) | wise(X0) | tall(X0)) [flattening 32]
35. ! [X0] : (old(X0) | (~humble(X0) & funny(X0))) [ennf transformation 13]
44. ! [X0] : (((~humble(X0) | strong(X0)) | (~wise(X0) & brave(X0))) & ((wise(X0) | ~brave(X0)) | (humble(X0) & ~strong(X0)))) [nnf transformation 4]
45. ! [X0] : ((~humble(X0) | strong(X0) | (~wise(X0) & brave(X0))) & (wise(X0) | ~brave(X0) | (humble(X0) & ~strong(X0)))) [flattening 44]
46. (? [X0] : (~generous(X0) & kind(X0)) | ! [X1] : (~calm(X1) | funny(X1))) & (? [X1] : (calm(X1) & ~funny(X1)) | ! [X0] : (generous(X0) | ~kind(X0))) [nnf transformation 25]
47. (? [X0] : (~generous(X0) & kind(X0)) | ! [X1] : (~calm(X1) | funny(X1))) & (? [X2] : (calm(X2) & ~funny(X2)) | ! [X3] : (generous(X3) | ~kind(X3))) [rectify 46]
48. ? [X0] : (~generous(X0) & kind(X0)) => (~generous(sK2) & kind(sK2)) [choice axiom]
49. ? [X2] : (calm(X2) & ~funny(X2)) => (calm(sK3) & ~funny(sK3)) [choice axiom]
50. ((~generous(sK2) & kind(sK2)) | ! [X1] : (~calm(X1) | funny(X1))) & ((calm(sK3) & ~funny(sK3)) | ! [X3] : (generous(X3) | ~kind(X3))) [skolemisation 47,49,48]
51. ! [X0] : (((tall(X0) & creative(X0)) | (~wise(X0) & calm(X0))) & ((wise(X0) | ~calm(X0)) | (~tall(X0) | ~creative(X0)))) [nnf transformation 6]
52. ! [X0] : (((tall(X0) & creative(X0)) | (~wise(X0) & calm(X0))) & (wise(X0) | ~calm(X0) | ~tall(X0) | ~creative(X0))) [flattening 51]
57. ((patient(lucy) & ~old(lucy)) | (calm(john) & tall(john))) & ((~calm(john) | ~tall(john)) | (~patient(lucy) | old(lucy))) [nnf transformation 8]
58. ((patient(lucy) & ~old(lucy)) | (calm(john) & tall(john))) & (~calm(john) | ~tall(john) | ~patient(lucy) | old(lucy)) [flattening 57]
65. ! [X0] : (((kind(X0) | tall(X0)) | (~generous(X0) | wise(X0))) & ((generous(X0) & ~wise(X0)) | (~kind(X0) & ~tall(X0)))) [nnf transformation 16]
66. ! [X0] : ((kind(X0) | tall(X0) | ~generous(X0) | wise(X0)) & ((generous(X0) & ~wise(X0)) | (~kind(X0) & ~tall(X0)))) [flattening 65]
71. humble(X0) | brave(X0) [cnf transformation 27]
81. wise(X0) | ~brave(X0) | humble(X0) [cnf transformation 45]
87. ~generous(sK2) | ~calm(X1) | funny(X1) [cnf transformation 50]
91. tall(X0) | calm(X0) [cnf transformation 52]
92. ~wise(X0) | tall(X0) [cnf transformation 52]
99. ~old(lucy) | calm(john) [cnf transformation 58]
104. ~funny(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 31]
106. ~calm(X0) | wise(X0) | tall(X0) [cnf transformation 33]
110. ~humble(X0) | old(X0) [cnf transformation 35]
117. ~wise(X0) | ~tall(X0) [cnf transformation 66]
119. generous(X0) | ~tall(X0) [cnf transformation 66]
130. kind(john) [cnf transformation 23]
166. wise(X0) | humble(X0) [subsumption resolution 81,71]
168. 9 <=> ! [X1] : (~calm(X1) | funny(X1)) [avatar definition]
169. ~calm(X1) | funny(X1) <- (9) [avatar component clause 168]
171. 10 <=> generous(sK2) [avatar definition]
173. ~generous(sK2) <- (~10) [avatar component clause 171]
174. 9 | ~10 [avatar split clause 87,171,168]
216. 20 <=> calm(john) [avatar definition]
218. calm(john) <- (20) [avatar component clause 216]
230. 23 <=> old(lucy) [avatar definition]
232. ~old(lucy) <- (~23) [avatar component clause 230]
233. 20 | ~23 [avatar split clause 99,230,216]
236. wise(X0) | tall(X0) [subsumption resolution 106,91]
237. tall(X0) [subsumption resolution 236,92]
266. generous(X0) [subsumption resolution 119,237]
267. ~wise(X0) [subsumption resolution 117,237]
300. humble(X3) [resolution 166,267]
301. funny(john) <- (9, 20) [resolution 169,218]
303. old(X0) [resolution 300,110]
306. $false <- (~23) [resolution 303,232]
307. 23 [avatar contradiction clause 306]
321. ~generous(john) | ~kind(john) <- (9, 20) [resolution 104,301]
323. ~kind(john) <- (9, 20) [subsumption resolution 321,266]
324. $false <- (9, 20) [subsumption resolution 323,130]
325. ~9 | ~20 [avatar contradiction clause 324]
326. $false <- (~10) [subsumption resolution 173,266]
327. 10 [avatar contradiction clause 326]
328. $false [avatar sat refutation 174,233,307,325,327]
% SZS output end Proof for 8023539052688002110984824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 both not curious and rich is either strong or not generous and vice versa. If someone is both rich and not calm then lucy is either strong or curious. If mary is not wise then someone is not tall or kind. Everyone who is not humble is tall or not happy. If someone is both strong and quiet then susan is happy and vice versa. Everyone who is quiet is not wise or not rich. Everyone who is both not rich and tall is not generous. Everyone who is brave is patient and vice versa. Everyone who is either patient or not strong is both not calm and brave and vice versa. Everyone who is not strong is kind or not calm and vice versa. If susan is old or not tall then someone is quiet. If someone is both quiet and happy then fred is happy or generous and vice versa. Everyone who is not wise or not rich is both not happy and not brave. Everyone who is either not curious or not brave is curious or funny and vice versa. Everyone who is not curious or not calm is not calm and vice versa. Everyone who is either rich or curious is brave or not quiet and vice versa. Paul is both not humble and not generous. Someone is either not funny or not wise. Someone is either not brave or not funny. Alice is both calm and not tall. Susan is not funny or funny. Someone is both not tall and not wise. | Paul is strong. | entailment | (![X]:((~curious(X)&rich(X))<=>(strong(X)<~>~generous(X))))&
((?[X]:((rich(X)&~calm(X))))=>((strong(lucy)<~>curious(lucy))))&
((~wise(mary))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:(~humble(X)=>(tall(X)|~happy(X))))&
((?[X]:((strong(X)&quiet(X))))<=>(happy(susan)))&
(![X]:(quiet(X)=>(~wise(X)|~rich(X))))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((~humble(paul)&~generous(paul)))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((~brave(X)<~>~funny(X))))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X)))) | strong(paul) | [
"p7",
"p8",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6668168732304552793414224
% SZS output start Proof for 6668168732304552793414224
8. ! [X0] : (brave(X0) <=> patient(X0)) [input p7]
9. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p8]
10. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p9]
14. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (funny(X0) | curious(X0))) [input p13]
15. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p14]
23. ~strong(paul) [input hypothesis]
44. ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))) [nnf transformation 8]
45. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 9]
46. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 45]
47. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 10]
48. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 47]
56. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 14]
57. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 56]
58. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 15]
59. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 58]
85. ~brave(X0) | patient(X0) [cnf transformation 44]
86. ~patient(X0) | brave(X0) [cnf transformation 44]
90. brave(X0) | patient(X0) | strong(X0) [cnf transformation 46]
92. strong(X0) | ~patient(X0) | ~brave(X0) | calm(X0) [cnf transformation 46]
95. ~strong(X0) | calm(X0) [cnf transformation 48]
108. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 57]
112. ~calm(X0) | curious(X0) [cnf transformation 59]
132. ~strong(paul) [cnf transformation 23]
134. ~brave(X0) | ~curious(X0) [duplicate literal removal 108]
179. ~brave(X0) | strong(X0) | calm(X0) [subsumption resolution 92,85]
180. patient(X0) | strong(X0) [subsumption resolution 90,85]
241. brave(X0) | strong(X0) [resolution 180,86]
435. strong(X0) | strong(X0) | calm(X0) [resolution 241,179]
437. ~curious(X2) | strong(X2) [resolution 241,134]
442. strong(X0) | calm(X0) [duplicate literal removal 435]
444. calm(X0) [subsumption resolution 442,95]
491. curious(X1) [resolution 444,112]
522. strong(X0) [resolution 437,491]
554. $false [resolution 522,132]
% SZS output end Proof for 6668168732304552793414224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and generous then mary is both brave and not quiet and vice versa. Everyone who is not strong is not wise and vice versa. Everyone who is not quiet or not happy is both creative and not funny. If someone is both quiet and not patient then fred is not humble. Everyone who is both creative and tall is not kind or not happy and vice versa. Everyone who is generous or not quiet is both not patient and wise. If lucy is funny or not creative then someone is either not curious or not brave and vice versa. Everyone who is either creative or rich is not funny or old and vice versa. Everyone who is either not tall or not kind is both not strong and not patient and vice versa. If susan is both curious and generous then someone is curious and vice versa. Everyone who is both generous and not humble is not strong and vice versa. Everyone who is either creative or old is both tall and humble and vice versa. Everyone who is either strong or creative is both generous and curious. If someone is either not wise or not rich then someone is rich or not funny. Someone is not happy. Someone is not quiet or not old. Mary is either not patient or not wise. Someone is not funny or kind. Alice is strong. | Lucy is not rich. | neutral | ((?[X]:((humble(X)&generous(X))))<=>((brave(mary)&~quiet(mary))))&
(![X]:(~strong(X)<=>~wise(X)))&
(![X]:((~quiet(X)|~happy(X))=>(creative(X)&~funny(X))))&
((?[X]:((quiet(X)&~patient(X))))=>(~humble(fred)))&
(![X]:((creative(X)&tall(X))<=>(~kind(X)|~happy(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
((?[X]:((~wise(X)<~>~rich(X))))=>(?[X]:((rich(X)|~funny(X)))))&
(?[X]:(~happy(X)))&
(?[X]:((~quiet(X)|~old(X))))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X))))&
(strong(alice)) | ~rich(lucy) | [] | null | 0 |
Everyone who is not creative or kind is not brave. Everyone who is not rich or kind is either not kind or brave. If someone is curious or not humble then lucy is not funny and vice versa. If someone is either not calm or not curious then someone is either happy or not patient and vice versa. Everyone who is either not humble or calm is both wise and quiet. Everyone who is not happy or not curious is both happy and kind and vice versa. Everyone who is not kind is not funny or not patient. If alice is not humble or not funny then someone is both not quiet and creative. If someone is patient or wise then paul is both not happy and patient. If alice is either strong or not patient then someone is not funny or not creative. Everyone who is either brave or not patient is not curious or calm. If fred is not strong then someone is brave or happy. Everyone who is either not kind or humble is not old. If someone is tall or not generous then alice is not curious and vice versa. If alice is brave or rich then lucy is not humble. Mary is both not patient and rich. Mary is either strong or quiet. Someone is both not kind and not humble. Someone is strong or not calm. Susan is not kind or calm. Someone is both quiet and not patient. Someone is not wise or curious. | Alice is not kind. | entailment | (![X]:((~creative(X)|kind(X))=>~brave(X)))&
(![X]:((~rich(X)|kind(X))=>(~kind(X)<~>brave(X))))&
((?[X]:((curious(X)|~humble(X))))<=>(~funny(lucy)))&
((?[X]:((~calm(X)<~>~curious(X))))<=>(?[X]:((happy(X)<~>~patient(X)))))&
(![X]:((~humble(X)<~>calm(X))=>(wise(X)&quiet(X))))&
(![X]:((~happy(X)|~curious(X))<=>(happy(X)&kind(X))))&
(![X]:(~kind(X)=>(~funny(X)|~patient(X))))&
(((~humble(alice)|~funny(alice)))=>(?[X]:((~quiet(X)&creative(X)))))&
((?[X]:((patient(X)|wise(X))))=>((~happy(paul)&patient(paul))))&
(((strong(alice)<~>~patient(alice)))=>(?[X]:((~funny(X)|~creative(X)))))&
(![X]:((brave(X)<~>~patient(X))=>(~curious(X)|calm(X))))&
((~strong(fred))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((~kind(X)<~>humble(X))=>~old(X)))&
((?[X]:((tall(X)|~generous(X))))<=>(~curious(alice)))&
(((brave(alice)|rich(alice)))=>(~humble(lucy)))&
((~patient(mary)&rich(mary)))&
((strong(mary)<~>quiet(mary)))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((strong(X)|~calm(X))))&
((~kind(susan)|calm(susan)))&
(?[X]:((quiet(X)&~patient(X))))&
(?[X]:((~wise(X)|curious(X)))) | ~kind(alice) | [
"p0",
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 9074151190458015290597623
% SZS output start Proof for 9074151190458015290597623
1. ! [X0] : ((kind(X0) | ~creative(X0)) => ~brave(X0)) [input p0]
2. ! [X0] : ((kind(X0) | ~rich(X0)) => (~kind(X0) <~> brave(X0))) [input p1]
23. kind(alice) [input hypothesis]
26. ! [X0] : (~brave(X0) | (~kind(X0) & creative(X0))) [ennf transformation 1]
27. ! [X0] : ((~kind(X0) <~> brave(X0)) | (~kind(X0) & rich(X0))) [ennf transformation 2]
38. ! [X0] : (((~brave(X0) | kind(X0)) & (brave(X0) | ~kind(X0))) | (~kind(X0) & rich(X0))) [nnf transformation 27]
73. ~brave(X0) | ~kind(X0) [cnf transformation 26]
75. brave(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
128. kind(alice) [cnf transformation 23]
131. brave(X0) | ~kind(X0) [duplicate literal removal 75]
133. ~kind(X0) [subsumption resolution 131,73]
285. $false [subsumption resolution 128,133]
% SZS output end Proof for 9074151190458015290597623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and not rich then someone is both not creative and happy. Everyone who is either wise or humble is both not patient and calm and vice versa. Everyone who is either calm or tall is either old or quiet and vice versa. If mary is either not curious or not patient then lucy is wise or rich and vice versa. Everyone who is brave or not happy is both not curious and curious. If susan is strong then lucy is both not curious and happy and vice versa. Everyone who is either generous or not curious is either not happy or not rich and vice versa. If someone is not happy or not quiet then someone is not wise or not calm. If someone is either patient or creative then someone is either not generous or not funny and vice versa. Everyone who is either not rich or not calm is both not kind and not generous and vice versa. If someone is either patient or strong then mary is both not humble and old. Everyone who is funny is kind. If someone is not old or not humble then someone is funny. Everyone who is either funny or tall is both not patient and calm and vice versa. If susan is strong or curious then fred is both not quiet and not tall and vice versa. Someone is calm or kind. Someone is not brave or not old. Someone is rich. Susan is kind or not happy. Someone is not brave. Fred is either not kind or not tall. Someone is either not happy or wise. Mary is tall or not creative. | Susan is not humble. | neutral | ((?[X]:((tall(X)&~rich(X))))=>(?[X]:((~creative(X)&happy(X)))))&
(![X]:((wise(X)<~>humble(X))<=>(~patient(X)&calm(X))))&
(![X]:((calm(X)<~>tall(X))<=>(old(X)<~>quiet(X))))&
(((~curious(mary)<~>~patient(mary)))<=>((wise(lucy)|rich(lucy))))&
(![X]:((brave(X)|~happy(X))=>(~curious(X)&curious(X))))&
((strong(susan))<=>((~curious(lucy)&happy(lucy))))&
(![X]:((generous(X)<~>~curious(X))<=>(~happy(X)<~>~rich(X))))&
((?[X]:((~happy(X)|~quiet(X))))=>(?[X]:((~wise(X)|~calm(X)))))&
((?[X]:((patient(X)<~>creative(X))))<=>(?[X]:((~generous(X)<~>~funny(X)))))&
(![X]:((~rich(X)<~>~calm(X))<=>(~kind(X)&~generous(X))))&
((?[X]:((patient(X)<~>strong(X))))=>((~humble(mary)&old(mary))))&
(![X]:(funny(X)=>kind(X)))&
((?[X]:((~old(X)|~humble(X))))=>(?[X]:(funny(X))))&
(![X]:((funny(X)<~>tall(X))<=>(~patient(X)&calm(X))))&
(((strong(susan)|curious(susan)))<=>((~quiet(fred)&~tall(fred))))&
(?[X]:((calm(X)|kind(X))))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:(rich(X)))&
((kind(susan)|~happy(susan)))&
(?[X]:(~brave(X)))&
((~kind(fred)<~>~tall(fred)))&
(?[X]:((~happy(X)<~>wise(X))))&
((tall(mary)|~creative(mary))) | ~humble(susan) | [] | null | 0 |
If lucy is strong then susan is not kind and vice versa.
If fred is both strong and not curious then lucy is quiet.
Everyone who is either quiet or generous is either happy or rich.
If someone is not old then lucy is both creative and strong and vice versa.
If someone is not rich then john is either quiet or kind.
If lucy is funny or not rich then someone is not funny or tall and vice versa.
If lucy is old then someone is wise or not brave and vice versa.
Everyone who is quiet is both humble and not patient and vice versa.
If someone is not old then someone is not wise and vice versa.
Everyone who is not old or not tall is not patient.
If someone is either not wise or humble then someone is not quiet or rich and vice versa.
Everyone who is both funny and generous is not creative and vice versa.
Everyone who is patient is both kind and generous.
Everyone who is not rich is both not calm and not funny.
If someone is not calm or not creative then someone is funny or not creative.
Everyone who is either not creative or wise is either old or brave and vice versa.
Mary is creative.
Lucy is either not patient or not old.
Someone is either not curious or not happy.
Lucy is both creative and kind.
Susan is patient.
Mary is either kind or happy.
Someone is not humble. | Mary is not brave. | entailment | ((strong(lucy))<=>(~kind(susan)))&
(((strong(fred)&~curious(fred)))=>(quiet(lucy)))&
(![X]:((quiet(X)<~>generous(X))=>(happy(X)<~>rich(X))))&
((?[X]:(~old(X)))<=>((creative(lucy)&strong(lucy))))&
((?[X]:(~rich(X)))=>((quiet(john)<~>kind(john))))&
(((funny(lucy)|~rich(lucy)))<=>(?[X]:((~funny(X)|tall(X)))))&
((old(lucy))<=>(?[X]:((wise(X)|~brave(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~patient(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~wise(X))))&
(![X]:((~old(X)|~tall(X))=>~patient(X)))&
((?[X]:((~wise(X)<~>humble(X))))<=>(?[X]:((~quiet(X)|rich(X)))))&
(![X]:((funny(X)&generous(X))<=>~creative(X)))&
(![X]:(patient(X)=>(kind(X)&generous(X))))&
(![X]:(~rich(X)=>(~calm(X)&~funny(X))))&
((?[X]:((~calm(X)|~creative(X))))=>(?[X]:((funny(X)|~creative(X)))))&
(![X]:((~creative(X)<~>wise(X))<=>(old(X)<~>brave(X))))&
(creative(mary))&
((~patient(lucy)<~>~old(lucy)))&
(?[X]:((~curious(X)<~>~happy(X))))&
((creative(lucy)&kind(lucy)))&
(patient(susan))&
((kind(mary)<~>happy(mary)))&
(?[X]:(~humble(X))) | ~brave(mary) | [
"p0",
"p3",
"p8",
"p12",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8996849796966390704776243
% SZS output start Proof for 8996849796966390704776243
1. strong(lucy) <=> ~kind(susan) [input p0]
4. ? [X0] : ~old(X0) <=> (strong(lucy) & creative(lucy)) [input p3]
9. ? [X0] : ~old(X0) <=> ? [X0] : ~wise(X0) [input p8]
13. ! [X0] : (patient(X0) => (generous(X0) & kind(X0))) [input p12]
16. ! [X0] : ((~creative(X0) <~> wise(X0)) <=> (old(X0) <~> brave(X0))) [input p15]
17. creative(mary) [input p16]
21. patient(susan) [input p20]
24. brave(mary) [input hypothesis]
25. ? [X0] : ~old(X0) <=> ? [X1] : ~wise(X1) [rectify 9]
33. ! [X0] : ((generous(X0) & kind(X0)) | ~patient(X0)) [ennf transformation 13]
36. (strong(lucy) | kind(susan)) & (~kind(susan) | ~strong(lucy)) [nnf transformation 1]
38. (? [X0] : ~old(X0) | (~strong(lucy) | ~creative(lucy))) & ((strong(lucy) & creative(lucy)) | ! [X0] : old(X0)) [nnf transformation 4]
39. (? [X0] : ~old(X0) | ~strong(lucy) | ~creative(lucy)) & ((strong(lucy) & creative(lucy)) | ! [X0] : old(X0)) [flattening 38]
40. (? [X0] : ~old(X0) | ~strong(lucy) | ~creative(lucy)) & ((strong(lucy) & creative(lucy)) | ! [X1] : old(X1)) [rectify 39]
41. ? [X0] : ~old(X0) => ~old(sK0) [choice axiom]
42. (~old(sK0) | ~strong(lucy) | ~creative(lucy)) & ((strong(lucy) & creative(lucy)) | ! [X1] : old(X1)) [skolemisation 40,41]
55. (? [X0] : ~old(X0) | ! [X1] : wise(X1)) & (? [X1] : ~wise(X1) | ! [X0] : old(X0)) [nnf transformation 25]
56. (? [X0] : ~old(X0) | ! [X1] : wise(X1)) & (? [X2] : ~wise(X2) | ! [X3] : old(X3)) [rectify 55]
57. ? [X0] : ~old(X0) => ~old(sK3) [choice axiom]
58. ? [X2] : ~wise(X2) => ~wise(sK4) [choice axiom]
59. (~old(sK3) | ! [X1] : wise(X1)) & (~wise(sK4) | ! [X3] : old(X3)) [skolemisation 56,58,57]
70. ! [X0] : ((((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0)))) & (((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0))))) [nnf transformation 16]
78. ~kind(susan) | ~strong(lucy) [cnf transformation 36]
86. strong(lucy) | old(X1) [cnf transformation 42]
101. ~old(sK3) | wise(X1) [cnf transformation 59]
113. ~patient(X0) | kind(X0) [cnf transformation 33]
122. ~brave(X0) | ~old(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 70]
127. creative(mary) [cnf transformation 17]
134. patient(susan) [cnf transformation 21]
138. brave(mary) [cnf transformation 24]
140. 1 <=> kind(susan) [avatar definition]
144. 2 <=> strong(lucy) [avatar definition]
148. ~2 | ~1 [avatar split clause 78,140,144]
172. 8 <=> ! [X1] : old(X1) [avatar definition]
173. old(X1) <- (8) [avatar component clause 172]
174. 8 | 2 [avatar split clause 86,144,172]
237. 23 <=> ! [X1] : wise(X1) [avatar definition]
238. wise(X1) <- (23) [avatar component clause 237]
240. 24 <=> old(sK3) [avatar definition]
242. ~old(sK3) <- (~24) [avatar component clause 240]
243. 23 | ~24 [avatar split clause 101,240,237]
328. kind(susan) [resolution 113,134]
331. 1 [avatar split clause 328,140]
333. $false <- (8, ~24) [resolution 173,242]
334. ~8 | 24 [avatar contradiction clause 333]
443. ~old(mary) | ~creative(mary) | ~wise(mary) [resolution 122,138]
445. ~creative(mary) | ~wise(mary) <- (8) [subsumption resolution 443,173]
446. ~wise(mary) <- (8) [subsumption resolution 445,127]
447. $false <- (8, 23) [subsumption resolution 446,238]
448. ~8 | ~23 [avatar contradiction clause 447]
449. $false [avatar sat refutation 148,174,243,331,334,448]
% SZS output end Proof for 8996849796966390704776243
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both funny and generous then lucy is not humble or humble. Everyone who is both wise and not happy is not rich or not happy and vice versa. Everyone who is generous is both not calm and not brave and vice versa. Everyone who is either strong or not patient is either tall or wise and vice versa. Everyone who is not brave is not wise or funny and vice versa. If paul is both not calm and curious then fred is quiet or not strong. Everyone who is not wise is not kind. Everyone who is not funny or not humble is curious or not old. Everyone who is both not funny and not old is both not funny and not tall and vice versa. Everyone who is not humble is not old and vice versa. Everyone who is both not creative and generous is happy or not brave. Everyone who is funny or old is wise and vice versa. If someone is both brave and funny then someone is funny or curious and vice versa. If someone is not rich then lucy is either happy or generous. Everyone who is either old or strong is either not tall or brave. If lucy is old then someone is kind. Alice is not generous or not happy. Fred is either not generous or not wise. Paul is either tall or creative. Someone is quiet. | Paul is not happy. | contradiction | (((funny(mary)&generous(mary)))=>((~humble(lucy)|humble(lucy))))&
(![X]:((wise(X)&~happy(X))<=>(~rich(X)|~happy(X))))&
(![X]:(generous(X)<=>(~calm(X)&~brave(X))))&
(![X]:((strong(X)<~>~patient(X))<=>(tall(X)<~>wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)|funny(X))))&
(((~calm(paul)&curious(paul)))=>((quiet(fred)|~strong(fred))))&
(![X]:(~wise(X)=>~kind(X)))&
(![X]:((~funny(X)|~humble(X))=>(curious(X)|~old(X))))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&~tall(X))))&
(![X]:(~humble(X)<=>~old(X)))&
(![X]:((~creative(X)&generous(X))=>(happy(X)|~brave(X))))&
(![X]:((funny(X)|old(X))<=>wise(X)))&
((?[X]:((brave(X)&funny(X))))<=>(?[X]:((funny(X)|curious(X)))))&
((?[X]:(~rich(X)))=>((happy(lucy)<~>generous(lucy))))&
(![X]:((old(X)<~>strong(X))=>(~tall(X)<~>brave(X))))&
((old(lucy))=>(?[X]:(kind(X))))&
((~generous(alice)|~happy(alice)))&
((~generous(fred)<~>~wise(fred)))&
((tall(paul)<~>creative(paul)))&
(?[X]:(quiet(X))) | ~happy(paul) | [
"p1",
"p4",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3163752539277460470696418
% SZS output start Proof for 3163752539277460470696418
2. ! [X0] : ((~happy(X0) & wise(X0)) <=> (~happy(X0) | ~rich(X0))) [input p1]
5. ! [X0] : (~brave(X0) <=> (funny(X0) | ~wise(X0))) [input p4]
8. ! [X0] : ((~humble(X0) | ~funny(X0)) => (~old(X0) | curious(X0))) [input p7]
12. ! [X0] : ((old(X0) | funny(X0)) <=> wise(X0)) [input p11]
13. ? [X0] : (funny(X0) & brave(X0)) <=> ? [X0] : (curious(X0) | funny(X0)) [input p12]
21. ~happy(paul) [input hypothesis]
22. ? [X0] : (funny(X0) & brave(X0)) <=> ? [X1] : (curious(X1) | funny(X1)) [rectify 13]
28. ! [X0] : ((~old(X0) | curious(X0)) | (humble(X0) & funny(X0))) [ennf transformation 8]
29. ! [X0] : (~old(X0) | curious(X0) | (humble(X0) & funny(X0))) [flattening 28]
35. ! [X0] : (((~happy(X0) & wise(X0)) | (happy(X0) & rich(X0))) & ((~happy(X0) | ~rich(X0)) | (happy(X0) | ~wise(X0)))) [nnf transformation 2]
36. ! [X0] : (((~happy(X0) & wise(X0)) | (happy(X0) & rich(X0))) & (~happy(X0) | ~rich(X0) | happy(X0) | ~wise(X0))) [flattening 35]
40. ! [X0] : ((~brave(X0) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | brave(X0))) [nnf transformation 5]
41. ! [X0] : ((~brave(X0) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | brave(X0))) [flattening 40]
45. ! [X0] : (((old(X0) | funny(X0)) | ~wise(X0)) & (wise(X0) | (~old(X0) & ~funny(X0)))) [nnf transformation 12]
46. ! [X0] : ((old(X0) | funny(X0) | ~wise(X0)) & (wise(X0) | (~old(X0) & ~funny(X0)))) [flattening 45]
47. (? [X0] : (funny(X0) & brave(X0)) | ! [X1] : (~curious(X1) & ~funny(X1))) & (? [X1] : (curious(X1) | funny(X1)) | ! [X0] : (~funny(X0) | ~brave(X0))) [nnf transformation 22]
48. (? [X0] : (funny(X0) & brave(X0)) | ! [X1] : (~curious(X1) & ~funny(X1))) & (? [X2] : (curious(X2) | funny(X2)) | ! [X3] : (~funny(X3) | ~brave(X3))) [rectify 47]
49. ? [X0] : (funny(X0) & brave(X0)) => (funny(sK0) & brave(sK0)) [choice axiom]
50. ? [X2] : (curious(X2) | funny(X2)) => (curious(sK1) | funny(sK1)) [choice axiom]
51. ((funny(sK0) & brave(sK0)) | ! [X1] : (~curious(X1) & ~funny(X1))) & ((curious(sK1) | funny(sK1)) | ! [X3] : (~funny(X3) | ~brave(X3))) [skolemisation 48,50,49]
61. happy(X0) | wise(X0) [cnf transformation 36]
77. ~brave(X0) | ~funny(X0) [cnf transformation 41]
79. ~old(X0) | curious(X0) | funny(X0) [cnf transformation 29]
90. ~wise(X0) | funny(X0) | old(X0) [cnf transformation 46]
92. brave(sK0) | ~funny(X1) [cnf transformation 51]
93. brave(sK0) | ~curious(X1) [cnf transformation 51]
94. funny(sK0) | ~funny(X1) [cnf transformation 51]
95. funny(sK0) | ~curious(X1) [cnf transformation 51]
108. ~happy(paul) [cnf transformation 21]
110. 1 <=> ! [X1] : ~curious(X1) [avatar definition]
111. ~curious(X1) <- (1) [avatar component clause 110]
113. 2 <=> funny(sK0) [avatar definition]
116. 1 | 2 [avatar split clause 95,113,110]
118. 3 <=> ! [X1] : ~funny(X1) [avatar definition]
119. ~funny(X1) <- (3) [avatar component clause 118]
120. 3 | 2 [avatar split clause 94,113,118]
122. 4 <=> brave(sK0) [avatar definition]
124. brave(sK0) <- (4) [avatar component clause 122]
125. 1 | 4 [avatar split clause 93,122,110]
126. 3 | 4 [avatar split clause 92,122,118]
178. wise(paul) [resolution 61,108]
182. ~funny(sK0) <- (4) [resolution 77,124]
185. ~2 | ~4 [avatar split clause 182,122,113]
205. funny(paul) | old(paul) [resolution 90,178]
207. old(paul) <- (3) [subsumption resolution 205,119]
211. curious(paul) | funny(paul) <- (3) [resolution 207,79]
218. funny(paul) <- (1, 3) [subsumption resolution 211,111]
219. $false <- (1, 3) [subsumption resolution 218,119]
220. ~1 | ~3 [avatar contradiction clause 219]
221. $false [avatar sat refutation 116,120,125,126,185,220]
% SZS output end Proof for 3163752539277460470696418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or funny is either not generous or not happy and vice versa.
If someone is funny then paul is humble or not brave.
Everyone who is both not tall and happy is not humble and vice versa.
Everyone who is not patient is rich.
Everyone who is calm or not calm is both not humble and curious and vice versa.
Everyone who is generous is not quiet and vice versa.
If someone is calm or not rich then someone is both wise and not calm and vice versa.
Everyone who is both not curious and not brave is both creative and not creative and vice versa.
If paul is both calm and funny then john is either not tall or not generous.
Everyone who is both not quiet and humble is either not kind or wise.
If paul is not wise or creative then john is both generous and not kind.
Everyone who is either not old or not patient is both quiet and kind and vice versa.
If john is not creative or patient then lucy is both not brave and quiet.
Everyone who is not creative is calm or not old and vice versa.
If someone is not generous then someone is funny or not wise and vice versa.
If someone is not brave then someone is both kind and calm.
Someone is both curious and old.
Someone is both not patient and not wise.
Someone is not old.
Fred is both curious and not funny.
Someone is not patient.
Someone is both kind and not tall.
Susan is tall or kind. | Susan is not patient. | neutral | (![X]:((~patient(X)<~>funny(X))<=>(~generous(X)<~>~happy(X))))&
((?[X]:(funny(X)))=>((humble(paul)|~brave(paul))))&
(![X]:((~tall(X)&happy(X))<=>~humble(X)))&
(![X]:(~patient(X)=>rich(X)))&
(![X]:((calm(X)|~calm(X))<=>(~humble(X)&curious(X))))&
(![X]:(generous(X)<=>~quiet(X)))&
((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((~curious(X)&~brave(X))<=>(creative(X)&~creative(X))))&
(((calm(paul)&funny(paul)))=>((~tall(john)<~>~generous(john))))&
(![X]:((~quiet(X)&humble(X))=>(~kind(X)<~>wise(X))))&
(((~wise(paul)|creative(paul)))=>((generous(john)&~kind(john))))&
(![X]:((~old(X)<~>~patient(X))<=>(quiet(X)&kind(X))))&
(((~creative(john)|patient(john)))=>((~brave(lucy)&quiet(lucy))))&
(![X]:(~creative(X)<=>(calm(X)|~old(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((funny(X)|~wise(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((kind(X)&calm(X)))))&
(?[X]:((curious(X)&old(X))))&
(?[X]:((~patient(X)&~wise(X))))&
(?[X]:(~old(X)))&
((curious(fred)&~funny(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((kind(X)&~tall(X))))&
((tall(susan)|kind(susan))) | ~patient(susan) | [] | null | 0 |
Everyone who is either not quiet or brave is both not rich and brave. Everyone who is either old or quiet is either not patient or not happy. Everyone who is not patient or generous is either not quiet or happy. Everyone who is wise or not calm is both not strong and strong. If paul is not funny or rich then someone is either not calm or happy and vice versa. Everyone who is not humble or not quiet is generous or not quiet. Everyone who is humble is quiet or patient and vice versa. If mary is not brave then someone is either brave or not wise. If mary is humble or old then someone is both kind and not funny and vice versa. Everyone who is funny is both not rich and tall. Everyone who is either humble or not tall is either not kind or rich. If someone is both quiet and not happy then paul is not strong and vice versa. Everyone who is not tall or patient is curious and vice versa. Everyone who is not generous is either happy or strong and vice versa. Everyone who is not humble or happy is both not brave and not old and vice versa. Everyone who is not kind or not funny is not patient and vice versa. Paul is either not humble or generous. Paul is either humble or funny. Someone is quiet or not creative. Susan is wise or not kind. Alice is not wise or not humble. Someone is not tall. Mary is either not patient or not quiet. | Alice is happy. | entailment | (![X]:((~quiet(X)<~>brave(X))=>(~rich(X)&brave(X))))&
(![X]:((old(X)<~>quiet(X))=>(~patient(X)<~>~happy(X))))&
(![X]:((~patient(X)|generous(X))=>(~quiet(X)<~>happy(X))))&
(![X]:((wise(X)|~calm(X))=>(~strong(X)&strong(X))))&
(((~funny(paul)|rich(paul)))<=>(?[X]:((~calm(X)<~>happy(X)))))&
(![X]:((~humble(X)|~quiet(X))=>(generous(X)|~quiet(X))))&
(![X]:(humble(X)<=>(quiet(X)|patient(X))))&
((~brave(mary))=>(?[X]:((brave(X)<~>~wise(X)))))&
(((humble(mary)|old(mary)))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:(funny(X)=>(~rich(X)&tall(X))))&
(![X]:((humble(X)<~>~tall(X))=>(~kind(X)<~>rich(X))))&
((?[X]:((quiet(X)&~happy(X))))<=>(~strong(paul)))&
(![X]:((~tall(X)|patient(X))<=>curious(X)))&
(![X]:(~generous(X)<=>(happy(X)<~>strong(X))))&
(![X]:((~humble(X)|happy(X))<=>(~brave(X)&~old(X))))&
(![X]:((~kind(X)|~funny(X))<=>~patient(X)))&
((~humble(paul)<~>generous(paul)))&
((humble(paul)<~>funny(paul)))&
(?[X]:((quiet(X)|~creative(X))))&
((wise(susan)|~kind(susan)))&
((~wise(alice)|~humble(alice)))&
(?[X]:(~tall(X)))&
((~patient(mary)<~>~quiet(mary))) | happy(alice) | [
"p0",
"p2",
"p6",
"p9",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 919677567382591559945239
% SZS output start Proof for 919677567382591559945239
1. ! [X0] : ((~quiet(X0) <~> brave(X0)) => (brave(X0) & ~rich(X0))) [input p0]
3. ! [X0] : ((generous(X0) | ~patient(X0)) => (~quiet(X0) <~> happy(X0))) [input p2]
7. ! [X0] : (humble(X0) <=> (patient(X0) | quiet(X0))) [input p6]
10. ! [X0] : (funny(X0) => (tall(X0) & ~rich(X0))) [input p9]
11. ! [X0] : ((humble(X0) <~> ~tall(X0)) => (~kind(X0) <~> rich(X0))) [input p10]
12. ? [X0] : (~happy(X0) & quiet(X0)) <=> ~strong(paul) [input p11]
15. ! [X0] : ((happy(X0) | ~humble(X0)) <=> (~old(X0) & ~brave(X0))) [input p14]
16. ! [X0] : ((~funny(X0) | ~kind(X0)) <=> ~patient(X0)) [input p15]
24. ~happy(alice) [input hypothesis]
26. ! [X0] : ((brave(X0) & ~rich(X0)) | (~quiet(X0) <=> brave(X0))) [ennf transformation 1]
28. ! [X0] : ((~quiet(X0) <~> happy(X0)) | (~generous(X0) & patient(X0))) [ennf transformation 3]
33. ! [X0] : ((tall(X0) & ~rich(X0)) | ~funny(X0)) [ennf transformation 10]
34. ! [X0] : ((~kind(X0) <~> rich(X0)) | (humble(X0) <=> ~tall(X0))) [ennf transformation 11]
35. ! [X0] : ((brave(X0) & ~rich(X0)) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0)))) [nnf transformation 26]
37. ! [X0] : (((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (~generous(X0) & patient(X0))) [nnf transformation 28]
43. ! [X0] : ((humble(X0) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | ~humble(X0))) [nnf transformation 7]
44. ! [X0] : ((humble(X0) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~humble(X0))) [flattening 43]
53. ! [X0] : (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0)))) [nnf transformation 34]
54. (? [X0] : (~happy(X0) & quiet(X0)) | strong(paul)) & (~strong(paul) | ! [X0] : (happy(X0) | ~quiet(X0))) [nnf transformation 12]
55. (? [X0] : (~happy(X0) & quiet(X0)) | strong(paul)) & (~strong(paul) | ! [X1] : (happy(X1) | ~quiet(X1))) [rectify 54]
56. ? [X0] : (~happy(X0) & quiet(X0)) => (~happy(sK3) & quiet(sK3)) [choice axiom]
57. ((~happy(sK3) & quiet(sK3)) | strong(paul)) & (~strong(paul) | ! [X1] : (happy(X1) | ~quiet(X1))) [skolemisation 55,56]
59. ! [X0] : (((happy(X0) | ~humble(X0)) | (old(X0) | brave(X0))) & ((~old(X0) & ~brave(X0)) | (~happy(X0) & humble(X0)))) [nnf transformation 15]
60. ! [X0] : ((happy(X0) | ~humble(X0) | old(X0) | brave(X0)) & ((~old(X0) & ~brave(X0)) | (~happy(X0) & humble(X0)))) [flattening 59]
61. ! [X0] : (((~funny(X0) | ~kind(X0)) | patient(X0)) & (~patient(X0) | (funny(X0) & kind(X0)))) [nnf transformation 16]
62. ! [X0] : ((~funny(X0) | ~kind(X0) | patient(X0)) & (~patient(X0) | (funny(X0) & kind(X0)))) [flattening 61]
70. brave(X0) | brave(X0) | quiet(X0) [cnf transformation 35]
76. ~quiet(X0) | happy(X0) | patient(X0) [cnf transformation 37]
92. ~humble(X0) | quiet(X0) | patient(X0) [cnf transformation 44]
93. ~quiet(X0) | humble(X0) [cnf transformation 44]
102. ~funny(X0) | ~rich(X0) [cnf transformation 33]
103. ~funny(X0) | tall(X0) [cnf transformation 33]
104. ~tall(X0) | ~kind(X0) | rich(X0) | ~humble(X0) [cnf transformation 53]
108. ~strong(paul) | happy(X1) | ~quiet(X1) [cnf transformation 57]
110. ~happy(sK3) | strong(paul) [cnf transformation 57]
115. ~brave(X0) | humble(X0) [cnf transformation 60]
120. ~patient(X0) | kind(X0) [cnf transformation 62]
121. ~patient(X0) | funny(X0) [cnf transformation 62]
132. ~happy(alice) [cnf transformation 24]
133. brave(X0) | quiet(X0) [duplicate literal removal 70]
192. 12 <=> strong(paul) [avatar definition]
196. 13 <=> happy(sK3) [avatar definition]
198. ~happy(sK3) <- (~13) [avatar component clause 196]
199. 12 | ~13 [avatar split clause 110,196,192]
201. 14 <=> quiet(sK3) [avatar definition]
202. ~quiet(sK3) <- (~14) [avatar component clause 201]
203. quiet(sK3) <- (14) [avatar component clause 201]
206. 15 <=> ! [X1] : (happy(X1) | ~quiet(X1)) [avatar definition]
207. ~quiet(X1) | happy(X1) <- (15) [avatar component clause 206]
208. 15 | ~12 [avatar split clause 108,192,206]
233. humble(sK3) <- (14) [resolution 93,203]
248. quiet(X0) | humble(X0) [resolution 133,115]
250. humble(X0) [subsumption resolution 248,93]
268. happy(sK3) | patient(sK3) <- (14) [resolution 76,203]
270. patient(sK3) <- (~13, 14) [subsumption resolution 268,198]
294. funny(sK3) <- (~13, 14) [resolution 270,121]
295. kind(sK3) <- (~13, 14) [resolution 270,120]
305. patient(X0) | quiet(X0) [resolution 92,250]
335. tall(sK3) <- (~13, 14) [resolution 294,103]
336. ~rich(sK3) <- (~13, 14) [resolution 294,102]
368. ~kind(sK3) | rich(sK3) | ~humble(sK3) <- (~13, 14) [resolution 335,104]
369. rich(sK3) | ~humble(sK3) <- (~13, 14) [subsumption resolution 368,295]
370. ~humble(sK3) <- (~13, 14) [subsumption resolution 369,336]
371. $false <- (~13, 14) [subsumption resolution 370,233]
372. 13 | ~14 [avatar contradiction clause 371]
433. funny(X0) | quiet(X0) [resolution 305,121]
434. kind(X1) | quiet(X1) [resolution 305,120]
471. tall(X0) | quiet(X0) [resolution 433,103]
472. ~rich(X1) | quiet(X1) [resolution 433,102]
490. quiet(X1) | ~kind(X1) | rich(X1) | ~humble(X1) [resolution 471,104]
491. quiet(X1) | ~kind(X1) | rich(X1) [subsumption resolution 490,250]
492. quiet(X1) | rich(X1) [subsumption resolution 491,434]
493. quiet(X1) [subsumption resolution 492,472]
532. happy(X0) <- (15) [resolution 493,207]
537. $false <- (~14) [resolution 493,202]
538. 14 [avatar contradiction clause 537]
564. $false <- (15) [resolution 532,132]
565. ~15 [avatar contradiction clause 564]
567. $false [avatar sat refutation 199,208,372,538,565]
% SZS output end Proof for 919677567382591559945239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not funny is creative and vice versa. Everyone who is brave or not happy is not strong or not wise. If someone is curious or not funny then someone is both not patient and quiet. If susan is not humble then lucy is both rich and calm and vice versa. Everyone who is either not quiet or rich is either not funny or not wise. Everyone who is both not rich and kind is not generous. Everyone who is both wise and patient is either not generous or not tall. If john is either not calm or creative then mary is old or patient and vice versa. Everyone who is either not rich or humble is either creative or not rich and vice versa. If someone is either strong or not calm then someone is either rich or humble and vice versa. If alice is quiet then alice is creative or quiet and vice versa. Everyone who is either not curious or curious is both happy and wise. If someone is both not funny and wise then john is not rich and vice versa. If someone is either not patient or not tall then someone is both not tall and brave. Everyone who is not quiet is not creative and vice versa. If someone is either humble or not generous then mary is strong and vice versa. Paul is not funny. Mary is both not generous and rich. Someone is not tall or not curious. Alice is not funny or kind. Someone is either not rich or old. Someone is both not funny and not brave. Someone is calm. | John is quiet. | entailment | (![X]:((~wise(X)<~>~funny(X))<=>creative(X)))&
(![X]:((brave(X)|~happy(X))=>(~strong(X)|~wise(X))))&
((?[X]:((curious(X)|~funny(X))))=>(?[X]:((~patient(X)&quiet(X)))))&
((~humble(susan))<=>((rich(lucy)&calm(lucy))))&
(![X]:((~quiet(X)<~>rich(X))=>(~funny(X)<~>~wise(X))))&
(![X]:((~rich(X)&kind(X))=>~generous(X)))&
(![X]:((wise(X)&patient(X))=>(~generous(X)<~>~tall(X))))&
(((~calm(john)<~>creative(john)))<=>((old(mary)|patient(mary))))&
(![X]:((~rich(X)<~>humble(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((strong(X)<~>~calm(X))))<=>(?[X]:((rich(X)<~>humble(X)))))&
((quiet(alice))<=>((creative(alice)|quiet(alice))))&
(![X]:((~curious(X)<~>curious(X))=>(happy(X)&wise(X))))&
((?[X]:((~funny(X)&wise(X))))<=>(~rich(john)))&
((?[X]:((~patient(X)<~>~tall(X))))=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:(~quiet(X)<=>~creative(X)))&
((?[X]:((humble(X)<~>~generous(X))))<=>(strong(mary)))&
(~funny(paul))&
((~generous(mary)&rich(mary)))&
(?[X]:((~tall(X)|~curious(X))))&
((~funny(alice)|kind(alice)))&
(?[X]:((~rich(X)<~>old(X))))&
(?[X]:((~funny(X)&~brave(X))))&
(?[X]:(calm(X))) | quiet(john) | [
"p0",
"p4",
"p11",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1658620022553228787424685
% SZS output start Proof for 1658620022553228787424685
1. ! [X0] : ((~wise(X0) <~> ~funny(X0)) <=> creative(X0)) [input p0]
5. ! [X0] : ((~quiet(X0) <~> rich(X0)) => (~funny(X0) <~> ~wise(X0))) [input p4]
12. ! [X0] : ((~curious(X0) <~> curious(X0)) => (wise(X0) & happy(X0))) [input p11]
13. ? [X0] : (wise(X0) & ~funny(X0)) <=> ~rich(john) [input p12]
15. ! [X0] : (~quiet(X0) <=> ~creative(X0)) [input p14]
17. ~funny(paul) [input p16]
24. ~quiet(john) [input hypothesis]
29. ! [X0] : ((~curious(X0) <~> curious(X0)) => wise(X0)) [pure predicate removal 12]
33. ! [X0] : ((~funny(X0) <~> ~wise(X0)) | (~quiet(X0) <=> rich(X0))) [ennf transformation 5]
38. ! [X0] : (wise(X0) | (~curious(X0) <=> curious(X0))) [ennf transformation 29]
40. ! [X0] : ((((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | ~creative(X0)) & (creative(X0) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0))))) [nnf transformation 1]
46. ! [X0] : (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) [nnf transformation 33]
58. ! [X0] : (wise(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) [nnf transformation 38]
59. (? [X0] : (wise(X0) & ~funny(X0)) | rich(john)) & (~rich(john) | ! [X0] : (~wise(X0) | funny(X0))) [nnf transformation 13]
60. (? [X0] : (wise(X0) & ~funny(X0)) | rich(john)) & (~rich(john) | ! [X1] : (~wise(X1) | funny(X1))) [rectify 59]
61. ? [X0] : (wise(X0) & ~funny(X0)) => (wise(sK3) & ~funny(sK3)) [choice axiom]
62. ((wise(sK3) & ~funny(sK3)) | rich(john)) & (~rich(john) | ! [X1] : (~wise(X1) | funny(X1))) [skolemisation 60,61]
67. ! [X0] : ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0))) [nnf transformation 15]
82. ~wise(X0) | creative(X0) | funny(X0) [cnf transformation 40]
93. ~funny(X0) | ~wise(X0) | rich(X0) | quiet(X0) [cnf transformation 46]
125. wise(X0) | curious(X0) | curious(X0) [cnf transformation 58]
126. wise(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 58]
127. ~rich(john) | ~wise(X1) | funny(X1) [cnf transformation 62]
134. ~creative(X0) | quiet(X0) [cnf transformation 67]
140. ~funny(paul) [cnf transformation 17]
150. ~quiet(john) [cnf transformation 24]
151. wise(X0) | curious(X0) [duplicate literal removal 125]
152. ~curious(X0) | wise(X0) [duplicate literal removal 126]
158. 1 <=> ! [X1] : funny(X1) [avatar definition]
159. funny(X1) <- (1) [avatar component clause 158]
199. 10 <=> creative(john) [avatar definition]
200. creative(john) <- (10) [avatar component clause 199]
201. ~creative(john) <- (~10) [avatar component clause 199]
259. wise(X0) [subsumption resolution 151,152]
261. 22 <=> rich(john) [avatar definition]
262. ~rich(john) <- (~22) [avatar component clause 261]
269. ~rich(john) | funny(X1) [subsumption resolution 127,259]
270. 1 | ~22 [avatar split clause 269,261,158]
343. creative(X0) | funny(X0) [resolution 82,259]
347. funny(john) <- (~10) [resolution 343,201]
375. ~wise(john) | rich(john) | quiet(john) <- (~10) [resolution 93,347]
376. rich(john) | quiet(john) <- (~10) [subsumption resolution 375,259]
377. quiet(john) <- (~10, ~22) [subsumption resolution 376,262]
378. $false <- (~10, ~22) [subsumption resolution 377,150]
379. 10 | 22 [avatar contradiction clause 378]
383. quiet(john) <- (10) [resolution 200,134]
385. $false <- (10) [subsumption resolution 383,150]
386. ~10 [avatar contradiction clause 385]
390. $false <- (1) [resolution 159,140]
397. ~1 [avatar contradiction clause 390]
400. $false [avatar sat refutation 270,379,386,397]
% SZS output end Proof for 1658620022553228787424685
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not generous is strong or not calm.
Everyone who is rich or brave is humble or creative and vice versa.
If someone is not generous then someone is not funny.
If someone is either tall or funny then someone is either not strong or kind and vice versa.
If fred is both not tall and not generous then someone is not wise or not quiet.
Everyone who is kind is happy.
Everyone who is not happy or tall is not brave and vice versa.
Everyone who is both not brave and not strong is not generous and vice versa.
Everyone who is not calm is both not curious and brave and vice versa.
If alice is either strong or not humble then someone is old or not happy and vice versa.
Everyone who is generous or happy is either not wise or not tall and vice versa.
Everyone who is both quiet and not kind is either not old or quiet.
If lucy is either not creative or patient then john is both not rich and not curious.
If alice is either not humble or not brave then alice is not creative or not kind.
If someone is wise or not tall then someone is funny.
Everyone who is not creative or not brave is not kind or strong.
Alice is calm or generous.
John is not kind.
Mary is both happy and funny.
Susan is either rich or not kind.
Someone is either not tall or not funny.
Susan is both old and not quiet.
Mary is happy or not curious.
Someone is not calm. | Alice is brave. | neutral | (![X]:((funny(X)<~>~generous(X))=>(strong(X)|~calm(X))))&
(![X]:((rich(X)|brave(X))<=>(humble(X)|creative(X))))&
((?[X]:(~generous(X)))=>(?[X]:(~funny(X))))&
((?[X]:((tall(X)<~>funny(X))))<=>(?[X]:((~strong(X)<~>kind(X)))))&
(((~tall(fred)&~generous(fred)))=>(?[X]:((~wise(X)|~quiet(X)))))&
(![X]:(kind(X)=>happy(X)))&
(![X]:((~happy(X)|tall(X))<=>~brave(X)))&
(![X]:((~brave(X)&~strong(X))<=>~generous(X)))&
(![X]:(~calm(X)<=>(~curious(X)&brave(X))))&
(((strong(alice)<~>~humble(alice)))<=>(?[X]:((old(X)|~happy(X)))))&
(![X]:((generous(X)|happy(X))<=>(~wise(X)<~>~tall(X))))&
(![X]:((quiet(X)&~kind(X))=>(~old(X)<~>quiet(X))))&
(((~creative(lucy)<~>patient(lucy)))=>((~rich(john)&~curious(john))))&
(((~humble(alice)<~>~brave(alice)))=>((~creative(alice)|~kind(alice))))&
((?[X]:((wise(X)|~tall(X))))=>(?[X]:(funny(X))))&
(![X]:((~creative(X)|~brave(X))=>(~kind(X)|strong(X))))&
((calm(alice)|generous(alice)))&
(~kind(john))&
((happy(mary)&funny(mary)))&
((rich(susan)<~>~kind(susan)))&
(?[X]:((~tall(X)<~>~funny(X))))&
((old(susan)&~quiet(susan)))&
((happy(mary)|~curious(mary)))&
(?[X]:(~calm(X))) | brave(alice) | [] | null | 0 |
Everyone who is both strong and curious is either not humble or tall. Everyone who is either not old or not strong is either wise or tall. Everyone who is either not humble or strong is both kind and wise. Everyone who is both curious and not strong is both rich and generous. Everyone who is both not kind and not tall is both not kind and wise. If someone is not creative or not quiet then mary is both not generous and patient. If someone is not patient or not old then someone is both not wise and not kind and vice versa. Everyone who is humble is both humble and not strong. Everyone who is tall is not funny. Everyone who is either generous or wise is quiet or not kind and vice versa. Everyone who is strong is humble and vice versa. Everyone who is both quiet and not patient is either brave or old and vice versa. Everyone who is not generous is quiet or creative and vice versa. If someone is both happy and not tall then someone is either old or creative and vice versa. Someone is either curious or tall. Paul is not calm or old. Fred is happy. Paul is not creative or kind. | Mary is old. | entailment | (![X]:((strong(X)&curious(X))=>(~humble(X)<~>tall(X))))&
(![X]:((~old(X)<~>~strong(X))=>(wise(X)<~>tall(X))))&
(![X]:((~humble(X)<~>strong(X))=>(kind(X)&wise(X))))&
(![X]:((curious(X)&~strong(X))=>(rich(X)&generous(X))))&
(![X]:((~kind(X)&~tall(X))=>(~kind(X)&wise(X))))&
((?[X]:((~creative(X)|~quiet(X))))=>((~generous(mary)&patient(mary))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(humble(X)=>(humble(X)&~strong(X))))&
(![X]:(tall(X)=>~funny(X)))&
(![X]:((generous(X)<~>wise(X))<=>(quiet(X)|~kind(X))))&
(![X]:(strong(X)<=>humble(X)))&
(![X]:((quiet(X)&~patient(X))<=>(brave(X)<~>old(X))))&
(![X]:(~generous(X)<=>(quiet(X)|creative(X))))&
((?[X]:((happy(X)&~tall(X))))<=>(?[X]:((old(X)<~>creative(X)))))&
(?[X]:((curious(X)<~>tall(X))))&
((~calm(paul)|old(paul)))&
(happy(fred))&
((~creative(paul)|kind(paul))) | old(mary) | [
"p2",
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7561319478101460696512236
% SZS output start Proof for 7561319478101460696512236
3. ! [X0] : ((~humble(X0) <~> strong(X0)) => (wise(X0) & kind(X0))) [input p2]
7. ? [X0] : (~old(X0) | ~patient(X0)) <=> ? [X0] : (~kind(X0) & ~wise(X0)) [input p6]
8. ! [X0] : (humble(X0) => (~strong(X0) & humble(X0))) [input p7]
11. ! [X0] : (strong(X0) <=> humble(X0)) [input p10]
19. ~old(mary) [input hypothesis]
20. ? [X0] : (~old(X0) | ~patient(X0)) <=> ? [X1] : (~kind(X1) & ~wise(X1)) [rectify 7]
28. ! [X0] : ((wise(X0) & kind(X0)) | (~humble(X0) <=> strong(X0))) [ennf transformation 3]
34. ! [X0] : ((~strong(X0) & humble(X0)) | ~humble(X0)) [ennf transformation 8]
37. ! [X0] : ((wise(X0) & kind(X0)) | ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0)))) [nnf transformation 28]
38. (? [X0] : (~old(X0) | ~patient(X0)) | ! [X1] : (kind(X1) | wise(X1))) & (? [X1] : (~kind(X1) & ~wise(X1)) | ! [X0] : (old(X0) & patient(X0))) [nnf transformation 20]
39. (? [X0] : (~old(X0) | ~patient(X0)) | ! [X1] : (kind(X1) | wise(X1))) & (? [X2] : (~kind(X2) & ~wise(X2)) | ! [X3] : (old(X3) & patient(X3))) [rectify 38]
40. ? [X0] : (~old(X0) | ~patient(X0)) => (~old(sK0) | ~patient(sK0)) [choice axiom]
41. ? [X2] : (~kind(X2) & ~wise(X2)) => (~kind(sK1) & ~wise(sK1)) [choice axiom]
42. ((~old(sK0) | ~patient(sK0)) | ! [X1] : (kind(X1) | wise(X1))) & ((~kind(sK1) & ~wise(sK1)) | ! [X3] : (old(X3) & patient(X3))) [skolemisation 39,41,40]
45. ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))) [nnf transformation 11]
64. kind(X0) | strong(X0) | humble(X0) [cnf transformation 37]
78. ~kind(sK1) | old(X3) [cnf transformation 42]
81. ~humble(X0) | ~strong(X0) [cnf transformation 34]
88. humble(X0) | ~strong(X0) [cnf transformation 45]
89. strong(X0) | ~humble(X0) [cnf transformation 45]
109. ~old(mary) [cnf transformation 19]
141. 8 <=> ! [X3] : old(X3) [avatar definition]
142. old(X3) <- (8) [avatar component clause 141]
144. 9 <=> kind(sK1) [avatar definition]
146. ~kind(sK1) <- (~9) [avatar component clause 144]
147. 8 | ~9 [avatar split clause 78,144,141]
158. ~humble(X0) [subsumption resolution 89,81]
159. ~strong(X0) [subsumption resolution 88,158]
211. strong(sK1) | humble(sK1) <- (~9) [resolution 64,146]
212. humble(sK1) <- (~9) [subsumption resolution 211,159]
213. $false <- (~9) [subsumption resolution 212,158]
214. 9 [avatar contradiction clause 213]
215. $false <- (8) [resolution 142,109]
219. ~8 [avatar contradiction clause 215]
221. $false [avatar sat refutation 147,214,219]
% SZS output end Proof for 7561319478101460696512236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% 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 generous or humble then someone is either not happy or creative. If someone is both not brave and not happy then mary is old and vice versa. If susan is not creative or funny then susan is not kind or not old. Everyone who is both not kind and not old is not curious or not patient. Everyone who is either not brave or not wise is happy and vice versa. If someone is either not old or patient then someone is both funny and curious and vice versa. Everyone who is not old is funny or calm and vice versa. Everyone who is funny is not happy or happy and vice versa. If fred is not brave or not patient then fred is both not old and brave. If someone is both not strong and not rich then mary is both not patient and not wise and vice versa. If someone is not rich then mary is generous or brave. Everyone who is not kind is calm and vice versa. Everyone who is not creative is not rich or calm. Everyone who is either not kind or quiet is both not creative and not happy and vice versa. Everyone who is both calm and kind is either old or not tall and vice versa. If someone is quiet or wise then susan is both wise and not old. Someone is both not strong and brave. Fred is either not humble or not curious. Susan is quiet. Someone is both creative and brave. Someone is both not humble and not strong. Mary is not strong or not kind. | Susan is curious. | neutral | ((?[X]:((generous(X)|humble(X))))=>(?[X]:((~happy(X)<~>creative(X)))))&
((?[X]:((~brave(X)&~happy(X))))<=>(old(mary)))&
(((~creative(susan)|funny(susan)))=>((~kind(susan)|~old(susan))))&
(![X]:((~kind(X)&~old(X))=>(~curious(X)|~patient(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>happy(X)))&
((?[X]:((~old(X)<~>patient(X))))<=>(?[X]:((funny(X)&curious(X)))))&
(![X]:(~old(X)<=>(funny(X)|calm(X))))&
(![X]:(funny(X)<=>(~happy(X)|happy(X))))&
(((~brave(fred)|~patient(fred)))=>((~old(fred)&brave(fred))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~patient(mary)&~wise(mary))))&
((?[X]:(~rich(X)))=>((generous(mary)|brave(mary))))&
(![X]:(~kind(X)<=>calm(X)))&
(![X]:(~creative(X)=>(~rich(X)|calm(X))))&
(![X]:((~kind(X)<~>quiet(X))<=>(~creative(X)&~happy(X))))&
(![X]:((calm(X)&kind(X))<=>(old(X)<~>~tall(X))))&
((?[X]:((quiet(X)|wise(X))))=>((wise(susan)&~old(susan))))&
(?[X]:((~strong(X)&brave(X))))&
((~humble(fred)<~>~curious(fred)))&
(quiet(susan))&
(?[X]:((creative(X)&brave(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~strong(mary)|~kind(mary))) | curious(susan) | [] | null | 0 |
Everyone who is both curious and not generous is curious or old and vice versa.
Everyone who is both funny and not curious is both not brave and not calm and vice versa.
Everyone who is brave or patient is both not quiet and quiet and vice versa.
If susan is not strong then someone is both not strong and not patient and vice versa.
If paul is either patient or not happy then john is strong or quiet and vice versa.
If someone is not creative or humble then paul is wise.
Everyone who is both not funny and not patient is either not funny or not creative.
If someone is either old or not happy then someone is both not brave and not kind and vice versa.
Everyone who is humble or happy is both generous and not kind and vice versa.
Everyone who is humble is not wise or not calm and vice versa.
Everyone who is both funny and not brave is not quiet or patient.
If someone is either happy or funny then john is either not rich or not brave.
Everyone who is not wise or not strong is both not tall and creative.
If mary is either not curious or calm then paul is either not generous or funny and vice versa.
If fred is kind or humble then someone is both not quiet and wise and vice versa.
If someone is not creative or not rich then alice is both not kind and strong and vice versa.
Someone is not curious or not quiet.
Susan is generous.
John is funny or not patient.
Someone is either happy or patient.
Fred is either tall or strong.
Susan is wise.
Someone is curious or creative. | John is generous. | neutral | (![X]:((curious(X)&~generous(X))<=>(curious(X)|old(X))))&
(![X]:((funny(X)&~curious(X))<=>(~brave(X)&~calm(X))))&
(![X]:((brave(X)|patient(X))<=>(~quiet(X)&quiet(X))))&
((~strong(susan))<=>(?[X]:((~strong(X)&~patient(X)))))&
(((patient(paul)<~>~happy(paul)))<=>((strong(john)|quiet(john))))&
((?[X]:((~creative(X)|humble(X))))=>(wise(paul)))&
(![X]:((~funny(X)&~patient(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:((old(X)<~>~happy(X))))<=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((humble(X)|happy(X))<=>(generous(X)&~kind(X))))&
(![X]:(humble(X)<=>(~wise(X)|~calm(X))))&
(![X]:((funny(X)&~brave(X))=>(~quiet(X)|patient(X))))&
((?[X]:((happy(X)<~>funny(X))))=>((~rich(john)<~>~brave(john))))&
(![X]:((~wise(X)|~strong(X))=>(~tall(X)&creative(X))))&
(((~curious(mary)<~>calm(mary)))<=>((~generous(paul)<~>funny(paul))))&
(((kind(fred)|humble(fred)))<=>(?[X]:((~quiet(X)&wise(X)))))&
((?[X]:((~creative(X)|~rich(X))))<=>((~kind(alice)&strong(alice))))&
(?[X]:((~curious(X)|~quiet(X))))&
(generous(susan))&
((funny(john)|~patient(john)))&
(?[X]:((happy(X)<~>patient(X))))&
((tall(fred)<~>strong(fred)))&
(wise(susan))&
(?[X]:((curious(X)|creative(X)))) | generous(john) | [] | null | 0 |
If someone is not creative then someone is not tall.
If paul is either curious or patient then paul is both not happy and rich and vice versa.
If john is either patient or not brave then mary is either not generous or not calm and vice versa.
If lucy is both not kind and curious then someone is creative or not quiet.
Everyone who is either not strong or not patient is both not strong and not happy and vice versa.
If someone is both happy and not creative then mary is quiet and vice versa.
If paul is not happy or not tall then someone is happy or humble and vice versa.
Everyone who is either curious or not happy is both curious and kind and vice versa.
Everyone who is both not calm and tall is calm and vice versa.
Everyone who is both tall and funny is either funny or quiet.
If fred is either not strong or not kind then someone is funny or rich.
Everyone who is both not creative and not patient is either not old or not wise and vice versa.
If paul is tall then fred is happy and vice versa.
Everyone who is either not creative or quiet is either curious or not patient.
If someone is kind then paul is humble.
If someone is both humble and strong then paul is either tall or not strong and vice versa.
Someone is not kind or not generous.
Someone is quiet.
Someone is strong.
Mary is both not tall and humble.
Alice is wise.
Mary is brave. | John is wise. | neutral | ((?[X]:(~creative(X)))=>(?[X]:(~tall(X))))&
(((curious(paul)<~>patient(paul)))<=>((~happy(paul)&rich(paul))))&
(((patient(john)<~>~brave(john)))<=>((~generous(mary)<~>~calm(mary))))&
(((~kind(lucy)&curious(lucy)))=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((~strong(X)<~>~patient(X))<=>(~strong(X)&~happy(X))))&
((?[X]:((happy(X)&~creative(X))))<=>(quiet(mary)))&
(((~happy(paul)|~tall(paul)))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((curious(X)<~>~happy(X))<=>(curious(X)&kind(X))))&
(![X]:((~calm(X)&tall(X))<=>calm(X)))&
(![X]:((tall(X)&funny(X))=>(funny(X)<~>quiet(X))))&
(((~strong(fred)<~>~kind(fred)))=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((~creative(X)&~patient(X))<=>(~old(X)<~>~wise(X))))&
((tall(paul))<=>(happy(fred)))&
(![X]:((~creative(X)<~>quiet(X))=>(curious(X)<~>~patient(X))))&
((?[X]:(kind(X)))=>(humble(paul)))&
((?[X]:((humble(X)&strong(X))))<=>((tall(paul)<~>~strong(paul))))&
(?[X]:((~kind(X)|~generous(X))))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X)))&
((~tall(mary)&humble(mary)))&
(wise(alice))&
(brave(mary)) | wise(john) | [] | null | 0 |
If someone is not happy then fred is not rich.
Everyone who is not quiet or not rich is not humble or not wise.
Everyone who is either calm or tall is creative and vice versa.
Everyone who is either tall or not quiet is wise or kind.
Everyone who is either creative or patient is not old and vice versa.
If someone is either tall or happy then mary is either not kind or happy.
If john is curious then someone is not curious or rich and vice versa.
If someone is both generous and kind then someone is both not brave and kind.
Everyone who is creative is both strong and not happy.
Everyone who is either not happy or not wise is not brave and vice versa.
If someone is not tall or not wise then someone is not quiet.
Everyone who is quiet is both funny and not funny and vice versa.
Everyone who is either not creative or not patient is either not happy or not patient.
Everyone who is both quiet and not kind is either not wise or old.
Everyone who is not quiet is wise and vice versa.
If mary is both brave and tall then fred is not quiet or not old and vice versa.
Susan is both not calm and not strong.
Someone is tall or not old.
Someone is tall.
Someone is kind.
Mary is both old and calm.
Someone is either rich or not happy. | Mary is not happy. | contradiction | ((?[X]:(~happy(X)))=>(~rich(fred)))&
(![X]:((~quiet(X)|~rich(X))=>(~humble(X)|~wise(X))))&
(![X]:((calm(X)<~>tall(X))<=>creative(X)))&
(![X]:((tall(X)<~>~quiet(X))=>(wise(X)|kind(X))))&
(![X]:((creative(X)<~>patient(X))<=>~old(X)))&
((?[X]:((tall(X)<~>happy(X))))=>((~kind(mary)<~>happy(mary))))&
((curious(john))<=>(?[X]:((~curious(X)|rich(X)))))&
((?[X]:((generous(X)&kind(X))))=>(?[X]:((~brave(X)&kind(X)))))&
(![X]:(creative(X)=>(strong(X)&~happy(X))))&
(![X]:((~happy(X)<~>~wise(X))<=>~brave(X)))&
((?[X]:((~tall(X)|~wise(X))))=>(?[X]:(~quiet(X))))&
(![X]:(quiet(X)<=>(funny(X)&~funny(X))))&
(![X]:((~creative(X)<~>~patient(X))=>(~happy(X)<~>~patient(X))))&
(![X]:((quiet(X)&~kind(X))=>(~wise(X)<~>old(X))))&
(![X]:(~quiet(X)<=>wise(X)))&
(((brave(mary)&tall(mary)))<=>((~quiet(fred)|~old(fred))))&
((~calm(susan)&~strong(susan)))&
(?[X]:((tall(X)|~old(X))))&
(?[X]:(tall(X)))&
(?[X]:(kind(X)))&
((old(mary)&calm(mary)))&
(?[X]:((rich(X)<~>~happy(X)))) | ~happy(mary) | [
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8721663706863221260598961
% SZS output start Proof for 8721663706863221260598961
10. ! [X0] : ((~happy(X0) <~> ~wise(X0)) <=> ~brave(X0)) [input p9]
12. ! [X0] : (quiet(X0) <=> (~funny(X0) & funny(X0))) [input p11]
15. ! [X0] : (~quiet(X0) <=> wise(X0)) [input p14]
16. (tall(mary) & brave(mary)) <=> (~old(fred) | ~quiet(fred)) [input p15]
23. ~happy(mary) [input hypothesis]
45. ! [X0] : ((((wise(X0) | happy(X0)) & (~wise(X0) | ~happy(X0))) | brave(X0)) & (~brave(X0) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0))))) [nnf transformation 10]
49. ! [X0] : ((quiet(X0) | (funny(X0) | ~funny(X0))) & ((~funny(X0) & funny(X0)) | ~quiet(X0))) [nnf transformation 12]
50. ! [X0] : ((quiet(X0) | funny(X0) | ~funny(X0)) & ((~funny(X0) & funny(X0)) | ~quiet(X0))) [flattening 49]
53. ! [X0] : ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))) [nnf transformation 15]
54. ((tall(mary) & brave(mary)) | (old(fred) & quiet(fred))) & ((~old(fred) | ~quiet(fred)) | (~tall(mary) | ~brave(mary))) [nnf transformation 16]
55. ((tall(mary) & brave(mary)) | (old(fred) & quiet(fred))) & (~old(fred) | ~quiet(fred) | ~tall(mary) | ~brave(mary)) [flattening 54]
85. ~brave(X0) | ~wise(X0) | happy(X0) [cnf transformation 45]
91. funny(X0) | ~quiet(X0) [cnf transformation 50]
92. ~funny(X0) | ~quiet(X0) [cnf transformation 50]
100. wise(X0) | quiet(X0) [cnf transformation 53]
103. brave(mary) | quiet(fred) [cnf transformation 55]
116. ~happy(mary) [cnf transformation 23]
135. 5 <=> happy(mary) [avatar definition]
137. ~happy(mary) <- (~5) [avatar component clause 135]
167. 12 <=> ! [X1] : wise(X1) [avatar definition]
168. wise(X1) <- (12) [avatar component clause 167]
178. ~quiet(X0) [subsumption resolution 91,92]
181. wise(X0) [subsumption resolution 100,178]
182. 12 [avatar split clause 181,167]
195. 17 <=> brave(mary) [avatar definition]
197. brave(mary) <- (17) [avatar component clause 195]
199. brave(mary) [subsumption resolution 103,178]
200. 17 [avatar split clause 199,195]
220. ~5 [avatar split clause 116,135]
263. ~wise(mary) | happy(mary) <- (17) [resolution 85,197]
264. happy(mary) <- (12, 17) [subsumption resolution 263,168]
265. $false <- (~5, 12, 17) [subsumption resolution 264,137]
266. 5 | ~12 | ~17 [avatar contradiction clause 265]
267. $false [avatar sat refutation 182,200,220,266]
% SZS output end Proof for 8721663706863221260598961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both calm and not kind then someone is not humble or not old and vice versa. If mary is either not brave or not tall then mary is either generous or not calm and vice versa. Everyone who is either not patient or not quiet is either not quiet or quiet and vice versa. If someone is both not brave and creative then someone is not kind and vice versa. If someone is not quiet or humble then someone is either not rich or not creative. If susan is old or not humble then someone is both calm and not rich. If someone is not tall or not rich then mary is funny or creative and vice versa. Everyone who is funny or old is not kind or not strong and vice versa. If lucy is humble then someone is strong and vice versa. Everyone who is both not humble and not kind is not curious or not tall and vice versa. Everyone who is either not humble or not curious is either not old or not strong and vice versa. Everyone who is creative or generous is either not patient or calm. If someone is either not humble or not wise then alice is kind and vice versa. Everyone who is funny or patient is either happy or not strong. Everyone who is both not happy and humble is rich. If alice is old or humble then someone is calm or tall and vice versa. Fred is both not funny and not patient. Someone is either not brave or not calm. Someone is brave or creative. Someone is either not happy or strong. Susan is both not patient and not humble. Someone is either brave or not strong. | Susan is not humble. | entailment | (((calm(lucy)&~kind(lucy)))<=>(?[X]:((~humble(X)|~old(X)))))&
(((~brave(mary)<~>~tall(mary)))<=>((generous(mary)<~>~calm(mary))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~quiet(X)<~>quiet(X))))&
((?[X]:((~brave(X)&creative(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((~quiet(X)|humble(X))))=>(?[X]:((~rich(X)<~>~creative(X)))))&
(((old(susan)|~humble(susan)))=>(?[X]:((calm(X)&~rich(X)))))&
((?[X]:((~tall(X)|~rich(X))))<=>((funny(mary)|creative(mary))))&
(![X]:((funny(X)|old(X))<=>(~kind(X)|~strong(X))))&
((humble(lucy))<=>(?[X]:(strong(X))))&
(![X]:((~humble(X)&~kind(X))<=>(~curious(X)|~tall(X))))&
(![X]:((~humble(X)<~>~curious(X))<=>(~old(X)<~>~strong(X))))&
(![X]:((creative(X)|generous(X))=>(~patient(X)<~>calm(X))))&
((?[X]:((~humble(X)<~>~wise(X))))<=>(kind(alice)))&
(![X]:((funny(X)|patient(X))=>(happy(X)<~>~strong(X))))&
(![X]:((~happy(X)&humble(X))=>rich(X)))&
(((old(alice)|humble(alice)))<=>(?[X]:((calm(X)|tall(X)))))&
((~funny(fred)&~patient(fred)))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((brave(X)|creative(X))))&
(?[X]:((~happy(X)<~>strong(X))))&
((~patient(susan)&~humble(susan)))&
(?[X]:((brave(X)<~>~strong(X)))) | ~humble(susan) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 441827025404637555955233
% SZS output start Proof for 441827025404637555955233
21. ~humble(susan) & ~patient(susan) [input p20]
23. humble(susan) [input hypothesis]
166. ~humble(susan) [cnf transformation 21]
169. humble(susan) [cnf transformation 23]
269. 20 <=> humble(susan) [avatar definition]
408. ~20 [avatar split clause 166,269]
419. 20 [avatar split clause 169,269]
420. $false [avatar sat refutation 408,419]
% SZS output end Proof for 441827025404637555955233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not kind is not old and vice versa. Everyone who is both brave and patient is wise and vice versa. Everyone who is both not creative and not brave is kind or not humble and vice versa. If susan is either not humble or not quiet then john is both brave and kind and vice versa. Everyone who is either happy or not strong is not happy or patient and vice versa. If alice is not funny then paul is both not happy and not wise and vice versa. Everyone who is both not kind and not strong is not strong and vice versa. If paul is either not patient or wise then someone is generous. Everyone who is generous is both kind and not kind and vice versa. If someone is funny or creative then someone is not strong or not tall. Everyone who is both calm and not tall is both happy and brave. Everyone who is not curious is creative or brave and vice versa. Everyone who is not funny or humble is not brave or not funny and vice versa. If someone is strong then mary is generous and vice versa. Everyone who is either rich or not kind is either not generous or rich. Alice is not tall or not happy. Someone is not humble. Someone is both not wise and creative. Paul is not curious or strong. Susan is not generous. Someone is not tall. Susan is not quiet. Someone is brave. | Alice is not patient. | neutral | (![X]:((~tall(X)|~kind(X))<=>~old(X)))&
(![X]:((brave(X)&patient(X))<=>wise(X)))&
(![X]:((~creative(X)&~brave(X))<=>(kind(X)|~humble(X))))&
(((~humble(susan)<~>~quiet(susan)))<=>((brave(john)&kind(john))))&
(![X]:((happy(X)<~>~strong(X))<=>(~happy(X)|patient(X))))&
((~funny(alice))<=>((~happy(paul)&~wise(paul))))&
(![X]:((~kind(X)&~strong(X))<=>~strong(X)))&
(((~patient(paul)<~>wise(paul)))=>(?[X]:(generous(X))))&
(![X]:(generous(X)<=>(kind(X)&~kind(X))))&
((?[X]:((funny(X)|creative(X))))=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:((calm(X)&~tall(X))=>(happy(X)&brave(X))))&
(![X]:(~curious(X)<=>(creative(X)|brave(X))))&
(![X]:((~funny(X)|humble(X))<=>(~brave(X)|~funny(X))))&
((?[X]:(strong(X)))<=>(generous(mary)))&
(![X]:((rich(X)<~>~kind(X))=>(~generous(X)<~>rich(X))))&
((~tall(alice)|~happy(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((~wise(X)&creative(X))))&
((~curious(paul)|strong(paul)))&
(~generous(susan))&
(?[X]:(~tall(X)))&
(~quiet(susan))&
(?[X]:(brave(X))) | ~patient(alice) | [] | null | 0 |
Everyone who is not quiet is both not quiet and not curious and vice versa.
If alice is old then john is tall.
Everyone who is patient or not funny is not rich or funny and vice versa.
If someone is not calm or generous then someone is either not kind or not wise.
Everyone who is either not old or not brave is both not strong and not rich and vice versa.
If alice is either not creative or not quiet then someone is both not rich and not calm.
Everyone who is not old or not humble is either tall or not old and vice versa.
Everyone who is either wise or strong is not strong and vice versa.
Everyone who is either not patient or not curious is not tall or generous.
If fred is strong or happy then mary is funny or quiet and vice versa.
Everyone who is humble or quiet is tall or not kind.
Everyone who is not creative or not wise is quiet or not quiet.
Everyone who is old or humble is not brave and vice versa.
If someone is tall or brave then lucy is not calm or curious.
Everyone who is calm is not calm or strong and vice versa.
Everyone who is both quiet and not tall is not calm.
Alice is not old.
Paul is not generous or not calm.
Lucy is not happy.
Susan is not curious. | Paul is rich. | neutral | (![X]:(~quiet(X)<=>(~quiet(X)&~curious(X))))&
((old(alice))=>(tall(john)))&
(![X]:((patient(X)|~funny(X))<=>(~rich(X)|funny(X))))&
((?[X]:((~calm(X)|generous(X))))=>(?[X]:((~kind(X)<~>~wise(X)))))&
(![X]:((~old(X)<~>~brave(X))<=>(~strong(X)&~rich(X))))&
(((~creative(alice)<~>~quiet(alice)))=>(?[X]:((~rich(X)&~calm(X)))))&
(![X]:((~old(X)|~humble(X))<=>(tall(X)<~>~old(X))))&
(![X]:((wise(X)<~>strong(X))<=>~strong(X)))&
(![X]:((~patient(X)<~>~curious(X))=>(~tall(X)|generous(X))))&
(((strong(fred)|happy(fred)))<=>((funny(mary)|quiet(mary))))&
(![X]:((humble(X)|quiet(X))=>(tall(X)|~kind(X))))&
(![X]:((~creative(X)|~wise(X))=>(quiet(X)|~quiet(X))))&
(![X]:((old(X)|humble(X))<=>~brave(X)))&
((?[X]:((tall(X)|brave(X))))=>((~calm(lucy)|curious(lucy))))&
(![X]:(calm(X)<=>(~calm(X)|strong(X))))&
(![X]:((quiet(X)&~tall(X))=>~calm(X)))&
(~old(alice))&
((~generous(paul)|~calm(paul)))&
(~happy(lucy))&
(~curious(susan)) | rich(paul) | [] | null | 0 |
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