premise
stringlengths 12
3.12k
| hypothesis
stringlengths 10
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| label
stringclasses 3
values | premise_tptp
stringlengths 51
8k
| hypothesis_tptp
stringlengths 41
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| proof_inputs
sequencelengths 0
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| proof
stringlengths 767
76.8k
⌀ | rule_concentration
float64 0
0.72
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|---|---|---|---|---|---|---|---|
Charles, Eric, Miguel are the only persons in the room.
Eric neither does not frequently participates in hackathons and coding competitions nor is a client of LVMH.
Not everyone outside the room who is an expert in identifying and foraging wild edible plants is a certified yoga instructor teaching classes weekly.
Eric who neither is an avid hiker nor does enjoy mountain biking neither creates large-scale murals for public art installations nor enjoys camping and organizing outdoor survival workshops.
Eric collects limited-edition art prints from contemporary artists.
Eric is an expert in identifying and foraging wild edible plants.
Eric who practices digital art collects modern art.
Everyone anywhere practices and performs acrobatic dance routines if and only if they composes and performs experimental electronic music.
Everyone outside the room collects modern art if and only if they practices and performs acrobatic dance routines.
Everyone in the room who practices and performs acrobatic dance routines enjoys wildlife photography.
Everyone in the room enjoys camping and organizing outdoor survival workshops if they enjoys wildlife photography. | Eric creates large-scale murals for public art installations. | contradiction | room(charles)&room(eric)&room(miguel)&(![X]:(room(X)=>(X='charles'|X='eric'|X='miguel')))&
(~((does_not_frequently_participates_in_hackathons_and_coding_competitions(eric))|(is_a_client_of_LVMH(eric))))&
(~![X]:(~room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))&
((~((is_an_avid_hiker(eric))|(does_enjoy_mountain_biking(eric))))&(~((creates_large-scale_murals_for_public_art_installations(eric))|(enjoys_camping_and_organizing_outdoor_survival_workshops(eric)))))&
(collects_limited-edition_art_prints_from_contemporary_artists(eric))&
(is_an_expert_in_identifying_and_foraging_wild_edible_plants(eric))&
((practices_digital_art(eric))&(collects_modern_art(eric)))&
(![X]:(anywhere(X)=>(((practices_and_performs_acrobatic_dance_routines(X))<=>(composes_and_performs_experimental_electronic_music(X))))))&
(![X]:(~room(X)=>(((collects_modern_art(X))<=>(practices_and_performs_acrobatic_dance_routines(X))))))&
(![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(enjoys_wildlife_photography(X))))))&
(![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))) | room(charles)&room(eric)&room(miguel)&(![X]:(room(X)=>(X='charles'|X='eric'|X='miguel')))&
creates_large-scale_murals_for_public_art_installations(eric) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 983378338588578495256424
% SZS output start Proof for 983378338588578495256424
47. ~(predr(paul) | predf(paul)) & ~(predd(paul) | predc(paul)) [input p3]
55. predf(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
58. ~(predr(paul) | predf(paul)) & ~predc(paul) [pure predicate removal 47]
59. ~(predr(paul) | predf(paul)) [pure predicate removal 58]
139. ~predr(paul) & ~predf(paul) [ennf transformation 59]
146. predf(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 55]
147. predf(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 146]
239. ~predf(paul) [cnf transformation 139]
252. predf(paul) [cnf transformation 147]
255. $false [subsumption resolution 252,239]
% SZS output end Proof for 983378338588578495256424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Larry, Melanie, Timothy, William, Andrew are the only persons in the room.
Everyone in the room who is a client of Meta collects rare and antique scientific instruments if not everyone in the room is a client of Meta or does not collect rare and antique scientific instruments.
Larry collects rare and antique scientific instruments if everyone in the room regularly contributes to tech forums and online communities or does not collect rare and antique scientific instruments.
Melanie is a client of Meta.
At least one person in the room either builds model airplanes or is a client of Meta but not both.
Only one person in the room is a client of Meta.
Everyone in the room does not collect rare and antique scientific instruments if they is a member of a local theater group specializing in improv.
Everyone in the room builds model airplanes or does not have a piercing.
Everyone in the room is a member of a local theater group specializing in improv if they builds model airplanes.
Only one person in the room is a member of a local theater group specializing in improv.
Someone anywhere builds model airplanes and has a piercing.
Larry collects rare and antique scientific instruments. | Melanie builds model airplanes. | contradiction | room(larry)&room(melanie)&room(timothy)&room(william)&room(andrew)&(![X]:(room(X)=>(X='larry'|X='melanie'|X='timothy'|X='william'|X='andrew')))&
((~![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(is_a_client_of_Meta(X))))))=>(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(collects_rare_and_antique_scientific_instruments(X)))))))&
((![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))=>(collects_rare_and_antique_scientific_instruments(larry)))&
(is_a_client_of_Meta(melanie))&
(((?[X]:(room(X)&((builds_model_airplanes(X))<~>(is_a_client_of_Meta(X)))))))&
(((?[X]:(room(X)&is_a_client_of_Meta(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_client_of_Meta(X))&(is_a_client_of_Meta(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(does_not_collect_rare_and_antique_scientific_instruments(X))))))&
(![X]:(room(X)=>(((does_not_have_a_piercing(X))|(builds_model_airplanes(X))))))&
(![X]:(room(X)=>(((builds_model_airplanes(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
(((?[X]:(room(X)&is_a_member_of_a_local_theater_group_specializing_in_improv(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(Y)))=>(X=Y)))))&
(?[X]:(anywhere(X)&(((builds_model_airplanes(X))&(has_a_piercing(X))))))&
(collects_rare_and_antique_scientific_instruments(larry))&
(~![X]:(anywhere(X)=>(((is_a_client_of_Meta(X))=>(has_a_piercing(X)))))) | room(larry)&room(melanie)&room(timothy)&room(william)&room(andrew)&(![X]:(room(X)=>(X='larry'|X='melanie'|X='timothy'|X='william'|X='andrew')))&
builds_model_airplanes(melanie) | [
"b42",
"p0",
"p1",
"p3",
"p5",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8142993651230815447825022
% SZS output start Proof for 8142993651230815447825022
43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42]
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. ~! [X0] : (room(X0) => (predf(X0) | ~predd(X0))) => ! [X0] : (room(X0) => (predf(X0) => predd(X0))) [input p1]
47. predf(paul) [input p3]
49. ! [X0,X1] : ((predf(X1) & predf(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predf(X0) & room(X0)) [input p5]
50. ! [X0] : (room(X0) => (preda(X0) => ~predd(X0))) [input p6]
52. ! [X0] : (room(X0) => (prede(X0) => preda(X0))) [input p8]
55. predd(mary) [input p11]
57. prede(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
58. ~! [X0] : (room(X0) => (predf(X0) | ~predd(X0))) => ! [X1] : (room(X1) => (predf(X1) => predd(X1))) [rectify 45]
59. ! [X0,X1] : ((predf(X1) & predf(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predf(X2) & room(X2)) [rectify 49]
136. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
137. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 136]
138. ! [X1] : ((predd(X1) | ~predf(X1)) | ~room(X1)) | ! [X0] : ((predf(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 58]
139. ! [X1] : (predd(X1) | ~predf(X1) | ~room(X1)) | ! [X0] : (predf(X0) | ~predd(X0) | ~room(X0)) [flattening 138]
141. ! [X0,X1] : (X0 = X1 | (~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predf(X2) & room(X2)) [ennf transformation 59]
142. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predf(X2) & room(X2)) [flattening 141]
143. ! [X0] : ((~predd(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 50]
144. ! [X0] : (~predd(X0) | ~preda(X0) | ~room(X0)) [flattening 143]
147. ! [X0] : ((preda(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 52]
148. ! [X0] : (preda(X0) | ~prede(X0) | ~room(X0)) [flattening 147]
152. prede(paul) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 57]
153. prede(paul) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 152]
155. ! [X0] : (predd(X0) | ~predf(X0) | ~room(X0)) | ! [X1] : (predf(X1) | ~predd(X1) | ~room(X1)) [rectify 139]
162. ? [X2] : (predf(X2) & room(X2)) => (predf(sK2) & room(sK2)) [choice axiom]
163. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0)) & (predf(sK2) & room(sK2)) [skolemisation 142,162]
214. mary != paul [cnf transformation 43]
250. room(mary) [cnf transformation 137]
251. room(paul) [cnf transformation 137]
256. predd(X0) | ~predf(X0) | ~room(X0) | predf(X1) | ~predd(X1) | ~room(X1) [cnf transformation 155]
259. predf(paul) [cnf transformation 47]
265. ~predf(X1) | X0 = X1 | ~predf(X0) | ~room(X1) | ~room(X0) [cnf transformation 163]
266. ~preda(X0) | ~predd(X0) | ~room(X0) [cnf transformation 144]
268. ~prede(X0) | preda(X0) | ~room(X0) [cnf transformation 148]
274. predd(mary) [cnf transformation 55]
283. prede(paul) [cnf transformation 153]
285. 1 <=> ! [X1] : (predf(X1) | ~room(X1) | ~predd(X1)) [avatar definition]
286. ~predd(X1) | ~room(X1) | predf(X1) <- (1) [avatar component clause 285]
288. 2 <=> ! [X0] : (predd(X0) | ~room(X0) | ~predf(X0)) [avatar definition]
289. ~predf(X0) | ~room(X0) | predd(X0) <- (2) [avatar component clause 288]
290. 1 | 2 [avatar split clause 256,288,285]
296. 4 <=> predd(mary) [avatar definition]
298. predd(mary) <- (4) [avatar component clause 296]
315. 4 [avatar split clause 274,296]
320. preda(paul) | ~room(paul) [resolution 268,283]
331. preda(paul) [subsumption resolution 320,251]
333. ~room(paul) | predd(paul) <- (2) [resolution 289,259]
336. predd(paul) <- (2) [subsumption resolution 333,251]
347. ~predd(paul) | ~room(paul) [resolution 331,266]
348. ~room(paul) <- (2) [subsumption resolution 347,336]
349. $false <- (2) [subsumption resolution 348,251]
350. ~2 [avatar contradiction clause 349]
352. ~room(mary) | predf(mary) <- (1, 4) [resolution 286,298]
353. predf(mary) <- (1, 4) [subsumption resolution 352,250]
393. paul = X1 | ~predf(X1) | ~room(paul) | ~room(X1) [resolution 265,259]
397. ~predf(X1) | paul = X1 | ~room(X1) [subsumption resolution 393,251]
399. mary = paul | ~room(mary) <- (1, 4) [resolution 397,353]
403. ~room(mary) <- (1, 4) [subsumption resolution 399,214]
404. $false <- (1, 4) [subsumption resolution 403,250]
405. ~1 | ~4 [avatar contradiction clause 404]
410. $false [avatar sat refutation 290,315,350,405]
% SZS output end Proof for 8142993651230815447825022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0.181463 |
Elizabeth, George, Donald are the only persons in the room.
“Everyone in the room has lived in exactly three countries” if “everyone anywhere is a skilled home brewer experimenting with craft beer recipes or does not travel domestically frequently” and vice versa.
Either “Elizabeth does not have lived in exactly three countries” or “everyone outside the room does not travel domestically frequently or travels domestically frequently” but not both.
Not everyone outside the room who is an avid collector of autographed memorabilia from famous musicians practices archery.
Elizabeth regularly goes on multi-day backpacking trips in national parks.
Elizabeth practices archery. | Elizabeth regularly goes on multi-day backpacking trips in national parks. | entailment | room(elizabeth)&room(george)&room(donald)&(![X]:(room(X)=>(X='elizabeth'|X='george'|X='donald')))&
((![X]:(anywhere(X)=>(((does_not_travel_domestically_frequently(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))<=>(![X]:(room(X)=>(has_lived_in_exactly_three_countries(X)))))&
((does_not_have_lived_in_exactly_three_countries(elizabeth))<~>(![X]:(~room(X)=>(((travels_domestically_frequently(X))|(does_not_travel_domestically_frequently(X)))))))&
(~![X]:(~room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(practices_archery(X))))))&
(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(elizabeth))&
(practices_archery(elizabeth))&
(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(elizabeth))&
(travels_domestically_frequently(elizabeth)) | room(elizabeth)&room(george)&room(donald)&(![X]:(room(X)=>(X='elizabeth'|X='george'|X='donald')))&
regularly_goes_on_multi-day_backpacking_trips_in_national_parks(elizabeth) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8249984968941676102769195
% SZS output start Proof for 8249984968941676102769195
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
48. predb(mary) [input p4]
52. ~(predb(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
127. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
128. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 127]
134. ~predb(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 52]
135. ~predb(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 134]
148. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
149. ~predb(mary) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 135,148]
231. room(mary) [cnf transformation 128]
232. room(paul) [cnf transformation 128]
233. room(fred) [cnf transformation 128]
234. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 128]
246. predb(mary) [cnf transformation 48]
249. ~predb(mary) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 149]
250. ~predb(mary) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 149]
251. ~predb(mary) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 149]
252. ~predb(mary) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 149]
296. fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 252,246]
297. fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 296,233]
298. fred != sK4 | ~room(mary) [subsumption resolution 297,232]
299. fred != sK4 [subsumption resolution 298,231]
300. paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 251,246]
301. paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 300,233]
302. paul != sK4 | ~room(mary) [subsumption resolution 301,232]
303. paul != sK4 [subsumption resolution 302,231]
304. mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 250,246]
305. mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 304,233]
306. mary != sK4 | ~room(mary) [subsumption resolution 305,232]
307. mary != sK4 [subsumption resolution 306,231]
308. room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 249,246]
309. room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 308,233]
310. room(sK4) | ~room(mary) [subsumption resolution 309,232]
311. room(sK4) [subsumption resolution 310,231]
356. paul = sK4 | mary = sK4 | fred = sK4 [resolution 234,311]
357. mary = sK4 | fred = sK4 [subsumption resolution 356,303]
358. fred = sK4 [subsumption resolution 357,307]
359. $false [subsumption resolution 358,299]
% SZS output end Proof for 8249984968941676102769195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Sarah, Howard are the only persons in the room. Someone anywhere hosts themed dinner parties featuring gourmet home-cooked meals or does not know morse code or both if Sarah enjoys landscape photography and vice versa. Everyone in the room collects luxury watches. | It is true that Sarah collects luxury watches. | entailment | room(sarah)&room(howard)&(![X]:(room(X)=>(X='sarah'|X='howard')))&
((enjoys_landscape_photography(sarah))<=>(?[X]:(anywhere(X)&(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_know_morse_code(X)))))))&
((~![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(is_allergic_to_anything(howard)))&
((?[X]:(room(X)&(((writes_poetry(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(hosts_regular_workshops_on_creative_writing(X))))))=>((![X]:((does_not_enjoy_mountain_biking(X))<=>(enjoys_landscape_photography(X))))))&
((owns_a_smart_tv(sarah))=>((maintains_a_large,_organic_vegetable_garden_year-round(sarah))&(hosts_regular_workshops_on_creative_writing(sarah))))&
(((![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))=>(![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(owns_an_Android_phone(X)))))))&((~(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))=>(~![X]:(~room(X)=>(((owns_an_Android_phone(X))=>(((writes_poetry(X))&(does_enjoy_trail_running(X))&(hosts_regular_workshops_on_creative_writing(X))))))))))&
(![X]:(room(X)=>(((((writes_poetry(X))&(does_enjoy_trail_running(X))&(hosts_regular_workshops_on_creative_writing(X))))=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))&
(((owns_an_Android_phone(sarah))|(does_not_enjoy_mountain_biking(sarah))|(enjoys_windsurfing(sarah))))&
((![X]:((collects_vintage_vinyl_records(X))<=>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))&
(![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(is_a_night_owl(X))))))&
(![X]:(room(X)=>(collects_luxury_watches(X))))&
((![X]:((cannot_play_the_flute(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))&
(((?[X]:(room(X)&hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))&
(![X]:(room(X)=>(((((enjoys_windsurfing(X))&(can_play_the_flute(X))&(plays_the_violin(X))))=>(is_an_active_member_of_a_local_robotics_club(X))))))&
(![X]:(~room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(does_not_play_eSports_competitively(X))))))&
(enjoys_deep-sea_diving_and_exploring_underwater_caves(howard))&
(![X]:(room(X)=>(((does_not_host_regular_workshops_on_creative_writing(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(does_not_host_regular_workshops_on_creative_writing(X)))))))) | room(sarah)&room(howard)&(![X]:(room(X)=>(X='sarah'|X='howard')))&
collects_luxury_watches(sarah) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6000245351963510149888704
% SZS output start Proof for 6000245351963510149888704
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
54. ! [X0] : (room(X0) => predn(X0)) [input p10]
62. ~(predn(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
150. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
151. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 150]
152. ! [X0] : (predn(X0) | ~room(X0)) [ennf transformation 54]
157. ~predn(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 62]
158. ~predn(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 157]
166. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom]
167. ~predn(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 158,166]
249. room(mary) [cnf transformation 151]
250. room(paul) [cnf transformation 151]
251. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 151]
256. ~room(X0) | predn(X0) [cnf transformation 152]
262. ~predn(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 167]
263. ~predn(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 167]
264. ~predn(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 167]
288. ~predn(mary) | paul != sK2 | ~room(mary) [subsumption resolution 264,250]
289. ~predn(mary) | paul != sK2 [subsumption resolution 288,249]
291. 6 <=> paul = sK2 [avatar definition]
293. paul != sK2 <- (~6) [avatar component clause 291]
295. 7 <=> predn(mary) [avatar definition]
298. ~6 | ~7 [avatar split clause 289,295,291]
299. ~predn(mary) | mary != sK2 | ~room(mary) [subsumption resolution 263,250]
300. ~predn(mary) | mary != sK2 [subsumption resolution 299,249]
302. 8 <=> mary = sK2 [avatar definition]
304. mary != sK2 <- (~8) [avatar component clause 302]
305. ~8 | ~7 [avatar split clause 300,295,302]
306. ~predn(mary) | room(sK2) | ~room(mary) [subsumption resolution 262,250]
307. ~predn(mary) | room(sK2) [subsumption resolution 306,249]
309. 9 <=> room(sK2) [avatar definition]
311. room(sK2) <- (9) [avatar component clause 309]
312. 9 | ~7 [avatar split clause 307,295,309]
313. predn(mary) [resolution 256,249]
318. 7 [avatar split clause 313,295]
368. mary = sK2 | paul = sK2 <- (9) [resolution 251,311]
378. paul = sK2 <- (~8, 9) [subsumption resolution 368,304]
379. $false <- (~6, ~8, 9) [subsumption resolution 378,293]
380. 6 | 8 | ~9 [avatar contradiction clause 379]
381. $false [avatar sat refutation 298,305,312,318,380]
% SZS output end Proof for 6000245351963510149888704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Clay, Kirk, Travis are the only persons in the room. If “Travis collects limited-edition art prints from contemporary artists” then “if someone collects luxury watches then he/she develops open-source software projects in their free time and vice versa”. If “everyone in the room enjoys fishing or does not play the violin” then “everyone in the room plays eSports competitively or does not collect luxury watches”. “Everyone in the room has a vast collection of first-edition science fiction novels or does not have a vast collection of first-edition science fiction novels” only if “everyone in the room who collect rare sneakers collects limited-edition art prints from contemporary artists and is a client of Meta”. Everyone in the room who develops open-source software projects in their free time frequently participates in hackathons and coding competitions. Everyone in the room who frequently participates in hackathons and coding competitions is not a member of a local theater group specializing in improv. Everyone in the room competes in national level swimming championships and collect rare sneakers if they is not a member of a local theater group specializing in improv. If someone does not collect rare sneakers then he/she neither plays eSports competitively nor enjoys camping and organizing outdoor survival workshops and vice versa. Everyone in the room develops open-source software projects in their free time only if they does not compete in national level swimming championships. Everyone in the room enjoys fishing or does not play the violin. | Travis collects luxury watches. | contradiction | room(clay)&room(kirk)&room(travis)&(![X]:(room(X)=>(X='clay'|X='kirk'|X='travis')))&
((((?[X]:(anywhere(X)&trains_for_and_competes_in_international_triathlons(X)))))<~>(![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(does_not_compete_in_national_level_swimming_championships(X)))))))&
((![X]:(room(X)=>(((plays_eSports_competitively(X))|(does_not_collect_luxury_watches(X))))))=>(![X]:(~room(X)=>(((does_not_collect_luxury_watches(X))<=>(enjoys_wildlife_photography(X)))))))&
((![X]:(room(X)=>(((does_not_collect_rare_minerals(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))=>(enjoys_fishing(kirk)))&
(~(![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_collect_first_edition_books(X))))))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(clay)))&
((~?[X]:(room(X)=>(((enjoys_cross-country_skiing(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))=>((enjoys_cross-country_skiing(kirk))&(frequently_participates_in_hackathons_and_coding_competitions(kirk))))&
((enjoys_stand-up_paddleboarding(clay))=>(~?[X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(collects_luxury_watches(X)))))))&
((![X]:(anywhere(X)=>(((enjoys_windsurfing(X))|(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))=>(?[X]:(room(X)&(streams_on_Twitch(X)))))&
((collects_limited-edition_art_prints_from_contemporary_artists(travis))=>((![X]:((collects_luxury_watches(X))<=>(develops_open-source_software_projects_in_their_free_time(X))))))&
((![X]:(room(X)=>(((does_not_play_the_violin(X))|(enjoys_fishing(X))))))=>(![X]:(room(X)=>(((does_not_collect_luxury_watches(X))|(plays_eSports_competitively(X)))))))&
((frequently_participates_in_hackathons_and_coding_competitions(travis))=>(![X]:(anywhere(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(collects_first_edition_books(X))&(enjoys_wildlife_photography(X)))))))))&
((enjoys_cross-country_skiing(clay))=>(develops_open-source_software_projects_in_their_free_time(kirk)))&
((![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))=>(![X]:(room(X)=>(((collect_rare_sneakers(X))=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))&(is_a_client_of_Meta(X)))))))))&
((~?[X]:(room(X)=>(((collects_vintage_vinyl_records(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))=>(![X]:(~room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))=>(collects_first_edition_books(X)))))))&
((![X]:((((plays_eSports_competitively(X))|(competes_in_national_level_swimming_championships(X))))<=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))&
(?[X]:(room(X)&(streams_on_Twitch(X))))&
(![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))&
(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
(![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(((competes_in_national_level_swimming_championships(X))&(collect_rare_sneakers(X))))))))&
(does_not_enjoy_watercolor_painting(kirk))&
((![X]:((does_not_collect_rare_sneakers(X))<=>(~((plays_eSports_competitively(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))&
(![X]:(room(X)=>(((does_not_own_a_microscope(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))<=(develops_open-source_software_projects_in_their_free_time(X))))))&
(is_not_a_client_of_Meta(clay))&
((clay_dream=>(![X]:(~room(X)=>(((((competes_in_national_level_swimming_championships(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(develops_open-source_software_projects_in_their_free_time(X))))))))&
(![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(collects_first_edition_books(X))))))&
(![X]:(anywhere(X)=>(((collects_first_edition_books(X))<=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<~>(enjoys_cross-country_skiing(X))))))))&
(![X]:(room(X)=>(((does_not_play_the_violin(X))|(enjoys_fishing(X))))))&
(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(((enjoys_cross-country_skiing(X))<~>(collects_vintage_vinyl_records(X)))))))) | room(clay)&room(kirk)&room(travis)&(![X]:(room(X)=>(X='clay'|X='kirk'|X='travis')))&
collects_luxury_watches(travis) | [
"p0",
"p8",
"p9",
"p12",
"p16",
"p17",
"p18",
"p20",
"p23",
"p28",
"hypothesis"
] | % SZS status Unsatisfiable for 8229102962586326932309207
% SZS output start Proof for 8229102962586326932309207
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
52. predi(fred) => ! [X0] : (predz(X0) <=> predp(X0)) [input p8]
53. ! [X0] : (room(X0) => (predo(X0) | ~predf(X0))) => ! [X0] : (room(X0) => (predt(X0) | ~predz(X0))) [input p9]
56. ! [X0] : (room(X0) => (predy(X0) | ~predy(X0))) => ! [X0] : (room(X0) => (predx(X0) => (prede(X0) & predi(X0)))) [input p12]
60. ! [X0] : (room(X0) => (predp(X0) => predv(X0))) [input p16]
61. ! [X0] : (room(X0) => (predv(X0) => ~predu(X0))) [input p17]
62. ! [X0] : (room(X0) => (~predu(X0) => (predx(X0) & predg(X0)))) [input p18]
64. ! [X0] : (~predx(X0) <=> ~(preda(X0) | predt(X0))) [input p20]
67. ! [X0] : (room(X0) => (predp(X0) => ~predg(X0))) [input p23]
72. ! [X0] : (room(X0) => (predo(X0) | ~predf(X0))) [input p28]
74. predz(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
78. ! [X0] : (room(X0) => (predo(X0) | ~predf(X0))) => ! [X1] : (room(X1) => (predt(X1) | ~predz(X1))) [rectify 53]
79. ! [X0] : (room(X0) => (predy(X0) | ~predy(X0))) => ! [X1] : (room(X1) => (predx(X1) => (prede(X1) & predi(X1)))) [rectify 56]
159. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
160. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 159]
173. ! [X0] : (predz(X0) <=> predp(X0)) | ~predi(fred) [ennf transformation 52]
174. ! [X1] : ((predt(X1) | ~predz(X1)) | ~room(X1)) | ? [X0] : ((~predo(X0) & predf(X0)) & room(X0)) [ennf transformation 78]
175. ! [X1] : (predt(X1) | ~predz(X1) | ~room(X1)) | ? [X0] : (~predo(X0) & predf(X0) & room(X0)) [flattening 174]
178. ! [X1] : (((prede(X1) & predi(X1)) | ~predx(X1)) | ~room(X1)) | ? [X0] : ((~predy(X0) & predy(X0)) & room(X0)) [ennf transformation 79]
179. ! [X1] : ((prede(X1) & predi(X1)) | ~predx(X1) | ~room(X1)) | ? [X0] : (~predy(X0) & predy(X0) & room(X0)) [flattening 178]
182. ! [X0] : ((predv(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 60]
183. ! [X0] : (predv(X0) | ~predp(X0) | ~room(X0)) [flattening 182]
184. ! [X0] : ((~predu(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 61]
185. ! [X0] : (~predu(X0) | ~predv(X0) | ~room(X0)) [flattening 184]
186. ! [X0] : (((predx(X0) & predg(X0)) | predu(X0)) | ~room(X0)) [ennf transformation 62]
187. ! [X0] : ((predx(X0) & predg(X0)) | predu(X0) | ~room(X0)) [flattening 186]
188. ! [X0] : (~predx(X0) <=> (~preda(X0) & ~predt(X0))) [ennf transformation 64]
191. ! [X0] : ((~predg(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 67]
192. ! [X0] : (~predg(X0) | ~predp(X0) | ~room(X0)) [flattening 191]
196. ! [X0] : ((predo(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 72]
197. ! [X0] : (predo(X0) | ~predf(X0) | ~room(X0)) [flattening 196]
200. predz(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 74]
201. predz(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 200]
220. ! [X0] : ((predz(X0) | ~predp(X0)) & (predp(X0) | ~predz(X0))) | ~predi(fred) [nnf transformation 173]
221. ! [X0] : (predt(X0) | ~predz(X0) | ~room(X0)) | ? [X1] : (~predo(X1) & predf(X1) & room(X1)) [rectify 175]
222. ? [X1] : (~predo(X1) & predf(X1) & room(X1)) => (~predo(sK7) & predf(sK7) & room(sK7)) [choice axiom]
223. ! [X0] : (predt(X0) | ~predz(X0) | ~room(X0)) | (~predo(sK7) & predf(sK7) & room(sK7)) [skolemisation 221,222]
226. ! [X0] : ((prede(X0) & predi(X0)) | ~predx(X0) | ~room(X0)) | ? [X1] : (~predy(X1) & predy(X1) & room(X1)) [rectify 179]
227. ? [X1] : (~predy(X1) & predy(X1) & room(X1)) => (~predy(sK8) & predy(sK8) & room(sK8)) [choice axiom]
228. ! [X0] : ((prede(X0) & predi(X0)) | ~predx(X0) | ~room(X0)) | (~predy(sK8) & predy(sK8) & room(sK8)) [skolemisation 226,227]
236. ! [X0] : ((~predx(X0) | (preda(X0) | predt(X0))) & ((~preda(X0) & ~predt(X0)) | predx(X0))) [nnf transformation 188]
237. ! [X0] : ((~predx(X0) | preda(X0) | predt(X0)) & ((~preda(X0) & ~predt(X0)) | predx(X0))) [flattening 236]
323. room(fred) [cnf transformation 160]
346. predp(X0) | ~predz(X0) | ~predi(fred) [cnf transformation 220]
348. predt(X0) | ~predz(X0) | ~room(X0) | room(sK7) [cnf transformation 223]
349. predt(X0) | ~predz(X0) | ~room(X0) | predf(sK7) [cnf transformation 223]
350. predt(X0) | ~predz(X0) | ~room(X0) | ~predo(sK7) [cnf transformation 223]
357. predi(X0) | ~predx(X0) | ~room(X0) | predy(sK8) [cnf transformation 228]
358. predi(X0) | ~predx(X0) | ~room(X0) | ~predy(sK8) [cnf transformation 228]
367. ~predp(X0) | predv(X0) | ~room(X0) [cnf transformation 183]
368. ~predu(X0) | ~predv(X0) | ~room(X0) [cnf transformation 185]
369. ~room(X0) | predu(X0) | predg(X0) [cnf transformation 187]
371. ~predt(X0) | predx(X0) [cnf transformation 237]
375. ~predp(X0) | ~predg(X0) | ~room(X0) [cnf transformation 192]
382. ~predf(X0) | predo(X0) | ~room(X0) [cnf transformation 197]
389. predz(fred) [cnf transformation 201]
513. 28 <=> predi(fred) [avatar definition]
521. 30 <=> ! [X0] : (predp(X0) | ~predz(X0)) [avatar definition]
522. ~predz(X0) | predp(X0) <- (30) [avatar component clause 521]
523. ~28 | 30 [avatar split clause 346,521,513]
525. 31 <=> predo(sK7) [avatar definition]
529. 32 <=> ! [X0] : (predt(X0) | ~room(X0) | ~predz(X0)) [avatar definition]
530. ~predz(X0) | ~room(X0) | predt(X0) <- (32) [avatar component clause 529]
531. ~31 | 32 [avatar split clause 350,529,525]
533. 33 <=> predf(sK7) [avatar definition]
535. predf(sK7) <- (33) [avatar component clause 533]
536. 33 | 32 [avatar split clause 349,529,533]
538. 34 <=> room(sK7) [avatar definition]
540. room(sK7) <- (34) [avatar component clause 538]
541. 34 | 32 [avatar split clause 348,529,538]
544. 35 <=> predv(fred) [avatar definition]
546. ~predv(fred) <- (~35) [avatar component clause 544]
576. 42 <=> predy(sK8) [avatar definition]
590. 45 <=> ! [X0] : (predi(X0) | ~room(X0) | ~predx(X0)) [avatar definition]
591. ~predx(X0) | ~room(X0) | predi(X0) <- (45) [avatar component clause 590]
592. ~42 | 45 [avatar split clause 358,590,576]
593. 42 | 45 [avatar split clause 357,590,576]
619. predu(fred) | predg(fred) [resolution 369,323]
642. 54 <=> predg(fred) [avatar definition]
644. predg(fred) <- (54) [avatar component clause 642]
646. 55 <=> predu(fred) [avatar definition]
648. predu(fred) <- (55) [avatar component clause 646]
649. 54 | 55 [avatar split clause 619,646,642]
684. 62 <=> predx(fred) [avatar definition]
686. predx(fred) <- (62) [avatar component clause 684]
724. 69 <=> predp(fred) [avatar definition]
726. predp(fred) <- (69) [avatar component clause 724]
765. ~predv(fred) | ~room(fred) <- (55) [resolution 648,368]
773. ~room(fred) | predt(fred) <- (32) [resolution 530,389]
775. predt(fred) <- (32) [subsumption resolution 773,323]
803. ~predg(fred) | ~room(fred) <- (69) [resolution 726,375]
804. predv(fred) | ~room(fred) <- (69) [resolution 726,367]
806. ~room(fred) <- (54, 69) [subsumption resolution 803,644]
807. $false <- (54, 69) [subsumption resolution 806,323]
808. ~54 | ~69 [avatar contradiction clause 807]
809. ~room(fred) <- (~35, 69) [subsumption resolution 804,546]
810. $false <- (~35, 69) [subsumption resolution 809,323]
811. 35 | ~69 [avatar contradiction clause 810]
824. predx(fred) <- (32) [resolution 775,371]
826. 62 | ~32 [avatar split clause 824,529,684]
827. predo(sK7) | ~room(sK7) <- (33) [resolution 535,382]
831. predo(sK7) <- (33, 34) [subsumption resolution 827,540]
832. 31 | ~33 | ~34 [avatar split clause 831,538,533,525]
862. ~room(fred) | predi(fred) <- (45, 62) [resolution 686,591]
865. predi(fred) <- (45, 62) [subsumption resolution 862,323]
869. 28 | ~45 | ~62 [avatar split clause 865,684,590,513]
884. predp(fred) <- (30) [resolution 522,389]
888. ~predv(fred) <- (55) [subsumption resolution 765,323]
889. ~35 | ~55 [avatar split clause 888,646,544]
890. 69 | ~30 [avatar split clause 884,521,724]
891. $false [avatar sat refutation 523,531,536,541,592,593,649,808,811,826,832,869,889,890]
% SZS output end Proof for 8229102962586326932309207
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
There is a room.
Everyone anywhere does not collect vintage stamps or is not a client of Meta.
Everyone in the room who practices digital art either volunteers for local environmental conservation projects or is a culinary enthusiast who experiments with international cuisines but not both.
If someone does not practice digital art then he/she is a client of Meta.
At least one person in the room enjoys watercolor painting.
Everyone in the room neither practices graffiti art nor is a culinary enthusiast who experiments with international cuisines if they is not a certified scuba diver with advanced underwater photography skills.
It is true that “everyone in the room collects vintage stamps if they neither practices graffiti art nor is a culinary enthusiast who experiments with international cuisines”.
Everyone in the room who collects vintage stamps practices graffiti art.
Everyone outside the room who collects vintage stamps is a client of Meta.
No one in the room is a culinary enthusiast who experiments with international cuisines.
Everyone in the room who has completed a triathlon either enjoys macrame or is a culinary enthusiast who experiments with international cuisines but not both.
Everyone in the room has a curated collection of mid-century modern furniture.
Not everyone in the room does not maintain a large, organic vegetable garden year-round if and only if they is a client of Meta.
Everyone in the room enjoys watercolor painting, practices calligraphy and enjoys making ceramics if they is a client of Meta.
Everyone in the room has a curated collection of mid-century modern furniture if they enjoys watercolor painting, practices calligraphy and enjoys making ceramics.
If someone is a certified scuba diver with advanced underwater photography skills then he/she collects vintage stamps.
If someone does not enjoy macrame then he/she is not an expert in identifying and foraging wild edible plants and vice versa.
Not everyone in the room does not host regular game nights featuring complex strategy games if they enjoys macrame, volunteers for local environmental conservation projects or uses contact lenses.
Everyone in the room uses contact lenses if they does not host regular game nights featuring complex strategy games.
If someone is a certified scuba diver with advanced underwater photography skills then he/she enjoys macrame.
Everyone in the room who does not have completed a triathlon, enjoys stand-up paddleboarding and enjoys macrame writes a travel blog. | Everyone outside the room does not host regular game nights featuring complex strategy games. | entailment | (there_is_a_room)&
(![X]:(anywhere(X)=>(((is_not_a_client_of_Meta(X))|(does_not_collect_vintage_stamps(X))))))&
(![X]:(room(X)=>(((practices_digital_art(X))=>(((volunteers_for_local_environmental_conservation_projects(X))<~>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))))&
((![X]:((does_not_practice_digital_art(X))=>(is_a_client_of_Meta(X)))))&
(((?[X]:(room(X)&enjoys_watercolor_painting(X)))))&
(![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(~((practices_graffiti_art(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))))&
(![X]:(room(X)=>(((~((practices_graffiti_art(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))=>(collects_vintage_stamps(X))))))&
(![X]:(room(X)=>(((collects_vintage_stamps(X))=>(practices_graffiti_art(X))))))&
(![X]:(~room(X)=>(((collects_vintage_stamps(X))=>(is_a_client_of_Meta(X))))))&
(~?[X]:(room(X)=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))&
(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(((enjoys_macrame(X))<~>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))))&
(![X]:(room(X)=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))&
(~![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))<=>(is_a_client_of_Meta(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(((enjoys_watercolor_painting(X))&(practices_calligraphy(X))&(enjoys_making_ceramics(X))))))))&
(![X]:(room(X)=>(((((enjoys_watercolor_painting(X))&(practices_calligraphy(X))&(enjoys_making_ceramics(X))))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))&
((![X]:((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(collects_vintage_stamps(X)))))&
((![X]:((does_not_enjoy_macrame(X))<=>(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))&
(~![X]:(room(X)=>(((((enjoys_macrame(X))|(volunteers_for_local_environmental_conservation_projects(X))|(uses_contact_lenses(X))))=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))=>(uses_contact_lenses(X))))))&
((![X]:((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(enjoys_macrame(X)))))&
(![X]:(room(X)=>(((((does_not_have_completed_a_triathlon(X))&(enjoys_stand-up_paddleboarding(X))&(enjoys_macrame(X))))=>(writes_a_travel_blog(X))))))&
(![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(enjoys_making_ceramics(X))))))&
(![X]:(room(X)=>(((does_not_practice_graffiti_art(X))=>(reads_mystery_novels(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7354091031375020269306158
% SZS output start Proof for 7354091031375020269306158
44. there_is_a_room [input p0]
53. ~? [X0] : (room(X0) => predu(X0)) [input p9]
68. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis]
166. ! [X0] : (~predu(X0) & room(X0)) [ennf transformation 53]
176. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 68]
187. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK3) & ~room(sK3)) [choice axiom]
188. (preda(sK3) & ~room(sK3)) | ~there_is_a_room [skolemisation 176,187]
270. there_is_a_room [cnf transformation 44]
281. room(X0) [cnf transformation 166]
292. ~room(sK3) | ~there_is_a_room [cnf transformation 188]
310. ~there_is_a_room [subsumption resolution 292,281]
311. $false [subsumption resolution 310,270]
% SZS output end Proof for 7354091031375020269306158
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
There is a room.
Not everyone in the room hosts a YouTube channel dedicated to art tutorials if they plays as a goalkeeper for a local amateur soccer team.
Everyone in the room does not enjoy fishing if they hosts a YouTube channel dedicated to art tutorials.
More than one person outside the room hosts themed dinner parties featuring gourmet home-cooked meals.
Only one person in the room does not enjoy kayaking.
Everyone anywhere who either does not create bespoke furniture pieces from reclaimed wood or practices digital art but not both writes in-depth travel guides for off-the-beaten-path destinations, does not practice digital art or enjoys fishing.
At least one person in the room hosts a YouTube channel dedicated to art tutorials, participates in long-distance cycling events across the country or enjoys salsa dancing.
If someone neither hosts regular game nights featuring complex strategy games nor enjoys fishing then he/she is a client of LVMH.
If someone is a client of LVMH then he/she travels domestically frequently.
Everyone in the room who hosts regular game nights featuring complex strategy games enjoys skydiving.
Not everyone in the room is a client of LVMH and practices digital art if they enjoys skydiving.
Everyone in the room owns a microscope if they either owns a microscope or creates bespoke furniture pieces from reclaimed wood but not both.
If someone enjoys fishing then he/she enjoys skydiving.
It is not the case that 'someone in the room writes in-depth travel guides for off-the-beaten-path destinations and owns a microscope'.
Everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations if and only if they plays as a goalkeeper for a local amateur soccer team.
If someone enjoys camping and organizing outdoor survival workshops then he/she creates bespoke furniture pieces from reclaimed wood. | Everyone in the room plays as a goalkeeper for a local amateur soccer team. | neutral | (there_is_a_room)&
(~![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(does_not_enjoy_fishing(X))))))&
((?[X,Y]:(~room(X)&~room(Y)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)&hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(Y))&(X!=Y))))&
(((?[X]:(room(X)&does_not_enjoy_kayaking(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_enjoy_kayaking(X))&(does_not_enjoy_kayaking(Y)))=>(X=Y)))))&
(![X]:(anywhere(X)=>(((((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))<~>(practices_digital_art(X))))=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(does_not_practice_digital_art(X))|(enjoys_fishing(X))))))))&
(((?[X]:(room(X)&((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(participates_in_long-distance_cycling_events_across_the_country(X))|(enjoys_salsa_dancing(X)))))))&
((![X]:((~((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(enjoys_fishing(X))))=>(is_a_client_of_LVMH(X)))))&
((![X]:((is_a_client_of_LVMH(X))=>(travels_domestically_frequently(X)))))&
(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(enjoys_skydiving(X))))))&
(~![X]:(room(X)=>(((enjoys_skydiving(X))=>(((is_a_client_of_LVMH(X))&(practices_digital_art(X))))))))&
(![X]:(room(X)=>(((((owns_a_microscope(X))<~>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(owns_a_microscope(X))))))&
((![X]:((enjoys_fishing(X))=>(enjoys_skydiving(X)))))&
(~(?[X]:(room(X)&(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(owns_a_microscope(X)))))))&
(![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
((![X]:((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))) | (there_is_a_room)&
![X]:(room(X)=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))) | [] | null | 0.088244 |
Laura, Jorge, Nathaniel are the only persons in the room.
Everyone in the room is not a creative person.
No creative person is wise.
Everyone anywhere is an avid hiker.
Everyone in the room enjoys stargazing.
Everyone in the room is creative.
All wise persons are creative.
Everyone in the room either is creative or practices archery but not both.
Not everyone outside the room is wise.
Everyone in the room is an avid hiker.
If someone is creative then he/she is wise or does not practice archery or both and vice versa.
More than one person outside the room is an avid hiker.
Everyone in the room is not wise. | Nathaniel is creative. | entailment | room(laura)&room(jorge)&room(nathaniel)&(![X]:(room(X)=>(X='laura'|X='jorge'|X='nathaniel')))&
(![X]:(room(X)=>(~(creative(X)&person(X)))))&
(~?[X]:(creative(X)=>wise(X)))&
(![X]:(anywhere(X)=>(is_an_avid_hiker(X))))&
(![X]:(room(X)=>(enjoys_stargazing(X))))&
(![X]:(room(X)=>(creative(X))))&
(![X]:(wise(X)=>creative(X)))&
(![X]:(room(X)=>(((creative(X))<~>(practices_archery(X))))))&
(~![X]:(~room(X)=>(wise(X))))&
(![X]:(room(X)=>(is_an_avid_hiker(X))))&
((![X]:((creative(X))<=>(((wise(X))|(does_not_practice_archery(X)))))))&
((?[X,Y]:(~room(X)&~room(Y)&(is_an_avid_hiker(X)&is_an_avid_hiker(Y))&(X!=Y))))&
(![X]:(room(X)=>(~wise(X)))) | room(laura)&room(jorge)&room(nathaniel)&(![X]:(room(X)=>(X='laura'|X='jorge'|X='nathaniel')))&
creative(nathaniel) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 2643652365571811225991723
% SZS output start Proof for 2643652365571811225991723
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
46. ~? [X0] : (creative(X0) => wise(X0)) [input p2]
57. ~(creative(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
135. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
136. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 135]
137. ! [X0] : (~wise(X0) & creative(X0)) [ennf transformation 46]
143. ~creative(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57]
144. ~creative(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 143]
153. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
154. ~creative(fred) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 144,153]
235. room(mary) [cnf transformation 136]
236. room(paul) [cnf transformation 136]
237. room(fred) [cnf transformation 136]
238. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 136]
239. creative(X0) [cnf transformation 137]
254. ~creative(fred) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154]
255. ~creative(fred) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154]
256. ~creative(fred) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154]
257. ~creative(fred) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154]
261. fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 257,239]
262. fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 261,237]
263. fred != sK3 | ~room(mary) [subsumption resolution 262,236]
264. fred != sK3 [subsumption resolution 263,235]
265. paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 256,239]
266. paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 265,237]
267. paul != sK3 | ~room(mary) [subsumption resolution 266,236]
268. paul != sK3 [subsumption resolution 267,235]
269. mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 255,239]
270. mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 269,237]
271. mary != sK3 | ~room(mary) [subsumption resolution 270,236]
272. mary != sK3 [subsumption resolution 271,235]
273. room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 254,239]
274. room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 273,237]
275. room(sK3) | ~room(mary) [subsumption resolution 274,236]
276. room(sK3) [subsumption resolution 275,235]
322. paul = sK3 | mary = sK3 | fred = sK3 [resolution 238,276]
323. mary = sK3 | fred = sK3 [subsumption resolution 322,268]
324. fred = sK3 [subsumption resolution 323,272]
325. $false [subsumption resolution 324,264]
% SZS output end Proof for 2643652365571811225991723
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.040106 |
There is a room. "Not everyone outside the room is quiet" if "everyone outside the room is not a tall person" and vice versa. Either "everyone in the room is a tall person" or "someone in the room is quiet" but not both. Everyone in the room is not a quiet person. Everyone in the room is tall. Everyone in the room is quiet. Not everyone outside the room is quiet. All quiet persons are old. | Everyone in the room is a tall person. | neutral | (there_is_a_room)&
((![X]:(~room(X)=>(~(tall(X)&person(X)))))<=>(~![X]:(~room(X)=>(quiet(X)))))&
((![X]:(room(X)=>(tall(X)&person(X))))<~>(?[X]:(room(X)&(quiet(X)))))&
(![X]:(room(X)=>(~(quiet(X)&person(X)))))&
(![X]:(room(X)=>(tall(X))))&
(![X]:(room(X)=>(quiet(X))))&
(~![X]:(~room(X)=>(quiet(X))))&
(![X]:(quiet(X)=>old(X))) | (there_is_a_room)&
![X]:(room(X)=>(tall(X)&person(X))) | [] | null | 0.051634 |
Reva, Donna, Rodney, Geraldine are the only persons in the room.
“Everyone in the room makes intricate hand-cut paper art for exhibitions or does not design and sews custom cosplay costumes for conventions” if “someone in the room enjoys stand-up paddleboarding” and vice versa.
If “everyone outside the room does not collect modern art or makes homemade pastries” then “everyone in the room who does not collect modern art makes homemade pastries”.
If “everyone in the room is not a certified scuba diver with advanced underwater photography skills or is a certified scuba diver with advanced underwater photography skills” then “everyone in the room who is not a certified scuba diver with advanced underwater photography skills is a certified scuba diver with advanced underwater photography skills”.
“No one anywhere who enjoys cross-country skiing enjoys camping and organizing outdoor survival workshops” if “at least one person in the room enjoys origami”.
“Rodney makes homemade pastries” if “not everyone in the room does not enjoy camping and organizing outdoor survival workshops or has a pet dog”.
“Everyone in the room does not play the violin or enjoys cross-country skiing” if “everyone anywhere does not make intricate hand-cut paper art for exhibitions or enjoys stand-up paddleboarding” and vice versa.
If “everyone in the room maintains a large, organic vegetable garden year-round or does not use contact lenses” then “everyone in the room who maintains a large, organic vegetable garden year-round designs and sews custom cosplay costumes for conventions”.
Either “everyone in the room does not collect classic novels or collects classic novels” or “Rodney uses contact lenses” but not both.
Everyone in the room collects modern art or does not enjoy fishing.
Everyone in the room uses contact lenses if they plays the violin.
Everyone in the room who makes intricate hand-cut paper art for exhibitions plays the violin.
Everyone outside the room does not enjoy fishing or mentors a youth basketball team on weekends.
Everyone in the room does not enjoy fishing only if they has lived in exactly three countries.
Everyone in the room who has lived in exactly three countries collects classic novels.
Reva neither has a specialized collection of handmade artisan pottery nor enjoys camping and organizing outdoor survival workshops.
Everyone in the room who plays the violin enjoys camping and organizing outdoor survival workshops.
Everyone anywhere who enjoys camping and organizing outdoor survival workshops either has a pet dog or has lived in exactly three countries but not both. | Rodney makes intricate hand-cut paper art for exhibitions. | contradiction | room(reva)&room(donna)&room(rodney)&room(geraldine)&(![X]:(room(X)=>(X='reva'|X='donna'|X='rodney'|X='geraldine')))&
((?[X]:(room(X)&(enjoys_stand-up_paddleboarding(X))))<=>(![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))))&
((![X]:(~room(X)=>(((makes_homemade_pastries(X))|(does_not_collect_modern_art(X))))))=>(![X]:(room(X)=>(((does_not_collect_modern_art(X))=>(makes_homemade_pastries(X)))))))&
((![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>(![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))&
((((?[X]:(room(X)&enjoys_origami(X)))))=>(~?[X]:(anywhere(X)=>(((enjoys_cross-country_skiing(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))&
((~![X]:(room(X)=>(((has_a_pet_dog(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))=>(makes_homemade_pastries(rodney)))&
((![X]:(anywhere(X)=>(((enjoys_stand-up_paddleboarding(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))<=>(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))|(does_not_play_the_violin(X)))))))&
((![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))=>(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))))&
((![X]:(room(X)=>(((collects_classic_novels(X))|(does_not_collect_classic_novels(X))))))<~>(uses_contact_lenses(rodney)))&
(![X]:(room(X)=>(((does_not_enjoy_fishing(X))|(collects_modern_art(X))))))&
(![X]:(room(X)=>(((plays_the_violin(X))=>(uses_contact_lenses(X))))))&
(![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(plays_the_violin(X))))))&
(![X]:(~room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(does_not_enjoy_fishing(X))))))&
(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))<=(does_not_enjoy_fishing(X))))))&
(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(collects_classic_novels(X))))))&
(~((has_a_specialized_collection_of_handmade_artisan_pottery(reva))|(enjoys_camping_and_organizing_outdoor_survival_workshops(reva))))&
(![X]:(room(X)=>(((plays_the_violin(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(![X]:(anywhere(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(((has_a_pet_dog(X))<~>(has_lived_in_exactly_three_countries(X)))))))) | room(reva)&room(donna)&room(rodney)&room(geraldine)&(![X]:(room(X)=>(X='reva'|X='donna'|X='rodney'|X='geraldine')))&
makes_intricate_hand-cut_paper_art_for_exhibitions(rodney) | [
"p0",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2413855703777055389182454
% SZS output start Proof for 2413855703777055389182454
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
52. ! [X0] : (room(X0) => (~predo(X0) | predo(X0))) <~> predu(fred) [input p8]
54. ! [X0] : (room(X0) => (predn(X0) => predu(X0))) [input p10]
55. ! [X0] : (room(X0) => (predk(X0) => predn(X0))) [input p11]
62. predk(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
148. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
149. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 148]
156. ! [X0] : ((~predo(X0) | predo(X0)) | ~room(X0)) <~> predu(fred) [ennf transformation 52]
157. ! [X0] : (~predo(X0) | predo(X0) | ~room(X0)) <~> predu(fred) [flattening 156]
158. ! [X0] : ((predu(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 54]
159. ! [X0] : (predu(X0) | ~predn(X0) | ~room(X0)) [flattening 158]
160. ! [X0] : ((predn(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 55]
161. ! [X0] : (predn(X0) | ~predk(X0) | ~room(X0)) [flattening 160]
169. predk(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 62]
170. predk(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 169]
185. (~predu(fred) | ? [X0] : (predo(X0) & ~predo(X0) & room(X0))) & (predu(fred) | ! [X0] : (~predo(X0) | predo(X0) | ~room(X0))) [nnf transformation 157]
186. (~predu(fred) | ? [X0] : (predo(X0) & ~predo(X0) & room(X0))) & (predu(fred) | ! [X1] : (~predo(X1) | predo(X1) | ~room(X1))) [rectify 185]
187. ? [X0] : (predo(X0) & ~predo(X0) & room(X0)) => (predo(sK5) & ~predo(sK5) & room(sK5)) [choice axiom]
188. (~predu(fred) | (predo(sK5) & ~predo(sK5) & room(sK5))) & (predu(fred) | ! [X1] : (~predo(X1) | predo(X1) | ~room(X1))) [skolemisation 186,187]
273. room(fred) [cnf transformation 149]
294. ~predu(fred) | ~predo(sK5) [cnf transformation 188]
295. ~predu(fred) | predo(sK5) [cnf transformation 188]
296. ~predn(X0) | predu(X0) | ~room(X0) [cnf transformation 159]
297. ~predk(X0) | predn(X0) | ~room(X0) [cnf transformation 161]
308. predk(fred) [cnf transformation 170]
394. 18 <=> predo(sK5) [avatar definition]
398. 19 <=> predu(fred) [avatar definition]
400. ~predu(fred) <- (~19) [avatar component clause 398]
401. 18 | ~19 [avatar split clause 295,398,394]
402. ~18 | ~19 [avatar split clause 294,398,394]
422. predn(fred) | ~room(fred) [resolution 297,308]
424. predn(fred) [subsumption resolution 422,273]
437. predu(fred) | ~room(fred) [resolution 424,296]
439. ~room(fred) <- (~19) [subsumption resolution 437,400]
440. $false <- (~19) [subsumption resolution 439,273]
441. 19 [avatar contradiction clause 440]
442. $false [avatar sat refutation 401,402,441]
% SZS output end Proof for 2413855703777055389182454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.347196 |
Iva is the only person in the room. If 'everyone in the room practices archery or does not have a specialized collection of handmade artisan pottery' then 'Iva who owns a telescope and works on fridays does not have a specialized collection of handmade artisan pottery'. If 'Iva is a tea enthusiast and does not enjoy writing detailed reviews of new and classic board games' then 'not everyone anywhere neither does not enjoy making ceramics nor is not a cybersecurity expert only if they enjoys camping and organizing outdoor survival workshops'. If 'Iva develops open-source software projects in their free time' then 'Iva owns a telescope'. 'Everyone in the room enjoys writing detailed reviews of new and classic board games' only if 'everyone in the room does not have a specialized collection of handmade artisan pottery if they is a dedicated advocate for digital privacy and encryption'. 'Not everyone in the room is not an avid hiker or plays eSports competitively' only if 'Iva develops open-source software projects in their free time or hosts themed dinner parties featuring gourmet home-cooked meals or both'. Either 'everyone in the room does not enjoy writing detailed reviews of new and classic board games or plays eSports competitively' or 'Iva regularly contributes to tech forums and online communities' but not both. Iva enjoys camping and organizing outdoor survival workshops. Iva who does not have a specialized collection of handmade artisan pottery is a cybersecurity expert. Everyone in the room who is a dedicated advocate for digital privacy and encryption has a specialized collection of handmade artisan pottery. Not everyone in the room is not an avid hiker or plays eSports competitively, does not own a telescope or is a dedicated advocate for digital privacy and encryption. Everyone in the room owns a telescope if they is not an avid hiker. Everyone in the room develops open-source software projects in their free time. Everyone in the room collects action figures if they practices archery. Everyone outside the room who bakes bread at home develops open-source software projects in their free time. Iva either does not enjoy making ceramics or is a tea enthusiast but not both. If someone regularly contributes to tech forums and online communities then he/she is a dedicated advocate for digital privacy and encryption. Everyone in the room who neither works on fridays nor regularly contributes to tech forums and online communities enjoys camping and organizing outdoor survival workshops. | Iva owns a telescope. | entailment | room(iva)&(![X]:(room(X)=>(X='iva')))&
((![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(practices_archery(X))))))=>((((owns_a_telescope(iva))&(works_on_fridays(iva))))&(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(iva))))&
((((is_a_tea_enthusiast(iva))&(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(iva))))=>(~![X]:(anywhere(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<=(~((does_not_enjoy_making_ceramics(X))|(is_not_a_cybersecurity_expert(X)))))))))&
((develops_open-source_software_projects_in_their_free_time(iva))=>(owns_a_telescope(iva)))&
((![X]:(room(X)=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))=>(![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X)))))))&
((~![X]:(room(X)=>(((plays_eSports_competitively(X))|(is_not_an_avid_hiker(X))))))=>(((develops_open-source_software_projects_in_their_free_time(iva))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(iva)))))&
((![X]:(room(X)=>(((plays_eSports_competitively(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))<~>(regularly_contributes_to_tech_forums_and_online_communities(iva)))&
(enjoys_camping_and_organizing_outdoor_survival_workshops(iva))&
((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(iva))&(is_a_cybersecurity_expert(iva)))&
(![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))&
(~![X]:(room(X)=>(((((plays_eSports_competitively(X))|(does_not_own_a_telescope(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))|(is_not_an_avid_hiker(X))))))&
(![X]:(room(X)=>(((is_not_an_avid_hiker(X))=>(owns_a_telescope(X))))))&
(![X]:(room(X)=>(develops_open-source_software_projects_in_their_free_time(X))))&
(![X]:(room(X)=>(((practices_archery(X))=>(collects_action_figures(X))))))&
(![X]:(~room(X)=>(((bakes_bread_at_home(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(((does_not_enjoy_making_ceramics(iva))<~>(is_a_tea_enthusiast(iva))))&
((![X]:((regularly_contributes_to_tech_forums_and_online_communities(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))&
(![X]:(room(X)=>(((~((works_on_fridays(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))) | room(iva)&(![X]:(room(X)=>(X='iva')))&
owns_a_telescope(iva) | [
"p0",
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6209141901271846123601531
% SZS output start Proof for 6209141901271846123601531
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
47. predq(mary) => predo(mary) [input p3]
56. ! [X0] : (room(X0) => predq(X0)) [input p12]
62. ~(predo(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
147. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
151. predo(mary) | ~predq(mary) [ennf transformation 47]
160. ! [X0] : (predq(X0) | ~room(X0)) [ennf transformation 56]
162. ~predo(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 62]
178. ? [X0] : (mary != X0 & room(X0)) => (mary != sK5 & room(sK5)) [choice axiom]
179. ~predo(mary) | (mary != sK5 & room(sK5)) | ~room(mary) [skolemisation 162,178]
260. room(mary) [cnf transformation 147]
261. ~room(X0) | mary = X0 [cnf transformation 147]
268. predo(mary) | ~predq(mary) [cnf transformation 151]
282. ~room(X0) | predq(X0) [cnf transformation 160]
286. ~predo(mary) | room(sK5) | ~room(mary) [cnf transformation 179]
287. ~predo(mary) | mary != sK5 | ~room(mary) [cnf transformation 179]
303. 4 <=> predo(mary) [avatar definition]
327. 9 <=> predq(mary) [avatar definition]
330. ~9 | 4 [avatar split clause 268,303,327]
374. ~predo(mary) | mary != sK5 [subsumption resolution 287,260]
376. 19 <=> mary = sK5 [avatar definition]
378. mary != sK5 <- (~19) [avatar component clause 376]
379. ~19 | ~4 [avatar split clause 374,303,376]
380. ~predo(mary) | room(sK5) [subsumption resolution 286,260]
382. 20 <=> room(sK5) [avatar definition]
384. room(sK5) <- (20) [avatar component clause 382]
385. 20 | ~4 [avatar split clause 380,303,382]
387. predq(mary) [resolution 282,260]
391. 9 [avatar split clause 387,327]
396. mary = sK5 <- (20) [resolution 261,384]
409. $false <- (~19, 20) [subsumption resolution 396,378]
410. 19 | ~20 [avatar contradiction clause 409]
411. $false [avatar sat refutation 330,379,385,391,410]
% SZS output end Proof for 6209141901271846123601531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.015209 |
Chung is the only person in the room.
Either “Chung is quieter than Johnnie” or “everyone outside the room does not create augmented reality experiences for mobile applications or creates augmented reality experiences for mobile applications” but not both.
If “Chung does not create augmented reality experiences for mobile applications” then “Chung creates augmented reality experiences for mobile applications”.
If “Chung creates augmented reality experiences for mobile applications” then “at least one person in the room creates augmented reality experiences for mobile applications”.
If “everyone in the room is quiet or does not create augmented reality experiences for mobile applications” then “Chung is the least quiet in the room”.
“Everyone in the room is quieter than Johnnie or does not create augmented reality experiences for mobile applications” only if “Chung is quieter than Johnnie or creates augmented reality experiences for mobile applications or both”.
Chung creates augmented reality experiences for mobile applications.
Everyone in the room creates augmented reality experiences for mobile applications if they is quieter than Johnnie.
Everyone in the room creates augmented reality experiences for mobile applications. | Chung is quieter than Johnnie. | contradiction | room(chung)&(![X]:(room(X)=>(X='chung')))&
((quieter(johnnienie,chung))<~>(![X]:(~room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X)))))))&
((does_not_create_augmented_reality_experiences_for_mobile_applications(chung))=>(creates_augmented_reality_experiences_for_mobile_applications(chung)))&
((creates_augmented_reality_experiences_for_mobile_applications(chung))=>(((?[X]:(room(X)&creates_augmented_reality_experiences_for_mobile_applications(X))))))&
((![X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(quiet(X))))))=>(![X]:((room(X)&(X!=chung))=>quieter(chung,X))))&
((![X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(quieter(johnnienie,X))))))=>(((quieter(johnnienie,chung))|(creates_augmented_reality_experiences_for_mobile_applications(chung)))))&
(creates_augmented_reality_experiences_for_mobile_applications(chung))&
(![X]:(room(X)=>(((quieter(johnnienie,X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(![X]:(room(X)=>(creates_augmented_reality_experiences_for_mobile_applications(X)))) | room(chung)&(![X]:(room(X)=>(X='chung')))&
quieter(johnnienie,chung) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6864921491287720152247644
% SZS output start Proof for 6864921491287720152247644
45. quieter(john,mary) <~> ! [X0] : (~room(X0) => (~predq(X0) | predq(X0))) [input p1]
53. quieter(john,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
128. quieter(john,mary) <~> ! [X0] : ((~predq(X0) | predq(X0)) | room(X0)) [ennf transformation 45]
129. quieter(john,mary) <~> ! [X0] : (~predq(X0) | predq(X0) | room(X0)) [flattening 128]
139. quieter(john,mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 53]
141. (? [X0] : (predq(X0) & ~predq(X0) & ~room(X0)) | ~quieter(john,mary)) & (! [X0] : (~predq(X0) | predq(X0) | room(X0)) | quieter(john,mary)) [nnf transformation 129]
142. (? [X0] : (predq(X0) & ~predq(X0) & ~room(X0)) | ~quieter(john,mary)) & (! [X1] : (~predq(X1) | predq(X1) | room(X1)) | quieter(john,mary)) [rectify 141]
143. ? [X0] : (predq(X0) & ~predq(X0) & ~room(X0)) => (predq(sK0) & ~predq(sK0) & ~room(sK0)) [choice axiom]
144. ((predq(sK0) & ~predq(sK0) & ~room(sK0)) | ~quieter(john,mary)) & (! [X1] : (~predq(X1) | predq(X1) | room(X1)) | quieter(john,mary)) [skolemisation 142,143]
236. ~predq(sK0) | ~quieter(john,mary) [cnf transformation 144]
237. predq(sK0) | ~quieter(john,mary) [cnf transformation 144]
252. quieter(john,mary) [cnf transformation 139]
255. 1 <=> quieter(john,mary) [avatar definition]
259. 2 <=> predq(sK0) [avatar definition]
262. ~1 | 2 [avatar split clause 237,259,255]
263. ~1 | ~2 [avatar split clause 236,259,255]
271. 1 [avatar split clause 252,255]
272. $false [avatar sat refutation 262,263,271]
% SZS output end Proof for 6864921491287720152247644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.272669 |
There is a room.
If “everyone anywhere does not enjoy rooftop gardening or practices zumba” then “everyone in the room who does not enjoy rooftop gardening collects antique jewelry”.
If “everyone anywhere collects vintage stamps” then “only one person in the room creates large-scale murals for public art installations”.
If “everyone anywhere practices digital art” then “everyone in the room is a cybersecurity expert if they has a pet dog”.
If “everyone anywhere is not a member of a local theater group specializing in improv or collects antique jewelry” then “everyone in the room who is not a member of a local theater group specializing in improv uses a Windows laptop”.
“Everyone in the room who collect rare sneakers enjoys watercolor painting” unless “everyone in the room does not collect rare sneakers or does not collect antique jewelry”. | Everyone in the room does not use a Windows laptop or makes homemade pastries. | neutral | (there_is_a_room)&
((![X]:(anywhere(X)=>(((practices_zumba(X))|(does_not_enjoy_rooftop_gardening(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))=>(collects_antique_jewelry(X)))))))&
((![X]:(anywhere(X)=>(collects_vintage_stamps(X))))=>(((?[X]:(room(X)&creates_large-scale_murals_for_public_art_installations(X)))&(![X,Y]:((room(X)&room(Y)&(creates_large-scale_murals_for_public_art_installations(X))&(creates_large-scale_murals_for_public_art_installations(Y)))=>(X=Y))))))&
((![X]:(anywhere(X)=>(practices_digital_art(X))))=>(![X]:(room(X)=>(((has_a_pet_dog(X))=>(is_a_cybersecurity_expert(X)))))))&
((![X]:(anywhere(X)=>(((collects_antique_jewelry(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(uses_a_Windows_laptop(X)))))))&
(~(![X]:(room(X)=>(((does_not_collect_antique_jewelry(X))|(does_not_collect_rare_sneakers(X))))))=>(![X]:(room(X)=>(((collect_rare_sneakers(X))=>(enjoys_watercolor_painting(X)))))))&
((![X]:(room(X)=>(((collects_luxury_watches(X))|(does_not_collect_antique_jewelry(X))))))=>(![X]:(anywhere(X)=>(((does_not_collect_antique_jewelry(X))=>(practices_digital_art(X)))))))&
(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(practices_zumba(X))))))&
(((?[X]:(room(X)&owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))&(![X,Y]:((room(X)&room(Y)&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(Y)))=>(X=Y)))))&
(![X]:(anywhere(X)=>(((has_a_pet_dog(X))=>(((makes_homemade_pastries(X))&(does_not_collect_rare_sneakers(X))&(collects_vintage_stamps(X))))))))&
(![X]:(room(X)=>(((((uses_a_Windows_laptop(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))=>(practices_digital_art(X))))))&
(~![X]:(room(X)=>(((practices_digital_art(X))=>(collects_antique_jewelry(X))))))&
(![X]:(~room(X)=>(((collects_antique_jewelry(X))=>(has_a_pet_dog(X))))))&
(![X]:(room(X)=>(((collects_antique_jewelry(X))=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))&
(![X]:(anywhere(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(own_a_television(X))))))&
(~?[X]:(room(X)=>(does_not_play_video_games(X))))&
(((?[X]:(room(X)&makes_homemade_pastries(X)))&(![X,Y]:((room(X)&room(Y)&(makes_homemade_pastries(X))&(makes_homemade_pastries(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(collect_rare_sneakers(X))))))&
(![X]:(room(X)=>(((collect_rare_sneakers(X))|(does_not_practice_zumba(X))))))&
(![X]:(anywhere(X)=>(((does_not_practice_zumba(X))=>(plays_the_drums(X))))))&
(![X]:(room(X)=>(((plays_the_drums(X))=>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
((![X]:((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(is_a_chess_master_who_participates_in_national_tournaments(X))))) | (there_is_a_room)&
![X]:(room(X)=>(((makes_homemade_pastries(X))|(does_not_use_a_Windows_laptop(X))))) | [] | null | 0.542589 |
Gilbert, Valarie, Forrest, Merle, Rose are the only persons in the room.
If “everyone in the room uses contact lenses or does not collect vintage vinyl records” then “everyone in the room has a saltwater aquarium or does not collect rare sneakers”.
If “not everyone outside the room enjoys wildlife photography or does not practice zumba” then “Forrest enjoys wildlife photography”.
If “everyone in the room does not enjoy kayaking and exploring remote waterways or uses contact lenses” then “Forrest has lived in exactly three countries”.
“Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals” unless “everyone in the room does not enjoy coding in Python or does not enjoy salsa dancing”.
“Valarie writes a travel blog” unless “everyone in the room does not create bespoke furniture pieces from reclaimed wood or does not develop open-source software projects in their free time”.
“Valarie does not use contact lenses” only if “everyone in the room who reads mystery novels has a vast collection of first-edition science fiction novels”.
Everyone anywhere does not write a travel blog, does not have lived in exactly three countries and does not create bespoke furniture pieces from reclaimed wood if they has a vast collection of first-edition science fiction novels.
Not everyone anywhere does not play the violin or enjoys windsurfing.
Someone in the room collects vintage vinyl records. | Everyone in the room does not collect vintage vinyl records. | contradiction | room(gilbert)&room(valarie)&room(forrest)&room(merle)&room(rose)&(![X]:(room(X)=>(X='gilbert'|X='valarie'|X='forrest'|X='merle'|X='rose')))&
((![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))|(uses_contact_lenses(X))))))=>(![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))|(has_a_saltwater_aquarium(X)))))))&
((~![X]:(~room(X)=>(((does_not_practice_zumba(X))|(enjoys_wildlife_photography(X))))))=>(enjoys_wildlife_photography(forrest)))&
((![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))=>(has_lived_in_exactly_three_countries(forrest)))&
(~(![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(does_not_enjoy_coding_in_Python(X))))))=>(![X]:(room(X)=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))&
(~(![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>(writes_a_travel_blog(valarie)))&
((does_not_use_contact_lenses(valarie))=>(![X]:(room(X)=>(((reads_mystery_novels(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))&
(![X]:(anywhere(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(((does_not_write_a_travel_blog(X))&(does_not_have_lived_in_exactly_three_countries(X))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))&
(~![X]:(anywhere(X)=>(((enjoys_windsurfing(X))|(does_not_play_the_violin(X))))))&
((![X]:((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(collect_rare_sneakers(X)))))&
(uses_contact_lenses(gilbert))&
(?[X]:(room(X)&(collects_vintage_vinyl_records(X))))&
(![X]:(room(X)=>(((enjoys_wildlife_photography(X))<=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))&
(![X]:(room(X)=>(enjoys_kayaking_and_exploring_remote_waterways(X))))&
(![X]:(room(X)=>(((practices_zumba(X))=>(streams_on_Twitch(X))))))&
(makes_homemade_pastries(valarie))&
(![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=>(((enjoys_wildlife_photography(X))&(streams_on_Twitch(X))&(enjoys_windsurfing(X))))))))&
(![X]:(anywhere(X)=>(((((enjoys_wildlife_photography(X))&(streams_on_Twitch(X))&(enjoys_windsurfing(X))))=>(plays_the_violin(X))))))&
(![X]:(room(X)=>(((plays_the_violin(X))|(does_not_enjoy_salsa_dancing(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(((has_lived_in_exactly_three_countries(X))&(does_enjoy_trail_running(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))))))))&
(~![X]:(room(X)=>(((((has_lived_in_exactly_three_countries(X))&(does_enjoy_trail_running(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))))=>(is_a_tea_enthusiast(X))))))&
(![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(uses_an_ios_phone(X))))))&
(![X]:(~room(X)=>(((uses_an_ios_phone(X))=>(writes_a_travel_blog(X))))))&
((?[X,Y]:(room(X)&room(Y)&(does_not_make_homemade_pastries(X)&does_not_make_homemade_pastries(Y))&(X!=Y)))) | room(gilbert)&room(valarie)&room(forrest)&room(merle)&room(rose)&(![X]:(room(X)=>(X='gilbert'|X='valarie'|X='forrest'|X='merle'|X='rose')))&
![X]:(room(X)=>(does_not_collect_vintage_vinyl_records(X))) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1323047796605273006876523
% SZS output start Proof for 1323047796605273006876523
55. ? [X0] : (predk(X0) & room(X0)) [input p11]
68. ! [X0] : (room(X0) => ~predk(X0)) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
71. ! [X0] : (room(X0) => ~predk(X0)) & ! [X1] : (room(X1) => (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 68]
173. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : ((john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 71]
174. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 173]
180. ? [X0] : (predk(X0) & room(X0)) => (predk(sK2) & room(sK2)) [choice axiom]
181. predk(sK2) & room(sK2) [skolemisation 55,180]
282. room(sK2) [cnf transformation 181]
283. predk(sK2) [cnf transformation 181]
304. ~predk(X0) | ~room(X0) [cnf transformation 174]
320. ~room(sK2) [resolution 304,283]
321. $false [subsumption resolution 320,282]
% SZS output end Proof for 1323047796605273006876523
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.288288 |
There is a room. “No one in the room is not right-handed if they cannot play the piano” if “everyone in the room cannot play the piano or is right-handed”. Everyone in the room can play the harmonica or cannot play the harmonica. Everyone in the room can play the harmonica only if they can play the piano. Everyone in the room who can play the piano is not a scotch connoisseur. Everyone outside the room is a kind generous person if they is not a scotch connoisseur. Everyone in the room can play the piano, is a scotch connoisseur or is not not generous if they enjoys skydiving, makes homemade pastries or does not make homemade pastries. Everyone in the room is right-handed. Everyone in the room makes homemade pastries. If someone enjoys spelunking then he/she cannot play the piano or enjoys spelunking or both. No one in the room who is right-handed, is a kind person and is a kind generous person is not a scotch connoisseur. Everyone outside the room cannot play the harmonica or can play the piano. Everyone in the room who is a scotch connoisseur is right-handed. Everyone in the room is not a generous person only if they is not generous. Everyone in the room is a kind person only if they is right-handed. Everyone in the room enjoys spelunking or cannot play the piano. Everyone in the room who enjoys spelunking makes homemade pastries. Everyone outside the room enjoys spelunking if they makes homemade pastries. | Everyone outside the room is a scotch connoisseur. | entailment | (there_is_a_room)&
((![X]:(room(X)=>(((is_right-handed(X))|(cannot_play_the_piano(X))))))=>(~?[X]:(room(X)=>(((cannot_play_the_piano(X))=>(is_not_right-handed(X)))))))&
(![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(can_play_the_harmonica(X))))))&
(![X]:(room(X)=>(((can_play_the_piano(X))<=(can_play_the_harmonica(X))))))&
(![X]:(room(X)=>(((can_play_the_piano(X))=>(is_not_a_scotch_connoisseur(X))))))&
(![X]:(~room(X)=>(((is_not_a_scotch_connoisseur(X))=>(kind(X)&generous(X)&person(X))))))&
(![X]:(room(X)=>(((((enjoys_skydiving(X))|(makes_homemade_pastries(X))|(does_not_make_homemade_pastries(X))))=>(((can_play_the_piano(X))|(is_a_scotch_connoisseur(X))|(~~generous(X))))))))&
(![X]:(room(X)=>(is_right-handed(X))))&
(![X]:(room(X)=>(makes_homemade_pastries(X))))&
((![X]:((enjoys_spelunking(X))=>(((cannot_play_the_piano(X))|(enjoys_spelunking(X)))))))&
(~?[X]:(room(X)=>(((((is_right-handed(X))&(kind(X)&person(X))&(kind(X)&generous(X)&person(X))))=>(is_not_a_scotch_connoisseur(X))))))&
(![X]:(~room(X)=>(((can_play_the_piano(X))|(cannot_play_the_harmonica(X))))))&
(![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(is_right-handed(X))))))&
(![X]:(room(X)=>(((~generous(X))<=(~(generous(X)&person(X)))))))&
(![X]:(room(X)=>(((is_right-handed(X))<=(kind(X)&person(X))))))&
(![X]:(room(X)=>(((cannot_play_the_piano(X))|(enjoys_spelunking(X))))))&
(![X]:(room(X)=>(((enjoys_spelunking(X))=>(makes_homemade_pastries(X))))))&
(![X]:(~room(X)=>(((makes_homemade_pastries(X))=>(enjoys_spelunking(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(is_a_scotch_connoisseur(X))) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1560824793297393314792401
% SZS output start Proof for 1560824793297393314792401
44. there_is_a_room [input p0]
54. ~? [X0] : (room(X0) => ((person(X0) & generous(X0) & kind(X0) & person(X0) & kind(X0) & predp(X0)) => ~predc(X0))) [input p10]
62. ~(! [X0] : (~room(X0) => predc(X0)) & there_is_a_room) [input hypothesis]
153. ! [X0] : ((predc(X0) & (person(X0) & generous(X0) & kind(X0) & person(X0) & kind(X0) & predp(X0))) & room(X0)) [ennf transformation 54]
154. ! [X0] : (predc(X0) & person(X0) & generous(X0) & kind(X0) & person(X0) & kind(X0) & predp(X0) & room(X0)) [flattening 153]
169. ? [X0] : (~predc(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 62]
177. ? [X0] : (~predc(X0) & ~room(X0)) => (~predc(sK2) & ~room(sK2)) [choice axiom]
178. (~predc(sK2) & ~room(sK2)) | ~there_is_a_room [skolemisation 169,177]
259. there_is_a_room [cnf transformation 44]
284. predc(X0) [cnf transformation 154]
294. ~predc(sK2) | ~there_is_a_room [cnf transformation 178]
332. ~there_is_a_room [subsumption resolution 294,284]
333. $false [subsumption resolution 332,259]
% SZS output end Proof for 1560824793297393314792401
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.222169 |
Virgina is the only person in the room.
“Virgina creates YouTube content” only if “Virgina is a Linux enthusiast”.
“Virgina practices kickboxing” unless “no one anywhere participates in long-distance cycling events across the country or is not allergic to anything”.
If “at least one person in the room is not a certified scuba diver with advanced underwater photography skills” then “if someone mentors a youth basketball team on weekends then he/she enjoys spelunking and vice versa” otherwise “if someone is an enthusiastic bird watcher who travels for rare sightings then he/she neither does not enjoy cross-country skiing nor does enjoy trail running and vice versa”.
Either “no one in the room is not an enthusiastic bird watcher who travels for rare sightings or is a Linux enthusiast” or “Virgina is a coffee connoisseur” but not both. | Virgina is a Linux enthusiast. | neutral | room(virgina)&(![X]:(room(X)=>(X='virgina')))&
((creates_YouTube_content(virgina))=>(is_a_Linux_enthusiast(virgina)))&
(~(~?[X]:(anywhere(X)=>(((is_not_allergic_to_anything(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))))=>(practices_kickboxing(virgina)))&
(((((?[X]:(room(X)&is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))=>((![X]:((mentors_a_youth_basketball_team_on_weekends(X))<=>(enjoys_spelunking(X))))))&((~(((?[X]:(room(X)&is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>((![X]:((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=>(~((does_not_enjoy_cross-country_skiing(X))|(does_enjoy_trail_running(X)))))))))&
((~?[X]:(room(X)=>(((is_a_Linux_enthusiast(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))<~>(is_a_coffee_connoisseur(virgina)))&
(~(?[X]:(room(X)&(does_not_create_YouTube_content(X))))=>((?[X,Y]:(room(X)&room(Y)&(~((is_a_coffee_connoisseur(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))&~((is_a_coffee_connoisseur(Y))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(Y))))&(X!=Y)))))&
((creates_YouTube_content(virgina))=>(does_not_drive_a_hybrid_car(virgina)))&
((((does_enjoy_trail_running(virgina))|(enjoys_watercolor_painting(virgina))))=>(![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(enjoys_virtual_reality_gaming(X)))))))&
(does_not_collect_vintage_vinyl_records(virgina))&
(![X]:(room(X)=>(((((collects_vintage_vinyl_records(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(is_a_Linux_enthusiast(X))))))&
(![X]:(room(X)=>(((((practices_kickboxing(X))&(practices_calligraphy(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))<=(is_a_Linux_enthusiast(X))))))&
(enjoys_landscape_photography(virgina))&
(is_a_coffee_connoisseur(virgina))&
(~(enjoys_cross-country_skiing(virgina)))&
(is_allergic_to_anything(virgina))&
(![X]:(room(X)=>(((((has_lived_in_exactly_three_countries(X))<~>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))=>(uses_an_ios_phone(X)))))) | room(virgina)&(![X]:(room(X)=>(X='virgina')))&
is_a_Linux_enthusiast(virgina) | [] | null | 0.039127 |
Leonard, Patrick, Lamar, Robert, Carmine are the only persons in the room. It is true that 'everyone in the room who is a client of Cassandra is not a calm happy person'. Everyone in the room is calm if they is a client of Albert. Everyone in the room hosts regular game nights featuring complex strategy games only if they practices calligraphy. Everyone in the room is a generous creative brave quiet tall happy tourist. Everyone in the room is a client of Cassandra if they is a generous tourist. Everyone anywhere is a client of Albert if they practices calligraphy. | Lamar does not host regular game nights featuring complex strategy games. | entailment | room(leonard)&room(patrick)&room(lamar)&room(robert)&room(carmine)&(![X]:(room(X)=>(X='leonard'|X='patrick'|X='lamar'|X='robert'|X='carmine')))&
(![X]:((room(X)&(X!=carmine))=>older(carmine,X)))&
(![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))&
(strong(patrick)&strong(robert))&
(![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(~(tall(X)&curious(X)&tourist(X)))))))&
(![X]:((anywhere(X)&(X!=patrick))=>louder(patrick,X)))&
(sibling(carmine,albert))&
(((?[X]:(room(X)&~patient(X)))&(![X,Y]:((room(X)&room(Y)&(~patient(X))&(~patient(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((client(cassandra,X))=>(~(calm(X)&happy(X)&person(X)))))))&
(![X]:(anywhere(X)=>(((is_a_client_of_Costco(X))<=>(writes_poetry(X))))))&
(client(carmine,albert))&
((like(cassandra,carmine) & like(carmine,cassandra)))&
((like(cassandra,robert) & like(robert,cassandra)))&
(?[X]:(room(X)&(~(calm(X)&person(X)))))&
(![X]:(room(X)=>(((patient(X))=>(~(generous(X)&wise(X)&tourist(X)))))))&
(![X]:(room(X)=>(((client(albert,X))=>(calm(X))))))&
(![X]:(room(X)=>(((hate(X,albert))<=(~~~brave(X))))))&
(((?[X]:(room(X)&~humble(X)&~strong(X)&~curious(X)))&(![X,Y]:((room(X)&room(Y)&(~humble(X)&~strong(X)&~curious(X))&(~humble(Y)&~strong(Y)&~curious(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((practices_calligraphy(X))<=(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
((![X]:((practices_and_performs_acrobatic_dance_routines(X))<=>(~calm(X)))))&
(![X]:(room(X)=>(generous(X)&creative(X)&brave(X)&quiet(X)&tall(X)&happy(X)&tourist(X))))&
(![X]:(room(X)=>(((generous(X)&tourist(X))=>(client(cassandra,X))))))&
(~![X]:(~room(X)=>(((sibling(albert,X))=>(~(old(X)&humble(X)&european(X)))))))&
(![X]:(anywhere(X)=>(((like(X,albert))=>(client(cassandra,X))))))&
(![X]:(room(X)=>(((((~(generous(X)&person(X)))&(hate(X,cassandra))&(client(albert,X))))=>(wise(X))))))&
(![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=(practices_and_performs_acrobatic_dance_routines(X))))))&
(![X]:(anywhere(X)=>(((practices_calligraphy(X))=>(client(albert,X))))))&
(![X]:(room(X)=>(((sibling(cassandra,X))<=>(client(cassandra,X)))))) | room(leonard)&room(patrick)&room(lamar)&room(robert)&room(carmine)&(![X]:(room(X)=>(X='leonard'|X='patrick'|X='lamar'|X='robert'|X='carmine')))&
does_not_host_regular_game_nights_featuring_complex_strategy_games(lamar) | [
"b3",
"b4",
"p0",
"p8",
"p15",
"p18",
"p20",
"p21",
"p26",
"hypothesis"
] | % SZS status Unsatisfiable for 2522651145051068320401536
% SZS output start Proof for 2522651145051068320401536
4. ! [X0] : (tourist(X0) => person(X0)) [input b3]
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
52. ! [X0] : (room(X0) => (client(lucy,X0) => ~(person(X0) & happy(X0) & calm(X0)))) [input p8]
59. ! [X0] : (room(X0) => (client(susan,X0) => calm(X0))) [input p15]
62. ! [X0] : (room(X0) => (predd(X0) => predg(X0))) [input p18]
64. ! [X0] : (room(X0) => (tourist(X0) & happy(X0) & tall(X0) & quiet(X0) & brave(X0) & creative(X0) & generous(X0))) [input p20]
65. ! [X0] : (room(X0) => ((tourist(X0) & generous(X0)) => client(lucy,X0))) [input p21]
70. ! [X0] : (anywhere(X0) => (predg(X0) => client(susan,X0))) [input p26]
72. ~(~predd(fred) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
76. ! [X0] : (room(X0) => (tourist(X0) & happy(X0) & tall(X0) & quiet(X0) & brave(X0) & generous(X0))) [pure predicate removal 64]
77. ! [X0] : (room(X0) => (tourist(X0) & happy(X0) & tall(X0) & quiet(X0) & generous(X0))) [pure predicate removal 76]
84. ! [X0] : (room(X0) => (tourist(X0) & happy(X0) & quiet(X0) & generous(X0))) [pure predicate removal 77]
87. ! [X0] : (person(X0) | ~tourist(X0)) [ennf transformation 4]
155. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
156. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 155]
163. ! [X0] : (((~person(X0) | ~happy(X0) | ~calm(X0)) | ~client(lucy,X0)) | ~room(X0)) [ennf transformation 52]
164. ! [X0] : (~person(X0) | ~happy(X0) | ~calm(X0) | ~client(lucy,X0) | ~room(X0)) [flattening 163]
167. ! [X0] : ((calm(X0) | ~client(susan,X0)) | ~room(X0)) [ennf transformation 59]
168. ! [X0] : (calm(X0) | ~client(susan,X0) | ~room(X0)) [flattening 167]
171. ! [X0] : ((predg(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 62]
172. ! [X0] : (predg(X0) | ~predd(X0) | ~room(X0)) [flattening 171]
173. ! [X0] : ((tourist(X0) & happy(X0) & quiet(X0) & generous(X0)) | ~room(X0)) [ennf transformation 84]
174. ! [X0] : ((client(lucy,X0) | (~tourist(X0) | ~generous(X0))) | ~room(X0)) [ennf transformation 65]
175. ! [X0] : (client(lucy,X0) | ~tourist(X0) | ~generous(X0) | ~room(X0)) [flattening 174]
180. ! [X0] : ((client(susan,X0) | ~predg(X0)) | ~anywhere(X0)) [ennf transformation 70]
181. ! [X0] : (client(susan,X0) | ~predg(X0) | ~anywhere(X0)) [flattening 180]
183. predd(fred) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 72]
184. predd(fred) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 183]
196. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
197. predd(fred) | (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 184,196]
199. ~tourist(X0) | person(X0) [cnf transformation 87]
200. anywhere(X0) [cnf transformation 5]
281. room(mary) [cnf transformation 156]
282. room(paul) [cnf transformation 156]
283. room(fred) [cnf transformation 156]
284. room(alice) [cnf transformation 156]
285. room(john) [cnf transformation 156]
286. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 156]
295. ~client(lucy,X0) | ~happy(X0) | ~calm(X0) | ~person(X0) | ~room(X0) [cnf transformation 164]
305. ~client(susan,X0) | calm(X0) | ~room(X0) [cnf transformation 168]
311. ~predd(X0) | predg(X0) | ~room(X0) [cnf transformation 172]
312. ~room(X0) | generous(X0) [cnf transformation 173]
314. ~room(X0) | happy(X0) [cnf transformation 173]
315. ~room(X0) | tourist(X0) [cnf transformation 173]
316. client(lucy,X0) | ~tourist(X0) | ~generous(X0) | ~room(X0) [cnf transformation 175]
323. client(susan,X0) | ~predg(X0) | ~anywhere(X0) [cnf transformation 181]
326. predd(fred) | room(sK4) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
327. predd(fred) | mary != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
328. predd(fred) | paul != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
329. predd(fred) | fred != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
330. predd(fred) | alice != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
331. predd(fred) | john != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
344. client(lucy,X0) | ~generous(X0) | ~room(X0) [subsumption resolution 316,315]
345. client(lucy,X0) | ~room(X0) [subsumption resolution 344,312]
347. client(susan,X0) | ~predg(X0) [subsumption resolution 323,200]
349. predd(fred) | john != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 331,285]
350. predd(fred) | john != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 349,284]
351. predd(fred) | john != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 350,283]
352. predd(fred) | john != sK4 | ~room(mary) [subsumption resolution 351,282]
353. predd(fred) | john != sK4 [subsumption resolution 352,281]
355. 3 <=> john = sK4 [avatar definition]
357. john != sK4 <- (~3) [avatar component clause 355]
359. 4 <=> predd(fred) [avatar definition]
361. predd(fred) <- (4) [avatar component clause 359]
362. ~3 | 4 [avatar split clause 353,359,355]
363. predd(fred) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 330,285]
364. predd(fred) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 363,284]
365. predd(fred) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 364,283]
366. predd(fred) | alice != sK4 | ~room(mary) [subsumption resolution 365,282]
367. predd(fred) | alice != sK4 [subsumption resolution 366,281]
369. 5 <=> alice = sK4 [avatar definition]
371. alice != sK4 <- (~5) [avatar component clause 369]
372. ~5 | 4 [avatar split clause 367,359,369]
373. predd(fred) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 329,285]
374. predd(fred) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 373,284]
375. predd(fred) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 374,283]
376. predd(fred) | fred != sK4 | ~room(mary) [subsumption resolution 375,282]
377. predd(fred) | fred != sK4 [subsumption resolution 376,281]
379. 6 <=> fred = sK4 [avatar definition]
381. fred != sK4 <- (~6) [avatar component clause 379]
382. ~6 | 4 [avatar split clause 377,359,379]
383. predd(fred) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,285]
384. predd(fred) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 383,284]
385. predd(fred) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 384,283]
386. predd(fred) | paul != sK4 | ~room(mary) [subsumption resolution 385,282]
387. predd(fred) | paul != sK4 [subsumption resolution 386,281]
389. 7 <=> paul = sK4 [avatar definition]
391. paul != sK4 <- (~7) [avatar component clause 389]
392. ~7 | 4 [avatar split clause 387,359,389]
393. predd(fred) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,285]
394. predd(fred) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 393,284]
395. predd(fred) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 394,283]
396. predd(fred) | mary != sK4 | ~room(mary) [subsumption resolution 395,282]
397. predd(fred) | mary != sK4 [subsumption resolution 396,281]
399. 8 <=> mary = sK4 [avatar definition]
401. mary != sK4 <- (~8) [avatar component clause 399]
402. ~8 | 4 [avatar split clause 397,359,399]
403. predd(fred) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,285]
404. predd(fred) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 403,284]
405. predd(fred) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 404,283]
406. predd(fred) | room(sK4) | ~room(mary) [subsumption resolution 405,282]
407. predd(fred) | room(sK4) [subsumption resolution 406,281]
409. 9 <=> room(sK4) [avatar definition]
411. room(sK4) <- (9) [avatar component clause 409]
412. 9 | 4 [avatar split clause 407,359,409]
440. tourist(fred) [resolution 315,283]
446. predg(fred) | ~room(fred) <- (4) [resolution 311,361]
447. predg(fred) <- (4) [subsumption resolution 446,283]
448. ~predg(X0) | ~room(X0) | calm(X0) [resolution 305,347]
480. person(fred) [resolution 440,199]
608. ~happy(X0) | ~calm(X0) | ~person(X0) | ~room(X0) | ~room(X0) [resolution 295,345]
609. ~happy(X0) | ~calm(X0) | ~person(X0) | ~room(X0) [duplicate literal removal 608]
610. ~calm(X0) | ~person(X0) | ~room(X0) [subsumption resolution 609,314]
726. ~room(fred) | calm(fred) <- (4) [resolution 448,447]
727. calm(fred) <- (4) [subsumption resolution 726,283]
780. ~person(fred) | ~room(fred) <- (4) [resolution 610,727]
781. ~room(fred) <- (4) [subsumption resolution 780,480]
782. $false <- (4) [subsumption resolution 781,283]
783. ~4 [avatar contradiction clause 782]
784. alice = sK4 | fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (9) [resolution 411,286]
791. fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (~5, 9) [subsumption resolution 784,371]
792. paul = sK4 | mary = sK4 | john = sK4 <- (~5, ~6, 9) [subsumption resolution 791,381]
793. mary = sK4 | john = sK4 <- (~5, ~6, ~7, 9) [subsumption resolution 792,391]
794. john = sK4 <- (~5, ~6, ~7, ~8, 9) [subsumption resolution 793,401]
795. $false <- (~3, ~5, ~6, ~7, ~8, 9) [subsumption resolution 794,357]
796. 3 | 5 | 6 | 7 | 8 | ~9 [avatar contradiction clause 795]
821. $false [avatar sat refutation 362,372,382,392,402,412,783,796]
% SZS output end Proof for 2522651145051068320401536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.043 s
% ------------------------------
% ------------------------------
| 0.048532 |
Elizabeth, Jody are the only persons in the room. Jody is richer than Teresa. | Teresa is richer than Jody. | contradiction | room(elizabeth)&room(jody)&(![X]:(room(X)=>(X='elizabeth'|X='jody')))&
((?[X]:(~room(X)&(richer(teresa,X))))=>(![X]:((anywhere(X)&(X!=jody))=>richer(X,jody))))&
(~(?[X]:(room(X)&(richer(teresa,X))))=>(richer(jody,nancy)))&
(richer(nancy,jody))&
(richer(teresa,jody))&
(![X]:((~room(X)&(X!=elizabeth))=>richer(X,elizabeth)))&
(?[X]:(room(X)&(richer(teresa,X))))&
(![X]:(room(X)=>(((richer(teresa,X))=>(richer(nancy,X))))))&
(~(~(richer(teresa,elizabeth)&richer(teresa,jody))))&
(richer(teresa,jody)&richer(teresa,elizabeth))&
(richer(teresa,elizabeth)) | room(elizabeth)&room(jody)&(![X]:(room(X)=>(X='elizabeth'|X='jody')))&
richer(jody,teresa) | [
"b7",
"b42",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5190693534593821851411747
% SZS output start Proof for 5190693534593821851411747
8. ! [X0,X1] : (X0 != X1 => (richer(X0,X1) => ~richer(X1,X0))) [input b7]
43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42]
48. richer(alice,paul) [input p4]
55. richer(paul,alice) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
65. ! [X0,X1] : ((~richer(X1,X0) | ~richer(X0,X1)) | X0 = X1) [ennf transformation 8]
66. ! [X0,X1] : (~richer(X1,X0) | ~richer(X0,X1) | X0 = X1) [flattening 65]
138. richer(paul,alice) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 55]
139. richer(paul,alice) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 138]
150. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 66]
204. paul != alice [cnf transformation 43]
234. richer(alice,paul) [cnf transformation 48]
247. richer(paul,alice) [cnf transformation 139]
293. ~richer(paul,alice) | paul = alice [resolution 150,234]
304. paul = alice [subsumption resolution 293,247]
305. $false [subsumption resolution 304,204]
% SZS output end Proof for 5190693534593821851411747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.268316 |
Joyce, Lawrence are the only persons in the room.
If 'Lawrence is not a quiet person' then 'it is not the case that 'Joyce is a old tall person'' otherwise 'Joyce is a old person'.
If 'Lawrence either is a quiet old person or is a quiet person but not both' then 'someone who is a quiet person is older than someone who is not old' otherwise 'someone who is a old person is quieter than someone who is richer than Veronica'.
'Lawrence is a tall person' if 'Joyce is quiet' and vice versa.
At least one person anywhere is older than Veronica. | Lawrence is older than Veronica. | neutral | room(joyce)&room(lawrence)&(![X]:(room(X)=>(X='joyce'|X='lawrence')))&
(((~(quiet(lawrence)&person(lawrence)))=>(~(old(joyce)&tall(joyce)&person(joyce))))&((~(~(quiet(lawrence)&person(lawrence))))=>(old(joyce)&person(joyce))))&
(((((quiet(lawrence)&old(lawrence)&person(lawrence))<~>(quiet(lawrence)&person(lawrence))))=>(?[X,Y]:((quiet(X)&person(X))&(~old(Y))&(older(X,Y)))))&((~(((quiet(lawrence)&old(lawrence)&person(lawrence))<~>(quiet(lawrence)&person(lawrence)))))=>(?[X,Y]:((old(X)&person(X))&(richer(veronica,Y))&(quieter(X,Y))))))&
((quiet(joyce))<=>(tall(lawrence)&person(lawrence)))&
(((?[X]:(anywhere(X)&older(veronica,X)))))&
(quieter(lawrence,veronica))&
(![X]:((room(X)&(X!=lawrence))=>quieter(lawrence,X)))&
(quieter(lawrence,lois))&
(richer(veronica,joyce))&
((joyce_dream=>(quiet(lawrence)&old(lawrence)&person(lawrence))))&
(old(joyce)&person(joyce))&
((quiet(lawrence))&(tall(joyce)))&
(![X]:(tall(X)=>quiet(X)))&
(richer(joyce,brian))&
(tall(lawrence)&person(lawrence))&
(?[X,Y]:((quiet(X)&person(X))&(quieter(brian,Y))&(older(X,Y))))&
(~(?[X]:(anywhere(X)&(~(quiet(X)&person(X))))))&
(older(lois,lawrence))&
(((~(quiet(lawrence)&old(lawrence)&person(lawrence)))<~>(richer(veronica,lawrence))))&
(old(joyce)&quiet(joyce)&person(joyce))&
(quiet(lawrence)&person(lawrence))&
(richer(veronica,lawrence))&
(?[X,Y]:((richer(veronica,X))&(older(lois,Y))&(richer(X,Y))))&
(quieter(brian,lawrence))&
(older(veronica,joyce))&
(richer(lawrence,brian))&
(((older(veronica,lawrence))|(tall(lawrence)&person(lawrence)))) | room(joyce)&room(lawrence)&(![X]:(room(X)=>(X='joyce'|X='lawrence')))&
older(veronica,lawrence) | [] | null | 0.001711 |
Tamara, Richard, Elizabeth, Brandon are the only persons in the room.
If “everyone in the room does not own a high-end gaming PC with custom-built components or has a curated collection of mid-century modern furniture” then “everyone anywhere who does not own a high-end gaming PC with custom-built components enjoys kayaking”.
“Everyone anywhere does not own a high-end gaming PC with custom-built components or owns a high-end gaming PC with custom-built components” only if “everyone in the room who does not own a high-end gaming PC with custom-built components practices zumba”. | Brandon drives a hybrid car. | neutral | room(tamara)&room(richard)&room(elizabeth)&room(brandon)&(![X]:(room(X)=>(X='tamara'|X='richard'|X='elizabeth'|X='brandon')))&
((![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(![X]:(anywhere(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))=>(enjoys_kayaking(X)))))))&
((![X]:(anywhere(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))=>(practices_zumba(X)))))))&
((![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))|(enjoys_kayaking(X))))))=>(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))<=>(enjoys_kayaking(X)))))))&
((![X]:(room(X)=>(((does_not_practice_zumba(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))=>(![X]:(anywhere(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))<=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))&(practices_zumba(X)))))))))&
((~![X]:(room(X)=>(((enjoys_kayaking(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))=>(![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))=>(enjoys_kayaking(X)))))))&
(((![X]:(~room(X)=>(((enjoys_kayaking(X))|(does_not_enjoy_kayaking(X))))))=>(![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=>(practices_zumba(X)))))))&((~(![X]:(~room(X)=>(((enjoys_kayaking(X))|(does_not_enjoy_kayaking(X)))))))=>(((?[X]:(room(X)&is_passionate_about_collecting_and_restoring_classic_cars(X)))&(![X,Y]:((room(X)&room(Y)&(is_passionate_about_collecting_and_restoring_classic_cars(X))&(is_passionate_about_collecting_and_restoring_classic_cars(Y)))=>(X=Y)))))))&
((![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))<=>(![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(drives_a_hybrid_car(X)))))))&
((![X]:(anywhere(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))<=>(![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_enjoy_kayaking(X)))))))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))<=>(enjoys_kayaking(X))))))&
(![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))&
(![X]:(room(X)=>(((drives_a_hybrid_car(X))<=>(((enjoys_kayaking(X))&(is_passionate_about_collecting_and_restoring_classic_cars(X))))))))&
(((?[X]:(anywhere(X)&has_a_curated_collection_of_mid-century_modern_furniture(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(has_a_curated_collection_of_mid-century_modern_furniture(X))&(has_a_curated_collection_of_mid-century_modern_furniture(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_enjoy_kayaking(X))))))&
(![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))&
(![X]:(room(X)=>(((enjoys_kayaking(X))=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))) | room(tamara)&room(richard)&room(elizabeth)&room(brandon)&(![X]:(room(X)=>(X='tamara'|X='richard'|X='elizabeth'|X='brandon')))&
drives_a_hybrid_car(brandon) | [] | null | 0.71002 |
Orval, Tammy, Marian, Salvatore are the only persons in the room.
Orval and Tammy are quieter than Margaret.
No tall person is old.
Someone in the room is quieter than Margaret.
Everyone in the room who is a old person is quieter than Margaret.
Marian and Salvatore are quieter than Margaret.
No tall person is quiet.
Someone in the room is older than Margaret.
Tammy and Orval are richer than Margaret. | Marian is old. | contradiction | room(orval)&room(tammy)&room(marian)&room(salvatore)&(![X]:(room(X)=>(X='orval'|X='tammy'|X='marian'|X='salvatore')))&
(quieter(margaret,orval)&quieter(margaret,tammy))&
(~?[X]:(tall(X)=>old(X)))&
(?[X]:(room(X)&(quieter(margaret,X))))&
(![X]:(room(X)=>(((old(X)&person(X))=>(quieter(margaret,X))))))&
(quieter(margaret,marian)&quieter(margaret,salvatore))&
(~?[X]:(tall(X)=>quiet(X)))&
(?[X]:(room(X)&(older(margaret,X))))&
(richer(margaret,tammy)&richer(margaret,orval)) | room(orval)&room(tammy)&room(marian)&room(salvatore)&(![X]:(room(X)=>(X='orval'|X='tammy'|X='marian'|X='salvatore')))&
old(marian) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 849995228046833601107682
% SZS output start Proof for 849995228046833601107682
46. ~? [X0] : (tall(X0) => old(X0)) [input p2]
53. old(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
55. ~? [X0] : old(X0) [pure predicate removal 46]
131. ! [X0] : ~old(X0) [ennf transformation 55]
133. old(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 53]
134. old(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133]
227. ~old(X0) [cnf transformation 131]
242. old(fred) [cnf transformation 134]
243. $false [subsumption resolution 242,227]
% SZS output end Proof for 849995228046833601107682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0.004537 |
Mark, Jessie, Jennifer are the only persons in the room.
Everyone in the room is not a funny person if they is calm and vice versa.
Only one person outside the room either is a humble old curious generous brave tall person or is older than Rose but not both.
Everyone in the room is quieter than Rose only if they either is not humble, not quiet or is not brave, not happy, not tall but not both.
Jennifer who is a funny person is a humble person, is quieter than Rose or is richer than Rose.
Jessie who is a kind happy wise strong person is not a calm person.
Everyone in the room is a old person and is richer than Rose if they is older than Rose.
Mark and Jennifer are not a wise kind persons.
At least one person in the room is quieter than Rose, is richer than Rose and is not a brave person.
If someone is a creative person then he/she is a brave happy strong person and vice versa. | Jessie and Mark are not a funny quiet tall generous wise persons. | neutral | room(mark)&room(jessie)&room(jennifer)&(![X]:(room(X)=>(X='mark'|X='jessie'|X='jennifer')))&
(![X]:(room(X)=>(((~(funny(X)&person(X)))<=>(calm(X))))))&
(((?[X]:(~room(X)&((humble(X)&old(X)&curious(X)&generous(X)&brave(X)&tall(X)&person(X))<~>(older(rose,X)))))&(![X,Y]:((~room(X)&~room(Y)&(((humble(X)&old(X)&curious(X)&generous(X)&brave(X)&tall(X)&person(X))<~>(older(rose,X))))&(((humble(Y)&old(Y)&curious(Y)&generous(Y)&brave(Y)&tall(Y)&person(Y))<~>(older(rose,Y)))))=>(X=Y)))))&
(![X]:(room(X)=>(((((~humble(X)&~quiet(X))<~>(~brave(X)&~happy(X)&~tall(X))))<=(quieter(rose,X))))))&
((funny(jennifer)&person(jennifer))&(((humble(jennifer)&person(jennifer))|(quieter(rose,jennifer))|(richer(rose,jennifer)))))&
((kind(jessie)&happy(jessie)&wise(jessie)&strong(jessie)&person(jessie))&(~(calm(jessie)&person(jessie))))&
(![X]:(room(X)=>(((older(rose,X))=>(((old(X)&person(X))&(richer(rose,X))))))))&
(~(wise(mark)&kind(mark)&person(mark))&~(wise(jennifer)&kind(jennifer)&person(jennifer)))&
(((?[X]:(room(X)&((quieter(rose,X))&(richer(rose,X))&(~(brave(X)&person(X))))))))&
((![X]:((creative(X)&person(X))<=>(brave(X)&happy(X)&strong(X)&person(X))))) | room(mark)&room(jessie)&room(jennifer)&(![X]:(room(X)=>(X='mark'|X='jessie'|X='jennifer')))&
~(funny(jessie)&quiet(jessie)&tall(jessie)&generous(jessie)&wise(jessie)&person(jessie))&~(funny(mark)&quiet(mark)&tall(mark)&generous(mark)&wise(mark)&person(mark)) | [] | null | 0.131289 |
Herbert, Lucille, Nicholas are the only persons in the room.
Someone outside the room is not a funny strong person.
Nicholas is a generous person or is a generous calm person or both.
Nicholas and Herbert are wise persons, are brave and are not creative.
Jackie is richer than Nicholas.
Everyone in the room is not creative and is not a happy person if they is not quiet, is a wise person or is not a creative funny person.
Everyone in the room who is not creative and is not a happy person is not a funny brave person.
Someone who is richer than Jackie is older than someone who is not brave, not funny, not creative, not patient.
Everyone in the room is richer than Geneva if they is not a old person.
Nicholas and Herbert are quieter than Jackie.
Lucille and Nicholas are respectively wise and tall.
Everyone in the room who is a humble person is a happy person. | All brave persons are funny. | contradiction | room(herbert)&room(lucille)&room(nicholas)&(![X]:(room(X)=>(X='herbert'|X='lucille'|X='nicholas')))&
(?[X]:(~room(X)&(~(funny(X)&strong(X)&person(X)))))&
(((generous(nicholas)&person(nicholas))|(generous(nicholas)&calm(nicholas)&person(nicholas))))&
(((wise(nicholas)&person(nicholas))&(brave(nicholas))&(~creative(nicholas)))&((wise(herbert)&person(herbert))&(brave(herbert))&(~creative(herbert))))&
(richer(nicholas,jackie))&
(![X]:(room(X)=>(((((~quiet(X))|(wise(X)&person(X))|(~(creative(X)&funny(X)&person(X)))))=>(((~creative(X))&(~(happy(X)&person(X)))))))))&
(![X]:(room(X)=>(((((~creative(X))&(~(happy(X)&person(X)))))=>(~(funny(X)&brave(X)&person(X)))))))&
(?[X,Y]:((richer(jackie,X))&(~brave(Y)&~funny(Y)&~creative(Y)&~patient(Y))&(older(X,Y))))&
(![X]:(room(X)=>(((~(old(X)&person(X)))=>(richer(geneva,X))))))&
(quieter(jackie,nicholas)&quieter(jackie,herbert))&
((wise(lucille))&(tall(nicholas)))&
(![X]:(room(X)=>(((humble(X)&person(X))=>(happy(X)&person(X)))))) | room(herbert)&room(lucille)&room(nicholas)&(![X]:(room(X)=>(X='herbert'|X='lucille'|X='nicholas')))&
![X]:(brave(X)=>funny(X)) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 237129101084771309633961
% SZS output start Proof for 237129101084771309633961
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
46. (person(fred) & calm(fred) & generous(fred)) | (person(fred) & generous(fred)) [input p2]
47. ~creative(mary) & brave(mary) & person(mary) & wise(mary) & ~creative(fred) & brave(fred) & person(fred) & wise(fred) [input p3]
49. ! [X0] : (room(X0) => ((~(person(X0) & funny(X0) & creative(X0)) | (person(X0) & wise(X0)) | ~quiet(X0)) => (~(person(X0) & happy(X0)) & ~creative(X0)))) [input p5]
50. ! [X0] : (room(X0) => ((~(person(X0) & happy(X0)) & ~creative(X0)) => ~(person(X0) & brave(X0) & funny(X0)))) [input p6]
56. ! [X0] : (brave(X0) => funny(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
57. ! [X0] : (brave(X0) => funny(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 56]
61. (person(fred) & generous(fred)) | (person(fred) & generous(fred)) [pure predicate removal 46]
62. person(fred) | person(fred) [pure predicate removal 61]
136. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
137. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 136]
138. ! [X0] : ((((~person(X0) | ~happy(X0)) & ~creative(X0)) | ((person(X0) & funny(X0) & creative(X0)) & (~person(X0) | ~wise(X0)) & quiet(X0))) | ~room(X0)) [ennf transformation 49]
139. ! [X0] : (((~person(X0) | ~happy(X0)) & ~creative(X0)) | (person(X0) & funny(X0) & creative(X0) & (~person(X0) | ~wise(X0)) & quiet(X0)) | ~room(X0)) [flattening 138]
140. ! [X0] : (((~person(X0) | ~brave(X0) | ~funny(X0)) | ((person(X0) & happy(X0)) | creative(X0))) | ~room(X0)) [ennf transformation 50]
141. ! [X0] : (~person(X0) | ~brave(X0) | ~funny(X0) | (person(X0) & happy(X0)) | creative(X0) | ~room(X0)) [flattening 140]
144. ! [X0] : (funny(X0) | ~brave(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 57]
145. ! [X0] : (funny(X0) | ~brave(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 144]
146. ! [X0] : ((person(X0) & funny(X0) & creative(X0) & (~person(X0) | ~wise(X0)) & quiet(X0)) | ~sP0(X0)) [predicate definition introduction]
147. ! [X0] : (((~person(X0) | ~happy(X0)) & ~creative(X0)) | sP0(X0) | ~room(X0)) [definition folding 139,146]
151. ! [X0] : ((person(X0) & funny(X0) & creative(X0) & (~person(X0) | ~wise(X0)) & quiet(X0)) | ~sP0(X0)) [nnf transformation 146]
236. room(fred) [cnf transformation 137]
239. person(fred) | person(fred) [cnf transformation 62]
240. wise(fred) [cnf transformation 47]
242. brave(fred) [cnf transformation 47]
243. ~creative(fred) [cnf transformation 47]
250. ~person(X0) | ~wise(X0) | ~sP0(X0) [cnf transformation 151]
253. ~sP0(X0) | person(X0) [cnf transformation 151]
255. ~happy(X0) | ~person(X0) | sP0(X0) | ~room(X0) [cnf transformation 147]
256. ~brave(X0) | ~person(X0) | ~funny(X0) | happy(X0) | creative(X0) | ~room(X0) [cnf transformation 141]
272. ~brave(X0) | funny(X0) [cnf transformation 145]
273. person(fred) [duplicate literal removal 239]
274. ~sP0(X0) | ~wise(X0) [subsumption resolution 250,253]
275. funny(fred) [resolution 272,242]
514. ~person(fred) | ~funny(fred) | happy(fred) | creative(fred) | ~room(fred) [resolution 256,242]
516. ~funny(fred) | happy(fred) | creative(fred) | ~room(fred) [subsumption resolution 514,273]
517. happy(fred) | creative(fred) | ~room(fred) [subsumption resolution 516,275]
518. happy(fred) | ~room(fred) [subsumption resolution 517,243]
519. happy(fred) [subsumption resolution 518,236]
524. ~person(fred) | sP0(fred) | ~room(fred) [resolution 519,255]
525. sP0(fred) | ~room(fred) [subsumption resolution 524,273]
526. sP0(fred) [subsumption resolution 525,236]
544. ~wise(fred) [resolution 526,274]
549. $false [subsumption resolution 544,240]
% SZS output end Proof for 237129101084771309633961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.641019 |
Ada is the only person in the room. Either “Ada is a skilled home brewer experimenting with craft beer recipes” or “no one anywhere is a client of Meta or does not have completed a triathlon” but not both. If “someone in the room enjoys kayaking” then “Ada is a member of a local theater group specializing in improv”. If “Ada enjoys kayaking” then “Ada enjoys landscape photography”. If “Ada practices pilates” then “Ada has completed a triathlon”. If “Ada practices pilates” then “Ada is a member of a local theater group specializing in improv” otherwise “not everyone in the room who regularly contributes to tech forums and online communities has completed a triathlon”. “Ada does not have completed a triathlon” if “everyone in the room practices pilates or is not a chess master who participates in national tournaments”. “Ada enjoys kayaking and regularly contributes to tech forums and online communities” only if “everyone in the room does not maintain a personal blog focused on cybersecurity tips or does not enjoy deep-sea diving and exploring underwater caves”. If “someone in the room is a member of a local theater group specializing in improv” then “if someone is a tea enthusiast then he/she enjoys fishing and vice versa”. It is not the case that “Ada enjoys landscape photography”. Ada is a certified scuba diver with advanced underwater photography skills. Ada own a television and enjoys deep-sea diving and exploring underwater caves. Everyone in the room who has completed a triathlon enjoys landscape photography. | Ada is a member of a local theater group specializing in improv. | neutral | room(ada)&(![X]:(room(X)=>(X='ada')))&
((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(ada))<~>(~?[X]:(anywhere(X)=>(((does_not_have_completed_a_triathlon(X))|(is_a_client_of_Meta(X)))))))&
((?[X]:(room(X)&(enjoys_kayaking(X))))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(ada)))&
((enjoys_kayaking(ada))=>(enjoys_landscape_photography(ada)))&
((practices_pilates(ada))=>(has_completed_a_triathlon(ada)))&
(((practices_pilates(ada))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(ada)))&((~(practices_pilates(ada)))=>(~![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(has_completed_a_triathlon(X))))))))&
((![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(practices_pilates(X))))))=>(does_not_have_completed_a_triathlon(ada)))&
((((enjoys_kayaking(ada))&(regularly_contributes_to_tech_forums_and_online_communities(ada))))=>(![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X)))))))&
((?[X]:(room(X)&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>((![X]:((is_a_tea_enthusiast(X))<=>(enjoys_fishing(X))))))&
(~(enjoys_landscape_photography(ada)))&
(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(ada))&
(((own_a_television(ada))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(ada))))&
(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(enjoys_landscape_photography(X))))))&
(![X]:(room(X)=>(((~((is_a_tea_enthusiast(X))|(has_completed_a_triathlon(X))))=>(has_completed_a_triathlon(X))))))&
((![X]:((collects_action_figures(X))<=>(own_a_television(X)))))&
(is_a_client_of_Meta(ada))&
(~(~(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(ada))|(own_a_television(ada))|(has_completed_a_triathlon(ada))))))&
(![X]:(room(X)=>(((practices_pilates(X))=>(~((is_a_client_of_Meta(X))|(enjoys_kayaking(X))))))))&
(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(((collects_action_figures(X))|(owns_a_telescope(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))))&
(![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(enjoys_making_ceramics(ada)) | room(ada)&(![X]:(room(X)=>(X='ada')))&
is_a_member_of_a_local_theater_group_specializing_in_improv(ada) | [] | null | 0.19395 |
Barbara, Francis, Donald are the only persons in the room. Everyone in the room who is a member of a local theater group specializing in improv is not humble. Everyone in the room is a tea enthusiast only if they is humble. Francis is a member of a local theater group specializing in improv. | Francis is a tea enthusiast. | contradiction | room(barbara)&room(francis)&room(donald)&(![X]:(room(X)=>(X='barbara'|X='francis'|X='donald')))&
(?[X]:(anywhere(X)&(curious(X))))&
(collects_vintage_stamps(francis))&
(![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(~humble(X))))))&
(A_shadow_appears_only_at_noon.)&
(![X]:(room(X)=>(((humble(X))<=(is_a_tea_enthusiast(X))))))&
(![X]:(room(X)=>(((((humble(X))&(is_a_tea_enthusiast(X))))=>(humble(X))))))&
(((?[X]:(room(X)&((~hate(chong,X))|(~humble(X)))))))&
(is_a_member_of_a_local_theater_group_specializing_in_improv(francis)) | room(barbara)&room(francis)&room(donald)&(![X]:(room(X)=>(X='barbara'|X='francis'|X='donald')))&
is_a_tea_enthusiast(francis) | [
"p0",
"p3",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2860492865435745797430481
% SZS output start Proof for 2860492865435745797430481
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
47. ! [X0] : (room(X0) => (predh(X0) => ~humble(X0))) [input p3]
49. ! [X0] : (room(X0) => (predx(X0) => humble(X0))) [input p5]
52. predh(paul) [input p8]
53. predx(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
131. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
132. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 131]
133. ! [X0] : ((~humble(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 47]
134. ! [X0] : (~humble(X0) | ~predh(X0) | ~room(X0)) [flattening 133]
135. ! [X0] : ((humble(X0) | ~predx(X0)) | ~room(X0)) [ennf transformation 49]
136. ! [X0] : (humble(X0) | ~predx(X0) | ~room(X0)) [flattening 135]
139. predx(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 53]
140. predx(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 139]
225. room(paul) [cnf transformation 132]
228. ~humble(X0) | ~predh(X0) | ~room(X0) [cnf transformation 134]
229. ~predx(X0) | humble(X0) | ~room(X0) [cnf transformation 136]
232. predh(paul) [cnf transformation 52]
237. predx(paul) [cnf transformation 140]
238. humble(paul) | ~room(paul) [resolution 229,237]
239. humble(paul) [subsumption resolution 238,225]
240. ~predh(paul) | ~room(paul) [resolution 239,228]
241. ~room(paul) [subsumption resolution 240,232]
242. $false [subsumption resolution 241,225]
% SZS output end Proof for 2860492865435745797430481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.191502 |
Sarah is the only person in the room.
Sarah is dedicated to sustainable living and zero-waste practices if everyone in the room practices graffiti art or is not a wine connoisseur with a private cellar of vintage wines and vice versa.
Either everyone in the room practices graffiti art or is not a wine connoisseur with a private cellar of vintage wines or everyone in the room enjoys stand-up paddleboarding or is not an active member of a local robotics club but not both.
Sarah is a night owl.
Everyone in the room enjoys stand-up paddleboarding or is not an active member of a local robotics club.
Not everyone in the room who collects rare and antique scientific instruments writes in-depth travel guides for off-the-beaten-path destinations.
Everyone in the room who writes in-depth travel guides for off-the-beaten-path destinations collects classic novels.
Everyone in the room who collects classic novels writes in-depth travel guides for off-the-beaten-path destinations.
Everyone in the room who regularly contributes to tech forums and online communities collects vintage vinyl records.
Everyone in the room collects vintage vinyl records if they hosts regular game nights featuring complex strategy games and vice versa. | Sarah is dedicated to sustainable living and zero-waste practices. | contradiction | room(sarah)&(![X]:(room(X)=>(X='sarah')))&
((![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(practices_graffiti_art(X))))))<=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(sarah)))&
((![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(practices_graffiti_art(X))))))<~>(![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))|(enjoys_stand-up_paddleboarding(X)))))))&
(is_a_night_owl(sarah))&
(![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))|(enjoys_stand-up_paddleboarding(X))))))&
(~![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))&
(![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(collects_classic_novels(X))))))&
(![X]:(room(X)=>(((collects_classic_novels(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(collects_vintage_vinyl_records(X))))))&
(![X]:(room(X)=>(((collects_vintage_vinyl_records(X))<=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))) | room(sarah)&(![X]:(room(X)=>(X='sarah')))&
is_dedicated_to_sustainable_living_and_zero-waste_practices(sarah) | [
"p0",
"p1",
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6312963662879090067396231
% SZS output start Proof for 6312963662879090067396231
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
45. ! [X0] : (room(X0) => (prede(X0) | ~predh(X0))) <=> predu(mary) [input p1]
46. ! [X0] : (room(X0) => (prede(X0) | ~predh(X0))) <~> ! [X0] : (room(X0) => (predx(X0) | ~predf(X0))) [input p2]
48. ! [X0] : (room(X0) => (predx(X0) | ~predf(X0))) [input p4]
54. predu(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
55. ! [X0] : (room(X0) => (prede(X0) | ~predh(X0))) <~> ! [X1] : (room(X1) => (predx(X1) | ~predf(X1))) [rectify 46]
131. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
132. ! [X0] : ((prede(X0) | ~predh(X0)) | ~room(X0)) <=> predu(mary) [ennf transformation 45]
133. ! [X0] : (prede(X0) | ~predh(X0) | ~room(X0)) <=> predu(mary) [flattening 132]
134. ! [X0] : ((prede(X0) | ~predh(X0)) | ~room(X0)) <~> ! [X1] : ((predx(X1) | ~predf(X1)) | ~room(X1)) [ennf transformation 55]
135. ! [X0] : (prede(X0) | ~predh(X0) | ~room(X0)) <~> ! [X1] : (predx(X1) | ~predf(X1) | ~room(X1)) [flattening 134]
136. ! [X0] : ((predx(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 48]
137. ! [X0] : (predx(X0) | ~predf(X0) | ~room(X0)) [flattening 136]
144. predu(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 54]
146. (! [X0] : (prede(X0) | ~predh(X0) | ~room(X0)) | ~predu(mary)) & (predu(mary) | ? [X0] : (~prede(X0) & predh(X0) & room(X0))) [nnf transformation 133]
147. (! [X0] : (prede(X0) | ~predh(X0) | ~room(X0)) | ~predu(mary)) & (predu(mary) | ? [X1] : (~prede(X1) & predh(X1) & room(X1))) [rectify 146]
148. ? [X1] : (~prede(X1) & predh(X1) & room(X1)) => (~prede(sK0) & predh(sK0) & room(sK0)) [choice axiom]
149. (! [X0] : (prede(X0) | ~predh(X0) | ~room(X0)) | ~predu(mary)) & (predu(mary) | (~prede(sK0) & predh(sK0) & room(sK0))) [skolemisation 147,148]
150. (? [X1] : (~predx(X1) & predf(X1) & room(X1)) | ? [X0] : (~prede(X0) & predh(X0) & room(X0))) & (! [X1] : (predx(X1) | ~predf(X1) | ~room(X1)) | ! [X0] : (prede(X0) | ~predh(X0) | ~room(X0))) [nnf transformation 135]
151. (? [X0] : (~predx(X0) & predf(X0) & room(X0)) | ? [X1] : (~prede(X1) & predh(X1) & room(X1))) & (! [X2] : (predx(X2) | ~predf(X2) | ~room(X2)) | ! [X3] : (prede(X3) | ~predh(X3) | ~room(X3))) [rectify 150]
152. ? [X0] : (~predx(X0) & predf(X0) & room(X0)) => (~predx(sK1) & predf(sK1) & room(sK1)) [choice axiom]
153. ? [X1] : (~prede(X1) & predh(X1) & room(X1)) => (~prede(sK2) & predh(sK2) & room(sK2)) [choice axiom]
154. ((~predx(sK1) & predf(sK1) & room(sK1)) | (~prede(sK2) & predh(sK2) & room(sK2))) & (! [X2] : (predx(X2) | ~predf(X2) | ~room(X2)) | ! [X3] : (prede(X3) | ~predh(X3) | ~room(X3))) [skolemisation 151,153,152]
238. room(mary) [cnf transformation 131]
239. ~room(X0) | mary = X0 [cnf transformation 131]
243. prede(X0) | ~predh(X0) | ~room(X0) | ~predu(mary) [cnf transformation 149]
245. room(sK1) | room(sK2) [cnf transformation 154]
246. room(sK1) | predh(sK2) [cnf transformation 154]
247. room(sK1) | ~prede(sK2) [cnf transformation 154]
248. predf(sK1) | room(sK2) [cnf transformation 154]
249. predf(sK1) | predh(sK2) [cnf transformation 154]
250. predf(sK1) | ~prede(sK2) [cnf transformation 154]
251. ~predx(sK1) | room(sK2) [cnf transformation 154]
252. ~predx(sK1) | predh(sK2) [cnf transformation 154]
253. ~predx(sK1) | ~prede(sK2) [cnf transformation 154]
254. predx(X0) | ~predf(X0) | ~room(X0) [cnf transformation 137]
263. predu(mary) [cnf transformation 144]
265. 1 <=> predu(mary) [avatar definition]
269. 2 <=> ! [X0] : (prede(X0) | ~room(X0) | ~predh(X0)) [avatar definition]
270. ~predh(X0) | ~room(X0) | prede(X0) <- (2) [avatar component clause 269]
271. ~1 | 2 [avatar split clause 243,269,265]
288. 6 <=> prede(sK2) [avatar definition]
290. ~prede(sK2) <- (~6) [avatar component clause 288]
292. 7 <=> predx(sK1) [avatar definition]
294. ~predx(sK1) <- (~7) [avatar component clause 292]
295. ~6 | ~7 [avatar split clause 253,292,288]
297. 8 <=> predh(sK2) [avatar definition]
299. predh(sK2) <- (8) [avatar component clause 297]
300. 8 | ~7 [avatar split clause 252,292,297]
302. 9 <=> room(sK2) [avatar definition]
304. room(sK2) <- (9) [avatar component clause 302]
305. 9 | ~7 [avatar split clause 251,292,302]
307. 10 <=> predf(sK1) [avatar definition]
309. predf(sK1) <- (10) [avatar component clause 307]
310. ~6 | 10 [avatar split clause 250,307,288]
311. 8 | 10 [avatar split clause 249,307,297]
312. 9 | 10 [avatar split clause 248,307,302]
314. 11 <=> room(sK1) [avatar definition]
316. room(sK1) <- (11) [avatar component clause 314]
317. ~6 | 11 [avatar split clause 247,314,288]
318. 8 | 11 [avatar split clause 246,314,297]
319. 9 | 11 [avatar split clause 245,314,302]
321. 12 <=> ! [X2] : (predx(X2) | ~room(X2) | ~predf(X2)) [avatar definition]
322. ~predf(X2) | ~room(X2) | predx(X2) <- (12) [avatar component clause 321]
324. 12 [avatar split clause 254,321]
325. 1 [avatar split clause 263,265]
328. mary = sK2 <- (9) [resolution 239,304]
331. ~prede(mary) <- (~6, 9) [backward demodulation 290,328]
332. predh(mary) <- (8, 9) [backward demodulation 299,328]
334. ~room(mary) | prede(mary) <- (2, 8, 9) [resolution 270,332]
335. prede(mary) <- (2, 8, 9) [subsumption resolution 334,238]
336. $false <- (2, ~6, 8, 9) [subsumption resolution 335,331]
337. ~2 | 6 | ~8 | ~9 [avatar contradiction clause 336]
339. mary = sK1 <- (11) [resolution 316,239]
340. ~predx(mary) <- (~7, 11) [backward demodulation 294,339]
341. predf(mary) <- (10, 11) [backward demodulation 309,339]
343. ~room(mary) | predx(mary) <- (10, 11, 12) [resolution 322,341]
344. predx(mary) <- (10, 11, 12) [subsumption resolution 343,238]
345. $false <- (~7, 10, 11, 12) [subsumption resolution 344,340]
346. 7 | ~10 | ~11 | ~12 [avatar contradiction clause 345]
347. $false [avatar sat refutation 271,295,300,305,310,311,312,317,318,319,324,325,337,346]
% SZS output end Proof for 6312963662879090067396231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0.598984 |
Deena is the only person in the room.
“Everyone in the room who is not a client of Meta practices and performs acrobatic dance routines or trains for and competes in international triathlons or both” if “everyone in the room is not a client of Meta or practices and performs acrobatic dance routines”.
“Not everyone outside the room owns a smartwatch” if “everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals or does not enjoy virtual reality gaming” and vice versa.
“Not everyone in the room enjoys kayaking and exploring remote waterways or is not an expert in identifying and foraging wild edible plants” if “everyone in the room collects modern art or does not have a specialized collection of handmade artisan pottery” and vice versa.
If “not everyone in the room collects vintage stamps or does not collect vintage stamps” then “everyone in the room who collects vintage stamps is a drone photographer”.
If “everyone anywhere enjoys virtual reality gaming or does not develop open-source software projects in their free time” then “not everyone in the room enjoys windsurfing if they enjoys virtual reality gaming”.
If “at least one person in the room collects modern art” then “Deena makes intricate hand-cut paper art for exhibitions”.
Deena hosts themed dinner parties featuring gourmet home-cooked meals.
At least one person anywhere plays the violin.
Everyone in the room practices archery if they is right-handed.
Everyone in the room who practices archery is an expert in identifying and foraging wild edible plants.
Deena makes intricate hand-cut paper art for exhibitions.
Everyone in the room who is right-handed bakes bread at home.
Everyone in the room who trains for and competes in international triathlons practices and performs acrobatic dance routines.
Not everyone in the room who practices archery trains for and competes in international triathlons.
Everyone anywhere who plays the violin is a drone photographer.
Everyone in the room who is a drone photographer practices calligraphy.
Everyone anywhere enjoys virtual reality gaming or does not develop open-source software projects in their free time.
Not everyone in the room is a cybersecurity expert if they collects first edition books and vice versa.
Everyone in the room who collects first edition books practices and performs acrobatic dance routines.
Deena neither collects first edition books nor enjoys windsurfing. | Deena plays the violin. | neutral | room(deena)&(![X]:(room(X)=>(X='deena')))&
((![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(is_not_a_client_of_Meta(X))))))=>(![X]:(room(X)=>(((is_not_a_client_of_Meta(X))=>(((practices_and_performs_acrobatic_dance_routines(X))|(trains_for_and_competes_in_international_triathlons(X)))))))))&
((![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))<=>(~![X]:(~room(X)=>(owns_a_smartwatch(X)))))&
((![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(collects_modern_art(X))))))<=>(~![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(enjoys_kayaking_and_exploring_remote_waterways(X)))))))&
((~![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(collects_vintage_stamps(X))))))=>(![X]:(room(X)=>(((collects_vintage_stamps(X))=>(is_a_drone_photographer(X)))))))&
((![X]:(anywhere(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(enjoys_virtual_reality_gaming(X))))))=>(~![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(enjoys_windsurfing(X)))))))&
((((?[X]:(room(X)&collects_modern_art(X)))))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(deena)))&
(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(deena))&
(((?[X]:(anywhere(X)&plays_the_violin(X)))))&
(![X]:(room(X)=>(((is_right-handed(X))=>(practices_archery(X))))))&
(![X]:(room(X)=>(((practices_archery(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))&
(makes_intricate_hand-cut_paper_art_for_exhibitions(deena))&
(![X]:(room(X)=>(((is_right-handed(X))=>(bakes_bread_at_home(X))))))&
(![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))&
(~![X]:(room(X)=>(((practices_archery(X))=>(trains_for_and_competes_in_international_triathlons(X))))))&
(![X]:(anywhere(X)=>(((plays_the_violin(X))=>(is_a_drone_photographer(X))))))&
(![X]:(room(X)=>(((is_a_drone_photographer(X))=>(practices_calligraphy(X))))))&
(![X]:(anywhere(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(enjoys_virtual_reality_gaming(X))))))&
(~![X]:(room(X)=>(((is_a_cybersecurity_expert(X))<=>(collects_first_edition_books(X))))))&
(![X]:(room(X)=>(((collects_first_edition_books(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))&
(~((collects_first_edition_books(deena))|(enjoys_windsurfing(deena))))&
(![X]:(room(X)=>(((collects_modern_art(X))=>(plays_the_violin(X))))))&
(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=(bakes_bread_at_home(X)))))) | room(deena)&(![X]:(room(X)=>(X='deena')))&
plays_the_violin(deena) | [] | null | 0.326017 |
Alex, Jean are the only persons in the room.
Jean is calm.
At least one person anywhere is a calm happy person. | Alex is calm. | neutral | room(alex)&room(jean)&(![X]:(room(X)=>(X='alex'|X='jean')))&
(calm(jean))&
(((?[X]:(anywhere(X)&calm(X)&happy(X)&person(X)))))&
(?[X]:(room(X)&(~(happy(X)&wise(X)&person(X)))))&
(does_not_enjoy_trail_running(alex))&
(?[X]:(room(X)&(~happy(X))))&
((![X]:((~(wise(X)&person(X)))=>(~(wise(X)&calm(X)&happy(X)&person(X))))))&
(((wise(jean)&happy(jean)&person(jean))|(~(wise(jean)&happy(jean)&calm(jean)&person(jean)))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(jean))))&
(?[X]:(room(X)&(calm(X)&wise(X)&person(X))))&
(![X]:(wise(X)=>happy(X)))&
(?[X]:(room(X)&(((happy(X))|(~(wise(X)&person(X)))|(wise(X)&person(X))))))&
(((happy(jean)&person(jean))|(~(wise(jean)&happy(jean)&person(jean)))|(calm(jean)&person(jean))))&
(does_not_enjoy_skydiving(jean))&
(~(does_not_collect_modern_art(alex)))&
((![X]:((happy(X)&wise(X)&person(X))=>(happy(X)&person(X)))))&
(wise(jean))&
(~(happy(alex)))&
(![X]:(happy(X)=>wise(X))) | room(alex)&room(jean)&(![X]:(room(X)=>(X='alex'|X='jean')))&
calm(alex) | [] | null | 0.527627 |
Dolores, Douglas are the only persons in the room.
“Douglas does enjoy mountain biking” only if “if someone bakes bread at home or does not collect luxury watches or both then he/she does not write poetry or uses contact lenses or both”. | It is true that “Douglas enjoys cross-country skiing”. | neutral | room(dolores)&room(douglas)&(![X]:(room(X)=>(X='dolores'|X='douglas')))&
((does_enjoy_mountain_biking(douglas))=>((![X]:((((bakes_bread_at_home(X))|(does_not_collect_luxury_watches(X))))=>(((does_not_write_poetry(X))|(uses_contact_lenses(X))))))))&
((~((collects_luxury_watches(douglas))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(douglas))))<~>(((writes_poetry(dolores))|(is_not_passionate_about_collecting_and_restoring_classic_cars(dolores)))))&
((((is_not_a_certified_yoga_instructor_teaching_classes_weekly(dolores))&(does_not_bake_bread_at_home(dolores))))=>(is_not_passionate_about_collecting_and_restoring_classic_cars(dolores)))&
((((is_passionate_about_collecting_and_restoring_classic_cars(dolores))&(does_not_create_augmented_reality_experiences_for_mobile_applications(dolores))))<~>(((is_passionate_about_collecting_and_restoring_classic_cars(douglas))&(does_not_write_poetry(douglas)))))&
((((does_not_enjoy_mountain_biking(dolores))|(does_not_have_a_tattoo(dolores))))<=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(dolores)))&
(does_not_have_a_tattoo(douglas))&
(is_not_a_certified_yoga_instructor_teaching_classes_weekly(dolores))&
(collects_luxury_watches(douglas))&
((![X]:((((bakes_bread_at_home(X))|(does_not_collect_luxury_watches(X))))=>(((does_not_write_poetry(X))|(uses_contact_lenses(X)))))))&
(collects_first_edition_books(douglas))&
(is_a_client_of_Costco(dolores))&
(~((does_not_enjoy_cross-country_skiing(dolores))|(uses_contact_lenses(dolores))))&
(does_not_practice_zumba(douglas))&
(does_not_write_poetry(dolores))&
(~((does_not_volunteer_for_local_environmental_conservation_projects(dolores))|(does_not_bake_bread_at_home(dolores))))&
(((does_not_enjoy_landscape_photography(dolores))<~>(collects_luxury_watches(dolores))))&
(~((does_not_practice_zumba(dolores))|(does_not_collect_luxury_watches(dolores))))&
(does_not_enjoy_mountain_biking(dolores))&
(does_not_use_contact_lenses(douglas))&
(enjoys_landscape_photography(dolores))&
(~((does_not_create_augmented_reality_experiences_for_mobile_applications(douglas))|(does_not_bake_bread_at_home(douglas))))&
(is_not_a_client_of_Costco(douglas))&
(((is_passionate_about_collecting_and_restoring_classic_cars(dolores))<~>(does_not_collect_first_edition_books(dolores)))) | room(dolores)&room(douglas)&(![X]:(room(X)=>(X='dolores'|X='douglas')))&
enjoys_cross-country_skiing(douglas) | [] | null | 0.478572 |
Wallace, Hector, Louis, Charles are the only persons in the room.
All quiet persons are kind.
Someone in the room is calm.
Someone in the room is strong.
All generous persons are quiet.
All strong persons are generous. | Everyone in the room is not quiet. | contradiction | room(wallace)&room(hector)&room(louis)&room(charles)&(![X]:(room(X)=>(X='wallace'|X='hector'|X='louis'|X='charles')))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:(room(X)&(calm(X))))&
((?[X,Y]:(room(X)&room(Y)&(funny(X)&funny(Y))&(X!=Y))))&
(![X]:(old(X)=>happy(X)))&
(![X]:(funny(X)=>creative(X)))&
(?[X]:(room(X)&(~humble(X))))&
(![X]:(creative(X)=>funny(X)))&
(?[X]:(room(X)&(strong(X))))&
(![X]:(brave(X)=>quiet(X)))&
(![X]:(humble(X)=>happy(X)))&
(![X]:(happy(X)=>funny(X)))&
(((?[X]:(room(X)&kind(X)))&(![X,Y]:((room(X)&room(Y)&(kind(X))&(kind(Y)))=>(X=Y)))))&
(((?[X]:(room(X)&strong(X)))&(![X,Y]:((room(X)&room(Y)&(strong(X))&(strong(Y)))=>(X=Y)))))&
((?[X,Y]:(room(X)&room(Y)&(calm(X)&calm(Y))&(X!=Y))))&
(((?[X]:(room(X)&wise(X)))&(![X,Y]:((room(X)&room(Y)&(wise(X))&(wise(Y)))=>(X=Y)))))&
(![X]:(generous(X)=>quiet(X)))&
(![X]:(kind(X)=>wise(X)))&
(?[X]:(room(X)&(~~~tall(X))))&
(![X]:(tall(X)=>funny(X)))&
(?[X]:(room(X)&(~creative(X)&~happy(X)&~brave(X)&~tall(X)&~wise(X)&~patient(X))))&
(?[X]:(room(X)&(tall(X))))&
(![X]:(strong(X)=>generous(X)))&
(?[X]:(room(X)&(brave(X))))&
(?[X]:(room(X)&(~strong(X))))&
(![X]:(humble(X)=>generous(X))) | room(wallace)&room(hector)&room(louis)&room(charles)&(![X]:(room(X)=>(X='wallace'|X='hector'|X='louis'|X='charles')))&
![X]:(room(X)=>(~quiet(X))) | [
"p8",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2377145106966414411260004
% SZS output start Proof for 2377145106966414411260004
52. ? [X0] : (strong(X0) & room(X0)) [input p8]
60. ! [X0] : (generous(X0) => quiet(X0)) [input p16]
66. ! [X0] : (strong(X0) => generous(X0)) [input p22]
70. ! [X0] : (room(X0) => ~quiet(X0)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
74. ! [X0] : (room(X0) => ~quiet(X0)) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 70]
167. ! [X0] : (quiet(X0) | ~generous(X0)) [ennf transformation 60]
170. ! [X0] : (generous(X0) | ~strong(X0)) [ennf transformation 66]
171. ! [X0] : (~quiet(X0) | ~room(X0)) & ! [X1] : ((alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 74]
172. ! [X0] : (~quiet(X0) | ~room(X0)) & ! [X1] : (alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 171]
180. ? [X0] : (strong(X0) & room(X0)) => (strong(sK4) & room(sK4)) [choice axiom]
181. strong(sK4) & room(sK4) [skolemisation 52,180]
296. room(sK4) [cnf transformation 181]
297. strong(sK4) [cnf transformation 181]
312. ~generous(X0) | quiet(X0) [cnf transformation 167]
325. ~strong(X0) | generous(X0) [cnf transformation 170]
335. ~room(X0) | ~quiet(X0) [cnf transformation 172]
346. generous(sK4) [resolution 325,297]
348. quiet(sK4) [resolution 346,312]
357. ~quiet(sK4) [resolution 335,296]
368. $false [subsumption resolution 357,348]
% SZS output end Proof for 2377145106966414411260004
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.558027 |
Charles, Dora, Paula are the only persons in the room.
"Dora is quiet" only if "everyone outside the room is old and is not a quiet person if and only if they is old".
It is true that "Paula is old".
All old persons are quiet.
Everyone outside the room is old and is not a quiet person if and only if they is old.
Dora is not a quiet old person.
Everyone in the room is not a old quiet person if they is not a old person.
Charles is not not not not quiet.
Charles is a quiet person.
Paula is quiet.
Everyone in the room is quiet if and only if they is not a old person and is quiet. | Dora is old. | neutral | room(charles)&room(dora)&room(paula)&(![X]:(room(X)=>(X='charles'|X='dora'|X='paula')))&
((quiet(dora))=>(![X]:(~room(X)=>(((((old(X))&(~(quiet(X)&person(X)))))<=>(old(X)))))))&
(old(paula))&
(![X]:(old(X)=>quiet(X)))&
(![X]:(~room(X)=>(((((old(X))&(~(quiet(X)&person(X)))))<=>(old(X))))))&
(~(quiet(dora)&old(dora)&person(dora)))&
(![X]:(room(X)=>(((~(old(X)&person(X)))=>(~(old(X)&quiet(X)&person(X)))))))&
(~~~~quiet(charles))&
(quiet(charles)&person(charles))&
(quiet(paula))&
(![X]:(room(X)=>(((quiet(X))<=>(((~(old(X)&person(X)))&(quiet(X)))))))) | room(charles)&room(dora)&room(paula)&(![X]:(room(X)=>(X='charles'|X='dora'|X='paula')))&
old(dora) | [] | null | 0.334977 |
Terri, Mark, Joseph, Valeria are the only persons in the room.
"Terri does not collect first edition books" unless "Joseph is a client of Costco".
Everyone anywhere plays eSports competitively if they builds model airplanes and vice versa.
Mark who is a dedicated volunteer for local community service projects is not a coffee connoisseur.
Mark collects rare and antique scientific instruments.
If someone owns a 3D printer then he/she own a television.
Everyone in the room is not a client of Meta if they is a client of Meta.
Everyone in the room collects first edition books, is not a client of Costco or is a client of Costco if they is not a client of Meta. | Mark is a client of Meta. | contradiction | room(terri)&room(mark)&room(joseph)&room(valeria)&(![X]:(room(X)=>(X='terri'|X='mark'|X='joseph'|X='valeria')))&
(~(is_a_client_of_Costco(joseph))=>(does_not_collect_first_edition_books(terri)))&
(![X]:(anywhere(X)=>(((plays_eSports_competitively(X))<=>(builds_model_airplanes(X))))))&
((is_a_dedicated_volunteer_for_local_community_service_projects(mark))&(is_not_a_coffee_connoisseur(mark)))&
(collects_rare_and_antique_scientific_instruments(mark))&
((![X]:((owns_a_3D_printer(X))=>(own_a_television(X)))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(is_not_a_client_of_Meta(X))))))&
(![X]:(room(X)=>(((is_not_a_client_of_Meta(X))=>(((collects_first_edition_books(X))|(is_not_a_client_of_Costco(X))|(is_a_client_of_Costco(X))))))))&
((![X]:((((is_a_Linux_enthusiast(X))|(cannot_play_the_harmonica(X))|(plays_the_drums(X))))=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))&
(~(((regularly_contributes_to_tech_forums_and_online_communities(joseph))|(plays_eSports_competitively(joseph))|(collects_rare_and_antique_scientific_instruments(joseph)))))&
(![X]:(anywhere(X)=>(((~((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(is_a_coffee_connoisseur(X))))=>(((does_not_own_a_television(X))<~>(develops_open-source_software_projects_in_their_free_time(X))))))))&
(?[X]:(room(X)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))&
(builds_model_airplanes(terri))&
(is_a_client_of_Costco(joseph))&
(![X]:(room(X)=>(((plays_eSports_competitively(X))<=(enjoys_snowboarding(X))))))&
(![X]:(room(X)=>(((does_not_build_model_airplanes(X))=>(can_play_the_harmonica(X)))))) | room(terri)&room(mark)&room(joseph)&room(valeria)&(![X]:(room(X)=>(X='terri'|X='mark'|X='joseph'|X='valeria')))&
is_a_client_of_Meta(mark) | [
"p0",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7226557732648629916638555
% SZS output start Proof for 7226557732648629916638555
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
50. ! [X0] : (room(X0) => (predc(X0) => ~predc(X0))) [input p6]
60. predc(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
143. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
144. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 143]
147. ! [X0] : ((~predc(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 50]
148. ! [X0] : (~predc(X0) | ~predc(X0) | ~room(X0)) [flattening 147]
152. predc(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 60]
153. predc(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 152]
240. room(paul) [cnf transformation 144]
248. ~predc(X0) | ~predc(X0) | ~room(X0) [cnf transformation 148]
260. predc(paul) [cnf transformation 153]
261. ~predc(X0) | ~room(X0) [duplicate literal removal 248]
274. ~room(paul) [resolution 261,260]
275. $false [subsumption resolution 274,240]
% SZS output end Proof for 7226557732648629916638555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
There is a room.
More than one person in the room is a calm generous person or is not not not not not humble or both.
No calm person is happy.
Everyone in the room who is humble is not a generous happy humble person, is a humble happy person and is a generous person.
Everyone in the room who is a generous person is calm.
Everyone in the room is a humble person if they is a happy generous person and vice versa. | Everyone in the room is a happy person. | contradiction | (there_is_a_room)&
((?[X,Y]:(room(X)&room(Y)&(((calm(X)&generous(X)&person(X))|(~~~~~humble(X)))&((calm(Y)&generous(Y)&person(Y))|(~~~~~humble(Y))))&(X!=Y))))&
(~?[X]:(calm(X)=>happy(X)))&
(![X]:(room(X)=>(((humble(X))=>(((~(generous(X)&happy(X)&humble(X)&person(X)))&(humble(X)&happy(X)&person(X))&(generous(X)&person(X))))))))&
(![X]:(room(X)=>(((generous(X)&person(X))=>(calm(X))))))&
(![X]:(room(X)=>(((humble(X)&person(X))<=>(happy(X)&generous(X)&person(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(happy(X)&person(X))) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1085760595364262775676205
% SZS output start Proof for 1085760595364262775676205
45. ? [X0,X1] : (X0 != X1 & (~humble(X1) | (person(X1) & generous(X1) & calm(X1))) & (~humble(X0) | (person(X0) & generous(X0) & calm(X0))) & room(X1) & room(X0)) [input p1]
46. ~? [X0] : (calm(X0) => happy(X0)) [input p2]
50. ! [X0] : (room(X0) => (person(X0) & happy(X0))) & there_is_a_room [input hypothesis]
52. ~? [X0] : happy(X0) [pure predicate removal 46]
53. ? [X0,X1] : (X0 != X1 & (~humble(X1) | (person(X1) & generous(X1))) & (~humble(X0) | (person(X0) & generous(X0))) & room(X1) & room(X0)) [pure predicate removal 45]
54. ! [X0] : (room(X0) => (person(X0) & happy(X0))) [pure predicate removal 50]
128. ! [X0] : ~happy(X0) [ennf transformation 52]
132. ! [X0] : ((person(X0) & happy(X0)) | ~room(X0)) [ennf transformation 54]
134. ? [X0,X1] : (X0 != X1 & (~humble(X1) | (person(X1) & generous(X1))) & (~humble(X0) | (person(X0) & generous(X0))) & room(X1) & room(X0)) => (sK0 != sK1 & (~humble(sK1) | (person(sK1) & generous(sK1))) & (~humble(sK0) | (person(sK0) & generous(sK0))) & room(sK1) & room(sK0)) [choice axiom]
135. sK0 != sK1 & (~humble(sK1) | (person(sK1) & generous(sK1))) & (~humble(sK0) | (person(sK0) & generous(sK0))) & room(sK1) & room(sK0) [skolemisation 53,134]
219. room(sK1) [cnf transformation 135]
225. ~happy(X0) [cnf transformation 128]
237. happy(X0) | ~room(X0) [cnf transformation 132]
269. ~room(X0) [subsumption resolution 237,225]
271. $false [resolution 269,219]
% SZS output end Proof for 1085760595364262775676205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.002714 |
Cory is the only person in the room.
If "someone in the room makes intricate hand-cut paper art for exhibitions" then "if someone participates in long-distance cycling events across the country then he/she does not travel domestically frequently and vice versa".
If "everyone in the room is a dedicated volunteer for local community service projects or is not a tea enthusiast" then "more than one person in the room is a dedicated volunteer for local community service projects".
If "everyone in the room creates large-scale murals for public art installations or is not a dedicated volunteer for local community service projects" then "everyone anywhere does not enjoy kayaking or is not a night owl".
Everyone anywhere does not enjoy kayaking or is not a night owl.
Cory enjoys deep-sea diving and exploring underwater caves.
Cory can play the piano.
Cory writes poetry.
Everyone anywhere who is an avid mountain climber who has scaled several peaks does not make intricate hand-cut paper art for exhibitions.
Everyone outside the room is not a client of LVMH if they does not make intricate hand-cut paper art for exhibitions.
Everyone in the room who does not own a television enjoys kayaking and is a Linux enthusiast.
Cory does not make intricate hand-cut paper art for exhibitions.
Only one person in the room is a client of LVMH.
Everyone in the room who is a client of LVMH creates large-scale murals for public art installations.
More than one person outside the room is a client of LVMH.
Everyone in the room is a night owl.
Not everyone in the room who has a tattoo is an enthusiastic bird watcher who travels for rare sightings.
More than one person outside the room is not a tea enthusiast.
Everyone in the room owns a significant collection of rare gemstones and minerals if they own a television.
If someone is an avid hiker then he/she makes intricate hand-cut paper art for exhibitions.
Someone outside the room writes poetry. | Cory owns a significant collection of rare gemstones and minerals. | entailment | room(cory)&(![X]:(room(X)=>(X='cory')))&
((?[X]:(room(X)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))=>((![X]:((participates_in_long-distance_cycling_events_across_the_country(X))<=>(does_not_travel_domestically_frequently(X))))))&
((![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))=>((?[X,Y]:(room(X)&room(Y)&(is_a_dedicated_volunteer_for_local_community_service_projects(X)&is_a_dedicated_volunteer_for_local_community_service_projects(Y))&(X!=Y)))))&
((![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(creates_large-scale_murals_for_public_art_installations(X))))))=>(![X]:(anywhere(X)=>(((is_not_a_night_owl(X))|(does_not_enjoy_kayaking(X)))))))&
(![X]:(anywhere(X)=>(((is_not_a_night_owl(X))|(does_not_enjoy_kayaking(X))))))&
(enjoys_deep-sea_diving_and_exploring_underwater_caves(cory))&
(can_play_the_piano(cory))&
(writes_poetry(cory))&
(![X]:(anywhere(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))&
(![X]:(~room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))=>(is_not_a_client_of_LVMH(X))))))&
(![X]:(room(X)=>(((does_not_own_a_television(X))=>(((enjoys_kayaking(X))&(is_a_Linux_enthusiast(X))))))))&
(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(cory))&
(((?[X]:(room(X)&is_a_client_of_LVMH(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_client_of_LVMH(X))&(is_a_client_of_LVMH(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))&
((?[X,Y]:(~room(X)&~room(Y)&(is_a_client_of_LVMH(X)&is_a_client_of_LVMH(Y))&(X!=Y))))&
(![X]:(room(X)=>(is_a_night_owl(X))))&
(~![X]:(room(X)=>(((has_a_tattoo(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
((?[X,Y]:(~room(X)&~room(Y)&(is_not_a_tea_enthusiast(X)&is_not_a_tea_enthusiast(Y))&(X!=Y))))&
(![X]:(room(X)=>(((own_a_television(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
((![X]:((is_an_avid_hiker(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))&
(?[X]:(~room(X)&(writes_poetry(X)))) | room(cory)&(![X]:(room(X)=>(X='cory')))&
owns_a_significant_collection_of_rare_gemstones_and_minerals(cory) | [
"b4",
"p0",
"p4",
"p10",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7462487467451997544763034
% SZS output start Proof for 7462487467451997544763034
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
48. ! [X0] : (anywhere(X0) => (~predt(X0) | ~predd(X0))) [input p4]
54. ! [X0] : (room(X0) => (~predc(X0) => (predk(X0) & predt(X0)))) [input p10]
59. ! [X0] : (room(X0) => predd(X0)) [input p15]
62. ! [X0] : (room(X0) => (predc(X0) => predb(X0))) [input p18]
65. ~(predb(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
73. ! [X0] : (room(X0) => (~predc(X0) => predt(X0))) [pure predicate removal 54]
150. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
156. ! [X0] : ((~predt(X0) | ~predd(X0)) | ~anywhere(X0)) [ennf transformation 48]
157. ! [X0] : (~predt(X0) | ~predd(X0) | ~anywhere(X0)) [flattening 156]
160. ! [X0] : ((predt(X0) | predc(X0)) | ~room(X0)) [ennf transformation 73]
161. ! [X0] : (predt(X0) | predc(X0) | ~room(X0)) [flattening 160]
166. ! [X0] : (predd(X0) | ~room(X0)) [ennf transformation 59]
168. ! [X0] : ((predb(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 62]
169. ! [X0] : (predb(X0) | ~predc(X0) | ~room(X0)) [flattening 168]
170. ~predb(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 65]
195. ? [X0] : (mary != X0 & room(X0)) => (mary != sK12 & room(sK12)) [choice axiom]
196. ~predb(mary) | (mary != sK12 & room(sK12)) | ~room(mary) [skolemisation 170,195]
197. anywhere(X0) [cnf transformation 5]
278. room(mary) [cnf transformation 150]
279. ~room(X0) | mary = X0 [cnf transformation 150]
293. ~predt(X0) | ~predd(X0) | ~anywhere(X0) [cnf transformation 157]
295. ~room(X0) | predc(X0) | predt(X0) [cnf transformation 161]
306. ~room(X0) | predd(X0) [cnf transformation 166]
313. ~predc(X0) | predb(X0) | ~room(X0) [cnf transformation 169]
315. ~predb(mary) | room(sK12) | ~room(mary) [cnf transformation 196]
316. ~predb(mary) | mary != sK12 | ~room(mary) [cnf transformation 196]
378. 14 <=> ! [X0] : (~predt(X0) | ~predd(X0)) [avatar definition]
379. ~predt(X0) | ~predd(X0) <- (14) [avatar component clause 378]
393. ~predt(X0) | ~predd(X0) [subsumption resolution 293,197]
394. 14 [avatar split clause 393,378]
395. ~predb(mary) | mary != sK12 [subsumption resolution 316,278]
397. 17 <=> mary = sK12 [avatar definition]
399. mary != sK12 <- (~17) [avatar component clause 397]
401. 18 <=> predb(mary) [avatar definition]
404. ~17 | ~18 [avatar split clause 395,401,397]
405. ~predb(mary) | room(sK12) [subsumption resolution 315,278]
407. 19 <=> room(sK12) [avatar definition]
409. room(sK12) <- (19) [avatar component clause 407]
410. 19 | ~18 [avatar split clause 405,401,407]
411. predd(mary) [resolution 306,278]
447. predc(mary) | predt(mary) [resolution 295,278]
449. 20 <=> predt(mary) [avatar definition]
451. predt(mary) <- (20) [avatar component clause 449]
453. 21 <=> predc(mary) [avatar definition]
455. predc(mary) <- (21) [avatar component clause 453]
456. 20 | 21 [avatar split clause 447,453,449]
461. ~predd(mary) <- (14, 20) [resolution 451,379]
462. $false <- (14, 20) [subsumption resolution 461,411]
463. ~14 | ~20 [avatar contradiction clause 462]
464. predb(mary) | ~room(mary) <- (21) [resolution 455,313]
468. predb(mary) <- (21) [subsumption resolution 464,278]
469. 18 | ~21 [avatar split clause 468,453,401]
471. mary = sK12 <- (19) [resolution 409,279]
482. $false <- (~17, 19) [subsumption resolution 471,399]
483. 17 | ~19 [avatar contradiction clause 482]
484. $false [avatar sat refutation 394,404,410,456,463,469,483]
% SZS output end Proof for 7462487467451997544763034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.009717 |
Marsha is the only person in the room.
Everyone anywhere who frequently participates in hackathons and coding competitions bakes bread at home.
No one anywhere practices pilates if they writes and illustrates their own graphic novels.
Everyone in the room is a member of a local theater group specializing in improv if and only if they practices pilates. | Marsha is a member of a local theater group specializing in improv. | contradiction | room(marsha)&(![X]:(room(X)=>(X='marsha')))&
(![X]:(anywhere(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(bakes_bread_at_home(X))))))&
(![X]:(room(X)=>(((plays_the_violin(X))=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(writes_and_illustrates_their_own_graphic_novels(X))|(plays_the_violin(X))))))))&
(~?[X]:(anywhere(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(practices_pilates(X))))))&
((uses_an_ios_phone(marsha))&(has_a_curated_collection_of_mid-century_modern_furniture(marsha)))&
(![X]:(room(X)=>(((plays_the_violin(X))=>(enjoys_watercolor_painting(X))))))&
(![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
(![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<=>(practices_pilates(X))))))&
(![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(bakes_bread_at_home(X))))))&
(![X]:(~room(X)=>(is_a_cybersecurity_expert(X))))&
(![X]:(room(X)=>(((practices_pilates(X))=>(does_not_enjoy_making_ceramics(X))))))&
(![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(plays_the_drums(X))))))&
((plays_the_drums(marsha))&(reads_mystery_novels(marsha))) | room(marsha)&(![X]:(room(X)=>(X='marsha')))&
is_a_member_of_a_local_theater_group_specializing_in_improv(marsha) | [
"p0",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 231230107390629100021478
% SZS output start Proof for 231230107390629100021478
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
47. ~? [X0] : (anywhere(X0) => (predb(X0) => predg(X0))) [input p3]
51. ! [X0] : (room(X0) => (predd(X0) <=> predg(X0))) [input p7]
58. predd(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
68. ~? [X0] : (anywhere(X0) => predg(X0)) [pure predicate removal 47]
73. ~? [X0] : predg(X0) [pure predicate removal 68]
146. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
147. ! [X0] : ~predg(X0) [ennf transformation 73]
148. ! [X0] : ((predd(X0) <=> predg(X0)) | ~room(X0)) [ennf transformation 51]
149. predd(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 58]
151. ! [X0] : (((predd(X0) | ~predg(X0)) & (predg(X0) | ~predd(X0))) | ~room(X0)) [nnf transformation 148]
232. room(mary) [cnf transformation 146]
234. ~predg(X0) [cnf transformation 147]
235. predg(X0) | ~predd(X0) | ~room(X0) [cnf transformation 151]
239. predd(mary) [cnf transformation 149]
240. ~predd(X0) | ~room(X0) [subsumption resolution 235,234]
241. ~room(mary) [resolution 240,239]
242. $false [subsumption resolution 241,232]
% SZS output end Proof for 231230107390629100021478
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0.000259 |
Juan, Teresa, Robert, Della are the only persons in the room. If 'at least one person in the room does not make intricate hand-cut paper art for exhibitions' then 'someone in the room does not enjoy cross-country skiing'. If 'someone in the room does not enjoy cross-country skiing' then 'someone in the room does not host a popular podcast about emerging technologies or does not have lived in exactly three countries or both'. | Everyone outside the room either does not create bespoke furniture pieces from reclaimed wood or does not make intricate hand-cut paper art for exhibitions but not both. | neutral | room(juan)&room(teresa)&room(robert)&room(della)&(![X]:(room(X)=>(X='juan'|X='teresa'|X='robert'|X='della')))&
(((((?[X]:(room(X)&does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X)))))=>(?[X]:(room(X)&(does_not_enjoy_cross-country_skiing(X)))))&
((?[X]:(room(X)&(does_not_enjoy_cross-country_skiing(X))))=>(?[X]:(room(X)&(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(does_not_have_lived_in_exactly_three_countries(X))))))))&
(?[X]:(room(X)&(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))&
(?[X]:(room(X)&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))&
(?[X]:(room(X)&(does_not_enjoy_cross-country_skiing(X))))&
(?[X]:(anywhere(X)&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))&
(?[X]:(anywhere(X)&(((does_not_own_a_telescope(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
((![X]:((does_not_practice_archery(X))<=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(does_not_enjoy_cross-country_skiing(X)))))))&
(?[X]:(~room(X)&(does_not_collect_rare_sneakers(X))))&
(((?[X]:(room(X)&does_not_enjoy_landscape_photography(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_enjoy_landscape_photography(X))&(does_not_enjoy_landscape_photography(Y)))=>(X=Y)))))&
(?[X]:(room(X)&(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(does_not_have_lived_in_exactly_three_countries(X))))))&
(?[X]:(room(X)&(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))&
(((?[X]:(room(X)&is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))&
(((?[X]:(room(X)&does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(Y)))=>(X=Y)))))&
(((?[X]:(room(X)&is_not_an_active_member_of_a_local_robotics_club(X)))&(![X,Y]:((room(X)&room(Y)&(is_not_an_active_member_of_a_local_robotics_club(X))&(is_not_an_active_member_of_a_local_robotics_club(Y)))=>(X=Y)))))&
(?[X]:(room(X)&(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))&
((![X]:((does_not_train_for_and_competes_in_international_triathlons(X))<=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X)))))&
(((?[X]:(room(X)&does_not_train_for_and_competes_in_international_triathlons(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_train_for_and_competes_in_international_triathlons(X))&(does_not_train_for_and_competes_in_international_triathlons(Y)))=>(X=Y)))))&
(?[X]:(room(X)&(does_not_drive_a_hybrid_car(X))))&
(((?[X]:(room(X)&is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))&(![X,Y]:((room(X)&room(Y)&(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))&(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(Y)))=>(X=Y)))))&
(((?[X]:(room(X)&does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))&
((![X]:((does_not_drive_a_hybrid_car(X))<=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))&
(?[X]:(room(X)&(((does_not_drive_a_hybrid_car(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))&
(?[X]:(room(X)&(does_not_have_lived_in_exactly_three_countries(X))))&
(((?[X]:(room(X)&does_not_drive_a_hybrid_car(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_drive_a_hybrid_car(X))&(does_not_drive_a_hybrid_car(Y)))=>(X=Y)))))&
((![X]:((does_not_have_lived_in_exactly_three_countries(X))<=>(((does_not_collect_classic_novels(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))))&
((![X]:((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))<=>(does_not_have_a_tattoo(X)))))&
(((?[X]:(room(X)&does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X)))))&
((![X]:((((does_not_have_lived_in_exactly_three_countries(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))<=>(((is_not_an_active_member_of_a_local_robotics_club(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))&
((![X]:((((does_not_own_a_telescope(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))<=>(does_not_own_a_telescope(X)))))&
(((?[X]:(anywhere(X)&does_not_own_a_telescope(X))))) | room(juan)&room(teresa)&room(robert)&room(della)&(![X]:(room(X)=>(X='juan'|X='teresa'|X='robert'|X='della')))&
![X]:(~room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))<~>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))) | [] | null | 0.548183 |
Linda is the only person in the room.
If “Linda practices archery” then “Linda enjoys bird watching”.
If “Linda does not mentor a youth basketball team on weekends” then “not everyone outside the room who is a tea enthusiast enjoys watercolor painting”.
If “Linda does not host regular game nights featuring complex strategy games” then “more than one person outside the room is a skilled home brewer experimenting with craft beer recipes” otherwise “no one in the room who does not enjoy bird watching practices urban gardening”.
If “someone in the room travels domestically frequently” then “Linda is a tea enthusiast”. | Linda has a specialized collection of handmade artisan pottery. | neutral | room(linda)&(![X]:(room(X)=>(X='linda')))&
((practices_archery(linda))=>(enjoys_bird_watching(linda)))&
((does_not_mentor_a_youth_basketball_team_on_weekends(linda))=>(~![X]:(~room(X)=>(((is_a_tea_enthusiast(X))=>(enjoys_watercolor_painting(X)))))))&
(((does_not_host_regular_game_nights_featuring_complex_strategy_games(linda))=>((?[X,Y]:(~room(X)&~room(Y)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)&is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(Y))&(X!=Y)))))&((~(does_not_host_regular_game_nights_featuring_complex_strategy_games(linda)))=>(~?[X]:(room(X)=>(((does_not_enjoy_bird_watching(X))=>(practices_urban_gardening(X))))))))&
((?[X]:(room(X)&(travels_domestically_frequently(X))))=>(is_a_tea_enthusiast(linda)))&
(does_not_collect_limited-edition_art_prints_from_contemporary_artists(linda))&
(![X]:(anywhere(X)=>(((is_not_right-handed(X))=>(works_on_fridays(X))))))&
(~![X]:(room(X)=>(((works_on_fridays(X))=>(does_not_practice_urban_gardening(X))))))&
(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(linda))&
(![X]:(room(X)=>(((~((practices_archery(X))|(uses_contact_lenses(X))))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(enjoys_kayaking(X))))))&
(is_a_tea_enthusiast(linda))&
(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(linda))&
(~![X]:(anywhere(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))&
(does_not_enjoy_bird_watching(linda))&
(![X]:(room(X)=>(((enjoys_fishing(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(is_an_avid_hiker(linda))&
(![X]:(room(X)=>(((does_not_enjoy_kayaking(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))&
(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))&
(~?[X]:(anywhere(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(practices_archery(X))))))&
(uses_contact_lenses(linda))&
(enjoys_stand-up_paddleboarding(linda))&
(?[X]:(anywhere(X)&(works_on_fridays(X))))&
(is_a_coffee_connoisseur(linda))&
(![X]:(room(X)=>(((uses_contact_lenses(X))=>(enjoys_watercolor_painting(X)))))) | room(linda)&(![X]:(room(X)=>(X='linda')))&
has_a_specialized_collection_of_handmade_artisan_pottery(linda) | [] | null | 0.592851 |
Demetrius, Donna are the only persons in the room.
All strong persons are humble.
Someone in the room is happy.
Someone in the room is tall.
Everyone in the room is not a wise person.
Everyone in the room is a kind person.
Someone in the room is a kind person.
Everyone in the room is tall, is old or is not a old person.
Donna and Demetrius are generous.
All humble persons are creative.
Not everyone in the room is a wise person.
All humble persons are strong.
All quiet persons are patient.
Everyone in the room is not a humble person.
Demetrius and Donna are quiet persons. | All patient persons are humble. | contradiction | room(demetrius)&room(donna)&(![X]:(room(X)=>(X='demetrius'|X='donna')))&
(![X]:(strong(X)=>humble(X)))&
(?[X]:(room(X)&(happy(X))))&
(?[X]:(room(X)&(tall(X))))&
(![X]:(room(X)=>(~(wise(X)&person(X)))))&
(![X]:(room(X)=>(kind(X)&person(X))))&
(?[X]:(room(X)&(kind(X)&person(X))))&
(![X]:(room(X)=>(((tall(X))|(old(X))|(~(old(X)&person(X)))))))&
(generous(donna)&generous(demetrius))&
(![X]:(humble(X)=>creative(X)))&
(~![X]:(room(X)=>(wise(X)&person(X))))&
(![X]:(humble(X)=>strong(X)))&
(![X]:(calm(X)=>old(X)))&
(![X]:(quiet(X)=>patient(X)))&
(![X]:(~room(X)=>(~(kind(X)&person(X)))))&
(![X]:(room(X)=>(~(humble(X)&person(X)))))&
(![X]:(room(X)=>(((wise(X)&person(X))|(quiet(X))|(calm(X)&person(X))))))&
(quiet(demetrius)&person(demetrius)&quiet(donna)&person(donna)) | room(demetrius)&room(donna)&(![X]:(room(X)=>(X='demetrius'|X='donna')))&
![X]:(patient(X)=>humble(X)) | [
"p0",
"p5",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 377869144995074521479285
% SZS output start Proof for 377869144995074521479285
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
49. ! [X0] : (room(X0) => (person(X0) & kind(X0))) [input p5]
57. ! [X0] : (quiet(X0) => patient(X0)) [input p13]
59. ! [X0] : (room(X0) => ~(person(X0) & humble(X0))) [input p15]
61. person(paul) & quiet(paul) & person(mary) & quiet(mary) [input p17]
62. ! [X0] : (patient(X0) => humble(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
63. ! [X0] : (patient(X0) => humble(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 62]
141. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
142. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 141]
146. ! [X0] : ((person(X0) & kind(X0)) | ~room(X0)) [ennf transformation 49]
150. ! [X0] : (patient(X0) | ~quiet(X0)) [ennf transformation 57]
153. ! [X0] : ((~person(X0) | ~humble(X0)) | ~room(X0)) [ennf transformation 59]
154. ! [X0] : (~person(X0) | ~humble(X0) | ~room(X0)) [flattening 153]
157. ! [X0] : (humble(X0) | ~patient(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 63]
158. ! [X0] : (humble(X0) | ~patient(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 157]
248. room(mary) [cnf transformation 142]
256. ~room(X0) | person(X0) [cnf transformation 146]
264. ~quiet(X0) | patient(X0) [cnf transformation 150]
266. ~person(X0) | ~humble(X0) | ~room(X0) [cnf transformation 154]
271. quiet(mary) [cnf transformation 61]
278. ~patient(X0) | humble(X0) [cnf transformation 158]
289. ~humble(X0) | ~room(X0) [subsumption resolution 266,256]
303. patient(mary) [resolution 264,271]
368. humble(mary) [resolution 303,278]
370. ~room(mary) [resolution 368,289]
372. $false [subsumption resolution 370,248]
% SZS output end Proof for 377869144995074521479285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.262279 |
Omer, Christopher are the only persons in the room. “Everyone anywhere is happy” if “Christopher is not old” and vice versa. “Christopher is a strong person” only if “everyone in the room neither is a generous person nor is a happy person”. “Everyone in the room is a creative person” only if “not everyone in the room is a funny person”. “Christopher is strong” if “Omer is a generous person” and vice versa. Christopher is a funny person. All calm persons are kind. Everyone in the room is quiet if they is a kind person, is wise and is funny. Everyone in the room is a quiet person. Everyone in the room is a brave person. Someone outside the room is a creative person. It is not the case that “Christopher is a patient person”. Omer is the oldest in the room. At least one person in the room is a old person. It is not the case that “Christopher is calm”. All happy persons are humble. | Omer is kind. | neutral | room(omer)&room(christopher)&(![X]:(room(X)=>(X='omer'|X='christopher')))&
((~old(christopher))<=>(![X]:(anywhere(X)=>(happy(X)))))&
((strong(christopher)&person(christopher))=>(![X]:(room(X)=>(~((generous(X)&person(X))|(happy(X)&person(X)))))))&
((![X]:(room(X)=>(creative(X)&person(X))))=>(~![X]:(room(X)=>(funny(X)&person(X)))))&
((generous(omer)&person(omer))<=>(strong(christopher)))&
(funny(christopher)&person(christopher))&
(![X]:(calm(X)=>kind(X)))&
(![X]:(room(X)=>(((((kind(X)&person(X))&(wise(X))&(funny(X))))=>(quiet(X))))))&
(![X]:(room(X)=>(quiet(X)&person(X))))&
(![X]:(room(X)=>(brave(X)&person(X))))&
(?[X]:(~room(X)&(creative(X)&person(X))))&
(~(patient(christopher)&person(christopher)))&
(![X]:((room(X)&(X!=omer))=>older(X,omer)))&
(((?[X]:(room(X)&old(X)&person(X)))))&
(~(calm(christopher)))&
(![X]:(happy(X)=>humble(X)))&
(~(~(wise(christopher))))&
(![X]:(tall(X)=>old(X)))&
(![X]:((~room(X)&(X!=omer))=>older(X,omer)))&
(generous(christopher))&
(old(omer))&
(![X]:((anywhere(X)&(X!=omer))=>quieter(X,omer)))&
(![X]:(room(X)=>(tall(X))))&
(![X]:(room(X)=>(happy(X)&person(X))))&
(![X]:((room(X)&(X!=omer))=>richer(X,omer)))&
(~![X]:(room(X)=>(~(patient(X)&person(X))))) | room(omer)&room(christopher)&(![X]:(room(X)=>(X='omer'|X='christopher')))&
kind(omer) | [] | null | 0.129297 |
Jean, Laura are the only persons in the room. Laura is a Linux enthusiast. Everyone in the room plays as a goalkeeper for a local amateur soccer team if they has a specialized collection of handmade artisan pottery. Someone in the room enjoys writing detailed reviews of new and classic board games. Laura writes in-depth travel guides for off-the-beaten-path destinations. Jean has a specialized collection of handmade artisan pottery. Jean who plays as a goalkeeper for a local amateur soccer team has a specialized collection of handmade artisan pottery. Everyone in the room who either enjoys writing detailed reviews of new and classic board games or is a Linux enthusiast but not both neither does not make homemade pastries nor collects first edition books. Jean is not a Linux enthusiast. | Everyone in the room does not enjoy writing detailed reviews of new and classic board games. | contradiction | room(jean)&room(laura)&(![X]:(room(X)=>(X='jean'|X='laura')))&
(is_a_Linux_enthusiast(laura))&
(![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(?[X]:(room(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))&
(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(laura))&
(has_a_specialized_collection_of_handmade_artisan_pottery(jean))&
((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(jean))&(has_a_specialized_collection_of_handmade_artisan_pottery(jean)))&
(![X]:(room(X)=>(((((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<~>(is_a_Linux_enthusiast(X))))=>(~((does_not_make_homemade_pastries(X))|(collects_first_edition_books(X))))))))&
(is_not_a_Linux_enthusiast(jean))&
(![X]:(room(X)=>(((collects_antique_jewelry(X))=>(practices_kickboxing(X)))))) | room(jean)&room(laura)&(![X]:(room(X)=>(X='jean'|X='laura')))&
![X]:(room(X)=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 325165256353291076642694
% SZS output start Proof for 325165256353291076642694
47. ? [X0] : (predn(X0) & room(X0)) [input p3]
54. ! [X0] : (room(X0) => ~predn(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
55. ! [X0] : (room(X0) => ~predn(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 54]
138. ! [X0] : (~predn(X0) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 55]
139. ! [X0] : (~predn(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 138]
141. ? [X0] : (predn(X0) & room(X0)) => (predn(sK0) & room(sK0)) [choice axiom]
142. predn(sK0) & room(sK0) [skolemisation 47,141]
227. room(sK0) [cnf transformation 142]
228. predn(sK0) [cnf transformation 142]
233. ~predn(X0) | ~room(X0) [cnf transformation 139]
234. ~room(sK0) [resolution 233,228]
235. $false [subsumption resolution 234,227]
% SZS output end Proof for 325165256353291076642694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.010769 |
There is a room.
If 'everyone in the room practices kickboxing or does not host regular game nights featuring complex strategy games' then 'everyone in the room who practices kickboxing hosts regular game nights featuring complex strategy games'.
If 'someone in the room can play the flute' then 'everyone in the room hosts regular game nights featuring complex strategy games if they can play the flute'.
'Everyone outside the room cannot play the flute or participates in citizen science projects related to wildlife monitoring' only if 'someone in the room can play the flute'.
Everyone in the room who cannot play the flute practices kickboxing.
At least one person in the room participates in citizen science projects related to wildlife monitoring.
Everyone in the room can play the flute or does not participate in citizen science projects related to wildlife monitoring.
If someone participates in citizen science projects related to wildlife monitoring then he/she practices kickboxing. | Everyone outside the room hosts regular game nights featuring complex strategy games. | neutral | (there_is_a_room)&
((![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(practices_kickboxing(X))))))=>(![X]:(room(X)=>(((practices_kickboxing(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))&
((?[X]:(room(X)&(can_play_the_flute(X))))=>(![X]:(room(X)=>(((can_play_the_flute(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))&
((![X]:(~room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(cannot_play_the_flute(X))))))=>(?[X]:(room(X)&(can_play_the_flute(X)))))&
(![X]:(room(X)=>(((cannot_play_the_flute(X))=>(practices_kickboxing(X))))))&
(((?[X]:(room(X)&participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))&
(![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(can_play_the_flute(X))))))&
((![X]:((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(practices_kickboxing(X)))))&
((anthony_dream=>(![X]:(room(X)=>(((practices_kickboxing(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))&
(![X]:(room(X)=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))&
(![X]:(room(X)=>(((owns_a_3D_printer(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(~room(X)=>(practices_kickboxing(X)))) | (there_is_a_room)&
![X]:(~room(X)=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))) | [] | null | 0.18255 |
Terry, Robert, Thomas, Edwardo are the only persons in the room.
Terry is a wine connoisseur with a private cellar of vintage wines, enjoys stand-up paddleboarding and composes and performs experimental electronic music.
Everyone anywhere is a wine connoisseur with a private cellar of vintage wines if they can play the flute and is a wine connoisseur with a private cellar of vintage wines and vice versa.
Everyone in the room hosts a popular podcast about emerging technologies if they can play the flute and volunteers for local environmental conservation projects.
No one anywhere who enjoys watercolor painting hosts a popular podcast about emerging technologies.
If someone collects classic novels then he/she volunteers for local environmental conservation projects and vice versa. | Terry collects classic novels. | contradiction | room(terry)&room(robert)&room(thomas)&room(edwardo)&(![X]:(room(X)=>(X='terry'|X='robert'|X='thomas'|X='edwardo')))&
(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(terry))&(enjoys_stand-up_paddleboarding(terry))&(composes_and_performs_experimental_electronic_music(terry))))&
(![X]:(anywhere(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(((can_play_the_flute(X))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))))&
((![X]:((((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(is_a_scotch_connoisseur(X))&(does_not_collect_action_figures(X))))=>(collects_action_figures(X)))))&
(![X]:(room(X)=>(((((can_play_the_flute(X))&(volunteers_for_local_environmental_conservation_projects(X))))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(~room(X)=>(((drives_a_hybrid_car(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(enjoys_origami(terry))&
(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(terry))&
(?[X]:(room(X)&(collects_historical_artifacts_related_to_ancient_civilizations(X))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_enjoy_coding_in_Python(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))&
(![X]:(anywhere(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(((enjoys_cross-country_skiing(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))))&
(![X]:(room(X)=>(((((enjoys_cross-country_skiing(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))|(does_not_practice_tai_chi(X))))))&
(does_not_drive_a_hybrid_car(terry))&
(![X]:(~room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))=>(enjoys_watercolor_painting(X))))))&
(~?[X]:(anywhere(X)=>(((enjoys_watercolor_painting(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(~(hosts_regular_game_nights_featuring_complex_strategy_games(terry)))&
(![X]:(~room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))))&
(![X]:(~room(X)=>(((((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))&
(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(terry))&
(~(does_not_enjoy_coding_in_Python(terry)))&
((![X]:((collects_classic_novels(X))<=>(volunteers_for_local_environmental_conservation_projects(X)))))&
(![X]:(~room(X)=>(((collects_action_figures(X))<=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(practices_tai_chi(X))|(is_a_scotch_connoisseur(X)))))))) | room(terry)&room(robert)&room(thomas)&room(edwardo)&(![X]:(room(X)=>(X='terry'|X='robert'|X='thomas'|X='edwardo')))&
collects_classic_novels(terry) | [
"b4",
"p0",
"p1",
"p2",
"p4",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7323209111203112970237206
% SZS output start Proof for 7323209111203112970237206
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. prede(mary) & predr(mary) & predc(mary) [input p1]
46. ! [X0] : (anywhere(X0) => (predc(X0) <=> (predc(X0) & predg(X0)))) [input p2]
48. ! [X0] : (room(X0) => ((predi(X0) & predg(X0)) => predp(X0))) [input p4]
59. ~? [X0] : (anywhere(X0) => (predw(X0) => predp(X0))) [input p15]
65. ! [X0] : (predz(X0) <=> predi(X0)) [input p21]
67. predz(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
68. ! [X0] : (predz(X0) => predi(X0)) [unused predicate definition removal 65]
71. ~? [X0] : (anywhere(X0) => predp(X0)) [pure predicate removal 59]
85. predr(mary) & predc(mary) [pure predicate removal 45]
86. predc(mary) [pure predicate removal 85]
158. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
159. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 158]
160. ! [X0] : ((predc(X0) <=> (predc(X0) & predg(X0))) | ~anywhere(X0)) [ennf transformation 46]
161. ! [X0] : ((predp(X0) | (~predi(X0) | ~predg(X0))) | ~room(X0)) [ennf transformation 48]
162. ! [X0] : (predp(X0) | ~predi(X0) | ~predg(X0) | ~room(X0)) [flattening 161]
163. ! [X0] : (~predp(X0) & anywhere(X0)) [ennf transformation 71]
164. ! [X0] : (predi(X0) | ~predz(X0)) [ennf transformation 68]
166. predz(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 67]
167. predz(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 166]
169. ! [X0] : (((predc(X0) | (~predc(X0) | ~predg(X0))) & ((predc(X0) & predg(X0)) | ~predc(X0))) | ~anywhere(X0)) [nnf transformation 160]
170. ! [X0] : (((predc(X0) | ~predc(X0) | ~predg(X0)) & ((predc(X0) & predg(X0)) | ~predc(X0))) | ~anywhere(X0)) [flattening 169]
175. anywhere(X0) [cnf transformation 5]
256. room(mary) [cnf transformation 159]
261. predc(mary) [cnf transformation 86]
262. predg(X0) | ~predc(X0) | ~anywhere(X0) [cnf transformation 170]
265. ~predi(X0) | predp(X0) | ~predg(X0) | ~room(X0) [cnf transformation 162]
269. ~predp(X0) [cnf transformation 163]
270. ~predz(X0) | predi(X0) [cnf transformation 164]
280. predz(mary) [cnf transformation 167]
281. ~predc(X0) | predg(X0) [subsumption resolution 262,175]
282. predi(mary) [resolution 270,280]
283. predg(mary) [resolution 281,261]
284. predp(mary) | ~predg(mary) | ~room(mary) [resolution 265,282]
285. ~predg(mary) | ~room(mary) [subsumption resolution 284,269]
286. ~room(mary) [subsumption resolution 285,283]
287. $false [subsumption resolution 286,256]
% SZS output end Proof for 7323209111203112970237206
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Todd is the only person in the room.
It is not the case that more than one person in the room is a client of Costco.
It is not the case that it is not the case that more than one person anywhere makes intricate hand-cut paper art for exhibitions.
More than one person anywhere participates in long-distance cycling events across the country.
It is not the case that it is not the case that it is not the case that more than one person in the room is a client of Costco. | It is not the case that Todd is a client of Costco. | neutral | room(todd)&(![X]:(room(X)=>(X='todd')))&
(~((?[X,Y]:(room(X)&room(Y)&(is_a_client_of_Costco(X)&is_a_client_of_Costco(Y))&(X!=Y)))))&
(~(~((?[X,Y]:(anywhere(X)&anywhere(Y)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X)&makes_intricate_hand-cut_paper_art_for_exhibitions(Y))&(X!=Y))))))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(participates_in_long-distance_cycling_events_across_the_country(X)&participates_in_long-distance_cycling_events_across_the_country(Y))&(X!=Y))))&
(~(~(~((?[X,Y]:(room(X)&room(Y)&(is_a_client_of_Costco(X)&is_a_client_of_Costco(Y))&(X!=Y))))))) | room(todd)&(![X]:(room(X)=>(X='todd')))&
~(is_a_client_of_Costco(todd)) | [] | null | 0.699961 |
Angelo, Selma are the only persons in the room.
“Everyone in the room participates in citizen science projects related to wildlife monitoring” only if “everyone in the room is a skilled home brewer experimenting with craft beer recipes”.
Everyone anywhere enjoys wildlife photography.
Everyone in the room enjoys landscape photography and does not enjoy wildlife photography if they does not collect foreign coins. | It is true that “Angelo does not collect foreign coins”. | contradiction | room(angelo)&room(selma)&(![X]:(room(X)=>(X='angelo'|X='selma')))&
((![X]:(room(X)=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))=>(![X]:(room(X)=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))&
(![X]:(room(X)=>(does_not_enjoy_kayaking(X))))&
(![X]:(anywhere(X)=>(enjoys_wildlife_photography(X))))&
(![X]:(room(X)=>(((does_not_collect_foreign_coins(X))=>(((enjoys_landscape_photography(X))&(does_not_enjoy_wildlife_photography(X))))))))&
(![X]:(anywhere(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))&(does_not_collect_vintage_stamps(X))))))&
(![X]:(anywhere(X)=>(does_not_enjoy_windsurfing(X))))&
(![X]:(room(X)=>(((does_not_collect_antique_clocks(X))&(collects_foreign_coins(X))))))&
(?[X]:(room(X)&(does_not_collect_rare_sneakers(X))))&
(~![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X)))))) | room(angelo)&room(selma)&(![X]:(room(X)=>(X='angelo'|X='selma')))&
does_not_collect_foreign_coins(angelo) | [
"b4",
"p0",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6011746301599468644687232
% SZS output start Proof for 6011746301599468644687232
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
47. ! [X0] : (anywhere(X0) => preda(X0)) [input p3]
48. ! [X0] : (room(X0) => (~predk(X0) => (~preda(X0) & predy(X0)))) [input p4]
54. ~predk(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
63. ! [X0] : (room(X0) => (~predk(X0) => ~preda(X0))) [pure predicate removal 48]
137. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
138. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 137]
139. ! [X0] : (preda(X0) | ~anywhere(X0)) [ennf transformation 47]
140. ! [X0] : ((~preda(X0) | predk(X0)) | ~room(X0)) [ennf transformation 63]
141. ! [X0] : (~preda(X0) | predk(X0) | ~room(X0)) [flattening 140]
144. ~predk(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 54]
145. ~predk(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 144]
151. anywhere(X0) [cnf transformation 5]
232. room(mary) [cnf transformation 138]
235. preda(X0) | ~anywhere(X0) [cnf transformation 139]
236. ~preda(X0) | predk(X0) | ~room(X0) [cnf transformation 141]
243. ~predk(mary) [cnf transformation 145]
244. preda(X0) [subsumption resolution 235,151]
245. ~room(X0) | predk(X0) [subsumption resolution 236,244]
246. predk(mary) [resolution 245,232]
250. $false [subsumption resolution 246,243]
% SZS output end Proof for 6011746301599468644687232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0.232915 |
Jane, James, Forest, Keven, Clarence are the only persons in the room. “James collects antique jewelry” only if “Forest practices zumba”. If “not everyone in the room does not frequently participates in hackathons and coding competitions or does not use a Windows laptop” then “Keven does not use a Windows laptop”. Everyone in the room neither is allergic to anything nor is an enthusiastic bird watcher who travels for rare sightings if they does not frequently participates in hackathons and coding competitions. Everyone anywhere enjoys stargazing if they collects antique jewelry and practices calligraphy. Only one person in the room does not bake bread at home. Everyone anywhere who participates in citizen science projects related to wildlife monitoring is a scotch connoisseur. Everyone in the room does not practice zumba. Everyone anywhere collects historical artifacts related to ancient civilizations if they uses a Windows laptop. Jane frequently participates in hackathons and coding competitions. Everyone in the room collects historical artifacts related to ancient civilizations if they collects foreign coins. Everyone in the room enjoys windsurfing if they collects historical artifacts related to ancient civilizations. Keven enjoys kayaking. Everyone in the room who frequently participates in hackathons and coding competitions does enjoy mountain biking. Everyone in the room participates in citizen science projects related to wildlife monitoring if they is allergic to anything. Not everyone in the room uses a Windows laptop or does not bake bread at home. Everyone in the room who enjoys stargazing uses contact lenses. Not everyone in the room watches fantasy movies if they uses contact lenses. Clarence uses a Windows laptop. | Clarence enjoys windsurfing. | entailment | room(jane)&room(james)&room(forest)&room(keven)&room(clarence)&(![X]:(room(X)=>(X='jane'|X='james'|X='forest'|X='keven'|X='clarence')))&
((collects_antique_jewelry(james))=>(practices_zumba(forest)))&
((~![X]:(room(X)=>(((does_not_use_a_Windows_laptop(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(does_not_use_a_Windows_laptop(keven)))&
(![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))=>(~((is_allergic_to_anything(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))&
(![X]:(anywhere(X)=>(((((collects_antique_jewelry(X))&(practices_calligraphy(X))))=>(enjoys_stargazing(X))))))&
(((?[X]:(room(X)&does_not_bake_bread_at_home(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_bake_bread_at_home(X))&(does_not_bake_bread_at_home(Y)))=>(X=Y)))))&
(![X]:(anywhere(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(is_a_scotch_connoisseur(X))))))&
(![X]:(room(X)=>(does_not_practice_zumba(X))))&
(![X]:(anywhere(X)=>(((uses_a_Windows_laptop(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))&
(frequently_participates_in_hackathons_and_coding_competitions(jane))&
(![X]:(room(X)=>(((collects_foreign_coins(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))&
(![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(enjoys_windsurfing(X))))))&
(enjoys_kayaking(keven))&
(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(does_enjoy_mountain_biking(X))))))&
(![X]:(room(X)=>(((is_allergic_to_anything(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))&
(~![X]:(room(X)=>(((does_not_bake_bread_at_home(X))|(uses_a_Windows_laptop(X))))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))=>(uses_contact_lenses(X))))))&
(~![X]:(room(X)=>(((uses_contact_lenses(X))=>(watches_fantasy_movies(X))))))&
(![X]:(room(X)=>(((watches_fantasy_movies(X))=>(does_not_enjoy_windsurfing(X))))))&
(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))&
(uses_a_Windows_laptop(clarence))&
(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(jane))&
(is_a_Linux_enthusiast(forest))&
(((?[X]:(room(X)&participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))&(![X,Y]:((room(X)&room(Y)&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(Y)))=>(X=Y)))))&
(enjoys_stargazing(forest))&
(![X]:(room(X)=>(((is_a_scotch_connoisseur(X))<=>(collects_antique_jewelry(X)))))) | room(jane)&room(james)&room(forest)&room(keven)&room(clarence)&(![X]:(room(X)=>(X='jane'|X='james'|X='forest'|X='keven'|X='clarence')))&
enjoys_windsurfing(clarence) | [
"b4",
"p0",
"p8",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2417049115595123909545609
% SZS output start Proof for 2417049115595123909545609
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
52. ! [X0] : (anywhere(X0) => (predy(X0) => predp(X0))) [input p8]
55. ! [X0] : (room(X0) => (predp(X0) => predb(X0))) [input p11]
64. predy(john) [input p20]
70. ~(predb(john) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
159. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
160. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 159]
169. ! [X0] : ((predp(X0) | ~predy(X0)) | ~anywhere(X0)) [ennf transformation 52]
170. ! [X0] : (predp(X0) | ~predy(X0) | ~anywhere(X0)) [flattening 169]
171. ! [X0] : ((predb(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 55]
172. ! [X0] : (predb(X0) | ~predp(X0) | ~room(X0)) [flattening 171]
179. ~predb(john) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70]
180. ~predb(john) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 179]
191. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
192. ~predb(john) | (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 180,191]
193. anywhere(X0) [cnf transformation 5]
274. room(mary) [cnf transformation 160]
275. room(paul) [cnf transformation 160]
276. room(fred) [cnf transformation 160]
277. room(alice) [cnf transformation 160]
278. room(john) [cnf transformation 160]
279. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 160]
287. predp(X0) | ~predy(X0) | ~anywhere(X0) [cnf transformation 170]
289. ~predp(X0) | predb(X0) | ~room(X0) [cnf transformation 172]
294. predy(john) [cnf transformation 64]
300. ~predb(john) | room(sK4) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192]
301. ~predb(john) | mary != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192]
302. ~predb(john) | paul != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192]
303. ~predb(john) | fred != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192]
304. ~predb(john) | alice != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192]
305. ~predb(john) | john != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192]
324. ~predy(X0) | predp(X0) [subsumption resolution 287,193]
325. ~predb(john) | john != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,278]
326. ~predb(john) | john != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 325,277]
327. ~predb(john) | john != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 326,276]
328. ~predb(john) | john != sK4 | ~room(mary) [subsumption resolution 327,275]
329. ~predb(john) | john != sK4 [subsumption resolution 328,274]
331. 5 <=> john = sK4 [avatar definition]
333. john != sK4 <- (~5) [avatar component clause 331]
335. 6 <=> predb(john) [avatar definition]
338. ~5 | ~6 [avatar split clause 329,335,331]
339. ~predb(john) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,278]
340. ~predb(john) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 339,277]
341. ~predb(john) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 340,276]
342. ~predb(john) | alice != sK4 | ~room(mary) [subsumption resolution 341,275]
343. ~predb(john) | alice != sK4 [subsumption resolution 342,274]
345. 7 <=> alice = sK4 [avatar definition]
347. alice != sK4 <- (~7) [avatar component clause 345]
348. ~7 | ~6 [avatar split clause 343,335,345]
349. ~predb(john) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,278]
350. ~predb(john) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 349,277]
351. ~predb(john) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 350,276]
352. ~predb(john) | fred != sK4 | ~room(mary) [subsumption resolution 351,275]
353. ~predb(john) | fred != sK4 [subsumption resolution 352,274]
355. 8 <=> fred = sK4 [avatar definition]
357. fred != sK4 <- (~8) [avatar component clause 355]
358. ~8 | ~6 [avatar split clause 353,335,355]
359. ~predb(john) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,278]
360. ~predb(john) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 359,277]
361. ~predb(john) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 360,276]
362. ~predb(john) | paul != sK4 | ~room(mary) [subsumption resolution 361,275]
363. ~predb(john) | paul != sK4 [subsumption resolution 362,274]
365. 9 <=> paul = sK4 [avatar definition]
367. paul != sK4 <- (~9) [avatar component clause 365]
368. ~9 | ~6 [avatar split clause 363,335,365]
369. ~predb(john) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,278]
370. ~predb(john) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 369,277]
371. ~predb(john) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 370,276]
372. ~predb(john) | mary != sK4 | ~room(mary) [subsumption resolution 371,275]
373. ~predb(john) | mary != sK4 [subsumption resolution 372,274]
375. 10 <=> mary = sK4 [avatar definition]
377. mary != sK4 <- (~10) [avatar component clause 375]
378. ~10 | ~6 [avatar split clause 373,335,375]
379. ~predb(john) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 300,278]
380. ~predb(john) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 379,277]
381. ~predb(john) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 380,276]
382. ~predb(john) | room(sK4) | ~room(mary) [subsumption resolution 381,275]
383. ~predb(john) | room(sK4) [subsumption resolution 382,274]
385. 11 <=> room(sK4) [avatar definition]
387. room(sK4) <- (11) [avatar component clause 385]
388. 11 | ~6 [avatar split clause 383,335,385]
390. predp(john) [resolution 324,294]
391. predb(john) | ~room(john) [resolution 390,289]
395. predb(john) [subsumption resolution 391,278]
396. 6 [avatar split clause 395,335]
564. alice = sK4 | fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (11) [resolution 279,387]
641. fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (~7, 11) [subsumption resolution 564,347]
642. paul = sK4 | mary = sK4 | john = sK4 <- (~7, ~8, 11) [subsumption resolution 641,357]
643. mary = sK4 | john = sK4 <- (~7, ~8, ~9, 11) [subsumption resolution 642,367]
644. john = sK4 <- (~7, ~8, ~9, ~10, 11) [subsumption resolution 643,377]
645. $false <- (~5, ~7, ~8, ~9, ~10, 11) [subsumption resolution 644,333]
646. 5 | 7 | 8 | 9 | 10 | ~11 [avatar contradiction clause 645]
647. $false [avatar sat refutation 338,348,358,368,378,388,396,646]
% SZS output end Proof for 2417049115595123909545609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s
% ------------------------------
% ------------------------------
| 0.017125 |
Clinton, Quinton are the only persons in the room.
“Clinton and Quinton are richer than Burt” unless “Quinton is a quiet person”.
If “Quinton is a old quiet person” then “Quinton neither is richer than George nor is quiet” otherwise “everyone in the room is a quiet person if they is older than George and is not a quiet old person”.
Everyone in the room who is a old person is quieter than Burt.
Quinton and Clinton are respectively old and quiet.
Clinton and Quinton are not a old quiet persons.
Someone who is quieter than George is quieter than someone who is quieter than Burt.
Clinton is quieter than James.
Everyone in the room who is richer than James, is quieter than James and is old is richer than James.
Everyone in the room either is richer than Burt or is older than Burt but not both if and only if they is a old quiet person. | Quinton is richer than Burt. | entailment | room(clinton)&room(quinton)&(![X]:(room(X)=>(X='clinton'|X='quinton')))&
(~(quiet(quinton)&person(quinton))=>(richer(burt,clinton)&richer(burt,quinton)))&
(((old(quinton)&quiet(quinton)&person(quinton))=>(~((richer(george,quinton))|(quiet(quinton)))))&((~(old(quinton)&quiet(quinton)&person(quinton)))=>(![X]:(room(X)=>(((((older(george,X))&(~(quiet(X)&old(X)&person(X)))))=>(quiet(X)&person(X))))))))&
(![X]:(room(X)=>(((old(X)&person(X))=>(quieter(burt,X))))))&
((old(quinton))&(quiet(clinton)))&
(~(old(clinton)&quiet(clinton)&person(clinton))&~(old(quinton)&quiet(quinton)&person(quinton)))&
(?[X,Y]:((quieter(george,X))&(quieter(burt,Y))&(quieter(X,Y))))&
(quieter(james,clinton))&
(![X]:(room(X)=>(((((richer(james,X))&(quieter(james,X))&(old(X))))=>(richer(james,X))))))&
(![X]:(room(X)=>(((((richer(burt,X))<~>(older(burt,X))))<=>(old(X)&quiet(X)&person(X)))))) | room(clinton)&room(quinton)&(![X]:(room(X)=>(X='clinton'|X='quinton')))&
richer(burt,quinton) | [
"p0",
"p1",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6323031985192480216841746
% SZS output start Proof for 6323031985192480216841746
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
45. ~(person(paul) & quiet(paul)) => (richer(fred,paul) & richer(fred,mary)) [input p1]
48. quiet(mary) & old(paul) [input p4]
49. ~(person(paul) & quiet(paul) & old(paul)) & ~(person(mary) & quiet(mary) & old(mary)) [input p5]
54. ~(richer(fred,paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
127. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
128. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 127]
129. (richer(fred,paul) & richer(fred,mary)) | (person(paul) & quiet(paul)) [ennf transformation 45]
134. (~person(paul) | ~quiet(paul) | ~old(paul)) & (~person(mary) | ~quiet(mary) | ~old(mary)) [ennf transformation 49]
138. ~richer(fred,paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 54]
139. ~richer(fred,paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 138]
148. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
149. ~richer(fred,paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 139,148]
230. room(mary) [cnf transformation 128]
231. room(paul) [cnf transformation 128]
232. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 128]
235. richer(fred,paul) | quiet(paul) [cnf transformation 129]
236. richer(fred,paul) | person(paul) [cnf transformation 129]
249. old(paul) [cnf transformation 48]
252. ~person(paul) | ~quiet(paul) | ~old(paul) [cnf transformation 134]
266. ~richer(fred,paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 149]
267. ~richer(fred,paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 149]
268. ~richer(fred,paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 149]
273. 1 <=> person(paul) [avatar definition]
277. 2 <=> richer(fred,paul) [avatar definition]
280. 1 | 2 [avatar split clause 236,277,273]
282. 3 <=> quiet(paul) [avatar definition]
285. 3 | 2 [avatar split clause 235,277,282]
320. 11 <=> old(paul) [avatar definition]
330. 11 [avatar split clause 249,320]
331. ~11 | ~3 | ~1 [avatar split clause 252,273,282,320]
342. ~richer(fred,paul) | paul != sK3 | ~room(mary) [subsumption resolution 268,231]
343. ~richer(fred,paul) | paul != sK3 [subsumption resolution 342,230]
345. 15 <=> paul = sK3 [avatar definition]
347. paul != sK3 <- (~15) [avatar component clause 345]
348. ~15 | ~2 [avatar split clause 343,277,345]
349. ~richer(fred,paul) | mary != sK3 | ~room(mary) [subsumption resolution 267,231]
350. ~richer(fred,paul) | mary != sK3 [subsumption resolution 349,230]
352. 16 <=> mary = sK3 [avatar definition]
354. mary != sK3 <- (~16) [avatar component clause 352]
355. ~16 | ~2 [avatar split clause 350,277,352]
356. ~richer(fred,paul) | room(sK3) | ~room(mary) [subsumption resolution 266,231]
357. ~richer(fred,paul) | room(sK3) [subsumption resolution 356,230]
359. 17 <=> room(sK3) [avatar definition]
361. room(sK3) <- (17) [avatar component clause 359]
362. 17 | ~2 [avatar split clause 357,277,359]
365. mary = sK3 | paul = sK3 <- (17) [resolution 232,361]
366. paul = sK3 <- (~16, 17) [subsumption resolution 365,354]
367. $false <- (~15, ~16, 17) [subsumption resolution 366,347]
368. 15 | 16 | ~17 [avatar contradiction clause 367]
369. $false [avatar sat refutation 280,285,330,331,348,355,362,368]
% SZS output end Proof for 6323031985192480216841746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Dorothy, Patricia, Holly, Roland, Roland are the only persons in the room.
Roland plays the drums.
Patricia plays the drums.
Patricia does not create augmented reality experiences for mobile applications.
Dorothy is not passionate about collecting and restoring classic cars, does not collect action figures and can play the harmonica.
If someone neither cannot play the harmonica nor does not play the drums then he/she does not create augmented reality experiences for mobile applications and does not collect action figures and vice versa.
Dorothy does not enjoy kayaking and exploring remote waterways.
Everyone in the room does not collect action figures if they does not create augmented reality experiences for mobile applications or is passionate about collecting and restoring classic cars or both.
Dorothy neither does not create augmented reality experiences for mobile applications nor cannot play the harmonica.
Patricia is passionate about collecting and restoring classic cars or does not enjoy kayaking and exploring remote waterways or both.
If someone enjoys kayaking and exploring remote waterways and does not create augmented reality experiences for mobile applications then he/she cannot play the harmonica and does not collect action figures.
Dorothy is not passionate about collecting and restoring classic cars.
Holly who cannot play the harmonica, does not enjoy kayaking and exploring remote waterways or is not passionate about collecting and restoring classic cars does not collect action figures, is not passionate about collecting and restoring classic cars and cannot play the harmonica. | Holly creates augmented reality experiences for mobile applications. | entailment | room(dorothy)&room(patricia)&room(holly)&room(roland)&room(roland)&(![X]:(room(X)=>(X='dorothy'|X='patricia'|X='holly'|X='roland'|X='roland')))&
(plays_the_drums(roland))&
(plays_the_drums(patricia))&
(does_not_create_augmented_reality_experiences_for_mobile_applications(patricia))&
(((is_not_passionate_about_collecting_and_restoring_classic_cars(dorothy))&(does_not_collect_action_figures(dorothy))&(can_play_the_harmonica(dorothy))))&
((![X]:((~((cannot_play_the_harmonica(X))|(does_not_play_the_drums(X))))<=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))&(does_not_collect_action_figures(X)))))))&
(does_not_enjoy_kayaking_and_exploring_remote_waterways(dorothy))&
(![X]:(room(X)=>(((((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))=>(does_not_collect_action_figures(X))))))&
(~((does_not_create_augmented_reality_experiences_for_mobile_applications(dorothy))|(cannot_play_the_harmonica(dorothy))))&
(((is_passionate_about_collecting_and_restoring_classic_cars(patricia))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(patricia))))&
((![X]:((((enjoys_kayaking_and_exploring_remote_waterways(X))&(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))=>(((cannot_play_the_harmonica(X))&(does_not_collect_action_figures(X)))))))&
(is_not_passionate_about_collecting_and_restoring_classic_cars(dorothy))&
((((cannot_play_the_harmonica(holly))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(holly))|(is_not_passionate_about_collecting_and_restoring_classic_cars(holly))))&(((does_not_collect_action_figures(holly))&(is_not_passionate_about_collecting_and_restoring_classic_cars(holly))&(cannot_play_the_harmonica(holly))))) | room(dorothy)&room(patricia)&room(holly)&room(roland)&room(roland)&(![X]:(room(X)=>(X='dorothy'|X='patricia'|X='holly'|X='roland'|X='roland')))&
creates_augmented_reality_experiences_for_mobile_applications(holly) | [
"p0",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5283536250726709078988090
% SZS output start Proof for 5283536250726709078988090
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
49. ! [X0] : (~(~predb(X0) | ~preda(X0)) <=> (~predf(X0) & ~predd(X0))) [input p5]
56. ~preda(fred) & ~prede(fred) & ~predf(fred) & (~prede(fred) | ~predc(fred) | ~preda(fred)) [input p12]
57. ~(predd(fred) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
59. ~preda(fred) & ~prede(fred) & ~predf(fred) [pure predicate removal 56]
64. ~preda(fred) & ~predf(fred) [pure predicate removal 59]
138. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
139. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 138]
140. ! [X0] : ((predb(X0) & preda(X0)) <=> (~predf(X0) & ~predd(X0))) [ennf transformation 49]
144. ~predd(fred) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57]
145. ~predd(fred) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 144]
147. ! [X0] : (((predb(X0) & preda(X0)) | (predf(X0) | predd(X0))) & ((~predf(X0) & ~predd(X0)) | (~predb(X0) | ~preda(X0)))) [nnf transformation 140]
148. ! [X0] : (((predb(X0) & preda(X0)) | predf(X0) | predd(X0)) & ((~predf(X0) & ~predd(X0)) | ~predb(X0) | ~preda(X0))) [flattening 147]
149. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom]
150. ~predd(fred) | (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 145,149]
231. room(mary) [cnf transformation 139]
232. room(paul) [cnf transformation 139]
233. room(fred) [cnf transformation 139]
234. room(alice) [cnf transformation 139]
235. room(john) [cnf transformation 139]
236. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 139]
244. preda(X0) | predf(X0) | predd(X0) [cnf transformation 148]
249. ~predf(fred) [cnf transformation 64]
250. ~preda(fred) [cnf transformation 64]
251. ~predd(fred) | room(sK0) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150]
252. ~predd(fred) | mary != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150]
253. ~predd(fred) | paul != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150]
254. ~predd(fred) | fred != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150]
255. ~predd(fred) | alice != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150]
256. ~predd(fred) | john != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150]
257. ~predd(fred) | john != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 256,235]
258. ~predd(fred) | john != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 257,234]
259. ~predd(fred) | john != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 258,233]
260. ~predd(fred) | john != sK0 | ~room(mary) [subsumption resolution 259,232]
261. ~predd(fred) | john != sK0 [subsumption resolution 260,231]
263. 1 <=> john = sK0 [avatar definition]
265. john != sK0 <- (~1) [avatar component clause 263]
267. 2 <=> predd(fred) [avatar definition]
270. ~1 | ~2 [avatar split clause 261,267,263]
271. ~predd(fred) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 255,235]
272. ~predd(fred) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,234]
273. ~predd(fred) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 272,233]
274. ~predd(fred) | alice != sK0 | ~room(mary) [subsumption resolution 273,232]
275. ~predd(fred) | alice != sK0 [subsumption resolution 274,231]
277. 3 <=> alice = sK0 [avatar definition]
279. alice != sK0 <- (~3) [avatar component clause 277]
280. ~3 | ~2 [avatar split clause 275,267,277]
281. ~predd(fred) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 254,235]
282. ~predd(fred) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 281,234]
283. ~predd(fred) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 282,233]
284. ~predd(fred) | fred != sK0 | ~room(mary) [subsumption resolution 283,232]
285. ~predd(fred) | fred != sK0 [subsumption resolution 284,231]
287. 4 <=> fred = sK0 [avatar definition]
289. fred != sK0 <- (~4) [avatar component clause 287]
290. ~4 | ~2 [avatar split clause 285,267,287]
291. ~predd(fred) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 253,235]
292. ~predd(fred) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,234]
293. ~predd(fred) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 292,233]
294. ~predd(fred) | paul != sK0 | ~room(mary) [subsumption resolution 293,232]
295. ~predd(fred) | paul != sK0 [subsumption resolution 294,231]
297. 5 <=> paul = sK0 [avatar definition]
299. paul != sK0 <- (~5) [avatar component clause 297]
300. ~5 | ~2 [avatar split clause 295,267,297]
301. ~predd(fred) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 252,235]
302. ~predd(fred) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,234]
303. ~predd(fred) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 302,233]
304. ~predd(fred) | mary != sK0 | ~room(mary) [subsumption resolution 303,232]
305. ~predd(fred) | mary != sK0 [subsumption resolution 304,231]
307. 6 <=> mary = sK0 [avatar definition]
309. mary != sK0 <- (~6) [avatar component clause 307]
310. ~6 | ~2 [avatar split clause 305,267,307]
311. ~predd(fred) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 251,235]
312. ~predd(fred) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 311,234]
313. ~predd(fred) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 312,233]
314. ~predd(fred) | room(sK0) | ~room(mary) [subsumption resolution 313,232]
315. ~predd(fred) | room(sK0) [subsumption resolution 314,231]
317. 7 <=> room(sK0) [avatar definition]
319. room(sK0) <- (7) [avatar component clause 317]
320. 7 | ~2 [avatar split clause 315,267,317]
324. predf(fred) | predd(fred) [resolution 244,250]
327. predd(fred) [subsumption resolution 324,249]
330. 2 [avatar split clause 327,267]
400. alice = sK0 | fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (7) [resolution 236,319]
401. fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (~3, 7) [subsumption resolution 400,279]
402. paul = sK0 | mary = sK0 | john = sK0 <- (~3, ~4, 7) [subsumption resolution 401,289]
403. mary = sK0 | john = sK0 <- (~3, ~4, ~5, 7) [subsumption resolution 402,299]
404. john = sK0 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 403,309]
405. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 404,265]
406. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 405]
407. $false [avatar sat refutation 270,280,290,300,310,320,330,406]
% SZS output end Proof for 5283536250726709078988090
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.000054 |
Russell, Justine, Nancy are the only persons in the room.
Nancy is a wise person.
Everyone anywhere does not have lived in exactly three countries.
Someone who is a quiet person is poorer than someone who is a quiet person, is not wise and is not a night owl.
Everyone in the room is wise.
Nancy is the least poor outside the room.
Everyone in the room does not collect classic novels.
All wise persons are kind.
It is not the case that “Nancy and Russell are not wise”.
Everyone in the room is not a night owl.
Everyone in the room is a quiet person.
Russell who is not a night owl or does not collect rare sneakers or both is a wise person.
Everyone in the room is kind and is a kind person.
Everyone in the room is a wise person.
Nancy is kind.
Everyone in the room does not have lived in exactly three countries.
Nancy either is a quiet person or does not collect rare sneakers but not both. | Russell is quiet. | entailment | room(russell)&room(justine)&room(nancy)&(![X]:(room(X)=>(X='russell'|X='justine'|X='nancy')))&
(wise(nancy)&person(nancy))&
(![X]:(anywhere(X)=>(does_not_have_lived_in_exactly_three_countries(X))))&
(?[X,Y]:((quiet(X)&person(X))&(((quiet(Y)&person(Y))&(~wise(Y))&(is_not_a_night_owl(Y))))&(poorer(X,Y))))&
(![X]:(room(X)=>(wise(X))))&
(![X]:((~room(X)&(X!=nancy))=>poorer(nancy,X)))&
(![X]:(room(X)=>(does_not_collect_classic_novels(X))))&
(![X]:(wise(X)=>kind(X)))&
(~(~wise(nancy)&~wise(russell)))&
(![X]:(room(X)=>(is_not_a_night_owl(X))))&
(![X]:(room(X)=>(quiet(X)&person(X))))&
((((is_not_a_night_owl(russell))|(does_not_collect_rare_sneakers(russell))))&(wise(russell)&person(russell)))&
(![X]:(room(X)=>(((kind(X))&(kind(X)&person(X))))))&
(![X]:(room(X)=>(wise(X)&person(X))))&
(kind(nancy))&
(![X]:(room(X)=>(does_not_have_lived_in_exactly_three_countries(X))))&
(((quiet(nancy)&person(nancy))<~>(does_not_collect_rare_sneakers(nancy)))) | room(russell)&room(justine)&room(nancy)&(![X]:(room(X)=>(X='russell'|X='justine'|X='nancy')))&
quiet(russell) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3930633432510000527978144
% SZS output start Proof for 3930633432510000527978144
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
54. ! [X0] : (room(X0) => (person(X0) & quiet(X0))) [input p10]
61. ~(quiet(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
143. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
144. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 143]
149. ! [X0] : ((person(X0) & quiet(X0)) | ~room(X0)) [ennf transformation 54]
152. ~quiet(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 61]
153. ~quiet(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 152]
159. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom]
160. ~quiet(mary) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 153,159]
241. room(mary) [cnf transformation 144]
242. room(paul) [cnf transformation 144]
243. room(fred) [cnf transformation 144]
244. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 144]
256. ~room(X0) | quiet(X0) [cnf transformation 149]
266. ~quiet(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160]
267. ~quiet(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160]
268. ~quiet(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160]
269. ~quiet(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160]
281. ~quiet(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 269,243]
282. ~quiet(mary) | fred != sK2 | ~room(mary) [subsumption resolution 281,242]
283. ~quiet(mary) | fred != sK2 [subsumption resolution 282,241]
285. 3 <=> fred = sK2 [avatar definition]
287. fred != sK2 <- (~3) [avatar component clause 285]
289. 4 <=> quiet(mary) [avatar definition]
292. ~3 | ~4 [avatar split clause 283,289,285]
293. ~quiet(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 268,243]
294. ~quiet(mary) | paul != sK2 | ~room(mary) [subsumption resolution 293,242]
295. ~quiet(mary) | paul != sK2 [subsumption resolution 294,241]
297. 5 <=> paul = sK2 [avatar definition]
299. paul != sK2 <- (~5) [avatar component clause 297]
300. ~5 | ~4 [avatar split clause 295,289,297]
301. ~quiet(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 267,243]
302. ~quiet(mary) | mary != sK2 | ~room(mary) [subsumption resolution 301,242]
303. ~quiet(mary) | mary != sK2 [subsumption resolution 302,241]
305. 6 <=> mary = sK2 [avatar definition]
307. mary != sK2 <- (~6) [avatar component clause 305]
308. ~6 | ~4 [avatar split clause 303,289,305]
309. ~quiet(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 266,243]
310. ~quiet(mary) | room(sK2) | ~room(mary) [subsumption resolution 309,242]
311. ~quiet(mary) | room(sK2) [subsumption resolution 310,241]
313. 7 <=> room(sK2) [avatar definition]
315. room(sK2) <- (7) [avatar component clause 313]
316. 7 | ~4 [avatar split clause 311,289,313]
320. quiet(mary) [resolution 256,241]
328. 4 [avatar split clause 320,289]
445. paul = sK2 | mary = sK2 | fred = sK2 <- (7) [resolution 244,315]
446. mary = sK2 | fred = sK2 <- (~5, 7) [subsumption resolution 445,299]
447. fred = sK2 <- (~5, ~6, 7) [subsumption resolution 446,307]
448. $false <- (~3, ~5, ~6, 7) [subsumption resolution 447,287]
449. 3 | 5 | 6 | ~7 [avatar contradiction clause 448]
450. $false [avatar sat refutation 292,300,308,316,328,449]
% SZS output end Proof for 3930633432510000527978144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.200908 |
There is a room. “Someone in the room writes a travel blog” unless “everyone in the room has a piercing or does not participate in citizen science projects related to wildlife monitoring”. “Everyone outside the room does not own a microscope or is not an avid collector of autographed memorabilia from famous musicians” only if “everyone in the room who maintains a large, organic vegetable garden year-round is an amateur astronomer who builds and uses custom telescopes”. Either “everyone in the room does not write a travel blog or maintains a large, organic vegetable garden year-round” or “no one in the room writes a travel blog or does not write a travel blog” but not both. If “everyone in the room does not maintain a large, organic vegetable garden year-round or maintains a large, organic vegetable garden year-round” then “everyone in the room does practice yoga, is an avid hiker or hosts regular game nights featuring complex strategy games if they does not maintain a large, organic vegetable garden year-round” otherwise “everyone in the room who does practice yoga, is an avid hiker or hosts regular game nights featuring complex strategy games hosts regular game nights featuring complex strategy games”. “Everyone in the room watches fantasy movies or does not own a microscope” only if “everyone in the room watches fantasy movies only if they builds model airplanes”. If “everyone outside the room does not maintain a large, organic vegetable garden year-round or plays video games” then “if someone is passionate about collecting and restoring classic cars then he/she watches fantasy movies”. Someone in the room writes a travel blog. Everyone in the room builds model airplanes if they watches fantasy movies and vice versa. Everyone in the room who enjoys stargazing does practice yoga. Everyone in the room who does practice yoga neither is an amateur astronomer who builds and uses custom telescopes nor has a piercing. Everyone in the room neither is an amateur astronomer who builds and uses custom telescopes nor has a piercing only if they participates in citizen science projects related to wildlife monitoring. Everyone in the room is an avid collector of autographed memorabilia from famous musicians only if they does practice yoga. Everyone in the room who either has a piercing or maintains a large, organic vegetable garden year-round but not both enjoys stargazing, practices and performs acrobatic dance routines or builds model airplanes. Everyone anywhere does not have a piercing only if they builds model airplanes. | Everyone in the room is not passionate about collecting and restoring classic cars or is an amateur astronomer who builds and uses custom telescopes. | neutral | (there_is_a_room)&
(~(![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(has_a_piercing(X))))))=>(?[X]:(room(X)&(writes_a_travel_blog(X)))))&
((![X]:(~room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_own_a_microscope(X))))))=>(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))))&
((![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_write_a_travel_blog(X))))))<~>(~?[X]:(room(X)=>(((does_not_write_a_travel_blog(X))|(writes_a_travel_blog(X)))))))&
(((![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))=>(![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))=>(((does_practice_yoga(X))|(is_an_avid_hiker(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))))&((~(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X)))))))=>(![X]:(room(X)=>(((((does_practice_yoga(X))|(is_an_avid_hiker(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))&
((![X]:(room(X)=>(((does_not_own_a_microscope(X))|(watches_fantasy_movies(X))))))=>(![X]:(room(X)=>(((builds_model_airplanes(X))<=(watches_fantasy_movies(X)))))))&
((![X]:(~room(X)=>(((plays_video_games(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))=>((![X]:((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(watches_fantasy_movies(X))))))&
(?[X]:(room(X)&(writes_a_travel_blog(X))))&
(![X]:(room(X)=>(((builds_model_airplanes(X))<=>(watches_fantasy_movies(X))))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))=>(does_practice_yoga(X))))))&
(![X]:(room(X)=>(((does_practice_yoga(X))=>(~((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(has_a_piercing(X))))))))&
(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=(~((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(has_a_piercing(X))))))))&
(![X]:(room(X)=>(((does_practice_yoga(X))<=(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))&
(![X]:(room(X)=>(((((has_a_piercing(X))<~>(maintains_a_large,_organic_vegetable_garden_year-round(X))))=>(((enjoys_stargazing(X))|(practices_and_performs_acrobatic_dance_routines(X))|(builds_model_airplanes(X))))))))&
(![X]:(anywhere(X)=>(((builds_model_airplanes(X))<=(does_not_have_a_piercing(X))))))&
(![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_have_a_piercing(X))|(does_practice_yoga(X))))))&
((![X]:((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(watches_fantasy_movies(X)))))&
(![X]:(anywhere(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))&
(![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))) | [] | null | 0 |
Dorothy, Maurice, David are the only persons in the room.
“Dorothy has a curated collection of mid-century modern furniture” unless “Maurice is not a old person”.
Dorothy has a curated collection of mid-century modern furniture.
David collects antique clocks.
Everyone in the room is a old person only if they has a curated collection of mid-century modern furniture.
Someone in the room is a old person.
David has a curated collection of mid-century modern furniture.
It is true that “David is a old person”.
Dorothy collects antique clocks.
David is the least old in the room.
If someone has a curated collection of mid-century modern furniture then he/she collects antique clocks.
Maurice has a curated collection of mid-century modern furniture.
At least one person in the room is not a old person.
Maurice collects antique clocks.
Maurice is not a old person.
David is the least old anywhere. | Maurice is old. | entailment | room(dorothy)&room(maurice)&room(david)&(![X]:(room(X)=>(X='dorothy'|X='maurice'|X='david')))&
(~(~(old(maurice)&person(maurice)))=>(has_a_curated_collection_of_mid-century_modern_furniture(dorothy)))&
(has_a_curated_collection_of_mid-century_modern_furniture(dorothy))&
(collects_antique_clocks(david))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))<=(old(X)&person(X))))))&
(?[X]:(room(X)&(old(X)&person(X))))&
(has_a_curated_collection_of_mid-century_modern_furniture(david))&
(old(david)&person(david))&
(collects_antique_clocks(dorothy))&
(![X]:((room(X)&(X!=david))=>older(david,X)))&
((![X]:((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(collects_antique_clocks(X)))))&
(has_a_curated_collection_of_mid-century_modern_furniture(maurice))&
(((?[X]:(room(X)&~(old(X)&person(X))))))&
(collects_antique_clocks(maurice))&
(~(old(maurice)&person(maurice)))&
(![X]:((anywhere(X)&(X!=david))=>older(david,X))) | room(dorothy)&room(maurice)&room(david)&(![X]:(room(X)=>(X='dorothy'|X='maurice'|X='david')))&
old(maurice) | [
"b4",
"b20",
"b42",
"p0",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8831008591002381460121297
% SZS output start Proof for 8831008591002381460121297
5. ! [X0] : anywhere(X0) [input b4]
21. ! [X0,X1] : (X0 != X1 => ((old(X0) & older(X0,X1)) => old(X1))) [input b20]
43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42]
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
51. person(fred) & old(fred) [input p7]
59. ! [X0] : ((fred != X0 & anywhere(X0)) => older(fred,X0)) [input p15]
60. ~(old(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
102. ! [X0,X1] : ((old(X1) | (~old(X0) | ~older(X0,X1))) | X0 = X1) [ennf transformation 21]
103. ! [X0,X1] : (old(X1) | ~old(X0) | ~older(X0,X1) | X0 = X1) [flattening 102]
142. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
143. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 142]
148. ! [X0] : (older(fred,X0) | (fred = X0 | ~anywhere(X0))) [ennf transformation 59]
149. ! [X0] : (older(fred,X0) | fred = X0 | ~anywhere(X0)) [flattening 148]
150. ~old(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60]
151. ~old(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 150]
157. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom]
158. ~old(paul) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 151,157]
159. anywhere(X0) [cnf transformation 5]
176. ~older(X0,X1) | ~old(X0) | old(X1) | X0 = X1 [cnf transformation 103]
211. paul != fred [cnf transformation 43]
240. room(mary) [cnf transformation 143]
241. room(paul) [cnf transformation 143]
242. room(fred) [cnf transformation 143]
243. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143]
247. old(fred) [cnf transformation 51]
253. older(fred,X0) | fred = X0 | ~anywhere(X0) [cnf transformation 149]
254. ~old(paul) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 158]
255. ~old(paul) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 158]
256. ~old(paul) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 158]
257. ~old(paul) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 158]
268. 3 <=> old(paul) [avatar definition]
270. ~old(paul) <- (~3) [avatar component clause 268]
276. older(fred,X0) | fred = X0 [subsumption resolution 253,159]
277. ~old(paul) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 257,242]
278. ~old(paul) | fred != sK2 | ~room(mary) [subsumption resolution 277,241]
279. ~old(paul) | fred != sK2 [subsumption resolution 278,240]
281. 5 <=> fred = sK2 [avatar definition]
283. fred != sK2 <- (~5) [avatar component clause 281]
284. ~5 | ~3 [avatar split clause 279,268,281]
285. ~old(paul) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 256,242]
286. ~old(paul) | paul != sK2 | ~room(mary) [subsumption resolution 285,241]
287. ~old(paul) | paul != sK2 [subsumption resolution 286,240]
289. 6 <=> paul = sK2 [avatar definition]
291. paul != sK2 <- (~6) [avatar component clause 289]
292. ~6 | ~3 [avatar split clause 287,268,289]
293. ~old(paul) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 255,242]
294. ~old(paul) | mary != sK2 | ~room(mary) [subsumption resolution 293,241]
295. ~old(paul) | mary != sK2 [subsumption resolution 294,240]
297. 7 <=> mary = sK2 [avatar definition]
299. mary != sK2 <- (~7) [avatar component clause 297]
300. ~7 | ~3 [avatar split clause 295,268,297]
301. ~old(paul) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 254,242]
302. ~old(paul) | room(sK2) | ~room(mary) [subsumption resolution 301,241]
303. ~old(paul) | room(sK2) [subsumption resolution 302,240]
305. 8 <=> room(sK2) [avatar definition]
307. room(sK2) <- (8) [avatar component clause 305]
308. 8 | ~3 [avatar split clause 303,268,305]
354. ~old(fred) | old(X1) | fred = X1 | fred = X1 [resolution 176,276]
355. ~old(fred) | old(X1) | fred = X1 [duplicate literal removal 354]
358. old(X1) | fred = X1 [subsumption resolution 355,247]
359. paul = fred <- (~3) [resolution 358,270]
360. $false <- (~3) [subsumption resolution 359,211]
361. 3 [avatar contradiction clause 360]
424. paul = sK2 | mary = sK2 | fred = sK2 <- (8) [resolution 243,307]
451. mary = sK2 | fred = sK2 <- (~6, 8) [subsumption resolution 424,291]
452. fred = sK2 <- (~6, ~7, 8) [subsumption resolution 451,299]
453. $false <- (~5, ~6, ~7, 8) [subsumption resolution 452,283]
454. 5 | 6 | 7 | ~8 [avatar contradiction clause 453]
455. $false [avatar sat refutation 284,292,300,308,361,454]
% SZS output end Proof for 8831008591002381460121297
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.135999 |
Ron, Stephen, Ronald are the only persons in the room. “Everyone in the room is old or does not practice and performs acrobatic dance routines” if “everyone outside the room is tall” and vice versa. If “everyone in the room practices and performs acrobatic dance routines” then “everyone outside the room is tall”. If “everyone in the room does not practice and performs acrobatic dance routines or is older than Lydia” then “everyone anywhere is not tall if they is older than Lydia and vice versa”. “Stephen is a tall person” if “no one in the room does not practice and performs acrobatic dance routines or is a tall person” and vice versa. If “everyone outside the room is not old, not tall or does not practice and performs acrobatic dance routines” then “all old persons are tall” otherwise “no one in the room is not old, not tall”. If “everyone in the room is older than Lydia or does not practice and performs acrobatic dance routines” then “it is true that “everyone in the room is older than Lydia if they is not old, not tall””. Everyone in the room is old. Everyone anywhere is tall if they practices and performs acrobatic dance routines. All tall persons are old. Everyone in the room who is a tall person is old. Ron is a old tall person. Everyone in the room is older than Lydia if they is not old, not tall. Not everyone anywhere is a old person or does not practice and performs acrobatic dance routines. Everyone outside the room is a tall person if they is old. | Ron practices and performs acrobatic dance routines. | neutral | room(ron)&room(stephen)&room(ronald)&(![X]:(room(X)=>(X='ron'|X='stephen'|X='ronald')))&
((![X]:(~room(X)=>(tall(X))))<=>(![X]:(room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(old(X)))))))&
((![X]:(room(X)=>(practices_and_performs_acrobatic_dance_routines(X))))=>(![X]:(~room(X)=>(tall(X)))))&
((![X]:(room(X)=>(((older(lydia,X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))=>(![X]:(anywhere(X)=>(((~tall(X))<=>(older(lydia,X)))))))&
((~?[X]:(room(X)=>(((tall(X)&person(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))<=>(tall(stephen)&person(stephen)))&
(((![X]:(~room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(~old(X)&~tall(X))))))=>(![X]:(old(X)=>tall(X))))&((~(![X]:(~room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(~old(X)&~tall(X)))))))=>(~?[X]:(room(X)=>(~old(X)&~tall(X))))))&
((![X]:(room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(older(lydia,X))))))=>(![X]:(room(X)=>(((~old(X)&~tall(X))=>(older(lydia,X)))))))&
(![X]:(room(X)=>(old(X))))&
(![X]:(anywhere(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(tall(X))))))&
(![X]:(tall(X)=>old(X)))&
(![X]:(room(X)=>(((tall(X)&person(X))=>(old(X))))))&
(old(ron)&tall(ron)&person(ron))&
(![X]:(room(X)=>(((~old(X)&~tall(X))=>(older(lydia,X))))))&
(~![X]:(anywhere(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(old(X)&person(X))))))&
(![X]:(~room(X)=>(((old(X))=>(tall(X)&person(X)))))) | room(ron)&room(stephen)&room(ronald)&(![X]:(room(X)=>(X='ron'|X='stephen'|X='ronald')))&
practices_and_performs_acrobatic_dance_routines(ron) | [] | null | 0.685379 |
Gladys, Megan, Esther are the only persons in the room.
Someone anywhere is not a wine connoisseur.
Everyone in the room does not train for and competes in international triathlons.
Everyone in the room does not write poetry, does not enjoy stand-up paddleboarding and does not enjoy origami.
If someone either is not dedicated to sustainable living and zero-waste practices or does not enjoy stand-up paddleboarding but not both then he/she does not host a popular podcast about emerging technologies.
Everyone in the room does not collect historical artifacts related to ancient civilizations.
No one anywhere does not collect action figures, does not write poetry and does not own a significant collection of rare gemstones and minerals.
Megan who either does not collect action figures or is not a scotch connoisseur but not both either does not own a smartwatch or does not own an Android phone but not both.
Everyone in the room either is not a scotch connoisseur or does not own a smartwatch but not both.
Gladys who does not own a significant collection of rare gemstones and minerals, does not collect action figures or does not have a pet dog does not use a Windows laptop, does not own an Android phone and does not host a popular podcast about emerging technologies.
Everyone in the room either is not an active member of a local robotics club or does not own a significant collection of rare gemstones and minerals but not both.
Everyone in the room does not write poetry.
Someone in the room does not collect action figures.
Everyone in the room does not make homemade pastries, does not train for and competes in international triathlons or does not use a Windows laptop.
Everyone anywhere either does not collect action figures or is not dedicated to sustainable living and zero-waste practices but not both.
Everyone anywhere does not collect historical artifacts related to ancient civilizations, does not own a smartwatch and does not use a Windows laptop.
If someone does not host a popular podcast about emerging technologies then he/she does not watche fantasy movies and vice versa.
Everyone in the room does not use an ios phone, does not make homemade pastries or does not train for and competes in international triathlons.
Everyone in the room is not a client of Costco. | Megan watches fantasy movies. | contradiction | room(gladys)&room(megan)&room(esther)&(![X]:(room(X)=>(X='gladys'|X='megan'|X='esther')))&
(?[X]:(anywhere(X)&(is_not_a_wine_connoisseur(X))))&
(![X]:(room(X)=>(does_not_train_for_and_competes_in_international_triathlons(X))))&
(![X]:(room(X)=>(((does_not_write_poetry(X))&(does_not_enjoy_stand-up_paddleboarding(X))&(does_not_enjoy_origami(X))))))&
((![X]:((((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))<~>(does_not_enjoy_stand-up_paddleboarding(X))))=>(does_not_host_a_popular_podcast_about_emerging_technologies(X)))))&
(![X]:(room(X)=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))&
(~?[X]:(anywhere(X)=>(((does_not_collect_action_figures(X))&(does_not_write_poetry(X))&(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
((((does_not_collect_action_figures(megan))<~>(is_not_a_scotch_connoisseur(megan))))&(((does_not_own_a_smartwatch(megan))<~>(does_not_own_an_Android_phone(megan)))))&
(![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))<~>(does_not_own_a_smartwatch(X))))))&
((((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(gladys))|(does_not_collect_action_figures(gladys))|(does_not_have_a_pet_dog(gladys))))&(((does_not_use_a_Windows_laptop(gladys))&(does_not_own_an_Android_phone(gladys))&(does_not_host_a_popular_podcast_about_emerging_technologies(gladys)))))&
(![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))<~>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
(![X]:(room(X)=>(does_not_write_poetry(X))))&
(?[X]:(room(X)&(does_not_collect_action_figures(X))))&
(![X]:(room(X)=>(((does_not_make_homemade_pastries(X))|(does_not_train_for_and_competes_in_international_triathlons(X))|(does_not_use_a_Windows_laptop(X))))))&
(![X]:(anywhere(X)=>(((does_not_collect_action_figures(X))<~>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))&
(![X]:(anywhere(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))&(does_not_own_a_smartwatch(X))&(does_not_use_a_Windows_laptop(X))))))&
((![X]:((does_not_host_a_popular_podcast_about_emerging_technologies(X))<=>(does_not_watche_fantasy_movies(X)))))&
(![X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(does_not_make_homemade_pastries(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))&
(![X]:(room(X)=>(is_not_a_client_of_Costco(X)))) | room(gladys)&room(megan)&room(esther)&(![X]:(room(X)=>(X='gladys'|X='megan'|X='esther')))&
watches_fantasy_movies(megan) | [
"b4",
"p0",
"p3",
"p4",
"p7",
"p8",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 814108921159582866775756
% SZS output start Proof for 814108921159582866775756
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
47. ! [X0] : (room(X0) => (~predq(X0) & ~predm(X0) & ~predi(X0))) [input p3]
48. ! [X0] : ((~predo(X0) <~> ~predm(X0)) => ~predp(X0)) [input p4]
51. (~predb(paul) <~> ~predd(paul)) & (~predl(paul) <~> ~predw(paul)) [input p7]
52. ! [X0] : (room(X0) => (~predw(X0) <~> ~predb(X0))) [input p8]
58. ! [X0] : (anywhere(X0) => (~predl(X0) <~> ~predo(X0))) [input p14]
59. ! [X0] : (anywhere(X0) => (~predf(X0) & ~predb(X0) & ~predj(X0))) [input p15]
60. ! [X0] : (~predp(X0) <=> ~predn(X0)) [input p16]
63. predn(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
64. ! [X0] : (~predp(X0) => ~predn(X0)) [unused predicate definition removal 60]
68. ! [X0] : (anywhere(X0) => (~predb(X0) & ~predj(X0))) [pure predicate removal 59]
72. ! [X0] : (anywhere(X0) => ~predb(X0)) [pure predicate removal 68]
73. ! [X0] : (room(X0) => (~predm(X0) & ~predi(X0))) [pure predicate removal 47]
147. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
148. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 147]
149. ! [X0] : ((~predm(X0) & ~predi(X0)) | ~room(X0)) [ennf transformation 73]
150. ! [X0] : (~predp(X0) | (~predo(X0) <=> ~predm(X0))) [ennf transformation 48]
152. ! [X0] : ((~predw(X0) <~> ~predb(X0)) | ~room(X0)) [ennf transformation 52]
155. ! [X0] : ((~predl(X0) <~> ~predo(X0)) | ~anywhere(X0)) [ennf transformation 58]
156. ! [X0] : (~predb(X0) | ~anywhere(X0)) [ennf transformation 72]
157. ! [X0] : (~predn(X0) | predp(X0)) [ennf transformation 64]
158. predn(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 63]
159. predn(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 158]
163. ! [X0] : (~predp(X0) | ((~predo(X0) | predm(X0)) & (~predm(X0) | predo(X0)))) [nnf transformation 150]
164. ((predd(paul) | predb(paul)) & (~predd(paul) | ~predb(paul))) & ((predw(paul) | predl(paul)) & (~predw(paul) | ~predl(paul))) [nnf transformation 51]
165. (predd(paul) | predb(paul)) & (~predd(paul) | ~predb(paul)) & (predw(paul) | predl(paul)) & (~predw(paul) | ~predl(paul)) [flattening 164]
166. ! [X0] : (((predb(X0) | predw(X0)) & (~predb(X0) | ~predw(X0))) | ~room(X0)) [nnf transformation 152]
170. ! [X0] : (((predo(X0) | predl(X0)) & (~predo(X0) | ~predl(X0))) | ~anywhere(X0)) [nnf transformation 155]
171. anywhere(X0) [cnf transformation 5]
253. room(paul) [cnf transformation 148]
258. ~predm(X0) | ~room(X0) [cnf transformation 149]
260. ~predp(X0) | ~predo(X0) | predm(X0) [cnf transformation 163]
263. ~predw(paul) | ~predl(paul) [cnf transformation 165]
268. ~room(X0) | predw(X0) | predb(X0) [cnf transformation 166]
277. predo(X0) | predl(X0) | ~anywhere(X0) [cnf transformation 170]
278. ~predb(X0) | ~anywhere(X0) [cnf transformation 156]
279. ~predn(X0) | predp(X0) [cnf transformation 157]
284. predn(paul) [cnf transformation 159]
296. 3 <=> predl(paul) [avatar definition]
297. ~predl(paul) <- (~3) [avatar component clause 296]
300. 4 <=> predw(paul) [avatar definition]
304. ~3 | ~4 [avatar split clause 263,300,296]
305. predl(X0) | predo(X0) [subsumption resolution 277,171]
307. ~predb(X0) [subsumption resolution 278,171]
308. predp(paul) [resolution 279,284]
314. ~predo(paul) | predm(paul) [resolution 260,308]
316. predw(paul) | predb(paul) [resolution 268,253]
326. 5 <=> predm(paul) [avatar definition]
328. predm(paul) <- (5) [avatar component clause 326]
330. 6 <=> predo(paul) [avatar definition]
333. 5 | ~6 [avatar split clause 314,330,326]
335. predw(paul) [subsumption resolution 316,307]
336. 4 [avatar split clause 335,300]
337. predo(paul) <- (~3) [resolution 297,305]
340. 6 | 3 [avatar split clause 337,296,330]
381. ~room(paul) <- (5) [resolution 328,258]
382. $false <- (5) [subsumption resolution 381,253]
383. ~5 [avatar contradiction clause 382]
384. $false [avatar sat refutation 304,333,336,340,383]
% SZS output end Proof for 814108921159582866775756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.261523 |
There is a room.
If “everyone in the room is a wine connoisseur with a private cellar of vintage wines or does not own a microscope” then “everyone in the room owns a microscope if they is a wine connoisseur with a private cellar of vintage wines”.
Everyone in the room is a drone photographer if they does not write and illustrates their own graphic novels.
Everyone in the room collects limited-edition art prints from contemporary artists and is a drone photographer if they is a drone photographer.
At least one person anywhere collects limited-edition art prints from contemporary artists.
Not everyone in the room writes and illustrates their own graphic novels.
Not everyone anywhere owns a microscope if they has completed a triathlon or is a drone photographer or both.
Not everyone outside the room who owns a telescope is a chess master who participates in national tournaments.
Everyone in the room is a chess master who participates in national tournaments only if they is a drone photographer.
Everyone in the room is a wine connoisseur with a private cellar of vintage wines or does not own a microscope.
Everyone anywhere owns a telescope if and only if they owns a microscope and has completed a triathlon.
Not everyone in the room is a chess master who participates in national tournaments if they has completed a triathlon.
Everyone in the room who is a chess master who participates in national tournaments does not collect comic books.
Everyone in the room who either is a wine connoisseur with a private cellar of vintage wines or owns a telescope but not both collects vintage vinyl records.
Everyone in the room who collects vintage vinyl records is a drone photographer, writes and illustrates their own graphic novels or owns a telescope.
Everyone in the room who is a chess master who participates in national tournaments writes and illustrates their own graphic novels.
Everyone in the room who is a chess master who participates in national tournaments is a drone photographer. | Everyone in the room is not a chess master who participates in national tournaments or is a wine connoisseur with a private cellar of vintage wines. | neutral | (there_is_a_room)&
((![X]:(room(X)=>(((does_not_own_a_microscope(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))=>(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(owns_a_microscope(X)))))))&
(![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))=>(is_a_drone_photographer(X))))))&
(![X]:(room(X)=>(((is_a_drone_photographer(X))=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))&(is_a_drone_photographer(X))))))))&
(((?[X]:(anywhere(X)&collects_limited-edition_art_prints_from_contemporary_artists(X)))))&
(~![X]:(room(X)=>(writes_and_illustrates_their_own_graphic_novels(X))))&
(~![X]:(anywhere(X)=>(((((has_completed_a_triathlon(X))|(is_a_drone_photographer(X))))=>(owns_a_microscope(X))))))&
(~![X]:(~room(X)=>(((owns_a_telescope(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))&
(![X]:(room(X)=>(((is_a_drone_photographer(X))<=(is_a_chess_master_who_participates_in_national_tournaments(X))))))&
(![X]:(room(X)=>(((does_not_own_a_microscope(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(![X]:(anywhere(X)=>(((owns_a_telescope(X))<=>(((owns_a_microscope(X))&(has_completed_a_triathlon(X))))))))&
(~![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))&
(![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(does_not_collect_comic_books(X))))))&
(![X]:(room(X)=>(((((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<~>(owns_a_telescope(X))))=>(collects_vintage_vinyl_records(X))))))&
(![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(((is_a_drone_photographer(X))|(writes_and_illustrates_their_own_graphic_novels(X))|(owns_a_telescope(X))))))))&
(![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))&
(![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(is_a_drone_photographer(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))) | [] | null | 0.335956 |
Lisa, Sandra, Adam, Anthony, Robert are the only persons in the room.
If “Anthony and Lisa are respectively tall and curious” then “Anthony collects rare and antique scientific instruments”.
“Adam and Anthony are respectively tall and curious” if “Adam is tall”.
Everyone in the room does not enjoy spelunking or enjoys spelunking.
Anthony collects rare and antique scientific instruments.
Everyone in the room enjoys coding in Python.
If someone is curious then he/she is not tall, not curious.
If someone drives a hybrid car then he/she does not drive a hybrid car, is a curious european or drives a hybrid car.
Everyone in the room is not a curious tall european if they enjoys spelunking.
Robert is the least loud outside the room. | Lisa enjoys coding in Python. | entailment | room(lisa)&room(sandra)&room(adam)&room(anthony)&room(robert)&(![X]:(room(X)=>(X='lisa'|X='sandra'|X='adam'|X='anthony'|X='robert')))&
(((tall(anthony))&(curious(lisa)))=>(collects_rare_and_antique_scientific_instruments(anthony)))&
((tall(adam))=>((tall(adam))&(curious(anthony))))&
(![X]:(room(X)=>(((enjoys_spelunking(X))|(does_not_enjoy_spelunking(X))))))&
(collects_rare_and_antique_scientific_instruments(anthony))&
(![X]:(room(X)=>(enjoys_coding_in_Python(X))))&
((![X]:((curious(X))=>(~tall(X)&~curious(X)))))&
((![X]:((drives_a_hybrid_car(X))=>(((does_not_drive_a_hybrid_car(X))|(curious(X)&european(X))|(drives_a_hybrid_car(X)))))))&
(![X]:(room(X)=>(((enjoys_spelunking(X))=>(~(curious(X)&tall(X)&european(X)))))))&
(![X]:((~room(X)&(X!=robert))=>louder(robert,X))) | room(lisa)&room(sandra)&room(adam)&room(anthony)&room(robert)&(![X]:(room(X)=>(X='lisa'|X='sandra'|X='adam'|X='anthony'|X='robert')))&
enjoys_coding_in_Python(lisa) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 737843249360521284709500
% SZS output start Proof for 737843249360521284709500
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
49. ! [X0] : (room(X0) => predo(X0)) [input p5]
54. ~(predo(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
129. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
130. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 129]
134. ! [X0] : (predo(X0) | ~room(X0)) [ennf transformation 49]
142. ~predo(mary) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 54]
143. ~predo(mary) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 142]
145. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom]
146. ~predo(mary) | (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 143,145]
227. room(mary) [cnf transformation 130]
228. room(paul) [cnf transformation 130]
229. room(fred) [cnf transformation 130]
230. room(alice) [cnf transformation 130]
231. room(john) [cnf transformation 130]
232. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 130]
236. ~room(X0) | predo(X0) [cnf transformation 134]
243. ~predo(mary) | room(sK0) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146]
244. ~predo(mary) | mary != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146]
245. ~predo(mary) | paul != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146]
246. ~predo(mary) | fred != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146]
247. ~predo(mary) | alice != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146]
248. ~predo(mary) | john != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146]
261. ~predo(mary) | john != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 248,231]
262. ~predo(mary) | john != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,230]
263. ~predo(mary) | john != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 262,229]
264. ~predo(mary) | john != sK0 | ~room(mary) [subsumption resolution 263,228]
265. ~predo(mary) | john != sK0 [subsumption resolution 264,227]
267. 3 <=> john = sK0 [avatar definition]
269. john != sK0 <- (~3) [avatar component clause 267]
271. 4 <=> predo(mary) [avatar definition]
274. ~3 | ~4 [avatar split clause 265,271,267]
275. ~predo(mary) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 247,231]
276. ~predo(mary) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,230]
277. ~predo(mary) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 276,229]
278. ~predo(mary) | alice != sK0 | ~room(mary) [subsumption resolution 277,228]
279. ~predo(mary) | alice != sK0 [subsumption resolution 278,227]
281. 5 <=> alice = sK0 [avatar definition]
283. alice != sK0 <- (~5) [avatar component clause 281]
284. ~5 | ~4 [avatar split clause 279,271,281]
285. ~predo(mary) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 246,231]
286. ~predo(mary) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,230]
287. ~predo(mary) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 286,229]
288. ~predo(mary) | fred != sK0 | ~room(mary) [subsumption resolution 287,228]
289. ~predo(mary) | fred != sK0 [subsumption resolution 288,227]
291. 6 <=> fred = sK0 [avatar definition]
293. fred != sK0 <- (~6) [avatar component clause 291]
294. ~6 | ~4 [avatar split clause 289,271,291]
295. ~predo(mary) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 245,231]
296. ~predo(mary) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,230]
297. ~predo(mary) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 296,229]
298. ~predo(mary) | paul != sK0 | ~room(mary) [subsumption resolution 297,228]
299. ~predo(mary) | paul != sK0 [subsumption resolution 298,227]
301. 7 <=> paul = sK0 [avatar definition]
303. paul != sK0 <- (~7) [avatar component clause 301]
304. ~7 | ~4 [avatar split clause 299,271,301]
305. ~predo(mary) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 244,231]
306. ~predo(mary) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,230]
307. ~predo(mary) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 306,229]
308. ~predo(mary) | mary != sK0 | ~room(mary) [subsumption resolution 307,228]
309. ~predo(mary) | mary != sK0 [subsumption resolution 308,227]
311. 8 <=> mary = sK0 [avatar definition]
313. mary != sK0 <- (~8) [avatar component clause 311]
314. ~8 | ~4 [avatar split clause 309,271,311]
315. ~predo(mary) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 243,231]
316. ~predo(mary) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,230]
317. ~predo(mary) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 316,229]
318. ~predo(mary) | room(sK0) | ~room(mary) [subsumption resolution 317,228]
319. ~predo(mary) | room(sK0) [subsumption resolution 318,227]
321. 9 <=> room(sK0) [avatar definition]
323. room(sK0) <- (9) [avatar component clause 321]
324. 9 | ~4 [avatar split clause 319,271,321]
325. predo(mary) [resolution 236,227]
332. 4 [avatar split clause 325,271]
417. alice = sK0 | fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (9) [resolution 232,323]
418. fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (~5, 9) [subsumption resolution 417,283]
419. paul = sK0 | mary = sK0 | john = sK0 <- (~5, ~6, 9) [subsumption resolution 418,293]
420. mary = sK0 | john = sK0 <- (~5, ~6, ~7, 9) [subsumption resolution 419,303]
421. john = sK0 <- (~5, ~6, ~7, ~8, 9) [subsumption resolution 420,313]
422. $false <- (~3, ~5, ~6, ~7, ~8, 9) [subsumption resolution 421,269]
423. 3 | 5 | 6 | 7 | 8 | ~9 [avatar contradiction clause 422]
424. $false [avatar sat refutation 274,284,294,304,314,324,332,423]
% SZS output end Proof for 737843249360521284709500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.029268 |
Lisa, Joseph, Roger are the only persons in the room.
Either "Joseph has completed a triathlon or enjoys virtual reality gaming or both" or "Lisa enjoys wildlife photography" but not both.
Everyone in the room is right-handed only if they enjoys macrame or can play the harmonica or both.
Lisa is a client of Costco.
Only one person in the room volunteers for local environmental conservation projects, is right-handed or is a night owl.
Everyone in the room who is a night owl or plays the violin or both maintains a personal blog focused on cybersecurity tips.
If someone either maintains a personal blog focused on cybersecurity tips or creates large-scale murals for public art installations but not both then he/she creates large-scale murals for public art installations and vice versa. | Lisa is a night owl. | contradiction | room(lisa)&room(joseph)&room(roger)&(![X]:(room(X)=>(X='lisa'|X='joseph'|X='roger')))&
((((has_completed_a_triathlon(joseph))|(enjoys_virtual_reality_gaming(joseph))))<~>(enjoys_wildlife_photography(lisa)))&
(![X]:(room(X)=>(((((enjoys_macrame(X))|(can_play_the_harmonica(X))))<=(is_right-handed(X))))))&
(is_a_client_of_Costco(lisa))&
(((?[X]:(room(X)&((volunteers_for_local_environmental_conservation_projects(X))|(is_right-handed(X))|(is_a_night_owl(X)))))&(![X,Y]:((room(X)&room(Y)&(((volunteers_for_local_environmental_conservation_projects(X))|(is_right-handed(X))|(is_a_night_owl(X))))&(((volunteers_for_local_environmental_conservation_projects(Y))|(is_right-handed(Y))|(is_a_night_owl(Y)))))=>(X=Y)))))&
(![X]:(room(X)=>(((((enjoys_snowboarding(X))<~>(uses_an_ios_phone(X))))<=(plays_the_violin(X))))))&
((![X]:((((has_completed_a_triathlon(X))<~>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))&
(((?[X]:(room(X)&~((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_right-handed(X)))))&(![X,Y]:((room(X)&room(Y)&(~((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_right-handed(X))))&(~((is_an_avid_mountain_climber_who_has_scaled_several_peaks(Y))|(is_right-handed(Y)))))=>(X=Y)))))&
(![X]:(anywhere(X)=>(((((enjoys_spelunking(X))|(enjoys_macrame(X))))=>(is_a_client_of_Costco(X))))))&
(((has_completed_a_triathlon(joseph))<~>(is_a_tea_enthusiast(joseph))))&
(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(collects_first_edition_books(X))))))&
(![X]:(room(X)=>(((collects_first_edition_books(X))=>(((is_a_night_owl(X))|(plays_the_violin(X))))))))&
(![X]:(room(X)=>(((((is_a_night_owl(X))|(plays_the_violin(X))))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(collects_limited-edition_art_prints_from_contemporary_artists(joseph))&
(![X]:(room(X)=>(((is_right-handed(X))=>(enjoys_macrame(X))))))&
(![X]:(~room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(collects_limited-edition_art_prints_from_contemporary_artists(X))))))&
(![X]:(room(X)=>(((has_completed_a_triathlon(X))<=(collects_limited-edition_art_prints_from_contemporary_artists(X))))))&
(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(enjoys_virtual_reality_gaming(X))))))&
(((is_a_dedicated_volunteer_for_local_community_service_projects(lisa))<~>(does_not_play_the_violin(lisa))))&
(![X]:(room(X)=>(can_play_the_harmonica(X))))&
(![X]:(room(X)=>(((is_not_a_night_owl(X))|(creates_large-scale_murals_for_public_art_installations(X))))))&
(~(is_a_dedicated_volunteer_for_local_community_service_projects(lisa)))&
((![X]:((((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<~>(creates_large-scale_murals_for_public_art_installations(X))))<=>(creates_large-scale_murals_for_public_art_installations(X))))) | room(lisa)&room(joseph)&room(roger)&(![X]:(room(X)=>(X='lisa'|X='joseph'|X='roger')))&
is_a_night_owl(lisa) | [
"p0",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 390135285914226609725105
% SZS output start Proof for 390135285914226609725105
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
56. ! [X0] : (room(X0) => ((predq(X0) | predh(X0)) => predg(X0))) [input p12]
66. ! [X0] : ((predg(X0) <~> predu(X0)) <=> predu(X0)) [input p22]
67. predh(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
149. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
150. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 149]
161. ! [X0] : ((predg(X0) | (~predq(X0) & ~predh(X0))) | ~room(X0)) [ennf transformation 56]
162. ! [X0] : (predg(X0) | (~predq(X0) & ~predh(X0)) | ~room(X0)) [flattening 161]
171. predh(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 67]
172. predh(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 171]
186. ! [X0] : ((((~predu(X0) | ~predg(X0)) & (predu(X0) | predg(X0))) | ~predu(X0)) & (predu(X0) | ((predg(X0) | ~predu(X0)) & (predu(X0) | ~predg(X0))))) [nnf transformation 66]
267. room(mary) [cnf transformation 150]
292. ~predh(X0) | predg(X0) | ~room(X0) [cnf transformation 162]
302. predu(X0) | predu(X0) | ~predg(X0) [cnf transformation 186]
305. ~predu(X0) | ~predg(X0) | ~predu(X0) [cnf transformation 186]
310. predh(mary) [cnf transformation 172]
311. predu(X0) | ~predg(X0) [duplicate literal removal 302]
312. ~predu(X0) | ~predg(X0) [duplicate literal removal 305]
358. ~predg(X0) [subsumption resolution 311,312]
359. predg(mary) | ~room(mary) [resolution 292,310]
360. ~room(mary) [subsumption resolution 359,358]
361. $false [subsumption resolution 360,267]
% SZS output end Proof for 390135285914226609725105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.118295 |
Sean, Edward, Yuki, Frederick are the only persons in the room.
Everyone anywhere who is an active member of a local robotics club or plays the drums or both does practice yoga.
Everyone anywhere maintains a large, organic vegetable garden year-round or is not an active member of a local robotics club.
At least one person outside the room enjoys cross-country skiing.
Someone outside the room uses contact lenses.
Everyone in the room who maintains a large, organic vegetable garden year-round and collects vintage vinyl records uses contact lenses.
Everyone in the room who enjoys cross-country skiing is an active member of a local robotics club.
Sean enjoys cross-country skiing.
Everyone in the room who is a culinary enthusiast who experiments with international cuisines or does practice yoga or both enjoys logic puzzles.
It is not the case that “it is not the case that “Sean collects antique clocks””.
If someone is a culinary enthusiast who experiments with international cuisines then he/she collects vintage vinyl records and vice versa.
Everyone in the room is a culinary enthusiast who experiments with international cuisines only if they has a curated collection of mid-century modern furniture.
If someone either enjoys cross-country skiing or collects vintage vinyl records but not both then he/she plays the drums and vice versa.
More than one person in the room either does practice yoga or enjoys logic puzzles but not both. | Sean enjoys logic puzzles. | entailment | room(sean)&room(edward)&room(yuki)&room(frederick)&(![X]:(room(X)=>(X='sean'|X='edward'|X='yuki'|X='frederick')))&
(![X]:(anywhere(X)=>(((((is_an_active_member_of_a_local_robotics_club(X))|(plays_the_drums(X))))=>(does_practice_yoga(X))))))&
(![X]:(anywhere(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(((?[X]:(~room(X)&enjoys_cross-country_skiing(X)))))&
(?[X]:(~room(X)&(uses_contact_lenses(X))))&
(![X]:(room(X)=>(((((maintains_a_large,_organic_vegetable_garden_year-round(X))&(collects_vintage_vinyl_records(X))))=>(uses_contact_lenses(X))))))&
(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))&
(enjoys_cross-country_skiing(sean))&
(![X]:(room(X)=>(((((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_practice_yoga(X))))=>(enjoys_logic_puzzles(X))))))&
(~(~(collects_antique_clocks(sean))))&
((![X]:((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<=>(collects_vintage_vinyl_records(X)))))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))<=(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
((![X]:((((enjoys_cross-country_skiing(X))<~>(collects_vintage_vinyl_records(X))))<=>(plays_the_drums(X)))))&
((?[X,Y]:(room(X)&room(Y)&(((does_practice_yoga(X))<~>(enjoys_logic_puzzles(X)))&((does_practice_yoga(Y))<~>(enjoys_logic_puzzles(Y))))&(X!=Y))))&
((![X]:((does_practice_yoga(X))=>(collects_antique_clocks(X))))) | room(sean)&room(edward)&room(yuki)&room(frederick)&(![X]:(room(X)=>(X='sean'|X='edward'|X='yuki'|X='frederick')))&
enjoys_logic_puzzles(sean) | [
"b4",
"p0",
"p1",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3687305078284494896522781
% SZS output start Proof for 3687305078284494896522781
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. ! [X0] : (anywhere(X0) => ((predb(X0) | predj(X0)) => predc(X0))) [input p1]
50. ! [X0] : (room(X0) => (predf(X0) => predj(X0))) [input p6]
51. predf(mary) [input p7]
52. ! [X0] : (room(X0) => ((predc(X0) | predh(X0)) => preda(X0))) [input p8]
59. ~(preda(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
139. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
140. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 139]
141. ! [X0] : ((predc(X0) | (~predb(X0) & ~predj(X0))) | ~anywhere(X0)) [ennf transformation 45]
142. ! [X0] : (predc(X0) | (~predb(X0) & ~predj(X0)) | ~anywhere(X0)) [flattening 141]
143. ! [X0] : ((predj(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 50]
144. ! [X0] : (predj(X0) | ~predf(X0) | ~room(X0)) [flattening 143]
145. ! [X0] : ((preda(X0) | (~predc(X0) & ~predh(X0))) | ~room(X0)) [ennf transformation 52]
146. ! [X0] : (preda(X0) | (~predc(X0) & ~predh(X0)) | ~room(X0)) [flattening 145]
149. ~preda(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59]
150. ~preda(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 149]
161. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
162. ~preda(mary) | (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 150,161]
163. anywhere(X0) [cnf transformation 5]
244. room(mary) [cnf transformation 140]
245. room(paul) [cnf transformation 140]
246. room(fred) [cnf transformation 140]
247. room(alice) [cnf transformation 140]
248. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 140]
249. predc(X0) | ~predj(X0) | ~anywhere(X0) [cnf transformation 142]
254. ~predf(X0) | predj(X0) | ~room(X0) [cnf transformation 144]
255. predf(mary) [cnf transformation 51]
257. ~predc(X0) | preda(X0) | ~room(X0) [cnf transformation 146]
268. ~preda(mary) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
269. ~preda(mary) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
270. ~preda(mary) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
271. ~preda(mary) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
272. ~preda(mary) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
274. ~predj(X0) | predc(X0) [subsumption resolution 249,163]
295. ~preda(mary) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,247]
296. ~preda(mary) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 295,246]
297. ~preda(mary) | alice != sK4 | ~room(mary) [subsumption resolution 296,245]
298. ~preda(mary) | alice != sK4 [subsumption resolution 297,244]
300. 5 <=> alice = sK4 [avatar definition]
302. alice != sK4 <- (~5) [avatar component clause 300]
304. 6 <=> preda(mary) [avatar definition]
307. ~5 | ~6 [avatar split clause 298,304,300]
308. ~preda(mary) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,247]
309. ~preda(mary) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 308,246]
310. ~preda(mary) | fred != sK4 | ~room(mary) [subsumption resolution 309,245]
311. ~preda(mary) | fred != sK4 [subsumption resolution 310,244]
313. 7 <=> fred = sK4 [avatar definition]
315. fred != sK4 <- (~7) [avatar component clause 313]
316. ~7 | ~6 [avatar split clause 311,304,313]
317. ~preda(mary) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,247]
318. ~preda(mary) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 317,246]
319. ~preda(mary) | paul != sK4 | ~room(mary) [subsumption resolution 318,245]
320. ~preda(mary) | paul != sK4 [subsumption resolution 319,244]
322. 8 <=> paul = sK4 [avatar definition]
324. paul != sK4 <- (~8) [avatar component clause 322]
325. ~8 | ~6 [avatar split clause 320,304,322]
326. ~preda(mary) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,247]
327. ~preda(mary) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 326,246]
328. ~preda(mary) | mary != sK4 | ~room(mary) [subsumption resolution 327,245]
329. ~preda(mary) | mary != sK4 [subsumption resolution 328,244]
331. 9 <=> mary = sK4 [avatar definition]
333. mary != sK4 <- (~9) [avatar component clause 331]
334. ~9 | ~6 [avatar split clause 329,304,331]
335. ~preda(mary) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,247]
336. ~preda(mary) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 335,246]
337. ~preda(mary) | room(sK4) | ~room(mary) [subsumption resolution 336,245]
338. ~preda(mary) | room(sK4) [subsumption resolution 337,244]
340. 10 <=> room(sK4) [avatar definition]
342. room(sK4) <- (10) [avatar component clause 340]
343. 10 | ~6 [avatar split clause 338,304,340]
345. predj(mary) | ~room(mary) [resolution 254,255]
346. predj(mary) [subsumption resolution 345,244]
347. predc(mary) [resolution 346,274]
352. preda(mary) | ~room(mary) [resolution 347,257]
356. preda(mary) [subsumption resolution 352,244]
357. 6 [avatar split clause 356,304]
423. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 <- (10) [resolution 248,342]
458. paul = sK4 | mary = sK4 | alice = sK4 <- (~7, 10) [subsumption resolution 423,315]
459. mary = sK4 | alice = sK4 <- (~7, ~8, 10) [subsumption resolution 458,324]
460. alice = sK4 <- (~7, ~8, ~9, 10) [subsumption resolution 459,333]
461. $false <- (~5, ~7, ~8, ~9, 10) [subsumption resolution 460,302]
462. 5 | 7 | 8 | 9 | ~10 [avatar contradiction clause 461]
463. $false [avatar sat refutation 307,316,325,334,343,357,462]
% SZS output end Proof for 3687305078284494896522781
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0.128388 |
There is a room. If someone hates Francis then he/she neither does not like Francis nor is not hated by David. At least one person in the room does not like Joseph or does not like Francis or both. Everyone in the room does not like David if they is hated by David. Everyone in the room who does not like David does not hate Joseph. If someone is not liked by David or does not hate Francis or both then he/she is not hated by Joseph. Everyone in the room who neither hates David nor is not liked by Joseph is not liked by David. Everyone in the room who is not liked by David does not like Francis. Everyone anywhere neither is not hated by David nor does not hate Francis if they is not liked by Joseph. Everyone anywhere either likes David or likes Francis but not both if they neither is not hated by David nor does not hate Francis. Everyone in the room either likes David or likes Francis but not both only if they is liked by David. Everyone anywhere is liked by David. Everyone in the room either does not hate Joseph or is not hated by Francis but not both if they neither does not hate David nor is not liked by Francis. | Everyone in the room hates Joseph. | contradiction | (there_is_a_room)&
((![X]:((hate(francis,X))=>(~((~like(francis,X))|(~hate(X,david)))))))&
(((?[X]:(room(X)&((~like(joseph,X))|(~like(francis,X)))))))&
(![X]:(room(X)=>(((hate(X,david))=>(~like(david,X))))))&
(![X]:(room(X)=>(((~like(david,X))=>(~hate(joseph,X))))))&
((![X]:((((~like(X,david))|(~hate(francis,X))))=>(~hate(X,joseph)))))&
(![X]:(room(X)=>(((~((hate(david,X))|(~like(X,joseph))))=>(~like(X,david))))))&
(![X]:(room(X)=>(((~like(X,david))=>(~like(francis,X))))))&
(![X]:(anywhere(X)=>(((~like(X,joseph))=>(~((~hate(X,david))|(~hate(francis,X))))))))&
(![X]:(anywhere(X)=>(((~((~hate(X,david))|(~hate(francis,X))))=>(((like(david,X))<~>(like(francis,X))))))))&
(![X]:(room(X)=>(((like(X,david))<=(((like(david,X))<~>(like(francis,X))))))))&
(![X]:(anywhere(X)=>(like(X,david))))&
(![X]:(room(X)=>(((~((~hate(david,X))|(~like(X,francis))))=>(((~hate(joseph,X))<~>(~hate(X,francis)))))))) | (there_is_a_room)&
![X]:(room(X)=>(hate(joseph,X))) | [
"b0",
"b4",
"p1",
"p2",
"p3",
"p4",
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3141412742609284914520687
% SZS output start Proof for 3141412742609284914520687
1. ! [X0,X1] : (X0 != X1 => (like(X0,X1) => ~hate(X0,X1))) [input b0]
5. ! [X0] : anywhere(X0) [input b4]
45. ! [X0] : (hate(mary,X0) => ~(~hate(X0,fred) | ~like(mary,X0))) [input p1]
46. ? [X0] : ((~like(mary,X0) | ~like(paul,X0)) & room(X0)) [input p2]
47. ! [X0] : (room(X0) => (hate(X0,fred) => ~like(fred,X0))) [input p3]
48. ! [X0] : (room(X0) => (~like(fred,X0) => ~hate(paul,X0))) [input p4]
50. ! [X0] : (room(X0) => (~(~like(X0,paul) | hate(fred,X0)) => ~like(X0,fred))) [input p6]
52. ! [X0] : (anywhere(X0) => (~like(X0,paul) => ~(~hate(mary,X0) | ~hate(X0,fred)))) [input p8]
53. ! [X0] : (anywhere(X0) => (~(~hate(mary,X0) | ~hate(X0,fred)) => (like(fred,X0) <~> like(mary,X0)))) [input p9]
55. ! [X0] : (anywhere(X0) => like(X0,fred)) [input p11]
57. ! [X0] : (room(X0) => hate(paul,X0)) & there_is_a_room [input hypothesis]
59. ! [X0] : (room(X0) => hate(paul,X0)) [pure predicate removal 57]
62. ! [X0,X1] : ((~hate(X0,X1) | ~like(X0,X1)) | X0 = X1) [ennf transformation 1]
63. ! [X0,X1] : (~hate(X0,X1) | ~like(X0,X1) | X0 = X1) [flattening 62]
133. ! [X0] : ((hate(X0,fred) & like(mary,X0)) | ~hate(mary,X0)) [ennf transformation 45]
134. ! [X0] : ((~like(fred,X0) | ~hate(X0,fred)) | ~room(X0)) [ennf transformation 47]
135. ! [X0] : (~like(fred,X0) | ~hate(X0,fred) | ~room(X0)) [flattening 134]
136. ! [X0] : ((~hate(paul,X0) | like(fred,X0)) | ~room(X0)) [ennf transformation 48]
137. ! [X0] : (~hate(paul,X0) | like(fred,X0) | ~room(X0)) [flattening 136]
139. ! [X0] : ((~like(X0,fred) | (~like(X0,paul) | hate(fred,X0))) | ~room(X0)) [ennf transformation 50]
140. ! [X0] : (~like(X0,fred) | ~like(X0,paul) | hate(fred,X0) | ~room(X0)) [flattening 139]
143. ! [X0] : (((hate(mary,X0) & hate(X0,fred)) | like(X0,paul)) | ~anywhere(X0)) [ennf transformation 52]
144. ! [X0] : ((hate(mary,X0) & hate(X0,fred)) | like(X0,paul) | ~anywhere(X0)) [flattening 143]
145. ! [X0] : (((like(fred,X0) <~> like(mary,X0)) | (~hate(mary,X0) | ~hate(X0,fred))) | ~anywhere(X0)) [ennf transformation 53]
146. ! [X0] : ((like(fred,X0) <~> like(mary,X0)) | ~hate(mary,X0) | ~hate(X0,fred) | ~anywhere(X0)) [flattening 145]
149. ! [X0] : (like(X0,fred) | ~anywhere(X0)) [ennf transformation 55]
152. ! [X0] : (hate(paul,X0) | ~room(X0)) [ennf transformation 59]
154. ? [X0] : ((~like(mary,X0) | ~like(paul,X0)) & room(X0)) => ((~like(mary,sK0) | ~like(paul,sK0)) & room(sK0)) [choice axiom]
155. (~like(mary,sK0) | ~like(paul,sK0)) & room(sK0) [skolemisation 46,154]
156. ! [X0] : (((~like(mary,X0) | ~like(fred,X0)) & (like(mary,X0) | like(fred,X0))) | ~hate(mary,X0) | ~hate(X0,fred) | ~anywhere(X0)) [nnf transformation 146]
159. ~hate(X0,X1) | ~like(X0,X1) | X0 = X1 [cnf transformation 63]
161. anywhere(X0) [cnf transformation 5]
242. ~hate(mary,X0) | like(mary,X0) [cnf transformation 133]
243. ~hate(mary,X0) | hate(X0,fred) [cnf transformation 133]
244. room(sK0) [cnf transformation 155]
246. ~hate(X0,fred) | ~like(fred,X0) | ~room(X0) [cnf transformation 135]
247. ~hate(paul,X0) | like(fred,X0) | ~room(X0) [cnf transformation 137]
250. ~like(X0,fred) | ~like(X0,paul) | hate(fred,X0) | ~room(X0) [cnf transformation 140]
253. hate(mary,X0) | like(X0,paul) | ~anywhere(X0) [cnf transformation 144]
255. ~like(mary,X0) | ~like(fred,X0) | ~hate(mary,X0) | ~hate(X0,fred) | ~anywhere(X0) [cnf transformation 156]
258. like(X0,fred) | ~anywhere(X0) [cnf transformation 149]
261. hate(paul,X0) | ~room(X0) [cnf transformation 152]
271. hate(mary,X0) | like(X0,paul) [subsumption resolution 253,161]
273. ~like(mary,X0) | ~like(fred,X0) | ~hate(mary,X0) | ~hate(X0,fred) [subsumption resolution 255,161]
274. ~like(mary,X0) | ~like(fred,X0) | ~hate(mary,X0) [subsumption resolution 273,243]
275. ~hate(mary,X0) | ~like(fred,X0) [subsumption resolution 274,242]
277. like(X0,fred) [subsumption resolution 258,161]
315. ~like(fred,X0) | like(X0,paul) [resolution 275,271]
325. like(fred,X0) | ~room(X0) | ~room(X0) [resolution 247,261]
327. like(fred,X0) | ~room(X0) [duplicate literal removal 325]
359. like(X0,paul) | ~room(X0) [resolution 315,327]
417. ~like(X0,paul) | hate(fred,X0) | ~room(X0) [resolution 250,277]
421. hate(fred,X0) | ~room(X0) [subsumption resolution 417,359]
424. ~room(fred) | ~like(fred,fred) | ~room(fred) [resolution 421,246]
425. ~room(X0) | ~like(fred,X0) | fred = X0 [resolution 421,159]
426. ~room(fred) | ~like(fred,fred) [duplicate literal removal 424]
427. ~room(X0) | fred = X0 [subsumption resolution 425,327]
433. fred = sK0 [resolution 427,244]
435. room(fred) [backward demodulation 244,433]
440. ~like(fred,fred) [subsumption resolution 426,435]
441. $false [subsumption resolution 440,277]
% SZS output end Proof for 3141412742609284914520687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0.131344 |
Louraie, Monica are the only persons in the room.
Louraie does not work on fridays.
It is not the case that “Louraie does not work as a freelance web developer specializing in e-commerce sites, enjoys writing detailed reviews of new and classic board games and bakes bread at home”.
If someone does not create YouTube content then he/she does not use an ios phone and does not enjoy camping and organizing outdoor survival workshops.
Louraie is a member of a local theater group specializing in improv.
Louraie neither does not enjoy origami nor does not compete in national level swimming championships.
Only one person in the room is not a professional photographer specializing in portrait photography.
Louraie enjoys writing detailed reviews of new and classic board games, does not use an ios phone and is an avid collector of autographed memorabilia from famous musicians.
Louraie who does not create augmented reality experiences for mobile applications, participates in long-distance cycling events across the country or is not a craft beer aficionado cannot play the flute, participates in long-distance cycling events across the country and does not create YouTube content.
Louraie is a craft beer aficionado, uses a Windows laptop or is not an avid collector of autographed memorabilia from famous musicians.
If someone does not write poetry then he/she is not a dedicated advocate for digital privacy and encryption and does not use a Windows laptop and vice versa.
Louraie can play the guitar.
Louraie collects modern art.
If someone is not a member of a local theater group specializing in improv then he/she cannot play the guitar and enjoys stand-up paddleboarding.
Only one person in the room does not have a piercing.
Louraie does not write poetry. | Everyone in the room is not a craft beer aficionado or works on fridays. | contradiction | room(louraie)&room(monica)&(![X]:(room(X)=>(X='louraie'|X='monica')))&
(does_not_work_on_fridays(louraie))&
(~(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(louraie))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(louraie))&(bakes_bread_at_home(louraie)))))&
((![X]:((does_not_create_YouTube_content(X))=>(((does_not_use_an_ios_phone(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X)))))))&
(is_a_member_of_a_local_theater_group_specializing_in_improv(louraie))&
(~((does_not_enjoy_origami(louraie))|(does_not_compete_in_national_level_swimming_championships(louraie))))&
(((?[X]:(room(X)&is_not_a_professional_photographer_specializing_in_portrait_photography(X)))&(![X,Y]:((room(X)&room(Y)&(is_not_a_professional_photographer_specializing_in_portrait_photography(X))&(is_not_a_professional_photographer_specializing_in_portrait_photography(Y)))=>(X=Y)))))&
(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(louraie))&(does_not_use_an_ios_phone(louraie))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(louraie))))&
((((does_not_create_augmented_reality_experiences_for_mobile_applications(louraie))|(participates_in_long-distance_cycling_events_across_the_country(louraie))|(is_not_a_craft_beer_aficionado(louraie))))&(((cannot_play_the_flute(louraie))&(participates_in_long-distance_cycling_events_across_the_country(louraie))&(does_not_create_YouTube_content(louraie)))))&
(((is_a_craft_beer_aficionado(louraie))|(uses_a_Windows_laptop(louraie))|(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(louraie))))&
((![X]:((does_not_write_poetry(X))<=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(does_not_use_a_Windows_laptop(X)))))))&
(can_play_the_guitar(louraie))&
(collects_modern_art(louraie))&
((![X]:((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(((cannot_play_the_guitar(X))&(enjoys_stand-up_paddleboarding(X)))))))&
(((?[X]:(room(X)&does_not_have_a_piercing(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_have_a_piercing(X))&(does_not_have_a_piercing(Y)))=>(X=Y)))))&
(does_not_write_poetry(louraie)) | room(louraie)&room(monica)&(![X]:(room(X)=>(X='louraie'|X='monica')))&
![X]:(room(X)=>(((works_on_fridays(X))|(is_not_a_craft_beer_aficionado(X))))) | [
"p0",
"p1",
"p7",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3841406497933304128369238
% SZS output start Proof for 3841406497933304128369238
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
45. ~predd(mary) [input p1]
51. predx(mary) & ~predq(mary) & predk(mary) [input p7]
53. ~predx(mary) | predw(mary) | predg(mary) [input p9]
54. ! [X0] : (~predb(X0) <=> (~predw(X0) & ~predr(X0))) [input p10]
59. ~predb(mary) [input p15]
60. ! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
63. ! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 60]
64. ! [X0] : (~predb(X0) => (~predw(X0) & ~predr(X0))) [unused predicate definition removal 54]
65. ! [X0] : (~predb(X0) => ~predw(X0)) [pure predicate removal 64]
76. predx(mary) & predk(mary) [pure predicate removal 51]
80. predx(mary) [pure predicate removal 76]
153. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
154. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 153]
157. ! [X0] : (~predw(X0) | predb(X0)) [ennf transformation 65]
160. ! [X0] : ((~predg(X0) | predd(X0)) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 63]
161. ! [X0] : (~predg(X0) | predd(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 160]
247. room(mary) [cnf transformation 154]
250. ~predd(mary) [cnf transformation 45]
254. predx(mary) [cnf transformation 80]
255. ~predx(mary) | predw(mary) | predg(mary) [cnf transformation 53]
256. ~predw(X0) | predb(X0) [cnf transformation 157]
260. ~predb(mary) [cnf transformation 59]
264. ~predg(X0) | predd(X0) | ~room(X0) [cnf transformation 161]
265. predw(mary) | predg(mary) [subsumption resolution 255,254]
267. 1 <=> predg(mary) [avatar definition]
269. predg(mary) <- (1) [avatar component clause 267]
271. 2 <=> predw(mary) [avatar definition]
273. predw(mary) <- (2) [avatar component clause 271]
274. 1 | 2 [avatar split clause 265,271,267]
275. predb(mary) <- (2) [resolution 256,273]
276. $false <- (2) [subsumption resolution 275,260]
277. ~2 [avatar contradiction clause 276]
278. predd(mary) | ~room(mary) <- (1) [resolution 264,269]
279. ~room(mary) <- (1) [subsumption resolution 278,250]
280. $false <- (1) [subsumption resolution 279,247]
281. ~1 [avatar contradiction clause 280]
282. $false [avatar sat refutation 274,277,281]
% SZS output end Proof for 3841406497933304128369238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.304275 |
Francis, Laura, Kari, Frank are the only persons in the room. Francis likes Kim. | Everyone anywhere neither is a happy person nor is a kind happy person. | neutral | room(francis)&room(laura)&room(kari)&room(frank)&(![X]:(room(X)=>(X='francis'|X='laura'|X='kari'|X='frank')))&
(like(kim,francis))&
(![X]:(room(X)=>(((curious(X))=>(~like(patricia,X))))))&
(louder(patricia,kari))&
(~?[X]:(old(X)=>kind(X)))&
(~((sibling(kim,frank))|(~(curious(frank)&calm(frank)&person(frank)))))&
(enjoys_snowboarding(laura))&
(![X]:(room(X)=>(((enjoys_snowboarding(X))=>(younger(kim,X))))))&
(![X]:(anywhere(X)=>(((~((~hate(scot,X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(is_a_coffee_connoisseur(X))))))&
((francis_dream=>((like(kim,francis) & like(francis,kim)))))&
(![X]:(room(X)=>(((~happy(X))=>(quiet(X)&tourist(X)))))) | room(francis)&room(laura)&room(kari)&room(frank)&(![X]:(room(X)=>(X='francis'|X='laura'|X='kari'|X='frank')))&
![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X))))) | [] | null | 0 |
Jillian, Henry, Betty, Sylvia are the only persons in the room.
Everyone in the room builds model airplanes.
Everyone in the room practices zumba only if they enjoys rooftop gardening.
Everyone in the room drives a hybrid car if they enjoys rooftop gardening.
Everyone in the room who drives a hybrid car enjoys stargazing.
Betty is an amateur astronomer who builds and uses custom telescopes.
Jillian is an amateur astronomer who builds and uses custom telescopes.
Henry who drives a hybrid car enjoys rooftop gardening.
Everyone in the room competes in national level swimming championships if they enjoys kayaking and vice versa.
Everyone in the room enjoys writing detailed reviews of new and classic board games if they practices urban gardening.
Everyone in the room does not enjoy kayaking if they builds model airplanes.
Henry who drives a hybrid car practices urban gardening.
Not everyone in the room who practices zumba creates bespoke furniture pieces from reclaimed wood.
Henry enjoys rooftop gardening.
Not everyone in the room does not enjoy rooftop gardening if they is not an amateur astronomer who builds and uses custom telescopes.
Not everyone in the room drives a hybrid car.
Henry collects comic books.
Jillian dreamt that 'Betty enjoys kayaking'.
Everyone in the room who does not own a television does not collect comic books.
Everyone in the room who enjoys kayaking practices kickboxing.
If someone is an amateur astronomer who builds and uses custom telescopes then he/she does not practice kickboxing and vice versa.
Sylvia does not compete in national level swimming championships. | Betty practices kickboxing. | contradiction | room(jillian)&room(henry)&room(betty)&room(sylvia)&(![X]:(room(X)=>(X='jillian'|X='henry'|X='betty'|X='sylvia')))&
(![X]:(room(X)=>(builds_model_airplanes(X))))&
(![X]:(room(X)=>(((enjoys_rooftop_gardening(X))<=(practices_zumba(X))))))&
(![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(drives_a_hybrid_car(X))))))&
(![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(enjoys_stargazing(X))))))&
(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(betty))&
(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(jillian))&
((drives_a_hybrid_car(henry))&(enjoys_rooftop_gardening(henry)))&
(![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))<=>(enjoys_kayaking(X))))))&
(![X]:(room(X)=>(((practices_urban_gardening(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))&
(![X]:(room(X)=>(((builds_model_airplanes(X))=>(does_not_enjoy_kayaking(X))))))&
((drives_a_hybrid_car(henry))&(practices_urban_gardening(henry)))&
(~![X]:(room(X)=>(((practices_zumba(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(enjoys_rooftop_gardening(henry))&
(~![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(does_not_enjoy_rooftop_gardening(X))))))&
(~![X]:(room(X)=>(drives_a_hybrid_car(X))))&
(collects_comic_books(henry))&
((jillian_dream=>(enjoys_kayaking(betty))))&
(![X]:(room(X)=>(((does_not_own_a_television(X))=>(does_not_collect_comic_books(X))))))&
(![X]:(room(X)=>(((enjoys_kayaking(X))=>(practices_kickboxing(X))))))&
((![X]:((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=>(does_not_practice_kickboxing(X)))))&
(does_not_compete_in_national_level_swimming_championships(sylvia))&
(![X]:(~room(X)=>(((enjoys_rooftop_gardening(X))=>(does_not_enjoy_rooftop_gardening(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))=>(own_a_television(X))))))&
(?[X]:(room(X)&(own_a_television(X)))) | room(jillian)&room(henry)&room(betty)&room(sylvia)&(![X]:(room(X)=>(X='jillian'|X='henry'|X='betty'|X='sylvia')))&
practices_kickboxing(betty) | [
"p5",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2771645297103006338358238
% SZS output start Proof for 2771645297103006338358238
49. predj(fred) [input p5]
64. ! [X0] : (predj(X0) <=> ~prede(X0)) [input p20]
69. prede(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
169. prede(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 69]
170. prede(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 169]
179. ! [X0] : ((predj(X0) | prede(X0)) & (~prede(X0) | ~predj(X0))) [nnf transformation 64]
270. predj(fred) [cnf transformation 49]
287. ~prede(X0) | ~predj(X0) [cnf transformation 179]
297. prede(fred) [cnf transformation 170]
308. ~predj(fred) [resolution 287,297]
309. $false [subsumption resolution 308,270]
% SZS output end Proof for 2771645297103006338358238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.142784 |
Hoyt, Linda are the only persons in the room.
Either “Hoyt is not hated by Diane or is liked by Diane or both” or “Hoyt and Herbert like each other” but not both.
“Someone outside the room does not hate Diane” only if “Herbert and Hoyt hate each other”.
“Hoyt is liked by Herbert or is not liked by Herbert or both” only if “if someone is hated by Diane then he/she hates Herbert and vice versa”.
If “Linda is not hated by Herbert” then “Hoyt is liked by Herbert and is not liked by Herbert”.
“It is not the case that “it is not the case that “Linda does not like Herbert””” if “Diane and Linda like each other”.
“Diane and Linda like each other” only if “Linda is not liked by Herbert”.
“Hoyt does not like Herbert or likes Herbert or both” only if “Hoyt is not liked by Herbert”.
“Linda does not hate Herbert” if “Linda and Herbert hate each other”.
If someone does not hate Diane then he/she either likes Herbert or is not liked by Herbert but not both.
Linda does not hate Herbert.
Hoyt is not liked by Diane.
Linda does not hate Diane or is hated by Diane or both. | Hoyt is hated by Herbert. | neutral | room(hoyt)&room(linda)&(![X]:(room(X)=>(X='hoyt'|X='linda')))&
((((~hate(hoyt,diane))|(like(hoyt,diane))))<~>((like(hoyt,herbert) & like(herbert,hoyt))))&
((?[X]:(~room(X)&(~hate(diane,X))))=>((hate(herbert,hoyt) & hate(hoyt,herbert))))&
((((like(hoyt,herbert))|(~like(hoyt,herbert))))=>((![X]:((hate(X,diane))<=>(hate(herbert,X))))))&
((~hate(linda,herbert))=>(((like(hoyt,herbert))&(~like(hoyt,herbert)))))&
(((like(diane,linda) & like(linda,diane)))=>(~(~(~like(herbert,linda)))))&
(((like(diane,linda) & like(linda,diane)))=>(~like(linda,herbert)))&
((((~like(herbert,hoyt))|(like(herbert,hoyt))))=>(~like(hoyt,herbert)))&
(((hate(linda,herbert) & hate(herbert,linda)))=>(~hate(herbert,linda)))&
((![X]:((~hate(diane,X))=>(((like(herbert,X))<~>(~like(X,herbert)))))))&
(~hate(herbert,linda))&
(~like(hoyt,diane))&
(((~hate(diane,linda))|(hate(linda,diane))))&
((hoyt_dream=>(~hate(hoyt,herbert)&~hate(linda,herbert))))&
((![X]:((((hate(X,herbert))&(like(X,herbert))))=>(like(X,herbert))))) | room(hoyt)&room(linda)&(![X]:(room(X)=>(X='hoyt'|X='linda')))&
hate(hoyt,herbert) | [] | null | 0.180378 |
Ivan, Adolph, Franklin, Anthony are the only persons in the room.
Everyone in the room either collects comic books or enjoys watercolor painting but not both if they is not an avid mountain climber who has scaled several peaks.
Everyone in the room is an avid mountain climber who has scaled several peaks if they either collects comic books or enjoys watercolor painting but not both.
Ivan either does not enjoy kayaking and exploring remote waterways or is an avid mountain climber who has scaled several peaks but not both.
Everyone in the room plays the violin if they neither trains for and competes in international triathlons nor is a wine connoisseur with a private cellar of vintage wines.
Everyone in the room who plays the violin is a wine connoisseur with a private cellar of vintage wines.
Everyone in the room is a wine connoisseur with a private cellar of vintage wines only if they has a tattoo.
Everyone anywhere is a wine connoisseur with a private cellar of vintage wines if they has a tattoo.
Everyone in the room does not play the violin if they is an avid mountain climber who has scaled several peaks. | Adolph plays the violin. | contradiction | room(ivan)&room(adolph)&room(franklin)&room(anthony)&(![X]:(room(X)=>(X='ivan'|X='adolph'|X='franklin'|X='anthony')))&
(![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(((collects_comic_books(X))<~>(enjoys_watercolor_painting(X))))))))&
(![X]:(room(X)=>(((((collects_comic_books(X))<~>(enjoys_watercolor_painting(X))))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))&
(((does_not_enjoy_kayaking_and_exploring_remote_waterways(ivan))<~>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(ivan))))&
(![X]:(room(X)=>(((~((trains_for_and_competes_in_international_triathlons(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))=>(plays_the_violin(X))))))&
(![X]:(room(X)=>(((plays_the_violin(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(![X]:(room(X)=>(((has_a_tattoo(X))<=(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(![X]:(anywhere(X)=>(((has_a_tattoo(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(![X]:(room(X)=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))&
(![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))&
(![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(does_not_play_the_violin(X))))))&
(has_a_tattoo(adolph)) | room(ivan)&room(adolph)&room(franklin)&room(anthony)&(![X]:(room(X)=>(X='ivan'|X='adolph'|X='franklin'|X='anthony')))&
plays_the_violin(adolph) | [
"p0",
"p1",
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5298564262484883475949319
% SZS output start Proof for 5298564262484883475949319
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. ! [X0] : (room(X0) => (~predi(X0) => (predc(X0) <~> predk(X0)))) [input p1]
46. ! [X0] : (room(X0) => ((predc(X0) <~> predk(X0)) => predi(X0))) [input p2]
55. ! [X0] : (room(X0) => (predi(X0) => ~predh(X0))) [input p11]
57. predh(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
131. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
132. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 131]
133. ! [X0] : (((predc(X0) <~> predk(X0)) | predi(X0)) | ~room(X0)) [ennf transformation 45]
134. ! [X0] : ((predc(X0) <~> predk(X0)) | predi(X0) | ~room(X0)) [flattening 133]
135. ! [X0] : ((predi(X0) | (predc(X0) <=> predk(X0))) | ~room(X0)) [ennf transformation 46]
136. ! [X0] : (predi(X0) | (predc(X0) <=> predk(X0)) | ~room(X0)) [flattening 135]
146. ! [X0] : ((~predh(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 55]
147. ! [X0] : (~predh(X0) | ~predi(X0) | ~room(X0)) [flattening 146]
148. predh(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 57]
149. predh(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 148]
151. ! [X0] : (((~predk(X0) | ~predc(X0)) & (predk(X0) | predc(X0))) | predi(X0) | ~room(X0)) [nnf transformation 134]
152. ! [X0] : (predi(X0) | ((predc(X0) | ~predk(X0)) & (predk(X0) | ~predc(X0))) | ~room(X0)) [nnf transformation 136]
236. room(paul) [cnf transformation 132]
240. ~room(X0) | predc(X0) | predi(X0) | predk(X0) [cnf transformation 151]
241. ~predk(X0) | ~predc(X0) | predi(X0) | ~room(X0) [cnf transformation 151]
242. predi(X0) | predk(X0) | ~predc(X0) | ~room(X0) [cnf transformation 152]
243. predi(X0) | predc(X0) | ~predk(X0) | ~room(X0) [cnf transformation 152]
251. ~predh(X0) | ~predi(X0) | ~room(X0) [cnf transformation 147]
258. predh(paul) [cnf transformation 149]
259. ~room(X0) | predc(X0) | predi(X0) [subsumption resolution 243,240]
260. ~room(X0) | predk(X0) | predi(X0) [subsumption resolution 242,240]
285. ~predi(paul) | ~room(paul) [resolution 251,258]
286. ~predi(paul) [subsumption resolution 285,236]
288. predc(paul) | predi(paul) [resolution 259,236]
292. predc(paul) [subsumption resolution 288,286]
312. predk(paul) | predi(paul) [resolution 260,236]
316. predk(paul) [subsumption resolution 312,286]
337. ~predc(paul) | predi(paul) | ~room(paul) [resolution 316,241]
338. predi(paul) | ~room(paul) [subsumption resolution 337,292]
339. ~room(paul) [subsumption resolution 338,286]
340. $false [subsumption resolution 339,236]
% SZS output end Proof for 5298564262484883475949319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.076939 |
Lula is the only person in the room.
Lula is a night owl.
Lula collects action figures.
Lula either is not an avid hiker or can play the flute but not both.
It is not the case that “Lula does not make homemade pastries”.
Lula who enjoys kayaking enjoys wildlife photography.
If someone collects action figures then he/she owns a telescope and vice versa.
Lula creates large-scale murals for public art installations.
Lula enjoys wildlife photography.
Lula enjoys kayaking.
Lula has a specialized collection of handmade artisan pottery.
Lula is an avid hiker.
Lula maintains a personal blog focused on cybersecurity tips.
Only one person in the room maintains a personal blog focused on cybersecurity tips.
Lula dreamt that “someone in the room hosts themed dinner parties featuring gourmet home-cooked meals, makes homemade pastries or does not own a smartwatch”.
Lula has a vast collection of first-edition science fiction novels and hosts themed dinner parties featuring gourmet home-cooked meals. | Lula is an avid hiker. | entailment | room(lula)&(![X]:(room(X)=>(X='lula')))&
(is_a_night_owl(lula))&
(collects_action_figures(lula))&
(((is_not_an_avid_hiker(lula))<~>(can_play_the_flute(lula))))&
(~(does_not_make_homemade_pastries(lula)))&
((enjoys_kayaking(lula))&(enjoys_wildlife_photography(lula)))&
((![X]:((collects_action_figures(X))<=>(owns_a_telescope(X)))))&
(creates_large-scale_murals_for_public_art_installations(lula))&
(enjoys_wildlife_photography(lula))&
(enjoys_kayaking(lula))&
(has_a_specialized_collection_of_handmade_artisan_pottery(lula))&
(is_an_avid_hiker(lula))&
(maintains_a_personal_blog_focused_on_cybersecurity_tips(lula))&
(((?[X]:(room(X)&maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))&(![X,Y]:((room(X)&room(Y)&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(Y)))=>(X=Y)))))&
((lula_dream=>(?[X]:(room(X)&(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(makes_homemade_pastries(X))|(does_not_own_a_smartwatch(X))))))))&
(((has_a_vast_collection_of_first-edition_science_fiction_novels(lula))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(lula)))) | room(lula)&(![X]:(room(X)=>(X='lula')))&
is_an_avid_hiker(lula) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8406538283582784450710163
% SZS output start Proof for 8406538283582784450710163
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
55. predg(mary) [input p11]
60. ~(predg(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
149. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
152. ~predg(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 60]
157. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom]
158. ~predg(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 152,157]
239. room(mary) [cnf transformation 149]
240. ~room(X0) | mary = X0 [cnf transformation 149]
243. predg(mary) [cnf transformation 55]
248. ~predg(mary) | room(sK1) | ~room(mary) [cnf transformation 158]
249. ~predg(mary) | mary != sK1 | ~room(mary) [cnf transformation 158]
251. 1 <=> predg(mary) [avatar definition]
260. 1 [avatar split clause 243,251]
261. ~predg(mary) | mary != sK1 [subsumption resolution 249,239]
263. 3 <=> mary = sK1 [avatar definition]
265. mary != sK1 <- (~3) [avatar component clause 263]
266. ~3 | ~1 [avatar split clause 261,251,263]
267. ~predg(mary) | room(sK1) [subsumption resolution 248,239]
269. 4 <=> room(sK1) [avatar definition]
271. room(sK1) <- (4) [avatar component clause 269]
272. 4 | ~1 [avatar split clause 267,251,269]
275. mary = sK1 <- (4) [resolution 240,271]
278. $false <- (~3, 4) [subsumption resolution 275,265]
279. 3 | ~4 [avatar contradiction clause 278]
280. $false [avatar sat refutation 260,266,272,279]
% SZS output end Proof for 8406538283582784450710163
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.431513 |
There is a room. Everyone in the room is a client of Meta only if they hosts a YouTube channel dedicated to art tutorials. Everyone in the room who hosts a YouTube channel dedicated to art tutorials is a dedicated advocate for digital privacy and encryption. Everyone in the room frequently participates in hackathons and coding competitions if they does not host a YouTube channel dedicated to art tutorials and vice versa. Everyone in the room does not host a YouTube channel dedicated to art tutorials only if they does enjoy trail running. Everyone in the room who either enjoys bird watching or does not make homemade pastries but not both is a night owl or enjoys bird watching or both. Everyone in the room who enjoys spelunking does not make homemade pastries. Everyone in the room is a drone photographer if they is a dedicated advocate for digital privacy and encryption. Everyone in the room hosts a YouTube channel dedicated to art tutorials, enjoys watercolor painting and frequently participates in hackathons and coding competitions. Everyone in the room does practice yoga or does not enjoy watercolor painting. | Everyone in the room does practice yoga. | entailment | (there_is_a_room)&
(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))<=(is_a_client_of_Meta(X))))))&
(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))&
(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))<=>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(![X]:(room(X)=>(((does_enjoy_trail_running(X))<=(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(![X]:(room(X)=>(((((enjoys_bird_watching(X))<~>(does_not_make_homemade_pastries(X))))=>(((is_a_night_owl(X))|(enjoys_bird_watching(X))))))))&
(![X]:(room(X)=>(((enjoys_spelunking(X))=>(does_not_make_homemade_pastries(X))))))&
(![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(is_a_drone_photographer(X))))))&
((![X]:((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_enjoy_trail_running(X))|(frequently_participates_in_hackathons_and_coding_competitions(X)))))))&
(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(enjoys_watercolor_painting(X))&(frequently_participates_in_hackathons_and_coding_competitions(X))))))&
(![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_a_drone_photographer(X))))))&
(![X]:(room(X)=>(((((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(enjoys_landscape_photography(X))&(enjoys_spelunking(X))))<=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(enjoys_watercolor_painting(X))))))))&
(![X]:(room(X)=>(((((makes_homemade_pastries(X))&(is_not_a_client_of_Meta(X))))<=(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(does_practice_yoga(X))))))&
(![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(is_a_client_of_Meta(X))))))&
((![X]:((makes_homemade_pastries(X))<=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(makes_homemade_pastries(X))|(enjoys_landscape_photography(X)))))))&
(![X]:(room(X)=>(((does_practice_yoga(X))=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(does_enjoy_trail_running(X))&(enjoys_watercolor_painting(X))))))))&
((![X]:((collects_first_edition_books(X))<=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))&
(![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(enjoys_rooftop_gardening(X))))))&
((![X]:((does_not_enjoy_spelunking(X))=>(((has_lived_in_exactly_three_countries(X))&(is_a_drone_photographer(X))&(does_not_collect_first_edition_books(X))))))) | (there_is_a_room)&
![X]:(room(X)=>(does_practice_yoga(X))) | [
"p0",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1753416316656055306579485
% SZS output start Proof for 1753416316656055306579485
44. there_is_a_room [input p0]
53. ! [X0] : (room(X0) => (predp(X0) & prede(X0) & predi(X0))) [input p9]
57. ! [X0] : (room(X0) => (predk(X0) | ~prede(X0))) [input p13]
64. ~(! [X0] : (room(X0) => predk(X0)) & there_is_a_room) [input hypothesis]
156. ! [X0] : ((predp(X0) & prede(X0) & predi(X0)) | ~room(X0)) [ennf transformation 53]
160. ! [X0] : ((predk(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 57]
161. ! [X0] : (predk(X0) | ~prede(X0) | ~room(X0)) [flattening 160]
166. ? [X0] : (~predk(X0) & room(X0)) | ~there_is_a_room [ennf transformation 64]
173. ? [X0] : (~predk(X0) & room(X0)) => (~predk(sK0) & room(sK0)) [choice axiom]
174. (~predk(sK0) & room(sK0)) | ~there_is_a_room [skolemisation 166,173]
255. there_is_a_room [cnf transformation 44]
262. ~room(X0) | prede(X0) [cnf transformation 156]
271. predk(X0) | ~prede(X0) | ~room(X0) [cnf transformation 161]
279. room(sK0) | ~there_is_a_room [cnf transformation 174]
280. ~predk(sK0) | ~there_is_a_room [cnf transformation 174]
287. ~room(X0) | predk(X0) [subsumption resolution 271,262]
288. ~predk(sK0) [subsumption resolution 280,255]
289. room(sK0) [subsumption resolution 279,255]
294. predk(sK0) [resolution 287,289]
295. $false [subsumption resolution 294,288]
% SZS output end Proof for 1753416316656055306579485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
David is the only person in the room.
David uses an ios phone.
Everyone in the room collects foreign coins if they knows morse code, works on fridays or is a scotch connoisseur.
Someone in the room practices calligraphy.
Everyone in the room does not use an ios phone or has a curated collection of mid-century modern furniture. | David knows morse code. | neutral | room(david)&(![X]:(room(X)=>(X='david')))&
(uses_an_ios_phone(david))&
(![X]:(room(X)=>(((((knows_morse_code(X))|(works_on_fridays(X))|(is_a_scotch_connoisseur(X))))=>(collects_foreign_coins(X))))))&
(?[X]:(room(X)&(practices_calligraphy(X))))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_use_an_ios_phone(X))))))&
(![X]:(~room(X)=>(((does_not_use_an_ios_phone(X))=>(((owns_a_microscope(X))&(practices_calligraphy(X))))))))&
((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(david))&(practices_calligraphy(david)))&
(((knows_morse_code(david))|(works_on_fridays(david))|(is_a_scotch_connoisseur(david))))&
((owns_a_3D_printer(david))&(collects_comic_books(david)))&
(![X]:(room(X)=>(((((does_not_enjoy_watercolor_painting(X))|(owns_a_smartwatch(X))))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(?[X]:(room(X)&(((owns_a_3D_printer(X))|(is_a_client_of_LVMH(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))&
(![X]:(room(X)=>(((works_on_fridays(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))) | room(david)&(![X]:(room(X)=>(X='david')))&
knows_morse_code(david) | [] | null | 0.007869 |
Ronnie, Emma are the only persons in the room.
It is not the case that “Emma is not happy”.
Ronnie is funny.
If someone is not wise then he/she is not patient.
If someone is kind then he/she neither is not happy nor is a happy person.
Ronnie is a old person.
Ronnie is not wise.
Emma is a strong person.
Ronnie is calm.
Ronnie neither is a humble person nor is a kind person. | All calm persons are humble. | contradiction | room(ronnie)&room(emma)&(![X]:(room(X)=>(X='ronnie'|X='emma')))&
(~(~happy(emma)))&
(funny(ronnie))&
((![X]:((~wise(X))=>(~patient(X)))))&
((![X]:((kind(X))=>(~((~happy(X))|(happy(X)&person(X)))))))&
(old(ronnie)&person(ronnie))&
(~wise(ronnie))&
(strong(emma)&person(emma))&
(~(kind(emma)&person(emma)))&
((ronnie_dream=>(generous(emma)&person(emma))))&
(~(~quiet(emma)))&
(((~(generous(emma)&person(emma)))&(curious(emma))))&
(?[X,Y]:((brave(X)&person(X))&(quiet(Y)&person(Y))&(quieter(X,Y))))&
(calm(ronnie))&
(happy(emma))&
(~((humble(ronnie)&person(ronnie))|(kind(ronnie)&person(ronnie))))&
(![X]:(wise(X)=>old(X)))&
(((brave(ronnie)&person(ronnie))<~>(~(tall(ronnie)&person(ronnie)))))&
((![X]:((patient(X))=>(happy(X)))))&
(strong(emma))&
(~(calm(emma)&person(emma)))&
(~humble(emma))&
(happy(ronnie)&person(ronnie))&
(?[X,Y]:((~generous(X))&(funny(Y)&person(Y))&(richer(X,Y))))&
(tall(emma))&
(tall(ronnie)&person(ronnie))&
((![X]:((quiet(X)&person(X))=>(tall(X))))) | room(ronnie)&room(emma)&(![X]:(room(X)=>(X='ronnie'|X='emma')))&
![X]:(calm(X)=>humble(X)) | [
"p5",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6289551327716147954792024
% SZS output start Proof for 6289551327716147954792024
49. person(mary) & old(mary) [input p5]
57. calm(mary) [input p13]
59. ~((person(mary) & kind(mary)) | (person(mary) & humble(mary))) [input p15]
71. ! [X0] : (calm(X0) => humble(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
72. ! [X0] : (calm(X0) => humble(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 71]
80. ~(person(mary) & humble(mary)) [pure predicate removal 59]
165. ~person(mary) | ~humble(mary) [ennf transformation 80]
170. ! [X0] : (humble(X0) | ~calm(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 72]
171. ! [X0] : (humble(X0) | ~calm(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 170]
263. person(mary) [cnf transformation 49]
271. calm(mary) [cnf transformation 57]
272. ~person(mary) | ~humble(mary) [cnf transformation 165]
289. ~calm(X0) | humble(X0) [cnf transformation 171]
290. ~humble(mary) [subsumption resolution 272,263]
305. humble(mary) [resolution 289,271]
306. $false [subsumption resolution 305,290]
% SZS output end Proof for 6289551327716147954792024
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.65444 |
Chaya, Eunice, Frank are the only persons in the room.
If “not everyone in the room hosts regular game nights featuring complex strategy games” then “everyone in the room collects comic books if they cannot play the harmonica”.
Someone in the room does not host regular game nights featuring complex strategy games.
Everyone outside the room is not an avid hiker or maintains a large, organic vegetable garden year-round.
Eunice cannot play the harmonica.
Chaya who collects rare and antique scientific instruments does not enjoy stargazing.
Everyone anywhere neither owns a smartwatch nor collects rare and antique scientific instruments if they does not watche fantasy movies.
Eunice who maintains a large, organic vegetable garden year-round does not enjoy stargazing.
More than one person in the room owns a smartwatch.
Eunice is an avid hiker or does not collect rare and antique scientific instruments or both.
Everyone outside the room is a client of LVMH or owns a smart tv or both if they does not maintain a large, organic vegetable garden year-round.
Everyone in the room is an avid hiker if they is a client of LVMH or owns a smart tv or both.
Eunice is a client of LVMH.
Chaya who collects comic books does not own a high-end gaming PC with custom-built components.
Chaya is not a client of LVMH.
If someone does not watche fantasy movies then he/she owns a smart tv.
Eunice who maintains a large, organic vegetable garden year-round owns a smartwatch.
Everyone in the room collects comic books if they cannot play the harmonica.
If someone does not own a smartwatch then he/she owns a high-end gaming PC with custom-built components. | Chaya neither hosts regular game nights featuring complex strategy games nor owns a high-end gaming PC with custom-built components. | neutral | room(chaya)&room(eunice)&room(frank)&(![X]:(room(X)=>(X='chaya'|X='eunice'|X='frank')))&
((~![X]:(room(X)=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(![X]:(room(X)=>(((cannot_play_the_harmonica(X))=>(collects_comic_books(X)))))))&
(?[X]:(room(X)&(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))&
(![X]:(~room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(is_not_an_avid_hiker(X))))))&
(cannot_play_the_harmonica(eunice))&
((collects_rare_and_antique_scientific_instruments(chaya))&(does_not_enjoy_stargazing(chaya)))&
(![X]:(anywhere(X)=>(((does_not_watche_fantasy_movies(X))=>(~((owns_a_smartwatch(X))|(collects_rare_and_antique_scientific_instruments(X))))))))&
((maintains_a_large,_organic_vegetable_garden_year-round(eunice))&(does_not_enjoy_stargazing(eunice)))&
((?[X,Y]:(room(X)&room(Y)&(owns_a_smartwatch(X)&owns_a_smartwatch(Y))&(X!=Y))))&
(((is_an_avid_hiker(eunice))|(does_not_collect_rare_and_antique_scientific_instruments(eunice))))&
(![X]:(~room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))=>(((is_a_client_of_LVMH(X))|(owns_a_smart_tv(X))))))))&
(![X]:(room(X)=>(((((is_a_client_of_LVMH(X))|(owns_a_smart_tv(X))))=>(is_an_avid_hiker(X))))))&
(is_a_client_of_LVMH(eunice))&
((collects_comic_books(chaya))&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(chaya)))&
(is_not_a_client_of_LVMH(chaya))&
((![X]:((does_not_watche_fantasy_movies(X))=>(owns_a_smart_tv(X)))))&
((maintains_a_large,_organic_vegetable_garden_year-round(eunice))&(owns_a_smartwatch(eunice)))&
(![X]:(room(X)=>(((cannot_play_the_harmonica(X))=>(collects_comic_books(X))))))&
((![X]:((does_not_own_a_smartwatch(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))) | room(chaya)&room(eunice)&room(frank)&(![X]:(room(X)=>(X='chaya'|X='eunice'|X='frank')))&
~((hosts_regular_game_nights_featuring_complex_strategy_games(chaya))|(owns_a_high-end_gaming_PC_with_custom-built_components(chaya))) | [] | null | 0.215894 |
Betty, Debra are the only persons in the room.
Debra is not tall.
If someone is a quiet generous person then he/she is a humble strong creative curious funny person and vice versa.
Betty is a calm curious brave generous person.
If someone is a happy person then he/she is wise and vice versa.
All kind persons are wise.
Someone in the room neither is generous nor is not old.
Someone in the room is a quiet person.
All brave persons are curious.
Debra either is a generous person or is wise but not both. | Debra is not happy. | contradiction | room(betty)&room(debra)&(![X]:(room(X)=>(X='betty'|X='debra')))&
(~tall(debra))&
((![X]:((quiet(X)&generous(X)&person(X))<=>(humble(X)&strong(X)&creative(X)&curious(X)&funny(X)&person(X)))))&
(calm(betty)&curious(betty)&brave(betty)&generous(betty)&person(betty))&
((![X]:((happy(X)&person(X))<=>(wise(X)))))&
(![X]:(kind(X)=>wise(X)))&
(?[X]:(room(X)&(~((generous(X))|(~old(X))))))&
(?[X]:(room(X)&(quiet(X)&person(X))))&
(![X]:(brave(X)=>curious(X)))&
(?[X]:(room(X)&(happy(X))))&
(old(betty)&creative(betty)&quiet(betty)&person(betty))&
(![X]:((room(X)&(X!=betty))=>older(betty,X)))&
(((generous(debra)&person(debra))<~>(wise(debra)))) | room(betty)&room(debra)&(![X]:(room(X)=>(X='betty'|X='debra')))&
~happy(debra) | [
"p0",
"p3",
"p4",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2403245425723564893386488
% SZS output start Proof for 2403245425723564893386488
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
47. person(mary) & generous(mary) & brave(mary) & curious(mary) & calm(mary) [input p3]
48. ! [X0] : ((person(X0) & happy(X0)) <=> wise(X0)) [input p4]
50. ? [X0] : (~(~old(X0) | generous(X0)) & room(X0)) [input p6]
56. (person(paul) & generous(paul)) <~> wise(paul) [input p12]
57. ~happy(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
59. person(mary) & generous(mary) & brave(mary) & curious(mary) [pure predicate removal 47]
133. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
134. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 133]
135. ? [X0] : ((old(X0) & ~generous(X0)) & room(X0)) [ennf transformation 50]
136. ? [X0] : (old(X0) & ~generous(X0) & room(X0)) [flattening 135]
140. ~happy(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 57]
141. ~happy(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 140]
145. ! [X0] : (((person(X0) & happy(X0)) | ~wise(X0)) & (wise(X0) | (~person(X0) | ~happy(X0)))) [nnf transformation 48]
146. ! [X0] : (((person(X0) & happy(X0)) | ~wise(X0)) & (wise(X0) | ~person(X0) | ~happy(X0))) [flattening 145]
147. ? [X0] : (old(X0) & ~generous(X0) & room(X0)) => (old(sK0) & ~generous(sK0) & room(sK0)) [choice axiom]
148. old(sK0) & ~generous(sK0) & room(sK0) [skolemisation 136,147]
153. (~wise(paul) | (~person(paul) | ~generous(paul))) & (wise(paul) | (person(paul) & generous(paul))) [nnf transformation 56]
154. (~wise(paul) | ~person(paul) | ~generous(paul)) & (wise(paul) | (person(paul) & generous(paul))) [flattening 153]
237. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 134]
249. generous(mary) [cnf transformation 59]
252. ~wise(X0) | happy(X0) [cnf transformation 146]
254. room(sK0) [cnf transformation 148]
255. ~generous(sK0) [cnf transformation 148]
268. wise(paul) | generous(paul) [cnf transformation 154]
274. ~happy(paul) [cnf transformation 141]
277. 1 <=> generous(paul) [avatar definition]
278. generous(paul) <- (1) [avatar component clause 277]
281. 2 <=> wise(paul) [avatar definition]
282. wise(paul) <- (2) [avatar component clause 281]
286. 1 | 2 [avatar split clause 268,281,277]
287. happy(paul) <- (2) [resolution 252,282]
288. $false <- (2) [subsumption resolution 287,274]
289. ~2 [avatar contradiction clause 288]
303. mary = sK0 | paul = sK0 [resolution 237,254]
307. 5 <=> paul = sK0 [avatar definition]
309. paul = sK0 <- (5) [avatar component clause 307]
311. 6 <=> mary = sK0 [avatar definition]
313. mary = sK0 <- (6) [avatar component clause 311]
314. 5 | 6 [avatar split clause 303,311,307]
344. ~generous(paul) <- (5) [backward demodulation 255,309]
346. $false <- (1, 5) [subsumption resolution 344,278]
347. ~1 | ~5 [avatar contradiction clause 346]
355. ~generous(mary) <- (6) [backward demodulation 255,313]
357. $false <- (6) [subsumption resolution 355,249]
358. ~6 [avatar contradiction clause 357]
360. $false [avatar sat refutation 286,289,314,347,358]
% SZS output end Proof for 2403245425723564893386488
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.091682 |
Jeffrey is the only person in the room. If “Jeffrey volunteers for local environmental conservation projects” then “someone anywhere plays the violin”. If “Jeffrey is right-handed” then “Jeffrey volunteers for local environmental conservation projects and enjoys landscape photography”. Either “Jeffrey is right-handed” or “everyone in the room is right-handed or does not volunteer for local environmental conservation projects” but not both. It is not the case that “more than one person in the room is a dedicated volunteer for local community service projects”. Only one person in the room plays the violin. Jeffrey collects antique jewelry. | Jeffrey enjoys landscape photography, collects antique jewelry and is a dedicated volunteer for local community service projects. | neutral | room(jeffrey)&(![X]:(room(X)=>(X='jeffrey')))&
((volunteers_for_local_environmental_conservation_projects(jeffrey))=>(?[X]:(anywhere(X)&(plays_the_violin(X)))))&
((is_right-handed(jeffrey))=>(((volunteers_for_local_environmental_conservation_projects(jeffrey))&(enjoys_landscape_photography(jeffrey)))))&
((is_right-handed(jeffrey))<~>(![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(is_right-handed(X)))))))&
(~((?[X,Y]:(room(X)&room(Y)&(is_a_dedicated_volunteer_for_local_community_service_projects(X)&is_a_dedicated_volunteer_for_local_community_service_projects(Y))&(X!=Y)))))&
(((?[X]:(room(X)&plays_the_violin(X)))&(![X,Y]:((room(X)&room(Y)&(plays_the_violin(X))&(plays_the_violin(Y)))=>(X=Y)))))&
(collects_antique_jewelry(jeffrey)) | room(jeffrey)&(![X]:(room(X)=>(X='jeffrey')))&
((enjoys_landscape_photography(jeffrey))&(collects_antique_jewelry(jeffrey))&(is_a_dedicated_volunteer_for_local_community_service_projects(jeffrey))) | [] | null | 0.313277 |
Eula, Christopher are the only persons in the room.
If 'everyone in the room is allergic to anything or does not own a high-end gaming PC with custom-built components' then 'it is not the case that 'Eula enjoys making ceramics''.
'Christopher collects vintage stamps or is a dedicated volunteer for local community service projects or both' if 'not everyone anywhere is a dedicated advocate for digital privacy and encryption' and vice versa.
If 'everyone in the room is a dedicated volunteer for local community service projects or does not write in-depth travel guides for off-the-beaten-path destinations' then 'not everyone in the room practices tai chi, is an enthusiastic bird watcher who travels for rare sightings or own a television'.
If 'not everyone in the room practices tai chi, is an enthusiastic bird watcher who travels for rare sightings or own a television' then 'Eula owns a high-end gaming PC with custom-built components'.
If someone collects antique jewelry then he/she practices kickboxing.
Everyone in the room enjoys deep-sea diving and exploring underwater caves.
Only one person in the room either regularly goes on multi-day backpacking trips in national parks or does not own a high-end gaming PC with custom-built components but not both.
Eula practices kickboxing. | Christopher collects vintage stamps. | neutral | room(eula)&room(christopher)&(![X]:(room(X)=>(X='eula'|X='christopher')))&
((![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(is_allergic_to_anything(X))))))=>(~(enjoys_making_ceramics(eula))))&
((~![X]:(anywhere(X)=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))<=>(((collects_vintage_stamps(christopher))|(is_a_dedicated_volunteer_for_local_community_service_projects(christopher)))))&
(((![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))=>(~![X]:(room(X)=>(((practices_tai_chi(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(own_a_television(X)))))))&
((~![X]:(room(X)=>(((practices_tai_chi(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(own_a_television(X))))))=>(owns_a_high-end_gaming_PC_with_custom-built_components(eula))))&
((![X]:((collects_antique_jewelry(X))=>(practices_kickboxing(X)))))&
(![X]:(room(X)=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))&
(((?[X]:(room(X)&((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X)))))&(![X,Y]:((room(X)&room(Y)&(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))&(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(Y))<~>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(Y)))))=>(X=Y)))))&
(practices_kickboxing(eula))&
(~![X]:(~room(X)=>(((collects_luxury_watches(X))=>(collects_antique_jewelry(X))))))&
(~![X]:(room(X)=>(((practices_tai_chi(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(own_a_television(X))))))&
(owns_a_high-end_gaming_PC_with_custom-built_components(eula))&
(![X]:(room(X)=>(((practices_tai_chi(X))<=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(![X]:(room(X)=>(((collects_luxury_watches(X))=>(practices_archery(X))))))&
(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(christopher))&
(![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))&
(collects_antique_jewelry(christopher))&
(((?[X]:(room(X)&collects_luxury_watches(X)))&(![X,Y]:((room(X)&room(Y)&(collects_luxury_watches(X))&(collects_luxury_watches(Y)))=>(X=Y)))))&
(![X]:(anywhere(X)=>(((does_not_have_a_tattoo(X))=>(((is_a_cybersecurity_expert(X))|(develops_open-source_software_projects_in_their_free_time(X))|(collects_luxury_watches(X))))))))&
(![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))&
(![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X)))))) | room(eula)&room(christopher)&(![X]:(room(X)=>(X='eula'|X='christopher')))&
collects_vintage_stamps(christopher) | [] | null | 0.411046 |
Tona, Russell, Alphonso, Audrey are the only persons in the room. "Everyone in the room does not collect rare and antique scientific instruments" unless "not everyone in the room is not dedicated to sustainable living and zero-waste practices". Everyone outside the room is not a tea enthusiast, does not use an ios phone and is not a wine connoisseur with a private cellar of vintage wines. Everyone in the room is a certified yoga instructor teaching classes weekly and does not host a YouTube channel dedicated to art tutorials. | Tona is a certified yoga instructor teaching classes weekly. | entailment | room(tona)&room(russell)&room(alphonso)&room(audrey)&(![X]:(room(X)=>(X='tona'|X='russell'|X='alphonso'|X='audrey')))&
(~(~![X]:(room(X)=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))=>(![X]:(room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X)))))&
(![X]:(~room(X)=>(((is_not_a_tea_enthusiast(X))&(does_not_use_an_ios_phone(X))&(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(~![X]:(room(X)=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))&
(![X]:(~room(X)=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))&
(((?[X]:(~room(X)&is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(does_not_regularly_contributes_to_tech_forums_and_online_communities(X))))&
(![X]:(room(X)=>(does_not_enjoy_trail_running(X))))&
(![X]:(~room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(does_not_compete_in_national_level_swimming_championships(X))&(is_not_a_coffee_connoisseur(X))))))&
(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(((is_not_a_tea_enthusiast(X))&(does_not_collect_rare_and_antique_scientific_instruments(X))))))))&
(![X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(does_not_own_a_telescope(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))&
(~![X]:(anywhere(X)=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))&
(![X]:(room(X)=>(((does_not_collect_luxury_watches(X))|(is_not_a_coffee_connoisseur(X))))))&
(![X]:(~room(X)=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(![X]:(room(X)=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<~>(is_not_an_avid_hiker(X))))))&
(![X]:(anywhere(X)=>(((does_not_enjoy_fishing(X))=>(is_not_an_avid_hiker(X))))))&
(![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X)))))) | room(tona)&room(russell)&room(alphonso)&room(audrey)&(![X]:(room(X)=>(X='tona'|X='russell'|X='alphonso'|X='audrey')))&
is_a_certified_yoga_instructor_teaching_classes_weekly(tona) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2030369223210275589839180
% SZS output start Proof for 2030369223210275589839180
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
58. ! [X0] : (room(X0) => (~predx(X0) & predz(X0))) [input p14]
63. ~(predz(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
70. ! [X0] : (room(X0) => predz(X0)) [pure predicate removal 58]
159. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
160. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 159]
165. ! [X0] : (predz(X0) | ~room(X0)) [ennf transformation 70]
167. ~predz(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63]
168. ~predz(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 167]
177. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
178. ~predz(mary) | (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 168,177]
259. room(mary) [cnf transformation 160]
260. room(paul) [cnf transformation 160]
261. room(fred) [cnf transformation 160]
262. room(alice) [cnf transformation 160]
263. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 160]
269. ~room(X0) | predz(X0) [cnf transformation 165]
272. ~predz(mary) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
273. ~predz(mary) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
274. ~predz(mary) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
275. ~predz(mary) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
276. ~predz(mary) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
278. ~predz(mary) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,262]
279. ~predz(mary) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 278,261]
280. ~predz(mary) | alice != sK3 | ~room(mary) [subsumption resolution 279,260]
281. ~predz(mary) | alice != sK3 [subsumption resolution 280,259]
283. 1 <=> alice = sK3 [avatar definition]
285. alice != sK3 <- (~1) [avatar component clause 283]
287. 2 <=> predz(mary) [avatar definition]
290. ~1 | ~2 [avatar split clause 281,287,283]
291. ~predz(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,262]
292. ~predz(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 291,261]
293. ~predz(mary) | fred != sK3 | ~room(mary) [subsumption resolution 292,260]
294. ~predz(mary) | fred != sK3 [subsumption resolution 293,259]
296. 3 <=> fred = sK3 [avatar definition]
298. fred != sK3 <- (~3) [avatar component clause 296]
299. ~3 | ~2 [avatar split clause 294,287,296]
300. ~predz(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,262]
301. ~predz(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 300,261]
302. ~predz(mary) | paul != sK3 | ~room(mary) [subsumption resolution 301,260]
303. ~predz(mary) | paul != sK3 [subsumption resolution 302,259]
305. 4 <=> paul = sK3 [avatar definition]
307. paul != sK3 <- (~4) [avatar component clause 305]
308. ~4 | ~2 [avatar split clause 303,287,305]
309. ~predz(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,262]
310. ~predz(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 309,261]
311. ~predz(mary) | mary != sK3 | ~room(mary) [subsumption resolution 310,260]
312. ~predz(mary) | mary != sK3 [subsumption resolution 311,259]
314. 5 <=> mary = sK3 [avatar definition]
316. mary != sK3 <- (~5) [avatar component clause 314]
317. ~5 | ~2 [avatar split clause 312,287,314]
318. ~predz(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,262]
319. ~predz(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 318,261]
320. ~predz(mary) | room(sK3) | ~room(mary) [subsumption resolution 319,260]
321. ~predz(mary) | room(sK3) [subsumption resolution 320,259]
323. 6 <=> room(sK3) [avatar definition]
325. room(sK3) <- (6) [avatar component clause 323]
326. 6 | ~2 [avatar split clause 321,287,323]
327. predz(mary) [resolution 269,259]
334. 2 [avatar split clause 327,287]
390. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (6) [resolution 263,325]
408. paul = sK3 | mary = sK3 | alice = sK3 <- (~3, 6) [subsumption resolution 390,298]
409. mary = sK3 | alice = sK3 <- (~3, ~4, 6) [subsumption resolution 408,307]
410. alice = sK3 <- (~3, ~4, ~5, 6) [subsumption resolution 409,316]
411. $false <- (~1, ~3, ~4, ~5, 6) [subsumption resolution 410,285]
412. 1 | 3 | 4 | 5 | ~6 [avatar contradiction clause 411]
413. $false [avatar sat refutation 290,299,308,317,326,334,412]
% SZS output end Proof for 2030369223210275589839180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.359358 |
Flossie, Linda, Teri are the only persons in the room.
Linda regularly contributes to tech forums and online communities.
Everyone outside the room enjoys landscape photography.
Everyone in the room who regularly contributes to tech forums and online communities enjoys landscape photography.
Flossie regularly contributes to tech forums and online communities. | Linda enjoys landscape photography. | entailment | room(flossie)&room(linda)&room(teri)&(![X]:(room(X)=>(X='flossie'|X='linda'|X='teri')))&
(regularly_contributes_to_tech_forums_and_online_communities(linda))&
(![X]:(~room(X)=>(enjoys_landscape_photography(X))))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(enjoys_landscape_photography(X))))))&
(regularly_contributes_to_tech_forums_and_online_communities(flossie)) | room(flossie)&room(linda)&room(teri)&(![X]:(room(X)=>(X='flossie'|X='linda'|X='teri')))&
enjoys_landscape_photography(linda) | [
"p0",
"p1",
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3077099760652142186950384
% SZS output start Proof for 3077099760652142186950384
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
45. predc(paul) [input p1]
46. ! [X0] : (~room(X0) => predb(X0)) [input p2]
47. ! [X0] : (room(X0) => (predc(X0) => predb(X0))) [input p3]
49. ~(predb(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
122. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
123. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 122]
124. ! [X0] : (predb(X0) | room(X0)) [ennf transformation 46]
125. ! [X0] : ((predb(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 47]
126. ! [X0] : (predb(X0) | ~predc(X0) | ~room(X0)) [flattening 125]
127. ~predb(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 49]
128. ~predb(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 127]
130. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom]
131. ~predb(paul) | (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 128,130]
212. room(mary) [cnf transformation 123]
213. room(paul) [cnf transformation 123]
214. room(fred) [cnf transformation 123]
215. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 123]
216. predc(paul) [cnf transformation 45]
217. predb(X0) | room(X0) [cnf transformation 124]
218. predb(X0) | ~predc(X0) | ~room(X0) [cnf transformation 126]
220. ~predb(paul) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 131]
221. ~predb(paul) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 131]
222. ~predb(paul) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 131]
223. ~predb(paul) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 131]
224. ~predc(X0) | predb(X0) [subsumption resolution 218,217]
225. ~predb(paul) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 223,214]
226. ~predb(paul) | fred != sK0 | ~room(mary) [subsumption resolution 225,213]
227. ~predb(paul) | fred != sK0 [subsumption resolution 226,212]
229. 1 <=> fred = sK0 [avatar definition]
231. fred != sK0 <- (~1) [avatar component clause 229]
233. 2 <=> predb(paul) [avatar definition]
236. ~1 | ~2 [avatar split clause 227,233,229]
237. ~predb(paul) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 222,214]
238. ~predb(paul) | paul != sK0 | ~room(mary) [subsumption resolution 237,213]
239. ~predb(paul) | paul != sK0 [subsumption resolution 238,212]
241. 3 <=> paul = sK0 [avatar definition]
243. paul != sK0 <- (~3) [avatar component clause 241]
244. ~3 | ~2 [avatar split clause 239,233,241]
245. ~predb(paul) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 221,214]
246. ~predb(paul) | mary != sK0 | ~room(mary) [subsumption resolution 245,213]
247. ~predb(paul) | mary != sK0 [subsumption resolution 246,212]
249. 4 <=> mary = sK0 [avatar definition]
251. mary != sK0 <- (~4) [avatar component clause 249]
252. ~4 | ~2 [avatar split clause 247,233,249]
253. ~predb(paul) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 220,214]
254. ~predb(paul) | room(sK0) | ~room(mary) [subsumption resolution 253,213]
255. ~predb(paul) | room(sK0) [subsumption resolution 254,212]
257. 5 <=> room(sK0) [avatar definition]
259. room(sK0) <- (5) [avatar component clause 257]
260. 5 | ~2 [avatar split clause 255,233,257]
262. predb(paul) [resolution 224,216]
266. 2 [avatar split clause 262,233]
306. paul = sK0 | mary = sK0 | fred = sK0 <- (5) [resolution 215,259]
307. mary = sK0 | fred = sK0 <- (~3, 5) [subsumption resolution 306,243]
308. fred = sK0 <- (~3, ~4, 5) [subsumption resolution 307,251]
309. $false <- (~1, ~3, ~4, 5) [subsumption resolution 308,231]
310. 1 | 3 | 4 | ~5 [avatar contradiction clause 309]
311. $false [avatar sat refutation 236,244,252,260,266,310]
% SZS output end Proof for 3077099760652142186950384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.036525 |
Thaddeus, Wendy, Wilford, Jackie, Paul are the only persons in the room.
“Thaddeus does not write and illustrates their own graphic novels” if “everyone in the room does not develop open-source software projects in their free time, does not enjoy stargazing and writes and illustrates their own graphic novels” and vice versa.
“Wendy is not an avid hiker” unless “Thaddeus does not enjoy salsa dancing, is not a culinary enthusiast who experiments with international cuisines or does not enjoy logic puzzles”.
“Everyone in the room does not enjoy salsa dancing” if “everyone in the room does not practice tai chi or does not own a television or both” and vice versa.
Either “Wendy does not enjoy logic puzzles or does not write and illustrates their own graphic novels or both” or “someone in the room does not drive a hybrid car, does not own a significant collection of rare gemstones and minerals and does not know morse code” but not both.
Either “Thaddeus neither does not collect luxury watches nor does not enjoy salsa dancing” or “Thaddeus does not read mystery novels, is not a certified yoga instructor teaching classes weekly or does not enjoy logic puzzles” but not both.
Someone in the room does not enjoy salsa dancing or does not develop open-source software projects in their free time or both.
Wendy does not host a YouTube channel dedicated to art tutorials.
Thaddeus does not read mystery novels, is not a certified yoga instructor teaching classes weekly or does not enjoy logic puzzles.
Everyone in the room neither does not enjoy salsa dancing nor is not an avid hiker. | Thaddeus is an avid hiker. | entailment | room(thaddeus)&room(wendy)&room(wilford)&room(jackie)&room(paul)&(![X]:(room(X)=>(X='thaddeus'|X='wendy'|X='wilford'|X='jackie'|X='paul')))&
((![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))&(does_not_enjoy_stargazing(X))&(writes_and_illustrates_their_own_graphic_novels(X))))))<=>(does_not_write_and_illustrates_their_own_graphic_novels(thaddeus)))&
(~(((does_not_enjoy_salsa_dancing(thaddeus))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(thaddeus))|(does_not_enjoy_logic_puzzles(thaddeus))))=>(is_not_an_avid_hiker(wendy)))&
((![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(does_not_own_a_television(X))))))<=>(![X]:(room(X)=>(does_not_enjoy_salsa_dancing(X)))))&
((((does_not_enjoy_logic_puzzles(wendy))|(does_not_write_and_illustrates_their_own_graphic_novels(wendy))))<~>(?[X]:(room(X)&(((does_not_drive_a_hybrid_car(X))&(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))&(does_not_know_morse_code(X)))))))&
((~((does_not_collect_luxury_watches(thaddeus))|(does_not_enjoy_salsa_dancing(thaddeus))))<~>(((does_not_read_mystery_novels(thaddeus))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(thaddeus))|(does_not_enjoy_logic_puzzles(thaddeus)))))&
(?[X]:(room(X)&(((does_not_enjoy_salsa_dancing(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))&
(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(wendy))&
(((does_not_read_mystery_novels(thaddeus))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(thaddeus))|(does_not_enjoy_logic_puzzles(thaddeus))))&
(?[X]:(room(X)&(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_enjoy_salsa_dancing(X))))))&
(![X]:(room(X)=>(~((does_not_enjoy_salsa_dancing(X))|(is_not_an_avid_hiker(X)))))) | room(thaddeus)&room(wendy)&room(wilford)&room(jackie)&room(paul)&(![X]:(room(X)=>(X='thaddeus'|X='wendy'|X='wilford'|X='jackie'|X='paul')))&
is_an_avid_hiker(thaddeus) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2085306400687140165977028
% SZS output start Proof for 2085306400687140165977028
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
54. ! [X0] : (room(X0) => ~(~predf(X0) | ~predj(X0))) [input p10]
55. ~(predf(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
131. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
132. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 131]
137. ! [X0] : ((predf(X0) & predj(X0)) | ~room(X0)) [ennf transformation 54]
138. ~predf(mary) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 55]
139. ~predf(mary) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 138]
164. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK7 & alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom]
165. ~predf(mary) | (john != sK7 & alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 139,164]
246. room(mary) [cnf transformation 132]
247. room(paul) [cnf transformation 132]
248. room(fred) [cnf transformation 132]
249. room(alice) [cnf transformation 132]
250. room(john) [cnf transformation 132]
251. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 132]
281. ~room(X0) | predf(X0) [cnf transformation 137]
282. ~predf(mary) | room(sK7) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165]
283. ~predf(mary) | mary != sK7 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165]
284. ~predf(mary) | paul != sK7 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165]
285. ~predf(mary) | fred != sK7 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165]
286. ~predf(mary) | alice != sK7 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165]
287. ~predf(mary) | john != sK7 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165]
436. ~predf(mary) | john != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,250]
437. ~predf(mary) | john != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 436,249]
438. ~predf(mary) | john != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 437,248]
439. ~predf(mary) | john != sK7 | ~room(mary) [subsumption resolution 438,247]
440. ~predf(mary) | john != sK7 [subsumption resolution 439,246]
442. 33 <=> john = sK7 [avatar definition]
444. john != sK7 <- (~33) [avatar component clause 442]
446. 34 <=> predf(mary) [avatar definition]
449. ~33 | ~34 [avatar split clause 440,446,442]
450. ~predf(mary) | alice != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,250]
451. ~predf(mary) | alice != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 450,249]
452. ~predf(mary) | alice != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 451,248]
453. ~predf(mary) | alice != sK7 | ~room(mary) [subsumption resolution 452,247]
454. ~predf(mary) | alice != sK7 [subsumption resolution 453,246]
456. 35 <=> alice = sK7 [avatar definition]
458. alice != sK7 <- (~35) [avatar component clause 456]
459. ~35 | ~34 [avatar split clause 454,446,456]
460. ~predf(mary) | fred != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,250]
461. ~predf(mary) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 460,249]
462. ~predf(mary) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 461,248]
463. ~predf(mary) | fred != sK7 | ~room(mary) [subsumption resolution 462,247]
464. ~predf(mary) | fred != sK7 [subsumption resolution 463,246]
466. 36 <=> fred = sK7 [avatar definition]
468. fred != sK7 <- (~36) [avatar component clause 466]
469. ~36 | ~34 [avatar split clause 464,446,466]
470. ~predf(mary) | paul != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,250]
471. ~predf(mary) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 470,249]
472. ~predf(mary) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 471,248]
473. ~predf(mary) | paul != sK7 | ~room(mary) [subsumption resolution 472,247]
474. ~predf(mary) | paul != sK7 [subsumption resolution 473,246]
476. 37 <=> paul = sK7 [avatar definition]
478. paul != sK7 <- (~37) [avatar component clause 476]
479. ~37 | ~34 [avatar split clause 474,446,476]
480. ~predf(mary) | mary != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,250]
481. ~predf(mary) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 480,249]
482. ~predf(mary) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 481,248]
483. ~predf(mary) | mary != sK7 | ~room(mary) [subsumption resolution 482,247]
484. ~predf(mary) | mary != sK7 [subsumption resolution 483,246]
486. 38 <=> mary = sK7 [avatar definition]
488. mary != sK7 <- (~38) [avatar component clause 486]
489. ~38 | ~34 [avatar split clause 484,446,486]
490. ~predf(mary) | room(sK7) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,250]
491. ~predf(mary) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 490,249]
492. ~predf(mary) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 491,248]
493. ~predf(mary) | room(sK7) | ~room(mary) [subsumption resolution 492,247]
494. ~predf(mary) | room(sK7) [subsumption resolution 493,246]
496. 39 <=> room(sK7) [avatar definition]
498. room(sK7) <- (39) [avatar component clause 496]
499. 39 | ~34 [avatar split clause 494,446,496]
532. predf(mary) [resolution 281,246]
542. 34 [avatar split clause 532,446]
780. alice = sK7 | fred = sK7 | paul = sK7 | mary = sK7 | john = sK7 <- (39) [resolution 251,498]
907. fred = sK7 | paul = sK7 | mary = sK7 | john = sK7 <- (~35, 39) [subsumption resolution 780,458]
908. paul = sK7 | mary = sK7 | john = sK7 <- (~35, ~36, 39) [subsumption resolution 907,468]
909. mary = sK7 | john = sK7 <- (~35, ~36, ~37, 39) [subsumption resolution 908,478]
910. john = sK7 <- (~35, ~36, ~37, ~38, 39) [subsumption resolution 909,488]
911. $false <- (~33, ~35, ~36, ~37, ~38, 39) [subsumption resolution 910,444]
912. 33 | 35 | 36 | 37 | 38 | ~39 [avatar contradiction clause 911]
913. $false [avatar sat refutation 449,459,469,479,489,499,542,912]
% SZS output end Proof for 2085306400687140165977028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0.498635 |
Maria, Pauline are the only persons in the room.
Pauline is a wise person.
Pauline is the quietest in the room.
Everyone in the room who is older than Robert is a wise creative generous patient person.
Everyone in the room who is a creative humble person is older than Robert.
All humble persons are creative.
Maria is a patient kind curious happy funny person.
Everyone outside the room who is older than Marie is older than Robert.
Marie is older than Pauline.
Pauline is older than Robert.
Robert is richer than Maria.
Everyone in the room is not a wise funny old person if they is not strong, not tall.
Pauline is a brave person.
Pauline who is richer than Marie is richer than Robert.
Everyone in the room is a brave person if they is not a patient kind person.
Everyone anywhere who is a brave person is a generous person.
Pauline is a quiet person. | It is not the case that “it is not the case that “it is not the case that “more than one person in the room is not tall, is a kind person and is a old person”””. | neutral | room(maria)&room(pauline)&(![X]:(room(X)=>(X='maria'|X='pauline')))&
(wise(pauline)&person(pauline))&
(![X]:((room(X)&(X!=pauline))=>quieter(X,pauline)))&
(![X]:(room(X)=>(((older(robert,X))=>(wise(X)&creative(X)&generous(X)&patient(X)&person(X))))))&
(![X]:(room(X)=>(((creative(X)&humble(X)&person(X))=>(older(robert,X))))))&
(![X]:(humble(X)=>creative(X)))&
(patient(maria)&kind(maria)&curious(maria)&happy(maria)&funny(maria)&person(maria))&
(![X]:(~room(X)=>(((older(marie,X))=>(older(robert,X))))))&
(older(pauline,marie))&
(older(robert,pauline))&
(richer(maria,robert))&
(![X]:(room(X)=>(((~strong(X)&~tall(X))=>(~(wise(X)&funny(X)&old(X)&person(X)))))))&
(brave(pauline)&person(pauline))&
((richer(marie,pauline))&(richer(robert,pauline)))&
(![X]:(room(X)=>(((~(patient(X)&kind(X)&person(X)))=>(brave(X)&person(X))))))&
(![X]:(anywhere(X)=>(((brave(X)&person(X))=>(generous(X)&person(X))))))&
(quiet(pauline)&person(pauline)) | room(maria)&room(pauline)&(![X]:(room(X)=>(X='maria'|X='pauline')))&
~(~(~((?[X,Y]:(room(X)&room(Y)&(((~tall(X))&(kind(X)&person(X))&(old(X)&person(X)))&((~tall(Y))&(kind(Y)&person(Y))&(old(Y)&person(Y))))&(X!=Y)))))) | [] | null | 0.206123 |
Lindsay is the only person in the room. 'Everyone anywhere is a Linux enthusiast if and only if they knows morse code' unless 'Lindsay plays eSports competitively'. Everyone outside the room does not practice and performs acrobatic dance routines or knows morse code. Everyone anywhere is a Linux enthusiast if and only if they knows morse code. Lindsay owns a smartwatch. If someone creates augmented reality experiences for mobile applications then he/she owns a significant collection of rare gemstones and minerals. Lindsay enjoys virtual reality gaming. Lindsay uses an ios phone. Lindsay knows morse code. Lindsay plays eSports competitively. Everyone in the room is an amateur astronomer who builds and uses custom telescopes, plays eSports competitively and enjoys virtual reality gaming if they cannot play the guitar and vice versa. If someone enjoys origami then he/she is a Linux enthusiast or can play the guitar or both. Lindsay has a piercing. Lindsay is dedicated to sustainable living and zero-waste practices, plays eSports competitively and enjoys rooftop gardening. Everyone in the room who plays eSports competitively is a certified yoga instructor teaching classes weekly. Lindsay builds model airplanes. If someone does not enjoy camping and organizing outdoor survival workshops then he/she is a certified yoga instructor teaching classes weekly and vice versa. | Lindsay enjoys camping and organizing outdoor survival workshops. | contradiction | room(lindsay)&(![X]:(room(X)=>(X='lindsay')))&
(~(plays_eSports_competitively(lindsay))=>(![X]:(anywhere(X)=>(((is_a_Linux_enthusiast(X))<=>(knows_morse_code(X)))))))&
(![X]:(~room(X)=>(((knows_morse_code(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))&
(![X]:(anywhere(X)=>(((is_a_Linux_enthusiast(X))<=>(knows_morse_code(X))))))&
(owns_a_smartwatch(lindsay))&
((![X]:((creates_augmented_reality_experiences_for_mobile_applications(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))&
(enjoys_virtual_reality_gaming(lindsay))&
(uses_an_ios_phone(lindsay))&
(knows_morse_code(lindsay))&
(plays_eSports_competitively(lindsay))&
(![X]:(room(X)=>(((((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))&(plays_eSports_competitively(X))&(enjoys_virtual_reality_gaming(X))))<=>(cannot_play_the_guitar(X))))))&
((![X]:((enjoys_origami(X))=>(((is_a_Linux_enthusiast(X))|(can_play_the_guitar(X)))))))&
(has_a_piercing(lindsay))&
(((is_dedicated_to_sustainable_living_and_zero-waste_practices(lindsay))&(plays_eSports_competitively(lindsay))&(enjoys_rooftop_gardening(lindsay))))&
(![X]:(room(X)=>(((plays_eSports_competitively(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))&
(builds_model_airplanes(lindsay))&
((![X]:((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))<=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))) | room(lindsay)&(![X]:(room(X)=>(X='lindsay')))&
enjoys_camping_and_organizing_outdoor_survival_workshops(lindsay) | [
"p0",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4645744302844386966381457
% SZS output start Proof for 4645744302844386966381457
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
57. prede(mary) & predj(mary) & predw(mary) [input p13]
58. ! [X0] : (room(X0) => (predj(X0) => predh(X0))) [input p14]
60. ! [X0] : (~predc(X0) <=> predh(X0)) [input p16]
61. predc(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
62. ! [X0] : (predh(X0) => ~predc(X0)) [unused predicate definition removal 60]
64. predj(mary) & predw(mary) [pure predicate removal 57]
65. predj(mary) [pure predicate removal 64]
143. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
147. ! [X0] : ((predh(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 58]
148. ! [X0] : (predh(X0) | ~predj(X0) | ~room(X0)) [flattening 147]
149. ! [X0] : (~predc(X0) | ~predh(X0)) [ennf transformation 62]
150. predc(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 61]
237. room(mary) [cnf transformation 143]
250. predj(mary) [cnf transformation 65]
251. ~predj(X0) | predh(X0) | ~room(X0) [cnf transformation 148]
252. ~predc(X0) | ~predh(X0) [cnf transformation 149]
255. predc(mary) [cnf transformation 150]
258. 1 <=> predj(mary) [avatar definition]
260. predj(mary) <- (1) [avatar component clause 258]
275. 1 [avatar split clause 250,258]
276. ~predh(mary) [resolution 252,255]
292. predh(mary) | ~room(mary) <- (1) [resolution 251,260]
293. ~room(mary) <- (1) [subsumption resolution 292,276]
294. $false <- (1) [subsumption resolution 293,237]
295. ~1 [avatar contradiction clause 294]
296. $false [avatar sat refutation 275,295]
% SZS output end Proof for 4645744302844386966381457
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
There is a room.
Everyone outside the room either does not own a smartwatch or does not create YouTube content but not both.
Everyone in the room makes intricate hand-cut paper art for exhibitions and does not collect vintage stamps.
Everyone in the room does not write a travel blog if they does not write a travel blog, makes intricate hand-cut paper art for exhibitions and does not own a smartwatch.
Everyone in the room writes a travel blog or does not create YouTube content.
Everyone in the room does not mentor a youth basketball team on weekends. | Everyone outside the room does not write a travel blog. | neutral | (there_is_a_room)&
(![X]:(~room(X)=>(((does_not_own_a_smartwatch(X))<~>(does_not_create_YouTube_content(X))))))&
(![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(does_not_collect_vintage_stamps(X))))))&
(![X]:(room(X)=>(((((does_not_write_a_travel_blog(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(does_not_own_a_smartwatch(X))))=>(does_not_write_a_travel_blog(X))))))&
(![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(writes_a_travel_blog(X))))))&
(![X]:(room(X)=>(does_not_mentor_a_youth_basketball_team_on_weekends(X))))&
(![X]:(anywhere(X)=>(((((makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))&(does_not_own_a_smartwatch(X))))=>(collects_vintage_stamps(X))))))&
(![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(writes_a_travel_blog(X))))))&
(![X]:(~room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(does_not_write_a_travel_blog(X))))))&
(![X]:(room(X)=>(does_not_write_a_travel_blog(X))))&
(![X]:(room(X)=>(does_not_collect_vintage_stamps(X)))) | (there_is_a_room)&
![X]:(~room(X)=>(does_not_write_a_travel_blog(X))) | [] | null | 0.620256 |
Connie, James are the only persons in the room.
Everyone in the room is a old person if and only if they is richer than Janice.
Connie either is a tall person or is quiet but not both.
Connie is richer than Lucille. | James is quieter than Janice. | neutral | room(connie)&room(james)&(![X]:(room(X)=>(X='connie'|X='james')))&
(![X]:(room(X)=>(((old(X)&person(X))<=>(richer(janice,X))))))&
(((tall(connie)&person(connie))<~>(quiet(connie))))&
(richer(lucille,connie))&
(quieter(lucille,connie))&
(![X]:(tall(X)=>old(X)))&
(![X]:(room(X)=>(((~~~~quiet(X))=>(tall(X)&quiet(X)&old(X)&person(X))))))&
(richer(lucille,james))&
(richer(janice,james))&
(old(james))&
(quiet(james)&old(james)&person(james))&
(![X]:(room(X)=>(((~(tall(X)&old(X)&person(X)))=>(~(old(X)&person(X)))))))&
(old(james)&person(james))&
(old(connie))&
(richer(janice,connie))&
(~(((?[X]:(~room(X)&richer(janice,X))))))&
(old(james)&person(james)&old(connie)&person(connie)) | room(connie)&room(james)&(![X]:(room(X)=>(X='connie'|X='james')))&
quieter(janice,james) | [] | null | 0.0353 |
Conrad is the only person in the room. If someone regularly goes on multi-day backpacking trips in national parks then he/she has lived in exactly three countries. Everyone outside the room who has a tattoo practices calligraphy. Everyone in the room does not have a tattoo or practices calligraphy. Conrad enjoys making ceramics. Everyone in the room who practices tai chi is an expert in identifying and foraging wild edible plants. Everyone outside the room is an expert in identifying and foraging wild edible plants if and only if they enjoys bird watching. Only one person outside the room regularly goes on multi-day backpacking trips in national parks or creates YouTube content or both. Conrad works on fridays, creates YouTube content and collects vintage stamps. Everyone in the room collect rare sneakers only if they is a skilled home brewer experimenting with craft beer recipes. Everyone in the room who creates YouTube content is a scotch connoisseur. Everyone in the room is a skilled home brewer experimenting with craft beer recipes, practices tai chi and collects vintage stamps if they is a scotch connoisseur and vice versa. | Conrad practices tai chi. | entailment | room(conrad)&(![X]:(room(X)=>(X='conrad')))&
((![X]:((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(has_lived_in_exactly_three_countries(X)))))&
(![X]:(~room(X)=>(((has_a_tattoo(X))=>(practices_calligraphy(X))))))&
(![X]:(room(X)=>(((practices_calligraphy(X))|(does_not_have_a_tattoo(X))))))&
(enjoys_making_ceramics(conrad))&
(![X]:(room(X)=>(((practices_tai_chi(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))&
(![X]:(~room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=>(enjoys_bird_watching(X))))))&
(((?[X]:(~room(X)&((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(creates_YouTube_content(X)))))&(![X,Y]:((~room(X)&~room(Y)&(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(creates_YouTube_content(X))))&(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(Y))|(creates_YouTube_content(Y)))))=>(X=Y)))))&
(((works_on_fridays(conrad))&(creates_YouTube_content(conrad))&(collects_vintage_stamps(conrad))))&
(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=(collect_rare_sneakers(X))))))&
(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(((enjoys_kayaking(X))&(enjoys_bird_watching(X))))))))&
(![X]:(room(X)=>(((creates_YouTube_content(X))=>(is_a_scotch_connoisseur(X))))))&
(has_lived_in_exactly_three_countries(conrad))&
(![X]:(room(X)=>(((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(practices_tai_chi(X))&(collects_vintage_stamps(X))))<=>(is_a_scotch_connoisseur(X))))))&
(collect_rare_sneakers(conrad))&
(has_a_tattoo(conrad))&
(is_an_expert_in_identifying_and_foraging_wild_edible_plants(conrad))&
((![X]:((((collects_vintage_stamps(X))&(has_lived_in_exactly_three_countries(X))))=>(creates_YouTube_content(X)))))&
(((enjoys_making_ceramics(conrad))|(is_a_scotch_connoisseur(conrad))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(conrad))))&
(![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))&
(~![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(~((collects_vintage_stamps(X))|(enjoys_bird_watching(X))))))))&
(is_a_wine_connoisseur(conrad))&
(![X]:(anywhere(X)=>(((is_a_wine_connoisseur(X))=>(collects_vintage_stamps(X)))))) | room(conrad)&(![X]:(room(X)=>(X='conrad')))&
practices_tai_chi(conrad) | [
"p0",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5816669672871126524698742
% SZS output start Proof for 5816669672871126524698742
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
52. preda(mary) & predm(mary) & predp(mary) [input p8]
55. ! [X0] : (room(X0) => (predm(X0) => predk(X0))) [input p11]
57. ! [X0] : (room(X0) => ((preda(X0) & predo(X0) & predf(X0)) <=> predk(X0))) [input p13]
67. ~(predo(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
70. preda(mary) & predm(mary) [pure predicate removal 52]
147. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
158. ! [X0] : ((predk(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 55]
159. ! [X0] : (predk(X0) | ~predm(X0) | ~room(X0)) [flattening 158]
160. ! [X0] : (((preda(X0) & predo(X0) & predf(X0)) <=> predk(X0)) | ~room(X0)) [ennf transformation 57]
169. ~predo(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 67]
174. ! [X0] : ((((preda(X0) & predo(X0) & predf(X0)) | ~predk(X0)) & (predk(X0) | (~preda(X0) | ~predo(X0) | ~predf(X0)))) | ~room(X0)) [nnf transformation 160]
175. ! [X0] : ((((preda(X0) & predo(X0) & predf(X0)) | ~predk(X0)) & (predk(X0) | ~preda(X0) | ~predo(X0) | ~predf(X0))) | ~room(X0)) [flattening 174]
178. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom]
179. ~predo(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 169,178]
261. room(mary) [cnf transformation 147]
262. ~room(X0) | mary = X0 [cnf transformation 147]
273. predm(mary) [cnf transformation 70]
277. ~predm(X0) | predk(X0) | ~room(X0) [cnf transformation 159]
281. ~predk(X0) | predo(X0) | ~room(X0) [cnf transformation 175]
292. ~predo(mary) | room(sK2) | ~room(mary) [cnf transformation 179]
293. ~predo(mary) | mary != sK2 | ~room(mary) [cnf transformation 179]
313. ~predo(mary) | mary != sK2 [subsumption resolution 293,261]
315. 5 <=> mary = sK2 [avatar definition]
317. mary != sK2 <- (~5) [avatar component clause 315]
319. 6 <=> predo(mary) [avatar definition]
322. ~5 | ~6 [avatar split clause 313,319,315]
323. ~predo(mary) | room(sK2) [subsumption resolution 292,261]
325. 7 <=> room(sK2) [avatar definition]
327. room(sK2) <- (7) [avatar component clause 325]
328. 7 | ~6 [avatar split clause 323,319,325]
341. predk(mary) | ~room(mary) [resolution 277,273]
343. predk(mary) [subsumption resolution 341,261]
345. predo(mary) | ~room(mary) [resolution 281,343]
349. predo(mary) [subsumption resolution 345,261]
350. 6 [avatar split clause 349,319]
352. mary = sK2 <- (7) [resolution 327,262]
353. $false <- (~5, 7) [subsumption resolution 352,317]
354. 5 | ~7 [avatar contradiction clause 353]
355. $false [avatar sat refutation 322,328,350,354]
% SZS output end Proof for 5816669672871126524698742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.201265 |
Timothy is the only person in the room. “Everyone outside the room is not a certified scuba diver with advanced underwater photography skills or regularly contributes to tech forums and online communities” if “everyone anywhere creates augmented reality experiences for mobile applications or is not an avid mountain climber who has scaled several peaks” and vice versa. “Everyone in the room is a scotch connoisseur or is not a certified scuba diver with advanced underwater photography skills” only if “everyone in the room who is a scotch connoisseur either creates augmented reality experiences for mobile applications or is a night owl but not both”. “It is true that “Timothy is a scotch connoisseur”” if “Timothy regularly contributes to tech forums and online communities” and vice versa. Either “everyone in the room creates augmented reality experiences for mobile applications or does not regularly contributes to tech forums and online communities” or “Timothy is not a scotch connoisseur or does not regularly contributes to tech forums and online communities or both” but not both. Timothy is a certified scuba diver with advanced underwater photography skills. Everyone in the room is a certified scuba diver with advanced underwater photography skills. Everyone outside the room regularly contributes to tech forums and online communities and creates augmented reality experiences for mobile applications if they is a certified scuba diver with advanced underwater photography skills. Everyone anywhere creates augmented reality experiences for mobile applications or is not an avid mountain climber who has scaled several peaks. Everyone outside the room who is a scotch connoisseur is a certified scuba diver with advanced underwater photography skills. | Timothy is an avid mountain climber who has scaled several peaks. | neutral | room(timothy)&(![X]:(room(X)=>(X='timothy')))&
((![X]:(anywhere(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))<=>(![X]:(~room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))&
((![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_a_scotch_connoisseur(X))))))=>(![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))<~>(is_a_night_owl(X)))))))))&
((regularly_contributes_to_tech_forums_and_online_communities(timothy))<=>(is_a_scotch_connoisseur(timothy)))&
((![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))<~>(((is_not_a_scotch_connoisseur(timothy))|(does_not_regularly_contributes_to_tech_forums_and_online_communities(timothy)))))&
(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(timothy))&
(![X]:(room(X)=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))&
(![X]:(~room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(((regularly_contributes_to_tech_forums_and_online_communities(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))))))))&
(![X]:(anywhere(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(![X]:(~room(X)=>(((is_a_scotch_connoisseur(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))) | room(timothy)&(![X]:(room(X)=>(X='timothy')))&
is_an_avid_mountain_climber_who_has_scaled_several_peaks(timothy) | [] | null | 0.062418 |
Brad is the only person in the room.
If “everyone outside the room practices calligraphy or does not enjoy kayaking and exploring remote waterways” then “everyone in the room who practices calligraphy creates large-scale murals for public art installations”.
Either “not everyone in the room is not passionate about collecting and restoring classic cars or is a wine connoisseur with a private cellar of vintage wines” or “everyone in the room is not a wine connoisseur with a private cellar of vintage wines or does not maintain a personal blog focused on cybersecurity tips” but not both.
“At least one person in the room either is a client of LVMH or hosts regular workshops on creative writing but not both” if “everyone in the room does not host regular game nights featuring complex strategy games or is a wine connoisseur with a private cellar of vintage wines” and vice versa.
Everyone in the room enjoys deep-sea diving and exploring underwater caves.
Everyone outside the room who is passionate about collecting and restoring classic cars, trains for and competes in international triathlons and enjoys deep-sea diving and exploring underwater caves is a wine connoisseur with a private cellar of vintage wines.
Everyone in the room does not create augmented reality experiences for mobile applications or creates large-scale murals for public art installations.
Everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations or does not create augmented reality experiences for mobile applications.
Everyone in the room who does not write in-depth travel guides for off-the-beaten-path destinations collects vintage vinyl records.
Everyone anywhere participates in long-distance cycling events across the country if they collects vintage vinyl records.
Everyone outside the room who is a wine connoisseur with a private cellar of vintage wines enjoys wildlife photography.
Not everyone in the room who enjoys wildlife photography has a vast collection of first-edition science fiction novels.
Only one person in the room maintains a personal blog focused on cybersecurity tips or is a wine connoisseur with a private cellar of vintage wines or both.
Everyone outside the room is a client of LVMH or is not a wine connoisseur.
Everyone anywhere does not enjoy kayaking and exploring remote waterways or is a client of LVMH.
At least one person in the room is a wine connoisseur with a private cellar of vintage wines.
Everyone anywhere who owns a high-end gaming PC with custom-built components maintains a personal blog focused on cybersecurity tips. | Brad owns a high-end gaming PC with custom-built components. | contradiction | room(brad)&(![X]:(room(X)=>(X='brad')))&
((![X]:(~room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(practices_calligraphy(X))))))=>(![X]:(room(X)=>(((practices_calligraphy(X))=>(creates_large-scale_murals_for_public_art_installations(X)))))))&
((~![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))<~>(![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))&
((![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))<=>(((?[X]:(room(X)&((is_a_client_of_LVMH(X))<~>(hosts_regular_workshops_on_creative_writing(X))))))))&
(![X]:(room(X)=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))&
(![X]:(~room(X)=>(((((is_passionate_about_collecting_and_restoring_classic_cars(X))&(trains_for_and_competes_in_international_triathlons(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))&
(![X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))&
(![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(collects_vintage_vinyl_records(X))))))&
(![X]:(anywhere(X)=>(((collects_vintage_vinyl_records(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))&
(![X]:(~room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(enjoys_wildlife_photography(X))))))&
(~![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))&
(((?[X]:(room(X)&((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))&(![X,Y]:((room(X)&room(Y)&(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))&(((maintains_a_personal_blog_focused_on_cybersecurity_tips(Y))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(Y)))))=>(X=Y)))))&
(![X]:(~room(X)=>(((is_not_a_wine_connoisseur(X))|(is_a_client_of_LVMH(X))))))&
(![X]:(anywhere(X)=>(((is_a_client_of_LVMH(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))&
(![X]:(~room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))&
(![X]:(room(X)=>(((practices_calligraphy(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))&
(![X]:(anywhere(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))&
(((?[X]:(room(X)&is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))&
(?[X]:(room(X)&(practices_calligraphy(X))))&
(![X]:(room(X)=>(((practices_calligraphy(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(((trains_for_and_competes_in_international_triathlons(X))&(creates_large-scale_murals_for_public_art_installations(X))&(enjoys_wildlife_photography(X))))))))&
(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(practices_urban_gardening(X))))))&
(?[X]:(room(X)&(((owns_a_microscope(X))<~>(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))&
(![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))&
(![X]:(anywhere(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))) | room(brad)&(![X]:(room(X)=>(X='brad')))&
owns_a_high-end_gaming_PC_with_custom-built_components(brad) | [
"b4",
"p0",
"p2",
"p18",
"p25",
"hypothesis"
] | % SZS status Unsatisfiable for 3955331835763050232270400
% SZS output start Proof for 3955331835763050232270400
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
46. ~! [X0] : (room(X0) => (~predq(X0) | predu(X0))) <~> ! [X0] : (room(X0) => (~predu(X0) | ~prede(X0))) [input p2]
62. ? [X0] : (predu(X0) & room(X0)) [input p18]
69. ! [X0] : (anywhere(X0) => (predk(X0) => prede(X0))) [input p25]
70. predk(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
72. ~! [X0] : (room(X0) => (~predq(X0) | predu(X0))) <~> ! [X1] : (room(X1) => (~predu(X1) | ~prede(X1))) [rectify 46]
159. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
160. ? [X0] : ((predq(X0) & ~predu(X0)) & room(X0)) <~> ! [X1] : ((~predu(X1) | ~prede(X1)) | ~room(X1)) [ennf transformation 72]
161. ? [X0] : (predq(X0) & ~predu(X0) & room(X0)) <~> ! [X1] : (~predu(X1) | ~prede(X1) | ~room(X1)) [flattening 160]
180. ! [X0] : ((prede(X0) | ~predk(X0)) | ~anywhere(X0)) [ennf transformation 69]
181. ! [X0] : (prede(X0) | ~predk(X0) | ~anywhere(X0)) [flattening 180]
182. predk(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 70]
183. sP0 <=> ? [X0] : (predq(X0) & ~predu(X0) & room(X0)) [predicate definition introduction]
184. sP0 <~> ! [X1] : (~predu(X1) | ~prede(X1) | ~room(X1)) [definition folding 161,183]
188. (sP0 | ! [X0] : (~predq(X0) | predu(X0) | ~room(X0))) & (? [X0] : (predq(X0) & ~predu(X0) & room(X0)) | ~sP0) [nnf transformation 183]
189. (sP0 | ! [X0] : (~predq(X0) | predu(X0) | ~room(X0))) & (? [X1] : (predq(X1) & ~predu(X1) & room(X1)) | ~sP0) [rectify 188]
190. ? [X1] : (predq(X1) & ~predu(X1) & room(X1)) => (predq(sK2) & ~predu(sK2) & room(sK2)) [choice axiom]
191. (sP0 | ! [X0] : (~predq(X0) | predu(X0) | ~room(X0))) & ((predq(sK2) & ~predu(sK2) & room(sK2)) | ~sP0) [skolemisation 189,190]
192. (? [X1] : (predu(X1) & prede(X1) & room(X1)) | ~sP0) & (! [X1] : (~predu(X1) | ~prede(X1) | ~room(X1)) | sP0) [nnf transformation 184]
193. (? [X0] : (predu(X0) & prede(X0) & room(X0)) | ~sP0) & (! [X1] : (~predu(X1) | ~prede(X1) | ~room(X1)) | sP0) [rectify 192]
194. ? [X0] : (predu(X0) & prede(X0) & room(X0)) => (predu(sK3) & prede(sK3) & room(sK3)) [choice axiom]
195. ((predu(sK3) & prede(sK3) & room(sK3)) | ~sP0) & (! [X1] : (~predu(X1) | ~prede(X1) | ~room(X1)) | sP0) [skolemisation 193,194]
209. ? [X0] : (predu(X0) & room(X0)) => (predu(sK8) & room(sK8)) [choice axiom]
210. predu(sK8) & room(sK8) [skolemisation 62,209]
217. anywhere(X0) [cnf transformation 5]
298. room(mary) [cnf transformation 159]
299. ~room(X0) | mary = X0 [cnf transformation 159]
300. room(sK2) | ~sP0 [cnf transformation 191]
301. ~predu(sK2) | ~sP0 [cnf transformation 191]
304. ~predu(X1) | ~prede(X1) | ~room(X1) | sP0 [cnf transformation 195]
330. room(sK8) [cnf transformation 210]
331. predu(sK8) [cnf transformation 210]
339. prede(X0) | ~predk(X0) | ~anywhere(X0) [cnf transformation 181]
342. predk(mary) [cnf transformation 182]
348. 2 <=> sP0 [avatar definition]
358. 4 <=> predu(sK2) [avatar definition]
360. ~predu(sK2) <- (~4) [avatar component clause 358]
361. ~2 | ~4 [avatar split clause 301,358,348]
363. 5 <=> room(sK2) [avatar definition]
365. room(sK2) <- (5) [avatar component clause 363]
366. ~2 | 5 [avatar split clause 300,363,348]
383. 9 <=> ! [X1] : (~predu(X1) | ~room(X1) | ~prede(X1)) [avatar definition]
384. ~prede(X1) | ~room(X1) | ~predu(X1) <- (9) [avatar component clause 383]
385. 2 | 9 [avatar split clause 304,383,348]
453. ~predk(X0) | prede(X0) [subsumption resolution 339,217]
464. prede(mary) [resolution 453,342]
466. mary = sK2 <- (5) [resolution 299,365]
471. mary = sK8 [resolution 299,330]
476. ~predu(mary) <- (~4, 5) [backward demodulation 360,466]
496. predu(mary) [backward demodulation 331,471]
497. $false <- (~4, 5) [subsumption resolution 496,476]
498. 4 | ~5 [avatar contradiction clause 497]
523. ~room(mary) | ~predu(mary) <- (9) [resolution 384,464]
524. ~predu(mary) <- (9) [subsumption resolution 523,298]
525. $false <- (9) [subsumption resolution 524,496]
526. ~9 [avatar contradiction clause 525]
527. $false [avatar sat refutation 361,366,385,498,526]
% SZS output end Proof for 3955331835763050232270400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.395115 |
There is a room. "Someone in the room neither is a client of Meta nor owns a microscope" only if "everyone in the room who is a client of Meta uses an ios phone". If "everyone in the room does not use an ios phone or owns a microscope" then "at least one person in the room uses an ios phone". If "everyone in the room is not a client of Meta or is a client of Meta" then "everyone in the room who is not a client of Meta collect rare sneakers". If "everyone in the room does not collect rare sneakers or uses an ios phone" then "everyone in the room who does not collect rare sneakers collect rare sneakers". If "everyone in the room uses an ios phone or does not use an ios phone" then "everyone in the room who neither collect rare sneakers nor uses an ios phone uses an ios phone". If "not everyone outside the room does not own a microscope or collect rare sneakers" then "no one in the room uses an ios phone or does not use an ios phone". If "no one in the room collect rare sneakers or does not own a microscope" then "everyone in the room who uses an ios phone collect rare sneakers". | Everyone outside the room does not collect rare sneakers. | neutral | (there_is_a_room)&
((?[X]:(room(X)&(~((is_a_client_of_Meta(X))|(owns_a_microscope(X))))))=>(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(uses_an_ios_phone(X)))))))&
((![X]:(room(X)=>(((owns_a_microscope(X))|(does_not_use_an_ios_phone(X))))))=>(((?[X]:(room(X)&uses_an_ios_phone(X))))))&
((![X]:(room(X)=>(((is_a_client_of_Meta(X))|(is_not_a_client_of_Meta(X))))))=>(![X]:(room(X)=>(((is_not_a_client_of_Meta(X))=>(collect_rare_sneakers(X)))))))&
((![X]:(room(X)=>(((uses_an_ios_phone(X))|(does_not_collect_rare_sneakers(X))))))=>(![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))=>(collect_rare_sneakers(X)))))))&
((![X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(uses_an_ios_phone(X))))))=>(![X]:(room(X)=>(((~((collect_rare_sneakers(X))|(uses_an_ios_phone(X))))=>(uses_an_ios_phone(X)))))))&
((~![X]:(~room(X)=>(((collect_rare_sneakers(X))|(does_not_own_a_microscope(X))))))=>(~?[X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(uses_an_ios_phone(X)))))))&
((~?[X]:(room(X)=>(((does_not_own_a_microscope(X))|(collect_rare_sneakers(X))))))=>(![X]:(room(X)=>(((uses_an_ios_phone(X))=>(collect_rare_sneakers(X)))))))&
((![X]:(room(X)=>(((collect_rare_sneakers(X))|(does_not_collect_rare_sneakers(X))))))=>(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(uses_an_ios_phone(X)))))))&
(![X]:(~room(X)=>(((uses_an_ios_phone(X))<=>(is_not_a_client_of_Meta(X))))))&
(![X]:(anywhere(X)=>(((is_not_a_client_of_Meta(X))=>(collect_rare_sneakers(X))))))&
(![X]:(room(X)=>(((collect_rare_sneakers(X))=>(is_not_a_client_of_Meta(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(uses_an_ios_phone(X))))))&
(![X]:(anywhere(X)=>(((uses_an_ios_phone(X))=>(owns_a_microscope(X))))))&
(![X]:(room(X)=>(((owns_a_microscope(X))=>(uses_an_ios_phone(X))))))&
((![X]:((((uses_an_ios_phone(X))&(collect_rare_sneakers(X))&(owns_a_microscope(X))))<=>(uses_an_ios_phone(X)))))&
(![X]:(room(X)=>(((owns_a_microscope(X))=>(collect_rare_sneakers(X))))))&
(~![X]:(room(X)=>(((collect_rare_sneakers(X))=>(is_a_client_of_Meta(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(~((owns_a_microscope(X))|(collect_rare_sneakers(X)))))))) | (there_is_a_room)&
![X]:(~room(X)=>(does_not_collect_rare_sneakers(X))) | [] | null | 0.099619 |
Leslie is the only person in the room.
It is true that “it is not the case that “someone in the room does not practice tai chi””.
Someone anywhere has a specialized collection of handmade artisan pottery.
Someone in the room enjoys logic puzzles.
It is not the case that “it is not the case that “it is not the case that “someone in the room does not own a high-end gaming PC with custom-built components”””.
Someone in the room regularly goes on multi-day backpacking trips in national parks.
Someone in the room practices tai chi.
It is not the case that “it is not the case that “someone in the room regularly goes on multi-day backpacking trips in national parks””.
Someone in the room has a specialized collection of handmade artisan pottery.
It is not the case that “more than one person in the room owns a high-end gaming PC with custom-built components”.
Someone in the room owns a high-end gaming PC with custom-built components.
It is not the case that “more than one person in the room enjoys logic puzzles”. | Leslie owns a high-end gaming PC with custom-built components. | entailment | room(leslie)&(![X]:(room(X)=>(X='leslie')))&
(~(?[X]:(room(X)&(does_not_practice_tai_chi(X)))))&
(?[X]:(anywhere(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))&
(?[X]:(room(X)&(enjoys_logic_puzzles(X))))&
(~(~(~(?[X]:(room(X)&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X)))))))&
(?[X]:(room(X)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))&
(?[X]:(room(X)&(practices_tai_chi(X))))&
(~(~(?[X]:(room(X)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))&
(?[X]:(room(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))&
(~((?[X,Y]:(room(X)&room(Y)&(owns_a_high-end_gaming_PC_with_custom-built_components(X)&owns_a_high-end_gaming_PC_with_custom-built_components(Y))&(X!=Y)))))&
(?[X]:(room(X)&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))&
(~((?[X,Y]:(room(X)&room(Y)&(enjoys_logic_puzzles(X)&enjoys_logic_puzzles(Y))&(X!=Y))))) | room(leslie)&(![X]:(room(X)=>(X='leslie')))&
owns_a_high-end_gaming_PC_with_custom-built_components(leslie) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3621847192623288161598326
% SZS output start Proof for 3621847192623288161598326
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
48. ~~~? [X0] : (~predc(X0) & room(X0)) [input p4]
56. ~(predc(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
57. ~? [X0] : (~predc(X0) & room(X0)) [flattening 48]
138. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
139. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 57]
142. ~predc(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 56]
156. ? [X0] : (mary != X0 & room(X0)) => (mary != sK6 & room(sK6)) [choice axiom]
157. ~predc(mary) | (mary != sK6 & room(sK6)) | ~room(mary) [skolemisation 142,156]
238. room(mary) [cnf transformation 138]
239. ~room(X0) | mary = X0 [cnf transformation 138]
242. ~room(X0) | predc(X0) [cnf transformation 139]
251. ~predc(mary) | room(sK6) | ~room(mary) [cnf transformation 157]
252. ~predc(mary) | mary != sK6 | ~room(mary) [cnf transformation 157]
255. ~predc(mary) | mary != sK6 [subsumption resolution 252,238]
257. 1 <=> mary = sK6 [avatar definition]
259. mary != sK6 <- (~1) [avatar component clause 257]
261. 2 <=> predc(mary) [avatar definition]
264. ~1 | ~2 [avatar split clause 255,261,257]
265. ~predc(mary) | room(sK6) [subsumption resolution 251,238]
267. 3 <=> room(sK6) [avatar definition]
269. room(sK6) <- (3) [avatar component clause 267]
270. 3 | ~2 [avatar split clause 265,261,267]
271. predc(mary) [resolution 242,238]
280. 2 [avatar split clause 271,261]
289. mary = sK6 <- (3) [resolution 239,269]
303. $false <- (~1, 3) [subsumption resolution 289,259]
304. 1 | ~3 [avatar contradiction clause 303]
305. $false [avatar sat refutation 264,270,280,304]
% SZS output end Proof for 3621847192623288161598326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.571603 |
There is a room.
Only one person in the room is hated by Gregory and is not hated by Norma.
Everyone outside the room is not hated by Gregory if they either is not hated by Robert or does not hate Gregory but not both.
At least one person in the room does not hate Gregory.
Everyone in the room is hated by Gregory if they does not hate Irene, does not hate Norma or is not hated by Norma.
Everyone outside the room is hated by Deja if they does not hate Deja or hates Irene or both.
Everyone in the room is hated by Deja only if they is hated by Robert, is not hated by Irene and does not hate Irene.
Everyone in the room does not hate Deja and does not hate Irene if they either does not hate Gregory or does not hate Norma but not both.
If someone does not hate Norma then he/she is not hated by Gregory or hates Deja or both.
Only one person in the room is not hated by Gregory.
Everyone in the room who is not hated by Norma and is hated by Robert does not hate Irene.
Someone in the room either is not hated by Gregory or is not hated by Irene but not both. | Everyone in the room hates Deja. | neutral | (there_is_a_room)&
(((?[X]:(room(X)&((hate(X,gregory))&(~hate(X,norma)))))&(![X,Y]:((room(X)&room(Y)&(((hate(X,gregory))&(~hate(X,norma))))&(((hate(Y,gregory))&(~hate(Y,norma)))))=>(X=Y)))))&
(![X]:(~room(X)=>(((((~hate(X,robert))<~>(~hate(gregory,X))))=>(~hate(X,gregory))))))&
(((?[X]:(room(X)&~hate(gregory,X)))))&
(![X]:(room(X)=>(((((~hate(irene,X))|(~hate(norma,X))|(~hate(X,norma))))=>(hate(X,gregory))))))&
(![X]:(~room(X)=>(((((~hate(deja,X))|(hate(irene,X))))=>(hate(X,deja))))))&
(![X]:(room(X)=>(((((hate(X,robert))&(~hate(X,irene))&(~hate(irene,X))))<=(hate(X,deja))))))&
(![X]:(room(X)=>(((((~hate(gregory,X))<~>(~hate(norma,X))))=>(((~hate(deja,X))&(~hate(irene,X))))))))&
((![X]:((~hate(norma,X))=>(((~hate(X,gregory))|(hate(deja,X)))))))&
(((?[X]:(room(X)&~hate(X,gregory)))&(![X,Y]:((room(X)&room(Y)&(~hate(X,gregory))&(~hate(Y,gregory)))=>(X=Y)))))&
(![X]:(room(X)=>(((((~hate(X,norma))&(hate(X,robert))))=>(~hate(irene,X))))))&
(?[X]:(room(X)&(((~hate(X,gregory))<~>(~hate(X,irene)))))) | (there_is_a_room)&
![X]:(room(X)=>(hate(deja,X))) | [] | null | 0.054224 |
Darlene, Lorraine, Michael, Angelita, Heather are the only persons in the room.
If “no one in the room is not a tall person” then “no happy person is patient” otherwise “everyone in the room is a wise person”.
“Everyone in the room is not a quiet person” only if “no old person is wise”.
“It is not the case that “Lorraine and Michael are not a old persons”” only if “no brave person is quiet”.
Lorraine is the oldest in the room.
Everyone in the room is not a patient person, is a curious person and is a tall person. | Angelita is old. | contradiction | room(darlene)&room(lorraine)&room(michael)&room(angelita)&room(heather)&(![X]:(room(X)=>(X='darlene'|X='lorraine'|X='michael'|X='angelita'|X='heather')))&
(((kind(michael))&(tall(lorraine)))=>(~![X]:(~room(X)=>(~(happy(X)&person(X))))))&
(((~?[X]:(room(X)=>(~(tall(X)&person(X)))))=>(~?[X]:(happy(X)=>patient(X))))&((~(~?[X]:(room(X)=>(~(tall(X)&person(X))))))=>(![X]:(room(X)=>(wise(X)&person(X))))))&
((![X]:(room(X)=>(~(quiet(X)&person(X)))))=>(~?[X]:(old(X)=>wise(X))))&
((~(~(old(lorraine)&person(lorraine))&~(old(michael)&person(michael))))=>(~?[X]:(brave(X)=>quiet(X))))&
(![X]:((room(X)&(X!=lorraine))=>older(X,lorraine)))&
(![X]:(room(X)=>(tall(X)&person(X))))&
(![X]:(room(X)=>(((~(patient(X)&person(X)))&(curious(X)&person(X))&(tall(X)&person(X))))))&
(![X]:((room(X)&(X!=heather))=>quieter(heather,X)))&
(![X]:(room(X)=>(((~(funny(X)&person(X)))<=>(((patient(X)&person(X))|(~(curious(X)&person(X)))|(strong(X)))))))) | room(darlene)&room(lorraine)&room(michael)&room(angelita)&room(heather)&(![X]:(room(X)=>(X='darlene'|X='lorraine'|X='michael'|X='angelita'|X='heather')))&
old(angelita) | [
"b20",
"b42",
"p0",
"p2",
"p3",
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2622771370748470808862450
% SZS output start Proof for 2622771370748470808862450
21. ! [X0,X1] : (X0 != X1 => ((old(X0) & older(X0,X1)) => old(X1))) [input b20]
43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42]
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
46. (~~? [X0] : (room(X0) => ~(person(X0) & tall(X0))) => ! [X0] : (room(X0) => (person(X0) & wise(X0)))) & (~? [X0] : (room(X0) => ~(person(X0) & tall(X0))) => ~? [X0] : (happy(X0) => patient(X0))) [input p2]
47. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) => ~? [X0] : (old(X0) => wise(X0)) [input p3]
48. ~(~(person(fred) & old(fred)) & ~(person(paul) & old(paul))) => ~? [X0] : (brave(X0) => quiet(X0)) [input p4]
49. ! [X0] : ((paul != X0 & room(X0)) => older(X0,paul)) [input p5]
51. ! [X0] : (room(X0) => (person(X0) & tall(X0) & person(X0) & curious(X0) & ~(person(X0) & patient(X0)))) [input p7]
54. old(alice) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
55. (~~? [X0] : (room(X0) => ~(person(X0) & tall(X0))) => ! [X1] : (room(X1) => (person(X1) & wise(X1)))) & (~? [X2] : (room(X2) => ~(person(X2) & tall(X2))) => ~? [X3] : (happy(X3) => patient(X3))) [rectify 46]
56. (? [X0] : (room(X0) => ~(person(X0) & tall(X0))) => ! [X1] : (room(X1) => (person(X1) & wise(X1)))) & (~? [X2] : (room(X2) => ~(person(X2) & tall(X2))) => ~? [X3] : (happy(X3) => patient(X3))) [flattening 55]
57. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) => ~? [X1] : (old(X1) => wise(X1)) [rectify 47]
58. ~(~(person(fred) & old(fred)) & ~(person(paul) & old(paul))) => ~? [X0] : quiet(X0) [pure predicate removal 48]
59. (? [X0] : (room(X0) => ~(person(X0) & tall(X0))) => ! [X1] : (room(X1) => (person(X1) & wise(X1)))) & (~? [X2] : (room(X2) => ~(person(X2) & tall(X2))) => ~? [X3] : patient(X3)) [pure predicate removal 56]
94. ! [X0,X1] : ((old(X1) | (~old(X0) | ~older(X0,X1))) | X0 = X1) [ennf transformation 21]
95. ! [X0,X1] : (old(X1) | ~old(X0) | ~older(X0,X1) | X0 = X1) [flattening 94]
134. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
135. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134]
136. (! [X1] : ((person(X1) & wise(X1)) | ~room(X1)) | ! [X0] : ((person(X0) & tall(X0)) & room(X0))) & (! [X3] : ~patient(X3) | ? [X2] : ((~person(X2) | ~tall(X2)) | ~room(X2))) [ennf transformation 59]
137. (! [X1] : ((person(X1) & wise(X1)) | ~room(X1)) | ! [X0] : (person(X0) & tall(X0) & room(X0))) & (! [X3] : ~patient(X3) | ? [X2] : (~person(X2) | ~tall(X2) | ~room(X2))) [flattening 136]
138. ! [X1] : (~wise(X1) & old(X1)) | ? [X0] : ((person(X0) & quiet(X0)) & room(X0)) [ennf transformation 57]
139. ! [X1] : (~wise(X1) & old(X1)) | ? [X0] : (person(X0) & quiet(X0) & room(X0)) [flattening 138]
140. ! [X0] : ~quiet(X0) | ((~person(fred) | ~old(fred)) & (~person(paul) | ~old(paul))) [ennf transformation 58]
141. ! [X0] : (older(X0,paul) | (paul = X0 | ~room(X0))) [ennf transformation 49]
142. ! [X0] : (older(X0,paul) | paul = X0 | ~room(X0)) [flattening 141]
144. ! [X0] : ((person(X0) & tall(X0) & person(X0) & curious(X0) & (~person(X0) | ~patient(X0))) | ~room(X0)) [ennf transformation 51]
149. old(alice) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 54]
150. old(alice) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 149]
152. (! [X0] : ((person(X0) & wise(X0)) | ~room(X0)) | ! [X1] : (person(X1) & tall(X1) & room(X1))) & (! [X2] : ~patient(X2) | ? [X3] : (~person(X3) | ~tall(X3) | ~room(X3))) [rectify 137]
153. ? [X3] : (~person(X3) | ~tall(X3) | ~room(X3)) => (~person(sK0) | ~tall(sK0) | ~room(sK0)) [choice axiom]
154. (! [X0] : ((person(X0) & wise(X0)) | ~room(X0)) | ! [X1] : (person(X1) & tall(X1) & room(X1))) & (! [X2] : ~patient(X2) | (~person(sK0) | ~tall(sK0) | ~room(sK0))) [skolemisation 152,153]
155. ! [X0] : (~wise(X0) & old(X0)) | ? [X1] : (person(X1) & quiet(X1) & room(X1)) [rectify 139]
156. ? [X1] : (person(X1) & quiet(X1) & room(X1)) => (person(sK1) & quiet(sK1) & room(sK1)) [choice axiom]
157. ! [X0] : (~wise(X0) & old(X0)) | (person(sK1) & quiet(sK1) & room(sK1)) [skolemisation 155,156]
176. ~older(X0,X1) | ~old(X0) | old(X1) | X0 = X1 [cnf transformation 95]
217. paul != alice [cnf transformation 43]
234. mary != lucy [cnf transformation 43]
235. paul != lucy [cnf transformation 43]
236. fred != lucy [cnf transformation 43]
237. alice != lucy [cnf transformation 43]
238. john != lucy [cnf transformation 43]
240. room(mary) [cnf transformation 135]
241. room(paul) [cnf transformation 135]
243. room(alice) [cnf transformation 135]
245. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 135]
247. wise(X0) | ~room(X0) | room(X1) [cnf transformation 154]
257. ~wise(X0) | quiet(sK1) [cnf transformation 157]
259. ~quiet(X0) | ~person(paul) | ~old(paul) [cnf transformation 140]
261. older(X0,paul) | paul = X0 | ~room(X0) [cnf transformation 142]
266. person(X0) | ~room(X0) [cnf transformation 144]
284. old(alice) [cnf transformation 150]
291. 2 <=> ! [X0] : (person(X0) | ~room(X0)) [avatar definition]
292. ~room(X0) | person(X0) <- (2) [avatar component clause 291]
299. 4 <=> ! [X1] : room(X1) [avatar definition]
300. room(X1) <- (4) [avatar component clause 299]
303. 5 <=> ! [X0] : (wise(X0) | ~room(X0)) [avatar definition]
304. ~room(X0) | wise(X0) <- (5) [avatar component clause 303]
307. 4 | 5 [avatar split clause 247,303,299]
329. 11 <=> ! [X0] : ~wise(X0) [avatar definition]
330. ~wise(X0) <- (11) [avatar component clause 329]
333. 12 <=> quiet(sK1) [avatar definition]
335. quiet(sK1) <- (12) [avatar component clause 333]
336. 12 | 11 [avatar split clause 257,329,333]
357. 17 <=> ! [X0] : ~quiet(X0) [avatar definition]
358. ~quiet(X0) <- (17) [avatar component clause 357]
361. 18 <=> old(paul) [avatar definition]
363. ~old(paul) <- (~18) [avatar component clause 361]
365. 19 <=> person(paul) [avatar definition]
368. ~18 | ~19 | 17 [avatar split clause 259,357,365,361]
371. 2 [avatar split clause 266,291]
387. person(paul) <- (2) [resolution 292,241]
392. 19 | ~2 [avatar split clause 387,291,365]
394. wise(mary) <- (5) [resolution 304,240]
472. $false <- (12, 17) [resolution 358,335]
473. ~12 | ~17 [avatar contradiction clause 472]
482. $false <- (5, 11) [resolution 394,330]
483. ~5 | ~11 [avatar contradiction clause 482]
546. ~old(X0) | old(paul) | paul = X0 | paul = X0 | ~room(X0) [resolution 176,261]
547. ~old(X0) | old(paul) | paul = X0 | ~room(X0) [duplicate literal removal 546]
548. ~room(X0) | paul = X0 | ~old(X0) <- (~18) [subsumption resolution 547,363]
649. paul = alice | ~old(alice) <- (~18) [resolution 548,243]
652. ~old(alice) <- (~18) [subsumption resolution 649,217]
653. $false <- (~18) [subsumption resolution 652,284]
654. 18 [avatar contradiction clause 653]
660. john = X0 | fred = X0 | paul = X0 | mary = X0 | alice = X0 <- (4) [resolution 300,245]
806. john != john | fred = lucy | paul = lucy | mary = lucy | alice = lucy <- (4) [superposition 238,660]
818. fred = lucy | paul = lucy | mary = lucy | alice = lucy <- (4) [trivial inequality removal 806]
828. paul = lucy | mary = lucy | alice = lucy <- (4) [subsumption resolution 818,236]
829. mary = lucy | alice = lucy <- (4) [subsumption resolution 828,235]
830. alice = lucy <- (4) [subsumption resolution 829,234]
831. $false <- (4) [subsumption resolution 830,237]
832. ~4 [avatar contradiction clause 831]
833. $false [avatar sat refutation 307,336,368,371,392,473,483,654,832]
% SZS output end Proof for 2622771370748470808862450
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0.036878 |
There is a room. 'Everyone in the room collects vintage stamps or does not have a vast collection of first-edition science fiction novels' if 'everyone in the room is a dedicated advocate for digital privacy and encryption or does not practice pilates'. Either 'everyone outside the room does not practice pilates or does not participate in citizen science projects related to wildlife monitoring' or 'not everyone in the room is a client of Costco or does not watche fantasy movies' but not both. If 'no one in the room does not practice yoga or does not compete in national level swimming championships' then 'everyone anywhere enjoys rooftop gardening'. If 'everyone outside the room is a certified yoga instructor teaching classes weekly or does not enjoy bird watching' then 'everyone in the room is not passionate about collecting and restoring classic cars if they has a pet dog' otherwise 'everyone in the room is not passionate about collecting and restoring classic cars only if they does not use contact lenses'. | Everyone in the room does not have a pet dog or watches fantasy movies. | neutral | (there_is_a_room)&
((![X]:(room(X)=>(((does_not_practice_pilates(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(collects_vintage_stamps(X)))))))&
((![X]:(~room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_practice_pilates(X))))))<~>(~![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(is_a_client_of_Costco(X)))))))&
((~?[X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))|(does_not_practice_yoga(X))))))=>(![X]:(anywhere(X)=>(enjoys_rooftop_gardening(X)))))&
(((![X]:(~room(X)=>(((does_not_enjoy_bird_watching(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((has_a_pet_dog(X))=>(is_not_passionate_about_collecting_and_restoring_classic_cars(X)))))))&((~(![X]:(~room(X)=>(((does_not_enjoy_bird_watching(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))=>(![X]:(room(X)=>(((does_not_use_contact_lenses(X))<=(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))))&
((~?[X]:(room(X)=>(((is_a_client_of_Costco(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))))&
((~![X]:(room(X)=>(((can_play_the_piano(X))|(uses_contact_lenses(X))|(has_a_pet_dog(X))))))=>((![X]:((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(does_practice_yoga(X))))))&
((![X]:(room(X)=>(((cannot_play_the_piano(X))|(does_not_enjoy_bird_watching(X))))))=>(~?[X]:(anywhere(X)=>(((does_not_enjoy_bird_watching(X))=>(enjoys_rooftop_gardening(X)))))))&
((![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((~((creates_large-scale_murals_for_public_art_installations(X))|(enjoys_bird_watching(X))))=>(enjoys_rooftop_gardening(X)))))))&
(![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(((watches_fantasy_movies(X))<~>(uses_contact_lenses(X))))))))&
(![X]:(room(X)=>(((((watches_fantasy_movies(X))<~>(uses_contact_lenses(X))))=>(enjoys_bird_watching(X))))))&
(~![X]:(room(X)=>(((enjoys_bird_watching(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(room(X)=>(((uses_contact_lenses(X))<=(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(((?[X]:(room(X)&is_a_client_of_Costco(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_client_of_Costco(X))&(is_a_client_of_Costco(Y)))=>(X=Y)))))&
(![X]:(~room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_practice_pilates(X))))))&
(![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(((has_a_pet_dog(X))&(does_not_practice_pilates(X))))))))&
(![X]:(room(X)=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))&
(![X]:(room(X)=>(((~((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(can_play_the_piano(X))))<=(((collects_vintage_stamps(X))<~>(uses_contact_lenses(X))))))))&
((![X]:((((has_a_pet_dog(X))&(can_play_the_piano(X))))<=>(uses_contact_lenses(X)))))&
(?[X]:(room(X)&(uses_contact_lenses(X))))&
(![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))&
(![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(?[X]:(room(X)&(is_a_client_of_Costco(X)))) | (there_is_a_room)&
![X]:(room(X)=>(((watches_fantasy_movies(X))|(does_not_have_a_pet_dog(X))))) | [] | null | 0 |
There is a room.
Everyone in the room is tall if they is a patient person, is a patient tall person and is not a brave patient person and vice versa.
Everyone outside the room who is a patient person, is a patient tall person and is not a brave patient person is tall.
It is not the case that “at least one person in the room practices pilates”.
If someone practices pilates then he/she maintains a large, organic vegetable garden year-round and vice versa.
It is true that “everyone outside the room maintains a large, organic vegetable garden year-round if they practices urban gardening”.
Everyone in the room who makes intricate hand-cut paper art for exhibitions is patient, is a tall person or does not make intricate hand-cut paper art for exhibitions.
Everyone in the room maintains a large, organic vegetable garden year-round if they is patient, is a tall person or does not make intricate hand-cut paper art for exhibitions.
Everyone in the room is not brave if and only if they is a brave patient tall person.
All brave persons are patient.
Everyone in the room who practices urban gardening does not practice urban gardening.
Everyone in the room who does not practice urban gardening does not maintain a large, organic vegetable garden year-round. | Everyone in the room is a tall person. | entailment | (there_is_a_room)&
(![X]:(room(X)=>(((tall(X))<=>(((patient(X)&person(X))&(patient(X)&tall(X)&person(X))&(~(brave(X)&patient(X)&person(X)))))))))&
(![X]:(~room(X)=>(((((patient(X)&person(X))&(patient(X)&tall(X)&person(X))&(~(brave(X)&patient(X)&person(X)))))=>(tall(X))))))&
(~(((?[X]:(room(X)&practices_pilates(X))))))&
((![X]:((practices_pilates(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))&
(![X]:(~room(X)=>(((practices_urban_gardening(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(((patient(X))|(tall(X)&person(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))))&
(![X]:(room(X)=>(((((patient(X))|(tall(X)&person(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(![X]:(room(X)=>(((~brave(X))<=>(brave(X)&patient(X)&tall(X)&person(X))))))&
(![X]:(brave(X)=>patient(X)))&
(![X]:(room(X)=>(((practices_urban_gardening(X))=>(does_not_practice_urban_gardening(X))))))&
(![X]:(room(X)=>(((does_not_practice_urban_gardening(X))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(tall(X)&person(X))) | [
"p0",
"p7",
"p8",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3109335521559737018996324
% SZS output start Proof for 3109335521559737018996324
44. there_is_a_room [input p0]
51. ! [X0] : (room(X0) => ((~predb(X0) | (person(X0) & tall(X0)) | patient(X0)) => predu(X0))) [input p7]
52. ! [X0] : (room(X0) => (~brave(X0) <=> (person(X0) & tall(X0) & patient(X0) & brave(X0)))) [input p8]
53. ! [X0] : (brave(X0) => patient(X0)) [input p9]
54. ! [X0] : (room(X0) => (predm(X0) => ~predm(X0))) [input p10]
55. ! [X0] : (room(X0) => (~predm(X0) => ~predu(X0))) [input p11]
56. ~(! [X0] : (room(X0) => (person(X0) & tall(X0))) & there_is_a_room) [input hypothesis]
139. ! [X0] : ((predu(X0) | (predb(X0) & (~person(X0) | ~tall(X0)) & ~patient(X0))) | ~room(X0)) [ennf transformation 51]
140. ! [X0] : (predu(X0) | (predb(X0) & (~person(X0) | ~tall(X0)) & ~patient(X0)) | ~room(X0)) [flattening 139]
141. ! [X0] : ((~brave(X0) <=> (person(X0) & tall(X0) & patient(X0) & brave(X0))) | ~room(X0)) [ennf transformation 52]
142. ! [X0] : (patient(X0) | ~brave(X0)) [ennf transformation 53]
143. ! [X0] : ((~predm(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 54]
144. ! [X0] : (~predm(X0) | ~predm(X0) | ~room(X0)) [flattening 143]
145. ! [X0] : ((~predu(X0) | predm(X0)) | ~room(X0)) [ennf transformation 55]
146. ! [X0] : (~predu(X0) | predm(X0) | ~room(X0)) [flattening 145]
147. ? [X0] : ((~person(X0) | ~tall(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 56]
155. ! [X0] : (((~brave(X0) | (~person(X0) | ~tall(X0) | ~patient(X0) | ~brave(X0))) & ((person(X0) & tall(X0) & patient(X0) & brave(X0)) | brave(X0))) | ~room(X0)) [nnf transformation 141]
156. ! [X0] : (((~brave(X0) | ~person(X0) | ~tall(X0) | ~patient(X0) | ~brave(X0)) & ((person(X0) & tall(X0) & patient(X0) & brave(X0)) | brave(X0))) | ~room(X0)) [flattening 155]
157. ? [X0] : ((~person(X0) | ~tall(X0)) & room(X0)) => ((~person(sK2) | ~tall(sK2)) & room(sK2)) [choice axiom]
158. ((~person(sK2) | ~tall(sK2)) & room(sK2)) | ~there_is_a_room [skolemisation 147,157]
239. there_is_a_room [cnf transformation 44]
260. ~patient(X0) | predu(X0) | ~room(X0) [cnf transformation 140]
263. brave(X0) | brave(X0) | ~room(X0) [cnf transformation 156]
268. ~brave(X0) | patient(X0) [cnf transformation 142]
269. ~predm(X0) | ~predm(X0) | ~room(X0) [cnf transformation 144]
270. ~predu(X0) | predm(X0) | ~room(X0) [cnf transformation 146]
271. room(sK2) | ~there_is_a_room [cnf transformation 158]
273. ~predm(X0) | ~room(X0) [duplicate literal removal 269]
274. ~room(X0) | brave(X0) [duplicate literal removal 263]
284. ~predu(X0) | ~room(X0) [subsumption resolution 270,273]
295. room(sK2) [subsumption resolution 271,239]
297. brave(sK2) [resolution 274,295]
298. patient(sK2) [resolution 297,268]
301. predu(sK2) | ~room(sK2) [resolution 260,298]
302. predu(sK2) [subsumption resolution 301,295]
303. ~room(sK2) [resolution 302,284]
305. $false [subsumption resolution 303,295]
% SZS output end Proof for 3109335521559737018996324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Earl, Debra, Daniel, Bobby, James are the only persons in the room. James writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room is a client of Costco if they enjoys spelunking. Not everyone in the room who is a client of Costco owns a high-end gaming PC with custom-built components. Everyone in the room who owns a high-end gaming PC with custom-built components is a client of Costco. Everyone in the room enjoys spelunking if they is a client of Costco. Bobby owns a telescope. Debra writes in-depth travel guides for off-the-beaten-path destinations. Someone in the room is a client of Costco. Debra who does not have a curated collection of mid-century modern furniture enjoys spelunking. Everyone anywhere who either bakes bread at home or owns a telescope but not both bakes bread at home. Everyone in the room who has a specialized collection of handmade artisan pottery owns a high-end gaming PC with custom-built components. At least one person in the room enjoys spelunking. Everyone in the room who does not enjoy spelunking, has a curated collection of mid-century modern furniture and has a specialized collection of handmade artisan pottery writes in-depth travel guides for off-the-beaten-path destinations. Daniel who is a client of Costco is an active member of a local robotics club. | Everyone in the room is not a client of Costco or is an active member of a local robotics club. | neutral | room(earl)&room(debra)&room(daniel)&room(bobby)&room(james)&(![X]:(room(X)=>(X='earl'|X='debra'|X='daniel'|X='bobby'|X='james')))&
(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(james))&
(![X]:(room(X)=>(((enjoys_spelunking(X))=>(is_a_client_of_Costco(X))))))&
(~![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))&
(![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_a_client_of_Costco(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(enjoys_spelunking(X))))))&
(owns_a_telescope(bobby))&
(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(debra))&
(?[X]:(room(X)&(is_a_client_of_Costco(X))))&
((does_not_have_a_curated_collection_of_mid-century_modern_furniture(debra))&(enjoys_spelunking(debra)))&
(![X]:(anywhere(X)=>(((((bakes_bread_at_home(X))<~>(owns_a_telescope(X))))=>(bakes_bread_at_home(X))))))&
(![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))&
(((?[X]:(room(X)&enjoys_spelunking(X)))))&
(![X]:(room(X)=>(((((does_not_enjoy_spelunking(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))&
((is_a_client_of_Costco(daniel))&(is_an_active_member_of_a_local_robotics_club(daniel))) | room(earl)&room(debra)&room(daniel)&room(bobby)&room(james)&(![X]:(room(X)=>(X='earl'|X='debra'|X='daniel'|X='bobby'|X='james')))&
![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))|(is_not_a_client_of_Costco(X))))) | [] | null | 0.001647 |
There is a room.
If "everyone in the room has a specialized collection of handmade artisan pottery" then "everyone in the room is dedicated to sustainable living and zero-waste practices or does not collect limited-edition art prints from contemporary artists".
If "everyone in the room is dedicated to sustainable living and zero-waste practices or does not collect limited-edition art prints from contemporary artists" then "everyone in the room is dedicated to sustainable living and zero-waste practices or does not create YouTube content or both if they has a saltwater aquarium".
Everyone outside the room who is dedicated to sustainable living and zero-waste practices or does not create YouTube content or both does not collect rare sneakers.
Everyone in the room collect rare sneakers if they does not collect rare sneakers.
Everyone in the room is dedicated to sustainable living and zero-waste practices or does not collect limited-edition art prints from contemporary artists.
Everyone in the room is dedicated to sustainable living and zero-waste practices or enjoys rooftop gardening or both if they practices tai chi.
Everyone in the room has lived in exactly three countries. | Everyone in the room is not a dedicated volunteer for local community service projects or owns an Android phone. | neutral | (there_is_a_room)&
(((![X]:(room(X)=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))&
((![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))=>(![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(does_not_create_YouTube_content(X))))))))))&
(![X]:(~room(X)=>(((((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(does_not_create_YouTube_content(X))))=>(does_not_collect_rare_sneakers(X))))))&
(![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))=>(collect_rare_sneakers(X))))))&
(![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))&
(![X]:(room(X)=>(((practices_tai_chi(X))=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(enjoys_rooftop_gardening(X))))))))&
(![X]:(room(X)=>(has_lived_in_exactly_three_countries(X))))&
(?[X]:(room(X)&(~((owns_a_3D_printer(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))&
(~![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(practices_graffiti_art(X))))))&
(![X]:(room(X)=>(((owns_a_3D_printer(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))&
(((?[X]:(anywhere(X)&does_not_collect_rare_sneakers(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(does_not_collect_rare_sneakers(X))&(does_not_collect_rare_sneakers(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(owns_a_3D_printer(X))))))&
(![X]:(room(X)=>(((owns_a_3D_printer(X))=>(((regularly_contributes_to_tech_forums_and_online_communities(X))|(owns_an_Android_phone(X))))))))&
(![X]:(room(X)=>(((((regularly_contributes_to_tech_forums_and_online_communities(X))|(owns_an_Android_phone(X))))=>(collect_rare_sneakers(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((owns_an_Android_phone(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))) | [] | null | 0.261783 |
There is a room.
If "everyone in the room does not enjoy wildlife photography or trains for and competes in international triathlons" then "more than one person in the room does not enjoy virtual reality gaming".
If "everyone in the room is not dedicated to sustainable living and zero-waste practices or trains for and competes in international triathlons" then "everyone in the room who is a skilled home brewer experimenting with craft beer recipes is an avid hiker".
If "everyone in the room does not enjoy making ceramics or enjoys virtual reality gaming" then "everyone in the room who does not enjoy making ceramics collects antique jewelry".
If "everyone in the room does not design and sews custom cosplay costumes for conventions or creates large-scale murals for public art installations" then "everyone in the room regularly contributes to tech forums and online communities if they does not design and sews custom cosplay costumes for conventions".
"Everyone in the room who does not own an extensive assortment of vintage comic book memorabilia designs and sews custom cosplay costumes for conventions" unless "everyone in the room does not participate in long-distance cycling events across the country or is an avid mountain climber who has scaled several peaks".
If "everyone anywhere does not enjoy virtual reality gaming or enjoys wildlife photography" then "everyone in the room who does not enjoy virtual reality gaming owns an extensive assortment of vintage comic book memorabilia".
Everyone in the room regularly contributes to tech forums and online communities if they enjoys virtual reality gaming.
Everyone in the room is dedicated to sustainable living and zero-waste practices if they regularly contributes to tech forums and online communities.
Everyone in the room who is dedicated to sustainable living and zero-waste practices enjoys making ceramics.
Everyone in the room travels domestically frequently, collects antique jewelry and enjoys virtual reality gaming if they enjoys origami.
If someone enjoys origami then he/she is a culinary enthusiast who experiments with international cuisines and vice versa.
No one in the room who is not an avid mountain climber who has scaled several peaks enjoys making ceramics. | Everyone in the room does not design and sews custom cosplay costumes for conventions or is a culinary enthusiast who experiments with international cuisines. | contradiction | (there_is_a_room)&
((![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))|(does_not_enjoy_wildlife_photography(X))))))=>((?[X,Y]:(room(X)&room(Y)&(does_not_enjoy_virtual_reality_gaming(X)&does_not_enjoy_virtual_reality_gaming(Y))&(X!=Y)))))&
((![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))=>(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(is_an_avid_hiker(X)))))))&
((![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))|(does_not_enjoy_making_ceramics(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))=>(collects_antique_jewelry(X)))))))&
((![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))))&
(~(![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))=>(![X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))))&
((![X]:(anywhere(X)=>(((enjoys_wildlife_photography(X))|(does_not_enjoy_virtual_reality_gaming(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))))&
(~(![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))=>(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(enjoys_salsa_dancing(X)))))))&
((![X]:(anywhere(X)=>(((does_not_enjoy_logic_puzzles(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))=>(![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(is_not_an_avid_hiker(X)))))))&
((~?[X]:(room(X)=>(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(![X]:(~room(X)=>(((can_play_the_piano(X))=>(enjoys_virtual_reality_gaming(X)))))))&
(![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))&
(![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(enjoys_making_ceramics(X))))))&
(![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(owns_a_smart_tv(X))))))&
(![X]:(~room(X)=>(((owns_a_smart_tv(X))=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(creates_large-scale_murals_for_public_art_installations(X))&(owns_a_smartwatch(X))))))))&
(![X]:(room(X)=>(((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(creates_large-scale_murals_for_public_art_installations(X))&(owns_a_smartwatch(X))))=>(is_an_avid_hiker(X))))))&
(![X]:(room(X)=>(((is_an_avid_hiker(X))|(does_not_own_a_smart_tv(X))))))&
(![X]:(room(X)=>(((enjoys_origami(X))=>(((travels_domestically_frequently(X))&(collects_antique_jewelry(X))&(enjoys_virtual_reality_gaming(X))))))))&
((![X]:((enjoys_origami(X))<=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))&
(![X]:(room(X)=>(((travels_domestically_frequently(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))&
(![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))&
(?[X]:(room(X)&(owns_a_smartwatch(X))))&
(~(?[X]:(room(X)&(trains_for_and_competes_in_international_triathlons(X)))))&
(![X]:(room(X)=>(((owns_a_smart_tv(X))=>(is_a_client_of_LVMH(X))))))&
(~?[X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(enjoys_making_ceramics(X))))))&
((![X]:((((enjoys_salsa_dancing(X))<~>(participates_in_long-distance_cycling_events_across_the_country(X))))<=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))&
(![X]:(anywhere(X)=>(((does_not_enjoy_origami(X))=>(is_not_a_client_of_LVMH(X))))))&
(![X]:(room(X)=>(((enjoys_making_ceramics(X))<=(participates_in_long-distance_cycling_events_across_the_country(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))) | [
"p4",
"p10",
"p11",
"p12",
"p17",
"p18",
"p24",
"hypothesis"
] | % SZS status Unsatisfiable for 805091268032794353570019
% SZS output start Proof for 805091268032794353570019
48. ! [X0] : (room(X0) => (~predd(X0) | predl(X0))) => ! [X0] : (room(X0) => (~predd(X0) => predn(X0))) [input p4]
54. ! [X0] : (room(X0) => (prede(X0) => predn(X0))) [input p10]
55. ! [X0] : (room(X0) => (predn(X0) => preda(X0))) [input p11]
56. ! [X0] : (room(X0) => (preda(X0) => predu(X0))) [input p12]
61. ! [X0] : (room(X0) => (predt(X0) => (prede(X0) & predx(X0) & predz(X0)))) [input p17]
62. ! [X0] : (predt(X0) <=> predj(X0)) [input p18]
68. ~? [X0] : (room(X0) => (~predr(X0) => predu(X0))) [input p24]
72. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room [input hypothesis]
76. ! [X0] : (room(X0) => (~predd(X0) | predl(X0))) => ! [X1] : (room(X1) => (~predd(X1) => predn(X1))) [rectify 48]
88. ! [X0] : (room(X0) => (predt(X0) => (prede(X0) & predx(X0)))) [pure predicate removal 61]
90. ! [X0] : (room(X0) => (predt(X0) => prede(X0))) [pure predicate removal 88]
95. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [pure predicate removal 72]
172. ! [X1] : ((predn(X1) | predd(X1)) | ~room(X1)) | ? [X0] : ((predd(X0) & ~predl(X0)) & room(X0)) [ennf transformation 76]
173. ! [X1] : (predn(X1) | predd(X1) | ~room(X1)) | ? [X0] : (predd(X0) & ~predl(X0) & room(X0)) [flattening 172]
178. ! [X0] : ((predn(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 54]
179. ! [X0] : (predn(X0) | ~prede(X0) | ~room(X0)) [flattening 178]
180. ! [X0] : ((preda(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 55]
181. ! [X0] : (preda(X0) | ~predn(X0) | ~room(X0)) [flattening 180]
182. ! [X0] : ((predu(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 56]
183. ! [X0] : (predu(X0) | ~preda(X0) | ~room(X0)) [flattening 182]
192. ! [X0] : ((prede(X0) | ~predt(X0)) | ~room(X0)) [ennf transformation 90]
193. ! [X0] : (prede(X0) | ~predt(X0) | ~room(X0)) [flattening 192]
198. ! [X0] : ((~predu(X0) & ~predr(X0)) & room(X0)) [ennf transformation 68]
199. ! [X0] : (~predu(X0) & ~predr(X0) & room(X0)) [flattening 198]
205. ! [X0] : ((~predd(X0) | predj(X0)) | ~room(X0)) [ennf transformation 95]
206. ! [X0] : (~predd(X0) | predj(X0) | ~room(X0)) [flattening 205]
215. ! [X0] : (predn(X0) | predd(X0) | ~room(X0)) | ? [X1] : (predd(X1) & ~predl(X1) & room(X1)) [rectify 173]
216. ? [X1] : (predd(X1) & ~predl(X1) & room(X1)) => (predd(sK4) & ~predl(sK4) & room(sK4)) [choice axiom]
217. ! [X0] : (predn(X0) | predd(X0) | ~room(X0)) | (predd(sK4) & ~predl(sK4) & room(sK4)) [skolemisation 215,216]
222. ! [X0] : ((predt(X0) | ~predj(X0)) & (predj(X0) | ~predt(X0))) [nnf transformation 62]
316. predn(X0) | predd(X0) | ~room(X0) | predd(sK4) [cnf transformation 217]
319. ~prede(X0) | predn(X0) | ~room(X0) [cnf transformation 179]
320. ~predn(X0) | preda(X0) | ~room(X0) [cnf transformation 181]
321. ~preda(X0) | predu(X0) | ~room(X0) [cnf transformation 183]
328. ~predt(X0) | prede(X0) | ~room(X0) [cnf transformation 193]
330. ~predj(X0) | predt(X0) [cnf transformation 222]
335. room(X0) [cnf transformation 199]
337. ~predu(X0) [cnf transformation 199]
342. ~predd(X0) | predj(X0) | ~room(X0) [cnf transformation 206]
353. 3 <=> prede(sK1) [avatar definition]
354. prede(sK1) <- (3) [avatar component clause 353]
355. ~prede(sK1) <- (~3) [avatar component clause 353]
386. 10 <=> predd(sK4) [avatar definition]
388. predd(sK4) <- (10) [avatar component clause 386]
390. 11 <=> ! [X0] : (predn(X0) | ~room(X0) | predd(X0)) [avatar definition]
391. predn(X0) | ~room(X0) | predd(X0) <- (11) [avatar component clause 390]
392. 10 | 11 [avatar split clause 316,390,386]
415. ~predd(X0) | predj(X0) [subsumption resolution 342,335]
416. predn(X0) | predd(X0) <- (11) [subsumption resolution 391,335]
418. preda(X0) | ~room(X0) | predd(X0) <- (11) [resolution 320,416]
419. predd(X0) | preda(X0) <- (11) [subsumption resolution 418,335]
420. predj(X0) | preda(X0) <- (11) [resolution 419,415]
421. predt(X0) | preda(X0) <- (11) [resolution 420,330]
423. prede(X0) | ~room(X0) | preda(X0) <- (11) [resolution 328,421]
424. preda(X0) | prede(X0) <- (11) [subsumption resolution 423,335]
425. prede(X0) | predu(X0) | ~room(X0) <- (11) [resolution 424,321]
426. prede(X0) | ~room(X0) <- (11) [subsumption resolution 425,337]
427. prede(X0) <- (11) [subsumption resolution 426,335]
428. $false <- (~3, 11) [resolution 427,355]
432. 3 | ~11 [avatar contradiction clause 428]
434. predj(sK4) <- (10) [resolution 388,415]
435. predt(sK4) <- (10) [resolution 434,330]
436. prede(sK4) | ~room(sK4) <- (10) [resolution 435,328]
438. prede(sK4) <- (10) [subsumption resolution 436,335]
439. predn(sK4) | ~room(sK4) <- (10) [resolution 438,319]
440. predn(sK4) <- (10) [subsumption resolution 439,335]
441. preda(sK4) | ~room(sK4) <- (10) [resolution 440,320]
442. preda(sK4) <- (10) [subsumption resolution 441,335]
443. predu(sK4) | ~room(sK4) <- (10) [resolution 442,321]
444. ~room(sK4) <- (10) [subsumption resolution 443,337]
445. $false <- (10) [subsumption resolution 444,335]
446. ~10 [avatar contradiction clause 445]
448. predn(sK1) | ~room(sK1) <- (3) [resolution 354,319]
449. predn(sK1) <- (3) [subsumption resolution 448,335]
452. preda(sK1) | ~room(sK1) <- (3) [resolution 449,320]
453. preda(sK1) <- (3) [subsumption resolution 452,335]
458. predu(sK1) | ~room(sK1) <- (3) [resolution 453,321]
459. ~room(sK1) <- (3) [subsumption resolution 458,337]
460. $false <- (3) [subsumption resolution 459,335]
461. ~3 [avatar contradiction clause 460]
462. $false [avatar sat refutation 392,432,446,461]
% SZS output end Proof for 805091268032794353570019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.119226 |
Mildred is the only person in the room. If 'Geneva is older than Mildred' then 'someone outside the room is older than Christy'. If 'Mildred is older than William' then 'Mildred is richer than William'. If 'Mildred is richer than William' then 'Mildred is quieter than Christy'. Mildred is richer than William. Someone who is richer than William and is quieter than Christy is quieter than someone who is richer than Geneva. If someone is richer than William then he/she is older than William. Mildred is quieter than Christy. If someone is quieter than Geneva then he/she is quieter than Christy. Mildred is richer than Geneva. | Geneva is older than Mildred. | neutral | room(mildred)&(![X]:(room(X)=>(X='mildred')))&
((older(mildred,geneva))=>(?[X]:(~room(X)&(older(christy,X)))))&
((older(william,mildred))=>(richer(william,mildred)))&
((richer(william,mildred))=>(quieter(christy,mildred)))&
(richer(william,mildred))&
(?[X,Y]:((((richer(william,X))&(quieter(christy,X))))&(richer(geneva,Y))&(quieter(X,Y))))&
((![X]:((richer(william,X))=>(older(william,X)))))&
(quieter(christy,mildred))&
((![X]:((quieter(geneva,X))=>(quieter(christy,X)))))&
(richer(geneva,mildred)) | room(mildred)&(![X]:(room(X)=>(X='mildred')))&
older(mildred,geneva) | [] | null | 0.477707 |
Ronnie, Virgina, Brett, Ollie, Graham are the only persons in the room.
"Everyone in the room either is not a wine connoisseur with a private cellar of vintage wines or is not an avid collector of autographed memorabilia from famous musicians but not both" if "everyone in the room cannot play the piano, does not collect antique jewelry and does not write a travel blog".
"Everyone in the room does not use a Windows laptop" if "everyone in the room either does not enjoy coding in Python or does not use a Windows laptop but not both".
"Everyone in the room either cannot play the harmonica or cannot play the piano but not both" only if "everyone outside the room cannot play the harmonica and is not dedicated to sustainable living and zero-waste practices".
Everyone in the room does not enjoy coding in Python, does not enjoy virtual reality gaming or does not practice calligraphy.
Everyone in the room is not a wine connoisseur with a private cellar of vintage wines and does not collect action figures.
Everyone in the room does not collect antique jewelry.
If someone does not use contact lenses and is not dedicated to sustainable living and zero-waste practices then he/she does not practice calligraphy, is not dedicated to sustainable living and zero-waste practices or does not make homemade pastries.
Everyone anywhere cannot play the piano.
Everyone in the room does not enjoy kayaking.
Everyone in the room does not enjoy logic puzzles, does not make intricate hand-cut paper art for exhibitions and does not have lived in exactly three countries.
Everyone in the room does not make homemade pastries, does not use contact lenses or does not play as a goalkeeper for a local amateur soccer team.
Everyone in the room cannot play the harmonica, does not write a travel blog or is not dedicated to sustainable living and zero-waste practices.
Not everyone in the room does not collect classic novels.
Everyone outside the room does not write a travel blog.
Everyone in the room does not make intricate hand-cut paper art for exhibitions.
Everyone outside the room does not enjoy logic puzzles, does not make intricate hand-cut paper art for exhibitions or does not enjoy coding in Python.
Not everyone in the room is not a cybersecurity expert, does not enjoy kayaking and does not have a pet dog.
Everyone in the room cannot play the harmonica, does not enjoy coding in Python or is not a cybersecurity expert.
Everyone in the room does not enjoy coding in Python.
Everyone in the room does not make homemade pastries and does not write a travel blog. | Ronnie is an avid collector of autographed memorabilia from famous musicians. | entailment | room(ronnie)&room(virgina)&room(brett)&room(ollie)&room(graham)&(![X]:(room(X)=>(X='ronnie'|X='virgina'|X='brett'|X='ollie'|X='graham')))&
((![X]:(room(X)=>(((cannot_play_the_piano(X))&(does_not_collect_antique_jewelry(X))&(does_not_write_a_travel_blog(X))))))=>(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<~>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))))&
((![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))<~>(does_not_use_a_Windows_laptop(X))))))=>(![X]:(room(X)=>(does_not_use_a_Windows_laptop(X)))))&
((![X]:(room(X)=>(((cannot_play_the_harmonica(X))<~>(cannot_play_the_piano(X))))))=>(![X]:(~room(X)=>(((cannot_play_the_harmonica(X))&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))&
(![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))|(does_not_enjoy_virtual_reality_gaming(X))|(does_not_practice_calligraphy(X))))))&
(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(does_not_collect_action_figures(X))))))&
(![X]:(room(X)=>(does_not_collect_antique_jewelry(X))))&
((![X]:((((does_not_use_contact_lenses(X))&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))=>(((does_not_practice_calligraphy(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(does_not_make_homemade_pastries(X)))))))&
(![X]:(anywhere(X)=>(cannot_play_the_piano(X))))&
(![X]:(room(X)=>(does_not_enjoy_kayaking(X))))&
(![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))&(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))&(does_not_have_lived_in_exactly_three_countries(X))))))&
(![X]:(room(X)=>(((does_not_make_homemade_pastries(X))|(does_not_use_contact_lenses(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(does_not_write_a_travel_blog(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))&
(~![X]:(room(X)=>(does_not_collect_classic_novels(X))))&
(![X]:(~room(X)=>(does_not_write_a_travel_blog(X))))&
(![X]:(room(X)=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))&
(![X]:(~room(X)=>(((does_not_enjoy_logic_puzzles(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_enjoy_coding_in_Python(X))))))&
(~![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))&(does_not_enjoy_kayaking(X))&(does_not_have_a_pet_dog(X))))))&
(![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(does_not_enjoy_coding_in_Python(X))|(is_not_a_cybersecurity_expert(X))))))&
(![X]:(room(X)=>(does_not_enjoy_coding_in_Python(X))))&
(![X]:(room(X)=>(((does_not_make_homemade_pastries(X))&(does_not_write_a_travel_blog(X)))))) | room(ronnie)&room(virgina)&room(brett)&room(ollie)&room(graham)&(![X]:(room(X)=>(X='ronnie'|X='virgina'|X='brett'|X='ollie'|X='graham')))&
is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(ronnie) | [
"b4",
"p0",
"p1",
"p5",
"p6",
"p8",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 297982004722615130394124
% SZS output start Proof for 297982004722615130394124
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. ! [X0] : (room(X0) => (~predd(X0) & ~predt(X0) & ~predf(X0))) => ! [X0] : (room(X0) => (~predk(X0) <~> ~predc(X0))) [input p1]
49. ! [X0] : (room(X0) => (~predq(X0) & ~predk(X0))) [input p5]
50. ! [X0] : (room(X0) => ~predt(X0)) [input p6]
52. ! [X0] : (anywhere(X0) => ~predf(X0)) [input p8]
58. ! [X0] : (~room(X0) => ~predd(X0)) [input p14]
64. ! [X0] : (room(X0) => (~predd(X0) & ~predo(X0))) [input p20]
65. ~(predc(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
66. ! [X0] : (room(X0) => (~predd(X0) & ~predt(X0) & ~predf(X0))) => ! [X1] : (room(X1) => (~predk(X1) <~> ~predc(X1))) [rectify 45]
82. ! [X0] : (room(X0) => ~predd(X0)) [pure predicate removal 64]
83. ! [X0] : (room(X0) => ~predk(X0)) [pure predicate removal 49]
156. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
157. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 156]
158. ! [X1] : ((~predk(X1) <~> ~predc(X1)) | ~room(X1)) | ? [X0] : ((predd(X0) | predt(X0) | predf(X0)) & room(X0)) [ennf transformation 66]
161. ! [X0] : (~predk(X0) | ~room(X0)) [ennf transformation 83]
162. ! [X0] : (~predt(X0) | ~room(X0)) [ennf transformation 50]
163. ! [X0] : (~predf(X0) | ~anywhere(X0)) [ennf transformation 52]
165. ! [X0] : (~predd(X0) | room(X0)) [ennf transformation 58]
168. ! [X0] : (~predd(X0) | ~room(X0)) [ennf transformation 82]
169. ~predc(mary) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 65]
170. ~predc(mary) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 169]
172. ! [X1] : (((predc(X1) | predk(X1)) & (~predc(X1) | ~predk(X1))) | ~room(X1)) | ? [X0] : ((predd(X0) | predt(X0) | predf(X0)) & room(X0)) [nnf transformation 158]
173. ! [X0] : (((predc(X0) | predk(X0)) & (~predc(X0) | ~predk(X0))) | ~room(X0)) | ? [X1] : ((predd(X1) | predt(X1) | predf(X1)) & room(X1)) [rectify 172]
174. ? [X1] : ((predd(X1) | predt(X1) | predf(X1)) & room(X1)) => ((predd(sK0) | predt(sK0) | predf(sK0)) & room(sK0)) [choice axiom]
175. ! [X0] : (((predc(X0) | predk(X0)) & (~predc(X0) | ~predk(X0))) | ~room(X0)) | ((predd(sK0) | predt(sK0) | predf(sK0)) & room(sK0)) [skolemisation 173,174]
190. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom]
191. ~predc(mary) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 170,190]
192. anywhere(X0) [cnf transformation 5]
273. room(mary) [cnf transformation 157]
274. room(paul) [cnf transformation 157]
275. room(fred) [cnf transformation 157]
276. room(alice) [cnf transformation 157]
277. room(john) [cnf transformation 157]
278. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 157]
281. predc(X0) | predk(X0) | ~room(X0) | room(sK0) [cnf transformation 175]
282. predc(X0) | predk(X0) | ~room(X0) | predd(sK0) | predt(sK0) | predf(sK0) [cnf transformation 175]
289. ~predk(X0) | ~room(X0) [cnf transformation 161]
290. ~predt(X0) | ~room(X0) [cnf transformation 162]
291. ~predf(X0) | ~anywhere(X0) [cnf transformation 163]
293. ~predd(X0) | room(X0) [cnf transformation 165]
296. ~predd(X0) | ~room(X0) [cnf transformation 168]
297. ~predc(mary) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191]
298. ~predc(mary) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191]
299. ~predc(mary) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191]
300. ~predc(mary) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191]
301. ~predc(mary) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191]
302. ~predc(mary) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191]
304. 1 <=> predf(sK0) [avatar definition]
306. predf(sK0) <- (1) [avatar component clause 304]
308. 2 <=> predt(sK0) [avatar definition]
310. predt(sK0) <- (2) [avatar component clause 308]
312. 3 <=> predd(sK0) [avatar definition]
314. predd(sK0) <- (3) [avatar component clause 312]
316. 4 <=> ! [X0] : (predc(X0) | ~room(X0) | predk(X0)) [avatar definition]
317. predc(X0) | ~room(X0) | predk(X0) <- (4) [avatar component clause 316]
318. 1 | 2 | 3 | 4 [avatar split clause 282,316,312,308,304]
320. 5 <=> room(sK0) [avatar definition]
323. 5 | 4 [avatar split clause 281,316,320]
365. ~predf(X0) [subsumption resolution 291,192]
366. ~predd(X0) [subsumption resolution 296,293]
367. ~predc(mary) | john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,277]
368. ~predc(mary) | john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 367,276]
369. ~predc(mary) | john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 368,275]
370. ~predc(mary) | john != sK5 | ~room(mary) [subsumption resolution 369,274]
371. ~predc(mary) | john != sK5 [subsumption resolution 370,273]
373. 15 <=> john = sK5 [avatar definition]
375. john != sK5 <- (~15) [avatar component clause 373]
377. 16 <=> predc(mary) [avatar definition]
380. ~15 | ~16 [avatar split clause 371,377,373]
381. ~predc(mary) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,277]
382. ~predc(mary) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 381,276]
383. ~predc(mary) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 382,275]
384. ~predc(mary) | alice != sK5 | ~room(mary) [subsumption resolution 383,274]
385. ~predc(mary) | alice != sK5 [subsumption resolution 384,273]
387. 17 <=> alice = sK5 [avatar definition]
389. alice != sK5 <- (~17) [avatar component clause 387]
390. ~17 | ~16 [avatar split clause 385,377,387]
391. ~predc(mary) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 300,277]
392. ~predc(mary) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 391,276]
393. ~predc(mary) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 392,275]
394. ~predc(mary) | fred != sK5 | ~room(mary) [subsumption resolution 393,274]
395. ~predc(mary) | fred != sK5 [subsumption resolution 394,273]
397. 18 <=> fred = sK5 [avatar definition]
399. fred != sK5 <- (~18) [avatar component clause 397]
400. ~18 | ~16 [avatar split clause 395,377,397]
401. ~predc(mary) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 299,277]
402. ~predc(mary) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 401,276]
403. ~predc(mary) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 402,275]
404. ~predc(mary) | paul != sK5 | ~room(mary) [subsumption resolution 403,274]
405. ~predc(mary) | paul != sK5 [subsumption resolution 404,273]
407. 19 <=> paul = sK5 [avatar definition]
410. ~19 | ~16 [avatar split clause 405,377,407]
411. ~predc(mary) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 298,277]
412. ~predc(mary) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 411,276]
413. ~predc(mary) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 412,275]
414. ~predc(mary) | mary != sK5 | ~room(mary) [subsumption resolution 413,274]
415. ~predc(mary) | mary != sK5 [subsumption resolution 414,273]
417. 20 <=> mary = sK5 [avatar definition]
419. mary != sK5 <- (~20) [avatar component clause 417]
420. ~20 | ~16 [avatar split clause 415,377,417]
421. ~predc(mary) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 297,277]
422. ~predc(mary) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 421,276]
423. ~predc(mary) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 422,275]
424. ~predc(mary) | room(sK5) | ~room(mary) [subsumption resolution 423,274]
425. ~predc(mary) | room(sK5) [subsumption resolution 424,273]
427. 21 <=> room(sK5) [avatar definition]
429. room(sK5) <- (21) [avatar component clause 427]
430. 21 | ~16 [avatar split clause 425,377,427]
431. ~room(sK0) <- (2) [resolution 290,310]
434. ~5 | ~2 [avatar split clause 431,308,320]
435. ~room(X0) | predc(X0) <- (4) [subsumption resolution 317,289]
436. predc(mary) <- (4) [resolution 435,273]
445. 16 | ~4 [avatar split clause 436,316,377]
496. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (21) [resolution 278,429]
539. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~17, 21) [subsumption resolution 496,389]
540. paul = sK5 | mary = sK5 | john = sK5 <- (~17, ~18, 21) [subsumption resolution 539,399]
545. paul = sK5 | john = sK5 <- (~17, ~18, ~20, 21) [subsumption resolution 540,419]
546. paul = sK5 <- (~15, ~17, ~18, ~20, 21) [subsumption resolution 545,375]
547. 19 | 15 | 17 | 18 | 20 | ~21 [avatar split clause 546,427,417,397,387,373,407]
554. $false <- (1) [subsumption resolution 306,365]
555. ~1 [avatar contradiction clause 554]
556. $false <- (3) [subsumption resolution 314,366]
557. ~3 [avatar contradiction clause 556]
558. $false [avatar sat refutation 318,323,380,390,400,410,420,430,434,445,547,555,557]
% SZS output end Proof for 297982004722615130394124
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s
% ------------------------------
% ------------------------------
| 0.540184 |
Jody, Diana, Jonathan, Dennis are the only persons in the room. Jody does not host themed dinner parties featuring gourmet home-cooked meals. Everyone outside the room hosts themed dinner parties featuring gourmet home-cooked meals if they does not enjoy watercolor painting. Everyone in the room participates in citizen science projects related to wildlife monitoring if they hosts themed dinner parties featuring gourmet home-cooked meals. Everyone in the room who plays video games has completed a triathlon, does not collect first edition books or frequently participates in hackathons and coding competitions. Everyone in the room who has completed a triathlon, does not collect first edition books or frequently participates in hackathons and coding competitions develops open-source software projects in their free time. Everyone in the room develops open-source software projects in their free time if they enjoys rooftop gardening and vice versa. Jody who owns a microscope enjoys rooftop gardening or participates in citizen science projects related to wildlife monitoring or both. Jody participates in citizen science projects related to wildlife monitoring. Jody is a certified scuba diver with advanced underwater photography skills. Everyone in the room is a certified scuba diver with advanced underwater photography skills or does not play video games. Only one person in the room owns a microscope. | Dennis owns a microscope. | contradiction | room(jody)&room(diana)&room(jonathan)&room(dennis)&(![X]:(room(X)=>(X='jody'|X='diana'|X='jonathan'|X='dennis')))&
(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(jody))&
(![X]:(~room(X)=>(((does_not_enjoy_watercolor_painting(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))&
(![X]:(room(X)=>(((plays_video_games(X))=>(((has_completed_a_triathlon(X))|(does_not_collect_first_edition_books(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))))&
(![X]:(room(X)=>(((((has_completed_a_triathlon(X))|(does_not_collect_first_edition_books(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))<=>(enjoys_rooftop_gardening(X))))))&
((owns_a_microscope(jody))&(((enjoys_rooftop_gardening(jody))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(jody)))))&
(participates_in_citizen_science_projects_related_to_wildlife_monitoring(jody))&
(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(jody))&
(![X]:(room(X)=>(((does_not_play_video_games(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))&
(((?[X]:(room(X)&collects_first_edition_books(X)))))&
(((?[X]:(room(X)&owns_a_microscope(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_microscope(X))&(owns_a_microscope(Y)))=>(X=Y)))))&
(does_not_enjoy_windsurfing(jody)) | room(jody)&room(diana)&room(jonathan)&room(dennis)&(![X]:(room(X)=>(X='jody'|X='diana'|X='jonathan'|X='dennis')))&
owns_a_microscope(dennis) | [
"b42",
"p0",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6301643603996777089463676
% SZS output start Proof for 6301643603996777089463676
43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42]
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
51. (prede(mary) | predu(mary)) & predt(mary) [input p7]
56. ! [X0,X1] : ((predt(X1) & predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predt(X0) & room(X0)) [input p12]
58. predt(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
59. ! [X0,X1] : ((predt(X1) & predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predt(X2) & room(X2)) [rectify 56]
68. predt(mary) [pure predicate removal 51]
145. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
146. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 145]
148. ! [X0,X1] : (X0 = X1 | (~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predt(X2) & room(X2)) [ennf transformation 59]
149. ! [X0,X1] : (X0 = X1 | ~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predt(X2) & room(X2)) [flattening 148]
150. predt(alice) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 58]
151. predt(alice) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 150]
156. ? [X2] : (predt(X2) & room(X2)) => (predt(sK1) & room(sK1)) [choice axiom]
157. ! [X0,X1] : (X0 = X1 | ~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0)) & (predt(sK1) & room(sK1)) [skolemisation 149,156]
214. mary != alice [cnf transformation 43]
238. room(mary) [cnf transformation 146]
241. room(alice) [cnf transformation 146]
245. predt(mary) [cnf transformation 68]
249. ~predt(X1) | X0 = X1 | ~predt(X0) | ~room(X1) | ~room(X0) [cnf transformation 157]
255. predt(alice) [cnf transformation 151]
298. mary = X0 | ~predt(X0) | ~room(mary) | ~room(X0) [resolution 249,245]
301. ~predt(X0) | mary = X0 | ~room(X0) [subsumption resolution 298,238]
306. mary = alice | ~room(alice) [resolution 301,255]
311. ~room(alice) [subsumption resolution 306,214]
312. $false [subsumption resolution 311,241]
% SZS output end Proof for 6301643603996777089463676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
There is a room. “Not everyone in the room is not a culinary enthusiast who experiments with international cuisines or does not enjoy kayaking” if “everyone in the room does not enjoy kayaking or does practice yoga”. Not everyone in the room is not a culinary enthusiast who experiments with international cuisines or does not enjoy kayaking. Everyone anywhere plays as a goalkeeper for a local amateur soccer team, is a culinary enthusiast who experiments with international cuisines and is not a certified yoga instructor teaching classes weekly if they competes in national level swimming championships. Everyone in the room who plays as a goalkeeper for a local amateur soccer team, is a culinary enthusiast who experiments with international cuisines and is not a certified yoga instructor teaching classes weekly is a certified yoga instructor teaching classes weekly. Someone in the room owns a 3D printer, is a culinary enthusiast who experiments with international cuisines and can play the harmonica. Not everyone in the room is not a culinary enthusiast who experiments with international cuisines if they does not have a piercing. Everyone in the room who can play the harmonica or is not a certified yoga instructor teaching classes weekly or both owns a 3D printer and is an active member of a local robotics club. Everyone in the room cannot play the harmonica or owns a 3D printer and is an active member of a local robotics club. Everyone outside the room neither does practice yoga nor enjoys stargazing if they is an active member of a local robotics club. Everyone in the room who neither does practice yoga nor enjoys stargazing is a drone photographer and enjoys kayaking. Everyone in the room does not compete in national level swimming championships if they is a drone photographer and enjoys kayaking. Everyone in the room is passionate about collecting and restoring classic cars and plays as a goalkeeper for a local amateur soccer team. Everyone in the room who has a piercing is an active member of a local robotics club. Dora dreamt that “someone outside the room is not a certified yoga instructor teaching classes weekly”. At least one person in the room has a piercing, is passionate about collecting and restoring classic cars and is a certified yoga instructor teaching classes weekly. Everyone in the room does practice yoga if they does not enjoy stargazing and vice versa. Everyone in the room who enjoys salsa dancing or cannot play the harmonica or both enjoys stargazing. Everyone in the room who enjoys stargazing has a piercing. | Everyone in the room is passionate about collecting and restoring classic cars. | entailment | (there_is_a_room)&
((![X]:(room(X)=>(((does_practice_yoga(X))|(does_not_enjoy_kayaking(X))))))=>(~![X]:(room(X)=>(((does_not_enjoy_kayaking(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))&
(~![X]:(room(X)=>(((does_not_enjoy_kayaking(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(![X]:(anywhere(X)=>(((competes_in_national_level_swimming_championships(X))=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))&
(![X]:(room(X)=>(((((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))&
(?[X]:(room(X)&(((owns_a_3D_printer(X))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(can_play_the_harmonica(X))))))&
(~![X]:(room(X)=>(((does_not_have_a_piercing(X))=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(![X]:(room(X)=>(((((can_play_the_harmonica(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))=>(((owns_a_3D_printer(X))&(is_an_active_member_of_a_local_robotics_club(X))))))))&
(![X]:(room(X)=>(((((owns_a_3D_printer(X))&(is_an_active_member_of_a_local_robotics_club(X))))|(cannot_play_the_harmonica(X))))))&
(![X]:(~room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(~((does_practice_yoga(X))|(enjoys_stargazing(X))))))))&
(![X]:(room(X)=>(((~((does_practice_yoga(X))|(enjoys_stargazing(X))))=>(((is_a_drone_photographer(X))&(enjoys_kayaking(X))))))))&
(![X]:(room(X)=>(((((is_a_drone_photographer(X))&(enjoys_kayaking(X))))=>(does_not_compete_in_national_level_swimming_championships(X))))))&
(![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(![X]:(room(X)=>(((has_a_piercing(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))&
((dora_dream=>(?[X]:(~room(X)&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))&
(((?[X]:(room(X)&((has_a_piercing(X))&(is_passionate_about_collecting_and_restoring_classic_cars(X))&(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))&
(![X]:(room(X)=>(((does_practice_yoga(X))<=>(does_not_enjoy_stargazing(X))))))&
(![X]:(room(X)=>(((((enjoys_salsa_dancing(X))|(cannot_play_the_harmonica(X))))=>(enjoys_stargazing(X))))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))=>(has_a_piercing(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(is_passionate_about_collecting_and_restoring_classic_cars(X))) | [
"p0",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 632645232893982196918716
% SZS output start Proof for 632645232893982196918716
44. there_is_a_room [input p0]
56. ! [X0] : (room(X0) => (preda(X0) & predk(X0))) [input p12]
63. ~(! [X0] : (room(X0) => predk(X0)) & there_is_a_room) [input hypothesis]
83. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 56]
165. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 83]
173. ? [X0] : (~predk(X0) & room(X0)) | ~there_is_a_room [ennf transformation 63]
188. ? [X0] : (~predk(X0) & room(X0)) => (~predk(sK6) & room(sK6)) [choice axiom]
189. (~predk(sK6) & room(sK6)) | ~there_is_a_room [skolemisation 173,188]
270. there_is_a_room [cnf transformation 44]
282. ~room(X0) | predk(X0) [cnf transformation 165]
291. room(sK6) | ~there_is_a_room [cnf transformation 189]
292. ~predk(sK6) | ~there_is_a_room [cnf transformation 189]
307. ~predk(sK6) [subsumption resolution 292,270]
308. room(sK6) [subsumption resolution 291,270]
314. predk(sK6) [resolution 282,308]
315. $false [subsumption resolution 314,307]
% SZS output end Proof for 632645232893982196918716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.528212 |
Larry is the only person in the room.
'Larry is not a quiet tall old person' only if 'Larry is quieter than Bennie'.
If 'Larry is old' then 'Larry is a old person'.
If 'it is not the case that 'Larry is quieter than Bennie'' then 'Larry neither is not not old nor is old'.
If 'Larry is richer than Robert' then 'everyone in the room who is richer than Elise neither is richer than Bennie nor is quieter than Bennie'.
Larry is a old person.
Larry is richer than Elise. | Larry is richer than Robert. | contradiction | room(larry)&(![X]:(room(X)=>(X='larry')))&
((~(quiet(larry)&tall(larry)&old(larry)&person(larry)))=>(quieter(bennie,larry)))&
((old(larry))=>(old(larry)&person(larry)))&
((quieter(brian,larry))=>(richer(bennie,larry)))&
((~(quieter(bennie,larry)))=>(~((~~old(larry))|(old(larry)))))&
((richer(larry,elise))=>(~~old(larry)))&
((old(larry)&person(larry))=>(older(elise,larry)))&
((~quiet(larry))=>(quieter(elise,larry)))&
((richer(robert,larry))=>(![X]:(room(X)=>(((richer(elise,X))=>(~((richer(bennie,X))|(quieter(bennie,X)))))))))&
((~~~quiet(larry))=>((?[X,Y]:(room(X)&room(Y)&(~((quieter(elise,X))|(richer(robert,X)))&~((quieter(elise,Y))|(richer(robert,Y))))&(X!=Y)))))&
((older(elise,larry))<~>(~~tall(larry)))&
(older(bennie,larry))&
(older(brian,larry))&
(richer(brian,larry))&
(old(larry)&person(larry))&
(older(robert,larry))&
(older(elise,larry))&
(richer(elise,larry))&
(quieter(brian,larry))&
(richer(bennie,larry)) | room(larry)&(![X]:(room(X)=>(X='larry')))&
richer(robert,larry) | [
"p0",
"p4",
"p8",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5892930487794545404608327
% SZS output start Proof for 5892930487794545404608327
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
48. ~quieter(alice,mary) => ~(old(mary) | old(mary)) [input p4]
52. richer(fred,mary) => ! [X0] : (room(X0) => (richer(paul,X0) => ~(quieter(alice,X0) | richer(alice,X0)))) [input p8]
58. person(mary) & old(mary) [input p14]
61. richer(paul,mary) [input p17]
64. richer(fred,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
137. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
141. (~old(mary) & ~old(mary)) | quieter(alice,mary) [ennf transformation 48]
146. ! [X0] : (((~quieter(alice,X0) & ~richer(alice,X0)) | ~richer(paul,X0)) | ~room(X0)) | ~richer(fred,mary) [ennf transformation 52]
147. ! [X0] : ((~quieter(alice,X0) & ~richer(alice,X0)) | ~richer(paul,X0) | ~room(X0)) | ~richer(fred,mary) [flattening 146]
150. richer(fred,mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 64]
235. room(mary) [cnf transformation 137]
244. ~old(mary) | quieter(alice,mary) [cnf transformation 141]
250. ~quieter(alice,X0) | ~richer(paul,X0) | ~room(X0) | ~richer(fred,mary) [cnf transformation 147]
263. old(mary) [cnf transformation 58]
267. richer(paul,mary) [cnf transformation 61]
272. richer(fred,mary) [cnf transformation 150]
278. 2 <=> quieter(alice,mary) [avatar definition]
280. quieter(alice,mary) <- (2) [avatar component clause 278]
283. 3 <=> old(mary) [avatar definition]
308. 2 | ~3 [avatar split clause 244,283,278]
325. 11 <=> richer(fred,mary) [avatar definition]
329. 12 <=> ! [X0] : (~quieter(alice,X0) | ~room(X0) | ~richer(paul,X0)) [avatar definition]
330. ~quieter(alice,X0) | ~room(X0) | ~richer(paul,X0) <- (12) [avatar component clause 329]
331. ~11 | 12 [avatar split clause 250,329,325]
374. 3 [avatar split clause 263,283]
378. 11 [avatar split clause 272,325]
400. ~room(mary) | ~richer(paul,mary) <- (2, 12) [resolution 330,280]
401. ~richer(paul,mary) <- (2, 12) [subsumption resolution 400,235]
402. $false <- (2, 12) [subsumption resolution 401,267]
403. ~2 | ~12 [avatar contradiction clause 402]
404. $false [avatar sat refutation 308,331,374,378,403]
% SZS output end Proof for 5892930487794545404608327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.67163 |
Theodore is the only person in the room. Everyone in the room does not like Maurice, is liked by William and is not liked by William if they does not like William and is not liked by Gary. Theodore does not like Lonny or does not like Maurice or both. Everyone outside the room does not like Lonny, does not like Gary and is not liked by William if they does not like Lonny. Theodore is liked by William, is not liked by Maurice and does not like Maurice. Someone in the room is liked by William. If someone is not liked by William then he/she does not like William. Theodore does not like Gary, is not liked by Maurice and is not liked by Lonny. Everyone in the room is not liked by Maurice if they is not liked by Gary. | Theodore likes Maurice. | contradiction | room(theodore)&(![X]:(room(X)=>(X='theodore')))&
(![X]:(room(X)=>(((((~like(william,X))&(~like(X,gary))))=>(((~like(maurice,X))&(like(X,william))&(~like(X,william))))))))&
(((~like(lonny,theodore))|(~like(maurice,theodore))))&
(![X]:(~room(X)=>(((~like(lonny,X))=>(((~like(lonny,X))&(~like(gary,X))&(~like(X,william))))))))&
(((like(theodore,william))&(~like(theodore,maurice))&(~like(maurice,theodore))))&
(?[X]:(room(X)&(like(X,william))))&
((![X]:((~like(X,william))=>(~like(william,X)))))&
(((~like(gary,theodore))&(~like(theodore,maurice))&(~like(theodore,lonny))))&
(![X]:(room(X)=>(((~like(X,gary))=>(~like(X,maurice)))))) | room(theodore)&(![X]:(room(X)=>(X='theodore')))&
like(maurice,theodore) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6365280637105396276715835
% SZS output start Proof for 6365280637105396276715835
48. ~like(paul,mary) & ~like(mary,paul) & like(mary,john) [input p4]
53. like(paul,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
134. like(paul,mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 53]
229. ~like(paul,mary) [cnf transformation 48]
239. like(paul,mary) [cnf transformation 134]
246. 2 <=> like(paul,mary) [avatar definition]
250. ~2 [avatar split clause 229,246]
251. 2 [avatar split clause 239,246]
252. $false [avatar sat refutation 250,251]
% SZS output end Proof for 6365280637105396276715835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.318949 |
Daniel is the only person in the room.
"Daniel develops open-source software projects in their free time" if "Daniel practices and performs acrobatic dance routines" and vice versa.
If "everyone in the room does not have a pet dog or has a pet dog" then "everyone in the room who has a pet dog practices and performs acrobatic dance routines".
If "Daniel develops open-source software projects in their free time" then "it is not the case that "someone outside the room has a pet dog, practices and performs acrobatic dance routines and regularly contributes to tech forums and online communities"" otherwise "everyone in the room who has a pet dog enjoys stargazing".
"Daniel enjoys stargazing" only if "it is true that "Daniel who practices and performs acrobatic dance routines or has a pet dog or both regularly contributes to tech forums and online communities"".
Daniel practices and performs acrobatic dance routines.
Everyone in the room who has a pet dog develops open-source software projects in their free time.
Daniel develops open-source software projects in their free time.
Daniel has a pet dog.
Daniel regularly contributes to tech forums and online communities.
More than one person anywhere practices and performs acrobatic dance routines.
Everyone in the room who practices and performs acrobatic dance routines develops open-source software projects in their free time.
Everyone in the room who practices and performs acrobatic dance routines regularly contributes to tech forums and online communities. | Daniel enjoys stargazing. | neutral | room(daniel)&(![X]:(room(X)=>(X='daniel')))&
((practices_and_performs_acrobatic_dance_routines(daniel))<=>(develops_open-source_software_projects_in_their_free_time(daniel)))&
((![X]:(room(X)=>(((has_a_pet_dog(X))|(does_not_have_a_pet_dog(X))))))=>(![X]:(room(X)=>(((has_a_pet_dog(X))=>(practices_and_performs_acrobatic_dance_routines(X)))))))&
(((develops_open-source_software_projects_in_their_free_time(daniel))=>(~(?[X]:(~room(X)&(((has_a_pet_dog(X))&(practices_and_performs_acrobatic_dance_routines(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))))))&((~(develops_open-source_software_projects_in_their_free_time(daniel)))=>(![X]:(room(X)=>(((has_a_pet_dog(X))=>(enjoys_stargazing(X))))))))&
((enjoys_stargazing(daniel))=>((((practices_and_performs_acrobatic_dance_routines(daniel))|(has_a_pet_dog(daniel))))&(regularly_contributes_to_tech_forums_and_online_communities(daniel))))&
(practices_and_performs_acrobatic_dance_routines(daniel))&
(![X]:(room(X)=>(((has_a_pet_dog(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(develops_open-source_software_projects_in_their_free_time(daniel))&
(has_a_pet_dog(daniel))&
(regularly_contributes_to_tech_forums_and_online_communities(daniel))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(practices_and_performs_acrobatic_dance_routines(X)&practices_and_performs_acrobatic_dance_routines(Y))&(X!=Y))))&
(![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))) | room(daniel)&(![X]:(room(X)=>(X='daniel')))&
enjoys_stargazing(daniel) | [] | null | 0.112953 |
Laura is the only person in the room.
Either “Laura enjoys logic puzzles” or “Laura enjoys wildlife photography” but not both.
If “Laura is an avid collector of autographed memorabilia from famous musicians” then “someone in the room enjoys wildlife photography”.
Laura is an avid collector of autographed memorabilia from famous musicians. | It is not the case that “Laura enjoys logic puzzles”. | entailment | room(laura)&(![X]:(room(X)=>(X='laura')))&
((?[X]:(room(X)&(enjoys_wildlife_photography(X))))=>(![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))<=>(does_not_collect_antique_clocks(X)))))))&
((~(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(laura)))=>(~(~(~(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(laura))))))&
((enjoys_logic_puzzles(laura))<~>(enjoys_wildlife_photography(laura)))&
((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(laura))=>(?[X]:(room(X)&(enjoys_wildlife_photography(X)))))&
((collects_antique_clocks(laura))=>((![X]:((enjoys_logic_puzzles(X))=>(((collects_antique_clocks(X))|(does_not_enjoy_wildlife_photography(X))))))))&
(![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))<=>(does_not_collect_antique_clocks(X))))))&
((![X]:((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(enjoys_logic_puzzles(X)))))&
(~(?[X]:(room(X)&(collects_antique_clocks(X)))))&
(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(laura))&
((![X]:((enjoys_logic_puzzles(X))=>(((collects_antique_clocks(X))|(does_not_enjoy_wildlife_photography(X))))))) | room(laura)&(![X]:(room(X)=>(X='laura')))&
~(enjoys_logic_puzzles(laura)) | [
"p0",
"p3",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8160438523458455993327688
% SZS output start Proof for 8160438523458455993327688
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
47. preda(mary) <~> prede(mary) [input p3]
48. predd(mary) => ? [X0] : (prede(X0) & room(X0)) [input p4]
53. predd(mary) [input p9]
55. ~(~preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
130. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
133. ? [X0] : (prede(X0) & room(X0)) | ~predd(mary) [ennf transformation 48]
140. preda(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 55]
144. (~prede(mary) | ~preda(mary)) & (prede(mary) | preda(mary)) [nnf transformation 47]
145. ? [X0] : (prede(X0) & room(X0)) => (prede(sK0) & room(sK0)) [choice axiom]
146. (prede(sK0) & room(sK0)) | ~predd(mary) [skolemisation 133,145]
148. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom]
149. preda(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 140,148]
230. room(mary) [cnf transformation 130]
231. ~room(X0) | mary = X0 [cnf transformation 130]
236. ~prede(mary) | ~preda(mary) [cnf transformation 144]
237. room(sK0) | ~predd(mary) [cnf transformation 146]
238. prede(sK0) | ~predd(mary) [cnf transformation 146]
243. predd(mary) [cnf transformation 53]
245. preda(mary) | room(sK1) | ~room(mary) [cnf transformation 149]
246. preda(mary) | mary != sK1 | ~room(mary) [cnf transformation 149]
259. 4 <=> preda(mary) [avatar definition]
263. 5 <=> prede(mary) [avatar definition]
266. ~4 | ~5 [avatar split clause 236,263,259]
269. 6 <=> predd(mary) [avatar definition]
273. 7 <=> prede(sK0) [avatar definition]
275. prede(sK0) <- (7) [avatar component clause 273]
276. ~6 | 7 [avatar split clause 238,273,269]
278. 8 <=> room(sK0) [avatar definition]
280. room(sK0) <- (8) [avatar component clause 278]
281. ~6 | 8 [avatar split clause 237,278,269]
292. 6 [avatar split clause 243,269]
294. preda(mary) | mary != sK1 [subsumption resolution 246,230]
296. 11 <=> mary = sK1 [avatar definition]
298. mary != sK1 <- (~11) [avatar component clause 296]
299. ~11 | 4 [avatar split clause 294,259,296]
300. preda(mary) | room(sK1) [subsumption resolution 245,230]
302. 12 <=> room(sK1) [avatar definition]
304. room(sK1) <- (12) [avatar component clause 302]
305. 12 | 4 [avatar split clause 300,259,302]
310. mary = sK0 <- (8) [resolution 231,280]
312. prede(mary) <- (7, 8) [backward demodulation 275,310]
316. 5 | ~7 | ~8 [avatar split clause 312,278,273,263]
317. mary = sK1 <- (12) [resolution 304,231]
319. $false <- (~11, 12) [subsumption resolution 317,298]
320. 11 | ~12 [avatar contradiction clause 319]
321. $false [avatar sat refutation 266,276,281,292,299,305,316,320]
% SZS output end Proof for 8160438523458455993327688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.024811 |
Sandra, Edith, Vince, Robert, Miriam are the only persons in the room. “Everyone in the room does not have a pet dog” if “everyone in the room is a coffee connoisseur or does not collect comic books” and vice versa. Everyone in the room enjoys snowboarding or enjoys macrame or both if they is a coffee connoisseur. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings if they enjoys snowboarding or enjoys macrame or both. If someone enjoys spelunking then he/she practices pilates and vice versa. Everyone anywhere is a skilled home brewer experimenting with craft beer recipes if they is a client of Meta. Robert makes homemade pastries. Vince makes homemade pastries. Sandra collects comic books. Sandra who collects comic books has a pet dog. Not everyone in the room who maintains a personal blog focused on cybersecurity tips can play the harmonica, practices pilates and participates in citizen science projects related to wildlife monitoring. Vince is a client of Meta. Everyone in the room who is an enthusiastic bird watcher who travels for rare sightings neither practices pilates nor is a coffee connoisseur. | Sandra is a coffee connoisseur. | contradiction | room(sandra)&room(edith)&room(vince)&room(robert)&room(miriam)&(![X]:(room(X)=>(X='sandra'|X='edith'|X='vince'|X='robert'|X='miriam')))&
((![X]:(room(X)=>(((does_not_collect_comic_books(X))|(is_a_coffee_connoisseur(X))))))<=>(![X]:(room(X)=>(does_not_have_a_pet_dog(X)))))&
(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(((enjoys_snowboarding(X))|(enjoys_macrame(X))))))))&
(![X]:(room(X)=>(((((enjoys_snowboarding(X))|(enjoys_macrame(X))))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
((![X]:((enjoys_spelunking(X))<=>(practices_pilates(X)))))&
(![X]:(anywhere(X)=>(((is_a_client_of_Meta(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))&
(makes_homemade_pastries(robert))&
(makes_homemade_pastries(vince))&
(collects_comic_books(sandra))&
((collects_comic_books(sandra))&(has_a_pet_dog(sandra)))&
(~![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(((can_play_the_harmonica(X))&(practices_pilates(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))))&
(is_a_client_of_Meta(vince))&
((![X]:((~((enjoys_rooftop_gardening(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))=>(((collects_foreign_coins(X))|(enjoys_rooftop_gardening(X))|(enjoys_snowboarding(X)))))))&
(~(((can_play_the_harmonica(vince))&(does_not_practice_pilates(vince)))))&
(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(vince))&
(![X]:(room(X)=>(((((enjoys_rooftop_gardening(X))&(hosts_regular_workshops_on_creative_writing(X))))=>(enjoys_macrame(X))))))&
((![X]:((can_play_the_harmonica(X))<=>(collects_classic_novels(X)))))&
(has_a_pet_dog(vince))&
(![X]:(room(X)=>(((((creates_YouTube_content(X))<~>(enjoys_rooftop_gardening(X))))=>(((does_not_enjoy_macrame(X))&(volunteers_for_local_environmental_conservation_projects(X))&(is_a_client_of_Meta(X))))))))&
((volunteers_for_local_environmental_conservation_projects(vince))&(hosts_regular_workshops_on_creative_writing(vince)))&
(![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(~((practices_pilates(X))|(is_a_coffee_connoisseur(X)))))))) | room(sandra)&room(edith)&room(vince)&room(robert)&room(miriam)&(![X]:(room(X)=>(X='sandra'|X='edith'|X='vince'|X='robert'|X='miriam')))&
is_a_coffee_connoisseur(sandra) | [
"p0",
"p2",
"p3",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3859445307639190980852778
% SZS output start Proof for 3859445307639190980852778
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
46. ! [X0] : (room(X0) => (predg(X0) => (predk(X0) | prede(X0)))) [input p2]
47. ! [X0] : (room(X0) => ((predk(X0) | prede(X0)) => predl(X0))) [input p3]
64. ! [X0] : (room(X0) => (predl(X0) => ~(predg(X0) | predt(X0)))) [input p20]
65. predg(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
71. ! [X0] : (room(X0) => (predl(X0) => ~predg(X0))) [pure predicate removal 64]
153. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
154. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 153]
157. ! [X0] : (((predk(X0) | prede(X0)) | ~predg(X0)) | ~room(X0)) [ennf transformation 46]
158. ! [X0] : (predk(X0) | prede(X0) | ~predg(X0) | ~room(X0)) [flattening 157]
159. ! [X0] : ((predl(X0) | (~predk(X0) & ~prede(X0))) | ~room(X0)) [ennf transformation 47]
160. ! [X0] : (predl(X0) | (~predk(X0) & ~prede(X0)) | ~room(X0)) [flattening 159]
166. ! [X0] : ((~predg(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 71]
167. ! [X0] : (~predg(X0) | ~predl(X0) | ~room(X0)) [flattening 166]
168. predg(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 65]
169. predg(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 168]
259. room(mary) [cnf transformation 154]
270. ~predg(X0) | prede(X0) | predk(X0) | ~room(X0) [cnf transformation 158]
271. ~prede(X0) | predl(X0) | ~room(X0) [cnf transformation 160]
272. ~predk(X0) | predl(X0) | ~room(X0) [cnf transformation 160]
283. ~predl(X0) | ~predg(X0) | ~room(X0) [cnf transformation 167]
290. predg(mary) [cnf transformation 169]
333. prede(mary) | predk(mary) | ~room(mary) [resolution 270,290]
334. prede(mary) | predk(mary) [subsumption resolution 333,259]
336. 8 <=> predk(mary) [avatar definition]
338. predk(mary) <- (8) [avatar component clause 336]
340. 9 <=> prede(mary) [avatar definition]
342. prede(mary) <- (9) [avatar component clause 340]
343. 8 | 9 [avatar split clause 334,340,336]
355. predl(mary) | ~room(mary) <- (9) [resolution 342,271]
356. predl(mary) <- (9) [subsumption resolution 355,259]
357. ~predg(mary) | ~room(mary) <- (9) [resolution 356,283]
358. ~room(mary) <- (9) [subsumption resolution 357,290]
359. $false <- (9) [subsumption resolution 358,259]
360. ~9 [avatar contradiction clause 359]
361. predl(mary) | ~room(mary) <- (8) [resolution 338,272]
362. predl(mary) <- (8) [subsumption resolution 361,259]
363. ~predg(mary) | ~room(mary) <- (8) [resolution 362,283]
364. ~room(mary) <- (8) [subsumption resolution 363,290]
365. $false <- (8) [subsumption resolution 364,259]
366. ~8 [avatar contradiction clause 365]
367. $false [avatar sat refutation 343,360,366]
% SZS output end Proof for 3859445307639190980852778
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.237148 |
There is a room. Everyone anywhere creates YouTube content or is a tea enthusiast or both only if they practices archery. Not everyone in the room who practices archery is not a dedicated volunteer for local community service projects. Everyone in the room is not a dedicated volunteer for local community service projects if and only if they neither owns an extensive assortment of vintage comic book memorabilia nor practices tai chi. Everyone in the room does not make intricate hand-cut paper art for exhibitions. Everyone in the room who makes intricate hand-cut paper art for exhibitions does enjoy mountain biking. Everyone in the room who does enjoy mountain biking has completed a triathlon. If someone has completed a triathlon, collects antique clocks or does not have a pet dog then he/she has completed a triathlon and vice versa. Everyone in the room either has a pet dog or is an avid collector of autographed memorabilia from famous musicians but not both if they practices zumba. Everyone in the room makes intricate hand-cut paper art for exhibitions if they either has a pet dog or is an avid collector of autographed memorabilia from famous musicians but not both. Everyone in the room who has a pet dog, does not practice tai chi or is a tea enthusiast collects antique clocks. Everyone in the room has a pet dog if they collects antique clocks. Everyone in the room who has a pet dog has completed a triathlon and has a pet dog. More than one person in the room does enjoy mountain biking. Everyone in the room who practices tai chi and has completed a triathlon has a pet dog. Everyone in the room is a cybersecurity expert or owns a smart tv or both if they has a pet dog. No one in the room who is a cybersecurity expert or owns a smart tv or both practices urban gardening. Everyone in the room owns a smart tv. Everyone in the room has a pet dog only if they practices archery. | Everyone in the room collects antique clocks. | entailment | (there_is_a_room)&
(![X]:(anywhere(X)=>(((practices_archery(X))<=(((creates_YouTube_content(X))|(is_a_tea_enthusiast(X))))))))&
(~![X]:(room(X)=>(((practices_archery(X))=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))&
(![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))<=>(~((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(practices_tai_chi(X))))))))&
(![X]:(room(X)=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))&
(![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(does_enjoy_mountain_biking(X))))))&
(![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(has_completed_a_triathlon(X))))))&
((![X]:((((has_completed_a_triathlon(X))|(collects_antique_clocks(X))|(does_not_have_a_pet_dog(X))))<=>(has_completed_a_triathlon(X)))))&
(![X]:(room(X)=>(((practices_zumba(X))=>(((has_a_pet_dog(X))<~>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))&
(![X]:(room(X)=>(((((has_a_pet_dog(X))<~>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))&
(![X]:(room(X)=>(((((has_a_pet_dog(X))|(does_not_practice_tai_chi(X))|(is_a_tea_enthusiast(X))))=>(collects_antique_clocks(X))))))&
(![X]:(room(X)=>(((collects_antique_clocks(X))=>(has_a_pet_dog(X))))))&
(![X]:(room(X)=>(((has_a_pet_dog(X))=>(((has_completed_a_triathlon(X))&(has_a_pet_dog(X))))))))&
((?[X,Y]:(room(X)&room(Y)&(does_enjoy_mountain_biking(X)&does_enjoy_mountain_biking(Y))&(X!=Y))))&
(![X]:(room(X)=>(((((practices_tai_chi(X))&(has_completed_a_triathlon(X))))=>(has_a_pet_dog(X))))))&
(![X]:(room(X)=>(((has_a_pet_dog(X))=>(((is_a_cybersecurity_expert(X))|(owns_a_smart_tv(X))))))))&
(~?[X]:(room(X)=>(((((is_a_cybersecurity_expert(X))|(owns_a_smart_tv(X))))=>(practices_urban_gardening(X))))))&
(![X]:(room(X)=>(owns_a_smart_tv(X))))&
(![X]:(room(X)=>(((practices_archery(X))<=(has_a_pet_dog(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(collects_antique_clocks(X))) | [
"p0",
"p7",
"p10",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8154584123978312495312815
% SZS output start Proof for 8154584123978312495312815
44. there_is_a_room [input p0]
51. ! [X0] : ((~predi(X0) | predc(X0) | predb(X0)) <=> predb(X0)) [input p7]
54. ! [X0] : (room(X0) => ((predk(X0) | ~predl(X0) | predi(X0)) => predc(X0))) [input p10]
56. ! [X0] : (room(X0) => (predi(X0) => (predi(X0) & predb(X0)))) [input p12]
58. ! [X0] : (room(X0) => ((predb(X0) & predl(X0)) => predi(X0))) [input p14]
60. ~? [X0] : (room(X0) => ((predp(X0) | predj(X0)) => predh(X0))) [input p16]
63. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis]
64. ~? [X0] : (room(X0) => ~(predp(X0) | predj(X0))) [pure predicate removal 60]
67. ~? [X0] : ~room(X0) [pure predicate removal 64]
69. ! [X0] : (room(X0) => ((~predl(X0) | predi(X0)) => predc(X0))) [pure predicate removal 54]
155. ! [X0] : ((predc(X0) | (predl(X0) & ~predi(X0))) | ~room(X0)) [ennf transformation 69]
156. ! [X0] : (predc(X0) | (predl(X0) & ~predi(X0)) | ~room(X0)) [flattening 155]
159. ! [X0] : (((predi(X0) & predb(X0)) | ~predi(X0)) | ~room(X0)) [ennf transformation 56]
160. ! [X0] : ((predi(X0) & predb(X0)) | ~predi(X0) | ~room(X0)) [flattening 159]
161. ! [X0] : ((predi(X0) | (~predb(X0) | ~predl(X0))) | ~room(X0)) [ennf transformation 58]
162. ! [X0] : (predi(X0) | ~predb(X0) | ~predl(X0) | ~room(X0)) [flattening 161]
163. ! [X0] : room(X0) [ennf transformation 67]
164. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 63]
170. ! [X0] : (((~predi(X0) | predc(X0) | predb(X0)) | ~predb(X0)) & (predb(X0) | (predi(X0) & ~predc(X0) & ~predb(X0)))) [nnf transformation 51]
171. ! [X0] : ((~predi(X0) | predc(X0) | predb(X0) | ~predb(X0)) & (predb(X0) | (predi(X0) & ~predc(X0) & ~predb(X0)))) [flattening 170]
175. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK3) & room(sK3)) [choice axiom]
176. (~predc(sK3) & room(sK3)) | ~there_is_a_room [skolemisation 164,175]
257. there_is_a_room [cnf transformation 44]
268. predi(X0) | predb(X0) [cnf transformation 171]
272. ~predi(X0) | predc(X0) | ~room(X0) [cnf transformation 156]
273. ~room(X0) | predl(X0) | predc(X0) [cnf transformation 156]
275. predb(X0) | ~predi(X0) | ~room(X0) [cnf transformation 160]
282. predi(X0) | ~predb(X0) | ~predl(X0) | ~room(X0) [cnf transformation 162]
283. room(X0) [cnf transformation 163]
285. ~predc(sK3) | ~there_is_a_room [cnf transformation 176]
288. ~room(X0) | predb(X0) [subsumption resolution 275,268]
289. ~predl(X0) | predi(X0) | ~room(X0) [subsumption resolution 282,288]
290. ~predc(sK3) [subsumption resolution 285,257]
298. predc(X0) | predl(X0) [resolution 273,283]
302. predl(sK3) [resolution 298,290]
312. predi(sK3) | ~room(sK3) [resolution 289,302]
313. predi(sK3) [subsumption resolution 312,283]
315. predc(sK3) | ~room(sK3) [resolution 313,272]
317. ~room(sK3) [subsumption resolution 315,290]
318. $false [subsumption resolution 317,283]
% SZS output end Proof for 8154584123978312495312815
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.32437 |
Brandon is the only person in the room.
"Brandon enjoys skydiving" if "everyone in the room does not collect rare sneakers or can play the flute" and vice versa. | Brandon collects classic novels. | neutral | room(brandon)&(![X]:(room(X)=>(X='brandon')))&
((![X]:(room(X)=>(((can_play_the_flute(X))|(does_not_collect_rare_sneakers(X))))))<=>(enjoys_skydiving(brandon)))&
((((streams_on_Twitch(brandon))&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(brandon))&(practices_pilates(brandon))))=>((((practices_and_performs_acrobatic_dance_routines(brandon))<~>(enjoys_skydiving(brandon))))&(collects_vintage_stamps(brandon))))&
((collects_classic_novels(brandon))=>((![X]:((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(owns_a_microscope(X))))))&
((![X]:(room(X)=>(((can_play_the_harmonica(X))|(cannot_play_the_harmonica(X))))))<=>(is_not_a_tea_enthusiast(brandon)))&
((uses_contact_lenses(brandon))=>(practices_pilates(brandon)))&
(practices_pilates(brandon))&
(practices_and_performs_acrobatic_dance_routines(brandon))&
(travels_domestically_frequently(brandon))&
(((composes_and_performs_experimental_electronic_music(brandon))|(streams_on_Twitch(brandon))))&
(![X]:(room(X)=>(((can_play_the_flute(X))=>(is_a_tea_enthusiast(X))))))&
((brandon_dream=>(is_a_tea_enthusiast(brandon))))&
(?[X]:(room(X)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))&
(![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(collects_luxury_watches(X))))))&
(~(?[X]:(room(X)&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))&
(collects_vintage_stamps(brandon))&
(![X]:(room(X)=>(((travels_domestically_frequently(X))<=>(uses_contact_lenses(X))))))&
(enjoys_wildlife_photography(brandon))&
(watches_fantasy_movies(brandon)) | room(brandon)&(![X]:(room(X)=>(X='brandon')))&
collects_classic_novels(brandon) | [] | null | 0.036491 |