premise
stringlengths 12
3.12k
| hypothesis
stringlengths 10
236
| label
stringclasses 3
values | premise_tptp
stringlengths 51
8k
| hypothesis_tptp
stringlengths 41
352
| proof_inputs
sequencelengths 0
20
| proof
stringlengths 767
76.8k
⌀ | rule_concentration
float64 0
0.72
|
|---|---|---|---|---|---|---|---|
Patricia, Jose, William are the only persons in the room.
William is quieter than Paul.
Everyone outside the room is quieter than Paul.
Jose is richer than Paul. | Paul is richer than Jose. | contradiction | room(patricia)&room(jose)&room(william)&(![X]:(room(X)=>(X='patricia'|X='jose'|X='william')))&
(quieter(paul,william))&
(![X]:(~room(X)=>(quieter(paul,X))))&
((![X]:((((~(quiet(X)&person(X)))<~>(richer(paul,X))))=>(old(X)))))&
(![X]:(room(X)=>(quiet(X)&old(X)&person(X))))&
(![X]:(room(X)=>(((old(X)&person(X))=>(quiet(X)&old(X)&person(X))))))&
(![X]:(~room(X)=>(((quiet(X)&old(X)&person(X))=>(quieter(paul,X))))))&
(quieter(paul,patricia)&quieter(paul,william))&
(![X]:(room(X)=>(((quiet(X))=>(old(X)&person(X))))))&
(![X]:(room(X)=>(((~(quiet(X)&person(X)))=>(quiet(X))))))&
(![X]:(anywhere(X)=>(((~quiet(X)&~old(X))=>(older(paul,X))))))&
(richer(paul,jose)) | room(patricia)&room(jose)&room(william)&(![X]:(room(X)=>(X='patricia'|X='jose'|X='william')))&
richer(jose,paul) | [
"b7",
"b42",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4516572107371806969736533
% SZS output start Proof for 4516572107371806969736533
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]
55. richer(alice,paul) [input p11]
56. richer(paul,alice) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
64. ! [X0,X1] : ((~richer(X1,X0) | ~richer(X0,X1)) | X0 = X1) [ennf transformation 8]
65. ! [X0,X1] : (~richer(X1,X0) | ~richer(X0,X1) | X0 = X1) [flattening 64]
143. richer(paul,alice) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 56]
144. richer(paul,alice) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 143]
152. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 65]
206. paul != alice [cnf transformation 43]
252. richer(alice,paul) [cnf transformation 55]
257. richer(paul,alice) [cnf transformation 144]
269. ~richer(paul,alice) | paul = alice [resolution 152,252]
273. paul = alice [subsumption resolution 269,257]
274. $false [subsumption resolution 273,206]
% SZS output end Proof for 4516572107371806969736533
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Arnold, Jeffrey, Melissa are the only persons in the room. Arnold neither enjoys stand-up paddleboarding nor is a Linux enthusiast. | Arnold is a Linux enthusiast. | contradiction | room(arnold)&room(jeffrey)&room(melissa)&(![X]:(room(X)=>(X='arnold'|X='jeffrey'|X='melissa')))&
((![X]:(room(X)=>(((does_not_make_homemade_pastries(X))|(cannot_play_the_guitar(X))))))=>(((is_a_Linux_enthusiast(arnold))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(arnold)))))&
((~?[X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(cannot_play_the_guitar(X))))))<=>(((?[X]:(room(X)&((collects_foreign_coins(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))))&
((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(arnold))<~>(((plays_eSports_competitively(arnold))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(arnold)))))&
(~((enjoys_stand-up_paddleboarding(arnold))|(is_a_Linux_enthusiast(arnold))))&
(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(arnold)) | room(arnold)&room(jeffrey)&room(melissa)&(![X]:(room(X)=>(X='arnold'|X='jeffrey'|X='melissa')))&
is_a_Linux_enthusiast(arnold) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6870370580397021700345915
% SZS output start Proof for 6870370580397021700345915
48. ~(predi(mary) | predb(mary)) [input p4]
50. predi(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
52. ~predi(mary) [pure predicate removal 48]
131. ~predi(mary) [ennf transformation 52]
132. predi(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 50]
133. predi(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 132]
244. ~predi(mary) [cnf transformation 131]
250. predi(mary) [cnf transformation 133]
256. 2 <=> predi(mary) [avatar definition]
329. ~2 [avatar split clause 244,256]
331. 2 [avatar split clause 250,256]
332. $false [avatar sat refutation 329,331]
% SZS output end Proof for 6870370580397021700345915
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.031014 |
There is a room.
Either “everyone anywhere does not write and illustrates their own graphic novels or does not practice yoga” or “everyone in the room does not collect antique jewelry or creates bespoke furniture pieces from reclaimed wood” but not both.
“Everyone in the room builds model airplanes if and only if they does not build model airplanes” unless “everyone in the room writes and illustrates their own graphic novels or does not create bespoke furniture pieces from reclaimed wood”.
Everyone in the room writes and illustrates their own graphic novels if and only if they builds model airplanes.
No one outside the room collects antique jewelry or does not practice yoga.
Everyone in the room collects antique jewelry if they creates bespoke furniture pieces from reclaimed wood. | Everyone outside the room writes and illustrates their own graphic novels. | neutral | (there_is_a_room)&
((![X]:(anywhere(X)=>(((does_not_practice_yoga(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))))<~>(![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_collect_antique_jewelry(X)))))))&
(~(![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(writes_and_illustrates_their_own_graphic_novels(X))))))=>(![X]:(room(X)=>(((builds_model_airplanes(X))<=>(does_not_build_model_airplanes(X)))))))&
(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))<=>(builds_model_airplanes(X))))))&
(~?[X]:(~room(X)=>(((does_not_practice_yoga(X))|(collects_antique_jewelry(X))))))&
(![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(collects_antique_jewelry(X))))))&
(![X]:(room(X)=>(((does_practice_yoga(X))=>(collects_antique_jewelry(X))))))&
(![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(writes_and_illustrates_their_own_graphic_novels(X))))))&
(~![X]:(~room(X)=>(((collects_antique_jewelry(X))<=(does_practice_yoga(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(writes_and_illustrates_their_own_graphic_novels(X))) | [] | null | 0 |
There is a room.
Everyone in the room enjoys snowboarding if they hosts regular game nights featuring complex strategy games.
No one in the room who enjoys snowboarding practices urban gardening.
Everyone in the room plays as a goalkeeper for a local amateur soccer team if they practices urban gardening.
Not everyone in the room who collects foreign coins hosts a YouTube channel dedicated to art tutorials.
Everyone outside the room who hosts a YouTube channel dedicated to art tutorials volunteers for local environmental conservation projects.
Everyone in the room does not host a popular podcast about emerging technologies if they volunteers for local environmental conservation projects.
Everyone in the room is a client of Meta if they does not host a popular podcast about emerging technologies.
Everyone in the room who plays the drums plays as a goalkeeper for a local amateur soccer team.
Someone in the room hosts regular game nights featuring complex strategy games.
Not everyone in the room who mentors a youth basketball team on weekends enjoys salsa dancing.
Everyone in the room enjoys salsa dancing if they trains for and competes in international triathlons and vice versa.
Everyone in the room who hosts regular game nights featuring complex strategy games hosts a YouTube channel dedicated to art tutorials.
Everyone in the room who hosts a YouTube channel dedicated to art tutorials trains for and competes in international triathlons.
Everyone outside the room who is an amateur astronomer who builds and uses custom telescopes does not mentor a youth basketball team on weekends.
Everyone in the room who does not mentor a youth basketball team on weekends is a culinary enthusiast who experiments with international cuisines.
Not everyone in the room collects comic books if they is a culinary enthusiast who experiments with international cuisines.
Everyone in the room who collects modern art enjoys salsa dancing.
Everyone anywhere does not have completed a triathlon or hosts regular workshops on creative writing.
Everyone in the room who does not have completed a triathlon has completed a triathlon.
Everyone in the room plays as a goalkeeper for a local amateur soccer team if they trains for and competes in international triathlons. | Everyone in the room does not host a popular podcast about emerging technologies or is a client of Meta. | neutral | (there_is_a_room)&
(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(enjoys_snowboarding(X))))))&
(~?[X]:(room(X)=>(((enjoys_snowboarding(X))=>(practices_urban_gardening(X))))))&
(![X]:(room(X)=>(((practices_urban_gardening(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(~![X]:(room(X)=>(((collects_foreign_coins(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(![X]:(~room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))&
(![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))=>(is_a_client_of_Meta(X))))))&
(![X]:(room(X)=>(((plays_the_drums(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))&
(~![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(enjoys_salsa_dancing(X))))))&
(![X]:(room(X)=>(((enjoys_salsa_dancing(X))<=>(trains_for_and_competes_in_international_triathlons(X))))))&
(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(trains_for_and_competes_in_international_triathlons(X))))))&
(![X]:(~room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))&
(![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(~![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(collects_comic_books(X))))))&
(![X]:(room(X)=>(((collects_modern_art(X))=>(enjoys_salsa_dancing(X))))))&
(![X]:(anywhere(X)=>(((hosts_regular_workshops_on_creative_writing(X))|(does_not_have_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))=>(has_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(![X]:(~room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(practices_urban_gardening(X))))))&
((?[X,Y]:(room(X)&room(Y)&(volunteers_for_local_environmental_conservation_projects(X)&volunteers_for_local_environmental_conservation_projects(Y))&(X!=Y))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(collects_foreign_coins(X))))))&
(![X]:(~room(X)=>(((collects_foreign_coins(X))<=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))&
(![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))&
(![X]:(~room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((is_a_client_of_Meta(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))))) | [] | null | 0.145331 |
Jose is the only person in the room. If everyone outside the room is a happy creative european or does not write a travel blog then Jose is a client of LVMH. If Jose is a strong person then all curious person is funny. If everyone in the room develops open-source software projects in their free time or is not an avid mountain climber who has scaled several peaks then Jose is the quietest in the room otherwise all funny person is brave. Everyone in the room who volunteers for local environmental conservation projects builds model airplanes. Everyone in the room who is a strong european is not quiet. Jose dreamt that all old person is patient. Everyone outside the room does not enjoy coding in Python or is older than Kyle. Michael is quieter than Jose. Everyone in the room is a client of LVMH if they is a calm tall person and vice versa. Jose is a strong european. Jose does not like Kyle. Everyone outside the room is a client of LVMH if and only if they is liked by Michael. Jose is a wine connoisseur. Jose is a curious person. Jose is not hated by Michael. Everyone in the room is wise, is louder than James or mentors a youth basketball team on weekends if they is richer than Kyle. It is not the case that Lisbeth is a sibling of Jose. Not everyone anywhere is not hated by Freddie. All funny person is brave. Jose owns a 3D printer. | Jose is brave. | entailment | room(jose)&(![X]:(room(X)=>(X='jose')))&
((![X]:(~room(X)=>(((does_not_write_a_travel_blog(X))|(happy(X)&creative(X)&european(X))))))=>(is_a_client_of_LVMH(jose)))&
((strong(jose)&person(jose))=>(![X]:(curious(X)=>funny(X))))&
(((![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(develops_open-source_software_projects_in_their_free_time(X))))))=>(![X]:((room(X)&(X!=jose))=>quieter(X,jose))))&((~(![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(develops_open-source_software_projects_in_their_free_time(X)))))))=>(![X]:(funny(X)=>brave(X)))))&
(![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(builds_model_airplanes(X))))))&
(![X]:(room(X)=>(((strong(X)&european(X))=>(~quiet(X))))))&
((jose_dream=>(![X]:(old(X)=>patient(X)))))&
(![X]:(~room(X)=>(((older(kyle,X))|(does_not_enjoy_coding_in_Python(X))))))&
(quieter(jose,michael))&
(![X]:(room(X)=>(((is_a_client_of_LVMH(X))<=>(calm(X)&tall(X)&person(X))))))&
(strong(jose)&european(jose))&
(~like(kyle,jose))&
(![X]:(~room(X)=>(((is_a_client_of_LVMH(X))<=>(like(X,michael))))))&
(is_a_wine_connoisseur(jose))&
(curious(jose)&person(jose))&
(~hate(jose,michael))&
(![X]:(room(X)=>(((richer(kyle,X))=>(((wise(X))|(louder(james,X))|(mentors_a_youth_basketball_team_on_weekends(X))))))))&
(~(sibling(jose,lisbeth)))&
(~![X]:(anywhere(X)=>(~hate(X,freddie))))&
(![X]:(funny(X)=>brave(X)))&
(owns_a_3D_printer(jose)) | room(jose)&(![X]:(room(X)=>(X='jose')))&
brave(jose) | [
"p0",
"p2",
"p10",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3008680031826746286292663
% SZS output start Proof for 3008680031826746286292663
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
46. (person(mary) & strong(mary)) => ! [X0] : (curious(X0) => funny(X0)) [input p2]
54. european(mary) & strong(mary) [input p10]
58. person(mary) & curious(mary) [input p14]
63. ! [X0] : (funny(X0) => brave(X0)) [input p19]
65. ~(brave(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
150. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
152. ! [X0] : (funny(X0) | ~curious(X0)) | (~person(mary) | ~strong(mary)) [ennf transformation 46]
153. ! [X0] : (funny(X0) | ~curious(X0)) | ~person(mary) | ~strong(mary) [flattening 152]
161. ! [X0] : (brave(X0) | ~funny(X0)) [ennf transformation 63]
162. ~brave(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 65]
174. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom]
175. ~brave(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 162,174]
259. room(mary) [cnf transformation 150]
260. ~room(X0) | mary = X0 [cnf transformation 150]
262. funny(X0) | ~curious(X0) | ~person(mary) | ~strong(mary) [cnf transformation 153]
273. strong(mary) [cnf transformation 54]
278. curious(mary) [cnf transformation 58]
279. person(mary) [cnf transformation 58]
283. brave(X0) | ~funny(X0) [cnf transformation 161]
284. ~brave(mary) | room(sK3) | ~room(mary) [cnf transformation 175]
285. ~brave(mary) | mary != sK3 | ~room(mary) [cnf transformation 175]
296. 3 <=> strong(mary) [avatar definition]
300. 4 <=> person(mary) [avatar definition]
304. 5 <=> ! [X0] : (funny(X0) | ~curious(X0)) [avatar definition]
305. ~curious(X0) | funny(X0) <- (5) [avatar component clause 304]
306. ~3 | ~4 | 5 [avatar split clause 262,304,300,296]
311. 7 <=> ! [X0] : (brave(X0) | ~funny(X0)) [avatar definition]
312. ~funny(X0) | brave(X0) <- (7) [avatar component clause 311]
314. 3 [avatar split clause 273,296]
315. 4 [avatar split clause 279,300]
316. 7 [avatar split clause 283,311]
317. ~brave(mary) | mary != sK3 [subsumption resolution 285,259]
319. 8 <=> mary = sK3 [avatar definition]
321. mary != sK3 <- (~8) [avatar component clause 319]
323. 9 <=> brave(mary) [avatar definition]
326. ~8 | ~9 [avatar split clause 317,323,319]
327. ~brave(mary) | room(sK3) [subsumption resolution 284,259]
329. 10 <=> room(sK3) [avatar definition]
331. room(sK3) <- (10) [avatar component clause 329]
332. 10 | ~9 [avatar split clause 327,323,329]
334. funny(mary) <- (5) [resolution 305,278]
335. brave(mary) <- (5, 7) [resolution 312,334]
338. 9 | ~5 | ~7 [avatar split clause 335,311,304,323]
340. mary = sK3 <- (10) [resolution 260,331]
341. $false <- (~8, 10) [subsumption resolution 340,321]
342. 8 | ~10 [avatar contradiction clause 341]
343. $false [avatar sat refutation 306,314,315,316,326,332,338,342]
% SZS output end Proof for 3008680031826746286292663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.269007 |
Ana, Maxine, Marcus are the only persons in the room.
If "everyone in the room has a curated collection of mid-century modern furniture or does not make intricate hand-cut paper art for exhibitions" then "Ana is a craft beer aficionado".
If "Ana has a saltwater aquarium" then "Maxine is a client of Costco".
If "Maxine practices kickboxing" then "Maxine is a client of Meta" otherwise "Maxine practices archery".
If "someone in the room is a scotch connoisseur" then "Ana neither is a scotch connoisseur nor enjoys fishing".
If "everyone in the room mentors a youth basketball team on weekends or does not host a YouTube channel dedicated to art tutorials" then "Ana practices archery".
"Everyone in the room has a curated collection of mid-century modern furniture only if they enjoys logic puzzles" unless "everyone in the room is not a scotch connoisseur or practices kickboxing".
If "everyone in the room does not have a saltwater aquarium or develops open-source software projects in their free time" then "someone in the room uses contact lenses".
"Someone anywhere practices archery" unless "not everyone in the room is a craft beer aficionado or does not use contact lenses".
If "everyone in the room does not have a curated collection of mid-century modern furniture or is a scotch connoisseur" then "Maxine can play the flute".
"No one in the room does not enjoy windsurfing or collects action figures" only if "not everyone in the room plays eSports competitively only if they practices archery".
"Maxine develops open-source software projects in their free time" unless "Maxine enjoys windsurfing".
Maxine enjoys fishing.
Only one person in the room enjoys fishing.
Maxine makes intricate hand-cut paper art for exhibitions.
Ana hosts a YouTube channel dedicated to art tutorials.
Not everyone outside the room is a client of Costco only if they develops open-source software projects in their free time.
Maxine does not practice kickboxing.
Everyone in the room who mentors a youth basketball team on weekends develops open-source software projects in their free time.
Everyone in the room who enjoys windsurfing practices graffiti art.
Everyone in the room who practices graffiti art practices archery, enjoys fishing and volunteers for local environmental conservation projects. | Ana enjoys fishing. | contradiction | room(ana)&room(maxine)&room(marcus)&(![X]:(room(X)=>(X='ana'|X='maxine'|X='marcus')))&
((![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))=>(is_a_craft_beer_aficionado(ana)))&
((has_a_saltwater_aquarium(ana))=>(is_a_client_of_Costco(maxine)))&
(((practices_kickboxing(maxine))=>(is_a_client_of_Meta(maxine)))&((~(practices_kickboxing(maxine)))=>(practices_archery(maxine))))&
((?[X]:(room(X)&(is_a_scotch_connoisseur(X))))=>(~((is_a_scotch_connoisseur(ana))|(enjoys_fishing(ana)))))&
((![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))=>(practices_archery(ana)))&
(~(![X]:(room(X)=>(((practices_kickboxing(X))|(is_not_a_scotch_connoisseur(X))))))=>(![X]:(room(X)=>(((enjoys_logic_puzzles(X))<=(has_a_curated_collection_of_mid-century_modern_furniture(X)))))))&
((![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(does_not_have_a_saltwater_aquarium(X))))))=>(?[X]:(room(X)&(uses_contact_lenses(X)))))&
(~(~![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(is_a_craft_beer_aficionado(X))))))=>(?[X]:(anywhere(X)&(practices_archery(X)))))&
((![X]:(room(X)=>(((is_a_scotch_connoisseur(X))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))=>(can_play_the_flute(maxine)))&
((~?[X]:(room(X)=>(((collects_action_figures(X))|(does_not_enjoy_windsurfing(X))))))=>(~![X]:(room(X)=>(((practices_archery(X))<=(plays_eSports_competitively(X)))))))&
(~(enjoys_windsurfing(maxine))=>(develops_open-source_software_projects_in_their_free_time(maxine)))&
(enjoys_fishing(maxine))&
(((?[X]:(room(X)&enjoys_fishing(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_fishing(X))&(enjoys_fishing(Y)))=>(X=Y)))))&
(makes_intricate_hand-cut_paper_art_for_exhibitions(maxine))&
(hosts_a_YouTube_channel_dedicated_to_art_tutorials(ana))&
(~![X]:(~room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))<=(is_a_client_of_Costco(X))))))&
(does_not_practice_kickboxing(maxine))&
(![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(![X]:(room(X)=>(((enjoys_windsurfing(X))=>(practices_graffiti_art(X))))))&
(![X]:(room(X)=>(((practices_graffiti_art(X))=>(((practices_archery(X))&(enjoys_fishing(X))&(volunteers_for_local_environmental_conservation_projects(X))))))))&
(enjoys_stand-up_paddleboarding(maxine))&
(![X]:(room(X)=>(((practices_archery(X))|(cannot_play_the_flute(X))))))&
(![X]:(~room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(enjoys_fishing(X)))))) | room(ana)&room(maxine)&room(marcus)&(![X]:(room(X)=>(X='ana'|X='maxine'|X='marcus')))&
enjoys_fishing(ana) | [
"b42",
"p0",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6709789119381857028400906
% SZS output start Proof for 6709789119381857028400906
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]
56. predb(paul) [input p12]
57. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predb(X0) & room(X0)) [input p13]
68. predb(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
74. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) [rectify 57]
173. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
174. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 173]
177. ! [X0,X1] : (X0 = X1 | (~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predb(X2) & room(X2)) [ennf transformation 74]
178. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predb(X2) & room(X2)) [flattening 177]
186. predb(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 68]
187. predb(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 186]
193. ? [X2] : (predb(X2) & room(X2)) => (predb(sK2) & room(sK2)) [choice axiom]
194. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & (predb(sK2) & room(sK2)) [skolemisation 178,193]
241. mary != paul [cnf transformation 43]
277. room(mary) [cnf transformation 174]
278. room(paul) [cnf transformation 174]
284. predb(paul) [cnf transformation 56]
287. ~predb(X1) | X0 = X1 | ~predb(X0) | ~room(X1) | ~room(X0) [cnf transformation 194]
297. predb(mary) [cnf transformation 187]
400. paul = X0 | ~predb(X0) | ~room(paul) | ~room(X0) [resolution 287,284]
403. ~predb(X0) | paul = X0 | ~room(X0) [subsumption resolution 400,278]
411. mary = paul | ~room(mary) [resolution 403,297]
413. ~room(mary) [subsumption resolution 411,241]
414. $false [subsumption resolution 413,277]
% SZS output end Proof for 6709789119381857028400906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.391833 |
Barbara, Stephanie are the only persons in the room.
“Everyone in the room does not enjoy spelunking or does not enjoy logic puzzles” if “everyone outside the room is not a night owl or enjoys windsurfing” and vice versa.
If “everyone in the room is a night owl or does not enjoy spelunking” then “if someone enjoys logic puzzles then he/she is a night owl”.
“Everyone in the room is not a night owl or composes and performs experimental electronic music” if “everyone outside the room enjoys logic puzzles or is not a night owl” and vice versa.
Everyone in the room enjoys logic puzzles.
Everyone in the room is not a night owl or composes and performs experimental electronic music.
Everyone in the room is a night owl if they composes and performs experimental electronic music.
Everyone in the room enjoys spelunking if they is a night owl.
Everyone outside the room enjoys logic puzzles or is not a night owl.
Barbara who composes and performs experimental electronic music is a night owl.
Not everyone in the room enjoys windsurfing if they does not compose and performs experimental electronic music.
Everyone in the room composes and performs experimental electronic music and enjoys windsurfing if they enjoys windsurfing.
Everyone anywhere enjoys spelunking if they practices pilates.
Stephanie does not compose and performs experimental electronic music. | Barbara practices pilates. | neutral | room(barbara)&room(stephanie)&(![X]:(room(X)=>(X='barbara'|X='stephanie')))&
((![X]:(~room(X)=>(((enjoys_windsurfing(X))|(is_not_a_night_owl(X))))))<=>(![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))|(does_not_enjoy_spelunking(X)))))))&
((![X]:(room(X)=>(((does_not_enjoy_spelunking(X))|(is_a_night_owl(X))))))=>((![X]:((enjoys_logic_puzzles(X))=>(is_a_night_owl(X))))))&
((![X]:(~room(X)=>(((is_not_a_night_owl(X))|(enjoys_logic_puzzles(X))))))<=>(![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))|(is_not_a_night_owl(X)))))))&
(![X]:(room(X)=>(enjoys_logic_puzzles(X))))&
(![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))|(is_not_a_night_owl(X))))))&
(![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(is_a_night_owl(X))))))&
(![X]:(room(X)=>(((is_a_night_owl(X))=>(enjoys_spelunking(X))))))&
(![X]:(~room(X)=>(((is_not_a_night_owl(X))|(enjoys_logic_puzzles(X))))))&
((composes_and_performs_experimental_electronic_music(barbara))&(is_a_night_owl(barbara)))&
(~![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))=>(enjoys_windsurfing(X))))))&
(![X]:(room(X)=>(((enjoys_windsurfing(X))=>(((composes_and_performs_experimental_electronic_music(X))&(enjoys_windsurfing(X))))))))&
(![X]:(anywhere(X)=>(((practices_pilates(X))=>(enjoys_spelunking(X))))))&
(does_not_compose_and_performs_experimental_electronic_music(stephanie)) | room(barbara)&room(stephanie)&(![X]:(room(X)=>(X='barbara'|X='stephanie')))&
practices_pilates(barbara) | [] | null | 0.001995 |
Ora, Melanie, James, Beatrice, Brenda are the only persons in the room.
Everyone in the room is an avid collector of autographed memorabilia from famous musicians or develops open-source software projects in their free time or both if they plays video games.
Everyone in the room who is an avid collector of autographed memorabilia from famous musicians or develops open-source software projects in their free time or both does not own a significant collection of rare gemstones and minerals or has a piercing or both.
Everyone in the room enjoys spelunking.
Everyone in the room collects action figures if they is a certified scuba diver with advanced underwater photography skills.
Everyone in the room enjoys bird watching.
Everyone in the room either has a piercing or enjoys salsa dancing but not both if they is a cybersecurity expert.
Everyone in the room does not regularly goes on multi-day backpacking trips in national parks.
If someone does not regularly goes on multi-day backpacking trips in national parks then he/she does not own a significant collection of rare gemstones and minerals and vice versa.
Everyone in the room collects action figures.
Everyone in the room is not an avid collector of autographed memorabilia from famous musicians or can play the guitar or both.
Not everyone in the room who enjoys writing detailed reviews of new and classic board games does not enjoy salsa dancing.
More than one person in the room either enjoys salsa dancing or enjoys skydiving but not both.
Everyone anywhere works on fridays if they is a cybersecurity expert.
Everyone anywhere who does not play video games can play the guitar.
If someone uses a Windows laptop then he/she does enjoy mountain biking and vice versa. | Ora owns a significant collection of rare gemstones and minerals. | contradiction | room(ora)&room(melanie)&room(james)&room(beatrice)&room(brenda)&(![X]:(room(X)=>(X='ora'|X='melanie'|X='james'|X='beatrice'|X='brenda')))&
(![X]:(room(X)=>(((plays_video_games(X))=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(develops_open-source_software_projects_in_their_free_time(X))))))))&
(![X]:(room(X)=>(((((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(develops_open-source_software_projects_in_their_free_time(X))))=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(has_a_piercing(X))))))))&
(![X]:(room(X)=>(enjoys_spelunking(X))))&
(![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(collects_action_figures(X))))))&
(![X]:(room(X)=>(enjoys_bird_watching(X))))&
(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(((has_a_piercing(X))<~>(enjoys_salsa_dancing(X))))))))&
(![X]:(room(X)=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))&
((![X]:((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<=>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X)))))&
(![X]:(room(X)=>(collects_action_figures(X))))&
(![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(can_play_the_guitar(X))))))&
(~![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(does_not_enjoy_salsa_dancing(X))))))&
((?[X,Y]:(room(X)&room(Y)&(((enjoys_salsa_dancing(X))<~>(enjoys_skydiving(X)))&((enjoys_salsa_dancing(Y))<~>(enjoys_skydiving(Y))))&(X!=Y))))&
(![X]:(anywhere(X)=>(((is_a_cybersecurity_expert(X))=>(works_on_fridays(X))))))&
(![X]:(anywhere(X)=>(((does_not_play_video_games(X))=>(can_play_the_guitar(X))))))&
((![X]:((uses_a_Windows_laptop(X))<=>(does_enjoy_mountain_biking(X))))) | room(ora)&room(melanie)&room(james)&room(beatrice)&room(brenda)&(![X]:(room(X)=>(X='ora'|X='melanie'|X='james'|X='beatrice'|X='brenda')))&
owns_a_significant_collection_of_rare_gemstones_and_minerals(ora) | [
"p0",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4189352585650557196451316
% SZS output start Proof for 4189352585650557196451316
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]
51. ! [X0] : (room(X0) => ~predc(X0)) [input p7]
52. ! [X0] : (~predc(X0) <=> ~predd(X0)) [input p8]
60. predd(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]
61. ! [X0] : (~predc(X0) => ~predd(X0)) [unused predicate definition removal 52]
146. ! [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]
147. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 146]
148. ! [X0] : (~predc(X0) | ~room(X0)) [ennf transformation 51]
149. ! [X0] : (~predd(X0) | predc(X0)) [ennf transformation 61]
151. predd(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 60]
152. predd(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 151]
240. room(mary) [cnf transformation 147]
246. ~predc(X0) | ~room(X0) [cnf transformation 148]
247. ~predd(X0) | predc(X0) [cnf transformation 149]
263. predd(mary) [cnf transformation 152]
284. predc(mary) [resolution 247,263]
285. ~room(mary) [resolution 284,246]
286. $false [subsumption resolution 285,240]
% SZS output end Proof for 4189352585650557196451316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.391412 |
Bonnie is the only person in the room. If "Bonnie is not dedicated to sustainable living and zero-waste practices" then "everyone in the room who enjoys virtual reality gaming, hosts regular game nights featuring complex strategy games or hosts a YouTube channel dedicated to art tutorials enjoys fishing, enjoys windsurfing and does not enjoy logic puzzles" otherwise "Bonnie collects limited-edition art prints from contemporary artists". If "everyone in the room practices urban gardening" then "everyone in the room does not collect action figures or enjoys fishing". If "everyone in the room does not collect action figures or enjoys fishing" then "everyone in the room is a professional photographer specializing in portrait photography if they has a specialized collection of handmade artisan pottery". If "Bonnie enjoys windsurfing" then "everyone in the room plays as a goalkeeper for a local amateur soccer team if they practices pilates". If "everyone anywhere does not enjoy writing detailed reviews of new and classic board games or enjoys fishing" then "everyone in the room who collects rare minerals or collects action figures or both is not a professional photographer specializing in portrait photography". If "Bonnie hosts a YouTube channel dedicated to art tutorials" then "it is not the case that "it is not the case that "Bonnie enjoys stargazing""". If "everyone anywhere hosts regular workshops on creative writing" then "Bonnie has a vast collection of first-edition science fiction novels" otherwise "everyone in the room hosts regular game nights featuring complex strategy games if they is a professional photographer specializing in portrait photography". Someone in the room is a professional photographer specializing in portrait photography. Not everyone outside the room who practices pilates is dedicated to sustainable living and zero-waste practices. Everyone in the room who is dedicated to sustainable living and zero-waste practices neither hosts regular workshops on creative writing nor is not a professional photographer specializing in portrait photography. Bonnie who does not collect rare minerals, does not create bespoke furniture pieces from reclaimed wood and hosts a YouTube channel dedicated to art tutorials enjoys logic puzzles. Bonnie who has a vast collection of first-edition science fiction novels enjoys virtual reality gaming, hosts regular game nights featuring complex strategy games or hosts a YouTube channel dedicated to art tutorials. Bonnie enjoys stargazing. Bonnie is a professional photographer specializing in portrait photography. | Everyone in the room is not a professional photographer specializing in portrait photography or is a professional photographer specializing in portrait photography. | entailment | room(bonnie)&(![X]:(room(X)=>(X='bonnie')))&
(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(bonnie))=>(![X]:(room(X)=>(((((enjoys_virtual_reality_gaming(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))=>(((enjoys_fishing(X))&(enjoys_windsurfing(X))&(does_not_enjoy_logic_puzzles(X)))))))))&((~(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(bonnie)))=>(collects_limited-edition_art_prints_from_contemporary_artists(bonnie))))&
(((![X]:(room(X)=>(practices_urban_gardening(X))))=>(![X]:(room(X)=>(((enjoys_fishing(X))|(does_not_collect_action_figures(X)))))))&
((![X]:(room(X)=>(((enjoys_fishing(X))|(does_not_collect_action_figures(X))))))=>(![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))))&
((enjoys_windsurfing(bonnie))=>(![X]:(room(X)=>(((practices_pilates(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))&
((![X]:(anywhere(X)=>(((enjoys_fishing(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))=>(![X]:(room(X)=>(((((collects_rare_minerals(X))|(collects_action_figures(X))))=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))))&
((hosts_a_YouTube_channel_dedicated_to_art_tutorials(bonnie))=>(~(~(enjoys_stargazing(bonnie)))))&
(((![X]:(anywhere(X)=>(hosts_regular_workshops_on_creative_writing(X))))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(bonnie)))&((~(![X]:(anywhere(X)=>(hosts_regular_workshops_on_creative_writing(X)))))=>(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))&
(?[X]:(room(X)&(is_a_professional_photographer_specializing_in_portrait_photography(X))))&
(~![X]:(~room(X)=>(((practices_pilates(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))&
(![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(~((hosts_regular_workshops_on_creative_writing(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))))&
((((does_not_collect_rare_minerals(bonnie))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(bonnie))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(bonnie))))&(enjoys_logic_puzzles(bonnie)))&
((has_a_vast_collection_of_first-edition_science_fiction_novels(bonnie))&(((enjoys_virtual_reality_gaming(bonnie))|(hosts_regular_game_nights_featuring_complex_strategy_games(bonnie))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(bonnie)))))&
(enjoys_stargazing(bonnie))&
(is_a_professional_photographer_specializing_in_portrait_photography(bonnie)) | room(bonnie)&(![X]:(room(X)=>(X='bonnie')))&
![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 2766377286624303458550807
% SZS output start Proof for 2766377286624303458550807
44. predb(mary) & preds(mary) & (predt(mary) | predp(mary) | predy(mary)) & predm(mary) & prede(mary) & predt(mary) & ~predl(mary) & ~predu(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X0] : (~room(X0) => (predq(X0) => preda(X0))) & ? [X0] : (predb(X0) & room(X0)) & (~! [X0] : (anywhere(X0) => predd(X0)) => ! [X0] : (room(X0) => (predb(X0) => predp(X0)))) & (! [X0] : (anywhere(X0) => predd(X0)) => predm(mary)) & (predt(mary) => preds(mary)) & (! [X0] : (anywhere(X0) => (~predk(X0) | predz(X0))) => ! [X0] : (room(X0) => ((predg(X0) | predu(X0)) => ~predb(X0)))) & (predr(mary) => ! [X0] : (room(X0) => (predq(X0) => predc(X0)))) & (! [X0] : (room(X0) => (~predg(X0) | predz(X0))) => ! [X0] : (room(X0) => (predw(X0) => predb(X0)))) & (! [X0] : (room(X0) => predx(X0)) => ! [X0] : (room(X0) => (~predg(X0) | predz(X0)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X0] : (room(X0) => ((predt(X0) | predp(X0) | predy(X0)) => (~prede(X0) & predr(X0) & predz(X0))))) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
45. ~(! [X0] : (room(X0) => (~predb(X0) | predb(X0))) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
46. predb(mary) & preds(mary) & (predt(mary) | predp(mary) | predy(mary)) & predm(mary) & prede(mary) & predt(mary) & ~predl(mary) & ~predu(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => (predq(X1) => preda(X1))) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (! [X5] : (anywhere(X5) => predd(X5)) => predm(mary)) & (predt(mary) => preds(mary)) & (! [X6] : (anywhere(X6) => (~predk(X6) | predz(X6))) => ! [X7] : (room(X7) => ((predg(X7) | predu(X7)) => ~predb(X7)))) & (predr(mary) => ! [X8] : (room(X8) => (predq(X8) => predc(X8)))) & (! [X9] : (room(X9) => (~predg(X9) | predz(X9))) => ! [X10] : (room(X10) => (predw(X10) => predb(X10)))) & (! [X11] : (room(X11) => predx(X11)) => ! [X12] : (room(X12) => (~predg(X12) | predz(X12)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predr(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [rectify 44]
47. ~(! [X0] : (room(X0) => (~predb(X0) | predb(X0))) & ! [X1] : (room(X1) => mary = X1) & room(mary)) [rectify 45]
48. predb(mary) & preds(mary) & (predt(mary) | predp(mary) | predy(mary)) & predm(mary) & prede(mary) & predt(mary) & ~predu(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => (predq(X1) => preda(X1))) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (! [X5] : (anywhere(X5) => predd(X5)) => predm(mary)) & (predt(mary) => preds(mary)) & (! [X6] : (anywhere(X6) => (~predk(X6) | predz(X6))) => ! [X7] : (room(X7) => ((predg(X7) | predu(X7)) => ~predb(X7)))) & (predr(mary) => ! [X8] : (room(X8) => (predq(X8) => predc(X8)))) & (! [X9] : (room(X9) => (~predg(X9) | predz(X9))) => ! [X10] : (room(X10) => (predw(X10) => predb(X10)))) & (! [X11] : (room(X11) => predx(X11)) => ! [X12] : (room(X12) => (~predg(X12) | predz(X12)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predr(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 46]
49. predb(mary) & preds(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ~predu(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => (predq(X1) => preda(X1))) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (predt(mary) => preds(mary)) & (! [X6] : (anywhere(X6) => (~predk(X6) | predz(X6))) => ! [X7] : (room(X7) => ((predg(X7) | predu(X7)) => ~predb(X7)))) & (predr(mary) => ! [X8] : (room(X8) => (predq(X8) => predc(X8)))) & (! [X9] : (room(X9) => (~predg(X9) | predz(X9))) => ! [X10] : (room(X10) => (predw(X10) => predb(X10)))) & (! [X11] : (room(X11) => predx(X11)) => ! [X12] : (room(X12) => (~predg(X12) | predz(X12)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predr(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 48]
50. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ~predu(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => (predq(X1) => preda(X1))) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (! [X6] : (anywhere(X6) => (~predk(X6) | predz(X6))) => ! [X7] : (room(X7) => ((predg(X7) | predu(X7)) => ~predb(X7)))) & (predr(mary) => ! [X8] : (room(X8) => (predq(X8) => predc(X8)))) & (! [X9] : (room(X9) => (~predg(X9) | predz(X9))) => ! [X10] : (room(X10) => (predw(X10) => predb(X10)))) & (! [X11] : (room(X11) => predx(X11)) => ! [X12] : (room(X12) => (~predg(X12) | predz(X12)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predr(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 49]
51. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => (predq(X1) => preda(X1))) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (! [X6] : (anywhere(X6) => (~predk(X6) | predz(X6))) => ! [X7] : (room(X7) => (predg(X7) => ~predb(X7)))) & (predr(mary) => ! [X8] : (room(X8) => (predq(X8) => predc(X8)))) & (! [X9] : (room(X9) => (~predg(X9) | predz(X9))) => ! [X10] : (room(X10) => (predw(X10) => predb(X10)))) & (! [X11] : (room(X11) => predx(X11)) => ! [X12] : (room(X12) => (~predg(X12) | predz(X12)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predr(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 50]
52. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => (predq(X1) => preda(X1))) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (! [X6] : (anywhere(X6) => predz(X6)) => ! [X7] : (room(X7) => (predg(X7) => ~predb(X7)))) & (predr(mary) => ! [X8] : (room(X8) => (predq(X8) => predc(X8)))) & (! [X9] : (room(X9) => (~predg(X9) | predz(X9))) => ! [X10] : (room(X10) => (predw(X10) => predb(X10)))) & (! [X11] : (room(X11) => predx(X11)) => ! [X12] : (room(X12) => (~predg(X12) | predz(X12)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predr(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 51]
53. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => (predq(X1) => preda(X1))) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (! [X6] : (anywhere(X6) => predz(X6)) => ! [X7] : (room(X7) => (predg(X7) => ~predb(X7)))) & (! [X9] : (room(X9) => (~predg(X9) | predz(X9))) => ! [X10] : (room(X10) => (predw(X10) => predb(X10)))) & (! [X11] : (room(X11) => predx(X11)) => ! [X12] : (room(X12) => (~predg(X12) | predz(X12)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predr(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 52]
54. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => preda(X1)) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (! [X6] : (anywhere(X6) => predz(X6)) => ! [X7] : (room(X7) => (predg(X7) => ~predb(X7)))) & (! [X9] : (room(X9) => (~predg(X9) | predz(X9))) => ! [X10] : (room(X10) => (predw(X10) => predb(X10)))) & (! [X11] : (room(X11) => predx(X11)) => ! [X12] : (room(X12) => (~predg(X12) | predz(X12)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predr(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 53]
55. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => preda(X1)) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (! [X6] : (anywhere(X6) => predz(X6)) => ! [X7] : (room(X7) => (predg(X7) => ~predb(X7)))) & (! [X9] : (room(X9) => (~predg(X9) | predz(X9))) => ! [X10] : (room(X10) => (predw(X10) => predb(X10)))) & (! [X11] : (room(X11) => predx(X11)) => ! [X12] : (room(X12) => (~predg(X12) | predz(X12)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 54]
56. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => preda(X1)) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (! [X6] : (anywhere(X6) => predz(X6)) => ! [X7] : (room(X7) => (predg(X7) => ~predb(X7)))) & (! [X11] : (room(X11) => predx(X11)) => ! [X12] : (room(X12) => (~predg(X12) | predz(X12)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 55]
57. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => preda(X1)) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => (~prede(X13) & predz(X13))))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 56]
58. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => preda(X1)) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (preda(mary) => predn(mary)) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => ~prede(X13)))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 57]
59. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : (room(X0) => (preda(X0) => ~(~predb(X0) | predd(X0)))) & ~! [X1] : (~room(X1) => preda(X1)) & ? [X2] : (predb(X2) & room(X2)) & (~! [X3] : (anywhere(X3) => predd(X3)) => ! [X4] : (room(X4) => (predb(X4) => predp(X4)))) & (~preda(mary) => ! [X13] : (room(X13) => ((predt(X13) | predp(X13) | predy(X13)) => ~prede(X13)))) & ! [X14] : (room(X14) => mary = X14) & room(mary) [pure predicate removal 58]
131. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : (((predb(X0) & ~predd(X0)) | ~preda(X0)) | ~room(X0)) & ? [X1] : (~preda(X1) & ~room(X1)) & ? [X2] : (predb(X2) & room(X2)) & (! [X4] : ((predp(X4) | ~predb(X4)) | ~room(X4)) | ! [X3] : (predd(X3) | ~anywhere(X3))) & (! [X13] : ((~prede(X13) | (~predt(X13) & ~predp(X13) & ~predy(X13))) | ~room(X13)) | preda(mary)) & ! [X14] : (mary = X14 | ~room(X14)) & room(mary) [ennf transformation 59]
132. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : ((predb(X0) & ~predd(X0)) | ~preda(X0) | ~room(X0)) & ? [X1] : (~preda(X1) & ~room(X1)) & ? [X2] : (predb(X2) & room(X2)) & (! [X4] : (predp(X4) | ~predb(X4) | ~room(X4)) | ! [X3] : (predd(X3) | ~anywhere(X3))) & (! [X13] : (~prede(X13) | (~predt(X13) & ~predp(X13) & ~predy(X13)) | ~room(X13)) | preda(mary)) & ! [X14] : (mary = X14 | ~room(X14)) & room(mary) [flattening 131]
133. ? [X0] : ((predb(X0) & ~predb(X0)) & room(X0)) | ? [X1] : (mary != X1 & room(X1)) | ~room(mary) [ennf transformation 47]
134. ? [X0] : (predb(X0) & ~predb(X0) & room(X0)) | ? [X1] : (mary != X1 & room(X1)) | ~room(mary) [flattening 133]
136. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : ((predb(X0) & ~predd(X0)) | ~preda(X0) | ~room(X0)) & ? [X1] : (~preda(X1) & ~room(X1)) & ? [X2] : (predb(X2) & room(X2)) & (! [X3] : (predp(X3) | ~predb(X3) | ~room(X3)) | ! [X4] : (predd(X4) | ~anywhere(X4))) & (! [X5] : (~prede(X5) | (~predt(X5) & ~predp(X5) & ~predy(X5)) | ~room(X5)) | preda(mary)) & ! [X6] : (mary = X6 | ~room(X6)) & room(mary) [rectify 132]
137. ? [X1] : (~preda(X1) & ~room(X1)) => (~preda(sK0) & ~room(sK0)) [choice axiom]
138. ? [X2] : (predb(X2) & room(X2)) => (predb(sK1) & room(sK1)) [choice axiom]
139. predb(mary) & (predt(mary) | predp(mary) | predy(mary)) & prede(mary) & predt(mary) & ! [X0] : ((predb(X0) & ~predd(X0)) | ~preda(X0) | ~room(X0)) & (~preda(sK0) & ~room(sK0)) & (predb(sK1) & room(sK1)) & (! [X3] : (predp(X3) | ~predb(X3) | ~room(X3)) | ! [X4] : (predd(X4) | ~anywhere(X4))) & (! [X5] : (~prede(X5) | (~predt(X5) & ~predp(X5) & ~predy(X5)) | ~room(X5)) | preda(mary)) & ! [X6] : (mary = X6 | ~room(X6)) & room(mary) [skolemisation 136,138,137]
140. ? [X0] : (predb(X0) & ~predb(X0) & room(X0)) => (predb(sK2) & ~predb(sK2) & room(sK2)) [choice axiom]
141. ? [X1] : (mary != X1 & room(X1)) => (mary != sK3 & room(sK3)) [choice axiom]
142. (predb(sK2) & ~predb(sK2) & room(sK2)) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 134,141,140]
224. room(mary) [cnf transformation 139]
225. ~room(X6) | mary = X6 [cnf transformation 139]
242. ~predb(sK2) | room(sK3) | ~room(mary) [cnf transformation 142]
243. ~predb(sK2) | mary != sK3 | ~room(mary) [cnf transformation 142]
244. predb(sK2) | room(sK3) | ~room(mary) [cnf transformation 142]
245. predb(sK2) | mary != sK3 | ~room(mary) [cnf transformation 142]
284. predb(sK2) | mary != sK3 [subsumption resolution 245,224]
286. 10 <=> mary = sK3 [avatar definition]
288. mary != sK3 <- (~10) [avatar component clause 286]
290. 11 <=> predb(sK2) [avatar definition]
293. ~10 | 11 [avatar split clause 284,290,286]
294. predb(sK2) | room(sK3) [subsumption resolution 244,224]
296. 12 <=> room(sK3) [avatar definition]
298. room(sK3) <- (12) [avatar component clause 296]
299. 12 | 11 [avatar split clause 294,290,296]
300. ~predb(sK2) | mary != sK3 [subsumption resolution 243,224]
301. ~10 | ~11 [avatar split clause 300,290,286]
302. ~predb(sK2) | room(sK3) [subsumption resolution 242,224]
303. 12 | ~11 [avatar split clause 302,290,296]
314. mary = sK3 <- (12) [resolution 225,298]
317. $false <- (~10, 12) [subsumption resolution 314,288]
318. 10 | ~12 [avatar contradiction clause 317]
319. $false [avatar sat refutation 293,299,301,303,318]
% SZS output end Proof for 2766377286624303458550807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.612211 |
Gladys, Jana are the only persons in the room.
Either “Gladys is not right-handed, does not collect first edition books or is a tea enthusiast” or “Gladys bakes bread at home, does not host a popular podcast about emerging technologies or does not enjoy windsurfing” but not both.
“Jana neither does not collect classic novels nor cannot play the piano” if “at least one person in the room is not allergic to anything, creates YouTube content or does not own a smartwatch” and vice versa.
Gladys is not dedicated to sustainable living and zero-waste practices, does not bake bread at home or does not use a Windows laptop.
Gladys does not write a travel blog.
Everyone outside the room neither is not passionate about collecting and restoring classic cars nor does not enjoy coding in Python.
Gladys does not practice pilates or does not own a smartwatch or both.
Gladys does not collect rare minerals and does not practice graffiti art.
Everyone in the room does not host a popular podcast about emerging technologies or does not own a 3D printer.
Everyone in the room does not host a popular podcast about emerging technologies or does not bake bread at home or both.
Gladys is not right-handed, does not practice pilates or bakes bread at home.
Everyone outside the room either does not write a travel blog or can play the piano but not both.
Jana does not own a 3D printer.
Gladys either is not passionate about collecting and restoring classic cars or does not own a smartwatch but not both.
Gladys either does not write a travel blog or enjoys landscape photography but not both.
Jana does not practice pilates or does not use a Windows laptop or both.
At least one person in the room develops open-source software projects in their free time and does not collect classic novels.
Jana neither does not collect classic novels nor cannot play the piano.
Everyone anywhere does not collect rare minerals or does not enjoy logic puzzles or both. | Everyone in the room does not practice graffiti art and cannot play the piano. | contradiction | room(gladys)&room(jana)&(![X]:(room(X)=>(X='gladys'|X='jana')))&
((((is_not_right-handed(gladys))|(does_not_collect_first_edition_books(gladys))|(is_a_tea_enthusiast(gladys))))<~>(((bakes_bread_at_home(gladys))|(does_not_host_a_popular_podcast_about_emerging_technologies(gladys))|(does_not_enjoy_windsurfing(gladys)))))&
((((?[X]:(room(X)&((is_not_allergic_to_anything(X))|(creates_YouTube_content(X))|(does_not_own_a_smartwatch(X)))))))<=>(~((does_not_collect_classic_novels(jana))|(cannot_play_the_piano(jana)))))&
(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(gladys))|(does_not_bake_bread_at_home(gladys))|(does_not_use_a_Windows_laptop(gladys))))&
(does_not_write_a_travel_blog(gladys))&
(![X]:(~room(X)=>(~((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_enjoy_coding_in_Python(X))))))&
(((does_not_practice_pilates(gladys))|(does_not_own_a_smartwatch(gladys))))&
(((does_not_collect_rare_minerals(gladys))&(does_not_practice_graffiti_art(gladys))))&
(![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(does_not_bake_bread_at_home(X))))))&
(((is_not_right-handed(gladys))|(does_not_practice_pilates(gladys))|(bakes_bread_at_home(gladys))))&
(![X]:(~room(X)=>(((does_not_write_a_travel_blog(X))<~>(can_play_the_piano(X))))))&
(does_not_own_a_3D_printer(jana))&
(((is_not_passionate_about_collecting_and_restoring_classic_cars(gladys))<~>(does_not_own_a_smartwatch(gladys))))&
(((does_not_write_a_travel_blog(gladys))<~>(enjoys_landscape_photography(gladys))))&
(((does_not_practice_pilates(jana))|(does_not_use_a_Windows_laptop(jana))))&
(((?[X]:(room(X)&((develops_open-source_software_projects_in_their_free_time(X))&(does_not_collect_classic_novels(X)))))))&
(~((does_not_collect_classic_novels(jana))|(cannot_play_the_piano(jana))))&
(![X]:(anywhere(X)=>(((does_not_collect_rare_minerals(X))|(does_not_enjoy_logic_puzzles(X)))))) | room(gladys)&room(jana)&(![X]:(room(X)=>(X='gladys'|X='jana')))&
![X]:(room(X)=>(((does_not_practice_graffiti_art(X))&(cannot_play_the_piano(X))))) | [
"p0",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4467160587801809004931070
% SZS output start Proof for 4467160587801809004931070
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
61. ~(~preda(paul) | ~predm(paul)) [input p17]
63. ! [X0] : (room(X0) => (~preda(X0) & ~predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
64. ! [X0] : (room(X0) => (~preda(X0) & ~predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 63]
71. ! [X0] : (room(X0) => ~preda(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [pure predicate removal 64]
149. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
150. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 149]
156. preda(paul) & predm(paul) [ennf transformation 61]
157. ! [X0] : (~preda(X0) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 71]
158. ! [X0] : (~preda(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 157]
253. room(paul) [cnf transformation 150]
285. preda(paul) [cnf transformation 156]
289. ~preda(X0) | ~room(X0) [cnf transformation 158]
329. 8 <=> preda(paul) [avatar definition]
330. preda(paul) <- (8) [avatar component clause 329]
376. 8 [avatar split clause 285,329]
378. ~room(paul) <- (8) [resolution 289,330]
379. $false <- (8) [subsumption resolution 378,253]
380. ~8 [avatar contradiction clause 379]
381. $false [avatar sat refutation 376,380]
% SZS output end Proof for 4467160587801809004931070
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.553478 |
There is a room.
“Everyone in the room has a saltwater aquarium or is not a culinary enthusiast who experiments with international cuisines” if “everyone in the room is not a certified yoga instructor teaching classes weekly or is not a culinary enthusiast who experiments with international cuisines” and vice versa.
Everyone in the room is a certified yoga instructor teaching classes weekly.
Everyone anywhere does not practice archery.
If someone either is a culinary enthusiast who experiments with international cuisines or practices archery but not both then he/she is a certified yoga instructor teaching classes weekly and is a professional photographer specializing in portrait photography and vice versa.
Everyone in the room practices archery.
Everyone in the room who does not practice archery is a certified yoga instructor teaching classes weekly.
Everyone in the room who is a certified yoga instructor teaching classes weekly is a culinary enthusiast who experiments with international cuisines.
If someone is a culinary enthusiast who experiments with international cuisines then he/she practices archery and vice versa.
Everyone in the room is a certified yoga instructor teaching classes weekly if they practices archery.
Everyone in the room who is a certified yoga instructor teaching classes weekly practices archery. | Everyone outside the room is not a certified yoga instructor teaching classes weekly. | neutral | (there_is_a_room)&
((![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))<=>(![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(has_a_saltwater_aquarium(X)))))))&
(![X]:(room(X)=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))&
(![X]:(anywhere(X)=>(does_not_practice_archery(X))))&
((![X]:((((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<~>(practices_archery(X))))<=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))&
(![X]:(room(X)=>(practices_archery(X))))&
(![X]:(room(X)=>(((does_not_practice_archery(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
((![X]:((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<=>(practices_archery(X)))))&
(![X]:(room(X)=>(((practices_archery(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(practices_archery(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))) | [] | null | 0 |
Jean is the only person in the room.
If “Jean uses an ios phone” then “Jean works as a freelance web developer specializing in e-commerce sites”.
“It is true that “it is not the case that “Jean uses an ios phone””” unless “Jean travels domestically frequently”.
“Everyone in the room who practices tai chi competes in national level swimming championships” unless “Jean collects foreign coins”.
“Jean practices tai chi” if “Jean enjoys skydiving”.
“Everyone in the room collects foreign coins if they enjoys writing detailed reviews of new and classic board games” if “everyone in the room does not own an Android phone or hosts regular game nights featuring complex strategy games”.
If “Jean owns an Android phone” then “Jean practices tai chi”.
Jean who plays as a goalkeeper for a local amateur soccer team travels domestically frequently.
It is not the case that “at least one person in the room enjoys skydiving”.
Jean enjoys writing detailed reviews of new and classic board games.
Someone in the room collects foreign coins.
More than one person anywhere enjoys skydiving.
Someone anywhere enjoys skydiving.
If someone works as a freelance web developer specializing in e-commerce sites then he/she enjoys writing detailed reviews of new and classic board games and vice versa. | Jean owns an Android phone. | neutral | room(jean)&(![X]:(room(X)=>(X='jean')))&
((uses_an_ios_phone(jean))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(jean)))&
(~(travels_domestically_frequently(jean))=>(~(uses_an_ios_phone(jean))))&
(~(collects_foreign_coins(jean))=>(![X]:(room(X)=>(((practices_tai_chi(X))=>(competes_in_national_level_swimming_championships(X)))))))&
((enjoys_skydiving(jean))=>(practices_tai_chi(jean)))&
((![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(does_not_own_an_Android_phone(X))))))=>(![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(collects_foreign_coins(X)))))))&
((owns_an_Android_phone(jean))=>(practices_tai_chi(jean)))&
((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(jean))&(travels_domestically_frequently(jean)))&
(~(((?[X]:(room(X)&enjoys_skydiving(X))))))&
(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(jean))&
(?[X]:(room(X)&(collects_foreign_coins(X))))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(enjoys_skydiving(X)&enjoys_skydiving(Y))&(X!=Y))))&
(?[X]:(anywhere(X)&(enjoys_skydiving(X))))&
((![X]:((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))) | room(jean)&(![X]:(room(X)=>(X='jean')))&
owns_an_Android_phone(jean) | [] | null | 0.017659 |
Gary, Aaron, Myrna, Lauren, Elwood are the only persons in the room.
Everyone in the room is old if they is tall or is not a creative person or both.
Everyone in the room is wise if they is a happy person.
Everyone in the room is wise only if they is not a curious person.
Everyone in the room is tall if they is not a curious person.
Everyone in the room is not funny if they is tall.
Not everyone in the room is a curious person if and only if they is not a wise person.
Everyone in the room is not a patient person.
All brave persons are creative.
Everyone in the room is a calm person.
All brave persons are old.
Everyone in the room is a patient calm person only if they is a tall person.
Everyone in the room is a strong person if they is a tall person.
Everyone in the room is humble if they is a strong person.
Everyone in the room either is wise or is a brave person but not both.
Someone who is a funny person, is old and is not a kind person is quieter than someone who is not a old person.
Everyone in the room is tall and is a tall person if they is not a happy person. | Gary is old. | entailment | room(gary)&room(aaron)&room(myrna)&room(lauren)&room(elwood)&(![X]:(room(X)=>(X='gary'|X='aaron'|X='myrna'|X='lauren'|X='elwood')))&
(![X]:(room(X)=>(((((tall(X))|(~(creative(X)&person(X)))))=>(old(X))))))&
(![X]:(room(X)=>(((happy(X)&person(X))=>(wise(X))))))&
(![X]:(room(X)=>(((~(curious(X)&person(X)))<=(wise(X))))))&
(![X]:(room(X)=>(((~(curious(X)&person(X)))=>(tall(X))))))&
(![X]:(room(X)=>(((tall(X))=>(~funny(X))))))&
(~![X]:(room(X)=>(((curious(X)&person(X))<=>(~(wise(X)&person(X)))))))&
(![X]:(room(X)=>(~(patient(X)&person(X)))))&
(![X]:(brave(X)=>creative(X)))&
(![X]:(room(X)=>(calm(X)&person(X))))&
(![X]:(brave(X)=>old(X)))&
(![X]:(room(X)=>(((tall(X)&person(X))<=(patient(X)&calm(X)&person(X))))))&
(![X]:(room(X)=>(((tall(X)&person(X))=>(strong(X)&person(X))))))&
(![X]:(room(X)=>(((strong(X)&person(X))=>(humble(X))))))&
(![X]:(room(X)=>(((wise(X))<~>(brave(X)&person(X))))))&
(?[X,Y]:((((funny(X)&person(X))&(old(X))&(~(kind(X)&person(X)))))&(~(old(Y)&person(Y)))&(quieter(X,Y))))&
(![X]:(room(X)=>(((~(happy(X)&person(X)))=>(((tall(X))&(tall(X)&person(X)))))))) | room(gary)&room(aaron)&room(myrna)&room(lauren)&room(elwood)&(![X]:(room(X)=>(X='gary'|X='aaron'|X='myrna'|X='lauren'|X='elwood')))&
old(gary) | [
"p0",
"p1",
"p3",
"p4",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 576901688325335948522257
% SZS output start Proof for 576901688325335948522257
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) => ((~(person(X0) & creative(X0)) | tall(X0)) => old(X0))) [input p1]
47. ! [X0] : (room(X0) => (wise(X0) => ~(person(X0) & curious(X0)))) [input p3]
48. ! [X0] : (room(X0) => (~(person(X0) & curious(X0)) => tall(X0))) [input p4]
53. ! [X0] : (room(X0) => (person(X0) & calm(X0))) [input p9]
54. ! [X0] : (brave(X0) => old(X0)) [input p10]
58. ! [X0] : (room(X0) => (wise(X0) <~> (person(X0) & brave(X0)))) [input p14]
61. ~(old(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]
67. ! [X0] : (room(X0) => person(X0)) [pure predicate removal 53]
68. ! [X0] : (room(X0) => ((~person(X0) | tall(X0)) => old(X0))) [pure predicate removal 45]
142. ! [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]
143. ! [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]
144. ! [X0] : ((old(X0) | (person(X0) & ~tall(X0))) | ~room(X0)) [ennf transformation 68]
145. ! [X0] : (old(X0) | (person(X0) & ~tall(X0)) | ~room(X0)) [flattening 144]
148. ! [X0] : (((~person(X0) | ~curious(X0)) | ~wise(X0)) | ~room(X0)) [ennf transformation 47]
149. ! [X0] : (~person(X0) | ~curious(X0) | ~wise(X0) | ~room(X0)) [flattening 148]
150. ! [X0] : ((tall(X0) | (person(X0) & curious(X0))) | ~room(X0)) [ennf transformation 48]
151. ! [X0] : (tall(X0) | (person(X0) & curious(X0)) | ~room(X0)) [flattening 150]
155. ! [X0] : (person(X0) | ~room(X0)) [ennf transformation 67]
156. ! [X0] : (old(X0) | ~brave(X0)) [ennf transformation 54]
159. ! [X0] : ((wise(X0) <~> (person(X0) & brave(X0))) | ~room(X0)) [ennf transformation 58]
163. ~old(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 61]
164. ~old(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 163]
170. ! [X0] : ((((~person(X0) | ~brave(X0)) | ~wise(X0)) & ((person(X0) & brave(X0)) | wise(X0))) | ~room(X0)) [nnf transformation 159]
171. ! [X0] : (((~person(X0) | ~brave(X0) | ~wise(X0)) & ((person(X0) & brave(X0)) | wise(X0))) | ~room(X0)) [flattening 170]
174. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
175. ~old(mary) | (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 164,174]
256. room(mary) [cnf transformation 143]
257. room(paul) [cnf transformation 143]
258. room(fred) [cnf transformation 143]
259. room(alice) [cnf transformation 143]
260. room(john) [cnf transformation 143]
261. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 143]
262. ~tall(X0) | old(X0) | ~room(X0) [cnf transformation 145]
265. ~curious(X0) | ~person(X0) | ~wise(X0) | ~room(X0) [cnf transformation 149]
266. ~room(X0) | curious(X0) | tall(X0) [cnf transformation 151]
274. ~room(X0) | person(X0) [cnf transformation 155]
275. ~brave(X0) | old(X0) [cnf transformation 156]
277. ~room(X0) | wise(X0) | brave(X0) [cnf transformation 171]
291. ~old(mary) | room(sK3) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175]
292. ~old(mary) | mary != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175]
293. ~old(mary) | paul != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175]
294. ~old(mary) | fred != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175]
295. ~old(mary) | alice != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175]
296. ~old(mary) | john != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175]
322. ~old(mary) | john != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,260]
323. ~old(mary) | john != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,259]
324. ~old(mary) | john != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 323,258]
325. ~old(mary) | john != sK3 | ~room(mary) [subsumption resolution 324,257]
326. ~old(mary) | john != sK3 [subsumption resolution 325,256]
328. 6 <=> john = sK3 [avatar definition]
330. john != sK3 <- (~6) [avatar component clause 328]
332. 7 <=> old(mary) [avatar definition]
335. ~6 | ~7 [avatar split clause 326,332,328]
336. ~old(mary) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,260]
337. ~old(mary) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 336,259]
338. ~old(mary) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 337,258]
339. ~old(mary) | alice != sK3 | ~room(mary) [subsumption resolution 338,257]
340. ~old(mary) | alice != sK3 [subsumption resolution 339,256]
342. 8 <=> alice = sK3 [avatar definition]
344. alice != sK3 <- (~8) [avatar component clause 342]
345. ~8 | ~7 [avatar split clause 340,332,342]
346. ~old(mary) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,260]
347. ~old(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 346,259]
348. ~old(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 347,258]
349. ~old(mary) | fred != sK3 | ~room(mary) [subsumption resolution 348,257]
350. ~old(mary) | fred != sK3 [subsumption resolution 349,256]
352. 9 <=> fred = sK3 [avatar definition]
354. fred != sK3 <- (~9) [avatar component clause 352]
355. ~9 | ~7 [avatar split clause 350,332,352]
356. ~old(mary) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 293,260]
357. ~old(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 356,259]
358. ~old(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 357,258]
359. ~old(mary) | paul != sK3 | ~room(mary) [subsumption resolution 358,257]
360. ~old(mary) | paul != sK3 [subsumption resolution 359,256]
362. 10 <=> paul = sK3 [avatar definition]
364. paul != sK3 <- (~10) [avatar component clause 362]
365. ~10 | ~7 [avatar split clause 360,332,362]
366. ~old(mary) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,260]
367. ~old(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 366,259]
368. ~old(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 367,258]
369. ~old(mary) | mary != sK3 | ~room(mary) [subsumption resolution 368,257]
370. ~old(mary) | mary != sK3 [subsumption resolution 369,256]
372. 11 <=> mary = sK3 [avatar definition]
374. mary != sK3 <- (~11) [avatar component clause 372]
375. ~11 | ~7 [avatar split clause 370,332,372]
376. ~old(mary) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,260]
377. ~old(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 376,259]
378. ~old(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 377,258]
379. ~old(mary) | room(sK3) | ~room(mary) [subsumption resolution 378,257]
380. ~old(mary) | room(sK3) [subsumption resolution 379,256]
382. 12 <=> room(sK3) [avatar definition]
384. room(sK3) <- (12) [avatar component clause 382]
385. 12 | ~7 [avatar split clause 380,332,382]
386. person(mary) [resolution 274,256]
401. curious(mary) | tall(mary) [resolution 266,256]
408. 13 <=> tall(mary) [avatar definition]
410. tall(mary) <- (13) [avatar component clause 408]
412. 14 <=> curious(mary) [avatar definition]
414. curious(mary) <- (14) [avatar component clause 412]
415. 13 | 14 [avatar split clause 401,412,408]
469. old(mary) | ~room(mary) <- (13) [resolution 410,262]
473. old(mary) <- (13) [subsumption resolution 469,256]
474. 7 | ~13 [avatar split clause 473,408,332]
509. wise(mary) | brave(mary) [resolution 277,256]
517. 29 <=> brave(mary) [avatar definition]
519. brave(mary) <- (29) [avatar component clause 517]
521. 30 <=> wise(mary) [avatar definition]
524. 29 | 30 [avatar split clause 509,521,517]
579. ~person(mary) | ~wise(mary) | ~room(mary) <- (14) [resolution 265,414]
580. ~wise(mary) | ~room(mary) <- (14) [subsumption resolution 579,386]
581. ~wise(mary) <- (14) [subsumption resolution 580,256]
582. ~30 | ~14 [avatar split clause 581,412,521]
584. old(mary) <- (29) [resolution 519,275]
587. 7 | ~29 [avatar split clause 584,517,332]
714. alice = sK3 | fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (12) [resolution 261,384]
736. fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (~8, 12) [subsumption resolution 714,344]
737. paul = sK3 | mary = sK3 | john = sK3 <- (~8, ~9, 12) [subsumption resolution 736,354]
738. mary = sK3 | john = sK3 <- (~8, ~9, ~10, 12) [subsumption resolution 737,364]
739. john = sK3 <- (~8, ~9, ~10, ~11, 12) [subsumption resolution 738,374]
740. $false <- (~6, ~8, ~9, ~10, ~11, 12) [subsumption resolution 739,330]
741. 6 | 8 | 9 | 10 | 11 | ~12 [avatar contradiction clause 740]
742. $false [avatar sat refutation 335,345,355,365,375,385,415,474,524,582,587,741]
% SZS output end Proof for 576901688325335948522257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0.030733 |
There is a room. If “everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or has lived in exactly three countries” then “everyone in the room who can play the flute enjoys bird watching”. If “everyone outside the room develops open-source software projects in their free time or does not practice zumba” then “everyone in the room who collects modern art writes in-depth travel guides for off-the-beaten-path destinations”. If “not everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals or is not right-handed” then “everyone in the room has a saltwater aquarium if they hosts a YouTube channel dedicated to art tutorials”. “Everyone in the room does not host a YouTube channel dedicated to art tutorials or practices zumba” only if “everyone in the room who hosts a YouTube channel dedicated to art tutorials, is an expert in identifying and foraging wild edible plants or writes in-depth travel guides for off-the-beaten-path destinations hosts themed dinner parties featuring gourmet home-cooked meals”. “No one outside the room does not host a YouTube channel dedicated to art tutorials or enjoys bird watching” if “everyone outside the room does not develop open-source software projects in their free time or enjoys bird watching” and vice versa. Not everyone anywhere who collects modern art hosts themed dinner parties featuring gourmet home-cooked meals. Everyone outside the room creates augmented reality experiences for mobile applications if they can play the flute, has lived in exactly three countries or hosts a YouTube channel dedicated to art tutorials. Everyone in the room does not collect vintage stamps or creates augmented reality experiences for mobile applications. Everyone in the room who hosts a YouTube channel dedicated to art tutorials practices zumba. More than one person anywhere hosts a YouTube channel dedicated to art tutorials. At least one person in the room practices zumba. Everyone in the room who hosts a YouTube channel dedicated to art tutorials, is an expert in identifying and foraging wild edible plants or writes in-depth travel guides for off-the-beaten-path destinations hosts themed dinner parties featuring gourmet home-cooked meals. At least one person in the room collects vintage stamps. At least one person in the room writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room collects vintage stamps if they develops open-source software projects in their free time. Everyone outside the room who hosts themed dinner parties featuring gourmet home-cooked meals is right-handed. | Everyone outside the room has lived in exactly three countries. | neutral | (there_is_a_room)&
((![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))=>(![X]:(room(X)=>(((can_play_the_flute(X))=>(enjoys_bird_watching(X)))))))&
((![X]:(~room(X)=>(((does_not_practice_zumba(X))|(develops_open-source_software_projects_in_their_free_time(X))))))=>(![X]:(room(X)=>(((collects_modern_art(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))&
((~![X]:(room(X)=>(((is_not_right-handed(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))=>(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(has_a_saltwater_aquarium(X)))))))&
((![X]:(room(X)=>(((practices_zumba(X))|(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))=>(![X]:(room(X)=>(((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))&
((![X]:(~room(X)=>(((enjoys_bird_watching(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))<=>(~?[X]:(~room(X)=>(((enjoys_bird_watching(X))|(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X)))))))&
(~![X]:(anywhere(X)=>(((collects_modern_art(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(![X]:(~room(X)=>(((((can_play_the_flute(X))|(has_lived_in_exactly_three_countries(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_collect_vintage_stamps(X))))))&
(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(practices_zumba(X))))))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)&hosts_a_YouTube_channel_dedicated_to_art_tutorials(Y))&(X!=Y))))&
(((?[X]:(room(X)&practices_zumba(X)))))&
(![X]:(room(X)=>(((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(((?[X]:(room(X)&collects_vintage_stamps(X)))))&
(((?[X]:(room(X)&writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))&
(![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(collects_vintage_stamps(X))))))&
(![X]:(~room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(is_right-handed(X))))))&
(![X]:(anywhere(X)=>(((uses_contact_lenses(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(has_lived_in_exactly_three_countries(X))) | [] | null | 0.007998 |
Chad, Jorge are the only persons in the room. Everyone in the room does not own a microscope, is a culinary enthusiast who experiments with international cuisines or is not a dedicated advocate for digital privacy and encryption. Everyone outside the room neither does not have a piercing nor can play the piano. Not everyone outside the room does not enjoy skydiving and has a tattoo if they neither does not host a popular podcast about emerging technologies nor writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room neither owns a microscope nor has lived in exactly three countries. Jorge neither does not host a popular podcast about emerging technologies nor does not mentor a youth basketball team on weekends. Chad does not stream on Twitch and does not enjoy skydiving. Everyone in the room neither does not mentor a youth basketball team on weekends nor does not enjoy making ceramics. Chad is a culinary enthusiast who experiments with international cuisines. Jorge does not own a microscope and does not have a tattoo. Jorge enjoys skydiving and is not a culinary enthusiast who experiments with international cuisines. Everyone in the room neither is not a dedicated advocate for digital privacy and encryption nor does not have a piercing. Everyone in the room uses a Windows laptop and enjoys making ceramics if and only if they can play the piano and has a tattoo. Everyone in the room is a client of LVMH and does not have a tattoo if they can play the piano and has a tattoo. Everyone outside the room enjoys skydiving. Everyone in the room does not practice graffiti art if and only if they does not enjoy skydiving and is not a client of LVMH. Jorge does not own a microscope. Everyone in the room is not a culinary enthusiast who experiments with international cuisines and cannot play the piano if they is not a dedicated advocate for digital privacy and encryption and is a client of Meta. Jorge does not stream on Twitch. | Jorge practices graffiti art. | entailment | room(chad)&room(jorge)&(![X]:(room(X)=>(X='chad'|X='jorge')))&
(![X]:(room(X)=>(((does_not_own_a_microscope(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))&
(![X]:(~room(X)=>(~((does_not_have_a_piercing(X))|(can_play_the_piano(X))))))&
(~![X]:(~room(X)=>(((~((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))=>(((does_not_enjoy_skydiving(X))&(has_a_tattoo(X))))))))&
(![X]:(room(X)=>(~((owns_a_microscope(X))|(has_lived_in_exactly_three_countries(X))))))&
(~((does_not_host_a_popular_podcast_about_emerging_technologies(jorge))|(does_not_mentor_a_youth_basketball_team_on_weekends(jorge))))&
(((does_not_stream_on_Twitch(chad))&(does_not_enjoy_skydiving(chad))))&
(![X]:(room(X)=>(~((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(does_not_enjoy_making_ceramics(X))))))&
(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(chad))&
(((does_not_own_a_microscope(jorge))&(does_not_have_a_tattoo(jorge))))&
(((enjoys_skydiving(jorge))&(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(jorge))))&
(![X]:(room(X)=>(~((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_have_a_piercing(X))))))&
(![X]:(room(X)=>(((((uses_a_Windows_laptop(X))&(enjoys_making_ceramics(X))))<=>(((can_play_the_piano(X))&(has_a_tattoo(X))))))))&
(![X]:(room(X)=>(((((can_play_the_piano(X))&(has_a_tattoo(X))))=>(((is_a_client_of_LVMH(X))&(does_not_have_a_tattoo(X))))))))&
(![X]:(~room(X)=>(enjoys_skydiving(X))))&
(![X]:(room(X)=>(((does_not_practice_graffiti_art(X))<=>(((does_not_enjoy_skydiving(X))&(is_not_a_client_of_LVMH(X))))))))&
(does_not_own_a_microscope(jorge))&
(![X]:(room(X)=>(((((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(is_a_client_of_Meta(X))))=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(cannot_play_the_piano(X))))))))&
(does_not_stream_on_Twitch(jorge)) | room(chad)&room(jorge)&(![X]:(room(X)=>(X='chad'|X='jorge')))&
practices_graffiti_art(jorge) | [
"p0",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6074261973194571963693406
% SZS output start Proof for 6074261973194571963693406
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
54. ~predr(paul) & preda(paul) [input p10]
59. ! [X0] : (room(X0) => (~predg(X0) <=> (~predl(X0) & ~preda(X0)))) [input p15]
63. ~(predg(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
152. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
153. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 152]
161. ! [X0] : ((~predg(X0) <=> (~predl(X0) & ~preda(X0))) | ~room(X0)) [ennf transformation 59]
162. ~predg(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 63]
163. ~predg(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 162]
169. ! [X0] : (((~predg(X0) | (predl(X0) | preda(X0))) & ((~predl(X0) & ~preda(X0)) | predg(X0))) | ~room(X0)) [nnf transformation 161]
170. ! [X0] : (((~predg(X0) | predl(X0) | preda(X0)) & ((~predl(X0) & ~preda(X0)) | predg(X0))) | ~room(X0)) [flattening 169]
171. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom]
172. ~predg(paul) | (paul != sK1 & mary != sK1 & room(sK1)) | ~room(paul) | ~room(mary) [skolemisation 163,171]
253. room(mary) [cnf transformation 153]
254. room(paul) [cnf transformation 153]
255. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 153]
263. preda(paul) [cnf transformation 54]
272. ~preda(X0) | predg(X0) | ~room(X0) [cnf transformation 170]
275. ~predg(paul) | room(sK1) | ~room(paul) | ~room(mary) [cnf transformation 172]
276. ~predg(paul) | mary != sK1 | ~room(paul) | ~room(mary) [cnf transformation 172]
277. ~predg(paul) | paul != sK1 | ~room(paul) | ~room(mary) [cnf transformation 172]
293. ~predg(paul) | paul != sK1 | ~room(mary) [subsumption resolution 277,254]
294. ~predg(paul) | paul != sK1 [subsumption resolution 293,253]
296. 3 <=> paul = sK1 [avatar definition]
298. paul != sK1 <- (~3) [avatar component clause 296]
300. 4 <=> predg(paul) [avatar definition]
303. ~3 | ~4 [avatar split clause 294,300,296]
304. ~predg(paul) | mary != sK1 | ~room(mary) [subsumption resolution 276,254]
305. ~predg(paul) | mary != sK1 [subsumption resolution 304,253]
307. 5 <=> mary = sK1 [avatar definition]
309. mary != sK1 <- (~5) [avatar component clause 307]
310. ~5 | ~4 [avatar split clause 305,300,307]
311. ~predg(paul) | room(sK1) | ~room(mary) [subsumption resolution 275,254]
312. ~predg(paul) | room(sK1) [subsumption resolution 311,253]
314. 6 <=> room(sK1) [avatar definition]
316. room(sK1) <- (6) [avatar component clause 314]
317. 6 | ~4 [avatar split clause 312,300,314]
321. predg(paul) | ~room(paul) [resolution 272,263]
326. predg(paul) [subsumption resolution 321,254]
327. 4 [avatar split clause 326,300]
332. mary = sK1 | paul = sK1 <- (6) [resolution 255,316]
333. paul = sK1 <- (~5, 6) [subsumption resolution 332,309]
334. $false <- (~3, ~5, 6) [subsumption resolution 333,298]
335. 3 | 5 | ~6 [avatar contradiction clause 334]
336. $false [avatar sat refutation 303,310,317,327,335]
% SZS output end Proof for 6074261973194571963693406
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.106093 |
There is a room.
Everyone in the room neither is not hated by Tammy nor does not like Francis only if they hates Tammy.
Everyone in the room is hated by Tammy and likes Roseanna.
Everyone in the room likes Francis if they is hated by Tammy.
Not everyone in the room is hated by Tammy and is hated by Roseanna if they likes Francis.
Everyone outside the room is not liked by Patrick.
Everyone outside the room is not liked by Roseanna, is liked by Tammy and does not like Patrick.
Not everyone outside the room is hated by Francis only if they likes Roseanna.
Everyone outside the room is hated by Patrick. | More than one person in the room is liked by Francis. | neutral | (there_is_a_room)&
(![X]:(room(X)=>(((hate(tammy,X))<=(~((~hate(X,tammy))|(~like(francis,X))))))))&
(![X]:(room(X)=>(((hate(X,tammy))&(like(roseanna,X))))))&
(![X]:(room(X)=>(((hate(X,tammy))=>(like(francis,X))))))&
(~![X]:(room(X)=>(((like(francis,X))=>(((hate(X,tammy))&(hate(X,roseanna))))))))&
(![X]:(~room(X)=>(~like(X,patrick))))&
(![X]:(~room(X)=>(((~like(X,roseanna))&(like(X,tammy))&(~like(patrick,X))))))&
(~![X]:(~room(X)=>(((like(roseanna,X))<=(hate(X,francis))))))&
(![X]:(~room(X)=>(hate(X,patrick))))&
(![X]:(room(X)=>(((((like(patrick,X))&(like(roseanna,X))))<=(like(patrick,X))))))&
(![X]:(room(X)=>(((((like(patrick,X))&(like(roseanna,X))))=>(~hate(patrick,X))))))&
(![X]:(room(X)=>(((like(X,roseanna))<=(~hate(patrick,X))))))&
((![X]:((~like(X,roseanna))=>(((hate(X,patrick))|(~like(X,roseanna))|(~hate(francis,X)))))))&
(![X]:(room(X)=>(((((like(X,roseanna))&(hate(roseanna,X))&(like(X,patrick))))=>(((hate(patrick,X))&(~hate(X,tammy))&(hate(roseanna,X))))))))&
(?[X]:(~room(X)&(like(X,francis)))) | (there_is_a_room)&
(?[X,Y]:(room(X)&room(Y)&(like(X,francis)&like(Y,francis))&(X!=Y))) | [] | null | 0.554912 |
Lula, Victor, Mark are the only persons in the room.
If "everyone in the room does not collect first edition books or collects limited-edition art prints from contemporary artists" then "everyone outside the room who does not collect first edition books enjoys deep-sea diving and exploring underwater caves" otherwise "not everyone outside the room enjoys deep-sea diving and exploring underwater caves".
Everyone anywhere collects first edition books.
Everyone in the room does not collect first edition books or does not enjoy deep-sea diving and exploring underwater caves.
Everyone in the room collects first edition books if they does not collect first edition books.
Everyone in the room collects limited-edition art prints from contemporary artists or does not collect first edition books.
Lula who collects limited-edition art prints from contemporary artists collects first edition books.
If someone collects limited-edition art prints from contemporary artists then he/she collects first edition books.
Everyone in the room collects first edition books if they enjoys deep-sea diving and exploring underwater caves.
Lula collects limited-edition art prints from contemporary artists.
Everyone anywhere collects first edition books if they enjoys deep-sea diving and exploring underwater caves or does not enjoy deep-sea diving and exploring underwater caves or both. | Lula collects first edition books. | entailment | room(lula)&room(victor)&room(mark)&(![X]:(room(X)=>(X='lula'|X='victor'|X='mark')))&
(((![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_collect_first_edition_books(X))))))=>(![X]:(~room(X)=>(((does_not_collect_first_edition_books(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))&((~(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_collect_first_edition_books(X)))))))=>(~![X]:(~room(X)=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))&
(![X]:(anywhere(X)=>(collects_first_edition_books(X))))&
(![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(does_not_collect_first_edition_books(X))))))&
(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))=>(collects_first_edition_books(X))))))&
(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(collects_limited-edition_art_prints_from_contemporary_artists(X))))))&
((collects_limited-edition_art_prints_from_contemporary_artists(lula))&(collects_first_edition_books(lula)))&
((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(collects_first_edition_books(X)))))&
(![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(collects_first_edition_books(X))))))&
(collects_limited-edition_art_prints_from_contemporary_artists(lula))&
(![X]:(anywhere(X)=>(((((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))=>(collects_first_edition_books(X)))))) | room(lula)&room(victor)&room(mark)&(![X]:(room(X)=>(X='lula'|X='victor'|X='mark')))&
collects_first_edition_books(lula) | [
"b4",
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 6015787801095573426239941
% SZS output start Proof for 6015787801095573426239941
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
46. ! [X0] : (anywhere(X0) => predc(X0)) [input p2]
55. ~(predc(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
128. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
129. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 128]
132. ! [X0] : (predc(X0) | ~anywhere(X0)) [ennf transformation 46]
144. ~predc(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 55]
145. ~predc(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 144]
151. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom]
152. ~predc(mary) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 145,151]
153. anywhere(X0) [cnf transformation 5]
234. room(mary) [cnf transformation 129]
235. room(paul) [cnf transformation 129]
236. room(fred) [cnf transformation 129]
237. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 129]
243. predc(X0) | ~anywhere(X0) [cnf transformation 132]
254. ~predc(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152]
255. ~predc(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152]
256. ~predc(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152]
257. ~predc(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152]
290. predc(X0) [subsumption resolution 243,153]
293. fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 257,290]
294. fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 293,236]
295. fred != sK2 | ~room(mary) [subsumption resolution 294,235]
296. fred != sK2 [subsumption resolution 295,234]
297. paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 256,290]
298. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 297,236]
299. paul != sK2 | ~room(mary) [subsumption resolution 298,235]
300. paul != sK2 [subsumption resolution 299,234]
301. mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 255,290]
302. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 301,236]
303. mary != sK2 | ~room(mary) [subsumption resolution 302,235]
304. mary != sK2 [subsumption resolution 303,234]
305. room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 254,290]
306. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 305,236]
307. room(sK2) | ~room(mary) [subsumption resolution 306,235]
308. room(sK2) [subsumption resolution 307,234]
358. paul = sK2 | mary = sK2 | fred = sK2 [resolution 237,308]
359. mary = sK2 | fred = sK2 [subsumption resolution 358,300]
360. fred = sK2 [subsumption resolution 359,304]
361. $false [subsumption resolution 360,296]
% SZS output end Proof for 6015787801095573426239941
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.363957 |
Britt, Joan are the only persons in the room. If “everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations or creates bespoke furniture pieces from reclaimed wood” then “everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations only if they watches fantasy movies”. “Everyone outside the room is not a chess master who participates in national tournaments or creates bespoke furniture pieces from reclaimed wood” only if “everyone in the room writes in-depth travel guides for off-the-beaten-path destinations”. “Everyone in the room creates bespoke furniture pieces from reclaimed wood” unless “at least one person in the room streams on Twitch”. If someone practices archery then he/she creates bespoke furniture pieces from reclaimed wood and vice versa. Everyone in the room does not create large-scale murals for public art installations if they streams on Twitch. Everyone in the room who streams on Twitch creates large-scale murals for public art installations, is a chess master who participates in national tournaments and practices archery. | Britt practices archery. | entailment | room(britt)&room(joan)&(![X]:(room(X)=>(X='britt'|X='joan')))&
((![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))=>(![X]:(room(X)=>(((watches_fantasy_movies(X))<=(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))&
((![X]:(~room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))=>(![X]:(room(X)=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))&
((![X]:(~room(X)=>(((is_not_a_tea_enthusiast(X))|(does_not_practice_graffiti_art(X))))))=>(![X]:(~room(X)=>(((((watches_fantasy_movies(X))&(is_right-handed(X))))=>(((is_right-handed(X))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(is_a_tea_enthusiast(X)))))))))&
((![X]:(~room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))=>(![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))=>(does_not_practice_graffiti_art(X)))))))&
((![X]:(room(X)=>(((is_right-handed(X))|(does_not_practice_graffiti_art(X))))))=>(~?[X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(practices_graffiti_art(X)))))))&
((![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>((creates_bespoke_furniture_pieces_from_reclaimed_wood(joan))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(joan))))&
(~(((?[X]:(room(X)&streams_on_Twitch(X)))))=>(![X]:(room(X)=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))&
(![X]:(room(X)=>(((practices_graffiti_art(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
((creates_large-scale_murals_for_public_art_installations(joan))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(joan)))&
(?[X]:(room(X)&(is_not_a_chess_master_who_participates_in_national_tournaments(X))))&
((![X]:((practices_archery(X))<=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))&
(![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(practices_graffiti_art(X))))))&
(![X]:(room(X)=>(((streams_on_Twitch(X))=>(does_not_create_large-scale_murals_for_public_art_installations(X))))))&
(![X]:(room(X)=>(((is_right-handed(X))<=(is_a_tea_enthusiast(X))))))&
(![X]:(room(X)=>(((streams_on_Twitch(X))=>(((creates_large-scale_murals_for_public_art_installations(X))&(is_a_chess_master_who_participates_in_national_tournaments(X))&(practices_archery(X))))))))&
(![X]:(room(X)=>(((streams_on_Twitch(X))=>(enjoys_snowboarding(X))))))&
(![X]:(room(X)=>(((((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(is_right-handed(X))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))<=(enjoys_snowboarding(X))))))&
(![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<=(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(is_right-handed(X))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))))&
(![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<=(((does_not_create_large-scale_murals_for_public_art_installations(X))&(is_right-handed(X)))))))) | room(britt)&room(joan)&(![X]:(room(X)=>(X='britt'|X='joan')))&
practices_archery(britt) | [
"p0",
"p7",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5171656328829748901592374
% SZS output start Proof for 5171656328829748901592374
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
51. ~? [X0] : (prede(X0) & room(X0)) => ! [X0] : (room(X0) => preda(X0)) [input p7]
55. ! [X0] : (predd(X0) <=> preda(X0)) [input p11]
57. ! [X0] : (room(X0) => (prede(X0) => ~predh(X0))) [input p13]
59. ! [X0] : (room(X0) => (prede(X0) => (predd(X0) & predk(X0) & predh(X0)))) [input p15]
64. ~(predd(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
70. ~? [X0] : (prede(X0) & room(X0)) => ! [X1] : (room(X1) => preda(X1)) [rectify 51]
143. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
144. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 143]
157. ! [X1] : (preda(X1) | ~room(X1)) | ? [X0] : (prede(X0) & room(X0)) [ennf transformation 70]
162. ! [X0] : ((~predh(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 57]
163. ! [X0] : (~predh(X0) | ~prede(X0) | ~room(X0)) [flattening 162]
166. ! [X0] : (((predd(X0) & predk(X0) & predh(X0)) | ~prede(X0)) | ~room(X0)) [ennf transformation 59]
167. ! [X0] : ((predd(X0) & predk(X0) & predh(X0)) | ~prede(X0) | ~room(X0)) [flattening 166]
176. ~predd(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 64]
177. ~predd(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 176]
202. ! [X0] : (preda(X0) | ~room(X0)) | ? [X1] : (prede(X1) & room(X1)) [rectify 157]
203. ? [X1] : (prede(X1) & room(X1)) => (prede(sK8) & room(sK8)) [choice axiom]
204. ! [X0] : (preda(X0) | ~room(X0)) | (prede(sK8) & room(sK8)) [skolemisation 202,203]
207. ! [X0] : ((predd(X0) | ~preda(X0)) & (preda(X0) | ~predd(X0))) [nnf transformation 55]
208. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK10 & mary != sK10 & room(sK10)) [choice axiom]
209. ~predd(mary) | (paul != sK10 & mary != sK10 & room(sK10)) | ~room(paul) | ~room(mary) [skolemisation 177,208]
290. room(mary) [cnf transformation 144]
291. room(paul) [cnf transformation 144]
292. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 144]
320. preda(X0) | ~room(X0) | room(sK8) [cnf transformation 204]
321. preda(X0) | ~room(X0) | prede(sK8) [cnf transformation 204]
328. ~preda(X0) | predd(X0) [cnf transformation 207]
330. ~prede(X0) | ~predh(X0) | ~room(X0) [cnf transformation 163]
332. predh(X0) | ~prede(X0) | ~room(X0) [cnf transformation 167]
341. ~predd(mary) | room(sK10) | ~room(paul) | ~room(mary) [cnf transformation 209]
342. ~predd(mary) | mary != sK10 | ~room(paul) | ~room(mary) [cnf transformation 209]
343. ~predd(mary) | paul != sK10 | ~room(paul) | ~room(mary) [cnf transformation 209]
483. 31 <=> prede(sK8) [avatar definition]
485. prede(sK8) <- (31) [avatar component clause 483]
487. 32 <=> ! [X0] : (preda(X0) | ~room(X0)) [avatar definition]
488. ~room(X0) | preda(X0) <- (32) [avatar component clause 487]
489. 31 | 32 [avatar split clause 321,487,483]
491. 33 <=> room(sK8) [avatar definition]
494. 33 | 32 [avatar split clause 320,487,491]
496. ~prede(X0) | ~room(X0) [subsumption resolution 332,330]
498. ~predd(mary) | paul != sK10 | ~room(mary) [subsumption resolution 343,291]
499. ~predd(mary) | paul != sK10 [subsumption resolution 498,290]
501. 34 <=> paul = sK10 [avatar definition]
503. paul != sK10 <- (~34) [avatar component clause 501]
505. 35 <=> predd(mary) [avatar definition]
507. ~predd(mary) <- (~35) [avatar component clause 505]
508. ~34 | ~35 [avatar split clause 499,505,501]
509. ~predd(mary) | mary != sK10 | ~room(mary) [subsumption resolution 342,291]
510. ~predd(mary) | mary != sK10 [subsumption resolution 509,290]
512. 36 <=> mary = sK10 [avatar definition]
514. mary != sK10 <- (~36) [avatar component clause 512]
515. ~36 | ~35 [avatar split clause 510,505,512]
516. ~predd(mary) | room(sK10) | ~room(mary) [subsumption resolution 341,291]
517. ~predd(mary) | room(sK10) [subsumption resolution 516,290]
519. 37 <=> room(sK10) [avatar definition]
521. room(sK10) <- (37) [avatar component clause 519]
522. 37 | ~35 [avatar split clause 517,505,519]
525. preda(mary) <- (32) [resolution 488,290]
532. predd(mary) <- (32) [resolution 525,328]
533. $false <- (32, ~35) [subsumption resolution 532,507]
534. ~32 | 35 [avatar contradiction clause 533]
535. ~room(sK8) <- (31) [resolution 485,496]
538. ~33 | ~31 [avatar split clause 535,483,491]
636. mary = sK10 | paul = sK10 <- (37) [resolution 292,521]
655. paul = sK10 <- (~36, 37) [subsumption resolution 636,514]
656. $false <- (~34, ~36, 37) [subsumption resolution 655,503]
657. 34 | 36 | ~37 [avatar contradiction clause 656]
658. $false [avatar sat refutation 489,494,508,515,522,534,538,657]
% SZS output end Proof for 5171656328829748901592374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0.295607 |
Jorge is the only person in the room.
If “someone in the room drives a hybrid car” then “Jorge frequently participates in hackathons and coding competitions”.
“Only one person in the room enjoys camping and organizing outdoor survival workshops” unless “Jorge frequently participates in hackathons and coding competitions”.
If “someone in the room drives a hybrid car” then “Jorge is a chess master who participates in national tournaments”.
“Jorge neither can play the flute nor enjoys camping and organizing outdoor survival workshops” if “Jorge can play the flute, cannot play the flute and drives a hybrid car”.
If “Jorge is a drone photographer” then “Jorge has completed a triathlon”.
If “someone in the room collects foreign coins” then “Jorge enjoys camping and organizing outdoor survival workshops, has completed a triathlon and writes a travel blog”. | Jorge collects foreign coins. | neutral | room(jorge)&(![X]:(room(X)=>(X='jorge')))&
((?[X]:(room(X)&(drives_a_hybrid_car(X))))=>(frequently_participates_in_hackathons_and_coding_competitions(jorge)))&
(~(frequently_participates_in_hackathons_and_coding_competitions(jorge))=>(((?[X]:(room(X)&enjoys_camping_and_organizing_outdoor_survival_workshops(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(Y)))=>(X=Y))))))&
((?[X]:(room(X)&(drives_a_hybrid_car(X))))=>(is_a_chess_master_who_participates_in_national_tournaments(jorge)))&
((((can_play_the_flute(jorge))&(cannot_play_the_flute(jorge))&(drives_a_hybrid_car(jorge))))=>(~((can_play_the_flute(jorge))|(enjoys_camping_and_organizing_outdoor_survival_workshops(jorge)))))&
((is_a_drone_photographer(jorge))=>(has_completed_a_triathlon(jorge)))&
((?[X]:(room(X)&(collects_foreign_coins(X))))=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(jorge))&(has_completed_a_triathlon(jorge))&(writes_a_travel_blog(jorge)))))&
((does_not_collect_foreign_coins(jorge))=>(writes_a_travel_blog(jorge)))&
((can_play_the_flute(jorge))=>((?[X,Y]:(room(X)&room(Y)&(((enjoys_kayaking_and_exploring_remote_waterways(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))|(writes_a_travel_blog(X)))&((enjoys_kayaking_and_exploring_remote_waterways(Y))|(is_a_chess_master_who_participates_in_national_tournaments(Y))|(writes_a_travel_blog(Y))))&(X!=Y)))))&
(~(is_a_chess_master_who_participates_in_national_tournaments(jorge))=>(creates_YouTube_content(jorge)))&
(((enjoys_landscape_photography(jorge))=>(((?[X]:(room(X)&has_completed_a_triathlon(X))))))&((~(enjoys_landscape_photography(jorge)))=>((jorge_dream=>(does_not_enjoy_landscape_photography(jorge))))))&
((~((enjoys_landscape_photography(jorge))|(writes_and_illustrates_their_own_graphic_novels(jorge))))=>(((enjoys_stargazing(jorge))&(can_play_the_flute(jorge))&(writes_and_illustrates_their_own_graphic_novels(jorge)))))&
(((does_not_drive_a_hybrid_car(jorge))&(enjoys_kayaking_and_exploring_remote_waterways(jorge))&(creates_YouTube_content(jorge))))&
(enjoys_landscape_photography(jorge))&
(enjoys_stargazing(jorge))&
(writes_and_illustrates_their_own_graphic_novels(jorge))&
(enjoys_camping_and_organizing_outdoor_survival_workshops(jorge))&
((![X]:((frequently_participates_in_hackathons_and_coding_competitions(X))=>(can_play_the_flute(X)))))&
(writes_a_travel_blog(jorge))&
(is_not_a_client_of_LVMH(jorge))&
(is_a_chess_master_who_participates_in_national_tournaments(jorge))&
((jorge_dream=>(has_completed_a_triathlon(jorge))))&
(has_completed_a_triathlon(jorge))&
(?[X]:(room(X)&(has_completed_a_triathlon(X))))&
(is_not_a_drone_photographer(jorge))&
((enjoys_camping_and_organizing_outdoor_survival_workshops(jorge))&(creates_YouTube_content(jorge)))&
((![X]:((((writes_a_travel_blog(X))<~>(enjoys_kayaking_and_exploring_remote_waterways(X))))=>(enjoys_stargazing(X))))) | room(jorge)&(![X]:(room(X)=>(X='jorge')))&
collects_foreign_coins(jorge) | [] | null | 0.2483 |
Mildred is the only person in the room.
Mildred who likes William either does not like Sarah or is liked by William but not both.
Everyone in the room who is not liked by William does not hate Sarah and does not like Sarah.
If someone hates William then he/she is hated by Sarah.
Everyone in the room either is liked by Sarah or does not like William but not both if they is not liked by William.
Mildred dreamt that 'everyone outside the room does not like Sarah if they either is liked by Sarah or does not like William but not both'.
Everyone in the room who does not like Sarah either likes William or is liked by Sarah but not both.
Mildred is hated by Sarah. | Mildred likes Sarah. | entailment | room(mildred)&(![X]:(room(X)=>(X='mildred')))&
((like(william,mildred))&(((~like(sarah,mildred))<~>(like(mildred,william)))))&
(![X]:(room(X)=>(((~like(X,william))=>(((~hate(sarah,X))&(~like(sarah,X))))))))&
((![X]:((hate(william,X))=>(hate(X,sarah)))))&
(![X]:(room(X)=>(((~like(X,william))=>(((like(X,sarah))<~>(~like(william,X))))))))&
((mildred_dream=>(![X]:(~room(X)=>(((((like(X,sarah))<~>(~like(william,X))))=>(~like(sarah,X))))))))&
(![X]:(room(X)=>(((~like(sarah,X))=>(((like(william,X))<~>(like(X,sarah))))))))&
(hate(mildred,sarah)) | room(mildred)&(![X]:(room(X)=>(X='mildred')))&
like(sarah,mildred) | [
"b0",
"b42",
"p0",
"p1",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7391756938224581790620319
% SZS output start Proof for 7391756938224581790620319
1. ! [X0,X1] : (X0 != X1 => (like(X0,X1) => ~hate(X0,X1))) [input b0]
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) => mary = X0) & room(mary) [input p0]
45. (~like(paul,mary) <~> like(mary,fred)) & like(fred,mary) [input p1]
48. ! [X0] : (room(X0) => (~like(X0,fred) => (like(X0,paul) <~> ~like(fred,X0)))) [input p4]
51. hate(mary,paul) [input p7]
52. ~(like(paul,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
57. ! [X0,X1] : ((~hate(X0,X1) | ~like(X0,X1)) | X0 = X1) [ennf transformation 1]
58. ! [X0,X1] : (~hate(X0,X1) | ~like(X0,X1) | X0 = X1) [flattening 57]
128. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
132. ! [X0] : (((like(X0,paul) <~> ~like(fred,X0)) | like(X0,fred)) | ~room(X0)) [ennf transformation 48]
133. ! [X0] : ((like(X0,paul) <~> ~like(fred,X0)) | like(X0,fred) | ~room(X0)) [flattening 132]
136. ~like(paul,mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 52]
138. ((~like(mary,fred) | like(paul,mary)) & (like(mary,fred) | ~like(paul,mary))) & like(fred,mary) [nnf transformation 45]
139. (~like(mary,fred) | like(paul,mary)) & (like(mary,fred) | ~like(paul,mary)) & like(fred,mary) [flattening 138]
140. ! [X0] : (((like(fred,X0) | ~like(X0,paul)) & (~like(fred,X0) | like(X0,paul))) | like(X0,fred) | ~room(X0)) [nnf transformation 133]
142. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom]
143. ~like(paul,mary) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 136,142]
144. ~hate(X0,X1) | ~like(X0,X1) | X0 = X1 [cnf transformation 58]
190. mary != paul [cnf transformation 43]
226. room(mary) [cnf transformation 128]
227. ~room(X0) | mary = X0 [cnf transformation 128]
228. like(fred,mary) [cnf transformation 139]
230. ~like(mary,fred) | like(paul,mary) [cnf transformation 139]
234. ~like(fred,X0) | like(X0,paul) | like(X0,fred) | ~room(X0) [cnf transformation 140]
238. hate(mary,paul) [cnf transformation 51]
239. ~like(paul,mary) | room(sK0) | ~room(mary) [cnf transformation 143]
240. ~like(paul,mary) | mary != sK0 | ~room(mary) [cnf transformation 143]
242. 1 <=> like(paul,mary) [avatar definition]
246. 2 <=> like(mary,fred) [avatar definition]
249. 1 | ~2 [avatar split clause 230,246,242]
251. ~like(paul,mary) | mary != sK0 [subsumption resolution 240,226]
253. 3 <=> mary = sK0 [avatar definition]
255. mary != sK0 <- (~3) [avatar component clause 253]
256. ~3 | ~1 [avatar split clause 251,242,253]
257. ~like(paul,mary) | room(sK0) [subsumption resolution 239,226]
259. 4 <=> room(sK0) [avatar definition]
261. room(sK0) <- (4) [avatar component clause 259]
262. 4 | ~1 [avatar split clause 257,242,259]
264. ~like(mary,paul) | mary = paul [resolution 144,238]
265. ~like(mary,paul) [subsumption resolution 264,190]
308. like(mary,paul) | like(mary,fred) | ~room(mary) [resolution 234,228]
309. like(mary,fred) | ~room(mary) [subsumption resolution 308,265]
313. like(mary,fred) [subsumption resolution 309,226]
314. 2 [avatar split clause 313,246]
315. mary = sK0 <- (4) [resolution 261,227]
316. $false <- (~3, 4) [subsumption resolution 315,255]
317. 3 | ~4 [avatar contradiction clause 316]
318. $false [avatar sat refutation 249,256,262,314,317]
% SZS output end Proof for 7391756938224581790620319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Barbara, Victor, David, Billie, Louise are the only persons in the room.
No quiet person is tall.
At least one person in the room is old.
If someone is not a tall person then he/she is a old person and vice versa.
Everyone in the room is old if they is not old.
Everyone in the room is tall if they is not a quiet person and vice versa.
Everyone in the room is tall if they is not a quiet person.
All tall persons are quiet.
All tall persons are old. | Victor and David are respectively old and quiet. | entailment | room(barbara)&room(victor)&room(david)&room(billie)&room(louise)&(![X]:(room(X)=>(X='barbara'|X='victor'|X='david'|X='billie'|X='louise')))&
(~?[X]:(quiet(X)=>tall(X)))&
(((?[X]:(room(X)&old(X)))))&
((![X]:((~(tall(X)&person(X)))<=>(old(X)&person(X)))))&
(![X]:(room(X)=>(((~old(X))=>(old(X))))))&
(![X]:(room(X)=>(((tall(X))<=>(~(quiet(X)&person(X)))))))&
(![X]:(room(X)=>(((~(quiet(X)&person(X)))=>(tall(X))))))&
(![X]:(tall(X)=>quiet(X)))&
(![X]:(tall(X)=>old(X))) | room(barbara)&room(victor)&room(david)&room(billie)&room(louise)&(![X]:(room(X)=>(X='barbara'|X='victor'|X='david'|X='billie'|X='louise')))&
(old(victor))&(quiet(david)) | [
"p0",
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6464756781866050048731044
% SZS output start Proof for 6464756781866050048731044
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] : (quiet(X0) => tall(X0)) [input p1]
47. ! [X0] : (~(person(X0) & tall(X0)) <=> (person(X0) & old(X0))) [input p3]
53. ~(quiet(fred) & old(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]
126. ! [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]
127. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126]
128. ! [X0] : (~tall(X0) & quiet(X0)) [ennf transformation 45]
129. ! [X0] : ((~person(X0) | ~tall(X0)) <=> (person(X0) & old(X0))) [ennf transformation 47]
137. ~quiet(fred) | ~old(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 53]
138. ~quiet(fred) | ~old(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 137]
142. ! [X0] : (((~person(X0) | ~tall(X0)) | (~person(X0) | ~old(X0))) & ((person(X0) & old(X0)) | (person(X0) & tall(X0)))) [nnf transformation 129]
143. ! [X0] : ((~person(X0) | ~tall(X0) | ~person(X0) | ~old(X0)) & ((person(X0) & old(X0)) | (person(X0) & tall(X0)))) [flattening 142]
146. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK1 & alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom]
147. ~quiet(fred) | ~old(paul) | (john != sK1 & alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 138,146]
228. room(mary) [cnf transformation 127]
229. room(paul) [cnf transformation 127]
230. room(fred) [cnf transformation 127]
231. room(alice) [cnf transformation 127]
232. room(john) [cnf transformation 127]
233. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 127]
234. quiet(X0) [cnf transformation 128]
235. ~tall(X0) [cnf transformation 128]
238. old(X0) | tall(X0) [cnf transformation 143]
251. ~quiet(fred) | ~old(paul) | room(sK1) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147]
252. ~quiet(fred) | ~old(paul) | mary != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147]
253. ~quiet(fred) | ~old(paul) | paul != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147]
254. ~quiet(fred) | ~old(paul) | fred != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147]
255. ~quiet(fred) | ~old(paul) | alice != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147]
256. ~quiet(fred) | ~old(paul) | john != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147]
260. old(X0) [subsumption resolution 238,235]
261. ~old(paul) | john != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 256,234]
262. john != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,260]
263. john != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,232]
264. john != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 263,231]
265. john != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 264,230]
266. john != sK1 | ~room(mary) [subsumption resolution 265,229]
267. john != sK1 [subsumption resolution 266,228]
268. ~old(paul) | alice != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 255,234]
269. alice != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,260]
270. alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,232]
271. alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,231]
272. alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 271,230]
273. alice != sK1 | ~room(mary) [subsumption resolution 272,229]
274. alice != sK1 [subsumption resolution 273,228]
275. ~old(paul) | fred != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 254,234]
276. fred != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,260]
277. fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,232]
278. fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,231]
279. fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 278,230]
280. fred != sK1 | ~room(mary) [subsumption resolution 279,229]
281. fred != sK1 [subsumption resolution 280,228]
282. ~old(paul) | paul != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 253,234]
283. paul != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,260]
284. paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,232]
285. paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,231]
286. paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 285,230]
287. paul != sK1 | ~room(mary) [subsumption resolution 286,229]
288. paul != sK1 [subsumption resolution 287,228]
289. ~old(paul) | mary != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 252,234]
290. mary != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,260]
291. mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,232]
292. mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,231]
293. mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 292,230]
294. mary != sK1 | ~room(mary) [subsumption resolution 293,229]
295. mary != sK1 [subsumption resolution 294,228]
296. ~old(paul) | room(sK1) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 251,234]
297. room(sK1) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,260]
298. room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 297,232]
299. room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 298,231]
300. room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 299,230]
301. room(sK1) | ~room(mary) [subsumption resolution 300,229]
302. room(sK1) [subsumption resolution 301,228]
351. alice = sK1 | fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 [resolution 233,302]
373. fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 [subsumption resolution 351,274]
374. paul = sK1 | mary = sK1 | john = sK1 [subsumption resolution 373,281]
375. mary = sK1 | john = sK1 [subsumption resolution 374,288]
376. john = sK1 [subsumption resolution 375,295]
377. $false [subsumption resolution 376,267]
% SZS output end Proof for 6464756781866050048731044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Daniel, Donna are the only persons in the room.
Everyone in the room who does not work on fridays bakes bread at home.
Everyone in the room who bakes bread at home does enjoy mountain biking.
Only one person in the room works on fridays. | Everyone in the room does not enjoy mountain biking. | contradiction | room(daniel)&room(donna)&(![X]:(room(X)=>(X='daniel'|X='donna')))&
(![X]:(room(X)=>(((bakes_bread_at_home(X))=>(collect_rare_sneakers(X))))))&
(![X]:(room(X)=>(((collects_antique_jewelry(X))=>(enjoys_stand-up_paddleboarding(X))))))&
(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(is_a_client_of_Meta(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))&
((![X]:((owns_a_3D_printer(X))<=>(~((collects_comic_books(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))&
(![X]:(room(X)=>(((does_not_bake_bread_at_home(X))<=>(has_lived_in_exactly_three_countries(X))))))&
((?[X,Y]:(room(X)&room(Y)&(does_not_participate_in_long-distance_cycling_events_across_the_country(X)&does_not_participate_in_long-distance_cycling_events_across_the_country(Y))&(X!=Y))))&
(![X]:(room(X)=>(((does_not_work_on_fridays(X))=>(makes_homemade_pastries(X))))))&
(![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))&
(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(does_enjoy_mountain_biking(X))))))&
(![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<=>(does_not_work_on_fridays(X))))))&
(![X]:(room(X)=>(((does_not_work_on_fridays(X))=>(bakes_bread_at_home(X))))))&
(![X]:(room(X)=>(((bakes_bread_at_home(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
((![X]:((has_lived_in_exactly_three_countries(X))=>(makes_homemade_pastries(X)))))&
(![X]:(room(X)=>(((bakes_bread_at_home(X))=>(does_enjoy_mountain_biking(X))))))&
(((?[X]:(room(X)&~((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))&(![X,Y]:((room(X)&room(Y)&(~((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))&(~((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(Y))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(Y)))))=>(X=Y)))))&
(![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(((collect_rare_sneakers(X))&(enjoys_coding_in_Python(X))))))))&
(![X]:(room(X)=>(((((collect_rare_sneakers(X))&(enjoys_coding_in_Python(X))))<=>(collects_antique_jewelry(X))))))&
(![X]:(room(X)=>(((collects_antique_jewelry(X))=>(owns_a_3D_printer(X))))))&
(((?[X]:(room(X)&is_a_Linux_enthusiast(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_Linux_enthusiast(X))&(is_a_Linux_enthusiast(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(((?[X]:(room(X)&works_on_fridays(X)))&(![X,Y]:((room(X)&room(Y)&(works_on_fridays(X))&(works_on_fridays(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((((bakes_bread_at_home(X))&(enjoys_coding_in_Python(X))))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
((![X]:((owns_a_3D_printer(X))<=>(is_a_Linux_enthusiast(X)))))&
(![X]:(room(X)=>(((works_on_fridays(X))<=>(is_a_coffee_connoisseur(X)))))) | room(daniel)&room(donna)&(![X]:(room(X)=>(X='daniel'|X='donna')))&
![X]:(room(X)=>(does_not_enjoy_mountain_biking(X))) | [
"b42",
"p0",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2977763795434700826154582
% SZS output start Proof for 2977763795434700826154582
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) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
56. ! [X0] : (room(X0) => (~predd(X0) => predl(X0))) [input p12]
59. ! [X0] : (room(X0) => (predl(X0) => predn(X0))) [input p15]
66. ! [X0,X1] : ((predd(X1) & predd(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predd(X0) & room(X0)) [input p22]
70. ! [X0] : (room(X0) => ~predn(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
73. ! [X0,X1] : ((predd(X1) & predd(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predd(X2) & room(X2)) [rectify 66]
74. ! [X0] : (room(X0) => ~predn(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 70]
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]
168. ! [X0] : ((predl(X0) | predd(X0)) | ~room(X0)) [ennf transformation 56]
169. ! [X0] : (predl(X0) | predd(X0) | ~room(X0)) [flattening 168]
170. ! [X0] : ((predn(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 59]
171. ! [X0] : (predn(X0) | ~predl(X0) | ~room(X0)) [flattening 170]
181. ! [X0,X1] : (X0 = X1 | (~predd(X1) | ~predd(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predd(X2) & room(X2)) [ennf transformation 73]
182. ! [X0,X1] : (X0 = X1 | ~predd(X1) | ~predd(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predd(X2) & room(X2)) [flattening 181]
186. ! [X0] : (~predn(X0) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 74]
187. ! [X0] : (~predn(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 186]
201. ? [X2] : (predd(X2) & room(X2)) => (predd(sK4) & room(sK4)) [choice axiom]
202. ! [X0,X1] : (X0 = X1 | ~predd(X1) | ~predd(X0) | ~room(X1) | ~room(X0)) & (predd(sK4) & room(sK4)) [skolemisation 182,201]
249. mary != paul [cnf transformation 43]
285. room(mary) [cnf transformation 154]
286. room(paul) [cnf transformation 154]
303. ~room(X0) | predd(X0) | predl(X0) [cnf transformation 169]
304. ~predl(X0) | predn(X0) | ~room(X0) [cnf transformation 171]
320. ~predd(X1) | X0 = X1 | ~predd(X0) | ~room(X1) | ~room(X0) [cnf transformation 202]
329. ~predn(X0) | ~room(X0) [cnf transformation 187]
346. 2 <=> predl(mary) [avatar definition]
348. predl(mary) <- (2) [avatar component clause 346]
355. 4 <=> predl(paul) [avatar definition]
357. predl(paul) <- (4) [avatar component clause 355]
426. 16 <=> predd(mary) [avatar definition]
428. predd(mary) <- (16) [avatar component clause 426]
435. 18 <=> predd(paul) [avatar definition]
437. predd(paul) <- (18) [avatar component clause 435]
475. predd(mary) | predl(mary) [resolution 303,285]
476. predd(paul) | predl(paul) [resolution 303,286]
489. 4 | 18 [avatar split clause 476,435,355]
491. predn(mary) | ~room(mary) <- (2) [resolution 304,348]
492. predn(mary) <- (2) [subsumption resolution 491,285]
652. ~room(mary) <- (2) [resolution 492,329]
653. $false <- (2) [subsumption resolution 652,285]
654. ~2 [avatar contradiction clause 653]
655. 2 | 16 [avatar split clause 475,426,346]
725. paul = X0 | ~predd(X0) | ~room(paul) | ~room(X0) <- (18) [resolution 320,437]
727. ~predd(X0) | paul = X0 | ~room(X0) <- (18) [subsumption resolution 725,286]
730. mary = paul | ~room(mary) <- (16, 18) [resolution 727,428]
731. ~room(mary) <- (16, 18) [subsumption resolution 730,249]
732. $false <- (16, 18) [subsumption resolution 731,285]
733. ~16 | ~18 [avatar contradiction clause 732]
788. predn(paul) | ~room(paul) <- (4) [resolution 357,304]
790. predn(paul) <- (4) [subsumption resolution 788,286]
830. ~room(paul) <- (4) [resolution 790,329]
831. $false <- (4) [subsumption resolution 830,286]
832. ~4 [avatar contradiction clause 831]
833. $false [avatar sat refutation 489,654,655,733,832]
% SZS output end Proof for 2977763795434700826154582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0.264763 |
Kirk is the only person in the room. Kirk is a cybersecurity expert. No one anywhere does not practice tai chi or practices tai chi or both only if they uses a Windows laptop. Everyone in the room can play the piano. Everyone in the room collects luxury watches if they is a cybersecurity expert. Kirk practices tai chi. Someone outside the room practices tai chi. Everyone in the room can play the piano if they does not use a Windows laptop and vice versa. | Kirk collects luxury watches, practices tai chi and can play the piano. | entailment | room(kirk)&(![X]:(room(X)=>(X='kirk')))&
(is_a_cybersecurity_expert(kirk))&
(~?[X]:(anywhere(X)=>(((uses_a_Windows_laptop(X))<=(((does_not_practice_tai_chi(X))|(practices_tai_chi(X))))))))&
(![X]:(room(X)=>(can_play_the_piano(X))))&
(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(collects_luxury_watches(X))))))&
(practices_tai_chi(kirk))&
(?[X]:(~room(X)&(practices_tai_chi(X))))&
(![X]:(room(X)=>(((can_play_the_piano(X))<=>(does_not_use_a_Windows_laptop(X)))))) | room(kirk)&(![X]:(room(X)=>(X='kirk')))&
((collects_luxury_watches(kirk))&(practices_tai_chi(kirk))&(can_play_the_piano(kirk))) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 69176234147208534179807
% SZS output start Proof for 69176234147208534179807
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
45. predf(mary) [input p1]
47. ! [X0] : (room(X0) => predb(X0)) [input p3]
48. ! [X0] : (room(X0) => (predf(X0) => prede(X0))) [input p4]
49. preda(mary) [input p5]
52. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
126. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
128. ! [X0] : (predb(X0) | ~room(X0)) [ennf transformation 47]
129. ! [X0] : ((prede(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 48]
130. ! [X0] : (prede(X0) | ~predf(X0) | ~room(X0)) [flattening 129]
132. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 52]
137. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom]
138. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 132,137]
219. room(mary) [cnf transformation 126]
220. ~room(X0) | mary = X0 [cnf transformation 126]
221. predf(mary) [cnf transformation 45]
224. ~room(X0) | predb(X0) [cnf transformation 128]
225. ~predf(X0) | prede(X0) | ~room(X0) [cnf transformation 130]
226. preda(mary) [cnf transformation 49]
231. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK1) | ~room(mary) [cnf transformation 138]
232. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [cnf transformation 138]
233. ~predb(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 232,226]
234. ~predb(mary) | ~prede(mary) | mary != sK1 [subsumption resolution 233,219]
236. 1 <=> mary = sK1 [avatar definition]
238. mary != sK1 <- (~1) [avatar component clause 236]
240. 2 <=> prede(mary) [avatar definition]
244. 3 <=> predb(mary) [avatar definition]
247. ~1 | ~2 | ~3 [avatar split clause 234,244,240,236]
248. ~predb(mary) | ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 231,226]
249. ~predb(mary) | ~prede(mary) | room(sK1) [subsumption resolution 248,219]
251. 4 <=> room(sK1) [avatar definition]
253. room(sK1) <- (4) [avatar component clause 251]
254. 4 | ~2 | ~3 [avatar split clause 249,244,240,251]
255. predb(mary) [resolution 224,219]
256. 3 [avatar split clause 255,244]
258. prede(mary) | ~room(mary) [resolution 225,221]
262. prede(mary) [subsumption resolution 258,219]
263. 2 [avatar split clause 262,240]
264. mary = sK1 <- (4) [resolution 253,220]
266. $false <- (~1, 4) [subsumption resolution 264,238]
267. 1 | ~4 [avatar contradiction clause 266]
268. $false [avatar sat refutation 247,254,256,263,267]
% SZS output end Proof for 69176234147208534179807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Tommie is the only person in the room.
Only one person in the room neither does not like Sherry nor does not like Mattie.
Everyone in the room who is liked by Anthony does not like Anthony.
If someone does not like Mattie then he/she either does not like Anthony or likes Anthony but not both.
Tommie does not like Anthony.
Tommie and Mattie like each other. | Tommie is liked by Sherry. | neutral | room(tommie)&(![X]:(room(X)=>(X='tommie')))&
(((?[X]:(room(X)&~((~like(sherry,X))|(~like(mattie,X)))))&(![X,Y]:((room(X)&room(Y)&(~((~like(sherry,X))|(~like(mattie,X))))&(~((~like(sherry,Y))|(~like(mattie,Y)))))=>(X=Y)))))&
(![X]:(room(X)=>(((like(X,anthony))=>(~like(anthony,X))))))&
((![X]:((~like(mattie,X))=>(((~like(anthony,X))<~>(like(anthony,X)))))))&
(~like(anthony,tommie))&
((like(tommie,mattie) & like(mattie,tommie))) | room(tommie)&(![X]:(room(X)=>(X='tommie')))&
like(tommie,sherry) | [] | null | 0.677419 |
Lisa, Joseph, Steven, Brian, Rose are the only persons in the room.
“Everyone in the room is an avid collector of autographed memorabilia from famous musicians or does not collect luxury watches” only if “Joseph is an avid collector of autographed memorabilia from famous musicians”.
Everyone anywhere designs and sews custom cosplay costumes for conventions if and only if they enjoys virtual reality gaming.
Joseph is an avid collector of autographed memorabilia from famous musicians.
Everyone in the room who enjoys landscape photography has a tattoo.
Joseph is passionate about collecting and restoring classic cars.
Someone in the room does not host themed dinner parties featuring gourmet home-cooked meals.
Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations, is a skilled home brewer experimenting with craft beer recipes and has a specialized collection of handmade artisan pottery if they does not enjoy landscape photography, does not have a tattoo or has a tattoo.
Everyone in the room who neither enjoys landscape photography nor enjoys skydiving is right-handed.
Everyone in the room is right-handed only if they enjoys landscape photography.
Everyone in the room who enjoys landscape photography writes in-depth travel guides for off-the-beaten-path destinations.
Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations if and only if they collects luxury watches.
Brian hosts regular workshops on creative writing.
Joseph enjoys wildlife photography. | It is not the case that “Lisa has a specialized collection of handmade artisan pottery”. | contradiction | room(lisa)&room(joseph)&room(steven)&room(brian)&room(rose)&(![X]:(room(X)=>(X='lisa'|X='joseph'|X='steven'|X='brian'|X='rose')))&
((![X]:(room(X)=>(((does_not_collect_luxury_watches(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(joseph)))&
(![X]:(anywhere(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(enjoys_virtual_reality_gaming(X))))))&
(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(joseph))&
(![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(has_a_tattoo(X))))))&
(is_passionate_about_collecting_and_restoring_classic_cars(joseph))&
(?[X]:(room(X)&(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))&
(![X]:(room(X)=>(((((does_not_enjoy_landscape_photography(X))|(does_not_have_a_tattoo(X))|(has_a_tattoo(X))))=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))&
(![X]:(room(X)=>(((~((enjoys_landscape_photography(X))|(enjoys_skydiving(X))))=>(is_right-handed(X))))))&
(![X]:(room(X)=>(((enjoys_landscape_photography(X))<=(is_right-handed(X))))))&
(![X]:(room(X)=>(((enjoys_landscape_photography(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_luxury_watches(X))))))&
(hosts_regular_workshops_on_creative_writing(brian))&
(enjoys_wildlife_photography(joseph)) | room(lisa)&room(joseph)&room(steven)&room(brian)&room(rose)&(![X]:(room(X)=>(X='lisa'|X='joseph'|X='steven'|X='brian'|X='rose')))&
~(has_a_specialized_collection_of_handmade_artisan_pottery(lisa)) | [
"p0",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1524421121413537731143754
% SZS output start Proof for 1524421121413537731143754
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]
51. ! [X0] : (room(X0) => ((predv(X0) | ~predv(X0) | ~preda(X0)) => (predl(X0) & predg(X0) & predy(X0)))) [input p7]
58. ~predl(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]
63. ! [X0] : (room(X0) => ((predv(X0) | ~predv(X0) | ~preda(X0)) => (predl(X0) & predy(X0)))) [pure predicate removal 51]
137. ! [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]
138. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 137]
144. ! [X0] : (((predl(X0) & predy(X0)) | (~predv(X0) & predv(X0) & preda(X0))) | ~room(X0)) [ennf transformation 63]
145. ! [X0] : ((predl(X0) & predy(X0)) | (~predv(X0) & predv(X0) & preda(X0)) | ~room(X0)) [flattening 144]
149. ~predl(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 58]
150. ~predl(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 149]
239. room(mary) [cnf transformation 138]
257. predl(X0) | predv(X0) | ~room(X0) [cnf transformation 145]
258. predl(X0) | ~predv(X0) | ~room(X0) [cnf transformation 145]
268. ~predl(mary) [cnf transformation 150]
291. ~room(X0) | predl(X0) [subsumption resolution 257,258]
294. predl(mary) [resolution 291,239]
300. $false [subsumption resolution 294,268]
% SZS output end Proof for 1524421121413537731143754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
There is a room.
If no one anywhere is not a craft beer aficionado or is a Linux enthusiast then if someone hosts a popular podcast about emerging technologies then he/she enjoys wildlife photography and vice versa.
Not everyone outside the room is an expert in identifying and foraging wild edible plants if they makes homemade pastries.
Not everyone in the room who is an expert in identifying and foraging wild edible plants makes homemade pastries.
Everyone outside the room who travels domestically frequently can play the flute.
If someone collects luxury watches then he/she collects classic novels and vice versa.
Everyone in the room who enjoys windsurfing is an amateur astronomer who builds and uses custom telescopes.
Someone in the room enjoys landscape photography.
Everyone in the room who regularly goes on multi-day backpacking trips in national parks creates large-scale murals for public art installations. | Everyone outside the room is an expert in identifying and foraging wild edible plants. | contradiction | (there_is_a_room)&
((~?[X]:(anywhere(X)=>(((is_a_Linux_enthusiast(X))|(is_not_a_craft_beer_aficionado(X))))))=>((![X]:((hosts_a_popular_podcast_about_emerging_technologies(X))<=>(enjoys_wildlife_photography(X))))))&
(~![X]:(~room(X)=>(((makes_homemade_pastries(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))=>(makes_homemade_pastries(X))))))&
(![X]:(~room(X)=>(((travels_domestically_frequently(X))=>(can_play_the_flute(X))))))&
((![X]:((collects_luxury_watches(X))<=>(collects_classic_novels(X)))))&
(![X]:(room(X)=>(((enjoys_windsurfing(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))&
(?[X]:(room(X)&(enjoys_landscape_photography(X))))&
(![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))&
(![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(hosts_regular_workshops_on_creative_writing(X))))))&
(![X]:(room(X)=>(((enjoys_windsurfing(X))=>(travels_domestically_frequently(X))))))&
((?[X,Y]:(room(X)&room(Y)&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)&is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(Y))&(X!=Y))))&
((![X]:((plays_video_games(X))<=>(enjoys_windsurfing(X))))) | (there_is_a_room)&
![X]:(~room(X)=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1010012082333606475525051
% SZS output start Proof for 1010012082333606475525051
46. ~! [X0] : (~room(X0) => (predo(X0) => predc(X0))) [input p2]
57. ! [X0] : (~room(X0) => predc(X0)) & there_is_a_room [input hypothesis]
69. ! [X0] : (~room(X0) => predc(X0)) [pure predicate removal 57]
141. ? [X0] : ((~predc(X0) & predo(X0)) & ~room(X0)) [ennf transformation 46]
142. ? [X0] : (~predc(X0) & predo(X0) & ~room(X0)) [flattening 141]
145. ! [X0] : (predc(X0) | room(X0)) [ennf transformation 69]
147. ? [X0] : (~predc(X0) & predo(X0) & ~room(X0)) => (~predc(sK0) & predo(sK0) & ~room(sK0)) [choice axiom]
148. ~predc(sK0) & predo(sK0) & ~room(sK0) [skolemisation 142,147]
235. ~room(sK0) [cnf transformation 148]
237. ~predc(sK0) [cnf transformation 148]
245. predc(X0) | room(X0) [cnf transformation 145]
246. room(sK0) [resolution 245,237]
247. $false [subsumption resolution 246,235]
% SZS output end Proof for 1010012082333606475525051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.491135 |
There is a room.
Everyone in the room who maintains a personal blog focused on cybersecurity tips either plays the drums or drives a hybrid car but not both.
Everyone in the room does not play the drums or either plays the drums or drives a hybrid car but not both.
Everyone in the room who does not play the drums does not volunteer for local environmental conservation projects.
If someone can play the flute or enjoys spelunking or both then he/she can play the piano.
Everyone anywhere collects luxury watches if they either does not own a microscope or can play the flute but not both.
Everyone in the room who collects luxury watches either cannot play the flute or is a client of Meta but not both.
If someone drives a hybrid car then he/she enjoys spelunking, plays eSports competitively and can play the flute.
Everyone in the room who does not maintain a personal blog focused on cybersecurity tips is a client of Meta.
If someone is right-handed then he/she competes in national level swimming championships and vice versa.
Everyone anywhere who plays the drums owns a microscope.
Everyone anywhere can play the piano if they owns a microscope.
Everyone in the room plays eSports competitively.
Everyone in the room plays as a goalkeeper for a local amateur soccer team if they plays eSports competitively.
Everyone in the room is right-handed if they plays as a goalkeeper for a local amateur soccer team. | Everyone in the room is not a client of Meta or can play the piano. | entailment | (there_is_a_room)&
(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(((plays_the_drums(X))<~>(drives_a_hybrid_car(X))))))))&
(![X]:(room(X)=>(((((plays_the_drums(X))<~>(drives_a_hybrid_car(X))))|(does_not_play_the_drums(X))))))&
(![X]:(room(X)=>(((does_not_play_the_drums(X))=>(does_not_volunteer_for_local_environmental_conservation_projects(X))))))&
((![X]:((((can_play_the_flute(X))|(enjoys_spelunking(X))))=>(can_play_the_piano(X)))))&
(![X]:(anywhere(X)=>(((((does_not_own_a_microscope(X))<~>(can_play_the_flute(X))))=>(collects_luxury_watches(X))))))&
(![X]:(room(X)=>(((collects_luxury_watches(X))=>(((cannot_play_the_flute(X))<~>(is_a_client_of_Meta(X))))))))&
((![X]:((drives_a_hybrid_car(X))=>(((enjoys_spelunking(X))&(plays_eSports_competitively(X))&(can_play_the_flute(X)))))))&
(![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))=>(is_a_client_of_Meta(X))))))&
((![X]:((is_right-handed(X))<=>(competes_in_national_level_swimming_championships(X)))))&
(![X]:(anywhere(X)=>(((plays_the_drums(X))=>(owns_a_microscope(X))))))&
(![X]:(anywhere(X)=>(((owns_a_microscope(X))=>(can_play_the_piano(X))))))&
(![X]:(room(X)=>(plays_eSports_competitively(X))))&
(![X]:(room(X)=>(((plays_eSports_competitively(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(is_right-handed(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((can_play_the_piano(X))|(is_not_a_client_of_Meta(X))))) | [
"b4",
"p0",
"p4",
"p5",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2218241674405897121675416
% SZS output start Proof for 2218241674405897121675416
5. ! [X0] : anywhere(X0) [input b4]
44. there_is_a_room [input p0]
48. ! [X0] : ((predh(X0) | predo(X0)) => predj(X0)) [input p4]
49. ! [X0] : (anywhere(X0) => ((~predi(X0) <~> predo(X0)) => predb(X0))) [input p5]
50. ! [X0] : (room(X0) => (predb(X0) => (~predo(X0) <~> predd(X0)))) [input p6]
55. ! [X0] : (anywhere(X0) => (predi(X0) => predj(X0))) [input p11]
59. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis]
142. ! [X0] : (predj(X0) | (~predh(X0) & ~predo(X0))) [ennf transformation 48]
143. ! [X0] : ((predb(X0) | (~predi(X0) <=> predo(X0))) | ~anywhere(X0)) [ennf transformation 49]
144. ! [X0] : (predb(X0) | (~predi(X0) <=> predo(X0)) | ~anywhere(X0)) [flattening 143]
145. ! [X0] : (((~predo(X0) <~> predd(X0)) | ~predb(X0)) | ~room(X0)) [ennf transformation 50]
146. ! [X0] : ((~predo(X0) <~> predd(X0)) | ~predb(X0) | ~room(X0)) [flattening 145]
152. ! [X0] : ((predj(X0) | ~predi(X0)) | ~anywhere(X0)) [ennf transformation 55]
153. ! [X0] : (predj(X0) | ~predi(X0) | ~anywhere(X0)) [flattening 152]
154. ? [X0] : ((predd(X0) & ~predj(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 59]
155. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ~there_is_a_room [flattening 154]
159. ! [X0] : (predb(X0) | ((~predi(X0) | ~predo(X0)) & (predo(X0) | predi(X0))) | ~anywhere(X0)) [nnf transformation 144]
160. ! [X0] : (((~predd(X0) | predo(X0)) & (predd(X0) | ~predo(X0))) | ~predb(X0) | ~room(X0)) [nnf transformation 146]
161. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK0) & ~predj(sK0) & room(sK0)) [choice axiom]
162. (predd(sK0) & ~predj(sK0) & room(sK0)) | ~there_is_a_room [skolemisation 155,161]
163. anywhere(X0) [cnf transformation 5]
244. there_is_a_room [cnf transformation 44]
249. ~predo(X0) | predj(X0) [cnf transformation 142]
251. predb(X0) | predo(X0) | predi(X0) | ~anywhere(X0) [cnf transformation 159]
254. ~predd(X0) | predo(X0) | ~predb(X0) | ~room(X0) [cnf transformation 160]
259. predj(X0) | ~predi(X0) | ~anywhere(X0) [cnf transformation 153]
260. room(sK0) | ~there_is_a_room [cnf transformation 162]
261. ~predj(sK0) | ~there_is_a_room [cnf transformation 162]
262. predd(sK0) | ~there_is_a_room [cnf transformation 162]
265. predb(X0) | predo(X0) | predi(X0) [subsumption resolution 251,163]
267. ~predi(X0) | predj(X0) [subsumption resolution 259,163]
268. predd(sK0) [subsumption resolution 262,244]
269. ~predj(sK0) [subsumption resolution 261,244]
270. room(sK0) [subsumption resolution 260,244]
273. predo(sK0) | ~predb(sK0) | ~room(sK0) [resolution 254,268]
274. predo(sK0) | ~predb(sK0) [subsumption resolution 273,270]
276. 1 <=> predb(sK0) [avatar definition]
278. ~predb(sK0) <- (~1) [avatar component clause 276]
280. 2 <=> predo(sK0) [avatar definition]
282. predo(sK0) <- (2) [avatar component clause 280]
283. ~1 | 2 [avatar split clause 274,280,276]
284. predo(sK0) | predi(sK0) <- (~1) [resolution 278,265]
286. 3 <=> predi(sK0) [avatar definition]
288. predi(sK0) <- (3) [avatar component clause 286]
289. 3 | 2 | 1 [avatar split clause 284,276,280,286]
291. predj(sK0) <- (3) [resolution 288,267]
294. $false <- (3) [subsumption resolution 291,269]
295. ~3 [avatar contradiction clause 294]
296. predj(sK0) <- (2) [resolution 282,249]
297. $false <- (2) [subsumption resolution 296,269]
298. ~2 [avatar contradiction clause 297]
299. $false [avatar sat refutation 283,289,295,298]
% SZS output end Proof for 2218241674405897121675416
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Pedro, Sharron are the only persons in the room.
If “everyone in the room does not collect classic novels or collects limited-edition art prints from contemporary artists” then “everyone in the room who does not collect classic novels participates in long-distance cycling events across the country, uses a Windows laptop or is a wine connoisseur”.
If “everyone in the room does not enjoy watercolor painting or is a tea enthusiast” then “if someone is a chess master who participates in national tournaments then he/she regularly contributes to tech forums and online communities and vice versa”.
Everyone in the room who collects classic novels participates in long-distance cycling events across the country.
Everyone in the room who is a chess master who participates in national tournaments collects limited-edition art prints from contemporary artists, does not enjoy wildlife photography or uses contact lenses.
Everyone in the room who collects limited-edition art prints from contemporary artists is a client of Costco.
Everyone in the room who designs and sews custom cosplay costumes for conventions own a television.
Everyone in the room who own a television collects classic novels.
Everyone in the room who is a wine connoisseur with a private cellar of vintage wines participates in long-distance cycling events across the country.
If someone enjoys bird watching, enjoys origami or is a tea enthusiast then he/she is a wine connoisseur with a private cellar of vintage wines.
More than one person in the room is a wine connoisseur with a private cellar of vintage wines. | Pedro is a wine connoisseur with a private cellar of vintage wines. | entailment | room(pedro)&room(sharron)&(![X]:(room(X)=>(X='pedro'|X='sharron')))&
((![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_collect_classic_novels(X))))))=>(![X]:(room(X)=>(((does_not_collect_classic_novels(X))=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(uses_a_Windows_laptop(X))|(is_a_wine_connoisseur(X)))))))))&
((![X]:(room(X)=>(((is_a_tea_enthusiast(X))|(does_not_enjoy_watercolor_painting(X))))))=>((![X]:((is_a_chess_master_who_participates_in_national_tournaments(X))<=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))&
(![X]:(room(X)=>(((collects_classic_novels(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))&
(![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_enjoy_wildlife_photography(X))|(uses_contact_lenses(X))))))))&
(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(is_a_client_of_Costco(X))))))&
(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(own_a_television(X))))))&
(![X]:(room(X)=>(((own_a_television(X))=>(collects_classic_novels(X))))))&
(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))&
((![X]:((((enjoys_bird_watching(X))|(enjoys_origami(X))|(is_a_tea_enthusiast(X))))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))&
(![X]:(anywhere(X)=>(((is_not_a_coffee_connoisseur(X))=>(uses_a_Windows_laptop(X))))))&
(![X]:(~room(X)=>(((uses_a_Windows_laptop(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))=>(is_a_coffee_connoisseur(X))))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(reads_mystery_novels(X))))))&
(![X]:(~room(X)=>(((uses_contact_lenses(X))=>(is_a_coffee_connoisseur(X))))))&
((?[X,Y]:(room(X)&room(Y)&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)&is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(Y))&(X!=Y))))&
(![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(own_a_television(X))))))&
(![X]:(room(X)=>(((enjoys_bird_watching(X))=>(is_a_coffee_connoisseur(X))))))&
(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(practices_kickboxing(X))))))&
(![X]:(room(X)=>(((enjoys_watercolor_painting(X))<=(practices_kickboxing(X))))))&
(![X]:(room(X)=>(((own_a_television(X))=>(writes_a_travel_blog(X)))))) | room(pedro)&room(sharron)&(![X]:(room(X)=>(X='pedro'|X='sharron')))&
is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(pedro) | [
"p0",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8624338040118785629291394
% SZS output start Proof for 8624338040118785629291394
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
60. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) [input p16]
66. ~(predc(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
161. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
162. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 161]
170. ~predc(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 66]
171. ~predc(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 170]
179. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) => (sK2 != sK3 & predc(sK3) & predc(sK2) & room(sK3) & room(sK2)) [choice axiom]
180. sK2 != sK3 & predc(sK3) & predc(sK2) & room(sK3) & room(sK2) [skolemisation 60,179]
181. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
182. ~predc(mary) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 171,181]
264. room(mary) [cnf transformation 162]
265. room(paul) [cnf transformation 162]
266. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 162]
274. room(sK2) [cnf transformation 180]
275. room(sK3) [cnf transformation 180]
276. predc(sK2) [cnf transformation 180]
277. predc(sK3) [cnf transformation 180]
278. sK2 != sK3 [cnf transformation 180]
279. ~predc(mary) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 182]
280. ~predc(mary) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 182]
281. ~predc(mary) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 182]
295. ~predc(mary) | paul != sK4 | ~room(mary) [subsumption resolution 281,265]
296. ~predc(mary) | paul != sK4 [subsumption resolution 295,264]
298. 4 <=> paul = sK4 [avatar definition]
300. paul != sK4 <- (~4) [avatar component clause 298]
302. 5 <=> predc(mary) [avatar definition]
304. ~predc(mary) <- (~5) [avatar component clause 302]
305. ~4 | ~5 [avatar split clause 296,302,298]
306. ~predc(mary) | mary != sK4 | ~room(mary) [subsumption resolution 280,265]
307. ~predc(mary) | mary != sK4 [subsumption resolution 306,264]
309. 6 <=> mary = sK4 [avatar definition]
311. mary != sK4 <- (~6) [avatar component clause 309]
312. ~6 | ~5 [avatar split clause 307,302,309]
313. ~predc(mary) | room(sK4) | ~room(mary) [subsumption resolution 279,265]
314. ~predc(mary) | room(sK4) [subsumption resolution 313,264]
316. 7 <=> room(sK4) [avatar definition]
318. room(sK4) <- (7) [avatar component clause 316]
319. 7 | ~5 [avatar split clause 314,302,316]
325. mary = sK2 | paul = sK2 [resolution 266,274]
326. mary = sK3 | paul = sK3 [resolution 266,275]
337. 10 <=> paul = sK2 [avatar definition]
341. 11 <=> mary = sK2 [avatar definition]
343. mary = sK2 <- (11) [avatar component clause 341]
344. 10 | 11 [avatar split clause 325,341,337]
346. 12 <=> paul = sK3 [avatar definition]
348. paul = sK3 <- (12) [avatar component clause 346]
350. 13 <=> mary = sK3 [avatar definition]
352. mary = sK3 <- (13) [avatar component clause 350]
353. 12 | 13 [avatar split clause 326,350,346]
370. predc(mary) <- (13) [backward demodulation 277,352]
372. $false <- (~5, 13) [subsumption resolution 370,304]
373. 5 | ~13 [avatar contradiction clause 372]
380. paul != sK2 <- (12) [backward demodulation 278,348]
381. ~10 | ~12 [avatar split clause 380,346,337]
383. predc(mary) <- (11) [backward demodulation 276,343]
384. 5 | ~11 [avatar split clause 383,341,302]
386. mary = sK4 | paul = sK4 <- (7) [resolution 318,266]
387. paul = sK4 <- (~6, 7) [subsumption resolution 386,311]
388. $false <- (~4, ~6, 7) [subsumption resolution 387,300]
389. 4 | 6 | ~7 [avatar contradiction clause 388]
390. $false [avatar sat refutation 305,312,319,344,353,373,381,384,389]
% SZS output end Proof for 8624338040118785629291394
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.492053 |
Earl, Diana are the only persons in the room.
Not everyone in the room is a sibling of Robert if they is a sibling of Joan.
Everyone in the room is a sibling of Robert and is a sibling of Joan if they is a sibling of Robert.
Everyone in the room who neither is a sibling of Robert nor is a sibling of Joan is a sibling of Robert.
Everyone in the room is a sibling of Teresa.
Not everyone anywhere is a sibling of Joan if they is a sibling of Teresa.
Everyone in the room is a sibling of Joan if they either is a sibling of Teresa or is a sibling of Joan but not both.
Everyone in the room is a sibling of Joan if they is a sibling of Teresa.
Everyone in the room is a sibling of Teresa if they is a sibling of Joan.
Earl either is a sibling of Robert or is a sibling of Teresa but not both.
Everyone in the room is a sibling of Joan if they is a sibling of Robert. | Diana is a sibling of Joan. | entailment | room(earl)&room(diana)&(![X]:(room(X)=>(X='earl'|X='diana')))&
(~![X]:(room(X)=>(((sibling(joan,X))=>(sibling(robert,X))))))&
(![X]:(room(X)=>(((sibling(robert,X))=>(((sibling(robert,X))&(sibling(joan,X))))))))&
(![X]:(room(X)=>(((~((sibling(robert,X))|(sibling(joan,X))))=>(sibling(robert,X))))))&
(![X]:(room(X)=>(sibling(teresa,X))))&
(~![X]:(anywhere(X)=>(((sibling(teresa,X))=>(sibling(joan,X))))))&
(![X]:(room(X)=>(((((sibling(teresa,X))<~>(sibling(joan,X))))=>(sibling(joan,X))))))&
(![X]:(room(X)=>(((sibling(teresa,X))=>(sibling(joan,X))))))&
(![X]:(room(X)=>(((sibling(joan,X))=>(sibling(teresa,X))))))&
(((sibling(robert,earl))<~>(sibling(teresa,earl))))&
(![X]:(room(X)=>(((sibling(robert,X))=>(sibling(joan,X)))))) | room(earl)&room(diana)&(![X]:(room(X)=>(X='earl'|X='diana')))&
sibling(joan,diana) | [
"p0",
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3490498958336829387998058
% SZS output start Proof for 3490498958336829387998058
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
46. ! [X0] : (room(X0) => (sibling(john,X0) => (sibling(alice,X0) & sibling(john,X0)))) [input p2]
47. ! [X0] : (room(X0) => (~(sibling(alice,X0) | sibling(john,X0)) => sibling(john,X0))) [input p3]
55. ~(sibling(alice,paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
129. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
130. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 129]
133. ! [X0] : (((sibling(alice,X0) & sibling(john,X0)) | ~sibling(john,X0)) | ~room(X0)) [ennf transformation 46]
134. ! [X0] : ((sibling(alice,X0) & sibling(john,X0)) | ~sibling(john,X0) | ~room(X0)) [flattening 133]
135. ! [X0] : ((sibling(john,X0) | (sibling(alice,X0) | sibling(john,X0))) | ~room(X0)) [ennf transformation 47]
136. ! [X0] : (sibling(john,X0) | sibling(alice,X0) | sibling(john,X0) | ~room(X0)) [flattening 135]
147. ~sibling(alice,paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 55]
148. ~sibling(alice,paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 147]
156. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom]
157. ~sibling(alice,paul) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 148,156]
238. room(mary) [cnf transformation 130]
239. room(paul) [cnf transformation 130]
240. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 130]
245. sibling(alice,X0) | ~sibling(john,X0) | ~room(X0) [cnf transformation 134]
246. sibling(john,X0) | sibling(alice,X0) | sibling(john,X0) | ~room(X0) [cnf transformation 136]
257. ~sibling(alice,paul) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 157]
258. ~sibling(alice,paul) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 157]
259. ~sibling(alice,paul) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 157]
261. sibling(john,X0) | sibling(alice,X0) | ~room(X0) [duplicate literal removal 246]
262. sibling(alice,X0) | ~room(X0) [subsumption resolution 261,245]
273. ~sibling(alice,paul) | paul != sK2 | ~room(mary) [subsumption resolution 259,239]
274. ~sibling(alice,paul) | paul != sK2 [subsumption resolution 273,238]
276. 3 <=> paul = sK2 [avatar definition]
278. paul != sK2 <- (~3) [avatar component clause 276]
280. 4 <=> sibling(alice,paul) [avatar definition]
282. ~sibling(alice,paul) <- (~4) [avatar component clause 280]
283. ~3 | ~4 [avatar split clause 274,280,276]
284. ~sibling(alice,paul) | mary != sK2 | ~room(mary) [subsumption resolution 258,239]
285. ~sibling(alice,paul) | mary != sK2 [subsumption resolution 284,238]
287. 5 <=> mary = sK2 [avatar definition]
289. mary != sK2 <- (~5) [avatar component clause 287]
290. ~5 | ~4 [avatar split clause 285,280,287]
291. ~sibling(alice,paul) | room(sK2) | ~room(mary) [subsumption resolution 257,239]
292. ~sibling(alice,paul) | room(sK2) [subsumption resolution 291,238]
294. 6 <=> room(sK2) [avatar definition]
296. room(sK2) <- (6) [avatar component clause 294]
297. 6 | ~4 [avatar split clause 292,280,294]
299. ~room(paul) <- (~4) [resolution 262,282]
300. $false <- (~4) [subsumption resolution 299,239]
301. 4 [avatar contradiction clause 300]
305. mary = sK2 | paul = sK2 <- (6) [resolution 240,296]
315. paul = sK2 <- (~5, 6) [subsumption resolution 305,289]
316. $false <- (~3, ~5, 6) [subsumption resolution 315,278]
317. 3 | 5 | ~6 [avatar contradiction clause 316]
318. $false [avatar sat refutation 283,290,297,301,317]
% SZS output end Proof for 3490498958336829387998058
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.156299 |
There is a room.
Only one person in the room is kind, is a old person and is a kind person.
It is not the case that 'it is not the case that 'more than one person anywhere is kind, is old and is not a kind person''.
All tall persons are quiet.
All quiet persons are kind.
Only one person in the room is quiet.
It is true that 'someone who is kind is older than someone who is a kind person'.
More than one person in the room is kind.
All quiet persons are old.
All tall persons are kind.
All old persons are quiet.
All quiet persons are tall.
It is not the case that 'more than one person in the room is not a kind person'.
All tall persons are old.
More than one person outside the room is not a tall person or is a old person or both.
At least one person in the room is tall.
Only one person in the room is a old person. | Everyone in the room is a tall person. | contradiction | (there_is_a_room)&
(((?[X]:(room(X)&((kind(X))&(old(X)&person(X))&(kind(X)&person(X)))))&(![X,Y]:((room(X)&room(Y)&(((kind(X))&(old(X)&person(X))&(kind(X)&person(X))))&(((kind(Y))&(old(Y)&person(Y))&(kind(Y)&person(Y)))))=>(X=Y)))))&
(~(~((?[X,Y]:(anywhere(X)&anywhere(Y)&(((kind(X))&(old(X))&(~(kind(X)&person(X))))&((kind(Y))&(old(Y))&(~(kind(Y)&person(Y)))))&(X!=Y))))))&
(![X]:(tall(X)=>quiet(X)))&
(![X]:(quiet(X)=>kind(X)))&
(((?[X]:(room(X)&quiet(X)))&(![X,Y]:((room(X)&room(Y)&(quiet(X))&(quiet(Y)))=>(X=Y)))))&
(?[X,Y]:((kind(X))&(kind(Y)&person(Y))&(older(X,Y))))&
((?[X,Y]:(room(X)&room(Y)&(kind(X)&kind(Y))&(X!=Y))))&
(![X]:(quiet(X)=>old(X)))&
(![X]:(tall(X)=>kind(X)))&
(![X]:(old(X)=>quiet(X)))&
(![X]:(quiet(X)=>tall(X)))&
(~((?[X,Y]:(room(X)&room(Y)&(~(kind(X)&person(X))&~(kind(Y)&person(Y)))&(X!=Y)))))&
(![X]:(tall(X)=>old(X)))&
((?[X,Y]:(~room(X)&~room(Y)&(((~(tall(X)&person(X)))|(old(X)&person(X)))&((~(tall(Y)&person(Y)))|(old(Y)&person(Y))))&(X!=Y))))&
(((?[X]:(room(X)&tall(X)))))&
(((?[X]:(room(X)&old(X)&person(X)))&(![X,Y]:((room(X)&room(Y)&(old(X)&person(X))&(old(Y)&person(Y)))=>(X=Y)))))&
(?[X,Y]:((~old(X))&(tall(Y)&person(Y))&(older(X,Y)))) | (there_is_a_room)&
![X]:(room(X)=>(tall(X)&person(X))) | [
"p1",
"p3",
"p5",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4015611768266687057102587
% SZS output start Proof for 4015611768266687057102587
45. ! [X0,X1] : ((person(X1) & kind(X1) & person(X1) & old(X1) & kind(X1) & person(X0) & kind(X0) & person(X0) & old(X0) & kind(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (person(X0) & kind(X0) & person(X0) & old(X0) & kind(X0) & room(X0)) [input p1]
47. ! [X0] : (tall(X0) => quiet(X0)) [input p3]
49. ! [X0,X1] : ((quiet(X1) & quiet(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (quiet(X0) & room(X0)) [input p5]
51. ? [X0,X1] : (X0 != X1 & kind(X1) & kind(X0) & room(X1) & room(X0)) [input p7]
54. ! [X0] : (old(X0) => quiet(X0)) [input p10]
62. ! [X0] : (room(X0) => (person(X0) & tall(X0))) & there_is_a_room [input hypothesis]
63. ! [X0,X1] : ((person(X1) & kind(X1) & person(X1) & old(X1) & kind(X1) & person(X0) & kind(X0) & person(X0) & old(X0) & kind(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (person(X2) & kind(X2) & person(X2) & old(X2) & kind(X2) & room(X2)) [rectify 45]
65. ! [X0,X1] : ((quiet(X1) & quiet(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (quiet(X2) & room(X2)) [rectify 49]
68. ! [X0] : (room(X0) => (person(X0) & tall(X0))) [pure predicate removal 62]
142. ! [X0,X1] : (X0 = X1 | (~person(X1) | ~kind(X1) | ~person(X1) | ~old(X1) | ~kind(X1) | ~person(X0) | ~kind(X0) | ~person(X0) | ~old(X0) | ~kind(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (person(X2) & kind(X2) & person(X2) & old(X2) & kind(X2) & room(X2)) [ennf transformation 63]
143. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~kind(X1) | ~person(X1) | ~old(X1) | ~kind(X1) | ~person(X0) | ~kind(X0) | ~person(X0) | ~old(X0) | ~kind(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (person(X2) & kind(X2) & person(X2) & old(X2) & kind(X2) & room(X2)) [flattening 142]
145. ! [X0] : (quiet(X0) | ~tall(X0)) [ennf transformation 47]
147. ! [X0,X1] : (X0 = X1 | (~quiet(X1) | ~quiet(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (quiet(X2) & room(X2)) [ennf transformation 65]
148. ! [X0,X1] : (X0 = X1 | ~quiet(X1) | ~quiet(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (quiet(X2) & room(X2)) [flattening 147]
151. ! [X0] : (quiet(X0) | ~old(X0)) [ennf transformation 54]
159. ! [X0] : ((person(X0) & tall(X0)) | ~room(X0)) [ennf transformation 68]
161. ? [X2] : (person(X2) & kind(X2) & person(X2) & old(X2) & kind(X2) & room(X2)) => (person(sK0) & kind(sK0) & person(sK0) & old(sK0) & kind(sK0) & room(sK0)) [choice axiom]
162. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~kind(X1) | ~person(X1) | ~old(X1) | ~kind(X1) | ~person(X0) | ~kind(X0) | ~person(X0) | ~old(X0) | ~kind(X0) | ~room(X1) | ~room(X0)) & (person(sK0) & kind(sK0) & person(sK0) & old(sK0) & kind(sK0) & room(sK0)) [skolemisation 143,161]
165. ? [X2] : (quiet(X2) & room(X2)) => (quiet(sK3) & room(sK3)) [choice axiom]
166. ! [X0,X1] : (X0 = X1 | ~quiet(X1) | ~quiet(X0) | ~room(X1) | ~room(X0)) & (quiet(sK3) & room(sK3)) [skolemisation 148,165]
169. ? [X0,X1] : (X0 != X1 & kind(X1) & kind(X0) & room(X1) & room(X0)) => (sK6 != sK7 & kind(sK7) & kind(sK6) & room(sK7) & room(sK6)) [choice axiom]
170. sK6 != sK7 & kind(sK7) & kind(sK6) & room(sK7) & room(sK6) [skolemisation 51,169]
259. room(sK0) [cnf transformation 162]
261. old(sK0) [cnf transformation 162]
273. ~tall(X0) | quiet(X0) [cnf transformation 145]
277. ~room(X1) | ~quiet(X1) | ~quiet(X0) | X0 = X1 | ~room(X0) [cnf transformation 166]
282. room(sK6) [cnf transformation 170]
283. room(sK7) [cnf transformation 170]
286. sK6 != sK7 [cnf transformation 170]
289. ~old(X0) | quiet(X0) [cnf transformation 151]
313. ~room(X0) | tall(X0) [cnf transformation 159]
346. quiet(sK0) [resolution 289,261]
364. tall(sK6) [resolution 313,282]
365. tall(sK7) [resolution 313,283]
385. quiet(sK6) [resolution 364,273]
388. quiet(sK7) [resolution 365,273]
515. ~quiet(sK0) | ~quiet(X0) | sK0 = X0 | ~room(X0) [resolution 277,259]
521. ~room(X0) | sK0 = X0 | ~quiet(X0) [subsumption resolution 515,346]
590. sK0 = sK6 | ~quiet(sK6) [resolution 521,282]
591. sK0 = sK7 | ~quiet(sK7) [resolution 521,283]
603. sK0 = sK6 [subsumption resolution 590,385]
606. sK0 != sK7 [backward demodulation 286,603]
613. ~quiet(sK7) [subsumption resolution 591,606]
614. $false [subsumption resolution 613,388]
% SZS output end Proof for 4015611768266687057102587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.402862 |
Pinkie, Thomas are the only persons in the room.
“Everyone in the room does not play the drums or enjoys landscape photography” if “no one outside the room is not a skilled home brewer experimenting with craft beer recipes or is a dedicated advocate for digital privacy and encryption” and vice versa.
“Not everyone in the room does not collect antique jewelry or hosts themed dinner parties featuring gourmet home-cooked meals” only if “Pinkie who is a certified yoga instructor teaching classes weekly hosts a popular podcast about emerging technologies”.
“At least one person outside the room collects luxury watches” unless “everyone in the room is not an avid hiker or owns a significant collection of rare gemstones and minerals”.
If “everyone in the room is not a culinary enthusiast who experiments with international cuisines or is a skilled home brewer experimenting with craft beer recipes” then “Pinkie who hosts themed dinner parties featuring gourmet home-cooked meals owns a microscope”.
Everyone in the room owns a significant collection of rare gemstones and minerals, does not collect antique clocks and does not collect luxury watches if they is not a culinary enthusiast who experiments with international cuisines.
If someone enjoys stargazing then he/she collects vintage stamps, does not play the drums and enjoys snowboarding.
Pinkie does not enjoy snowboarding, practices calligraphy and is a cybersecurity expert.
Everyone in the room enjoys stargazing, is a dedicated advocate for digital privacy and encryption or plays the drums.
Pinkie who is a dedicated advocate for digital privacy and encryption collects antique clocks.
Everyone in the room does not enjoy landscape photography or does not own an extensive assortment of vintage comic book memorabilia.
Everyone in the room who does not host regular game nights featuring complex strategy games plays the drums, is a culinary enthusiast who experiments with international cuisines and practices pilates.
Pinkie who enjoys landscape photography practices calligraphy.
Everyone in the room writes and illustrates their own graphic novels if they does not collect antique jewelry. | Thomas plays the drums. | entailment | room(pinkie)&room(thomas)&(![X]:(room(X)=>(X='pinkie'|X='thomas')))&
((~?[X]:(~room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))<=>(![X]:(room(X)=>(((enjoys_landscape_photography(X))|(does_not_play_the_drums(X)))))))&
((~![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_collect_antique_jewelry(X))))))=>((is_a_certified_yoga_instructor_teaching_classes_weekly(pinkie))&(hosts_a_popular_podcast_about_emerging_technologies(pinkie))))&
(~(![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_not_an_avid_hiker(X))))))=>(((?[X]:(~room(X)&collects_luxury_watches(X))))))&
((![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))=>((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(pinkie))&(owns_a_microscope(pinkie))))&
(![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(does_not_collect_antique_clocks(X))&(does_not_collect_luxury_watches(X))))))))&
((![X]:((enjoys_stargazing(X))=>(((collects_vintage_stamps(X))&(does_not_play_the_drums(X))&(enjoys_snowboarding(X)))))))&
(((does_not_enjoy_snowboarding(pinkie))&(practices_calligraphy(pinkie))&(is_a_cybersecurity_expert(pinkie))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(plays_the_drums(X))))))&
((is_a_dedicated_advocate_for_digital_privacy_and_encryption(pinkie))&(collects_antique_clocks(pinkie)))&
(![X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_enjoy_landscape_photography(X))))))&
(![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))=>(((plays_the_drums(X))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(practices_pilates(X))))))))&
((enjoys_landscape_photography(pinkie))&(practices_calligraphy(pinkie)))&
(![X]:(room(X)=>(((does_not_collect_antique_jewelry(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))&
(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(enjoys_landscape_photography(X))))))&
(![X]:(room(X)=>(collects_antique_jewelry(X))))&
(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))|(is_not_an_avid_hiker(X))))))&
(![X]:(room(X)=>(((is_not_an_avid_hiker(X))<=>(practices_pilates(X))))))&
(![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(enjoys_stargazing(X))))))))&
(![X]:(room(X)=>(((((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(enjoys_stargazing(X))))=>(((writes_and_illustrates_their_own_graphic_novels(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(collects_luxury_watches(X))))))))&
(![X]:(room(X)=>(((collects_antique_clocks(X))=>(((enjoys_landscape_photography(X))|(is_an_avid_hiker(X))|(hosts_a_popular_podcast_about_emerging_technologies(X)))))))) | room(pinkie)&room(thomas)&(![X]:(room(X)=>(X='pinkie'|X='thomas')))&
plays_the_drums(thomas) | [
"p0",
"p1",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7020565933356095967800332
% SZS output start Proof for 7020565933356095967800332
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
45. ~? [X0] : (~room(X0) => (~preda(X0) | predb(X0))) <=> ! [X0] : (room(X0) => (~predi(X0) | predx(X0))) [input p1]
53. predz(mary) & predb(mary) [input p9]
56. predy(mary) & predx(mary) [input p12]
65. ~(predi(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
66. ~? [X0] : (~room(X0) => (~preda(X0) | predb(X0))) <=> ! [X1] : (room(X1) => (~predi(X1) | predx(X1))) [rectify 45]
73. predx(mary) [pure predicate removal 56]
157. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
158. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 157]
159. ! [X0] : ((preda(X0) & ~predb(X0)) & ~room(X0)) <=> ! [X1] : ((~predi(X1) | predx(X1)) | ~room(X1)) [ennf transformation 66]
160. ! [X0] : (preda(X0) & ~predb(X0) & ~room(X0)) <=> ! [X1] : (~predi(X1) | predx(X1) | ~room(X1)) [flattening 159]
173. ~predi(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 65]
174. ~predi(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 173]
175. sP0 <=> ! [X0] : (preda(X0) & ~predb(X0) & ~room(X0)) [predicate definition introduction]
176. sP0 <=> ! [X1] : (~predi(X1) | predx(X1) | ~room(X1)) [definition folding 160,175]
178. (sP0 | ? [X0] : (~preda(X0) | predb(X0) | room(X0))) & (! [X0] : (preda(X0) & ~predb(X0) & ~room(X0)) | ~sP0) [nnf transformation 175]
179. (sP0 | ? [X0] : (~preda(X0) | predb(X0) | room(X0))) & (! [X1] : (preda(X1) & ~predb(X1) & ~room(X1)) | ~sP0) [rectify 178]
180. ? [X0] : (~preda(X0) | predb(X0) | room(X0)) => (~preda(sK1) | predb(sK1) | room(sK1)) [choice axiom]
181. (sP0 | (~preda(sK1) | predb(sK1) | room(sK1))) & (! [X1] : (preda(X1) & ~predb(X1) & ~room(X1)) | ~sP0) [skolemisation 179,180]
182. (sP0 | ? [X1] : (predi(X1) & ~predx(X1) & room(X1))) & (! [X1] : (~predi(X1) | predx(X1) | ~room(X1)) | ~sP0) [nnf transformation 176]
183. (sP0 | ? [X0] : (predi(X0) & ~predx(X0) & room(X0))) & (! [X1] : (~predi(X1) | predx(X1) | ~room(X1)) | ~sP0) [rectify 182]
184. ? [X0] : (predi(X0) & ~predx(X0) & room(X0)) => (predi(sK2) & ~predx(sK2) & room(sK2)) [choice axiom]
185. (sP0 | (predi(sK2) & ~predx(sK2) & room(sK2))) & (! [X1] : (~predi(X1) | predx(X1) | ~room(X1)) | ~sP0) [skolemisation 183,184]
187. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
188. ~predi(paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 174,187]
269. room(mary) [cnf transformation 158]
270. room(paul) [cnf transformation 158]
271. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 158]
273. ~predb(X1) | ~sP0 [cnf transformation 181]
277. sP0 | room(sK2) [cnf transformation 185]
278. sP0 | ~predx(sK2) [cnf transformation 185]
279. sP0 | predi(sK2) [cnf transformation 185]
286. predb(mary) [cnf transformation 53]
288. predx(mary) [cnf transformation 73]
295. ~predi(paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 188]
296. ~predi(paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 188]
297. ~predi(paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 188]
311. 4 <=> sP0 [avatar definition]
320. 6 <=> ! [X1] : ~predb(X1) [avatar definition]
321. ~predb(X1) <- (6) [avatar component clause 320]
322. ~4 | 6 [avatar split clause 273,320,311]
328. 8 <=> predi(sK2) [avatar definition]
330. predi(sK2) <- (8) [avatar component clause 328]
331. 8 | 4 [avatar split clause 279,311,328]
333. 9 <=> predx(sK2) [avatar definition]
335. ~predx(sK2) <- (~9) [avatar component clause 333]
336. ~9 | 4 [avatar split clause 278,311,333]
338. 10 <=> room(sK2) [avatar definition]
340. room(sK2) <- (10) [avatar component clause 338]
341. 10 | 4 [avatar split clause 277,311,338]
346. ~predi(paul) | paul != sK3 | ~room(mary) [subsumption resolution 297,270]
347. ~predi(paul) | paul != sK3 [subsumption resolution 346,269]
349. 12 <=> paul = sK3 [avatar definition]
351. paul != sK3 <- (~12) [avatar component clause 349]
353. 13 <=> predi(paul) [avatar definition]
356. ~12 | ~13 [avatar split clause 347,353,349]
357. ~predi(paul) | mary != sK3 | ~room(mary) [subsumption resolution 296,270]
358. ~predi(paul) | mary != sK3 [subsumption resolution 357,269]
360. 14 <=> mary = sK3 [avatar definition]
362. mary != sK3 <- (~14) [avatar component clause 360]
363. ~14 | ~13 [avatar split clause 358,353,360]
364. ~predi(paul) | room(sK3) | ~room(mary) [subsumption resolution 295,270]
365. ~predi(paul) | room(sK3) [subsumption resolution 364,269]
367. 15 <=> room(sK3) [avatar definition]
369. room(sK3) <- (15) [avatar component clause 367]
370. 15 | ~13 [avatar split clause 365,353,367]
407. $false <- (6) [resolution 321,286]
408. ~6 [avatar contradiction clause 407]
419. mary = sK2 | paul = sK2 <- (10) [resolution 271,340]
421. 22 <=> paul = sK2 [avatar definition]
423. paul = sK2 <- (22) [avatar component clause 421]
425. 23 <=> mary = sK2 [avatar definition]
427. mary = sK2 <- (23) [avatar component clause 425]
428. 22 | 23 | ~10 [avatar split clause 419,338,425,421]
431. predi(paul) <- (8, 22) [backward demodulation 330,423]
435. 13 | ~8 | ~22 [avatar split clause 431,421,328,353]
436. mary = sK3 | paul = sK3 <- (15) [resolution 369,271]
438. paul = sK3 <- (~14, 15) [subsumption resolution 436,362]
439. $false <- (~12, ~14, 15) [subsumption resolution 438,351]
440. 12 | 14 | ~15 [avatar contradiction clause 439]
453. ~predx(mary) <- (~9, 23) [backward demodulation 335,427]
454. $false <- (~9, 23) [subsumption resolution 453,288]
455. 9 | ~23 [avatar contradiction clause 454]
457. $false [avatar sat refutation 322,331,336,341,356,363,370,408,428,435,440,455]
% SZS output end Proof for 7020565933356095967800332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.522494 |
There is a room.
All creative persons are quiet.
Everyone in the room either is old or is a patient person but not both.
Everyone in the room is a tall person.
If someone either is not calm or is a happy person but not both then he/she neither is humble nor is creative.
Someone who is patient is richer than someone who is a patient person.
No brave person is happy.
It is not the case that “at least one person outside the room is a patient person”.
Everyone in the room is creative.
Everyone outside the room is a funny person.
Everyone in the room is a calm person.
Someone who is quiet, is a strong person or is a old person is richer than someone who is a creative person.
Everyone outside the room is a tall person.
Someone who is a patient person is quieter than someone who is a humble person, is not curious or is patient.
Someone who neither is strong nor is a strong person is quieter than someone who is a tall person. | All tall persons are old. | contradiction | (there_is_a_room)&
(![X]:(creative(X)=>quiet(X)))&
(![X]:(room(X)=>(((old(X))<~>(patient(X)&person(X))))))&
(![X]:(room(X)=>(tall(X)&person(X))))&
((![X]:((((~calm(X))<~>(happy(X)&person(X))))=>(~((humble(X))|(creative(X)))))))&
(?[X,Y]:((patient(X))&(patient(Y)&person(Y))&(richer(X,Y))))&
(~?[X]:(brave(X)=>happy(X)))&
(~(((?[X]:(~room(X)&patient(X)&person(X))))))&
(![X]:(room(X)=>(creative(X))))&
(![X]:(~room(X)=>(funny(X)&person(X))))&
(![X]:(room(X)=>(calm(X)&person(X))))&
(?[X,Y]:((((quiet(X))|(strong(X)&person(X))|(old(X)&person(X))))&(creative(Y)&person(Y))&(richer(X,Y))))&
(![X]:(~room(X)=>(tall(X)&person(X))))&
(?[X,Y]:((patient(X)&person(X))&(((humble(Y)&person(Y))|(~curious(Y))|(patient(Y))))&(quieter(X,Y))))&
(?[X,Y]:((~((strong(X))|(strong(X)&person(X))))&(tall(Y)&person(Y))&(quieter(X,Y)))) | (there_is_a_room)&
![X]:(tall(X)=>old(X)) | [
"p2",
"p3",
"p5",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 714041024647824330192218
% SZS output start Proof for 714041024647824330192218
46. ! [X0] : (room(X0) => (old(X0) <~> (person(X0) & patient(X0)))) [input p2]
47. ! [X0] : (room(X0) => (person(X0) & tall(X0))) [input p3]
49. ? [X0,X1] : (richer(X0,X1) & person(X1) & patient(X1) & patient(X0)) [input p5]
51. ~? [X0] : (person(X0) & patient(X0) & ~room(X0)) [input p7]
53. ! [X0] : (~room(X0) => (person(X0) & funny(X0))) [input p9]
56. ! [X0] : (~room(X0) => (person(X0) & tall(X0))) [input p12]
59. ! [X0] : (tall(X0) => old(X0)) & there_is_a_room [input hypothesis]
62. ! [X0] : (~room(X0) => person(X0)) [pure predicate removal 53]
64. ! [X0] : (tall(X0) => old(X0)) [pure predicate removal 59]
139. ! [X0] : ((old(X0) <~> (person(X0) & patient(X0))) | ~room(X0)) [ennf transformation 46]
140. ! [X0] : ((person(X0) & tall(X0)) | ~room(X0)) [ennf transformation 47]
143. ! [X0] : (~person(X0) | ~patient(X0) | room(X0)) [ennf transformation 51]
145. ! [X0] : (person(X0) | room(X0)) [ennf transformation 62]
147. ! [X0] : ((person(X0) & tall(X0)) | room(X0)) [ennf transformation 56]
150. ! [X0] : (old(X0) | ~tall(X0)) [ennf transformation 64]
152. ! [X0] : ((((~person(X0) | ~patient(X0)) | ~old(X0)) & ((person(X0) & patient(X0)) | old(X0))) | ~room(X0)) [nnf transformation 139]
153. ! [X0] : (((~person(X0) | ~patient(X0) | ~old(X0)) & ((person(X0) & patient(X0)) | old(X0))) | ~room(X0)) [flattening 152]
156. ? [X0,X1] : (richer(X0,X1) & person(X1) & patient(X1) & patient(X0)) => (richer(sK0,sK1) & person(sK1) & patient(sK1) & patient(sK0)) [choice axiom]
157. richer(sK0,sK1) & person(sK1) & patient(sK1) & patient(sK0) [skolemisation 49,156]
247. ~patient(X0) | ~person(X0) | ~old(X0) | ~room(X0) [cnf transformation 153]
248. ~room(X0) | tall(X0) [cnf transformation 140]
249. ~room(X0) | person(X0) [cnf transformation 140]
253. patient(sK0) [cnf transformation 157]
258. ~patient(X0) | ~person(X0) | room(X0) [cnf transformation 143]
260. person(X0) | room(X0) [cnf transformation 145]
270. tall(X0) | room(X0) [cnf transformation 147]
280. old(X0) | ~tall(X0) [cnf transformation 150]
282. person(X0) [subsumption resolution 260,249]
296. tall(X0) [subsumption resolution 270,248]
298. old(X0) [subsumption resolution 280,296]
303. ~person(sK0) | room(sK0) [resolution 258,253]
306. room(sK0) [subsumption resolution 303,282]
309. ~person(sK0) | ~old(sK0) | ~room(sK0) [resolution 247,253]
312. ~old(sK0) | ~room(sK0) [subsumption resolution 309,282]
313. ~room(sK0) [subsumption resolution 312,298]
314. $false [subsumption resolution 313,306]
% SZS output end Proof for 714041024647824330192218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.221325 |
Jennifer, Sabrina are the only persons in the room.
'It is not the case that 'Sabrina does not practice urban gardening'' only if 'Jennifer is a curious person'.
'Sabrina is not a generous person' if 'Jennifer is a generous person' and vice versa.
Jennifer is a curious person.
Jennifer is not a generous person. | Jennifer is not generous. | entailment | room(jennifer)&room(sabrina)&(![X]:(room(X)=>(X='jennifer'|X='sabrina')))&
((~(does_not_practice_urban_gardening(sabrina)))=>(curious(jennifer)&person(jennifer)))&
((generous(jennifer)&person(jennifer))<=>(~(generous(sabrina)&person(sabrina))))&
((((?[X]:(anywhere(X)&curious(X)&person(X)))))=>(~curious(sabrina)))&
((~(curious(jennifer)&person(jennifer)))=>(~(generous(jennifer)&person(jennifer))))&
((generous(jennifer))=>(~(generous(jennifer)&person(jennifer))))&
((?[X,Y]:(room(X)&room(Y)&(does_not_practice_urban_gardening(X)&does_not_practice_urban_gardening(Y))&(X!=Y))))&
(curious(jennifer)&person(jennifer))&
(~(generous(jennifer)&person(jennifer)))&
(((?[X]:(room(X)&~(generous(X)&person(X)))))) | room(jennifer)&room(sabrina)&(![X]:(room(X)=>(X='jennifer'|X='sabrina')))&
~generous(jennifer) | [
"p0",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2027665748253579794440426
% SZS output start Proof for 2027665748253579794440426
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
51. person(mary) & curious(mary) [input p7]
52. ~(person(mary) & generous(mary)) [input p8]
54. ~(~generous(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
128. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
129. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 128]
136. ~person(mary) | ~generous(mary) [ennf transformation 52]
138. generous(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 54]
139. generous(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 138]
147. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
148. generous(mary) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 139,147]
230. room(mary) [cnf transformation 129]
231. room(paul) [cnf transformation 129]
232. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 129]
246. person(mary) [cnf transformation 51]
247. ~person(mary) | ~generous(mary) [cnf transformation 136]
250. generous(mary) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 148]
251. generous(mary) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 148]
252. generous(mary) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 148]
259. 2 <=> person(mary) [avatar definition]
269. 4 <=> generous(mary) [avatar definition]
290. 2 [avatar split clause 246,259]
292. ~4 | ~2 [avatar split clause 247,259,269]
302. generous(mary) | paul != sK3 | ~room(mary) [subsumption resolution 252,231]
303. generous(mary) | paul != sK3 [subsumption resolution 302,230]
305. 10 <=> paul = sK3 [avatar definition]
307. paul != sK3 <- (~10) [avatar component clause 305]
308. ~10 | 4 [avatar split clause 303,269,305]
309. generous(mary) | mary != sK3 | ~room(mary) [subsumption resolution 251,231]
310. generous(mary) | mary != sK3 [subsumption resolution 309,230]
312. 11 <=> mary = sK3 [avatar definition]
314. mary != sK3 <- (~11) [avatar component clause 312]
315. ~11 | 4 [avatar split clause 310,269,312]
316. generous(mary) | room(sK3) | ~room(mary) [subsumption resolution 250,231]
317. generous(mary) | room(sK3) [subsumption resolution 316,230]
319. 12 <=> room(sK3) [avatar definition]
321. room(sK3) <- (12) [avatar component clause 319]
322. 12 | 4 [avatar split clause 317,269,319]
328. mary = sK3 | paul = sK3 <- (12) [resolution 232,321]
356. paul = sK3 <- (~11, 12) [subsumption resolution 328,314]
357. $false <- (~10, ~11, 12) [subsumption resolution 356,307]
358. 10 | 11 | ~12 [avatar contradiction clause 357]
359. $false [avatar sat refutation 290,292,308,315,322,358]
% SZS output end Proof for 2027665748253579794440426
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.572982 |
Barbara, Gladys, Melissa are the only persons in the room.
If “Barbara does not collect luxury watches or enjoys kayaking or both” then “everyone outside the room does not own a smart tv or plays the violin”.
“Someone in the room makes intricate hand-cut paper art for exhibitions” only if “Barbara neither is an avid collector of autographed memorabilia from famous musicians nor makes intricate hand-cut paper art for exhibitions”.
“Everyone outside the room does not compose and performs experimental electronic music or has lived in exactly three countries” only if “Barbara has lived in exactly three countries”.
If “at least one person in the room does not host a popular podcast about emerging technologies” then “Barbara collects luxury watches”.
“Everyone anywhere composes and performs experimental electronic music or does not compose and performs experimental electronic music” if “everyone outside the room is an avid collector of autographed memorabilia from famous musicians or does not play the violin” and vice versa.
“Everyone in the room does not drive a hybrid car or does not host a popular podcast about emerging technologies” only if “Barbara does not play the violin”.
If “no one anywhere is an avid collector of autographed memorabilia from famous musicians” then “Barbara plays the violin”.
If “Barbara neither makes intricate hand-cut paper art for exhibitions nor drives a hybrid car” then “everyone in the room has lived in exactly three countries only if they hosts a popular podcast about emerging technologies” otherwise “Barbara who plays the violin either drives a hybrid car or trains for and competes in international triathlons but not both”.
Everyone in the room hosts a popular podcast about emerging technologies if they does not train for and competes in international triathlons.
Barbara does not host a popular podcast about emerging technologies.
Barbara neither composes and performs experimental electronic music nor makes intricate hand-cut paper art for exhibitions. | Barbara has lived in exactly three countries. | contradiction | room(barbara)&room(gladys)&room(melissa)&(![X]:(room(X)=>(X='barbara'|X='gladys'|X='melissa')))&
((((does_not_collect_luxury_watches(barbara))|(enjoys_kayaking(barbara))))=>(![X]:(~room(X)=>(((plays_the_violin(X))|(does_not_own_a_smart_tv(X)))))))&
((?[X]:(room(X)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(~((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(barbara))|(makes_intricate_hand-cut_paper_art_for_exhibitions(barbara)))))&
((![X]:(~room(X)=>(((has_lived_in_exactly_three_countries(X))|(does_not_compose_and_performs_experimental_electronic_music(X))))))=>(has_lived_in_exactly_three_countries(barbara)))&
((((?[X]:(room(X)&does_not_host_a_popular_podcast_about_emerging_technologies(X)))))=>(collects_luxury_watches(barbara)))&
((![X]:(~room(X)=>(((does_not_play_the_violin(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))<=>(![X]:(anywhere(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(composes_and_performs_experimental_electronic_music(X)))))))&
((![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(does_not_drive_a_hybrid_car(X))))))=>(does_not_play_the_violin(barbara)))&
((~?[X]:(anywhere(X)=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))=>(plays_the_violin(barbara)))&
(((~((makes_intricate_hand-cut_paper_art_for_exhibitions(barbara))|(drives_a_hybrid_car(barbara))))=>(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))<=(has_lived_in_exactly_three_countries(X)))))))&((~(~((makes_intricate_hand-cut_paper_art_for_exhibitions(barbara))|(drives_a_hybrid_car(barbara)))))=>((plays_the_violin(barbara))&(((drives_a_hybrid_car(barbara))<~>(trains_for_and_competes_in_international_triathlons(barbara)))))))&
((![X]:((enjoys_kayaking(X))=>(collects_luxury_watches(X)))))&
(![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(does_not_host_a_popular_podcast_about_emerging_technologies(barbara))&
(((collects_luxury_watches(barbara))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(barbara))|(has_lived_in_exactly_three_countries(barbara))))&
(plays_the_violin(barbara))&
(~![X]:(anywhere(X)=>(((does_not_play_the_violin(X))=>(drives_a_hybrid_car(X))))))&
(![X]:(room(X)=>(((drives_a_hybrid_car(X))<=>(does_not_play_the_violin(X))))))&
(~((composes_and_performs_experimental_electronic_music(barbara))|(makes_intricate_hand-cut_paper_art_for_exhibitions(barbara))))&
(![X]:(room(X)=>(((((does_not_have_lived_in_exactly_three_countries(X))&(has_lived_in_exactly_three_countries(X))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))=>(owns_a_smart_tv(X))))))&
(![X]:(room(X)=>(((((drives_a_hybrid_car(X))&(enjoys_kayaking(X))&(does_not_train_for_and_competes_in_international_triathlons(X))))<=(owns_a_smart_tv(X)))))) | room(barbara)&room(gladys)&room(melissa)&(![X]:(room(X)=>(X='barbara'|X='gladys'|X='melissa')))&
has_lived_in_exactly_three_countries(barbara) | [
"p0",
"p8",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1006089201847536280703447
% SZS output start Proof for 1006089201847536280703447
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
52. (~~(preda(mary) | predh(mary)) => ((preda(mary) <~> predj(mary)) & predd(mary))) & (~(preda(mary) | predh(mary)) => ! [X0] : (room(X0) => (predc(X0) => prede(X0)))) [input p8]
54. ! [X0] : (room(X0) => (~predj(X0) => prede(X0))) [input p10]
55. ~prede(mary) [input p11]
60. ~(predh(mary) | predi(mary)) [input p16]
63. predc(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
65. ((preda(mary) | predh(mary)) => ((preda(mary) <~> predj(mary)) & predd(mary))) & (~(preda(mary) | predh(mary)) => ! [X0] : (room(X0) => (predc(X0) => prede(X0)))) [flattening 52]
141. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
142. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 141]
153. (((preda(mary) <~> predj(mary)) & predd(mary)) | (~preda(mary) & ~predh(mary))) & (! [X0] : ((prede(X0) | ~predc(X0)) | ~room(X0)) | (preda(mary) | predh(mary))) [ennf transformation 65]
154. (((preda(mary) <~> predj(mary)) & predd(mary)) | (~preda(mary) & ~predh(mary))) & (! [X0] : (prede(X0) | ~predc(X0) | ~room(X0)) | preda(mary) | predh(mary)) [flattening 153]
155. ! [X0] : ((prede(X0) | predj(X0)) | ~room(X0)) [ennf transformation 54]
156. ! [X0] : (prede(X0) | predj(X0) | ~room(X0)) [flattening 155]
160. ~predh(mary) & ~predi(mary) [ennf transformation 60]
165. predc(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 63]
166. predc(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 165]
179. ((((~predj(mary) | ~preda(mary)) & (predj(mary) | preda(mary))) & predd(mary)) | (~preda(mary) & ~predh(mary))) & (! [X0] : (prede(X0) | ~predc(X0) | ~room(X0)) | preda(mary) | predh(mary)) [nnf transformation 154]
180. (((~predj(mary) | ~preda(mary)) & (predj(mary) | preda(mary)) & predd(mary)) | (~preda(mary) & ~predh(mary))) & (! [X0] : (prede(X0) | ~predc(X0) | ~room(X0)) | preda(mary) | predh(mary)) [flattening 179]
265. room(mary) [cnf transformation 142]
285. prede(X0) | ~predc(X0) | ~room(X0) | preda(mary) | predh(mary) [cnf transformation 180]
291. ~predj(mary) | ~preda(mary) | ~preda(mary) [cnf transformation 180]
292. ~room(X0) | predj(X0) | prede(X0) [cnf transformation 156]
293. ~prede(mary) [cnf transformation 55]
301. ~predh(mary) [cnf transformation 160]
310. predc(mary) [cnf transformation 166]
311. ~predj(mary) | ~preda(mary) [duplicate literal removal 291]
324. 4 <=> predh(mary) [avatar definition]
338. 7 <=> predc(mary) [avatar definition]
340. predc(mary) <- (7) [avatar component clause 338]
387. 17 <=> preda(mary) [avatar definition]
391. 18 <=> predj(mary) [avatar definition]
394. ~17 | ~18 [avatar split clause 311,391,387]
400. 19 <=> ! [X0] : (prede(X0) | ~room(X0) | ~predc(X0)) [avatar definition]
401. ~predc(X0) | ~room(X0) | prede(X0) <- (19) [avatar component clause 400]
402. 4 | 17 | 19 [avatar split clause 285,400,387,324]
404. ~4 [avatar split clause 301,324]
405. 7 [avatar split clause 310,338]
406. predj(mary) | prede(mary) [resolution 292,265]
431. predj(mary) [subsumption resolution 406,293]
432. 18 [avatar split clause 431,391]
466. ~room(mary) | prede(mary) <- (7, 19) [resolution 401,340]
467. prede(mary) <- (7, 19) [subsumption resolution 466,265]
468. $false <- (7, 19) [subsumption resolution 467,293]
469. ~7 | ~19 [avatar contradiction clause 468]
470. $false [avatar sat refutation 394,402,404,405,432,469]
% SZS output end Proof for 1006089201847536280703447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.048682 |
Cythia, Sarah, Thomas, Rodney, Virginia are the only persons in the room.
Cythia enjoys macrame.
Not everyone in the room does not enjoy macrame if they practices archery.
Everyone anywhere either does not play as a goalkeeper for a local amateur soccer team or plays as a goalkeeper for a local amateur soccer team but not both if and only if they is an avid hiker.
If someone enjoys macrame then he/she is an avid hiker.
Everyone in the room who can play the piano is an avid hiker.
Thomas either does not play as a goalkeeper for a local amateur soccer team or plays as a goalkeeper for a local amateur soccer team but not both.
Everyone in the room who does not watche fantasy movies hosts a popular podcast about emerging technologies.
Sarah enjoys macrame.
Everyone in the room can play the piano if they owns a smart tv, owns a 3D printer or can play the piano.
Cythia practices archery.
Thomas cannot play the piano.
Thomas plays as a goalkeeper for a local amateur soccer team and watches fantasy movies.
Everyone in the room who owns a 3D printer practices archery.
Sarah plays as a goalkeeper for a local amateur soccer team. | Thomas can play the piano. | contradiction | room(cythia)&room(sarah)&room(thomas)&room(rodney)&room(virginia)&(![X]:(room(X)=>(X='cythia'|X='sarah'|X='thomas'|X='rodney'|X='virginia')))&
(enjoys_macrame(cythia))&
(~![X]:(room(X)=>(((practices_archery(X))=>(does_not_enjoy_macrame(X))))))&
(![X]:(anywhere(X)=>(((((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))<=>(is_an_avid_hiker(X))))))&
((![X]:((enjoys_macrame(X))=>(is_an_avid_hiker(X)))))&
(![X]:(room(X)=>(((can_play_the_piano(X))=>(is_an_avid_hiker(X))))))&
(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(thomas))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(thomas))))&
(![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(enjoys_macrame(sarah))&
(![X]:(room(X)=>(((((owns_a_smart_tv(X))|(owns_a_3D_printer(X))|(can_play_the_piano(X))))=>(can_play_the_piano(X))))))&
(practices_archery(cythia))&
(cannot_play_the_piano(thomas))&
(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(thomas))&(watches_fantasy_movies(thomas))))&
(![X]:(room(X)=>(((owns_a_3D_printer(X))=>(practices_archery(X))))))&
(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(sarah))&
(![X]:(room(X)=>(((can_play_the_piano(X))=>(((can_play_the_piano(X))<~>(watches_fantasy_movies(X)))))))) | room(cythia)&room(sarah)&room(thomas)&room(rodney)&room(virginia)&(![X]:(room(X)=>(X='cythia'|X='sarah'|X='thomas'|X='rodney'|X='virginia')))&
can_play_the_piano(thomas) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7036899608000741490217895
% SZS output start Proof for 7036899608000741490217895
55. ~predc(fred) [input p11]
60. predc(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]
149. predc(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 60]
150. predc(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 149]
257. ~predc(fred) [cnf transformation 55]
269. predc(fred) [cnf transformation 150]
276. $false [subsumption resolution 269,257]
% SZS output end Proof for 7036899608000741490217895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Renee, Latoya, Gloria are the only persons in the room.
If “everyone outside the room does not own a high-end gaming PC with custom-built components or makes intricate hand-cut paper art for exhibitions” then “everyone in the room who does not own a high-end gaming PC with custom-built components is a dedicated volunteer for local community service projects or enjoys fishing or both”.
“No one outside the room cannot play the flute or does not collect first edition books” if “no one in the room does not own a microscope or enjoys fishing” and vice versa.
“If someone is allergic to anything and is a drone photographer then he/she either is not a wine connoisseur with a private cellar of vintage wines or can play the flute but not both” if “everyone in the room does not enjoy fishing or is not a client of Meta”.
“Everyone in the room does not make intricate hand-cut paper art for exhibitions if they owns a microscope, owns a high-end gaming PC with custom-built components and enjoys fishing and vice versa” if “everyone in the room does not make intricate hand-cut paper art for exhibitions or cannot play the guitar”.
If someone does not own a microscope or can play the guitar or both then he/she is not a drone photographer and owns a microscope.
Everyone in the room does not enjoy fishing, has a curated collection of mid-century modern furniture and is an avid mountain climber who has scaled several peaks. | Gloria enjoys fishing. | contradiction | room(renee)&room(latoya)&room(gloria)&(![X]:(room(X)=>(X='renee'|X='latoya'|X='gloria')))&
((![X]:(~room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(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))=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(enjoys_fishing(X)))))))))&
((~?[X]:(room(X)=>(((enjoys_fishing(X))|(does_not_own_a_microscope(X))))))<=>(~?[X]:(~room(X)=>(((does_not_collect_first_edition_books(X))|(cannot_play_the_flute(X)))))))&
((![X]:(room(X)=>(((is_not_a_client_of_Meta(X))|(does_not_enjoy_fishing(X))))))=>((![X]:((((is_allergic_to_anything(X))&(is_a_drone_photographer(X))))=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<~>(can_play_the_flute(X))))))))&
((![X]:(room(X)=>(((cannot_play_the_guitar(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))<=>(((owns_a_microscope(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))&(enjoys_fishing(X)))))))))&
((![X]:((((does_not_own_a_microscope(X))|(can_play_the_guitar(X))))=>(((is_not_a_drone_photographer(X))&(owns_a_microscope(X)))))))&
(![X]:(~room(X)=>(((is_a_client_of_Meta(X))=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))&
(![X]:(anywhere(X)=>(((((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))<=>(is_allergic_to_anything(X))))))&
(?[X]:(room(X)&(((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_fishing(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))) | room(renee)&room(latoya)&room(gloria)&(![X]:(room(X)=>(X='renee'|X='latoya'|X='gloria')))&
enjoys_fishing(gloria) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3829787250267380683538052
% SZS output start Proof for 3829787250267380683538052
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
53. ! [X0] : (room(X0) => (predm(X0) & predc(X0) & ~preda(X0))) [input p9]
54. preda(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
59. ! [X0] : (room(X0) => (predc(X0) & ~preda(X0))) [pure predicate removal 53]
134. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
135. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 134]
144. ! [X0] : ((predc(X0) & ~preda(X0)) | ~room(X0)) [ennf transformation 59]
145. preda(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 54]
146. preda(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 145]
250. room(fred) [cnf transformation 135]
277. ~preda(X0) | ~room(X0) [cnf transformation 144]
283. preda(fred) [cnf transformation 146]
393. ~room(fred) [resolution 277,283]
394. $false [subsumption resolution 393,250]
% SZS output end Proof for 3829787250267380683538052
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0.058216 |
Mark, Ernest, Matthew are the only persons in the room.
If Ernest is a kind old quiet person then everyone in the room is richer than Michael and is a old quiet person if they is richer than Bessie.
If Matthew is quieter than Bessie and is not a quiet kind person then it is not the case that Mark is quieter than Michael.
If someone is quieter than Bessie then he/she is a quiet person, is quieter than Michael and is older than Bessie.
Mark dreamt that Matthew is the least old outside the room.
Everyone anywhere who is quiet is not a quiet person.
If someone is richer than Michael then he/she is tall.
Michael is quieter than Matthew.
Everyone in the room is quieter than Bessie if they is quieter than Michael, is not tall or is not kind, not quiet.
If someone is older than Bessie then he/she is not kind.
Ernest is a tall person.
Everyone in the room is a tall person if they is a kind old person.
No one anywhere who is a tall person neither is kind nor is older than Michael.
Everyone anywhere neither is kind nor is older than Michael if they is quieter than Bessie, is older than Michael and is not a tall person and vice versa.
Mark is the least quiet in the room. | Ernest is older than Bessie. | contradiction | room(mark)&room(ernest)&room(matthew)&(![X]:(room(X)=>(X='mark'|X='ernest'|X='matthew')))&
((kind(ernest)&old(ernest)&quiet(ernest)&person(ernest))=>(![X]:(room(X)=>(((richer(bessie,X))=>(((richer(michael,X))&(old(X)&quiet(X)&person(X)))))))))&
((((quieter(bessie,matthew))&(~(quiet(matthew)&kind(matthew)&person(matthew)))))=>(~(quieter(michael,mark))))&
((![X]:((quieter(bessie,X))=>(((quiet(X)&person(X))&(quieter(michael,X))&(older(bessie,X)))))))&
((mark_dream=>(![X]:((~room(X)&(X!=matthew))=>older(matthew,X)))))&
(![X]:(anywhere(X)=>(((quiet(X))=>(~(quiet(X)&person(X)))))))&
((![X]:((richer(michael,X))=>(tall(X)))))&
(quieter(matthew,michael))&
(![X]:(room(X)=>(((((quieter(michael,X))|(~tall(X))|(~kind(X)&~quiet(X))))=>(quieter(bessie,X))))))&
((![X]:((older(bessie,X))=>(~kind(X)))))&
(tall(ernest)&person(ernest))&
(![X]:(room(X)=>(((kind(X)&old(X)&person(X))=>(tall(X)&person(X))))))&
(~?[X]:(anywhere(X)=>(((tall(X)&person(X))=>(~((kind(X))|(older(michael,X))))))))&
(![X]:(anywhere(X)=>(((~((kind(X))|(older(michael,X))))<=>(((quieter(bessie,X))&(older(michael,X))&(~(tall(X)&person(X)))))))))&
(![X]:((room(X)&(X!=mark))=>quieter(mark,X))) | room(mark)&room(ernest)&room(matthew)&(![X]:(room(X)=>(X='mark'|X='ernest'|X='matthew')))&
older(bessie,ernest) | [
"b4",
"p0",
"p3",
"p5",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7621475012683740558877748
% SZS output start Proof for 7621475012683740558877748
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] : (quieter(alice,X0) => (older(alice,X0) & quieter(john,X0) & person(X0) & quiet(X0))) [input p3]
49. ! [X0] : (anywhere(X0) => (quiet(X0) => ~(person(X0) & quiet(X0)))) [input p5]
52. ! [X0] : (room(X0) => (((~quiet(X0) & ~kind(X0)) | ~tall(X0) | quieter(john,X0)) => quieter(alice,X0))) [input p8]
53. ! [X0] : (older(alice,X0) => ~kind(X0)) [input p9]
56. ~? [X0] : (anywhere(X0) => ((person(X0) & tall(X0)) => ~(older(john,X0) | kind(X0)))) [input p12]
59. older(alice,paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
132. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
133. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 132]
138. ! [X0] : ((older(alice,X0) & quieter(john,X0) & person(X0) & quiet(X0)) | ~quieter(alice,X0)) [ennf transformation 47]
139. ! [X0] : (((~person(X0) | ~quiet(X0)) | ~quiet(X0)) | ~anywhere(X0)) [ennf transformation 49]
140. ! [X0] : (~person(X0) | ~quiet(X0) | ~quiet(X0) | ~anywhere(X0)) [flattening 139]
142. ! [X0] : ((quieter(alice,X0) | ((quiet(X0) | kind(X0)) & tall(X0) & ~quieter(john,X0))) | ~room(X0)) [ennf transformation 52]
143. ! [X0] : (quieter(alice,X0) | ((quiet(X0) | kind(X0)) & tall(X0) & ~quieter(john,X0)) | ~room(X0)) [flattening 142]
144. ! [X0] : (~kind(X0) | ~older(alice,X0)) [ennf transformation 53]
147. ! [X0] : (((older(john,X0) | kind(X0)) & (person(X0) & tall(X0))) & anywhere(X0)) [ennf transformation 56]
148. ! [X0] : ((older(john,X0) | kind(X0)) & person(X0) & tall(X0) & anywhere(X0)) [flattening 147]
152. older(alice,paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 59]
153. older(alice,paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 152]
157. anywhere(X0) [cnf transformation 5]
239. room(paul) [cnf transformation 133]
249. ~quieter(alice,X0) | quiet(X0) [cnf transformation 138]
253. ~person(X0) | ~quiet(X0) | ~quiet(X0) | ~anywhere(X0) [cnf transformation 140]
258. quieter(alice,X0) | quiet(X0) | kind(X0) | ~room(X0) [cnf transformation 143]
259. ~older(alice,X0) | ~kind(X0) [cnf transformation 144]
266. person(X0) [cnf transformation 148]
280. older(alice,paul) [cnf transformation 153]
284. ~person(X0) | ~quiet(X0) | ~anywhere(X0) [duplicate literal removal 253]
286. 1 <=> kind(paul) [avatar definition]
294. 3 <=> quiet(paul) [avatar definition]
295. quiet(paul) <- (3) [avatar component clause 294]
340. ~quiet(X0) | ~person(X0) [subsumption resolution 284,157]
341. ~room(X0) | kind(X0) | quiet(X0) [subsumption resolution 258,249]
343. ~kind(paul) [resolution 259,280]
345. kind(paul) | quiet(paul) [resolution 341,239]
359. ~person(paul) <- (3) [resolution 295,340]
360. $false <- (3) [subsumption resolution 359,266]
361. ~3 [avatar contradiction clause 360]
362. 3 | 1 [avatar split clause 345,286,294]
363. ~1 [avatar split clause 343,286]
364. $false [avatar sat refutation 361,362,363]
% SZS output end Proof for 7621475012683740558877748
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.193285 |
Beulah is the only person in the room.
If Beulah is a skilled home brewer experimenting with craft beer recipes then Beulah is an expert in identifying and foraging wild edible plants.
Beulah owns a 3D printer.
Beulah volunteers for local environmental conservation projects.
Beulah does not have completed a triathlon.
Beulah is an expert in identifying and foraging wild edible plants.
Beulah is a skilled home brewer experimenting with craft beer recipes.
Beulah collects action figures.
Beulah neither regularly contributes to tech forums and online communities nor can play the guitar.
Beulah owns a smart tv.
Beulah is right-handed.
Beulah is a scotch connoisseur.
Beulah dreamt that Beulah collects action figures.
Beulah dreamt that Beulah neither enjoys camping and organizing outdoor survival workshops nor collects action figures.
Beulah is a dedicated advocate for digital privacy and encryption.
Beulah knows morse code.
Beulah maintains a large, organic vegetable garden year-round.
Beulah enjoys bird watching.
Beulah reads mystery novels.
If someone is not an expert in identifying and foraging wild edible plants then he/she enjoys virtual reality gaming.
Beulah does practice yoga.
More than one person outside the room volunteers for local environmental conservation projects.
Beulah owns a high-end gaming PC with custom-built components. | Beulah dreamt that Beulah is an expert in identifying and foraging wild edible plants. | entailment | room(beulah)&(![X]:(room(X)=>(X='beulah')))&
((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(beulah))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(beulah)))&
(owns_a_3D_printer(beulah))&
(volunteers_for_local_environmental_conservation_projects(beulah))&
(does_not_have_completed_a_triathlon(beulah))&
(is_an_expert_in_identifying_and_foraging_wild_edible_plants(beulah))&
(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(beulah))&
(collects_action_figures(beulah))&
(~((regularly_contributes_to_tech_forums_and_online_communities(beulah))|(can_play_the_guitar(beulah))))&
(owns_a_smart_tv(beulah))&
(is_right-handed(beulah))&
(is_a_scotch_connoisseur(beulah))&
((beulah_dream=>(collects_action_figures(beulah))))&
((beulah_dream=>(~((enjoys_camping_and_organizing_outdoor_survival_workshops(beulah))|(collects_action_figures(beulah))))))&
(is_a_dedicated_advocate_for_digital_privacy_and_encryption(beulah))&
(knows_morse_code(beulah))&
(maintains_a_large,_organic_vegetable_garden_year-round(beulah))&
(enjoys_bird_watching(beulah))&
(reads_mystery_novels(beulah))&
((![X]:((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(enjoys_virtual_reality_gaming(X)))))&
(does_practice_yoga(beulah))&
((?[X,Y]:(~room(X)&~room(Y)&(volunteers_for_local_environmental_conservation_projects(X)&volunteers_for_local_environmental_conservation_projects(Y))&(X!=Y))))&
(owns_a_high-end_gaming_PC_with_custom-built_components(beulah)) | room(beulah)&(![X]:(room(X)=>(X='beulah')))&
(beulah_dream=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(beulah))) | [
"p0",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4479183874384070269661694
% SZS output start Proof for 4479183874384070269661694
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
51. predz(mary) [input p7]
57. mary_dream => ~(predz(mary) | predq(mary)) [input p13]
67. ~((mary_dream => predi(mary)) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
76. mary_dream => ~predz(mary) [pure predicate removal 57]
158. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
161. ~predz(mary) | ~mary_dream [ennf transformation 76]
162. (~predi(mary) & mary_dream) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 67]
166. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom]
167. (~predi(mary) & mary_dream) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 162,166]
248. room(mary) [cnf transformation 158]
249. ~room(X0) | mary = X0 [cnf transformation 158]
253. predz(mary) [cnf transformation 51]
255. ~predz(mary) | ~mary_dream [cnf transformation 161]
259. mary_dream | room(sK2) | ~room(mary) [cnf transformation 167]
260. mary_dream | mary != sK2 | ~room(mary) [cnf transformation 167]
274. ~mary_dream [subsumption resolution 255,253]
277. 3 <=> mary = sK2 [avatar definition]
279. mary != sK2 <- (~3) [avatar component clause 277]
283. 4 <=> room(sK2) [avatar definition]
285. room(sK2) <- (4) [avatar component clause 283]
287. mary != sK2 | ~room(mary) [subsumption resolution 260,274]
288. mary != sK2 [subsumption resolution 287,248]
289. ~3 [avatar split clause 288,277]
290. room(sK2) | ~room(mary) [subsumption resolution 259,274]
291. room(sK2) [subsumption resolution 290,248]
292. 4 [avatar split clause 291,283]
294. mary = sK2 <- (4) [resolution 249,285]
295. $false <- (~3, 4) [subsumption resolution 294,279]
296. 3 | ~4 [avatar contradiction clause 295]
297. $false [avatar sat refutation 289,292,296]
% SZS output end Proof for 4479183874384070269661694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.626225 |
Lupe, Patrice, Jason are the only persons in the room.
Everyone in the room is a quiet person.
If someone either is a old person or is a kind person but not both then he/she is a old person and is not old.
Everyone in the room is not old.
More than one person in the room either is a quiet person or is a tall person but not both.
Everyone in the room is not kind.
Lupe is the quietest in the room.
If someone is a tall person then he/she either is a old person or is a quiet person but not both.
Everyone in the room is not old, is not a kind person or is not quiet. | Lupe is tall. | neutral | room(lupe)&room(patrice)&room(jason)&(![X]:(room(X)=>(X='lupe'|X='patrice'|X='jason')))&
(![X]:(room(X)=>(quiet(X)&person(X))))&
((![X]:((((old(X)&person(X))<~>(kind(X)&person(X))))=>(((old(X)&person(X))&(~old(X)))))))&
(![X]:(room(X)=>(~old(X))))&
((?[X,Y]:(room(X)&room(Y)&(((quiet(X)&person(X))<~>(tall(X)&person(X)))&((quiet(Y)&person(Y))<~>(tall(Y)&person(Y))))&(X!=Y))))&
(![X]:(room(X)=>(~kind(X))))&
(![X]:((room(X)&(X!=lupe))=>quieter(X,lupe)))&
((![X]:((tall(X)&person(X))=>(((old(X)&person(X))<~>(quiet(X)&person(X)))))))&
(![X]:(room(X)=>(((~old(X))|(~(kind(X)&person(X)))|(~quiet(X)))))) | room(lupe)&room(patrice)&room(jason)&(![X]:(room(X)=>(X='lupe'|X='patrice'|X='jason')))&
tall(lupe) | [] | null | 0.253854 |
Jeffrey, Brandon, Maria, Karen, Valerie are the only persons in the room.
Everyone in the room is not a scotch connoisseur or enjoys deep-sea diving and exploring underwater caves.
Only one person in the room has completed a triathlon.
Everyone in the room who has completed a triathlon does not enjoy deep-sea diving and exploring underwater caves.
It is true that “everyone in the room has completed a triathlon if they enjoys deep-sea diving and exploring underwater caves”.
Everyone in the room who creates YouTube content has completed a triathlon or is a scotch connoisseur or both. | Not everyone in the room creates YouTube content. | entailment | room(jeffrey)&room(brandon)&room(maria)&room(karen)&room(valerie)&(![X]:(room(X)=>(X='jeffrey'|X='brandon'|X='maria'|X='karen'|X='valerie')))&
((![X]:((enjoys_landscape_photography(X))<=>(~((has_completed_a_triathlon(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X)))))))&
((![X]:((streams_on_Twitch(X))=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X)))))&
(![X]:(room(X)=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))&
(![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(is_not_a_scotch_connoisseur(X))))))&
(((?[X]:(room(X)&has_completed_a_triathlon(X)))&(![X,Y]:((room(X)&room(Y)&(has_completed_a_triathlon(X))&(has_completed_a_triathlon(Y)))=>(X=Y)))))&
(?[X]:(room(X)&(has_completed_a_triathlon(X))))&
((![X]:((((cannot_play_the_flute(X))|(does_not_collect_antique_jewelry(X))))=>(creates_YouTube_content(X)))))&
(![X]:(~room(X)=>(((collects_antique_jewelry(X))=>(has_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))&
(~![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))=>(enjoys_fishing(X))))))&
(![X]:(room(X)=>(collects_luxury_watches(X))))&
(![X]:(~room(X)=>(((has_completed_a_triathlon(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))&
(![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(has_completed_a_triathlon(X))))))&
(?[X]:(anywhere(X)&(can_play_the_flute(X))))&
(![X]:(room(X)=>(((creates_YouTube_content(X))=>(((has_completed_a_triathlon(X))|(is_a_scotch_connoisseur(X))))))))&
(![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(((enjoys_fishing(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))|(hosts_a_popular_podcast_about_emerging_technologies(X)))))))) | room(jeffrey)&room(brandon)&room(maria)&room(karen)&room(valerie)&(![X]:(room(X)=>(X='jeffrey'|X='brandon'|X='maria'|X='karen'|X='valerie')))&
~![X]:(room(X)=>(creates_YouTube_content(X))) | [
"b42",
"p0",
"p4",
"p5",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2848807815209250209843539
% SZS output start Proof for 2848807815209250209843539
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]
48. ! [X0] : (room(X0) => (~predi(X0) | predk(X0))) [input p4]
49. ! [X0,X1] : ((predf(X1) & predf(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predf(X0) & room(X0)) [input p5]
53. ! [X0] : (room(X0) => (predf(X0) => ~predk(X0))) [input p9]
57. ! [X0] : (room(X0) => (predk(X0) => predf(X0))) [input p13]
59. ! [X0] : (room(X0) => (predj(X0) => (predi(X0) | predf(X0)))) [input p15]
61. ~(~! [X0] : (room(X0) => predj(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]
62. ! [X0,X1] : ((predf(X1) & predf(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predf(X2) & room(X2)) [rectify 49]
63. ~(~! [X0] : (room(X0) => predj(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 61]
143. ! [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]
144. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 143]
145. ! [X0] : ((~predi(X0) | predk(X0)) | ~room(X0)) [ennf transformation 48]
146. ! [X0] : (~predi(X0) | predk(X0) | ~room(X0)) [flattening 145]
147. ! [X0,X1] : (X0 = X1 | (~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predf(X2) & room(X2)) [ennf transformation 62]
148. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predf(X2) & room(X2)) [flattening 147]
152. ! [X0] : ((~predk(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 53]
153. ! [X0] : (~predk(X0) | ~predf(X0) | ~room(X0)) [flattening 152]
157. ! [X0] : ((predf(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 57]
158. ! [X0] : (predf(X0) | ~predk(X0) | ~room(X0)) [flattening 157]
159. ! [X0] : (((predi(X0) | predf(X0)) | ~predj(X0)) | ~room(X0)) [ennf transformation 59]
160. ! [X0] : (predi(X0) | predf(X0) | ~predj(X0) | ~room(X0)) [flattening 159]
163. ! [X0] : (predj(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 63]
164. ! [X0] : (predj(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 163]
166. ? [X2] : (predf(X2) & room(X2)) => (predf(sK0) & room(sK0)) [choice axiom]
167. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0)) & (predf(sK0) & room(sK0)) [skolemisation 148,166]
172. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) => (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
173. ! [X0] : (predj(X0) | ~room(X0)) | (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 164,172]
238. fred != john [cnf transformation 43]
254. room(mary) [cnf transformation 144]
255. room(paul) [cnf transformation 144]
256. room(fred) [cnf transformation 144]
257. room(alice) [cnf transformation 144]
258. room(john) [cnf transformation 144]
259. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 144]
260. ~predi(X0) | predk(X0) | ~room(X0) [cnf transformation 146]
261. room(sK0) [cnf transformation 167]
262. predf(sK0) [cnf transformation 167]
263. ~predf(X1) | X0 = X1 | ~predf(X0) | ~room(X1) | ~room(X0) [cnf transformation 167]
268. ~predk(X0) | ~predf(X0) | ~room(X0) [cnf transformation 153]
272. predf(X0) | ~predk(X0) | ~room(X0) [cnf transformation 158]
273. ~predj(X0) | predf(X0) | predi(X0) | ~room(X0) [cnf transformation 160]
275. predj(X0) | ~room(X0) | room(sK3) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173]
276. predj(X0) | ~room(X0) | mary != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173]
277. predj(X0) | ~room(X0) | paul != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173]
278. predj(X0) | ~room(X0) | fred != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173]
279. predj(X0) | ~room(X0) | alice != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173]
280. predj(X0) | ~room(X0) | john != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173]
281. ~predk(X0) | ~room(X0) [subsumption resolution 272,268]
282. predj(X0) | ~room(X0) | john != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,258]
283. predj(X0) | ~room(X0) | john != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,257]
284. predj(X0) | ~room(X0) | john != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 283,256]
285. predj(X0) | ~room(X0) | john != sK3 | ~room(mary) [subsumption resolution 284,255]
286. predj(X0) | ~room(X0) | john != sK3 [subsumption resolution 285,254]
288. 1 <=> john = sK3 [avatar definition]
290. john != sK3 <- (~1) [avatar component clause 288]
292. 2 <=> ! [X0] : (predj(X0) | ~room(X0)) [avatar definition]
293. ~room(X0) | predj(X0) <- (2) [avatar component clause 292]
294. ~1 | 2 [avatar split clause 286,292,288]
295. predj(X0) | ~room(X0) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,258]
296. predj(X0) | ~room(X0) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,257]
297. predj(X0) | ~room(X0) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 296,256]
298. predj(X0) | ~room(X0) | alice != sK3 | ~room(mary) [subsumption resolution 297,255]
299. predj(X0) | ~room(X0) | alice != sK3 [subsumption resolution 298,254]
301. 3 <=> alice = sK3 [avatar definition]
303. alice != sK3 <- (~3) [avatar component clause 301]
304. ~3 | 2 [avatar split clause 299,292,301]
305. predj(X0) | ~room(X0) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,258]
306. predj(X0) | ~room(X0) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,257]
307. predj(X0) | ~room(X0) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 306,256]
308. predj(X0) | ~room(X0) | fred != sK3 | ~room(mary) [subsumption resolution 307,255]
309. predj(X0) | ~room(X0) | fred != sK3 [subsumption resolution 308,254]
311. 4 <=> fred = sK3 [avatar definition]
313. fred != sK3 <- (~4) [avatar component clause 311]
314. ~4 | 2 [avatar split clause 309,292,311]
315. predj(X0) | ~room(X0) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,258]
316. predj(X0) | ~room(X0) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,257]
317. predj(X0) | ~room(X0) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 316,256]
318. predj(X0) | ~room(X0) | paul != sK3 | ~room(mary) [subsumption resolution 317,255]
319. predj(X0) | ~room(X0) | paul != sK3 [subsumption resolution 318,254]
321. 5 <=> paul = sK3 [avatar definition]
323. paul != sK3 <- (~5) [avatar component clause 321]
324. ~5 | 2 [avatar split clause 319,292,321]
325. predj(X0) | ~room(X0) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,258]
326. predj(X0) | ~room(X0) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 325,257]
327. predj(X0) | ~room(X0) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 326,256]
328. predj(X0) | ~room(X0) | mary != sK3 | ~room(mary) [subsumption resolution 327,255]
329. predj(X0) | ~room(X0) | mary != sK3 [subsumption resolution 328,254]
331. 6 <=> mary = sK3 [avatar definition]
333. mary != sK3 <- (~6) [avatar component clause 331]
334. ~6 | 2 [avatar split clause 329,292,331]
335. predj(X0) | ~room(X0) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,258]
336. predj(X0) | ~room(X0) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 335,257]
337. predj(X0) | ~room(X0) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 336,256]
338. predj(X0) | ~room(X0) | room(sK3) | ~room(mary) [subsumption resolution 337,255]
339. predj(X0) | ~room(X0) | room(sK3) [subsumption resolution 338,254]
341. 7 <=> room(sK3) [avatar definition]
343. room(sK3) <- (7) [avatar component clause 341]
344. 7 | 2 [avatar split clause 339,292,341]
383. 12 <=> predi(fred) [avatar definition]
385. predi(fred) <- (12) [avatar component clause 383]
387. 13 <=> predf(fred) [avatar definition]
389. predf(fred) <- (13) [avatar component clause 387]
403. 16 <=> predi(john) [avatar definition]
405. predi(john) <- (16) [avatar component clause 403]
407. 17 <=> predf(john) [avatar definition]
409. predf(john) <- (17) [avatar component clause 407]
474. predj(fred) <- (2) [resolution 293,256]
476. predj(john) <- (2) [resolution 293,258]
482. predf(fred) | predi(fred) | ~room(fred) <- (2) [resolution 474,273]
484. predf(john) | predi(john) | ~room(john) <- (2) [resolution 476,273]
492. predk(fred) | ~room(fred) <- (12) [resolution 385,260]
493. predk(fred) <- (12) [subsumption resolution 492,256]
496. predk(john) | ~room(john) <- (16) [resolution 405,260]
497. predk(john) <- (16) [subsumption resolution 496,258]
522. ~room(fred) <- (12) [resolution 493,281]
525. $false <- (12) [subsumption resolution 522,256]
526. ~12 [avatar contradiction clause 525]
527. predf(fred) | predi(fred) <- (2) [subsumption resolution 482,256]
528. 12 | 13 | ~2 [avatar split clause 527,292,387,383]
558. ~room(john) <- (16) [resolution 497,281]
561. $false <- (16) [subsumption resolution 558,258]
562. ~16 [avatar contradiction clause 561]
563. predf(john) | predi(john) <- (2) [subsumption resolution 484,258]
564. 16 | 17 | ~2 [avatar split clause 563,292,407,403]
577. sK0 = X5 | ~predf(X5) | ~room(sK0) | ~room(X5) [resolution 263,262]
585. ~predf(X5) | sK0 = X5 | ~room(X5) [subsumption resolution 577,261]
590. fred = sK0 | ~room(fred) <- (13) [resolution 585,389]
592. john = sK0 | ~room(john) <- (17) [resolution 585,409]
605. fred = sK0 <- (13) [subsumption resolution 590,256]
613. john = sK0 <- (17) [subsumption resolution 592,258]
669. fred = john <- (13, 17) [forward demodulation 613,605]
670. $false <- (13, 17) [subsumption resolution 669,238]
671. ~13 | ~17 [avatar contradiction clause 670]
688. alice = sK3 | fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (7) [resolution 259,343]
689. fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (~3, 7) [subsumption resolution 688,303]
690. paul = sK3 | mary = sK3 | john = sK3 <- (~3, ~4, 7) [subsumption resolution 689,313]
691. mary = sK3 | john = sK3 <- (~3, ~4, ~5, 7) [subsumption resolution 690,323]
692. john = sK3 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 691,333]
693. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 692,290]
694. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 693]
695. $false [avatar sat refutation 294,304,314,324,334,344,526,528,562,564,671,694]
% SZS output end Proof for 2848807815209250209843539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.042 s
% ------------------------------
% ------------------------------
| 0.060146 |
Joseph, Lilian are the only persons in the room.
If “neither “A frog sings opera in the swamp at night.” nor “Stars are visible during the daytime only on Sundays.”” then “everyone anywhere makes intricate hand-cut paper art for exhibitions if they enjoys stand-up paddleboarding”.
“It is not the case that “neither “A pen does not exist that only writes secrets.” nor “A shadow does not appear only at noon.””” unless “Joseph and Lilian are kind tourists or are liked by Ruth or both”.
Joseph is the least rich in the room.
No wise person is old.
It is not the case that “it is not the case that ““A frog does not sing opera in the swamp at night.” or “A bird does not tweet using morse code.” or both””.
“A shadow does not appear only at noon.” or “A shadow appears only at noon.” but not both.
Everyone outside the room is a tall person if they plays as a goalkeeper for a local amateur soccer team.
Everyone in the room is a certified yoga instructor teaching classes weekly.
Everyone in the room can play the piano.
“A pen exists that only writes secrets.” or “A shadow does not appear only at noon.” but not both.
Everyone in the room builds model airplanes or does not have a curated collection of mid-century modern furniture.
Everyone in the room streams on Twitch if they is a quiet european.
No wise person is curious.
Lilian is not liked by Ruth.
Everyone outside the room streams on Twitch.
“A bird does not tweet using morse code.” and “A shadow does not appear only at noon.”.
It is not the case that “it is not the case that ““A frog sings opera in the swamp at night.” and “A pen does not exist that only writes secrets.”””.
Everyone in the room has a curated collection of mid-century modern furniture if they plays as a goalkeeper for a local amateur soccer team.
Everyone in the room drives a hybrid car.
Everyone in the room is not liked by Alice.
Everyone in the room hates Annie.
Not everyone in the room is a quiet person.
Everyone anywhere is a funny person if they has a vast collection of first-edition science fiction novels. | A shadow appears only at noon. | contradiction | room(joseph)&room(lilian)&(![X]:(room(X)=>(X='joseph'|X='lilian')))&
((~((A_frog_sings_opera_in_the_swamp_at_night.)|(Stars_are_visible_during_the_daytime_only_on_Sundays.)))=>(![X]:(anywhere(X)=>(((enjoys_stand-up_paddleboarding(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))))&
(~(((kind(joseph)&tourist(joseph))|(like(joseph,ruth)))&((kind(lilian)&tourist(lilian))|(like(lilian,ruth))))=>(~(~((A_pen_does_not_exist_that_only_writes_secrets.)|(A_shadow_does_not_appear_only_at_noon.)))))&
(![X]:((room(X)&(X!=joseph))=>richer(joseph,X)))&
(~?[X]:(wise(X)=>old(X)))&
(~(~(((A_frog_does_not_sing_opera_in_the_swamp_at_night.)|(A_bird_does_not_tweet_using_morse_code.)))))&
(((A_shadow_does_not_appear_only_at_noon.)<~>(A_shadow_appears_only_at_noon.)))&
(![X]:(~room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(tall(X)&person(X))))))&
(![X]:(room(X)=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))&
(![X]:(room(X)=>(can_play_the_piano(X))))&
(((A_pen_exists_that_only_writes_secrets.)<~>(A_shadow_does_not_appear_only_at_noon.)))&
(![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(builds_model_airplanes(X))))))&
(![X]:(room(X)=>(((quiet(X)&european(X))=>(streams_on_Twitch(X))))))&
(~?[X]:(wise(X)=>curious(X)))&
(~like(lilian,ruth))&
(![X]:(~room(X)=>(streams_on_Twitch(X))))&
(((A_bird_does_not_tweet_using_morse_code.)&(A_shadow_does_not_appear_only_at_noon.)))&
(~(~(((A_frog_sings_opera_in_the_swamp_at_night.)&(A_pen_does_not_exist_that_only_writes_secrets.)))))&
(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))&
(![X]:(room(X)=>(drives_a_hybrid_car(X))))&
(![X]:(room(X)=>(~like(X,alice))))&
(![X]:(room(X)=>(hate(annie,X))))&
(~![X]:(room(X)=>(quiet(X)&person(X))))&
(![X]:(anywhere(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(funny(X)&person(X)))))) | room(joseph)&room(lilian)&(![X]:(room(X)=>(X='joseph'|X='lilian')))&
A_shadow_appears_only_at_noon. | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 842526922821277057113034
% SZS output start Proof for 842526922821277057113034
60. ~propositiona & ~propositione [input p16]
68. propositiona & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
85. ~propositiona [pure predicate removal 60]
175. propositiona & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 68]
176. propositiona & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 175]
277. ~propositiona [cnf transformation 85]
286. propositiona [cnf transformation 176]
300. 4 <=> propositiona [avatar definition]
316. ~4 [avatar split clause 277,300]
327. 4 [avatar split clause 286,300]
328. $false [avatar sat refutation 316,327]
% SZS output end Proof for 842526922821277057113034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.684014 |
Carola is the only person in the room.
If “it is true that “Chad is a sibling of Carola”” then “if someone is a sibling of Raymond then he/she does not practice pilates and vice versa”.
If “Carola maintains a large, organic vegetable garden year-round” then “Carola is a client of Anthony” otherwise “no generous person is tall”.
“Carola who collects antique jewelry makes homemade pastries, competes in national level swimming championships and is a sibling of Chad” unless “Carola uses a Windows laptop”.
“Carola is a patient european” if “Carola is a old person”.
If “not everyone anywhere designs and sews custom cosplay costumes for conventions or does not work on fridays” then “all funny person is wise”.
If “Carola hates Willie” then “everyone in the room does not enjoy origami or writes and illustrates their own graphic novels” otherwise “someone in the room works on fridays”.
“All strong person is funny” unless “it is not the case that “Janine is older than Carola””.
If “everyone in the room is not a happy european or is not right-handed” then “all calm person is funny”. | Carola practices pilates. | neutral | room(carola)&(![X]:(room(X)=>(X='carola')))&
((sibling(carola,chad))=>((![X]:((sibling(raymond,X))<=>(does_not_practice_pilates(X))))))&
(((maintains_a_large,_organic_vegetable_garden_year-round(carola))=>(client(anthony,carola)))&((~(maintains_a_large,_organic_vegetable_garden_year-round(carola)))=>(~?[X]:(generous(X)=>tall(X)))))&
(~(uses_a_Windows_laptop(carola))=>((collects_antique_jewelry(carola))&(((makes_homemade_pastries(carola))&(competes_in_national_level_swimming_championships(carola))&(sibling(chad,carola))))))&
((old(carola)&person(carola))=>(patient(carola)&european(carola)))&
((~![X]:(anywhere(X)=>(((does_not_work_on_fridays(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(![X]:(funny(X)=>wise(X))))&
(((hate(willie,carola))=>(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))|(does_not_enjoy_origami(X)))))))&((~(hate(willie,carola)))=>(?[X]:(room(X)&(works_on_fridays(X))))))&
(~(~(older(carola,janine)))=>(![X]:(strong(X)=>funny(X))))&
((![X]:(room(X)=>(((is_not_right-handed(X))|(~(happy(X)&european(X)))))))=>(![X]:(calm(X)=>funny(X))))&
((collects_action_figures(carola))=>(![X]:(room(X)=>(((practices_urban_gardening(X))<=>(collects_antique_jewelry(X)))))))&
((![X]:((louder(robert,X))=>(writes_and_illustrates_their_own_graphic_novels(X)))))&
(sibling(janine,carola))&
((![X]:((practices_urban_gardening(X))=>(louder(anthony,X)))))&
(poorer(carola,willie))&
((competes_in_national_level_swimming_championships(carola))&(((~hate(chad,carola))&(works_on_fridays(carola))&(kind(carola)&european(carola)))))&
(![X]:((room(X)&(X!=carola))=>richer(X,carola)))&
(![X]:(funny(X)=>strong(X)))&
(((?[X]:(~room(X)&volunteers_for_local_environmental_conservation_projects(X)))))&
(![X]:(room(X)=>(((~like(chad,X))=>(sibling(robert,X))))))&
(![X]:(funny(X)=>generous(X))) | room(carola)&(![X]:(room(X)=>(X='carola')))&
practices_pilates(carola) | [] | null | 0.084009 |
Tracy, Victor, Debora are the only persons in the room. Debora is not a happy person. Tracy is not patient. Tracy who is not a humble person is wise. At least one person in the room neither is strong nor is not a wise person. Victor and Tracy are respectively old and strong. Tracy is not kind. It is true that "everyone outside the room is not a calm strong person or is humble or both only if they is humble". More than one person in the room is not strong. Everyone in the room is not a old person only if they is not creative. Everyone in the room is a brave person. Victor is a patient person. Someone in the room is not a calm person. Someone in the room is not calm. Debora is a generous person. Victor is old, is not brave or is curious. Everyone in the room is not a funny person. | Victor is funny. | contradiction | room(tracy)&room(victor)&room(debora)&(![X]:(room(X)=>(X='tracy'|X='victor'|X='debora')))&
(~(happy(debora)&person(debora)))&
(~patient(tracy))&
((~(humble(tracy)&person(tracy)))&(wise(tracy)))&
(((?[X]:(room(X)&~((strong(X))|(~(wise(X)&person(X))))))))&
((old(victor))&(strong(tracy)))&
(~kind(tracy))&
(![X]:(~room(X)=>(((humble(X))<=(((~(calm(X)&strong(X)&person(X)))|(humble(X))))))))&
((?[X,Y]:(room(X)&room(Y)&(~strong(X)&~strong(Y))&(X!=Y))))&
(![X]:(room(X)=>(((~creative(X))<=(~(old(X)&person(X)))))))&
(![X]:(room(X)=>(brave(X)&person(X))))&
(patient(victor)&person(victor))&
(?[X]:(room(X)&(~(calm(X)&person(X)))))&
(?[X]:(room(X)&(~calm(X))))&
(generous(debora)&person(debora))&
(((old(victor))|(~brave(victor))|(curious(victor))))&
(![X]:(room(X)=>(~(funny(X)&person(X)))))&
(![X]:(room(X)=>(((((~(funny(X)&person(X)))&(~kind(X))&(generous(X))))<=(~((~(wise(X)&funny(X)&person(X)))|(calm(X))))))))&
(![X]:(room(X)=>(((((~(funny(X)&person(X)))&(~kind(X))&(generous(X))))<=>(((~(brave(X)&person(X)))|(~(tall(X)&person(X))))))))) | room(tracy)&room(victor)&room(debora)&(![X]:(room(X)=>(X='tracy'|X='victor'|X='debora')))&
funny(victor) | [
"p0",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4876666461371313921407324
% SZS output start Proof for 4876666461371313921407324
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
54. ! [X0] : (room(X0) => (person(X0) & brave(X0))) [input p10]
60. ! [X0] : (room(X0) => ~(person(X0) & funny(X0))) [input p16]
63. funny(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
139. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
140. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 139]
146. ! [X0] : ((person(X0) & brave(X0)) | ~room(X0)) [ennf transformation 54]
148. ! [X0] : ((~person(X0) | ~funny(X0)) | ~room(X0)) [ennf transformation 60]
149. ! [X0] : (~person(X0) | ~funny(X0) | ~room(X0)) [flattening 148]
154. funny(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 63]
155. funny(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 154]
253. room(paul) [cnf transformation 140]
276. ~room(X0) | person(X0) [cnf transformation 146]
285. ~person(X0) | ~funny(X0) | ~room(X0) [cnf transformation 149]
304. funny(paul) [cnf transformation 155]
325. ~funny(X0) | ~room(X0) [subsumption resolution 285,276]
354. ~room(paul) [resolution 325,304]
355. $false [subsumption resolution 354,253]
% SZS output end Proof for 4876666461371313921407324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.280094 |
Juan, Mark, Janet are the only persons in the room. "A tower does not lean significantly without falling." and "A city has not outlawed the use of round tables." and "A door randomly teleports those who pass through it.". Juan plays as a goalkeeper for a local amateur soccer team. "A bird does not tweet using morse code." or "A door does not randomly teleport those who pass through it." or both. Everyone in the room who enjoys stand-up paddleboarding is passionate about collecting and restoring classic cars. "A city has not outlawed the use of round tables." or "A door does not randomly teleport those who pass through it." but not both. If someone plays video games then he/she enjoys making ceramics. Not everyone in the room who plays as a goalkeeper for a local amateur soccer team plays video games. "A door does not randomly teleport those who pass through it." or "A city has not outlawed the use of round tables." or both. Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings if they is passionate about collecting and restoring classic cars. Everyone in the room who regularly contributes to tech forums and online communities designs and sews custom cosplay costumes for conventions. "A door randomly teleports those who pass through it." or "A city has not outlawed the use of round tables." or both. Everyone anywhere who plays as a goalkeeper for a local amateur soccer team enjoys making ceramics. "A bird does not tweet using morse code." or "Socks do not disappear worldwide every full moon." or both. Juan who plays as a goalkeeper for a local amateur soccer team is an enthusiastic bird watcher who travels for rare sightings. A door randomly teleports those who pass through it. Everyone outside the room plays video games if they designs and sews custom cosplay costumes for conventions. Everyone in the room enjoys stand-up paddleboarding if they plays video games. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings if they plays video games. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings only if they designs and sews custom cosplay costumes for conventions. | Juan plays video games. | contradiction | room(juan)&room(mark)&room(janet)&(![X]:(room(X)=>(X='juan'|X='mark'|X='janet')))&
(((A_tower_does_not_lean_significantly_without_falling.)&(A_city_has_not_outlawed_the_use_of_round_tables.)&(A_door_randomly_teleports_those_who_pass_through_it.)))&
(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(juan))&
(((A_bird_does_not_tweet_using_morse_code.)|(A_door_does_not_randomly_teleport_those_who_pass_through_it.)))&
(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))&
(((A_city_has_not_outlawed_the_use_of_round_tables.)<~>(A_door_does_not_randomly_teleport_those_who_pass_through_it.)))&
((![X]:((plays_video_games(X))=>(enjoys_making_ceramics(X)))))&
(~![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(plays_video_games(X))))))&
(((A_door_does_not_randomly_teleport_those_who_pass_through_it.)|(A_city_has_not_outlawed_the_use_of_round_tables.)))&
(![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))&
(((A_door_randomly_teleports_those_who_pass_through_it.)|(A_city_has_not_outlawed_the_use_of_round_tables.)))&
(![X]:(anywhere(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(enjoys_making_ceramics(X))))))&
(((A_bird_does_not_tweet_using_morse_code.)|(Socks_do_not_disappear_worldwide_every_full_moon.)))&
((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(juan))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(juan)))&
(A_door_randomly_teleports_those_who_pass_through_it.)&
(![X]:(~room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(plays_video_games(X))))))&
(![X]:(room(X)=>(((plays_video_games(X))=>(enjoys_stand-up_paddleboarding(X))))))&
(![X]:(room(X)=>(((plays_video_games(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))&
(~(~((A_city_has_not_outlawed_the_use_of_round_tables.)|(A_bird_does_not_tweet_using_morse_code.))))&
(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(((A_city_has_not_outlawed_the_use_of_round_tables.)|(A_door_randomly_teleports_those_who_pass_through_it.))) | room(juan)&room(mark)&room(janet)&(![X]:(room(X)=>(X='juan'|X='mark'|X='janet')))&
plays_video_games(juan) | [
"p0",
"p4",
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5972756442719928486455803
% SZS output start Proof for 5972756442719928486455803
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
48. ! [X0] : (room(X0) => (predk(X0) => predo(X0))) [input p4]
53. ! [X0] : (room(X0) => (predo(X0) => ~predw(X0))) [input p9]
58. predw(mary) & predg(mary) [input p14]
61. ! [X0] : (room(X0) => (predq(X0) => predk(X0))) [input p17]
69. predq(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
150. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
151. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 150]
152. ! [X0] : ((predo(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 48]
153. ! [X0] : (predo(X0) | ~predk(X0) | ~room(X0)) [flattening 152]
156. ! [X0] : ((~predw(X0) | ~predo(X0)) | ~room(X0)) [ennf transformation 53]
157. ! [X0] : (~predw(X0) | ~predo(X0) | ~room(X0)) [flattening 156]
160. ! [X0] : ((predk(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 61]
161. ! [X0] : (predk(X0) | ~predq(X0) | ~room(X0)) [flattening 160]
172. predq(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 69]
173. predq(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 172]
258. room(mary) [cnf transformation 151]
265. ~predk(X0) | predo(X0) | ~room(X0) [cnf transformation 153]
272. ~predw(X0) | ~predo(X0) | ~room(X0) [cnf transformation 157]
275. predw(mary) [cnf transformation 58]
278. ~predq(X0) | predk(X0) | ~room(X0) [cnf transformation 161]
289. predq(mary) [cnf transformation 173]
290. ~predo(mary) | ~room(mary) [resolution 272,275]
291. ~predo(mary) [subsumption resolution 290,258]
292. predk(mary) | ~room(mary) [resolution 278,289]
293. predk(mary) [subsumption resolution 292,258]
294. predo(mary) | ~room(mary) [resolution 293,265]
295. ~room(mary) [subsumption resolution 294,291]
296. $false [subsumption resolution 295,258]
% SZS output end Proof for 5972756442719928486455803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.39583 |
There is a room. “Everyone in the room does not stream on Twitch or trains for and competes in international triathlons” only if “everyone in the room does not stream on Twitch only if they does practice yoga”. If “at least one person anywhere is a member of a local theater group specializing in improv” then “no one in the room either plays the drums or owns an Android phone but not both only if they participates in citizen science projects related to wildlife monitoring”. If “everyone in the room does not stream on Twitch or does not enjoy camping and organizing outdoor survival workshops” then “more than one person outside the room either plays the drums or owns an Android phone but not both”. “Not everyone outside the room who streams on Twitch is passionate about collecting and restoring classic cars” if “everyone in the room does not work as a freelance web developer specializing in e-commerce sites or participates in citizen science projects related to wildlife monitoring”. If “everyone anywhere is not a certified yoga instructor teaching classes weekly or plays video games” then “everyone in the room does not enjoy spelunking or is not a certified yoga instructor teaching classes weekly”. Everyone in the room either enjoys spelunking or practices zumba but not both if they does not enjoy spelunking. Everyone in the room either enjoys spelunking or practices zumba but not both if they participates in citizen science projects related to wildlife monitoring and vice versa. Everyone in the room who participates in citizen science projects related to wildlife monitoring neither has a pet dog nor does not own an Android phone. Everyone in the room who neither has a pet dog nor does not own an Android phone plays the drums. Everyone in the room who plays the drums plays video games, is an avid collector of autographed memorabilia from famous musicians and enjoys spelunking. Not everyone in the room plays video games, is an avid collector of autographed memorabilia from famous musicians and enjoys spelunking if they does not play the drums and vice versa. Everyone in the room does not play the drums only if they has a pet dog. Everyone in the room does not enjoy spelunking or is not a certified yoga instructor teaching classes weekly. | Everyone in the room is not a certified yoga instructor teaching classes weekly. | entailment | (there_is_a_room)&
((![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))|(does_not_stream_on_Twitch(X))))))=>(![X]:(room(X)=>(((does_practice_yoga(X))<=(does_not_stream_on_Twitch(X)))))))&
((((?[X]:(anywhere(X)&is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))=>(~?[X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=(((plays_the_drums(X))<~>(owns_an_Android_phone(X)))))))))&
((![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_stream_on_Twitch(X))))))=>((?[X,Y]:(~room(X)&~room(Y)&(((plays_the_drums(X))<~>(owns_an_Android_phone(X)))&((plays_the_drums(Y))<~>(owns_an_Android_phone(Y))))&(X!=Y)))))&
((![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))=>(~![X]:(~room(X)=>(((streams_on_Twitch(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))))&
((![X]:(anywhere(X)=>(((plays_video_games(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_enjoy_spelunking(X)))))))&
(![X]:(room(X)=>(((does_not_enjoy_spelunking(X))=>(((enjoys_spelunking(X))<~>(practices_zumba(X))))))))&
(![X]:(room(X)=>(((((enjoys_spelunking(X))<~>(practices_zumba(X))))<=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))&
(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(~((has_a_pet_dog(X))|(does_not_own_an_Android_phone(X))))))))&
(![X]:(room(X)=>(((~((has_a_pet_dog(X))|(does_not_own_an_Android_phone(X))))=>(plays_the_drums(X))))))&
(![X]:(room(X)=>(((plays_the_drums(X))=>(((plays_video_games(X))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(enjoys_spelunking(X))))))))&
(~![X]:(room(X)=>(((((plays_video_games(X))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(enjoys_spelunking(X))))<=>(does_not_play_the_drums(X))))))&
(![X]:(room(X)=>(((has_a_pet_dog(X))<=(does_not_play_the_drums(X))))))&
(![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_enjoy_spelunking(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))) | [
"p0",
"p6",
"p7",
"p8",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5840843942891186885996307
% SZS output start Proof for 5840843942891186885996307
44. there_is_a_room [input p0]
50. ! [X0] : (room(X0) => (~predv(X0) => (predv(X0) <~> predc(X0)))) [input p6]
51. ! [X0] : (room(X0) => ((predv(X0) <~> predc(X0)) <=> predx(X0))) [input p7]
52. ! [X0] : (room(X0) => (predx(X0) => ~(~predd(X0) | preds(X0)))) [input p8]
54. ! [X0] : (room(X0) => (predk(X0) => (predv(X0) & predq(X0) & predg(X0)))) [input p10]
56. ! [X0] : (room(X0) => (~predk(X0) => preds(X0))) [input p12]
57. ! [X0] : (room(X0) => (~predv(X0) | ~predm(X0))) [input p13]
58. ~(! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room) [input hypothesis]
148. ! [X0] : (((predv(X0) <~> predc(X0)) | predv(X0)) | ~room(X0)) [ennf transformation 50]
149. ! [X0] : ((predv(X0) <~> predc(X0)) | predv(X0) | ~room(X0)) [flattening 148]
150. ! [X0] : (((predv(X0) <~> predc(X0)) <=> predx(X0)) | ~room(X0)) [ennf transformation 51]
151. ! [X0] : (((predd(X0) & ~preds(X0)) | ~predx(X0)) | ~room(X0)) [ennf transformation 52]
152. ! [X0] : ((predd(X0) & ~preds(X0)) | ~predx(X0) | ~room(X0)) [flattening 151]
155. ! [X0] : (((predv(X0) & predq(X0) & predg(X0)) | ~predk(X0)) | ~room(X0)) [ennf transformation 54]
156. ! [X0] : ((predv(X0) & predq(X0) & predg(X0)) | ~predk(X0) | ~room(X0)) [flattening 155]
158. ! [X0] : ((preds(X0) | predk(X0)) | ~room(X0)) [ennf transformation 56]
159. ! [X0] : (preds(X0) | predk(X0) | ~room(X0)) [flattening 158]
160. ! [X0] : ((~predv(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 57]
161. ! [X0] : (~predv(X0) | ~predm(X0) | ~room(X0)) [flattening 160]
162. ? [X0] : (predm(X0) & room(X0)) | ~there_is_a_room [ennf transformation 58]
177. ! [X0] : (((~predc(X0) | ~predv(X0)) & (predc(X0) | predv(X0))) | predv(X0) | ~room(X0)) [nnf transformation 149]
178. ! [X0] : (((((~predc(X0) | ~predv(X0)) & (predc(X0) | predv(X0))) | ~predx(X0)) & (predx(X0) | ((predv(X0) | ~predc(X0)) & (predc(X0) | ~predv(X0))))) | ~room(X0)) [nnf transformation 150]
183. ? [X0] : (predm(X0) & room(X0)) => (predm(sK7) & room(sK7)) [choice axiom]
184. (predm(sK7) & room(sK7)) | ~there_is_a_room [skolemisation 162,183]
265. there_is_a_room [cnf transformation 44]
277. predc(X0) | predv(X0) | predv(X0) | ~room(X0) [cnf transformation 177]
280. predx(X0) | predv(X0) | ~predc(X0) | ~room(X0) [cnf transformation 178]
283. ~preds(X0) | ~predx(X0) | ~room(X0) [cnf transformation 152]
288. ~predk(X0) | predv(X0) | ~room(X0) [cnf transformation 156]
294. ~room(X0) | predk(X0) | preds(X0) [cnf transformation 159]
295. ~predv(X0) | ~predm(X0) | ~room(X0) [cnf transformation 161]
296. room(sK7) | ~there_is_a_room [cnf transformation 184]
297. predm(sK7) | ~there_is_a_room [cnf transformation 184]
298. ~room(X0) | predv(X0) | predc(X0) [duplicate literal removal 277]
357. 13 <=> ! [X0] : (~predv(X0) | ~room(X0) | ~predm(X0)) [avatar definition]
358. ~predv(X0) | ~room(X0) | ~predm(X0) <- (13) [avatar component clause 357]
365. ~room(X0) | predv(X0) | predx(X0) [subsumption resolution 280,298]
387. 13 [avatar split clause 295,357]
388. predm(sK7) [subsumption resolution 297,265]
389. room(sK7) [subsumption resolution 296,265]
397. predk(sK7) | preds(sK7) [resolution 294,389]
400. 19 <=> preds(sK7) [avatar definition]
402. preds(sK7) <- (19) [avatar component clause 400]
404. 20 <=> predk(sK7) [avatar definition]
406. predk(sK7) <- (20) [avatar component clause 404]
407. 19 | 20 [avatar split clause 397,404,400]
418. 22 <=> predv(sK7) [avatar definition]
420. predv(sK7) <- (22) [avatar component clause 418]
422. ~predx(sK7) | ~room(sK7) <- (19) [resolution 402,283]
423. ~predx(sK7) <- (19) [subsumption resolution 422,389]
425. predv(sK7) | predx(sK7) [resolution 365,389]
429. predv(sK7) <- (19) [subsumption resolution 425,423]
430. 22 | ~19 [avatar split clause 429,400,418]
462. predv(sK7) | ~room(sK7) <- (20) [resolution 406,288]
471. ~room(sK7) | ~predm(sK7) <- (13, 22) [resolution 420,358]
472. ~predm(sK7) <- (13, 22) [subsumption resolution 471,389]
473. $false <- (13, 22) [subsumption resolution 472,388]
474. ~13 | ~22 [avatar contradiction clause 473]
477. predv(sK7) <- (20) [subsumption resolution 462,389]
478. 22 | ~20 [avatar split clause 477,404,418]
479. $false [avatar sat refutation 387,407,430,474,478]
% SZS output end Proof for 5840843942891186885996307
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.255972 |
Shaunna, Lionel, Adam, Valerie are the only persons in the room. "Everyone in the room is not passionate about collecting and restoring classic cars or does not build model airplanes" if "everyone in the room has a specialized collection of handmade artisan pottery or is not a dedicated volunteer for local community service projects" and vice versa. If "Shaunna neither builds model airplanes nor does not enjoy windsurfing" then "everyone in the room neither is a dedicated volunteer for local community service projects nor does not write and illustrates their own graphic novels if they is not a tea enthusiast and vice versa". If "not everyone in the room does not host a YouTube channel dedicated to art tutorials or practices archery or both" then "Shaunna writes poetry". If "Shaunna writes poetry" then "Shaunna neither writes and illustrates their own graphic novels nor does not collect foreign coins". "Shaunna neither writes poetry nor owns a 3D printer" if "Lionel does not write poetry" and vice versa. "Lionel enjoys macrame or hosts a YouTube channel dedicated to art tutorials or both" if "Lionel does not own a 3D printer or has a specialized collection of handmade artisan pottery or both" and vice versa. If "someone in the room writes and illustrates their own graphic novels and is passionate about collecting and restoring classic cars" then "someone in the room does not enjoy coding in Python". "Someone in the room builds model airplanes" only if "more than one person in the room is not a dedicated volunteer for local community service projects". Adam is not a tea enthusiast. | Adam is a tea enthusiast. | contradiction | room(shaunna)&room(lionel)&room(adam)&room(valerie)&(![X]:(room(X)=>(X='shaunna'|X='lionel'|X='adam'|X='valerie')))&
((![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))<=>(![X]:(room(X)=>(((does_not_build_model_airplanes(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X)))))))&
((~((builds_model_airplanes(shaunna))|(does_not_enjoy_windsurfing(shaunna))))=>(![X]:(room(X)=>(((~((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))<=>(is_not_a_tea_enthusiast(X)))))))&
(((~![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(practices_archery(X))))))=>(writes_poetry(shaunna)))&
((writes_poetry(shaunna))=>(~((writes_and_illustrates_their_own_graphic_novels(shaunna))|(does_not_collect_foreign_coins(shaunna))))))&
((does_not_write_poetry(lionel))<=>(~((writes_poetry(shaunna))|(owns_a_3D_printer(shaunna)))))&
((((does_not_own_a_3D_printer(lionel))|(has_a_specialized_collection_of_handmade_artisan_pottery(lionel))))<=>(((enjoys_macrame(lionel))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(lionel)))))&
((?[X]:(room(X)&(((writes_and_illustrates_their_own_graphic_novels(X))&(is_passionate_about_collecting_and_restoring_classic_cars(X))))))=>(?[X]:(room(X)&(does_not_enjoy_coding_in_Python(X)))))&
((?[X]:(room(X)&(builds_model_airplanes(X))))=>((?[X,Y]:(room(X)&room(Y)&(is_not_a_dedicated_volunteer_for_local_community_service_projects(X)&is_not_a_dedicated_volunteer_for_local_community_service_projects(Y))&(X!=Y)))))&
(is_not_a_tea_enthusiast(adam))&
(does_not_enjoy_windsurfing(adam))&
(~((is_a_dedicated_volunteer_for_local_community_service_projects(lionel))|(does_not_write_and_illustrates_their_own_graphic_novels(lionel))))&
((?[X,Y]:(room(X)&room(Y)&(is_not_a_dedicated_volunteer_for_local_community_service_projects(X)&is_not_a_dedicated_volunteer_for_local_community_service_projects(Y))&(X!=Y))))&
(~((builds_model_airplanes(adam))|(practices_archery(adam))))&
((![X]:((((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(does_not_collect_foreign_coins(X))))=>(~((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(writes_poetry(X)))))))&
(?[X]:(~room(X)&(writes_and_illustrates_their_own_graphic_novels(X))))&
(![X]:(~room(X)=>(enjoys_windsurfing(X))))&
(((is_a_tea_enthusiast(lionel))|(is_a_dedicated_volunteer_for_local_community_service_projects(lionel))))&
(is_not_a_dedicated_volunteer_for_local_community_service_projects(adam))&
(![X]:(room(X)=>(((does_not_collect_foreign_coins(X))<=>(collects_modern_art(X))))))&
((![X]:((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))=>(((enjoys_macrame(X))|(does_not_own_a_3D_printer(X)))))))&
((![X]:((plays_the_drums(X))=>(~((enjoys_macrame(X))|(does_not_collect_foreign_coins(X)))))))&
(~((does_not_enjoy_macrame(adam))|(writes_and_illustrates_their_own_graphic_novels(adam)))) | room(shaunna)&room(lionel)&room(adam)&room(valerie)&(![X]:(room(X)=>(X='shaunna'|X='lionel'|X='adam'|X='valerie')))&
is_a_tea_enthusiast(adam) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 2038761496512925773397460
% SZS output start Proof for 2038761496512925773397460
44. ~(predj(fred) | ~preda(fred)) & ! [X0] : (predc(X0) => ~(~predo(X0) | preda(X0))) & ! [X0] : (~predp(X0) => (~predi(X0) | preda(X0))) & ! [X0] : (room(X0) => (~predo(X0) <=> predg(X0))) & ~predk(fred) & (predk(paul) | predf(paul)) & ! [X0] : (~room(X0) => predm(X0)) & ? [X0] : (predj(X0) & ~room(X0)) & ! [X0] : ((~predo(X0) | predp(X0)) => ~(predb(X0) | predp(X0))) & ~(predh(fred) | predn(fred)) & ? [X0,X1] : (X0 != X1 & ~predk(X1) & ~predk(X0) & room(X1) & room(X0)) & ~(~predj(paul) | predk(paul)) & ~predm(fred) & ~predf(fred) & (? [X0] : (predn(X0) & room(X0)) => ? [X0,X1] : (X0 != X1 & ~predk(X1) & ~predk(X0) & room(X1) & room(X0))) & (? [X0] : (predl(X0) & predj(X0) & room(X0)) => ? [X0] : (~prede(X0) & room(X0))) & ((predp(paul) | ~predi(paul)) <=> (predd(paul) | preda(paul))) & (~predb(paul) <=> ~(predi(mary) | predb(mary))) & (predb(mary) => ~(~predo(mary) | predj(mary))) & (~! [X0] : (room(X0) => (predh(X0) | ~predd(X0))) => predb(mary)) & (~(~predm(mary) | predn(mary)) => ! [X0] : (room(X0) => (~(~predj(X0) | predk(X0)) <=> ~predf(X0)))) & (! [X0] : (room(X0) => (predp(X0) | ~predk(X0))) <=> ! [X0] : (room(X0) => (~predl(X0) | ~predn(X0)))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. predf(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
46. ~(predj(fred) | ~preda(fred)) & ! [X0] : (predc(X0) => ~(~predo(X0) | preda(X0))) & ! [X1] : (~predp(X1) => (~predi(X1) | preda(X1))) & ! [X2] : (room(X2) => (~predo(X2) <=> predg(X2))) & ~predk(fred) & (predk(paul) | predf(paul)) & ! [X3] : (~room(X3) => predm(X3)) & ? [X4] : (predj(X4) & ~room(X4)) & ! [X5] : ((~predo(X5) | predp(X5)) => ~(predb(X5) | predp(X5))) & ~(predh(fred) | predn(fred)) & ? [X6,X7] : (X6 != X7 & ~predk(X7) & ~predk(X6) & room(X7) & room(X6)) & ~(~predj(paul) | predk(paul)) & ~predm(fred) & ~predf(fred) & (? [X8] : (predn(X8) & room(X8)) => ? [X9,X10] : (X9 != X10 & ~predk(X10) & ~predk(X9) & room(X10) & room(X9))) & (? [X11] : (predl(X11) & predj(X11) & room(X11)) => ? [X12] : (~prede(X12) & room(X12))) & ((predp(paul) | ~predi(paul)) <=> (predd(paul) | preda(paul))) & (~predb(paul) <=> ~(predi(mary) | predb(mary))) & (predb(mary) => ~(~predo(mary) | predj(mary))) & (~! [X13] : (room(X13) => (predh(X13) | ~predd(X13))) => predb(mary)) & (~(~predm(mary) | predn(mary)) => ! [X14] : (room(X14) => (~(~predj(X14) | predk(X14)) <=> ~predf(X14)))) & (! [X15] : (room(X15) => (predp(X15) | ~predk(X15))) <=> ! [X16] : (room(X16) => (~predl(X16) | ~predn(X16)))) & ! [X17] : (room(X17) => (alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44]
47. ~(predj(fred) | ~preda(fred)) & ! [X1] : (~predp(X1) => (~predi(X1) | preda(X1))) & ! [X2] : (room(X2) => (~predo(X2) <=> predg(X2))) & ~predk(fred) & (predk(paul) | predf(paul)) & ! [X3] : (~room(X3) => predm(X3)) & ? [X4] : (predj(X4) & ~room(X4)) & ! [X5] : ((~predo(X5) | predp(X5)) => ~(predb(X5) | predp(X5))) & ~(predh(fred) | predn(fred)) & ? [X6,X7] : (X6 != X7 & ~predk(X7) & ~predk(X6) & room(X7) & room(X6)) & ~(~predj(paul) | predk(paul)) & ~predm(fred) & ~predf(fred) & (? [X8] : (predn(X8) & room(X8)) => ? [X9,X10] : (X9 != X10 & ~predk(X10) & ~predk(X9) & room(X10) & room(X9))) & (? [X11] : (predl(X11) & predj(X11) & room(X11)) => ? [X12] : (~prede(X12) & room(X12))) & ((predp(paul) | ~predi(paul)) <=> (predd(paul) | preda(paul))) & (~predb(paul) <=> ~(predi(mary) | predb(mary))) & (predb(mary) => ~(~predo(mary) | predj(mary))) & (~! [X13] : (room(X13) => (predh(X13) | ~predd(X13))) => predb(mary)) & (~(~predm(mary) | predn(mary)) => ! [X14] : (room(X14) => (~(~predj(X14) | predk(X14)) <=> ~predf(X14)))) & (! [X15] : (room(X15) => (predp(X15) | ~predk(X15))) <=> ! [X16] : (room(X16) => (~predl(X16) | ~predn(X16)))) & ! [X17] : (room(X17) => (alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46]
48. ~(predj(fred) | ~preda(fred)) & ! [X1] : (~predp(X1) => (~predi(X1) | preda(X1))) & ! [X2] : (room(X2) => (~predo(X2) <=> predg(X2))) & ~predk(fred) & (predk(paul) | predf(paul)) & ! [X3] : (~room(X3) => predm(X3)) & ? [X4] : (predj(X4) & ~room(X4)) & ! [X5] : ((~predo(X5) | predp(X5)) => ~(predb(X5) | predp(X5))) & ~(predh(fred) | predn(fred)) & ? [X6,X7] : (X6 != X7 & ~predk(X7) & ~predk(X6) & room(X7) & room(X6)) & ~(~predj(paul) | predk(paul)) & ~predm(fred) & ~predf(fred) & (? [X8] : (predn(X8) & room(X8)) => ? [X9,X10] : (X9 != X10 & ~predk(X10) & ~predk(X9) & room(X10) & room(X9))) & (? [X11] : (predl(X11) & predj(X11) & room(X11)) => ? [X12] : room(X12)) & ((predp(paul) | ~predi(paul)) <=> (predd(paul) | preda(paul))) & (~predb(paul) <=> ~(predi(mary) | predb(mary))) & (predb(mary) => ~(~predo(mary) | predj(mary))) & (~! [X13] : (room(X13) => (predh(X13) | ~predd(X13))) => predb(mary)) & (~(~predm(mary) | predn(mary)) => ! [X14] : (room(X14) => (~(~predj(X14) | predk(X14)) <=> ~predf(X14)))) & (! [X15] : (room(X15) => (predp(X15) | ~predk(X15))) <=> ! [X16] : (room(X16) => (~predl(X16) | ~predn(X16)))) & ! [X17] : (room(X17) => (alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47]
121. (~predj(fred) & preda(fred)) & ! [X1] : ((~predi(X1) | preda(X1)) | predp(X1)) & ! [X2] : ((~predo(X2) <=> predg(X2)) | ~room(X2)) & ~predk(fred) & (predk(paul) | predf(paul)) & ! [X3] : (predm(X3) | room(X3)) & ? [X4] : (predj(X4) & ~room(X4)) & ! [X5] : ((~predb(X5) & ~predp(X5)) | (predo(X5) & ~predp(X5))) & (~predh(fred) & ~predn(fred)) & ? [X6,X7] : (X6 != X7 & ~predk(X7) & ~predk(X6) & room(X7) & room(X6)) & (predj(paul) & ~predk(paul)) & ~predm(fred) & ~predf(fred) & (? [X9,X10] : (X9 != X10 & ~predk(X10) & ~predk(X9) & room(X10) & room(X9)) | ! [X8] : (~predn(X8) | ~room(X8))) & (? [X12] : room(X12) | ! [X11] : (~predl(X11) | ~predj(X11) | ~room(X11))) & ((predp(paul) | ~predi(paul)) <=> (predd(paul) | preda(paul))) & (~predb(paul) <=> (~predi(mary) & ~predb(mary))) & ((predo(mary) & ~predj(mary)) | ~predb(mary)) & (predb(mary) | ! [X13] : ((predh(X13) | ~predd(X13)) | ~room(X13))) & (! [X14] : (((predj(X14) & ~predk(X14)) <=> ~predf(X14)) | ~room(X14)) | (~predm(mary) | predn(mary))) & (! [X15] : ((predp(X15) | ~predk(X15)) | ~room(X15)) <=> ! [X16] : ((~predl(X16) | ~predn(X16)) | ~room(X16))) & ! [X17] : ((alice = X17 | fred = X17 | paul = X17 | mary = X17) | ~room(X17)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 48]
122. ~predj(fred) & preda(fred) & ! [X1] : (~predi(X1) | preda(X1) | predp(X1)) & ! [X2] : ((~predo(X2) <=> predg(X2)) | ~room(X2)) & ~predk(fred) & (predk(paul) | predf(paul)) & ! [X3] : (predm(X3) | room(X3)) & ? [X4] : (predj(X4) & ~room(X4)) & ! [X5] : ((~predb(X5) & ~predp(X5)) | (predo(X5) & ~predp(X5))) & ~predh(fred) & ~predn(fred) & ? [X6,X7] : (X6 != X7 & ~predk(X7) & ~predk(X6) & room(X7) & room(X6)) & predj(paul) & ~predk(paul) & ~predm(fred) & ~predf(fred) & (? [X9,X10] : (X9 != X10 & ~predk(X10) & ~predk(X9) & room(X10) & room(X9)) | ! [X8] : (~predn(X8) | ~room(X8))) & (? [X12] : room(X12) | ! [X11] : (~predl(X11) | ~predj(X11) | ~room(X11))) & ((predp(paul) | ~predi(paul)) <=> (predd(paul) | preda(paul))) & (~predb(paul) <=> (~predi(mary) & ~predb(mary))) & ((predo(mary) & ~predj(mary)) | ~predb(mary)) & (predb(mary) | ! [X13] : (predh(X13) | ~predd(X13) | ~room(X13))) & (! [X14] : (((predj(X14) & ~predk(X14)) <=> ~predf(X14)) | ~room(X14)) | ~predm(mary) | predn(mary)) & (! [X15] : (predp(X15) | ~predk(X15) | ~room(X15)) <=> ! [X16] : (~predl(X16) | ~predn(X16) | ~room(X16))) & ! [X17] : (alice = X17 | fred = X17 | paul = X17 | mary = X17 | ~room(X17)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 121]
123. predf(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 45]
124. predf(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 123]
126. ~predj(fred) & preda(fred) & ! [X1] : (~predi(X1) | preda(X1) | predp(X1)) & ! [X2] : (((~predo(X2) | ~predg(X2)) & (predg(X2) | predo(X2))) | ~room(X2)) & ~predk(fred) & (predk(paul) | predf(paul)) & ! [X3] : (predm(X3) | room(X3)) & ? [X4] : (predj(X4) & ~room(X4)) & ! [X5] : ((~predb(X5) & ~predp(X5)) | (predo(X5) & ~predp(X5))) & ~predh(fred) & ~predn(fred) & ? [X6,X7] : (X6 != X7 & ~predk(X7) & ~predk(X6) & room(X7) & room(X6)) & predj(paul) & ~predk(paul) & ~predm(fred) & ~predf(fred) & (? [X9,X10] : (X9 != X10 & ~predk(X10) & ~predk(X9) & room(X10) & room(X9)) | ! [X8] : (~predn(X8) | ~room(X8))) & (? [X12] : room(X12) | ! [X11] : (~predl(X11) | ~predj(X11) | ~room(X11))) & (((predp(paul) | ~predi(paul)) | (~predd(paul) & ~preda(paul))) & ((predd(paul) | preda(paul)) | (~predp(paul) & predi(paul)))) & ((~predb(paul) | (predi(mary) | predb(mary))) & ((~predi(mary) & ~predb(mary)) | predb(paul))) & ((predo(mary) & ~predj(mary)) | ~predb(mary)) & (predb(mary) | ! [X13] : (predh(X13) | ~predd(X13) | ~room(X13))) & (! [X14] : ((((predj(X14) & ~predk(X14)) | predf(X14)) & (~predf(X14) | (~predj(X14) | predk(X14)))) | ~room(X14)) | ~predm(mary) | predn(mary)) & ((! [X15] : (predp(X15) | ~predk(X15) | ~room(X15)) | ? [X16] : (predl(X16) & predn(X16) & room(X16))) & (! [X16] : (~predl(X16) | ~predn(X16) | ~room(X16)) | ? [X15] : (~predp(X15) & predk(X15) & room(X15)))) & ! [X17] : (alice = X17 | fred = X17 | paul = X17 | mary = X17 | ~room(X17)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 122]
127. ~predj(fred) & preda(fred) & ! [X1] : (~predi(X1) | preda(X1) | predp(X1)) & ! [X2] : (((~predo(X2) | ~predg(X2)) & (predg(X2) | predo(X2))) | ~room(X2)) & ~predk(fred) & (predk(paul) | predf(paul)) & ! [X3] : (predm(X3) | room(X3)) & ? [X4] : (predj(X4) & ~room(X4)) & ! [X5] : ((~predb(X5) & ~predp(X5)) | (predo(X5) & ~predp(X5))) & ~predh(fred) & ~predn(fred) & ? [X6,X7] : (X6 != X7 & ~predk(X7) & ~predk(X6) & room(X7) & room(X6)) & predj(paul) & ~predk(paul) & ~predm(fred) & ~predf(fred) & (? [X9,X10] : (X9 != X10 & ~predk(X10) & ~predk(X9) & room(X10) & room(X9)) | ! [X8] : (~predn(X8) | ~room(X8))) & (? [X12] : room(X12) | ! [X11] : (~predl(X11) | ~predj(X11) | ~room(X11))) & (predp(paul) | ~predi(paul) | (~predd(paul) & ~preda(paul))) & (predd(paul) | preda(paul) | (~predp(paul) & predi(paul))) & (~predb(paul) | predi(mary) | predb(mary)) & ((~predi(mary) & ~predb(mary)) | predb(paul)) & ((predo(mary) & ~predj(mary)) | ~predb(mary)) & (predb(mary) | ! [X13] : (predh(X13) | ~predd(X13) | ~room(X13))) & (! [X14] : ((((predj(X14) & ~predk(X14)) | predf(X14)) & (~predf(X14) | ~predj(X14) | predk(X14))) | ~room(X14)) | ~predm(mary) | predn(mary)) & (! [X15] : (predp(X15) | ~predk(X15) | ~room(X15)) | ? [X16] : (predl(X16) & predn(X16) & room(X16))) & (! [X16] : (~predl(X16) | ~predn(X16) | ~room(X16)) | ? [X15] : (~predp(X15) & predk(X15) & room(X15))) & ! [X17] : (alice = X17 | fred = X17 | paul = X17 | mary = X17 | ~room(X17)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126]
128. ~predj(fred) & preda(fred) & ! [X0] : (~predi(X0) | preda(X0) | predp(X0)) & ! [X1] : (((~predo(X1) | ~predg(X1)) & (predg(X1) | predo(X1))) | ~room(X1)) & ~predk(fred) & (predk(paul) | predf(paul)) & ! [X2] : (predm(X2) | room(X2)) & ? [X3] : (predj(X3) & ~room(X3)) & ! [X4] : ((~predb(X4) & ~predp(X4)) | (predo(X4) & ~predp(X4))) & ~predh(fred) & ~predn(fred) & ? [X5,X6] : (X5 != X6 & ~predk(X6) & ~predk(X5) & room(X6) & room(X5)) & predj(paul) & ~predk(paul) & ~predm(fred) & ~predf(fred) & (? [X7,X8] : (X7 != X8 & ~predk(X8) & ~predk(X7) & room(X8) & room(X7)) | ! [X9] : (~predn(X9) | ~room(X9))) & (? [X10] : room(X10) | ! [X11] : (~predl(X11) | ~predj(X11) | ~room(X11))) & (predp(paul) | ~predi(paul) | (~predd(paul) & ~preda(paul))) & (predd(paul) | preda(paul) | (~predp(paul) & predi(paul))) & (~predb(paul) | predi(mary) | predb(mary)) & ((~predi(mary) & ~predb(mary)) | predb(paul)) & ((predo(mary) & ~predj(mary)) | ~predb(mary)) & (predb(mary) | ! [X12] : (predh(X12) | ~predd(X12) | ~room(X12))) & (! [X13] : ((((predj(X13) & ~predk(X13)) | predf(X13)) & (~predf(X13) | ~predj(X13) | predk(X13))) | ~room(X13)) | ~predm(mary) | predn(mary)) & (! [X14] : (predp(X14) | ~predk(X14) | ~room(X14)) | ? [X15] : (predl(X15) & predn(X15) & room(X15))) & (! [X16] : (~predl(X16) | ~predn(X16) | ~room(X16)) | ? [X17] : (~predp(X17) & predk(X17) & room(X17))) & ! [X18] : (alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 127]
129. ? [X3] : (predj(X3) & ~room(X3)) => (predj(sK0) & ~room(sK0)) [choice axiom]
130. ? [X5,X6] : (X5 != X6 & ~predk(X6) & ~predk(X5) & room(X6) & room(X5)) => (sK1 != sK2 & ~predk(sK2) & ~predk(sK1) & room(sK2) & room(sK1)) [choice axiom]
131. ? [X7,X8] : (X7 != X8 & ~predk(X8) & ~predk(X7) & room(X8) & room(X7)) => (sK3 != sK4 & ~predk(sK4) & ~predk(sK3) & room(sK4) & room(sK3)) [choice axiom]
132. ? [X10] : room(X10) => room(sK5) [choice axiom]
133. ? [X15] : (predl(X15) & predn(X15) & room(X15)) => (predl(sK6) & predn(sK6) & room(sK6)) [choice axiom]
134. ? [X17] : (~predp(X17) & predk(X17) & room(X17)) => (~predp(sK7) & predk(sK7) & room(sK7)) [choice axiom]
135. ~predj(fred) & preda(fred) & ! [X0] : (~predi(X0) | preda(X0) | predp(X0)) & ! [X1] : (((~predo(X1) | ~predg(X1)) & (predg(X1) | predo(X1))) | ~room(X1)) & ~predk(fred) & (predk(paul) | predf(paul)) & ! [X2] : (predm(X2) | room(X2)) & (predj(sK0) & ~room(sK0)) & ! [X4] : ((~predb(X4) & ~predp(X4)) | (predo(X4) & ~predp(X4))) & ~predh(fred) & ~predn(fred) & (sK1 != sK2 & ~predk(sK2) & ~predk(sK1) & room(sK2) & room(sK1)) & predj(paul) & ~predk(paul) & ~predm(fred) & ~predf(fred) & ((sK3 != sK4 & ~predk(sK4) & ~predk(sK3) & room(sK4) & room(sK3)) | ! [X9] : (~predn(X9) | ~room(X9))) & (room(sK5) | ! [X11] : (~predl(X11) | ~predj(X11) | ~room(X11))) & (predp(paul) | ~predi(paul) | (~predd(paul) & ~preda(paul))) & (predd(paul) | preda(paul) | (~predp(paul) & predi(paul))) & (~predb(paul) | predi(mary) | predb(mary)) & ((~predi(mary) & ~predb(mary)) | predb(paul)) & ((predo(mary) & ~predj(mary)) | ~predb(mary)) & (predb(mary) | ! [X12] : (predh(X12) | ~predd(X12) | ~room(X12))) & (! [X13] : ((((predj(X13) & ~predk(X13)) | predf(X13)) & (~predf(X13) | ~predj(X13) | predk(X13))) | ~room(X13)) | ~predm(mary) | predn(mary)) & (! [X14] : (predp(X14) | ~predk(X14) | ~room(X14)) | (predl(sK6) & predn(sK6) & room(sK6))) & (! [X16] : (~predl(X16) | ~predn(X16) | ~room(X16)) | (~predp(sK7) & predk(sK7) & room(sK7))) & ! [X18] : (alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 128,134,133,132,131,130,129]
246. ~predf(fred) [cnf transformation 135]
276. predf(fred) [cnf transformation 124]
419. $false [subsumption resolution 276,246]
% SZS output end Proof for 2038761496512925773397460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0.580734 |
There is a room.
“Everyone outside the room does not have completed a triathlon or hosts a popular podcast about emerging technologies” only if “everyone anywhere is a skilled home brewer experimenting with craft beer recipes”.
If “everyone in the room is not a drone photographer or enjoys stand-up paddleboarding” then “everyone in the room owns a significant collection of rare gemstones and minerals if and only if they is a skilled home brewer experimenting with craft beer recipes”.
“Everyone in the room does not have completed a triathlon or is a skilled home brewer experimenting with craft beer recipes” if “everyone anywhere is not an avid mountain climber who has scaled several peaks or collects vintage stamps” and vice versa.
“Everyone in the room collects vintage stamps, plays eSports competitively or collects foreign coins if they does not collect vintage stamps” if “everyone in the room does not collect vintage stamps or does not enjoy stand-up paddleboarding”.
If “everyone in the room is not a skilled home brewer experimenting with craft beer recipes or own a television” then “everyone in the room who is not a skilled home brewer experimenting with craft beer recipes plays eSports competitively”.
No one in the room who plays eSports competitively either writes a travel blog or enjoys stand-up paddleboarding but not both.
Everyone in the room either writes a travel blog or enjoys stand-up paddleboarding but not both only if they writes a travel blog.
Everyone in the room writes a travel blog if and only if they either does not host a YouTube channel dedicated to art tutorials or develops open-source software projects in their free time but not both.
Everyone in the room either is a skilled home brewer experimenting with craft beer recipes or enjoys stand-up paddleboarding but not both if and only if they owns a significant collection of rare gemstones and minerals.
Everyone in the room owns a significant collection of rare gemstones and minerals only if they is an avid mountain climber who has scaled several peaks.
Everyone in the room who is an avid mountain climber who has scaled several peaks has completed a triathlon.
Everyone in the room who has completed a triathlon is a drone photographer.
Everyone in the room plays eSports competitively only if they collects foreign coins and writes in-depth travel guides for off-the-beaten-path destinations.
Everyone in the room who collects foreign coins and writes in-depth travel guides for off-the-beaten-path destinations owns a significant collection of rare gemstones and minerals.
Someone in the room collects foreign coins. | Everyone in the room is an avid mountain climber who has scaled several peaks. | entailment | (there_is_a_room)&
((![X]:(~room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))|(does_not_have_completed_a_triathlon(X))))))=>(![X]:(anywhere(X)=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))&
((![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))|(is_not_a_drone_photographer(X))))))=>(![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))&
((![X]:(anywhere(X)=>(((collects_vintage_stamps(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))<=>(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_have_completed_a_triathlon(X)))))))&
((![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(does_not_collect_vintage_stamps(X))))))=>(![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))=>(((collects_vintage_stamps(X))|(plays_eSports_competitively(X))|(collects_foreign_coins(X)))))))))&
((![X]:(room(X)=>(((own_a_television(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(plays_eSports_competitively(X)))))))&
(~?[X]:(room(X)=>(((plays_eSports_competitively(X))=>(((writes_a_travel_blog(X))<~>(enjoys_stand-up_paddleboarding(X))))))))&
(![X]:(room(X)=>(((writes_a_travel_blog(X))<=(((writes_a_travel_blog(X))<~>(enjoys_stand-up_paddleboarding(X))))))))&
(![X]:(room(X)=>(((writes_a_travel_blog(X))<=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))<~>(develops_open-source_software_projects_in_their_free_time(X))))))))&
(![X]:(room(X)=>(((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<~>(enjoys_stand-up_paddleboarding(X))))<=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
(![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
(![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(has_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(is_a_drone_photographer(X))))))&
(![X]:(room(X)=>(((((collects_foreign_coins(X))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))<=(plays_eSports_competitively(X))))))&
(![X]:(room(X)=>(((((collects_foreign_coins(X))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
(?[X]:(room(X)&(collects_foreign_coins(X)))) | (there_is_a_room)&
![X]:(room(X)=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))) | [
"p0",
"p6",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4188715489973169252279166
% SZS output start Proof for 4188715489973169252279166
44. there_is_a_room [input p0]
50. ~? [X0] : (room(X0) => (predc(X0) => (preda(X0) <~> predh(X0)))) [input p6]
54. ! [X0] : (room(X0) => (predm(X0) => predk(X0))) [input p10]
57. ! [X0] : (room(X0) => (predc(X0) => (predf(X0) & predn(X0)))) [input p13]
58. ! [X0] : (room(X0) => ((predf(X0) & predn(X0)) => predm(X0))) [input p14]
60. ~(! [X0] : (room(X0) => predk(X0)) & there_is_a_room) [input hypothesis]
149. ! [X0] : (((preda(X0) <=> predh(X0)) & predc(X0)) & room(X0)) [ennf transformation 50]
150. ! [X0] : ((preda(X0) <=> predh(X0)) & predc(X0) & room(X0)) [flattening 149]
155. ! [X0] : ((predk(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 54]
156. ! [X0] : (predk(X0) | ~predm(X0) | ~room(X0)) [flattening 155]
159. ! [X0] : (((predf(X0) & predn(X0)) | ~predc(X0)) | ~room(X0)) [ennf transformation 57]
160. ! [X0] : ((predf(X0) & predn(X0)) | ~predc(X0) | ~room(X0)) [flattening 159]
161. ! [X0] : ((predm(X0) | (~predf(X0) | ~predn(X0))) | ~room(X0)) [ennf transformation 58]
162. ! [X0] : (predm(X0) | ~predf(X0) | ~predn(X0) | ~room(X0)) [flattening 161]
163. ? [X0] : (~predk(X0) & room(X0)) | ~there_is_a_room [ennf transformation 60]
183. ! [X0] : (((preda(X0) | ~predh(X0)) & (predh(X0) | ~preda(X0))) & predc(X0) & room(X0)) [nnf transformation 150]
184. ! [X0] : ((preda(X0) | ~predh(X0)) & (predh(X0) | ~preda(X0)) & predc(X0) & room(X0)) [flattening 183]
190. ? [X0] : (~predk(X0) & room(X0)) => (~predk(sK7) & room(sK7)) [choice axiom]
191. (~predk(sK7) & room(sK7)) | ~there_is_a_room [skolemisation 163,190]
273. there_is_a_room [cnf transformation 44]
291. room(X0) [cnf transformation 184]
292. predc(X0) [cnf transformation 184]
305. predk(X0) | ~predm(X0) | ~room(X0) [cnf transformation 156]
307. predn(X0) | ~predc(X0) | ~room(X0) [cnf transformation 160]
308. predf(X0) | ~predc(X0) | ~room(X0) [cnf transformation 160]
309. predm(X0) | ~predf(X0) | ~predn(X0) | ~room(X0) [cnf transformation 162]
313. ~predk(sK7) | ~there_is_a_room [cnf transformation 191]
424. ~predm(X0) | predk(X0) [subsumption resolution 305,291]
426. predf(X0) | ~room(X0) [subsumption resolution 308,292]
427. predf(X0) [subsumption resolution 426,291]
428. predn(X0) | ~room(X0) [subsumption resolution 307,292]
429. predn(X0) [subsumption resolution 428,291]
430. predm(X0) | ~predn(X0) | ~room(X0) [subsumption resolution 309,427]
431. predm(X0) | ~room(X0) [subsumption resolution 430,429]
432. predm(X0) [subsumption resolution 431,291]
433. ~predk(sK7) [subsumption resolution 313,273]
439. predk(X0) [resolution 424,432]
440. $false [resolution 439,433]
% SZS output end Proof for 4188715489973169252279166
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.258936 |
Mark is the only person in the room.
Either Mark is a culinary enthusiast who experiments with international cuisines or Mark enjoys cross-country skiing but not both.
If everyone in the room is not a certified yoga instructor teaching classes weekly or reads mystery novels then everyone in the room reads mystery novels if and only if they enjoys logic puzzles or enjoys fishing or both.
Mark who is an expert in identifying and foraging wild edible plants is a tea enthusiast, does not collect antique jewelry or is a coffee connoisseur.
Mark reads mystery novels.
Mark participates in long-distance cycling events across the country.
Everyone in the room plays eSports competitively if they is not a coffee connoisseur and vice versa.
Everyone in the room is a certified yoga instructor teaching classes weekly, enjoys spelunking and enjoys fishing.
Everyone in the room is a tea enthusiast if they can play the harmonica.
Everyone outside the room owns a smart tv if they is a tea enthusiast.
Mark enjoys logic puzzles.
Everyone in the room reads mystery novels if and only if they enjoys logic puzzles or enjoys fishing or both. | Mark is a culinary enthusiast who experiments with international cuisines. | neutral | room(mark)&(![X]:(room(X)=>(X='mark')))&
((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(mark))<~>(enjoys_cross-country_skiing(mark)))&
((![X]:(room(X)=>(((reads_mystery_novels(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((reads_mystery_novels(X))<=>(((enjoys_logic_puzzles(X))|(enjoys_fishing(X)))))))))&
((is_an_expert_in_identifying_and_foraging_wild_edible_plants(mark))&(((is_a_tea_enthusiast(mark))|(does_not_collect_antique_jewelry(mark))|(is_a_coffee_connoisseur(mark)))))&
(reads_mystery_novels(mark))&
(participates_in_long-distance_cycling_events_across_the_country(mark))&
(![X]:(room(X)=>(((plays_eSports_competitively(X))<=>(is_not_a_coffee_connoisseur(X))))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(enjoys_spelunking(X))&(enjoys_fishing(X))))))&
(![X]:(room(X)=>(((can_play_the_harmonica(X))=>(is_a_tea_enthusiast(X))))))&
(![X]:(~room(X)=>(((is_a_tea_enthusiast(X))=>(owns_a_smart_tv(X))))))&
(enjoys_logic_puzzles(mark))&
(![X]:(room(X)=>(((reads_mystery_novels(X))<=>(((enjoys_logic_puzzles(X))|(enjoys_fishing(X)))))))) | room(mark)&(![X]:(room(X)=>(X='mark')))&
is_a_culinary_enthusiast_who_experiments_with_international_cuisines(mark) | [] | null | 0.035004 |
Barry is the only person in the room.
Either 'no one in the room does not enjoy landscape photography or is a culinary enthusiast who experiments with international cuisines' or 'Barry enjoys making ceramics' but not both.
'Everyone in the room uses an ios phone if they uses a Windows laptop or watches fantasy movies or both' unless 'everyone anywhere does not enjoy stargazing or uses a Windows laptop'.
If 'no one in the room enjoys deep-sea diving and exploring underwater caves or is not an avid mountain climber who has scaled several peaks' then 'Barry enjoys stargazing'.
If 'everyone anywhere watches fantasy movies or does not practice archery' then 'no one in the room who watches fantasy movies enjoys deep-sea diving and exploring underwater caves'.
If 'Barry enjoys cross-country skiing' then 'no one anywhere does not write in-depth travel guides for off-the-beaten-path destinations or enjoys origami'.
If 'no one anywhere does not write in-depth travel guides for off-the-beaten-path destinations or enjoys origami' then 'Barry is not an avid mountain climber who has scaled several peaks'.
If 'everyone in the room does not watche fantasy movies or enjoys making ceramics' then 'everyone outside the room who does not watche fantasy movies is an avid mountain climber who has scaled several peaks'. | Barry enjoys stargazing. | neutral | room(barry)&(![X]:(room(X)=>(X='barry')))&
((~?[X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_enjoy_landscape_photography(X))))))<~>(enjoys_making_ceramics(barry)))&
(~(![X]:(anywhere(X)=>(((uses_a_Windows_laptop(X))|(does_not_enjoy_stargazing(X))))))=>(![X]:(room(X)=>(((((uses_a_Windows_laptop(X))|(watches_fantasy_movies(X))))=>(uses_an_ios_phone(X)))))))&
((~?[X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(enjoys_stargazing(barry)))&
((![X]:(anywhere(X)=>(((does_not_practice_archery(X))|(watches_fantasy_movies(X))))))=>(~?[X]:(room(X)=>(((watches_fantasy_movies(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))&
(((enjoys_cross-country_skiing(barry))=>(~?[X]:(anywhere(X)=>(((enjoys_origami(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))&
((~?[X]:(anywhere(X)=>(((enjoys_origami(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))=>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(barry))))&
((![X]:(room(X)=>(((enjoys_making_ceramics(X))|(does_not_watche_fantasy_movies(X))))))=>(![X]:(~room(X)=>(((does_not_watche_fantasy_movies(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))&
((cannot_play_the_flute(barry))=>(![X]:(room(X)=>(((enjoys_stargazing(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))&
(![X]:(anywhere(X)=>(((uses_a_Windows_laptop(X))|(does_not_enjoy_stargazing(X))))))&
(![X]:(room(X)=>(((uses_an_ios_phone(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(~room(X)=>(((owns_a_smart_tv(X))<=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
(is_a_certified_yoga_instructor_teaching_classes_weekly(barry))&
(![X]:(room(X)=>(((does_not_own_a_smart_tv(X))=>(enjoys_logic_puzzles(X))))))&
(![X]:(anywhere(X)=>(((enjoys_logic_puzzles(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))&
(![X]:(room(X)=>(((enjoys_origami(X))=>(enjoys_stargazing(X))))))&
(hosts_regular_game_nights_featuring_complex_strategy_games(barry))&
(uses_an_ios_phone(barry))&
(![X]:(room(X)=>(((enjoys_logic_puzzles(X))|(cannot_play_the_flute(X)))))) | room(barry)&(![X]:(room(X)=>(X='barry')))&
enjoys_stargazing(barry) | [] | null | 0.135665 |
Terry, Heidi, Ashley, Teresa are the only persons in the room. If “Ashley neither is not a old person nor is quiet” then “everyone anywhere is a quiet person” otherwise “Terry and Heidi are old persons”. Either “Ashley is not quiet” or “everyone anywhere is a quiet person” but not both. “Everyone anywhere is a quiet person” if “Ashley and Heidi are not a quiet persons or are not old or both”. If “everyone in the room is quiet or is not a quiet person or both” then “more than one person in the room is a quiet person” otherwise “everyone anywhere is a old person”. Terry is a old person. Terry is old and is a old person. All quiet persons are old. Terry and Heidi are quiet persons. | Ashley is quiet. | neutral | room(terry)&room(heidi)&room(ashley)&room(teresa)&(![X]:(room(X)=>(X='terry'|X='heidi'|X='ashley'|X='teresa')))&
(((~((~(old(ashley)&person(ashley)))|(quiet(ashley))))=>(![X]:(anywhere(X)=>(quiet(X)&person(X)))))&((~(~((~(old(ashley)&person(ashley)))|(quiet(ashley)))))=>(old(terry)&person(terry)&old(heidi)&person(heidi))))&
((~quiet(ashley))<~>(![X]:(anywhere(X)=>(quiet(X)&person(X)))))&
((((~(quiet(ashley)&person(ashley)))|(~old(ashley)))&((~(quiet(heidi)&person(heidi)))|(~old(heidi))))=>(![X]:(anywhere(X)=>(quiet(X)&person(X)))))&
(((![X]:(room(X)=>(((quiet(X))|(~(quiet(X)&person(X)))))))=>((?[X,Y]:(room(X)&room(Y)&(quiet(X)&person(X)&quiet(Y)&person(Y))&(X!=Y)))))&((~(![X]:(room(X)=>(((quiet(X))|(~(quiet(X)&person(X))))))))=>(![X]:(anywhere(X)=>(old(X)&person(X))))))&
(old(terry)&person(terry))&
(((old(terry))&(old(terry)&person(terry))))&
(![X]:(quiet(X)=>old(X)))&
(quiet(terry)&person(terry)&quiet(heidi)&person(heidi)) | room(terry)&room(heidi)&room(ashley)&room(teresa)&(![X]:(room(X)=>(X='terry'|X='heidi'|X='ashley'|X='teresa')))&
quiet(ashley) | [] | null | 0.182686 |
There is a room. If “not everyone in the room collects vintage vinyl records or does not make intricate hand-cut paper art for exhibitions” then “it is true that “everyone in the room who collects vintage vinyl records neither is not a member of a local theater group specializing in improv nor owns a 3D printer””. Someone in the room is an enthusiastic bird watcher who travels for rare sightings. It is true that “everyone in the room who collects vintage vinyl records neither is not a member of a local theater group specializing in improv nor owns a 3D printer”. Everyone outside the room owns an Android phone if they owns an Android phone or owns a 3D printer or both. Everyone in the room who competes in national level swimming championships is a scotch connoisseur. Everyone in the room neither does not enjoy coding in Python nor owns an Android phone only if they owns a microscope. Everyone in the room who owns a microscope is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room who neither makes intricate hand-cut paper art for exhibitions nor collects first edition books enjoys origami. Not everyone in the room owns a 3D printer if they enjoys origami. Everyone in the room owns a 3D printer if and only if they hosts a popular podcast about emerging technologies. Everyone in the room collects first edition books or is a craft beer aficionado or both if they collects antique clocks and vice versa. Not everyone in the room enjoys stargazing if they enjoys coding in Python. Everyone in the room who enjoys origami is a tea enthusiast. Everyone in the room who is a tea enthusiast can play the flute. Everyone anywhere enjoys origami, is a craft beer aficionado or is a member of a local theater group specializing in improv if they can play the guitar. Everyone in the room who enjoys coding in Python, is a cybersecurity expert or enjoys stargazing collects first edition books. Everyone in the room who does not own an Android phone cannot play the flute. | Everyone in the room does not own an Android phone. | contradiction | (there_is_a_room)&
((~![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(collects_vintage_vinyl_records(X))))))=>(![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(~((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(owns_a_3D_printer(X)))))))))&
(?[X]:(room(X)&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))&
(![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(~((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(owns_a_3D_printer(X))))))))&
(![X]:(~room(X)=>(((((owns_an_Android_phone(X))|(owns_a_3D_printer(X))))=>(owns_an_Android_phone(X))))))&
(![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(is_a_scotch_connoisseur(X))))))&
(![X]:(room(X)=>(((owns_a_microscope(X))<=(~((does_not_enjoy_coding_in_Python(X))|(owns_an_Android_phone(X))))))))&
(![X]:(room(X)=>(((owns_a_microscope(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(![X]:(room(X)=>(((~((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(collects_first_edition_books(X))))=>(enjoys_origami(X))))))&
(~![X]:(room(X)=>(((enjoys_origami(X))=>(owns_a_3D_printer(X))))))&
(![X]:(room(X)=>(((owns_a_3D_printer(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(room(X)=>(((((collects_first_edition_books(X))|(is_a_craft_beer_aficionado(X))))<=>(collects_antique_clocks(X))))))&
(~![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(enjoys_stargazing(X))))))&
(![X]:(room(X)=>(((enjoys_origami(X))=>(is_a_tea_enthusiast(X))))))&
(![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(can_play_the_flute(X))))))&
(![X]:(anywhere(X)=>(((can_play_the_guitar(X))=>(((enjoys_origami(X))|(is_a_craft_beer_aficionado(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))))&
(![X]:(room(X)=>(((((enjoys_coding_in_Python(X))|(is_a_cybersecurity_expert(X))|(enjoys_stargazing(X))))=>(collects_first_edition_books(X))))))&
(![X]:(room(X)=>(((does_not_own_a_microscope(X))|(enjoys_origami(X))))))&
(![X]:(~room(X)=>(((enjoys_origami(X))=>(does_not_compete_in_national_level_swimming_championships(X))))))&
(![X]:(room(X)=>(((does_not_own_an_Android_phone(X))=>(cannot_play_the_flute(X))))))&
(![X]:(anywhere(X)=>(((((has_a_piercing(X))&(does_not_own_a_3D_printer(X))))=>(((is_not_a_scotch_connoisseur(X))|(does_not_enjoy_origami(X))|(enjoys_origami(X))))))))&
(~![X]:(room(X)=>(((is_not_a_client_of_LVMH(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))&
(![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<=>(collects_antique_clocks(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(does_not_own_an_Android_phone(X))) | [
"p9",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 789628569763389067150125
% SZS output start Proof for 789628569763389067150125
53. ~! [X0] : (room(X0) => (predv(X0) => predc(X0))) [input p9]
57. ! [X0] : (room(X0) => (predv(X0) => predw(X0))) [input p13]
58. ! [X0] : (room(X0) => (predw(X0) => predg(X0))) [input p14]
63. ! [X0] : (room(X0) => (~predm(X0) => ~predg(X0))) [input p19]
67. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis]
83. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 67]
165. ? [X0] : ((~predc(X0) & predv(X0)) & room(X0)) [ennf transformation 53]
166. ? [X0] : (~predc(X0) & predv(X0) & room(X0)) [flattening 165]
170. ! [X0] : ((predw(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 57]
171. ! [X0] : (predw(X0) | ~predv(X0) | ~room(X0)) [flattening 170]
172. ! [X0] : ((predg(X0) | ~predw(X0)) | ~room(X0)) [ennf transformation 58]
173. ! [X0] : (predg(X0) | ~predw(X0) | ~room(X0)) [flattening 172]
178. ! [X0] : ((~predg(X0) | predm(X0)) | ~room(X0)) [ennf transformation 63]
179. ! [X0] : (~predg(X0) | predm(X0) | ~room(X0)) [flattening 178]
182. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 83]
187. ? [X0] : (~predc(X0) & predv(X0) & room(X0)) => (~predc(sK1) & predv(sK1) & room(sK1)) [choice axiom]
188. ~predc(sK1) & predv(sK1) & room(sK1) [skolemisation 166,187]
284. room(sK1) [cnf transformation 188]
285. predv(sK1) [cnf transformation 188]
294. ~predv(X0) | predw(X0) | ~room(X0) [cnf transformation 171]
295. ~predw(X0) | predg(X0) | ~room(X0) [cnf transformation 173]
298. ~predg(X0) | predm(X0) | ~room(X0) [cnf transformation 179]
303. ~predm(X0) | ~room(X0) [cnf transformation 182]
312. predw(sK1) | ~room(sK1) [resolution 294,285]
313. predw(sK1) [subsumption resolution 312,284]
314. predg(sK1) | ~room(sK1) [resolution 313,295]
315. predg(sK1) [subsumption resolution 314,284]
320. predm(sK1) | ~room(sK1) [resolution 298,315]
321. predm(sK1) [subsumption resolution 320,284]
322. ~room(sK1) [resolution 321,303]
323. $false [subsumption resolution 322,284]
% SZS output end Proof for 789628569763389067150125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.588302 |
Gladys, Anna are the only persons in the room. All kind persons are old. Everyone in the room is kind. Anna and Gladys are old or are kind or both. More than one person in the room is not a kind person, is not a old person and is old. Everyone in the room is not tall, is a kind person or is not a old person if they is tall, is a kind person or is a tall person and vice versa. Everyone in the room is tall, is a tall person or is kind if they is not quiet. Everyone in the room is old or is a tall person or both if they is tall, is a tall person or is kind. | Gladys is tall. | entailment | room(gladys)&room(anna)&(![X]:(room(X)=>(X='gladys'|X='anna')))&
(![X]:(kind(X)=>old(X)))&
(![X]:(room(X)=>(kind(X))))&
(((old(anna))|(kind(anna)))&((old(gladys))|(kind(gladys))))&
((?[X,Y]:(room(X)&room(Y)&(((~(kind(X)&person(X)))&(~(old(X)&person(X)))&(old(X)))&((~(kind(Y)&person(Y)))&(~(old(Y)&person(Y)))&(old(Y))))&(X!=Y))))&
(![X]:(room(X)=>(((((~tall(X))|(kind(X)&person(X))|(~(old(X)&person(X)))))<=>(((tall(X))|(kind(X)&person(X))|(tall(X)&person(X))))))))&
(![X]:(room(X)=>(((~quiet(X))=>(((tall(X))|(tall(X)&person(X))|(kind(X))))))))&
(![X]:(room(X)=>(((((tall(X))|(tall(X)&person(X))|(kind(X))))=>(((old(X))|(tall(X)&person(X)))))))) | room(gladys)&room(anna)&(![X]:(room(X)=>(X='gladys'|X='anna')))&
tall(gladys) | [
"p0",
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1619004950886540184284020
% SZS output start Proof for 1619004950886540184284020
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
46. ! [X0] : (room(X0) => kind(X0)) [input p2]
48. ? [X0,X1] : (X0 != X1 & old(X1) & ~(person(X1) & old(X1)) & ~(person(X1) & kind(X1)) & old(X0) & ~(person(X0) & old(X0)) & ~(person(X0) & kind(X0)) & room(X1) & room(X0)) [input p4]
49. ! [X0] : (room(X0) => ((~(person(X0) & old(X0)) | (person(X0) & kind(X0)) | ~tall(X0)) <=> ((person(X0) & tall(X0)) | (person(X0) & kind(X0)) | tall(X0)))) [input p5]
52. ~(tall(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
125. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
126. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 125]
128. ! [X0] : (kind(X0) | ~room(X0)) [ennf transformation 46]
129. ? [X0,X1] : (X0 != X1 & old(X1) & (~person(X1) | ~old(X1)) & (~person(X1) | ~kind(X1)) & old(X0) & (~person(X0) | ~old(X0)) & (~person(X0) | ~kind(X0)) & room(X1) & room(X0)) [ennf transformation 48]
130. ! [X0] : ((((~person(X0) | ~old(X0)) | (person(X0) & kind(X0)) | ~tall(X0)) <=> ((person(X0) & tall(X0)) | (person(X0) & kind(X0)) | tall(X0))) | ~room(X0)) [ennf transformation 49]
131. ! [X0] : (((~person(X0) | ~old(X0) | (person(X0) & kind(X0)) | ~tall(X0)) <=> ((person(X0) & tall(X0)) | (person(X0) & kind(X0)) | tall(X0))) | ~room(X0)) [flattening 130]
136. ~tall(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 52]
137. ~tall(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 136]
138. ! [X0] : (sP0(X0) <=> (~person(X0) | ~old(X0) | (person(X0) & kind(X0)) | ~tall(X0))) [predicate definition introduction]
139. ! [X0] : ((sP0(X0) <=> ((person(X0) & tall(X0)) | (person(X0) & kind(X0)) | tall(X0))) | ~sP1(X0)) [predicate definition introduction]
140. ! [X0] : (sP1(X0) | ~room(X0)) [definition folding 131,139,138]
142. ? [X0,X1] : (X0 != X1 & old(X1) & (~person(X1) | ~old(X1)) & (~person(X1) | ~kind(X1)) & old(X0) & (~person(X0) | ~old(X0)) & (~person(X0) | ~kind(X0)) & room(X1) & room(X0)) => (sK2 != sK3 & old(sK3) & (~person(sK3) | ~old(sK3)) & (~person(sK3) | ~kind(sK3)) & old(sK2) & (~person(sK2) | ~old(sK2)) & (~person(sK2) | ~kind(sK2)) & room(sK3) & room(sK2)) [choice axiom]
143. sK2 != sK3 & old(sK3) & (~person(sK3) | ~old(sK3)) & (~person(sK3) | ~kind(sK3)) & old(sK2) & (~person(sK2) | ~old(sK2)) & (~person(sK2) | ~kind(sK2)) & room(sK3) & room(sK2) [skolemisation 129,142]
144. ! [X0] : (((sP0(X0) | ((~person(X0) | ~tall(X0)) & (~person(X0) | ~kind(X0)) & ~tall(X0))) & (((person(X0) & tall(X0)) | (person(X0) & kind(X0)) | tall(X0)) | ~sP0(X0))) | ~sP1(X0)) [nnf transformation 139]
145. ! [X0] : (((sP0(X0) | ((~person(X0) | ~tall(X0)) & (~person(X0) | ~kind(X0)) & ~tall(X0))) & ((person(X0) & tall(X0)) | (person(X0) & kind(X0)) | tall(X0) | ~sP0(X0))) | ~sP1(X0)) [flattening 144]
146. ! [X0] : ((sP0(X0) | (person(X0) & old(X0) & (~person(X0) | ~kind(X0)) & tall(X0))) & ((~person(X0) | ~old(X0) | (person(X0) & kind(X0)) | ~tall(X0)) | ~sP0(X0))) [nnf transformation 138]
147. ! [X0] : ((sP0(X0) | (person(X0) & old(X0) & (~person(X0) | ~kind(X0)) & tall(X0))) & (~person(X0) | ~old(X0) | (person(X0) & kind(X0)) | ~tall(X0) | ~sP0(X0))) [flattening 146]
148. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
149. ~tall(mary) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 137,148]
230. room(mary) [cnf transformation 126]
231. room(paul) [cnf transformation 126]
232. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 126]
234. ~room(X0) | kind(X0) [cnf transformation 128]
237. room(sK2) [cnf transformation 143]
238. room(sK3) [cnf transformation 143]
240. ~person(sK2) | ~old(sK2) [cnf transformation 143]
241. old(sK2) [cnf transformation 143]
243. ~person(sK3) | ~old(sK3) [cnf transformation 143]
244. old(sK3) [cnf transformation 143]
245. sK2 != sK3 [cnf transformation 143]
249. person(X0) | person(X0) | tall(X0) | ~sP0(X0) | ~sP1(X0) [cnf transformation 145]
256. sP0(X0) | ~person(X0) | ~kind(X0) [cnf transformation 147]
258. sP0(X0) | person(X0) [cnf transformation 147]
259. ~room(X0) | sP1(X0) [cnf transformation 140]
268. ~tall(mary) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 149]
269. ~tall(mary) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 149]
270. ~tall(mary) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 149]
274. ~sP1(X0) | tall(X0) | ~sP0(X0) | person(X0) [duplicate literal removal 249]
277. ~person(sK3) [subsumption resolution 243,244]
278. ~person(sK2) [subsumption resolution 240,241]
279. ~kind(X0) | sP0(X0) [subsumption resolution 256,258]
280. ~tall(mary) | paul != sK4 | ~room(mary) [subsumption resolution 270,231]
281. ~tall(mary) | paul != sK4 [subsumption resolution 280,230]
283. 1 <=> paul = sK4 [avatar definition]
285. paul != sK4 <- (~1) [avatar component clause 283]
287. 2 <=> tall(mary) [avatar definition]
289. ~tall(mary) <- (~2) [avatar component clause 287]
290. ~1 | ~2 [avatar split clause 281,287,283]
291. ~tall(mary) | mary != sK4 | ~room(mary) [subsumption resolution 269,231]
292. ~tall(mary) | mary != sK4 [subsumption resolution 291,230]
294. 3 <=> mary = sK4 [avatar definition]
296. mary != sK4 <- (~3) [avatar component clause 294]
297. ~3 | ~2 [avatar split clause 292,287,294]
298. ~tall(mary) | room(sK4) | ~room(mary) [subsumption resolution 268,231]
299. ~tall(mary) | room(sK4) [subsumption resolution 298,230]
301. 4 <=> room(sK4) [avatar definition]
303. room(sK4) <- (4) [avatar component clause 301]
304. 4 | ~2 [avatar split clause 299,287,301]
305. kind(mary) [resolution 234,230]
313. sP1(mary) [resolution 259,230]
317. sP0(mary) [resolution 279,305]
326. mary = sK2 | paul = sK2 [resolution 232,237]
327. mary = sK3 | paul = sK3 [resolution 232,238]
329. 5 <=> paul = sK2 [avatar definition]
333. 6 <=> mary = sK2 [avatar definition]
335. mary = sK2 <- (6) [avatar component clause 333]
336. 5 | 6 [avatar split clause 326,333,329]
338. 7 <=> paul = sK3 [avatar definition]
340. paul = sK3 <- (7) [avatar component clause 338]
342. 8 <=> mary = sK3 [avatar definition]
344. mary = sK3 <- (8) [avatar component clause 342]
345. 7 | 8 [avatar split clause 327,342,338]
362. ~person(mary) <- (6) [backward demodulation 278,335]
373. tall(mary) | ~sP0(mary) | person(mary) [resolution 274,313]
375. ~sP0(mary) | person(mary) <- (~2) [subsumption resolution 373,289]
376. person(mary) <- (~2) [subsumption resolution 375,317]
377. $false <- (~2, 6) [subsumption resolution 376,362]
378. 2 | ~6 [avatar contradiction clause 377]
393. ~person(mary) <- (8) [backward demodulation 277,344]
398. $false <- (~2, 8) [subsumption resolution 393,376]
399. 2 | ~8 [avatar contradiction clause 398]
416. paul != sK2 <- (7) [backward demodulation 245,340]
421. ~5 | ~7 [avatar split clause 416,338,329]
434. mary = sK4 | paul = sK4 <- (4) [resolution 303,232]
437. paul = sK4 <- (~3, 4) [subsumption resolution 434,296]
438. $false <- (~1, ~3, 4) [subsumption resolution 437,285]
439. 1 | 3 | ~4 [avatar contradiction clause 438]
440. $false [avatar sat refutation 290,297,304,336,345,378,399,421,439]
% SZS output end Proof for 1619004950886540184284020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0.590376 |
Jerry, Henry, Jesse, Jessica, Marie are the only persons in the room. Everyone in the room neither does not have a vast collection of first-edition science fiction novels nor is not a craft beer aficionado. | Jerry has a vast collection of first-edition science fiction novels. | entailment | room(jerry)&room(henry)&room(jesse)&room(jessica)&room(marie)&(![X]:(room(X)=>(X='jerry'|X='henry'|X='jesse'|X='jessica'|X='marie')))&
![X]:(room(X)=>(~((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(is_not_a_craft_beer_aficionado(X))))) | room(jerry)&room(henry)&room(jesse)&room(jessica)&room(marie)&(![X]:(room(X)=>(X='jerry'|X='henry'|X='jesse'|X='jessica'|X='marie')))&
has_a_vast_collection_of_first-edition_science_fiction_novels(jerry) | [
"p0",
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 376829545909353342111938
% SZS output start Proof for 376829545909353342111938
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) => ~(~predc(X0) | ~prede(X0))) [input p1]
46. ~(prede(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]
47. ! [X0] : (room(X0) => ~~prede(X0)) [pure predicate removal 45]
120. ! [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]
121. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 120]
122. ! [X0] : (prede(X0) | ~room(X0)) [ennf transformation 47]
123. ~prede(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 46]
124. ~prede(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 123]
126. ? [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]
127. ~prede(mary) | (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 124,126]
208. room(mary) [cnf transformation 121]
209. room(paul) [cnf transformation 121]
210. room(fred) [cnf transformation 121]
211. room(alice) [cnf transformation 121]
212. room(john) [cnf transformation 121]
213. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 121]
214. ~room(X0) | prede(X0) [cnf transformation 122]
215. ~prede(mary) | room(sK0) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 127]
216. ~prede(mary) | mary != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 127]
217. ~prede(mary) | paul != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 127]
218. ~prede(mary) | fred != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 127]
219. ~prede(mary) | alice != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 127]
220. ~prede(mary) | john != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 127]
221. ~prede(mary) | john != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 220,212]
222. ~prede(mary) | john != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 221,211]
223. ~prede(mary) | john != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 222,210]
224. ~prede(mary) | john != sK0 | ~room(mary) [subsumption resolution 223,209]
225. ~prede(mary) | john != sK0 [subsumption resolution 224,208]
227. 1 <=> john = sK0 [avatar definition]
229. john != sK0 <- (~1) [avatar component clause 227]
231. 2 <=> prede(mary) [avatar definition]
234. ~1 | ~2 [avatar split clause 225,231,227]
235. ~prede(mary) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 219,212]
236. ~prede(mary) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 235,211]
237. ~prede(mary) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 236,210]
238. ~prede(mary) | alice != sK0 | ~room(mary) [subsumption resolution 237,209]
239. ~prede(mary) | alice != sK0 [subsumption resolution 238,208]
241. 3 <=> alice = sK0 [avatar definition]
243. alice != sK0 <- (~3) [avatar component clause 241]
244. ~3 | ~2 [avatar split clause 239,231,241]
245. ~prede(mary) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 218,212]
246. ~prede(mary) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 245,211]
247. ~prede(mary) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 246,210]
248. ~prede(mary) | fred != sK0 | ~room(mary) [subsumption resolution 247,209]
249. ~prede(mary) | fred != sK0 [subsumption resolution 248,208]
251. 4 <=> fred = sK0 [avatar definition]
253. fred != sK0 <- (~4) [avatar component clause 251]
254. ~4 | ~2 [avatar split clause 249,231,251]
255. ~prede(mary) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 217,212]
256. ~prede(mary) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 255,211]
257. ~prede(mary) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 256,210]
258. ~prede(mary) | paul != sK0 | ~room(mary) [subsumption resolution 257,209]
259. ~prede(mary) | paul != sK0 [subsumption resolution 258,208]
261. 5 <=> paul = sK0 [avatar definition]
263. paul != sK0 <- (~5) [avatar component clause 261]
264. ~5 | ~2 [avatar split clause 259,231,261]
265. ~prede(mary) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 216,212]
266. ~prede(mary) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,211]
267. ~prede(mary) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 266,210]
268. ~prede(mary) | mary != sK0 | ~room(mary) [subsumption resolution 267,209]
269. ~prede(mary) | mary != sK0 [subsumption resolution 268,208]
271. 6 <=> mary = sK0 [avatar definition]
273. mary != sK0 <- (~6) [avatar component clause 271]
274. ~6 | ~2 [avatar split clause 269,231,271]
275. ~prede(mary) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 215,212]
276. ~prede(mary) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,211]
277. ~prede(mary) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 276,210]
278. ~prede(mary) | room(sK0) | ~room(mary) [subsumption resolution 277,209]
279. ~prede(mary) | room(sK0) [subsumption resolution 278,208]
281. 7 <=> room(sK0) [avatar definition]
283. room(sK0) <- (7) [avatar component clause 281]
284. 7 | ~2 [avatar split clause 279,231,281]
285. prede(mary) [resolution 214,208]
292. 2 [avatar split clause 285,231]
341. alice = sK0 | fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (7) [resolution 213,283]
342. fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (~3, 7) [subsumption resolution 341,243]
343. paul = sK0 | mary = sK0 | john = sK0 <- (~3, ~4, 7) [subsumption resolution 342,253]
344. mary = sK0 | john = sK0 <- (~3, ~4, ~5, 7) [subsumption resolution 343,263]
345. john = sK0 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 344,273]
346. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 345,229]
347. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 346]
348. $false [avatar sat refutation 234,244,254,264,274,284,292,347]
% SZS output end Proof for 376829545909353342111938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.014701 |
There is a room.
If “at least one person outside the room is a client of LVMH” then “no one in the room bakes bread at home only if they is a craft beer aficionado”.
Everyone in the room who is a craft beer aficionado neither does not bake bread at home nor is a craft beer aficionado.
Everyone in the room has a tattoo if they is a craft beer aficionado.
If someone bakes bread at home then he/she either does not bake bread at home or has a tattoo but not both and vice versa.
Joseph dreamt that “everyone in the room is a craft beer aficionado or is not a craft beer aficionado”.
If someone bakes bread at home then he/she has a tattoo and vice versa.
At least one person anywhere has a tattoo.
At least one person anywhere bakes bread at home.
Everyone in the room is a client of LVMH if they is a craft beer aficionado and has a tattoo.
Everyone outside the room is a craft beer aficionado if they is a client of LVMH.
Everyone in the room bakes bread at home if they is a craft beer aficionado.
Everyone in the room who bakes bread at home neither does not bake bread at home nor is not a craft beer aficionado.
Everyone anywhere is a client of LVMH if they is a craft beer aficionado. | Everyone in the room is a client of LVMH. | entailment | (there_is_a_room)&
((((?[X]:(~room(X)&is_a_client_of_LVMH(X)))))=>(~?[X]:(room(X)=>(((is_a_craft_beer_aficionado(X))<=(bakes_bread_at_home(X)))))))&
(![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(~((does_not_bake_bread_at_home(X))|(is_a_craft_beer_aficionado(X))))))))&
(![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(has_a_tattoo(X))))))&
((![X]:((bakes_bread_at_home(X))<=>(((does_not_bake_bread_at_home(X))<~>(has_a_tattoo(X)))))))&
((joseph_dream=>(![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(is_a_craft_beer_aficionado(X))))))))&
((![X]:((bakes_bread_at_home(X))<=>(has_a_tattoo(X)))))&
(((?[X]:(anywhere(X)&has_a_tattoo(X)))))&
(((?[X]:(anywhere(X)&bakes_bread_at_home(X)))))&
(![X]:(room(X)=>(((((is_a_craft_beer_aficionado(X))&(has_a_tattoo(X))))=>(is_a_client_of_LVMH(X))))))&
(![X]:(~room(X)=>(((is_a_client_of_LVMH(X))=>(is_a_craft_beer_aficionado(X))))))&
(![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(bakes_bread_at_home(X))))))&
(![X]:(room(X)=>(((bakes_bread_at_home(X))=>(~((does_not_bake_bread_at_home(X))|(is_not_a_craft_beer_aficionado(X))))))))&
(![X]:(anywhere(X)=>(((is_a_craft_beer_aficionado(X))=>(is_a_client_of_LVMH(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(is_a_client_of_LVMH(X))) | [
"p0",
"p2",
"p4",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4968630872117547268446869
% SZS output start Proof for 4968630872117547268446869
44. there_is_a_room [input p0]
46. ! [X0] : (room(X0) => (preda(X0) => ~(preda(X0) | ~predb(X0)))) [input p2]
48. ! [X0] : (predb(X0) <=> (~predb(X0) <~> predd(X0))) [input p4]
50. ! [X0] : (predb(X0) <=> predd(X0)) [input p6]
56. ! [X0] : (room(X0) => (predb(X0) => ~(~preda(X0) | ~predb(X0)))) [input p12]
58. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis]
134. ! [X0] : (((~preda(X0) & predb(X0)) | ~preda(X0)) | ~room(X0)) [ennf transformation 46]
135. ! [X0] : ((~preda(X0) & predb(X0)) | ~preda(X0) | ~room(X0)) [flattening 134]
144. ! [X0] : (((preda(X0) & predb(X0)) | ~predb(X0)) | ~room(X0)) [ennf transformation 56]
145. ! [X0] : ((preda(X0) & predb(X0)) | ~predb(X0) | ~room(X0)) [flattening 144]
148. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 58]
151. ! [X0] : ((predb(X0) | ((~predb(X0) | ~predd(X0)) & (predd(X0) | predb(X0)))) & (((~predd(X0) | predb(X0)) & (predd(X0) | ~predb(X0))) | ~predb(X0))) [nnf transformation 48]
152. ! [X0] : ((predb(X0) | ~predd(X0)) & (predd(X0) | ~predb(X0))) [nnf transformation 50]
157. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK2) & room(sK2)) [choice axiom]
158. (~predc(sK2) & room(sK2)) | ~there_is_a_room [skolemisation 148,157]
240. there_is_a_room [cnf transformation 44]
245. ~preda(X0) | ~preda(X0) | ~room(X0) [cnf transformation 135]
247. predd(X0) | ~predb(X0) | ~predb(X0) [cnf transformation 151]
249. predb(X0) | predd(X0) | predb(X0) [cnf transformation 151]
252. predb(X0) | ~predd(X0) [cnf transformation 152]
261. preda(X0) | ~predb(X0) | ~room(X0) [cnf transformation 145]
263. room(sK2) | ~there_is_a_room [cnf transformation 158]
265. predd(X0) | ~predb(X0) [duplicate literal removal 247]
266. predd(X0) | predb(X0) [duplicate literal removal 249]
267. ~preda(X0) | ~room(X0) [duplicate literal removal 245]
276. 3 <=> ! [X0] : predb(X0) [avatar definition]
277. predb(X0) <- (3) [avatar component clause 276]
283. predd(X0) [subsumption resolution 265,266]
284. predb(X0) [subsumption resolution 252,283]
285. 3 [avatar split clause 284,276]
286. ~predb(X0) | ~room(X0) [subsumption resolution 261,267]
289. room(sK2) [subsumption resolution 263,240]
291. ~room(X0) <- (3) [resolution 286,277]
297. $false <- (3) [resolution 291,289]
298. ~3 [avatar contradiction clause 297]
299. $false [avatar sat refutation 285,298]
% SZS output end Proof for 4968630872117547268446869
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.385522 |
Lashandra, Katherine, Robert are the only persons in the room.
Either "everyone outside the room enjoys kayaking or does not practice urban gardening" or "Lashandra is a coffee connoisseur" but not both.
It is not the case that "Lashandra enjoys cross-country skiing". | Lashandra enjoys cross-country skiing. | contradiction | room(lashandra)&room(katherine)&room(robert)&(![X]:(room(X)=>(X='lashandra'|X='katherine'|X='robert')))&
((![X]:(~room(X)=>(((does_not_practice_urban_gardening(X))|(enjoys_kayaking(X))))))<~>(is_a_coffee_connoisseur(lashandra)))&
((![X]:(room(X)=>(((does_not_collect_luxury_watches(X))|(collects_action_figures(X))))))=>(![X]:(~room(X)=>(((~((is_an_avid_hiker(X))|(practices_kickboxing(X))))=>(is_an_avid_hiker(X)))))))&
((is_right-handed(katherine))=>(does_not_practice_urban_gardening(lashandra)))&
((collects_antique_clocks(lashandra))=>((![X]:((practices_kickboxing(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(katherine))=>(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))&
(((![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))|(collects_action_figures(X))))))=>(((is_a_professional_photographer_specializing_in_portrait_photography(lashandra))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(lashandra)))))&((~(![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))|(collects_action_figures(X)))))))=>(practices_kickboxing(katherine))))&
((enjoys_windsurfing(katherine))=>((?[X,Y]:(room(X)&room(Y)&(enjoys_windsurfing(X)&enjoys_windsurfing(Y))&(X!=Y)))))&
((collects_foreign_coins(katherine))=>(~(enjoys_cross-country_skiing(lashandra))))&
((creates_bespoke_furniture_pieces_from_reclaimed_wood(katherine))=>(?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))&
(((collects_antique_clocks(lashandra))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(lashandra)))&((~(collects_antique_clocks(lashandra)))=>((![X]:((((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<~>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))=>(practices_graffiti_art(X)))))))&
((is_an_avid_hiker(lashandra))=>(practices_kickboxing(lashandra)))&
(practices_graffiti_art(lashandra))&
(?[X]:(~room(X)&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))&
(collects_luxury_watches(katherine))&
(![X]:(room(X)=>(((collects_action_figures(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(is_an_avid_hiker(lashandra))&
(~(is_an_avid_hiker(katherine)))&
(does_not_practice_urban_gardening(katherine))&
(~(((?[X]:(anywhere(X)&does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))&
(enjoys_salsa_dancing(lashandra))&
((does_not_practice_urban_gardening(katherine))&(collects_foreign_coins(katherine)))&
(~(enjoys_cross-country_skiing(lashandra))) | room(lashandra)&room(katherine)&room(robert)&(![X]:(room(X)=>(X='lashandra'|X='katherine'|X='robert')))&
enjoys_cross-country_skiing(lashandra) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1116902791719362923683295
% SZS output start Proof for 1116902791719362923683295
66. ~predu(mary) [input p22]
67. predu(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
167. predu(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 67]
168. predu(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 167]
286. ~predu(mary) [cnf transformation 66]
291. predu(mary) [cnf transformation 168]
363. 16 <=> predu(mary) [avatar definition]
377. ~16 [avatar split clause 286,363]
378. 16 [avatar split clause 291,363]
379. $false [avatar sat refutation 377,378]
% SZS output end Proof for 1116902791719362923683295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.548335 |
There is a room. “Everyone in the room who is not hated by Elizabeth, is not liked by Mark and is not hated by Mark likes Dorothy, likes Elizabeth and is liked by Brian” unless “not everyone in the room does not hate Charles”. Everyone in the room who likes Dorothy, likes Elizabeth and is liked by Brian likes Elizabeth or is not hated by Elizabeth or both. If someone is hated by Brian then he/she likes Mark and likes Dorothy and vice versa. If someone is not hated by Elizabeth and does not hate Dorothy then he/she likes Elizabeth and likes Brian and vice versa. Only one person in the room hates Brian and is not hated by Mark. Everyone in the room does not like Elizabeth if they likes Brian. Not everyone outside the room is hated by Dorothy and does not like Mark if they does not like Elizabeth. | Everyone in the room hates Mark. | neutral | (there_is_a_room)&
(~(~![X]:(room(X)=>(~hate(charles,X))))=>(![X]:(room(X)=>(((((~hate(X,elizabeth))&(~like(X,mark))&(~hate(X,mark))))=>(((like(dorothy,X))&(like(elizabeth,X))&(like(X,brian)))))))))&
(![X]:(room(X)=>(((((like(dorothy,X))&(like(elizabeth,X))&(like(X,brian))))=>(((like(elizabeth,X))|(~hate(X,elizabeth))))))))&
((![X]:((hate(X,brian))<=>(((like(mark,X))&(like(dorothy,X)))))))&
((![X]:((((~hate(X,elizabeth))&(~hate(dorothy,X))))<=>(((like(elizabeth,X))&(like(brian,X)))))))&
(((?[X]:(room(X)&((hate(brian,X))&(~hate(X,mark)))))&(![X,Y]:((room(X)&room(Y)&(((hate(brian,X))&(~hate(X,mark))))&(((hate(brian,Y))&(~hate(Y,mark)))))=>(X=Y)))))&
(![X]:(room(X)=>(((like(brian,X))=>(~like(elizabeth,X))))))&
(~![X]:(~room(X)=>(((~like(elizabeth,X))=>(((hate(X,dorothy))&(~like(mark,X))))))))&
(![X]:(room(X)=>(((((~like(X,brian))<~>(~hate(dorothy,X))))<=(((hate(X,dorothy))&(~like(mark,X))))))))&
(![X]:(room(X)=>(((~like(X,charles))=>(hate(X,dorothy))))))&
(![X]:(anywhere(X)=>(((hate(X,dorothy))=>(like(mark,X))))))&
(![X]:(room(X)=>(((like(mark,X))=>(hate(X,dorothy))))))&
(~![X]:(room(X)=>(~hate(charles,X))))&
(![X]:(room(X)=>(((((hate(X,dorothy))&(like(mark,X))))=>(((hate(charles,X))|(~hate(X,dorothy))))))))&
(![X]:(room(X)=>(((((hate(charles,X))|(~hate(X,dorothy))))=>(hate(elizabeth,X))))))&
(?[X,Y]:((((like(X,mark))&(hate(brian,X))&(hate(dorothy,X))))&(like(Y,mark))&(like(X,Y))))&
(![X]:(~room(X)=>(((((like(X,elizabeth))&(~hate(X,brian))))=>(((~hate(X,brian))|(hate(charles,X))))))))&
(![X]:(anywhere(X)=>(~like(X,dorothy)))) | (there_is_a_room)&
![X]:(room(X)=>(hate(mark,X))) | [] | null | 0.255799 |
Lisa, Stephen are the only persons in the room.
Everyone in the room does not drive a hybrid car.
Everyone in the room does not write and illustrates their own graphic novels.
Everyone outside the room does not have lived in exactly three countries.
Someone in the room does not collect antique jewelry.
Someone in the room does not enjoy windsurfing. | Lisa is an enthusiastic bird watcher who travels for rare sightings. | neutral | room(lisa)&room(stephen)&(![X]:(room(X)=>(X='lisa'|X='stephen')))&
(![X]:(room(X)=>(does_not_drive_a_hybrid_car(X))))&
(![X]:(room(X)=>(does_not_write_and_illustrates_their_own_graphic_novels(X))))&
(![X]:(~room(X)=>(does_not_have_lived_in_exactly_three_countries(X))))&
(?[X]:(room(X)&(does_not_collect_antique_jewelry(X))))&
(?[X]:(room(X)&(does_not_enjoy_windsurfing(X))))&
(~![X]:(room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))&
(![X]:(room(X)=>(does_not_have_lived_in_exactly_three_countries(X))))&
(![X]:(room(X)=>(does_not_create_YouTube_content(X))))&
(![X]:(room(X)=>(does_not_collect_antique_jewelry(X))))&
(![X]:(room(X)=>(does_not_use_an_ios_phone(X))))&
(![X]:(room(X)=>(is_not_an_active_member_of_a_local_robotics_club(X))))&
(~![X]:(room(X)=>(does_not_collect_antique_clocks(X))))&
(![X]:(room(X)=>(does_not_enjoy_windsurfing(X))))&
(?[X]:(room(X)&(does_not_collect_antique_clocks(X))))&
(![X]:(room(X)=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))&
(![X]:(~room(X)=>(does_not_use_an_ios_phone(X)))) | room(lisa)&room(stephen)&(![X]:(room(X)=>(X='lisa'|X='stephen')))&
is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(lisa) | [] | null | 0.66975 |
Gary is the only person in the room.
“It is not the case that “it is not the case that “it is not the case that “Gary hosts themed dinner parties featuring gourmet home-cooked meals”””” if “everyone in the room is not a member of a local theater group specializing in improv or enjoys rooftop gardening”.
Gary is a chess master who participates in national tournaments.
If someone is a chess master who participates in national tournaments then he/she either hosts themed dinner parties featuring gourmet home-cooked meals or works as a freelance web developer specializing in e-commerce sites but not both.
Everyone in the room is not a member of a local theater group specializing in improv or enjoys rooftop gardening. | Gary works as a freelance web developer specializing in e-commerce sites. | entailment | room(gary)&(![X]:(room(X)=>(X='gary')))&
((![X]:(room(X)=>(((enjoys_rooftop_gardening(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(~(~(~(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(gary))))))&
((~(collect_rare_sneakers(gary)))=>(is_a_chess_master_who_participates_in_national_tournaments(gary)))&
(is_a_chess_master_who_participates_in_national_tournaments(gary))&
(builds_model_airplanes(gary))&
(![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(![X]:(room(X)=>(practices_zumba(X))))&
((![X]:((is_a_chess_master_who_participates_in_national_tournaments(X))=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<~>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))&
(travels_domestically_frequently(gary))&
(![X]:(room(X)=>(((enjoys_rooftop_gardening(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X)))))) | room(gary)&(![X]:(room(X)=>(X='gary')))&
works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(gary) | [
"p0",
"p1",
"p3",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5524246025035800004814139
% SZS output start Proof for 5524246025035800004814139
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
45. ! [X0] : (room(X0) => (~preda(X0) | predr(X0))) => ~predi(mary) [input p1]
47. prede(mary) [input p3]
51. ! [X0] : (prede(X0) => (predi(X0) <~> predl(X0))) [input p7]
53. ! [X0] : (room(X0) => (~preda(X0) | predr(X0))) [input p9]
54. ~(predl(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
132. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
133. ~predi(mary) | ? [X0] : ((preda(X0) & ~predr(X0)) & room(X0)) [ennf transformation 45]
134. ~predi(mary) | ? [X0] : (preda(X0) & ~predr(X0) & room(X0)) [flattening 133]
135. ! [X0] : ((predi(X0) <~> predl(X0)) | ~prede(X0)) [ennf transformation 51]
136. ! [X0] : ((~preda(X0) | predr(X0)) | ~room(X0)) [ennf transformation 53]
137. ! [X0] : (~preda(X0) | predr(X0) | ~room(X0)) [flattening 136]
138. ~predl(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 54]
140. ? [X0] : (preda(X0) & ~predr(X0) & room(X0)) => (preda(sK0) & ~predr(sK0) & room(sK0)) [choice axiom]
141. ~predi(mary) | (preda(sK0) & ~predr(sK0) & room(sK0)) [skolemisation 134,140]
142. ! [X0] : (((~predl(X0) | ~predi(X0)) & (predl(X0) | predi(X0))) | ~prede(X0)) [nnf transformation 135]
143. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom]
144. ~predl(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 138,143]
225. room(mary) [cnf transformation 132]
226. ~room(X0) | mary = X0 [cnf transformation 132]
227. ~predi(mary) | room(sK0) [cnf transformation 141]
228. ~predi(mary) | ~predr(sK0) [cnf transformation 141]
229. ~predi(mary) | preda(sK0) [cnf transformation 141]
230. prede(mary) [cnf transformation 47]
231. ~prede(X0) | predi(X0) | predl(X0) [cnf transformation 142]
233. ~preda(X0) | predr(X0) | ~room(X0) [cnf transformation 137]
234. ~predl(mary) | room(sK1) | ~room(mary) [cnf transformation 144]
235. ~predl(mary) | mary != sK1 | ~room(mary) [cnf transformation 144]
237. 1 <=> preda(sK0) [avatar definition]
239. preda(sK0) <- (1) [avatar component clause 237]
241. 2 <=> predi(mary) [avatar definition]
244. 1 | ~2 [avatar split clause 229,241,237]
246. 3 <=> predr(sK0) [avatar definition]
248. ~predr(sK0) <- (~3) [avatar component clause 246]
249. ~3 | ~2 [avatar split clause 228,241,246]
251. 4 <=> room(sK0) [avatar definition]
253. room(sK0) <- (4) [avatar component clause 251]
254. 4 | ~2 [avatar split clause 227,241,251]
255. ~predl(mary) | mary != sK1 [subsumption resolution 235,225]
257. 5 <=> mary = sK1 [avatar definition]
259. mary != sK1 <- (~5) [avatar component clause 257]
261. 6 <=> predl(mary) [avatar definition]
264. ~5 | ~6 [avatar split clause 255,261,257]
265. ~predl(mary) | room(sK1) [subsumption resolution 234,225]
267. 7 <=> room(sK1) [avatar definition]
269. room(sK1) <- (7) [avatar component clause 267]
270. 7 | ~6 [avatar split clause 265,261,267]
272. predi(mary) | predl(mary) [resolution 231,230]
277. mary = sK1 <- (7) [resolution 269,226]
278. $false <- (~5, 7) [subsumption resolution 277,259]
279. 5 | ~7 [avatar contradiction clause 278]
280. 6 | 2 [avatar split clause 272,241,261]
281. mary = sK0 <- (4) [resolution 253,226]
282. preda(mary) <- (1, 4) [backward demodulation 239,281]
283. ~predr(mary) <- (~3, 4) [backward demodulation 248,281]
285. predr(mary) | ~room(mary) <- (1, 4) [resolution 233,282]
286. ~room(mary) <- (1, ~3, 4) [subsumption resolution 285,283]
287. $false <- (1, ~3, 4) [subsumption resolution 286,225]
288. ~1 | 3 | ~4 [avatar contradiction clause 287]
289. $false [avatar sat refutation 244,249,254,264,270,279,280,288]
% SZS output end Proof for 5524246025035800004814139
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.332156 |
There is a room. No tall person is quiet. Everyone in the room is a kind person. Everyone outside the room either is old or is quieter than Shauna but not both only if they is richer than Shauna. Everyone anywhere is richer than Shauna only if they either is a old person or is a kind person but not both. If someone is a kind tall person then he/she is a old tall person and vice versa. No one in the room is not a kind person if they is older than Shauna. Everyone in the room who is a old person is tall. Everyone in the room is richer than Thomas if they is not a tall person. All quiet persons are kind. Everyone in the room is a old person, is richer than Jason or is quieter than Thomas. All tall persons are old. Everyone in the room is a quiet person if they is quieter than Thomas. More than one person in the room is not a quiet person. All old persons are tall. Everyone in the room is richer than Thomas if they neither is kind nor is a tall kind old person. | More than one person anywhere is richer than Shauna and is quieter than Shauna. | contradiction | (there_is_a_room)&
(~?[X]:(tall(X)=>quiet(X)))&
(![X]:(room(X)=>(kind(X)&person(X))))&
(![X]:(~room(X)=>(((richer(shauna,X))<=(((old(X))<~>(quieter(shauna,X))))))))&
(![X]:(anywhere(X)=>(((((old(X)&person(X))<~>(kind(X)&person(X))))<=(richer(shauna,X))))))&
((![X]:((kind(X)&tall(X)&person(X))<=>(old(X)&tall(X)&person(X)))))&
(~?[X]:(room(X)=>(((older(shauna,X))=>(~(kind(X)&person(X)))))))&
(![X]:(room(X)=>(((old(X)&person(X))=>(tall(X))))))&
(![X]:(room(X)=>(((~(tall(X)&person(X)))=>(richer(thomas,X))))))&
(![X]:(quiet(X)=>kind(X)))&
(![X]:(room(X)=>(((old(X)&person(X))|(richer(jason,X))|(quieter(thomas,X))))))&
(![X]:(tall(X)=>old(X)))&
(![X]:(room(X)=>(((quieter(thomas,X))=>(quiet(X)&person(X))))))&
((?[X,Y]:(room(X)&room(Y)&(~(quiet(X)&person(X))&~(quiet(Y)&person(Y)))&(X!=Y))))&
(![X]:(old(X)=>tall(X)))&
(![X]:(room(X)=>(((~((kind(X))|(tall(X)&kind(X)&old(X)&person(X))))=>(richer(thomas,X)))))) | (there_is_a_room)&
(?[X,Y]:(anywhere(X)&anywhere(Y)&(((richer(shauna,X))&(quieter(shauna,X)))&((richer(shauna,Y))&(quieter(shauna,Y))))&(X!=Y))) | [
"b4",
"p1",
"p4",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2381262967738942584909719
% SZS output start Proof for 2381262967738942584909719
5. ! [X0] : anywhere(X0) [input b4]
45. ~? [X0] : (tall(X0) => quiet(X0)) [input p1]
48. ! [X0] : (anywhere(X0) => (richer(mary,X0) => ((person(X0) & old(X0)) <~> (person(X0) & kind(X0))))) [input p4]
50. ~? [X0] : (room(X0) => (older(mary,X0) => ~(person(X0) & kind(X0)))) [input p6]
55. ! [X0] : (tall(X0) => old(X0)) [input p11]
60. ? [X0,X1] : (X0 != X1 & quieter(mary,X1) & richer(mary,X1) & quieter(mary,X0) & richer(mary,X0) & anywhere(X1) & anywhere(X0)) & there_is_a_room [input hypothesis]
62. ? [X0,X1] : (X0 != X1 & quieter(mary,X1) & richer(mary,X1) & quieter(mary,X0) & richer(mary,X0) & anywhere(X1) & anywhere(X0)) [pure predicate removal 60]
134. ! [X0] : (~quiet(X0) & tall(X0)) [ennf transformation 45]
138. ! [X0] : ((((person(X0) & old(X0)) <~> (person(X0) & kind(X0))) | ~richer(mary,X0)) | ~anywhere(X0)) [ennf transformation 48]
139. ! [X0] : (((person(X0) & old(X0)) <~> (person(X0) & kind(X0))) | ~richer(mary,X0) | ~anywhere(X0)) [flattening 138]
140. ! [X0] : (((person(X0) & kind(X0)) & older(mary,X0)) & room(X0)) [ennf transformation 50]
141. ! [X0] : (person(X0) & kind(X0) & older(mary,X0) & room(X0)) [flattening 140]
149. ! [X0] : (old(X0) | ~tall(X0)) [ennf transformation 55]
158. ! [X0] : ((((~person(X0) | ~kind(X0)) | (~person(X0) | ~old(X0))) & ((person(X0) & kind(X0)) | (person(X0) & old(X0)))) | ~richer(mary,X0) | ~anywhere(X0)) [nnf transformation 139]
159. ! [X0] : (((~person(X0) | ~kind(X0) | ~person(X0) | ~old(X0)) & ((person(X0) & kind(X0)) | (person(X0) & old(X0)))) | ~richer(mary,X0) | ~anywhere(X0)) [flattening 158]
164. ? [X0,X1] : (X0 != X1 & quieter(mary,X1) & richer(mary,X1) & quieter(mary,X0) & richer(mary,X0) & anywhere(X1) & anywhere(X0)) => (sK2 != sK3 & quieter(mary,sK3) & richer(mary,sK3) & quieter(mary,sK2) & richer(mary,sK2) & anywhere(sK3) & anywhere(sK2)) [choice axiom]
165. sK2 != sK3 & quieter(mary,sK3) & richer(mary,sK3) & quieter(mary,sK2) & richer(mary,sK2) & anywhere(sK3) & anywhere(sK2) [skolemisation 62,164]
166. anywhere(X0) [cnf transformation 5]
247. tall(X0) [cnf transformation 134]
257. ~person(X0) | ~kind(X0) | ~person(X0) | ~old(X0) | ~richer(mary,X0) | ~anywhere(X0) [cnf transformation 159]
266. kind(X0) [cnf transformation 141]
267. person(X0) [cnf transformation 141]
274. old(X0) | ~tall(X0) [cnf transformation 149]
289. richer(mary,sK2) [cnf transformation 165]
296. ~person(X0) | ~kind(X0) | ~old(X0) | ~richer(mary,X0) | ~anywhere(X0) [duplicate literal removal 257]
297. ~richer(mary,X0) | ~kind(X0) | ~old(X0) | ~person(X0) [subsumption resolution 296,166]
303. old(X0) [subsumption resolution 274,247]
403. ~kind(sK2) | ~old(sK2) | ~person(sK2) [resolution 297,289]
405. ~old(sK2) | ~person(sK2) [subsumption resolution 403,266]
406. ~person(sK2) [subsumption resolution 405,303]
407. $false [subsumption resolution 406,267]
% SZS output end Proof for 2381262967738942584909719
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.029835 |
Linda, Jessica are the only persons in the room. Either “Linda is allergic to anything” or “everyone in the room is a chess master who participates in national tournaments or does not write poetry” but not both. “Linda neither does not host regular workshops on creative writing nor is a dedicated advocate for digital privacy and encryption” only if “Linda does not host regular workshops on creative writing”. Either “everyone in the room practices archery or does not volunteer for local environmental conservation projects” or “Linda is not a client of Meta” but not both. Either “everyone in the room does not enjoy bird watching or does not enjoy rooftop gardening” or “Linda neither does not own an extensive assortment of vintage comic book memorabilia nor is a dedicated advocate for digital privacy and encryption” but not both. Either “everyone in the room enjoys cross-country skiing” or “Linda neither owns an extensive assortment of vintage comic book memorabilia nor develops open-source software projects in their free time” but not both. “Everyone outside the room who writes poetry hosts a popular podcast about emerging technologies or does not read mystery novels or both” if “Linda writes poetry”. “Linda develops open-source software projects in their free time” if “Linda does not host a popular podcast about emerging technologies and reads mystery novels”. Either “everyone in the room practices archery or is not a client of Meta” or “Linda is a drone photographer” but not both. Linda neither writes poetry nor enjoys bird watching. Linda neither does not practice archery nor enjoys rooftop gardening. | More than one person in the room owns an extensive assortment of vintage comic book memorabilia. | neutral | room(linda)&room(jessica)&(![X]:(room(X)=>(X='linda'|X='jessica')))&
((is_allergic_to_anything(linda))<~>(![X]:(room(X)=>(((does_not_write_poetry(X))|(is_a_chess_master_who_participates_in_national_tournaments(X)))))))&
((~((does_not_host_regular_workshops_on_creative_writing(linda))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(linda))))=>(does_not_host_regular_workshops_on_creative_writing(linda)))&
((![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(practices_archery(X))))))<~>(is_not_a_client_of_Meta(linda)))&
((![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(does_not_enjoy_bird_watching(X))))))<~>(~((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(linda))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(linda)))))&
((![X]:(room(X)=>(enjoys_cross-country_skiing(X))))<~>(~((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(linda))|(develops_open-source_software_projects_in_their_free_time(linda)))))&
((writes_poetry(linda))=>(![X]:(~room(X)=>(((writes_poetry(X))=>(((hosts_a_popular_podcast_about_emerging_technologies(X))|(does_not_read_mystery_novels(X)))))))))&
((((does_not_host_a_popular_podcast_about_emerging_technologies(linda))&(reads_mystery_novels(linda))))=>(develops_open-source_software_projects_in_their_free_time(linda)))&
((![X]:(room(X)=>(((is_not_a_client_of_Meta(X))|(practices_archery(X))))))<~>(is_a_drone_photographer(linda)))&
(~((writes_poetry(linda))|(enjoys_bird_watching(linda))))&
(~((does_not_practice_archery(linda))|(enjoys_rooftop_gardening(linda))))&
(~((does_not_volunteer_for_local_environmental_conservation_projects(linda))|(is_not_a_chess_master_who_participates_in_national_tournaments(linda))))&
(~((is_not_allergic_to_anything(linda))|(develops_open-source_software_projects_in_their_free_time(linda))))&
(![X]:(~room(X)=>(((~((is_a_chess_master_who_participates_in_national_tournaments(X))|(reads_mystery_novels(X))))=>(~((hosts_regular_workshops_on_creative_writing(X))|(is_a_client_of_Meta(X))))))))&
((![X]:((hosts_regular_workshops_on_creative_writing(X))<=>(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))&
(has_a_vast_collection_of_first-edition_science_fiction_novels(linda))&
(is_a_dedicated_advocate_for_digital_privacy_and_encryption(linda))&
(~((enjoys_kayaking_and_exploring_remote_waterways(linda))|(writes_poetry(linda))))&
(~![X]:(room(X)=>(((~((volunteers_for_local_environmental_conservation_projects(X))|(writes_poetry(X))))<=(~((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_not_allergic_to_anything(X))))))))&
(does_not_enjoy_kayaking_and_exploring_remote_waterways(linda))&
(is_a_drone_photographer(linda))&
(cannot_play_the_flute(linda))&
(has_a_specialized_collection_of_handmade_artisan_pottery(linda))&
(![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))<=(enjoys_cross-country_skiing(X))))))&
(practices_archery(linda)) | room(linda)&room(jessica)&(![X]:(room(X)=>(X='linda'|X='jessica')))&
(?[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))) | [] | null | 0.595877 |
Douglas is the only person in the room.
If "Douglas collects vintage stamps" then "Douglas practices graffiti art".
If "everyone outside the room does not enjoy cross-country skiing or enjoys cross-country skiing" then "everyone in the room neither practices graffiti art nor is a night owl if they does not enjoy cross-country skiing".
"Everyone in the room competes in national level swimming championships or does not compete in national level swimming championships" only if "Douglas does not own a high-end gaming PC with custom-built components".
Douglas practices graffiti art.
Everyone anywhere is a skilled home brewer experimenting with craft beer recipes if they does not enjoy cross-country skiing.
Douglas does not compete in national level swimming championships.
Douglas is a chess master who participates in national tournaments.
Everyone anywhere is a skilled home brewer experimenting with craft beer recipes if they enjoys cross-country skiing.
Douglas is allergic to anything.
Everyone anywhere who practices tai chi enjoys cross-country skiing.
Everyone outside the room watches fantasy movies or is not a chess master who participates in national tournaments.
Everyone in the room who watches fantasy movies enjoys cross-country skiing. | Douglas practices tai chi. | neutral | room(douglas)&(![X]:(room(X)=>(X='douglas')))&
((collects_vintage_stamps(douglas))=>(practices_graffiti_art(douglas)))&
((![X]:(~room(X)=>(((enjoys_cross-country_skiing(X))|(does_not_enjoy_cross-country_skiing(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))=>(~((practices_graffiti_art(X))|(is_a_night_owl(X)))))))))&
((![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))|(competes_in_national_level_swimming_championships(X))))))=>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(douglas)))&
(practices_graffiti_art(douglas))&
(![X]:(anywhere(X)=>(((does_not_enjoy_cross-country_skiing(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))&
(does_not_compete_in_national_level_swimming_championships(douglas))&
(is_a_chess_master_who_participates_in_national_tournaments(douglas))&
(![X]:(anywhere(X)=>(((enjoys_cross-country_skiing(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))&
(is_allergic_to_anything(douglas))&
(![X]:(anywhere(X)=>(((practices_tai_chi(X))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(~room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(watches_fantasy_movies(X))))))&
(![X]:(room(X)=>(((watches_fantasy_movies(X))=>(enjoys_cross-country_skiing(X))))))&
(maintains_a_personal_blog_focused_on_cybersecurity_tips(douglas))&
(![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(competes_in_national_level_swimming_championships(X))))))&
(![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(collects_rare_and_antique_scientific_instruments(X))))))&
(collects_rare_and_antique_scientific_instruments(douglas))&
(![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(~((collects_foreign_coins(X))|(is_a_night_owl(X))))))))&
(![X]:(room(X)=>(((collects_foreign_coins(X))=>(is_a_night_owl(X)))))) | room(douglas)&(![X]:(room(X)=>(X='douglas')))&
practices_tai_chi(douglas) | [] | null | 0.423948 |
Evan, Eduardo, Olin, Melissa are the only persons in the room.
“Not everyone in the room does not enjoy stargazing or does not play video games” only if “everyone in the room does not enjoy stargazing if they does not own a smart tv and does not play video games and vice versa”.
“No one in the room is a chess master who participates in national tournaments” only if “someone in the room does not practice graffiti art and cannot play the piano”.
If someone has a pet dog and hosts regular game nights featuring complex strategy games then he/she either is not a chess master who participates in national tournaments or does not know morse code but not both and vice versa.
Everyone in the room designs and sews custom cosplay costumes for conventions and does not enjoy skydiving.
Not everyone in the room does not enjoy stargazing or does not play video games.
Everyone in the room does not enjoy origami and does not collect antique clocks.
Everyone anywhere does not have lived in exactly three countries.
Everyone in the room collects action figures and does not enjoy origami.
Everyone in the room does not enjoy skydiving and does not collect foreign coins.
Everyone in the room does not collect antique clocks and does not own a smart tv.
Everyone in the room either does not host themed dinner parties featuring gourmet home-cooked meals or does not design and sews custom cosplay costumes for conventions but not both.
Everyone in the room either does not enjoy stargazing or does not train for and competes in international triathlons but not both.
Someone in the room does not practice graffiti art and cannot play the piano.
Everyone in the room does not collect foreign coins and does not host a popular podcast about emerging technologies.
Everyone in the room either does not host a popular podcast about emerging technologies or does not have lived in exactly three countries but not both if and only if they either enjoys origami or trains for and competes in international triathlons but not both.
Everyone in the room either does not enjoy watercolor painting or does not own an Android phone but not both. | Evan plays video games. | entailment | room(evan)&room(eduardo)&room(olin)&room(melissa)&(![X]:(room(X)=>(X='evan'|X='eduardo'|X='olin'|X='melissa')))&
((~![X]:(room(X)=>(((does_not_play_video_games(X))|(does_not_enjoy_stargazing(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_stargazing(X))<=>(((does_not_own_a_smart_tv(X))&(does_not_play_video_games(X)))))))))&
((~?[X]:(room(X)=>(is_a_chess_master_who_participates_in_national_tournaments(X))))=>(?[X]:(room(X)&(((does_not_practice_graffiti_art(X))&(cannot_play_the_piano(X)))))))&
((![X]:((((has_a_pet_dog(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))<=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))<~>(does_not_know_morse_code(X)))))))&
(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(does_not_enjoy_skydiving(X))))))&
(~![X]:(room(X)=>(((does_not_play_video_games(X))|(does_not_enjoy_stargazing(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_origami(X))&(does_not_collect_antique_clocks(X))))))&
(![X]:(anywhere(X)=>(does_not_have_lived_in_exactly_three_countries(X))))&
(![X]:(room(X)=>(((collects_action_figures(X))&(does_not_enjoy_origami(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_skydiving(X))&(does_not_collect_foreign_coins(X))))))&
(![X]:(room(X)=>(((does_not_collect_antique_clocks(X))&(does_not_own_a_smart_tv(X))))))&
(![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<~>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_stargazing(X))<~>(does_not_train_for_and_competes_in_international_triathlons(X))))))&
(?[X]:(room(X)&(((does_not_practice_graffiti_art(X))&(cannot_play_the_piano(X))))))&
(![X]:(room(X)=>(((does_not_collect_foreign_coins(X))&(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(room(X)=>(((((does_not_host_a_popular_podcast_about_emerging_technologies(X))<~>(does_not_have_lived_in_exactly_three_countries(X))))<=>(((enjoys_origami(X))<~>(trains_for_and_competes_in_international_triathlons(X))))))))&
(![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))<~>(does_not_own_an_Android_phone(X)))))) | room(evan)&room(eduardo)&room(olin)&room(melissa)&(![X]:(room(X)=>(X='evan'|X='eduardo'|X='olin'|X='melissa')))&
plays_video_games(evan) | [
"b4",
"p0",
"p1",
"p5",
"p6",
"p7",
"p10",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3832910271491107095437973
% SZS output start Proof for 3832910271491107095437973
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] : (room(X0) => (~preda(X0) | ~predy(X0))) => ! [X0] : (room(X0) => (~preda(X0) <=> (~predy(X0) & ~preds(X0)))) [input p1]
49. ~! [X0] : (room(X0) => (~preda(X0) | ~predy(X0))) [input p5]
50. ! [X0] : (room(X0) => (~predr(X0) & ~predg(X0))) [input p6]
51. ! [X0] : (anywhere(X0) => ~predi(X0)) [input p7]
54. ! [X0] : (room(X0) => (~preds(X0) & ~predr(X0))) [input p10]
56. ! [X0] : (room(X0) => (~preda(X0) <~> ~predh(X0))) [input p12]
58. ! [X0] : (room(X0) => (~predk(X0) & ~predm(X0))) [input p14]
59. ! [X0] : (room(X0) => ((~predk(X0) <~> ~predi(X0)) <=> (predg(X0) <~> predh(X0)))) [input p15]
61. ~(predy(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
62. ~! [X0] : (room(X0) => (~preda(X0) | ~predy(X0))) => ! [X1] : (room(X1) => (~preda(X1) <=> (~predy(X1) & ~preds(X1)))) [rectify 45]
64. ! [X0] : (room(X0) => ~predk(X0)) [pure predicate removal 58]
67. ! [X0] : (room(X0) => ~predg(X0)) [pure predicate removal 50]
68. ! [X0] : (room(X0) => ~preds(X0)) [pure predicate removal 54]
146. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
147. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 146]
148. ! [X1] : ((~preda(X1) <=> (~predy(X1) & ~preds(X1))) | ~room(X1)) | ! [X0] : ((~preda(X0) | ~predy(X0)) | ~room(X0)) [ennf transformation 62]
149. ! [X1] : ((~preda(X1) <=> (~predy(X1) & ~preds(X1))) | ~room(X1)) | ! [X0] : (~preda(X0) | ~predy(X0) | ~room(X0)) [flattening 148]
152. ? [X0] : ((preda(X0) & predy(X0)) & room(X0)) [ennf transformation 49]
153. ? [X0] : (preda(X0) & predy(X0) & room(X0)) [flattening 152]
154. ! [X0] : (~predg(X0) | ~room(X0)) [ennf transformation 67]
155. ! [X0] : (~predi(X0) | ~anywhere(X0)) [ennf transformation 51]
157. ! [X0] : (~preds(X0) | ~room(X0)) [ennf transformation 68]
159. ! [X0] : ((~preda(X0) <~> ~predh(X0)) | ~room(X0)) [ennf transformation 56]
160. ! [X0] : (~predk(X0) | ~room(X0)) [ennf transformation 64]
161. ! [X0] : (((~predk(X0) <~> ~predi(X0)) <=> (predg(X0) <~> predh(X0))) | ~room(X0)) [ennf transformation 59]
163. ~predy(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 61]
164. ~predy(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 163]
166. ! [X1] : (((~preda(X1) | (predy(X1) | preds(X1))) & ((~predy(X1) & ~preds(X1)) | preda(X1))) | ~room(X1)) | ! [X0] : (~preda(X0) | ~predy(X0) | ~room(X0)) [nnf transformation 149]
167. ! [X1] : (((~preda(X1) | predy(X1) | preds(X1)) & ((~predy(X1) & ~preds(X1)) | preda(X1))) | ~room(X1)) | ! [X0] : (~preda(X0) | ~predy(X0) | ~room(X0)) [flattening 166]
168. ! [X0] : (((~preda(X0) | predy(X0) | preds(X0)) & ((~predy(X0) & ~preds(X0)) | preda(X0))) | ~room(X0)) | ! [X1] : (~preda(X1) | ~predy(X1) | ~room(X1)) [rectify 167]
175. ? [X0] : (preda(X0) & predy(X0) & room(X0)) => (preda(sK2) & predy(sK2) & room(sK2)) [choice axiom]
176. preda(sK2) & predy(sK2) & room(sK2) [skolemisation 153,175]
178. ! [X0] : (((predh(X0) | preda(X0)) & (~predh(X0) | ~preda(X0))) | ~room(X0)) [nnf transformation 159]
181. ! [X0] : (((((predi(X0) | predk(X0)) & (~predi(X0) | ~predk(X0))) | ((predg(X0) | ~predh(X0)) & (predh(X0) | ~predg(X0)))) & (((~predh(X0) | ~predg(X0)) & (predh(X0) | predg(X0))) | ((~predk(X0) | predi(X0)) & (~predi(X0) | predk(X0))))) | ~room(X0)) [nnf transformation 161]
183. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
184. ~predy(mary) | (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 164,183]
185. anywhere(X0) [cnf transformation 5]
266. room(mary) [cnf transformation 147]
267. room(paul) [cnf transformation 147]
268. room(fred) [cnf transformation 147]
269. room(alice) [cnf transformation 147]
270. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 147]
273. ~preda(X0) | predy(X0) | preds(X0) | ~room(X0) | ~preda(X1) | ~predy(X1) | ~room(X1) [cnf transformation 168]
282. room(sK2) [cnf transformation 176]
283. predy(sK2) [cnf transformation 176]
285. ~predg(X0) | ~room(X0) [cnf transformation 154]
286. ~predi(X0) | ~anywhere(X0) [cnf transformation 155]
288. ~preds(X0) | ~room(X0) [cnf transformation 157]
292. ~room(X0) | preda(X0) | predh(X0) [cnf transformation 178]
294. ~predk(X0) | ~room(X0) [cnf transformation 160]
302. predi(X0) | predk(X0) | predg(X0) | ~predh(X0) | ~room(X0) [cnf transformation 181]
305. ~predy(mary) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
306. ~predy(mary) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
307. ~predy(mary) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
308. ~predy(mary) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
309. ~predy(mary) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
311. 1 <=> ! [X1] : (~preda(X1) | ~room(X1) | ~predy(X1)) [avatar definition]
312. ~preda(X1) | ~room(X1) | ~predy(X1) <- (1) [avatar component clause 311]
314. 2 <=> ! [X0] : (~preda(X0) | ~room(X0) | preds(X0) | predy(X0)) [avatar definition]
315. ~preda(X0) | ~room(X0) | preds(X0) | predy(X0) <- (2) [avatar component clause 314]
316. 1 | 2 [avatar split clause 273,314,311]
338. ~predi(X0) [subsumption resolution 286,185]
340. predk(X0) | predg(X0) | ~predh(X0) | ~room(X0) [subsumption resolution 302,338]
341. predg(X0) | ~predh(X0) | ~room(X0) [subsumption resolution 340,294]
342. ~predh(X0) | ~room(X0) [subsumption resolution 341,285]
343. ~predy(mary) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,269]
344. ~predy(mary) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 343,268]
345. ~predy(mary) | alice != sK4 | ~room(mary) [subsumption resolution 344,267]
346. ~predy(mary) | alice != sK4 [subsumption resolution 345,266]
348. 8 <=> alice = sK4 [avatar definition]
350. alice != sK4 <- (~8) [avatar component clause 348]
352. 9 <=> predy(mary) [avatar definition]
354. ~predy(mary) <- (~9) [avatar component clause 352]
355. ~8 | ~9 [avatar split clause 346,352,348]
356. ~predy(mary) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,269]
357. ~predy(mary) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 356,268]
358. ~predy(mary) | fred != sK4 | ~room(mary) [subsumption resolution 357,267]
359. ~predy(mary) | fred != sK4 [subsumption resolution 358,266]
361. 10 <=> fred = sK4 [avatar definition]
363. fred != sK4 <- (~10) [avatar component clause 361]
364. ~10 | ~9 [avatar split clause 359,352,361]
365. ~predy(mary) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,269]
366. ~predy(mary) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 365,268]
367. ~predy(mary) | paul != sK4 | ~room(mary) [subsumption resolution 366,267]
368. ~predy(mary) | paul != sK4 [subsumption resolution 367,266]
370. 11 <=> paul = sK4 [avatar definition]
373. ~11 | ~9 [avatar split clause 368,352,370]
374. ~predy(mary) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,269]
375. ~predy(mary) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 374,268]
376. ~predy(mary) | mary != sK4 | ~room(mary) [subsumption resolution 375,267]
377. ~predy(mary) | mary != sK4 [subsumption resolution 376,266]
379. 12 <=> mary = sK4 [avatar definition]
381. mary != sK4 <- (~12) [avatar component clause 379]
382. ~12 | ~9 [avatar split clause 377,352,379]
383. ~predy(mary) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,269]
384. ~predy(mary) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 383,268]
385. ~predy(mary) | room(sK4) | ~room(mary) [subsumption resolution 384,267]
386. ~predy(mary) | room(sK4) [subsumption resolution 385,266]
388. 13 <=> room(sK4) [avatar definition]
390. room(sK4) <- (13) [avatar component clause 388]
391. 13 | ~9 [avatar split clause 386,352,388]
392. ~preda(X0) | ~room(X0) | predy(X0) <- (2) [subsumption resolution 315,288]
399. preda(mary) | predh(mary) [resolution 292,266]
400. preda(paul) | predh(paul) [resolution 292,267]
401. preda(fred) | predh(fred) [resolution 292,268]
402. preda(alice) | predh(alice) [resolution 292,269]
406. 14 <=> predh(mary) [avatar definition]
408. predh(mary) <- (14) [avatar component clause 406]
410. 15 <=> preda(mary) [avatar definition]
412. preda(mary) <- (15) [avatar component clause 410]
413. 14 | 15 [avatar split clause 399,410,406]
415. 16 <=> predh(paul) [avatar definition]
417. predh(paul) <- (16) [avatar component clause 415]
419. 17 <=> preda(paul) [avatar definition]
421. preda(paul) <- (17) [avatar component clause 419]
422. 16 | 17 [avatar split clause 400,419,415]
424. 18 <=> predh(fred) [avatar definition]
426. predh(fred) <- (18) [avatar component clause 424]
428. 19 <=> preda(fred) [avatar definition]
430. preda(fred) <- (19) [avatar component clause 428]
431. 18 | 19 [avatar split clause 401,428,424]
433. 20 <=> predh(alice) [avatar definition]
435. predh(alice) <- (20) [avatar component clause 433]
437. 21 <=> preda(alice) [avatar definition]
439. preda(alice) <- (21) [avatar component clause 437]
440. 20 | 21 [avatar split clause 402,437,433]
451. ~room(mary) <- (14) [resolution 408,342]
454. $false <- (14) [subsumption resolution 451,266]
455. ~14 [avatar contradiction clause 454]
518. ~room(paul) <- (16) [resolution 417,342]
521. $false <- (16) [subsumption resolution 518,267]
522. ~16 [avatar contradiction clause 521]
524. ~room(mary) | predy(mary) <- (2, 15) [resolution 392,412]
525. predy(mary) <- (2, 15) [subsumption resolution 524,266]
528. 9 | ~2 | ~15 [avatar split clause 525,410,314,352]
553. ~room(fred) <- (18) [resolution 426,342]
556. $false <- (18) [subsumption resolution 553,268]
557. ~18 [avatar contradiction clause 556]
567. ~room(alice) <- (20) [resolution 435,342]
570. $false <- (20) [subsumption resolution 567,269]
571. ~20 [avatar contradiction clause 570]
663. fred = sK2 | paul = sK2 | mary = sK2 | alice = sK2 [resolution 270,282]
665. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 <- (13) [resolution 270,390]
667. 40 <=> alice = sK2 [avatar definition]
669. alice = sK2 <- (40) [avatar component clause 667]
671. 41 <=> mary = sK2 [avatar definition]
673. mary = sK2 <- (41) [avatar component clause 671]
675. 42 <=> paul = sK2 [avatar definition]
677. paul = sK2 <- (42) [avatar component clause 675]
679. 43 <=> fred = sK2 [avatar definition]
681. fred = sK2 <- (43) [avatar component clause 679]
682. 40 | 41 | 42 | 43 [avatar split clause 663,679,675,671,667]
700. paul = sK4 | mary = sK4 | alice = sK4 <- (~10, 13) [subsumption resolution 665,363]
705. paul = sK4 | alice = sK4 <- (~10, ~12, 13) [subsumption resolution 700,381]
706. paul = sK4 <- (~8, ~10, ~12, 13) [subsumption resolution 705,350]
707. 11 | 8 | 10 | 12 | ~13 [avatar split clause 706,388,379,361,348,370]
718. predy(alice) <- (40) [backward demodulation 283,669]
730. ~room(paul) | ~predy(paul) <- (1, 17) [resolution 312,421]
731. ~room(fred) | ~predy(fred) <- (1, 19) [resolution 312,430]
732. ~room(alice) | ~predy(alice) <- (1, 21) [resolution 312,439]
733. ~predy(paul) <- (1, 17) [subsumption resolution 730,267]
734. ~predy(fred) <- (1, 19) [subsumption resolution 731,268]
735. ~predy(alice) <- (1, 21) [subsumption resolution 732,269]
736. $false <- (1, 21, 40) [subsumption resolution 735,718]
737. ~1 | ~21 | ~40 [avatar contradiction clause 736]
742. predy(mary) <- (41) [backward demodulation 283,673]
744. $false <- (~9, 41) [subsumption resolution 742,354]
745. 9 | ~41 [avatar contradiction clause 744]
748. predy(paul) <- (42) [backward demodulation 283,677]
754. $false <- (1, 17, 42) [subsumption resolution 748,733]
755. ~1 | ~17 | ~42 [avatar contradiction clause 754]
757. predy(fred) <- (43) [backward demodulation 283,681]
763. $false <- (1, 19, 43) [subsumption resolution 757,734]
764. ~1 | ~19 | ~43 [avatar contradiction clause 763]
765. $false [avatar sat refutation 316,355,364,373,382,391,413,422,431,440,455,522,528,557,571,682,707,737,745,755,764]
% SZS output end Proof for 3832910271491107095437973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0.029731 |
Lena is the only person in the room.
Everyone in the room collects historical artifacts related to ancient civilizations only if they practices pilates.
Everyone in the room does enjoy mountain biking if they enjoys spelunking and vice versa.
Lena enjoys rooftop gardening.
Lena enjoys spelunking.
Only one person in the room either collects antique jewelry or does enjoy mountain biking but not both.
Lena is a client of Costco.
Lena is a dedicated volunteer for local community service projects.
It is not the case that “Lena makes homemade pastries”.
Lena writes poetry.
Lena collects historical artifacts related to ancient civilizations.
Lena can play the harmonica. | Lena can play the harmonica, enjoys spelunking and collects historical artifacts related to ancient civilizations. | entailment | room(lena)&(![X]:(room(X)=>(X='lena')))&
(![X]:(room(X)=>(((practices_pilates(X))<=(collects_historical_artifacts_related_to_ancient_civilizations(X))))))&
(![X]:(room(X)=>(((does_enjoy_mountain_biking(X))<=>(enjoys_spelunking(X))))))&
(enjoys_rooftop_gardening(lena))&
(enjoys_spelunking(lena))&
(((?[X]:(room(X)&((collects_antique_jewelry(X))<~>(does_enjoy_mountain_biking(X)))))&(![X,Y]:((room(X)&room(Y)&(((collects_antique_jewelry(X))<~>(does_enjoy_mountain_biking(X))))&(((collects_antique_jewelry(Y))<~>(does_enjoy_mountain_biking(Y)))))=>(X=Y)))))&
(is_a_client_of_Costco(lena))&
(is_a_dedicated_volunteer_for_local_community_service_projects(lena))&
(~(makes_homemade_pastries(lena)))&
(writes_poetry(lena))&
(collects_historical_artifacts_related_to_ancient_civilizations(lena))&
(can_play_the_harmonica(lena)) | room(lena)&(![X]:(room(X)=>(X='lena')))&
((can_play_the_harmonica(lena))&(enjoys_spelunking(lena))&(collects_historical_artifacts_related_to_ancient_civilizations(lena))) | [
"p0",
"p4",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3149638367797903852484363
% SZS output start Proof for 3149638367797903852484363
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
48. preda(mary) [input p4]
54. predb(mary) [input p10]
55. prede(mary) [input p11]
56. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
136. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
140. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 56]
147. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom]
148. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 140,147]
229. room(mary) [cnf transformation 136]
230. ~room(X0) | mary = X0 [cnf transformation 136]
233. preda(mary) [cnf transformation 48]
241. predb(mary) [cnf transformation 54]
242. prede(mary) [cnf transformation 55]
243. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK1) | ~room(mary) [cnf transformation 148]
244. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [cnf transformation 148]
255. ~preda(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 244,241]
256. ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 255,233]
257. mary != sK1 | ~room(mary) [subsumption resolution 256,242]
258. mary != sK1 [subsumption resolution 257,229]
259. ~preda(mary) | ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 243,241]
260. ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 259,233]
261. room(sK1) | ~room(mary) [subsumption resolution 260,242]
262. room(sK1) [subsumption resolution 261,229]
265. mary = sK1 [resolution 230,262]
269. $false [subsumption resolution 265,258]
% SZS output end Proof for 3149638367797903852484363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0.591095 |
Dolores, Joseph, David are the only persons in the room. If not everyone in the room does not enjoy mountain biking then if someone does enjoy mountain biking or practices tai chi or both then he/she practices tai chi and vice versa. Everyone in the room who does enjoy mountain biking practices tai chi. If someone does enjoy mountain biking or practices tai chi or both then he/she practices tai chi and vice versa. At least one person in the room does enjoy mountain biking or practices tai chi or both. Everyone in the room practices tai chi or does not practice tai chi. Everyone outside the room who neither does not enjoy mountain biking nor practices tai chi practices tai chi. Joseph does not practice tai chi. Dolores dreamt that Joseph does not enjoy mountain biking. Dolores does enjoy mountain biking. More than one person outside the room practices tai chi. Everyone in the room who does enjoy mountain biking does not enjoy mountain biking or does enjoy mountain biking or both. Everyone in the room does enjoy mountain biking if they practices tai chi. | Dolores practices tai chi. | entailment | room(dolores)&room(joseph)&room(david)&(![X]:(room(X)=>(X='dolores'|X='joseph'|X='david')))&
((~![X]:(room(X)=>(does_not_enjoy_mountain_biking(X))))=>((![X]:((((does_enjoy_mountain_biking(X))|(practices_tai_chi(X))))<=>(practices_tai_chi(X))))))&
(![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(practices_tai_chi(X))))))&
((![X]:((((does_enjoy_mountain_biking(X))|(practices_tai_chi(X))))<=>(practices_tai_chi(X)))))&
(((?[X]:(room(X)&((does_enjoy_mountain_biking(X))|(practices_tai_chi(X)))))))&
(![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(practices_tai_chi(X))))))&
(![X]:(~room(X)=>(((~((does_not_enjoy_mountain_biking(X))|(practices_tai_chi(X))))=>(practices_tai_chi(X))))))&
(does_not_practice_tai_chi(joseph))&
((dolores_dream=>(does_not_enjoy_mountain_biking(joseph))))&
(does_enjoy_mountain_biking(dolores))&
((?[X,Y]:(~room(X)&~room(Y)&(practices_tai_chi(X)&practices_tai_chi(Y))&(X!=Y))))&
(![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(((does_not_enjoy_mountain_biking(X))|(does_enjoy_mountain_biking(X))))))))&
(![X]:(room(X)=>(((practices_tai_chi(X))=>(does_enjoy_mountain_biking(X)))))) | room(dolores)&room(joseph)&room(david)&(![X]:(room(X)=>(X='dolores'|X='joseph'|X='david')))&
practices_tai_chi(dolores) | [
"p0",
"p2",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5395939845123649537817325
% SZS output start Proof for 5395939845123649537817325
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
46. ! [X0] : (room(X0) => (predo(X0) => predu(X0))) [input p2]
50. ! [X0] : (~room(X0) => (~(predu(X0) | ~predo(X0)) => predu(X0))) [input p6]
53. predo(mary) [input p9]
57. ~(predu(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
132. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
133. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 132]
135. ! [X0] : ((predu(X0) | ~predo(X0)) | ~room(X0)) [ennf transformation 46]
136. ! [X0] : (predu(X0) | ~predo(X0) | ~room(X0)) [flattening 135]
139. ! [X0] : ((predu(X0) | (predu(X0) | ~predo(X0))) | room(X0)) [ennf transformation 50]
140. ! [X0] : (predu(X0) | predu(X0) | ~predo(X0) | room(X0)) [flattening 139]
145. ~predu(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57]
146. ~predu(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 145]
157. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
158. ~predu(mary) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 146,157]
239. room(mary) [cnf transformation 133]
240. room(paul) [cnf transformation 133]
241. room(fred) [cnf transformation 133]
242. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 133]
246. ~predo(X0) | predu(X0) | ~room(X0) [cnf transformation 136]
253. predu(X0) | predu(X0) | ~predo(X0) | room(X0) [cnf transformation 140]
255. predo(mary) [cnf transformation 53]
263. ~predu(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 158]
264. ~predu(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 158]
265. ~predu(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 158]
266. ~predu(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 158]
268. predu(X0) | ~predo(X0) | room(X0) [duplicate literal removal 253]
273. 2 <=> ! [X0] : (predu(X0) | ~predo(X0)) [avatar definition]
274. ~predo(X0) | predu(X0) <- (2) [avatar component clause 273]
286. predu(X0) | ~predo(X0) [subsumption resolution 268,246]
287. 2 [avatar split clause 286,273]
288. ~predu(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 266,241]
289. ~predu(mary) | fred != sK3 | ~room(mary) [subsumption resolution 288,240]
290. ~predu(mary) | fred != sK3 [subsumption resolution 289,239]
292. 5 <=> fred = sK3 [avatar definition]
294. fred != sK3 <- (~5) [avatar component clause 292]
296. 6 <=> predu(mary) [avatar definition]
299. ~5 | ~6 [avatar split clause 290,296,292]
300. ~predu(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 265,241]
301. ~predu(mary) | paul != sK3 | ~room(mary) [subsumption resolution 300,240]
302. ~predu(mary) | paul != sK3 [subsumption resolution 301,239]
304. 7 <=> paul = sK3 [avatar definition]
306. paul != sK3 <- (~7) [avatar component clause 304]
307. ~7 | ~6 [avatar split clause 302,296,304]
308. ~predu(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 264,241]
309. ~predu(mary) | mary != sK3 | ~room(mary) [subsumption resolution 308,240]
310. ~predu(mary) | mary != sK3 [subsumption resolution 309,239]
312. 8 <=> mary = sK3 [avatar definition]
314. mary != sK3 <- (~8) [avatar component clause 312]
315. ~8 | ~6 [avatar split clause 310,296,312]
316. ~predu(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 263,241]
317. ~predu(mary) | room(sK3) | ~room(mary) [subsumption resolution 316,240]
318. ~predu(mary) | room(sK3) [subsumption resolution 317,239]
320. 9 <=> room(sK3) [avatar definition]
322. room(sK3) <- (9) [avatar component clause 320]
323. 9 | ~6 [avatar split clause 318,296,320]
324. predu(mary) <- (2) [resolution 274,255]
329. 6 | ~2 [avatar split clause 324,273,296]
376. paul = sK3 | mary = sK3 | fred = sK3 <- (9) [resolution 242,322]
390. mary = sK3 | fred = sK3 <- (~7, 9) [subsumption resolution 376,306]
391. fred = sK3 <- (~7, ~8, 9) [subsumption resolution 390,314]
392. $false <- (~5, ~7, ~8, 9) [subsumption resolution 391,294]
393. 5 | 7 | 8 | ~9 [avatar contradiction clause 392]
394. $false [avatar sat refutation 287,299,307,315,323,329,393]
% SZS output end Proof for 5395939845123649537817325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.059626 |
There is a room. If “at least one person in the room does not have a saltwater aquarium” then “everyone in the room who has a saltwater aquarium creates bespoke furniture pieces from reclaimed wood” otherwise “someone in the room enjoys bird watching”. “Someone in the room has a saltwater aquarium” only if “everyone in the room hosts a popular podcast about emerging technologies if they does not enjoy bird watching”. Either “everyone in the room creates bespoke furniture pieces from reclaimed wood” or “not everyone in the room enjoys bird watching or does not enjoy bird watching” but not both. Everyone anywhere who enjoys bird watching creates bespoke furniture pieces from reclaimed wood. Everyone in the room creates bespoke furniture pieces from reclaimed wood if and only if they does not host a popular podcast about emerging technologies. Everyone in the room who practices and performs acrobatic dance routines, does not enjoy bird watching and hosts a popular podcast about emerging technologies does not create bespoke furniture pieces from reclaimed wood. Everyone in the room hosts a popular podcast about emerging technologies if they does not create bespoke furniture pieces from reclaimed wood. Everyone anywhere enjoys bird watching if they creates bespoke furniture pieces from reclaimed wood. Everyone in the room who has a saltwater aquarium creates bespoke furniture pieces from reclaimed wood. | Everyone outside the room does not have a saltwater aquarium. | neutral | (there_is_a_room)&
(((((?[X]:(room(X)&does_not_have_a_saltwater_aquarium(X)))))=>(![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))&((~(((?[X]:(room(X)&does_not_have_a_saltwater_aquarium(X))))))=>(?[X]:(room(X)&(enjoys_bird_watching(X))))))&
((?[X]:(room(X)&(has_a_saltwater_aquarium(X))))=>(![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))))&
((![X]:(room(X)=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))<~>(~![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))|(enjoys_bird_watching(X)))))))&
(![X]:(anywhere(X)=>(((enjoys_bird_watching(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(room(X)=>(((((practices_and_performs_acrobatic_dance_routines(X))&(does_not_enjoy_bird_watching(X))&(hosts_a_popular_podcast_about_emerging_technologies(X))))=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(anywhere(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(enjoys_bird_watching(X))))))&
(![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(does_not_have_a_saltwater_aquarium(X))) | [] | null | 0 |
Jillian, Diane, Jason are the only persons in the room. If 'Diane is a client of Costco' then 'everyone in the room who owns a telescope frequently participates in hackathons and coding competitions'. Everyone in the room who owns a telescope frequently participates in hackathons and coding competitions. It is not the case that 'at least one person in the room frequently participates in hackathons and coding competitions'. If someone is a certified scuba diver with advanced underwater photography skills then he/she drives a hybrid car and vice versa. Diane enjoys origami. At least one person in the room writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room is a certified scuba diver with advanced underwater photography skills or is not a client of Costco. Jason plays as a goalkeeper for a local amateur soccer team. It is not the case that 'someone in the room drives a hybrid car'. Jillian can play the harmonica. Diane plays as a goalkeeper for a local amateur soccer team. Everyone in the room who enjoys kayaking and exploring remote waterways frequently participates in hackathons and coding competitions. It is not the case that 'someone in the room enjoys kayaking and exploring remote waterways'. Everyone in the room owns a telescope only if they writes in-depth travel guides for off-the-beaten-path destinations. Everyone outside the room who frequently participates in hackathons and coding competitions or can play the harmonica or both is a certified scuba diver with advanced underwater photography skills. Everyone in the room enjoys origami only if they is a certified scuba diver with advanced underwater photography skills, enjoys kayaking and exploring remote waterways or can play the harmonica. Everyone in the room who plays as a goalkeeper for a local amateur soccer team enjoys origami. Everyone in the room who is a client of Costco can play the harmonica. | Diane is a client of Costco. | contradiction | room(jillian)&room(diane)&room(jason)&(![X]:(room(X)=>(X='jillian'|X='diane'|X='jason')))&
((is_a_client_of_Costco(diane))=>(![X]:(room(X)=>(((owns_a_telescope(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))))&
(![X]:(room(X)=>(((owns_a_telescope(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))&
(~(((?[X]:(room(X)&frequently_participates_in_hackathons_and_coding_competitions(X))))))&
((![X]:((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=>(drives_a_hybrid_car(X)))))&
(enjoys_origami(diane))&
(((?[X]:(room(X)&writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))&
(![X]:(room(X)=>(((is_not_a_client_of_Costco(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))&
(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(jason))&
(~(?[X]:(room(X)&(drives_a_hybrid_car(X)))))&
(can_play_the_harmonica(jillian))&
(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(diane))&
(![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))&
(~(?[X]:(room(X)&(enjoys_kayaking_and_exploring_remote_waterways(X)))))&
(![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=(owns_a_telescope(X))))))&
(![X]:(~room(X)=>(((((frequently_participates_in_hackathons_and_coding_competitions(X))|(can_play_the_harmonica(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))|(enjoys_kayaking_and_exploring_remote_waterways(X))|(can_play_the_harmonica(X))))<=(enjoys_origami(X))))))&
(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(enjoys_origami(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(can_play_the_harmonica(X)))))) | room(jillian)&room(diane)&room(jason)&(![X]:(room(X)=>(X='jillian'|X='diane'|X='jason')))&
is_a_client_of_Costco(diane) | [
"p0",
"p4",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 71596993328313683210807
% SZS output start Proof for 71596993328313683210807
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
48. ! [X0] : (predg(X0) <=> predb(X0)) [input p4]
51. ! [X0] : (room(X0) => (predg(X0) | ~preda(X0))) [input p7]
53. ~? [X0] : (predb(X0) & room(X0)) [input p9]
63. preda(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
64. ! [X0] : (predg(X0) => predb(X0)) [unused predicate definition removal 48]
141. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
142. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 141]
144. ! [X0] : (predb(X0) | ~predg(X0)) [ennf transformation 64]
145. ! [X0] : ((predg(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 51]
146. ! [X0] : (predg(X0) | ~preda(X0) | ~room(X0)) [flattening 145]
147. ! [X0] : (~predb(X0) | ~room(X0)) [ennf transformation 53]
159. preda(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 63]
160. preda(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 159]
245. room(paul) [cnf transformation 142]
249. ~predg(X0) | predb(X0) [cnf transformation 144]
252. ~preda(X0) | predg(X0) | ~room(X0) [cnf transformation 146]
254. ~predb(X0) | ~room(X0) [cnf transformation 147]
268. preda(paul) [cnf transformation 160]
272. predg(paul) | ~room(paul) [resolution 252,268]
273. predg(paul) [subsumption resolution 272,245]
275. predb(paul) [resolution 273,249]
294. ~room(paul) [resolution 275,254]
295. $false [subsumption resolution 294,245]
% SZS output end Proof for 71596993328313683210807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.013137 |
Kristy, David are the only persons in the room.
If “everyone in the room does not use contact lenses or uses contact lenses” then “everyone anywhere is not right-handed if they collects antique clocks”.
“Everyone in the room is not an avid mountain climber who has scaled several peaks or is a Linux enthusiast” only if “everyone in the room is not a culinary enthusiast who experiments with international cuisines if they participates in citizen science projects related to wildlife monitoring”.
If “it is true that “no one in the room is not an amateur astronomer who builds and uses custom telescopes or enjoys watercolor painting”” then “everyone in the room does not participate in citizen science projects related to wildlife monitoring or uses contact lenses”.
If “everyone in the room does not participate in citizen science projects related to wildlife monitoring or uses contact lenses” then “if someone does not enjoy mountain biking then he/she is right-handed”.
“Everyone in the room plays eSports competitively or is not a professional photographer specializing in portrait photography” only if “if someone uses contact lenses then he/she does enjoy trail running”.
Everyone in the room is a skilled home brewer experimenting with craft beer recipes.
Everyone in the room who is not a coffee connoisseur is not a dedicated advocate for digital privacy and encryption.
Not everyone in the room collects rare and antique scientific instruments if they is not a dedicated advocate for digital privacy and encryption.
Everyone in the room collects rare and antique scientific instruments if and only if they is right-handed.
If someone enjoys watercolor painting and is not a Linux enthusiast then he/she is a Linux enthusiast.
If someone is a Linux enthusiast then he/she is a skilled home brewer experimenting with craft beer recipes and vice versa.
Everyone in the room does not collect vintage stamps or is a coffee connoisseur or both if they composes and performs experimental electronic music.
If someone is right-handed then he/she is an amateur astronomer who builds and uses custom telescopes and vice versa.
More than one person anywhere does not make homemade pastries. | David is a skilled home brewer experimenting with craft beer recipes. | entailment | room(kristy)&room(david)&(![X]:(room(X)=>(X='kristy'|X='david')))&
((![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_use_contact_lenses(X))))))=>(![X]:(anywhere(X)=>(((collects_antique_clocks(X))=>(is_not_right-handed(X)))))))&
((![X]:(room(X)=>(((is_a_Linux_enthusiast(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))&
(((~?[X]:(room(X)=>(((enjoys_watercolor_painting(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))=>(![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))))&
((![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>((![X]:((does_not_enjoy_mountain_biking(X))=>(is_right-handed(X)))))))&
((![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(plays_eSports_competitively(X))))))=>((![X]:((uses_contact_lenses(X))=>(does_enjoy_trail_running(X))))))&
(![X]:(room(X)=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))&
(![X]:(room(X)=>(((is_not_a_coffee_connoisseur(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))=>(collects_rare_and_antique_scientific_instruments(X))))))&
(![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))<=>(is_right-handed(X))))))&
((![X]:((((enjoys_watercolor_painting(X))&(is_not_a_Linux_enthusiast(X))))=>(is_a_Linux_enthusiast(X)))))&
((![X]:((is_a_Linux_enthusiast(X))<=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))&
(![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(((does_not_collect_vintage_stamps(X))|(is_a_coffee_connoisseur(X))))))))&
((![X]:((is_right-handed(X))<=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(does_not_make_homemade_pastries(X)&does_not_make_homemade_pastries(Y))&(X!=Y)))) | room(kristy)&room(david)&(![X]:(room(X)=>(X='kristy'|X='david')))&
is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(david) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1563154888615392214482121
% SZS output start Proof for 1563154888615392214482121
44. ? [X0,X1] : (X0 != X1 & ~predc(X1) & ~predc(X0) & anywhere(X1) & anywhere(X0)) & ! [X0] : (predi(X0) <=> predu(X0)) & ! [X0] : (room(X0) => (predk(X0) => (predo(X0) | ~predp(X0)))) & ! [X0] : (predm(X0) <=> predj(X0)) & ! [X0] : ((~predm(X0) & predt(X0)) => predm(X0)) & ! [X0] : (room(X0) => (preds(X0) <=> predi(X0))) & ~! [X0] : (room(X0) => (~predg(X0) => preds(X0))) & ! [X0] : (room(X0) => (~predo(X0) => ~predg(X0))) & ! [X0] : (room(X0) => predj(X0)) & (! [X0] : (room(X0) => (predq(X0) | ~preda(X0))) => ! [X0] : (predy(X0) => predz(X0))) & (! [X0] : (room(X0) => (~prede(X0) | predy(X0))) => ! [X0] : (~predn(X0) => predi(X0))) & (~? [X0] : (room(X0) => (~predu(X0) | predt(X0))) => ! [X0] : (room(X0) => (~prede(X0) | predy(X0)))) & (! [X0] : (room(X0) => (~predr(X0) | predm(X0))) => ! [X0] : (room(X0) => (prede(X0) => ~predv(X0)))) & (! [X0] : (room(X0) => (~predy(X0) | predy(X0))) => ! [X0] : (anywhere(X0) => (predw(X0) => ~predi(X0)))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
45. ~(predj(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
46. ? [X0,X1] : (X0 != X1 & ~predc(X1) & ~predc(X0) & anywhere(X1) & anywhere(X0)) & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X3] : (room(X3) => (predk(X3) => (predo(X3) | ~predp(X3)))) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X5] : ((~predm(X5) & predt(X5)) => predm(X5)) & ! [X6] : (room(X6) => (preds(X6) <=> predi(X6))) & ~! [X7] : (room(X7) => (~predg(X7) => preds(X7))) & ! [X8] : (room(X8) => (~predo(X8) => ~predg(X8))) & ! [X9] : (room(X9) => predj(X9)) & (! [X10] : (room(X10) => (predq(X10) | ~preda(X10))) => ! [X11] : (predy(X11) => predz(X11))) & (! [X12] : (room(X12) => (~prede(X12) | predy(X12))) => ! [X13] : (~predn(X13) => predi(X13))) & (~? [X14] : (room(X14) => (~predu(X14) | predt(X14))) => ! [X15] : (room(X15) => (~prede(X15) | predy(X15)))) & (! [X16] : (room(X16) => (~predr(X16) | predm(X16))) => ! [X17] : (room(X17) => (prede(X17) => ~predv(X17)))) & (! [X18] : (room(X18) => (~predy(X18) | predy(X18))) => ! [X19] : (anywhere(X19) => (predw(X19) => ~predi(X19)))) & ! [X20] : (room(X20) => (paul = X20 | mary = X20)) & room(paul) & room(mary) [rectify 44]
47. ? [X0,X1] : (X0 != X1 & anywhere(X1) & anywhere(X0)) & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X3] : (room(X3) => (predk(X3) => (predo(X3) | ~predp(X3)))) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X5] : ((~predm(X5) & predt(X5)) => predm(X5)) & ! [X6] : (room(X6) => (preds(X6) <=> predi(X6))) & ~! [X7] : (room(X7) => (~predg(X7) => preds(X7))) & ! [X8] : (room(X8) => (~predo(X8) => ~predg(X8))) & ! [X9] : (room(X9) => predj(X9)) & (! [X10] : (room(X10) => (predq(X10) | ~preda(X10))) => ! [X11] : (predy(X11) => predz(X11))) & (! [X12] : (room(X12) => (~prede(X12) | predy(X12))) => ! [X13] : (~predn(X13) => predi(X13))) & (~? [X14] : (room(X14) => (~predu(X14) | predt(X14))) => ! [X15] : (room(X15) => (~prede(X15) | predy(X15)))) & (! [X16] : (room(X16) => (~predr(X16) | predm(X16))) => ! [X17] : (room(X17) => (prede(X17) => ~predv(X17)))) & (! [X18] : (room(X18) => (~predy(X18) | predy(X18))) => ! [X19] : (anywhere(X19) => (predw(X19) => ~predi(X19)))) & ! [X20] : (room(X20) => (paul = X20 | mary = X20)) & room(paul) & room(mary) [pure predicate removal 46]
48. ? [X0,X1] : (X0 != X1 & anywhere(X1) & anywhere(X0)) & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X5] : ((~predm(X5) & predt(X5)) => predm(X5)) & ! [X6] : (room(X6) => (preds(X6) <=> predi(X6))) & ~! [X7] : (room(X7) => (~predg(X7) => preds(X7))) & ! [X8] : (room(X8) => (~predo(X8) => ~predg(X8))) & ! [X9] : (room(X9) => predj(X9)) & (! [X10] : (room(X10) => (predq(X10) | ~preda(X10))) => ! [X11] : (predy(X11) => predz(X11))) & (! [X12] : (room(X12) => (~prede(X12) | predy(X12))) => ! [X13] : (~predn(X13) => predi(X13))) & (~? [X14] : (room(X14) => (~predu(X14) | predt(X14))) => ! [X15] : (room(X15) => (~prede(X15) | predy(X15)))) & (! [X16] : (room(X16) => (~predr(X16) | predm(X16))) => ! [X17] : (room(X17) => (prede(X17) => ~predv(X17)))) & (! [X18] : (room(X18) => (~predy(X18) | predy(X18))) => ! [X19] : (anywhere(X19) => (predw(X19) => ~predi(X19)))) & ! [X20] : (room(X20) => (paul = X20 | mary = X20)) & room(paul) & room(mary) [pure predicate removal 47]
49. ? [X0,X1] : (X0 != X1 & anywhere(X1) & anywhere(X0)) & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X5] : ((~predm(X5) & predt(X5)) => predm(X5)) & ! [X6] : (room(X6) => (preds(X6) <=> predi(X6))) & ~! [X7] : (room(X7) => preds(X7)) & ! [X9] : (room(X9) => predj(X9)) & (! [X10] : (room(X10) => (predq(X10) | ~preda(X10))) => ! [X11] : (predy(X11) => predz(X11))) & (! [X12] : (room(X12) => (~prede(X12) | predy(X12))) => ! [X13] : (~predn(X13) => predi(X13))) & (~? [X14] : (room(X14) => (~predu(X14) | predt(X14))) => ! [X15] : (room(X15) => (~prede(X15) | predy(X15)))) & (! [X16] : (room(X16) => (~predr(X16) | predm(X16))) => ! [X17] : (room(X17) => (prede(X17) => ~predv(X17)))) & (! [X18] : (room(X18) => (~predy(X18) | predy(X18))) => ! [X19] : (anywhere(X19) => (predw(X19) => ~predi(X19)))) & ! [X20] : (room(X20) => (paul = X20 | mary = X20)) & room(paul) & room(mary) [pure predicate removal 48]
50. ? [X0,X1] : (X0 != X1 & anywhere(X1) & anywhere(X0)) & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X5] : ((~predm(X5) & predt(X5)) => predm(X5)) & ! [X6] : (room(X6) => (preds(X6) <=> predi(X6))) & ~! [X7] : (room(X7) => preds(X7)) & ! [X9] : (room(X9) => predj(X9)) & (! [X12] : (room(X12) => (~prede(X12) | predy(X12))) => ! [X13] : (~predn(X13) => predi(X13))) & (~? [X14] : (room(X14) => (~predu(X14) | predt(X14))) => ! [X15] : (room(X15) => (~prede(X15) | predy(X15)))) & (! [X16] : (room(X16) => (~predr(X16) | predm(X16))) => ! [X17] : (room(X17) => (prede(X17) => ~predv(X17)))) & (! [X18] : (room(X18) => (~predy(X18) | predy(X18))) => ! [X19] : (anywhere(X19) => (predw(X19) => ~predi(X19)))) & ! [X20] : (room(X20) => (paul = X20 | mary = X20)) & room(paul) & room(mary) [pure predicate removal 49]
51. ? [X0,X1] : (X0 != X1 & anywhere(X1) & anywhere(X0)) & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X5] : ((~predm(X5) & predt(X5)) => predm(X5)) & ! [X6] : (room(X6) => (preds(X6) <=> predi(X6))) & ~! [X7] : (room(X7) => preds(X7)) & ! [X9] : (room(X9) => predj(X9)) & (~? [X14] : (room(X14) => (~predu(X14) | predt(X14))) => ! [X15] : (room(X15) => (~prede(X15) | predy(X15)))) & (! [X16] : (room(X16) => (~predr(X16) | predm(X16))) => ! [X17] : (room(X17) => (prede(X17) => ~predv(X17)))) & (! [X18] : (room(X18) => (~predy(X18) | predy(X18))) => ! [X19] : (anywhere(X19) => (predw(X19) => ~predi(X19)))) & ! [X20] : (room(X20) => (paul = X20 | mary = X20)) & room(paul) & room(mary) [pure predicate removal 50]
52. ? [X0,X1] : (X0 != X1 & anywhere(X1) & anywhere(X0)) & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X5] : ((~predm(X5) & predt(X5)) => predm(X5)) & ! [X6] : (room(X6) => (preds(X6) <=> predi(X6))) & ~! [X7] : (room(X7) => preds(X7)) & ! [X9] : (room(X9) => predj(X9)) & (! [X18] : (room(X18) => (~predy(X18) | predy(X18))) => ! [X19] : (anywhere(X19) => (predw(X19) => ~predi(X19)))) & ! [X20] : (room(X20) => (paul = X20 | mary = X20)) & room(paul) & room(mary) [pure predicate removal 51]
53. ? [X0,X1] : (X0 != X1 & anywhere(X1) & anywhere(X0)) & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X6] : (room(X6) => (preds(X6) <=> predi(X6))) & ~! [X7] : (room(X7) => preds(X7)) & ! [X9] : (room(X9) => predj(X9)) & (! [X18] : (room(X18) => (~predy(X18) | predy(X18))) => ! [X19] : (anywhere(X19) => (predw(X19) => ~predi(X19)))) & ! [X20] : (room(X20) => (paul = X20 | mary = X20)) & room(paul) & room(mary) [pure predicate removal 52]
54. ? [X0,X1] : (X0 != X1 & anywhere(X1) & anywhere(X0)) & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X6] : (room(X6) => (preds(X6) <=> predi(X6))) & ~! [X7] : (room(X7) => preds(X7)) & ! [X9] : (room(X9) => predj(X9)) & ! [X20] : (room(X20) => (paul = X20 | mary = X20)) & room(paul) & room(mary) [pure predicate removal 53]
55. ? [X0,X1] : X0 != X1 & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X6] : (room(X6) => (preds(X6) <=> predi(X6))) & ~! [X7] : (room(X7) => preds(X7)) & ! [X9] : (room(X9) => predj(X9)) & ! [X20] : (room(X20) => (paul = X20 | mary = X20)) & room(paul) & room(mary) [pure predicate removal 54]
128. ? [X0,X1] : X0 != X1 & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X6] : ((preds(X6) <=> predi(X6)) | ~room(X6)) & ? [X7] : (~preds(X7) & room(X7)) & ! [X9] : (predj(X9) | ~room(X9)) & ! [X20] : ((paul = X20 | mary = X20) | ~room(X20)) & room(paul) & room(mary) [ennf transformation 55]
129. ? [X0,X1] : X0 != X1 & ! [X2] : (predi(X2) <=> predu(X2)) & ! [X4] : (predm(X4) <=> predj(X4)) & ! [X6] : ((preds(X6) <=> predi(X6)) | ~room(X6)) & ? [X7] : (~preds(X7) & room(X7)) & ! [X9] : (predj(X9) | ~room(X9)) & ! [X20] : (paul = X20 | mary = X20 | ~room(X20)) & room(paul) & room(mary) [flattening 128]
130. ~predj(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 45]
131. ~predj(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 130]
133. ? [X0,X1] : X0 != X1 & ! [X2] : ((predi(X2) | ~predu(X2)) & (predu(X2) | ~predi(X2))) & ! [X4] : ((predm(X4) | ~predj(X4)) & (predj(X4) | ~predm(X4))) & ! [X6] : (((preds(X6) | ~predi(X6)) & (predi(X6) | ~preds(X6))) | ~room(X6)) & ? [X7] : (~preds(X7) & room(X7)) & ! [X9] : (predj(X9) | ~room(X9)) & ! [X20] : (paul = X20 | mary = X20 | ~room(X20)) & room(paul) & room(mary) [nnf transformation 129]
134. ? [X0,X1] : X0 != X1 & ! [X2] : ((predi(X2) | ~predu(X2)) & (predu(X2) | ~predi(X2))) & ! [X3] : ((predm(X3) | ~predj(X3)) & (predj(X3) | ~predm(X3))) & ! [X4] : (((preds(X4) | ~predi(X4)) & (predi(X4) | ~preds(X4))) | ~room(X4)) & ? [X5] : (~preds(X5) & room(X5)) & ! [X6] : (predj(X6) | ~room(X6)) & ! [X7] : (paul = X7 | mary = X7 | ~room(X7)) & room(paul) & room(mary) [rectify 133]
135. ? [X0,X1] : X0 != X1 => sK0 != sK1 [choice axiom]
136. ? [X5] : (~preds(X5) & room(X5)) => (~preds(sK2) & room(sK2)) [choice axiom]
137. sK0 != sK1 & ! [X2] : ((predi(X2) | ~predu(X2)) & (predu(X2) | ~predi(X2))) & ! [X3] : ((predm(X3) | ~predj(X3)) & (predj(X3) | ~predm(X3))) & ! [X4] : (((preds(X4) | ~predi(X4)) & (predi(X4) | ~preds(X4))) | ~room(X4)) & (~preds(sK2) & room(sK2)) & ! [X6] : (predj(X6) | ~room(X6)) & ! [X7] : (paul = X7 | mary = X7 | ~room(X7)) & room(paul) & room(mary) [skolemisation 134,136,135]
138. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
139. ~predj(paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 131,138]
220. room(mary) [cnf transformation 137]
221. room(paul) [cnf transformation 137]
222. ~room(X7) | mary = X7 | paul = X7 [cnf transformation 137]
223. ~room(X6) | predj(X6) [cnf transformation 137]
233. ~predj(paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 139]
234. ~predj(paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 139]
235. ~predj(paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 139]
236. ~predj(paul) | paul != sK3 | ~room(mary) [subsumption resolution 235,221]
237. ~predj(paul) | paul != sK3 [subsumption resolution 236,220]
239. 1 <=> paul = sK3 [avatar definition]
241. paul != sK3 <- (~1) [avatar component clause 239]
243. 2 <=> predj(paul) [avatar definition]
246. ~1 | ~2 [avatar split clause 237,243,239]
247. ~predj(paul) | mary != sK3 | ~room(mary) [subsumption resolution 234,221]
248. ~predj(paul) | mary != sK3 [subsumption resolution 247,220]
250. 3 <=> mary = sK3 [avatar definition]
252. mary != sK3 <- (~3) [avatar component clause 250]
253. ~3 | ~2 [avatar split clause 248,243,250]
254. ~predj(paul) | room(sK3) | ~room(mary) [subsumption resolution 233,221]
255. ~predj(paul) | room(sK3) [subsumption resolution 254,220]
257. 4 <=> room(sK3) [avatar definition]
259. room(sK3) <- (4) [avatar component clause 257]
260. 4 | ~2 [avatar split clause 255,243,257]
262. predj(paul) [resolution 223,221]
266. 2 [avatar split clause 262,243]
279. mary = sK3 | paul = sK3 <- (4) [resolution 222,259]
289. paul = sK3 <- (~3, 4) [subsumption resolution 279,252]
290. $false <- (~1, ~3, 4) [subsumption resolution 289,241]
291. 1 | 3 | ~4 [avatar contradiction clause 290]
292. $false [avatar sat refutation 246,253,260,266,291]
% SZS output end Proof for 1563154888615392214482121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.398691 |
Bonnie, Henry, Brandon are the only persons in the room. Everyone anywhere who can play the harmonica and is an expert in identifying and foraging wild edible plants can play the harmonica. Someone in the room has a pet dog. Someone in the room is a skilled home brewer experimenting with craft beer recipes. If someone collects limited-edition art prints from contemporary artists then he/she practices archery, is a dedicated volunteer for local community service projects and enjoys stargazing. Everyone in the room who collects limited-edition art prints from contemporary artists collects comic books. Everyone in the room collects comic books if they creates YouTube content and mentors a youth basketball team on weekends and vice versa. Everyone in the room who collects modern art, is a dedicated volunteer for local community service projects or does practice yoga neither collects modern art nor mentors a youth basketball team on weekends. | Bonnie collects limited-edition art prints from contemporary artists. | contradiction | room(bonnie)&room(henry)&room(brandon)&(![X]:(room(X)=>(X='bonnie'|X='henry'|X='brandon')))&
(![X]:(anywhere(X)=>(((((can_play_the_harmonica(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))=>(can_play_the_harmonica(X))))))&
(?[X]:(room(X)&(has_a_pet_dog(X))))&
(?[X]:(room(X)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))&
(![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))&(practices_archery(X))))<=(((collects_limited-edition_art_prints_from_contemporary_artists(X))&(enjoys_stargazing(X))&(has_a_pet_dog(X))))))))&
(![X]:(room(X)=>(((collects_luxury_watches(X))=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(practices_tai_chi(X))))))))&
(![X]:(room(X)=>(((enjoys_spelunking(X))=>(enjoys_watercolor_painting(X))))))&
(![X]:(room(X)=>(((does_not_own_a_telescope(X))|(own_a_television(X))))))&
(![X]:(room(X)=>(((own_a_television(X))<=>(((has_a_pet_dog(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))))&
(((?[X]:(room(X)&is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))&
((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(((practices_archery(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))&(enjoys_stargazing(X)))))))&
(((?[X]:(room(X)&((enjoys_stargazing(X))|(own_a_television(X)))))))&
(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(collects_comic_books(X))))))&
(![X]:(room(X)=>(((collects_comic_books(X))<=>(((creates_YouTube_content(X))&(mentors_a_youth_basketball_team_on_weekends(X))))))))&
(![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(collects_luxury_watches(X))))))&
(![X]:(room(X)=>(((collects_luxury_watches(X))<=>(collects_rare_minerals(X))))))&
(![X]:(room(X)=>(((can_play_the_harmonica(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))&
(![X]:(room(X)=>(((creates_YouTube_content(X))<=(bakes_bread_at_home(X))))))&
((![X]:((does_practice_yoga(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))&
(![X]:(~room(X)=>(((practices_tai_chi(X))=>(~((participates_in_long-distance_cycling_events_across_the_country(X))|(enjoys_watercolor_painting(X))))))))&
(![X]:(room(X)=>(((~((participates_in_long-distance_cycling_events_across_the_country(X))|(enjoys_watercolor_painting(X))))=>(((collects_modern_art(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X))|(does_practice_yoga(X))))))))&
(![X]:(room(X)=>(((((collects_modern_art(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X))|(does_practice_yoga(X))))=>(~((collects_modern_art(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))))&
(![X]:(room(X)=>(((~((collects_modern_art(X))|(mentors_a_youth_basketball_team_on_weekends(X))))=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(practices_tai_chi(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))))) | room(bonnie)&room(henry)&room(brandon)&(![X]:(room(X)=>(X='bonnie'|X='henry'|X='brandon')))&
collects_limited-edition_art_prints_from_contemporary_artists(bonnie) | [
"p0",
"p10",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2192931295012752137727552
% SZS output start Proof for 2192931295012752137727552
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
54. ! [X0] : (predj(X0) => (predo(X0) & predw(X0) & predp(X0))) [input p10]
56. ! [X0] : (room(X0) => (predj(X0) => preda(X0))) [input p12]
57. ! [X0] : (room(X0) => (preda(X0) <=> (predv(X0) & predm(X0)))) [input p13]
65. ! [X0] : (room(X0) => ((predc(X0) | predw(X0) | predy(X0)) => ~(predv(X0) | predy(X0)))) [input p21]
67. predj(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
73. ! [X0] : (predj(X0) => (predo(X0) & predw(X0))) [pure predicate removal 54]
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]
156. ! [X0] : ((predo(X0) & predw(X0)) | ~predj(X0)) [ennf transformation 73]
157. ! [X0] : ((preda(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 56]
158. ! [X0] : (preda(X0) | ~predj(X0) | ~room(X0)) [flattening 157]
159. ! [X0] : ((preda(X0) <=> (predv(X0) & predm(X0))) | ~room(X0)) [ennf transformation 57]
170. ! [X0] : (((~predv(X0) & ~predy(X0)) | (~predc(X0) & ~predw(X0) & ~predy(X0))) | ~room(X0)) [ennf transformation 65]
171. ! [X0] : ((~predv(X0) & ~predy(X0)) | (~predc(X0) & ~predw(X0) & ~predy(X0)) | ~room(X0)) [flattening 170]
174. predj(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 67]
175. predj(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 174]
187. ! [X0] : (((preda(X0) | (~predv(X0) | ~predm(X0))) & ((predv(X0) & predm(X0)) | ~preda(X0))) | ~room(X0)) [nnf transformation 159]
188. ! [X0] : (((preda(X0) | ~predv(X0) | ~predm(X0)) & ((predv(X0) & predm(X0)) | ~preda(X0))) | ~room(X0)) [flattening 187]
271. room(mary) [cnf transformation 150]
284. ~predj(X0) | predw(X0) [cnf transformation 156]
288. ~predj(X0) | preda(X0) | ~room(X0) [cnf transformation 158]
290. ~preda(X0) | predv(X0) | ~room(X0) [cnf transformation 188]
304. ~predv(X0) | ~predw(X0) | ~room(X0) [cnf transformation 171]
312. predj(mary) [cnf transformation 175]
325. predw(mary) [resolution 284,312]
329. preda(mary) | ~room(mary) [resolution 288,312]
330. preda(mary) [subsumption resolution 329,271]
333. predv(mary) | ~room(mary) [resolution 290,330]
334. predv(mary) [subsumption resolution 333,271]
335. ~predw(mary) | ~room(mary) [resolution 304,334]
336. ~room(mary) [subsumption resolution 335,325]
337. $false [subsumption resolution 336,271]
% SZS output end Proof for 2192931295012752137727552
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.075969 |
Earl is the only person in the room.
'Earl who either is a certified yoga instructor teaching classes weekly or plays the drums but not both frequently participates in hackathons and coding competitions' unless 'not everyone in the room does not create large-scale murals for public art installations or is a wine connoisseur with a private cellar of vintage wines'.
If 'not everyone anywhere is not a professional photographer specializing in portrait photography or makes intricate hand-cut paper art for exhibitions' then 'no one anywhere is not an amateur astronomer who builds and uses custom telescopes or is not a professional photographer specializing in portrait photography'.
If 'everyone in the room does not enjoy landscape photography or enjoys coding in Python' then 'everyone outside the room does not enjoy landscape photography if and only if they is right-handed'.
If 'everyone in the room does not use an ios phone or enjoys kayaking and exploring remote waterways' then 'everyone in the room who does not use an ios phone is a Linux enthusiast'.
If 'everyone in the room does not enjoy kayaking and exploring remote waterways or is a professional photographer specializing in portrait photography' then 'Earl who plays the drums is a wine connoisseur with a private cellar of vintage wines' otherwise 'no one in the room who is right-handed enjoys watercolor painting'.
Not everyone outside the room who enjoys watercolor painting enjoys landscape photography.
Everyone in the room who enjoys landscape photography collects antique jewelry.
Everyone outside the room is a dedicated advocate for digital privacy and encryption if and only if they is a Linux enthusiast.
Everyone outside the room is a Linux enthusiast only if they makes intricate hand-cut paper art for exhibitions.
Everyone in the room has a specialized collection of handmade artisan pottery only if they is right-handed.
No one anywhere who does practice yoga creates large-scale murals for public art installations.
Everyone in the room who creates large-scale murals for public art installations makes intricate hand-cut paper art for exhibitions.
Everyone in the room who is a certified yoga instructor teaching classes weekly collects antique jewelry.
Everyone in the room is not an amateur astronomer who builds and uses custom telescopes or enjoys landscape photography.
Someone in the room is a wine connoisseur with a private cellar of vintage wines. | Earl is a certified yoga instructor teaching classes weekly. | contradiction | room(earl)&(![X]:(room(X)=>(X='earl')))&
(~(~![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))=>((((is_a_certified_yoga_instructor_teaching_classes_weekly(earl))<~>(plays_the_drums(earl))))&(frequently_participates_in_hackathons_and_coding_competitions(earl))))&
((~![X]:(anywhere(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))=>(~?[X]:(anywhere(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))))&
((![X]:(room(X)=>(((enjoys_coding_in_Python(X))|(does_not_enjoy_landscape_photography(X))))))=>(![X]:(~room(X)=>(((does_not_enjoy_landscape_photography(X))<=>(is_right-handed(X)))))))&
((![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(does_not_use_an_ios_phone(X))))))=>(![X]:(room(X)=>(((does_not_use_an_ios_phone(X))=>(is_a_Linux_enthusiast(X)))))))&
(((![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))=>((plays_the_drums(earl))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(earl))))&((~(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X)))))))=>(~?[X]:(room(X)=>(((is_right-handed(X))=>(enjoys_watercolor_painting(X))))))))&
(~![X]:(~room(X)=>(((enjoys_watercolor_painting(X))=>(enjoys_landscape_photography(X))))))&
(![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(collects_antique_jewelry(X))))))&
(![X]:(~room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(is_a_Linux_enthusiast(X))))))&
(![X]:(~room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=(is_a_Linux_enthusiast(X))))))&
(![X]:(room(X)=>(((is_right-handed(X))<=(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))&
(~?[X]:(anywhere(X)=>(((does_practice_yoga(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))&
(![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(collects_antique_jewelry(X))))))&
(![X]:(room(X)=>(((enjoys_landscape_photography(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))&
(![X]:(anywhere(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(uses_an_ios_phone(X))))))&
(![X]:(room(X)=>(((((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(collects_antique_jewelry(X))|(creates_large-scale_murals_for_public_art_installations(X))))<=(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))&
(~![X]:(anywhere(X)=>(((((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(collects_antique_jewelry(X))|(creates_large-scale_murals_for_public_art_installations(X))))=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))<~>(uses_an_ios_phone(X))))))))&
(?[X]:(room(X)&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))&
(![X]:(room(X)=>(((collects_antique_jewelry(X))=>(enjoys_landscape_photography(X)))))) | room(earl)&(![X]:(room(X)=>(X='earl')))&
is_a_certified_yoga_instructor_teaching_classes_weekly(earl) | [
"p0",
"p1",
"p5",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 49149572838062570475300
% SZS output start Proof for 49149572838062570475300
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
45. ~~! [X0] : (room(X0) => (~preds(X0) | predu(X0))) => (predc(mary) & (predx(mary) <~> predv(mary))) [input p1]
49. (~! [X0] : (room(X0) => (~predm(X0) | preda(X0))) => ~? [X0] : (room(X0) => (predd(X0) => predr(X0)))) & (! [X0] : (room(X0) => (~predm(X0) | preda(X0))) => (predu(mary) & predv(mary))) [input p5]
50. ~! [X0] : (~room(X0) => (predr(X0) => predy(X0))) [input p6]
62. ? [X0] : (predu(X0) & room(X0)) [input p18]
64. predx(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
65. ! [X0] : (room(X0) => (~preds(X0) | predu(X0))) => (predc(mary) & (predx(mary) <~> predv(mary))) [flattening 45]
69. (~! [X0] : (room(X0) => (~predm(X0) | preda(X0))) => ~? [X1] : (room(X1) => (predd(X1) => predr(X1)))) & (! [X2] : (room(X2) => (~predm(X2) | preda(X2))) => (predu(mary) & predv(mary))) [rectify 49]
79. ! [X0] : (room(X0) => (~preds(X0) | predu(X0))) => (predx(mary) <~> predv(mary)) [pure predicate removal 65]
151. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
152. (predx(mary) <~> predv(mary)) | ? [X0] : ((preds(X0) & ~predu(X0)) & room(X0)) [ennf transformation 79]
153. (predx(mary) <~> predv(mary)) | ? [X0] : (preds(X0) & ~predu(X0) & room(X0)) [flattening 152]
157. (! [X1] : ((~predr(X1) & predd(X1)) & room(X1)) | ! [X0] : ((~predm(X0) | preda(X0)) | ~room(X0))) & ((predu(mary) & predv(mary)) | ? [X2] : ((predm(X2) & ~preda(X2)) & room(X2))) [ennf transformation 69]
158. (! [X1] : (~predr(X1) & predd(X1) & room(X1)) | ! [X0] : (~predm(X0) | preda(X0) | ~room(X0))) & ((predu(mary) & predv(mary)) | ? [X2] : (predm(X2) & ~preda(X2) & room(X2))) [flattening 157]
159. ? [X0] : ((~predy(X0) & predr(X0)) & ~room(X0)) [ennf transformation 50]
160. ? [X0] : (~predy(X0) & predr(X0) & ~room(X0)) [flattening 159]
172. predx(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 64]
174. ((~predv(mary) | ~predx(mary)) & (predv(mary) | predx(mary))) | ? [X0] : (preds(X0) & ~predu(X0) & room(X0)) [nnf transformation 153]
175. ? [X0] : (preds(X0) & ~predu(X0) & room(X0)) => (preds(sK0) & ~predu(sK0) & room(sK0)) [choice axiom]
176. ((~predv(mary) | ~predx(mary)) & (predv(mary) | predx(mary))) | (preds(sK0) & ~predu(sK0) & room(sK0)) [skolemisation 174,175]
184. (! [X0] : (~predr(X0) & predd(X0) & room(X0)) | ! [X1] : (~predm(X1) | preda(X1) | ~room(X1))) & ((predu(mary) & predv(mary)) | ? [X2] : (predm(X2) & ~preda(X2) & room(X2))) [rectify 158]
185. ? [X2] : (predm(X2) & ~preda(X2) & room(X2)) => (predm(sK3) & ~preda(sK3) & room(sK3)) [choice axiom]
186. (! [X0] : (~predr(X0) & predd(X0) & room(X0)) | ! [X1] : (~predm(X1) | preda(X1) | ~room(X1))) & ((predu(mary) & predv(mary)) | (predm(sK3) & ~preda(sK3) & room(sK3))) [skolemisation 184,185]
187. ? [X0] : (~predy(X0) & predr(X0) & ~room(X0)) => (~predy(sK4) & predr(sK4) & ~room(sK4)) [choice axiom]
188. ~predy(sK4) & predr(sK4) & ~room(sK4) [skolemisation 160,187]
194. ? [X0] : (predu(X0) & room(X0)) => (predu(sK6) & room(sK6)) [choice axiom]
195. predu(sK6) & room(sK6) [skolemisation 62,194]
277. room(mary) [cnf transformation 151]
278. ~room(X0) | mary = X0 [cnf transformation 151]
282. ~predv(mary) | ~predx(mary) | room(sK0) [cnf transformation 176]
283. ~predv(mary) | ~predx(mary) | ~predu(sK0) [cnf transformation 176]
292. predv(mary) | room(sK3) [cnf transformation 186]
293. predv(mary) | ~preda(sK3) [cnf transformation 186]
294. predv(mary) | predm(sK3) [cnf transformation 186]
300. ~predr(X0) | ~predm(X1) | preda(X1) | ~room(X1) [cnf transformation 186]
302. predr(sK4) [cnf transformation 188]
314. room(sK6) [cnf transformation 195]
315. predu(sK6) [cnf transformation 195]
319. predx(mary) [cnf transformation 172]
325. 2 <=> predx(mary) [avatar definition]
329. 3 <=> predv(mary) [avatar definition]
334. 4 <=> predu(sK0) [avatar definition]
336. ~predu(sK0) <- (~4) [avatar component clause 334]
337. ~4 | ~2 | ~3 [avatar split clause 283,329,325,334]
339. 5 <=> room(sK0) [avatar definition]
341. room(sK0) <- (5) [avatar component clause 339]
342. 5 | ~2 | ~3 [avatar split clause 282,329,325,339]
383. 14 <=> ! [X1] : (~predm(X1) | ~room(X1) | preda(X1)) [avatar definition]
384. ~predm(X1) | ~room(X1) | preda(X1) <- (14) [avatar component clause 383]
386. 15 <=> ! [X0] : ~predr(X0) [avatar definition]
387. ~predr(X0) <- (15) [avatar component clause 386]
388. 14 | 15 [avatar split clause 300,386,383]
398. 18 <=> predm(sK3) [avatar definition]
400. predm(sK3) <- (18) [avatar component clause 398]
402. 19 <=> predu(mary) [avatar definition]
404. predu(mary) <- (19) [avatar component clause 402]
407. 20 <=> preda(sK3) [avatar definition]
409. ~preda(sK3) <- (~20) [avatar component clause 407]
412. 21 <=> room(sK3) [avatar definition]
414. room(sK3) <- (21) [avatar component clause 412]
416. 18 | 3 [avatar split clause 294,329,398]
417. ~20 | 3 [avatar split clause 293,329,407]
418. 21 | 3 [avatar split clause 292,329,412]
430. 2 [avatar split clause 319,325]
433. mary = sK3 <- (21) [resolution 278,414]
434. mary = sK6 [resolution 278,314]
437. predm(mary) <- (18, 21) [backward demodulation 400,433]
438. ~preda(mary) <- (~20, 21) [backward demodulation 409,433]
441. predu(mary) [backward demodulation 315,434]
442. 19 [avatar split clause 441,402]
466. ~room(mary) | preda(mary) <- (14, 18, 21) [resolution 384,437]
467. preda(mary) <- (14, 18, 21) [subsumption resolution 466,277]
468. $false <- (14, 18, ~20, 21) [subsumption resolution 467,438]
469. ~14 | ~18 | 20 | ~21 [avatar contradiction clause 468]
477. mary = sK0 <- (5) [resolution 341,278]
487. ~predu(mary) <- (~4, 5) [backward demodulation 336,477]
489. $false <- (~4, 5, 19) [subsumption resolution 487,404]
490. 4 | ~5 | ~19 [avatar contradiction clause 489]
496. $false <- (15) [resolution 387,302]
497. ~15 [avatar contradiction clause 496]
498. $false [avatar sat refutation 337,342,388,416,417,418,430,442,469,490,497]
% SZS output end Proof for 49149572838062570475300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.377626 |
Sue, Sylvia, Herbert, Guillermo, Jeff are the only persons in the room. Everyone in the room owns an Android phone only if they does enjoy trail running. Everyone anywhere reads mystery novels only if they does enjoy trail running. Everyone in the room creates bespoke furniture pieces from reclaimed wood if they does enjoy trail running. Everyone in the room owns an Android phone. Everyone in the room is not a skilled home brewer experimenting with craft beer recipes if they owns an Android phone, is a dedicated advocate for digital privacy and encryption or cannot play the flute. Everyone in the room either trains for and competes in international triathlons or collects comic books but not both if they is a dedicated advocate for digital privacy and encryption. Everyone in the room is a skilled home brewer experimenting with craft beer recipes if they either trains for and competes in international triathlons or collects comic books but not both. | Herbert is a dedicated advocate for digital privacy and encryption. | contradiction | room(sue)&room(sylvia)&room(herbert)&room(guillermo)&room(jeff)&(![X]:(room(X)=>(X='sue'|X='sylvia'|X='herbert'|X='guillermo'|X='jeff')))&
(![X]:(room(X)=>(((does_enjoy_trail_running(X))<=(owns_an_Android_phone(X))))))&
(![X]:(anywhere(X)=>(((does_enjoy_trail_running(X))<=(reads_mystery_novels(X))))))&
(![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
((![X]:((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(((collects_first_edition_books(X))<~>(practices_pilates(X)))))))&
(![X]:(room(X)=>(((owns_an_Android_phone(X))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(owns_a_3D_printer(X))))))&
(![X]:(room(X)=>(((reads_mystery_novels(X))<=(owns_a_3D_printer(X))))))&
(![X]:(room(X)=>(((reads_mystery_novels(X))=>(can_play_the_flute(X))))))&
(![X]:(room(X)=>(((can_play_the_flute(X))=>(collects_comic_books(X))))))&
(![X]:(room(X)=>(((collects_comic_books(X))=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<~>(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))))&
(![X]:(room(X)=>(((((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<~>(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))=>(enjoys_kayaking(X))))))&
(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))<=(collects_comic_books(X))))))&
(![X]:(room(X)=>(owns_an_Android_phone(X))))&
(![X]:(room(X)=>(((owns_a_3D_printer(X))=>(practices_pilates(X))))))&
(![X]:(room(X)=>(((practices_pilates(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(![X]:(room(X)=>(((((collects_first_edition_books(X))<~>(collects_limited-edition_art_prints_from_contemporary_artists(X))))=>(trains_for_and_competes_in_international_triathlons(X))))))&
(![X]:(~room(X)=>(((owns_an_Android_phone(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))&
(~((?[X,Y]:(room(X)&room(Y)&(enjoys_kayaking_and_exploring_remote_waterways(X)&enjoys_kayaking_and_exploring_remote_waterways(Y))&(X!=Y)))))&
(![X]:(room(X)=>(((((enjoys_salsa_dancing(X))|(does_not_have_a_pet_dog(X))|(is_passionate_about_collecting_and_restoring_classic_cars(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]:(room(X)=>(((collects_comic_books(X))=>(does_enjoy_trail_running(X))))))&
((![X]:((is_passionate_about_collecting_and_restoring_classic_cars(X))<=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(trains_for_and_competes_in_international_triathlons(X)))))))&
(![X]:(~room(X)=>(((owns_a_3D_printer(X))=>(((owns_an_Android_phone(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(cannot_play_the_flute(X))))))))&
(![X]:(room(X)=>(((((owns_an_Android_phone(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(cannot_play_the_flute(X))))=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))&
(![X]:(anywhere(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(enjoys_salsa_dancing(X))))))&
(![X]:(room(X)=>(((((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))<~>(reads_mystery_novels(X))))=>(enjoys_macrame(X))))))&
(![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(((trains_for_and_competes_in_international_triathlons(X))<~>(collects_comic_books(X))))))))&
(![X]:(room(X)=>(((((trains_for_and_competes_in_international_triathlons(X))<~>(collects_comic_books(X))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))) | room(sue)&room(sylvia)&room(herbert)&room(guillermo)&room(jeff)&(![X]:(room(X)=>(X='sue'|X='sylvia'|X='herbert'|X='guillermo'|X='jeff')))&
is_a_dedicated_advocate_for_digital_privacy_and_encryption(herbert) | [
"p0",
"p13",
"p24",
"p27",
"p28",
"hypothesis"
] | % SZS status Unsatisfiable for 7243369899797468928478403
% SZS output start Proof for 7243369899797468928478403
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]
57. ! [X0] : (room(X0) => predo(X0)) [input p13]
68. ! [X0] : (room(X0) => ((~predd(X0) | preda(X0) | predo(X0)) => ~predk(X0))) [input p24]
71. ! [X0] : (room(X0) => (preda(X0) => (predv(X0) <~> predp(X0)))) [input p27]
72. ! [X0] : (room(X0) => ((predv(X0) <~> predp(X0)) => predk(X0))) [input p28]
73. preda(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]
158. ! [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]
159. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 158]
173. ! [X0] : (predo(X0) | ~room(X0)) [ennf transformation 57]
188. ! [X0] : ((~predk(X0) | (predd(X0) & ~preda(X0) & ~predo(X0))) | ~room(X0)) [ennf transformation 68]
189. ! [X0] : (~predk(X0) | (predd(X0) & ~preda(X0) & ~predo(X0)) | ~room(X0)) [flattening 188]
190. ! [X0] : (((predv(X0) <~> predp(X0)) | ~preda(X0)) | ~room(X0)) [ennf transformation 71]
191. ! [X0] : ((predv(X0) <~> predp(X0)) | ~preda(X0) | ~room(X0)) [flattening 190]
192. ! [X0] : ((predk(X0) | (predv(X0) <=> predp(X0))) | ~room(X0)) [ennf transformation 72]
193. ! [X0] : (predk(X0) | (predv(X0) <=> predp(X0)) | ~room(X0)) [flattening 192]
194. preda(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 73]
195. preda(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 194]
202. ! [X0] : (((~predp(X0) | ~predv(X0)) & (predp(X0) | predv(X0))) | ~preda(X0) | ~room(X0)) [nnf transformation 191]
203. ! [X0] : (predk(X0) | ((predv(X0) | ~predp(X0)) & (predp(X0) | ~predv(X0))) | ~room(X0)) [nnf transformation 193]
286. room(fred) [cnf transformation 159]
299. ~room(X0) | predo(X0) [cnf transformation 173]
313. ~predk(X0) | ~predo(X0) | ~room(X0) [cnf transformation 189]
316. ~preda(X0) | predv(X0) | predp(X0) | ~room(X0) [cnf transformation 202]
317. ~preda(X0) | ~predv(X0) | ~predp(X0) | ~room(X0) [cnf transformation 202]
318. predk(X0) | predp(X0) | ~predv(X0) | ~room(X0) [cnf transformation 203]
319. predk(X0) | predv(X0) | ~predp(X0) | ~room(X0) [cnf transformation 203]
326. preda(fred) [cnf transformation 195]
328. ~predk(X0) | ~room(X0) [subsumption resolution 313,299]
329. ~predp(X0) | predv(X0) | ~room(X0) [subsumption resolution 319,328]
330. ~predv(X0) | predp(X0) | ~room(X0) [subsumption resolution 318,328]
351. 2 <=> predv(fred) [avatar definition]
352. predv(fred) <- (2) [avatar component clause 351]
353. ~predv(fred) <- (~2) [avatar component clause 351]
378. predv(fred) | predp(fred) | ~room(fred) [resolution 316,326]
379. predp(fred) | ~room(fred) <- (~2) [subsumption resolution 378,353]
380. predp(fred) <- (~2) [subsumption resolution 379,286]
381. predv(fred) | ~room(fred) <- (~2) [resolution 380,329]
383. ~room(fred) <- (~2) [subsumption resolution 381,353]
384. $false <- (~2) [subsumption resolution 383,286]
385. 2 [avatar contradiction clause 384]
389. 7 <=> predp(fred) [avatar definition]
390. ~predp(fred) <- (~7) [avatar component clause 389]
393. ~predv(fred) | ~predp(fred) | ~room(fred) [resolution 317,326]
394. ~predp(fred) | ~room(fred) <- (2) [subsumption resolution 393,352]
395. ~predp(fred) <- (2) [subsumption resolution 394,286]
396. ~7 | ~2 [avatar split clause 395,351,389]
399. predp(fred) | ~room(fred) <- (2) [resolution 352,330]
400. ~room(fred) <- (2, ~7) [subsumption resolution 399,390]
401. $false <- (2, ~7) [subsumption resolution 400,286]
402. ~2 | 7 [avatar contradiction clause 401]
403. $false [avatar sat refutation 385,396,402]
% SZS output end Proof for 7243369899797468928478403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.348461 |
Stephen, Bradley, Victoria, Allison, James are the only persons in the room. Everyone outside the room does not enjoy kayaking. It is not the case that “Stephen drives a hybrid car”. Stephen enjoys kayaking or drives a hybrid car or both. Everyone in the room uses contact lenses if they enjoys kayaking and vice versa. | Stephen uses contact lenses. | entailment | room(stephen)&room(bradley)&room(victoria)&room(allison)&room(james)&(![X]:(room(X)=>(X='stephen'|X='bradley'|X='victoria'|X='allison'|X='james')))&
(![X]:(room(X)=>(((does_not_enjoy_macrame(X))|(bakes_bread_at_home(X))))))&
(enjoys_camping_and_organizing_outdoor_survival_workshops(stephen))&
(has_a_tattoo(bradley))&
(![X]:(~room(X)=>(does_not_enjoy_kayaking(X))))&
(![X]:(room(X)=>(((((enjoys_bird_watching(X))|(collects_rare_and_antique_scientific_instruments(X))))=>(is_right-handed(X))))))&
(~((is_not_an_avid_hiker(stephen))|(does_not_collect_rare_and_antique_scientific_instruments(stephen))))&
(~(drives_a_hybrid_car(stephen)))&
(((enjoys_kayaking(stephen))|(drives_a_hybrid_car(stephen))))&
(![X]:(room(X)=>(((enjoys_kayaking(X))<=(collects_rare_and_antique_scientific_instruments(X))))))&
(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(![X]:(room(X)=>(((is_right-handed(X))<=(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(![X]:(~room(X)=>(((is_right-handed(X))=>(enjoys_kayaking(X))))))&
(((is_right-handed(bradley))|(does_not_enjoy_kayaking(bradley))|(is_allergic_to_anything(bradley))))&
(does_enjoy_trail_running(bradley))&
(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(is_right-handed(bradley))&
(![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(collects_rare_and_antique_scientific_instruments(X))))))&
(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(is_not_allergic_to_anything(X))))))&
(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(bradley))&
(does_not_enjoy_kayaking(bradley))&
(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(is_an_avid_hiker(X))))))&
(![X]:(room(X)=>(((((is_allergic_to_anything(X))<~>(does_enjoy_trail_running(X))))=>(enjoys_macrame(X))))))&
(![X]:(anywhere(X)=>(((((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<~>(enjoys_bird_watching(X))))=>(uses_contact_lenses(X))))))&
(![X]:(room(X)=>(((uses_contact_lenses(X))<=>(enjoys_kayaking(X))))))&
(![X]:(anywhere(X)=>(((enjoys_kayaking(X))=>(enjoys_macrame(X))))))&
(![X]:(room(X)=>(((enjoys_macrame(X))|(enjoys_kayaking(X)))))) | room(stephen)&room(bradley)&room(victoria)&room(allison)&room(james)&(![X]:(room(X)=>(X='stephen'|X='bradley'|X='victoria'|X='allison'|X='james')))&
uses_contact_lenses(stephen) | [
"p0",
"p4",
"p7",
"p8",
"p24",
"hypothesis"
] | % SZS status Unsatisfiable for 3964583056274705324907691
% SZS output start Proof for 3964583056274705324907691
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]
48. ! [X0] : (~room(X0) => ~predj(X0)) [input p4]
51. ~predg(mary) [input p7]
52. predg(mary) | predj(mary) [input p8]
68. ! [X0] : (room(X0) => (predf(X0) <=> predj(X0))) [input p24]
71. ~(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]
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]
155. ! [X0] : (~predj(X0) | room(X0)) [ennf transformation 48]
171. ! [X0] : ((predf(X0) <=> predj(X0)) | ~room(X0)) [ennf transformation 68]
172. ~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 71]
173. ~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 172]
176. ! [X0] : (((predf(X0) | ~predj(X0)) & (predj(X0) | ~predf(X0))) | ~room(X0)) [nnf transformation 171]
177. ? [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]
178. ~predf(mary) | (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,177]
260. room(mary) [cnf transformation 154]
261. room(paul) [cnf transformation 154]
262. room(fred) [cnf transformation 154]
263. room(alice) [cnf transformation 154]
264. room(john) [cnf transformation 154]
265. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 154]
267. ~predj(X0) | room(X0) [cnf transformation 155]
271. ~predg(mary) [cnf transformation 51]
272. predg(mary) | predj(mary) [cnf transformation 52]
285. predf(X0) | ~predj(X0) | ~room(X0) [cnf transformation 176]
286. ~predf(mary) | room(sK0) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
287. ~predf(mary) | mary != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
288. ~predf(mary) | paul != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
289. ~predf(mary) | fred != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
290. ~predf(mary) | alice != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
291. ~predf(mary) | john != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
292. predj(mary) [subsumption resolution 272,271]
311. ~predj(X0) | predf(X0) [subsumption resolution 285,267]
312. ~predf(mary) | john != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,264]
313. ~predf(mary) | john != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,263]
314. ~predf(mary) | john != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 313,262]
315. ~predf(mary) | john != sK0 | ~room(mary) [subsumption resolution 314,261]
316. ~predf(mary) | john != sK0 [subsumption resolution 315,260]
318. 4 <=> john = sK0 [avatar definition]
320. john != sK0 <- (~4) [avatar component clause 318]
322. 5 <=> predf(mary) [avatar definition]
325. ~4 | ~5 [avatar split clause 316,322,318]
326. ~predf(mary) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,264]
327. ~predf(mary) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,263]
328. ~predf(mary) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 327,262]
329. ~predf(mary) | alice != sK0 | ~room(mary) [subsumption resolution 328,261]
330. ~predf(mary) | alice != sK0 [subsumption resolution 329,260]
332. 6 <=> alice = sK0 [avatar definition]
334. alice != sK0 <- (~6) [avatar component clause 332]
335. ~6 | ~5 [avatar split clause 330,322,332]
336. ~predf(mary) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,264]
337. ~predf(mary) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 336,263]
338. ~predf(mary) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 337,262]
339. ~predf(mary) | fred != sK0 | ~room(mary) [subsumption resolution 338,261]
340. ~predf(mary) | fred != sK0 [subsumption resolution 339,260]
342. 7 <=> fred = sK0 [avatar definition]
344. fred != sK0 <- (~7) [avatar component clause 342]
345. ~7 | ~5 [avatar split clause 340,322,342]
346. ~predf(mary) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,264]
347. ~predf(mary) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 346,263]
348. ~predf(mary) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 347,262]
349. ~predf(mary) | paul != sK0 | ~room(mary) [subsumption resolution 348,261]
350. ~predf(mary) | paul != sK0 [subsumption resolution 349,260]
352. 8 <=> paul = sK0 [avatar definition]
354. paul != sK0 <- (~8) [avatar component clause 352]
355. ~8 | ~5 [avatar split clause 350,322,352]
356. ~predf(mary) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,264]
357. ~predf(mary) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 356,263]
358. ~predf(mary) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 357,262]
359. ~predf(mary) | mary != sK0 | ~room(mary) [subsumption resolution 358,261]
360. ~predf(mary) | mary != sK0 [subsumption resolution 359,260]
362. 9 <=> mary = sK0 [avatar definition]
364. mary != sK0 <- (~9) [avatar component clause 362]
365. ~9 | ~5 [avatar split clause 360,322,362]
366. ~predf(mary) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,264]
367. ~predf(mary) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 366,263]
368. ~predf(mary) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 367,262]
369. ~predf(mary) | room(sK0) | ~room(mary) [subsumption resolution 368,261]
370. ~predf(mary) | room(sK0) [subsumption resolution 369,260]
372. 10 <=> room(sK0) [avatar definition]
374. room(sK0) <- (10) [avatar component clause 372]
375. 10 | ~5 [avatar split clause 370,322,372]
378. predf(mary) [resolution 311,292]
381. 5 [avatar split clause 378,322]
512. alice = sK0 | fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (10) [resolution 265,374]
513. fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (~6, 10) [subsumption resolution 512,334]
514. paul = sK0 | mary = sK0 | john = sK0 <- (~6, ~7, 10) [subsumption resolution 513,344]
515. mary = sK0 | john = sK0 <- (~6, ~7, ~8, 10) [subsumption resolution 514,354]
516. john = sK0 <- (~6, ~7, ~8, ~9, 10) [subsumption resolution 515,364]
517. $false <- (~4, ~6, ~7, ~8, ~9, 10) [subsumption resolution 516,320]
518. 4 | 6 | 7 | 8 | 9 | ~10 [avatar contradiction clause 517]
519. $false [avatar sat refutation 325,335,345,355,365,375,381,518]
% SZS output end Proof for 3964583056274705324907691
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.175504 |
Charles, Genevieve, Mika are the only persons in the room.
Mika who is not a wise person is quiet.
Mika is the oldest in the room.
All wise persons are generous.
Mika is not a calm person, is richer than Jessica or is kind.
Genevieve and Charles are not a strong creative old humble persons.
It is true that “it is true that “all quiet persons are calm””.
If someone is patient then he/she is brave and vice versa.
All old persons are wise.
More than one person in the room is not a quiet brave happy person. | Everyone anywhere is a quiet person. | neutral | room(charles)&room(genevieve)&room(mika)&(![X]:(room(X)=>(X='charles'|X='genevieve'|X='mika')))&
((~(wise(mika)&person(mika)))&(quiet(mika)))&
(![X]:((room(X)&(X!=mika))=>older(X,mika)))&
(![X]:(wise(X)=>generous(X)))&
(((~(calm(mika)&person(mika)))|(richer(jessica,mika))|(kind(mika))))&
(~(strong(genevieve)&creative(genevieve)&old(genevieve)&humble(genevieve)&person(genevieve))&~(strong(charles)&creative(charles)&old(charles)&humble(charles)&person(charles)))&
(![X]:(quiet(X)=>calm(X)))&
((![X]:((patient(X))<=>(brave(X)))))&
(![X]:(old(X)=>wise(X)))&
((?[X,Y]:(room(X)&room(Y)&(~(quiet(X)&brave(X)&happy(X)&person(X))&~(quiet(Y)&brave(Y)&happy(Y)&person(Y)))&(X!=Y))))&
((![X]:((wise(X))=>(calm(X)))))&
(![X]:(happy(X)=>funny(X)))&
(?[X,Y]:((older(jessica,X))&(~(funny(Y)&strong(Y)&wise(Y)&humble(Y)&curious(Y)&brave(Y)&person(Y)))&(richer(X,Y))))&
(![X]:(humble(X)=>creative(X)))&
(((?[X]:(anywhere(X)&older(james,X)))))&
(![X]:(room(X)=>(((~funny(X)&~wise(X)&~strong(X)&~old(X))=>(happy(X))))))&
(richer(mika,james))&
((![X]:((~(creative(X)&humble(X)&brave(X)&tall(X)&happy(X)&calm(X)&person(X)))=>(~(brave(X)&calm(X)&kind(X)&wise(X)&happy(X)&patient(X)&person(X))))))&
(richer(jessica,genevieve)&richer(jessica,charles))&
(richer(genevieve,james))&
((charles_dream=>((![X]:((richer(james,X))<=>(((~(brave(X)&person(X)))|(quieter(james,X))|(funny(X)))))))))&
(![X]:(room(X)=>(((~(creative(X)&person(X)))=>(older(jessica,X)))))) | room(charles)&room(genevieve)&room(mika)&(![X]:(room(X)=>(X='charles'|X='genevieve'|X='mika')))&
![X]:(anywhere(X)=>(quiet(X)&person(X))) | [] | null | 0.421619 |
There is a room.
“More than one person in the room is an enthusiastic bird watcher who travels for rare sightings” unless “no one in the room does not frequently participates in hackathons and coding competitions or creates augmented reality experiences for mobile applications”.
“Everyone in the room does enjoy trail running, reads mystery novels and is a drone photographer if they collects foreign coins and vice versa” unless “everyone in the room does not collect rare and antique scientific instruments or practices and performs acrobatic dance routines”.
“Everyone outside the room creates augmented reality experiences for mobile applications only if they is a certified scuba diver with advanced underwater photography skills” unless “everyone in the room is not a chess master who participates in national tournaments or is not a culinary enthusiast who experiments with international cuisines”.
“Everyone in the room does not read mystery novels only if they uses an ios phone” if “no one anywhere does not read mystery novels or is not an avid hiker”.
Everyone in the room who uses an ios phone hosts regular game nights featuring complex strategy games.
Everyone in the room hosts regular game nights featuring complex strategy games only if they does not write a travel blog, hosts a YouTube channel dedicated to art tutorials and is a client of Meta.
Everyone in the room does not enjoy wildlife photography or does not write a travel blog, hosts a YouTube channel dedicated to art tutorials and is a client of Meta.
Everyone in the room does not enjoy wildlife photography only if they practices zumba.
Everyone in the room practices zumba only if they creates augmented reality experiences for mobile applications.
If someone either develops open-source software projects in their free time or enjoys wildlife photography but not both then he/she collects foreign coins.
Everyone anywhere enjoys wildlife photography only if they frequently participates in hackathons and coding competitions.
More than one person anywhere does enjoy trail running, reads mystery novels and is a drone photographer.
Everyone in the room either is an avid hiker or frequently participates in hackathons and coding competitions but not both if they neither hosts regular game nights featuring complex strategy games nor frequently participates in hackathons and coding competitions and vice versa.
Everyone in the room neither hosts regular game nights featuring complex strategy games nor frequently participates in hackathons and coding competitions only if they is a client of Meta.
If someone does enjoy trail running, practices graffiti art and frequently participates in hackathons and coding competitions then he/she has a tattoo.
Everyone in the room creates augmented reality experiences for mobile applications if they is a client of Meta and vice versa. | Everyone in the room is a client of Meta. | entailment | (there_is_a_room)&
(~(~?[X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>((?[X,Y]:(room(X)&room(Y)&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)&is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(Y))&(X!=Y)))))&
(~(![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))=>(![X]:(room(X)=>(((((does_enjoy_trail_running(X))&(reads_mystery_novels(X))&(is_a_drone_photographer(X))))<=>(collects_foreign_coins(X)))))))&
(~(![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))=>(![X]:(~room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=(creates_augmented_reality_experiences_for_mobile_applications(X)))))))&
((~?[X]:(anywhere(X)=>(((is_not_an_avid_hiker(X))|(does_not_read_mystery_novels(X))))))=>(![X]:(room(X)=>(((uses_an_ios_phone(X))<=(does_not_read_mystery_novels(X)))))))&
(![X]:(room(X)=>(((uses_an_ios_phone(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(room(X)=>(((((does_not_write_a_travel_blog(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(is_a_client_of_Meta(X))))<=(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(room(X)=>(((((does_not_write_a_travel_blog(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(is_a_client_of_Meta(X))))|(does_not_enjoy_wildlife_photography(X))))))&
(![X]:(room(X)=>(((practices_zumba(X))<=(does_not_enjoy_wildlife_photography(X))))))&
(![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))<=(practices_zumba(X))))))&
((![X]:((((develops_open-source_software_projects_in_their_free_time(X))<~>(enjoys_wildlife_photography(X))))=>(collects_foreign_coins(X)))))&
(![X]:(anywhere(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))<=(enjoys_wildlife_photography(X))))))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(((does_enjoy_trail_running(X))&(reads_mystery_novels(X))&(is_a_drone_photographer(X)))&((does_enjoy_trail_running(Y))&(reads_mystery_novels(Y))&(is_a_drone_photographer(Y))))&(X!=Y))))&
(![X]:(room(X)=>(((((is_an_avid_hiker(X))<~>(frequently_participates_in_hackathons_and_coding_competitions(X))))<=>(~((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))<=(~((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))))&
((![X]:((((does_enjoy_trail_running(X))&(practices_graffiti_art(X))&(frequently_participates_in_hackathons_and_coding_competitions(X))))=>(has_a_tattoo(X)))))&
(![X]:(room(X)=>(((((bakes_bread_at_home(X))&(has_a_tattoo(X))&(collects_foreign_coins(X))))=>(writes_a_travel_blog(X))))))&
(![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))<=>(((practices_zumba(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))))))))&
(~![X]:(room(X)=>(((((practices_zumba(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))))<=>(is_an_avid_hiker(X))))))&
(![X]:(room(X)=>(((is_an_avid_hiker(X))=>(does_not_have_a_tattoo(X))))))&
(![X]:(anywhere(X)=>(((does_not_have_a_tattoo(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))<=>(is_a_client_of_Meta(X))))))&
((?[X,Y]:(room(X)&room(Y)&(does_enjoy_trail_running(X)&does_enjoy_trail_running(Y))&(X!=Y))))&
(![X]:(~room(X)=>(((is_a_drone_photographer(X))=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<~>(collects_foreign_coins(X))))))))&
(![X]:(room(X)=>(((((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<~>(collects_foreign_coins(X))))=>(is_an_avid_hiker(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(is_a_client_of_Meta(X))) | [
"p0",
"p7",
"p8",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8946559610201403671783709
% SZS output start Proof for 8946559610201403671783709
44. there_is_a_room [input p0]
51. ! [X0] : (room(X0) => (~prede(X0) | (predc(X0) & predk(X0) & ~predm(X0)))) [input p7]
52. ! [X0] : (room(X0) => (~prede(X0) => predo(X0))) [input p8]
53. ! [X0] : (room(X0) => (predo(X0) => predp(X0))) [input p9]
65. ! [X0] : (room(X0) => (predp(X0) <=> predc(X0))) [input p21]
69. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis]
77. ! [X0] : (room(X0) => (~prede(X0) | (predc(X0) & predk(X0)))) [pure predicate removal 51]
80. ! [X0] : (room(X0) => (~prede(X0) | predc(X0))) [pure predicate removal 77]
165. ! [X0] : ((~prede(X0) | predc(X0)) | ~room(X0)) [ennf transformation 80]
166. ! [X0] : (~prede(X0) | predc(X0) | ~room(X0)) [flattening 165]
167. ! [X0] : ((predo(X0) | prede(X0)) | ~room(X0)) [ennf transformation 52]
168. ! [X0] : (predo(X0) | prede(X0) | ~room(X0)) [flattening 167]
169. ! [X0] : ((predp(X0) | ~predo(X0)) | ~room(X0)) [ennf transformation 53]
170. ! [X0] : (predp(X0) | ~predo(X0) | ~room(X0)) [flattening 169]
183. ! [X0] : ((predp(X0) <=> predc(X0)) | ~room(X0)) [ennf transformation 65]
188. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 69]
210. ! [X0] : (((predp(X0) | ~predc(X0)) & (predc(X0) | ~predp(X0))) | ~room(X0)) [nnf transformation 183]
215. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK9) & room(sK9)) [choice axiom]
216. (~predc(sK9) & room(sK9)) | ~there_is_a_room [skolemisation 188,215]
298. there_is_a_room [cnf transformation 44]
308. ~prede(X0) | predc(X0) | ~room(X0) [cnf transformation 166]
309. ~room(X0) | prede(X0) | predo(X0) [cnf transformation 168]
310. ~predo(X0) | predp(X0) | ~room(X0) [cnf transformation 170]
337. ~predp(X0) | predc(X0) | ~room(X0) [cnf transformation 210]
346. room(sK9) | ~there_is_a_room [cnf transformation 216]
347. ~predc(sK9) | ~there_is_a_room [cnf transformation 216]
412. ~predc(sK9) [subsumption resolution 347,298]
413. room(sK9) [subsumption resolution 346,298]
419. prede(sK9) | predo(sK9) [resolution 309,413]
457. 22 <=> predo(sK9) [avatar definition]
459. predo(sK9) <- (22) [avatar component clause 457]
461. 23 <=> prede(sK9) [avatar definition]
463. prede(sK9) <- (23) [avatar component clause 461]
464. 22 | 23 [avatar split clause 419,461,457]
476. predp(sK9) | ~room(sK9) <- (22) [resolution 459,310]
477. predp(sK9) <- (22) [subsumption resolution 476,413]
740. predc(sK9) | ~room(sK9) <- (22) [resolution 477,337]
742. ~room(sK9) <- (22) [subsumption resolution 740,412]
743. $false <- (22) [subsumption resolution 742,413]
744. ~22 [avatar contradiction clause 743]
752. predc(sK9) | ~room(sK9) <- (23) [resolution 463,308]
763. ~room(sK9) <- (23) [subsumption resolution 752,412]
764. $false <- (23) [subsumption resolution 763,413]
765. ~23 [avatar contradiction clause 764]
766. $false [avatar sat refutation 464,744,765]
% SZS output end Proof for 8946559610201403671783709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0.585093 |
Georgia, Barbara are the only persons in the room.
Georgia does not collect historical artifacts related to ancient civilizations or is not a craft beer aficionado or both.
Only one person in the room either is not an avid hiker or is not dedicated to sustainable living and zero-waste practices but not both.
Georgia neither does not read mystery novels nor does not write in-depth travel guides for off-the-beaten-path destinations.
Someone in the room either is not a tea enthusiast or is not dedicated to sustainable living and zero-waste practices but not both.
At least one person in the room is not a tea enthusiast.
Someone outside the room does not play as a goalkeeper for a local amateur soccer team.
Georgia does not have a specialized collection of handmade artisan pottery.
Georgia neither does not practice archery nor is not a scotch connoisseur.
Someone in the room does not practice archery.
Georgia does not practice archery or does not have a specialized collection of handmade artisan pottery or both.
Georgia does not play as a goalkeeper for a local amateur soccer team.
Georgia is not a craft beer aficionado. | Everyone in the room does not practice archery or reads mystery novels. | entailment | room(georgia)&room(barbara)&(![X]:(room(X)=>(X='georgia'|X='barbara')))&
(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(georgia))|(is_not_a_craft_beer_aficionado(georgia))))&
(((?[X]:(room(X)&((is_not_an_avid_hiker(X))<~>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))&(![X,Y]:((room(X)&room(Y)&(((is_not_an_avid_hiker(X))<~>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))&(((is_not_an_avid_hiker(Y))<~>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(Y)))))=>(X=Y)))))&
(~((does_not_read_mystery_novels(georgia))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(georgia))))&
(?[X]:(room(X)&(((is_not_a_tea_enthusiast(X))<~>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))&
(((?[X]:(room(X)&is_not_a_tea_enthusiast(X)))))&
(?[X]:(~room(X)&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))&
(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(georgia))&
(~((does_not_practice_archery(georgia))|(is_not_a_scotch_connoisseur(georgia))))&
(?[X]:(room(X)&(does_not_practice_archery(X))))&
(((does_not_practice_archery(georgia))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(georgia))))&
(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(georgia))&
(is_not_a_craft_beer_aficionado(georgia)) | room(georgia)&room(barbara)&(![X]:(room(X)=>(X='georgia'|X='barbara')))&
![X]:(room(X)=>(((reads_mystery_novels(X))|(does_not_practice_archery(X))))) | [
"p0",
"p3",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 475258723865543010988955
% SZS output start Proof for 475258723865543010988955
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
47. ~(~predi(mary) | ~predd(mary)) [input p3]
52. ~(~predn(mary) | ~predg(mary)) [input p8]
53. ? [X0] : (~predg(X0) & room(X0)) [input p9]
57. ~(! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
59. ~(! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary)) [rectify 57]
60. ~~predg(mary) [pure predicate removal 52]
65. ~~predd(mary) [pure predicate removal 47]
140. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
141. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 140]
144. predd(mary) [ennf transformation 65]
145. predg(mary) [ennf transformation 60]
146. ? [X0] : ((predg(X0) & ~predd(X0)) & room(X0)) | ? [X1] : ((paul != X1 & mary != X1) & room(X1)) | ~room(paul) | ~room(mary) [ennf transformation 59]
147. ? [X0] : (predg(X0) & ~predd(X0) & room(X0)) | ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~room(paul) | ~room(mary) [flattening 146]
148. ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction]
149. ? [X0] : (predg(X0) & ~predd(X0) & room(X0)) | sP0 | ~room(paul) | ~room(mary) [definition folding 147,148]
163. ? [X0] : (~predg(X0) & room(X0)) => (~predg(sK5) & room(sK5)) [choice axiom]
164. ~predg(sK5) & room(sK5) [skolemisation 53,163]
165. ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 148]
166. ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 165]
167. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom]
168. (paul != sK6 & mary != sK6 & room(sK6)) | ~sP0 [skolemisation 166,167]
169. ? [X0] : (predg(X0) & ~predd(X0) & room(X0)) => (predg(sK7) & ~predd(sK7) & room(sK7)) [choice axiom]
170. (predg(sK7) & ~predd(sK7) & room(sK7)) | sP0 | ~room(paul) | ~room(mary) [skolemisation 149,169]
251. room(mary) [cnf transformation 141]
252. room(paul) [cnf transformation 141]
253. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 141]
261. predd(mary) [cnf transformation 144]
268. predg(mary) [cnf transformation 145]
269. room(sK5) [cnf transformation 164]
270. ~predg(sK5) [cnf transformation 164]
271. room(sK6) | ~sP0 [cnf transformation 168]
272. mary != sK6 | ~sP0 [cnf transformation 168]
273. paul != sK6 | ~sP0 [cnf transformation 168]
274. room(sK7) | sP0 | ~room(paul) | ~room(mary) [cnf transformation 170]
275. ~predd(sK7) | sP0 | ~room(paul) | ~room(mary) [cnf transformation 170]
276. predg(sK7) | sP0 | ~room(paul) | ~room(mary) [cnf transformation 170]
298. 5 <=> sP0 [avatar definition]
302. 6 <=> paul = sK6 [avatar definition]
304. paul != sK6 <- (~6) [avatar component clause 302]
305. ~5 | ~6 [avatar split clause 273,302,298]
307. 7 <=> mary = sK6 [avatar definition]
309. mary != sK6 <- (~7) [avatar component clause 307]
310. ~5 | ~7 [avatar split clause 272,307,298]
312. 8 <=> room(sK6) [avatar definition]
314. room(sK6) <- (8) [avatar component clause 312]
315. ~5 | 8 [avatar split clause 271,312,298]
316. predg(sK7) | sP0 | ~room(mary) [subsumption resolution 276,252]
317. predg(sK7) | sP0 [subsumption resolution 316,251]
319. 9 <=> predg(sK7) [avatar definition]
321. predg(sK7) <- (9) [avatar component clause 319]
322. 5 | 9 [avatar split clause 317,319,298]
323. ~predd(sK7) | sP0 | ~room(mary) [subsumption resolution 275,252]
324. ~predd(sK7) | sP0 [subsumption resolution 323,251]
326. 10 <=> predd(sK7) [avatar definition]
328. ~predd(sK7) <- (~10) [avatar component clause 326]
329. 5 | ~10 [avatar split clause 324,326,298]
330. room(sK7) | sP0 | ~room(mary) [subsumption resolution 274,252]
331. room(sK7) | sP0 [subsumption resolution 330,251]
333. 11 <=> room(sK7) [avatar definition]
335. room(sK7) <- (11) [avatar component clause 333]
336. 5 | 11 [avatar split clause 331,333,298]
342. mary = sK5 | paul = sK5 [resolution 253,269]
343. mary = sK6 | paul = sK6 <- (8) [resolution 253,314]
372. 18 <=> paul = sK5 [avatar definition]
374. paul = sK5 <- (18) [avatar component clause 372]
376. 19 <=> mary = sK5 [avatar definition]
378. mary = sK5 <- (19) [avatar component clause 376]
379. 18 | 19 [avatar split clause 342,376,372]
380. paul = sK6 <- (~7, 8) [subsumption resolution 343,309]
381. $false <- (~6, ~7, 8) [subsumption resolution 380,304]
382. 6 | 7 | ~8 [avatar contradiction clause 381]
384. ~predg(paul) <- (18) [backward demodulation 270,374]
399. mary = sK7 | paul = sK7 <- (11) [resolution 335,253]
401. 20 <=> paul = sK7 [avatar definition]
403. paul = sK7 <- (20) [avatar component clause 401]
405. 21 <=> mary = sK7 [avatar definition]
407. mary = sK7 <- (21) [avatar component clause 405]
408. 20 | 21 | ~11 [avatar split clause 399,333,405,401]
409. predg(paul) <- (9, 20) [backward demodulation 321,403]
412. $false <- (9, 18, 20) [subsumption resolution 409,384]
413. ~9 | ~18 | ~20 [avatar contradiction clause 412]
415. ~predd(mary) <- (~10, 21) [backward demodulation 328,407]
417. $false <- (~10, 21) [subsumption resolution 415,261]
418. 10 | ~21 [avatar contradiction clause 417]
424. ~predg(mary) <- (19) [backward demodulation 270,378]
425. $false <- (19) [subsumption resolution 424,268]
426. ~19 [avatar contradiction clause 425]
428. $false [avatar sat refutation 305,310,315,322,329,336,379,382,408,413,418,426]
% SZS output end Proof for 475258723865543010988955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.443989 |
Jana, Helen, Lucille, Steven, Jennifer are the only persons in the room. If “not everyone in the room is not a tea enthusiast or is a coffee connoisseur” then “everyone in the room enjoys cross-country skiing or is not a Linux enthusiast”. If “everyone in the room enjoys cross-country skiing or is not a Linux enthusiast” then “Lucille collects rare and antique scientific instruments”. Either “someone anywhere is a Linux enthusiast” or “everyone in the room is not a tea enthusiast or travels domestically frequently” but not both. If “Helen writes and illustrates their own graphic novels” then “Jana does not collect rare and antique scientific instruments”. If “Jana does not collect rare and antique scientific instruments” then “everyone in the room collects foreign coins if they is a coffee connoisseur”. If “Helen enjoys writing detailed reviews of new and classic board games” then “Helen collects foreign coins”. If “Helen collects foreign coins” then “everyone in the room collects foreign coins if they travels domestically frequently”. “Helen is a coffee connoisseur” if “no one in the room is not a tea enthusiast or collects comic books”. | Jana is a Linux enthusiast. | contradiction | room(jana)&room(helen)&room(lucille)&room(steven)&room(jennifer)&(![X]:(room(X)=>(X='jana'|X='helen'|X='lucille'|X='steven'|X='jennifer')))&
(((~![X]:(room(X)=>(((is_a_coffee_connoisseur(X))|(is_not_a_tea_enthusiast(X))))))=>(![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(enjoys_cross-country_skiing(X)))))))&
((![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(enjoys_cross-country_skiing(X))))))=>(collects_rare_and_antique_scientific_instruments(lucille))))&
((?[X]:(anywhere(X)&(is_a_Linux_enthusiast(X))))<~>(![X]:(room(X)=>(((travels_domestically_frequently(X))|(is_not_a_tea_enthusiast(X)))))))&
(((writes_and_illustrates_their_own_graphic_novels(helen))=>(does_not_collect_rare_and_antique_scientific_instruments(jana)))&
((does_not_collect_rare_and_antique_scientific_instruments(jana))=>(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(collects_foreign_coins(X))))))))&
(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(helen))=>(collects_foreign_coins(helen)))&
((collects_foreign_coins(helen))=>(![X]:(room(X)=>(((travels_domestically_frequently(X))=>(collects_foreign_coins(X))))))))&
((~?[X]:(room(X)=>(((collects_comic_books(X))|(is_not_a_tea_enthusiast(X))))))=>(is_a_coffee_connoisseur(helen)))&
((((?[X]:(room(X)&is_a_tea_enthusiast(X)))))=>(~![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(hosts_regular_workshops_on_creative_writing(X)))))))&
((((hosts_regular_workshops_on_creative_writing(lucille))<~>(is_a_Linux_enthusiast(lucille))))=>(![X]:(room(X)=>(((does_not_collect_comic_books(X))=>(hosts_regular_workshops_on_creative_writing(X)))))))&
((![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(collects_foreign_coins(X))))))=>(![X]:(room(X)=>(((collects_foreign_coins(X))=>(is_a_coffee_connoisseur(X)))))))&
((![X]:(room(X)=>(((is_a_coffee_connoisseur(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))=>(writes_and_illustrates_their_own_graphic_novels(lucille)))&
((((enjoys_cross-country_skiing(helen))<~>(collects_foreign_coins(helen))))<=>(travels_domestically_frequently(lucille)))&
((?[X]:(room(X)&(is_a_professional_photographer_specializing_in_portrait_photography(X))))=>(![X]:(room(X)=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))&
((~![X]:(anywhere(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(is_not_a_Linux_enthusiast(X))))))<=>(![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(is_a_Linux_enthusiast(X)))))))&
(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))&
(is_not_a_Linux_enthusiast(jana))&
(?[X]:(anywhere(X)&(streams_on_Twitch(X))))&
(does_not_enjoy_cross-country_skiing(lucille))&
(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(hosts_regular_workshops_on_creative_writing(X))))))&
(~((hosts_regular_workshops_on_creative_writing(lucille))|(enjoys_wildlife_photography(lucille))))&
(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(collects_comic_books(X))))))&
(![X]:(room(X)=>(((collects_comic_books(X))=>(is_a_Linux_enthusiast(X))))))&
(((is_a_Linux_enthusiast(lucille))&(collects_comic_books(lucille))&(does_not_write_and_illustrates_their_own_graphic_novels(lucille))))&
((((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(jana))<~>(is_a_coffee_connoisseur(jana))))&(is_a_coffee_connoisseur(jana)))&
(![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(is_a_Linux_enthusiast(X))))))&
(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))|(does_not_stream_on_Twitch(X))))))&
(![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(collects_rare_and_antique_scientific_instruments(X))))))&
(![X]:(anywhere(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))&
(((streams_on_Twitch(jana))|(owns_a_telescope(jana))))&
(((travels_domestically_frequently(jana))<~>(writes_and_illustrates_their_own_graphic_novels(jana)))) | room(jana)&room(helen)&room(lucille)&room(steven)&room(jennifer)&(![X]:(room(X)=>(X='jana'|X='helen'|X='lucille'|X='steven'|X='jennifer')))&
is_a_Linux_enthusiast(jana) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 4748045386944404395967343
% SZS output start Proof for 4748045386944404395967343
44. (predm(mary) <~> predn(mary)) & (predi(mary) | predh(mary)) & ! [X0] : (anywhere(X0) => (predg(X0) => ~predf(X0))) & ! [X0] : (room(X0) => (~predh(X0) => predg(X0))) & ! [X0] : (room(X0) => (~predh(X0) | predk(X0))) & ! [X0] : (room(X0) => (predf(X0) => predk(X0))) & predc(mary) & (predf(mary) <~> predc(mary)) & ~predn(fred) & predd(fred) & predk(fred) & ! [X0] : (room(X0) => (predd(X0) => predk(X0))) & ! [X0] : (room(X0) => (predp(X0) => predd(X0))) & ~(preda(fred) | prede(fred)) & ! [X0] : (room(X0) => (predc(X0) => prede(X0))) & ~predp(fred) & ? [X0] : (predh(X0) & anywhere(X0)) & ~predk(mary) & ! [X0] : (room(X0) => (predk(X0) => predl(X0))) & (~! [X0] : (anywhere(X0) => (~predk(X0) | ~predn(X0))) <=> ! [X0] : (room(X0) => (predk(X0) | ~predk(X0)))) & (? [X0] : (predl(X0) & room(X0)) => ! [X0] : (room(X0) => predl(X0))) & ((predp(paul) <~> predb(paul)) <=> predm(fred)) & (! [X0] : (room(X0) => (~predj(X0) | predc(X0))) => predn(fred)) & (! [X0] : (room(X0) => (predb(X0) | ~predf(X0))) => ! [X0] : (room(X0) => (predb(X0) => predc(X0)))) & ((prede(fred) <~> predk(fred)) => ! [X0] : (room(X0) => (~predd(X0) => prede(X0)))) & (? [X0] : (predo(X0) & room(X0)) => ~! [X0] : (room(X0) => (preda(X0) => prede(X0)))) & (~? [X0] : (room(X0) => (~predo(X0) | predd(X0))) => predc(paul)) & (predb(paul) => ! [X0] : (room(X0) => (predm(X0) => predb(X0)))) & (predf(paul) => predb(paul)) & (~predg(mary) => ! [X0] : (room(X0) => (predc(X0) => predb(X0)))) & (predn(paul) => ~predg(mary)) & (? [X0] : (predk(X0) & anywhere(X0)) <~> ! [X0] : (room(X0) => (~predo(X0) | predm(X0)))) & (! [X0] : (room(X0) => (predp(X0) | ~predk(X0))) => predg(fred)) & (~! [X0] : (room(X0) => (~predo(X0) | predc(X0))) => ! [X0] : (room(X0) => (predp(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 p0]
45. predk(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]
46. (predm(mary) <~> predn(mary)) & (predi(mary) | predh(mary)) & ! [X0] : (anywhere(X0) => (predg(X0) => ~predf(X0))) & ! [X1] : (room(X1) => (~predh(X1) => predg(X1))) & ! [X2] : (room(X2) => (~predh(X2) | predk(X2))) & ! [X3] : (room(X3) => (predf(X3) => predk(X3))) & predc(mary) & (predf(mary) <~> predc(mary)) & ~predn(fred) & predd(fred) & predk(fred) & ! [X4] : (room(X4) => (predd(X4) => predk(X4))) & ! [X5] : (room(X5) => (predp(X5) => predd(X5))) & ~(preda(fred) | prede(fred)) & ! [X6] : (room(X6) => (predc(X6) => prede(X6))) & ~predp(fred) & ? [X7] : (predh(X7) & anywhere(X7)) & ~predk(mary) & ! [X8] : (room(X8) => (predk(X8) => predl(X8))) & (~! [X9] : (anywhere(X9) => (~predk(X9) | ~predn(X9))) <=> ! [X10] : (room(X10) => (predk(X10) | ~predk(X10)))) & (? [X11] : (predl(X11) & room(X11)) => ! [X12] : (room(X12) => predl(X12))) & ((predp(paul) <~> predb(paul)) <=> predm(fred)) & (! [X13] : (room(X13) => (~predj(X13) | predc(X13))) => predn(fred)) & (! [X14] : (room(X14) => (predb(X14) | ~predf(X14))) => ! [X15] : (room(X15) => (predb(X15) => predc(X15)))) & ((prede(fred) <~> predk(fred)) => ! [X16] : (room(X16) => (~predd(X16) => prede(X16)))) & (? [X17] : (predo(X17) & room(X17)) => ~! [X18] : (room(X18) => (preda(X18) => prede(X18)))) & (~? [X19] : (room(X19) => (~predo(X19) | predd(X19))) => predc(paul)) & (predb(paul) => ! [X20] : (room(X20) => (predm(X20) => predb(X20)))) & (predf(paul) => predb(paul)) & (~predg(mary) => ! [X21] : (room(X21) => (predc(X21) => predb(X21)))) & (predn(paul) => ~predg(mary)) & (? [X22] : (predk(X22) & anywhere(X22)) <~> ! [X23] : (room(X23) => (~predo(X23) | predm(X23)))) & (! [X24] : (room(X24) => (predp(X24) | ~predk(X24))) => predg(fred)) & (~! [X25] : (room(X25) => (~predo(X25) | predc(X25))) => ! [X26] : (room(X26) => (predp(X26) | ~predk(X26)))) & ! [X27] : (room(X27) => (john = X27 | alice = X27 | fred = X27 | paul = X27 | mary = X27)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44]
47. (predm(mary) <~> predn(mary)) & ! [X0] : (anywhere(X0) => (predg(X0) => ~predf(X0))) & ! [X1] : (room(X1) => (~predh(X1) => predg(X1))) & ! [X2] : (room(X2) => (~predh(X2) | predk(X2))) & ! [X3] : (room(X3) => (predf(X3) => predk(X3))) & predc(mary) & (predf(mary) <~> predc(mary)) & ~predn(fred) & predd(fred) & predk(fred) & ! [X4] : (room(X4) => (predd(X4) => predk(X4))) & ! [X5] : (room(X5) => (predp(X5) => predd(X5))) & ~(preda(fred) | prede(fred)) & ! [X6] : (room(X6) => (predc(X6) => prede(X6))) & ~predp(fred) & ? [X7] : (predh(X7) & anywhere(X7)) & ~predk(mary) & ! [X8] : (room(X8) => (predk(X8) => predl(X8))) & (~! [X9] : (anywhere(X9) => (~predk(X9) | ~predn(X9))) <=> ! [X10] : (room(X10) => (predk(X10) | ~predk(X10)))) & (? [X11] : (predl(X11) & room(X11)) => ! [X12] : (room(X12) => predl(X12))) & ((predp(paul) <~> predb(paul)) <=> predm(fred)) & (! [X13] : (room(X13) => (~predj(X13) | predc(X13))) => predn(fred)) & (! [X14] : (room(X14) => (predb(X14) | ~predf(X14))) => ! [X15] : (room(X15) => (predb(X15) => predc(X15)))) & ((prede(fred) <~> predk(fred)) => ! [X16] : (room(X16) => (~predd(X16) => prede(X16)))) & (? [X17] : (predo(X17) & room(X17)) => ~! [X18] : (room(X18) => (preda(X18) => prede(X18)))) & (~? [X19] : (room(X19) => (~predo(X19) | predd(X19))) => predc(paul)) & (predb(paul) => ! [X20] : (room(X20) => (predm(X20) => predb(X20)))) & (predf(paul) => predb(paul)) & (~predg(mary) => ! [X21] : (room(X21) => (predc(X21) => predb(X21)))) & (predn(paul) => ~predg(mary)) & (? [X22] : (predk(X22) & anywhere(X22)) <~> ! [X23] : (room(X23) => (~predo(X23) | predm(X23)))) & (! [X24] : (room(X24) => (predp(X24) | ~predk(X24))) => predg(fred)) & (~! [X25] : (room(X25) => (~predo(X25) | predc(X25))) => ! [X26] : (room(X26) => (predp(X26) | ~predk(X26)))) & ! [X27] : (room(X27) => (john = X27 | alice = X27 | fred = X27 | paul = X27 | mary = X27)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46]
48. (predm(mary) <~> predn(mary)) & ! [X0] : (anywhere(X0) => (predg(X0) => ~predf(X0))) & ! [X1] : (room(X1) => (~predh(X1) => predg(X1))) & ! [X2] : (room(X2) => (~predh(X2) | predk(X2))) & ! [X3] : (room(X3) => (predf(X3) => predk(X3))) & predc(mary) & (predf(mary) <~> predc(mary)) & ~predn(fred) & predd(fred) & predk(fred) & ! [X4] : (room(X4) => (predd(X4) => predk(X4))) & ! [X5] : (room(X5) => (predp(X5) => predd(X5))) & ~(preda(fred) | prede(fred)) & ! [X6] : (room(X6) => (predc(X6) => prede(X6))) & ~predp(fred) & ? [X7] : (predh(X7) & anywhere(X7)) & ~predk(mary) & ! [X8] : (room(X8) => (predk(X8) => predl(X8))) & (~! [X9] : (anywhere(X9) => (~predk(X9) | ~predn(X9))) <=> ! [X10] : (room(X10) => (predk(X10) | ~predk(X10)))) & (? [X11] : (predl(X11) & room(X11)) => ! [X12] : (room(X12) => predl(X12))) & ((predp(paul) <~> predb(paul)) <=> predm(fred)) & (! [X13] : (room(X13) => predc(X13)) => predn(fred)) & (! [X14] : (room(X14) => (predb(X14) | ~predf(X14))) => ! [X15] : (room(X15) => (predb(X15) => predc(X15)))) & ((prede(fred) <~> predk(fred)) => ! [X16] : (room(X16) => (~predd(X16) => prede(X16)))) & (? [X17] : (predo(X17) & room(X17)) => ~! [X18] : (room(X18) => (preda(X18) => prede(X18)))) & (~? [X19] : (room(X19) => (~predo(X19) | predd(X19))) => predc(paul)) & (predb(paul) => ! [X20] : (room(X20) => (predm(X20) => predb(X20)))) & (predf(paul) => predb(paul)) & (~predg(mary) => ! [X21] : (room(X21) => (predc(X21) => predb(X21)))) & (predn(paul) => ~predg(mary)) & (? [X22] : (predk(X22) & anywhere(X22)) <~> ! [X23] : (room(X23) => (~predo(X23) | predm(X23)))) & (! [X24] : (room(X24) => (predp(X24) | ~predk(X24))) => predg(fred)) & (~! [X25] : (room(X25) => (~predo(X25) | predc(X25))) => ! [X26] : (room(X26) => (predp(X26) | ~predk(X26)))) & ! [X27] : (room(X27) => (john = X27 | alice = X27 | fred = X27 | paul = X27 | mary = X27)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47]
120. (predm(mary) <~> predn(mary)) & ! [X0] : ((~predf(X0) | ~predg(X0)) | ~anywhere(X0)) & ! [X1] : ((predg(X1) | predh(X1)) | ~room(X1)) & ! [X2] : ((~predh(X2) | predk(X2)) | ~room(X2)) & ! [X3] : ((predk(X3) | ~predf(X3)) | ~room(X3)) & predc(mary) & (predf(mary) <~> predc(mary)) & ~predn(fred) & predd(fred) & predk(fred) & ! [X4] : ((predk(X4) | ~predd(X4)) | ~room(X4)) & ! [X5] : ((predd(X5) | ~predp(X5)) | ~room(X5)) & (~preda(fred) & ~prede(fred)) & ! [X6] : ((prede(X6) | ~predc(X6)) | ~room(X6)) & ~predp(fred) & ? [X7] : (predh(X7) & anywhere(X7)) & ~predk(mary) & ! [X8] : ((predl(X8) | ~predk(X8)) | ~room(X8)) & (? [X9] : ((predk(X9) & predn(X9)) & anywhere(X9)) <=> ! [X10] : ((predk(X10) | ~predk(X10)) | ~room(X10))) & (! [X12] : (predl(X12) | ~room(X12)) | ! [X11] : (~predl(X11) | ~room(X11))) & ((predp(paul) <~> predb(paul)) <=> predm(fred)) & (predn(fred) | ? [X13] : (~predc(X13) & room(X13))) & (! [X15] : ((predc(X15) | ~predb(X15)) | ~room(X15)) | ? [X14] : ((~predb(X14) & predf(X14)) & room(X14))) & (! [X16] : ((prede(X16) | predd(X16)) | ~room(X16)) | (prede(fred) <=> predk(fred))) & (? [X18] : ((~prede(X18) & preda(X18)) & room(X18)) | ! [X17] : (~predo(X17) | ~room(X17))) & (predc(paul) | ? [X19] : ((~predo(X19) | predd(X19)) | ~room(X19))) & (! [X20] : ((predb(X20) | ~predm(X20)) | ~room(X20)) | ~predb(paul)) & (predb(paul) | ~predf(paul)) & (! [X21] : ((predb(X21) | ~predc(X21)) | ~room(X21)) | predg(mary)) & (~predg(mary) | ~predn(paul)) & (? [X22] : (predk(X22) & anywhere(X22)) <~> ! [X23] : ((~predo(X23) | predm(X23)) | ~room(X23))) & (predg(fred) | ? [X24] : ((~predp(X24) & predk(X24)) & room(X24))) & (! [X26] : ((predp(X26) | ~predk(X26)) | ~room(X26)) | ! [X25] : ((~predo(X25) | predc(X25)) | ~room(X25))) & ! [X27] : ((john = X27 | alice = X27 | fred = X27 | paul = X27 | mary = X27) | ~room(X27)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 48]
121. (predm(mary) <~> predn(mary)) & ! [X0] : (~predf(X0) | ~predg(X0) | ~anywhere(X0)) & ! [X1] : (predg(X1) | predh(X1) | ~room(X1)) & ! [X2] : (~predh(X2) | predk(X2) | ~room(X2)) & ! [X3] : (predk(X3) | ~predf(X3) | ~room(X3)) & predc(mary) & (predf(mary) <~> predc(mary)) & ~predn(fred) & predd(fred) & predk(fred) & ! [X4] : (predk(X4) | ~predd(X4) | ~room(X4)) & ! [X5] : (predd(X5) | ~predp(X5) | ~room(X5)) & ~preda(fred) & ~prede(fred) & ! [X6] : (prede(X6) | ~predc(X6) | ~room(X6)) & ~predp(fred) & ? [X7] : (predh(X7) & anywhere(X7)) & ~predk(mary) & ! [X8] : (predl(X8) | ~predk(X8) | ~room(X8)) & (? [X9] : (predk(X9) & predn(X9) & anywhere(X9)) <=> ! [X10] : (predk(X10) | ~predk(X10) | ~room(X10))) & (! [X12] : (predl(X12) | ~room(X12)) | ! [X11] : (~predl(X11) | ~room(X11))) & ((predp(paul) <~> predb(paul)) <=> predm(fred)) & (predn(fred) | ? [X13] : (~predc(X13) & room(X13))) & (! [X15] : (predc(X15) | ~predb(X15) | ~room(X15)) | ? [X14] : (~predb(X14) & predf(X14) & room(X14))) & (! [X16] : (prede(X16) | predd(X16) | ~room(X16)) | (prede(fred) <=> predk(fred))) & (? [X18] : (~prede(X18) & preda(X18) & room(X18)) | ! [X17] : (~predo(X17) | ~room(X17))) & (predc(paul) | ? [X19] : (~predo(X19) | predd(X19) | ~room(X19))) & (! [X20] : (predb(X20) | ~predm(X20) | ~room(X20)) | ~predb(paul)) & (predb(paul) | ~predf(paul)) & (! [X21] : (predb(X21) | ~predc(X21) | ~room(X21)) | predg(mary)) & (~predg(mary) | ~predn(paul)) & (? [X22] : (predk(X22) & anywhere(X22)) <~> ! [X23] : (~predo(X23) | predm(X23) | ~room(X23))) & (predg(fred) | ? [X24] : (~predp(X24) & predk(X24) & room(X24))) & (! [X26] : (predp(X26) | ~predk(X26) | ~room(X26)) | ! [X25] : (~predo(X25) | predc(X25) | ~room(X25))) & ! [X27] : (john = X27 | alice = X27 | fred = X27 | paul = X27 | mary = X27 | ~room(X27)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 120]
122. predk(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 45]
123. predk(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 122]
124. sP0 <=> ? [X9] : (predk(X9) & predn(X9) & anywhere(X9)) [predicate definition introduction]
125. (predm(mary) <~> predn(mary)) & ! [X0] : (~predf(X0) | ~predg(X0) | ~anywhere(X0)) & ! [X1] : (predg(X1) | predh(X1) | ~room(X1)) & ! [X2] : (~predh(X2) | predk(X2) | ~room(X2)) & ! [X3] : (predk(X3) | ~predf(X3) | ~room(X3)) & predc(mary) & (predf(mary) <~> predc(mary)) & ~predn(fred) & predd(fred) & predk(fred) & ! [X4] : (predk(X4) | ~predd(X4) | ~room(X4)) & ! [X5] : (predd(X5) | ~predp(X5) | ~room(X5)) & ~preda(fred) & ~prede(fred) & ! [X6] : (prede(X6) | ~predc(X6) | ~room(X6)) & ~predp(fred) & ? [X7] : (predh(X7) & anywhere(X7)) & ~predk(mary) & ! [X8] : (predl(X8) | ~predk(X8) | ~room(X8)) & (sP0 <=> ! [X10] : (predk(X10) | ~predk(X10) | ~room(X10))) & (! [X12] : (predl(X12) | ~room(X12)) | ! [X11] : (~predl(X11) | ~room(X11))) & ((predp(paul) <~> predb(paul)) <=> predm(fred)) & (predn(fred) | ? [X13] : (~predc(X13) & room(X13))) & (! [X15] : (predc(X15) | ~predb(X15) | ~room(X15)) | ? [X14] : (~predb(X14) & predf(X14) & room(X14))) & (! [X16] : (prede(X16) | predd(X16) | ~room(X16)) | (prede(fred) <=> predk(fred))) & (? [X18] : (~prede(X18) & preda(X18) & room(X18)) | ! [X17] : (~predo(X17) | ~room(X17))) & (predc(paul) | ? [X19] : (~predo(X19) | predd(X19) | ~room(X19))) & (! [X20] : (predb(X20) | ~predm(X20) | ~room(X20)) | ~predb(paul)) & (predb(paul) | ~predf(paul)) & (! [X21] : (predb(X21) | ~predc(X21) | ~room(X21)) | predg(mary)) & (~predg(mary) | ~predn(paul)) & (? [X22] : (predk(X22) & anywhere(X22)) <~> ! [X23] : (~predo(X23) | predm(X23) | ~room(X23))) & (predg(fred) | ? [X24] : (~predp(X24) & predk(X24) & room(X24))) & (! [X26] : (predp(X26) | ~predk(X26) | ~room(X26)) | ! [X25] : (~predo(X25) | predc(X25) | ~room(X25))) & ! [X27] : (john = X27 | alice = X27 | fred = X27 | paul = X27 | mary = X27 | ~room(X27)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [definition folding 121,124]
131. ((~predn(mary) | ~predm(mary)) & (predn(mary) | predm(mary))) & ! [X0] : (~predf(X0) | ~predg(X0) | ~anywhere(X0)) & ! [X1] : (predg(X1) | predh(X1) | ~room(X1)) & ! [X2] : (~predh(X2) | predk(X2) | ~room(X2)) & ! [X3] : (predk(X3) | ~predf(X3) | ~room(X3)) & predc(mary) & ((~predc(mary) | ~predf(mary)) & (predc(mary) | predf(mary))) & ~predn(fred) & predd(fred) & predk(fred) & ! [X4] : (predk(X4) | ~predd(X4) | ~room(X4)) & ! [X5] : (predd(X5) | ~predp(X5) | ~room(X5)) & ~preda(fred) & ~prede(fred) & ! [X6] : (prede(X6) | ~predc(X6) | ~room(X6)) & ~predp(fred) & ? [X7] : (predh(X7) & anywhere(X7)) & ~predk(mary) & ! [X8] : (predl(X8) | ~predk(X8) | ~room(X8)) & ((sP0 | ? [X10] : (~predk(X10) & predk(X10) & room(X10))) & (! [X10] : (predk(X10) | ~predk(X10) | ~room(X10)) | ~sP0)) & (! [X12] : (predl(X12) | ~room(X12)) | ! [X11] : (~predl(X11) | ~room(X11))) & ((((~predb(paul) | ~predp(paul)) & (predb(paul) | predp(paul))) | ~predm(fred)) & (predm(fred) | ((predp(paul) | ~predb(paul)) & (predb(paul) | ~predp(paul))))) & (predn(fred) | ? [X13] : (~predc(X13) & room(X13))) & (! [X15] : (predc(X15) | ~predb(X15) | ~room(X15)) | ? [X14] : (~predb(X14) & predf(X14) & room(X14))) & (! [X16] : (prede(X16) | predd(X16) | ~room(X16)) | ((prede(fred) | ~predk(fred)) & (predk(fred) | ~prede(fred)))) & (? [X18] : (~prede(X18) & preda(X18) & room(X18)) | ! [X17] : (~predo(X17) | ~room(X17))) & (predc(paul) | ? [X19] : (~predo(X19) | predd(X19) | ~room(X19))) & (! [X20] : (predb(X20) | ~predm(X20) | ~room(X20)) | ~predb(paul)) & (predb(paul) | ~predf(paul)) & (! [X21] : (predb(X21) | ~predc(X21) | ~room(X21)) | predg(mary)) & (~predg(mary) | ~predn(paul)) & ((? [X23] : (predo(X23) & ~predm(X23) & room(X23)) | ! [X22] : (~predk(X22) | ~anywhere(X22))) & (! [X23] : (~predo(X23) | predm(X23) | ~room(X23)) | ? [X22] : (predk(X22) & anywhere(X22)))) & (predg(fred) | ? [X24] : (~predp(X24) & predk(X24) & room(X24))) & (! [X26] : (predp(X26) | ~predk(X26) | ~room(X26)) | ! [X25] : (~predo(X25) | predc(X25) | ~room(X25))) & ! [X27] : (john = X27 | alice = X27 | fred = X27 | paul = X27 | mary = X27 | ~room(X27)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 125]
132. (~predn(mary) | ~predm(mary)) & (predn(mary) | predm(mary)) & ! [X0] : (~predf(X0) | ~predg(X0) | ~anywhere(X0)) & ! [X1] : (predg(X1) | predh(X1) | ~room(X1)) & ! [X2] : (~predh(X2) | predk(X2) | ~room(X2)) & ! [X3] : (predk(X3) | ~predf(X3) | ~room(X3)) & predc(mary) & (~predc(mary) | ~predf(mary)) & (predc(mary) | predf(mary)) & ~predn(fred) & predd(fred) & predk(fred) & ! [X4] : (predk(X4) | ~predd(X4) | ~room(X4)) & ! [X5] : (predd(X5) | ~predp(X5) | ~room(X5)) & ~preda(fred) & ~prede(fred) & ! [X6] : (prede(X6) | ~predc(X6) | ~room(X6)) & ~predp(fred) & ? [X7] : (predh(X7) & anywhere(X7)) & ~predk(mary) & ! [X8] : (predl(X8) | ~predk(X8) | ~room(X8)) & (sP0 | ? [X10] : (~predk(X10) & predk(X10) & room(X10))) & (! [X10] : (predk(X10) | ~predk(X10) | ~room(X10)) | ~sP0) & (! [X12] : (predl(X12) | ~room(X12)) | ! [X11] : (~predl(X11) | ~room(X11))) & (((~predb(paul) | ~predp(paul)) & (predb(paul) | predp(paul))) | ~predm(fred)) & (predm(fred) | ((predp(paul) | ~predb(paul)) & (predb(paul) | ~predp(paul)))) & (predn(fred) | ? [X13] : (~predc(X13) & room(X13))) & (! [X15] : (predc(X15) | ~predb(X15) | ~room(X15)) | ? [X14] : (~predb(X14) & predf(X14) & room(X14))) & (! [X16] : (prede(X16) | predd(X16) | ~room(X16)) | ((prede(fred) | ~predk(fred)) & (predk(fred) | ~prede(fred)))) & (? [X18] : (~prede(X18) & preda(X18) & room(X18)) | ! [X17] : (~predo(X17) | ~room(X17))) & (predc(paul) | ? [X19] : (~predo(X19) | predd(X19) | ~room(X19))) & (! [X20] : (predb(X20) | ~predm(X20) | ~room(X20)) | ~predb(paul)) & (predb(paul) | ~predf(paul)) & (! [X21] : (predb(X21) | ~predc(X21) | ~room(X21)) | predg(mary)) & (~predg(mary) | ~predn(paul)) & (? [X23] : (predo(X23) & ~predm(X23) & room(X23)) | ! [X22] : (~predk(X22) | ~anywhere(X22))) & (! [X23] : (~predo(X23) | predm(X23) | ~room(X23)) | ? [X22] : (predk(X22) & anywhere(X22))) & (predg(fred) | ? [X24] : (~predp(X24) & predk(X24) & room(X24))) & (! [X26] : (predp(X26) | ~predk(X26) | ~room(X26)) | ! [X25] : (~predo(X25) | predc(X25) | ~room(X25))) & ! [X27] : (john = X27 | alice = X27 | fred = X27 | paul = X27 | mary = X27 | ~room(X27)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 131]
133. (~predn(mary) | ~predm(mary)) & (predn(mary) | predm(mary)) & ! [X0] : (~predf(X0) | ~predg(X0) | ~anywhere(X0)) & ! [X1] : (predg(X1) | predh(X1) | ~room(X1)) & ! [X2] : (~predh(X2) | predk(X2) | ~room(X2)) & ! [X3] : (predk(X3) | ~predf(X3) | ~room(X3)) & predc(mary) & (~predc(mary) | ~predf(mary)) & (predc(mary) | predf(mary)) & ~predn(fred) & predd(fred) & predk(fred) & ! [X4] : (predk(X4) | ~predd(X4) | ~room(X4)) & ! [X5] : (predd(X5) | ~predp(X5) | ~room(X5)) & ~preda(fred) & ~prede(fred) & ! [X6] : (prede(X6) | ~predc(X6) | ~room(X6)) & ~predp(fred) & ? [X7] : (predh(X7) & anywhere(X7)) & ~predk(mary) & ! [X8] : (predl(X8) | ~predk(X8) | ~room(X8)) & (sP0 | ? [X9] : (~predk(X9) & predk(X9) & room(X9))) & (! [X10] : (predk(X10) | ~predk(X10) | ~room(X10)) | ~sP0) & (! [X11] : (predl(X11) | ~room(X11)) | ! [X12] : (~predl(X12) | ~room(X12))) & (((~predb(paul) | ~predp(paul)) & (predb(paul) | predp(paul))) | ~predm(fred)) & (predm(fred) | ((predp(paul) | ~predb(paul)) & (predb(paul) | ~predp(paul)))) & (predn(fred) | ? [X13] : (~predc(X13) & room(X13))) & (! [X14] : (predc(X14) | ~predb(X14) | ~room(X14)) | ? [X15] : (~predb(X15) & predf(X15) & room(X15))) & (! [X16] : (prede(X16) | predd(X16) | ~room(X16)) | ((prede(fred) | ~predk(fred)) & (predk(fred) | ~prede(fred)))) & (? [X17] : (~prede(X17) & preda(X17) & room(X17)) | ! [X18] : (~predo(X18) | ~room(X18))) & (predc(paul) | ? [X19] : (~predo(X19) | predd(X19) | ~room(X19))) & (! [X20] : (predb(X20) | ~predm(X20) | ~room(X20)) | ~predb(paul)) & (predb(paul) | ~predf(paul)) & (! [X21] : (predb(X21) | ~predc(X21) | ~room(X21)) | predg(mary)) & (~predg(mary) | ~predn(paul)) & (? [X22] : (predo(X22) & ~predm(X22) & room(X22)) | ! [X23] : (~predk(X23) | ~anywhere(X23))) & (! [X24] : (~predo(X24) | predm(X24) | ~room(X24)) | ? [X25] : (predk(X25) & anywhere(X25))) & (predg(fred) | ? [X26] : (~predp(X26) & predk(X26) & room(X26))) & (! [X27] : (predp(X27) | ~predk(X27) | ~room(X27)) | ! [X28] : (~predo(X28) | predc(X28) | ~room(X28))) & ! [X29] : (john = X29 | alice = X29 | fred = X29 | paul = X29 | mary = X29 | ~room(X29)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 132]
134. ? [X7] : (predh(X7) & anywhere(X7)) => (predh(sK2) & anywhere(sK2)) [choice axiom]
135. ? [X9] : (~predk(X9) & predk(X9) & room(X9)) => (~predk(sK3) & predk(sK3) & room(sK3)) [choice axiom]
136. ? [X13] : (~predc(X13) & room(X13)) => (~predc(sK4) & room(sK4)) [choice axiom]
137. ? [X15] : (~predb(X15) & predf(X15) & room(X15)) => (~predb(sK5) & predf(sK5) & room(sK5)) [choice axiom]
138. ? [X17] : (~prede(X17) & preda(X17) & room(X17)) => (~prede(sK6) & preda(sK6) & room(sK6)) [choice axiom]
139. ? [X19] : (~predo(X19) | predd(X19) | ~room(X19)) => (~predo(sK7) | predd(sK7) | ~room(sK7)) [choice axiom]
140. ? [X22] : (predo(X22) & ~predm(X22) & room(X22)) => (predo(sK8) & ~predm(sK8) & room(sK8)) [choice axiom]
141. ? [X25] : (predk(X25) & anywhere(X25)) => (predk(sK9) & anywhere(sK9)) [choice axiom]
142. ? [X26] : (~predp(X26) & predk(X26) & room(X26)) => (~predp(sK10) & predk(sK10) & room(sK10)) [choice axiom]
143. (~predn(mary) | ~predm(mary)) & (predn(mary) | predm(mary)) & ! [X0] : (~predf(X0) | ~predg(X0) | ~anywhere(X0)) & ! [X1] : (predg(X1) | predh(X1) | ~room(X1)) & ! [X2] : (~predh(X2) | predk(X2) | ~room(X2)) & ! [X3] : (predk(X3) | ~predf(X3) | ~room(X3)) & predc(mary) & (~predc(mary) | ~predf(mary)) & (predc(mary) | predf(mary)) & ~predn(fred) & predd(fred) & predk(fred) & ! [X4] : (predk(X4) | ~predd(X4) | ~room(X4)) & ! [X5] : (predd(X5) | ~predp(X5) | ~room(X5)) & ~preda(fred) & ~prede(fred) & ! [X6] : (prede(X6) | ~predc(X6) | ~room(X6)) & ~predp(fred) & (predh(sK2) & anywhere(sK2)) & ~predk(mary) & ! [X8] : (predl(X8) | ~predk(X8) | ~room(X8)) & (sP0 | (~predk(sK3) & predk(sK3) & room(sK3))) & (! [X10] : (predk(X10) | ~predk(X10) | ~room(X10)) | ~sP0) & (! [X11] : (predl(X11) | ~room(X11)) | ! [X12] : (~predl(X12) | ~room(X12))) & (((~predb(paul) | ~predp(paul)) & (predb(paul) | predp(paul))) | ~predm(fred)) & (predm(fred) | ((predp(paul) | ~predb(paul)) & (predb(paul) | ~predp(paul)))) & (predn(fred) | (~predc(sK4) & room(sK4))) & (! [X14] : (predc(X14) | ~predb(X14) | ~room(X14)) | (~predb(sK5) & predf(sK5) & room(sK5))) & (! [X16] : (prede(X16) | predd(X16) | ~room(X16)) | ((prede(fred) | ~predk(fred)) & (predk(fred) | ~prede(fred)))) & ((~prede(sK6) & preda(sK6) & room(sK6)) | ! [X18] : (~predo(X18) | ~room(X18))) & (predc(paul) | (~predo(sK7) | predd(sK7) | ~room(sK7))) & (! [X20] : (predb(X20) | ~predm(X20) | ~room(X20)) | ~predb(paul)) & (predb(paul) | ~predf(paul)) & (! [X21] : (predb(X21) | ~predc(X21) | ~room(X21)) | predg(mary)) & (~predg(mary) | ~predn(paul)) & ((predo(sK8) & ~predm(sK8) & room(sK8)) | ! [X23] : (~predk(X23) | ~anywhere(X23))) & (! [X24] : (~predo(X24) | predm(X24) | ~room(X24)) | (predk(sK9) & anywhere(sK9))) & (predg(fred) | (~predp(sK10) & predk(sK10) & room(sK10))) & (! [X27] : (predp(X27) | ~predk(X27) | ~room(X27)) | ! [X28] : (~predo(X28) | predc(X28) | ~room(X28))) & ! [X29] : (john = X29 | alice = X29 | fred = X29 | paul = X29 | mary = X29 | ~room(X29)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 133,142,141,140,139,138,137,136,135,134]
269. ~predk(mary) [cnf transformation 143]
296. predk(mary) [cnf transformation 123]
496. $false [subsumption resolution 296,269]
% SZS output end Proof for 4748045386944404395967343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0.0829 |
There is a room. If “everyone in the room does not have a piercing or collects antique clocks” then “someone in the room practices and performs acrobatic dance routines”. If “everyone in the room is not a wine connoisseur or owns a significant collection of rare gemstones and minerals” then “everyone in the room is not a wine connoisseur only if they is a night owl”. “At least one person in the room works as a freelance web developer specializing in e-commerce sites” if “everyone in the room does not collect vintage stamps or hosts regular workshops on creative writing”. “Everyone outside the room does not play the drums or owns a significant collection of rare gemstones and minerals” only if “if someone collects vintage stamps, enjoys logic puzzles and creates bespoke furniture pieces from reclaimed wood then he/she collects vintage stamps and vice versa”. Everyone in the room who enjoys kayaking and exploring remote waterways and enjoys macrame works as a freelance web developer specializing in e-commerce sites. Everyone in the room collects antique clocks if and only if they owns a significant collection of rare gemstones and minerals. Not everyone in the room who creates bespoke furniture pieces from reclaimed wood hosts regular workshops on creative writing, reads mystery novels or maintains a personal blog focused on cybersecurity tips. No one in the room is not an expert in identifying and foraging wild edible plants or practices and performs acrobatic dance routines. Everyone in the room who is not an expert in identifying and foraging wild edible plants drives a hybrid car. No one in the room who drives a hybrid car is a night owl. Everyone in the room reads mystery novels only if they hosts a popular podcast about emerging technologies. Everyone in the room does not participate in long-distance cycling events across the country or maintains a large, organic vegetable garden year-round. Everyone outside the room does not play the drums or owns a significant collection of rare gemstones and minerals. It is not the case that “more than one person in the room hosts a popular podcast about emerging technologies”. Everyone in the room who hosts regular workshops on creative writing or participates in long-distance cycling events across the country or both collects vintage stamps. Everyone outside the room who owns a significant collection of rare gemstones and minerals collects vintage stamps. Everyone in the room who collects vintage stamps enjoys bird watching. | Everyone in the room does not enjoy bird watching or maintains a large, organic vegetable garden year-round. | neutral | (there_is_a_room)&
((![X]:(room(X)=>(((collects_antique_clocks(X))|(does_not_have_a_piercing(X))))))=>(?[X]:(room(X)&(practices_and_performs_acrobatic_dance_routines(X)))))&
((![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_not_a_wine_connoisseur(X))))))=>(![X]:(room(X)=>(((is_a_night_owl(X))<=(is_not_a_wine_connoisseur(X)))))))&
((![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))|(does_not_collect_vintage_stamps(X))))))=>(((?[X]:(room(X)&works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))&
((![X]:(~room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_play_the_drums(X))))))=>((![X]:((((collects_vintage_stamps(X))&(enjoys_logic_puzzles(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))<=>(collects_vintage_stamps(X))))))&
(![X]:(room(X)=>(((((enjoys_kayaking_and_exploring_remote_waterways(X))&(enjoys_macrame(X))))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))&
(![X]:(room(X)=>(((collects_antique_clocks(X))<=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
(~![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(((hosts_regular_workshops_on_creative_writing(X))|(reads_mystery_novels(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))))&
(~?[X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))&
(![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(drives_a_hybrid_car(X))))))&
(~?[X]:(room(X)=>(((drives_a_hybrid_car(X))=>(is_a_night_owl(X))))))&
(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))<=(reads_mystery_novels(X))))))&
(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))&
(![X]:(~room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_play_the_drums(X))))))&
(~((?[X,Y]:(room(X)&room(Y)&(hosts_a_popular_podcast_about_emerging_technologies(X)&hosts_a_popular_podcast_about_emerging_technologies(Y))&(X!=Y)))))&
(![X]:(room(X)=>(((((hosts_regular_workshops_on_creative_writing(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))=>(collects_vintage_stamps(X))))))&
(![X]:(~room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(collects_vintage_stamps(X))))))&
(![X]:(room(X)=>(((collects_vintage_stamps(X))=>(enjoys_bird_watching(X))))))&
(![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))&
(~![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))&
(![X]:(room(X)=>(((is_a_night_owl(X))<=(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))&
((![X]:((((collects_vintage_stamps(X))&(enjoys_logic_puzzles(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))<=>(collects_vintage_stamps(X))))) | (there_is_a_room)&
![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_enjoy_bird_watching(X))))) | [] | null | 0.135623 |
Laura, Carol are the only persons in the room.
Not everyone in the room who collects rare and antique scientific instruments is not an avid collector of autographed memorabilia from famous musicians.
Everyone in the room is not an avid collector of autographed memorabilia from famous musicians only if they reads mystery novels.
Laura maintains a personal blog focused on cybersecurity tips.
Everyone in the room who regularly contributes to tech forums and online communities practices digital art.
Everyone anywhere collects antique clocks if they practices digital art.
If someone is a scotch connoisseur and practices digital art then he/she is an avid collector of autographed memorabilia from famous musicians.
Everyone in the room enjoys salsa dancing or can play the guitar or both if they plays video games, can play the harmonica or does not participate in long-distance cycling events across the country.
Carol practices calligraphy, hosts regular workshops on creative writing or is an avid collector of autographed memorabilia from famous musicians.
Carol participates in long-distance cycling events across the country.
Carol regularly contributes to tech forums and online communities.
Everyone in the room is a drone photographer if they practices calligraphy.
Everyone in the room practices calligraphy if they collects antique clocks.
Everyone in the room practices calligraphy only if they collects luxury watches. | Carol either does not collect luxury watches or is not a drone photographer but not both. | contradiction | room(laura)&room(carol)&(![X]:(room(X)=>(X='laura'|X='carol')))&
(~![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))&
(![X]:(room(X)=>(((reads_mystery_novels(X))<=(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))&
(maintains_a_personal_blog_focused_on_cybersecurity_tips(laura))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(practices_digital_art(X))))))&
(![X]:(anywhere(X)=>(((practices_digital_art(X))=>(collects_antique_clocks(X))))))&
((![X]:((((is_a_scotch_connoisseur(X))&(practices_digital_art(X))))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))&
(![X]:(room(X)=>(((((plays_video_games(X))|(can_play_the_harmonica(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))=>(((enjoys_salsa_dancing(X))|(can_play_the_guitar(X))))))))&
(((practices_calligraphy(carol))|(hosts_regular_workshops_on_creative_writing(carol))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(carol))))&
(participates_in_long-distance_cycling_events_across_the_country(carol))&
(regularly_contributes_to_tech_forums_and_online_communities(carol))&
(![X]:(room(X)=>(((practices_calligraphy(X))=>(is_a_drone_photographer(X))))))&
(![X]:(room(X)=>(((is_a_drone_photographer(X))=>(collects_rare_and_antique_scientific_instruments(X))))))&
(![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(collects_antique_clocks(X))))))&
(![X]:(room(X)=>(((collects_antique_clocks(X))=>(practices_calligraphy(X))))))&
(![X]:(room(X)=>(((collects_luxury_watches(X))<=(practices_calligraphy(X))))))&
(![X]:(room(X)=>(((is_a_drone_photographer(X))=>(practices_digital_art(X))))))&
(?[X]:(room(X)&(is_a_drone_photographer(X))))&
(![X]:(~room(X)=>(((((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))=>(is_a_drone_photographer(X))))))&
((![X]:((((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(collects_rare_and_antique_scientific_instruments(X))|(practices_digital_art(X))))=>(competes_in_national_level_swimming_championships(X)))))&
(![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(enjoys_salsa_dancing(X))))))&
(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(laura))&(is_a_scotch_connoisseur(laura))&(plays_video_games(laura)))) | room(laura)&room(carol)&(![X]:(room(X)=>(X='laura'|X='carol')))&
((does_not_collect_luxury_watches(carol))<~>(is_not_a_drone_photographer(carol))) | [
"b4",
"p0",
"p4",
"p5",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 132987059413847349798858
% SZS output start Proof for 132987059413847349798858
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
48. ! [X0] : (room(X0) => (predu(X0) => prede(X0))) [input p4]
49. ! [X0] : (anywhere(X0) => (prede(X0) => predy(X0))) [input p5]
54. predu(paul) [input p10]
55. ! [X0] : (room(X0) => (predw(X0) => predd(X0))) [input p11]
58. ! [X0] : (room(X0) => (predy(X0) => predw(X0))) [input p14]
59. ! [X0] : (room(X0) => (predw(X0) => predb(X0))) [input p15]
66. (~predb(paul) <~> ~predd(paul)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
148. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
149. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 148]
151. ! [X0] : ((prede(X0) | ~predu(X0)) | ~room(X0)) [ennf transformation 48]
152. ! [X0] : (prede(X0) | ~predu(X0) | ~room(X0)) [flattening 151]
153. ! [X0] : ((predy(X0) | ~prede(X0)) | ~anywhere(X0)) [ennf transformation 49]
154. ! [X0] : (predy(X0) | ~prede(X0) | ~anywhere(X0)) [flattening 153]
157. ! [X0] : ((predd(X0) | ~predw(X0)) | ~room(X0)) [ennf transformation 55]
158. ! [X0] : (predd(X0) | ~predw(X0) | ~room(X0)) [flattening 157]
161. ! [X0] : ((predw(X0) | ~predy(X0)) | ~room(X0)) [ennf transformation 58]
162. ! [X0] : (predw(X0) | ~predy(X0) | ~room(X0)) [flattening 161]
163. ! [X0] : ((predb(X0) | ~predw(X0)) | ~room(X0)) [ennf transformation 59]
164. ! [X0] : (predb(X0) | ~predw(X0) | ~room(X0)) [flattening 163]
167. (~predb(paul) <~> ~predd(paul)) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 66]
168. (~predb(paul) <~> ~predd(paul)) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 167]
174. ((predd(paul) | predb(paul)) & (~predd(paul) | ~predb(paul))) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [nnf transformation 168]
175. (predd(paul) | predb(paul)) & (~predd(paul) | ~predb(paul)) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 174]
176. anywhere(X0) [cnf transformation 5]
258. room(paul) [cnf transformation 149]
262. ~predu(X0) | prede(X0) | ~room(X0) [cnf transformation 152]
263. predy(X0) | ~prede(X0) | ~anywhere(X0) [cnf transformation 154]
266. predu(paul) [cnf transformation 54]
267. ~predw(X0) | predd(X0) | ~room(X0) [cnf transformation 158]
269. ~predy(X0) | predw(X0) | ~room(X0) [cnf transformation 162]
270. ~predw(X0) | predb(X0) | ~room(X0) [cnf transformation 164]
279. ~predd(paul) | ~predb(paul) [cnf transformation 175]
281. ~prede(X0) | predy(X0) [subsumption resolution 263,176]
283. 1 <=> predw(paul) [avatar definition]
285. predw(paul) <- (1) [avatar component clause 283]
296. 4 <=> predb(paul) [avatar definition]
297. ~predb(paul) <- (~4) [avatar component clause 296]
300. 5 <=> predd(paul) [avatar definition]
304. ~4 | ~5 [avatar split clause 279,300,296]
305. prede(paul) | ~room(paul) [resolution 262,266]
306. prede(paul) [subsumption resolution 305,258]
309. predy(paul) [resolution 306,281]
311. predw(paul) | ~room(paul) [resolution 269,309]
312. predw(paul) [subsumption resolution 311,258]
313. 1 [avatar split clause 312,283]
314. predd(paul) | ~room(paul) <- (1) [resolution 285,267]
318. predd(paul) <- (1) [subsumption resolution 314,258]
319. 5 | ~1 [avatar split clause 318,283,300]
320. predb(paul) | ~room(paul) <- (1) [resolution 270,285]
321. ~room(paul) <- (1, ~4) [subsumption resolution 320,297]
322. $false <- (1, ~4) [subsumption resolution 321,258]
323. ~1 | 4 [avatar contradiction clause 322]
324. $false [avatar sat refutation 304,313,319,323]
% SZS output end Proof for 132987059413847349798858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.191447 |
Lisa is the only person in the room.
'Everyone in the room is an avid hiker or does not own a smartwatch' if 'everyone in the room is not a certified yoga instructor teaching classes weekly or has a vast collection of first-edition science fiction novels'.
If 'everyone in the room is allergic to anything or does not create large-scale murals for public art installations' then 'if someone is a certified yoga instructor teaching classes weekly then he/she is a client of LVMH'.
It is not the case that 'at least one person in the room collects classic novels'.
Everyone anywhere who enjoys macrame is allergic to anything.
More than one person outside the room owns an extensive assortment of vintage comic book memorabilia.
Everyone anywhere who enjoys camping and organizing outdoor survival workshops develops open-source software projects in their free time.
Lisa has a vast collection of first-edition science fiction novels.
If someone is a certified yoga instructor teaching classes weekly then he/she is a client of LVMH.
Lisa is an expert in identifying and foraging wild edible plants.
Everyone outside the room makes homemade pastries if they is an expert in identifying and foraging wild edible plants. | Lisa collects classic novels. | contradiction | room(lisa)&(![X]:(room(X)=>(X='lisa')))&
((![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((does_not_own_a_smartwatch(X))|(is_an_avid_hiker(X)))))))&
((![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))|(is_allergic_to_anything(X))))))=>((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_client_of_LVMH(X))))))&
(~(((?[X]:(room(X)&collects_classic_novels(X))))))&
(![X]:(anywhere(X)=>(((enjoys_macrame(X))=>(is_allergic_to_anything(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)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(has_a_vast_collection_of_first-edition_science_fiction_novels(lisa))&
((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_client_of_LVMH(X)))))&
(is_an_expert_in_identifying_and_foraging_wild_edible_plants(lisa))&
(![X]:(~room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(makes_homemade_pastries(X)))))) | room(lisa)&(![X]:(room(X)=>(X='lisa')))&
collects_classic_novels(lisa) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1400192557836015170839464
% SZS output start Proof for 1400192557836015170839464
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
47. ~? [X0] : (predw(X0) & room(X0)) [input p3]
55. predw(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
141. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
142. ! [X0] : (~predw(X0) | ~room(X0)) [ennf transformation 47]
143. predw(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 55]
227. room(mary) [cnf transformation 141]
229. ~predw(X0) | ~room(X0) [cnf transformation 142]
235. predw(mary) [cnf transformation 143]
236. ~room(mary) [resolution 229,235]
237. $false [subsumption resolution 236,227]
% SZS output end Proof for 1400192557836015170839464
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.026835 |
Sonny, Ruth, Anthony are the only persons in the room. Either “no one in the room either is a certified yoga instructor teaching classes weekly or does not use an ios phone but not both” or “Sonny collects luxury watches” but not both. “Sonny neither does not use an ios phone nor does not collect luxury watches” if “everyone anywhere collects luxury watches and does not use an ios phone”. If “someone in the room does not write poetry” then “everyone anywhere either collects luxury watches or does not write poetry but not both” otherwise “Sonny who does not own a high-end gaming PC with custom-built components and does not collect luxury watches does not use an ios phone or is not a chess master who participates in national tournaments or both”. “Everyone in the room is not a certified yoga instructor teaching classes weekly” only if “everyone in the room does not write poetry, is a certified yoga instructor teaching classes weekly or is not a certified yoga instructor teaching classes weekly”. Someone outside the room does not write poetry. | Everyone outside the room writes poetry. | contradiction | room(sonny)&room(ruth)&room(anthony)&(![X]:(room(X)=>(X='sonny'|X='ruth'|X='anthony')))&
((~?[X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<~>(does_not_use_an_ios_phone(X))))))<~>(collects_luxury_watches(sonny)))&
((![X]:(anywhere(X)=>(((collects_luxury_watches(X))&(does_not_use_an_ios_phone(X))))))=>(~((does_not_use_an_ios_phone(sonny))|(does_not_collect_luxury_watches(sonny)))))&
(((?[X]:(room(X)&(does_not_write_poetry(X))))=>(![X]:(anywhere(X)=>(((collects_luxury_watches(X))<~>(does_not_write_poetry(X)))))))&((~(?[X]:(room(X)&(does_not_write_poetry(X)))))=>((((does_not_own_a_high-end_gaming_PC_with_custom-built_components(sonny))&(does_not_collect_luxury_watches(sonny))))&(((does_not_use_an_ios_phone(sonny))|(is_not_a_chess_master_who_participates_in_national_tournaments(sonny)))))))&
((![X]:(room(X)=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))=>(![X]:(room(X)=>(((does_not_write_poetry(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))&
((((?[X]:(room(X)&does_not_use_an_ios_phone(X)))))=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(sonny))|(is_not_a_chess_master_who_participates_in_national_tournaments(sonny))|(does_not_use_an_ios_phone(sonny)))))&
(?[X]:(~room(X)&(does_not_write_poetry(X))))&
(![X]:(room(X)=>(((~((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_collect_luxury_watches(X))))<=(((does_not_use_an_ios_phone(X))|(collects_luxury_watches(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))))&
(?[X]:(anywhere(X)&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))&
((((does_not_use_an_ios_phone(sonny))<~>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(sonny))))&(((is_a_chess_master_who_participates_in_national_tournaments(sonny))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(sonny))|(does_not_use_an_ios_phone(sonny)))))&
(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(sonny))|(is_not_a_chess_master_who_participates_in_national_tournaments(sonny))|(does_not_use_an_ios_phone(sonny)))) | room(sonny)&room(ruth)&room(anthony)&(![X]:(room(X)=>(X='sonny'|X='ruth'|X='anthony')))&
![X]:(~room(X)=>(writes_poetry(X))) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 853501082606667043034075
% SZS output start Proof for 853501082606667043034075
50. ? [X0] : (~prede(X0) & ~room(X0)) [input p6]
55. ! [X0] : (~room(X0) => prede(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
58. ! [X0] : (~room(X0) => prede(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 55]
141. ! [X0] : (prede(X0) | room(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 58]
142. ! [X0] : (prede(X0) | room(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 141]
158. ? [X0] : (~prede(X0) & ~room(X0)) => (~prede(sK4) & ~room(sK4)) [choice axiom]
159. ~prede(sK4) & ~room(sK4) [skolemisation 50,158]
269. ~room(sK4) [cnf transformation 159]
270. ~prede(sK4) [cnf transformation 159]
287. prede(X0) | room(X0) [cnf transformation 142]
384. room(sK4) [resolution 287,270]
386. $false [subsumption resolution 384,269]
% SZS output end Proof for 853501082606667043034075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0.082035 |
There is a room.
If “someone outside the room is a member of a local theater group specializing in improv” then “at least one person in the room is a chess master who participates in national tournaments”.
“Everyone in the room can play the flute if they does not enjoy trail running” if “everyone in the room does not enjoy trail running or does enjoy trail running”.
Everyone in the room either can play the flute or collects antique jewelry but not both.
At least one person in the room does enjoy trail running.
Everyone in the room owns a 3D printer, does enjoy trail running or does not collect luxury watches.
If someone owns a 3D printer, collects luxury watches and is a chess master who participates in national tournaments then he/she can play the flute and vice versa.
Everyone in the room who is not a chess master who participates in national tournaments owns a 3D printer.
If someone does enjoy trail running then he/she plays the violin and vice versa.
Everyone outside the room plays the violin if they does not host regular game nights featuring complex strategy games.
If someone does enjoy trail running then he/she hosts regular game nights featuring complex strategy games and vice versa.
Everyone outside the room either is passionate about collecting and restoring classic cars or owns a 3D printer but not both if they is a chess master who participates in national tournaments.
Everyone in the room does enjoy trail running if they collects antique jewelry and vice versa.
Everyone in the room is not a chess master who participates in national tournaments or plays the violin.
Someone outside the room can play the flute.
Everyone in the room is a member of a local theater group specializing in improv.
Everyone in the room does not host regular game nights featuring complex strategy games or does not own a 3D printer. | Everyone in the room is a chess master who participates in national tournaments. | entailment | (there_is_a_room)&
((?[X]:(~room(X)&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(((?[X]:(room(X)&is_a_chess_master_who_participates_in_national_tournaments(X))))))&
((![X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_enjoy_trail_running(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_trail_running(X))=>(can_play_the_flute(X)))))))&
(![X]:(room(X)=>(((can_play_the_flute(X))<~>(collects_antique_jewelry(X))))))&
(((?[X]:(room(X)&does_enjoy_trail_running(X)))))&
(![X]:(room(X)=>(((owns_a_3D_printer(X))|(does_enjoy_trail_running(X))|(does_not_collect_luxury_watches(X))))))&
((![X]:((((owns_a_3D_printer(X))&(collects_luxury_watches(X))&(is_a_chess_master_who_participates_in_national_tournaments(X))))<=>(can_play_the_flute(X)))))&
(![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))=>(owns_a_3D_printer(X))))))&
((![X]:((does_enjoy_trail_running(X))<=>(plays_the_violin(X)))))&
(![X]:(~room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))=>(plays_the_violin(X))))))&
((![X]:((does_enjoy_trail_running(X))<=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))&
(![X]:(~room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))<~>(owns_a_3D_printer(X))))))))&
(![X]:(room(X)=>(((does_enjoy_trail_running(X))<=>(collects_antique_jewelry(X))))))&
(![X]:(room(X)=>(((plays_the_violin(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))&
(?[X]:(~room(X)&(can_play_the_flute(X))))&
(![X]:(room(X)=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))&
(~(?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X)))))&
(![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))&
(~![X]:(room(X)=>(((does_not_collect_luxury_watches(X))|(does_not_collect_antique_jewelry(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_trail_running(X))=>(can_play_the_flute(X))))))&
(((?[X]:(room(X)&is_a_chess_master_who_participates_in_national_tournaments(X)))))&
(![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(does_enjoy_trail_running(X)))))))) | (there_is_a_room)&
![X]:(room(X)=>(is_a_chess_master_who_participates_in_national_tournaments(X))) | [
"p0",
"p3",
"p6",
"p7",
"p10",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8881201378080845047505990
% SZS output start Proof for 8881201378080845047505990
44. there_is_a_room [input p0]
47. ! [X0] : (room(X0) => (predf(X0) <~> prede(X0))) [input p3]
50. ! [X0] : ((predc(X0) & predb(X0) & predk(X0)) <=> predf(X0)) [input p6]
51. ! [X0] : (room(X0) => (~predc(X0) => predk(X0))) [input p7]
54. ! [X0] : (predi(X0) <=> preda(X0)) [input p10]
56. ! [X0] : (room(X0) => (predi(X0) <=> prede(X0))) [input p12]
61. ! [X0] : (room(X0) => (~preda(X0) | ~predk(X0))) [input p17]
66. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis]
144. ! [X0] : ((predf(X0) <~> prede(X0)) | ~room(X0)) [ennf transformation 47]
147. ! [X0] : ((predk(X0) | predc(X0)) | ~room(X0)) [ennf transformation 51]
148. ! [X0] : (predk(X0) | predc(X0) | ~room(X0)) [flattening 147]
153. ! [X0] : ((predi(X0) <=> prede(X0)) | ~room(X0)) [ennf transformation 56]
158. ! [X0] : ((~preda(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 61]
159. ! [X0] : (~preda(X0) | ~predk(X0) | ~room(X0)) [flattening 158]
166. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 66]
174. ! [X0] : (((~prede(X0) | ~predf(X0)) & (prede(X0) | predf(X0))) | ~room(X0)) [nnf transformation 144]
177. ! [X0] : (((predc(X0) & predb(X0) & predk(X0)) | ~predf(X0)) & (predf(X0) | (~predc(X0) | ~predb(X0) | ~predk(X0)))) [nnf transformation 50]
178. ! [X0] : (((predc(X0) & predb(X0) & predk(X0)) | ~predf(X0)) & (predf(X0) | ~predc(X0) | ~predb(X0) | ~predk(X0))) [flattening 177]
180. ! [X0] : ((predi(X0) | ~preda(X0)) & (preda(X0) | ~predi(X0))) [nnf transformation 54]
182. ! [X0] : (((predi(X0) | ~prede(X0)) & (prede(X0) | ~predi(X0))) | ~room(X0)) [nnf transformation 153]
189. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK6) & room(sK6)) [choice axiom]
190. (~predc(sK6) & room(sK6)) | ~there_is_a_room [skolemisation 166,189]
271. there_is_a_room [cnf transformation 44]
277. ~room(X0) | predf(X0) | prede(X0) [cnf transformation 174]
285. ~predf(X0) | predc(X0) [cnf transformation 178]
286. ~room(X0) | predc(X0) | predk(X0) [cnf transformation 148]
290. ~predi(X0) | preda(X0) [cnf transformation 180]
295. ~prede(X0) | predi(X0) | ~room(X0) [cnf transformation 182]
301. ~preda(X0) | ~predk(X0) | ~room(X0) [cnf transformation 159]
309. room(sK6) | ~there_is_a_room [cnf transformation 190]
310. ~predc(sK6) | ~there_is_a_room [cnf transformation 190]
339. ~predc(sK6) [subsumption resolution 310,271]
340. room(sK6) [subsumption resolution 309,271]
357. predf(sK6) | prede(sK6) [resolution 277,340]
386. 13 <=> prede(sK6) [avatar definition]
388. prede(sK6) <- (13) [avatar component clause 386]
390. 14 <=> predf(sK6) [avatar definition]
392. predf(sK6) <- (14) [avatar component clause 390]
393. 13 | 14 [avatar split clause 357,390,386]
401. predc(sK6) | predk(sK6) [resolution 286,340]
420. predk(sK6) [subsumption resolution 401,339]
453. 19 <=> predi(sK6) [avatar definition]
455. predi(sK6) <- (19) [avatar component clause 453]
457. predi(sK6) | ~room(sK6) <- (13) [resolution 388,295]
459. predi(sK6) <- (13) [subsumption resolution 457,340]
460. 19 | ~13 [avatar split clause 459,386,453]
471. predc(sK6) <- (14) [resolution 392,285]
474. $false <- (14) [subsumption resolution 471,339]
475. ~14 [avatar contradiction clause 474]
521. preda(sK6) <- (19) [resolution 455,290]
558. ~predk(sK6) | ~room(sK6) <- (19) [resolution 521,301]
560. ~room(sK6) <- (19) [subsumption resolution 558,420]
561. $false <- (19) [subsumption resolution 560,340]
562. ~19 [avatar contradiction clause 561]
563. $false [avatar sat refutation 393,460,475,562]
% SZS output end Proof for 8881201378080845047505990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.245324 |
Isaiah is the only person in the room.
'Isaiah enjoys skydiving' if 'Isaiah does not collect rare minerals'.
'Isaiah is dedicated to sustainable living and zero-waste practices, frequently participates in hackathons and coding competitions and own a television' unless 'at least one person in the room composes and performs experimental electronic music, is an enthusiastic bird watcher who travels for rare sightings and is a Linux enthusiast'.
Either 'someone outside the room is a certified scuba diver with advanced underwater photography skills' or 'Isaiah uses an ios phone' but not both.
If 'Isaiah composes and performs experimental electronic music' then 'it is not the case that 'more than one person in the room collects rare minerals''.
Isaiah who is a drone photographer writes in-depth travel guides for off-the-beaten-path destinations.
It is not the case that 'more than one person in the room collects rare minerals'.
Isaiah collects vintage vinyl records.
Isaiah uses contact lenses.
Isaiah who is a Linux enthusiast enjoys salsa dancing.
Isaiah who collect rare sneakers does not collect rare minerals. | Isaiah is dedicated to sustainable living and zero-waste practices. | neutral | room(isaiah)&(![X]:(room(X)=>(X='isaiah')))&
((does_not_collect_rare_minerals(isaiah))=>(enjoys_skydiving(isaiah)))&
(~(((?[X]:(room(X)&((composes_and_performs_experimental_electronic_music(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_a_Linux_enthusiast(X)))))))=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(isaiah))&(frequently_participates_in_hackathons_and_coding_competitions(isaiah))&(own_a_television(isaiah)))))&
((?[X]:(~room(X)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))<~>(uses_an_ios_phone(isaiah)))&
((composes_and_performs_experimental_electronic_music(isaiah))=>(~((?[X,Y]:(room(X)&room(Y)&(collects_rare_minerals(X)&collects_rare_minerals(Y))&(X!=Y))))))&
((is_a_drone_photographer(isaiah))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(isaiah)))&
(~((?[X,Y]:(room(X)&room(Y)&(collects_rare_minerals(X)&collects_rare_minerals(Y))&(X!=Y)))))&
(collects_vintage_vinyl_records(isaiah))&
(uses_contact_lenses(isaiah))&
((is_a_Linux_enthusiast(isaiah))&(enjoys_salsa_dancing(isaiah)))&
((collect_rare_sneakers(isaiah))&(does_not_collect_rare_minerals(isaiah))) | room(isaiah)&(![X]:(room(X)=>(X='isaiah')))&
is_dedicated_to_sustainable_living_and_zero-waste_practices(isaiah) | [] | null | 0.128132 |
Barbara, Leonardo are the only persons in the room.
“Leonardo is older than Melody” unless “Barbara is quieter than Melody”.
If “Barbara is a kind patient person” then “it is not the case that “Barbara is a curious tall quiet person””.
If “Barbara is a patient quiet tall creative curious person” then “someone who is quieter than Douglas is quieter than someone who is richer than Melody”.
If “Leonardo is older than Melody” then “Barbara is the least quiet in the room”.
“Leonardo and Barbara are respectively quiet and humble” unless “Barbara is a old creative person”.
It is not the case that “Leonardo is quieter than Melody”.
No humble person is happy.
Leonardo is a funny curious person.
Leonardo is strong.
Douglas is quieter than Leonardo.
Someone who is calm is richer than someone who is quieter than Douglas. | All calm persons are humble. | entailment | room(barbara)&room(leonardo)&(![X]:(room(X)=>(X='barbara'|X='leonardo')))&
(~(quieter(melody,barbara))=>(older(melody,leonardo)))&
((kind(barbara)&patient(barbara)&person(barbara))=>(~(curious(barbara)&tall(barbara)&quiet(barbara)&person(barbara))))&
((patient(barbara)&quiet(barbara)&tall(barbara)&creative(barbara)&curious(barbara)&person(barbara))=>(?[X,Y]:((quieter(douglas,X))&(richer(melody,Y))&(quieter(X,Y)))))&
((older(melody,leonardo))=>(![X]:((room(X)&(X!=barbara))=>quieter(barbara,X))))&
(~(old(barbara)&creative(barbara)&person(barbara))=>((quiet(leonardo))&(humble(barbara))))&
(~(quieter(melody,leonardo)))&
(~?[X]:(humble(X)=>happy(X)))&
(funny(leonardo)&curious(leonardo)&person(leonardo))&
(strong(leonardo))&
(quieter(leonardo,douglas))&
(?[X,Y]:((calm(X))&(quieter(douglas,Y))&(richer(X,Y))))&
(richer(melody,leonardo))&
(quieter(barbara,melody))&
(![X]:(curious(X)=>funny(X)))&
(![X]:(old(X)=>creative(X)))&
(richer(barbara,douglas)) | room(barbara)&room(leonardo)&(![X]:(room(X)=>(X='barbara'|X='leonardo')))&
![X]:(calm(X)=>humble(X)) | [
"p0",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2889335743647917441588000
% SZS output start Proof for 2889335743647917441588000
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
51. ~? [X0] : (humble(X0) => happy(X0)) [input p7]
61. ~(! [X0] : (calm(X0) => humble(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
62. ~(! [X0] : (calm(X0) => humble(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary)) [rectify 61]
64. ~(! [X0] : humble(X0) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary)) [pure predicate removal 62]
68. ~? [X0] : ~humble(X0) [pure predicate removal 51]
148. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
149. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 148]
154. ! [X0] : humble(X0) [ennf transformation 68]
155. ? [X0] : ~humble(X0) | ? [X1] : ((paul != X1 & mary != X1) & room(X1)) | ~room(paul) | ~room(mary) [ennf transformation 64]
156. ? [X0] : ~humble(X0) | ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~room(paul) | ~room(mary) [flattening 155]
160. ? [X0] : ~humble(X0) => ~humble(sK2) [choice axiom]
161. ? [X1] : (paul != X1 & mary != X1 & room(X1)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
162. ~humble(sK2) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 156,161,160]
243. room(mary) [cnf transformation 149]
244. room(paul) [cnf transformation 149]
245. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 149]
251. humble(X0) [cnf transformation 154]
258. ~humble(sK2) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 162]
259. ~humble(sK2) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 162]
260. ~humble(sK2) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 162]
288. paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 260,251]
289. paul != sK3 | ~room(mary) [subsumption resolution 288,244]
290. paul != sK3 [subsumption resolution 289,243]
291. mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 259,251]
292. mary != sK3 | ~room(mary) [subsumption resolution 291,244]
293. mary != sK3 [subsumption resolution 292,243]
294. room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 258,251]
295. room(sK3) | ~room(mary) [subsumption resolution 294,244]
296. room(sK3) [subsumption resolution 295,243]
299. mary = sK3 | paul = sK3 [resolution 245,296]
300. paul = sK3 [subsumption resolution 299,293]
301. $false [subsumption resolution 300,290]
% SZS output end Proof for 2889335743647917441588000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.318349 |
Charles is the only person in the room.
If “Charles writes a travel blog” then “it is not the case that “it is not the case that “Charles writes a travel blog”””.
If “Charles does not collect foreign coins” then “someone in the room uses contact lenses”.
“It is not the case that “someone in the room writes and illustrates their own graphic novels”” if “it is not the case that “Charles enjoys macrame”” and vice versa.
If “Charles has lived in exactly three countries” then “Charles who participates in long-distance cycling events across the country is passionate about collecting and restoring classic cars”.
“Not everyone in the room is not passionate about collecting and restoring classic cars or does not practice graffiti art” if “it is not the case that “Charles does not play video games”” and vice versa.
If someone uses an ios phone then he/she practices zumba and vice versa.
Charles collects foreign coins.
Not everyone anywhere has completed a triathlon if they uses an ios phone.
It is not the case that “it is not the case that “Charles practices zumba””.
It is not the case that “at least one person outside the room owns a telescope”.
Charles is passionate about collecting and restoring classic cars.
Charles collects antique jewelry.
Charles collects action figures. | Charles enjoys macrame. | neutral | room(charles)&(![X]:(room(X)=>(X='charles')))&
((writes_a_travel_blog(charles))=>(~(~(writes_a_travel_blog(charles)))))&
((does_not_collect_foreign_coins(charles))=>(?[X]:(room(X)&(uses_contact_lenses(X)))))&
((~(enjoys_macrame(charles)))<=>(~(?[X]:(room(X)&(writes_and_illustrates_their_own_graphic_novels(X))))))&
((has_lived_in_exactly_three_countries(charles))=>((participates_in_long-distance_cycling_events_across_the_country(charles))&(is_passionate_about_collecting_and_restoring_classic_cars(charles))))&
((~(does_not_play_video_games(charles)))<=>(~![X]:(room(X)=>(((does_not_practice_graffiti_art(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X)))))))&
((![X]:((uses_an_ios_phone(X))<=>(practices_zumba(X)))))&
(collects_foreign_coins(charles))&
(~![X]:(anywhere(X)=>(((uses_an_ios_phone(X))=>(has_completed_a_triathlon(X))))))&
(~(~(practices_zumba(charles))))&
(~(((?[X]:(~room(X)&owns_a_telescope(X))))))&
(is_passionate_about_collecting_and_restoring_classic_cars(charles))&
(collects_antique_jewelry(charles))&
(collects_action_figures(charles))&
(has_completed_a_triathlon(charles))&
((participates_in_long-distance_cycling_events_across_the_country(charles))&(is_passionate_about_collecting_and_restoring_classic_cars(charles)))&
(uses_contact_lenses(charles))&
(?[X]:(room(X)&(does_not_volunteer_for_local_environmental_conservation_projects(X))))&
((![X]:((~((collects_antique_clocks(X))|(volunteers_for_local_environmental_conservation_projects(X))))=>(plays_the_drums(X)))))&
(~(~(collects_antique_jewelry(charles))))&
(~![X]:(room(X)=>(((does_not_practice_graffiti_art(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X)))))) | room(charles)&(![X]:(room(X)=>(X='charles')))&
enjoys_macrame(charles) | [] | null | 0.095314 |
Earl, David are the only persons in the room. Everyone in the room does not have a curated collection of mid-century modern furniture, does not collect vintage stamps and does not enjoy spelunking. Earl does not collect vintage stamps and does not compete in national level swimming championships. Not everyone in the room does not compete in national level swimming championships. Earl does not compete in national level swimming championships. David who does not enjoy spelunking, does not collect vintage stamps and does not have a curated collection of mid-century modern furniture does not collect vintage stamps and does not have a curated collection of mid-century modern furniture. Everyone outside the room does not have a curated collection of mid-century modern furniture. David cannot play the harmonica. | Earl can play the harmonica. | neutral | room(earl)&room(david)&(![X]:(room(X)=>(X='earl'|X='david')))&
(![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))&(does_not_collect_vintage_stamps(X))&(does_not_enjoy_spelunking(X))))))&
(((does_not_collect_vintage_stamps(earl))&(does_not_compete_in_national_level_swimming_championships(earl))))&
(~![X]:(room(X)=>(does_not_compete_in_national_level_swimming_championships(X))))&
(does_not_compete_in_national_level_swimming_championships(earl))&
((((does_not_enjoy_spelunking(david))&(does_not_collect_vintage_stamps(david))&(does_not_have_a_curated_collection_of_mid-century_modern_furniture(david))))&(((does_not_collect_vintage_stamps(david))&(does_not_have_a_curated_collection_of_mid-century_modern_furniture(david)))))&
(![X]:(~room(X)=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))&
(cannot_play_the_harmonica(david)) | room(earl)&room(david)&(![X]:(room(X)=>(X='earl'|X='david')))&
can_play_the_harmonica(earl) | [] | null | 0.22085 |
Neither “A pizza does not exist that tastes like ice cream.” nor “A bird does not tweet using morse code.”.
“Mirrors do not fog permanently in one particular house.” or “A shadow does not appear only at noon.” but not both.
“A shadow does not appear only at noon.” or “A bird tweets using morse code.” but not both. | Mirrors fog permanently in one particular house. | contradiction | room(lara)&room(paulaa)&room(paul)&(![X]:(room(X)=>(X='lara'|X='paulaa'|X='paul')))&
((![X]:(room(X)=>(makes_homemade_pastries(X))))<~>(~?[X]:(room(X)=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))&
((![X]:((enjoys_kayaking(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))&
(~((A_pizza_does_not_exist_that_tastes_like_ice_cream.)|(A_bird_does_not_tweet_using_morse_code.)))&
(((A_book_can_be_opened_only_at_midnight.)|(A_pizza_does_not_exist_that_tastes_like_ice_cream.)))&
((![X]:((makes_homemade_pastries(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))&
(![X]:(room(X)=>(hosts_a_popular_podcast_about_emerging_technologies(X))))&
(((Mirrors_do_not_fog_permanently_in_one_particular_house.)<~>(A_shadow_does_not_appear_only_at_noon.)))&
((lara_dream=>(![X]:(anywhere(X)=>(makes_homemade_pastries(X))))))&
(![X]:(room(X)=>(makes_homemade_pastries(X))))&
((![X]:((enjoys_kayaking(X))=>(makes_homemade_pastries(X)))))&
((enjoys_kayaking(paul))&(makes_homemade_pastries(paul)))&
(((A_shadow_does_not_appear_only_at_noon.)<~>(A_bird_tweets_using_morse_code.)))&
(((A_bird_tweets_using_morse_code.)<~>(A_bird_does_not_tweet_using_morse_code.)))&
(![X]:(room(X)=>(enjoys_kayaking(X))))&
(![X]:(~room(X)=>(enjoys_kayaking(X)))) | room(lara)&room(paulaa)&room(paul)&(![X]:(room(X)=>(X='lara'|X='paulaa'|X='paul')))&
Mirrors_fog_permanently_in_one_particular_house. | [
"p3",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3450007642922410837343470
% SZS output start Proof for 3450007642922410837343470
47. ~(~propositiond | ~propositiona) [input p3]
51. ~propositionc <~> ~propositione [input p7]
56. ~propositione <~> propositiond [input p12]
60. propositionc & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
65. ~~propositiond [pure predicate removal 47]
141. propositiond [ennf transformation 65]
148. propositionc & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 60]
149. propositionc & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 148]
156. (propositione | propositionc) & (~propositione | ~propositionc) [nnf transformation 51]
157. (~propositiond | propositione) & (propositiond | ~propositione) [nnf transformation 56]
248. propositiond [cnf transformation 141]
251. ~propositione | ~propositionc [cnf transformation 156]
258. ~propositiond | propositione [cnf transformation 157]
267. propositionc [cnf transformation 149]
298. 8 <=> propositionc [avatar definition]
302. 9 <=> propositione [avatar definition]
306. ~8 | ~9 [avatar split clause 251,302,298]
308. propositione [subsumption resolution 258,248]
309. 9 [avatar split clause 308,302]
311. 8 [avatar split clause 267,298]
312. $false [avatar sat refutation 306,309,311]
% SZS output end Proof for 3450007642922410837343470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.712436 |
There is a room. “Everyone in the room collects rare minerals or does not collect historical artifacts related to ancient civilizations” if “everyone in the room does not practice graffiti art or volunteers for local environmental conservation projects” and vice versa. Either “no one in the room does practice yoga or does not collect classic novels” or “no one in the room collects foreign coins or does not practice digital art” but not both. Either “everyone in the room does not have a saltwater aquarium or does not collect foreign coins” or “everyone outside the room does not enjoy fishing or does practice yoga” but not both. “No one in the room who collects rare minerals practices graffiti art or does not mentor a youth basketball team on weekends or both” unless “someone in the room is a client of Costco”. Either “everyone in the room collects classic novels or does not collect classic novels” or “everyone in the room volunteers for local environmental conservation projects or does not collect foreign coins” but not both. Everyone in the room volunteers for local environmental conservation projects if they practices digital art and vice versa. Everyone in the room does not have a saltwater aquarium if they practices digital art. Everyone in the room who does not have a saltwater aquarium is a craft beer aficionado. Not everyone in the room practices digital art if they is a craft beer aficionado. Everyone in the room who has a saltwater aquarium collects historical artifacts related to ancient civilizations, volunteers for local environmental conservation projects or collects vintage stamps. Not everyone in the room who collects vintage stamps has a saltwater aquarium, practices digital art and does not volunteer for local environmental conservation projects. If someone collects classic novels then he/she enjoys fishing and vice versa. If someone enjoys fishing then he/she is a drone photographer. Someone in the room practices graffiti art. Everyone in the room is a client of Costco if they collects vintage stamps. At least one person in the room enjoys origami. Everyone in the room mentors a youth basketball team on weekends if they collects rare minerals or collects classic novels or both and vice versa. If someone mentors a youth basketball team on weekends then he/she collects foreign coins and vice versa. | Everyone in the room does not enjoy origami or mentors a youth basketball team on weekends. | entailment | (there_is_a_room)&
((![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))|(does_not_practice_graffiti_art(X))))))<=>(![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(collects_rare_minerals(X)))))))&
((~?[X]:(room(X)=>(((does_not_collect_classic_novels(X))|(does_practice_yoga(X))))))<~>(~?[X]:(room(X)=>(((does_not_practice_digital_art(X))|(collects_foreign_coins(X)))))))&
((![X]:(room(X)=>(((does_not_collect_foreign_coins(X))|(does_not_have_a_saltwater_aquarium(X))))))<~>(![X]:(~room(X)=>(((does_practice_yoga(X))|(does_not_enjoy_fishing(X)))))))&
(~(?[X]:(room(X)&(is_a_client_of_Costco(X))))=>(~?[X]:(room(X)=>(((collects_rare_minerals(X))=>(((practices_graffiti_art(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))))))&
((![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(collects_classic_novels(X))))))<~>(![X]:(room(X)=>(((does_not_collect_foreign_coins(X))|(volunteers_for_local_environmental_conservation_projects(X)))))))&
(![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))<=>(practices_digital_art(X))))))&
(![X]:(room(X)=>(((practices_digital_art(X))=>(does_not_have_a_saltwater_aquarium(X))))))&
(![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))=>(is_a_craft_beer_aficionado(X))))))&
(~![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(practices_digital_art(X))))))&
(![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(volunteers_for_local_environmental_conservation_projects(X))|(collects_vintage_stamps(X))))))))&
(~![X]:(room(X)=>(((collects_vintage_stamps(X))=>(((has_a_saltwater_aquarium(X))&(practices_digital_art(X))&(does_not_volunteer_for_local_environmental_conservation_projects(X))))))))&
((![X]:((collects_classic_novels(X))<=>(enjoys_fishing(X)))))&
((![X]:((enjoys_fishing(X))=>(is_a_drone_photographer(X)))))&
(?[X]:(room(X)&(practices_graffiti_art(X))))&
(![X]:(room(X)=>(((collects_vintage_stamps(X))=>(is_a_client_of_Costco(X))))))&
(((?[X]:(room(X)&enjoys_origami(X)))))&
(![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))<=>(((collects_rare_minerals(X))|(collects_classic_novels(X))))))))&
((![X]:((mentors_a_youth_basketball_team_on_weekends(X))<=>(collects_foreign_coins(X))))) | (there_is_a_room)&
![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(does_not_enjoy_origami(X))))) | [
"p0",
"p2",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2609163956776470411214066
% SZS output start Proof for 2609163956776470411214066
44. there_is_a_room [input p0]
46. ~? [X0] : (room(X0) => (predr(X0) | ~predg(X0))) <~> ~? [X0] : (room(X0) => (prede(X0) | ~predq(X0))) [input p2]
53. ~! [X0] : (room(X0) => (predm(X0) => predq(X0))) [input p9]
61. ! [X0] : (room(X0) => (predj(X0) <=> (predg(X0) | predi(X0)))) [input p17]
63. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis]
65. ~? [X0] : (room(X0) => (predr(X0) | ~predg(X0))) <~> ~? [X1] : (room(X1) => (prede(X1) | ~predq(X1))) [rectify 46]
69. ~(! [X0] : (room(X0) => predj(X0)) & there_is_a_room) [pure predicate removal 63]
73. ~! [X0] : (room(X0) => predq(X0)) [pure predicate removal 53]
152. ! [X0] : ((~predr(X0) & predg(X0)) & room(X0)) <~> ! [X1] : ((~prede(X1) & predq(X1)) & room(X1)) [ennf transformation 65]
153. ! [X0] : (~predr(X0) & predg(X0) & room(X0)) <~> ! [X1] : (~prede(X1) & predq(X1) & room(X1)) [flattening 152]
163. ? [X0] : (~predq(X0) & room(X0)) [ennf transformation 73]
165. ! [X0] : ((predj(X0) <=> (predg(X0) | predi(X0))) | ~room(X0)) [ennf transformation 61]
166. ? [X0] : (~predj(X0) & room(X0)) | ~there_is_a_room [ennf transformation 69]
173. (? [X1] : (prede(X1) | ~predq(X1) | ~room(X1)) | ? [X0] : (predr(X0) | ~predg(X0) | ~room(X0))) & (! [X1] : (~prede(X1) & predq(X1) & room(X1)) | ! [X0] : (~predr(X0) & predg(X0) & room(X0))) [nnf transformation 153]
174. (? [X0] : (prede(X0) | ~predq(X0) | ~room(X0)) | ? [X1] : (predr(X1) | ~predg(X1) | ~room(X1))) & (! [X2] : (~prede(X2) & predq(X2) & room(X2)) | ! [X3] : (~predr(X3) & predg(X3) & room(X3))) [rectify 173]
175. ? [X0] : (prede(X0) | ~predq(X0) | ~room(X0)) => (prede(sK2) | ~predq(sK2) | ~room(sK2)) [choice axiom]
176. ? [X1] : (predr(X1) | ~predg(X1) | ~room(X1)) => (predr(sK3) | ~predg(sK3) | ~room(sK3)) [choice axiom]
177. ((prede(sK2) | ~predq(sK2) | ~room(sK2)) | (predr(sK3) | ~predg(sK3) | ~room(sK3))) & (! [X2] : (~prede(X2) & predq(X2) & room(X2)) | ! [X3] : (~predr(X3) & predg(X3) & room(X3))) [skolemisation 174,176,175]
192. ? [X0] : (~predq(X0) & room(X0)) => (~predq(sK9) & room(sK9)) [choice axiom]
193. ~predq(sK9) & room(sK9) [skolemisation 163,192]
201. ! [X0] : (((predj(X0) | (~predg(X0) & ~predi(X0))) & ((predg(X0) | predi(X0)) | ~predj(X0))) | ~room(X0)) [nnf transformation 165]
202. ! [X0] : (((predj(X0) | (~predg(X0) & ~predi(X0))) & (predg(X0) | predi(X0) | ~predj(X0))) | ~room(X0)) [flattening 201]
204. ? [X0] : (~predj(X0) & room(X0)) => (~predj(sK13) & room(sK13)) [choice axiom]
205. (~predj(sK13) & room(sK13)) | ~there_is_a_room [skolemisation 166,204]
286. there_is_a_room [cnf transformation 44]
293. room(X2) | room(X3) [cnf transformation 177]
297. predq(X2) | predg(X3) [cnf transformation 177]
331. ~predq(sK9) [cnf transformation 193]
341. ~predg(X0) | predj(X0) | ~room(X0) [cnf transformation 202]
345. ~predj(sK13) | ~there_is_a_room [cnf transformation 205]
415. 17 <=> ! [X3] : predg(X3) [avatar definition]
416. predg(X3) <- (17) [avatar component clause 415]
419. 18 <=> ! [X3] : room(X3) [avatar definition]
420. room(X3) <- (18) [avatar component clause 419]
423. 19 <=> ! [X2] : predq(X2) [avatar definition]
424. predq(X2) <- (19) [avatar component clause 423]
426. 17 | 19 [avatar split clause 297,423,415]
430. 18 | 18 [avatar split clause 293,419,419]
476. 29 <=> ! [X0] : predj(X0) [avatar definition]
477. predj(X0) <- (29) [avatar component clause 476]
530. ~predj(sK13) [subsumption resolution 345,286]
536. $false <- (19) [resolution 424,331]
537. ~19 [avatar contradiction clause 536]
559. predj(X0) | ~room(X0) <- (17) [resolution 341,416]
560. predj(X0) <- (17, 18) [subsumption resolution 559,420]
561. 29 | ~17 | ~18 [avatar split clause 560,419,415,476]
562. $false <- (29) [resolution 477,530]
564. ~29 [avatar contradiction clause 562]
565. $false [avatar sat refutation 426,430,537,561,564]
% SZS output end Proof for 2609163956776470411214066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.042 s
% ------------------------------
% ------------------------------
| 0.094688 |
Jose, Deborah are the only persons in the room.
“Jose owns a smart tv or maintains a personal blog focused on cybersecurity tips or both” unless “everyone in the room does enjoy mountain biking or is not a night owl”.
Either “everyone in the room does not enjoy mountain biking or is a member of a local theater group specializing in improv” or “everyone in the room collects first edition books or does not regularly goes on multi-day backpacking trips in national parks” but not both.
If “Deborah can play the piano or regularly goes on multi-day backpacking trips in national parks or both” then “Jose does enjoy mountain biking”.
If “everyone anywhere regularly goes on multi-day backpacking trips in national parks or does not own a smart tv” then “Jose does not have completed a triathlon, collects rare and antique scientific instruments or does not own a smart tv”.
Either “Deborah maintains a personal blog focused on cybersecurity tips” or “Jose owns a smart tv” but not both.
Deborah cannot play the piano.
Everyone in the room who collects first edition books, has completed a triathlon or collects rare and antique scientific instruments does enjoy mountain biking.
Everyone in the room does not maintain a personal blog focused on cybersecurity tips.
Everyone in the room is a member of a local theater group specializing in improv if they has completed a triathlon.
If someone does not collect rare and antique scientific instruments then he/she can play the piano.
Everyone in the room is a night owl and collects rare and antique scientific instruments if they can play the guitar. | Everyone in the room cannot play the piano or does enjoy mountain biking. | neutral | room(jose)&room(deborah)&(![X]:(room(X)=>(X='jose'|X='deborah')))&
(~(![X]:(room(X)=>(((is_not_a_night_owl(X))|(does_enjoy_mountain_biking(X))))))=>(((owns_a_smart_tv(jose))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(jose)))))&
((![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))|(does_not_enjoy_mountain_biking(X))))))<~>(![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(collects_first_edition_books(X)))))))&
((((can_play_the_piano(deborah))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(deborah))))=>(does_enjoy_mountain_biking(jose)))&
((![X]:(anywhere(X)=>(((does_not_own_a_smart_tv(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))=>(((does_not_have_completed_a_triathlon(jose))|(collects_rare_and_antique_scientific_instruments(jose))|(does_not_own_a_smart_tv(jose)))))&
((maintains_a_personal_blog_focused_on_cybersecurity_tips(deborah))<~>(owns_a_smart_tv(jose)))&
(cannot_play_the_piano(deborah))&
(![X]:(room(X)=>(((((collects_first_edition_books(X))|(has_completed_a_triathlon(X))|(collects_rare_and_antique_scientific_instruments(X))))=>(does_enjoy_mountain_biking(X))))))&
(![X]:(room(X)=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))&
(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
((![X]:((does_not_collect_rare_and_antique_scientific_instruments(X))=>(can_play_the_piano(X)))))&
(![X]:(room(X)=>(((can_play_the_guitar(X))=>(((is_a_night_owl(X))&(collects_rare_and_antique_scientific_instruments(X)))))))) | room(jose)&room(deborah)&(![X]:(room(X)=>(X='jose'|X='deborah')))&
![X]:(room(X)=>(((does_enjoy_mountain_biking(X))|(cannot_play_the_piano(X))))) | [] | null | 0.085686 |
Monica, Ray are the only persons in the room.
If 'everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals' then 'someone in the room practices zumba'.
If 'someone in the room practices zumba' then 'everyone in the room who hosts themed dinner parties featuring gourmet home-cooked meals travels domestically frequently'.
If someone owns a significant collection of rare gemstones and minerals or uses an ios phone or both then he/she enjoys logic puzzles.
Everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals if they is an expert in identifying and foraging wild edible plants, owns a significant collection of rare gemstones and minerals and has completed a triathlon.
Everyone in the room is an enthusiastic bird watcher who travels for rare sightings.
Everyone in the room enjoys logic puzzles if they does not create YouTube content.
Monica is a skilled home brewer experimenting with craft beer recipes or creates YouTube content or both.
Monica develops open-source software projects in their free time or is an enthusiastic bird watcher who travels for rare sightings or both.
Everyone in the room has a tattoo if they writes poetry and vice versa.
Ray hosts themed dinner parties featuring gourmet home-cooked meals.
Ray travels domestically frequently.
Everyone in the room who collects first edition books enjoys cross-country skiing.
Everyone in the room who does not host themed dinner parties featuring gourmet home-cooked meals builds model airplanes.
Everyone in the room does not own a significant collection of rare gemstones and minerals or builds model airplanes.
Everyone in the room plays eSports competitively or uses an ios phone or both if they enjoys logic puzzles or hosts a YouTube channel dedicated to art tutorials or both.
Everyone in the room who practices zumba collects vintage stamps.
Someone outside the room travels domestically frequently.
Ray does not practice urban gardening.
Everyone in the room writes poetry if they is not an expert in identifying and foraging wild edible plants.
More than one person in the room collects vintage vinyl records.
Everyone in the room is an enthusiastic bird watcher who travels for rare sightings if they does not play eSports competitively. | Monica is a skilled home brewer experimenting with craft beer recipes. | neutral | room(monica)&room(ray)&(![X]:(room(X)=>(X='monica'|X='ray')))&
(((![X]:(room(X)=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))=>(?[X]:(room(X)&(practices_zumba(X)))))&
((?[X]:(room(X)&(practices_zumba(X))))=>(![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(travels_domestically_frequently(X))))))))&
((![X]:((((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(uses_an_ios_phone(X))))=>(enjoys_logic_puzzles(X)))))&
(![X]:(room(X)=>(((((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(has_completed_a_triathlon(X))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(![X]:(room(X)=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))&
(![X]:(room(X)=>(((does_not_create_YouTube_content(X))=>(enjoys_logic_puzzles(X))))))&
(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(monica))|(creates_YouTube_content(monica))))&
(((develops_open-source_software_projects_in_their_free_time(monica))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(monica))))&
(![X]:(room(X)=>(((has_a_tattoo(X))<=>(writes_poetry(X))))))&
(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(ray))&
(travels_domestically_frequently(ray))&
(![X]:(room(X)=>(((collects_first_edition_books(X))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(builds_model_airplanes(X))))))&
(![X]:(room(X)=>(((builds_model_airplanes(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
(![X]:(room(X)=>(((((enjoys_logic_puzzles(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))=>(((plays_eSports_competitively(X))|(uses_an_ios_phone(X))))))))&
(![X]:(room(X)=>(((practices_zumba(X))=>(collects_vintage_stamps(X))))))&
(?[X]:(~room(X)&(travels_domestically_frequently(X))))&
(does_not_practice_urban_gardening(ray))&
(![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(writes_poetry(X))))))&
((?[X,Y]:(room(X)&room(Y)&(collects_vintage_vinyl_records(X)&collects_vintage_vinyl_records(Y))&(X!=Y))))&
(![X]:(room(X)=>(((does_not_play_eSports_competitively(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))) | room(monica)&room(ray)&(![X]:(room(X)=>(X='monica'|X='ray')))&
is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(monica) | [] | null | 0.073588 |
Mildred, Christina, David, Deborah, Jennifer are the only persons in the room. “David does not hate Ruby” unless “Christina and Deborah are respectively generous and happy”. “It is true that “someone in the room is not a calm generous european”” if “someone in the room is creative” and vice versa. “David is liked by Ruby” if “Deborah is not an avid collector of autographed memorabilia from famous musicians, does not hate Michael or does not collect rare and antique scientific instruments” and vice versa. “Mildred dreamt that “Jennifer who is not a chess master who participates in national tournaments either does not hate Michael or is quiet but not both”” unless “Mildred is kind”. “David is calm” only if “Deborah is hated by Michael”. “Christina is the poorest in the room” if “Deborah neither does not hate Ruby nor is not a happy tourist”. “Jennifer is not generous, not calm, not strong” if “Jennifer is not a generous tourist” and vice versa. Jennifer is the youngest in the room. All happy persons are curious. At least one person in the room is not a quiet tall tourist. Mildred is not generous. All kind persons are creative. Mildred is the least poor in the room. Christina does not own a microscope. David is not hated by Ruby. David is liked by Ruby. Jennifer is not a strong european. David and Christina are respectively funny and generous. Christina does not work as a freelance web developer specializing in e-commerce sites. Jennifer and David are respectively quiet and tall. Christina who is calm, does not work as a freelance web developer specializing in e-commerce sites or does not create YouTube content is funny. Jennifer is patient. David does not hate Michael. No tall person is old. It is true that “Christina and Deborah are respectively strong and creative”. | Everyone in the room is not a curious person. | neutral | room(mildred)&room(christina)&room(david)&room(deborah)&room(jennifer)&(![X]:(room(X)=>(X='mildred'|X='christina'|X='david'|X='deborah'|X='jennifer')))&
(~((generous(christina))&(happy(deborah)))=>(~hate(ruby,david)))&
((?[X]:(room(X)&(creative(X))))<=>(?[X]:(room(X)&(~(calm(X)&generous(X)&european(X))))))&
((((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(deborah))|(~hate(michael,deborah))|(does_not_collect_rare_and_antique_scientific_instruments(deborah))))<=>(like(david,ruby)))&
(~(kind(mildred))=>((mildred_dream=>((is_not_a_chess_master_who_participates_in_national_tournaments(jennifer))&(((~hate(michael,jennifer))<~>(quiet(jennifer))))))))&
((calm(david))=>(hate(deborah,michael)))&
((~((~hate(ruby,deborah))|(~(happy(deborah)&tourist(deborah)))))=>(![X]:((room(X)&(X!=christina))=>poorer(X,christina))))&
((~(generous(jennifer)&tourist(jennifer)))<=>(~generous(jennifer)&~calm(jennifer)&~strong(jennifer)))&
(![X]:((room(X)&(X!=jennifer))=>younger(X,jennifer)))&
(![X]:(happy(X)=>curious(X)))&
(((?[X]:(room(X)&~(quiet(X)&tall(X)&tourist(X))))))&
(~generous(mildred))&
(![X]:(kind(X)=>creative(X)))&
(![X]:((room(X)&(X!=mildred))=>poorer(mildred,X)))&
(does_not_own_a_microscope(christina))&
(~hate(david,ruby))&
(like(david,ruby))&
(~(strong(jennifer)&european(jennifer)))&
((funny(david))&(generous(christina)))&
(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(christina))&
((quiet(jennifer))&(tall(david)))&
((((calm(christina))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(christina))|(does_not_create_YouTube_content(christina))))&(funny(christina)))&
(patient(jennifer))&
(~hate(michael,david))&
(~?[X]:(tall(X)=>old(X)))&
((strong(christina))&(creative(deborah)))&
(~(tall(david)&person(david)))&
(![X]:(strong(X)=>kind(X)))&
((![X]:((~wise(X))=>(~(funny(X)&tourist(X))))))&
(~generous(jennifer)&~calm(jennifer)&~strong(jennifer))&
(?[X]:(room(X)&(~like(ruby,X)))) | room(mildred)&room(christina)&room(david)&room(deborah)&room(jennifer)&(![X]:(room(X)=>(X='mildred'|X='christina'|X='david'|X='deborah'|X='jennifer')))&
![X]:(room(X)=>(~(curious(X)&person(X)))) | [] | null | 0.297403 |
Christine, Janna are the only persons in the room.
Everyone in the room neither is not an amateur astronomer who builds and uses custom telescopes nor mentors a youth basketball team on weekends.
Everyone anywhere does not enjoy camping and organizing outdoor survival workshops.
Everyone in the room can play the guitar, enjoys making ceramics or does not have completed a triathlon.
Everyone in the room enjoys windsurfing.
Everyone in the room is a certified yoga instructor teaching classes weekly. | Janna practices graffiti art. | neutral | room(christine)&room(janna)&(![X]:(room(X)=>(X='christine'|X='janna')))&
(![X]:(room(X)=>(~((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))&
(![X]:(anywhere(X)=>(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))&
(![X]:(room(X)=>(((can_play_the_guitar(X))|(enjoys_making_ceramics(X))|(does_not_have_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(enjoys_windsurfing(X))))&
(![X]:(room(X)=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))&
(![X]:(room(X)=>(((((does_not_enjoy_logic_puzzles(X))<~>(does_not_have_completed_a_triathlon(X))))=>(does_not_enjoy_logic_puzzles(X))))))&
(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(janna))&
(![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))=>(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))&
(![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))=>(does_not_have_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))&
(does_not_mentor_a_youth_basketball_team_on_weekends(christine))&
(![X]:(room(X)=>(is_not_a_craft_beer_aficionado(X))))&
(![X]:(room(X)=>(((((can_play_the_guitar(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_have_completed_a_triathlon(X))))))))&
(![X]:(anywhere(X)=>(is_not_right-handed(X))))&
(![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_have_completed_a_triathlon(X))))))&
(![X]:(~room(X)=>(mentors_a_youth_basketball_team_on_weekends(X))))&
(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(is_not_right-handed(X))))))&
(![X]:(room(X)=>(((does_not_practice_graffiti_art(X))|(does_not_enjoy_making_ceramics(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X)))))) | room(christine)&room(janna)&(![X]:(room(X)=>(X='christine'|X='janna')))&
practices_graffiti_art(janna) | [] | null | 0.273499 |
There is a room.
If everyone outside the room does not work on fridays then everyone in the room does not enjoy watercolor painting and does not collect comic books otherwise someone in the room either does not collect comic books or does not host a YouTube channel dedicated to art tutorials but not both.
Everyone in the room either does not collect comic books or does not practice zumba but not both only if everyone in the room does not enjoy macrame and does not have a pet dog.
Everyone in the room neither does not enjoy fishing nor cannot play the piano.
Everyone in the room does not enjoy watercolor painting.
Everyone in the room does not collect comic books, does not work on fridays or does not host a YouTube channel dedicated to art tutorials.
No one in the room does not collect modern art.
Everyone in the room is not dedicated to sustainable living and zero-waste practices and does not practice graffiti art. | Everyone outside the room does not practice graffiti art. | entailment | (there_is_a_room)&
(((![X]:(~room(X)=>(does_not_work_on_fridays(X))))=>(![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))&(does_not_collect_comic_books(X)))))))&((~(![X]:(~room(X)=>(does_not_work_on_fridays(X)))))=>(?[X]:(room(X)&(((does_not_collect_comic_books(X))<~>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))))&
((![X]:(room(X)=>(((does_not_collect_comic_books(X))<~>(does_not_practice_zumba(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_macrame(X))&(does_not_have_a_pet_dog(X)))))))&
(![X]:(room(X)=>(~((does_not_enjoy_fishing(X))|(cannot_play_the_piano(X))))))&
(![X]:(room(X)=>(does_not_enjoy_watercolor_painting(X))))&
(![X]:(room(X)=>(((does_not_collect_comic_books(X))|(does_not_work_on_fridays(X))|(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(~?[X]:(room(X)=>(does_not_collect_modern_art(X))))&
(![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(does_not_practice_graffiti_art(X))))))&
(![X]:(room(X)=>(does_not_collect_comic_books(X)))) | (there_is_a_room)&
![X]:(~room(X)=>(does_not_practice_graffiti_art(X))) | [
"p0",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1794903745055037569568660
% SZS output start Proof for 1794903745055037569568660
44. there_is_a_room [input p0]
50. ~? [X0] : (room(X0) => ~predp(X0)) [input p6]
51. ! [X0] : (room(X0) => (~preda(X0) & ~predh(X0))) [input p7]
53. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis]
56. ! [X0] : (room(X0) => ~preda(X0)) [pure predicate removal 51]
57. ~? [X0] : ~room(X0) [pure predicate removal 50]
139. ! [X0] : room(X0) [ennf transformation 57]
140. ! [X0] : (~preda(X0) | ~room(X0)) [ennf transformation 56]
142. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 53]
150. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK2) & ~room(sK2)) [choice axiom]
151. (preda(sK2) & ~room(sK2)) | ~there_is_a_room [skolemisation 142,150]
232. there_is_a_room [cnf transformation 44]
239. room(X0) [cnf transformation 139]
240. ~preda(X0) | ~room(X0) [cnf transformation 140]
243. preda(sK2) | ~there_is_a_room [cnf transformation 151]
275. ~preda(X0) [subsumption resolution 240,239]
277. ~there_is_a_room [subsumption resolution 243,275]
278. $false [subsumption resolution 277,232]
% SZS output end Proof for 1794903745055037569568660
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.406948 |
Lester, Cruz are the only persons in the room.
Lester does not host regular game nights featuring complex strategy games, does not own a significant collection of rare gemstones and minerals and does not use contact lenses. | Lester uses contact lenses. | contradiction | room(lester)&room(cruz)&(![X]:(room(X)=>(X='lester'|X='cruz')))&
(![X]:(room(X)=>(~((cannot_play_the_guitar(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))&(is_not_a_drone_photographer(X))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))&
(does_not_travel_domestically_frequently(lester))&
(does_not_collect_rare_minerals(lester))&
(((does_not_develop_open-source_software_projects_in_their_free_time(lester))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(lester))|(does_not_have_a_saltwater_aquarium(lester))))&
(does_not_play_the_drums(cruz))&
(((does_not_host_regular_game_nights_featuring_complex_strategy_games(lester))&(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(lester))&(does_not_use_contact_lenses(lester))))&
((![X]:((does_not_enjoy_stand-up_paddleboarding(X))<=>(is_not_passionate_about_collecting_and_restoring_classic_cars(X)))))&
(![X]:(room(X)=>(does_not_volunteer_for_local_environmental_conservation_projects(X))))&
(![X]:(~room(X)=>(does_not_develop_open-source_software_projects_in_their_free_time(X))))&
(![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(does_not_use_contact_lenses(X))|(does_not_build_model_airplanes(X))))))&
(((?[X]:(room(X)&~((does_not_travel_domestically_frequently(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X)))))&(![X,Y]:((room(X)&room(Y)&(~((does_not_travel_domestically_frequently(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))&(~((does_not_travel_domestically_frequently(Y))|(is_not_passionate_about_collecting_and_restoring_classic_cars(Y)))))=>(X=Y))))) | room(lester)&room(cruz)&(![X]:(room(X)=>(X='lester'|X='cruz')))&
uses_contact_lenses(lester) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2509101663862687907144572
% SZS output start Proof for 2509101663862687907144572
51. ~prede(mary) & ~predk(mary) & ~predy(mary) [input p7]
57. prede(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
61. ~prede(mary) & ~predy(mary) [pure predicate removal 51]
62. ~prede(mary) [pure predicate removal 61]
148. prede(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 57]
149. prede(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 148]
237. ~prede(mary) [cnf transformation 62]
245. prede(mary) [cnf transformation 149]
246. $false [subsumption resolution 245,237]
% SZS output end Proof for 2509101663862687907144572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.27498 |
Bridget, Joni, Heidi are the only persons in the room. If “everyone in the room does not like Andrew” then “all happy persons are generous”. All quiet persons are kind. Laverne and Heidi like each other. No funny person is calm. If someone is tall then he/she is not funny. Heidi enjoys fishing. Joni and Bridget are respectively old and creative. Heidi is generous. All tall persons are calm. All old persons are curious. All tall persons are humble. Everyone outside the room collects modern art if they hosts regular workshops on creative writing. Everyone in the room is not hated by Laverne only if they is a strong old tourist. Everyone in the room who is not a wise kind calm european, is dedicated to sustainable living and zero-waste practices or is a generous old strong funny person does not hate Angela. Everyone in the room is not hated by Lillian. Everyone in the room collects antique clocks if they is an avid collector of autographed memorabilia from famous musicians. | Joni and Heidi are curious. | entailment | room(bridget)&room(joni)&room(heidi)&(![X]:(room(X)=>(X='bridget'|X='joni'|X='heidi')))&
((![X]:(room(X)=>(~like(andrew,X))))=>(![X]:(happy(X)=>generous(X))))&
(![X]:(quiet(X)=>kind(X)))&
((like(laverne,heidi) & like(heidi,laverne)))&
(~?[X]:(funny(X)=>calm(X)))&
((![X]:((tall(X))=>(~funny(X)))))&
(enjoys_fishing(heidi))&
((old(joni))&(creative(bridget)))&
(generous(heidi))&
(![X]:(tall(X)=>calm(X)))&
(![X]:(old(X)=>curious(X)))&
(![X]:(tall(X)=>humble(X)))&
(![X]:(~room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(collects_modern_art(X))))))&
(![X]:(room(X)=>(((strong(X)&old(X)&tourist(X))<=(~hate(X,laverne))))))&
(![X]:(room(X)=>(((((~(wise(X)&kind(X)&calm(X)&european(X)))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(generous(X)&old(X)&strong(X)&funny(X)&person(X))))=>(~hate(angela,X))))))&
(![X]:(room(X)=>(~hate(X,lillian))))&
(![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(collects_antique_clocks(X)))))) | room(bridget)&room(joni)&room(heidi)&(![X]:(room(X)=>(X='bridget'|X='joni'|X='heidi')))&
curious(joni)&curious(heidi) | [
"b0",
"b42",
"p0",
"p3",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3874332160656713117210357
% SZS output start Proof for 3874332160656713117210357
1. ! [X0,X1] : (X0 != X1 => (like(X0,X1) => ~hate(X0,X1))) [input b0]
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]
47. like(fred,susan) & like(susan,fred) [input p3]
51. creative(mary) & old(paul) [input p7]
54. ! [X0] : (old(X0) => curious(X0)) [input p10]
57. ! [X0] : (room(X0) => (~hate(X0,susan) => (tourist(X0) & old(X0) & strong(X0)))) [input p13]
61. ~(curious(fred) & curious(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
68. old(paul) [pure predicate removal 51]
76. ! [X0,X1] : ((~hate(X0,X1) | ~like(X0,X1)) | X0 = X1) [ennf transformation 1]
77. ! [X0,X1] : (~hate(X0,X1) | ~like(X0,X1) | X0 = X1) [flattening 76]
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]
152. ! [X0] : (curious(X0) | ~old(X0)) [ennf transformation 54]
153. ! [X0] : (((tourist(X0) & old(X0) & strong(X0)) | hate(X0,susan)) | ~room(X0)) [ennf transformation 57]
154. ! [X0] : ((tourist(X0) & old(X0) & strong(X0)) | hate(X0,susan) | ~room(X0)) [flattening 153]
158. ~curious(fred) | ~curious(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 61]
159. ~curious(fred) | ~curious(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 158]
161. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom]
162. ~curious(fred) | ~curious(paul) | (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 159,161]
163. ~hate(X0,X1) | ~like(X0,X1) | X0 = X1 [cnf transformation 77]
237. fred != susan [cnf transformation 43]
247. room(mary) [cnf transformation 150]
248. room(paul) [cnf transformation 150]
249. room(fred) [cnf transformation 150]
250. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 150]
252. like(fred,susan) [cnf transformation 47]
255. old(paul) [cnf transformation 68]
257. ~old(X0) | curious(X0) [cnf transformation 152]
259. hate(X0,susan) | old(X0) | ~room(X0) [cnf transformation 154]
265. ~curious(fred) | ~curious(paul) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
266. ~curious(fred) | ~curious(paul) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
267. ~curious(fred) | ~curious(paul) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
268. ~curious(fred) | ~curious(paul) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
271. ~curious(fred) | ~curious(paul) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 268,249]
272. ~curious(fred) | ~curious(paul) | fred != sK0 | ~room(mary) [subsumption resolution 271,248]
273. ~curious(fred) | ~curious(paul) | fred != sK0 [subsumption resolution 272,247]
275. 1 <=> fred = sK0 [avatar definition]
277. fred != sK0 <- (~1) [avatar component clause 275]
279. 2 <=> curious(paul) [avatar definition]
283. 3 <=> curious(fred) [avatar definition]
286. ~1 | ~2 | ~3 [avatar split clause 273,283,279,275]
287. ~curious(fred) | ~curious(paul) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 267,249]
288. ~curious(fred) | ~curious(paul) | paul != sK0 | ~room(mary) [subsumption resolution 287,248]
289. ~curious(fred) | ~curious(paul) | paul != sK0 [subsumption resolution 288,247]
291. 4 <=> paul = sK0 [avatar definition]
293. paul != sK0 <- (~4) [avatar component clause 291]
294. ~4 | ~2 | ~3 [avatar split clause 289,283,279,291]
295. ~curious(fred) | ~curious(paul) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 266,249]
296. ~curious(fred) | ~curious(paul) | mary != sK0 | ~room(mary) [subsumption resolution 295,248]
297. ~curious(fred) | ~curious(paul) | mary != sK0 [subsumption resolution 296,247]
299. 5 <=> mary = sK0 [avatar definition]
301. mary != sK0 <- (~5) [avatar component clause 299]
302. ~5 | ~2 | ~3 [avatar split clause 297,283,279,299]
303. ~curious(fred) | ~curious(paul) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 265,249]
304. ~curious(fred) | ~curious(paul) | room(sK0) | ~room(mary) [subsumption resolution 303,248]
305. ~curious(fred) | ~curious(paul) | room(sK0) [subsumption resolution 304,247]
307. 6 <=> room(sK0) [avatar definition]
309. room(sK0) <- (6) [avatar component clause 307]
310. 6 | ~2 | ~3 [avatar split clause 305,283,279,307]
311. curious(paul) [resolution 257,255]
314. 2 [avatar split clause 311,279]
335. ~like(X1,susan) | susan = X1 | old(X1) | ~room(X1) [resolution 163,259]
385. fred = susan | old(fred) | ~room(fred) [resolution 335,252]
386. old(fred) | ~room(fred) [subsumption resolution 385,237]
387. old(fred) [subsumption resolution 386,249]
390. curious(fred) [resolution 387,257]
393. 3 [avatar split clause 390,283]
394. paul = sK0 | mary = sK0 | fred = sK0 <- (6) [resolution 309,250]
395. mary = sK0 | fred = sK0 <- (~4, 6) [subsumption resolution 394,293]
396. fred = sK0 <- (~4, ~5, 6) [subsumption resolution 395,301]
397. $false <- (~1, ~4, ~5, 6) [subsumption resolution 396,277]
398. 1 | 4 | 5 | ~6 [avatar contradiction clause 397]
399. $false [avatar sat refutation 286,294,302,310,314,393,398]
% SZS output end Proof for 3874332160656713117210357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Georgia is the only person in the room. “Georgia own a television” only if “Georgia collects modern art”. “Georgia has a piercing” if “everyone in the room does not host a popular podcast about emerging technologies or does not collect antique clocks” and vice versa. Either “Georgia owns a telescope, does not enjoy origami and is right-handed” or “not everyone in the room does not collect modern art or does not compose and performs experimental electronic music” but not both. If “Georgia does enjoy mountain biking” then “Georgia drives a hybrid car”. Georgia enjoys kayaking and exploring remote waterways. Everyone in the room enjoys origami. Everyone in the room who does enjoy mountain biking has a vast collection of first-edition science fiction novels. Everyone in the room neither owns a smartwatch nor collects modern art if they has a vast collection of first-edition science fiction novels. Georgia is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room practices and performs acrobatic dance routines or is an avid hiker or both only if they enjoys fishing. Everyone in the room who collects modern art collects antique clocks. Everyone in the room who collects antique clocks collects modern art. Everyone in the room collects antique clocks, practices and performs acrobatic dance routines and can play the flute if they collects modern art. | Georgia has a vast collection of first-edition science fiction novels. | contradiction | room(georgia)&(![X]:(room(X)=>(X='georgia')))&
((own_a_television(georgia))=>(collects_modern_art(georgia)))&
((![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))<=>(has_a_piercing(georgia)))&
((((owns_a_telescope(georgia))&(does_not_enjoy_origami(georgia))&(is_right-handed(georgia))))<~>(~![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(does_not_collect_modern_art(X)))))))&
((does_enjoy_mountain_biking(georgia))=>(drives_a_hybrid_car(georgia)))&
(enjoys_kayaking_and_exploring_remote_waterways(georgia))&
(![X]:(room(X)=>(enjoys_origami(X))))&
(![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))&
(![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(~((owns_a_smartwatch(X))|(collects_modern_art(X))))))))&
(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(georgia))&
(![X]:(room(X)=>(((enjoys_fishing(X))<=(((practices_and_performs_acrobatic_dance_routines(X))|(is_an_avid_hiker(X))))))))&
(![X]:(room(X)=>(((collects_modern_art(X))=>(collects_antique_clocks(X))))))&
(![X]:(room(X)=>(((collects_antique_clocks(X))=>(collects_modern_art(X))))))&
(![X]:(room(X)=>(((collects_modern_art(X))=>(((collects_antique_clocks(X))&(practices_and_performs_acrobatic_dance_routines(X))&(can_play_the_flute(X)))))))) | room(georgia)&(![X]:(room(X)=>(X='georgia')))&
has_a_vast_collection_of_first-edition_science_fiction_novels(georgia) | [
"p0",
"p3",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2357133586368479042512526
% SZS output start Proof for 2357133586368479042512526
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
47. (predy(mary) & ~predl(mary) & predz(mary)) <~> ~! [X0] : (room(X0) => (~predg(X0) | ~predh(X0))) [input p3]
50. ! [X0] : (room(X0) => predl(X0)) [input p6]
52. ! [X0] : (room(X0) => (predv(X0) => ~(predg(X0) | predr(X0)))) [input p8]
58. predv(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
64. ! [X0] : (room(X0) => (predv(X0) => ~predg(X0))) [pure predicate removal 52]
141. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
144. (predy(mary) & ~predl(mary) & predz(mary)) <~> ? [X0] : ((predg(X0) & predh(X0)) & room(X0)) [ennf transformation 47]
145. (predy(mary) & ~predl(mary) & predz(mary)) <~> ? [X0] : (predg(X0) & predh(X0) & room(X0)) [flattening 144]
146. ! [X0] : (predl(X0) | ~room(X0)) [ennf transformation 50]
147. ! [X0] : ((~predg(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 64]
148. ! [X0] : (~predg(X0) | ~predv(X0) | ~room(X0)) [flattening 147]
155. predv(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 58]
161. (! [X0] : (~predg(X0) | ~predh(X0) | ~room(X0)) | (~predy(mary) | predl(mary) | ~predz(mary))) & (? [X0] : (predg(X0) & predh(X0) & room(X0)) | (predy(mary) & ~predl(mary) & predz(mary))) [nnf transformation 145]
162. (! [X0] : (~predg(X0) | ~predh(X0) | ~room(X0)) | ~predy(mary) | predl(mary) | ~predz(mary)) & (? [X0] : (predg(X0) & predh(X0) & room(X0)) | (predy(mary) & ~predl(mary) & predz(mary))) [flattening 161]
163. (! [X0] : (~predg(X0) | ~predh(X0) | ~room(X0)) | ~predy(mary) | predl(mary) | ~predz(mary)) & (? [X1] : (predg(X1) & predh(X1) & room(X1)) | (predy(mary) & ~predl(mary) & predz(mary))) [rectify 162]
164. ? [X1] : (predg(X1) & predh(X1) & room(X1)) => (predg(sK1) & predh(sK1) & room(sK1)) [choice axiom]
165. (! [X0] : (~predg(X0) | ~predh(X0) | ~room(X0)) | ~predy(mary) | predl(mary) | ~predz(mary)) & ((predg(sK1) & predh(sK1) & room(sK1)) | (predy(mary) & ~predl(mary) & predz(mary))) [skolemisation 163,164]
246. room(mary) [cnf transformation 141]
247. ~room(X0) | mary = X0 [cnf transformation 141]
253. room(sK1) | ~predl(mary) [cnf transformation 165]
259. predg(sK1) | ~predl(mary) [cnf transformation 165]
262. ~room(X0) | predl(X0) [cnf transformation 146]
263. ~predv(X0) | ~predg(X0) | ~room(X0) [cnf transformation 148]
269. predv(mary) [cnf transformation 155]
298. 7 <=> predl(mary) [avatar definition]
310. 10 <=> predg(sK1) [avatar definition]
312. predg(sK1) <- (10) [avatar component clause 310]
314. ~7 | 10 [avatar split clause 259,310,298]
324. 12 <=> room(sK1) [avatar definition]
326. room(sK1) <- (12) [avatar component clause 324]
328. ~7 | 12 [avatar split clause 253,324,298]
330. predl(mary) [resolution 262,246]
334. 7 [avatar split clause 330,298]
338. mary = sK1 <- (12) [resolution 247,326]
344. predg(mary) <- (10, 12) [backward demodulation 312,338]
347. ~predg(mary) | ~room(mary) [resolution 263,269]
348. ~room(mary) <- (10, 12) [subsumption resolution 347,344]
349. $false <- (10, 12) [subsumption resolution 348,246]
350. ~10 | ~12 [avatar contradiction clause 349]
351. $false [avatar sat refutation 314,328,334,350]
% SZS output end Proof for 2357133586368479042512526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.083964 |
Laura is the only person in the room.
If someone does not enjoy fishing then he/she practices urban gardening and vice versa.
Laura does not practice yoga, is a wine connoisseur or is a wine connoisseur with a private cellar of vintage wines.
Laura is a craft beer aficionado.
Laura reads mystery novels.
Laura is a wine connoisseur.
Everyone in the room who does not practice kickboxing is a tea enthusiast and collects classic novels.
Only one person in the room either collects action figures or writes a travel blog but not both.
If someone hosts regular game nights featuring complex strategy games then he/she reads mystery novels and vice versa.
Laura practices calligraphy.
Laura enjoys stand-up paddleboarding.
Laura who plays as a goalkeeper for a local amateur soccer team hosts regular game nights featuring complex strategy games.
Laura who hosts regular game nights featuring complex strategy games or is a wine connoisseur or both practices graffiti art.
At least one person in the room uses an ios phone.
Laura does not practice yoga.
Laura hosts regular game nights featuring complex strategy games, collects action figures and enjoys fishing.
Not everyone in the room who practices kickboxing is a chess master who participates in national tournaments and collects vintage stamps.
Someone in the room collect rare sneakers and bakes bread at home.
Everyone in the room collects action figures if they is a client of Meta, hosts regular game nights featuring complex strategy games and is not a craft beer aficionado.
Someone in the room practices kickboxing.
Not everyone in the room reads mystery novels if and only if they writes a travel blog.
Laura collects luxury watches. | It is not the case that “it is not the case that “Laura practices urban gardening””. | contradiction | room(laura)&(![X]:(room(X)=>(X='laura')))&
((![X]:((does_not_enjoy_fishing(X))<=>(practices_urban_gardening(X)))))&
(((does_not_practice_yoga(laura))|(is_a_wine_connoisseur(laura))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(laura))))&
(is_a_craft_beer_aficionado(laura))&
(reads_mystery_novels(laura))&
(is_a_wine_connoisseur(laura))&
(![X]:(room(X)=>(((does_not_practice_kickboxing(X))=>(((is_a_tea_enthusiast(X))&(collects_classic_novels(X))))))))&
(((?[X]:(room(X)&((collects_action_figures(X))<~>(writes_a_travel_blog(X)))))&(![X,Y]:((room(X)&room(Y)&(((collects_action_figures(X))<~>(writes_a_travel_blog(X))))&(((collects_action_figures(Y))<~>(writes_a_travel_blog(Y)))))=>(X=Y)))))&
((![X]:((hosts_regular_game_nights_featuring_complex_strategy_games(X))<=>(reads_mystery_novels(X)))))&
(practices_calligraphy(laura))&
(enjoys_stand-up_paddleboarding(laura))&
((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(laura))&(hosts_regular_game_nights_featuring_complex_strategy_games(laura)))&
((((hosts_regular_game_nights_featuring_complex_strategy_games(laura))|(is_a_wine_connoisseur(laura))))&(practices_graffiti_art(laura)))&
(((?[X]:(room(X)&uses_an_ios_phone(X)))))&
(does_not_practice_yoga(laura))&
(((hosts_regular_game_nights_featuring_complex_strategy_games(laura))&(collects_action_figures(laura))&(enjoys_fishing(laura))))&
(~![X]:(room(X)=>(((practices_kickboxing(X))=>(((is_a_chess_master_who_participates_in_national_tournaments(X))&(collects_vintage_stamps(X))))))))&
(?[X]:(room(X)&(((collect_rare_sneakers(X))&(bakes_bread_at_home(X))))))&
(![X]:(room(X)=>(((((is_a_client_of_Meta(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))&(is_not_a_craft_beer_aficionado(X))))=>(collects_action_figures(X))))))&
(?[X]:(room(X)&(practices_kickboxing(X))))&
(~![X]:(room(X)=>(((reads_mystery_novels(X))<=>(writes_a_travel_blog(X))))))&
(collects_luxury_watches(laura)) | room(laura)&(![X]:(room(X)=>(X='laura')))&
~(~(practices_urban_gardening(laura))) | [
"p1",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5863065376017957256233592
% SZS output start Proof for 5863065376017957256233592
45. ! [X0] : (~predd(X0) <=> preda(X0)) [input p1]
59. predd(mary) & predb(mary) & predz(mary) [input p15]
66. preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
68. ! [X0] : (preda(X0) => ~predd(X0)) [unused predicate definition removal 45]
162. ! [X0] : (~predd(X0) | ~preda(X0)) [ennf transformation 68]
168. preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 66]
268. ~preda(X0) | ~predd(X0) [cnf transformation 162]
282. predd(mary) [cnf transformation 59]
291. preda(mary) [cnf transformation 168]
312. ~predd(mary) [resolution 268,291]
313. $false [subsumption resolution 312,282]
% SZS output end Proof for 5863065376017957256233592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Debra, Destiny, Terry are the only persons in the room.
“Everyone in the room does not use an ios phone” unless “everyone in the room does not enjoy kayaking”.
Everyone in the room either does not enjoy kayaking or does not create large-scale murals for public art installations but not both.
Everyone in the room does not create large-scale murals for public art installations.
Everyone anywhere does not travel domestically frequently.
Everyone in the room does not travel domestically frequently and does not create large-scale murals for public art installations.
Someone in the room does not travel domestically frequently.
Everyone outside the room does not travel domestically frequently.
Everyone in the room does not practice calligraphy.
Everyone in the room does not travel domestically frequently. | Terry uses an ios phone. | contradiction | room(debra)&room(destiny)&room(terry)&(![X]:(room(X)=>(X='debra'|X='destiny'|X='terry')))&
(~(![X]:(room(X)=>(does_not_enjoy_kayaking(X))))=>(![X]:(room(X)=>(does_not_use_an_ios_phone(X)))))&
(![X]:(room(X)=>(((does_not_enjoy_kayaking(X))<~>(does_not_create_large-scale_murals_for_public_art_installations(X))))))&
(![X]:(room(X)=>(does_not_create_large-scale_murals_for_public_art_installations(X))))&
(![X]:(anywhere(X)=>(does_not_travel_domestically_frequently(X))))&
(![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))&(does_not_create_large-scale_murals_for_public_art_installations(X))))))&
(?[X]:(room(X)&(does_not_travel_domestically_frequently(X))))&
(![X]:(~room(X)=>(does_not_travel_domestically_frequently(X))))&
(![X]:(room(X)=>(does_not_practice_calligraphy(X))))&
(![X]:(room(X)=>(does_not_travel_domestically_frequently(X)))) | room(debra)&room(destiny)&room(terry)&(![X]:(room(X)=>(X='debra'|X='destiny'|X='terry')))&
uses_an_ios_phone(terry) | [
"p0",
"p1",
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5704609386058144579342697
% SZS output start Proof for 5704609386058144579342697
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
45. ~! [X0] : (room(X0) => ~prede(X0)) => ! [X0] : (room(X0) => ~predc(X0)) [input p1]
46. ! [X0] : (room(X0) => (~prede(X0) <~> ~preda(X0))) [input p2]
47. ! [X0] : (room(X0) => ~preda(X0)) [input p3]
54. predc(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
55. ~! [X0] : (room(X0) => ~prede(X0)) => ! [X1] : (room(X1) => ~predc(X1)) [rectify 45]
134. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
135. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 134]
136. ! [X1] : (~predc(X1) | ~room(X1)) | ! [X0] : (~prede(X0) | ~room(X0)) [ennf transformation 55]
137. ! [X0] : ((~prede(X0) <~> ~preda(X0)) | ~room(X0)) [ennf transformation 46]
138. ! [X0] : (~preda(X0) | ~room(X0)) [ennf transformation 47]
140. predc(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 54]
141. predc(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 140]
143. ! [X0] : (~predc(X0) | ~room(X0)) | ! [X1] : (~prede(X1) | ~room(X1)) [rectify 136]
144. ! [X0] : (((preda(X0) | prede(X0)) & (~preda(X0) | ~prede(X0))) | ~room(X0)) [nnf transformation 137]
227. room(mary) [cnf transformation 135]
229. room(fred) [cnf transformation 135]
231. ~predc(X0) | ~room(X0) | ~prede(X1) | ~room(X1) [cnf transformation 143]
233. ~room(X0) | prede(X0) | preda(X0) [cnf transformation 144]
234. ~preda(X0) | ~room(X0) [cnf transformation 138]
241. predc(fred) [cnf transformation 141]
243. 1 <=> ! [X1] : (~prede(X1) | ~room(X1)) [avatar definition]
244. ~prede(X1) | ~room(X1) <- (1) [avatar component clause 243]
246. 2 <=> ! [X0] : (~predc(X0) | ~room(X0)) [avatar definition]
247. ~predc(X0) | ~room(X0) <- (2) [avatar component clause 246]
248. 1 | 2 [avatar split clause 231,246,243]
249. ~room(fred) <- (2) [resolution 247,241]
250. $false <- (2) [subsumption resolution 249,229]
251. ~2 [avatar contradiction clause 250]
252. prede(mary) | preda(mary) [resolution 233,227]
257. 3 <=> preda(mary) [avatar definition]
259. preda(mary) <- (3) [avatar component clause 257]
261. 4 <=> prede(mary) [avatar definition]
263. prede(mary) <- (4) [avatar component clause 261]
264. 3 | 4 [avatar split clause 252,261,257]
292. ~room(mary) <- (1, 4) [resolution 263,244]
293. $false <- (1, 4) [subsumption resolution 292,227]
294. ~1 | ~4 [avatar contradiction clause 293]
296. ~room(mary) <- (3) [resolution 259,234]
297. $false <- (3) [subsumption resolution 296,227]
298. ~3 [avatar contradiction clause 297]
299. $false [avatar sat refutation 248,251,264,294,298]
% SZS output end Proof for 5704609386058144579342697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.505781 |
Lewis, Mark, Jose are the only persons in the room. If “Blondell is quieter than Mark” then “everyone in the room does not collect historical artifacts related to ancient civilizations or collects historical artifacts related to ancient civilizations”. If “everyone anywhere does not collect historical artifacts related to ancient civilizations or collects modern art” then “only one person in the room owns a high-end gaming PC with custom-built components”. Everyone outside the room collects modern art or cannot play the flute. Everyone in the room who collects modern art owns a high-end gaming PC with custom-built components. Jose is quiet. Mark is quieter than Blondell. Everyone in the room is quieter than Blondell only if they maintains a personal blog focused on cybersecurity tips. Jose owns a high-end gaming PC with custom-built components. Everyone in the room is quieter than Blondell if they neither is quiet nor maintains a personal blog focused on cybersecurity tips. More than one person in the room is quieter than Blondell. Lewis is quieter than Blondell. Lewis is not a quiet person. Jose is the least quiet in the room. Not everyone in the room who is a client of Meta is not not not quiet. | Everyone anywhere is a quiet person. | contradiction | room(lewis)&room(mark)&room(jose)&(![X]:(room(X)=>(X='lewis'|X='mark'|X='jose')))&
((quieter(mark,blondell))=>(![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X)))))))&
((![X]:(anywhere(X)=>(((collects_modern_art(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))=>(((?[X]:(room(X)&owns_a_high-end_gaming_PC_with_custom-built_components(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)=>(((cannot_play_the_flute(X))|(collects_modern_art(X))))))&
(![X]:(room(X)=>(((collects_modern_art(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))&
(quiet(jose))&
(quieter(blondell,mark))&
(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<=(quieter(blondell,X))))))&
(owns_a_high-end_gaming_PC_with_custom-built_components(jose))&
(![X]:(room(X)=>(((~((quiet(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))=>(quieter(blondell,X))))))&
((?[X,Y]:(room(X)&room(Y)&(quieter(blondell,X)&quieter(blondell,Y))&(X!=Y))))&
(quieter(blondell,lewis))&
(~(quiet(lewis)&person(lewis)))&
(![X]:((room(X)&(X!=jose))=>quieter(jose,X)))&
(~![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(~~~quiet(X)))))) | room(lewis)&room(mark)&room(jose)&(![X]:(room(X)=>(X='lewis'|X='mark'|X='jose')))&
![X]:(anywhere(X)=>(quiet(X)&person(X))) | [
"b4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5692901241075125117767923
% SZS output start Proof for 5692901241075125117767923
5. ! [X0] : anywhere(X0) [input b4]
56. ~(person(mary) & quiet(mary)) [input p12]
59. ! [X0] : (anywhere(X0) => (person(X0) & quiet(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
61. ! [X0] : (anywhere(X0) => (person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 59]
145. ~person(mary) | ~quiet(mary) [ennf transformation 56]
149. ! [X0] : ((person(X0) & quiet(X0)) | ~anywhere(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 61]
150. ! [X0] : ((person(X0) & quiet(X0)) | ~anywhere(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 149]
160. anywhere(X0) [cnf transformation 5]
261. ~person(mary) | ~quiet(mary) [cnf transformation 145]
269. quiet(X0) | ~anywhere(X0) [cnf transformation 150]
270. person(X0) | ~anywhere(X0) [cnf transformation 150]
290. 5 <=> quiet(mary) [avatar definition]
292. ~quiet(mary) <- (~5) [avatar component clause 290]
294. 6 <=> person(mary) [avatar definition]
296. ~person(mary) <- (~6) [avatar component clause 294]
297. ~5 | ~6 [avatar split clause 261,294,290]
298. person(X0) [subsumption resolution 270,160]
299. quiet(X0) [subsumption resolution 269,160]
300. $false <- (~6) [subsumption resolution 296,298]
301. 6 [avatar contradiction clause 300]
302. $false <- (~5) [subsumption resolution 292,299]
303. 5 [avatar contradiction clause 302]
304. $false [avatar sat refutation 297,301,303]
% SZS output end Proof for 5692901241075125117767923
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.563431 |
David is the only person in the room. If “Debra is older than David” then “no happy person is humble”. No happy person is humble. Debra is richer than David. Someone who is richer than Steven is quieter than someone who is older than Debra. No generous person is wise. Steven is older than David. All happy person is curious. If someone either is strong or is quieter than Steven but not both then he/she either is kind or is richer than Steven but not both and vice versa. All happy person is brave. | David is wise. | contradiction | room(david)&(![X]:(room(X)=>(X='david')))&
((older(david,debra))=>(~?[X]:(happy(X)=>humble(X))))&
(~?[X]:(happy(X)=>humble(X)))&
(richer(david,debra))&
(?[X,Y]:((richer(steven,X))&(older(debra,Y))&(quieter(X,Y))))&
(~?[X]:(generous(X)=>wise(X)))&
(older(david,steven))&
(![X]:(happy(X)=>curious(X)))&
((![X]:((((strong(X))<~>(quieter(steven,X))))<=>(((kind(X))<~>(richer(steven,X)))))))&
(![X]:(happy(X)=>brave(X))) | room(david)&(![X]:(room(X)=>(X='david')))&
wise(david) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8469549308569355913451511
% SZS output start Proof for 8469549308569355913451511
49. ~? [X0] : (generous(X0) => wise(X0)) [input p5]
54. wise(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
59. ~? [X0] : wise(X0) [pure predicate removal 49]
135. ! [X0] : ~wise(X0) [ennf transformation 59]
136. wise(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 54]
227. ~wise(X0) [cnf transformation 135]
239. wise(mary) [cnf transformation 136]
240. $false [subsumption resolution 239,227]
% SZS output end Proof for 8469549308569355913451511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.625768 |
Debra, Rachel, Patricia, Peter are the only persons in the room.
“Debra competes in national level swimming championships or participates in citizen science projects related to wildlife monitoring or both” if “Debra neither competes in national level swimming championships nor enjoys snowboarding”.
“Peter knows morse code” only if “Patricia does not enjoy coding in Python”.
Either “Patricia enjoys coding in Python, does not own a 3D printer and does not enjoy writing detailed reviews of new and classic board games” or “Rachel either does not watche fantasy movies or is dedicated to sustainable living and zero-waste practices but not both” but not both.
Either “Patricia practices tai chi” or “Debra owns a telescope” but not both.
“Peter enjoys camping and organizing outdoor survival workshops” if “Peter collects antique clocks” and vice versa.
Either “Debra is a dedicated advocate for digital privacy and encryption” or “Peter does not volunteer for local environmental conservation projects” but not both.
Peter knows morse code.
Peter who is a wine connoisseur collects antique clocks or practices tai chi or both.
Peter neither practices tai chi nor does not own a 3D printer.
Patricia neither is dedicated to sustainable living and zero-waste practices nor is not a wine connoisseur.
If someone neither plays video games nor is not a wine connoisseur then he/she neither participates in citizen science projects related to wildlife monitoring nor plays video games.
Patricia participates in citizen science projects related to wildlife monitoring, practices graffiti art and does not compete in national level swimming championships. | Patricia plays video games. | entailment | room(debra)&room(rachel)&room(patricia)&room(peter)&(![X]:(room(X)=>(X='debra'|X='rachel'|X='patricia'|X='peter')))&
((~((competes_in_national_level_swimming_championships(debra))|(enjoys_snowboarding(debra))))=>(((competes_in_national_level_swimming_championships(debra))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(debra)))))&
((knows_morse_code(peter))=>(does_not_enjoy_coding_in_Python(patricia)))&
((((enjoys_coding_in_Python(patricia))&(does_not_own_a_3D_printer(patricia))&(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(patricia))))<~>(((does_not_watche_fantasy_movies(rachel))<~>(is_dedicated_to_sustainable_living_and_zero-waste_practices(rachel)))))&
((practices_tai_chi(patricia))<~>(owns_a_telescope(debra)))&
((collects_antique_clocks(peter))<=>(enjoys_camping_and_organizing_outdoor_survival_workshops(peter)))&
((is_a_dedicated_advocate_for_digital_privacy_and_encryption(debra))<~>(does_not_volunteer_for_local_environmental_conservation_projects(peter)))&
(knows_morse_code(peter))&
((is_a_wine_connoisseur(peter))&(((collects_antique_clocks(peter))|(practices_tai_chi(peter)))))&
(~((practices_tai_chi(peter))|(does_not_own_a_3D_printer(peter))))&
(~((is_dedicated_to_sustainable_living_and_zero-waste_practices(patricia))|(is_not_a_wine_connoisseur(patricia))))&
(~((owns_a_telescope(rachel))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(rachel))))&
((![X]:((~((plays_video_games(X))|(is_not_a_wine_connoisseur(X))))=>(~((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(plays_video_games(X)))))))&
(~((does_not_play_the_drums(rachel))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(rachel))))&
(does_not_volunteer_for_local_environmental_conservation_projects(peter))&
(((has_a_pet_dog(rachel))|(mentors_a_youth_basketball_team_on_weekends(rachel))))&
(~((competes_in_national_level_swimming_championships(debra))|(enjoys_snowboarding(debra))))&
(owns_a_telescope(debra))&
(((does_not_enjoy_stand-up_paddleboarding(patricia))<~>(does_not_own_a_telescope(patricia))))&
(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(patricia))&(practices_graffiti_art(patricia))&(does_not_compete_in_national_level_swimming_championships(patricia)))) | room(debra)&room(rachel)&room(patricia)&room(peter)&(![X]:(room(X)=>(X='debra'|X='rachel'|X='patricia'|X='peter')))&
plays_video_games(patricia) | [
"p0",
"p10",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5846407738814929010778233
% SZS output start Proof for 5846407738814929010778233
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
54. ~(~predv(fred) | predw(fred)) [input p10]
56. ! [X0] : (~(~predv(X0) | predx(X0)) => ~(predx(X0) | predd(X0))) [input p12]
63. ~predq(fred) & predb(fred) & predd(fred) [input p19]
64. ~(predx(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
65. ~predq(fred) & predd(fred) [pure predicate removal 63]
140. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
141. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 140]
146. predv(fred) & ~predw(fred) [ennf transformation 54]
148. ! [X0] : ((~predx(X0) & ~predd(X0)) | (~predv(X0) | predx(X0))) [ennf transformation 56]
149. ! [X0] : ((~predx(X0) & ~predd(X0)) | ~predv(X0) | predx(X0)) [flattening 148]
152. ~predx(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 64]
153. ~predx(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 152]
161. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom]
162. ~predx(fred) | (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 153,161]
243. room(mary) [cnf transformation 141]
244. room(paul) [cnf transformation 141]
245. room(fred) [cnf transformation 141]
246. room(alice) [cnf transformation 141]
247. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 141]
270. predv(fred) [cnf transformation 146]
273. ~predv(X0) | ~predd(X0) | predx(X0) [cnf transformation 149]
282. predd(fred) [cnf transformation 65]
284. ~predx(fred) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
285. ~predx(fred) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
286. ~predx(fred) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
287. ~predx(fred) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
288. ~predx(fred) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162]
387. ~predx(fred) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,246]
388. ~predx(fred) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 387,245]
389. ~predx(fred) | alice != sK0 | ~room(mary) [subsumption resolution 388,244]
390. ~predx(fred) | alice != sK0 [subsumption resolution 389,243]
392. 19 <=> alice = sK0 [avatar definition]
394. alice != sK0 <- (~19) [avatar component clause 392]
396. 20 <=> predx(fred) [avatar definition]
399. ~19 | ~20 [avatar split clause 390,396,392]
400. ~predx(fred) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,246]
401. ~predx(fred) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 400,245]
402. ~predx(fred) | fred != sK0 | ~room(mary) [subsumption resolution 401,244]
403. ~predx(fred) | fred != sK0 [subsumption resolution 402,243]
405. 21 <=> fred = sK0 [avatar definition]
407. fred != sK0 <- (~21) [avatar component clause 405]
408. ~21 | ~20 [avatar split clause 403,396,405]
409. ~predx(fred) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,246]
410. ~predx(fred) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 409,245]
411. ~predx(fred) | paul != sK0 | ~room(mary) [subsumption resolution 410,244]
412. ~predx(fred) | paul != sK0 [subsumption resolution 411,243]
414. 22 <=> paul = sK0 [avatar definition]
416. paul != sK0 <- (~22) [avatar component clause 414]
417. ~22 | ~20 [avatar split clause 412,396,414]
418. ~predx(fred) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,246]
419. ~predx(fred) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 418,245]
420. ~predx(fred) | mary != sK0 | ~room(mary) [subsumption resolution 419,244]
421. ~predx(fred) | mary != sK0 [subsumption resolution 420,243]
423. 23 <=> mary = sK0 [avatar definition]
425. mary != sK0 <- (~23) [avatar component clause 423]
426. ~23 | ~20 [avatar split clause 421,396,423]
427. ~predx(fred) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,246]
428. ~predx(fred) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 427,245]
429. ~predx(fred) | room(sK0) | ~room(mary) [subsumption resolution 428,244]
430. ~predx(fred) | room(sK0) [subsumption resolution 429,243]
432. 24 <=> room(sK0) [avatar definition]
434. room(sK0) <- (24) [avatar component clause 432]
435. 24 | ~20 [avatar split clause 430,396,432]
437. ~predd(fred) | predx(fred) [resolution 273,270]
447. predx(fred) [subsumption resolution 437,282]
450. 20 [avatar split clause 447,396]
491. fred = sK0 | paul = sK0 | mary = sK0 | alice = sK0 <- (24) [resolution 247,434]
492. paul = sK0 | mary = sK0 | alice = sK0 <- (~21, 24) [subsumption resolution 491,407]
493. mary = sK0 | alice = sK0 <- (~21, ~22, 24) [subsumption resolution 492,416]
494. alice = sK0 <- (~21, ~22, ~23, 24) [subsumption resolution 493,425]
495. $false <- (~19, ~21, ~22, ~23, 24) [subsumption resolution 494,394]
496. 19 | 21 | 22 | 23 | ~24 [avatar contradiction clause 495]
497. $false [avatar sat refutation 399,408,417,426,435,450,496]
% SZS output end Proof for 5846407738814929010778233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.132214 |
There is a room.
Everyone in the room who practices calligraphy owns a smart tv.
Everyone in the room does practice yoga if they owns a smart tv.
Everyone in the room has a tattoo only if they has lived in exactly three countries.
Everyone in the room enjoys salsa dancing if they has lived in exactly three countries.
Everyone in the room who designs and sews custom cosplay costumes for conventions is an expert in identifying and foraging wild edible plants.
If someone practices kickboxing then he/she designs and sews custom cosplay costumes for conventions.
Everyone outside the room designs and sews custom cosplay costumes for conventions if they has a vast collection of first-edition science fiction novels, is a culinary enthusiast who experiments with international cuisines or designs and sews custom cosplay costumes for conventions.
Everyone in the room who designs and sews custom cosplay costumes for conventions owns a smart tv.
Everyone in the room collects foreign coins.
No one in the room collects vintage stamps if they does not practice kickboxing and vice versa.
If someone does not use contact lenses then he/she enjoys virtual reality gaming, does not enjoy writing detailed reviews of new and classic board games or enjoys fishing and vice versa.
Everyone in the room who practices kickboxing neither practices kickboxing nor practices urban gardening.
More than one person in the room collects vintage stamps, does not collect vintage stamps or collects foreign coins.
Everyone in the room who enjoys salsa dancing practices kickboxing.
Everyone in the room who practices kickboxing regularly goes on multi-day backpacking trips in national parks.
If someone enjoys salsa dancing then he/she collects foreign coins. | Everyone in the room has lived in exactly three countries. | contradiction | (there_is_a_room)&
(![X]:(room(X)=>(((practices_calligraphy(X))=>(owns_a_smart_tv(X))))))&
(![X]:(room(X)=>(((owns_a_smart_tv(X))=>(does_practice_yoga(X))))))&
(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))<=(has_a_tattoo(X))))))&
(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(enjoys_salsa_dancing(X))))))&
(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))&
((![X]:((practices_kickboxing(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))&
(![X]:(~room(X)=>(((((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))&
(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(owns_a_smart_tv(X))))))&
(![X]:(room(X)=>(collects_foreign_coins(X))))&
(~?[X]:(room(X)=>(((collects_vintage_stamps(X))<=>(does_not_practice_kickboxing(X))))))&
((![X]:((does_not_use_contact_lenses(X))<=>(((enjoys_virtual_reality_gaming(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(enjoys_fishing(X)))))))&
(![X]:(room(X)=>(((practices_kickboxing(X))=>(~((practices_kickboxing(X))|(practices_urban_gardening(X))))))))&
((?[X,Y]:(room(X)&room(Y)&(((collects_vintage_stamps(X))|(does_not_collect_vintage_stamps(X))|(collects_foreign_coins(X)))&((collects_vintage_stamps(Y))|(does_not_collect_vintage_stamps(Y))|(collects_foreign_coins(Y))))&(X!=Y))))&
(![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(practices_kickboxing(X))))))&
(![X]:(room(X)=>(((practices_kickboxing(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))&
((![X]:((enjoys_salsa_dancing(X))=>(collects_foreign_coins(X))))) | (there_is_a_room)&
![X]:(room(X)=>(has_lived_in_exactly_three_countries(X))) | [
"p4",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 702333375719900193856744
% SZS output start Proof for 702333375719900193856744
48. ! [X0] : (room(X0) => (predk(X0) => predx(X0))) [input p4]
54. ~? [X0] : (room(X0) => (predl(X0) <=> ~predi(X0))) [input p10]
56. ! [X0] : (room(X0) => (predi(X0) => ~(predh(X0) | predi(X0)))) [input p12]
58. ! [X0] : (room(X0) => (predx(X0) => predi(X0))) [input p14]
61. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis]
63. ! [X0] : (room(X0) => (predi(X0) => ~predi(X0))) [pure predicate removal 56]
75. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 61]
148. ! [X0] : ((predx(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 48]
149. ! [X0] : (predx(X0) | ~predk(X0) | ~room(X0)) [flattening 148]
153. ! [X0] : ((predl(X0) <~> ~predi(X0)) & room(X0)) [ennf transformation 54]
154. ! [X0] : ((~predi(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 63]
155. ! [X0] : (~predi(X0) | ~predi(X0) | ~room(X0)) [flattening 154]
156. ! [X0] : ((predi(X0) | ~predx(X0)) | ~room(X0)) [ennf transformation 58]
157. ! [X0] : (predi(X0) | ~predx(X0) | ~room(X0)) [flattening 156]
158. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 75]
160. ! [X0] : (((predi(X0) | ~predl(X0)) & (~predi(X0) | predl(X0))) & room(X0)) [nnf transformation 153]
161. ! [X0] : ((predi(X0) | ~predl(X0)) & (~predi(X0) | predl(X0)) & room(X0)) [flattening 160]
244. ~predk(X0) | predx(X0) | ~room(X0) [cnf transformation 149]
247. room(X0) [cnf transformation 161]
250. ~predi(X0) | ~predi(X0) | ~room(X0) [cnf transformation 155]
254. predi(X0) | ~predx(X0) | ~room(X0) [cnf transformation 157]
255. predk(X0) | ~room(X0) [cnf transformation 158]
256. ~predi(X0) | ~room(X0) [duplicate literal removal 250]
257. ~predi(X0) [subsumption resolution 256,247]
258. ~predx(X0) | ~room(X0) [subsumption resolution 254,257]
259. ~predx(X0) [subsumption resolution 258,247]
260. predk(X0) [subsumption resolution 255,247]
261. predx(X0) | ~room(X0) [resolution 244,260]
262. ~room(X0) [subsumption resolution 261,259]
263. $false [subsumption resolution 262,247]
% SZS output end Proof for 702333375719900193856744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.188089 |