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
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|---|---|---|---|---|---|---|---|
Callie, Monica, Karen, James are the only persons in the room.
Not everyone in the room is not a quiet person if they is not a quiet old person.
Karen who is older than Elmer is a old person.
Everyone in the room is old if they is richer than Elmer.
Monica is richer than Elmer. | Monica is the least rich in the room. | contradiction | room(callie)&room(monica)&room(karen)&room(james)&(![X]:(room(X)=>(X='callie'|X='monica'|X='karen'|X='james')))&
(~![X]:(room(X)=>(((old(X)&person(X))<=>(older(elmer,X))))))&
(~![X]:(room(X)=>(((~(quiet(X)&old(X)&person(X)))=>(~(quiet(X)&person(X)))))))&
(?[X]:(anywhere(X)&(older(elmer,X))))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(~quiet(X)&~quiet(Y))&(X!=Y))))&
((older(elmer,karen))&(old(karen)&person(karen)))&
(![X]:(room(X)=>(((~quiet(X))=>(((quiet(X)&old(X)&person(X))&(~quiet(X)&~old(X))))))))&
(![X]:(room(X)=>(((((quiet(X)&old(X)&person(X))&(~quiet(X)&~old(X))))=>(richer(elmer,X))))))&
(![X]:(room(X)=>(((richer(elmer,X))=>(old(X))))))&
(![X]:(room(X)=>(((~old(X))=>(quiet(X))))))&
(![X]:(room(X)=>(((~(quiet(X)&person(X)))=>(((~(old(X)&quiet(X)&person(X)))|(~(quiet(X)&person(X)))))))))&
(richer(elmer,monica)) | room(callie)&room(monica)&room(karen)&room(james)&(![X]:(room(X)=>(X='callie'|X='monica'|X='karen'|X='james')))&
![X]:((room(X)&(X!=monica))=>richer(monica,X)) | [
"b6",
"b42",
"p0",
"p2",
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2129646301146494051310912
% SZS output start Proof for 2129646301146494051310912
7. ! [X0,X1,X2] : ((X0 != X2 & X1 != X2 & X0 != X1) => ((richer(X1,X2) & richer(X0,X1)) => richer(X0,X2))) [input b6]
43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42]
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
46. ~! [X0] : (room(X0) => (~(person(X0) & old(X0) & quiet(X0)) => ~(person(X0) & quiet(X0)))) [input p2]
49. person(fred) & old(fred) & older(john,fred) [input p5]
52. ! [X0] : (room(X0) => (richer(john,X0) => old(X0))) [input p8]
55. richer(john,paul) [input p11]
56. ! [X0] : ((paul != X0 & room(X0)) => richer(paul,X0)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
57. ! [X0] : ((paul != X0 & room(X0)) => richer(paul,X0)) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 56]
66. ! [X0,X1,X2] : ((richer(X0,X2) | (~richer(X1,X2) | ~richer(X0,X1))) | (X0 = X2 | X1 = X2 | X0 = X1)) [ennf transformation 7]
67. ! [X0,X1,X2] : (richer(X0,X2) | ~richer(X1,X2) | ~richer(X0,X1) | X0 = X2 | X1 = X2 | X0 = X1) [flattening 66]
132. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
133. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132]
135. ? [X0] : (((person(X0) & quiet(X0)) & (~person(X0) | ~old(X0) | ~quiet(X0))) & room(X0)) [ennf transformation 46]
136. ? [X0] : (person(X0) & quiet(X0) & (~person(X0) | ~old(X0) | ~quiet(X0)) & room(X0)) [flattening 135]
141. ! [X0] : ((old(X0) | ~richer(john,X0)) | ~room(X0)) [ennf transformation 52]
142. ! [X0] : (old(X0) | ~richer(john,X0) | ~room(X0)) [flattening 141]
147. ! [X0] : (richer(paul,X0) | (paul = X0 | ~room(X0))) & ! [X1] : ((alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 57]
148. ! [X0] : (richer(paul,X0) | paul = X0 | ~room(X0)) & ! [X1] : (alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147]
154. ? [X0] : (person(X0) & quiet(X0) & (~person(X0) | ~old(X0) | ~quiet(X0)) & room(X0)) => (person(sK1) & quiet(sK1) & (~person(sK1) | ~old(sK1) | ~quiet(sK1)) & room(sK1)) [choice axiom]
155. person(sK1) & quiet(sK1) & (~person(sK1) | ~old(sK1) | ~quiet(sK1)) & room(sK1) [skolemisation 136,154]
162. ~richer(X1,X2) | richer(X0,X2) | ~richer(X0,X1) | X0 = X2 | X1 = X2 | X0 = X1 [cnf transformation 67]
204. mary != paul [cnf transformation 43]
217. paul != alice [cnf transformation 43]
222. mary != john [cnf transformation 43]
223. paul != john [cnf transformation 43]
225. alice != john [cnf transformation 43]
240. room(mary) [cnf transformation 133]
241. room(paul) [cnf transformation 133]
243. room(alice) [cnf transformation 133]
244. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 133]
249. room(sK1) [cnf transformation 155]
250. ~person(sK1) | ~old(sK1) | ~quiet(sK1) [cnf transformation 155]
251. quiet(sK1) [cnf transformation 155]
252. person(sK1) [cnf transformation 155]
258. old(fred) [cnf transformation 49]
266. ~richer(john,X0) | old(X0) | ~room(X0) [cnf transformation 142]
270. richer(john,paul) [cnf transformation 55]
276. richer(paul,X0) | paul = X0 | ~room(X0) [cnf transformation 148]
295. ~old(sK1) | ~quiet(sK1) [subsumption resolution 250,252]
296. ~old(sK1) [subsumption resolution 295,251]
316. old(paul) | ~room(paul) [resolution 266,270]
317. old(paul) [subsumption resolution 316,241]
495. 18 <=> paul = sK1 [avatar definition]
497. paul = sK1 <- (18) [avatar component clause 495]
536. fred = sK1 | paul = sK1 | mary = sK1 | alice = sK1 [resolution 244,249]
551. 25 <=> alice = sK1 [avatar definition]
553. alice = sK1 <- (25) [avatar component clause 551]
555. 26 <=> mary = sK1 [avatar definition]
557. mary = sK1 <- (26) [avatar component clause 555]
559. 27 <=> fred = sK1 [avatar definition]
561. fred = sK1 <- (27) [avatar component clause 559]
562. 25 | 26 | 18 | 27 [avatar split clause 536,559,495,555,551]
565. ~old(paul) <- (18) [backward demodulation 296,497]
568. $false <- (18) [subsumption resolution 565,317]
569. ~18 [avatar contradiction clause 568]
584. ~old(alice) <- (25) [backward demodulation 296,553]
601. richer(X1,X2) | ~richer(X1,paul) | X1 = X2 | paul = X2 | paul = X1 | paul = X2 | ~room(X2) [resolution 162,276]
604. ~richer(X1,paul) | richer(X1,X2) | X1 = X2 | paul = X2 | paul = X1 | ~room(X2) [duplicate literal removal 601]
645. 29 <=> old(mary) [avatar definition]
647. old(mary) <- (29) [avatar component clause 645]
760. richer(john,X0) | john = X0 | paul = X0 | paul = john | ~room(X0) [resolution 604,270]
767. richer(john,X0) | john = X0 | paul = X0 | ~room(X0) [subsumption resolution 760,223]
836. john = X0 | paul = X0 | ~room(X0) | old(X0) | ~room(X0) [resolution 767,266]
855. ~room(X0) | paul = X0 | john = X0 | old(X0) [duplicate literal removal 836]
860. mary = paul | mary = john | old(mary) [resolution 855,240]
863. paul = alice | alice = john | old(alice) [resolution 855,243]
864. mary = john | old(mary) [subsumption resolution 860,204]
865. old(mary) [subsumption resolution 864,222]
866. 29 [avatar split clause 865,645]
867. alice = john | old(alice) [subsumption resolution 863,217]
868. old(alice) [subsumption resolution 867,225]
869. $false <- (25) [subsumption resolution 868,584]
870. ~25 [avatar contradiction clause 869]
875. ~old(mary) <- (26) [backward demodulation 296,557]
879. $false <- (26, 29) [subsumption resolution 875,647]
880. ~26 | ~29 [avatar contradiction clause 879]
885. ~old(fred) <- (27) [backward demodulation 296,561]
888. $false <- (27) [subsumption resolution 885,258]
889. ~27 [avatar contradiction clause 888]
904. $false [avatar sat refutation 562,569,866,870,880,889]
% SZS output end Proof for 2129646301146494051310912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Todd, Annette are the only persons in the room. If “everyone in the room is not a drone photographer” then “everyone in the room is not a wine connoisseur with a private cellar of vintage wines” otherwise “everyone in the room either does not create bespoke furniture pieces from reclaimed wood or does not enjoy camping and organizing outdoor survival workshops but not both”. If “everyone in the room does not create bespoke furniture pieces from reclaimed wood, does not host a YouTube channel dedicated to art tutorials or does not frequently participates in hackathons and coding competitions” then “not everyone in the room either does not enjoy making ceramics or is not a culinary enthusiast who experiments with international cuisines but not both”. If “not everyone in the room either does not enjoy making ceramics or is not a culinary enthusiast who experiments with international cuisines but not both” then “more than one person in the room does not read mystery novels”. Everyone in the room is not a drone photographer, does not develop open-source software projects in their free time or does not enjoy camping and organizing outdoor survival workshops. Someone in the room does not enjoy cross-country skiing. Everyone in the room does not develop open-source software projects in their free time. Everyone in the room is not a culinary enthusiast who experiments with international cuisines, does not develop open-source software projects in their free time or does not practice pilates. More than one person in the room does not read mystery novels. Someone in the room does not own an extensive assortment of vintage comic book memorabilia. Everyone in the room is not a wine connoisseur with a private cellar of vintage wines, does not have a pet dog or does not have completed a triathlon. Everyone in the room does not enjoy virtual reality gaming or does not create large-scale murals for public art installations or both. Everyone in the room does not create augmented reality experiences for mobile applications. Everyone in the room does not have completed a triathlon or does not read mystery novels or both. | Everyone in the room does not practice pilates and does not create large-scale murals for public art installations. | neutral | room(todd)&room(annette)&(![X]:(room(X)=>(X='todd'|X='annette')))&
(((![X]:(room(X)=>(is_not_a_drone_photographer(X))))=>(![X]:(room(X)=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))&((~(![X]:(room(X)=>(is_not_a_drone_photographer(X)))))=>(![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))<~>(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))))&
(((![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(~![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))<~>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))&
((~![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))<~>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))=>((?[X,Y]:(room(X)&room(Y)&(does_not_read_mystery_novels(X)&does_not_read_mystery_novels(Y))&(X!=Y))))))&
(![X]:(room(X)=>(((is_not_a_drone_photographer(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))&
(?[X]:(room(X)&(does_not_enjoy_cross-country_skiing(X))))&
(![X]:(room(X)=>(does_not_develop_open-source_software_projects_in_their_free_time(X))))&
(![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))|(does_not_practice_pilates(X))))))&
((?[X,Y]:(room(X)&room(Y)&(does_not_read_mystery_novels(X)&does_not_read_mystery_novels(Y))&(X!=Y))))&
(?[X]:(room(X)&(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))&
(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(does_not_have_a_pet_dog(X))|(does_not_have_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))&
(![X]:(room(X)=>(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))&
(![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(does_not_read_mystery_novels(X)))))) | room(todd)&room(annette)&(![X]:(room(X)=>(X='todd'|X='annette')))&
![X]:(room(X)=>(((does_not_practice_pilates(X))&(does_not_create_large-scale_murals_for_public_art_installations(X))))) | [] | null | 0.275947 |
Nanci, Thomas are the only persons in the room.
If Thomas owns a 3D printer then everyone in the room is an amateur astronomer who builds and uses custom telescopes only if they designs and sews custom cosplay costumes for conventions.
If not everyone in the room cannot play the guitar or is a culinary enthusiast who experiments with international cuisines then no one in the room is a culinary enthusiast who experiments with international cuisines or does not play video games.
If no one in the room is a culinary enthusiast who experiments with international cuisines or does not play video games then Nanci practices and performs acrobatic dance routines or develops open-source software projects in their free time or both.
If Thomas enjoys salsa dancing then Thomas practices calligraphy.
Everyone in the room who enjoys virtual reality gaming is a chess master who participates in national tournaments.
If someone does not practice calligraphy then he/she owns a microscope and vice versa.
Everyone in the room is an amateur astronomer who builds and uses custom telescopes only if they designs and sews custom cosplay costumes for conventions.
Thomas is a skilled home brewer experimenting with craft beer recipes or is a chess master who participates in national tournaments or both.
Thomas practices calligraphy.
Thomas is an amateur astronomer who builds and uses custom telescopes.
Someone in the room cannot play the guitar.
Everyone in the room does not play video games if they enjoys camping and organizing outdoor survival workshops.
Everyone in the room who does not play video games owns a microscope or is a night owl or both.
Everyone in the room either enjoys salsa dancing or owns a 3D printer but not both if they owns a microscope or is a night owl or both. | Thomas is a skilled home brewer experimenting with craft beer recipes. | neutral | room(nanci)&room(thomas)&(![X]:(room(X)=>(X='nanci'|X='thomas')))&
((owns_a_3D_printer(thomas))=>(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))))&
(((~![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(cannot_play_the_guitar(X))))))=>(~?[X]:(room(X)=>(((does_not_play_video_games(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))&
((~?[X]:(room(X)=>(((does_not_play_video_games(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))=>(((practices_and_performs_acrobatic_dance_routines(nanci))|(develops_open-source_software_projects_in_their_free_time(nanci))))))&
((enjoys_salsa_dancing(thomas))=>(practices_calligraphy(thomas)))&
(![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))&
((![X]:((does_not_practice_calligraphy(X))<=>(owns_a_microscope(X)))))&
(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))&
(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(thomas))|(is_a_chess_master_who_participates_in_national_tournaments(thomas))))&
(practices_calligraphy(thomas))&
(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(thomas))&
(?[X]:(room(X)&(cannot_play_the_guitar(X))))&
(![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(does_not_play_video_games(X))))))&
(![X]:(room(X)=>(((does_not_play_video_games(X))=>(((owns_a_microscope(X))|(is_a_night_owl(X))))))))&
(![X]:(room(X)=>(((((owns_a_microscope(X))|(is_a_night_owl(X))))=>(((enjoys_salsa_dancing(X))<~>(owns_a_3D_printer(X)))))))) | room(nanci)&room(thomas)&(![X]:(room(X)=>(X='nanci'|X='thomas')))&
is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(thomas) | [] | null | 0.024483 |
Stephen is the only person in the room. Everyone in the room hosts a popular podcast about emerging technologies if they can play the piano. Someone in the room hosts a popular podcast about emerging technologies. Everyone in the room who hosts a popular podcast about emerging technologies can play the piano. Everyone anywhere who can play the piano can play the harmonica. Everyone in the room hosts a popular podcast about emerging technologies if they can play the harmonica. Everyone in the room can play the harmonica if they hosts a popular podcast about emerging technologies. Stephen hosts a popular podcast about emerging technologies. Everyone in the room who does not host a popular podcast about emerging technologies can play the harmonica. Everyone in the room can play the harmonica if they hosts a popular podcast about emerging technologies and vice versa. Stephen can play the harmonica. Everyone in the room can play the harmonica if they can play the piano. Everyone in the room hosts a popular podcast about emerging technologies or can play the piano or both if they can play the harmonica. | Everyone outside the room does not host a popular podcast about emerging technologies. | neutral | room(stephen)&(![X]:(room(X)=>(X='stephen')))&
(![X]:(room(X)=>(((can_play_the_piano(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(?[X]:(room(X)&(hosts_a_popular_podcast_about_emerging_technologies(X))))&
(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(can_play_the_piano(X))))))&
(![X]:(anywhere(X)=>(((can_play_the_piano(X))=>(can_play_the_harmonica(X))))))&
(![X]:(room(X)=>(((can_play_the_harmonica(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(can_play_the_harmonica(X))))))&
(hosts_a_popular_podcast_about_emerging_technologies(stephen))&
(![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))=>(can_play_the_harmonica(X))))))&
(![X]:(room(X)=>(((can_play_the_harmonica(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(can_play_the_harmonica(stephen))&
(![X]:(room(X)=>(((can_play_the_piano(X))=>(can_play_the_harmonica(X))))))&
(![X]:(room(X)=>(((can_play_the_harmonica(X))=>(((hosts_a_popular_podcast_about_emerging_technologies(X))|(can_play_the_piano(X)))))))) | room(stephen)&(![X]:(room(X)=>(X='stephen')))&
![X]:(~room(X)=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))) | [] | null | 0.372174 |
There is a room. “Not everyone in the room is older than Donald” unless “at least one person in the room is a old tall person”. If “everyone in the room is richer than Jerry” then “it is not the case that “more than one person in the room is older than Jerry””. Everyone in the room who is quieter than Jerry is quiet, is richer than Donald and is a tall quiet person. Everyone in the room is quiet. Everyone in the room is a tall person only if they is not a old quiet tall person. Everyone in the room who is not a old quiet tall person is richer than Jerry. Everyone in the room who is a old tall person is tall. All old persons are quiet. All old persons are tall. Everyone in the room is not a old person if they is not a tall old quiet person. Everyone in the room is quieter than Donald if they is not a old person. Everyone in the room is older than Jerry if they is quieter than Donald. No quiet person is old. Everyone in the room who is not a tall person and is not a quiet person is older than Donald. Everyone in the room who is not quiet, not old is quieter than Jerry. Everyone anywhere is older than Donald if they is quieter than Jerry. Everyone in the room who is older than Donald is richer than Donald. Everyone in the room is a quiet person if they is quieter than Jerry. Everyone anywhere is richer than Donald if they is a quiet person. | More than one person anywhere is richer than Jerry and is quieter than Jerry. | neutral | (there_is_a_room)&
(~(((?[X]:(room(X)&old(X)&tall(X)&person(X)))))=>(~![X]:(room(X)=>(older(donald,X)))))&
((![X]:(room(X)=>(richer(jerry,X))))=>(~((?[X,Y]:(room(X)&room(Y)&(older(jerry,X)&older(jerry,Y))&(X!=Y))))))&
(![X]:(room(X)=>(((quieter(jerry,X))=>(((quiet(X))&(richer(donald,X))&(tall(X)&quiet(X)&person(X))))))))&
(![X]:(room(X)=>(quiet(X))))&
(![X]:(room(X)=>(((~(old(X)&quiet(X)&tall(X)&person(X)))<=(tall(X)&person(X))))))&
(![X]:(room(X)=>(((~(old(X)&quiet(X)&tall(X)&person(X)))=>(richer(jerry,X))))))&
(![X]:(room(X)=>(((old(X)&tall(X)&person(X))=>(tall(X))))))&
(![X]:(old(X)=>quiet(X)))&
(![X]:(old(X)=>tall(X)))&
(![X]:(room(X)=>(((~(tall(X)&old(X)&quiet(X)&person(X)))=>(~(old(X)&person(X)))))))&
(![X]:(room(X)=>(((~(old(X)&person(X)))=>(quieter(donald,X))))))&
(![X]:(room(X)=>(((quieter(donald,X))=>(older(jerry,X))))))&
(~?[X]:(quiet(X)=>old(X)))&
(![X]:(room(X)=>(((((~(tall(X)&person(X)))&(~(quiet(X)&person(X)))))=>(older(donald,X))))))&
(![X]:(room(X)=>(((~quiet(X)&~old(X))=>(quieter(jerry,X))))))&
(![X]:(anywhere(X)=>(((quieter(jerry,X))=>(older(donald,X))))))&
(![X]:(room(X)=>(((older(donald,X))=>(richer(donald,X))))))&
(![X]:(room(X)=>(((quieter(jerry,X))=>(quiet(X)&person(X))))))&
(![X]:(anywhere(X)=>(((quiet(X)&person(X))=>(richer(donald,X)))))) | (there_is_a_room)&
(?[X,Y]:(anywhere(X)&anywhere(Y)&(((richer(jerry,X))&(quieter(jerry,X)))&((richer(jerry,Y))&(quieter(jerry,Y))))&(X!=Y))) | [] | null | 0.363341 |
Lisa is the only person in the room. “At least one person in the room is a culinary enthusiast who experiments with international cuisines” if “not everyone outside the room enjoys bird watching or does not collect modern art” and vice versa. At least one person in the room is a culinary enthusiast who experiments with international cuisines. Someone in the room enjoys bird watching, is a culinary enthusiast who experiments with international cuisines or collects modern art. Lisa is a culinary enthusiast who experiments with international cuisines. Everyone anywhere who is a culinary enthusiast who experiments with international cuisines regularly contributes to tech forums and online communities. Everyone in the room who regularly contributes to tech forums and online communities is a culinary enthusiast who experiments with international cuisines. Lisa collects modern art or does not practice and performs acrobatic dance routines or both. Everyone outside the room who is not a culinary enthusiast who experiments with international cuisines is a client of Costco. If someone collects modern art then he/she is a client of Costco. Lisa who does not collect modern art is a client of Costco. Everyone in the room who regularly contributes to tech forums and online communities is a client of Costco. Lisa dreamt that “if someone practices and performs acrobatic dance routines then he/she is a culinary enthusiast who experiments with international cuisines and vice versa”. If someone regularly contributes to tech forums and online communities then he/she enjoys bird watching and vice versa. | Not everyone in the room enjoys bird watching. | contradiction | room(lisa)&(![X]:(room(X)=>(X='lisa')))&
((~![X]:(~room(X)=>(((does_not_collect_modern_art(X))|(enjoys_bird_watching(X))))))<=>(((?[X]:(room(X)&is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(((?[X]:(room(X)&is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))&
(?[X]:(room(X)&(((enjoys_bird_watching(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(collects_modern_art(X))))))&
(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(lisa))&
(![X]:(anywhere(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(((collects_modern_art(lisa))|(does_not_practice_and_performs_acrobatic_dance_routines(lisa))))&
(![X]:(~room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(is_a_client_of_Costco(X))))))&
((![X]:((collects_modern_art(X))=>(is_a_client_of_Costco(X)))))&
((does_not_collect_modern_art(lisa))&(is_a_client_of_Costco(lisa)))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(is_a_client_of_Costco(X))))))&
((lisa_dream=>((![X]:((practices_and_performs_acrobatic_dance_routines(X))<=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))&
((![X]:((regularly_contributes_to_tech_forums_and_online_communities(X))<=>(enjoys_bird_watching(X))))) | room(lisa)&(![X]:(room(X)=>(X='lisa')))&
~![X]:(room(X)=>(enjoys_bird_watching(X))) | [
"b4",
"p0",
"p4",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8014040282505382276949745
% SZS output start Proof for 8014040282505382276949745
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
48. predb(mary) [input p4]
49. ! [X0] : (anywhere(X0) => (predb(X0) => predf(X0))) [input p5]
57. ! [X0] : (predf(X0) <=> predd(X0)) [input p13]
58. ~! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
60. ~! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => mary = X1) & room(mary) [rectify 58]
138. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
141. ! [X0] : ((predf(X0) | ~predb(X0)) | ~anywhere(X0)) [ennf transformation 49]
142. ! [X0] : (predf(X0) | ~predb(X0) | ~anywhere(X0)) [flattening 141]
145. ? [X0] : (~predd(X0) & room(X0)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [ennf transformation 60]
156. ! [X0] : ((predf(X0) | ~predd(X0)) & (predd(X0) | ~predf(X0))) [nnf transformation 57]
157. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK4) & room(sK4)) [choice axiom]
158. (~predd(sK4) & room(sK4)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [skolemisation 145,157]
159. anywhere(X0) [cnf transformation 5]
241. ~room(X0) | mary = X0 [cnf transformation 138]
251. predb(mary) [cnf transformation 48]
252. predf(X0) | ~predb(X0) | ~anywhere(X0) [cnf transformation 142]
255. ~predf(X0) | predd(X0) [cnf transformation 156]
259. room(sK4) [cnf transformation 158]
260. ~predd(sK4) [cnf transformation 158]
305. ~predb(X0) | predf(X0) [subsumption resolution 252,159]
308. predf(mary) [resolution 305,251]
313. mary = sK4 [resolution 241,259]
321. ~predd(mary) [backward demodulation 260,313]
327. predd(mary) [resolution 308,255]
328. $false [subsumption resolution 327,321]
% SZS output end Proof for 8014040282505382276949745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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, Steven are the only persons in the room.
Barbara is the least rich in the room.
Steven who is a wise humble person is not a old curious brave tall person.
Everyone in the room is not old, not strong, not quiet, not humble, not generous or is a generous kind person or both if they is not a old kind person.
It is true that “Steven and Barbara are not a curious patient persons”.
Barbara is the least old in the room.
Everyone in the room who is calm is calm or is not a humble brave strong old person or both. | It is not the case that “it is not the case that “it is not the case that “more than one person in the room is not tall, is a kind person and is a old person”””. | neutral | room(barbara)&room(steven)&(![X]:(room(X)=>(X='barbara'|X='steven')))&
(![X]:((room(X)&(X!=barbara))=>richer(barbara,X)))&
((wise(steven)&humble(steven)&person(steven))&(~(old(steven)&curious(steven)&brave(steven)&tall(steven)&person(steven))))&
(![X]:(room(X)=>(((~(old(X)&kind(X)&person(X)))=>(((~old(X)&~strong(X)&~quiet(X)&~humble(X)&~generous(X))|(generous(X)&kind(X)&person(X))))))))&
(~(curious(steven)&patient(steven)&person(steven))&~(curious(barbara)&patient(barbara)&person(barbara)))&
(![X]:((room(X)&(X!=barbara))=>older(barbara,X)))&
(![X]:(room(X)=>(((calm(X))=>(((calm(X))|(~(humble(X)&brave(X)&strong(X)&old(X)&person(X)))))))))&
(![X]:(room(X)=>(((~(curious(X)&humble(X)&creative(X)&person(X)))=>(calm(X)&happy(X)&strong(X)&person(X))))))&
(((?[X]:(room(X)&~(curious(X)&humble(X)&creative(X)&person(X))))))&
(?[X,Y]:((brave(X))&(~wise(Y))&(quieter(X,Y))))&
(?[X,Y]:((((strong(X)&happy(X)&person(X))|(old(X))|(~(old(X)&person(X)))))&(generous(Y)&old(Y)&wise(Y)&creative(Y)&person(Y))&(older(X,Y))))&
(![X]:((anywhere(X)&(X!=barbara))=>older(barbara,X))) | room(barbara)&room(steven)&(![X]:(room(X)=>(X='barbara'|X='steven')))&
~(~(~((?[X,Y]:(room(X)&room(Y)&(((~tall(X))&(kind(X)&person(X))&(old(X)&person(X)))&((~tall(Y))&(kind(Y)&person(Y))&(old(Y)&person(Y))))&(X!=Y)))))) | [] | null | 0.077937 |
There is a room.
“Everyone in the room is a tall person, is a calm person or is a humble person” unless “everyone outside the room is a calm person”.
Either “everyone in the room is not tall or is a old person or both” or “everyone in the room is funny” but not both.
If “not everyone in the room is a tall person, is a quiet person and is a wise person” then “everyone in the room is a curious person” otherwise “no brave person is kind”.
Someone who is a calm person is older than someone who is not generous.
Everyone anywhere is a tall person or is not patient or both.
If someone is tall then he/she either is a brave person or is a patient person but not both.
Everyone in the room is strong.
All happy persons are old.
No calm person is creative. | Everyone in the room is a tall person. | neutral | (there_is_a_room)&
(~(![X]:(~room(X)=>(calm(X)&person(X))))=>(![X]:(room(X)=>(((tall(X)&person(X))|(calm(X)&person(X))|(humble(X)&person(X)))))))&
((![X]:(room(X)=>(((~tall(X))|(old(X)&person(X))))))<~>(![X]:(room(X)=>(funny(X)))))&
(((~![X]:(room(X)=>(((tall(X)&person(X))&(quiet(X)&person(X))&(wise(X)&person(X))))))=>(![X]:(room(X)=>(curious(X)&person(X)))))&((~(~![X]:(room(X)=>(((tall(X)&person(X))&(quiet(X)&person(X))&(wise(X)&person(X)))))))=>(~?[X]:(brave(X)=>kind(X)))))&
(?[X,Y]:((calm(X)&person(X))&(~generous(Y))&(older(X,Y))))&
(![X]:(anywhere(X)=>(((tall(X)&person(X))|(~patient(X))))))&
((![X]:((tall(X))=>(((brave(X)&person(X))<~>(patient(X)&person(X)))))))&
(![X]:(room(X)=>(strong(X))))&
(![X]:(happy(X)=>old(X)))&
(~?[X]:(calm(X)=>creative(X)))&
(![X]:(room(X)=>(brave(X)&person(X)))) | (there_is_a_room)&
![X]:(room(X)=>(tall(X)&person(X))) | [] | null | 0.444884 |
Claud, Stanley, Maura, Glenda, Frances are the only persons in the room. Frances builds model airplanes. Someone who enjoys landscape photography hate someone who is not an avid mountain climber who has scaled several peaks. All funny persons are strong. Someone who is a client of Costco hate someone who is a chess master who participates in national tournaments. Maura is curious. All wise persons are curious. Frances is a client of Meta. Glenda is not an active member of a local robotics club, builds model airplanes or does not have a saltwater aquarium. Glenda cannot play the harmonica. Maura is humble. All quiet persons are strong. Stanley is not old. Stanley practices digital art. If someone has a saltwater aquarium then he/she is creative and vice versa. Stanley practices tai chi. Someone who is an active member of a local robotics club hate someone who is not an avid mountain climber who has scaled several peaks. Stanley is a client of Meta. Glenda collects historical artifacts related to ancient civilizations. Stanley develops open-source software projects in their free time. All generous persons are brave. All funny persons are tall. Someone in the room is funny. Maura designs and sews custom cosplay costumes for conventions. If someone collects vintage vinyl records then he/she streams on Twitch and vice versa. | More than one person in the room is a client of Meta. | entailment | room(claud)&room(stanley)&room(maura)&room(glenda)&room(frances)&(![X]:(room(X)=>(X='claud'|X='stanley'|X='maura'|X='glenda'|X='frances')))&
(builds_model_airplanes(frances))&
(?[X,Y]:((enjoys_landscape_photography(X))&(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(Y))&(hate(X,Y))))&
(![X]:(funny(X)=>strong(X)))&
(?[X,Y]:((is_a_client_of_Costco(X))&(is_a_chess_master_who_participates_in_national_tournaments(Y))&(hate(X,Y))))&
(curious(maura))&
(![X]:(wise(X)=>curious(X)))&
(is_a_client_of_Meta(frances))&
(((is_not_an_active_member_of_a_local_robotics_club(glenda))|(builds_model_airplanes(glenda))|(does_not_have_a_saltwater_aquarium(glenda))))&
(cannot_play_the_harmonica(glenda))&
(humble(maura))&
(![X]:(quiet(X)=>strong(X)))&
(~old(stanley))&
(practices_digital_art(stanley))&
((![X]:((has_a_saltwater_aquarium(X))<=>(creative(X)))))&
(practices_tai_chi(stanley))&
(?[X,Y]:((is_an_active_member_of_a_local_robotics_club(X))&(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(Y))&(hate(X,Y))))&
(is_a_client_of_Meta(stanley))&
(collects_historical_artifacts_related_to_ancient_civilizations(glenda))&
(develops_open-source_software_projects_in_their_free_time(stanley))&
(![X]:(generous(X)=>brave(X)))&
(![X]:(funny(X)=>tall(X)))&
(?[X]:(room(X)&(funny(X))))&
(designs_and_sews_custom_cosplay_costumes_for_conventions(maura))&
((![X]:((collects_vintage_vinyl_records(X))<=>(streams_on_Twitch(X))))) | room(claud)&room(stanley)&room(maura)&room(glenda)&room(frances)&(![X]:(room(X)=>(X='claud'|X='stanley'|X='maura'|X='glenda'|X='frances')))&
(?[X,Y]:(room(X)&room(Y)&(is_a_client_of_Meta(X)&is_a_client_of_Meta(Y))&(X!=Y))) | [
"b42",
"p0",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8832020787776538937812926
% SZS output start Proof for 8832020787776538937812926
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]
51. predo(john) [input p7]
61. predo(paul) [input p17]
69. ~(? [X0,X1] : (X0 != X1 & predo(X1) & predo(X0) & room(X1) & room(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]
70. ~(? [X0,X1] : (X0 != X1 & predo(X1) & predo(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (john = X2 | alice = X2 | fred = X2 | paul = X2 | mary = X2)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 69]
170. ! [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]
171. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 170]
172. ! [X0,X1] : (X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0)) | ? [X2] : ((john != X2 & alice != X2 & fred != X2 & paul != X2 & mary != X2) & room(X2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70]
173. ! [X0,X1] : (X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0)) | ? [X2] : (john != X2 & alice != X2 & fred != X2 & paul != X2 & mary != X2 & room(X2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 172]
177. ? [X2] : (john != X2 & alice != X2 & fred != X2 & paul != X2 & mary != X2 & room(X2)) => (john != sK1 & alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom]
178. ! [X0,X1] : (X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0)) | (john != sK1 & alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,177]
242. paul != john [cnf transformation 43]
259. room(mary) [cnf transformation 171]
260. room(paul) [cnf transformation 171]
261. room(fred) [cnf transformation 171]
262. room(alice) [cnf transformation 171]
263. room(john) [cnf transformation 171]
264. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 171]
265. predo(john) [cnf transformation 51]
267. predo(paul) [cnf transformation 61]
269. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK1) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
270. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
271. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
272. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
273. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
274. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178]
275. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,263]
276. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,262]
277. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 276,261]
278. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK1 | ~room(mary) [subsumption resolution 277,260]
279. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK1 [subsumption resolution 278,259]
281. 1 <=> john = sK1 [avatar definition]
283. john != sK1 <- (~1) [avatar component clause 281]
285. 2 <=> ! [X0,X1] : (X0 = X1 | ~room(X0) | ~room(X1) | ~predo(X0) | ~predo(X1)) [avatar definition]
286. ~predo(X1) | ~room(X0) | ~room(X1) | ~predo(X0) | X0 = X1 <- (2) [avatar component clause 285]
287. ~1 | 2 [avatar split clause 279,285,281]
288. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,263]
289. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,262]
290. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 289,261]
291. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK1 | ~room(mary) [subsumption resolution 290,260]
292. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK1 [subsumption resolution 291,259]
294. 3 <=> alice = sK1 [avatar definition]
296. alice != sK1 <- (~3) [avatar component clause 294]
297. ~3 | 2 [avatar split clause 292,285,294]
298. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,263]
299. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 298,262]
300. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 299,261]
301. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK1 | ~room(mary) [subsumption resolution 300,260]
302. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK1 [subsumption resolution 301,259]
304. 4 <=> fred = sK1 [avatar definition]
306. fred != sK1 <- (~4) [avatar component clause 304]
307. ~4 | 2 [avatar split clause 302,285,304]
308. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,263]
309. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,262]
310. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 309,261]
311. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK1 | ~room(mary) [subsumption resolution 310,260]
312. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK1 [subsumption resolution 311,259]
314. 5 <=> paul = sK1 [avatar definition]
316. paul != sK1 <- (~5) [avatar component clause 314]
317. ~5 | 2 [avatar split clause 312,285,314]
318. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,263]
319. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,262]
320. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 319,261]
321. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK1 | ~room(mary) [subsumption resolution 320,260]
322. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK1 [subsumption resolution 321,259]
324. 6 <=> mary = sK1 [avatar definition]
326. mary != sK1 <- (~6) [avatar component clause 324]
327. ~6 | 2 [avatar split clause 322,285,324]
328. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,263]
329. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,262]
330. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 329,261]
331. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK1) | ~room(mary) [subsumption resolution 330,260]
332. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK1) [subsumption resolution 331,259]
334. 7 <=> room(sK1) [avatar definition]
336. room(sK1) <- (7) [avatar component clause 334]
337. 7 | 2 [avatar split clause 332,285,334]
380. ~room(X0) | ~room(john) | ~predo(X0) | john = X0 <- (2) [resolution 286,265]
382. ~predo(X0) | ~room(X0) | john = X0 <- (2) [subsumption resolution 380,263]
385. ~room(paul) | paul = john <- (2) [resolution 382,267]
386. paul = john <- (2) [subsumption resolution 385,260]
387. $false <- (2) [subsumption resolution 386,242]
388. ~2 [avatar contradiction clause 387]
395. alice = sK1 | fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (7) [resolution 264,336]
417. fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (~3, 7) [subsumption resolution 395,296]
418. paul = sK1 | mary = sK1 | john = sK1 <- (~3, ~4, 7) [subsumption resolution 417,306]
419. mary = sK1 | john = sK1 <- (~3, ~4, ~5, 7) [subsumption resolution 418,316]
420. john = sK1 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 419,326]
421. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 420,283]
422. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 421]
423. $false [avatar sat refutation 287,297,307,317,327,337,388,422]
% SZS output end Proof for 8832020787776538937812926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.635721 |
Todd, Juan, Toby, Judith, Marie are the only persons in the room.
“Todd creates bespoke furniture pieces from reclaimed wood” if “Todd does not enjoy wildlife photography” and vice versa.
If “Todd travels domestically frequently” then “Todd creates bespoke furniture pieces from reclaimed wood” otherwise “no one anywhere enjoys cross-country skiing if they neither owns a microscope nor enjoys wildlife photography”.
“No one in the room works on fridays or does not own a microscope” only if “everyone in the room who works on fridays does not have a curated collection of mid-century modern furniture”.
Either “Todd does not collect rare sneakers” or “everyone in the room collect rare sneakers or does not collect first edition books” but not both.
If “everyone in the room participates in citizen science projects related to wildlife monitoring or does not own a telescope” then “if someone does not travel domestically frequently then he/she enjoys wildlife photography and vice versa”.
Either “Todd enjoys snowboarding” or “no one in the room is a client of Meta or is not a certified scuba diver with advanced underwater photography skills” but not both.
If “not everyone in the room does not own a microscope” then “everyone in the room collects first edition books and works on fridays only if they either makes intricate hand-cut paper art for exhibitions or enjoys cross-country skiing but not both”.
“Todd does not write a travel blog, does not watche fantasy movies or enjoys snowboarding” if “Todd neither does not write a travel blog nor owns a telescope” and vice versa.
Everyone outside the room does not play the violin if they owns a microscope.
Everyone in the room who collect rare sneakers makes intricate hand-cut paper art for exhibitions.
Everyone outside the room plays the violin if they hosts regular workshops on creative writing.
Todd plays the violin.
Everyone in the room who does not collect first edition books hosts regular workshops on creative writing.
Todd hosts regular workshops on creative writing.
Everyone in the room travels domestically frequently if they owns a microscope.
Todd writes a travel blog.
Everyone in the room travels domestically frequently.
Todd does not collect rare sneakers.
Not everyone in the room travels domestically frequently only if they enjoys cross-country skiing. | Everyone in the room does not create bespoke furniture pieces from reclaimed wood. | contradiction | room(todd)&room(juan)&room(toby)&room(judith)&room(marie)&(![X]:(room(X)=>(X='todd'|X='juan'|X='toby'|X='judith'|X='marie')))&
((does_not_enjoy_wildlife_photography(todd))<=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(todd)))&
(((travels_domestically_frequently(todd))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(todd)))&((~(travels_domestically_frequently(todd)))=>(~?[X]:(anywhere(X)=>(((~((owns_a_microscope(X))|(enjoys_wildlife_photography(X))))=>(enjoys_cross-country_skiing(X))))))))&
((~?[X]:(room(X)=>(((does_not_own_a_microscope(X))|(works_on_fridays(X))))))=>(![X]:(room(X)=>(((works_on_fridays(X))=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X)))))))&
((does_not_collect_rare_sneakers(todd))<~>(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(collect_rare_sneakers(X)))))))&
((![X]:(room(X)=>(((does_not_own_a_telescope(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>((![X]:((does_not_travel_domestically_frequently(X))<=>(enjoys_wildlife_photography(X))))))&
((enjoys_snowboarding(todd))<~>(~?[X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_a_client_of_Meta(X)))))))&
((~![X]:(room(X)=>(does_not_own_a_microscope(X))))=>(![X]:(room(X)=>(((((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<~>(enjoys_cross-country_skiing(X))))<=(((collects_first_edition_books(X))&(works_on_fridays(X)))))))))&
((~((does_not_write_a_travel_blog(todd))|(owns_a_telescope(todd))))<=>(((does_not_write_a_travel_blog(todd))|(does_not_watche_fantasy_movies(todd))|(enjoys_snowboarding(todd)))))&
(![X]:(~room(X)=>(((owns_a_microscope(X))=>(does_not_play_the_violin(X))))))&
(![X]:(room(X)=>(((collect_rare_sneakers(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))&
(![X]:(~room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(plays_the_violin(X))))))&
(plays_the_violin(todd))&
(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))=>(hosts_regular_workshops_on_creative_writing(X))))))&
(hosts_regular_workshops_on_creative_writing(todd))&
(![X]:(room(X)=>(((owns_a_microscope(X))=>(travels_domestically_frequently(X))))))&
(writes_a_travel_blog(todd))&
(![X]:(room(X)=>(travels_domestically_frequently(X))))&
(does_not_collect_rare_sneakers(todd))&
(~![X]:(room(X)=>(((enjoys_cross-country_skiing(X))<=(travels_domestically_frequently(X)))))) | room(todd)&room(juan)&room(toby)&room(judith)&room(marie)&(![X]:(room(X)=>(X='todd'|X='juan'|X='toby'|X='judith'|X='marie')))&
![X]:(room(X)=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))) | [
"p0",
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 6960263072050527018990464
% SZS output start Proof for 6960263072050527018990464
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. ~predt(mary) <=> predk(mary) [input p1]
46. (~predu(mary) => ~? [X0] : (anywhere(X0) => (~(predt(X0) | prede(X0)) => predq(X0)))) & (predu(mary) => predk(mary)) [input p2]
64. ! [X0] : (room(X0) => ~predk(X0)) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
68. ! [X0] : (room(X0) => ~predk(X0)) & ! [X1] : (room(X1) => (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 64]
72. (~predu(mary) => ~? [X0] : (anywhere(X0) => ~~(predt(X0) | prede(X0)))) & (predu(mary) => predk(mary)) [pure predicate removal 46]
75. (~predu(mary) => ~? [X0] : (anywhere(X0) => ~~predt(X0))) & (predu(mary) => predk(mary)) [pure predicate removal 72]
83. (~predu(mary) => ~? [X0] : ~~predt(X0)) & (predu(mary) => predk(mary)) [pure predicate removal 75]
155. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
156. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 155]
157. (! [X0] : ~predt(X0) | predu(mary)) & (predk(mary) | ~predu(mary)) [ennf transformation 83]
166. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : ((john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 68]
167. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 166]
169. (~predt(mary) | ~predk(mary)) & (predk(mary) | predt(mary)) [nnf transformation 45]
266. room(mary) [cnf transformation 156]
272. predk(mary) | predt(mary) [cnf transformation 169]
274. predk(mary) | ~predu(mary) [cnf transformation 157]
275. ~predt(X0) | predu(mary) [cnf transformation 157]
306. ~predk(X0) | ~room(X0) [cnf transformation 167]
310. 1 <=> predk(mary) [avatar definition]
311. predk(mary) <- (1) [avatar component clause 310]
314. 2 <=> predt(mary) [avatar definition]
315. predt(mary) <- (2) [avatar component clause 314]
318. 2 | 1 [avatar split clause 272,310,314]
320. 3 <=> predu(mary) [avatar definition]
324. 4 <=> ! [X0] : ~predt(X0) [avatar definition]
325. ~predt(X0) <- (4) [avatar component clause 324]
326. 3 | 4 [avatar split clause 275,324,320]
327. ~3 | 1 [avatar split clause 274,310,320]
419. $false <- (2, 4) [subsumption resolution 315,325]
420. ~2 | ~4 [avatar contradiction clause 419]
429. ~room(mary) <- (1) [resolution 306,311]
430. $false <- (1) [subsumption resolution 429,266]
431. ~1 [avatar contradiction clause 430]
432. $false [avatar sat refutation 318,326,327,420,431]
% SZS output end Proof for 6960263072050527018990464
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.311567 |
Deloris, Leah are the only persons in the room. If "Donald is richer than Leah" then "everyone in the room is quieter than Donald if they is a quiet person and vice versa". At least one person in the room is not a old person. Deloris who is a quiet person is richer than Donald. Someone anywhere is a quiet person. Everyone in the room is quieter than Donald if they is a quiet person and vice versa. More than one person in the room either is a quiet person or is not a quiet person but not both. Deloris is the least quiet in the room. Donald is richer than Leah. | Leah is old. | neutral | room(deloris)&room(leah)&(![X]:(room(X)=>(X='deloris'|X='leah')))&
((richer(leah,donald))=>(![X]:(room(X)=>(((quieter(donald,X))<=>(quiet(X)&person(X)))))))&
(((?[X]:(room(X)&~(old(X)&person(X))))))&
((quiet(deloris)&person(deloris))&(richer(donald,deloris)))&
(?[X]:(anywhere(X)&(quiet(X)&person(X))))&
(![X]:(room(X)=>(((quieter(donald,X))<=>(quiet(X)&person(X))))))&
((?[X,Y]:(room(X)&room(Y)&(((quiet(X)&person(X))<~>(~(quiet(X)&person(X))))&((quiet(Y)&person(Y))<~>(~(quiet(Y)&person(Y)))))&(X!=Y))))&
(![X]:((room(X)&(X!=deloris))=>quieter(deloris,X)))&
(richer(leah,donald)) | room(deloris)&room(leah)&(![X]:(room(X)=>(X='deloris'|X='leah')))&
old(leah) | [] | null | 0.009358 |
Delbert, Rebecca, Salvatore, Miguel are the only persons in the room.
“Everyone in the room either does not use contact lenses or does not play eSports competitively but not both” if “everyone in the room does not participate in long-distance cycling events across the country”.
“Not everyone in the room neither does not have a piercing nor does not play eSports competitively” if “Salvatore does not have a specialized collection of handmade artisan pottery” and vice versa.
Either “no one in the room cannot play the flute” or “Delbert does not collect comic books” but not both.
Either “Rebecca does not collect comic books” or “Delbert is not right-handed” but not both.
“Everyone in the room is not a professional photographer specializing in portrait photography or does not mentor a youth basketball team on weekends or both” if “Salvatore does not enjoy origami” and vice versa.
Rebecca does not use contact lenses.
Rebecca is not a professional photographer specializing in portrait photography or does not make intricate hand-cut paper art for exhibitions or both.
Rebecca does not mentor a youth basketball team on weekends or does not use contact lenses or both.
Everyone in the room does not mentor a youth basketball team on weekends.
Everyone in the room has a specialized collection of handmade artisan pottery.
Rebecca does not collect comic books or is not right-handed or both.
Rebecca either does not participate in long-distance cycling events across the country or is not a professional photographer specializing in portrait photography but not both.
Salvatore either does not mentor a youth basketball team on weekends or does not have a curated collection of mid-century modern furniture but not both.
Rebecca is not a member of a local theater group specializing in improv.
Delbert cannot play the flute.
Everyone in the room does not make intricate hand-cut paper art for exhibitions.
Rebecca does not make intricate hand-cut paper art for exhibitions.
Everyone in the room does not use contact lenses.
Everyone in the room does not collect comic books.
Everyone in the room is not a professional photographer specializing in portrait photography. | Everyone outside the room does not play eSports competitively or has a specialized collection of handmade artisan pottery. | neutral | room(delbert)&room(rebecca)&room(salvatore)&room(miguel)&(![X]:(room(X)=>(X='delbert'|X='rebecca'|X='salvatore'|X='miguel')))&
((![X]:(room(X)=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))=>(![X]:(room(X)=>(((does_not_use_contact_lenses(X))<~>(does_not_play_eSports_competitively(X)))))))&
((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(salvatore))<=>(~![X]:(room(X)=>(~((does_not_have_a_piercing(X))|(does_not_play_eSports_competitively(X)))))))&
((~?[X]:(room(X)=>(cannot_play_the_flute(X))))<~>(does_not_collect_comic_books(delbert)))&
((does_not_collect_comic_books(rebecca))<~>(is_not_right-handed(delbert)))&
((does_not_enjoy_origami(salvatore))<=>(![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))))&
(does_not_use_contact_lenses(rebecca))&
(((is_not_a_professional_photographer_specializing_in_portrait_photography(rebecca))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(rebecca))))&
(((does_not_mentor_a_youth_basketball_team_on_weekends(rebecca))|(does_not_use_contact_lenses(rebecca))))&
(![X]:(room(X)=>(does_not_mentor_a_youth_basketball_team_on_weekends(X))))&
(![X]:(room(X)=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))&
(((does_not_collect_comic_books(rebecca))|(is_not_right-handed(rebecca))))&
(((does_not_participate_in_long-distance_cycling_events_across_the_country(rebecca))<~>(is_not_a_professional_photographer_specializing_in_portrait_photography(rebecca))))&
(((does_not_mentor_a_youth_basketball_team_on_weekends(salvatore))<~>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(salvatore))))&
(is_not_a_member_of_a_local_theater_group_specializing_in_improv(rebecca))&
(cannot_play_the_flute(delbert))&
(![X]:(room(X)=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))&
(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(rebecca))&
(![X]:(room(X)=>(does_not_use_contact_lenses(X))))&
(![X]:(room(X)=>(does_not_collect_comic_books(X))))&
(![X]:(room(X)=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))) | room(delbert)&room(rebecca)&room(salvatore)&room(miguel)&(![X]:(room(X)=>(X='delbert'|X='rebecca'|X='salvatore'|X='miguel')))&
![X]:(~room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(does_not_play_eSports_competitively(X))))) | [] | null | 0.416019 |
There is a room. “Everyone in the room is a member of a local theater group specializing in improv only if they collects limited-edition art prints from contemporary artists” unless “not everyone in the room does not collect limited-edition art prints from contemporary artists or collects antique clocks”. If “everyone in the room has a vast collection of first-edition science fiction novels or does not practice pilates” then “everyone in the room has a specialized collection of handmade artisan pottery or does not use an ios phone”. If “everyone in the room does not collect limited-edition art prints from contemporary artists or is a cybersecurity expert” then “only one person in the room either has a specialized collection of handmade artisan pottery or collects rare and antique scientific instruments but not both”. “Everyone outside the room collects antique clocks if they uses contact lenses and vice versa” if “everyone in the room does not enjoy logic puzzles or collects limited-edition art prints from contemporary artists”. Everyone in the room who enjoys coding in Python enjoys cross-country skiing. Everyone in the room is a member of a local theater group specializing in improv if they enjoys cross-country skiing. Everyone in the room is a member of a local theater group specializing in improv only if they collects limited-edition art prints from contemporary artists. Everyone in the room enjoys logic puzzles if and only if they enjoys coding in Python. | Everyone in the room does not enjoy logic puzzles or collects limited-edition art prints from contemporary artists. | entailment | (there_is_a_room)&
(~(~![X]:(room(X)=>(((collects_antique_clocks(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))=>(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))<=(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))&
((![X]:(room(X)=>(((does_not_practice_pilates(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))=>(![X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))&
((![X]:(room(X)=>(((is_a_cybersecurity_expert(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))=>(((?[X]:(room(X)&((has_a_specialized_collection_of_handmade_artisan_pottery(X))<~>(collects_rare_and_antique_scientific_instruments(X)))))&(![X,Y]:((room(X)&room(Y)&(((has_a_specialized_collection_of_handmade_artisan_pottery(X))<~>(collects_rare_and_antique_scientific_instruments(X))))&(((has_a_specialized_collection_of_handmade_artisan_pottery(Y))<~>(collects_rare_and_antique_scientific_instruments(Y)))))=>(X=Y))))))&
((![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_enjoy_logic_puzzles(X))))))=>(![X]:(~room(X)=>(((collects_antique_clocks(X))<=>(uses_contact_lenses(X)))))))&
((![X]:(room(X)=>(((is_a_client_of_Costco(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))<=>(![X]:(room(X)=>(((enjoys_stargazing(X))|(does_not_have_a_piercing(X)))))))&
(~(![X]:(~room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))=>((joseph_dream=>((![X]:((((collects_antique_clocks(X))|(is_a_cybersecurity_expert(X))))=>(((has_a_piercing(X))<~>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))))))&
(~(~?[X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_enjoy_stargazing(X))))))=>(((?[X]:(~room(X)&mentors_a_youth_basketball_team_on_weekends(X)))&(![X,Y]:((~room(X)&~room(Y)&(mentors_a_youth_basketball_team_on_weekends(X))&(mentors_a_youth_basketball_team_on_weekends(Y)))=>(X=Y))))))&
((![X]:(room(X)=>(((uses_an_ios_phone(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(collects_rare_and_antique_scientific_instruments(X)))))))&
((![X]:(room(X)=>(((enjoys_logic_puzzles(X))|(is_not_a_cybersecurity_expert(X))))))=>(![X]:(anywhere(X)=>(((is_not_a_cybersecurity_expert(X))<=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))|(does_not_have_a_piercing(X))))))&
(((?[X]:(~room(X)&does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X)))&(![X,Y]:((~room(X)&~room(Y)&(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))&(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
(![X]:(anywhere(X)=>(((is_not_a_cybersecurity_expert(X))<=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(((?[X]:(~room(X)&uses_contact_lenses(X)))&(![X,Y]:((~room(X)&~room(Y)&(uses_contact_lenses(X))&(uses_contact_lenses(Y)))=>(X=Y)))))&
((joseph_dream=>((![X]:((((collects_antique_clocks(X))|(is_a_cybersecurity_expert(X))))=>(((has_a_piercing(X))<~>(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))))&
(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))<=(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
(((?[X]:(room(X)&does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))&(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))|(does_not_use_an_ios_phone(X))))))&
((joseph_dream=>(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))))&
(~![X]:(room(X)=>(((collects_antique_clocks(X))<=(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(![X]:(~room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))&
(~![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))<=(~((uses_an_ios_phone(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))))&
(~![X]:(room(X)=>(((collects_antique_clocks(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))&
(![X]:(room(X)=>(((enjoys_logic_puzzles(X))|(is_not_a_cybersecurity_expert(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))<=>(enjoys_logic_puzzles(X))))))&
(![X]:(room(X)=>(((enjoys_logic_puzzles(X))<=>(enjoys_coding_in_Python(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_enjoy_logic_puzzles(X))))) | [
"p0",
"p12",
"p13",
"p17",
"p27",
"hypothesis"
] | % SZS status Unsatisfiable for 7893392766643755555774892
% SZS output start Proof for 7893392766643755555774892
44. there_is_a_room [input p0]
56. ! [X0] : (room(X0) => (predv(X0) => predf(X0))) [input p12]
57. ! [X0] : (room(X0) => (predf(X0) => predn(X0))) [input p13]
61. ! [X0] : (room(X0) => (predn(X0) => predj(X0))) [input p17]
71. ! [X0] : (room(X0) => (predd(X0) <=> predv(X0))) [input p27]
72. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis]
184. ! [X0] : ((predf(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 56]
185. ! [X0] : (predf(X0) | ~predv(X0) | ~room(X0)) [flattening 184]
186. ! [X0] : ((predn(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 57]
187. ! [X0] : (predn(X0) | ~predf(X0) | ~room(X0)) [flattening 186]
191. ! [X0] : ((predj(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 61]
192. ! [X0] : (predj(X0) | ~predn(X0) | ~room(X0)) [flattening 191]
206. ! [X0] : ((predd(X0) <=> predv(X0)) | ~room(X0)) [ennf transformation 71]
207. ? [X0] : ((predd(X0) & ~predj(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 72]
208. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ~there_is_a_room [flattening 207]
258. ! [X0] : (((predd(X0) | ~predv(X0)) & (predv(X0) | ~predd(X0))) | ~room(X0)) [nnf transformation 206]
259. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK17) & ~predj(sK17) & room(sK17)) [choice axiom]
260. (predd(sK17) & ~predj(sK17) & room(sK17)) | ~there_is_a_room [skolemisation 208,259]
342. there_is_a_room [cnf transformation 44]
386. ~predv(X0) | predf(X0) | ~room(X0) [cnf transformation 185]
387. ~predf(X0) | predn(X0) | ~room(X0) [cnf transformation 187]
393. predj(X0) | ~predn(X0) | ~room(X0) [cnf transformation 192]
410. ~predd(X0) | predv(X0) | ~room(X0) [cnf transformation 258]
412. room(sK17) | ~there_is_a_room [cnf transformation 260]
413. ~predj(sK17) | ~there_is_a_room [cnf transformation 260]
414. predd(sK17) | ~there_is_a_room [cnf transformation 260]
420. 2 <=> ! [X0] : (predj(X0) | ~room(X0) | ~predn(X0)) [avatar definition]
421. ~predn(X0) | ~room(X0) | predj(X0) <- (2) [avatar component clause 420]
618. 2 [avatar split clause 393,420]
619. predd(sK17) [subsumption resolution 414,342]
620. ~predj(sK17) [subsumption resolution 413,342]
621. room(sK17) [subsumption resolution 412,342]
649. predv(sK17) | ~room(sK17) [resolution 410,619]
652. predv(sK17) [subsumption resolution 649,621]
660. predf(sK17) | ~room(sK17) [resolution 652,386]
661. predf(sK17) [subsumption resolution 660,621]
717. predn(sK17) | ~room(sK17) [resolution 661,387]
718. predn(sK17) [subsumption resolution 717,621]
727. ~room(sK17) | predj(sK17) <- (2) [resolution 718,421]
728. predj(sK17) <- (2) [subsumption resolution 727,621]
729. $false <- (2) [subsumption resolution 728,620]
730. ~2 [avatar contradiction clause 729]
731. $false [avatar sat refutation 618,730]
% SZS output end Proof for 7893392766643755555774892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0.16946 |
Alana, Helene are the only persons in the room.
If Alana knows morse code then Alana neither is a member of a local theater group specializing in improv nor practices and performs acrobatic dance routines.
If it is not the case that at least one person in the room has a vast collection of first-edition science fiction novels then at least one person in the room practices and performs acrobatic dance routines.
Either Alana enjoys macrame or Alana enjoys windsurfing but not both.
If Alana neither creates augmented reality experiences for mobile applications nor enjoys spelunking then Alana enjoys landscape photography.
If Alana has a vast collection of first-edition science fiction novels then Alana trains for and competes in international triathlons.
If at least one person outside the room has a tattoo then Alana does not stream on Twitch.
If Alana participates in citizen science projects related to wildlife monitoring then Alana does not enjoy windsurfing.
If Alana neither knows morse code nor has a specialized collection of handmade artisan pottery then Alana is passionate about collecting and restoring classic cars.
If Alana has a vast collection of first-edition science fiction novels then Alana streams on Twitch.
Either Alana does not enjoy macrame or Alana enjoys macrame but not both.
If Alana hosts regular game nights featuring complex strategy games then Alana makes homemade pastries.
If Alana does not enjoy macrame then Alana enjoys windsurfing.
Either it is not the case that Alana makes homemade pastries or it is not the case that Alana is a member of a local theater group specializing in improv but not both.
Alana knows morse code.
Alana neither enjoys landscape photography nor hosts regular game nights featuring complex strategy games.
Alana has a tattoo.
Alana collects action figures.
Alana has a specialized collection of handmade artisan pottery.
It is not the case that it is not the case that Alana is a drone photographer.
Alana trains for and competes in international triathlons.
Alana has a pet dog.
Alana enjoys spelunking.
Alana streams on Twitch.
Alana enjoys macrame.
Alana has a vast collection of first-edition science fiction novels. | Alana hosts regular game nights featuring complex strategy games. | contradiction | room(alana)&room(helene)&(![X]:(room(X)=>(X='alana'|X='helene')))&
((knows_morse_code(alana))=>(~((is_a_member_of_a_local_theater_group_specializing_in_improv(alana))|(practices_and_performs_acrobatic_dance_routines(alana)))))&
((~(((?[X]:(room(X)&has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))=>(((?[X]:(room(X)&practices_and_performs_acrobatic_dance_routines(X))))))&
((enjoys_macrame(alana))<~>(enjoys_windsurfing(alana)))&
((~((creates_augmented_reality_experiences_for_mobile_applications(alana))|(enjoys_spelunking(alana))))=>(enjoys_landscape_photography(alana)))&
((has_a_vast_collection_of_first-edition_science_fiction_novels(alana))=>(trains_for_and_competes_in_international_triathlons(alana)))&
((((?[X]:(~room(X)&has_a_tattoo(X)))))=>(does_not_stream_on_Twitch(alana)))&
((participates_in_citizen_science_projects_related_to_wildlife_monitoring(alana))=>(does_not_enjoy_windsurfing(alana)))&
((~((knows_morse_code(alana))|(has_a_specialized_collection_of_handmade_artisan_pottery(alana))))=>(is_passionate_about_collecting_and_restoring_classic_cars(alana)))&
((has_a_vast_collection_of_first-edition_science_fiction_novels(alana))=>(streams_on_Twitch(alana)))&
((does_not_enjoy_macrame(alana))<~>(enjoys_macrame(alana)))&
((hosts_regular_game_nights_featuring_complex_strategy_games(alana))=>(makes_homemade_pastries(alana)))&
((does_not_enjoy_macrame(alana))=>(enjoys_windsurfing(alana)))&
((~(makes_homemade_pastries(alana)))<~>(~(is_a_member_of_a_local_theater_group_specializing_in_improv(alana))))&
(knows_morse_code(alana))&
(~((enjoys_landscape_photography(alana))|(hosts_regular_game_nights_featuring_complex_strategy_games(alana))))&
(has_a_tattoo(alana))&
(collects_action_figures(alana))&
(has_a_specialized_collection_of_handmade_artisan_pottery(alana))&
(~(~(is_a_drone_photographer(alana))))&
(trains_for_and_competes_in_international_triathlons(alana))&
(has_a_pet_dog(alana))&
(enjoys_spelunking(alana))&
(streams_on_Twitch(alana))&
(enjoys_macrame(alana))&
(has_a_vast_collection_of_first-edition_science_fiction_novels(alana))&
(~((?[X,Y]:(anywhere(X)&anywhere(Y)&(trains_for_and_competes_in_international_triathlons(X)&trains_for_and_competes_in_international_triathlons(Y))&(X!=Y)))))&
(~(does_not_stream_on_Twitch(alana))) | room(alana)&room(helene)&(![X]:(room(X)=>(X='alana'|X='helene')))&
hosts_regular_game_nights_featuring_complex_strategy_games(alana) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 381867141183040089376754
% SZS output start Proof for 381867141183040089376754
59. ~(predq(mary) | preda(mary)) [input p15]
72. predq(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
82. ~predq(mary) [pure predicate removal 59]
163. ~predq(mary) [ennf transformation 82]
165. predq(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 72]
166. predq(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 165]
277. ~predq(mary) [cnf transformation 163]
288. predq(mary) [cnf transformation 166]
352. 14 <=> predq(mary) [avatar definition]
364. ~14 [avatar split clause 277,352]
372. 14 [avatar split clause 288,352]
373. $false [avatar sat refutation 364,372]
% SZS output end Proof for 381867141183040089376754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.663606 |
Richard, David, Brandon are the only persons in the room. Richard is a wine connoisseur with a private cellar of vintage wines. Everyone in the room has lived in exactly three countries or does not enjoy writing detailed reviews of new and classic board games. Everyone in the room plays as a goalkeeper for a local amateur soccer team if they is a wine connoisseur with a private cellar of vintage wines. Everyone in the room enjoys writing detailed reviews of new and classic board games if they plays as a goalkeeper for a local amateur soccer team. | Richard has lived in exactly three countries. | entailment | room(richard)&room(david)&room(brandon)&(![X]:(room(X)=>(X='richard'|X='david'|X='brandon')))&
((![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))|(enjoys_making_ceramics(X))))))=>((![X]:((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(enjoys_origami(X))))))&
((~(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(richard)))=>(![X]:(room(X)=>(practices_kickboxing(X)))))&
((![X]:(room(X)=>(((is_a_client_of_Costco(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))=>(![X]:(anywhere(X)=>(((collects_vintage_vinyl_records(X))<=(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))&
(~(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(richard))=>(![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))&
((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(richard))<=>(owns_a_microscope(richard)))&
((![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_enjoy_making_ceramics(X))))))=>(~?[X]:(room(X)=>(((travels_domestically_frequently(X))|(is_not_a_client_of_Costco(X)))))))&
((![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))|(has_lived_in_exactly_three_countries(X))))))=>(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(is_a_craft_beer_aficionado(X)))))))&
(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(richard))&
(owns_an_Android_phone(richard))&
((![X]:((((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))=>(collect_rare_sneakers(X)))))&
(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(is_an_avid_hiker(X))))))&
((![X]:((((collect_rare_sneakers(X))|(enjoys_making_ceramics(X))))<=>(((is_a_craft_beer_aficionado(X))<~>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))))&
(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(is_a_craft_beer_aficionado(X))))))&
(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(richard))&
((?[X,Y]:(~room(X)&~room(Y)&(does_not_practice_kickboxing(X)&does_not_practice_kickboxing(Y))&(X!=Y))))&
(![X]:(room(X)=>(((is_a_client_of_Costco(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(has_lived_in_exactly_three_countries(X))))))&
(?[X]:(room(X)&(enjoys_origami(X))))&
(![X]:(room(X)=>(((is_an_avid_hiker(X))=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(collect_rare_sneakers(X))&(collects_vintage_vinyl_records(X))))))))&
(![X]:(room(X)=>(((does_not_enjoy_origami(X))|(is_a_craft_beer_aficionado(X))))))&
(![X]:(room(X)=>(((is_a_craft_beer_aficionado(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))=>(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))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))&
(is_not_a_scotch_connoisseur(richard))&
(![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))) | room(richard)&room(david)&room(brandon)&(![X]:(room(X)=>(X='richard'|X='david'|X='brandon')))&
has_lived_in_exactly_three_countries(richard) | [
"p0",
"p14",
"p17",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8494886933200099760387718
% SZS output start Proof for 8494886933200099760387718
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
58. predf(mary) [input p14]
61. ! [X0] : (room(X0) => (predh(X0) | ~predo(X0))) [input p17]
66. ! [X0] : (room(X0) => (predf(X0) => predm(X0))) [input p22]
67. ! [X0] : (room(X0) => (predm(X0) => predo(X0))) [input p23]
70. ~(predh(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
157. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
158. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 157]
170. ! [X0] : ((predh(X0) | ~predo(X0)) | ~room(X0)) [ennf transformation 61]
171. ! [X0] : (predh(X0) | ~predo(X0) | ~room(X0)) [flattening 170]
178. ! [X0] : ((predm(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 66]
179. ! [X0] : (predm(X0) | ~predf(X0) | ~room(X0)) [flattening 178]
180. ! [X0] : ((predo(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 67]
181. ! [X0] : (predo(X0) | ~predm(X0) | ~room(X0)) [flattening 180]
182. ~predh(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70]
183. ~predh(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 182]
201. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom]
202. ~predh(mary) | (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 183,201]
283. room(mary) [cnf transformation 158]
284. room(paul) [cnf transformation 158]
285. room(fred) [cnf transformation 158]
286. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 158]
308. predf(mary) [cnf transformation 58]
314. ~predo(X0) | predh(X0) | ~room(X0) [cnf transformation 171]
321. ~predf(X0) | predm(X0) | ~room(X0) [cnf transformation 179]
322. ~predm(X0) | predo(X0) | ~room(X0) [cnf transformation 181]
324. ~predh(mary) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 202]
325. ~predh(mary) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 202]
326. ~predh(mary) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 202]
327. ~predh(mary) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 202]
397. ~predh(mary) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 327,285]
398. ~predh(mary) | fred != sK6 | ~room(mary) [subsumption resolution 397,284]
399. ~predh(mary) | fred != sK6 [subsumption resolution 398,283]
401. 16 <=> fred = sK6 [avatar definition]
403. fred != sK6 <- (~16) [avatar component clause 401]
405. 17 <=> predh(mary) [avatar definition]
408. ~16 | ~17 [avatar split clause 399,405,401]
409. ~predh(mary) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 326,285]
410. ~predh(mary) | paul != sK6 | ~room(mary) [subsumption resolution 409,284]
411. ~predh(mary) | paul != sK6 [subsumption resolution 410,283]
413. 18 <=> paul = sK6 [avatar definition]
415. paul != sK6 <- (~18) [avatar component clause 413]
416. ~18 | ~17 [avatar split clause 411,405,413]
417. ~predh(mary) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 325,285]
418. ~predh(mary) | mary != sK6 | ~room(mary) [subsumption resolution 417,284]
419. ~predh(mary) | mary != sK6 [subsumption resolution 418,283]
421. 19 <=> mary = sK6 [avatar definition]
423. mary != sK6 <- (~19) [avatar component clause 421]
424. ~19 | ~17 [avatar split clause 419,405,421]
425. ~predh(mary) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 324,285]
426. ~predh(mary) | room(sK6) | ~room(mary) [subsumption resolution 425,284]
427. ~predh(mary) | room(sK6) [subsumption resolution 426,283]
429. 20 <=> room(sK6) [avatar definition]
431. room(sK6) <- (20) [avatar component clause 429]
432. 20 | ~17 [avatar split clause 427,405,429]
485. predm(mary) | ~room(mary) [resolution 321,308]
486. predm(mary) [subsumption resolution 485,283]
503. predo(mary) | ~room(mary) [resolution 486,322]
504. predo(mary) [subsumption resolution 503,283]
520. predh(mary) | ~room(mary) [resolution 504,314]
524. predh(mary) [subsumption resolution 520,283]
525. 17 [avatar split clause 524,405]
582. paul = sK6 | mary = sK6 | fred = sK6 <- (20) [resolution 286,431]
609. mary = sK6 | fred = sK6 <- (~18, 20) [subsumption resolution 582,415]
610. fred = sK6 <- (~18, ~19, 20) [subsumption resolution 609,423]
611. $false <- (~16, ~18, ~19, 20) [subsumption resolution 610,403]
612. 16 | 18 | 19 | ~20 [avatar contradiction clause 611]
613. $false [avatar sat refutation 408,416,424,432,525,612]
% SZS output end Proof for 8494886933200099760387718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Marian, Martin, Jonathan, William are the only persons in the room.
Jonathan does not practice urban gardening and does not like Joshua.
Martin is not creative, not old, not quiet.
Not everyone anywhere does not develop open-source software projects in their free time.
Jonathan who does not hate Florence does not enjoy cross-country skiing.
Everyone in the room does not have a pet dog only if they is not a happy european.
Everyone anywhere does not enjoy salsa dancing or is not a happy european.
Not everyone in the room does not have a pet dog or does not enjoy salsa dancing.
Everyone in the room does not build model airplanes or is not a old brave person.
Everyone in the room is not a quiet humble creative person only if they does not hate Florence.
Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or does not hate Florence.
No calm person is generous.
No strong person is old.
Everyone in the room does not hate Florence only if they does not create bespoke furniture pieces from reclaimed wood and does not like Randy.
Everyone anywhere does not enjoy trail running. | Martin does enjoy trail running. | contradiction | room(marian)&room(martin)&room(jonathan)&room(william)&(![X]:(room(X)=>(X='marian'|X='martin'|X='jonathan'|X='william')))&
(((does_not_practice_urban_gardening(jonathan))&(~like(joshua,jonathan))))&
(~creative(martin)&~old(martin)&~quiet(martin))&
(~![X]:(anywhere(X)=>(does_not_develop_open-source_software_projects_in_their_free_time(X))))&
((~hate(florence,jonathan))&(does_not_enjoy_cross-country_skiing(jonathan)))&
(![X]:(room(X)=>(((~(happy(X)&european(X)))<=(does_not_have_a_pet_dog(X))))))&
(![X]:(anywhere(X)=>(((~(happy(X)&european(X)))|(does_not_enjoy_salsa_dancing(X))))))&
(~![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(does_not_have_a_pet_dog(X))))))&
(![X]:(room(X)=>(((~(old(X)&brave(X)&person(X)))|(does_not_build_model_airplanes(X))))))&
(![X]:(room(X)=>(((~hate(florence,X))<=(~(quiet(X)&humble(X)&creative(X)&person(X)))))))&
(![X]:(room(X)=>(((~hate(florence,X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(~?[X]:(calm(X)=>generous(X)))&
(~?[X]:(strong(X)=>old(X)))&
(![X]:(room(X)=>(((((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))&(~like(randy,X))))<=(~hate(florence,X))))))&
(![X]:(anywhere(X)=>(does_not_enjoy_trail_running(X))))&
(does_not_have_a_pet_dog(marian))&
(![X]:(room(X)=>(((does_not_practice_pilates(X))<=(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))&
(((~(brave(martin)&tourist(martin)))&(~(patient(martin)&brave(martin)&creative(martin)&tall(martin)&european(martin)))&(~like(joshua,martin))))&
(![X]:(room(X)=>(((~(creative(X)&tall(X)&calm(X)&person(X)))<=>(~(funny(X)&person(X))))))) | room(marian)&room(martin)&room(jonathan)&room(william)&(![X]:(room(X)=>(X='marian'|X='martin'|X='jonathan'|X='william')))&
does_enjoy_trail_running(martin) | [
"b4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3749364634679565397514373
% SZS output start Proof for 3749364634679565397514373
5. ! [X0] : anywhere(X0) [input b4]
58. ! [X0] : (anywhere(X0) => ~prede(X0)) [input p14]
63. prede(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
161. ! [X0] : (~prede(X0) | ~anywhere(X0)) [ennf transformation 58]
163. prede(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 63]
164. prede(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 163]
172. anywhere(X0) [cnf transformation 5]
266. ~prede(X0) | ~anywhere(X0) [cnf transformation 161]
279. prede(paul) [cnf transformation 164]
280. ~prede(X0) [subsumption resolution 266,172]
282. $false [subsumption resolution 279,280]
% SZS output end Proof for 3749364634679565397514373
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.652641 |
Joseph, Trina, Antonia, Patrick are the only persons in the room. “Everyone in the room is a kind person” if “not everyone anywhere is a kind person and is not a old person” and vice versa. Either “everyone in the room is a quiet person” or “everyone in the room is a kind person” but not both. Either “everyone in the room is kind” or “everyone in the room is a tall person” but not both. Either “everyone in the room is a tall person” or “it is not the case that “Antonia and Trina are quiet”” but not both. If “everyone anywhere is a tall person” then “not everyone in the room is kind” otherwise “if someone is not a tall person then he/she is a quiet person and vice versa”. “Everyone in the room is a quiet person” only if “only one person outside the room is a kind person, is not kind and is a old person”. “If someone is a kind person, is not a quiet person and is not old then he/she is a kind person” if “everyone in the room is tall”. “Everyone in the room is a quiet person” if “Antonia and Trina are respectively quiet and old”. “Everyone in the room is not a old person” only if “not everyone in the room is quiet and is a old person”. If “everyone in the room is tall, is not a kind person or is a quiet person” then “everyone outside the room is old” otherwise “someone who is a quiet person is richer than someone who is a old person and is quiet”. Not everyone outside the room is not a kind person. Antonia who is a old person or is a quiet person or both is kind. Someone who is a quiet person is richer than someone who is a old person and is quiet. Joseph and Antonia are kind persons. Everyone in the room is not a old person. Someone in the room is not a quiet person or is a tall person or both. | Joseph is tall. | neutral | room(joseph)&room(trina)&room(antonia)&room(patrick)&(![X]:(room(X)=>(X='joseph'|X='trina'|X='antonia'|X='patrick')))&
((~![X]:(anywhere(X)=>(((kind(X)&person(X))&(~(old(X)&person(X)))))))<=>(![X]:(room(X)=>(kind(X)&person(X)))))&
((![X]:(room(X)=>(quiet(X)&person(X))))<~>(![X]:(room(X)=>(kind(X)&person(X)))))&
((![X]:(room(X)=>(kind(X))))<~>(![X]:(room(X)=>(tall(X)&person(X)))))&
((![X]:(room(X)=>(tall(X)&person(X))))<~>(~(quiet(antonia)&quiet(trina))))&
(((![X]:(anywhere(X)=>(tall(X)&person(X))))=>(~![X]:(room(X)=>(kind(X)))))&((~(![X]:(anywhere(X)=>(tall(X)&person(X)))))=>((![X]:((~(tall(X)&person(X)))<=>(quiet(X)&person(X)))))))&
((![X]:(room(X)=>(quiet(X)&person(X))))=>(((?[X]:(~room(X)&((kind(X)&person(X))&(~kind(X))&(old(X)&person(X)))))&(![X,Y]:((~room(X)&~room(Y)&(((kind(X)&person(X))&(~kind(X))&(old(X)&person(X))))&(((kind(Y)&person(Y))&(~kind(Y))&(old(Y)&person(Y)))))=>(X=Y))))))&
((![X]:(room(X)=>(tall(X))))=>((![X]:((((kind(X)&person(X))&(~(quiet(X)&person(X)))&(~old(X))))=>(kind(X)&person(X))))))&
(((quiet(antonia))&(old(trina)))=>(![X]:(room(X)=>(quiet(X)&person(X)))))&
((![X]:(room(X)=>(~(old(X)&person(X)))))=>(~![X]:(room(X)=>(((quiet(X))&(old(X)&person(X)))))))&
(((![X]:(room(X)=>(((tall(X))|(~(kind(X)&person(X)))|(quiet(X)&person(X))))))=>(![X]:(~room(X)=>(old(X)))))&((~(![X]:(room(X)=>(((tall(X))|(~(kind(X)&person(X)))|(quiet(X)&person(X)))))))=>(?[X,Y]:((quiet(X)&person(X))&(((old(Y)&person(Y))&(quiet(Y))))&(richer(X,Y))))))&
(~![X]:(~room(X)=>(~(kind(X)&person(X)))))&
((((old(antonia)&person(antonia))|(quiet(antonia)&person(antonia))))&(kind(antonia)))&
(?[X,Y]:((quiet(X)&person(X))&(((old(Y)&person(Y))&(quiet(Y))))&(richer(X,Y))))&
(kind(joseph)&person(joseph)&kind(antonia)&person(antonia))&
(![X]:(room(X)=>(~(old(X)&person(X)))))&
(?[X]:(room(X)&(((~(quiet(X)&person(X)))|(tall(X)&person(X)))))) | room(joseph)&room(trina)&room(antonia)&room(patrick)&(![X]:(room(X)=>(X='joseph'|X='trina'|X='antonia'|X='patrick')))&
tall(joseph) | [] | null | 0.379246 |
There is a room. If someone is right-handed then he/she is a cybersecurity expert and vice versa. At least one person in the room owns a telescope. If someone writes poetry then he/she uses a Windows laptop. Everyone in the room who is a craft beer aficionado has a piercing. Everyone in the room who travels domestically frequently drives a hybrid car. Everyone in the room is not a chess master who participates in national tournaments or drives a hybrid car. If someone has a piercing then he/she is an amateur astronomer who builds and uses custom telescopes and vice versa. If someone drives a hybrid car then he/she is a professional photographer specializing in portrait photography, owns a telescope or drives a hybrid car. Everyone in the room does not drive a hybrid car or mentors a youth basketball team on weekends. Only one person in the room mentors a youth basketball team on weekends. Everyone in the room is right-handed if they is right-handed and has a piercing and vice versa. Everyone anywhere who travels domestically frequently enjoys skydiving or is right-handed or both. Everyone anywhere does not have a piercing or has a piercing. Everyone in the room who drives a hybrid car enjoys kayaking and exploring remote waterways. If someone is a craft beer aficionado, enjoys skydiving and is a chess master who participates in national tournaments then he/she is a certified yoga instructor teaching classes weekly and vice versa. | Everyone in the room does not drive a hybrid car or is a professional photographer specializing in portrait photography. | neutral | (there_is_a_room)&
((![X]:((is_right-handed(X))<=>(is_a_cybersecurity_expert(X)))))&
(((?[X]:(room(X)&owns_a_telescope(X)))))&
((![X]:((writes_poetry(X))=>(uses_a_Windows_laptop(X)))))&
(![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(has_a_piercing(X))))))&
(![X]:(room(X)=>(((travels_domestically_frequently(X))=>(drives_a_hybrid_car(X))))))&
(![X]:(room(X)=>(((drives_a_hybrid_car(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))&
((![X]:((has_a_piercing(X))<=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))&
((![X]:((drives_a_hybrid_car(X))=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(owns_a_telescope(X))|(drives_a_hybrid_car(X)))))))&
(![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(does_not_drive_a_hybrid_car(X))))))&
(((?[X]:(room(X)&mentors_a_youth_basketball_team_on_weekends(X)))&(![X,Y]:((room(X)&room(Y)&(mentors_a_youth_basketball_team_on_weekends(X))&(mentors_a_youth_basketball_team_on_weekends(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((is_right-handed(X))<=>(((is_right-handed(X))&(has_a_piercing(X))))))))&
(![X]:(anywhere(X)=>(((travels_domestically_frequently(X))=>(((enjoys_skydiving(X))|(is_right-handed(X))))))))&
(![X]:(anywhere(X)=>(((has_a_piercing(X))|(does_not_have_a_piercing(X))))))&
(![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))&
((![X]:((((is_a_craft_beer_aficionado(X))&(enjoys_skydiving(X))&(is_a_chess_master_who_participates_in_national_tournaments(X))))<=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))&
(~![X]:(anywhere(X)=>(((is_a_cybersecurity_expert(X))=>(travels_domestically_frequently(X))))))&
(![X]:(~room(X)=>(((owns_a_telescope(X))|(does_not_own_a_telescope(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_drive_a_hybrid_car(X))))) | [] | null | 0.304219 |
Jerry, Sheree are the only persons in the room. “Everyone outside the room is quiet” only if “Jerry is richer than Douglas”. “All patient persons are funny” if “Douglas is quieter than Sheree”. If “Jerry is a old person” then “Sheree is a quiet person”. “Everyone in the room is not a old person if they is not a creative person” if “someone in the room is older than Douglas”. “Jerry dreamt that “Sheree is older than Douglas”” unless “Jerry is not brave”. Jerry is not brave. Sheree is the quietest in the room. Everyone in the room who is older than Douglas is strong. Someone in the room is a old person. Everyone in the room is not a old person if they is not a creative person. Everyone in the room who is a quiet person is old. Jerry dreamt that “Sheree is older than Douglas”. All happy persons are strong. Jerry is not brave, not tall. No kind person is patient. Sheree is the least old in the room. | Sheree is older than Douglas. | neutral | room(jerry)&room(sheree)&(![X]:(room(X)=>(X='jerry'|X='sheree')))&
((![X]:(~room(X)=>(quiet(X))))=>(richer(douglas,jerry)))&
((quieter(sheree,douglas))=>(![X]:(patient(X)=>funny(X))))&
((old(jerry)&person(jerry))=>(quiet(sheree)&person(sheree)))&
((?[X]:(room(X)&(older(douglas,X))))=>(![X]:(room(X)=>(((~(creative(X)&person(X)))=>(~(old(X)&person(X))))))))&
(~(~brave(jerry))=>((jerry_dream=>(older(douglas,sheree)))))&
(~brave(jerry))&
(![X]:((room(X)&(X!=sheree))=>quieter(X,sheree)))&
(![X]:(room(X)=>(((older(douglas,X))=>(strong(X))))))&
(?[X]:(room(X)&(old(X)&person(X))))&
(![X]:(room(X)=>(((~(creative(X)&person(X)))=>(~(old(X)&person(X)))))))&
(![X]:(room(X)=>(((quiet(X)&person(X))=>(old(X))))))&
((jerry_dream=>(older(douglas,sheree))))&
(![X]:(happy(X)=>strong(X)))&
(~brave(jerry)&~tall(jerry))&
(~?[X]:(kind(X)=>patient(X)))&
(![X]:((room(X)&(X!=sheree))=>older(sheree,X))) | room(jerry)&room(sheree)&(![X]:(room(X)=>(X='jerry'|X='sheree')))&
older(douglas,sheree) | [] | null | 0.558215 |
Henry is the only person in the room. If “everyone in the room maintains a personal blog focused on cybersecurity tips or does not have a piercing” then “everyone in the room does not host a popular podcast about emerging technologies only if they is a skilled home brewer experimenting with craft beer recipes”. “Everyone in the room does not enjoy mountain biking or is not a craft beer aficionado” only if “everyone in the room maintains a personal blog focused on cybersecurity tips if they does not enjoy mountain biking”. | It is not the case that “Henry does enjoy mountain biking”. | neutral | room(henry)&(![X]:(room(X)=>(X='henry')))&
((![X]:(room(X)=>(((does_not_have_a_piercing(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))=>(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=(does_not_host_a_popular_podcast_about_emerging_technologies(X)))))))&
((![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(does_not_enjoy_mountain_biking(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))))&
((![X]:(room(X)=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))=>(~?[X]:(~room(X)=>(((practices_zumba(X))=>(is_not_a_night_owl(X)))))))&
(![X]:(~room(X)=>(((practices_zumba(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))&
(![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))&
(~![X]:(room(X)=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))&
(![X]:(room(X)=>(((does_not_practice_zumba(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X)))))) | room(henry)&(![X]:(room(X)=>(X='henry')))&
~(does_enjoy_mountain_biking(henry)) | [] | null | 0.092115 |
Bonnie is the only person in the room. If "everyone in the room is not a professional photographer specializing in portrait photography or hosts regular workshops on creative writing" then "Bonnie has a curated collection of mid-century modern furniture". If "everyone in the room does not participate in citizen science projects related to wildlife monitoring or uses an ios phone" then "everyone in the room plays the drums if they does not participate in citizen science projects related to wildlife monitoring". If "Bonnie practices tai chi" then "everyone in the room owns a smartwatch if they hosts regular workshops on creative writing". If "everyone in the room does not play the drums or hosts a popular podcast about emerging technologies" then "Bonnie can play the harmonica". If "everyone in the room cannot play the harmonica or regularly contributes to tech forums and online communities" then "it is true that "Bonnie uses an ios phone"". If "everyone in the room owns a smartwatch or does not collect luxury watches" then "everyone in the room does not play the drums or owns a smartwatch". Bonnie participates in citizen science projects related to wildlife monitoring. Bonnie owns a smartwatch, collects foreign coins and collects luxury watches. Bonnie owns a smartwatch. If someone hosts regular workshops on creative writing then he/she collects foreign coins. | Bonnie is a professional photographer specializing in portrait photography, collects foreign coins and owns an extensive assortment of vintage comic book memorabilia. | neutral | room(bonnie)&(![X]:(room(X)=>(X='bonnie')))&
((![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))=>(has_a_curated_collection_of_mid-century_modern_furniture(bonnie)))&
((![X]:(room(X)=>(((uses_an_ios_phone(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>(![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(plays_the_drums(X)))))))&
((practices_tai_chi(bonnie))=>(![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(owns_a_smartwatch(X)))))))&
((![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))|(does_not_play_the_drums(X))))))=>(can_play_the_harmonica(bonnie)))&
((![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))|(cannot_play_the_harmonica(X))))))=>(uses_an_ios_phone(bonnie)))&
((![X]:(room(X)=>(((does_not_collect_luxury_watches(X))|(owns_a_smartwatch(X))))))=>(![X]:(room(X)=>(((owns_a_smartwatch(X))|(does_not_play_the_drums(X)))))))&
(participates_in_citizen_science_projects_related_to_wildlife_monitoring(bonnie))&
(((owns_a_smartwatch(bonnie))&(collects_foreign_coins(bonnie))&(collects_luxury_watches(bonnie))))&
(owns_a_smartwatch(bonnie))&
((![X]:((hosts_regular_workshops_on_creative_writing(X))=>(collects_foreign_coins(X)))))&
((![X]:((can_play_the_harmonica(X))=>(collects_luxury_watches(X)))))&
(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(bonnie))&
(practices_tai_chi(bonnie))&
(?[X]:(room(X)&(((uses_contact_lenses(X))&(collects_action_figures(X))))))&
(collects_foreign_coins(bonnie))&
((collects_historical_artifacts_related_to_ancient_civilizations(bonnie))&(has_a_curated_collection_of_mid-century_modern_furniture(bonnie)))&
(competes_in_national_level_swimming_championships(bonnie)) | room(bonnie)&(![X]:(room(X)=>(X='bonnie')))&
((is_a_professional_photographer_specializing_in_portrait_photography(bonnie))&(collects_foreign_coins(bonnie))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(bonnie))) | [] | null | 0.196092 |
Neal, Jeffrey, Jo, Kimberly are the only persons in the room.
If "no one outside the room does not build model airplanes or enjoys cross-country skiing" then "everyone in the room does not build model airplanes if and only if they creates YouTube content" otherwise "everyone in the room who creates YouTube content either is not an expert in identifying and foraging wild edible plants or makes intricate hand-cut paper art for exhibitions but not both".
"Neal does not make intricate hand-cut paper art for exhibitions or does not build model airplanes or both" only if "Neal has a saltwater aquarium".
If "Neal is a certified yoga instructor teaching classes weekly" then "only one person in the room does not play eSports competitively" otherwise "everyone in the room who is an expert in identifying and foraging wild edible plants is a certified yoga instructor teaching classes weekly".
"Jeffrey builds model airplanes" if "it is true that "everyone in the room is a cybersecurity expert or is not a certified yoga instructor teaching classes weekly"" and vice versa.
Someone in the room enjoys skydiving, is a cybersecurity expert or creates YouTube content.
If someone is a certified yoga instructor teaching classes weekly then he/she enjoys skydiving.
Everyone in the room who is a certified yoga instructor teaching classes weekly enjoys cross-country skiing.
Everyone outside the room is a cybersecurity expert and enjoys skydiving only if they does not build model airplanes.
Everyone in the room who enjoys cross-country skiing makes intricate hand-cut paper art for exhibitions.
Jeffrey does not make intricate hand-cut paper art for exhibitions. | Jeffrey enjoys cross-country skiing. | contradiction | room(neal)&room(jeffrey)&room(jo)&room(kimberly)&(![X]:(room(X)=>(X='neal'|X='jeffrey'|X='jo'|X='kimberly')))&
(((~?[X]:(~room(X)=>(((enjoys_cross-country_skiing(X))|(does_not_build_model_airplanes(X))))))=>(![X]:(room(X)=>(((does_not_build_model_airplanes(X))<=>(creates_YouTube_content(X)))))))&((~(~?[X]:(~room(X)=>(((enjoys_cross-country_skiing(X))|(does_not_build_model_airplanes(X)))))))=>(![X]:(room(X)=>(((creates_YouTube_content(X))=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<~>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))))))&
((((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(neal))|(does_not_build_model_airplanes(neal))))=>(has_a_saltwater_aquarium(neal)))&
(((is_a_certified_yoga_instructor_teaching_classes_weekly(neal))=>(((?[X]:(room(X)&does_not_play_eSports_competitively(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_play_eSports_competitively(X))&(does_not_play_eSports_competitively(Y)))=>(X=Y))))))&((~(is_a_certified_yoga_instructor_teaching_classes_weekly(neal)))=>(![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))&
((![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_a_cybersecurity_expert(X))))))<=>(builds_model_airplanes(jeffrey)))&
(?[X]:(room(X)&(((enjoys_skydiving(X))|(is_a_cybersecurity_expert(X))|(creates_YouTube_content(X))))))&
((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(enjoys_skydiving(X)))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(~room(X)=>(((does_not_build_model_airplanes(X))<=(((is_a_cybersecurity_expert(X))&(enjoys_skydiving(X))))))))&
(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))&
(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(jeffrey)) | room(neal)&room(jeffrey)&room(jo)&room(kimberly)&(![X]:(room(X)=>(X='neal'|X='jeffrey'|X='jo'|X='kimberly')))&
enjoys_cross-country_skiing(jeffrey) | [
"p0",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2265618442334549649370833
% SZS output start Proof for 2265618442334549649370833
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
53. ! [X0] : (room(X0) => (predj(X0) => preda(X0))) [input p9]
54. ~preda(paul) [input p10]
55. predj(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
132. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
133. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132]
145. ! [X0] : ((preda(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 53]
146. ! [X0] : (preda(X0) | ~predj(X0) | ~room(X0)) [flattening 145]
147. predj(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 55]
148. predj(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147]
243. room(paul) [cnf transformation 133]
268. ~predj(X0) | preda(X0) | ~room(X0) [cnf transformation 146]
269. ~preda(paul) [cnf transformation 54]
275. predj(paul) [cnf transformation 148]
375. preda(paul) | ~room(paul) [resolution 268,275]
376. ~room(paul) [subsumption resolution 375,269]
377. $false [subsumption resolution 376,243]
% SZS output end Proof for 2265618442334549649370833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Dina, Bridgette are the only persons in the room.
“Everyone in the room is not a client of LVMH or is an avid collector of autographed memorabilia from famous musicians” if “everyone in the room does not own an Android phone or watches fantasy movies” and vice versa.
If “everyone outside the room does not mentor a youth basketball team on weekends or has a vast collection of first-edition science fiction novels” then “Dina who makes homemade pastries collects foreign coins”.
If “someone anywhere makes homemade pastries” then “everyone anywhere owns an Android phone if they is a coffee connoisseur”.
Everyone in the room owns an Android phone.
Everyone in the room enjoys camping and organizing outdoor survival workshops if they makes intricate hand-cut paper art for exhibitions.
At least one person anywhere watches fantasy movies.
Everyone anywhere owns an Android phone if they is a coffee connoisseur.
Someone outside the room collects foreign coins.
Bridgette mentors a youth basketball team on weekends.
Everyone in the room does not have a vast collection of first-edition science fiction novels if they is an active member of a local robotics club.
Not everyone in the room has a vast collection of first-edition science fiction novels if they owns an Android phone.
Everyone in the room who has a vast collection of first-edition science fiction novels does not enjoy rooftop gardening.
Someone outside the room watches fantasy movies.
Dina has a vast collection of first-edition science fiction novels. | It is true that “Bridgette has a vast collection of first-edition science fiction novels”. | contradiction | room(dina)&room(bridgette)&(![X]:(room(X)=>(X='dina'|X='bridgette')))&
((![X]:(room(X)=>(((watches_fantasy_movies(X))|(does_not_own_an_Android_phone(X))))))<=>(![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(is_not_a_client_of_LVMH(X)))))))&
((![X]:(~room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))=>((makes_homemade_pastries(dina))&(collects_foreign_coins(dina))))&
((?[X]:(anywhere(X)&(makes_homemade_pastries(X))))=>(![X]:(anywhere(X)=>(((is_a_coffee_connoisseur(X))=>(owns_an_Android_phone(X)))))))&
(![X]:(room(X)=>(owns_an_Android_phone(X))))&
(![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(((?[X]:(anywhere(X)&watches_fantasy_movies(X)))))&
(![X]:(anywhere(X)=>(((is_a_coffee_connoisseur(X))=>(owns_an_Android_phone(X))))))&
(?[X]:(~room(X)&(collects_foreign_coins(X))))&
(mentors_a_youth_basketball_team_on_weekends(bridgette))&
(![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))&
(~![X]:(room(X)=>(((owns_an_Android_phone(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))=>(does_not_enjoy_rooftop_gardening(X))))))&
(?[X]:(~room(X)&(watches_fantasy_movies(X))))&
(has_a_vast_collection_of_first-edition_science_fiction_novels(dina)) | room(dina)&room(bridgette)&(![X]:(room(X)=>(X='dina'|X='bridgette')))&
has_a_vast_collection_of_first-edition_science_fiction_novels(bridgette) | [
"p0",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7555790544730984079516868
% SZS output start Proof for 7555790544730984079516868
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
55. ~! [X0] : (room(X0) => (preda(X0) => predm(X0))) [input p11]
58. predm(mary) [input p14]
59. predm(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
144. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
145. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 144]
149. ? [X0] : ((~predm(X0) & preda(X0)) & room(X0)) [ennf transformation 55]
150. ? [X0] : (~predm(X0) & preda(X0) & room(X0)) [flattening 149]
151. predm(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 59]
152. predm(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 151]
163. ? [X0] : (~predm(X0) & preda(X0) & room(X0)) => (~predm(sK4) & preda(sK4) & room(sK4)) [choice axiom]
164. ~predm(sK4) & preda(sK4) & room(sK4) [skolemisation 150,163]
249. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 145]
259. room(sK4) [cnf transformation 164]
261. ~predm(sK4) [cnf transformation 164]
264. predm(mary) [cnf transformation 58]
268. predm(paul) [cnf transformation 152]
314. mary = sK4 | paul = sK4 [resolution 249,259]
316. 9 <=> paul = sK4 [avatar definition]
318. paul = sK4 <- (9) [avatar component clause 316]
320. 10 <=> mary = sK4 [avatar definition]
322. mary = sK4 <- (10) [avatar component clause 320]
323. 9 | 10 [avatar split clause 314,320,316]
327. ~predm(paul) <- (9) [backward demodulation 261,318]
328. $false <- (9) [subsumption resolution 327,268]
329. ~9 [avatar contradiction clause 328]
333. ~predm(mary) <- (10) [backward demodulation 261,322]
334. $false <- (10) [subsumption resolution 333,264]
335. ~10 [avatar contradiction clause 334]
337. $false [avatar sat refutation 323,329,335]
% SZS output end Proof for 7555790544730984079516868
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Elizabeth, Patrick, Cornelius are the only persons in the room.
If “it is not the case that “Cornelius likes Cara”” then “Cornelius does not hate Cara”.
If “Cornelius is not hated by Kyle” then “at least one person in the room does not hate Cara and hates Cara”.
If “Cornelius likes Kyle” then “Elizabeth is not liked by Cara”.
If “Patrick either does not hate Cara or does not like Kyle but not both” then “it is not the case that “Patrick neither is liked by Kyle nor is not hated by Cara””.
It is true that “Cornelius does not like Kyle”.
Kyle and Cornelius hate each other.
Elizabeth neither likes Cara nor does not hate Cara.
Patrick does not hate Cara.
Only one person in the room is liked by Cara or likes Kyle or both.
Cornelius is not liked by Cara.
Elizabeth is not hated by Kyle.
If someone hates Kyle then he/she does not like Cara or is not liked by Cara or both.
Patrick is not hated by Cara.
It is not the case that “Patrick neither hates Cara nor hates Kyle”.
Patrick does not like Cara.
Elizabeth is not liked by Kyle or likes Cara or both. | Elizabeth likes Kyle. | neutral | room(elizabeth)&room(patrick)&room(cornelius)&(![X]:(room(X)=>(X='elizabeth'|X='patrick'|X='cornelius')))&
((~(like(cara,cornelius)))=>(~hate(cara,cornelius)))&
((~hate(cornelius,kyle))=>(((?[X]:(room(X)&((~hate(cara,X))&(hate(cara,X))))))))&
((like(kyle,cornelius))=>(~like(elizabeth,cara)))&
((((~hate(cara,patrick))<~>(~like(kyle,patrick))))=>(~(~((like(patrick,kyle))|(~hate(patrick,cara))))))&
(~like(kyle,cornelius))&
((hate(kyle,cornelius) & hate(cornelius,kyle)))&
(~((like(cara,elizabeth))|(~hate(cara,elizabeth))))&
(~hate(cara,patrick))&
(((?[X]:(room(X)&((like(X,cara))|(like(kyle,X)))))&(![X,Y]:((room(X)&room(Y)&(((like(X,cara))|(like(kyle,X))))&(((like(Y,cara))|(like(kyle,Y)))))=>(X=Y)))))&
(~like(cornelius,cara))&
(~hate(elizabeth,kyle))&
((![X]:((hate(kyle,X))=>(((~like(cara,X))|(~like(X,cara)))))))&
(~hate(patrick,cara))&
(~(~((hate(cara,patrick))|(hate(kyle,patrick)))))&
(~like(cara,patrick))&
(((~like(elizabeth,kyle))|(like(cara,elizabeth))))&
(~hate(kyle,elizabeth)) | room(elizabeth)&room(patrick)&room(cornelius)&(![X]:(room(X)=>(X='elizabeth'|X='patrick'|X='cornelius')))&
like(kyle,elizabeth) | [] | null | 0.082136 |
Jean, Daniel, Tiffany, Hector are the only persons in the room.
Tiffany participates in long-distance cycling events across the country only if Jean is the oldest in the room.
Tiffany is creative only if Tiffany is a scotch connoisseur, is a curious tourist or participates in long-distance cycling events across the country.
Daniel participates in long-distance cycling events across the country only if more than one person in the room participates in long-distance cycling events across the country.
If someone is a scotch connoisseur then he/she is creative, is curious or participates in long-distance cycling events across the country if Jean participates in long-distance cycling events across the country.
Daniel is old if Tiffany participates in long-distance cycling events across the country.
Jean is calm only if it is not the case that someone in the room is curious, is calm or is old.
All curious persons are old.
If someone is a scotch connoisseur then he/she participates in long-distance cycling events across the country.
Daniel participates in long-distance cycling events across the country.
Someone in the room is a scotch connoisseur.
Someone in the room either is old or is a scotch connoisseur but not both. | Tiffany is a scotch connoisseur. | neutral | room(jean)&room(daniel)&room(tiffany)&room(hector)&(![X]:(room(X)=>(X='jean'|X='daniel'|X='tiffany'|X='hector')))&
((participates_in_long-distance_cycling_events_across_the_country(tiffany))=>(![X]:((room(X)&(X!=jean))=>older(X,jean))))&
((creative(tiffany))=>(((is_a_scotch_connoisseur(tiffany))|(curious(tiffany)&tourist(tiffany))|(participates_in_long-distance_cycling_events_across_the_country(tiffany)))))&
((participates_in_long-distance_cycling_events_across_the_country(daniel))=>((?[X,Y]:(room(X)&room(Y)&(participates_in_long-distance_cycling_events_across_the_country(X)&participates_in_long-distance_cycling_events_across_the_country(Y))&(X!=Y)))))&
((participates_in_long-distance_cycling_events_across_the_country(jean))=>((![X]:((is_a_scotch_connoisseur(X))=>(((creative(X))|(curious(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))))))&
((participates_in_long-distance_cycling_events_across_the_country(tiffany))=>(old(daniel)))&
((calm(jean))=>(~(?[X]:(room(X)&(((curious(X))|(calm(X))|(old(X))))))))&
(![X]:(curious(X)=>old(X)))&
((![X]:((is_a_scotch_connoisseur(X))=>(participates_in_long-distance_cycling_events_across_the_country(X)))))&
(participates_in_long-distance_cycling_events_across_the_country(daniel))&
(?[X]:(room(X)&(is_a_scotch_connoisseur(X))))&
(?[X]:(room(X)&(((old(X))<~>(is_a_scotch_connoisseur(X))))))&
(creative(daniel))&
(old(daniel))&
(participates_in_long-distance_cycling_events_across_the_country(jean))&
(((creative(jean))|(is_a_scotch_connoisseur(jean))|(old(jean)&person(jean))))&
(((is_a_scotch_connoisseur(jean))|(~(curious(jean)&calm(jean)&tourist(jean)))|(old(jean)))) | room(jean)&room(daniel)&room(tiffany)&room(hector)&(![X]:(room(X)=>(X='jean'|X='daniel'|X='tiffany'|X='hector')))&
is_a_scotch_connoisseur(tiffany) | [] | null | 0.188432 |
There is a room.
Everyone in the room collects rare minerals if they does not watche fantasy movies, does not collect rare minerals and does practice yoga and vice versa.
Everyone in the room does not host a popular podcast about emerging technologies.
If someone either does not practice yoga or does not host a popular podcast about emerging technologies but not both then he/she does not host a popular podcast about emerging technologies.
Everyone in the room does not watche fantasy movies or does not practice yoga or both if they does not practice yoga.
Everyone in the room does not collect rare minerals, does not practice yoga or collects rare minerals if they collects rare minerals, does not watche fantasy movies or does not practice yoga.
Everyone in the room watches fantasy movies.
Everyone in the room either does not practice yoga or collects rare minerals but not both only if they neither does not host a popular podcast about emerging technologies nor hosts a popular podcast about emerging technologies. | Everyone outside the room collects rare minerals. | neutral | (there_is_a_room)&
(![X]:(room(X)=>(((collects_rare_minerals(X))<=>(((does_not_watche_fantasy_movies(X))&(does_not_collect_rare_minerals(X))&(does_practice_yoga(X))))))))&
(![X]:(room(X)=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))&
((![X]:((((does_not_practice_yoga(X))<~>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))=>(does_not_host_a_popular_podcast_about_emerging_technologies(X)))))&
(![X]:(room(X)=>(((does_not_practice_yoga(X))=>(((does_not_watche_fantasy_movies(X))|(does_not_practice_yoga(X))))))))&
(![X]:(room(X)=>(((((collects_rare_minerals(X))|(does_not_watche_fantasy_movies(X))|(does_not_practice_yoga(X))))=>(((does_not_collect_rare_minerals(X))|(does_not_practice_yoga(X))|(collects_rare_minerals(X))))))))&
(![X]:(room(X)=>(watches_fantasy_movies(X))))&
(![X]:(room(X)=>(((~((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(hosts_a_popular_podcast_about_emerging_technologies(X))))<=(((does_not_practice_yoga(X))<~>(collects_rare_minerals(X)))))))) | (there_is_a_room)&
![X]:(~room(X)=>(collects_rare_minerals(X))) | [] | null | 0.683493 |
Jesse is the only person in the room. “Betty is a client of Jesse” unless “everyone in the room does not own a telescope or does not hate Laura”. Not everyone in the room does not have a vast collection of first-edition science fiction novels or does not own a telescope. Someone who is not a happy funny tourist like someone who plays as a goalkeeper for a local amateur soccer team. Betty is a client of Jesse. Jesse and Frances like each other. All humble person is quiet. Everyone in the room who is a client of John designs and sews custom cosplay costumes for conventions. Neither “A pen exists that only writes secrets.” nor “A car runs solely on saltwater.”. Everyone in the room does not frequently participates in hackathons and coding competitions or owns a microscope. At least one person in the room creates augmented reality experiences for mobile applications. All curious person is funny. Everyone in the room does not own a telescope or collects foreign coins. Only one person anywhere owns a microscope. Everyone in the room who owns a 3D printer writes poetry. Jesse and Betty like each other. Everyone in the room who plays as a goalkeeper for a local amateur soccer team is a dedicated advocate for digital privacy and encryption. Everyone in the room does not own a telescope or does not hate Laura. At least one person in the room builds model airplanes. Everyone anywhere who does not like Betty writes poetry. All curious person is quiet. More than one person anywhere is louder than Charles. Everyone in the room has a vast collection of first-edition science fiction novels if and only if they creates augmented reality experiences for mobile applications. All wise person is patient. If someone is not a craft beer aficionado then he/she is a sibling of Frances. Everyone in the room is a sibling of John if they is louder than Frances and vice versa. | Jesse is wise. | neutral | room(jesse)&(![X]:(room(X)=>(X='jesse')))&
(~(![X]:(room(X)=>(((~hate(laura,X))|(does_not_own_a_telescope(X))))))=>(client(jesse,betty)))&
(~![X]:(room(X)=>(((does_not_own_a_telescope(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))&
(?[X,Y]:((~(happy(X)&funny(X)&tourist(X)))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(Y))&(like(X,Y))))&
(client(jesse,betty))&
((like(jesse,frances) & like(frances,jesse)))&
(![X]:(humble(X)=>quiet(X)))&
(![X]:(room(X)=>(((client(john,X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))&
(~((A_pen_exists_that_only_writes_secrets.)|(A_car_runs_solely_on_saltwater.)))&
(![X]:(room(X)=>(((owns_a_microscope(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))&
(((?[X]:(room(X)&creates_augmented_reality_experiences_for_mobile_applications(X)))))&
(![X]:(curious(X)=>funny(X)))&
(![X]:(room(X)=>(((collects_foreign_coins(X))|(does_not_own_a_telescope(X))))))&
(((?[X]:(anywhere(X)&owns_a_microscope(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(owns_a_microscope(X))&(owns_a_microscope(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((owns_a_3D_printer(X))=>(writes_poetry(X))))))&
((like(jesse,betty) & like(betty,jesse)))&
(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))&
(![X]:(room(X)=>(((~hate(laura,X))|(does_not_own_a_telescope(X))))))&
(((?[X]:(room(X)&builds_model_airplanes(X)))))&
(![X]:(anywhere(X)=>(((~like(betty,X))=>(writes_poetry(X))))))&
(![X]:(curious(X)=>quiet(X)))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(louder(charles,X)&louder(charles,Y))&(X!=Y))))&
(![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(![X]:(wise(X)=>patient(X)))&
((![X]:((is_not_a_craft_beer_aficionado(X))=>(sibling(frances,X)))))&
(![X]:(room(X)=>(((sibling(john,X))<=>(louder(frances,X)))))) | room(jesse)&(![X]:(room(X)=>(X='jesse')))&
wise(jesse) | [] | null | 0.362417 |
Edythe, Thomas, Kyle, Deborah, Deborah are the only persons in the room.
'Deborah and Kyle are not quiet' if 'Deborah and Edythe are old' and vice versa.
Either 'Deborah and Kyle are tall persons' or 'it is not the case that 'Deborah and Deborah are tall'' but not both.
'Deborah and Edythe are quiet persons' unless 'Deborah and Thomas are quiet persons'.
If 'it is not the case that 'Deborah and Edythe are tall'' then 'someone anywhere is a tall person'.
If 'someone anywhere is a tall person' then 'all old persons are quiet'.
All old persons are quiet.
It is not the case that 'it is not the case that 'someone in the room is a quiet person''.
Someone in the room is tall.
Deborah who is quiet is old.
Deborah and Kyle are tall persons. | Not everyone in the room is not a old person, is quiet and is not quiet. | entailment | room(edythe)&room(thomas)&room(kyle)&room(deborah)&room(deborah)&(![X]:(room(X)=>(X='edythe'|X='thomas'|X='kyle'|X='deborah'|X='deborah')))&
((old(deborah)&old(edythe))<=>(~quiet(deborah)&~quiet(kyle)))&
((tall(deborah)&person(deborah)&tall(kyle)&person(kyle))<~>(~(tall(deborah)&tall(deborah))))&
(~(quiet(deborah)&person(deborah)&quiet(thomas)&person(thomas))=>(quiet(deborah)&person(deborah)&quiet(edythe)&person(edythe)))&
(((~(tall(deborah)&tall(edythe)))=>(?[X]:(anywhere(X)&(tall(X)&person(X)))))&
((?[X]:(anywhere(X)&(tall(X)&person(X))))=>(![X]:(old(X)=>quiet(X)))))&
(![X]:(old(X)=>quiet(X)))&
(~(~(?[X]:(room(X)&(quiet(X)&person(X))))))&
(?[X]:(room(X)&(tall(X))))&
((quiet(deborah))&(old(deborah)))&
(tall(deborah)&person(deborah)&tall(kyle)&person(kyle)) | room(edythe)&room(thomas)&room(kyle)&room(deborah)&room(deborah)&(![X]:(room(X)=>(X='edythe'|X='thomas'|X='kyle'|X='deborah'|X='deborah')))&
~![X]:(room(X)=>(((~(old(X)&person(X)))&(quiet(X))&(~quiet(X))))) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 3270350205448695489279768
% SZS output start Proof for 3270350205448695489279768
44. person(fred) & tall(fred) & person(john) & tall(john) & old(alice) & quiet(alice) & ? [X0] : (tall(X0) & room(X0)) & ~~? [X0] : (person(X0) & quiet(X0) & room(X0)) & ! [X0] : (old(X0) => quiet(X0)) & (? [X0] : (person(X0) & tall(X0) & anywhere(X0)) => ! [X0] : (old(X0) => quiet(X0))) & (~(tall(mary) & tall(john)) => ? [X0] : (person(X0) & tall(X0) & anywhere(X0))) & (~(person(paul) & quiet(paul) & person(john) & quiet(john)) => (person(mary) & quiet(mary) & person(john) & quiet(john))) & ((person(fred) & tall(fred) & person(alice) & tall(alice)) <~> ~(tall(alice) & tall(john))) & ((old(mary) & old(alice)) <=> (~quiet(fred) & ~quiet(alice))) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. ~(~! [X0] : (room(X0) => (~quiet(X0) & quiet(X0) & ~(person(X0) & old(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]
46. person(fred) & tall(fred) & person(john) & tall(john) & old(alice) & quiet(alice) & ? [X0] : (tall(X0) & room(X0)) & ~~? [X1] : (person(X1) & quiet(X1) & room(X1)) & ! [X2] : (old(X2) => quiet(X2)) & (? [X3] : (person(X3) & tall(X3) & anywhere(X3)) => ! [X4] : (old(X4) => quiet(X4))) & (~(tall(mary) & tall(john)) => ? [X5] : (person(X5) & tall(X5) & anywhere(X5))) & (~(person(paul) & quiet(paul) & person(john) & quiet(john)) => (person(mary) & quiet(mary) & person(john) & quiet(john))) & ((person(fred) & tall(fred) & person(alice) & tall(alice)) <~> ~(tall(alice) & tall(john))) & ((old(mary) & old(alice)) <=> (~quiet(fred) & ~quiet(alice))) & ! [X6] : (room(X6) => (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44]
47. person(fred) & tall(fred) & person(john) & tall(john) & old(alice) & quiet(alice) & ? [X0] : (tall(X0) & room(X0)) & ? [X1] : (person(X1) & quiet(X1) & room(X1)) & ! [X2] : (old(X2) => quiet(X2)) & (? [X3] : (person(X3) & tall(X3) & anywhere(X3)) => ! [X4] : (old(X4) => quiet(X4))) & (~(tall(mary) & tall(john)) => ? [X5] : (person(X5) & tall(X5) & anywhere(X5))) & (~(person(paul) & quiet(paul) & person(john) & quiet(john)) => (person(mary) & quiet(mary) & person(john) & quiet(john))) & ((person(fred) & tall(fred) & person(alice) & tall(alice)) <~> ~(tall(alice) & tall(john))) & ((old(mary) & old(alice)) <=> (~quiet(fred) & ~quiet(alice))) & ! [X6] : (room(X6) => (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 46]
48. ~(~! [X0] : (room(X0) => (~quiet(X0) & quiet(X0) & ~(person(X0) & old(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 45]
120. person(fred) & tall(fred) & person(john) & tall(john) & old(alice) & quiet(alice) & ? [X0] : (tall(X0) & room(X0)) & ? [X1] : (person(X1) & quiet(X1) & room(X1)) & ! [X2] : (quiet(X2) | ~old(X2)) & (! [X4] : (quiet(X4) | ~old(X4)) | ! [X3] : (~person(X3) | ~tall(X3) | ~anywhere(X3))) & (? [X5] : (person(X5) & tall(X5) & anywhere(X5)) | (tall(mary) & tall(john))) & ((person(mary) & quiet(mary) & person(john) & quiet(john)) | (person(paul) & quiet(paul) & person(john) & quiet(john))) & ((person(fred) & tall(fred) & person(alice) & tall(alice)) <~> (~tall(alice) | ~tall(john))) & ((old(mary) & old(alice)) <=> (~quiet(fred) & ~quiet(alice))) & ! [X6] : ((john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6) | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 47]
121. person(fred) & tall(fred) & person(john) & tall(john) & old(alice) & quiet(alice) & ? [X0] : (tall(X0) & room(X0)) & ? [X1] : (person(X1) & quiet(X1) & room(X1)) & ! [X2] : (quiet(X2) | ~old(X2)) & (! [X4] : (quiet(X4) | ~old(X4)) | ! [X3] : (~person(X3) | ~tall(X3) | ~anywhere(X3))) & (? [X5] : (person(X5) & tall(X5) & anywhere(X5)) | (tall(mary) & tall(john))) & ((person(mary) & quiet(mary) & person(john) & quiet(john)) | (person(paul) & quiet(paul) & person(john) & quiet(john))) & ((person(fred) & tall(fred) & person(alice) & tall(alice)) <~> (~tall(alice) | ~tall(john))) & ((old(mary) & old(alice)) <=> (~quiet(fred) & ~quiet(alice))) & ! [X6] : (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 120]
122. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(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 48]
123. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(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 122]
124. sP0 <=> (person(fred) & tall(fred) & person(alice) & tall(alice)) [predicate definition introduction]
125. (person(paul) & quiet(paul) & person(john) & quiet(john)) | ~sP1 [predicate definition introduction]
126. person(fred) & tall(fred) & person(john) & tall(john) & old(alice) & quiet(alice) & ? [X0] : (tall(X0) & room(X0)) & ? [X1] : (person(X1) & quiet(X1) & room(X1)) & ! [X2] : (quiet(X2) | ~old(X2)) & (! [X4] : (quiet(X4) | ~old(X4)) | ! [X3] : (~person(X3) | ~tall(X3) | ~anywhere(X3))) & (? [X5] : (person(X5) & tall(X5) & anywhere(X5)) | (tall(mary) & tall(john))) & ((person(mary) & quiet(mary) & person(john) & quiet(john)) | sP1) & (sP0 <~> (~tall(alice) | ~tall(john))) & ((old(mary) & old(alice)) <=> (~quiet(fred) & ~quiet(alice))) & ! [X6] : (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [definition folding 121,125,124]
127. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP2 [predicate definition introduction]
128. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | sP2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 123,127]
133. person(fred) & tall(fred) & person(john) & tall(john) & old(alice) & quiet(alice) & ? [X0] : (tall(X0) & room(X0)) & ? [X1] : (person(X1) & quiet(X1) & room(X1)) & ! [X2] : (quiet(X2) | ~old(X2)) & (! [X4] : (quiet(X4) | ~old(X4)) | ! [X3] : (~person(X3) | ~tall(X3) | ~anywhere(X3))) & (? [X5] : (person(X5) & tall(X5) & anywhere(X5)) | (tall(mary) & tall(john))) & ((person(mary) & quiet(mary) & person(john) & quiet(john)) | sP1) & (((tall(alice) & tall(john)) | ~sP0) & ((~tall(alice) | ~tall(john)) | sP0)) & (((old(mary) & old(alice)) | (quiet(fred) | quiet(alice))) & ((~quiet(fred) & ~quiet(alice)) | (~old(mary) | ~old(alice)))) & ! [X6] : (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 126]
134. person(fred) & tall(fred) & person(john) & tall(john) & old(alice) & quiet(alice) & ? [X0] : (tall(X0) & room(X0)) & ? [X1] : (person(X1) & quiet(X1) & room(X1)) & ! [X2] : (quiet(X2) | ~old(X2)) & (! [X4] : (quiet(X4) | ~old(X4)) | ! [X3] : (~person(X3) | ~tall(X3) | ~anywhere(X3))) & (? [X5] : (person(X5) & tall(X5) & anywhere(X5)) | (tall(mary) & tall(john))) & ((person(mary) & quiet(mary) & person(john) & quiet(john)) | sP1) & ((tall(alice) & tall(john)) | ~sP0) & (~tall(alice) | ~tall(john) | sP0) & ((old(mary) & old(alice)) | quiet(fred) | quiet(alice)) & ((~quiet(fred) & ~quiet(alice)) | ~old(mary) | ~old(alice)) & ! [X6] : (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133]
135. person(fred) & tall(fred) & person(john) & tall(john) & old(alice) & quiet(alice) & ? [X0] : (tall(X0) & room(X0)) & ? [X1] : (person(X1) & quiet(X1) & room(X1)) & ! [X2] : (quiet(X2) | ~old(X2)) & (! [X3] : (quiet(X3) | ~old(X3)) | ! [X4] : (~person(X4) | ~tall(X4) | ~anywhere(X4))) & (? [X5] : (person(X5) & tall(X5) & anywhere(X5)) | (tall(mary) & tall(john))) & ((person(mary) & quiet(mary) & person(john) & quiet(john)) | sP1) & ((tall(alice) & tall(john)) | ~sP0) & (~tall(alice) | ~tall(john) | sP0) & ((old(mary) & old(alice)) | quiet(fred) | quiet(alice)) & ((~quiet(fred) & ~quiet(alice)) | ~old(mary) | ~old(alice)) & ! [X6] : (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 134]
136. ? [X0] : (tall(X0) & room(X0)) => (tall(sK3) & room(sK3)) [choice axiom]
137. ? [X1] : (person(X1) & quiet(X1) & room(X1)) => (person(sK4) & quiet(sK4) & room(sK4)) [choice axiom]
138. ? [X5] : (person(X5) & tall(X5) & anywhere(X5)) => (person(sK5) & tall(sK5) & anywhere(sK5)) [choice axiom]
139. person(fred) & tall(fred) & person(john) & tall(john) & old(alice) & quiet(alice) & (tall(sK3) & room(sK3)) & (person(sK4) & quiet(sK4) & room(sK4)) & ! [X2] : (quiet(X2) | ~old(X2)) & (! [X3] : (quiet(X3) | ~old(X3)) | ! [X4] : (~person(X4) | ~tall(X4) | ~anywhere(X4))) & ((person(sK5) & tall(sK5) & anywhere(sK5)) | (tall(mary) & tall(john))) & ((person(mary) & quiet(mary) & person(john) & quiet(john)) | sP1) & ((tall(alice) & tall(john)) | ~sP0) & (~tall(alice) | ~tall(john) | sP0) & ((old(mary) & old(alice)) | quiet(fred) | quiet(alice)) & ((~quiet(fred) & ~quiet(alice)) | ~old(mary) | ~old(alice)) & ! [X6] : (john = X6 | alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 135,138,137,136]
140. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP2 [nnf transformation 127]
141. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP2 [rectify 140]
142. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom]
143. (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~sP2 [skolemisation 141,142]
234. room(mary) [cnf transformation 139]
235. room(paul) [cnf transformation 139]
236. room(fred) [cnf transformation 139]
237. room(alice) [cnf transformation 139]
238. room(john) [cnf transformation 139]
239. ~room(X6) | alice = X6 | fred = X6 | paul = X6 | mary = X6 | john = X6 [cnf transformation 139]
270. room(sK6) | ~sP2 [cnf transformation 143]
271. mary != sK6 | ~sP2 [cnf transformation 143]
272. paul != sK6 | ~sP2 [cnf transformation 143]
273. fred != sK6 | ~sP2 [cnf transformation 143]
274. alice != sK6 | ~sP2 [cnf transformation 143]
275. john != sK6 | ~sP2 [cnf transformation 143]
277. quiet(X0) | ~room(X0) | sP2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 128]
278. ~quiet(X0) | ~room(X0) | sP2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 128]
374. 18 <=> sP2 [avatar definition]
378. 19 <=> john = sK6 [avatar definition]
380. john != sK6 <- (~19) [avatar component clause 378]
381. ~18 | ~19 [avatar split clause 275,378,374]
383. 20 <=> alice = sK6 [avatar definition]
385. alice != sK6 <- (~20) [avatar component clause 383]
386. ~18 | ~20 [avatar split clause 274,383,374]
388. 21 <=> fred = sK6 [avatar definition]
390. fred != sK6 <- (~21) [avatar component clause 388]
391. ~18 | ~21 [avatar split clause 273,388,374]
393. 22 <=> paul = sK6 [avatar definition]
396. ~18 | ~22 [avatar split clause 272,393,374]
398. 23 <=> mary = sK6 [avatar definition]
400. mary != sK6 <- (~23) [avatar component clause 398]
401. ~18 | ~23 [avatar split clause 271,398,374]
403. 24 <=> room(sK6) [avatar definition]
405. room(sK6) <- (24) [avatar component clause 403]
406. ~18 | 24 [avatar split clause 270,403,374]
407. ~quiet(X0) | ~room(X0) | sP2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,238]
408. ~quiet(X0) | ~room(X0) | sP2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 407,237]
409. ~quiet(X0) | ~room(X0) | sP2 | ~room(paul) | ~room(mary) [subsumption resolution 408,236]
410. ~quiet(X0) | ~room(X0) | sP2 | ~room(mary) [subsumption resolution 409,235]
411. ~quiet(X0) | ~room(X0) | sP2 [subsumption resolution 410,234]
413. 25 <=> ! [X0] : (~quiet(X0) | ~room(X0)) [avatar definition]
414. ~quiet(X0) | ~room(X0) <- (25) [avatar component clause 413]
415. 18 | 25 [avatar split clause 411,413,374]
416. quiet(X0) | ~room(X0) | sP2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,238]
417. quiet(X0) | ~room(X0) | sP2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 416,237]
418. quiet(X0) | ~room(X0) | sP2 | ~room(paul) | ~room(mary) [subsumption resolution 417,236]
419. quiet(X0) | ~room(X0) | sP2 | ~room(mary) [subsumption resolution 418,235]
420. quiet(X0) | ~room(X0) | sP2 [subsumption resolution 419,234]
422. 26 <=> ! [X0] : (quiet(X0) | ~room(X0)) [avatar definition]
423. quiet(X0) | ~room(X0) <- (26) [avatar component clause 422]
424. 18 | 26 [avatar split clause 420,422,374]
484. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (24) [resolution 239,405]
527. fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (~20, 24) [subsumption resolution 484,385]
528. paul = sK6 | mary = sK6 | john = sK6 <- (~20, ~21, 24) [subsumption resolution 527,390]
533. paul = sK6 | john = sK6 <- (~20, ~21, ~23, 24) [subsumption resolution 528,400]
534. paul = sK6 <- (~19, ~20, ~21, ~23, 24) [subsumption resolution 533,380]
535. 22 | 19 | 20 | 21 | 23 | ~24 [avatar split clause 534,403,398,388,383,378,393]
541. ~room(X0) <- (25, 26) [subsumption resolution 414,423]
546. $false <- (25, 26) [resolution 541,234]
555. ~25 | ~26 [avatar contradiction clause 546]
556. $false [avatar sat refutation 381,386,391,396,401,406,415,424,535,555]
% SZS output end Proof for 3270350205448695489279768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.342526 |
Shanda, Trinidad are the only persons in the room.
Everyone in the room who is an avid hiker and is a scotch connoisseur does not build model airplanes.
Everyone in the room enjoys camping and organizing outdoor survival workshops if they does not build model airplanes.
Everyone in the room does not collect action figures if they enjoys camping and organizing outdoor survival workshops.
Everyone outside the room is a wine connoisseur with a private cellar of vintage wines only if they participates in citizen science projects related to wildlife monitoring.
Not everyone anywhere plays video games if they participates in citizen science projects related to wildlife monitoring.
Not everyone in the room is an avid hiker and has completed a triathlon if they plays video games.
Not everyone anywhere who enjoys origami is a scotch connoisseur.
Everyone in the room is an expert in identifying and foraging wild edible plants if they is not an expert in identifying and foraging wild edible plants.
Everyone in the room who is an expert in identifying and foraging wild edible plants has completed a triathlon.
Everyone in the room is not a scotch connoisseur if they has completed a triathlon.
It is true that “it is true that “it is true that “everyone in the room who is not a scotch connoisseur enjoys origami”””. | Trinidad enjoys origami. | entailment | room(shanda)&room(trinidad)&(![X]:(room(X)=>(X='shanda'|X='trinidad')))&
(![X]:(room(X)=>(((((is_an_avid_hiker(X))&(is_a_scotch_connoisseur(X))))=>(does_not_build_model_airplanes(X))))))&
(![X]:(room(X)=>(((does_not_build_model_airplanes(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(does_not_collect_action_figures(X))))))&
(![X]:(~room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(~![X]:(anywhere(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(plays_video_games(X))))))&
(~![X]:(room(X)=>(((plays_video_games(X))=>(((is_an_avid_hiker(X))&(has_completed_a_triathlon(X))))))))&
(~![X]:(anywhere(X)=>(((enjoys_origami(X))=>(is_a_scotch_connoisseur(X))))))&
((![X]:((does_practice_yoga(X))<=>(((collects_antique_clocks(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))&
(![X]:(room(X)=>(((builds_model_airplanes(X))=>(does_not_compete_in_national_level_swimming_championships(X))))))&
(![X]:(room(X)=>(collects_antique_clocks(X))))&
(![X]:(~room(X)=>(((is_an_avid_hiker(X))=>(does_not_collect_antique_clocks(X))))))&
(![X]:(room(X)=>(((does_not_collect_antique_clocks(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))=>(builds_model_airplanes(X))))))&
(![X]:(room(X)=>(((builds_model_airplanes(X))=>(does_not_watche_fantasy_movies(X))))))&
(?[X]:(room(X)&(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))&
(![X]:(room(X)=>(((((collects_rare_minerals(X))&(practices_archery(X))))=>(((does_not_collect_rare_minerals(X))|(collect_rare_sneakers(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))))&
(![X]:(room(X)=>(((((does_not_collect_rare_minerals(X))|(collect_rare_sneakers(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))&
(?[X]:(room(X)&(collect_rare_sneakers(X))))&
(![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(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))=>(has_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(is_not_a_scotch_connoisseur(X))))))&
(![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))=>(enjoys_origami(X))))))&
(![X]:(anywhere(X)=>(((collects_antique_jewelry(X))=>(collects_action_figures(X))))))&
(![X]:(room(X)=>(((collects_action_figures(X))=>(collects_antique_jewelry(X)))))) | room(shanda)&room(trinidad)&(![X]:(room(X)=>(X='shanda'|X='trinidad')))&
enjoys_origami(trinidad) | [
"p0",
"p19",
"p20",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 615854867965749041413439
% SZS output start Proof for 615854867965749041413439
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
63. ! [X0] : (room(X0) => (~predo(X0) => predo(X0))) [input p19]
64. ! [X0] : (room(X0) => (predo(X0) => prede(X0))) [input p20]
65. ! [X0] : (room(X0) => (prede(X0) => ~predu(X0))) [input p21]
66. ! [X0] : (room(X0) => (~predu(X0) => predj(X0))) [input p22]
69. ~(predj(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
159. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
160. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 159]
165. ! [X0] : ((predo(X0) | predo(X0)) | ~room(X0)) [ennf transformation 63]
166. ! [X0] : (predo(X0) | predo(X0) | ~room(X0)) [flattening 165]
167. ! [X0] : ((prede(X0) | ~predo(X0)) | ~room(X0)) [ennf transformation 64]
168. ! [X0] : (prede(X0) | ~predo(X0) | ~room(X0)) [flattening 167]
169. ! [X0] : ((~predu(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 65]
170. ! [X0] : (~predu(X0) | ~prede(X0) | ~room(X0)) [flattening 169]
171. ! [X0] : ((predj(X0) | predu(X0)) | ~room(X0)) [ennf transformation 66]
172. ! [X0] : (predj(X0) | predu(X0) | ~room(X0)) [flattening 171]
177. ~predj(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 69]
178. ~predj(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 177]
190. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK5 & mary != sK5 & room(sK5)) [choice axiom]
191. ~predj(paul) | (paul != sK5 & mary != sK5 & room(sK5)) | ~room(paul) | ~room(mary) [skolemisation 178,190]
273. room(mary) [cnf transformation 160]
274. room(paul) [cnf transformation 160]
275. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 160]
285. predo(X0) | predo(X0) | ~room(X0) [cnf transformation 166]
286. prede(X0) | ~predo(X0) | ~room(X0) [cnf transformation 168]
287. ~predu(X0) | ~prede(X0) | ~room(X0) [cnf transformation 170]
288. predj(X0) | predu(X0) | ~room(X0) [cnf transformation 172]
291. ~predj(paul) | room(sK5) | ~room(paul) | ~room(mary) [cnf transformation 191]
292. ~predj(paul) | mary != sK5 | ~room(paul) | ~room(mary) [cnf transformation 191]
293. ~predj(paul) | paul != sK5 | ~room(paul) | ~room(mary) [cnf transformation 191]
294. ~room(X0) | predo(X0) [duplicate literal removal 285]
295. ~room(X0) | prede(X0) [subsumption resolution 286,294]
296. ~predu(X0) | ~room(X0) [subsumption resolution 287,295]
297. ~room(X0) | predj(X0) [subsumption resolution 288,296]
299. ~predj(paul) | paul != sK5 | ~room(mary) [subsumption resolution 293,274]
300. ~predj(paul) | paul != sK5 [subsumption resolution 299,273]
302. 1 <=> paul = sK5 [avatar definition]
304. paul != sK5 <- (~1) [avatar component clause 302]
306. 2 <=> predj(paul) [avatar definition]
309. ~1 | ~2 [avatar split clause 300,306,302]
310. ~predj(paul) | mary != sK5 | ~room(mary) [subsumption resolution 292,274]
311. ~predj(paul) | mary != sK5 [subsumption resolution 310,273]
313. 3 <=> mary = sK5 [avatar definition]
315. mary != sK5 <- (~3) [avatar component clause 313]
316. ~3 | ~2 [avatar split clause 311,306,313]
317. ~predj(paul) | room(sK5) | ~room(mary) [subsumption resolution 291,274]
318. ~predj(paul) | room(sK5) [subsumption resolution 317,273]
320. 4 <=> room(sK5) [avatar definition]
322. room(sK5) <- (4) [avatar component clause 320]
323. 4 | ~2 [avatar split clause 318,306,320]
335. predj(paul) [resolution 297,274]
341. 2 [avatar split clause 335,306]
350. mary = sK5 | paul = sK5 <- (4) [resolution 275,322]
378. paul = sK5 <- (~3, 4) [subsumption resolution 350,315]
379. $false <- (~1, ~3, 4) [subsumption resolution 378,304]
380. 1 | 3 | ~4 [avatar contradiction clause 379]
381. $false [avatar sat refutation 309,316,323,341,380]
% SZS output end Proof for 615854867965749041413439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.015875 |
There is a room. Everyone in the room is a member of a local theater group specializing in improv only if they collects action figures. Everyone in the room bakes bread at home, enjoys rooftop gardening or is a member of a local theater group specializing in improv if they collects action figures. Everyone in the room does not collect limited-edition art prints from contemporary artists or bakes bread at home, enjoys rooftop gardening or is a member of a local theater group specializing in improv. Everyone in the room who does not collect limited-edition art prints from contemporary artists bakes bread at home. Everyone in the room bakes bread at home only if they is an amateur astronomer who builds and uses custom telescopes. Everyone in the room who bakes bread at home and collects action figures either is a member of a local theater group specializing in improv or is an amateur astronomer who builds and uses custom telescopes but not both. Everyone in the room who either is a member of a local theater group specializing in improv or is an amateur astronomer who builds and uses custom telescopes but not both collects action figures. More than one person anywhere either does not collect limited-edition art prints from contemporary artists or does not bake bread at home but not both. | Everyone outside the room is an amateur astronomer who builds and uses custom telescopes. | neutral | (there_is_a_room)&
(![X]:(room(X)=>(((collects_action_figures(X))<=(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
(![X]:(room(X)=>(((collects_action_figures(X))=>(((bakes_bread_at_home(X))|(enjoys_rooftop_gardening(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))))&
(![X]:(room(X)=>(((((bakes_bread_at_home(X))|(enjoys_rooftop_gardening(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))&
(![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))=>(bakes_bread_at_home(X))))))&
(![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=(bakes_bread_at_home(X))))))&
(![X]:(room(X)=>(((((bakes_bread_at_home(X))&(collects_action_figures(X))))=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<~>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))))&
(![X]:(room(X)=>(((((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<~>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))=>(collects_action_figures(X))))))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))<~>(does_not_bake_bread_at_home(X)))&((does_not_collect_limited-edition_art_prints_from_contemporary_artists(Y))<~>(does_not_bake_bread_at_home(Y))))&(X!=Y)))) | (there_is_a_room)&
![X]:(~room(X)=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))) | [] | null | 0.019734 |
Larry is the only person in the room.
Larry practices zumba or collects action figures or both.
Only one person in the room is right-handed.
Larry neither has a tattoo nor knows morse code.
Larry is a client of Costco.
At least one person in the room trains for and competes in international triathlons.
If someone practices zumba or mentors a youth basketball team on weekends or both then he/she uses contact lenses.
It is not the case that “someone outside the room has a piercing”.
Larry trains for and competes in international triathlons.
Larry either competes in national level swimming championships or does enjoy mountain biking but not both. | Larry practices zumba. | neutral | room(larry)&(![X]:(room(X)=>(X='larry')))&
(((practices_zumba(larry))|(collects_action_figures(larry))))&
(((?[X]:(room(X)&is_right-handed(X)))&(![X,Y]:((room(X)&room(Y)&(is_right-handed(X))&(is_right-handed(Y)))=>(X=Y)))))&
(~((has_a_tattoo(larry))|(knows_morse_code(larry))))&
(is_a_client_of_Costco(larry))&
(((?[X]:(room(X)&trains_for_and_competes_in_international_triathlons(X)))))&
((![X]:((((practices_zumba(X))|(mentors_a_youth_basketball_team_on_weekends(X))))=>(uses_contact_lenses(X)))))&
(~(?[X]:(~room(X)&(has_a_piercing(X)))))&
(trains_for_and_competes_in_international_triathlons(larry))&
(((competes_in_national_level_swimming_championships(larry))<~>(does_enjoy_mountain_biking(larry)))) | room(larry)&(![X]:(room(X)=>(X='larry')))&
practices_zumba(larry) | [] | null | 0.02214 |
Larry, Wesley, Keira are the only persons in the room.
Either not everyone in the room does not create bespoke furniture pieces from reclaimed wood or is not a client of Costco or everyone in the room does not collect comic books or collects comic books but not both.
Everyone in the room practices tai chi if they mentors a youth basketball team on weekends.
Everyone in the room does not practice tai chi or is a client of Costco.
Everyone in the room who does not collect comic books is a drone photographer, owns a 3D printer and creates bespoke furniture pieces from reclaimed wood.
Everyone in the room is a drone photographer if and only if they mentors a youth basketball team on weekends. | Larry collects comic books. | entailment | room(larry)&room(wesley)&room(keira)&(![X]:(room(X)=>(X='larry'|X='wesley'|X='keira')))&
(~(~![X]:(~room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))=>(~?[X]:(room(X)=>(is_not_a_drone_photographer(X)))))&
((![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>((creates_large-scale_murals_for_public_art_installations(larry))&(((mentors_a_youth_basketball_team_on_weekends(larry))<~>(is_a_client_of_Costco(larry))))))&
(((![X]:(room(X)=>(((has_a_saltwater_aquarium(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>(![X]:(~room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_create_large-scale_murals_for_public_art_installations(X)))))))&((~(![X]:(room(X)=>(((has_a_saltwater_aquarium(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))=>(![X]:(~room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<~>(is_a_client_of_Costco(X))))))))&
((![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))|(does_not_practice_tai_chi(X))))))=>(![X]:(room(X)=>(((does_not_practice_tai_chi(X))<=>(creates_large-scale_murals_for_public_art_installations(X)))))))&
((~![X]:(room(X)=>(((is_not_a_client_of_Costco(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))<~>(![X]:(room(X)=>(((collects_comic_books(X))|(does_not_collect_comic_books(X)))))))&
((?[X]:(~room(X)&(((owns_a_3D_printer(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(does_not_own_a_3D_printer(X))))))=>(((is_a_client_of_Costco(larry))<~>(collects_comic_books(larry)))))&
((![X]:(room(X)=>(((practices_tai_chi(X))|(does_not_have_lived_in_exactly_three_countries(X))))))=>(![X]:(room(X)=>(((does_not_collect_comic_books(X))<=(does_not_have_lived_in_exactly_three_countries(X)))))))&
((~?[X]:(room(X)=>(((owns_a_3D_printer(X))|(is_not_a_drone_photographer(X))))))<=>(![X]:(room(X)=>(((has_a_saltwater_aquarium(X))|(does_not_have_lived_in_exactly_three_countries(X)))))))&
((![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(does_not_collect_comic_books(X))))))=>(![X]:(room(X)=>(((does_not_collect_comic_books(X))=>(((is_a_drone_photographer(X))&(owns_a_3D_printer(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))))&
(~![X]:(room(X)=>(((practices_tai_chi(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(is_a_client_of_Costco(X))))))&
(![X]:(room(X)=>(((((does_not_collect_comic_books(X))&(maintains_a_large,_organic_vegetable_garden_year-round(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(((is_a_client_of_Costco(X))<~>(practices_tai_chi(X))))))))&
(?[X]:(anywhere(X)&(is_not_a_drone_photographer(X))))&
(![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(practices_tai_chi(X))))))&
(![X]:(anywhere(X)=>(((practices_tai_chi(X))=>(((has_lived_in_exactly_three_countries(X))|(does_not_practice_tai_chi(X))))))))&
((larry_dream=>(((is_a_client_of_Costco(larry))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(larry))))))&
(![X]:(room(X)=>(((is_a_client_of_Costco(X))|(does_not_practice_tai_chi(X))))))&
(![X]:(~room(X)=>(((((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))<~>(is_not_a_drone_photographer(X))))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))<=(has_lived_in_exactly_three_countries(X))))))&
(~![X]:(room(X)=>(((((does_not_collect_comic_books(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(has_a_saltwater_aquarium(X))))<=(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))<=(((does_not_collect_comic_books(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(has_a_saltwater_aquarium(X))))))))&
(~![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))<=>(has_a_saltwater_aquarium(X))))))&
(![X]:(room(X)=>(((does_not_collect_comic_books(X))=>(((is_a_drone_photographer(X))&(owns_a_3D_printer(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))&
(![X]:(room(X)=>(((((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(owns_a_3D_printer(X))|(creates_large-scale_murals_for_public_art_installations(X))))<=>(((has_lived_in_exactly_three_countries(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))&
(![X]:(~room(X)=>(((((owns_a_3D_printer(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))<=(((has_lived_in_exactly_three_countries(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))&
(![X]:(room(X)=>(((is_a_drone_photographer(X))<=>(mentors_a_youth_basketball_team_on_weekends(X))))))&
(has_a_saltwater_aquarium(larry)) | room(larry)&room(wesley)&room(keira)&(![X]:(room(X)=>(X='larry'|X='wesley'|X='keira')))&
collects_comic_books(larry) | [
"p0",
"p5",
"p13",
"p16",
"p22",
"p25",
"hypothesis"
] | % SZS status Unsatisfiable for 20284484617684454861948
% SZS output start Proof for 20284484617684454861948
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
49. ~! [X0] : (room(X0) => (~predk(X0) | ~preda(X0))) <~> ! [X0] : (room(X0) => (~predh(X0) | predh(X0))) [input p5]
57. ! [X0] : (room(X0) => (predj(X0) => predf(X0))) [input p13]
60. ! [X0] : (room(X0) => (~predf(X0) | preda(X0))) [input p16]
66. ! [X0] : (room(X0) => (~predh(X0) => (predk(X0) & predd(X0) & prede(X0)))) [input p22]
69. ! [X0] : (room(X0) => (prede(X0) <=> predj(X0))) [input p25]
71. ~(predh(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
76. ~! [X0] : (room(X0) => (~predk(X0) | ~preda(X0))) <~> ! [X1] : (room(X1) => (~predh(X1) | predh(X1))) [rectify 49]
152. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
153. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 152]
162. ? [X0] : ((predk(X0) & preda(X0)) & room(X0)) <~> ! [X1] : ((~predh(X1) | predh(X1)) | ~room(X1)) [ennf transformation 76]
163. ? [X0] : (predk(X0) & preda(X0) & room(X0)) <~> ! [X1] : (~predh(X1) | predh(X1) | ~room(X1)) [flattening 162]
174. ! [X0] : ((predf(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 57]
175. ! [X0] : (predf(X0) | ~predj(X0) | ~room(X0)) [flattening 174]
178. ! [X0] : ((~predf(X0) | preda(X0)) | ~room(X0)) [ennf transformation 60]
179. ! [X0] : (~predf(X0) | preda(X0) | ~room(X0)) [flattening 178]
189. ! [X0] : (((predk(X0) & predd(X0) & prede(X0)) | predh(X0)) | ~room(X0)) [ennf transformation 66]
190. ! [X0] : ((predk(X0) & predd(X0) & prede(X0)) | predh(X0) | ~room(X0)) [flattening 189]
194. ! [X0] : ((prede(X0) <=> predj(X0)) | ~room(X0)) [ennf transformation 69]
195. ~predh(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 71]
196. ~predh(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 195]
199. sP1 <=> ? [X0] : (predk(X0) & preda(X0) & room(X0)) [predicate definition introduction]
200. sP1 <~> ! [X1] : (~predh(X1) | predh(X1) | ~room(X1)) [definition folding 163,199]
222. (sP1 | ! [X0] : (~predk(X0) | ~preda(X0) | ~room(X0))) & (? [X0] : (predk(X0) & preda(X0) & room(X0)) | ~sP1) [nnf transformation 199]
223. (sP1 | ! [X0] : (~predk(X0) | ~preda(X0) | ~room(X0))) & (? [X1] : (predk(X1) & preda(X1) & room(X1)) | ~sP1) [rectify 222]
224. ? [X1] : (predk(X1) & preda(X1) & room(X1)) => (predk(sK8) & preda(sK8) & room(sK8)) [choice axiom]
225. (sP1 | ! [X0] : (~predk(X0) | ~preda(X0) | ~room(X0))) & ((predk(sK8) & preda(sK8) & room(sK8)) | ~sP1) [skolemisation 223,224]
226. (? [X1] : (predh(X1) & ~predh(X1) & room(X1)) | ~sP1) & (! [X1] : (~predh(X1) | predh(X1) | ~room(X1)) | sP1) [nnf transformation 200]
227. (? [X0] : (predh(X0) & ~predh(X0) & room(X0)) | ~sP1) & (! [X1] : (~predh(X1) | predh(X1) | ~room(X1)) | sP1) [rectify 226]
228. ? [X0] : (predh(X0) & ~predh(X0) & room(X0)) => (predh(sK9) & ~predh(sK9) & room(sK9)) [choice axiom]
229. ((predh(sK9) & ~predh(sK9) & room(sK9)) | ~sP1) & (! [X1] : (~predh(X1) | predh(X1) | ~room(X1)) | sP1) [skolemisation 227,228]
260. ! [X0] : (((prede(X0) | ~predj(X0)) & (predj(X0) | ~prede(X0))) | ~room(X0)) [nnf transformation 194]
261. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK18 & paul != sK18 & mary != sK18 & room(sK18)) [choice axiom]
262. ~predh(mary) | (fred != sK18 & paul != sK18 & mary != sK18 & room(sK18)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 196,261]
344. room(mary) [cnf transformation 153]
345. room(paul) [cnf transformation 153]
346. room(fred) [cnf transformation 153]
347. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 153]
374. sP1 | ~predk(X0) | ~preda(X0) | ~room(X0) [cnf transformation 225]
377. ~predh(sK9) | ~sP1 [cnf transformation 229]
378. predh(sK9) | ~sP1 [cnf transformation 229]
404. ~predj(X0) | predf(X0) | ~room(X0) [cnf transformation 175]
406. ~predf(X0) | preda(X0) | ~room(X0) [cnf transformation 179]
421. prede(X0) | predh(X0) | ~room(X0) [cnf transformation 190]
423. predk(X0) | predh(X0) | ~room(X0) [cnf transformation 190]
431. ~prede(X0) | predj(X0) | ~room(X0) [cnf transformation 260]
434. ~predh(mary) | room(sK18) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 262]
435. ~predh(mary) | mary != sK18 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 262]
436. ~predh(mary) | paul != sK18 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 262]
437. ~predh(mary) | fred != sK18 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 262]
486. 10 <=> predj(mary) [avatar definition]
487. predj(mary) <- (10) [avatar component clause 486]
488. ~predj(mary) <- (~10) [avatar component clause 486]
490. 11 <=> preda(mary) [avatar definition]
491. preda(mary) <- (11) [avatar component clause 490]
492. ~preda(mary) <- (~11) [avatar component clause 490]
554. 25 <=> ! [X0] : (~predk(X0) | ~room(X0) | ~preda(X0)) [avatar definition]
555. ~preda(X0) | ~room(X0) | ~predk(X0) <- (25) [avatar component clause 554]
557. 26 <=> sP1 [avatar definition]
560. 25 | 26 [avatar split clause 374,557,554]
577. 30 <=> predh(sK9) [avatar definition]
580. ~26 | 30 [avatar split clause 378,577,557]
581. ~26 | ~30 [avatar split clause 377,577,557]
667. 49 <=> ! [X0] : (predk(X0) | ~room(X0) | predh(X0)) [avatar definition]
668. ~room(X0) | predk(X0) | predh(X0) <- (49) [avatar component clause 667]
675. 51 <=> ! [X0] : (prede(X0) | ~room(X0) | predh(X0)) [avatar definition]
676. ~room(X0) | prede(X0) | predh(X0) <- (51) [avatar component clause 675]
702. 49 [avatar split clause 423,667]
704. 51 [avatar split clause 421,675]
705. ~predh(mary) | fred != sK18 | ~room(paul) | ~room(mary) [subsumption resolution 437,346]
706. ~predh(mary) | fred != sK18 | ~room(mary) [subsumption resolution 705,345]
707. ~predh(mary) | fred != sK18 [subsumption resolution 706,344]
709. 57 <=> fred = sK18 [avatar definition]
713. 58 <=> predh(mary) [avatar definition]
716. ~57 | ~58 [avatar split clause 707,713,709]
717. ~predh(mary) | paul != sK18 | ~room(paul) | ~room(mary) [subsumption resolution 436,346]
718. ~predh(mary) | paul != sK18 | ~room(mary) [subsumption resolution 717,345]
719. ~predh(mary) | paul != sK18 [subsumption resolution 718,344]
721. 59 <=> paul = sK18 [avatar definition]
723. paul != sK18 <- (~59) [avatar component clause 721]
724. ~59 | ~58 [avatar split clause 719,713,721]
725. ~predh(mary) | mary != sK18 | ~room(paul) | ~room(mary) [subsumption resolution 435,346]
726. ~predh(mary) | mary != sK18 | ~room(mary) [subsumption resolution 725,345]
727. ~predh(mary) | mary != sK18 [subsumption resolution 726,344]
729. 60 <=> mary = sK18 [avatar definition]
732. ~60 | ~58 [avatar split clause 727,713,729]
733. ~predh(mary) | room(sK18) | ~room(paul) | ~room(mary) [subsumption resolution 434,346]
734. ~predh(mary) | room(sK18) | ~room(mary) [subsumption resolution 733,345]
735. ~predh(mary) | room(sK18) [subsumption resolution 734,344]
737. 61 <=> room(sK18) [avatar definition]
739. room(sK18) <- (61) [avatar component clause 737]
740. 61 | ~58 [avatar split clause 735,713,737]
809. 70 <=> predk(mary) [avatar definition]
811. predk(mary) <- (70) [avatar component clause 809]
865. ~room(mary) | ~predk(mary) <- (11, 25) [resolution 555,491]
867. ~predk(mary) <- (11, 25) [subsumption resolution 865,344]
868. $false <- (11, 25, 70) [subsumption resolution 867,811]
869. ~11 | ~25 | ~70 [avatar contradiction clause 868]
871. predf(mary) | ~room(mary) <- (10) [resolution 487,404]
873. predf(mary) <- (10) [subsumption resolution 871,344]
880. predk(mary) | predh(mary) <- (49) [resolution 668,344]
977. prede(mary) | predh(mary) <- (51) [resolution 676,344]
1035. preda(mary) | ~room(mary) <- (10) [resolution 873,406]
1037. ~room(mary) <- (10, ~11) [subsumption resolution 1035,492]
1038. $false <- (10, ~11) [subsumption resolution 1037,344]
1039. ~10 | 11 [avatar contradiction clause 1038]
1058. 96 <=> prede(mary) [avatar definition]
1060. prede(mary) <- (96) [avatar component clause 1058]
1061. 58 | 96 | ~51 [avatar split clause 977,675,1058,713]
1201. paul = sK18 | mary = sK18 | fred = sK18 <- (61) [resolution 347,739]
1280. mary = sK18 | fred = sK18 <- (~59, 61) [subsumption resolution 1201,723]
1306. 58 | 70 | ~49 [avatar split clause 880,667,809,713]
1385. 57 | 60 | 59 | ~61 [avatar split clause 1280,737,721,729,709]
1446. predj(mary) | ~room(mary) <- (96) [resolution 1060,431]
1447. ~room(mary) <- (~10, 96) [subsumption resolution 1446,488]
1448. $false <- (~10, 96) [subsumption resolution 1447,344]
1449. 10 | ~96 [avatar contradiction clause 1448]
1450. $false [avatar sat refutation 560,580,581,702,704,716,724,732,740,869,1039,1061,1306,1385,1449]
% SZS output end Proof for 20284484617684454861948
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5756
% Time elapsed: 0.043 s
% ------------------------------
% ------------------------------
| 0.410139 |
Johnny, Jean, Patrick, Roger are the only persons in the room.
“Someone in the room collects first edition books” only if “Johnny neither collects luxury watches nor owns a smartwatch”.
“Johnny has a curated collection of mid-century modern furniture and does not collect first edition books” unless “Patrick owns a smartwatch”.
“Everyone in the room does not enjoy stargazing if they enjoys windsurfing” unless “Johnny enjoys windsurfing or designs and sews custom cosplay costumes for conventions or both”.
If “someone anywhere does not have a curated collection of mid-century modern furniture or has a curated collection of mid-century modern furniture or both” then “not everyone in the room is dedicated to sustainable living and zero-waste practices”.
“Jean collects luxury watches” unless “Jean neither designs and sews custom cosplay costumes for conventions nor owns a smartwatch”.
“Someone in the room enjoys salsa dancing” unless “Patrick neither does not design and sews custom cosplay costumes for conventions nor has a piercing”. | Patrick owns a microscope. | entailment | room(johnny)&room(jean)&room(patrick)&room(roger)&(![X]:(room(X)=>(X='johnny'|X='jean'|X='patrick'|X='roger')))&
((?[X]:(room(X)&(collects_first_edition_books(X))))=>(~((collects_luxury_watches(johnny))|(owns_a_smartwatch(johnny)))))&
(~(owns_a_smartwatch(patrick))=>(((has_a_curated_collection_of_mid-century_modern_furniture(johnny))&(does_not_collect_first_edition_books(johnny)))))&
(~(((enjoys_windsurfing(johnny))|(designs_and_sews_custom_cosplay_costumes_for_conventions(johnny))))=>(![X]:(room(X)=>(((enjoys_windsurfing(X))=>(does_not_enjoy_stargazing(X)))))))&
((?[X]:(anywhere(X)&(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))=>(~![X]:(room(X)=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))&
(~(~((designs_and_sews_custom_cosplay_costumes_for_conventions(jean))|(owns_a_smartwatch(jean))))=>(collects_luxury_watches(jean)))&
(~(~((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(patrick))|(has_a_piercing(patrick))))=>(?[X]:(room(X)&(enjoys_salsa_dancing(X)))))&
(((collects_first_edition_books(johnny))=>(?[X]:(room(X)&(~((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(collects_luxury_watches(X)))))))&((~(collects_first_edition_books(johnny)))=>(((owns_a_microscope(patrick))&(designs_and_sews_custom_cosplay_costumes_for_conventions(patrick))))))&
(((~((has_a_piercing(jean))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(jean))))=>(does_not_have_a_piercing(johnny)))&
((does_not_have_a_piercing(johnny))=>(((?[X]:(room(X)&enjoys_windsurfing(X)))))))&
((does_not_have_a_curated_collection_of_mid-century_modern_furniture(patrick))<=>(?[X]:(anywhere(X)&(enjoys_salsa_dancing(X)))))&
(((((does_not_collect_luxury_watches(patrick))&(works_on_fridays(patrick))&(enjoys_cross-country_skiing(patrick))))=>(has_a_curated_collection_of_mid-century_modern_furniture(johnny)))&((~(((does_not_collect_luxury_watches(patrick))&(works_on_fridays(patrick))&(enjoys_cross-country_skiing(patrick)))))=>((enjoys_cross-country_skiing(patrick))&(enjoys_windsurfing(patrick)))))&
(![X]:(anywhere(X)=>(((enjoys_virtual_reality_gaming(X))=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(enjoys_windsurfing(X))|(does_not_collect_luxury_watches(X))))))))&
(![X]:(room(X)=>(((((enjoys_stargazing(X))&(enjoys_salsa_dancing(X))&(enjoys_windsurfing(X))))=>(collects_luxury_watches(X))))))&
((enjoys_cross-country_skiing(patrick))&(enjoys_windsurfing(patrick)))&
(collects_antique_jewelry(patrick))&
(((enjoys_stargazing(patrick))&(enjoys_salsa_dancing(patrick))&(enjoys_windsurfing(patrick))))&
(~((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(patrick))|(does_not_own_a_smartwatch(patrick))))&
(![X]:(room(X)=>(((does_not_have_a_piercing(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))&
(((enjoys_stargazing(johnny))&(enjoys_salsa_dancing(johnny))&(enjoys_windsurfing(johnny))))&
(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(patrick))&
(~((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(patrick))|(has_a_piercing(patrick))))&
(((?[X]:(room(X)&enjoys_cross-country_skiing(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_cross-country_skiing(X))&(enjoys_cross-country_skiing(Y)))=>(X=Y)))))&
(?[X]:(room(X)&(collects_luxury_watches(X))))&
(![X]:(room(X)=>(((collects_first_edition_books(X))<=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))) | room(johnny)&room(jean)&room(patrick)&room(roger)&(![X]:(room(X)=>(X='johnny'|X='jean'|X='patrick'|X='roger')))&
owns_a_microscope(patrick) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 6028462538060403928350581
% SZS output start Proof for 6028462538060403928350581
44. ! [X0] : (room(X0) => (predi(X0) <=> ~predp(X0))) & ? [X0] : (predf(X0) & room(X0)) & ! [X0,X1] : ((predc(X1) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predc(X0) & room(X0)) & ~(predd(fred) | ~predo(fred)) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X0] : (room(X0) => (predg(X0) | ~predd(X0))) & ~(~predj(fred) | ~predp(fred)) & predm(fred) & predn(fred) & predb(fred) & predh(fred) & predm(fred) & predc(fred) & ! [X0] : (room(X0) => ((predm(X0) & predn(X0) & predb(X0)) => predf(X0))) & ! [X0] : (anywhere(X0) => (predl(X0) => (~predf(X0) | predm(X0) | ~preda(X0)))) & (~(predc(fred) & prede(fred) & ~predf(fred)) => (predm(fred) & predc(fred))) & ((predc(fred) & prede(fred) & ~predf(fred)) => preda(mary)) & (~preda(fred) <=> ? [X0] : (predn(X0) & anywhere(X0))) & (~predd(mary) => ? [X0] : (predm(X0) & room(X0))) & (~(predg(paul) | predd(paul)) => ~predd(mary)) & (~predi(mary) => (predo(fred) & predk(fred))) & (predi(mary) => ? [X0] : (~(predf(X0) | ~preda(X0)) & room(X0))) & (~~(predd(fred) | ~predo(fred)) => ? [X0] : (predn(X0) & room(X0))) & (~~(predj(paul) | predo(paul)) => predf(paul)) & (? [X0] : ((preda(X0) | ~preda(X0)) & anywhere(X0)) => ~! [X0] : (room(X0) => predg(X0))) & (~(predo(mary) | predm(mary)) => ! [X0] : (room(X0) => (predm(X0) => ~predb(X0)))) & (~predj(fred) => (~predi(mary) & preda(mary))) & (? [X0] : (predi(X0) & room(X0)) => ~(predj(mary) | predf(mary))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. ~(predk(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
46. ! [X0] : (room(X0) => (predi(X0) <=> ~predp(X0))) & ? [X1] : (predf(X1) & room(X1)) & ! [X2,X3] : ((predc(X3) & predc(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (predc(X4) & room(X4)) & ~(predd(fred) | ~predo(fred)) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X5] : (room(X5) => (predg(X5) | ~predd(X5))) & ~(~predj(fred) | ~predp(fred)) & predm(fred) & predn(fred) & predb(fred) & predh(fred) & predm(fred) & predc(fred) & ! [X6] : (room(X6) => ((predm(X6) & predn(X6) & predb(X6)) => predf(X6))) & ! [X7] : (anywhere(X7) => (predl(X7) => (~predf(X7) | predm(X7) | ~preda(X7)))) & (~(predc(fred) & prede(fred) & ~predf(fred)) => (predm(fred) & predc(fred))) & ((predc(fred) & prede(fred) & ~predf(fred)) => preda(mary)) & (~preda(fred) <=> ? [X8] : (predn(X8) & anywhere(X8))) & (~predd(mary) => ? [X9] : (predm(X9) & room(X9))) & (~(predg(paul) | predd(paul)) => ~predd(mary)) & (~predi(mary) => (predo(fred) & predk(fred))) & (predi(mary) => ? [X10] : (~(predf(X10) | ~preda(X10)) & room(X10))) & (~~(predd(fred) | ~predo(fred)) => ? [X11] : (predn(X11) & room(X11))) & (~~(predj(paul) | predo(paul)) => predf(paul)) & (? [X12] : ((preda(X12) | ~preda(X12)) & anywhere(X12)) => ~! [X13] : (room(X13) => predg(X13))) & (~(predo(mary) | predm(mary)) => ! [X14] : (room(X14) => (predm(X14) => ~predb(X14)))) & (~predj(fred) => (~predi(mary) & preda(mary))) & (? [X15] : (predi(X15) & room(X15)) => ~(predj(mary) | predf(mary))) & ! [X16] : (room(X16) => (alice = X16 | fred = X16 | paul = X16 | mary = X16)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44]
47. ! [X0] : (room(X0) => (predi(X0) <=> ~predp(X0))) & ? [X1] : (predf(X1) & room(X1)) & ! [X2,X3] : ((predc(X3) & predc(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (predc(X4) & room(X4)) & ~(predd(fred) | ~predo(fred)) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X5] : (room(X5) => (predg(X5) | ~predd(X5))) & ~(~predj(fred) | ~predp(fred)) & predm(fred) & predn(fred) & predb(fred) & predh(fred) & predm(fred) & predc(fred) & ! [X6] : (room(X6) => ((predm(X6) & predn(X6) & predb(X6)) => predf(X6))) & ! [X7] : (anywhere(X7) => (predl(X7) => (~predf(X7) | predm(X7) | ~preda(X7)))) & (~(predc(fred) & prede(fred) & ~predf(fred)) => (predm(fred) & predc(fred))) & ((predc(fred) & prede(fred) & ~predf(fred)) => preda(mary)) & (~preda(fred) <=> ? [X8] : (predn(X8) & anywhere(X8))) & (~predd(mary) => ? [X9] : (predm(X9) & room(X9))) & (~(predg(paul) | predd(paul)) => ~predd(mary)) & (~predi(mary) => (predo(fred) & predk(fred))) & (predi(mary) => ? [X10] : (~(predf(X10) | ~preda(X10)) & room(X10))) & ((predd(fred) | ~predo(fred)) => ? [X11] : (predn(X11) & room(X11))) & ((predj(paul) | predo(paul)) => predf(paul)) & (? [X12] : ((preda(X12) | ~preda(X12)) & anywhere(X12)) => ~! [X13] : (room(X13) => predg(X13))) & (~(predo(mary) | predm(mary)) => ! [X14] : (room(X14) => (predm(X14) => ~predb(X14)))) & (~predj(fred) => (~predi(mary) & preda(mary))) & (? [X15] : (predi(X15) & room(X15)) => ~(predj(mary) | predf(mary))) & ! [X16] : (room(X16) => (alice = X16 | fred = X16 | paul = X16 | mary = X16)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 46]
48. ! [X0] : (room(X0) => (predi(X0) <=> ~predp(X0))) & ? [X1] : (predf(X1) & room(X1)) & ! [X2,X3] : ((predc(X3) & predc(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (predc(X4) & room(X4)) & ~(predd(fred) | ~predo(fred)) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X5] : (room(X5) => (predg(X5) | ~predd(X5))) & ~(~predj(fred) | ~predp(fred)) & predm(fred) & predn(fred) & predb(fred) & predm(fred) & predc(fred) & ! [X6] : (room(X6) => ((predm(X6) & predn(X6) & predb(X6)) => predf(X6))) & ! [X7] : (anywhere(X7) => (predl(X7) => (~predf(X7) | predm(X7) | ~preda(X7)))) & (~(predc(fred) & prede(fred) & ~predf(fred)) => (predm(fred) & predc(fred))) & ((predc(fred) & prede(fred) & ~predf(fred)) => preda(mary)) & (~preda(fred) <=> ? [X8] : (predn(X8) & anywhere(X8))) & (~predd(mary) => ? [X9] : (predm(X9) & room(X9))) & (~(predg(paul) | predd(paul)) => ~predd(mary)) & (~predi(mary) => (predo(fred) & predk(fred))) & (predi(mary) => ? [X10] : (~(predf(X10) | ~preda(X10)) & room(X10))) & ((predd(fred) | ~predo(fred)) => ? [X11] : (predn(X11) & room(X11))) & ((predj(paul) | predo(paul)) => predf(paul)) & (? [X12] : ((preda(X12) | ~preda(X12)) & anywhere(X12)) => ~! [X13] : (room(X13) => predg(X13))) & (~(predo(mary) | predm(mary)) => ! [X14] : (room(X14) => (predm(X14) => ~predb(X14)))) & (~predj(fred) => (~predi(mary) & preda(mary))) & (? [X15] : (predi(X15) & room(X15)) => ~(predj(mary) | predf(mary))) & ! [X16] : (room(X16) => (alice = X16 | fred = X16 | paul = X16 | mary = X16)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47]
49. ! [X0] : (room(X0) => (predi(X0) <=> ~predp(X0))) & ? [X1] : (predf(X1) & room(X1)) & ! [X2,X3] : ((predc(X3) & predc(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (predc(X4) & room(X4)) & ~(predd(fred) | ~predo(fred)) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X5] : (room(X5) => (predg(X5) | ~predd(X5))) & ~(~predj(fred) | ~predp(fred)) & predm(fred) & predn(fred) & predb(fred) & predm(fred) & predc(fred) & ! [X6] : (room(X6) => ((predm(X6) & predn(X6) & predb(X6)) => predf(X6))) & (~(predc(fred) & prede(fred) & ~predf(fred)) => (predm(fred) & predc(fred))) & ((predc(fred) & prede(fred) & ~predf(fred)) => preda(mary)) & (~preda(fred) <=> ? [X8] : (predn(X8) & anywhere(X8))) & (~predd(mary) => ? [X9] : (predm(X9) & room(X9))) & (~(predg(paul) | predd(paul)) => ~predd(mary)) & (~predi(mary) => (predo(fred) & predk(fred))) & (predi(mary) => ? [X10] : (~(predf(X10) | ~preda(X10)) & room(X10))) & ((predd(fred) | ~predo(fred)) => ? [X11] : (predn(X11) & room(X11))) & ((predj(paul) | predo(paul)) => predf(paul)) & (? [X12] : ((preda(X12) | ~preda(X12)) & anywhere(X12)) => ~! [X13] : (room(X13) => predg(X13))) & (~(predo(mary) | predm(mary)) => ! [X14] : (room(X14) => (predm(X14) => ~predb(X14)))) & (~predj(fred) => (~predi(mary) & preda(mary))) & (? [X15] : (predi(X15) & room(X15)) => ~(predj(mary) | predf(mary))) & ! [X16] : (room(X16) => (alice = X16 | fred = X16 | paul = X16 | mary = X16)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48]
121. ! [X0] : ((predi(X0) <=> ~predp(X0)) | ~room(X0)) & ? [X1] : (predf(X1) & room(X1)) & ! [X2,X3] : (X2 = X3 | (~predc(X3) | ~predc(X2) | ~room(X3) | ~room(X2))) & ? [X4] : (predc(X4) & room(X4)) & (~predd(fred) & predo(fred)) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X5] : ((predg(X5) | ~predd(X5)) | ~room(X5)) & (predj(fred) & predp(fred)) & predm(fred) & predn(fred) & predb(fred) & predm(fred) & predc(fred) & ! [X6] : ((predf(X6) | (~predm(X6) | ~predn(X6) | ~predb(X6))) | ~room(X6)) & ((predm(fred) & predc(fred)) | (predc(fred) & prede(fred) & ~predf(fred))) & (preda(mary) | (~predc(fred) | ~prede(fred) | predf(fred))) & (~preda(fred) <=> ? [X8] : (predn(X8) & anywhere(X8))) & (? [X9] : (predm(X9) & room(X9)) | predd(mary)) & (~predd(mary) | (predg(paul) | predd(paul))) & ((predo(fred) & predk(fred)) | predi(mary)) & (? [X10] : ((~predf(X10) & preda(X10)) & room(X10)) | ~predi(mary)) & (? [X11] : (predn(X11) & room(X11)) | (~predd(fred) & predo(fred))) & (predf(paul) | (~predj(paul) & ~predo(paul))) & (? [X13] : (~predg(X13) & room(X13)) | ! [X12] : ((~preda(X12) & preda(X12)) | ~anywhere(X12))) & (! [X14] : ((~predb(X14) | ~predm(X14)) | ~room(X14)) | (predo(mary) | predm(mary))) & ((~predi(mary) & preda(mary)) | predj(fred)) & ((~predj(mary) & ~predf(mary)) | ! [X15] : (~predi(X15) | ~room(X15))) & ! [X16] : ((alice = X16 | fred = X16 | paul = X16 | mary = X16) | ~room(X16)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 49]
122. ! [X0] : ((predi(X0) <=> ~predp(X0)) | ~room(X0)) & ? [X1] : (predf(X1) & room(X1)) & ! [X2,X3] : (X2 = X3 | ~predc(X3) | ~predc(X2) | ~room(X3) | ~room(X2)) & ? [X4] : (predc(X4) & room(X4)) & ~predd(fred) & predo(fred) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X5] : (predg(X5) | ~predd(X5) | ~room(X5)) & predj(fred) & predp(fred) & predm(fred) & predn(fred) & predb(fred) & predm(fred) & predc(fred) & ! [X6] : (predf(X6) | ~predm(X6) | ~predn(X6) | ~predb(X6) | ~room(X6)) & ((predm(fred) & predc(fred)) | (predc(fred) & prede(fred) & ~predf(fred))) & (preda(mary) | ~predc(fred) | ~prede(fred) | predf(fred)) & (~preda(fred) <=> ? [X8] : (predn(X8) & anywhere(X8))) & (? [X9] : (predm(X9) & room(X9)) | predd(mary)) & (~predd(mary) | predg(paul) | predd(paul)) & ((predo(fred) & predk(fred)) | predi(mary)) & (? [X10] : (~predf(X10) & preda(X10) & room(X10)) | ~predi(mary)) & (? [X11] : (predn(X11) & room(X11)) | (~predd(fred) & predo(fred))) & (predf(paul) | (~predj(paul) & ~predo(paul))) & (? [X13] : (~predg(X13) & room(X13)) | ! [X12] : ((~preda(X12) & preda(X12)) | ~anywhere(X12))) & (! [X14] : (~predb(X14) | ~predm(X14) | ~room(X14)) | predo(mary) | predm(mary)) & ((~predi(mary) & preda(mary)) | predj(fred)) & ((~predj(mary) & ~predf(mary)) | ! [X15] : (~predi(X15) | ~room(X15))) & ! [X16] : (alice = X16 | fred = X16 | paul = X16 | mary = X16 | ~room(X16)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 121]
123. ~predk(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45]
124. ~predk(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 123]
126. ! [X0] : (((predi(X0) | predp(X0)) & (~predp(X0) | ~predi(X0))) | ~room(X0)) & ? [X1] : (predf(X1) & room(X1)) & ! [X2,X3] : (X2 = X3 | ~predc(X3) | ~predc(X2) | ~room(X3) | ~room(X2)) & ? [X4] : (predc(X4) & room(X4)) & ~predd(fred) & predo(fred) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X5] : (predg(X5) | ~predd(X5) | ~room(X5)) & predj(fred) & predp(fred) & predm(fred) & predn(fred) & predb(fred) & predm(fred) & predc(fred) & ! [X6] : (predf(X6) | ~predm(X6) | ~predn(X6) | ~predb(X6) | ~room(X6)) & ((predm(fred) & predc(fred)) | (predc(fred) & prede(fred) & ~predf(fred))) & (preda(mary) | ~predc(fred) | ~prede(fred) | predf(fred)) & ((~preda(fred) | ! [X8] : (~predn(X8) | ~anywhere(X8))) & (? [X8] : (predn(X8) & anywhere(X8)) | preda(fred))) & (? [X9] : (predm(X9) & room(X9)) | predd(mary)) & (~predd(mary) | predg(paul) | predd(paul)) & ((predo(fred) & predk(fred)) | predi(mary)) & (? [X10] : (~predf(X10) & preda(X10) & room(X10)) | ~predi(mary)) & (? [X11] : (predn(X11) & room(X11)) | (~predd(fred) & predo(fred))) & (predf(paul) | (~predj(paul) & ~predo(paul))) & (? [X13] : (~predg(X13) & room(X13)) | ! [X12] : ((~preda(X12) & preda(X12)) | ~anywhere(X12))) & (! [X14] : (~predb(X14) | ~predm(X14) | ~room(X14)) | predo(mary) | predm(mary)) & ((~predi(mary) & preda(mary)) | predj(fred)) & ((~predj(mary) & ~predf(mary)) | ! [X15] : (~predi(X15) | ~room(X15))) & ! [X16] : (alice = X16 | fred = X16 | paul = X16 | mary = X16 | ~room(X16)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 122]
127. ! [X0] : (((predi(X0) | predp(X0)) & (~predp(X0) | ~predi(X0))) | ~room(X0)) & ? [X1] : (predf(X1) & room(X1)) & ! [X2,X3] : (X2 = X3 | ~predc(X3) | ~predc(X2) | ~room(X3) | ~room(X2)) & ? [X4] : (predc(X4) & room(X4)) & ~predd(fred) & predo(fred) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X5] : (predg(X5) | ~predd(X5) | ~room(X5)) & predj(fred) & predp(fred) & predm(fred) & predn(fred) & predb(fred) & predm(fred) & predc(fred) & ! [X6] : (predf(X6) | ~predm(X6) | ~predn(X6) | ~predb(X6) | ~room(X6)) & ((predm(fred) & predc(fred)) | (predc(fred) & prede(fred) & ~predf(fred))) & (preda(mary) | ~predc(fred) | ~prede(fred) | predf(fred)) & (~preda(fred) | ! [X8] : (~predn(X8) | ~anywhere(X8))) & (? [X8] : (predn(X8) & anywhere(X8)) | preda(fred)) & (? [X9] : (predm(X9) & room(X9)) | predd(mary)) & (~predd(mary) | predg(paul) | predd(paul)) & ((predo(fred) & predk(fred)) | predi(mary)) & (? [X10] : (~predf(X10) & preda(X10) & room(X10)) | ~predi(mary)) & (? [X11] : (predn(X11) & room(X11)) | (~predd(fred) & predo(fred))) & (predf(paul) | (~predj(paul) & ~predo(paul))) & (? [X13] : (~predg(X13) & room(X13)) | ! [X12] : ((~preda(X12) & preda(X12)) | ~anywhere(X12))) & (! [X14] : (~predb(X14) | ~predm(X14) | ~room(X14)) | predo(mary) | predm(mary)) & ((~predi(mary) & preda(mary)) | predj(fred)) & ((~predj(mary) & ~predf(mary)) | ! [X15] : (~predi(X15) | ~room(X15))) & ! [X16] : (alice = X16 | fred = X16 | paul = X16 | mary = X16 | ~room(X16)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126]
128. ! [X0] : (((predi(X0) | predp(X0)) & (~predp(X0) | ~predi(X0))) | ~room(X0)) & ? [X1] : (predf(X1) & room(X1)) & ! [X2,X3] : (X2 = X3 | ~predc(X3) | ~predc(X2) | ~room(X3) | ~room(X2)) & ? [X4] : (predc(X4) & room(X4)) & ~predd(fred) & predo(fred) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X5] : (predg(X5) | ~predd(X5) | ~room(X5)) & predj(fred) & predp(fred) & predm(fred) & predn(fred) & predb(fred) & predm(fred) & predc(fred) & ! [X6] : (predf(X6) | ~predm(X6) | ~predn(X6) | ~predb(X6) | ~room(X6)) & ((predm(fred) & predc(fred)) | (predc(fred) & prede(fred) & ~predf(fred))) & (preda(mary) | ~predc(fred) | ~prede(fred) | predf(fred)) & (~preda(fred) | ! [X7] : (~predn(X7) | ~anywhere(X7))) & (? [X8] : (predn(X8) & anywhere(X8)) | preda(fred)) & (? [X9] : (predm(X9) & room(X9)) | predd(mary)) & (~predd(mary) | predg(paul) | predd(paul)) & ((predo(fred) & predk(fred)) | predi(mary)) & (? [X10] : (~predf(X10) & preda(X10) & room(X10)) | ~predi(mary)) & (? [X11] : (predn(X11) & room(X11)) | (~predd(fred) & predo(fred))) & (predf(paul) | (~predj(paul) & ~predo(paul))) & (? [X12] : (~predg(X12) & room(X12)) | ! [X13] : ((~preda(X13) & preda(X13)) | ~anywhere(X13))) & (! [X14] : (~predb(X14) | ~predm(X14) | ~room(X14)) | predo(mary) | predm(mary)) & ((~predi(mary) & preda(mary)) | predj(fred)) & ((~predj(mary) & ~predf(mary)) | ! [X15] : (~predi(X15) | ~room(X15))) & ! [X16] : (alice = X16 | fred = X16 | paul = X16 | mary = X16 | ~room(X16)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 127]
129. ? [X1] : (predf(X1) & room(X1)) => (predf(sK0) & room(sK0)) [choice axiom]
130. ? [X4] : (predc(X4) & room(X4)) => (predc(sK1) & room(sK1)) [choice axiom]
131. ? [X8] : (predn(X8) & anywhere(X8)) => (predn(sK2) & anywhere(sK2)) [choice axiom]
132. ? [X9] : (predm(X9) & room(X9)) => (predm(sK3) & room(sK3)) [choice axiom]
133. ? [X10] : (~predf(X10) & preda(X10) & room(X10)) => (~predf(sK4) & preda(sK4) & room(sK4)) [choice axiom]
134. ? [X11] : (predn(X11) & room(X11)) => (predn(sK5) & room(sK5)) [choice axiom]
135. ? [X12] : (~predg(X12) & room(X12)) => (~predg(sK6) & room(sK6)) [choice axiom]
136. ! [X0] : (((predi(X0) | predp(X0)) & (~predp(X0) | ~predi(X0))) | ~room(X0)) & (predf(sK0) & room(sK0)) & ! [X2,X3] : (X2 = X3 | ~predc(X3) | ~predc(X2) | ~room(X3) | ~room(X2)) & (predc(sK1) & room(sK1)) & ~predd(fred) & predo(fred) & predp(fred) & predm(mary) & predn(mary) & predb(mary) & ! [X5] : (predg(X5) | ~predd(X5) | ~room(X5)) & predj(fred) & predp(fred) & predm(fred) & predn(fred) & predb(fred) & predm(fred) & predc(fred) & ! [X6] : (predf(X6) | ~predm(X6) | ~predn(X6) | ~predb(X6) | ~room(X6)) & ((predm(fred) & predc(fred)) | (predc(fred) & prede(fred) & ~predf(fred))) & (preda(mary) | ~predc(fred) | ~prede(fred) | predf(fred)) & (~preda(fred) | ! [X7] : (~predn(X7) | ~anywhere(X7))) & ((predn(sK2) & anywhere(sK2)) | preda(fred)) & ((predm(sK3) & room(sK3)) | predd(mary)) & (~predd(mary) | predg(paul) | predd(paul)) & ((predo(fred) & predk(fred)) | predi(mary)) & ((~predf(sK4) & preda(sK4) & room(sK4)) | ~predi(mary)) & ((predn(sK5) & room(sK5)) | (~predd(fred) & predo(fred))) & (predf(paul) | (~predj(paul) & ~predo(paul))) & ((~predg(sK6) & room(sK6)) | ! [X13] : ((~preda(X13) & preda(X13)) | ~anywhere(X13))) & (! [X14] : (~predb(X14) | ~predm(X14) | ~room(X14)) | predo(mary) | predm(mary)) & ((~predi(mary) & preda(mary)) | predj(fred)) & ((~predj(mary) & ~predf(mary)) | ! [X15] : (~predi(X15) | ~room(X15))) & ! [X16] : (alice = X16 | fred = X16 | paul = X16 | mary = X16 | ~room(X16)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 128,135,134,133,132,131,130,129]
137. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom]
138. ~predk(fred) | (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 124,137]
220. room(mary) [cnf transformation 136]
221. room(paul) [cnf transformation 136]
222. room(fred) [cnf transformation 136]
223. room(alice) [cnf transformation 136]
224. ~room(X16) | fred = X16 | paul = X16 | mary = X16 | alice = X16 [cnf transformation 136]
225. ~predf(mary) | ~predi(X15) | ~room(X15) [cnf transformation 136]
243. predk(fred) | predi(mary) [cnf transformation 136]
258. ~predn(X6) | ~predm(X6) | predf(X6) | ~predb(X6) | ~room(X6) [cnf transformation 136]
267. predb(mary) [cnf transformation 136]
268. predn(mary) [cnf transformation 136]
269. predm(mary) [cnf transformation 136]
280. ~predk(fred) | room(sK7) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138]
281. ~predk(fred) | mary != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138]
282. ~predk(fred) | paul != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138]
283. ~predk(fred) | fred != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138]
284. ~predk(fred) | alice != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138]
338. 12 <=> predi(mary) [avatar definition]
340. predi(mary) <- (12) [avatar component clause 338]
342. 13 <=> predk(fred) [avatar definition]
345. 12 | 13 [avatar split clause 243,342,338]
398. 24 <=> ! [X15] : (~predi(X15) | ~room(X15)) [avatar definition]
399. ~predi(X15) | ~room(X15) <- (24) [avatar component clause 398]
406. 26 <=> predf(mary) [avatar definition]
409. 24 | ~26 [avatar split clause 225,406,398]
410. ~predk(fred) | alice != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,223]
411. ~predk(fred) | alice != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 410,222]
412. ~predk(fred) | alice != sK7 | ~room(mary) [subsumption resolution 411,221]
413. ~predk(fred) | alice != sK7 [subsumption resolution 412,220]
415. 27 <=> alice = sK7 [avatar definition]
418. ~27 | ~13 [avatar split clause 413,342,415]
419. ~predk(fred) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,223]
420. ~predk(fred) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 419,222]
421. ~predk(fred) | fred != sK7 | ~room(mary) [subsumption resolution 420,221]
422. ~predk(fred) | fred != sK7 [subsumption resolution 421,220]
424. 28 <=> fred = sK7 [avatar definition]
426. fred != sK7 <- (~28) [avatar component clause 424]
427. ~28 | ~13 [avatar split clause 422,342,424]
428. ~predk(fred) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,223]
429. ~predk(fred) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 428,222]
430. ~predk(fred) | paul != sK7 | ~room(mary) [subsumption resolution 429,221]
431. ~predk(fred) | paul != sK7 [subsumption resolution 430,220]
433. 29 <=> paul = sK7 [avatar definition]
435. paul != sK7 <- (~29) [avatar component clause 433]
436. ~29 | ~13 [avatar split clause 431,342,433]
437. ~predk(fred) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 281,223]
438. ~predk(fred) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 437,222]
439. ~predk(fred) | mary != sK7 | ~room(mary) [subsumption resolution 438,221]
440. ~predk(fred) | mary != sK7 [subsumption resolution 439,220]
442. 30 <=> mary = sK7 [avatar definition]
444. mary != sK7 <- (~30) [avatar component clause 442]
445. ~30 | ~13 [avatar split clause 440,342,442]
446. ~predk(fred) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,223]
447. ~predk(fred) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 446,222]
448. ~predk(fred) | room(sK7) | ~room(mary) [subsumption resolution 447,221]
449. ~predk(fred) | room(sK7) [subsumption resolution 448,220]
451. 31 <=> room(sK7) [avatar definition]
453. room(sK7) <- (31) [avatar component clause 451]
454. 31 | ~13 [avatar split clause 449,342,451]
594. ~predm(mary) | predf(mary) | ~predb(mary) | ~room(mary) [resolution 258,268]
600. predf(mary) | ~predb(mary) | ~room(mary) [subsumption resolution 594,269]
622. predf(mary) | ~room(mary) [subsumption resolution 600,267]
623. predf(mary) [subsumption resolution 622,220]
624. 26 [avatar split clause 623,406]
652. fred = sK7 | paul = sK7 | mary = sK7 | alice = sK7 <- (31) [resolution 224,453]
704. paul = sK7 | mary = sK7 | alice = sK7 <- (~28, 31) [subsumption resolution 652,426]
705. mary = sK7 | alice = sK7 <- (~28, ~29, 31) [subsumption resolution 704,435]
706. alice = sK7 <- (~28, ~29, ~30, 31) [subsumption resolution 705,444]
714. 27 | 28 | 29 | 30 | ~31 [avatar split clause 706,451,442,433,424,415]
738. ~room(mary) <- (12, 24) [resolution 340,399]
739. $false <- (12, 24) [subsumption resolution 738,220]
740. ~12 | ~24 [avatar contradiction clause 739]
741. $false [avatar sat refutation 345,409,418,427,436,445,454,624,714,740]
% SZS output end Proof for 6028462538060403928350581
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0.164578 |
Ana is the only person in the room. If “everyone in the room practices calligraphy or is not a Linux enthusiast” then “Ana practices calligraphy”. If “everyone outside the room is a skilled home brewer experimenting with craft beer recipes or is not a skilled home brewer experimenting with craft beer recipes” then “it is not the case that “Ana creates bespoke furniture pieces from reclaimed wood””. If “Ana enjoys rooftop gardening or collects rare minerals or both” then “Ana plays as a goalkeeper for a local amateur soccer team or participates in citizen science projects related to wildlife monitoring or both”. If “at least one person outside the room is a wine connoisseur” then “Ana owns a smart tv”. If “everyone in the room does not own an extensive assortment of vintage comic book memorabilia or creates bespoke furniture pieces from reclaimed wood” then “if someone plays as a goalkeeper for a local amateur soccer team then he/she hosts a popular podcast about emerging technologies and vice versa”. Either “Ana is allergic to anything” or “everyone in the room practices calligraphy or does not collect antique clocks” but not both. “Everyone in the room uses an ios phone or is not allergic to anything” if “Ana is a skilled home brewer experimenting with craft beer recipes” and vice versa. Either “Ana hosts a YouTube channel dedicated to art tutorials” or “Ana is a wine connoisseur” but not both. Either “no one in the room regularly goes on multi-day backpacking trips in national parks or does not volunteer for local environmental conservation projects” or “everyone outside the room develops open-source software projects in their free time or is not allergic to anything” but not both. “Ana practices calligraphy and develops open-source software projects in their free time” if “everyone outside the room is allergic to anything or does not practice calligraphy” and vice versa. If “everyone in the room creates bespoke furniture pieces from reclaimed wood or does not regularly goes on multi-day backpacking trips in national parks” then “everyone in the room who enjoys stargazing creates bespoke furniture pieces from reclaimed wood”. Ana collects antique clocks. Everyone in the room who hosts a popular podcast about emerging technologies is a Linux enthusiast. Everyone in the room who enjoys stargazing creates bespoke furniture pieces from reclaimed wood. Everyone anywhere enjoys rooftop gardening if they regularly goes on multi-day backpacking trips in national parks. Ana is not a skilled home brewer experimenting with craft beer recipes. | Ana is a Linux enthusiast. | entailment | room(ana)&(![X]:(room(X)=>(X='ana')))&
((![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(practices_calligraphy(X))))))=>(practices_calligraphy(ana)))&
((![X]:(~room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(~(creates_bespoke_furniture_pieces_from_reclaimed_wood(ana))))&
((((enjoys_rooftop_gardening(ana))|(collects_rare_minerals(ana))))=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(ana))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(ana)))))&
((((?[X]:(~room(X)&is_a_wine_connoisseur(X)))))=>(owns_a_smart_tv(ana)))&
((![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))=>((![X]:((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
((is_allergic_to_anything(ana))<~>(![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(practices_calligraphy(X)))))))&
((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(ana))<=>(![X]:(room(X)=>(((is_not_allergic_to_anything(X))|(uses_an_ios_phone(X)))))))&
((hosts_a_YouTube_channel_dedicated_to_art_tutorials(ana))<~>(is_a_wine_connoisseur(ana)))&
((~?[X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))<~>(![X]:(~room(X)=>(((is_not_allergic_to_anything(X))|(develops_open-source_software_projects_in_their_free_time(X)))))))&
((![X]:(~room(X)=>(((does_not_practice_calligraphy(X))|(is_allergic_to_anything(X))))))<=>(((practices_calligraphy(ana))&(develops_open-source_software_projects_in_their_free_time(ana)))))&
((![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>(![X]:(room(X)=>(((enjoys_stargazing(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))&
(collects_antique_clocks(ana))&
(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(is_a_Linux_enthusiast(X))))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(![X]:(anywhere(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(enjoys_rooftop_gardening(X))))))&
(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(ana))&
(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(ana))&
((![X]:((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(trains_for_and_competes_in_international_triathlons(X)))))&
(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=>(has_a_piercing(X))))))&
(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(ana))&
(![X]:(room(X)=>(((practices_calligraphy(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(hosts_a_popular_podcast_about_emerging_technologies(ana)) | room(ana)&(![X]:(room(X)=>(X='ana')))&
is_a_Linux_enthusiast(ana) | [
"p0",
"p1",
"p6",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3535533511697825948487911
% SZS output start Proof for 3535533511697825948487911
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
45. ! [X0] : (room(X0) => (predv(X0) | ~predw(X0))) => predv(mary) [input p1]
50. predg(mary) <~> ! [X0] : (room(X0) => (predv(X0) | ~predx(X0))) [input p6]
51. predl(mary) <=> ! [X0] : (room(X0) => (predk(X0) | ~predg(X0))) [input p7]
61. ~predl(mary) [input p17]
67. ~(predw(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
150. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
151. predv(mary) | ? [X0] : ((~predv(X0) & predw(X0)) & room(X0)) [ennf transformation 45]
152. predv(mary) | ? [X0] : (~predv(X0) & predw(X0) & room(X0)) [flattening 151]
156. predg(mary) <~> ! [X0] : ((predv(X0) | ~predx(X0)) | ~room(X0)) [ennf transformation 50]
157. predg(mary) <~> ! [X0] : (predv(X0) | ~predx(X0) | ~room(X0)) [flattening 156]
158. predl(mary) <=> ! [X0] : ((predk(X0) | ~predg(X0)) | ~room(X0)) [ennf transformation 51]
159. predl(mary) <=> ! [X0] : (predk(X0) | ~predg(X0) | ~room(X0)) [flattening 158]
169. ~predw(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 67]
173. ? [X0] : (~predv(X0) & predw(X0) & room(X0)) => (~predv(sK1) & predw(sK1) & room(sK1)) [choice axiom]
174. predv(mary) | (~predv(sK1) & predw(sK1) & room(sK1)) [skolemisation 152,173]
181. (? [X0] : (~predv(X0) & predx(X0) & room(X0)) | ~predg(mary)) & (! [X0] : (predv(X0) | ~predx(X0) | ~room(X0)) | predg(mary)) [nnf transformation 157]
182. (? [X0] : (~predv(X0) & predx(X0) & room(X0)) | ~predg(mary)) & (! [X1] : (predv(X1) | ~predx(X1) | ~room(X1)) | predg(mary)) [rectify 181]
183. ? [X0] : (~predv(X0) & predx(X0) & room(X0)) => (~predv(sK4) & predx(sK4) & room(sK4)) [choice axiom]
184. ((~predv(sK4) & predx(sK4) & room(sK4)) | ~predg(mary)) & (! [X1] : (predv(X1) | ~predx(X1) | ~room(X1)) | predg(mary)) [skolemisation 182,183]
185. (predl(mary) | ? [X0] : (~predk(X0) & predg(X0) & room(X0))) & (! [X0] : (predk(X0) | ~predg(X0) | ~room(X0)) | ~predl(mary)) [nnf transformation 159]
186. (predl(mary) | ? [X0] : (~predk(X0) & predg(X0) & room(X0))) & (! [X1] : (predk(X1) | ~predg(X1) | ~room(X1)) | ~predl(mary)) [rectify 185]
187. ? [X0] : (~predk(X0) & predg(X0) & room(X0)) => (~predk(sK5) & predg(sK5) & room(sK5)) [choice axiom]
188. (predl(mary) | (~predk(sK5) & predg(sK5) & room(sK5))) & (! [X1] : (predk(X1) | ~predg(X1) | ~room(X1)) | ~predl(mary)) [skolemisation 186,187]
204. ? [X0] : (mary != X0 & room(X0)) => (mary != sK9 & room(sK9)) [choice axiom]
205. ~predw(mary) | (mary != sK9 & room(sK9)) | ~room(mary) [skolemisation 169,204]
286. room(mary) [cnf transformation 150]
287. ~room(X0) | mary = X0 [cnf transformation 150]
288. predv(mary) | room(sK1) [cnf transformation 174]
289. predv(mary) | predw(sK1) [cnf transformation 174]
299. room(sK4) | ~predg(mary) [cnf transformation 184]
301. ~predv(sK4) | ~predg(mary) [cnf transformation 184]
303. predl(mary) | room(sK5) [cnf transformation 188]
304. predl(mary) | predg(sK5) [cnf transformation 188]
326. ~predl(mary) [cnf transformation 61]
332. ~predw(mary) | room(sK9) | ~room(mary) [cnf transformation 205]
333. ~predw(mary) | mary != sK9 | ~room(mary) [cnf transformation 205]
339. 2 <=> predv(mary) [avatar definition]
344. 3 <=> predw(sK1) [avatar definition]
346. predw(sK1) <- (3) [avatar component clause 344]
347. 3 | 2 [avatar split clause 289,339,344]
349. 4 <=> room(sK1) [avatar definition]
351. room(sK1) <- (4) [avatar component clause 349]
352. 4 | 2 [avatar split clause 288,339,349]
387. 12 <=> predg(mary) [avatar definition]
391. 13 <=> predv(sK4) [avatar definition]
393. ~predv(sK4) <- (~13) [avatar component clause 391]
394. ~12 | ~13 [avatar split clause 301,391,387]
401. 15 <=> room(sK4) [avatar definition]
403. room(sK4) <- (15) [avatar component clause 401]
404. ~12 | 15 [avatar split clause 299,401,387]
414. 18 <=> predl(mary) [avatar definition]
419. 19 <=> predg(sK5) [avatar definition]
421. predg(sK5) <- (19) [avatar component clause 419]
422. 19 | 18 [avatar split clause 304,414,419]
424. 20 <=> room(sK5) [avatar definition]
426. room(sK5) <- (20) [avatar component clause 424]
427. 20 | 18 [avatar split clause 303,414,424]
516. ~18 [avatar split clause 326,414]
517. ~predw(mary) | mary != sK9 [subsumption resolution 333,286]
519. 40 <=> mary = sK9 [avatar definition]
521. mary != sK9 <- (~40) [avatar component clause 519]
523. 41 <=> predw(mary) [avatar definition]
526. ~40 | ~41 [avatar split clause 517,523,519]
527. ~predw(mary) | room(sK9) [subsumption resolution 332,286]
529. 42 <=> room(sK9) [avatar definition]
531. room(sK9) <- (42) [avatar component clause 529]
532. 42 | ~41 [avatar split clause 527,523,529]
543. mary = sK4 <- (15) [resolution 287,403]
544. mary = sK5 <- (20) [resolution 287,426]
555. predg(mary) <- (19, 20) [backward demodulation 421,544]
558. 12 | ~19 | ~20 [avatar split clause 555,424,419,387]
560. ~predv(mary) <- (~13, 15) [forward demodulation 393,543]
561. ~2 | 13 | ~15 [avatar split clause 560,401,391,339]
562. mary = sK1 <- (4) [resolution 351,287]
564. predw(mary) <- (3, 4) [backward demodulation 346,562]
568. 41 | ~3 | ~4 [avatar split clause 564,349,344,523]
569. mary = sK9 <- (42) [resolution 531,287]
570. $false <- (~40, 42) [subsumption resolution 569,521]
571. 40 | ~42 [avatar contradiction clause 570]
572. $false [avatar sat refutation 347,352,394,404,422,427,516,526,532,558,561,568,571]
% SZS output end Proof for 3535533511697825948487911
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0.497214 |
Ike, Evonne, Irma, Marian, Cherie are the only persons in the room. Evonne collects vintage stamps. Only one person in the room enjoys virtual reality gaming and does practice yoga. Someone in the room owns a high-end gaming PC with custom-built components. Only one person in the room enjoys watercolor painting. Ike collects luxury watches. Ike collects vintage stamps. Irma participates in citizen science projects related to wildlife monitoring. It is not the case that “it is not the case that “it is not the case that “Irma enjoys windsurfing”””. Ike collects vintage stamps and owns a high-end gaming PC with custom-built components. Evonne enjoys salsa dancing. Someone outside the room is a scotch connoisseur. It is not the case that “Irma owns a high-end gaming PC with custom-built components”. Irma enjoys virtual reality gaming. Evonne enjoys windsurfing. It is not the case that “Marian does practice yoga”. Evonne enjoys watercolor painting. Irma enjoys snowboarding. Marian hosts a YouTube channel dedicated to art tutorials. Ike dreamt that “it is not the case that “Irma does practice yoga””. Someone in the room collects antique clocks. Irma collects luxury watches. More than one person in the room enjoys salsa dancing. Marian writes poetry. Ike collects vintage stamps and participates in citizen science projects related to wildlife monitoring. Someone in the room maintains a large, organic vegetable garden year-round. Irma is a scotch connoisseur. | Ike enjoys watercolor painting. | contradiction | room(ike)&room(evonne)&room(irma)&room(marian)&room(cherie)&(![X]:(room(X)=>(X='ike'|X='evonne'|X='irma'|X='marian'|X='cherie')))&
(collects_vintage_stamps(evonne))&
(((?[X]:(room(X)&((enjoys_virtual_reality_gaming(X))&(does_practice_yoga(X)))))&(![X,Y]:((room(X)&room(Y)&(((enjoys_virtual_reality_gaming(X))&(does_practice_yoga(X))))&(((enjoys_virtual_reality_gaming(Y))&(does_practice_yoga(Y)))))=>(X=Y)))))&
(?[X]:(room(X)&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))&
(((?[X]:(room(X)&enjoys_watercolor_painting(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_watercolor_painting(X))&(enjoys_watercolor_painting(Y)))=>(X=Y)))))&
(collects_luxury_watches(ike))&
(collects_vintage_stamps(ike))&
(participates_in_citizen_science_projects_related_to_wildlife_monitoring(irma))&
(~(~(~(enjoys_windsurfing(irma)))))&
(((collects_vintage_stamps(ike))&(owns_a_high-end_gaming_PC_with_custom-built_components(ike))))&
(enjoys_salsa_dancing(evonne))&
(?[X]:(~room(X)&(is_a_scotch_connoisseur(X))))&
(~(owns_a_high-end_gaming_PC_with_custom-built_components(irma)))&
(enjoys_virtual_reality_gaming(irma))&
(enjoys_windsurfing(evonne))&
(~(does_practice_yoga(marian)))&
(enjoys_watercolor_painting(evonne))&
(enjoys_snowboarding(irma))&
(hosts_a_YouTube_channel_dedicated_to_art_tutorials(marian))&
((ike_dream=>(~(does_practice_yoga(irma)))))&
(?[X]:(room(X)&(collects_antique_clocks(X))))&
(collects_luxury_watches(irma))&
((?[X,Y]:(room(X)&room(Y)&(enjoys_salsa_dancing(X)&enjoys_salsa_dancing(Y))&(X!=Y))))&
(writes_poetry(marian))&
(((collects_vintage_stamps(ike))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(ike))))&
(?[X]:(room(X)&(maintains_a_large,_organic_vegetable_garden_year-round(X))))&
(is_a_scotch_connoisseur(irma)) | room(ike)&room(evonne)&room(irma)&room(marian)&room(cherie)&(![X]:(room(X)=>(X='ike'|X='evonne'|X='irma'|X='marian'|X='cherie')))&
enjoys_watercolor_painting(ike) | [
"b42",
"p0",
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8263458087859977500594084
% SZS output start Proof for 8263458087859977500594084
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,X1] : ((predd(X1) & predd(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predd(X0) & room(X0)) [input p4]
60. predd(paul) [input p16]
71. 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]
73. ! [X0,X1] : ((predd(X1) & predd(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predd(X2) & room(X2)) [rectify 48]
164. ! [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]
165. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 164]
168. ! [X0,X1] : (X0 = X1 | (~predd(X1) | ~predd(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predd(X2) & room(X2)) [ennf transformation 73]
169. ! [X0,X1] : (X0 = X1 | ~predd(X1) | ~predd(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predd(X2) & room(X2)) [flattening 168]
170. 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 71]
171. 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 170]
177. ? [X2] : (predd(X2) & room(X2)) => (predd(sK2) & room(sK2)) [choice axiom]
178. ! [X0,X1] : (X0 = X1 | ~predd(X1) | ~predd(X0) | ~room(X1) | ~room(X0)) & (predd(sK2) & room(sK2)) [skolemisation 169,177]
231. mary != paul [cnf transformation 43]
267. room(mary) [cnf transformation 165]
268. room(paul) [cnf transformation 165]
279. room(sK2) [cnf transformation 178]
280. predd(sK2) [cnf transformation 178]
281. ~predd(X1) | X0 = X1 | ~predd(X0) | ~room(X1) | ~room(X0) [cnf transformation 178]
289. predd(paul) [cnf transformation 60]
301. predd(mary) [cnf transformation 171]
338. sK2 = X0 | ~predd(X0) | ~room(sK2) | ~room(X0) [resolution 281,280]
341. ~predd(X0) | sK2 = X0 | ~room(X0) [subsumption resolution 338,279]
345. paul = sK2 | ~room(paul) [resolution 341,289]
346. mary = sK2 | ~room(mary) [resolution 341,301]
347. paul = sK2 [subsumption resolution 345,268]
351. mary = sK2 [subsumption resolution 346,267]
352. mary = paul [backward demodulation 347,351]
353. $false [subsumption resolution 352,231]
% SZS output end Proof for 8263458087859977500594084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.016677 |
Adam, Teresa, Frederick, Angie, Ramon are the only persons in the room.
Teresa has a saltwater aquarium.
Everyone anywhere enjoys cross-country skiing if they does not enjoy kayaking and exploring remote waterways.
Teresa maintains a personal blog focused on cybersecurity tips.
Everyone in the room either enjoys coding in Python or enjoys cross-country skiing but not both if they has a saltwater aquarium.
Everyone in the room enjoys coding in Python if they maintains a personal blog focused on cybersecurity tips. | Teresa enjoys kayaking and exploring remote waterways. | entailment | room(adam)&room(teresa)&room(frederickerick)&room(angie)&room(ramon)&(![X]:(room(X)=>(X='adam'|X='teresa'|X='frederickerick'|X='angie'|X='ramon')))&
((![X]:(~room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(does_not_make_homemade_pastries(X))))))=>(?[X]:(~room(X)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))&
((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(frederickerick))=>(makes_homemade_pastries(adam)))&
((![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_know_morse_code(X))))))=>(![X]:(anywhere(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(enjoys_cross-country_skiing(X)))))))&
(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(((is_not_a_night_owl(X))<~>(enjoys_coding_in_Python(X))))))))&
(![X]:(anywhere(X)=>(((((is_not_a_night_owl(X))<~>(enjoys_coding_in_Python(X))))=>(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))&
(has_a_saltwater_aquarium(teresa))&
(![X]:(anywhere(X)=>(((has_a_piercing(X))=>(makes_homemade_pastries(X))))))&
(does_not_enjoy_logic_puzzles(adam))&
(?[X]:(room(X)&(has_a_saltwater_aquarium(X))))&
(![X]:(anywhere(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(anywhere(X)=>(((has_a_pet_dog(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))&
((![X]:((collects_rare_minerals(X))<=>(knows_morse_code(X)))))&
(![X]:(room(X)=>(((((enjoys_cross-country_skiing(X))&(hosts_regular_workshops_on_creative_writing(X))&(has_completed_a_triathlon(X))))=>(does_not_enjoy_coding_in_Python(X))))))&
(![X]:(anywhere(X)=>(((((does_enjoy_mountain_biking(X))<~>(does_not_have_a_pet_dog(X))))<=(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))))&
(maintains_a_personal_blog_focused_on_cybersecurity_tips(teresa))&
(![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(room(X)=>(((((does_enjoy_mountain_biking(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))))=>(travels_domestically_frequently(X))))))&
(![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(enjoys_logic_puzzles(X))))))&
(?[X]:(room(X)&(collects_modern_art(X))))&
(![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(((enjoys_coding_in_Python(X))<~>(enjoys_cross-country_skiing(X))))))))&
(?[X]:(~room(X)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))&
(![X]:(~room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(enjoys_coding_in_Python(X))))))&
(![X]:(room(X)=>(((enjoys_coding_in_Python(X))|(does_not_have_a_saltwater_aquarium(X))))))&
(![X]:(room(X)=>(((collects_modern_art(X))<=(does_not_have_a_saltwater_aquarium(X))))))&
(collects_rare_minerals(adam))&
(![X]:(~room(X)=>(((does_not_enjoy_coding_in_Python(X))=>(((enjoys_logic_puzzles(X))<~>(does_enjoy_mountain_biking(X))))))))&
(![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))<=>(collects_rare_minerals(X)))))) | room(adam)&room(teresa)&room(frederickerick)&room(angie)&room(ramon)&(![X]:(room(X)=>(X='adam'|X='teresa'|X='frederickerick'|X='angie'|X='ramon')))&
enjoys_kayaking_and_exploring_remote_waterways(teresa) | [
"b4",
"p0",
"p6",
"p10",
"p15",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6598791006530759747224354
% SZS output start Proof for 6598791006530759747224354
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
50. predt(paul) [input p6]
54. ! [X0] : (anywhere(X0) => (~prede(X0) => predn(X0))) [input p10]
59. predv(paul) [input p15]
64. ! [X0] : (room(X0) => (predt(X0) => (predh(X0) <~> predn(X0)))) [input p20]
67. ! [X0] : (room(X0) => (predv(X0) => predh(X0))) [input p23]
73. ~(prede(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
159. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
160. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 159]
168. ! [X0] : ((predn(X0) | prede(X0)) | ~anywhere(X0)) [ennf transformation 54]
169. ! [X0] : (predn(X0) | prede(X0) | ~anywhere(X0)) [flattening 168]
172. ! [X0] : (((predh(X0) <~> predn(X0)) | ~predt(X0)) | ~room(X0)) [ennf transformation 64]
173. ! [X0] : ((predh(X0) <~> predn(X0)) | ~predt(X0) | ~room(X0)) [flattening 172]
176. ! [X0] : ((predh(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 67]
177. ! [X0] : (predh(X0) | ~predv(X0) | ~room(X0)) [flattening 176]
183. ~prede(paul) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 73]
184. ~prede(paul) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 183]
200. ! [X0] : (((~predn(X0) | ~predh(X0)) & (predn(X0) | predh(X0))) | ~predt(X0) | ~room(X0)) [nnf transformation 173]
205. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom]
206. ~prede(paul) | (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 184,205]
207. anywhere(X0) [cnf transformation 5]
288. room(mary) [cnf transformation 160]
289. room(paul) [cnf transformation 160]
290. room(fred) [cnf transformation 160]
291. room(alice) [cnf transformation 160]
292. room(john) [cnf transformation 160]
293. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 160]
303. predt(paul) [cnf transformation 50]
307. predn(X0) | prede(X0) | ~anywhere(X0) [cnf transformation 169]
310. predv(paul) [cnf transformation 59]
314. ~predt(X0) | ~predh(X0) | ~predn(X0) | ~room(X0) [cnf transformation 200]
318. ~predv(X0) | predh(X0) | ~room(X0) [cnf transformation 177]
325. ~prede(paul) | room(sK6) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 206]
326. ~prede(paul) | mary != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 206]
327. ~prede(paul) | paul != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 206]
328. ~prede(paul) | fred != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 206]
329. ~prede(paul) | alice != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 206]
330. ~prede(paul) | john != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 206]
351. 5 <=> ! [X0] : (predn(X0) | prede(X0)) [avatar definition]
352. predn(X0) | prede(X0) <- (5) [avatar component clause 351]
368. predn(X0) | prede(X0) [subsumption resolution 307,207]
369. 5 [avatar split clause 368,351]
370. ~prede(paul) | john != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 330,292]
371. ~prede(paul) | john != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 370,291]
372. ~prede(paul) | john != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 371,290]
373. ~prede(paul) | john != sK6 | ~room(mary) [subsumption resolution 372,289]
374. ~prede(paul) | john != sK6 [subsumption resolution 373,288]
376. 8 <=> john = sK6 [avatar definition]
378. john != sK6 <- (~8) [avatar component clause 376]
380. 9 <=> prede(paul) [avatar definition]
383. ~8 | ~9 [avatar split clause 374,380,376]
384. ~prede(paul) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 329,292]
385. ~prede(paul) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 384,291]
386. ~prede(paul) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 385,290]
387. ~prede(paul) | alice != sK6 | ~room(mary) [subsumption resolution 386,289]
388. ~prede(paul) | alice != sK6 [subsumption resolution 387,288]
390. 10 <=> alice = sK6 [avatar definition]
392. alice != sK6 <- (~10) [avatar component clause 390]
393. ~10 | ~9 [avatar split clause 388,380,390]
394. ~prede(paul) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,292]
395. ~prede(paul) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 394,291]
396. ~prede(paul) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 395,290]
397. ~prede(paul) | fred != sK6 | ~room(mary) [subsumption resolution 396,289]
398. ~prede(paul) | fred != sK6 [subsumption resolution 397,288]
400. 11 <=> fred = sK6 [avatar definition]
402. fred != sK6 <- (~11) [avatar component clause 400]
403. ~11 | ~9 [avatar split clause 398,380,400]
404. ~prede(paul) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,292]
405. ~prede(paul) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 404,291]
406. ~prede(paul) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 405,290]
407. ~prede(paul) | paul != sK6 | ~room(mary) [subsumption resolution 406,289]
408. ~prede(paul) | paul != sK6 [subsumption resolution 407,288]
410. 12 <=> paul = sK6 [avatar definition]
412. paul != sK6 <- (~12) [avatar component clause 410]
413. ~12 | ~9 [avatar split clause 408,380,410]
414. ~prede(paul) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,292]
415. ~prede(paul) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 414,291]
416. ~prede(paul) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 415,290]
417. ~prede(paul) | mary != sK6 | ~room(mary) [subsumption resolution 416,289]
418. ~prede(paul) | mary != sK6 [subsumption resolution 417,288]
420. 13 <=> mary = sK6 [avatar definition]
422. mary != sK6 <- (~13) [avatar component clause 420]
423. ~13 | ~9 [avatar split clause 418,380,420]
424. ~prede(paul) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 325,292]
425. ~prede(paul) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 424,291]
426. ~prede(paul) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 425,290]
427. ~prede(paul) | room(sK6) | ~room(mary) [subsumption resolution 426,289]
428. ~prede(paul) | room(sK6) [subsumption resolution 427,288]
430. 14 <=> room(sK6) [avatar definition]
432. room(sK6) <- (14) [avatar component clause 430]
433. 14 | ~9 [avatar split clause 428,380,430]
438. predh(paul) | ~room(paul) [resolution 318,310]
439. predh(paul) [subsumption resolution 438,289]
524. 29 <=> predn(paul) [avatar definition]
526. ~predn(paul) <- (~29) [avatar component clause 524]
542. ~predh(paul) | ~predn(paul) | ~room(paul) [resolution 314,303]
551. prede(paul) <- (5, ~29) [resolution 526,352]
554. 9 | ~5 | 29 [avatar split clause 551,524,351,380]
569. ~predn(paul) | ~room(paul) [subsumption resolution 542,439]
570. ~predn(paul) [subsumption resolution 569,289]
571. ~29 [avatar split clause 570,524]
631. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (14) [resolution 293,432]
674. fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (~10, 14) [subsumption resolution 631,392]
675. paul = sK6 | mary = sK6 | john = sK6 <- (~10, ~11, 14) [subsumption resolution 674,402]
676. mary = sK6 | john = sK6 <- (~10, ~11, ~12, 14) [subsumption resolution 675,412]
677. john = sK6 <- (~10, ~11, ~12, ~13, 14) [subsumption resolution 676,422]
678. $false <- (~8, ~10, ~11, ~12, ~13, 14) [subsumption resolution 677,378]
679. 8 | 10 | 11 | 12 | 13 | ~14 [avatar contradiction clause 678]
680. $false [avatar sat refutation 369,383,393,403,413,423,433,554,571,679]
% SZS output end Proof for 6598791006530759747224354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0.069462 |
Michaelne is the only person in the room.
Carol is richer than Michaelne.
Not everyone outside the room is a generous person only if they is not tall, not old.
Someone who neither is richer than Margaret nor is quieter than Carol is richer than someone who is a patient happy wise kind person.
Michaelne is a generous person.
Everyone in the room is older than Margaret if they is a calm person.
Michaelne is not a patient quiet funny calm person.
Michaelne is curious.
Michaelne is older than Carol.
Everyone in the room is a brave curious person if they is older than Carol.
Everyone in the room who is a brave curious person is kind.
Everyone outside the room is not a kind strong humble quiet person if they is a curious person.
Everyone in the room who is not a kind strong humble quiet person is not brave.
Only one person in the room is not a quiet curious patient happy wise old person.
All kind person is calm.
Someone who is a generous person is quieter than someone who is a quiet generous person and is quiet.
Everyone outside the room who is not a kind person is a calm old patient person.
If someone is a calm wise generous kind quiet person then he/she neither is not a patient brave kind old calm person nor is older than Carol and vice versa.
No patient person is tall.
Michaelne is older than Kelly. | Kelly is richer than Michaelne. | neutral | room(michaelne)&(![X]:(room(X)=>(X='michaelne')))&
(richer(michaelne,carol))&
(~![X]:(~room(X)=>(((~tall(X)&~old(X))<=(generous(X)&person(X))))))&
(?[X,Y]:((~((richer(margaret,X))|(quieter(carol,X))))&(patient(Y)&happy(Y)&wise(Y)&kind(Y)&person(Y))&(richer(X,Y))))&
(generous(michaelne)&person(michaelne))&
(![X]:(room(X)=>(((calm(X)&person(X))=>(older(margaret,X))))))&
(~(patient(michaelne)&quiet(michaelne)&funny(michaelne)&calm(michaelne)&person(michaelne)))&
(curious(michaelne))&
(older(carol,michaelne))&
(![X]:(room(X)=>(((older(carol,X))=>(brave(X)&curious(X)&person(X))))))&
(![X]:(room(X)=>(((brave(X)&curious(X)&person(X))=>(kind(X))))))&
(![X]:(~room(X)=>(((curious(X)&person(X))=>(~(kind(X)&strong(X)&humble(X)&quiet(X)&person(X)))))))&
(![X]:(room(X)=>(((~(kind(X)&strong(X)&humble(X)&quiet(X)&person(X)))=>(~brave(X))))))&
(((?[X]:(room(X)&~(quiet(X)&curious(X)&patient(X)&happy(X)&wise(X)&old(X)&person(X))))&(![X,Y]:((room(X)&room(Y)&(~(quiet(X)&curious(X)&patient(X)&happy(X)&wise(X)&old(X)&person(X)))&(~(quiet(Y)&curious(Y)&patient(Y)&happy(Y)&wise(Y)&old(Y)&person(Y))))=>(X=Y)))))&
(![X]:(kind(X)=>calm(X)))&
(?[X,Y]:((generous(X)&person(X))&(((quiet(Y)&generous(Y)&person(Y))&(quiet(Y))))&(quieter(X,Y))))&
(![X]:(~room(X)=>(((~(kind(X)&person(X)))=>(calm(X)&old(X)&patient(X)&person(X))))))&
((![X]:((calm(X)&wise(X)&generous(X)&kind(X)&quiet(X)&person(X))<=>(~((~(patient(X)&brave(X)&kind(X)&old(X)&calm(X)&person(X)))|(older(carol,X)))))))&
(~?[X]:(patient(X)=>tall(X)))&
(older(kelly,michaelne))&
(![X]:(room(X)=>(((~patient(X))<=>(((richer(kelly,X))|(~calm(X)&~happy(X))|(~(curious(X)&person(X)))))))))&
((![X]:((richer(margaret,X))=>(~(tall(X)&person(X))))))&
(![X]:(calm(X)=>creative(X)))&
(![X]:(room(X)=>(((quieter(kelly,X))=>(~patient(X)&~old(X)&~creative(X)&~generous(X)))))) | room(michaelne)&(![X]:(room(X)=>(X='michaelne')))&
richer(michaelne,kelly) | [] | null | 0.000445 |
There is a room.
Everyone in the room who collects rare and antique scientific instruments does not maintain a personal blog focused on cybersecurity tips.
Only one person in the room does not enjoy stargazing.
Only one person anywhere collects rare and antique scientific instruments.
Everyone outside the room enjoys stand-up paddleboarding if they watches fantasy movies and vice versa.
Everyone in the room collects modern art if they is right-handed.
Someone in the room uses contact lenses.
Everyone in the room watches fantasy movies, is a professional photographer specializing in portrait photography or collects rare and antique scientific instruments if they travels domestically frequently.
No one in the room enjoys stand-up paddleboarding if they enjoys macrame. | Everyone in the room enjoys macrame. | entailment | (there_is_a_room)&
(![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(((?[X]:(room(X)&does_not_enjoy_stargazing(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_enjoy_stargazing(X))&(does_not_enjoy_stargazing(Y)))=>(X=Y)))))&
(((?[X]:(anywhere(X)&collects_rare_and_antique_scientific_instruments(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(collects_rare_and_antique_scientific_instruments(X))&(collects_rare_and_antique_scientific_instruments(Y)))=>(X=Y)))))&
(![X]:(~room(X)=>(((enjoys_stand-up_paddleboarding(X))<=>(watches_fantasy_movies(X))))))&
(![X]:(room(X)=>(((is_right-handed(X))=>(collects_modern_art(X))))))&
(?[X]:(room(X)&(uses_contact_lenses(X))))&
(![X]:(room(X)=>(((travels_domestically_frequently(X))=>(((watches_fantasy_movies(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))|(collects_rare_and_antique_scientific_instruments(X))))))))&
(![X]:(room(X)=>(((((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(enjoys_stargazing(X))&(uses_contact_lenses(X))))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(![X]:(~room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(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))=>(((does_enjoy_mountain_biking(X))|(is_a_scotch_connoisseur(X))))))))&
(![X]:(room(X)=>(((((does_enjoy_mountain_biking(X))|(is_a_scotch_connoisseur(X))))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))=>(does_enjoy_mountain_biking(X))))))&
((![X]:((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<=>(does_not_collect_classic_novels(X)))))&
(~?[X]:(room(X)=>(((enjoys_macrame(X))=>(enjoys_stand-up_paddleboarding(X))))))&
(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(enjoys_macrame(X))))))&
((![X]:((competes_in_national_level_swimming_championships(X))=>(is_right-handed(X)))))&
(![X]:(~room(X)=>(((collects_modern_art(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))&
(![X]:(room(X)=>(((((plays_eSports_competitively(X))&(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))<=(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))&
(![X]:(room(X)=>(((travels_domestically_frequently(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(enjoys_macrame(X))) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5824530563592915066978624
% SZS output start Proof for 5824530563592915066978624
44. there_is_a_room [input p0]
58. ~? [X0] : (room(X0) => (predc(X0) => predx(X0))) [input p14]
64. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis]
158. ! [X0] : ((~predx(X0) & predc(X0)) & room(X0)) [ennf transformation 58]
159. ! [X0] : (~predx(X0) & predc(X0) & room(X0)) [flattening 158]
162. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 64]
172. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK3) & room(sK3)) [choice axiom]
173. (~predc(sK3) & room(sK3)) | ~there_is_a_room [skolemisation 162,172]
255. there_is_a_room [cnf transformation 44]
271. predc(X0) [cnf transformation 159]
275. ~predc(sK3) | ~there_is_a_room [cnf transformation 173]
278. ~there_is_a_room [subsumption resolution 275,271]
279. $false [subsumption resolution 278,255]
% SZS output end Proof for 5824530563592915066978624
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Jeffrey, Tonia are the only persons in the room.
If "it is true that "no one in the room does not practice urban gardening or is not an expert in identifying and foraging wild edible plants"" then "everyone in the room owns a significant collection of rare gemstones and minerals".
If "everyone in the room does not own a telescope or maintains a large, organic vegetable garden year-round" then "everyone outside the room who does not own a telescope owns a significant collection of rare gemstones and minerals".
If "everyone anywhere does not create YouTube content or collects antique clocks" then "everyone in the room does not mentor a youth basketball team on weekends or does not collect vintage vinyl records".
If "everyone in the room does not mentor a youth basketball team on weekends or does not collect vintage vinyl records" then "everyone in the room is right-handed or collects vintage vinyl records or both if they does not mentor a youth basketball team on weekends".
Either "no one outside the room is right-handed or is not an expert in identifying and foraging wild edible plants" or "someone in the room practices kickboxing" but not both.
Everyone anywhere who is right-handed mentors a youth basketball team on weekends, regularly contributes to tech forums and online communities and does not practice kickboxing.
Everyone outside the room who creates YouTube content collects vintage vinyl records.
Everyone in the room is an expert in identifying and foraging wild edible plants if they collects vintage vinyl records.
Everyone in the room collects vintage vinyl records.
Everyone anywhere who practices urban gardening, mentors a youth basketball team on weekends and does not practice kickboxing creates YouTube content.
Someone in the room practices kickboxing.
At least one person in the room is an expert in identifying and foraging wild edible plants or is a culinary enthusiast who experiments with international cuisines or both.
Everyone in the room maintains a large, organic vegetable garden year-round if they is a culinary enthusiast who experiments with international cuisines.
Everyone in the room does not own a telescope or maintains a large, organic vegetable garden year-round.
Everyone in the room either owns a significant collection of rare gemstones and minerals or knows morse code but not both.
Everyone in the room collects antique clocks only if they does not create YouTube content.
Everyone in the room does not create YouTube content only if they owns a telescope. | Tonia either is not a culinary enthusiast who experiments with international cuisines or is not an expert in identifying and foraging wild edible plants but not both. | neutral | room(jeffrey)&room(tonia)&(![X]:(room(X)=>(X='jeffrey'|X='tonia')))&
((~?[X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_practice_urban_gardening(X))))))=>(![X]:(room(X)=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))&
((![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_own_a_telescope(X))))))=>(![X]:(~room(X)=>(((does_not_own_a_telescope(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))))&
(((![X]:(anywhere(X)=>(((collects_antique_clocks(X))|(does_not_create_YouTube_content(X))))))=>(![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))))&
((![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(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_right-handed(X))|(collects_vintage_vinyl_records(X))))))))))&
((~?[X]:(~room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(is_right-handed(X))))))<~>(?[X]:(room(X)&(practices_kickboxing(X)))))&
(![X]:(anywhere(X)=>(((is_right-handed(X))=>(((mentors_a_youth_basketball_team_on_weekends(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))&(does_not_practice_kickboxing(X))))))))&
(![X]:(~room(X)=>(((creates_YouTube_content(X))=>(collects_vintage_vinyl_records(X))))))&
(![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))&
(![X]:(room(X)=>(collects_vintage_vinyl_records(X))))&
(![X]:(anywhere(X)=>(((((practices_urban_gardening(X))&(mentors_a_youth_basketball_team_on_weekends(X))&(does_not_practice_kickboxing(X))))=>(creates_YouTube_content(X))))))&
(?[X]:(room(X)&(practices_kickboxing(X))))&
(((?[X]:(room(X)&((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))&
(![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_own_a_telescope(X))))))&
(![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(knows_morse_code(X))))))&
(![X]:(room(X)=>(((does_not_create_YouTube_content(X))<=(collects_antique_clocks(X))))))&
(![X]:(room(X)=>(((owns_a_telescope(X))<=(does_not_create_YouTube_content(X)))))) | room(jeffrey)&room(tonia)&(![X]:(room(X)=>(X='jeffrey'|X='tonia')))&
((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(tonia))<~>(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(tonia))) | [] | null | 0 |
Everyone in the room collects vintage stamps if and only if they is a client of Costco and knows morse code.
No one in the room plays eSports competitively and enjoys bird watching if they either is a professional photographer specializing in portrait photography or is a drone photographer but not both and vice versa.
Everyone in the room knows morse code if and only if they enjoys windsurfing or is allergic to anything or both.
Everyone in the room who enjoys windsurfing or is allergic to anything or both enjoys kayaking and exploring remote waterways.
More than one person in the room owns a smartwatch and is an avid hiker.
Everyone in the room does not own a smartwatch or is an avid hiker and collects vintage stamps. | Everyone in the room does not enjoy kayaking and exploring remote waterways. | contradiction | (there_is_a_room)&
((~![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(is_not_right-handed(X))))))=>(![X]:(room(X)=>(((is_not_right-handed(X))<=>(plays_the_drums(X)))))))&
((![X]:(room(X)=>(((practices_digital_art(X))|(does_not_play_eSports_competitively(X))))))=>(![X]:(room(X)=>(((does_not_play_eSports_competitively(X))<=>(is_an_avid_hiker(X)))))))&
(![X]:(room(X)=>(((is_an_avid_hiker(X))<=>(collects_vintage_stamps(X))))))&
(![X]:(room(X)=>(((collects_vintage_stamps(X))<=>(((is_a_client_of_Costco(X))&(knows_morse_code(X))))))))&
(![X]:(room(X)=>(((((is_a_client_of_Costco(X))&(knows_morse_code(X))))=>(is_a_drone_photographer(X))))))&
(![X]:(room(X)=>(((is_not_right-handed(X))<=>(plays_the_drums(X))))))&
(~?[X]:(room(X)=>(((((plays_eSports_competitively(X))&(enjoys_bird_watching(X))))<=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))<~>(is_a_drone_photographer(X))))))))&
(~![X]:(room(X)=>(((((is_a_professional_photographer_specializing_in_portrait_photography(X))<~>(is_a_drone_photographer(X))))=>(((is_a_drone_photographer(X))|(owns_a_microscope(X))|(practices_kickboxing(X))))))))&
(![X]:(room(X)=>(((((is_a_drone_photographer(X))|(owns_a_microscope(X))|(practices_kickboxing(X))))=>(((is_a_drone_photographer(X))&(owns_a_3D_printer(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))))&
(![X]:(room(X)=>(((knows_morse_code(X))<=>(((enjoys_windsurfing(X))|(is_allergic_to_anything(X))))))))&
(![X]:(room(X)=>(((((enjoys_windsurfing(X))|(is_allergic_to_anything(X))))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))&
(~![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(is_not_right-handed(X))))))&
((?[X,Y]:(room(X)&room(Y)&(((owns_a_smartwatch(X))&(is_an_avid_hiker(X)))&((owns_a_smartwatch(Y))&(is_an_avid_hiker(Y))))&(X!=Y))))&
(![X]:(room(X)=>(((practices_kickboxing(X))<=>(((owns_a_smartwatch(X))&(owns_a_microscope(X))))))))&
(![X]:(room(X)=>(((((owns_a_smartwatch(X))&(owns_a_microscope(X))))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(![X]:(anywhere(X)=>(((((owns_a_3D_printer(X))|(practices_kickboxing(X))|(enjoys_bird_watching(X))))<=>(((practices_kickboxing(X))&(plays_eSports_competitively(X))&(is_an_avid_hiker(X))))))))&
(![X]:(room(X)=>(((((practices_kickboxing(X))&(plays_eSports_competitively(X))&(is_an_avid_hiker(X))))=>(((is_right-handed(X))|(owns_a_smartwatch(X))))))))&
(~![X]:(room(X)=>(((((is_an_avid_hiker(X))&(collects_vintage_stamps(X))))<=(practices_digital_art(X))))))&
(![X]:(room(X)=>(((((is_an_avid_hiker(X))&(collects_vintage_stamps(X))))|(does_not_own_a_smartwatch(X))))))&
(![X]:(room(X)=>(((owns_a_smartwatch(X))=>(practices_calligraphy(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))) | [
"p4",
"p7",
"p10",
"p11",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6586306959583937296236491
% SZS output start Proof for 6586306959583937296236491
48. ! [X0] : (room(X0) => (preda(X0) <=> (predq(X0) & predr(X0)))) [input p4]
51. ~? [X0] : (room(X0) => ((predk(X0) & predl(X0)) <=> (predb(X0) <~> predd(X0)))) [input p7]
54. ! [X0] : (room(X0) => (predq(X0) <=> (predn(X0) | predt(X0)))) [input p10]
55. ! [X0] : (room(X0) => ((predn(X0) | predt(X0)) => predm(X0))) [input p11]
57. ? [X0,X1] : (X0 != X1 & predy(X1) & predx(X1) & predy(X0) & predx(X0) & room(X1) & room(X0)) [input p13]
63. ! [X0] : (room(X0) => (~predx(X0) | (preda(X0) & predy(X0)))) [input p19]
65. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis]
71. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 65]
149. ! [X0] : ((preda(X0) <=> (predq(X0) & predr(X0))) | ~room(X0)) [ennf transformation 48]
153. ! [X0] : (((predk(X0) & predl(X0)) <~> (predb(X0) <~> predd(X0))) & room(X0)) [ennf transformation 51]
158. ! [X0] : ((predq(X0) <=> (predn(X0) | predt(X0))) | ~room(X0)) [ennf transformation 54]
159. ! [X0] : ((predm(X0) | (~predn(X0) & ~predt(X0))) | ~room(X0)) [ennf transformation 55]
160. ! [X0] : (predm(X0) | (~predn(X0) & ~predt(X0)) | ~room(X0)) [flattening 159]
169. ! [X0] : ((~predx(X0) | (preda(X0) & predy(X0))) | ~room(X0)) [ennf transformation 63]
170. ! [X0] : (~predx(X0) | (preda(X0) & predy(X0)) | ~room(X0)) [flattening 169]
171. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 71]
182. ! [X0] : (((preda(X0) | (~predq(X0) | ~predr(X0))) & ((predq(X0) & predr(X0)) | ~preda(X0))) | ~room(X0)) [nnf transformation 149]
183. ! [X0] : (((preda(X0) | ~predq(X0) | ~predr(X0)) & ((predq(X0) & predr(X0)) | ~preda(X0))) | ~room(X0)) [flattening 182]
185. ! [X0] : (((((predb(X0) | ~predd(X0)) & (predd(X0) | ~predb(X0))) | (~predk(X0) | ~predl(X0))) & (((~predd(X0) | ~predb(X0)) & (predd(X0) | predb(X0))) | (predk(X0) & predl(X0)))) & room(X0)) [nnf transformation 153]
186. ! [X0] : ((((predb(X0) | ~predd(X0)) & (predd(X0) | ~predb(X0))) | ~predk(X0) | ~predl(X0)) & (((~predd(X0) | ~predb(X0)) & (predd(X0) | predb(X0))) | (predk(X0) & predl(X0))) & room(X0)) [flattening 185]
191. ! [X0] : (((predq(X0) | (~predn(X0) & ~predt(X0))) & ((predn(X0) | predt(X0)) | ~predq(X0))) | ~room(X0)) [nnf transformation 158]
192. ! [X0] : (((predq(X0) | (~predn(X0) & ~predt(X0))) & (predn(X0) | predt(X0) | ~predq(X0))) | ~room(X0)) [flattening 191]
195. ? [X0,X1] : (X0 != X1 & predy(X1) & predx(X1) & predy(X0) & predx(X0) & room(X1) & room(X0)) => (sK4 != sK5 & predy(sK5) & predx(sK5) & predy(sK4) & predx(sK4) & room(sK5) & room(sK4)) [choice axiom]
196. sK4 != sK5 & predy(sK5) & predx(sK5) & predy(sK4) & predx(sK4) & room(sK5) & room(sK4) [skolemisation 57,195]
297. ~preda(X0) | predq(X0) | ~room(X0) [cnf transformation 183]
302. room(X0) [cnf transformation 186]
321. predn(X0) | predt(X0) | ~predq(X0) | ~room(X0) [cnf transformation 192]
324. predm(X0) | ~predt(X0) | ~room(X0) [cnf transformation 160]
325. predm(X0) | ~predn(X0) | ~room(X0) [cnf transformation 160]
331. predx(sK4) [cnf transformation 196]
352. ~predx(X0) | preda(X0) | ~room(X0) [cnf transformation 170]
353. ~predm(X0) | ~room(X0) [cnf transformation 171]
399. ~predq(X0) | predt(X0) | predn(X0) [subsumption resolution 321,302]
400. ~predn(X0) | predm(X0) [subsumption resolution 325,302]
401. ~predt(X0) | predm(X0) [subsumption resolution 324,302]
418. ~predx(X0) | preda(X0) [subsumption resolution 352,302]
420. ~predm(X0) [subsumption resolution 353,302]
423. preda(sK4) [resolution 418,331]
436. predq(sK4) | ~room(sK4) [resolution 297,423]
438. predq(sK4) [subsumption resolution 436,302]
448. predt(sK4) | predn(sK4) [resolution 399,438]
451. 11 <=> predn(sK4) [avatar definition]
453. predn(sK4) <- (11) [avatar component clause 451]
455. 12 <=> predt(sK4) [avatar definition]
457. predt(sK4) <- (12) [avatar component clause 455]
458. 11 | 12 [avatar split clause 448,455,451]
468. predm(sK4) <- (11) [resolution 453,400]
470. $false <- (11) [subsumption resolution 468,420]
471. ~11 [avatar contradiction clause 470]
500. predm(sK4) <- (12) [resolution 457,401]
502. $false <- (12) [subsumption resolution 500,420]
503. ~12 [avatar contradiction clause 502]
504. $false [avatar sat refutation 458,471,503]
% SZS output end Proof for 6586306959583937296236491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.182091 |
Either “Joseph enjoys rooftop gardening” or “Joseph does not own a microscope” but not both.
If “Joseph owns an Android phone” then “Joseph is a certified yoga instructor teaching classes weekly”.
If “Joseph plays video games” then “Joseph owns a microscope”.
If “it is not the case that “Joseph owns an Android phone”” then “Joseph is a client of LVMH”.
If “it is not the case that “Joseph is a drone photographer”” then “Joseph neither plays video games nor collects rare minerals”.
If “Joseph enjoys wildlife photography” then “Joseph neither plays video games nor owns a microscope”.
Joseph enjoys kayaking.
Joseph collects rare minerals.
Joseph is a certified yoga instructor teaching classes weekly.
Joseph enjoys wildlife photography.
Joseph can play the guitar.
Joseph owns an Android phone. | Joseph is a drone photographer. | entailment | room(joseph)&(![X]:(room(X)=>(X='joseph')))&
((enjoys_rooftop_gardening(joseph))<~>(does_not_own_a_microscope(joseph)))&
((owns_an_Android_phone(joseph))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(joseph)))&
((plays_video_games(joseph))=>(owns_a_microscope(joseph)))&
((~(owns_an_Android_phone(joseph)))=>(is_a_client_of_LVMH(joseph)))&
((~(is_a_drone_photographer(joseph)))=>(~((plays_video_games(joseph))|(collects_rare_minerals(joseph)))))&
((enjoys_wildlife_photography(joseph))=>(~((plays_video_games(joseph))|(owns_a_microscope(joseph)))))&
(enjoys_kayaking(joseph))&
(collects_rare_minerals(joseph))&
(is_a_certified_yoga_instructor_teaching_classes_weekly(joseph))&
(enjoys_wildlife_photography(joseph))&
(can_play_the_guitar(joseph))&
(owns_an_Android_phone(joseph)) | room(joseph)&(![X]:(room(X)=>(X='joseph')))&
is_a_drone_photographer(joseph) | [
"p0",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7709162111190204368736807
% SZS output start Proof for 7709162111190204368736807
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
49. ~predh(mary) => ~(predb(mary) | predf(mary)) [input p5]
52. predb(mary) [input p8]
57. ~(predh(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
62. ~predh(mary) => ~predb(mary) [pure predicate removal 49]
139. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
140. ~predb(mary) | predh(mary) [ennf transformation 62]
142. ~predh(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 57]
145. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom]
146. ~predh(mary) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 142,145]
227. room(mary) [cnf transformation 139]
228. ~room(X0) | mary = X0 [cnf transformation 139]
231. ~predb(mary) | predh(mary) [cnf transformation 140]
233. predb(mary) [cnf transformation 52]
235. ~predh(mary) | room(sK0) | ~room(mary) [cnf transformation 146]
236. ~predh(mary) | mary != sK0 | ~room(mary) [cnf transformation 146]
248. 3 <=> predh(mary) [avatar definition]
252. 4 <=> predb(mary) [avatar definition]
255. 3 | ~4 [avatar split clause 231,252,248]
261. 4 [avatar split clause 233,252]
263. ~predh(mary) | mary != sK0 [subsumption resolution 236,227]
265. 6 <=> mary = sK0 [avatar definition]
267. mary != sK0 <- (~6) [avatar component clause 265]
268. ~6 | ~3 [avatar split clause 263,248,265]
269. ~predh(mary) | room(sK0) [subsumption resolution 235,227]
271. 7 <=> room(sK0) [avatar definition]
273. room(sK0) <- (7) [avatar component clause 271]
274. 7 | ~3 [avatar split clause 269,248,271]
276. mary = sK0 <- (7) [resolution 228,273]
277. $false <- (~6, 7) [subsumption resolution 276,267]
278. 6 | ~7 [avatar contradiction clause 277]
279. $false [avatar sat refutation 255,261,268,274,278]
% SZS output end Proof for 7709162111190204368736807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.580568 |
Mark, Billy are the only persons in the room. If 'at least one person in the room creates large-scale murals for public art installations' then 'everyone outside the room does not practice urban gardening if they enjoys stand-up paddleboarding'. Everyone in the room works as a freelance web developer specializing in e-commerce sites. Everyone outside the room is a wine connoisseur with a private cellar of vintage wines if they works as a freelance web developer specializing in e-commerce sites. At least one person in the room is not an avid hiker. Everyone outside the room who has a pet dog either owns a smart tv or enjoys camping and organizing outdoor survival workshops but not both. Everyone in the room creates large-scale murals for public art installations. Everyone in the room does not practice urban gardening. Everyone in the room either is not a wine connoisseur with a private cellar of vintage wines or is a Linux enthusiast but not both. At least one person in the room collects historical artifacts related to ancient civilizations. Everyone in the room owns a telescope only if they does not own a telescope. | Billy owns a telescope. | contradiction | room(mark)&room(billy)&(![X]:(room(X)=>(X='mark'|X='billy')))&
((((?[X]:(room(X)&creates_large-scale_murals_for_public_art_installations(X)))))=>(![X]:(~room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(does_not_practice_urban_gardening(X)))))))&
(![X]:(room(X)=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))&
(![X]:(~room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(((?[X]:(room(X)&is_not_an_avid_hiker(X)))))&
(![X]:(~room(X)=>(((has_a_pet_dog(X))=>(((owns_a_smart_tv(X))<~>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))))&
(![X]:(room(X)=>(creates_large-scale_murals_for_public_art_installations(X))))&
(![X]:(room(X)=>(does_not_practice_urban_gardening(X))))&
(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<~>(is_a_Linux_enthusiast(X))))))&
(((?[X]:(room(X)&collects_historical_artifacts_related_to_ancient_civilizations(X)))))&
(![X]:(room(X)=>(((does_not_own_a_telescope(X))<=(owns_a_telescope(X)))))) | room(mark)&room(billy)&(![X]:(room(X)=>(X='mark'|X='billy')))&
owns_a_telescope(billy) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2988279204067022166291714
% SZS output start Proof for 2988279204067022166291714
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
54. ! [X0] : (room(X0) => (prede(X0) => ~prede(X0))) [input p10]
55. prede(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
135. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
136. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 135]
141. ! [X0] : ((~prede(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 54]
142. ! [X0] : (~prede(X0) | ~prede(X0) | ~room(X0)) [flattening 141]
143. prede(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 55]
144. prede(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 143]
232. room(paul) [cnf transformation 136]
240. ~prede(X0) | ~prede(X0) | ~room(X0) [cnf transformation 142]
244. prede(paul) [cnf transformation 144]
245. ~prede(X0) | ~room(X0) [duplicate literal removal 240]
250. ~room(paul) [resolution 245,244]
251. $false [subsumption resolution 250,232]
% SZS output end Proof for 2988279204067022166291714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.403012 |
Stephen, Felix, Kenneth, Cornelia are the only persons in the room. “Someone in the room is not a professional photographer specializing in portrait photography” if “no one in the room does not enjoy macrame or collects historical artifacts related to ancient civilizations” and vice versa. Felix collects historical artifacts related to ancient civilizations, has a pet dog or is a professional photographer specializing in portrait photography. Everyone in the room owns a microscope if they enjoys macrame. Everyone in the room who does not compete in national level swimming championships has a pet dog, is a professional photographer specializing in portrait photography or enjoys macrame. | Felix collects historical artifacts related to ancient civilizations. | neutral | room(stephen)&room(felix)&room(kenneth)&room(cornelia)&(![X]:(room(X)=>(X='stephen'|X='felix'|X='kenneth'|X='cornelia')))&
((~?[X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_enjoy_macrame(X))))))<=>(?[X]:(room(X)&(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))&
(((collects_historical_artifacts_related_to_ancient_civilizations(felix))|(has_a_pet_dog(felix))|(is_a_professional_photographer_specializing_in_portrait_photography(felix))))&
(![X]:(room(X)=>(((enjoys_macrame(X))=>(owns_a_microscope(X))))))&
(![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(((has_a_pet_dog(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))|(enjoys_macrame(X))))))))&
((![X]:((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(competes_in_national_level_swimming_championships(X)))))&
(owns_a_microscope(stephen))&
(![X]:(anywhere(X)=>(((competes_in_national_level_swimming_championships(X))<=(has_a_pet_dog(X))))))&
(![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(competes_in_national_level_swimming_championships(X))))))&
(![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))|(has_a_pet_dog(X)))))) | room(stephen)&room(felix)&room(kenneth)&room(cornelia)&(![X]:(room(X)=>(X='stephen'|X='felix'|X='kenneth'|X='cornelia')))&
collects_historical_artifacts_related_to_ancient_civilizations(felix) | [] | null | 0 |
Kristy, Joseph, Chris are the only persons in the room.
If 'Kristy uses contact lenses' then 'Chris uses contact lenses'.
'Kristy uses contact lenses' if 'everyone outside the room uses contact lenses'.
If 'everyone in the room collects luxury watches or does not have a curated collection of mid-century modern furniture' then 'everyone in the room collects luxury watches only if they maintains a personal blog focused on cybersecurity tips'.
If 'everyone anywhere does not collect luxury watches or has a curated collection of mid-century modern furniture' then 'everyone in the room uses contact lenses if they has a curated collection of mid-century modern furniture' otherwise 'it is not the case that 'Kristy has a curated collection of mid-century modern furniture''.
If 'everyone outside the room uses contact lenses or does not have a curated collection of mid-century modern furniture' then 'Kristy either does not use contact lenses or maintains a personal blog focused on cybersecurity tips but not both'.
Kristy uses contact lenses.
Everyone in the room who collects luxury watches uses contact lenses.
Everyone outside the room who uses contact lenses collects luxury watches.
Joseph collects luxury watches.
If someone neither maintains a personal blog focused on cybersecurity tips nor has a curated collection of mid-century modern furniture then he/she collects luxury watches.
If someone maintains a personal blog focused on cybersecurity tips then he/she collects luxury watches.
Chris collects luxury watches.
Kristy either does not use contact lenses or maintains a personal blog focused on cybersecurity tips but not both.
Everyone in the room collects luxury watches only if they maintains a personal blog focused on cybersecurity tips.
Everyone in the room maintains a personal blog focused on cybersecurity tips if they has a curated collection of mid-century modern furniture. | Kristy collects luxury watches. | entailment | room(kristy)&room(joseph)&room(chris)&(![X]:(room(X)=>(X='kristy'|X='joseph'|X='chris')))&
((uses_contact_lenses(kristy))=>(uses_contact_lenses(chris)))&
((![X]:(~room(X)=>(uses_contact_lenses(X))))=>(uses_contact_lenses(kristy)))&
((![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(collects_luxury_watches(X))))))=>(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<=(collects_luxury_watches(X)))))))&
(((![X]:(anywhere(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_collect_luxury_watches(X))))))=>(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(uses_contact_lenses(X)))))))&((~(![X]:(anywhere(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_collect_luxury_watches(X)))))))=>(~(has_a_curated_collection_of_mid-century_modern_furniture(kristy)))))&
((![X]:(~room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(uses_contact_lenses(X))))))=>(((does_not_use_contact_lenses(kristy))<~>(maintains_a_personal_blog_focused_on_cybersecurity_tips(kristy)))))&
(uses_contact_lenses(kristy))&
(![X]:(room(X)=>(((collects_luxury_watches(X))=>(uses_contact_lenses(X))))))&
(![X]:(~room(X)=>(((uses_contact_lenses(X))=>(collects_luxury_watches(X))))))&
(collects_luxury_watches(joseph))&
((![X]:((~((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))=>(collects_luxury_watches(X)))))&
((![X]:((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(collects_luxury_watches(X)))))&
(collects_luxury_watches(chris))&
(((does_not_use_contact_lenses(kristy))<~>(maintains_a_personal_blog_focused_on_cybersecurity_tips(kristy))))&
(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<=(collects_luxury_watches(X))))))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))) | room(kristy)&room(joseph)&room(chris)&(![X]:(room(X)=>(X='kristy'|X='joseph'|X='chris')))&
collects_luxury_watches(kristy) | [
"p0",
"p6",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2040062337291580135950769
% SZS output start Proof for 2040062337291580135950769
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
50. preda(mary) [input p6]
55. ! [X0] : (predb(X0) => predd(X0)) [input p11]
57. ~preda(mary) <~> predb(mary) [input p13]
60. ~(predd(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
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]
150. ! [X0] : (predd(X0) | ~predb(X0)) [ennf transformation 55]
155. ~predd(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60]
156. ~predd(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 155]
169. (~predb(mary) | preda(mary)) & (predb(mary) | ~preda(mary)) [nnf transformation 57]
170. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
171. ~predd(mary) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 156,170]
253. room(mary) [cnf transformation 135]
254. room(paul) [cnf transformation 135]
255. room(fred) [cnf transformation 135]
256. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 135]
273. preda(mary) [cnf transformation 50]
278. ~predb(X0) | predd(X0) [cnf transformation 150]
280. predb(mary) | ~preda(mary) [cnf transformation 169]
284. ~predd(mary) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171]
285. ~predd(mary) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171]
286. ~predd(mary) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171]
287. ~predd(mary) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171]
289. 1 <=> preda(mary) [avatar definition]
352. 15 <=> predb(mary) [avatar definition]
353. predb(mary) <- (15) [avatar component clause 352]
369. 1 [avatar split clause 273,289]
371. ~1 | 15 [avatar split clause 280,352,289]
373. ~predd(mary) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 287,255]
374. ~predd(mary) | fred != sK4 | ~room(mary) [subsumption resolution 373,254]
375. ~predd(mary) | fred != sK4 [subsumption resolution 374,253]
377. 18 <=> fred = sK4 [avatar definition]
379. fred != sK4 <- (~18) [avatar component clause 377]
381. 19 <=> predd(mary) [avatar definition]
384. ~18 | ~19 [avatar split clause 375,381,377]
385. ~predd(mary) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 286,255]
386. ~predd(mary) | paul != sK4 | ~room(mary) [subsumption resolution 385,254]
387. ~predd(mary) | paul != sK4 [subsumption resolution 386,253]
389. 20 <=> paul = sK4 [avatar definition]
391. paul != sK4 <- (~20) [avatar component clause 389]
392. ~20 | ~19 [avatar split clause 387,381,389]
393. ~predd(mary) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 285,255]
394. ~predd(mary) | mary != sK4 | ~room(mary) [subsumption resolution 393,254]
395. ~predd(mary) | mary != sK4 [subsumption resolution 394,253]
397. 21 <=> mary = sK4 [avatar definition]
399. mary != sK4 <- (~21) [avatar component clause 397]
400. ~21 | ~19 [avatar split clause 395,381,397]
401. ~predd(mary) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 284,255]
402. ~predd(mary) | room(sK4) | ~room(mary) [subsumption resolution 401,254]
403. ~predd(mary) | room(sK4) [subsumption resolution 402,253]
405. 22 <=> room(sK4) [avatar definition]
407. room(sK4) <- (22) [avatar component clause 405]
408. 22 | ~19 [avatar split clause 403,381,405]
409. predd(mary) <- (15) [resolution 278,353]
412. 19 | ~15 [avatar split clause 409,352,381]
493. paul = sK4 | mary = sK4 | fred = sK4 <- (22) [resolution 256,407]
494. mary = sK4 | fred = sK4 <- (~20, 22) [subsumption resolution 493,391]
495. fred = sK4 <- (~20, ~21, 22) [subsumption resolution 494,399]
496. $false <- (~18, ~20, ~21, 22) [subsumption resolution 495,379]
497. 18 | 20 | 21 | ~22 [avatar contradiction clause 496]
498. $false [avatar sat refutation 369,371,384,392,400,408,412,497]
% SZS output end Proof for 2040062337291580135950769
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Sandra, Christopher, Anthony are the only persons in the room.
If “Sandra enjoys skydiving” then “Sandra has a vast collection of first-edition science fiction novels”.
“Everyone in the room is a drone photographer or does not enjoy wildlife photography” if “everyone in the room is not a tea enthusiast or practices pilates”.
If “someone in the room works on fridays” then “only one person in the room practices pilates”.
If “Sandra does enjoy trail running” then “more than one person in the room streams on Twitch”.
If “it is not the case that “Sandra neither practices calligraphy nor has a vast collection of first-edition science fiction novels”” then “only one person in the room works on fridays”.
If “no one in the room does not practice graffiti art or practices graffiti art” then “everyone in the room who can play the guitar enjoys skydiving”.
“Sandra who is a tea enthusiast does not have a vast collection of first-edition science fiction novels” if “it is not the case that “someone in the room either enjoys writing detailed reviews of new and classic board games or is a chess master who participates in national tournaments but not both””.
“Everyone in the room either is a chess master who participates in national tournaments or writes poetry but not both if they practices pilates” if “Sandra does not collect rare minerals”.
If “someone outside the room builds model airplanes” then “more than one person outside the room is a chess master who participates in national tournaments”.
Either “everyone in the room can play the guitar or does not collect rare minerals” or “everyone in the room does not collect vintage stamps or writes poetry” but not both.
Everyone in the room who does not collect vintage stamps practices pilates.
Someone in the room practices graffiti art.
Sandra dreamt that “no one in the room who either is an avid hiker or writes poetry but not both collects vintage stamps”.
Sandra who does not collect vintage stamps has a vast collection of first-edition science fiction novels.
At least one person outside the room does enjoy trail running.
At least one person in the room either streams on Twitch or collects foreign coins but not both.
Everyone outside the room who is a certified yoga instructor teaching classes weekly practices calligraphy.
Everyone outside the room writes poetry only if they is a chess master who participates in national tournaments.
More than one person in the room writes poetry. | Anthony practices pilates. | contradiction | room(sandra)&room(christopher)&room(anthony)&(![X]:(room(X)=>(X='sandra'|X='christopher'|X='anthony')))&
((enjoys_skydiving(sandra))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(sandra)))&
((![X]:(room(X)=>(((practices_pilates(X))|(is_not_a_tea_enthusiast(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))|(is_a_drone_photographer(X)))))))&
((?[X]:(room(X)&(works_on_fridays(X))))=>(((?[X]:(room(X)&practices_pilates(X)))&(![X,Y]:((room(X)&room(Y)&(practices_pilates(X))&(practices_pilates(Y)))=>(X=Y))))))&
((does_enjoy_trail_running(sandra))=>((?[X,Y]:(room(X)&room(Y)&(streams_on_Twitch(X)&streams_on_Twitch(Y))&(X!=Y)))))&
((~(~((practices_calligraphy(sandra))|(has_a_vast_collection_of_first-edition_science_fiction_novels(sandra)))))=>(((?[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)=>(((practices_graffiti_art(X))|(does_not_practice_graffiti_art(X))))))=>(![X]:(room(X)=>(((can_play_the_guitar(X))=>(enjoys_skydiving(X)))))))&
((~(?[X]:(room(X)&(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<~>(is_a_chess_master_who_participates_in_national_tournaments(X)))))))=>((is_a_tea_enthusiast(sandra))&(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(sandra))))&
((does_not_collect_rare_minerals(sandra))=>(![X]:(room(X)=>(((practices_pilates(X))=>(((is_a_chess_master_who_participates_in_national_tournaments(X))<~>(writes_poetry(X)))))))))&
((?[X]:(~room(X)&(builds_model_airplanes(X))))=>((?[X,Y]:(~room(X)&~room(Y)&(is_a_chess_master_who_participates_in_national_tournaments(X)&is_a_chess_master_who_participates_in_national_tournaments(Y))&(X!=Y)))))&
((![X]:(room(X)=>(((does_not_collect_rare_minerals(X))|(can_play_the_guitar(X))))))<~>(![X]:(room(X)=>(((writes_poetry(X))|(does_not_collect_vintage_stamps(X)))))))&
(![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))=>(practices_pilates(X))))))&
(?[X]:(room(X)&(practices_graffiti_art(X))))&
((sandra_dream=>(~?[X]:(room(X)=>(((((is_an_avid_hiker(X))<~>(writes_poetry(X))))=>(collects_vintage_stamps(X))))))))&
((does_not_collect_vintage_stamps(sandra))&(has_a_vast_collection_of_first-edition_science_fiction_novels(sandra)))&
(((?[X]:(~room(X)&does_enjoy_trail_running(X)))))&
(((?[X]:(room(X)&((streams_on_Twitch(X))<~>(collects_foreign_coins(X)))))))&
(![X]:(~room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(practices_calligraphy(X))))))&
(![X]:(~room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))<=(writes_poetry(X))))))&
((?[X,Y]:(room(X)&room(Y)&(writes_poetry(X)&writes_poetry(Y))&(X!=Y))))&
(is_a_certified_yoga_instructor_teaching_classes_weekly(sandra))&
(((?[X]:(room(X)&does_not_collect_rare_minerals(X)))))&
((?[X,Y]:(room(X)&room(Y)&(practices_tai_chi(X)&practices_tai_chi(Y))&(X!=Y))))&
(![X]:(anywhere(X)=>(((is_an_avid_hiker(X))=>(practices_calligraphy(X))))))&
(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(sandra))&
(![X]:(~room(X)=>(((practices_tai_chi(X))=>(writes_a_travel_blog(X)))))) | room(sandra)&room(christopher)&room(anthony)&(![X]:(room(X)=>(X='sandra'|X='christopher'|X='anthony')))&
practices_pilates(anthony) | [
"b42",
"p0",
"p3",
"p5",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4188795571068695740197246
% SZS output start Proof for 4188795571068695740197246
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. ? [X0] : (predt(X0) & room(X0)) => (! [X0,X1] : ((predx(X1) & predx(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predx(X0) & room(X0))) [input p3]
49. ~~(predj(mary) | predl(mary)) => (! [X0,X1] : ((predt(X1) & predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predt(X0) & room(X0))) [input p5]
55. ! [X0] : (room(X0) => (~predy(X0) => predx(X0))) [input p11]
58. predj(mary) & ~predy(mary) [input p14]
70. predx(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
72. ? [X0] : (predt(X0) & room(X0)) => (! [X1,X2] : ((predx(X2) & predx(X1) & room(X2) & room(X1)) => X1 = X2) & ? [X3] : (predx(X3) & room(X3))) [rectify 47]
73. ~~(predj(mary) | predl(mary)) => (! [X0,X1] : ((predt(X1) & predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predt(X2) & room(X2))) [rectify 49]
74. (predj(mary) | predl(mary)) => (! [X0,X1] : ((predt(X1) & predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predt(X2) & room(X2))) [flattening 73]
158. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
159. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 158]
161. (! [X1,X2] : (X1 = X2 | (~predx(X2) | ~predx(X1) | ~room(X2) | ~room(X1))) & ? [X3] : (predx(X3) & room(X3))) | ! [X0] : (~predt(X0) | ~room(X0)) [ennf transformation 72]
162. (! [X1,X2] : (X1 = X2 | ~predx(X2) | ~predx(X1) | ~room(X2) | ~room(X1)) & ? [X3] : (predx(X3) & room(X3))) | ! [X0] : (~predt(X0) | ~room(X0)) [flattening 161]
164. (! [X0,X1] : (X0 = X1 | (~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predt(X2) & room(X2))) | (~predj(mary) & ~predl(mary)) [ennf transformation 74]
165. (! [X0,X1] : (X0 = X1 | ~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predt(X2) & room(X2))) | (~predj(mary) & ~predl(mary)) [flattening 164]
173. ! [X0] : ((predx(X0) | predy(X0)) | ~room(X0)) [ennf transformation 55]
174. ! [X0] : (predx(X0) | predy(X0) | ~room(X0)) [flattening 173]
179. predx(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 70]
180. predx(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 179]
182. (! [X0,X1] : (X0 = X1 | ~predx(X1) | ~predx(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predx(X2) & room(X2))) | ! [X3] : (~predt(X3) | ~room(X3)) [rectify 162]
183. ? [X2] : (predx(X2) & room(X2)) => (predx(sK0) & room(sK0)) [choice axiom]
184. (! [X0,X1] : (X0 = X1 | ~predx(X1) | ~predx(X0) | ~room(X1) | ~room(X0)) & (predx(sK0) & room(sK0))) | ! [X3] : (~predt(X3) | ~room(X3)) [skolemisation 182,183]
187. ? [X2] : (predt(X2) & room(X2)) => (predt(sK3) & room(sK3)) [choice axiom]
188. (! [X0,X1] : (X0 = X1 | ~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0)) & (predt(sK3) & room(sK3))) | (~predj(mary) & ~predl(mary)) [skolemisation 165,187]
266. mary != fred [cnf transformation 43]
296. room(mary) [cnf transformation 159]
298. room(fred) [cnf transformation 159]
303. X0 = X1 | ~predx(X1) | ~predx(X0) | ~room(X1) | ~room(X0) | ~predt(X3) | ~room(X3) [cnf transformation 184]
310. room(sK3) | ~predj(mary) [cnf transformation 188]
312. predt(sK3) | ~predj(mary) [cnf transformation 188]
331. ~room(X0) | predy(X0) | predx(X0) [cnf transformation 174]
334. ~predy(mary) [cnf transformation 58]
335. predj(mary) [cnf transformation 58]
358. predx(fred) [cnf transformation 180]
364. 2 <=> predj(mary) [avatar definition]
369. 3 <=> ! [X3] : (~predt(X3) | ~room(X3)) [avatar definition]
370. ~predt(X3) | ~room(X3) <- (3) [avatar component clause 369]
372. 4 <=> ! [X0,X1] : (X0 = X1 | ~room(X0) | ~room(X1) | ~predx(X0) | ~predx(X1)) [avatar definition]
373. ~predx(X1) | ~room(X0) | ~room(X1) | ~predx(X0) | X0 = X1 <- (4) [avatar component clause 372]
374. 3 | 4 [avatar split clause 303,372,369]
424. 15 <=> predt(sK3) [avatar definition]
426. predt(sK3) <- (15) [avatar component clause 424]
427. ~2 | 15 [avatar split clause 312,424,364]
430. 16 <=> room(sK3) [avatar definition]
432. room(sK3) <- (16) [avatar component clause 430]
433. ~2 | 16 [avatar split clause 310,430,364]
502. 2 [avatar split clause 335,364]
513. ~room(sK3) <- (3, 15) [resolution 370,426]
514. $false <- (3, 15, 16) [subsumption resolution 513,432]
515. ~3 | ~15 | ~16 [avatar contradiction clause 514]
516. predy(mary) | predx(mary) [resolution 331,296]
530. predx(mary) [subsumption resolution 516,334]
922. ~room(X2) | ~room(fred) | ~predx(X2) | fred = X2 <- (4) [resolution 373,358]
926. ~predx(X2) | ~room(X2) | fred = X2 <- (4) [subsumption resolution 922,298]
944. ~room(mary) | mary = fred <- (4) [resolution 926,530]
948. mary = fred <- (4) [subsumption resolution 944,296]
949. $false <- (4) [subsumption resolution 948,266]
950. ~4 [avatar contradiction clause 949]
954. $false [avatar sat refutation 374,427,433,502,515,950]
% SZS output end Proof for 4188795571068695740197246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5628
% Time elapsed: 0.042 s
% ------------------------------
% ------------------------------
| 0.306752 |
Adrian is the only person in the room.
If 'Adrian enjoys making ceramics' then 'Adrian mentors a youth basketball team on weekends'.
If 'no one in the room does not enjoy landscape photography or does not collect antique clocks' then 'at least one person anywhere is an avid mountain climber who has scaled several peaks'.
If 'it is true that 'it is not the case that 'Adrian has a tattoo''' then 'Adrian practices zumba'.
It is true that 'Adrian is allergic to anything'.
Adrian works on fridays.
Adrian mentors a youth basketball team on weekends.
Adrian hosts themed dinner parties featuring gourmet home-cooked meals.
It is not the case that 'Adrian has a tattoo'.
Everyone in the room enjoys making ceramics if they enjoys coding in Python.
Adrian practices zumba. | Adrian enjoys making ceramics. | neutral | room(adrian)&(![X]:(room(X)=>(X='adrian')))&
((enjoys_making_ceramics(adrian))=>(mentors_a_youth_basketball_team_on_weekends(adrian)))&
((~?[X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(does_not_enjoy_landscape_photography(X))))))=>(((?[X]:(anywhere(X)&is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))&
((~(has_a_tattoo(adrian)))=>(practices_zumba(adrian)))&
(is_allergic_to_anything(adrian))&
(works_on_fridays(adrian))&
(mentors_a_youth_basketball_team_on_weekends(adrian))&
(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(adrian))&
(~(has_a_tattoo(adrian)))&
(![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(enjoys_making_ceramics(X))))))&
(practices_zumba(adrian)) | room(adrian)&(![X]:(room(X)=>(X='adrian')))&
enjoys_making_ceramics(adrian) | [] | null | 0.002939 |
Sherri, Patricia are the only persons in the room.
Everyone in the room participates in citizen science projects related to wildlife monitoring and does not host a YouTube channel dedicated to art tutorials.
Everyone in the room is not a client of LVMH.
Everyone in the room participates in citizen science projects related to wildlife monitoring.
Everyone outside the room does not participate in citizen science projects related to wildlife monitoring or participates in citizen science projects related to wildlife monitoring or both.
Everyone in the room either is not a client of LVMH or does not participate in citizen science projects related to wildlife monitoring but not both.
Patricia does not practice urban gardening or is a client of LVMH or both.
Everyone in the room participates in citizen science projects related to wildlife monitoring if they does not practice urban gardening.
Everyone in the room does not practice yoga or is not a client of LVMH or both if they participates in citizen science projects related to wildlife monitoring.
Everyone in the room is not a client of LVMH if they does not practice yoga or is not a client of LVMH or both.
Everyone in the room does not host a YouTube channel dedicated to art tutorials. | Only one person in the room does practice yoga. | neutral | room(sherri)&room(patricia)&(![X]:(room(X)=>(X='sherri'|X='patricia')))&
(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(![X]:(room(X)=>(is_not_a_client_of_LVMH(X))))&
(![X]:(room(X)=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))&
(![X]:(~room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))&
(![X]:(room(X)=>(((is_not_a_client_of_LVMH(X))<~>(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))&
(((does_not_practice_urban_gardening(patricia))|(is_a_client_of_LVMH(patricia))))&
(![X]:(room(X)=>(((does_not_practice_urban_gardening(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_not_practice_yoga(X))|(is_not_a_client_of_LVMH(X))))))))&
(![X]:(room(X)=>(((((does_not_practice_yoga(X))|(is_not_a_client_of_LVMH(X))))=>(is_not_a_client_of_LVMH(X))))))&
(![X]:(room(X)=>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))&
(![X]:(~room(X)=>(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X)))) | room(sherri)&room(patricia)&(![X]:(room(X)=>(X='sherri'|X='patricia')))&
((?[X]:(room(X)&does_practice_yoga(X)))&(![X,Y]:((room(X)&room(Y)&(does_practice_yoga(X))&(does_practice_yoga(Y)))=>(X=Y)))) | [] | null | 0.130093 |
There is a room. Either “everyone in the room collects vintage stamps” or “no one in the room is not a certified yoga instructor teaching classes weekly or is a culinary enthusiast who experiments with international cuisines” but not both. If someone collects vintage stamps then he/she volunteers for local environmental conservation projects. Not everyone outside the room is a culinary enthusiast who experiments with international cuisines if they enjoys camping and organizing outdoor survival workshops. | Everyone in the room volunteers for local environmental conservation projects. | entailment | (there_is_a_room)&
((![X]:(room(X)=>(collects_vintage_stamps(X))))<~>(~?[X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))&
((![X]:(~room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(enjoys_stand-up_paddleboarding(X)))))))&
((~?[X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))=>((![X]:((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
((~![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_collect_first_edition_books(X))))))=>(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))=>(does_not_enjoy_stand-up_paddleboarding(X)))))))&
(~(![X]:(room(X)=>(is_a_wine_connoisseur(X))))=>(~?[X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(does_enjoy_trail_running(X)))))))&
((![X]:(room(X)=>(((has_a_piercing(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))<=>(((?[X]:(room(X)&is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
((![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))&(has_lived_in_exactly_three_countries(X))))))<=>(![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))&
((![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))=>(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))))&
((![X]:((does_enjoy_trail_running(X))=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))&
(~![X]:(anywhere(X)=>(((collects_first_edition_books(X))=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(develops_open-source_software_projects_in_their_free_time(X))))))))&
((![X]:((collects_vintage_stamps(X))=>(volunteers_for_local_environmental_conservation_projects(X)))))&
(![X]:(room(X)=>(is_a_client_of_LVMH(X))))&
(?[X]:(room(X)&(does_enjoy_trail_running(X))))&
(![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))))&
(![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(~![X]:(~room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(![X]:(room(X)=>(((((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(hosts_regular_workshops_on_creative_writing(X))))=>(~((does_enjoy_trail_running(X))|(enjoys_stand-up_paddleboarding(X))))))))&
(![X]:(room(X)=>(((~((does_enjoy_trail_running(X))|(enjoys_stand-up_paddleboarding(X))))=>(((has_lived_in_exactly_three_countries(X))|(does_enjoy_trail_running(X))|(is_a_tea_enthusiast(X))))))))&
(![X]:(room(X)=>(((((has_lived_in_exactly_three_countries(X))|(does_enjoy_trail_running(X))|(is_a_tea_enthusiast(X))))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(volunteers_for_local_environmental_conservation_projects(X))) | [
"p0",
"p1",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3631737369988972681962104
% SZS output start Proof for 3631737369988972681962104
44. there_is_a_room [input p0]
45. ! [X0] : (room(X0) => preda(X0)) <~> ~? [X0] : (room(X0) => (~predc(X0) | predr(X0))) [input p1]
55. ! [X0] : (preda(X0) => predk(X0)) [input p11]
60. ~! [X0] : (~room(X0) => (predf(X0) => predr(X0))) [input p16]
64. ~(! [X0] : (room(X0) => predk(X0)) & there_is_a_room) [input hypothesis]
65. ! [X0] : (room(X0) => preda(X0)) <~> ~? [X1] : (room(X1) => (~predc(X1) | predr(X1))) [rectify 45]
150. ! [X0] : (preda(X0) | ~room(X0)) <~> ! [X1] : ((predc(X1) & ~predr(X1)) & room(X1)) [ennf transformation 65]
151. ! [X0] : (preda(X0) | ~room(X0)) <~> ! [X1] : (predc(X1) & ~predr(X1) & room(X1)) [flattening 150]
167. ! [X0] : (predk(X0) | ~preda(X0)) [ennf transformation 55]
172. ? [X0] : ((~predr(X0) & predf(X0)) & ~room(X0)) [ennf transformation 60]
173. ? [X0] : (~predr(X0) & predf(X0) & ~room(X0)) [flattening 172]
178. ? [X0] : (~predk(X0) & room(X0)) | ~there_is_a_room [ennf transformation 64]
182. (? [X1] : (~predc(X1) | predr(X1) | ~room(X1)) | ? [X0] : (~preda(X0) & room(X0))) & (! [X1] : (predc(X1) & ~predr(X1) & room(X1)) | ! [X0] : (preda(X0) | ~room(X0))) [nnf transformation 151]
183. (? [X0] : (~predc(X0) | predr(X0) | ~room(X0)) | ? [X1] : (~preda(X1) & room(X1))) & (! [X2] : (predc(X2) & ~predr(X2) & room(X2)) | ! [X3] : (preda(X3) | ~room(X3))) [rectify 182]
184. ? [X0] : (~predc(X0) | predr(X0) | ~room(X0)) => (~predc(sK1) | predr(sK1) | ~room(sK1)) [choice axiom]
185. ? [X1] : (~preda(X1) & room(X1)) => (~preda(sK2) & room(sK2)) [choice axiom]
186. ((~predc(sK1) | predr(sK1) | ~room(sK1)) | (~preda(sK2) & room(sK2))) & (! [X2] : (predc(X2) & ~predr(X2) & room(X2)) | ! [X3] : (preda(X3) | ~room(X3))) [skolemisation 183,185,184]
214. ? [X0] : (~predr(X0) & predf(X0) & ~room(X0)) => (~predr(sK12) & predf(sK12) & ~room(sK12)) [choice axiom]
215. ~predr(sK12) & predf(sK12) & ~room(sK12) [skolemisation 173,214]
216. ? [X0] : (~predk(X0) & room(X0)) => (~predk(sK13) & room(sK13)) [choice axiom]
217. (~predk(sK13) & room(sK13)) | ~there_is_a_room [skolemisation 178,216]
298. there_is_a_room [cnf transformation 44]
299. room(X2) | preda(X3) | ~room(X3) [cnf transformation 186]
331. ~preda(X0) | predk(X0) [cnf transformation 167]
338. ~room(sK12) [cnf transformation 215]
345. room(sK13) | ~there_is_a_room [cnf transformation 217]
346. ~predk(sK13) | ~there_is_a_room [cnf transformation 217]
371. 6 <=> ! [X3] : (preda(X3) | ~room(X3)) [avatar definition]
372. ~room(X3) | preda(X3) <- (6) [avatar component clause 371]
382. 9 <=> ! [X2] : room(X2) [avatar definition]
383. room(X2) <- (9) [avatar component clause 382]
384. 6 | 9 [avatar split clause 299,382,371]
510. ~predk(sK13) [subsumption resolution 346,298]
511. room(sK13) [subsumption resolution 345,298]
624. $false <- (9) [resolution 383,338]
625. ~9 [avatar contradiction clause 624]
641. preda(sK13) <- (6) [resolution 372,511]
682. predk(sK13) <- (6) [resolution 641,331]
683. $false <- (6) [subsumption resolution 682,510]
684. ~6 [avatar contradiction clause 683]
685. $false [avatar sat refutation 384,625,684]
% SZS output end Proof for 3631737369988972681962104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.021865 |
Calvin, Sandra are the only persons in the room.
If Calvin collects first edition books or does not collect first edition books or both then everyone in the room who collects first edition books hosts a popular podcast about emerging technologies.
Sandra is a coffee connoisseur if Calvin hosts a popular podcast about emerging technologies and vice versa.
Everyone in the room who is a coffee connoisseur travels domestically frequently.
If someone collects first edition books then he/she travels domestically frequently and vice versa.
It is not the case that Calvin does not travel domestically frequently.
Sandra is a coffee connoisseur.
Sandra who is a coffee connoisseur owns a significant collection of rare gemstones and minerals.
It is not the case that it is not the case that more than one person in the room owns a significant collection of rare gemstones and minerals.
Sandra hosts a popular podcast about emerging technologies.
Sandra who hosts a popular podcast about emerging technologies is a coffee connoisseur.
At least one person anywhere is a coffee connoisseur.
If someone collects first edition books then he/she hosts a popular podcast about emerging technologies and vice versa.
Everyone in the room who hosts a popular podcast about emerging technologies owns a significant collection of rare gemstones and minerals. | Only one person in the room travels domestically frequently. | contradiction | room(calvin)&room(sandra)&(![X]:(room(X)=>(X='calvin'|X='sandra')))&
((((collects_first_edition_books(calvin))|(does_not_collect_first_edition_books(calvin))))=>(![X]:(room(X)=>(((collects_first_edition_books(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))))&
((hosts_a_popular_podcast_about_emerging_technologies(calvin))<=>(is_a_coffee_connoisseur(sandra)))&
(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(travels_domestically_frequently(X))))))&
((![X]:((collects_first_edition_books(X))<=>(travels_domestically_frequently(X)))))&
(~(does_not_travel_domestically_frequently(calvin)))&
(is_a_coffee_connoisseur(sandra))&
((is_a_coffee_connoisseur(sandra))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(sandra)))&
(~(~((?[X,Y]:(room(X)&room(Y)&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)&owns_a_significant_collection_of_rare_gemstones_and_minerals(Y))&(X!=Y))))))&
(hosts_a_popular_podcast_about_emerging_technologies(sandra))&
((hosts_a_popular_podcast_about_emerging_technologies(sandra))&(is_a_coffee_connoisseur(sandra)))&
(((?[X]:(anywhere(X)&is_a_coffee_connoisseur(X)))))&
((![X]:((collects_first_edition_books(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))&
(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))) | room(calvin)&room(sandra)&(![X]:(room(X)=>(X='calvin'|X='sandra')))&
((?[X]:(room(X)&travels_domestically_frequently(X)))&(![X,Y]:((room(X)&room(Y)&(travels_domestically_frequently(X))&(travels_domestically_frequently(Y)))=>(X=Y)))) | [
"b42",
"p0",
"p4",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3319316829523708063358197
% SZS output start Proof for 3319316829523708063358197
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]
48. ! [X0] : (predf(X0) <=> predc(X0)) [input p4]
49. predc(mary) [input p5]
53. predd(paul) [input p9]
56. ! [X0] : (predf(X0) <=> predd(X0)) [input p12]
58. ! [X0,X1] : ((predc(X1) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predc(X0) & room(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
60. ! [X0,X1] : ((predc(X1) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predc(X2) & room(X2)) & ! [X3] : (room(X3) => (paul = X3 | mary = X3)) & room(paul) & room(mary) [rectify 58]
137. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
138. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 137]
143. ! [X0,X1] : (X0 = X1 | (~predc(X1) | ~predc(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predc(X2) & room(X2)) & ! [X3] : ((paul = X3 | mary = X3) | ~room(X3)) & room(paul) & room(mary) [ennf transformation 60]
144. ! [X0,X1] : (X0 = X1 | ~predc(X1) | ~predc(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predc(X2) & room(X2)) & ! [X3] : (paul = X3 | mary = X3 | ~room(X3)) & room(paul) & room(mary) [flattening 143]
147. ! [X0] : ((predf(X0) | ~predc(X0)) & (predc(X0) | ~predf(X0))) [nnf transformation 48]
152. ! [X0] : ((predf(X0) | ~predd(X0)) & (predd(X0) | ~predf(X0))) [nnf transformation 56]
153. ? [X2] : (predc(X2) & room(X2)) => (predc(sK3) & room(sK3)) [choice axiom]
154. ! [X0,X1] : (X0 = X1 | ~predc(X1) | ~predc(X0) | ~room(X1) | ~room(X0)) & (predc(sK3) & room(sK3)) & ! [X3] : (paul = X3 | mary = X3 | ~room(X3)) & room(paul) & room(mary) [skolemisation 144,153]
199. mary != paul [cnf transformation 43]
235. room(mary) [cnf transformation 138]
236. room(paul) [cnf transformation 138]
243. ~predf(X0) | predc(X0) [cnf transformation 147]
245. predc(mary) [cnf transformation 49]
251. predd(paul) [cnf transformation 53]
256. ~predd(X0) | predf(X0) [cnf transformation 152]
262. ~predc(X1) | X0 = X1 | ~predc(X0) | ~room(X1) | ~room(X0) [cnf transformation 154]
292. predf(paul) [resolution 256,251]
295. predc(paul) [resolution 292,243]
388. mary = X0 | ~predc(X0) | ~room(mary) | ~room(X0) [resolution 262,245]
390. ~predc(X0) | mary = X0 | ~room(X0) [subsumption resolution 388,235]
393. mary = paul | ~room(paul) [resolution 390,295]
394. ~room(paul) [subsumption resolution 393,199]
395. $false [subsumption resolution 394,236]
% SZS output end Proof for 3319316829523708063358197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.097979 |
There is a room. Everyone in the room who neither is quieter than Joanne nor is a tall person is not a funny calm person. Everyone in the room is quieter than Tiffany only if they is older than Tiffany. Everyone in the room who is older than Tiffany is older than Joanne. If someone is a calm person then he/she is not a curious tall patient person, is older than Sophia and is a quiet person. Everyone in the room is richer than Tiffany if they is older than Joanne, is a happy kind creative quiet person and is richer than Sophia. Everyone in the room is not a old brave person if they is a old person. Not everyone in the room is richer than Sophia if they is not a old brave person. Everyone anywhere is a happy strong person, is quieter than Tiffany and is a old person if they is richer than Sophia. Everyone in the room who is a happy strong person, is quieter than Tiffany and is a old person is not not calm. No strong person is patient. Everyone in the room is a humble funny patient person if they is older than Joanne. | More than one person in the room is older than Joanne. | contradiction | (there_is_a_room)&
(![X]:(room(X)=>(((~((quieter(joanne,X))|(tall(X)&person(X))))=>(~(funny(X)&calm(X)&person(X)))))))&
(![X]:(room(X)=>(((older(tiffany,X))<=(quieter(tiffany,X))))))&
(![X]:(room(X)=>(((older(tiffany,X))=>(older(joanne,X))))))&
((![X]:((calm(X)&person(X))=>(((~(curious(X)&tall(X)&patient(X)&person(X)))&(older(sophia,X))&(quiet(X)&person(X)))))))&
(![X]:(room(X)=>(((((older(joanne,X))&(happy(X)&kind(X)&creative(X)&quiet(X)&person(X))&(richer(sophia,X))))=>(richer(tiffany,X))))))&
(![X]:(room(X)=>(((old(X)&person(X))=>(~(old(X)&brave(X)&person(X)))))))&
(~![X]:(room(X)=>(((~(old(X)&brave(X)&person(X)))=>(richer(sophia,X))))))&
(![X]:(anywhere(X)=>(((richer(sophia,X))=>(((happy(X)&strong(X)&person(X))&(quieter(tiffany,X))&(old(X)&person(X))))))))&
(![X]:(room(X)=>(((((happy(X)&strong(X)&person(X))&(quieter(tiffany,X))&(old(X)&person(X))))=>(~~calm(X))))))&
(![X]:(room(X)=>(((richer(sophia,X))<=(~~calm(X))))))&
(?[X,Y]:((richer(sophia,X))&(older(tiffany,Y))&(older(X,Y))))&
(![X]:(room(X)=>(((~funny(X)&~quiet(X)&~kind(X))=>(((older(tiffany,X))|(creative(X))|(older(sophia,X))))))))&
(![X]:(room(X)=>(((~(kind(X)&patient(X)&happy(X)&calm(X)&generous(X)&person(X)))=>(older(sophia,X))))))&
(~?[X]:(strong(X)=>patient(X)))&
((![X]:((creative(X)&funny(X)&person(X))<=>(quieter(joanne,X)))))&
(![X]:(anywhere(X)=>(((calm(X)&person(X))=>(generous(X))))))&
((?[X,Y]:(room(X)&room(Y)&(kind(X)&person(X)&kind(Y)&person(Y))&(X!=Y))))&
(?[X,Y]:((quieter(tiffany,X))&(~(strong(Y)&tall(Y)&person(Y)))&(quieter(X,Y))))&
(![X]:(room(X)=>(((~funny(X))<=(((older(tiffany,X))|(~(old(X)&happy(X)&brave(X)&person(X)))|(~kind(X))))))))&
((?[X,Y]:(room(X)&room(Y)&(humble(X)&kind(X)&person(X)&humble(Y)&kind(Y)&person(Y))&(X!=Y))))&
(![X]:(room(X)=>(((older(joanne,X))=>(humble(X)&funny(X)&patient(X)&person(X))))))&
(~![X]:(room(X)=>(((older(sophia,X))=>(calm(X))))))&
(![X]:(~room(X)=>(richer(sophia,X))))&
(![X]:(room(X)=>(((quieter(joanne,X))<=(brave(X))))))&
(![X]:(room(X)=>(((quieter(joanne,X))=>(quieter(sophia,X)))))) | (there_is_a_room)&
(?[X,Y]:(room(X)&room(Y)&(older(joanne,X)&older(joanne,Y))&(X!=Y))) | [
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8306921026535902684989705
% SZS output start Proof for 8306921026535902684989705
58. ~? [X0] : (strong(X0) => patient(X0)) [input p14]
65. ! [X0] : (room(X0) => (older(fred,X0) => (person(X0) & patient(X0) & funny(X0) & humble(X0)))) [input p21]
70. ? [X0,X1] : (X0 != X1 & older(fred,X1) & older(fred,X0) & room(X1) & room(X0)) & there_is_a_room [input hypothesis]
71. ! [X0] : (room(X0) => (older(fred,X0) => (person(X0) & patient(X0) & funny(X0)))) [pure predicate removal 65]
76. ? [X0,X1] : (X0 != X1 & older(fred,X1) & older(fred,X0) & room(X1) & room(X0)) [pure predicate removal 70]
173. ! [X0] : (~patient(X0) & strong(X0)) [ennf transformation 58]
177. ! [X0] : (((person(X0) & patient(X0) & funny(X0)) | ~older(fred,X0)) | ~room(X0)) [ennf transformation 71]
178. ! [X0] : ((person(X0) & patient(X0) & funny(X0)) | ~older(fred,X0) | ~room(X0)) [flattening 177]
201. ? [X0,X1] : (X0 != X1 & older(fred,X1) & older(fred,X0) & room(X1) & room(X0)) => (sK10 != sK11 & older(fred,sK11) & older(fred,sK10) & room(sK11) & room(sK10)) [choice axiom]
202. sK10 != sK11 & older(fred,sK11) & older(fred,sK10) & room(sK11) & room(sK10) [skolemisation 76,201]
314. ~patient(X0) [cnf transformation 173]
343. patient(X0) | ~older(fred,X0) | ~room(X0) [cnf transformation 178]
351. room(sK10) [cnf transformation 202]
353. older(fred,sK10) [cnf transformation 202]
386. ~older(fred,X0) | ~room(X0) [subsumption resolution 343,314]
396. ~room(sK10) [resolution 386,353]
398. $false [subsumption resolution 396,351]
% SZS output end Proof for 8306921026535902684989705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.0757 |
Larry is the only person in the room.
If “not everyone in the room has a piercing or does not enjoy deep-sea diving and exploring underwater caves” then “not everyone in the room does not collect rare minerals or is a wine connoisseur”.
If “not everyone in the room does not collect rare minerals or is a wine connoisseur” then “Larry can play the guitar”.
Either “everyone in the room enjoys deep-sea diving and exploring underwater caves or is not a certified scuba diver with advanced underwater photography skills” or “not everyone anywhere enjoys kayaking or does not practice and performs acrobatic dance routines” but not both.
If “everyone in the room collects historical artifacts related to ancient civilizations or does not maintain a personal blog focused on cybersecurity tips” then “Larry drives a hybrid car”. | Larry has a pet dog. | entailment | room(larry)&(![X]:(room(X)=>(X='larry')))&
(((~![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(has_a_piercing(X))))))=>(~![X]:(room(X)=>(((is_a_wine_connoisseur(X))|(does_not_collect_rare_minerals(X)))))))&
((~![X]:(room(X)=>(((is_a_wine_connoisseur(X))|(does_not_collect_rare_minerals(X))))))=>(can_play_the_guitar(larry))))&
((![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))<~>(~![X]:(anywhere(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(enjoys_kayaking(X)))))))&
((![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))=>(drives_a_hybrid_car(larry)))&
((![X]:(~room(X)=>(((does_not_practice_zumba(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))))=>(![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))&
((~![X]:(anywhere(X)=>(((has_a_pet_dog(X))|(does_not_use_an_ios_phone(X))))))=>(~?[X]:(anywhere(X)=>(((does_not_use_an_ios_phone(X))=>(has_a_pet_dog(X)))))))&
(maintains_a_personal_blog_focused_on_cybersecurity_tips(larry))&
(~![X]:(room(X)=>(((has_a_pet_dog(X))=>(bakes_bread_at_home(X))))))&
(((practices_and_performs_acrobatic_dance_routines(larry))|(is_a_wine_connoisseur(larry))|(collects_rare_minerals(larry))))&
(has_a_pet_dog(larry))&
(![X]:(anywhere(X)=>(((does_not_enjoy_snowboarding(X))|(can_play_the_flute(X))))))&
(~![X]:(room(X)=>(((can_play_the_flute(X))=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<~>(drives_a_hybrid_car(X))))))))&
(![X]:(~room(X)=>(((((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<~>(drives_a_hybrid_car(X))))=>(practices_kickboxing(X))))))&
(![X]:(room(X)=>(((practices_zumba(X))<=(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))) | room(larry)&(![X]:(room(X)=>(X='larry')))&
has_a_pet_dog(larry) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1577779224309647256862295
% SZS output start Proof for 1577779224309647256862295
44. ! [X0] : (room(X0) => (predd(X0) => predl(X0))) & ! [X0] : (~room(X0) => ((predm(X0) <~> predb(X0)) => predq(X0))) & ~! [X0] : (room(X0) => (predw(X0) => (predm(X0) <~> predb(X0)))) & ! [X0] : (anywhere(X0) => (predw(X0) | ~predu(X0))) & predt(mary) & (predh(mary) | predp(mary) | predx(mary)) & ~! [X0] : (room(X0) => (predt(X0) => predc(X0))) & predm(mary) & (~! [X0] : (anywhere(X0) => (~predf(X0) | predt(X0))) => ~? [X0] : (anywhere(X0) => (~predf(X0) => predt(X0)))) & (! [X0] : (~room(X0) => (predz(X0) | ~predl(X0))) => ! [X0] : (room(X0) => (predk(X0) => preds(X0)))) & (! [X0] : (room(X0) => (predn(X0) | ~predm(X0))) => predb(mary)) & (! [X0] : (room(X0) => (predg(X0) | ~predd(X0))) <~> ~! [X0] : (anywhere(X0) => (predr(X0) | ~predx(X0)))) & (~! [X0] : (room(X0) => (~predh(X0) | predp(X0))) => predy(mary)) & (~! [X0] : (room(X0) => (predj(X0) | ~predg(X0))) => ~! [X0] : (room(X0) => (~predh(X0) | predp(X0)))) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
45. ~(predt(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
46. ! [X0] : (room(X0) => (predd(X0) => predl(X0))) & ! [X1] : (~room(X1) => ((predm(X1) <~> predb(X1)) => predq(X1))) & ~! [X2] : (room(X2) => (predw(X2) => (predm(X2) <~> predb(X2)))) & ! [X3] : (anywhere(X3) => (predw(X3) | ~predu(X3))) & predt(mary) & (predh(mary) | predp(mary) | predx(mary)) & ~! [X4] : (room(X4) => (predt(X4) => predc(X4))) & predm(mary) & (~! [X5] : (anywhere(X5) => (~predf(X5) | predt(X5))) => ~? [X6] : (anywhere(X6) => (~predf(X6) => predt(X6)))) & (! [X7] : (~room(X7) => (predz(X7) | ~predl(X7))) => ! [X8] : (room(X8) => (predk(X8) => preds(X8)))) & (! [X9] : (room(X9) => (predn(X9) | ~predm(X9))) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X12] : (room(X12) => (~predh(X12) | predp(X12))) => predy(mary)) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : (room(X14) => (~predh(X14) | predp(X14)))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [rectify 44]
47. ! [X0] : (room(X0) => (predd(X0) => predl(X0))) & ~! [X2] : (room(X2) => (predw(X2) => (predm(X2) <~> predb(X2)))) & ! [X3] : (anywhere(X3) => (predw(X3) | ~predu(X3))) & predt(mary) & (predh(mary) | predp(mary) | predx(mary)) & ~! [X4] : (room(X4) => (predt(X4) => predc(X4))) & predm(mary) & (~! [X5] : (anywhere(X5) => (~predf(X5) | predt(X5))) => ~? [X6] : (anywhere(X6) => (~predf(X6) => predt(X6)))) & (! [X7] : (~room(X7) => (predz(X7) | ~predl(X7))) => ! [X8] : (room(X8) => (predk(X8) => preds(X8)))) & (! [X9] : (room(X9) => (predn(X9) | ~predm(X9))) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X12] : (room(X12) => (~predh(X12) | predp(X12))) => predy(mary)) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : (room(X14) => (~predh(X14) | predp(X14)))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 46]
48. ! [X0] : (room(X0) => (predd(X0) => predl(X0))) & ~! [X2] : (room(X2) => (predm(X2) <~> predb(X2))) & predt(mary) & (predh(mary) | predp(mary) | predx(mary)) & ~! [X4] : (room(X4) => (predt(X4) => predc(X4))) & predm(mary) & (~! [X5] : (anywhere(X5) => (~predf(X5) | predt(X5))) => ~? [X6] : (anywhere(X6) => (~predf(X6) => predt(X6)))) & (! [X7] : (~room(X7) => (predz(X7) | ~predl(X7))) => ! [X8] : (room(X8) => (predk(X8) => preds(X8)))) & (! [X9] : (room(X9) => (predn(X9) | ~predm(X9))) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X12] : (room(X12) => (~predh(X12) | predp(X12))) => predy(mary)) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : (room(X14) => (~predh(X14) | predp(X14)))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 47]
49. ! [X0] : (room(X0) => (predd(X0) => predl(X0))) & ~! [X2] : (room(X2) => (predm(X2) <~> predb(X2))) & predt(mary) & (predh(mary) | predp(mary) | predx(mary)) & ~! [X4] : (room(X4) => ~predt(X4)) & predm(mary) & (~! [X5] : (anywhere(X5) => (~predf(X5) | predt(X5))) => ~? [X6] : (anywhere(X6) => (~predf(X6) => predt(X6)))) & (! [X7] : (~room(X7) => (predz(X7) | ~predl(X7))) => ! [X8] : (room(X8) => (predk(X8) => preds(X8)))) & (! [X9] : (room(X9) => (predn(X9) | ~predm(X9))) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X12] : (room(X12) => (~predh(X12) | predp(X12))) => predy(mary)) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : (room(X14) => (~predh(X14) | predp(X14)))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 48]
50. ! [X0] : (room(X0) => (predd(X0) => predl(X0))) & ~! [X2] : (room(X2) => (predm(X2) <~> predb(X2))) & predt(mary) & (predh(mary) | predp(mary) | predx(mary)) & ~! [X4] : (room(X4) => ~predt(X4)) & predm(mary) & (! [X7] : (~room(X7) => (predz(X7) | ~predl(X7))) => ! [X8] : (room(X8) => (predk(X8) => preds(X8)))) & (! [X9] : (room(X9) => (predn(X9) | ~predm(X9))) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X12] : (room(X12) => (~predh(X12) | predp(X12))) => predy(mary)) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : (room(X14) => (~predh(X14) | predp(X14)))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 49]
51. ! [X0] : (room(X0) => (predd(X0) => predl(X0))) & ~! [X2] : (room(X2) => (predm(X2) <~> predb(X2))) & predt(mary) & (predh(mary) | predp(mary) | predx(mary)) & ~! [X4] : (room(X4) => ~predt(X4)) & predm(mary) & (! [X9] : (room(X9) => (predn(X9) | ~predm(X9))) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X12] : (room(X12) => (~predh(X12) | predp(X12))) => predy(mary)) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : (room(X14) => (~predh(X14) | predp(X14)))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 50]
52. ~! [X2] : (room(X2) => (predm(X2) <~> predb(X2))) & predt(mary) & (predh(mary) | predp(mary) | predx(mary)) & ~! [X4] : (room(X4) => ~predt(X4)) & predm(mary) & (! [X9] : (room(X9) => (predn(X9) | ~predm(X9))) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X12] : (room(X12) => (~predh(X12) | predp(X12))) => predy(mary)) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : (room(X14) => (~predh(X14) | predp(X14)))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 51]
53. ~! [X2] : (room(X2) => (predm(X2) <~> predb(X2))) & predt(mary) & (predh(mary) | predp(mary) | predx(mary)) & ~! [X4] : (room(X4) => ~predt(X4)) & predm(mary) & (! [X9] : (room(X9) => ~predm(X9)) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X12] : (room(X12) => (~predh(X12) | predp(X12))) => predy(mary)) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : (room(X14) => (~predh(X14) | predp(X14)))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 52]
54. ~! [X2] : (room(X2) => (predm(X2) <~> predb(X2))) & predt(mary) & (predh(mary) | predp(mary) | predx(mary)) & ~! [X4] : (room(X4) => ~predt(X4)) & predm(mary) & (! [X9] : (room(X9) => ~predm(X9)) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : (room(X14) => (~predh(X14) | predp(X14)))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 53]
55. ~! [X2] : (room(X2) => (predm(X2) <~> predb(X2))) & predt(mary) & ~! [X4] : (room(X4) => ~predt(X4)) & predm(mary) & (! [X9] : (room(X9) => ~predm(X9)) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : (room(X14) => predp(X14))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 54]
56. ~! [X2] : (room(X2) => (predm(X2) <~> predb(X2))) & predt(mary) & ~! [X4] : (room(X4) => ~predt(X4)) & predm(mary) & (! [X9] : (room(X9) => ~predm(X9)) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & (~! [X13] : (room(X13) => (predj(X13) | ~predg(X13))) => ~! [X14] : ~room(X14)) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 55]
57. ~! [X2] : (room(X2) => (predm(X2) <~> predb(X2))) & predt(mary) & ~! [X4] : (room(X4) => ~predt(X4)) & predm(mary) & (! [X9] : (room(X9) => ~predm(X9)) => predb(mary)) & (! [X10] : (room(X10) => (predg(X10) | ~predd(X10))) <~> ~! [X11] : (anywhere(X11) => (predr(X11) | ~predx(X11)))) & ! [X15] : (room(X15) => mary = X15) & room(mary) [pure predicate removal 56]
129. ? [X2] : ((predm(X2) <=> predb(X2)) & room(X2)) & predt(mary) & ? [X4] : (predt(X4) & room(X4)) & predm(mary) & (predb(mary) | ? [X9] : (predm(X9) & room(X9))) & (! [X10] : ((predg(X10) | ~predd(X10)) | ~room(X10)) <~> ? [X11] : ((~predr(X11) & predx(X11)) & anywhere(X11))) & ! [X15] : (mary = X15 | ~room(X15)) & room(mary) [ennf transformation 57]
130. ? [X2] : ((predm(X2) <=> predb(X2)) & room(X2)) & predt(mary) & ? [X4] : (predt(X4) & room(X4)) & predm(mary) & (predb(mary) | ? [X9] : (predm(X9) & room(X9))) & (! [X10] : (predg(X10) | ~predd(X10) | ~room(X10)) <~> ? [X11] : (~predr(X11) & predx(X11) & anywhere(X11))) & ! [X15] : (mary = X15 | ~room(X15)) & room(mary) [flattening 129]
131. ~predt(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 45]
132. sP0 <=> ! [X10] : (predg(X10) | ~predd(X10) | ~room(X10)) [predicate definition introduction]
133. ? [X2] : ((predm(X2) <=> predb(X2)) & room(X2)) & predt(mary) & ? [X4] : (predt(X4) & room(X4)) & predm(mary) & (predb(mary) | ? [X9] : (predm(X9) & room(X9))) & (sP0 <~> ? [X11] : (~predr(X11) & predx(X11) & anywhere(X11))) & ! [X15] : (mary = X15 | ~room(X15)) & room(mary) [definition folding 130,132]
139. ? [X2] : (((predm(X2) | ~predb(X2)) & (predb(X2) | ~predm(X2))) & room(X2)) & predt(mary) & ? [X4] : (predt(X4) & room(X4)) & predm(mary) & (predb(mary) | ? [X9] : (predm(X9) & room(X9))) & ((! [X11] : (predr(X11) | ~predx(X11) | ~anywhere(X11)) | ~sP0) & (? [X11] : (~predr(X11) & predx(X11) & anywhere(X11)) | sP0)) & ! [X15] : (mary = X15 | ~room(X15)) & room(mary) [nnf transformation 133]
140. ? [X2] : ((predm(X2) | ~predb(X2)) & (predb(X2) | ~predm(X2)) & room(X2)) & predt(mary) & ? [X4] : (predt(X4) & room(X4)) & predm(mary) & (predb(mary) | ? [X9] : (predm(X9) & room(X9))) & (! [X11] : (predr(X11) | ~predx(X11) | ~anywhere(X11)) | ~sP0) & (? [X11] : (~predr(X11) & predx(X11) & anywhere(X11)) | sP0) & ! [X15] : (mary = X15 | ~room(X15)) & room(mary) [flattening 139]
141. ? [X0] : ((predm(X0) | ~predb(X0)) & (predb(X0) | ~predm(X0)) & room(X0)) & predt(mary) & ? [X1] : (predt(X1) & room(X1)) & predm(mary) & (predb(mary) | ? [X2] : (predm(X2) & room(X2))) & (! [X3] : (predr(X3) | ~predx(X3) | ~anywhere(X3)) | ~sP0) & (? [X4] : (~predr(X4) & predx(X4) & anywhere(X4)) | sP0) & ! [X5] : (mary = X5 | ~room(X5)) & room(mary) [rectify 140]
142. ? [X0] : ((predm(X0) | ~predb(X0)) & (predb(X0) | ~predm(X0)) & room(X0)) => ((predm(sK2) | ~predb(sK2)) & (predb(sK2) | ~predm(sK2)) & room(sK2)) [choice axiom]
143. ? [X1] : (predt(X1) & room(X1)) => (predt(sK3) & room(sK3)) [choice axiom]
144. ? [X2] : (predm(X2) & room(X2)) => (predm(sK4) & room(sK4)) [choice axiom]
145. ? [X4] : (~predr(X4) & predx(X4) & anywhere(X4)) => (~predr(sK5) & predx(sK5) & anywhere(sK5)) [choice axiom]
146. ((predm(sK2) | ~predb(sK2)) & (predb(sK2) | ~predm(sK2)) & room(sK2)) & predt(mary) & (predt(sK3) & room(sK3)) & predm(mary) & (predb(mary) | (predm(sK4) & room(sK4))) & (! [X3] : (predr(X3) | ~predx(X3) | ~anywhere(X3)) | ~sP0) & ((~predr(sK5) & predx(sK5) & anywhere(sK5)) | sP0) & ! [X5] : (mary = X5 | ~room(X5)) & room(mary) [skolemisation 141,145,144,143,142]
147. ? [X0] : (mary != X0 & room(X0)) => (mary != sK6 & room(sK6)) [choice axiom]
148. ~predt(mary) | (mary != sK6 & room(sK6)) | ~room(mary) [skolemisation 131,147]
234. room(mary) [cnf transformation 146]
235. ~room(X5) | mary = X5 [cnf transformation 146]
245. predt(mary) [cnf transformation 146]
249. ~predt(mary) | room(sK6) | ~room(mary) [cnf transformation 148]
250. ~predt(mary) | mary != sK6 | ~room(mary) [cnf transformation 148]
313. mary != sK6 | ~room(mary) [subsumption resolution 250,245]
314. mary != sK6 [subsumption resolution 313,234]
315. room(sK6) | ~room(mary) [subsumption resolution 249,245]
316. room(sK6) [subsumption resolution 315,234]
320. mary = sK6 [resolution 235,316]
330. $false [subsumption resolution 320,314]
% SZS output end Proof for 1577779224309647256862295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.352175 |
Adrienne is the only person in the room.
“It is not the case that “Adrienne maintains a large, organic vegetable garden year-round”” if “everyone in the room volunteers for local environmental conservation projects or does not own an extensive assortment of vintage comic book memorabilia” and vice versa.
Adrienne enjoys writing detailed reviews of new and classic board games.
Everyone in the room who neither owns a microscope nor collects vintage vinyl records writes and illustrates their own graphic novels.
It is not the case that “Adrienne maintains a large, organic vegetable garden year-round”.
Everyone anywhere who collects rare minerals creates augmented reality experiences for mobile applications.
Someone in the room collects rare minerals.
Everyone outside the room who does not collect rare minerals has a curated collection of mid-century modern furniture.
Everyone in the room who has a curated collection of mid-century modern furniture hosts a popular podcast about emerging technologies.
Everyone outside the room who hosts a popular podcast about emerging technologies writes and illustrates their own graphic novels.
Everyone in the room who writes and illustrates their own graphic novels collects vintage vinyl records.
Adrienne owns a microscope.
Not everyone in the room travels domestically frequently if they makes intricate hand-cut paper art for exhibitions. | Adrienne maintains a large, organic vegetable garden year-round. | contradiction | room(adrienne)&(![X]:(room(X)=>(X='adrienne')))&
((![X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(volunteers_for_local_environmental_conservation_projects(X))))))<=>(~(maintains_a_large,_organic_vegetable_garden_year-round(adrienne))))&
(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(adrienne))&
(![X]:(room(X)=>(((~((owns_a_microscope(X))|(collects_vintage_vinyl_records(X))))=>(writes_and_illustrates_their_own_graphic_novels(X))))))&
(~(maintains_a_large,_organic_vegetable_garden_year-round(adrienne)))&
(![X]:(anywhere(X)=>(((collects_rare_minerals(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(?[X]:(room(X)&(collects_rare_minerals(X))))&
(![X]:(~room(X)=>(((does_not_collect_rare_minerals(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(~room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))&
(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(collects_vintage_vinyl_records(X))))))&
(owns_a_microscope(adrienne))&
(~![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(travels_domestically_frequently(X)))))) | room(adrienne)&(![X]:(room(X)=>(X='adrienne')))&
maintains_a_large,_organic_vegetable_garden_year-round(adrienne) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 135509233710606383999527
% SZS output start Proof for 135509233710606383999527
48. ~predu(mary) [input p4]
57. predu(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
145. predu(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 57]
241. ~predu(mary) [cnf transformation 48]
246. predu(mary) [cnf transformation 145]
248. 1 <=> predu(mary) [avatar definition]
270. ~1 [avatar split clause 241,248]
271. 1 [avatar split clause 246,248]
272. $false [avatar sat refutation 270,271]
% SZS output end Proof for 135509233710606383999527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.643993 |
Betty is the only person in the room. If "it is not the case that "Betty is richer than Carol"" then "someone who is a creative person is quieter than someone who is richer than David" otherwise "Betty is richer than David". "Betty neither is old nor is a kind calm generous humble person" only if "only one person in the room is not a funny person". If "Betty is quieter than Carol" then "all strong person is calm" otherwise "Betty is quiet". Someone who is brave is older than someone who is patient. Betty is the least old in the room. Carol is quieter than Betty. If someone is older than Douglas then he/she is quieter than Douglas. All kind person is funny. Betty is the least old anywhere. Betty is tall. If someone is a strong person then he/she is a brave person and vice versa. Douglas is quieter than Betty. Betty is richer than Douglas. Betty is richer than David. Only one person in the room is kind. Betty is not a creative kind generous person. Betty is not a happy generous person. Betty is richer than Carol. All strong person is patient. | Douglas is richer than Betty. | contradiction | room(betty)&(![X]:(room(X)=>(X='betty')))&
(((~(richer(carol,betty)))=>(?[X,Y]:((creative(X)&person(X))&(richer(david,Y))&(quieter(X,Y)))))&((~(~(richer(carol,betty))))=>(richer(david,betty))))&
((~((old(betty))|(kind(betty)&calm(betty)&generous(betty)&humble(betty)&person(betty))))=>(((?[X]:(room(X)&~(funny(X)&person(X))))&(![X,Y]:((room(X)&room(Y)&(~(funny(X)&person(X)))&(~(funny(Y)&person(Y))))=>(X=Y))))))&
(((quieter(carol,betty))=>(![X]:(strong(X)=>calm(X))))&((~(quieter(carol,betty)))=>(quiet(betty))))&
(?[X,Y]:((brave(X))&(patient(Y))&(older(X,Y))))&
(![X]:((room(X)&(X!=betty))=>older(betty,X)))&
(quieter(betty,carol))&
((![X]:((older(douglas,X))=>(quieter(douglas,X)))))&
(![X]:(kind(X)=>funny(X)))&
(![X]:((anywhere(X)&(X!=betty))=>older(betty,X)))&
(tall(betty))&
((![X]:((strong(X)&person(X))<=>(brave(X)&person(X)))))&
(quieter(betty,douglas))&
(richer(douglas,betty))&
(richer(david,betty))&
(((?[X]:(room(X)&kind(X)))&(![X,Y]:((room(X)&room(Y)&(kind(X))&(kind(Y)))=>(X=Y)))))&
(~(creative(betty)&kind(betty)&generous(betty)&person(betty)))&
(~(happy(betty)&generous(betty)&person(betty)))&
(richer(carol,betty))&
(![X]:(strong(X)=>patient(X))) | room(betty)&(![X]:(room(X)=>(X='betty')))&
richer(betty,douglas) | [
"b7",
"b42",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 226671644375003299538477
% SZS output start Proof for 226671644375003299538477
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]
57. richer(alice,mary) [input p13]
64. richer(mary,alice) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
81. ! [X0,X1] : ((~richer(X1,X0) | ~richer(X0,X1)) | X0 = X1) [ennf transformation 8]
82. ! [X0,X1] : (~richer(X1,X0) | ~richer(X0,X1) | X0 = X1) [flattening 81]
159. richer(mary,alice) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 64]
178. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 82]
231. mary != alice [cnf transformation 43]
284. richer(alice,mary) [cnf transformation 57]
293. richer(mary,alice) [cnf transformation 159]
418. ~richer(alice,mary) | mary = alice [resolution 178,293]
422. mary = alice [subsumption resolution 418,284]
423. $false [subsumption resolution 422,231]
% SZS output end Proof for 226671644375003299538477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.115803 |
Willie, Jan, Christopher, Rex are the only persons in the room. Everyone in the room is a kind person. Everyone outside the room is a tall person. Rex is the oldest outside the room. It is not the case that “Rex and Christopher are quiet persons”. Rex is a old person. It is not the case that “Rex and Willie are old persons”. Not everyone in the room is a quiet person, is a old person or is quiet. If someone is not tall then he/she is a quiet person. | Willie and Christopher are respectively old and quiet. | contradiction | room(willie)&room(jan)&room(christopher)&room(rex)&(![X]:(room(X)=>(X='willie'|X='jan'|X='christopher'|X='rex')))&
(![X]:(room(X)=>(kind(X)&person(X))))&
(![X]:(~room(X)=>(tall(X)&person(X))))&
(![X]:((~room(X)&(X!=rex))=>older(X,rex)))&
(~(quiet(rex)&person(rex)&quiet(christopher)&person(christopher)))&
(old(rex)&person(rex))&
(~(old(rex)&person(rex)&old(willie)&person(willie)))&
(~![X]:(room(X)=>(((quiet(X)&person(X))|(old(X)&person(X))|(quiet(X))))))&
((![X]:((~tall(X))=>(quiet(X)&person(X))))) | room(willie)&room(jan)&room(christopher)&room(rex)&(![X]:(room(X)=>(X='willie'|X='jan'|X='christopher'|X='rex')))&
(old(willie))&(quiet(christopher)) | [
"p1",
"p2",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1673260220501726854653424
% SZS output start Proof for 1673260220501726854653424
45. ! [X0] : (room(X0) => (person(X0) & kind(X0))) [input p1]
46. ! [X0] : (~room(X0) => (person(X0) & tall(X0))) [input p2]
49. person(alice) & old(alice) [input p5]
50. ~(person(mary) & old(mary) & person(alice) & old(alice)) [input p6]
53. quiet(fred) & old(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
54. ! [X0] : (~room(X0) => person(X0)) [pure predicate removal 46]
56. ! [X0] : (room(X0) => person(X0)) [pure predicate removal 45]
131. ! [X0] : (person(X0) | ~room(X0)) [ennf transformation 56]
132. ! [X0] : (person(X0) | room(X0)) [ennf transformation 54]
136. ~person(mary) | ~old(mary) | ~person(alice) | ~old(alice) [ennf transformation 50]
139. quiet(fred) & old(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 53]
140. quiet(fred) & old(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 139]
229. person(X0) | ~room(X0) [cnf transformation 131]
230. person(X0) | room(X0) [cnf transformation 132]
233. old(alice) [cnf transformation 49]
235. ~person(mary) | ~old(mary) | ~person(alice) | ~old(alice) [cnf transformation 136]
245. old(mary) [cnf transformation 140]
247. person(X0) [subsumption resolution 230,229]
259. ~old(mary) | ~person(alice) | ~old(alice) [subsumption resolution 235,247]
260. ~old(mary) | ~old(alice) [subsumption resolution 259,247]
261. ~old(mary) [subsumption resolution 260,233]
264. $false [subsumption resolution 245,261]
% SZS output end Proof for 1673260220501726854653424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0.000055 |
Janet, Rebecca, Gertrude, Curtis, Danny are the only persons in the room. “At least one person in the room enjoys stand-up paddleboarding, makes homemade pastries or is a craft beer aficionado” unless “Janet has a pet dog”. If “Janet hosts regular workshops on creative writing” then “Janet has a pet dog”. If “it is not the case that “someone in the room has a pet dog”” then “Rebecca enjoys stand-up paddleboarding, has a pet dog and hosts regular workshops on creative writing” otherwise “Rebecca who designs and sews custom cosplay costumes for conventions enjoys stand-up paddleboarding”. Janet who is a client of Costco enjoys stand-up paddleboarding, is a wine connoisseur and has a pet dog. | Rebecca designs and sews custom cosplay costumes for conventions. | entailment | room(janet)&room(rebecca)&room(gertrude)&room(curtis)&room(danny)&(![X]:(room(X)=>(X='janet'|X='rebecca'|X='gertrude'|X='curtis'|X='danny')))&
(~(has_a_pet_dog(janet))=>(((?[X]:(room(X)&((enjoys_stand-up_paddleboarding(X))|(makes_homemade_pastries(X))|(is_a_craft_beer_aficionado(X))))))))&
((hosts_regular_workshops_on_creative_writing(janet))=>(has_a_pet_dog(janet)))&
(((~(?[X]:(room(X)&(has_a_pet_dog(X)))))=>(((enjoys_stand-up_paddleboarding(rebecca))&(has_a_pet_dog(rebecca))&(hosts_regular_workshops_on_creative_writing(rebecca)))))&((~(~(?[X]:(room(X)&(has_a_pet_dog(X))))))=>((designs_and_sews_custom_cosplay_costumes_for_conventions(rebecca))&(enjoys_stand-up_paddleboarding(rebecca)))))&
(((enjoys_stand-up_paddleboarding(janet))=>(composes_and_performs_experimental_electronic_music(rebecca)))&((~(enjoys_stand-up_paddleboarding(janet)))=>(hosts_regular_workshops_on_creative_writing(janet))))&
(~(hosts_regular_workshops_on_creative_writing(janet))=>(((?[X]:(room(X)&is_a_client_of_Costco(X))))))&
(~(is_a_craft_beer_aficionado(janet))=>(((writes_and_illustrates_their_own_graphic_novels(rebecca))|(is_a_wine_connoisseur(rebecca))|(makes_homemade_pastries(rebecca)))))&
((enjoys_salsa_dancing(rebecca))<~>(has_a_pet_dog(rebecca)))&
(has_a_pet_dog(rebecca))&
(hosts_regular_workshops_on_creative_writing(janet))&
(makes_homemade_pastries(janet))&
((writes_and_illustrates_their_own_graphic_novels(janet))&(is_a_craft_beer_aficionado(janet)))&
(((?[X]:(room(X)&is_a_client_of_Costco(X)))))&
(composes_and_performs_experimental_electronic_music(janet))&
((![X]:((writes_and_illustrates_their_own_graphic_novels(X))<=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))&
((is_a_client_of_Costco(janet))&(((enjoys_stand-up_paddleboarding(janet))&(is_a_wine_connoisseur(janet))&(has_a_pet_dog(janet))))) | room(janet)&room(rebecca)&room(gertrude)&room(curtis)&room(danny)&(![X]:(room(X)=>(X='janet'|X='rebecca'|X='gertrude'|X='curtis'|X='danny')))&
designs_and_sews_custom_cosplay_costumes_for_conventions(rebecca) | [
"p0",
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4790515570104245144158583
% SZS output start Proof for 4790515570104245144158583
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]
47. (~~? [X0] : (predc(X0) & room(X0)) => (prede(paul) & predb(paul))) & (~? [X0] : (predc(X0) & room(X0)) => (predk(paul) & predc(paul) & prede(paul))) [input p3]
59. predc(mary) & predh(mary) & prede(mary) & preda(mary) [input p15]
60. ~(predb(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]
61. (~~? [X0] : (predc(X0) & room(X0)) => (prede(paul) & predb(paul))) & (~? [X1] : (predc(X1) & room(X1)) => (predk(paul) & predc(paul) & prede(paul))) [rectify 47]
62. (? [X0] : (predc(X0) & room(X0)) => (prede(paul) & predb(paul))) & (~? [X1] : (predc(X1) & room(X1)) => (predk(paul) & predc(paul) & prede(paul))) [flattening 61]
65. predc(mary) & prede(mary) & preda(mary) [pure predicate removal 59]
66. predc(mary) & prede(mary) [pure predicate removal 65]
73. (? [X0] : (predc(X0) & room(X0)) => predb(paul)) & (~? [X1] : (predc(X1) & room(X1)) => (predk(paul) & predc(paul))) [pure predicate removal 62]
74. predc(mary) [pure predicate removal 66]
149. ! [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]
150. ! [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]
153. (predb(paul) | ! [X0] : (~predc(X0) | ~room(X0))) & ((predk(paul) & predc(paul)) | ? [X1] : (predc(X1) & room(X1))) [ennf transformation 73]
156. ~predb(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 60]
157. ~predb(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 156]
161. ? [X1] : (predc(X1) & room(X1)) => (predc(sK1) & room(sK1)) [choice axiom]
162. (predb(paul) | ! [X0] : (~predc(X0) | ~room(X0))) & ((predk(paul) & predc(paul)) | (predc(sK1) & room(sK1))) [skolemisation 153,161]
168. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
169. ~predb(paul) | (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 157,168]
250. room(mary) [cnf transformation 150]
251. room(paul) [cnf transformation 150]
252. room(fred) [cnf transformation 150]
253. room(alice) [cnf transformation 150]
254. room(john) [cnf transformation 150]
255. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 150]
262. predb(paul) | ~predc(X0) | ~room(X0) [cnf transformation 162]
271. predc(mary) [cnf transformation 74]
272. ~predb(paul) | room(sK4) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
273. ~predb(paul) | mary != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
274. ~predb(paul) | paul != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
275. ~predb(paul) | fred != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
276. ~predb(paul) | alice != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
277. ~predb(paul) | john != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
279. 1 <=> predc(mary) [avatar definition]
281. predc(mary) <- (1) [avatar component clause 279]
293. 4 <=> ! [X0] : (~predc(X0) | ~room(X0)) [avatar definition]
294. ~predc(X0) | ~room(X0) <- (4) [avatar component clause 293]
296. 5 <=> predb(paul) [avatar definition]
299. 4 | 5 [avatar split clause 262,296,293]
333. 1 [avatar split clause 271,279]
334. ~predb(paul) | john != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,254]
335. ~predb(paul) | john != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 334,253]
336. ~predb(paul) | john != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 335,252]
337. ~predb(paul) | john != sK4 | ~room(mary) [subsumption resolution 336,251]
338. ~predb(paul) | john != sK4 [subsumption resolution 337,250]
340. 12 <=> john = sK4 [avatar definition]
342. john != sK4 <- (~12) [avatar component clause 340]
343. ~12 | ~5 [avatar split clause 338,296,340]
344. ~predb(paul) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,254]
345. ~predb(paul) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 344,253]
346. ~predb(paul) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 345,252]
347. ~predb(paul) | alice != sK4 | ~room(mary) [subsumption resolution 346,251]
348. ~predb(paul) | alice != sK4 [subsumption resolution 347,250]
350. 13 <=> alice = sK4 [avatar definition]
352. alice != sK4 <- (~13) [avatar component clause 350]
353. ~13 | ~5 [avatar split clause 348,296,350]
354. ~predb(paul) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,254]
355. ~predb(paul) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 354,253]
356. ~predb(paul) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 355,252]
357. ~predb(paul) | fred != sK4 | ~room(mary) [subsumption resolution 356,251]
358. ~predb(paul) | fred != sK4 [subsumption resolution 357,250]
360. 14 <=> fred = sK4 [avatar definition]
362. fred != sK4 <- (~14) [avatar component clause 360]
363. ~14 | ~5 [avatar split clause 358,296,360]
364. ~predb(paul) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,254]
365. ~predb(paul) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 364,253]
366. ~predb(paul) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 365,252]
367. ~predb(paul) | paul != sK4 | ~room(mary) [subsumption resolution 366,251]
368. ~predb(paul) | paul != sK4 [subsumption resolution 367,250]
370. 15 <=> paul = sK4 [avatar definition]
372. paul != sK4 <- (~15) [avatar component clause 370]
373. ~15 | ~5 [avatar split clause 368,296,370]
374. ~predb(paul) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,254]
375. ~predb(paul) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 374,253]
376. ~predb(paul) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 375,252]
377. ~predb(paul) | mary != sK4 | ~room(mary) [subsumption resolution 376,251]
378. ~predb(paul) | mary != sK4 [subsumption resolution 377,250]
380. 16 <=> mary = sK4 [avatar definition]
382. mary != sK4 <- (~16) [avatar component clause 380]
383. ~16 | ~5 [avatar split clause 378,296,380]
384. ~predb(paul) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,254]
385. ~predb(paul) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 384,253]
386. ~predb(paul) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 385,252]
387. ~predb(paul) | room(sK4) | ~room(mary) [subsumption resolution 386,251]
388. ~predb(paul) | room(sK4) [subsumption resolution 387,250]
390. 17 <=> room(sK4) [avatar definition]
392. room(sK4) <- (17) [avatar component clause 390]
393. 17 | ~5 [avatar split clause 388,296,390]
395. ~room(mary) <- (1, 4) [resolution 294,281]
397. $false <- (1, 4) [subsumption resolution 395,250]
398. ~1 | ~4 [avatar contradiction clause 397]
449. alice = sK4 | fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (17) [resolution 255,392]
471. fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (~13, 17) [subsumption resolution 449,352]
472. paul = sK4 | mary = sK4 | john = sK4 <- (~13, ~14, 17) [subsumption resolution 471,362]
473. mary = sK4 | john = sK4 <- (~13, ~14, ~15, 17) [subsumption resolution 472,372]
474. john = sK4 <- (~13, ~14, ~15, ~16, 17) [subsumption resolution 473,382]
475. $false <- (~12, ~13, ~14, ~15, ~16, 17) [subsumption resolution 474,342]
476. 12 | 13 | 14 | 15 | 16 | ~17 [avatar contradiction clause 475]
477. $false [avatar sat refutation 299,333,343,353,363,373,383,393,398,476]
% SZS output end Proof for 4790515570104245144158583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.611816 |
There is a room.
No one in the room who is old is older than Robert, is quiet and is older than Earl.
Everyone in the room is quiet.
Everyone in the room who is older than Earl is quieter than Toni. | Everyone in the room is a old person or is quieter than Earl or both. | neutral | (there_is_a_room)&
(~?[X]:(room(X)=>(((old(X))=>(((older(robert,X))&(quiet(X))&(older(earl,X))))))))&
(![X]:(room(X)=>(quiet(X))))&
(![X]:(room(X)=>(((older(earl,X))=>(quieter(toni,X))))))&
(![X]:(room(X)=>(old(X))))&
(![X]:(room(X)=>(((old(X)&person(X))<=>(((quiet(X))&(older(robert,X))&(older(earl,X))))))))&
(![X]:(room(X)=>(((quiet(X)&person(X))=>(quiet(X)&old(X)&person(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((old(X)&person(X))|(quieter(earl,X))))) | [] | null | 0.24695 |
Jerry, Mildred, Betty, Maria are the only persons in the room.
If someone practices tai chi then he/she can play the piano and vice versa.
Betty neither enjoys spelunking nor uses contact lenses.
If someone collects historical artifacts related to ancient civilizations then he/she enjoys rooftop gardening.
No one anywhere who is a night owl does not enjoy rooftop gardening.
Everyone in the room does not train for and competes in international triathlons or can play the piano.
Everyone in the room collects historical artifacts related to ancient civilizations if they does not train for and competes in international triathlons.
Jerry does not enjoy trail running.
Everyone in the room who does not make homemade pastries creates bespoke furniture pieces from reclaimed wood.
Betty is a night owl.
Jerry enjoys rooftop gardening.
Everyone anywhere creates bespoke furniture pieces from reclaimed wood only if they trains for and competes in international triathlons.
It is not the case that “Jerry practices tai chi”. | Jerry creates bespoke furniture pieces from reclaimed wood. | contradiction | room(jerry)&room(mildred)&room(betty)&room(maria)&(![X]:(room(X)=>(X='jerry'|X='mildred'|X='betty'|X='maria')))&
((![X]:((practices_tai_chi(X))<=>(can_play_the_piano(X)))))&
(~((enjoys_spelunking(betty))|(uses_contact_lenses(betty))))&
((![X]:((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(enjoys_rooftop_gardening(X)))))&
(~?[X]:(anywhere(X)=>(((is_a_night_owl(X))=>(does_not_enjoy_rooftop_gardening(X))))))&
(![X]:(room(X)=>(((can_play_the_piano(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))&
(![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))&
(does_not_enjoy_trail_running(jerry))&
(![X]:(room(X)=>(((does_not_make_homemade_pastries(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(is_a_night_owl(betty))&
(enjoys_rooftop_gardening(jerry))&
(trains_for_and_competes_in_international_triathlons(mildred))&
(![X]:(anywhere(X)=>(((trains_for_and_competes_in_international_triathlons(X))<=(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
((((is_an_avid_hiker(jerry))&(enjoys_stargazing(jerry))))&(enjoys_skydiving(jerry)))&
(![X]:(room(X)=>(((owns_an_Android_phone(X))<=(makes_homemade_pastries(X))))))&
(![X]:(room(X)=>(((owns_an_Android_phone(X))=>(is_an_avid_hiker(X))))))&
(~(practices_tai_chi(jerry)))&
(![X]:(room(X)=>(((does_not_build_model_airplanes(X))|(is_not_an_avid_hiker(X))))))&
(can_play_the_piano(mildred))&
(![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))<=(is_not_a_coffee_connoisseur(X))))))&
(((?[X]:(room(X)&does_enjoy_trail_running(X)))))&
(![X]:(room(X)=>(((uses_contact_lenses(X))=>(trains_for_and_competes_in_international_triathlons(X))))))&
(![X]:(anywhere(X)=>(((does_not_play_the_drums(X))|(does_not_make_homemade_pastries(X))))))&
(![X]:(anywhere(X)=>(((does_not_make_homemade_pastries(X))=>(collects_first_edition_books(X))))))&
(enjoys_stand-up_paddleboarding(jerry))&
((![X]:((mentors_a_youth_basketball_team_on_weekends(X))<=>(((is_a_chess_master_who_participates_in_national_tournaments(X))<~>(enjoys_stargazing(X))))))) | room(jerry)&room(mildred)&room(betty)&room(maria)&(![X]:(room(X)=>(X='jerry'|X='mildred'|X='betty'|X='maria')))&
creates_bespoke_furniture_pieces_from_reclaimed_wood(jerry) | [
"b4",
"p0",
"p1",
"p5",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8459448252240325779830396
% SZS output start Proof for 8459448252240325779830396
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] : (predn(X0) <=> predb(X0)) [input p1]
49. ! [X0] : (room(X0) => (~preda(X0) | predb(X0))) [input p5]
56. ! [X0] : (anywhere(X0) => (predz(X0) => preda(X0))) [input p12]
60. ~predn(mary) [input p16]
70. predz(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
71. ! [X0] : (predb(X0) => predn(X0)) [unused predicate definition removal 45]
163. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
164. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 163]
165. ! [X0] : (predn(X0) | ~predb(X0)) [ennf transformation 71]
167. ! [X0] : ((~preda(X0) | predb(X0)) | ~room(X0)) [ennf transformation 49]
168. ! [X0] : (~preda(X0) | predb(X0) | ~room(X0)) [flattening 167]
169. ! [X0] : ((preda(X0) | ~predz(X0)) | ~anywhere(X0)) [ennf transformation 56]
170. ! [X0] : (preda(X0) | ~predz(X0) | ~anywhere(X0)) [flattening 169]
171. predz(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 70]
172. predz(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 171]
176. anywhere(X0) [cnf transformation 5]
257. room(mary) [cnf transformation 164]
262. ~predb(X0) | predn(X0) [cnf transformation 165]
264. ~preda(X0) | predb(X0) | ~room(X0) [cnf transformation 168]
267. preda(X0) | ~predz(X0) | ~anywhere(X0) [cnf transformation 170]
268. ~predn(mary) [cnf transformation 60]
277. predz(mary) [cnf transformation 172]
278. ~predz(X0) | preda(X0) [subsumption resolution 267,176]
280. preda(mary) [resolution 278,277]
282. predb(mary) | ~room(mary) [resolution 280,264]
283. predb(mary) [subsumption resolution 282,257]
284. predn(mary) [resolution 283,262]
285. $false [subsumption resolution 284,268]
% SZS output end Proof for 8459448252240325779830396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Joseph, Diane, Denver are the only persons in the room.
If someone hosts a popular podcast about emerging technologies then he/she plays eSports competitively or is an amateur astronomer who builds and uses custom telescopes or both.
Not everyone in the room is a night owl if they practices calligraphy and is a client of Costco.
Joseph does not practice archery.
Everyone in the room is an amateur astronomer who builds and uses custom telescopes if they plays eSports competitively.
Joseph is a wine connoisseur.
Not everyone in the room plays eSports competitively.
Not everyone in the room is a coffee connoisseur if and only if they does not create bespoke furniture pieces from reclaimed wood or is a coffee connoisseur or both.
It is not the case that “Joseph is an amateur astronomer who builds and uses custom telescopes”.
Only one person outside the room does not host a popular podcast about emerging technologies.
Everyone in the room hosts a popular podcast about emerging technologies, is a client of Costco and creates large-scale murals for public art installations if they collects classic novels, is a night owl and collects first edition books.
Someone in the room is not a coffee connoisseur.
Everyone in the room practices archery only if they does not enjoy making ceramics.
Everyone in the room who hosts a popular podcast about emerging technologies is a Linux enthusiast, does not enjoy making ceramics and does not practice archery.
More than one person in the room hosts a popular podcast about emerging technologies. | Denver is a Linux enthusiast. | entailment | room(joseph)&room(diane)&room(denver)&(![X]:(room(X)=>(X='joseph'|X='diane'|X='denver')))&
((![X]:((hosts_a_popular_podcast_about_emerging_technologies(X))=>(((plays_eSports_competitively(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))))&
(~![X]:(room(X)=>(((((practices_calligraphy(X))&(is_a_client_of_Costco(X))))=>(is_a_night_owl(X))))))&
(does_not_practice_archery(joseph))&
(![X]:(room(X)=>(((plays_eSports_competitively(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))&
(is_a_wine_connoisseur(joseph))&
(~![X]:(room(X)=>(plays_eSports_competitively(X))))&
(~![X]:(room(X)=>(((is_a_coffee_connoisseur(X))<=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(is_a_coffee_connoisseur(X))))))))&
(~(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(joseph)))&
(((?[X]:(~room(X)&does_not_host_a_popular_podcast_about_emerging_technologies(X)))&(![X,Y]:((~room(X)&~room(Y)&(does_not_host_a_popular_podcast_about_emerging_technologies(X))&(does_not_host_a_popular_podcast_about_emerging_technologies(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((((collects_classic_novels(X))&(is_a_night_owl(X))&(collects_first_edition_books(X))))=>(((hosts_a_popular_podcast_about_emerging_technologies(X))&(is_a_client_of_Costco(X))&(creates_large-scale_murals_for_public_art_installations(X))))))))&
(?[X]:(room(X)&(is_not_a_coffee_connoisseur(X))))&
(![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))<=(practices_archery(X))))))&
(is_a_coffee_connoisseur(joseph))&
(((creates_large-scale_murals_for_public_art_installations(joseph))&(collects_first_edition_books(joseph))))&
(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(((is_a_Linux_enthusiast(X))&(does_not_enjoy_making_ceramics(X))&(does_not_practice_archery(X))))))))&
(![X]:(room(X)=>(((enjoys_snowboarding(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(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)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(practices_calligraphy(X))))))&
(practices_calligraphy(joseph))&
(![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(is_a_client_of_Costco(X))))))&
(is_a_Linux_enthusiast(joseph))&
((enjoys_snowboarding(joseph))&(is_a_coffee_connoisseur(joseph))) | room(joseph)&room(diane)&room(denver)&(![X]:(room(X)=>(X='joseph'|X='diane'|X='denver')))&
is_a_Linux_enthusiast(denver) | [
"p0",
"p1",
"p4",
"p8",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 611733175124956190637705
% SZS output start Proof for 611733175124956190637705
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
45. ! [X0] : (predp(X0) => (predo(X0) | preda(X0))) [input p1]
48. ! [X0] : (room(X0) => (preda(X0) => predo(X0))) [input p4]
52. ~predo(mary) [input p8]
59. ! [X0] : (room(X0) => (predp(X0) => (~prede(X0) & ~predd(X0) & predg(X0)))) [input p15]
61. ? [X0,X1] : (X0 != X1 & predp(X1) & predp(X0) & room(X1) & room(X0)) [input p17]
67. ~(predg(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
69. ! [X0] : (room(X0) => (predp(X0) => (~prede(X0) & predg(X0)))) [pure predicate removal 59]
78. ! [X0] : (room(X0) => (predp(X0) => predg(X0))) [pure predicate removal 69]
156. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
157. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 156]
158. ! [X0] : ((predo(X0) | preda(X0)) | ~predp(X0)) [ennf transformation 45]
159. ! [X0] : (predo(X0) | preda(X0) | ~predp(X0)) [flattening 158]
161. ! [X0] : ((predo(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 48]
162. ! [X0] : (predo(X0) | ~preda(X0) | ~room(X0)) [flattening 161]
167. ! [X0] : ((predg(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 78]
168. ! [X0] : (predg(X0) | ~predp(X0) | ~room(X0)) [flattening 167]
171. ~predg(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 67]
172. ~predg(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 171]
186. ? [X0,X1] : (X0 != X1 & predp(X1) & predp(X0) & room(X1) & room(X0)) => (sK5 != sK6 & predp(sK6) & predp(sK5) & room(sK6) & room(sK5)) [choice axiom]
187. sK5 != sK6 & predp(sK6) & predp(sK5) & room(sK6) & room(sK5) [skolemisation 61,186]
188. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom]
189. ~predg(fred) | (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 172,188]
270. room(mary) [cnf transformation 157]
271. room(paul) [cnf transformation 157]
272. room(fred) [cnf transformation 157]
273. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 157]
274. ~predp(X0) | preda(X0) | predo(X0) [cnf transformation 159]
276. ~preda(X0) | predo(X0) | ~room(X0) [cnf transformation 162]
283. ~predo(mary) [cnf transformation 52]
290. ~predp(X0) | predg(X0) | ~room(X0) [cnf transformation 168]
292. room(sK5) [cnf transformation 187]
293. room(sK6) [cnf transformation 187]
294. predp(sK5) [cnf transformation 187]
295. predp(sK6) [cnf transformation 187]
296. sK5 != sK6 [cnf transformation 187]
300. ~predg(fred) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189]
301. ~predg(fred) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189]
302. ~predg(fred) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189]
303. ~predg(fred) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189]
307. ~predg(fred) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 303,272]
308. ~predg(fred) | fred != sK7 | ~room(mary) [subsumption resolution 307,271]
309. ~predg(fred) | fred != sK7 [subsumption resolution 308,270]
311. 1 <=> fred = sK7 [avatar definition]
313. fred != sK7 <- (~1) [avatar component clause 311]
315. 2 <=> predg(fred) [avatar definition]
317. ~predg(fred) <- (~2) [avatar component clause 315]
318. ~1 | ~2 [avatar split clause 309,315,311]
319. ~predg(fred) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 302,272]
320. ~predg(fred) | paul != sK7 | ~room(mary) [subsumption resolution 319,271]
321. ~predg(fred) | paul != sK7 [subsumption resolution 320,270]
323. 3 <=> paul = sK7 [avatar definition]
325. paul != sK7 <- (~3) [avatar component clause 323]
326. ~3 | ~2 [avatar split clause 321,315,323]
327. ~predg(fred) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 301,272]
328. ~predg(fred) | mary != sK7 | ~room(mary) [subsumption resolution 327,271]
329. ~predg(fred) | mary != sK7 [subsumption resolution 328,270]
331. 4 <=> mary = sK7 [avatar definition]
334. ~4 | ~2 [avatar split clause 329,315,331]
335. ~predg(fred) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 300,272]
336. ~predg(fred) | room(sK7) | ~room(mary) [subsumption resolution 335,271]
337. ~predg(fred) | room(sK7) [subsumption resolution 336,270]
339. 5 <=> room(sK7) [avatar definition]
341. room(sK7) <- (5) [avatar component clause 339]
342. 5 | ~2 [avatar split clause 337,315,339]
343. preda(sK5) | predo(sK5) [resolution 274,294]
344. preda(sK6) | predo(sK6) [resolution 274,295]
346. 6 <=> predo(sK5) [avatar definition]
348. predo(sK5) <- (6) [avatar component clause 346]
350. 7 <=> preda(sK5) [avatar definition]
352. preda(sK5) <- (7) [avatar component clause 350]
353. 6 | 7 [avatar split clause 343,350,346]
355. 8 <=> predo(sK6) [avatar definition]
357. predo(sK6) <- (8) [avatar component clause 355]
359. 9 <=> preda(sK6) [avatar definition]
361. preda(sK6) <- (9) [avatar component clause 359]
362. 8 | 9 [avatar split clause 344,359,355]
363. predg(sK5) | ~room(sK5) [resolution 290,294]
364. predg(sK6) | ~room(sK6) [resolution 290,295]
365. predg(sK5) [subsumption resolution 363,292]
366. predg(sK6) [subsumption resolution 364,293]
412. paul = sK5 | mary = sK5 | fred = sK5 [resolution 273,292]
413. paul = sK6 | mary = sK6 | fred = sK6 [resolution 273,293]
467. 22 <=> fred = sK5 [avatar definition]
469. fred = sK5 <- (22) [avatar component clause 467]
471. 23 <=> mary = sK5 [avatar definition]
473. mary = sK5 <- (23) [avatar component clause 471]
475. 24 <=> paul = sK5 [avatar definition]
478. 22 | 23 | 24 [avatar split clause 412,475,471,467]
480. 25 <=> fred = sK6 [avatar definition]
482. fred = sK6 <- (25) [avatar component clause 480]
484. 26 <=> mary = sK6 [avatar definition]
486. mary = sK6 <- (26) [avatar component clause 484]
488. 27 <=> paul = sK6 [avatar definition]
490. paul = sK6 <- (27) [avatar component clause 488]
491. 25 | 26 | 27 [avatar split clause 413,488,484,480]
492. predg(fred) <- (25) [backward demodulation 366,482]
497. $false <- (~2, 25) [subsumption resolution 492,317]
498. 2 | ~25 [avatar contradiction clause 497]
515. predo(mary) <- (8, 26) [backward demodulation 357,486]
519. $false <- (8, 26) [subsumption resolution 515,283]
520. ~8 | ~26 [avatar contradiction clause 519]
524. predo(mary) <- (6, 23) [backward demodulation 348,473]
527. $false <- (6, 23) [subsumption resolution 524,283]
528. ~6 | ~23 [avatar contradiction clause 527]
535. preda(mary) <- (9, 26) [forward demodulation 361,486]
554. predo(mary) | ~room(mary) <- (9, 26) [resolution 535,276]
555. ~room(mary) <- (9, 26) [subsumption resolution 554,283]
556. $false <- (9, 26) [subsumption resolution 555,270]
557. ~9 | ~26 [avatar contradiction clause 556]
568. paul != sK5 <- (27) [forward demodulation 296,490]
569. ~24 | ~27 [avatar split clause 568,488,475]
570. predg(fred) <- (22) [backward demodulation 365,469]
574. 2 | ~22 [avatar split clause 570,467,315]
575. paul = sK7 | mary = sK7 | fred = sK7 <- (5) [resolution 341,273]
576. mary = sK7 | fred = sK7 <- (~3, 5) [subsumption resolution 575,325]
580. mary = sK7 <- (~1, ~3, 5) [subsumption resolution 576,313]
581. 4 | 1 | 3 | ~5 [avatar split clause 580,339,323,311,331]
587. preda(mary) <- (7, 23) [forward demodulation 352,473]
604. predo(mary) | ~room(mary) <- (7, 23) [resolution 587,276]
605. ~room(mary) <- (7, 23) [subsumption resolution 604,283]
606. $false <- (7, 23) [subsumption resolution 605,270]
607. ~7 | ~23 [avatar contradiction clause 606]
608. $false [avatar sat refutation 318,326,334,342,353,362,478,491,498,520,528,557,569,574,581,607]
% SZS output end Proof for 611733175124956190637705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.018963 |
Earl, Jeffrey, Anthony, Amy are the only persons in the room.
“Anthony is funny” if “Earl is strong or is funny or both” and vice versa.
Everyone in the room is not strong.
Everyone in the room is funny.
All strong persons are funny.
Anthony either is funny or is strong but not both.
Jeffrey is funny.
Anthony is not a funny person.
Earl dreamt that “more than one person in the room is not funny”. | Earl is strong. | contradiction | room(earl)&room(jeffrey)&room(anthony)&room(amy)&(![X]:(room(X)=>(X='earl'|X='jeffrey'|X='anthony'|X='amy')))&
((((strong(earl))|(funny(earl))))<=>(funny(anthony)))&
(![X]:(room(X)=>(~strong(X))))&
(![X]:(room(X)=>(funny(X))))&
(![X]:(strong(X)=>funny(X)))&
(((funny(anthony))<~>(strong(anthony))))&
(funny(jeffrey))&
(~(funny(anthony)&person(anthony)))&
((earl_dream=>((?[X,Y]:(room(X)&room(Y)&(~funny(X)&~funny(Y))&(X!=Y)))))) | room(earl)&room(jeffrey)&room(anthony)&room(amy)&(![X]:(room(X)=>(X='earl'|X='jeffrey'|X='anthony'|X='amy')))&
strong(earl) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 8037645304788420166103352
% SZS output start Proof for 8037645304788420166103352
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
46. ! [X0] : (room(X0) => ~strong(X0)) [input p2]
53. strong(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
128. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
129. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 128]
130. ! [X0] : (~strong(X0) | ~room(X0)) [ennf transformation 46]
133. strong(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 53]
134. strong(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133]
219. room(mary) [cnf transformation 129]
227. ~strong(X0) | ~room(X0) [cnf transformation 130]
238. strong(mary) [cnf transformation 134]
244. 2 <=> strong(mary) [avatar definition]
246. strong(mary) <- (2) [avatar component clause 244]
257. 2 [avatar split clause 238,244]
258. ~room(mary) <- (2) [resolution 227,246]
259. $false <- (2) [subsumption resolution 258,219]
260. ~2 [avatar contradiction clause 259]
261. $false [avatar sat refutation 257,260]
% SZS output end Proof for 8037645304788420166103352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.197627 |
Patricia, Elaine, Timothy are the only persons in the room. Either “everyone in the room own a television or does not practice zumba” or “Elaine volunteers for local environmental conservation projects and competes in national level swimming championships” but not both. If “everyone in the room does not participate in long-distance cycling events across the country or collects antique clocks” then “Patricia does not practice zumba”. “Everyone in the room is a tea enthusiast if they participates in long-distance cycling events across the country” unless “someone anywhere is a tea enthusiast”. “Timothy own a television” only if “at least one person in the room collects antique clocks”. If “everyone in the room uses an ios phone or does not participate in long-distance cycling events across the country” then “if someone collects antique clocks then he/she competes in national level swimming championships and vice versa”. Everyone in the room participates in long-distance cycling events across the country if they uses an ios phone. Elaine does not own a television. Patricia collects luxury watches. Timothy own a television and collects antique clocks. Elaine is dedicated to sustainable living and zero-waste practices. Timothy is a tea enthusiast. Patricia collects antique clocks. Everyone outside the room either practices zumba or is dedicated to sustainable living and zero-waste practices but not both only if they collects antique clocks. Everyone in the room is a tea enthusiast if they participates in long-distance cycling events across the country. If someone collects antique clocks then he/she competes in national level swimming championships and vice versa. Someone anywhere is a tea enthusiast. | Elaine volunteers for local environmental conservation projects. | neutral | room(patricia)&room(elaine)&room(timothy)&(![X]:(room(X)=>(X='patricia'|X='elaine'|X='timothy')))&
((![X]:(room(X)=>(((does_not_practice_zumba(X))|(own_a_television(X))))))<~>(((volunteers_for_local_environmental_conservation_projects(elaine))&(competes_in_national_level_swimming_championships(elaine)))))&
((![X]:(room(X)=>(((collects_antique_clocks(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))=>(does_not_practice_zumba(patricia)))&
(~(?[X]:(anywhere(X)&(is_a_tea_enthusiast(X))))=>(![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_a_tea_enthusiast(X)))))))&
((own_a_television(timothy))=>(((?[X]:(room(X)&collects_antique_clocks(X))))))&
((![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(uses_an_ios_phone(X))))))=>((![X]:((collects_antique_clocks(X))<=>(competes_in_national_level_swimming_championships(X))))))&
(![X]:(room(X)=>(((uses_an_ios_phone(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))&
(does_not_own_a_television(elaine))&
(collects_luxury_watches(patricia))&
(((own_a_television(timothy))&(collects_antique_clocks(timothy))))&
(is_dedicated_to_sustainable_living_and_zero-waste_practices(elaine))&
(is_a_tea_enthusiast(timothy))&
(collects_antique_clocks(patricia))&
(![X]:(~room(X)=>(((collects_antique_clocks(X))<=(((practices_zumba(X))<~>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))))&
(![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_a_tea_enthusiast(X))))))&
((![X]:((collects_antique_clocks(X))<=>(competes_in_national_level_swimming_championships(X)))))&
(?[X]:(anywhere(X)&(is_a_tea_enthusiast(X)))) | room(patricia)&room(elaine)&room(timothy)&(![X]:(room(X)=>(X='patricia'|X='elaine'|X='timothy')))&
volunteers_for_local_environmental_conservation_projects(elaine) | [] | null | 0.016609 |
There is a room. If “everyone in the room does not play eSports competitively or cannot play the flute” then “everyone anywhere plays as a goalkeeper for a local amateur soccer team if they is a dedicated advocate for digital privacy and encryption and is not dedicated to sustainable living and zero-waste practices”. If “everyone in the room does not own a high-end gaming PC with custom-built components or enjoys cross-country skiing” then “everyone in the room has a vast collection of first-edition science fiction novels if they enjoys cross-country skiing”. “Everyone in the room is not a chess master who participates in national tournaments if they is a night owl, is a professional photographer specializing in portrait photography and is an avid hiker” unless “someone in the room is a chess master who participates in national tournaments”. If “everyone in the room is not a night owl or drives a hybrid car” then “at least one person in the room cannot play the flute”. If “not everyone in the room uses a Windows laptop” then “everyone in the room does not drive a hybrid car if they uses a Windows laptop”. “Everyone in the room is not an avid hiker or is dedicated to sustainable living and zero-waste practices” only if “everyone in the room is not an avid hiker if and only if they owns a high-end gaming PC with custom-built components”. “At least one person in the room does not have a curated collection of mid-century modern furniture” only if “at least one person in the room enjoys cross-country skiing”. If “everyone in the room is a night owl” then “everyone in the room does not use an ios phone”. Everyone in the room plays as a goalkeeper for a local amateur soccer team if they is not dedicated to sustainable living and zero-waste practices. Everyone in the room does not use an ios phone. If someone enjoys cross-country skiing then he/she enjoys virtual reality gaming. Everyone outside the room plays eSports competitively or practices kickboxing or both if and only if they can play the flute. | Everyone outside the room is not allergic to anything. | neutral | (there_is_a_room)&
((![X]:(room(X)=>(((cannot_play_the_flute(X))|(does_not_play_eSports_competitively(X))))))=>(![X]:(anywhere(X)=>(((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))&
((![X]:(room(X)=>(((enjoys_cross-country_skiing(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))&
(~(?[X]:(room(X)&(is_a_chess_master_who_participates_in_national_tournaments(X))))=>(![X]:(room(X)=>(((((is_a_night_owl(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(is_an_avid_hiker(X))))=>(is_not_a_chess_master_who_participates_in_national_tournaments(X)))))))&
((![X]:(room(X)=>(((drives_a_hybrid_car(X))|(is_not_a_night_owl(X))))))=>(((?[X]:(room(X)&cannot_play_the_flute(X))))))&
((~![X]:(room(X)=>(uses_a_Windows_laptop(X))))=>(![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(does_not_drive_a_hybrid_car(X)))))))&
((![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(is_not_an_avid_hiker(X))))))=>(![X]:(room(X)=>(((is_not_an_avid_hiker(X))<=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))&
((((?[X]:(room(X)&does_not_have_a_curated_collection_of_mid-century_modern_furniture(X)))))=>(((?[X]:(room(X)&enjoys_cross-country_skiing(X))))))&
((![X]:(room(X)=>(is_a_night_owl(X))))=>(![X]:(room(X)=>(does_not_use_an_ios_phone(X)))))&
(![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(![X]:(room(X)=>(does_not_use_an_ios_phone(X))))&
((![X]:((enjoys_cross-country_skiing(X))=>(enjoys_virtual_reality_gaming(X)))))&
(![X]:(~room(X)=>(((((plays_eSports_competitively(X))|(practices_kickboxing(X))))<=>(can_play_the_flute(X))))))&
(![X]:(room(X)=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))&
(![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))&
(![X]:(room(X)=>(((drives_a_hybrid_car(X))|(is_not_a_night_owl(X))))))&
(![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(~room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))&
(![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(cannot_play_the_flute(X))))))))&
(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))&
((![X]:((uses_an_ios_phone(X))=>(((is_an_avid_hiker(X))&(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))&
(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(uses_an_ios_phone(X))))))&
(![X]:(room(X)=>(((uses_an_ios_phone(X))=>(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))&
(~![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))&
(![X]:(room(X)=>(((((is_a_professional_photographer_specializing_in_portrait_photography(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))=>(is_not_an_avid_hiker(X))))))&
(![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))&
(![X]:(anywhere(X)=>(((is_allergic_to_anything(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(is_not_allergic_to_anything(X))) | [] | null | 0.219448 |
Rachel is the only person in the room. If everyone in the room collects historical artifacts related to ancient civilizations or is not a craft beer aficionado then at least one person in the room hosts a popular podcast about emerging technologies otherwise everyone in the room who practices kickboxing practices pilates or is a craft beer aficionado or both. If no one outside the room collects historical artifacts related to ancient civilizations or does not collect rare and antique scientific instruments then everyone in the room is an enthusiastic bird watcher who travels for rare sightings or is not an enthusiastic bird watcher who travels for rare sightings. If Rachel practices kickboxing then Rachel is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings or is not a craft beer aficionado if everyone in the room practices pilates or does not collect historical artifacts related to ancient civilizations and vice versa. Rachel is a skilled home brewer experimenting with craft beer recipes. At least one person in the room owns a telescope. It is not the case that Rachel practices digital art or is an enthusiastic bird watcher who travels for rare sightings or both. Everyone in the room collects comic books if they is a skilled home brewer experimenting with craft beer recipes and vice versa. Everyone in the room practices kickboxing or does not practice pilates. Rachel owns a telescope or is a craft beer aficionado or both. Everyone in the room who neither is a craft beer aficionado nor practices digital art is an enthusiastic bird watcher who travels for rare sightings or collects comic books or both. | Rachel collects historical artifacts related to ancient civilizations. | neutral | room(rachel)&(![X]:(room(X)=>(X='rachel')))&
(((![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))=>(((?[X]:(room(X)&hosts_a_popular_podcast_about_emerging_technologies(X))))))&((~(![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X)))))))=>(![X]:(room(X)=>(((practices_kickboxing(X))=>(((practices_pilates(X))|(is_a_craft_beer_aficionado(X))))))))))&
((~?[X]:(~room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))=>(![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))&
((practices_kickboxing(rachel))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(rachel)))&
((![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(practices_pilates(X))))))<=>(![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))&
(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(rachel))&
(((?[X]:(room(X)&owns_a_telescope(X)))))&
(~(((practices_digital_art(rachel))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(rachel)))))&
(![X]:(room(X)=>(((collects_comic_books(X))<=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))&
(![X]:(room(X)=>(((does_not_practice_pilates(X))|(practices_kickboxing(X))))))&
(((owns_a_telescope(rachel))|(is_a_craft_beer_aficionado(rachel))))&
(![X]:(room(X)=>(((~((is_a_craft_beer_aficionado(X))|(practices_digital_art(X))))=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(collects_comic_books(X)))))))) | room(rachel)&(![X]:(room(X)=>(X='rachel')))&
collects_historical_artifacts_related_to_ancient_civilizations(rachel) | [] | null | 0.057874 |
Elroy, Joseph, Elizabeth, Lavinia, Kristi are the only persons in the room. Everyone in the room neither maintains a personal blog focused on cybersecurity tips nor is a night owl if they maintains a personal blog focused on cybersecurity tips and enjoys kayaking and exploring remote waterways and vice versa. At least one person in the room maintains a personal blog focused on cybersecurity tips. | Not everyone in the room enjoys kayaking and exploring remote waterways. | entailment | room(elroy)&room(joseph)&room(elizabeth)&room(lavinia)&room(kristi)&(![X]:(room(X)=>(X='elroy'|X='joseph'|X='elizabeth'|X='lavinia'|X='kristi')))&
((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(elroy))<~>(plays_eSports_competitively(joseph)))&
((is_a_night_owl(lavinia))<~>(enjoys_kayaking_and_exploring_remote_waterways(elroy)))&
((![X]:(~room(X)=>(((does_not_play_the_violin(X))|(is_a_night_owl(X))))))=>(![X]:(room(X)=>(((~((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_a_night_owl(X))))<=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(enjoys_kayaking_and_exploring_remote_waterways(X)))))))))&
(does_not_play_the_violin(elroy))&
(![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<=>(works_on_fridays(X))))))&
(does_not_play_the_violin(lavinia))&
(![X]:(room(X)=>(((plays_eSports_competitively(X))=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(plays_eSports_competitively(X))))))))&
(![X]:(room(X)=>(((~((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_a_night_owl(X))))<=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))))))))&
(![X]:(room(X)=>(((plays_the_violin(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(~((can_play_the_guitar(joseph))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(joseph))))&
(plays_eSports_competitively(elroy))&
(![X]:(anywhere(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(works_on_fridays(X))))))&
(plays_eSports_competitively(elizabeth))&
(~((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(elroy))|(can_play_the_guitar(elroy))))&
(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(elizabeth))<~>(maintains_a_personal_blog_focused_on_cybersecurity_tips(elizabeth))))&
(![X]:(room(X)=>(((does_not_work_on_fridays(X))|(enjoys_kayaking_and_exploring_remote_waterways(X))))))&
(~(plays_the_violin(joseph)))&
(~((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(lavinia))|(is_a_night_owl(lavinia))))&
(is_a_night_owl(joseph))&
(![X]:(room(X)=>(((~((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))=>(enjoys_macrame(X))))))&
(((?[X]:(room(X)&maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))&
(~(enjoys_macrame(elizabeth)))&
(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_play_the_violin(X)))))) | room(elroy)&room(joseph)&room(elizabeth)&room(lavinia)&room(kristi)&(![X]:(room(X)=>(X='elroy'|X='joseph'|X='elizabeth'|X='lavinia'|X='kristi')))&
~![X]:(room(X)=>(enjoys_kayaking_and_exploring_remote_waterways(X))) | [
"p0",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 645184839495708046181947
% SZS output start Proof for 645184839495708046181947
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
52. ! [X0] : (room(X0) => (~(predd(X0) | predi(X0)) <=> (predj(X0) & predi(X0)))) [input p8]
65. ? [X0] : (predi(X0) & room(X0)) [input p21]
68. ~(~! [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]
70. ~(~! [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 68]
144. ! [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]
145. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144]
151. ! [X0] : (((~predd(X0) & ~predi(X0)) <=> (predj(X0) & predi(X0))) | ~room(X0)) [ennf transformation 52]
165. ! [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 70]
166. ! [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 165]
178. ! [X0] : ((((~predd(X0) & ~predi(X0)) | (~predj(X0) | ~predi(X0))) & ((predj(X0) & predi(X0)) | (predd(X0) | predi(X0)))) | ~room(X0)) [nnf transformation 151]
179. ! [X0] : ((((~predd(X0) & ~predi(X0)) | ~predj(X0) | ~predi(X0)) & ((predj(X0) & predi(X0)) | predd(X0) | predi(X0))) | ~room(X0)) [flattening 178]
181. ? [X0] : (predi(X0) & room(X0)) => (predi(sK2) & room(sK2)) [choice axiom]
182. predi(sK2) & room(sK2) [skolemisation 65,181]
183. ? [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]
184. ! [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 166,183]
266. room(mary) [cnf transformation 145]
267. room(paul) [cnf transformation 145]
268. room(fred) [cnf transformation 145]
269. room(alice) [cnf transformation 145]
270. room(john) [cnf transformation 145]
271. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 145]
290. ~predi(X0) | ~predj(X0) | ~predi(X0) | ~room(X0) [cnf transformation 179]
306. room(sK2) [cnf transformation 182]
307. predi(sK2) [cnf transformation 182]
310. predj(X0) | ~room(X0) | room(sK3) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
311. predj(X0) | ~room(X0) | mary != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
312. predj(X0) | ~room(X0) | paul != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
313. predj(X0) | ~room(X0) | fred != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
314. predj(X0) | ~room(X0) | alice != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
315. predj(X0) | ~room(X0) | john != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
317. ~predi(X0) | ~predj(X0) | ~room(X0) [duplicate literal removal 290]
349. 7 <=> ! [X0] : (~predi(X0) | ~room(X0) | ~predj(X0)) [avatar definition]
350. ~predi(X0) | ~room(X0) | ~predj(X0) <- (7) [avatar component clause 349]
376. 7 [avatar split clause 317,349]
391. predj(X0) | ~room(X0) | john != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,270]
392. predj(X0) | ~room(X0) | john != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 391,269]
393. predj(X0) | ~room(X0) | john != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 392,268]
394. predj(X0) | ~room(X0) | john != sK3 | ~room(mary) [subsumption resolution 393,267]
395. predj(X0) | ~room(X0) | john != sK3 [subsumption resolution 394,266]
397. 15 <=> john = sK3 [avatar definition]
399. john != sK3 <- (~15) [avatar component clause 397]
401. 16 <=> ! [X0] : (predj(X0) | ~room(X0)) [avatar definition]
402. ~room(X0) | predj(X0) <- (16) [avatar component clause 401]
403. ~15 | 16 [avatar split clause 395,401,397]
404. predj(X0) | ~room(X0) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 314,270]
405. predj(X0) | ~room(X0) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 404,269]
406. predj(X0) | ~room(X0) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 405,268]
407. predj(X0) | ~room(X0) | alice != sK3 | ~room(mary) [subsumption resolution 406,267]
408. predj(X0) | ~room(X0) | alice != sK3 [subsumption resolution 407,266]
410. 17 <=> alice = sK3 [avatar definition]
412. alice != sK3 <- (~17) [avatar component clause 410]
413. ~17 | 16 [avatar split clause 408,401,410]
414. predj(X0) | ~room(X0) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,270]
415. predj(X0) | ~room(X0) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 414,269]
416. predj(X0) | ~room(X0) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 415,268]
417. predj(X0) | ~room(X0) | fred != sK3 | ~room(mary) [subsumption resolution 416,267]
418. predj(X0) | ~room(X0) | fred != sK3 [subsumption resolution 417,266]
420. 18 <=> fred = sK3 [avatar definition]
422. fred != sK3 <- (~18) [avatar component clause 420]
423. ~18 | 16 [avatar split clause 418,401,420]
424. predj(X0) | ~room(X0) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,270]
425. predj(X0) | ~room(X0) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 424,269]
426. predj(X0) | ~room(X0) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 425,268]
427. predj(X0) | ~room(X0) | paul != sK3 | ~room(mary) [subsumption resolution 426,267]
428. predj(X0) | ~room(X0) | paul != sK3 [subsumption resolution 427,266]
430. 19 <=> paul = sK3 [avatar definition]
432. paul != sK3 <- (~19) [avatar component clause 430]
433. ~19 | 16 [avatar split clause 428,401,430]
434. predj(X0) | ~room(X0) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 311,270]
435. predj(X0) | ~room(X0) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 434,269]
436. predj(X0) | ~room(X0) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 435,268]
437. predj(X0) | ~room(X0) | mary != sK3 | ~room(mary) [subsumption resolution 436,267]
438. predj(X0) | ~room(X0) | mary != sK3 [subsumption resolution 437,266]
440. 20 <=> mary = sK3 [avatar definition]
442. mary != sK3 <- (~20) [avatar component clause 440]
443. ~20 | 16 [avatar split clause 438,401,440]
444. predj(X0) | ~room(X0) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 310,270]
445. predj(X0) | ~room(X0) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 444,269]
446. predj(X0) | ~room(X0) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 445,268]
447. predj(X0) | ~room(X0) | room(sK3) | ~room(mary) [subsumption resolution 446,267]
448. predj(X0) | ~room(X0) | room(sK3) [subsumption resolution 447,266]
450. 21 <=> room(sK3) [avatar definition]
452. room(sK3) <- (21) [avatar component clause 450]
453. 21 | 16 [avatar split clause 448,401,450]
454. ~predi(X0) | ~room(X0) <- (7, 16) [subsumption resolution 350,402]
461. ~room(sK2) <- (7, 16) [resolution 454,307]
462. $false <- (7, 16) [subsumption resolution 461,306]
463. ~7 | ~16 [avatar contradiction clause 462]
637. alice = sK3 | fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (21) [resolution 271,452]
659. fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (~17, 21) [subsumption resolution 637,412]
660. paul = sK3 | mary = sK3 | john = sK3 <- (~17, ~18, 21) [subsumption resolution 659,422]
661. mary = sK3 | john = sK3 <- (~17, ~18, ~19, 21) [subsumption resolution 660,432]
662. john = sK3 <- (~17, ~18, ~19, ~20, 21) [subsumption resolution 661,442]
663. $false <- (~15, ~17, ~18, ~19, ~20, 21) [subsumption resolution 662,399]
664. 15 | 17 | 18 | 19 | 20 | ~21 [avatar contradiction clause 663]
665. $false [avatar sat refutation 376,403,413,423,433,443,453,463,664]
% SZS output end Proof for 645184839495708046181947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.075199 |
Sue, Thomas, Timothy are the only persons in the room.
If someone does not practice and performs acrobatic dance routines then he/she collects foreign coins and vice versa.
Everyone in the room does not practice yoga, is allergic to anything and does not practice pilates.
Timothy does not own a significant collection of rare gemstones and minerals or does not practice yoga or both.
Timothy does not practice and performs acrobatic dance routines.
Everyone in the room does not enjoy macrame.
Everyone in the room neither does not collect rare and antique scientific instruments nor cannot play the piano.
Sue either does not collect historical artifacts related to ancient civilizations or does not collect foreign coins but not both.
Everyone in the room does not have a curated collection of mid-century modern furniture or does not practice and performs acrobatic dance routines or both.
Sue is not right-handed.
Thomas is not a cybersecurity expert or does not own a high-end gaming PC with custom-built components or both.
Sue does not collect foreign coins, does not enjoy rooftop gardening or cannot play the piano.
Everyone in the room either does not know morse code or does not practice and performs acrobatic dance routines but not both. | Sue is allergic to anything. | entailment | room(sue)&room(thomas)&room(timothy)&(![X]:(room(X)=>(X='sue'|X='thomas'|X='timothy')))&
((![X]:((does_not_practice_and_performs_acrobatic_dance_routines(X))<=>(collects_foreign_coins(X)))))&
(![X]:(room(X)=>(((does_not_practice_yoga(X))&(is_allergic_to_anything(X))&(does_not_practice_pilates(X))))))&
(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(timothy))|(does_not_practice_yoga(timothy))))&
(does_not_practice_and_performs_acrobatic_dance_routines(timothy))&
(![X]:(room(X)=>(does_not_enjoy_macrame(X))))&
(![X]:(room(X)=>(~((does_not_collect_rare_and_antique_scientific_instruments(X))|(cannot_play_the_piano(X))))))&
(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(sue))<~>(does_not_collect_foreign_coins(sue))))&
(![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))&
(is_not_right-handed(sue))&
(((is_not_a_cybersecurity_expert(thomas))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(thomas))))&
(((does_not_collect_foreign_coins(sue))|(does_not_enjoy_rooftop_gardening(sue))|(cannot_play_the_piano(sue))))&
(![X]:(room(X)=>(((does_not_know_morse_code(X))<~>(does_not_practice_and_performs_acrobatic_dance_routines(X))))))&
(does_not_enjoy_macrame(thomas))&
(![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_know_morse_code(X))))))&
(does_not_enjoy_stand-up_paddleboarding(sue))&
(![X]:(~room(X)=>(does_not_enjoy_macrame(X))))&
(![X]:(anywhere(X)=>(((((does_not_train_for_and_competes_in_international_triathlons(X))&(does_not_practice_pilates(X))&(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(~((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_practice_pilates(X))))))))&
((![X]:((((is_not_allergic_to_anything(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))<=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))<~>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))))&
(![X]:(room(X)=>(does_not_practice_and_performs_acrobatic_dance_routines(X)))) | room(sue)&room(thomas)&room(timothy)&(![X]:(room(X)=>(X='sue'|X='thomas'|X='timothy')))&
is_allergic_to_anything(sue) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7442066062663383477270153
% SZS output start Proof for 7442066062663383477270153
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
46. ! [X0] : (room(X0) => (~predi(X0) & predg(X0) & ~predy(X0))) [input p2]
64. ~(predg(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
67. ! [X0] : (room(X0) => (predg(X0) & ~predy(X0))) [pure predicate removal 46]
81. ! [X0] : (room(X0) => predg(X0)) [pure predicate removal 67]
153. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
154. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 153]
155. ! [X0] : (predg(X0) | ~room(X0)) [ennf transformation 81]
158. ~predg(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 64]
159. ~predg(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 158]
166. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom]
167. ~predg(mary) | (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 159,166]
248. room(mary) [cnf transformation 154]
249. room(paul) [cnf transformation 154]
250. room(fred) [cnf transformation 154]
251. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 154]
254. ~room(X0) | predg(X0) [cnf transformation 155]
267. ~predg(mary) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167]
268. ~predg(mary) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167]
269. ~predg(mary) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167]
270. ~predg(mary) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167]
281. ~predg(mary) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 270,250]
282. ~predg(mary) | fred != sK0 | ~room(mary) [subsumption resolution 281,249]
283. ~predg(mary) | fred != sK0 [subsumption resolution 282,248]
285. 3 <=> fred = sK0 [avatar definition]
287. fred != sK0 <- (~3) [avatar component clause 285]
289. 4 <=> predg(mary) [avatar definition]
292. ~3 | ~4 [avatar split clause 283,289,285]
293. ~predg(mary) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 269,250]
294. ~predg(mary) | paul != sK0 | ~room(mary) [subsumption resolution 293,249]
295. ~predg(mary) | paul != sK0 [subsumption resolution 294,248]
297. 5 <=> paul = sK0 [avatar definition]
299. paul != sK0 <- (~5) [avatar component clause 297]
300. ~5 | ~4 [avatar split clause 295,289,297]
301. ~predg(mary) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 268,250]
302. ~predg(mary) | mary != sK0 | ~room(mary) [subsumption resolution 301,249]
303. ~predg(mary) | mary != sK0 [subsumption resolution 302,248]
305. 6 <=> mary = sK0 [avatar definition]
307. mary != sK0 <- (~6) [avatar component clause 305]
308. ~6 | ~4 [avatar split clause 303,289,305]
309. ~predg(mary) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 267,250]
310. ~predg(mary) | room(sK0) | ~room(mary) [subsumption resolution 309,249]
311. ~predg(mary) | room(sK0) [subsumption resolution 310,248]
313. 7 <=> room(sK0) [avatar definition]
315. room(sK0) <- (7) [avatar component clause 313]
316. 7 | ~4 [avatar split clause 311,289,313]
319. predg(mary) [resolution 254,248]
324. 4 [avatar split clause 319,289]
409. paul = sK0 | mary = sK0 | fred = sK0 <- (7) [resolution 251,315]
410. mary = sK0 | fred = sK0 <- (~5, 7) [subsumption resolution 409,299]
411. fred = sK0 <- (~5, ~6, 7) [subsumption resolution 410,307]
412. $false <- (~3, ~5, ~6, 7) [subsumption resolution 411,287]
413. 3 | 5 | 6 | ~7 [avatar contradiction clause 412]
414. $false [avatar sat refutation 292,300,308,316,324,413]
% SZS output end Proof for 7442066062663383477270153
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0.563134 |
David, Frank, Cara, Jennifer are the only persons in the room.
If someone owns a smart tv, plays the drums or practices digital art then he/she enjoys deep-sea diving and exploring underwater caves and vice versa.
Frank practices digital art.
Everyone anywhere composes and performs experimental electronic music if and only if they plays the drums.
Everyone in the room collects antique clocks or is not an avid collector of autographed memorabilia from famous musicians.
Cara neither collects antique clocks nor plays the drums.
David practices digital art.
Frank owns a smart tv.
If someone collects antique clocks then he/she practices digital art or is a skilled home brewer experimenting with craft beer recipes or both.
Frank is a skilled home brewer experimenting with craft beer recipes.
Everyone in the room who enjoys wildlife photography enjoys deep-sea diving and exploring underwater caves.
If someone plays the drums then he/she collect rare sneakers or is a skilled home brewer experimenting with craft beer recipes or both and vice versa.
Everyone in the room is a skilled home brewer experimenting with craft beer recipes or does not bake bread at home. | Cara bakes bread at home. | contradiction | room(david)&room(frank)&room(cara)&room(jennifer)&(![X]:(room(X)=>(X='david'|X='frank'|X='cara'|X='jennifer')))&
((![X]:((((owns_a_smart_tv(X))|(plays_the_drums(X))|(practices_digital_art(X))))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))&
(practices_digital_art(frank))&
(![X]:(anywhere(X)=>(((composes_and_performs_experimental_electronic_music(X))<=>(plays_the_drums(X))))))&
(![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(collects_antique_clocks(X))))))&
(~((collects_antique_clocks(cara))|(plays_the_drums(cara))))&
(practices_digital_art(david))&
(owns_a_smart_tv(frank))&
((![X]:((collects_antique_clocks(X))=>(((practices_digital_art(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))&
(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(frank))&
(![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))&
((![X]:((plays_the_drums(X))<=>(((collect_rare_sneakers(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))&
(![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))&
(![X]:(room(X)=>(((owns_a_smart_tv(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))&
(![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(collect_rare_sneakers(X))))))&
(~((plays_the_drums(cara))|(collects_antique_clocks(cara))))&
(![X]:(room(X)=>(((does_not_bake_bread_at_home(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))&
(![X]:(anywhere(X)=>(((plays_the_drums(X))=>(((collect_rare_sneakers(X))&(bakes_bread_at_home(X))))))))&
((![X]:((composes_and_performs_experimental_electronic_music(X))=>(practices_digital_art(X)))))&
(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(plays_the_drums(X))))))&
(![X]:(~room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))&
(collect_rare_sneakers(frank)) | room(david)&room(frank)&room(cara)&room(jennifer)&(![X]:(room(X)=>(X='david'|X='frank'|X='cara'|X='jennifer')))&
bakes_bread_at_home(cara) | [
"p0",
"p5",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 132180847996943873526674
% SZS output start Proof for 132180847996943873526674
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
49. ~(predi(fred) | preda(fred)) [input p5]
55. ! [X0] : (predi(X0) <=> (predc(X0) | prede(X0))) [input p11]
60. ! [X0] : (room(X0) => (predc(X0) | ~predg(X0))) [input p16]
66. predg(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
147. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
148. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147]
152. ~predi(fred) & ~preda(fred) [ennf transformation 49]
158. ! [X0] : ((predc(X0) | ~predg(X0)) | ~room(X0)) [ennf transformation 60]
159. ! [X0] : (predc(X0) | ~predg(X0) | ~room(X0)) [flattening 158]
164. predg(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 66]
165. predg(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 164]
168. ! [X0] : ((predi(X0) | (~predc(X0) & ~prede(X0))) & ((predc(X0) | prede(X0)) | ~predi(X0))) [nnf transformation 55]
169. ! [X0] : ((predi(X0) | (~predc(X0) & ~prede(X0))) & (predc(X0) | prede(X0) | ~predi(X0))) [flattening 168]
253. room(fred) [cnf transformation 148]
260. ~predi(fred) [cnf transformation 152]
265. ~predc(X0) | predi(X0) [cnf transformation 169]
270. ~predg(X0) | predc(X0) | ~room(X0) [cnf transformation 159]
280. predg(fred) [cnf transformation 165]
297. predc(fred) | ~room(fred) [resolution 270,280]
299. predc(fred) [subsumption resolution 297,253]
300. predi(fred) [resolution 299,265]
301. $false [subsumption resolution 300,260]
% SZS output end Proof for 132180847996943873526674
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0.540473 |
There is a room. 'At least one person in the room has a vast collection of first-edition science fiction novels' only if 'everyone in the room can play the harmonica if they plays the violin and vice versa'. If 'no one in the room does not create augmented reality experiences for mobile applications or can play the harmonica' then 'not everyone in the room who can play the harmonica, enjoys salsa dancing or has a vast collection of first-edition science fiction novels can play the harmonica'. If 'everyone in the room does not create augmented reality experiences for mobile applications or does not have a vast collection of first-edition science fiction novels' then 'only one person in the room enjoys salsa dancing, creates augmented reality experiences for mobile applications and watches fantasy movies'. If 'everyone in the room does not play the violin or enjoys salsa dancing' then 'everyone in the room does not play the violin if they enjoys salsa dancing'. Everyone in the room does not enjoy salsa dancing or does not play the violin. Everyone in the room watches fantasy movies, can play the harmonica or enjoys salsa dancing if they does not enjoy salsa dancing. Everyone in the room who enjoys salsa dancing can play the harmonica. At least one person anywhere does not have a vast collection of first-edition science fiction novels. Not everyone in the room who creates augmented reality experiences for mobile applications plays the violin. | Everyone outside the room creates augmented reality experiences for mobile applications. | neutral | (there_is_a_room)&
((((?[X]:(room(X)&has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))=>(![X]:(room(X)=>(((can_play_the_harmonica(X))<=>(plays_the_violin(X)))))))&
((~?[X]:(room(X)=>(((can_play_the_harmonica(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))=>(~![X]:(room(X)=>(((((can_play_the_harmonica(X))|(enjoys_salsa_dancing(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))=>(can_play_the_harmonica(X)))))))&
((![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))=>(((?[X]:(room(X)&((enjoys_salsa_dancing(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))&(watches_fantasy_movies(X)))))&(![X,Y]:((room(X)&room(Y)&(((enjoys_salsa_dancing(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))&(watches_fantasy_movies(X))))&(((enjoys_salsa_dancing(Y))&(creates_augmented_reality_experiences_for_mobile_applications(Y))&(watches_fantasy_movies(Y)))))=>(X=Y))))))&
((![X]:(room(X)=>(((enjoys_salsa_dancing(X))|(does_not_play_the_violin(X))))))=>(![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(does_not_play_the_violin(X)))))))&
(![X]:(room(X)=>(((does_not_play_the_violin(X))|(does_not_enjoy_salsa_dancing(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(((watches_fantasy_movies(X))|(can_play_the_harmonica(X))|(enjoys_salsa_dancing(X))))))))&
(![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(can_play_the_harmonica(X))))))&
(((?[X]:(anywhere(X)&does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X)))))&
(~![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(plays_the_violin(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(creates_augmented_reality_experiences_for_mobile_applications(X))) | [] | null | 0.044776 |
David is the only person in the room. David frequently participates in hackathons and coding competitions. David knows morse code, enjoys deep-sea diving and exploring underwater caves and mentors a youth basketball team on weekends. David does not practice digital art. David enjoys deep-sea diving and exploring underwater caves. David is a client of LVMH. David mentors a youth basketball team on weekends. Only one person outside the room is a client of LVMH. Everyone in the room mentors a youth basketball team on weekends. | David frequently participates in hackathons and coding competitions, enjoys deep-sea diving and exploring underwater caves and is a client of LVMH. | entailment | room(david)&(![X]:(room(X)=>(X='david')))&
(frequently_participates_in_hackathons_and_coding_competitions(david))&
(((knows_morse_code(david))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(david))&(mentors_a_youth_basketball_team_on_weekends(david))))&
(does_not_practice_digital_art(david))&
(enjoys_deep-sea_diving_and_exploring_underwater_caves(david))&
(is_a_client_of_LVMH(david))&
(mentors_a_youth_basketball_team_on_weekends(david))&
(((?[X]:(~room(X)&is_a_client_of_LVMH(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_a_client_of_LVMH(X))&(is_a_client_of_LVMH(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(mentors_a_youth_basketball_team_on_weekends(X)))) | room(david)&(![X]:(room(X)=>(X='david')))&
((frequently_participates_in_hackathons_and_coding_competitions(david))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(david))&(is_a_client_of_LVMH(david))) | [
"p0",
"p1",
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8369516920007979813938591
% SZS output start Proof for 8369516920007979813938591
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
45. prede(mary) [input p1]
46. predc(mary) & preda(mary) & predd(mary) [input p2]
49. predb(mary) [input p5]
53. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
57. preda(mary) & predd(mary) [pure predicate removal 46]
59. preda(mary) [pure predicate removal 57]
132. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
135. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 53]
139. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom]
140. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 135,139]
221. room(mary) [cnf transformation 132]
222. ~room(X0) | mary = X0 [cnf transformation 132]
223. prede(mary) [cnf transformation 45]
224. preda(mary) [cnf transformation 59]
226. predb(mary) [cnf transformation 49]
230. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK1) | ~room(mary) [cnf transformation 140]
231. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [cnf transformation 140]
232. ~preda(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 231,226]
233. ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 232,224]
234. mary != sK1 | ~room(mary) [subsumption resolution 233,223]
235. mary != sK1 [subsumption resolution 234,221]
236. ~preda(mary) | ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 230,226]
237. ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 236,224]
238. room(sK1) | ~room(mary) [subsumption resolution 237,223]
239. room(sK1) [subsumption resolution 238,221]
241. mary = sK1 [resolution 222,239]
242. $false [subsumption resolution 241,235]
% SZS output end Proof for 8369516920007979813938591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0.548615 |
There is a room.
If no one outside the room maintains a personal blog focused on cybersecurity tips or is not dedicated to sustainable living and zero-waste practices then everyone in the room who maintains a personal blog focused on cybersecurity tips can play the harmonica.
If everyone in the room maintains a personal blog focused on cybersecurity tips or is not dedicated to sustainable living and zero-waste practices then everyone in the room who maintains a personal blog focused on cybersecurity tips is dedicated to sustainable living and zero-waste practices.
If everyone in the room maintains a personal blog focused on cybersecurity tips or cannot play the harmonica then everyone anywhere who maintains a personal blog focused on cybersecurity tips is dedicated to sustainable living and zero-waste practices, plays eSports competitively or can play the harmonica.
Everyone in the room can play the harmonica if they is dedicated to sustainable living and zero-waste practices and vice versa.
Everyone in the room is dedicated to sustainable living and zero-waste practices or does not maintain a personal blog focused on cybersecurity tips.
No one outside the room maintains a personal blog focused on cybersecurity tips or is not dedicated to sustainable living and zero-waste practices.
Everyone in the room who is dedicated to sustainable living and zero-waste practices neither maintains a personal blog focused on cybersecurity tips nor plays eSports competitively.
Everyone in the room who neither maintains a personal blog focused on cybersecurity tips nor plays eSports competitively can play the harmonica.
Everyone outside the room who can play the harmonica maintains a personal blog focused on cybersecurity tips.
Everyone in the room maintains a personal blog focused on cybersecurity tips or cannot play the harmonica. | Everyone outside the room plays eSports competitively. | neutral | (there_is_a_room)&
((~?[X]:(~room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))=>(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(can_play_the_harmonica(X)))))))&
((![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))=>(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))&
((![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))=>(![X]:(anywhere(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(plays_eSports_competitively(X))|(can_play_the_harmonica(X)))))))))&
(![X]:(room(X)=>(((can_play_the_harmonica(X))<=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))&
(![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))&
(~?[X]:(~room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(~((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(plays_eSports_competitively(X))))))))&
(![X]:(room(X)=>(((~((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(plays_eSports_competitively(X))))=>(can_play_the_harmonica(X))))))&
(![X]:(~room(X)=>(((can_play_the_harmonica(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(plays_eSports_competitively(X))) | [] | null | 0.235666 |
Emma, David, Harriett are the only persons in the room.
More than one person in the room is richer than Lawrence unless Emma and Harriett are respectively humble and tall.
Someone in the room is a generous creative person or is wise or both only if everyone in the room who is richer than Lawrence is strong.
Someone in the room is richer than Lawrence if someone outside the room is richer than James, is not humble and is quieter than Lawrence.
David is a brave person.
Someone outside the room is richer than James, is not humble and is quieter than Lawrence.
Emma is not a funny patient person.
Not everyone in the room is kind if they is old.
Emma is older than Lawrence, is tall and is not a calm tall strong person.
Everyone in the room who is richer than Lawrence and is older than Lawrence is quieter than Lawrence.
Someone in the room is a quiet person.
Harriett is older than Lawrence.
Emma is richer than Lawrence.
Everyone in the room who is older than Lawrence is a happy quiet person.
Everyone in the room is a creative generous person if they is a happy quiet person.
Everyone outside the room either is richer than Lawrence or is funny but not both if they is a creative generous person. | David and Emma are not a funny quiet tall generous wise persons. | neutral | room(emma)&room(david)&room(harriett)&(![X]:(room(X)=>(X='emma'|X='david'|X='harriett')))&
(~((humble(emma))&(tall(harriett)))=>((?[X,Y]:(room(X)&room(Y)&(richer(lawrence,X)&richer(lawrence,Y))&(X!=Y)))))&
((?[X]:(room(X)&(((generous(X)&creative(X)&person(X))|(wise(X))))))=>(![X]:(room(X)=>(((richer(lawrence,X))=>(strong(X)))))))&
((?[X]:(~room(X)&(((richer(james,X))&(~humble(X))&(quieter(lawrence,X))))))=>(?[X]:(room(X)&(richer(lawrence,X)))))&
(brave(david)&person(david))&
(?[X]:(~room(X)&(((richer(james,X))&(~humble(X))&(quieter(lawrence,X))))))&
(~(funny(emma)&patient(emma)&person(emma)))&
(~![X]:(room(X)=>(((old(X))=>(kind(X))))))&
(((older(lawrence,emma))&(tall(emma))&(~(calm(emma)&tall(emma)&strong(emma)&person(emma)))))&
(![X]:(room(X)=>(((((richer(lawrence,X))&(older(lawrence,X))))=>(quieter(lawrence,X))))))&
(?[X]:(room(X)&(quiet(X)&person(X))))&
(older(lawrence,harriett))&
(richer(lawrence,emma))&
(![X]:(room(X)=>(((older(lawrence,X))=>(happy(X)&quiet(X)&person(X))))))&
(![X]:(room(X)=>(((happy(X)&quiet(X)&person(X))=>(creative(X)&generous(X)&person(X))))))&
(![X]:(~room(X)=>(((creative(X)&generous(X)&person(X))=>(((richer(lawrence,X))<~>(funny(X)))))))) | room(emma)&room(david)&room(harriett)&(![X]:(room(X)=>(X='emma'|X='david'|X='harriett')))&
~(funny(david)&quiet(david)&tall(david)&generous(david)&wise(david)&person(david))&~(funny(emma)&quiet(emma)&tall(emma)&generous(emma)&wise(emma)&person(emma)) | [] | null | 0.037304 |
There is a room.
Everyone in the room does not mentor a youth basketball team on weekends.
Everyone anywhere neither does not have a vast collection of first-edition science fiction novels nor does not host themed dinner parties featuring gourmet home-cooked meals.
Everyone in the room does not mentor a youth basketball team on weekends or is not a Linux enthusiast or both.
Not everyone in the room is not a drone photographer.
Only one person in the room is not a culinary enthusiast who experiments with international cuisines, does not collect foreign coins or is not a Linux enthusiast.
Everyone in the room does not watche fantasy movies, does not collect foreign coins or is not a Linux enthusiast.
Everyone anywhere does not mentor a youth basketball team on weekends, is not a culinary enthusiast who experiments with international cuisines or does not watche fantasy movies.
Everyone outside the room does not mentor a youth basketball team on weekends or is not a culinary enthusiast who experiments with international cuisines or both.
Everyone in the room does not practice kickboxing.
Everyone outside the room does not watche fantasy movies or does not practice kickboxing or both.
If someone either is not a drone photographer or does not have a vast collection of first-edition science fiction novels but not both then he/she does not host themed dinner parties featuring gourmet home-cooked meals, does not watche fantasy movies and does not practice kickboxing and vice versa.
No one in the room is not a culinary enthusiast who experiments with international cuisines, does not have a vast collection of first-edition science fiction novels or does not develop open-source software projects in their free time. | Everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals. | entailment | (there_is_a_room)&
(![X]:(room(X)=>(does_not_mentor_a_youth_basketball_team_on_weekends(X))))&
(![X]:(anywhere(X)=>(~((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(is_not_a_Linux_enthusiast(X))))))&
(~![X]:(room(X)=>(is_not_a_drone_photographer(X))))&
(((?[X]:(room(X)&((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_collect_foreign_coins(X))|(is_not_a_Linux_enthusiast(X)))))&(![X,Y]:((room(X)&room(Y)&(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_collect_foreign_coins(X))|(is_not_a_Linux_enthusiast(X))))&(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(Y))|(does_not_collect_foreign_coins(Y))|(is_not_a_Linux_enthusiast(Y)))))=>(X=Y)))))&
(![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(does_not_collect_foreign_coins(X))|(is_not_a_Linux_enthusiast(X))))))&
(![X]:(anywhere(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_watche_fantasy_movies(X))))))&
(![X]:(~room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(![X]:(room(X)=>(does_not_practice_kickboxing(X))))&
(![X]:(~room(X)=>(((does_not_watche_fantasy_movies(X))|(does_not_practice_kickboxing(X))))))&
((![X]:((((is_not_a_drone_photographer(X))<~>(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))<=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(does_not_watche_fantasy_movies(X))&(does_not_practice_kickboxing(X)))))))&
(~?[X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))) | [
"b4",
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 5647290033454309194537852
% SZS output start Proof for 5647290033454309194537852
5. ! [X0] : anywhere(X0) [input b4]
44. there_is_a_room [input p0]
46. ! [X0] : (anywhere(X0) => ~(~predc(X0) | ~predb(X0))) [input p2]
57. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis]
135. ! [X0] : ((predc(X0) & predb(X0)) | ~anywhere(X0)) [ennf transformation 46]
146. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 57]
157. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK3) & room(sK3)) [choice axiom]
158. (~predc(sK3) & room(sK3)) | ~there_is_a_room [skolemisation 146,157]
159. anywhere(X0) [cnf transformation 5]
240. there_is_a_room [cnf transformation 44]
242. predc(X0) | ~anywhere(X0) [cnf transformation 135]
268. ~predc(sK3) | ~there_is_a_room [cnf transformation 158]
269. predc(X0) [subsumption resolution 242,159]
289. ~there_is_a_room [subsumption resolution 268,269]
290. $false [subsumption resolution 289,240]
% SZS output end Proof for 5647290033454309194537852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.257387 |
Jane, Jeffrey, Lucio, Kenneth, Patricia are the only persons in the room. “It is not the case that “Jane is a happy person or is not generous or both”” only if “Jeffrey is a brave person”. “If someone is a calm person then he/she is a happy person and vice versa” if “everyone in the room is a old person”. “Jeffrey is a old person” only if “Jeffrey is the least quiet in the room”. Lucio is a brave person. Lucio is a patient person. Everyone in the room is a humble person if they is a wise person. Lucio is a strong person or is a funny person or both. Everyone in the room is a old person if they is a humble person. It is not the case that “Jane is a creative person”. Kenneth is humble. Jeffrey is a brave person. Jane is a brave person. Jeffrey is a patient person. Lucio is the quietest in the room. Jeffrey is the least quiet in the room. Jane is wise or is a humble person or both. | Jane is old. | entailment | room(jane)&room(jeffrey)&room(lucio)&room(kenneth)&room(patricia)&(![X]:(room(X)=>(X='jane'|X='jeffrey'|X='lucio'|X='kenneth'|X='patricia')))&
((~(((happy(jane)&person(jane))|(~generous(jane)))))=>(brave(jeffrey)&person(jeffrey)))&
((![X]:(room(X)=>(old(X)&person(X))))=>((![X]:((calm(X)&person(X))<=>(happy(X)&person(X))))))&
((old(jeffrey)&person(jeffrey))=>(![X]:((room(X)&(X!=jeffrey))=>quieter(jeffrey,X))))&
(brave(lucio)&person(lucio))&
(patient(lucio)&person(lucio))&
(![X]:(room(X)=>(((wise(X)&person(X))=>(humble(X)&person(X))))))&
(((strong(lucio)&person(lucio))|(funny(lucio)&person(lucio))))&
(![X]:(room(X)=>(((humble(X)&person(X))=>(old(X)&person(X))))))&
(~(creative(jane)&person(jane)))&
(humble(kenneth))&
(brave(jeffrey)&person(jeffrey))&
(brave(jane)&person(jane))&
(patient(jeffrey)&person(jeffrey))&
(![X]:((room(X)&(X!=lucio))=>quieter(X,lucio)))&
(![X]:((room(X)&(X!=jeffrey))=>quieter(jeffrey,X)))&
(wise(kenneth)&person(kenneth))&
((![X]:((((happy(X)&person(X))<~>(old(X))))=>(~(tall(X)&person(X))))))&
(tall(jane)&person(jane))&
(old(lucio)&person(lucio))&
(curious(kenneth)&person(kenneth))&
(~(tall(lucio)&person(lucio)))&
(~(generous(jane)&person(jane)))&
(((wise(jane))|(humble(jane)&person(jane))))&
(wise(jeffrey)&person(jeffrey))&
(kind(kenneth))&
(![X]:(room(X)=>(((tall(X)&person(X))<=(generous(X)&calm(X)&person(X))))))&
(kind(jeffrey)&person(jeffrey)) | room(jane)&room(jeffrey)&room(lucio)&room(kenneth)&room(patricia)&(![X]:(room(X)=>(X='jane'|X='jeffrey'|X='lucio'|X='kenneth'|X='patricia')))&
old(jane) | [
"p0",
"p6",
"p8",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5998888035273885844793218
% SZS output start Proof for 5998888035273885844793218
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]
50. ! [X0] : (room(X0) => ((person(X0) & wise(X0)) => (person(X0) & humble(X0)))) [input p6]
52. ! [X0] : (room(X0) => ((person(X0) & humble(X0)) => (person(X0) & old(X0)))) [input p8]
56. person(mary) & brave(mary) [input p12]
67. (person(mary) & humble(mary)) | wise(mary) [input p23]
72. ~(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]
83. person(mary) [pure predicate removal 56]
161. ! [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]
162. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 161]
166. ! [X0] : (((person(X0) & humble(X0)) | (~person(X0) | ~wise(X0))) | ~room(X0)) [ennf transformation 50]
167. ! [X0] : ((person(X0) & humble(X0)) | ~person(X0) | ~wise(X0) | ~room(X0)) [flattening 166]
168. ! [X0] : (((person(X0) & old(X0)) | (~person(X0) | ~humble(X0))) | ~room(X0)) [ennf transformation 52]
169. ! [X0] : ((person(X0) & old(X0)) | ~person(X0) | ~humble(X0) | ~room(X0)) [flattening 168]
177. ~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 72]
178. ~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 177]
187. ? [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]
188. ~old(mary) | (john != sK1 & alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 178,187]
269. room(mary) [cnf transformation 162]
270. room(paul) [cnf transformation 162]
271. room(fred) [cnf transformation 162]
272. room(alice) [cnf transformation 162]
273. room(john) [cnf transformation 162]
274. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 162]
286. ~wise(X0) | ~person(X0) | humble(X0) | ~room(X0) [cnf transformation 167]
289. ~humble(X0) | ~person(X0) | old(X0) | ~room(X0) [cnf transformation 169]
293. person(mary) [cnf transformation 83]
308. humble(mary) | wise(mary) [cnf transformation 67]
313. ~old(mary) | room(sK1) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188]
314. ~old(mary) | mary != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188]
315. ~old(mary) | paul != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188]
316. ~old(mary) | fred != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188]
317. ~old(mary) | alice != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188]
318. ~old(mary) | john != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188]
360. 9 <=> wise(mary) [avatar definition]
362. wise(mary) <- (9) [avatar component clause 360]
364. 10 <=> humble(mary) [avatar definition]
366. humble(mary) <- (10) [avatar component clause 364]
367. 9 | 10 [avatar split clause 308,364,360]
370. ~old(mary) | john != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,273]
371. ~old(mary) | john != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 370,272]
372. ~old(mary) | john != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 371,271]
373. ~old(mary) | john != sK1 | ~room(mary) [subsumption resolution 372,270]
374. ~old(mary) | john != sK1 [subsumption resolution 373,269]
376. 11 <=> john = sK1 [avatar definition]
378. john != sK1 <- (~11) [avatar component clause 376]
380. 12 <=> old(mary) [avatar definition]
383. ~11 | ~12 [avatar split clause 374,380,376]
384. ~old(mary) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,273]
385. ~old(mary) | alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 384,272]
386. ~old(mary) | alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 385,271]
387. ~old(mary) | alice != sK1 | ~room(mary) [subsumption resolution 386,270]
388. ~old(mary) | alice != sK1 [subsumption resolution 387,269]
390. 13 <=> alice = sK1 [avatar definition]
392. alice != sK1 <- (~13) [avatar component clause 390]
393. ~13 | ~12 [avatar split clause 388,380,390]
394. ~old(mary) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,273]
395. ~old(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 394,272]
396. ~old(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 395,271]
397. ~old(mary) | fred != sK1 | ~room(mary) [subsumption resolution 396,270]
398. ~old(mary) | fred != sK1 [subsumption resolution 397,269]
400. 14 <=> fred = sK1 [avatar definition]
402. fred != sK1 <- (~14) [avatar component clause 400]
403. ~14 | ~12 [avatar split clause 398,380,400]
404. ~old(mary) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,273]
405. ~old(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 404,272]
406. ~old(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 405,271]
407. ~old(mary) | paul != sK1 | ~room(mary) [subsumption resolution 406,270]
408. ~old(mary) | paul != sK1 [subsumption resolution 407,269]
410. 15 <=> paul = sK1 [avatar definition]
412. paul != sK1 <- (~15) [avatar component clause 410]
413. ~15 | ~12 [avatar split clause 408,380,410]
414. ~old(mary) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 314,273]
415. ~old(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 414,272]
416. ~old(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 415,271]
417. ~old(mary) | mary != sK1 | ~room(mary) [subsumption resolution 416,270]
418. ~old(mary) | mary != sK1 [subsumption resolution 417,269]
420. 16 <=> mary = sK1 [avatar definition]
422. mary != sK1 <- (~16) [avatar component clause 420]
423. ~16 | ~12 [avatar split clause 418,380,420]
424. ~old(mary) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,273]
425. ~old(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 424,272]
426. ~old(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 425,271]
427. ~old(mary) | room(sK1) | ~room(mary) [subsumption resolution 426,270]
428. ~old(mary) | room(sK1) [subsumption resolution 427,269]
430. 17 <=> room(sK1) [avatar definition]
432. room(sK1) <- (17) [avatar component clause 430]
433. 17 | ~12 [avatar split clause 428,380,430]
436. ~person(mary) | humble(mary) | ~room(mary) <- (9) [resolution 286,362]
439. humble(mary) | ~room(mary) <- (9) [subsumption resolution 436,293]
440. humble(mary) <- (9) [subsumption resolution 439,269]
441. 10 | ~9 [avatar split clause 440,360,364]
443. ~person(mary) | old(mary) | ~room(mary) <- (10) [resolution 289,366]
446. old(mary) | ~room(mary) <- (10) [subsumption resolution 443,293]
450. old(mary) <- (10) [subsumption resolution 446,269]
451. 12 | ~10 [avatar split clause 450,364,380]
581. alice = sK1 | fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (17) [resolution 274,432]
603. fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (~13, 17) [subsumption resolution 581,392]
604. paul = sK1 | mary = sK1 | john = sK1 <- (~13, ~14, 17) [subsumption resolution 603,402]
605. mary = sK1 | john = sK1 <- (~13, ~14, ~15, 17) [subsumption resolution 604,412]
606. john = sK1 <- (~13, ~14, ~15, ~16, 17) [subsumption resolution 605,422]
607. $false <- (~11, ~13, ~14, ~15, ~16, 17) [subsumption resolution 606,378]
608. 11 | 13 | 14 | 15 | 16 | ~17 [avatar contradiction clause 607]
609. $false [avatar sat refutation 367,383,393,403,413,423,433,441,451,608]
% SZS output end Proof for 5998888035273885844793218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.570453 |
Jane, Ivan, Michael are the only persons in the room. Michael has lived in exactly three countries. Everyone in the room who has a pet dog either can play the harmonica or collects action figures but not both. Michael has a pet dog. Michael either has lived in exactly three countries or collects action figures but not both. Jane makes intricate hand-cut paper art for exhibitions. Everyone in the room who collects foreign coins has lived in exactly three countries. Michael is a wine connoisseur. Jane collects foreign coins. Everyone in the room can play the harmonica or cannot play the harmonica. Jane collects action figures. Everyone in the room who collects action figures and makes intricate hand-cut paper art for exhibitions owns an Android phone. | Jane owns an Android phone. | entailment | room(jane)&room(ivan)&room(michael)&(![X]:(room(X)=>(X='jane'|X='ivan'|X='michael')))&
(has_lived_in_exactly_three_countries(michael))&
(![X]:(room(X)=>(((has_a_pet_dog(X))=>(((can_play_the_harmonica(X))<~>(collects_action_figures(X))))))))&
(has_a_pet_dog(michael))&
(((has_lived_in_exactly_three_countries(michael))<~>(collects_action_figures(michael))))&
(makes_intricate_hand-cut_paper_art_for_exhibitions(jane))&
(![X]:(room(X)=>(((collects_foreign_coins(X))=>(has_lived_in_exactly_three_countries(X))))))&
(is_a_wine_connoisseur(michael))&
(collects_foreign_coins(jane))&
(![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(can_play_the_harmonica(X))))))&
(![X]:(room(X)=>(((can_play_the_harmonica(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))&
(is_a_night_owl(michael))&
(![X]:(room(X)=>(((owns_a_smart_tv(X))<=(((is_a_wine_connoisseur(X))<~>(has_a_pet_dog(X))))))))&
(?[X]:(room(X)&(((has_lived_in_exactly_three_countries(X))&(can_play_the_harmonica(X))))))&
(![X]:(room(X)=>(((collects_action_figures(X))<=(collects_foreign_coins(X))))))&
(makes_intricate_hand-cut_paper_art_for_exhibitions(ivan))&
(is_a_night_owl(ivan))&
(collects_action_figures(jane))&
(can_play_the_harmonica(michael))&
(![X]:(room(X)=>(((((collects_action_figures(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(owns_an_Android_phone(X))))))&
(owns_an_Android_phone(ivan))&
(![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(collects_vintage_stamps(X)))))) | room(jane)&room(ivan)&room(michael)&(![X]:(room(X)=>(X='jane'|X='ivan'|X='michael')))&
owns_an_Android_phone(jane) | [
"p0",
"p5",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 480825999980670319118680
% SZS output start Proof for 480825999980670319118680
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
49. predi(mary) [input p5]
61. predj(mary) [input p17]
63. ! [X0] : (room(X0) => ((predi(X0) & predj(X0)) => preda(X0))) [input p19]
66. ~(preda(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
144. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
145. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 144]
156. ! [X0] : ((preda(X0) | (~predi(X0) | ~predj(X0))) | ~room(X0)) [ennf transformation 63]
157. ! [X0] : (preda(X0) | ~predi(X0) | ~predj(X0) | ~room(X0)) [flattening 156]
158. ~preda(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66]
159. ~preda(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 158]
165. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom]
166. ~preda(mary) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 159,165]
247. room(mary) [cnf transformation 145]
248. room(paul) [cnf transformation 145]
249. room(fred) [cnf transformation 145]
250. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 145]
257. predi(mary) [cnf transformation 49]
267. predj(mary) [cnf transformation 61]
269. ~predi(X0) | preda(X0) | ~predj(X0) | ~room(X0) [cnf transformation 157]
271. ~preda(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166]
272. ~preda(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166]
273. ~preda(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166]
274. ~preda(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166]
276. ~preda(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 274,249]
277. ~preda(mary) | fred != sK1 | ~room(mary) [subsumption resolution 276,248]
278. ~preda(mary) | fred != sK1 [subsumption resolution 277,247]
280. 1 <=> fred = sK1 [avatar definition]
282. fred != sK1 <- (~1) [avatar component clause 280]
284. 2 <=> preda(mary) [avatar definition]
287. ~1 | ~2 [avatar split clause 278,284,280]
288. ~preda(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 273,249]
289. ~preda(mary) | paul != sK1 | ~room(mary) [subsumption resolution 288,248]
290. ~preda(mary) | paul != sK1 [subsumption resolution 289,247]
292. 3 <=> paul = sK1 [avatar definition]
294. paul != sK1 <- (~3) [avatar component clause 292]
295. ~3 | ~2 [avatar split clause 290,284,292]
296. ~preda(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 272,249]
297. ~preda(mary) | mary != sK1 | ~room(mary) [subsumption resolution 296,248]
298. ~preda(mary) | mary != sK1 [subsumption resolution 297,247]
300. 4 <=> mary = sK1 [avatar definition]
302. mary != sK1 <- (~4) [avatar component clause 300]
303. ~4 | ~2 [avatar split clause 298,284,300]
304. ~preda(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 271,249]
305. ~preda(mary) | room(sK1) | ~room(mary) [subsumption resolution 304,248]
306. ~preda(mary) | room(sK1) [subsumption resolution 305,247]
308. 5 <=> room(sK1) [avatar definition]
310. room(sK1) <- (5) [avatar component clause 308]
311. 5 | ~2 [avatar split clause 306,284,308]
331. preda(mary) | ~predj(mary) | ~room(mary) [resolution 269,257]
349. preda(mary) | ~room(mary) [subsumption resolution 331,267]
350. preda(mary) [subsumption resolution 349,247]
351. 2 [avatar split clause 350,284]
392. paul = sK1 | mary = sK1 | fred = sK1 <- (5) [resolution 250,310]
406. mary = sK1 | fred = sK1 <- (~3, 5) [subsumption resolution 392,294]
407. fred = sK1 <- (~3, ~4, 5) [subsumption resolution 406,302]
408. $false <- (~1, ~3, ~4, 5) [subsumption resolution 407,282]
409. 1 | 3 | 4 | ~5 [avatar contradiction clause 408]
410. $false [avatar sat refutation 287,295,303,311,351,409]
% SZS output end Proof for 480825999980670319118680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0.073538 |
Milo, James, Rosalee are the only persons in the room. “Everyone outside the room is a calm person” if “not everyone in the room is a wise person”. If “everyone in the room is a wise person” then ““Mirrors do not fog permanently in one particular house.” or “Glass rain does not fall on a distant planet.” but not both” otherwise “someone who is not a calm person is poorer than someone who is not dedicated to sustainable living and zero-waste practices”. “Everyone in the room is a wise person” only if “more than one person in the room is a wise person”. “Everyone in the room is not a wise person” only if “all calm persons are kind”. Everyone in the room is not dedicated to sustainable living and zero-waste practices. | James is wise. | neutral | room(milo)&room(james)&room(rosalee)&(![X]:(room(X)=>(X='milo'|X='james'|X='rosalee')))&
((~![X]:(room(X)=>(wise(X)&person(X))))=>(![X]:(~room(X)=>(calm(X)&person(X)))))&
(((![X]:(room(X)=>(wise(X)&person(X))))=>(((Mirrors_do_not_fog_permanently_in_one_particular_house.)<~>(Glass_rain_does_not_fall_on_a_distant_planet.))))&((~(![X]:(room(X)=>(wise(X)&person(X)))))=>(?[X,Y]:((~(calm(X)&person(X)))&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(Y))&(poorer(X,Y))))))&
((![X]:(room(X)=>(wise(X)&person(X))))=>((?[X,Y]:(room(X)&room(Y)&(wise(X)&person(X)&wise(Y)&person(Y))&(X!=Y)))))&
((![X]:(room(X)=>(~(wise(X)&person(X)))))=>(![X]:(calm(X)=>kind(X))))&
(![X]:(room(X)=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(wise(X)&person(X)&wise(Y)&person(Y))&(X!=Y))))&
(![X]:(kind(X)=>calm(X)))&
(![X]:(~room(X)=>(kind(X)&person(X))))&
(![X]:(room(X)=>(((calm(X)&person(X))|(calm(X))|(wise(X)&person(X))))))&
(![X]:(room(X)=>(((wise(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))) | room(milo)&room(james)&room(rosalee)&(![X]:(room(X)=>(X='milo'|X='james'|X='rosalee')))&
wise(james) | [] | null | 0.193343 |
Jean, Karen are the only persons in the room.
'Someone outside the room either collect rare sneakers or collects vintage stamps but not both' if 'Jean collects vintage stamps'.
Jean who enjoys making ceramics enjoys making ceramics and owns a high-end gaming PC with custom-built components.
Jean writes a travel blog.
Karen writes a travel blog, does not collect rare sneakers and collects vintage stamps.
Karen drives a hybrid car.
It is not the case that 'Karen collect rare sneakers'.
Someone in the room enjoys making ceramics.
More than one person outside the room collect rare sneakers.
Someone outside the room drives a hybrid car.
Jean enjoys making ceramics.
Someone in the room collects vintage stamps.
More than one person anywhere drives a hybrid car.
Karen writes a travel blog. | Jean collects vintage stamps. | neutral | room(jean)&room(karen)&(![X]:(room(X)=>(X='jean'|X='karen')))&
((collects_vintage_stamps(jean))=>(?[X]:(~room(X)&(((collect_rare_sneakers(X))<~>(collects_vintage_stamps(X)))))))&
((enjoys_making_ceramics(jean))&(((enjoys_making_ceramics(jean))&(owns_a_high-end_gaming_PC_with_custom-built_components(jean)))))&
(writes_a_travel_blog(jean))&
(((writes_a_travel_blog(karen))&(does_not_collect_rare_sneakers(karen))&(collects_vintage_stamps(karen))))&
(drives_a_hybrid_car(karen))&
(~(collect_rare_sneakers(karen)))&
(?[X]:(room(X)&(enjoys_making_ceramics(X))))&
((?[X,Y]:(~room(X)&~room(Y)&(collect_rare_sneakers(X)&collect_rare_sneakers(Y))&(X!=Y))))&
(?[X]:(~room(X)&(drives_a_hybrid_car(X))))&
(enjoys_making_ceramics(jean))&
(?[X]:(room(X)&(collects_vintage_stamps(X))))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(drives_a_hybrid_car(X)&drives_a_hybrid_car(Y))&(X!=Y))))&
(writes_a_travel_blog(karen)) | room(jean)&room(karen)&(![X]:(room(X)=>(X='jean'|X='karen')))&
collects_vintage_stamps(jean) | [] | null | 0.139226 |
Rosario is the only person in the room.
Rosario who is a client of Costco collects classic novels.
Rosario who collects classic novels collects action figures.
Someone in the room is a certified scuba diver with advanced underwater photography skills.
Someone in the room practices kickboxing.
Someone outside the room collects classic novels.
If someone is an enthusiastic bird watcher who travels for rare sightings then he/she uses a Windows laptop and vice versa.
Someone in the room enjoys wildlife photography.
Only one person in the room practices kickboxing.
If someone uses a Windows laptop then he/she writes and illustrates their own graphic novels and vice versa.
If someone collects modern art then he/she writes and illustrates their own graphic novels and vice versa.
It is not the case that “it is not the case that “someone in the room collects vintage vinyl records””.
If someone is a client of Costco, practices urban gardening and uses a Windows laptop then he/she collects vintage vinyl records and vice versa. | Rosario collects modern art. | entailment | room(rosario)&(![X]:(room(X)=>(X='rosario')))&
((is_a_client_of_Costco(rosario))&(collects_classic_novels(rosario)))&
((collects_classic_novels(rosario))&(collects_action_figures(rosario)))&
(?[X]:(room(X)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))&
(?[X]:(room(X)&(practices_kickboxing(X))))&
(?[X]:(~room(X)&(collects_classic_novels(X))))&
((![X]:((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=>(uses_a_Windows_laptop(X)))))&
(?[X]:(room(X)&(enjoys_wildlife_photography(X))))&
(((?[X]:(room(X)&practices_kickboxing(X)))&(![X,Y]:((room(X)&room(Y)&(practices_kickboxing(X))&(practices_kickboxing(Y)))=>(X=Y)))))&
(?[X]:(room(X)&(collects_luxury_watches(X))))&
(~(?[X]:(room(X)&(plays_video_games(X)))))&
((enjoys_wildlife_photography(rosario))&(is_a_certified_yoga_instructor_teaching_classes_weekly(rosario)))&
(~(?[X]:(~room(X)&(writes_and_illustrates_their_own_graphic_novels(X)))))&
(?[X]:(room(X)&(collects_foreign_coins(X))))&
((![X]:((uses_a_Windows_laptop(X))<=>(writes_and_illustrates_their_own_graphic_novels(X)))))&
((![X]:((practices_urban_gardening(X))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))&
(((?[X]:(room(X)&writes_poetry(X)))&(![X,Y]:((room(X)&room(Y)&(writes_poetry(X))&(writes_poetry(Y)))=>(X=Y)))))&
((![X]:((collects_modern_art(X))<=>(writes_and_illustrates_their_own_graphic_novels(X)))))&
((![X]:((((owns_a_high-end_gaming_PC_with_custom-built_components(X))&(collects_vintage_vinyl_records(X))&(practices_kickboxing(X))))<=>(collects_historical_artifacts_related_to_ancient_civilizations(X)))))&
((![X]:((collects_historical_artifacts_related_to_ancient_civilizations(X))<=>(enjoys_wildlife_photography(X)))))&
(~(~(?[X]:(room(X)&(collects_vintage_vinyl_records(X))))))&
((![X]:((((is_a_client_of_Costco(X))&(practices_urban_gardening(X))&(uses_a_Windows_laptop(X))))<=>(collects_vintage_vinyl_records(X))))) | room(rosario)&(![X]:(room(X)=>(X='rosario')))&
collects_modern_art(rosario) | [
"p0",
"p14",
"p17",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2101301789608044834470231
% SZS output start Proof for 2101301789608044834470231
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
58. ! [X0] : (prede(X0) <=> predl(X0)) [input p14]
61. ! [X0] : (predr(X0) <=> predl(X0)) [input p17]
64. ~~? [X0] : (preda(X0) & room(X0)) [input p20]
65. ! [X0] : ((prede(X0) & predd(X0) & predx(X0)) <=> preda(X0)) [input p21]
66. ~(predr(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
69. ? [X0] : (preda(X0) & room(X0)) [flattening 64]
70. ! [X0] : (predl(X0) => predr(X0)) [unused predicate definition removal 61]
152. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
158. ! [X0] : (predr(X0) | ~predl(X0)) [ennf transformation 70]
159. ~predr(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 66]
175. ! [X0] : ((prede(X0) | ~predl(X0)) & (predl(X0) | ~prede(X0))) [nnf transformation 58]
182. ? [X0] : (preda(X0) & room(X0)) => (preda(sK8) & room(sK8)) [choice axiom]
183. preda(sK8) & room(sK8) [skolemisation 69,182]
184. ! [X0] : (((prede(X0) & predd(X0) & predx(X0)) | ~preda(X0)) & (preda(X0) | (~prede(X0) | ~predd(X0) | ~predx(X0)))) [nnf transformation 65]
185. ! [X0] : (((prede(X0) & predd(X0) & predx(X0)) | ~preda(X0)) & (preda(X0) | ~prede(X0) | ~predd(X0) | ~predx(X0))) [flattening 184]
186. ? [X0] : (mary != X0 & room(X0)) => (mary != sK9 & room(sK9)) [choice axiom]
187. ~predr(mary) | (mary != sK9 & room(sK9)) | ~room(mary) [skolemisation 159,186]
268. room(mary) [cnf transformation 152]
269. ~room(X0) | mary = X0 [cnf transformation 152]
284. ~prede(X0) | predl(X0) [cnf transformation 175]
291. ~predl(X0) | predr(X0) [cnf transformation 158]
298. room(sK8) [cnf transformation 183]
299. preda(sK8) [cnf transformation 183]
303. ~preda(X0) | prede(X0) [cnf transformation 185]
304. ~predr(mary) | room(sK9) | ~room(mary) [cnf transformation 187]
305. ~predr(mary) | mary != sK9 | ~room(mary) [cnf transformation 187]
306. ~predr(mary) | mary != sK9 [subsumption resolution 305,268]
308. 1 <=> mary = sK9 [avatar definition]
310. mary != sK9 <- (~1) [avatar component clause 308]
312. 2 <=> predr(mary) [avatar definition]
315. ~1 | ~2 [avatar split clause 306,312,308]
316. ~predr(mary) | room(sK9) [subsumption resolution 304,268]
318. 3 <=> room(sK9) [avatar definition]
320. room(sK9) <- (3) [avatar component clause 318]
321. 3 | ~2 [avatar split clause 316,312,318]
334. prede(sK8) [resolution 303,299]
343. mary = sK8 [resolution 269,298]
359. prede(mary) [backward demodulation 334,343]
364. predl(mary) [resolution 359,284]
371. predr(mary) [resolution 364,291]
376. 2 [avatar split clause 371,312]
377. mary = sK9 <- (3) [resolution 320,269]
378. $false <- (~1, 3) [subsumption resolution 377,310]
379. 1 | ~3 [avatar contradiction clause 378]
380. $false [avatar sat refutation 315,321,376,379]
% SZS output end Proof for 2101301789608044834470231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.669062 |
Jay is the only person in the room. If not everyone in the room does not practice yoga or enjoys snowboarding then everyone in the room enjoys making ceramics or is not a professional photographer specializing in portrait photography. If everyone in the room enjoys making ceramics or is not a professional photographer specializing in portrait photography then at least one person in the room builds model airplanes. If everyone in the room does not create bespoke furniture pieces from reclaimed wood or enjoys virtual reality gaming then Jay who is a client of LVMH does not enjoy virtual reality gaming, streams on Twitch or enjoys watercolor painting. Not everyone in the room does not enjoy watercolor painting if they does not create bespoke furniture pieces from reclaimed wood unless Jay does not collect vintage stamps. | Jay is a member of a local theater group specializing in improv. | neutral | room(jay)&(![X]:(room(X)=>(X='jay')))&
(((~![X]:(room(X)=>(((enjoys_snowboarding(X))|(does_not_practice_yoga(X))))))=>(![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(enjoys_making_ceramics(X)))))))&
((![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(enjoys_making_ceramics(X))))))=>(((?[X]:(room(X)&builds_model_airplanes(X)))))))&
((![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>((is_a_client_of_LVMH(jay))&(((does_not_enjoy_virtual_reality_gaming(jay))|(streams_on_Twitch(jay))|(enjoys_watercolor_painting(jay))))))&
(~(does_not_collect_vintage_stamps(jay))=>(~![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(does_not_enjoy_watercolor_painting(X)))))))&
(((enjoys_virtual_reality_gaming(jay))=>(![X]:(~room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_own_a_telescope(X)))))))&
((![X]:(~room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_own_a_telescope(X))))))=>(![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(creates_large-scale_murals_for_public_art_installations(X))))))))&
((~?[X]:(room(X)=>(((owns_a_telescope(X))|(does_not_enjoy_snowboarding(X))))))=>(~(~(enjoys_making_ceramics(jay)))))&
((creates_bespoke_furniture_pieces_from_reclaimed_wood(jay))=>(collects_rare_minerals(jay)))&
((enjoys_deep-sea_diving_and_exploring_underwater_caves(jay))<~>(![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))))&
((~![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_collect_rare_minerals(X))))))=>(((?[X]:(room(X)&enjoys_snowboarding(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_snowboarding(X))&(enjoys_snowboarding(Y)))=>(X=Y))))))&
(((is_a_coffee_connoisseur(jay))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(jay)))&
((is_a_member_of_a_local_theater_group_specializing_in_improv(jay))=>(collects_comic_books(jay))))&
(((?[X]:(~room(X)&is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))&
(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))<=(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))&
(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(jay))&
(![X]:(~room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(owns_a_telescope(X))))))))&
((streams_on_Twitch(jay))&(does_not_enjoy_making_ceramics(jay)))&
(enjoys_snowboarding(jay))&
(collects_comic_books(jay))&
(![X]:(room(X)=>(((((has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(does_not_own_a_telescope(X))&(does_not_practice_yoga(X))))=>(enjoys_spelunking(X))))))&
(designs_and_sews_custom_cosplay_costumes_for_conventions(jay))&
(![X]:(~room(X)=>(((collects_comic_books(X))<=>(does_not_practice_urban_gardening(X))))))&
(![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<=(does_not_practice_urban_gardening(X))))))&
(~(~((bakes_bread_at_home(jay))|(has_a_vast_collection_of_first-edition_science_fiction_novels(jay)))))&
(![X]:(room(X)=>(((does_not_own_a_telescope(X))|(builds_model_airplanes(X))))))&
(![X]:(anywhere(X)=>(((enjoys_watercolor_painting(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
(?[X]:(room(X)&(does_not_practice_yoga(X)))) | room(jay)&(![X]:(room(X)=>(X='jay')))&
is_a_member_of_a_local_theater_group_specializing_in_improv(jay) | [] | null | 0.11628 |
Larry, Henry, Edna, Gloria, William are the only persons in the room. If “everyone in the room does not build model airplanes or does not enjoy landscape photography” then “everyone anywhere who does not build model airplanes collects action figures”. If “everyone outside the room practices tai chi or is not a drone photographer” then “Gloria is not a drone photographer”. If “everyone in the room practices tai chi or does not practice zumba” then “no one in the room who does not collect vintage stamps is a professional photographer specializing in portrait photography”. “Larry hosts a popular podcast about emerging technologies” only if “Edna does not practice zumba”. Everyone in the room owns a high-end gaming PC with custom-built components if they does not host a popular podcast about emerging technologies. Gloria is a professional photographer specializing in portrait photography. Everyone in the room practices zumba. If someone owns a high-end gaming PC with custom-built components then he/she is a professional photographer specializing in portrait photography and vice versa. | Larry is a professional photographer specializing in portrait photography. | entailment | room(larry)&room(henry)&room(edna)&room(gloria)&room(william)&(![X]:(room(X)=>(X='larry'|X='henry'|X='edna'|X='gloria'|X='william')))&
((![X]:(room(X)=>(((does_not_enjoy_landscape_photography(X))|(does_not_build_model_airplanes(X))))))=>(![X]:(anywhere(X)=>(((does_not_build_model_airplanes(X))=>(collects_action_figures(X)))))))&
((![X]:(~room(X)=>(((is_not_a_drone_photographer(X))|(practices_tai_chi(X))))))=>(is_not_a_drone_photographer(gloria)))&
((![X]:(room(X)=>(((does_not_practice_zumba(X))|(practices_tai_chi(X))))))=>(~?[X]:(room(X)=>(((does_not_collect_vintage_stamps(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))&
((hosts_a_popular_podcast_about_emerging_technologies(larry))=>(does_not_practice_zumba(edna)))&
(![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))&
(is_a_professional_photographer_specializing_in_portrait_photography(gloria))&
(~(owns_a_high-end_gaming_PC_with_custom-built_components(edna)))&
(?[X]:(room(X)&(((practices_tai_chi(X))<~>(collects_vintage_stamps(X))))))&
(![X]:(room(X)=>(practices_zumba(X))))&
(![X]:(~room(X)=>(does_not_practice_zumba(X))))&
((?[X,Y]:(room(X)&room(Y)&(does_not_host_a_popular_podcast_about_emerging_technologies(X)&does_not_host_a_popular_podcast_about_emerging_technologies(Y))&(X!=Y))))&
((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))) | room(larry)&room(henry)&room(edna)&room(gloria)&room(william)&(![X]:(room(X)=>(X='larry'|X='henry'|X='edna'|X='gloria'|X='william')))&
is_a_professional_photographer_specializing_in_portrait_photography(larry) | [
"p0",
"p4",
"p5",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7400756628024699178158807
% SZS output start Proof for 7400756628024699178158807
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. preda(mary) => ~predh(fred) [input p4]
49. ! [X0] : (room(X0) => (~preda(X0) => predd(X0))) [input p5]
53. ! [X0] : (room(X0) => predh(X0)) [input p9]
56. ! [X0] : (predd(X0) <=> predk(X0)) [input p12]
57. ~(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]
133. ! [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]
134. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133]
139. ~predh(fred) | ~preda(mary) [ennf transformation 48]
140. ! [X0] : ((predd(X0) | preda(X0)) | ~room(X0)) [ennf transformation 49]
141. ! [X0] : (predd(X0) | preda(X0) | ~room(X0)) [flattening 140]
142. ! [X0] : (predh(X0) | ~room(X0)) [ennf transformation 53]
144. ~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 57]
145. ~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 144]
161. ! [X0] : ((predd(X0) | ~predk(X0)) & (predk(X0) | ~predd(X0))) [nnf transformation 56]
162. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom]
163. ~predk(mary) | (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 145,162]
244. room(mary) [cnf transformation 134]
245. room(paul) [cnf transformation 134]
246. room(fred) [cnf transformation 134]
247. room(alice) [cnf transformation 134]
248. room(john) [cnf transformation 134]
249. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 134]
259. ~predh(fred) | ~preda(mary) [cnf transformation 139]
260. ~room(X0) | preda(X0) | predd(X0) [cnf transformation 141]
266. ~room(X0) | predh(X0) [cnf transformation 142]
273. ~predd(X0) | predk(X0) [cnf transformation 161]
275. ~predk(mary) | room(sK6) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
276. ~predk(mary) | mary != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
277. ~predk(mary) | paul != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
278. ~predk(mary) | fred != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
279. ~predk(mary) | alice != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
280. ~predk(mary) | john != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
332. 12 <=> preda(mary) [avatar definition]
334. ~preda(mary) <- (~12) [avatar component clause 332]
336. 13 <=> predh(fred) [avatar definition]
339. ~12 | ~13 [avatar split clause 259,336,332]
350. ~predk(mary) | john != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,248]
351. ~predk(mary) | john != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 350,247]
352. ~predk(mary) | john != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 351,246]
353. ~predk(mary) | john != sK6 | ~room(mary) [subsumption resolution 352,245]
354. ~predk(mary) | john != sK6 [subsumption resolution 353,244]
356. 16 <=> john = sK6 [avatar definition]
358. john != sK6 <- (~16) [avatar component clause 356]
360. 17 <=> predk(mary) [avatar definition]
363. ~16 | ~17 [avatar split clause 354,360,356]
364. ~predk(mary) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,248]
365. ~predk(mary) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 364,247]
366. ~predk(mary) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 365,246]
367. ~predk(mary) | alice != sK6 | ~room(mary) [subsumption resolution 366,245]
368. ~predk(mary) | alice != sK6 [subsumption resolution 367,244]
370. 18 <=> alice = sK6 [avatar definition]
372. alice != sK6 <- (~18) [avatar component clause 370]
373. ~18 | ~17 [avatar split clause 368,360,370]
374. ~predk(mary) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,248]
375. ~predk(mary) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 374,247]
376. ~predk(mary) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 375,246]
377. ~predk(mary) | fred != sK6 | ~room(mary) [subsumption resolution 376,245]
378. ~predk(mary) | fred != sK6 [subsumption resolution 377,244]
380. 19 <=> fred = sK6 [avatar definition]
382. fred != sK6 <- (~19) [avatar component clause 380]
383. ~19 | ~17 [avatar split clause 378,360,380]
384. ~predk(mary) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,248]
385. ~predk(mary) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 384,247]
386. ~predk(mary) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 385,246]
387. ~predk(mary) | paul != sK6 | ~room(mary) [subsumption resolution 386,245]
388. ~predk(mary) | paul != sK6 [subsumption resolution 387,244]
390. 20 <=> paul = sK6 [avatar definition]
392. paul != sK6 <- (~20) [avatar component clause 390]
393. ~20 | ~17 [avatar split clause 388,360,390]
394. ~predk(mary) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,248]
395. ~predk(mary) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 394,247]
396. ~predk(mary) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 395,246]
397. ~predk(mary) | mary != sK6 | ~room(mary) [subsumption resolution 396,245]
398. ~predk(mary) | mary != sK6 [subsumption resolution 397,244]
400. 21 <=> mary = sK6 [avatar definition]
402. mary != sK6 <- (~21) [avatar component clause 400]
403. ~21 | ~17 [avatar split clause 398,360,400]
404. ~predk(mary) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,248]
405. ~predk(mary) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 404,247]
406. ~predk(mary) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 405,246]
407. ~predk(mary) | room(sK6) | ~room(mary) [subsumption resolution 406,245]
408. ~predk(mary) | room(sK6) [subsumption resolution 407,244]
410. 22 <=> room(sK6) [avatar definition]
412. room(sK6) <- (22) [avatar component clause 410]
413. 22 | ~17 [avatar split clause 408,360,410]
416. predh(fred) [resolution 266,246]
423. 13 [avatar split clause 416,336]
431. preda(mary) | predd(mary) [resolution 260,244]
440. predd(mary) <- (~12) [subsumption resolution 431,334]
491. predk(mary) <- (~12) [resolution 440,273]
494. 17 | 12 [avatar split clause 491,332,360]
567. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (22) [resolution 249,412]
652. fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (~18, 22) [subsumption resolution 567,372]
653. paul = sK6 | mary = sK6 | john = sK6 <- (~18, ~19, 22) [subsumption resolution 652,382]
654. mary = sK6 | john = sK6 <- (~18, ~19, ~20, 22) [subsumption resolution 653,392]
655. john = sK6 <- (~18, ~19, ~20, ~21, 22) [subsumption resolution 654,402]
656. $false <- (~16, ~18, ~19, ~20, ~21, 22) [subsumption resolution 655,358]
657. 16 | 18 | 19 | 20 | 21 | ~22 [avatar contradiction clause 656]
658. $false [avatar sat refutation 339,363,373,383,393,403,413,423,494,657]
% SZS output end Proof for 7400756628024699178158807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.25156 |
There is a room. Only one of the following is true:. -No one in the room is a quiet person if and only if they is richer than Jean. -Not everyone anywhere is richer than Franklin if they is quieter than Franklin. | More than one person anywhere is richer than Jean and is quieter than Jean. | neutral | (there_is_a_room)&
((~?[X]:(room(X)=>(((quiet(X)&person(X))<=>(richer(jean,X))))))<~>(~![X]:(anywhere(X)=>(((quieter(franklin,X))=>(richer(franklin,X))))))) | (there_is_a_room)&
(?[X,Y]:(anywhere(X)&anywhere(Y)&(((richer(jean,X))&(quieter(jean,X)))&((richer(jean,Y))&(quieter(jean,Y))))&(X!=Y))) | [] | null | 0.011839 |
There is a room.
Only one of the following is true:.
-Everyone in the room is a culinary enthusiast who experiments with international cuisines.
-Everyone in the room is a wise person. | Everyone in the room is a wise person. | neutral | (there_is_a_room)&
((![X]:(room(X)=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))<~>(![X]:(room(X)=>(wise(X)&person(X))))) | (there_is_a_room)&
![X]:(room(X)=>(wise(X)&person(X))) | [] | null | 0.19075 |
Leslie, Bernice, Donna are the only persons in the room. Everyone outside the room who writes poetry is a client of Meta. Everyone in the room who is a client of Meta collects rare minerals. Not everyone in the room owns an extensive assortment of vintage comic book memorabilia if they collects rare minerals. Bernice does not collect rare minerals. At least one person in the room enjoys landscape photography. Everyone outside the room who collects rare minerals travels domestically frequently. Donna is a client of Meta. Everyone in the room who writes poetry is a chess master who participates in national tournaments. | Everyone anywhere creates bespoke furniture pieces from reclaimed wood. | neutral | room(leslie)&room(bernice)&room(donna)&(![X]:(room(X)=>(X='leslie'|X='bernice'|X='donna')))&
(![X]:(~room(X)=>(((writes_poetry(X))=>(is_a_client_of_Meta(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(collects_rare_minerals(X))))))&
(~![X]:(room(X)=>(((collects_rare_minerals(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))&
(does_not_collect_rare_minerals(bernice))&
(((?[X]:(room(X)&enjoys_landscape_photography(X)))))&
(![X]:(~room(X)=>(((collects_rare_minerals(X))=>(travels_domestically_frequently(X))))))&
(is_a_client_of_Meta(donna))&
(![X]:(room(X)=>(((writes_poetry(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))&
(![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(knows_morse_code(X))))))&
(writes_poetry(bernice))&
(creates_bespoke_furniture_pieces_from_reclaimed_wood(leslie))&
(is_a_client_of_Meta(leslie))&
(((is_a_chess_master_who_participates_in_national_tournaments(donna))<~>(collects_rare_minerals(donna))))&
(enjoys_landscape_photography(donna))&
(![X]:(room(X)=>(((knows_morse_code(X))=>(travels_domestically_frequently(X))))))&
(![X]:(~room(X)=>(((travels_domestically_frequently(X))=>(is_a_client_of_Meta(X))))))&
(creates_bespoke_furniture_pieces_from_reclaimed_wood(donna))&
(![X]:(anywhere(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(enjoys_making_ceramics(X))))))&
(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(bernice))&
(![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(travels_domestically_frequently(X))))))&
(is_a_professional_photographer_specializing_in_portrait_photography(donna))&
(![X]:(~room(X)=>(((((is_a_professional_photographer_specializing_in_portrait_photography(X))<~>(knows_morse_code(X))))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))&
(is_a_chess_master_who_participates_in_national_tournaments(leslie))&
((![X]:((is_a_chess_master_who_participates_in_national_tournaments(X))=>(writes_poetry(X))))) | room(leslie)&room(bernice)&room(donna)&(![X]:(room(X)=>(X='leslie'|X='bernice'|X='donna')))&
![X]:(anywhere(X)=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))) | [] | null | 0.227692 |
Christine, Anthony, Frank are the only persons in the room.
“Christine is an avid hiker or creates bespoke furniture pieces from reclaimed wood or both” only if “everyone in the room owns a smartwatch or does not enjoy rooftop gardening”.
Either “Frank is a coffee connoisseur” or “everyone outside the room creates bespoke furniture pieces from reclaimed wood or does not own a smartwatch” but not both.
If “someone in the room owns a smartwatch” then “Christine does not own a smartwatch”.
If “Christine is an avid hiker” then “Frank is an avid hiker”.
Either “Anthony is an avid hiker” or “Christine owns a smartwatch” but not both.
Either “Christine either collects luxury watches or is an avid hiker but not both” or “it is not the case that “Anthony enjoys rooftop gardening”” but not both.
Christine collects luxury watches.
At least one person in the room owns a smartwatch.
Christine enjoys rooftop gardening.
Frank owns a smartwatch.
Frank enjoys rooftop gardening.
Anthony is a coffee connoisseur. | Everyone in the room creates bespoke furniture pieces from reclaimed wood. | contradiction | room(christine)&room(anthony)&room(frank)&(![X]:(room(X)=>(X='christine'|X='anthony'|X='frank')))&
((((is_an_avid_hiker(christine))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(christine))))=>(![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(owns_a_smartwatch(X)))))))&
((is_a_coffee_connoisseur(frank))<~>(![X]:(~room(X)=>(((does_not_own_a_smartwatch(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))&
((?[X]:(room(X)&(owns_a_smartwatch(X))))=>(does_not_own_a_smartwatch(christine)))&
((is_an_avid_hiker(christine))=>(is_an_avid_hiker(frank)))&
((is_an_avid_hiker(anthony))<~>(owns_a_smartwatch(christine)))&
((((collects_luxury_watches(christine))<~>(is_an_avid_hiker(christine))))<~>(~(enjoys_rooftop_gardening(anthony))))&
(collects_luxury_watches(christine))&
(((?[X]:(room(X)&owns_a_smartwatch(X)))))&
(enjoys_rooftop_gardening(christine))&
(owns_a_smartwatch(frank))&
(enjoys_rooftop_gardening(frank))&
(is_a_coffee_connoisseur(anthony)) | room(christine)&room(anthony)&room(frank)&(![X]:(room(X)=>(X='christine'|X='anthony'|X='frank')))&
![X]:(room(X)=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))) | [
"p0",
"p1",
"p3",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3429526352974842722804627
% SZS output start Proof for 3429526352974842722804627
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
45. (predd(mary) | predb(mary)) => ! [X0] : (room(X0) => (prede(X0) | ~preda(X0))) [input p1]
47. ? [X0] : (prede(X0) & room(X0)) => ~prede(mary) [input p3]
52. ? [X0] : (prede(X0) & room(X0)) [input p8]
53. preda(mary) [input p9]
57. ! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
58. ! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 57]
131. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
132. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 131]
133. ! [X0] : ((prede(X0) | ~preda(X0)) | ~room(X0)) | (~predd(mary) & ~predb(mary)) [ennf transformation 45]
134. ! [X0] : (prede(X0) | ~preda(X0) | ~room(X0)) | (~predd(mary) & ~predb(mary)) [flattening 133]
137. ~prede(mary) | ! [X0] : (~prede(X0) | ~room(X0)) [ennf transformation 47]
139. ! [X0] : (predd(X0) | ~room(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 58]
140. ! [X0] : (predd(X0) | ~room(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 139]
148. ? [X0] : (prede(X0) & room(X0)) => (prede(sK1) & room(sK1)) [choice axiom]
149. prede(sK1) & room(sK1) [skolemisation 52,148]
230. room(mary) [cnf transformation 132]
235. prede(X0) | ~preda(X0) | ~room(X0) | ~predd(mary) [cnf transformation 134]
240. ~prede(mary) | ~prede(X0) | ~room(X0) [cnf transformation 137]
249. room(sK1) [cnf transformation 149]
250. prede(sK1) [cnf transformation 149]
251. preda(mary) [cnf transformation 53]
259. ~room(X0) | predd(X0) [cnf transformation 140]
261. 1 <=> predd(mary) [avatar definition]
265. 2 <=> ! [X0] : (prede(X0) | ~room(X0) | ~preda(X0)) [avatar definition]
266. ~preda(X0) | ~room(X0) | prede(X0) <- (2) [avatar component clause 265]
267. ~1 | 2 [avatar split clause 235,265,261]
297. 9 <=> ! [X0] : (~prede(X0) | ~room(X0)) [avatar definition]
298. ~prede(X0) | ~room(X0) <- (9) [avatar component clause 297]
300. 10 <=> prede(mary) [avatar definition]
302. ~prede(mary) <- (~10) [avatar component clause 300]
303. 9 | ~10 [avatar split clause 240,300,297]
329. predd(mary) [resolution 259,230]
333. 1 [avatar split clause 329,261]
337. ~room(sK1) <- (9) [resolution 298,250]
342. $false <- (9) [subsumption resolution 337,249]
343. ~9 [avatar contradiction clause 342]
344. ~room(mary) | prede(mary) <- (2) [resolution 266,251]
346. prede(mary) <- (2) [subsumption resolution 344,230]
347. $false <- (2, ~10) [subsumption resolution 346,302]
348. ~2 | 10 [avatar contradiction clause 347]
349. $false [avatar sat refutation 267,303,333,343,348]
% SZS output end Proof for 3429526352974842722804627
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0.373639 |
Elaine, Jessica, Jennifer are the only persons in the room. “Jessica does not have a pet dog” if “someone in the room enjoys salsa dancing”. “Everyone in the room is an enthusiastic bird watcher who travels for rare sightings or does not use contact lenses” if “everyone in the room hosts a popular podcast about emerging technologies or is not an enthusiastic bird watcher who travels for rare sightings” and vice versa. “If someone is an enthusiastic bird watcher who travels for rare sightings then he/she is a professional photographer specializing in portrait photography or reads mystery novels or both and vice versa” unless “Jennifer neither is an enthusiastic bird watcher who travels for rare sightings nor can play the harmonica”. More than one person in the room practices zumba. Jessica has a pet dog. Elaine uses an ios phone. Everyone in the room uses an ios phone if they is an avid collector of autographed memorabilia from famous musicians. Only one person anywhere reads mystery novels. Everyone in the room who is not an enthusiastic bird watcher who travels for rare sightings enjoys skydiving. Everyone anywhere has a pet dog. Everyone outside the room collects vintage vinyl records if they reads mystery novels. Someone in the room is an avid collector of autographed memorabilia from famous musicians. Everyone in the room owns a microscope if and only if they hosts a popular podcast about emerging technologies. | Jennifer enjoys salsa dancing. | contradiction | room(elaine)&room(jessica)&room(jennifer)&(![X]:(room(X)=>(X='elaine'|X='jessica'|X='jennifer')))&
((?[X]:(room(X)&(enjoys_salsa_dancing(X))))=>(does_not_have_a_pet_dog(jessica)))&
((![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(hosts_a_popular_podcast_about_emerging_technologies(X))))))<=>(![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))&
(~(~((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jennifer))|(can_play_the_harmonica(jennifer))))=>((![X]:((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(reads_mystery_novels(X))))))))&
((?[X,Y]:(room(X)&room(Y)&(practices_zumba(X)&practices_zumba(Y))&(X!=Y))))&
(has_a_pet_dog(jessica))&
(uses_an_ios_phone(elaine))&
(![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(uses_an_ios_phone(X))))))&
(((?[X]:(anywhere(X)&reads_mystery_novels(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(reads_mystery_novels(X))&(reads_mystery_novels(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(enjoys_skydiving(X))))))&
(![X]:(anywhere(X)=>(has_a_pet_dog(X))))&
(![X]:(~room(X)=>(((reads_mystery_novels(X))=>(collects_vintage_vinyl_records(X))))))&
(?[X]:(room(X)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))&
(![X]:(room(X)=>(((owns_a_microscope(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))) | room(elaine)&room(jessica)&room(jennifer)&(![X]:(room(X)=>(X='elaine'|X='jessica'|X='jennifer')))&
enjoys_salsa_dancing(jennifer) | [
"p0",
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2685035671419822513762998
% SZS output start Proof for 2685035671419822513762998
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
45. ? [X0] : (preda(X0) & room(X0)) => ~predd(paul) [input p1]
49. predd(paul) [input p5]
58. preda(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
140. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
141. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 140]
142. ~predd(paul) | ! [X0] : (~preda(X0) | ~room(X0)) [ennf transformation 45]
150. preda(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 58]
151. preda(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 150]
250. room(fred) [cnf transformation 141]
252. ~predd(paul) | ~preda(X0) | ~room(X0) [cnf transformation 142]
265. predd(paul) [cnf transformation 49]
277. preda(fred) [cnf transformation 151]
279. 1 <=> ! [X0] : (~preda(X0) | ~room(X0)) [avatar definition]
280. ~preda(X0) | ~room(X0) <- (1) [avatar component clause 279]
282. 2 <=> predd(paul) [avatar definition]
285. 1 | ~2 [avatar split clause 252,282,279]
338. 2 [avatar split clause 265,282]
342. ~room(fred) <- (1) [resolution 280,277]
343. $false <- (1) [subsumption resolution 342,250]
344. ~1 [avatar contradiction clause 343]
345. $false [avatar sat refutation 285,338,344]
% SZS output end Proof for 2685035671419822513762998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.080943 |
Henry, Jeremy, Tony, Lila are the only persons in the room.
If someone either is a certified yoga instructor teaching classes weekly or enjoys virtual reality gaming but not both then he/she makes homemade pastries.
Everyone outside the room does not enjoy cross-country skiing if they writes in-depth travel guides for off-the-beaten-path destinations, is a skilled home brewer experimenting with craft beer recipes and is allergic to anything.
Everyone in the room either owns a significant collection of rare gemstones and minerals or is a coffee connoisseur but not both if they does not enjoy cross-country skiing.
More than one person in the room owns a significant collection of rare gemstones and minerals.
Everyone in the room hosts a popular podcast about emerging technologies.
Lila does not write in-depth travel guides for off-the-beaten-path destinations, does not practice archery and is not allergic to anything.
Everyone in the room has a tattoo if and only if they builds model airplanes.
Everyone in the room who builds model airplanes hosts regular workshops on creative writing, does not own a smartwatch and regularly goes on multi-day backpacking trips in national parks.
Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations if and only if they enjoys cross-country skiing.
If someone does not have a tattoo then he/she enjoys cross-country skiing.
Everyone outside the room hosts regular workshops on creative writing only if they hosts themed dinner parties featuring gourmet home-cooked meals.
Tony who enjoys salsa dancing hosts themed dinner parties featuring gourmet home-cooked meals.
Lila hosts a popular podcast about emerging technologies.
Everyone in the room can play the harmonica if they is a coffee connoisseur.
Everyone in the room is a professional photographer specializing in portrait photography if they can play the harmonica.
Everyone in the room is not a professional photographer specializing in portrait photography or is not a wine connoisseur with a private cellar of vintage wines.
Everyone outside the room who is not a professional photographer specializing in portrait photography is not allergic to anything.
If someone is a skilled home brewer experimenting with craft beer recipes then he/she hosts a popular podcast about emerging technologies. | Lila builds model airplanes. | entailment | room(henry)&room(jeremy)&room(tony)&room(lila)&(![X]:(room(X)=>(X='henry'|X='jeremy'|X='tony'|X='lila')))&
((![X]:((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<~>(enjoys_virtual_reality_gaming(X))))=>(makes_homemade_pastries(X)))))&
(![X]:(~room(X)=>(((((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(is_allergic_to_anything(X))))=>(does_not_enjoy_cross-country_skiing(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(is_a_coffee_connoisseur(X))))))))&
((?[X,Y]:(room(X)&room(Y)&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)&owns_a_significant_collection_of_rare_gemstones_and_minerals(Y))&(X!=Y))))&
(![X]:(room(X)=>(hosts_a_popular_podcast_about_emerging_technologies(X))))&
(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(lila))&(does_not_practice_archery(lila))&(is_not_allergic_to_anything(lila))))&
(![X]:(room(X)=>(((has_a_tattoo(X))<=>(builds_model_airplanes(X))))))&
(![X]:(room(X)=>(((builds_model_airplanes(X))=>(((hosts_regular_workshops_on_creative_writing(X))&(does_not_own_a_smartwatch(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))))&
(![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=>(enjoys_cross-country_skiing(X))))))&
((![X]:((does_not_have_a_tattoo(X))=>(enjoys_cross-country_skiing(X)))))&
(![X]:(~room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=(hosts_regular_workshops_on_creative_writing(X))))))&
((enjoys_salsa_dancing(tony))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(tony)))&
(hosts_a_popular_podcast_about_emerging_technologies(lila))&
(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(can_play_the_harmonica(X))))))&
(![X]:(room(X)=>(((can_play_the_harmonica(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))&
(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))&
(![X]:(~room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))=>(is_not_allergic_to_anything(X))))))&
((![X]:((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))) | room(henry)&room(jeremy)&room(tony)&room(lila)&(![X]:(room(X)=>(X='henry'|X='jeremy'|X='tony'|X='lila')))&
builds_model_airplanes(lila) | [
"p0",
"p6",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3023223192298669573680171
% SZS output start Proof for 3023223192298669573680171
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
50. ~predn(alice) & ~predd(alice) & ~preda(alice) [input p6]
51. ! [X0] : (room(X0) => (predz(X0) <=> predv(X0))) [input p7]
53. ! [X0] : (room(X0) => (preda(X0) <=> predc(X0))) [input p9]
54. ! [X0] : (~predz(X0) => predc(X0)) [input p10]
63. ~(predv(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
74. ~predn(alice) & ~preda(alice) [pure predicate removal 50]
79. ~preda(alice) [pure predicate removal 74]
153. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
154. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 153]
157. ! [X0] : ((predz(X0) <=> predv(X0)) | ~room(X0)) [ennf transformation 51]
158. ! [X0] : ((preda(X0) <=> predc(X0)) | ~room(X0)) [ennf transformation 53]
159. ! [X0] : (predc(X0) | predz(X0)) [ennf transformation 54]
160. ~predv(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63]
161. ~predv(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 160]
166. ! [X0] : (((predz(X0) | ~predv(X0)) & (predv(X0) | ~predz(X0))) | ~room(X0)) [nnf transformation 157]
167. ! [X0] : (((preda(X0) | ~predc(X0)) & (predc(X0) | ~preda(X0))) | ~room(X0)) [nnf transformation 158]
168. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom]
169. ~predv(alice) | (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 161,168]
250. room(mary) [cnf transformation 154]
251. room(paul) [cnf transformation 154]
252. room(fred) [cnf transformation 154]
253. room(alice) [cnf transformation 154]
254. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 154]
262. ~preda(alice) [cnf transformation 79]
263. ~predz(X0) | predv(X0) | ~room(X0) [cnf transformation 166]
266. ~predc(X0) | preda(X0) | ~room(X0) [cnf transformation 167]
267. predz(X0) | predc(X0) [cnf transformation 159]
268. ~predv(alice) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
269. ~predv(alice) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
270. ~predv(alice) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
271. ~predv(alice) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
272. ~predv(alice) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 169]
273. ~predv(alice) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,253]
274. ~predv(alice) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 273,252]
275. ~predv(alice) | alice != sK2 | ~room(mary) [subsumption resolution 274,251]
276. ~predv(alice) | alice != sK2 [subsumption resolution 275,250]
278. 1 <=> alice = sK2 [avatar definition]
280. alice != sK2 <- (~1) [avatar component clause 278]
282. 2 <=> predv(alice) [avatar definition]
284. ~predv(alice) <- (~2) [avatar component clause 282]
285. ~1 | ~2 [avatar split clause 276,282,278]
286. ~predv(alice) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,253]
287. ~predv(alice) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 286,252]
288. ~predv(alice) | fred != sK2 | ~room(mary) [subsumption resolution 287,251]
289. ~predv(alice) | fred != sK2 [subsumption resolution 288,250]
291. 3 <=> fred = sK2 [avatar definition]
293. fred != sK2 <- (~3) [avatar component clause 291]
294. ~3 | ~2 [avatar split clause 289,282,291]
295. ~predv(alice) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,253]
296. ~predv(alice) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 295,252]
297. ~predv(alice) | paul != sK2 | ~room(mary) [subsumption resolution 296,251]
298. ~predv(alice) | paul != sK2 [subsumption resolution 297,250]
300. 4 <=> paul = sK2 [avatar definition]
302. paul != sK2 <- (~4) [avatar component clause 300]
303. ~4 | ~2 [avatar split clause 298,282,300]
304. ~predv(alice) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,253]
305. ~predv(alice) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 304,252]
306. ~predv(alice) | mary != sK2 | ~room(mary) [subsumption resolution 305,251]
307. ~predv(alice) | mary != sK2 [subsumption resolution 306,250]
309. 5 <=> mary = sK2 [avatar definition]
311. mary != sK2 <- (~5) [avatar component clause 309]
312. ~5 | ~2 [avatar split clause 307,282,309]
313. ~predv(alice) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,253]
314. ~predv(alice) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 313,252]
315. ~predv(alice) | room(sK2) | ~room(mary) [subsumption resolution 314,251]
316. ~predv(alice) | room(sK2) [subsumption resolution 315,250]
318. 6 <=> room(sK2) [avatar definition]
320. room(sK2) <- (6) [avatar component clause 318]
321. 6 | ~2 [avatar split clause 316,282,318]
322. ~room(X0) | predv(X0) | predc(X0) [resolution 263,267]
326. predv(alice) | predc(alice) [resolution 322,253]
356. predc(alice) <- (~2) [subsumption resolution 326,284]
387. preda(alice) | ~room(alice) <- (~2) [resolution 356,266]
388. ~room(alice) <- (~2) [subsumption resolution 387,262]
389. $false <- (~2) [subsumption resolution 388,253]
390. 2 [avatar contradiction clause 389]
491. fred = sK2 | paul = sK2 | mary = sK2 | alice = sK2 <- (6) [resolution 254,320]
526. paul = sK2 | mary = sK2 | alice = sK2 <- (~3, 6) [subsumption resolution 491,293]
527. mary = sK2 | alice = sK2 <- (~3, ~4, 6) [subsumption resolution 526,302]
528. alice = sK2 <- (~3, ~4, ~5, 6) [subsumption resolution 527,311]
529. $false <- (~1, ~3, ~4, ~5, 6) [subsumption resolution 528,280]
530. 1 | 3 | 4 | 5 | ~6 [avatar contradiction clause 529]
531. $false [avatar sat refutation 285,294,303,312,321,390,530]
% SZS output end Proof for 3023223192298669573680171
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.038391 |
Linda, Gwen, Bryan, Kathy are the only persons in the room. Everyone in the room who either creates YouTube content or is a wine connoisseur with a private cellar of vintage wines but not both does not own a high-end gaming PC with custom-built components. Everyone in the room owns a high-end gaming PC with custom-built components if they does not own a high-end gaming PC with custom-built components. | Linda is not a wine connoisseur with a private cellar of vintage wines or creates YouTube content or both. | entailment | room(linda)&room(gwen)&room(bryan)&room(kathy)&(![X]:(room(X)=>(X='linda'|X='gwen'|X='bryan'|X='kathy')))&
(![X]:(~room(X)=>(((((does_not_practice_calligraphy(X))<~>(practices_calligraphy(X))))<=(has_a_piercing(X))))))&
(?[X]:(room(X)&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))&
(![X]:(room(X)=>(((((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(((can_play_the_guitar(X))&(enjoys_fishing(X))))))))&
(![X]:(room(X)=>(((((creates_YouTube_content(X))<~>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(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))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))&
(((has_a_piercing(linda))|(collects_classic_novels(linda))))&
(~![X]:(anywhere(X)=>(((has_a_piercing(X))=>(((collects_classic_novels(X))&(enjoys_bird_watching(X))))))))&
(((maintains_a_personal_blog_focused_on_cybersecurity_tips(linda))&(does_not_host_a_popular_podcast_about_emerging_technologies(linda))&(enjoys_logic_puzzles(linda))))&
(((enjoys_logic_puzzles(bryan))&(does_not_practice_calligraphy(bryan))))&
(has_a_piercing(linda)) | room(linda)&room(gwen)&room(bryan)&room(kathy)&(![X]:(room(X)=>(X='linda'|X='gwen'|X='bryan'|X='kathy')))&
((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(linda))|(creates_YouTube_content(linda))) | [
"p0",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1714581272759674344900790
% SZS output start Proof for 1714581272759674344900790
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
48. ! [X0] : (room(X0) => ((predd(X0) <~> predf(X0)) => ~prede(X0))) [input p4]
49. ! [X0] : (room(X0) => (~prede(X0) => prede(X0))) [input p5]
55. ~((predd(mary) | ~predf(mary)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
138. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
139. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 138]
142. ! [X0] : ((~prede(X0) | (predd(X0) <=> predf(X0))) | ~room(X0)) [ennf transformation 48]
143. ! [X0] : (~prede(X0) | (predd(X0) <=> predf(X0)) | ~room(X0)) [flattening 142]
144. ! [X0] : ((prede(X0) | prede(X0)) | ~room(X0)) [ennf transformation 49]
145. ! [X0] : (prede(X0) | prede(X0) | ~room(X0)) [flattening 144]
147. (~predd(mary) & predf(mary)) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 55]
148. (~predd(mary) & predf(mary)) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 147]
149. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [predicate definition introduction]
150. (~predd(mary) & predf(mary)) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 148,149]
155. ! [X0] : (~prede(X0) | ((predd(X0) | ~predf(X0)) & (predf(X0) | ~predd(X0))) | ~room(X0)) [nnf transformation 143]
158. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [nnf transformation 149]
159. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
160. (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~sP0 [skolemisation 158,159]
241. room(mary) [cnf transformation 139]
242. room(paul) [cnf transformation 139]
243. room(fred) [cnf transformation 139]
244. room(alice) [cnf transformation 139]
245. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 139]
250. ~prede(X0) | predd(X0) | ~predf(X0) | ~room(X0) [cnf transformation 155]
251. prede(X0) | prede(X0) | ~room(X0) [cnf transformation 145]
255. room(sK3) | ~sP0 [cnf transformation 160]
256. mary != sK3 | ~sP0 [cnf transformation 160]
257. paul != sK3 | ~sP0 [cnf transformation 160]
258. fred != sK3 | ~sP0 [cnf transformation 160]
259. alice != sK3 | ~sP0 [cnf transformation 160]
260. predf(mary) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150]
261. ~predd(mary) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150]
262. ~room(X0) | prede(X0) [duplicate literal removal 251]
264. 1 <=> sP0 [avatar definition]
268. 2 <=> alice = sK3 [avatar definition]
270. alice != sK3 <- (~2) [avatar component clause 268]
271. ~1 | ~2 [avatar split clause 259,268,264]
273. 3 <=> fred = sK3 [avatar definition]
275. fred != sK3 <- (~3) [avatar component clause 273]
276. ~1 | ~3 [avatar split clause 258,273,264]
278. 4 <=> paul = sK3 [avatar definition]
280. paul != sK3 <- (~4) [avatar component clause 278]
281. ~1 | ~4 [avatar split clause 257,278,264]
283. 5 <=> mary = sK3 [avatar definition]
285. mary != sK3 <- (~5) [avatar component clause 283]
286. ~1 | ~5 [avatar split clause 256,283,264]
288. 6 <=> room(sK3) [avatar definition]
290. room(sK3) <- (6) [avatar component clause 288]
291. ~1 | 6 [avatar split clause 255,288,264]
292. ~predd(mary) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,244]
293. ~predd(mary) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 292,243]
294. ~predd(mary) | sP0 | ~room(mary) [subsumption resolution 293,242]
295. ~predd(mary) | sP0 [subsumption resolution 294,241]
297. 7 <=> predd(mary) [avatar definition]
299. ~predd(mary) <- (~7) [avatar component clause 297]
300. 1 | ~7 [avatar split clause 295,297,264]
301. predf(mary) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,244]
302. predf(mary) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 301,243]
303. predf(mary) | sP0 | ~room(mary) [subsumption resolution 302,242]
304. predf(mary) | sP0 [subsumption resolution 303,241]
306. 8 <=> predf(mary) [avatar definition]
309. 1 | 8 [avatar split clause 304,306,264]
310. prede(mary) [resolution 262,241]
327. predd(mary) | ~predf(mary) | ~room(mary) [resolution 250,310]
329. ~predf(mary) | ~room(mary) <- (~7) [subsumption resolution 327,299]
336. ~predf(mary) <- (~7) [subsumption resolution 329,241]
337. ~8 | 7 [avatar split clause 336,297,306]
442. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (6) [resolution 245,290]
460. paul = sK3 | mary = sK3 | alice = sK3 <- (~3, 6) [subsumption resolution 442,275]
461. mary = sK3 | alice = sK3 <- (~3, ~4, 6) [subsumption resolution 460,280]
462. alice = sK3 <- (~3, ~4, ~5, 6) [subsumption resolution 461,285]
463. $false <- (~2, ~3, ~4, ~5, 6) [subsumption resolution 462,270]
464. 2 | 3 | 4 | 5 | ~6 [avatar contradiction clause 463]
465. $false [avatar sat refutation 271,276,281,286,291,300,309,337,464]
% SZS output end Proof for 1714581272759674344900790
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.175796 |
Phyllis, Gary, Thomas are the only persons in the room.
“Phyllis and Gary are not a humble europeans” if “Gary is a happy person” and vice versa.
If “Gary is a client of Donald” then “Thomas and Gary are respectively happy and calm” otherwise “Phyllis is hated by Billy”.
Either “Phyllis does not collect classic novels” or “Thomas is calm” but not both.
Phyllis is a client of Billy.
Billy is a client of Thomas.
If someone is a generous tourist then he/she is a patient european and vice versa.
Phyllis and Gary are not a humble europeans.
No quiet person is funny.
All wise persons are humble.
Thomas is calm. | Thomas is not funny. | entailment | room(phyllis)&room(gary)&room(thomas)&(![X]:(room(X)=>(X='phyllis'|X='gary'|X='thomas')))&
((happy(gary)&person(gary))<=>(~(humble(phyllis)&european(phyllis))&~(humble(gary)&european(gary))))&
(((client(donald,gary))=>((happy(thomas))&(calm(gary))))&((~(client(donald,gary)))=>(hate(phyllis,billy))))&
((does_not_collect_classic_novels(phyllis))<~>(calm(thomas)))&
(client(billy,phyllis))&
(client(thomas,billy))&
((![X]:((generous(X)&tourist(X))<=>(patient(X)&european(X)))))&
(~(humble(phyllis)&european(phyllis))&~(humble(gary)&european(gary)))&
(~?[X]:(quiet(X)=>funny(X)))&
(![X]:(wise(X)=>humble(X)))&
(calm(thomas)) | room(phyllis)&room(gary)&room(thomas)&(![X]:(room(X)=>(X='phyllis'|X='gary'|X='thomas')))&
~funny(thomas) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8897713167253189052176139
% SZS output start Proof for 8897713167253189052176139
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
52. ~? [X0] : (quiet(X0) => funny(X0)) [input p8]
55. ~(~funny(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
130. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
131. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 130]
135. ! [X0] : (~funny(X0) & quiet(X0)) [ennf transformation 52]
136. funny(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 55]
137. funny(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 136]
148. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom]
149. funny(fred) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 137,148]
232. room(mary) [cnf transformation 131]
233. room(paul) [cnf transformation 131]
234. room(fred) [cnf transformation 131]
235. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 131]
258. ~funny(X0) [cnf transformation 135]
260. funny(fred) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 149]
261. funny(fred) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 149]
262. funny(fred) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 149]
263. funny(fred) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 149]
328. fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 263,258]
329. fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 328,234]
330. fred != sK1 | ~room(mary) [subsumption resolution 329,233]
331. fred != sK1 [subsumption resolution 330,232]
332. paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,258]
333. paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 332,234]
334. paul != sK1 | ~room(mary) [subsumption resolution 333,233]
335. paul != sK1 [subsumption resolution 334,232]
336. mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,258]
337. mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 336,234]
338. mary != sK1 | ~room(mary) [subsumption resolution 337,233]
339. mary != sK1 [subsumption resolution 338,232]
340. room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,258]
341. room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 340,234]
342. room(sK1) | ~room(mary) [subsumption resolution 341,233]
343. room(sK1) [subsumption resolution 342,232]
389. paul = sK1 | mary = sK1 | fred = sK1 [resolution 235,343]
390. mary = sK1 | fred = sK1 [subsumption resolution 389,335]
391. fred = sK1 [subsumption resolution 390,339]
392. $false [subsumption resolution 391,331]
% SZS output end Proof for 8897713167253189052176139
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.219343 |
Oscar, Jean, Betty are the only persons in the room.
If “everyone in the room is not a skilled home brewer experimenting with craft beer recipes or collects comic books” then “everyone in the room who is a Linux enthusiast either is a Linux enthusiast or creates augmented reality experiences for mobile applications but not both”.
“Someone anywhere enjoys salsa dancing” if “someone in the room practices graffiti art”.
If “everyone in the room does not use an ios phone or practices tai chi” then “everyone outside the room makes homemade pastries only if they is a Linux enthusiast, collects antique clocks or makes homemade pastries”.
Someone in the room is a Linux enthusiast.
If someone either enjoys landscape photography or creates augmented reality experiences for mobile applications but not both then he/she practices tai chi, has lived in exactly three countries or is an avid collector of autographed memorabilia from famous musicians and vice versa.
Oscar dreamt that “if someone is a Linux enthusiast then he/she hosts a popular podcast about emerging technologies and vice versa”.
If someone either makes homemade pastries or enjoys landscape photography but not both then he/she either enjoys landscape photography or enjoys salsa dancing but not both and vice versa.
Someone in the room collects comic books.
If someone is an avid collector of autographed memorabilia from famous musicians then he/she does not practice tai chi.
Everyone in the room who enjoys landscape photography is an avid collector of autographed memorabilia from famous musicians.
If someone enjoys landscape photography then he/she enjoys salsa dancing and vice versa.
Everyone anywhere who is an avid collector of autographed memorabilia from famous musicians plays video games.
Not everyone in the room who has a specialized collection of handmade artisan pottery collects comic books.
Everyone in the room who is a Linux enthusiast collects comic books.
Everyone in the room plays video games only if they is a Linux enthusiast. | Everyone anywhere makes homemade pastries. | contradiction | room(oscar)&room(jean)&room(betty)&(![X]:(room(X)=>(X='oscar'|X='jean'|X='betty')))&
((![X]:(room(X)=>(((collects_comic_books(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(((is_a_Linux_enthusiast(X))<~>(creates_augmented_reality_experiences_for_mobile_applications(X)))))))))&
((?[X]:(room(X)&(practices_graffiti_art(X))))=>(?[X]:(anywhere(X)&(enjoys_salsa_dancing(X)))))&
((![X]:(room(X)=>(((practices_tai_chi(X))|(does_not_use_an_ios_phone(X))))))=>(![X]:(~room(X)=>(((((is_a_Linux_enthusiast(X))|(collects_antique_clocks(X))|(makes_homemade_pastries(X))))<=(makes_homemade_pastries(X)))))))&
(?[X]:(room(X)&(is_a_Linux_enthusiast(X))))&
((![X]:((((enjoys_landscape_photography(X))<~>(creates_augmented_reality_experiences_for_mobile_applications(X))))<=>(((practices_tai_chi(X))|(has_lived_in_exactly_three_countries(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))))&
((oscar_dream=>((![X]:((is_a_Linux_enthusiast(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))))&
((![X]:((((makes_homemade_pastries(X))<~>(enjoys_landscape_photography(X))))<=>(((enjoys_landscape_photography(X))<~>(enjoys_salsa_dancing(X)))))))&
(?[X]:(room(X)&(collects_comic_books(X))))&
((![X]:((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(does_not_practice_tai_chi(X)))))&
(![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))&
((![X]:((enjoys_landscape_photography(X))<=>(enjoys_salsa_dancing(X)))))&
((![X]:((practices_graffiti_art(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))&
(~(?[X]:(room(X)&(owns_a_smartwatch(X)))))&
(![X]:(anywhere(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(plays_video_games(X))))))&
((![X]:((is_a_tea_enthusiast(X))<=>(uses_an_ios_phone(X)))))&
(~![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(collects_comic_books(X))))))&
(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(collects_comic_books(X))))))&
(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))<=(hosts_a_popular_podcast_about_emerging_technologies(X))))))&
(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))<=(plays_video_games(X))))))&
(![X]:(room(X)=>(((owns_a_smartwatch(X))=>(makes_homemade_pastries(X)))))) | room(oscar)&room(jean)&room(betty)&(![X]:(room(X)=>(X='oscar'|X='jean'|X='betty')))&
![X]:(anywhere(X)=>(makes_homemade_pastries(X))) | [
"b4",
"p7",
"p10",
"p11",
"p14",
"p16",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2670175916504304729163696
% SZS output start Proof for 2670175916504304729163696
5. ! [X0] : anywhere(X0) [input b4]
51. ! [X0] : ((predb(X0) <~> predf(X0)) <=> (predf(X0) <~> predg(X0))) [input p7]
54. ! [X0] : (room(X0) => (predf(X0) => predq(X0))) [input p10]
55. ! [X0] : (predf(X0) <=> predg(X0)) [input p11]
58. ! [X0] : (anywhere(X0) => (predq(X0) => predm(X0))) [input p14]
60. ~! [X0] : (room(X0) => (preda(X0) => predu(X0))) [input p16]
61. ! [X0] : (room(X0) => (predp(X0) => predu(X0))) [input p17]
63. ! [X0] : (room(X0) => (predm(X0) => predp(X0))) [input p19]
65. ! [X0] : (anywhere(X0) => predb(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
69. ! [X0] : (anywhere(X0) => predb(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 65]
71. ~! [X0] : (room(X0) => predu(X0)) [pure predicate removal 60]
156. ! [X0] : ((predq(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 54]
157. ! [X0] : (predq(X0) | ~predf(X0) | ~room(X0)) [flattening 156]
158. ! [X0] : ((predm(X0) | ~predq(X0)) | ~anywhere(X0)) [ennf transformation 58]
159. ! [X0] : (predm(X0) | ~predq(X0) | ~anywhere(X0)) [flattening 158]
160. ? [X0] : (~predu(X0) & room(X0)) [ennf transformation 71]
161. ! [X0] : ((predu(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 61]
162. ! [X0] : (predu(X0) | ~predp(X0) | ~room(X0)) [flattening 161]
163. ! [X0] : ((predp(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 63]
164. ! [X0] : (predp(X0) | ~predm(X0) | ~room(X0)) [flattening 163]
165. ! [X0] : (predb(X0) | ~anywhere(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 69]
166. ! [X0] : (predb(X0) | ~anywhere(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 165]
176. ! [X0] : ((((~predf(X0) | ~predb(X0)) & (predf(X0) | predb(X0))) | ((predf(X0) | ~predg(X0)) & (predg(X0) | ~predf(X0)))) & (((~predg(X0) | ~predf(X0)) & (predg(X0) | predf(X0))) | ((predb(X0) | ~predf(X0)) & (predf(X0) | ~predb(X0))))) [nnf transformation 51]
179. ! [X0] : ((predf(X0) | ~predg(X0)) & (predg(X0) | ~predf(X0))) [nnf transformation 55]
180. ? [X0] : (~predu(X0) & room(X0)) => (~predu(sK3) & room(sK3)) [choice axiom]
181. ~predu(sK3) & room(sK3) [skolemisation 160,180]
182. anywhere(X0) [cnf transformation 5]
281. predg(X0) | predf(X0) | predf(X0) | ~predb(X0) [cnf transformation 176]
287. ~predf(X0) | ~predb(X0) | predg(X0) | ~predf(X0) [cnf transformation 176]
292. ~predf(X0) | predq(X0) | ~room(X0) [cnf transformation 157]
294. ~predg(X0) | predf(X0) [cnf transformation 179]
295. predm(X0) | ~predq(X0) | ~anywhere(X0) [cnf transformation 159]
296. room(sK3) [cnf transformation 181]
297. ~predu(sK3) [cnf transformation 181]
298. ~predp(X0) | predu(X0) | ~room(X0) [cnf transformation 162]
299. ~predm(X0) | predp(X0) | ~room(X0) [cnf transformation 164]
304. predb(X0) | ~anywhere(X0) [cnf transformation 166]
305. predg(X0) | predf(X0) | ~predb(X0) [duplicate literal removal 281]
308. ~predf(X0) | ~predb(X0) | predg(X0) [duplicate literal removal 287]
325. ~predb(X0) | predg(X0) [subsumption resolution 305,308]
326. ~predq(X0) | predm(X0) [subsumption resolution 295,182]
327. predb(X0) [subsumption resolution 304,182]
328. predg(X0) [resolution 325,327]
330. predf(X1) [resolution 328,294]
333. ~room(X0) | predq(X0) [resolution 292,330]
341. predq(sK3) [resolution 333,296]
371. predm(sK3) [resolution 341,326]
401. predp(sK3) | ~room(sK3) [resolution 371,299]
402. predp(sK3) [subsumption resolution 401,296]
429. predu(sK3) | ~room(sK3) [resolution 402,298]
430. ~room(sK3) [subsumption resolution 429,297]
431. $false [subsumption resolution 430,296]
% SZS output end Proof for 2670175916504304729163696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.222175 |
There is a room.
Everyone in the room travels domestically frequently or does not enjoy logic puzzles.
Everyone in the room does not have completed a triathlon or travels domestically frequently.
Everyone in the room who does not have completed a triathlon is a client of LVMH.
Everyone in the room who is a client of LVMH has lived in exactly three countries, has a saltwater aquarium and enjoys logic puzzles.
Everyone in the room is not a scotch connoisseur or neither enjoys logic puzzles nor travels domestically frequently. | Everyone in the room is not a scotch connoisseur or is a Linux enthusiast. | entailment | (there_is_a_room)&
((~![X]:(~room(X)=>(((is_not_a_scotch_connoisseur(X))|(travels_domestically_frequently(X))))))<~>(~?[X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(has_completed_a_triathlon(X)))))))&
((![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))<~>(![X]:(anywhere(X)=>(((is_not_a_client_of_LVMH(X))|(knows_morse_code(X)))))))&
((![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))=>(![X]:(anywhere(X)=>(((((knows_morse_code(X))|(collects_vintage_vinyl_records(X))|(writes_and_illustrates_their_own_graphic_novels(X))))=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))))&
((![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))=>(![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(enjoys_stargazing(X)))))))&
((![X]:(room(X)=>(((does_not_know_morse_code(X))|(collects_vintage_vinyl_records(X))))))<=>(![X]:(room(X)=>(((has_completed_a_triathlon(X))|(does_not_collect_vintage_vinyl_records(X)))))))&
(((~![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(plays_eSports_competitively(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_stargazing(X))|(enjoys_stargazing(X)))))))&((~(~![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(plays_eSports_competitively(X)))))))=>(![X]:(room(X)=>(((enjoys_stargazing(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))))&
(((![X]:(~room(X)=>(((enjoys_stargazing(X))|(does_not_have_a_saltwater_aquarium(X))))))=>(![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))=>(~((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(frequently_participates_in_hackathons_and_coding_competitions(X)))))))))&((~(![X]:(~room(X)=>(((enjoys_stargazing(X))|(does_not_have_a_saltwater_aquarium(X)))))))=>(![X]:(room(X)=>(((~((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))=>(travels_domestically_frequently(X))))))))&
((![X]:(room(X)=>(((is_a_Linux_enthusiast(X))|(does_not_enjoy_stargazing(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_stargazing(X))=>(does_not_play_eSports_competitively(X)))))))&
((![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_have_a_saltwater_aquarium(X))))))<~>(![X]:(room(X)=>(((does_not_enjoy_stargazing(X))|(plays_eSports_competitively(X)))))))&
(![X]:(room(X)=>(((plays_eSports_competitively(X))=>(enjoys_stargazing(X))))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))|(does_not_play_eSports_competitively(X))))))&
((?[X,Y]:(room(X)&room(Y)&(regularly_contributes_to_tech_forums_and_online_communities(X)®ularly_contributes_to_tech_forums_and_online_communities(Y))&(X!=Y))))&
(![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(practices_archery(X))))))&
(![X]:(room(X)=>(((practices_archery(X))<=>(knows_morse_code(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))|(travels_domestically_frequently(X))))))&
(![X]:(room(X)=>(((travels_domestically_frequently(X))|(does_not_have_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))=>(is_a_client_of_LVMH(X))))))&
(![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(((has_lived_in_exactly_three_countries(X))&(has_a_saltwater_aquarium(X))&(enjoys_logic_puzzles(X))))))))&
(![X]:(room(X)=>(((((has_lived_in_exactly_three_countries(X))&(has_a_saltwater_aquarium(X))&(enjoys_logic_puzzles(X))))<=>(enjoys_logic_puzzles(X))))))&
(![X]:(~room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(((is_a_client_of_LVMH(X))|(can_play_the_guitar(X))))))))&
(![X]:(room(X)=>(((~((enjoys_logic_puzzles(X))|(travels_domestically_frequently(X))))|(is_not_a_scotch_connoisseur(X))))))&
(~![X]:(room(X)=>(((does_not_practice_digital_art(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))&
(![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((is_a_Linux_enthusiast(X))|(is_not_a_scotch_connoisseur(X))))) | [
"p0",
"p15",
"p16",
"p17",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6193082823675222320503665
% SZS output start Proof for 6193082823675222320503665
44. there_is_a_room [input p0]
59. ! [X0] : (room(X0) => (predr(X0) | ~predp(X0))) [input p15]
60. ! [X0] : (room(X0) => (~predz(X0) | predr(X0))) [input p16]
61. ! [X0] : (room(X0) => (~predz(X0) => predm(X0))) [input p17]
62. ! [X0] : (room(X0) => (predm(X0) => (predp(X0) & predy(X0) & predn(X0)))) [input p18]
65. ! [X0] : (room(X0) => (~predd(X0) | ~(predr(X0) | predp(X0)))) [input p21]
68. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis]
83. ~(! [X0] : (room(X0) => ~predd(X0)) & there_is_a_room) [pure predicate removal 68]
179. ! [X0] : ((predr(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 59]
180. ! [X0] : (predr(X0) | ~predp(X0) | ~room(X0)) [flattening 179]
181. ! [X0] : ((~predz(X0) | predr(X0)) | ~room(X0)) [ennf transformation 60]
182. ! [X0] : (~predz(X0) | predr(X0) | ~room(X0)) [flattening 181]
183. ! [X0] : ((predm(X0) | predz(X0)) | ~room(X0)) [ennf transformation 61]
184. ! [X0] : (predm(X0) | predz(X0) | ~room(X0)) [flattening 183]
185. ! [X0] : (((predp(X0) & predy(X0) & predn(X0)) | ~predm(X0)) | ~room(X0)) [ennf transformation 62]
186. ! [X0] : ((predp(X0) & predy(X0) & predn(X0)) | ~predm(X0) | ~room(X0)) [flattening 185]
188. ! [X0] : ((~predd(X0) | (~predr(X0) & ~predp(X0))) | ~room(X0)) [ennf transformation 65]
189. ! [X0] : (~predd(X0) | (~predr(X0) & ~predp(X0)) | ~room(X0)) [flattening 188]
193. ? [X0] : (predd(X0) & room(X0)) | ~there_is_a_room [ennf transformation 83]
231. ? [X0] : (predd(X0) & room(X0)) => (predd(sK14) & room(sK14)) [choice axiom]
232. (predd(sK14) & room(sK14)) | ~there_is_a_room [skolemisation 193,231]
314. there_is_a_room [cnf transformation 44]
376. ~predp(X0) | predr(X0) | ~room(X0) [cnf transformation 180]
377. ~predz(X0) | predr(X0) | ~room(X0) [cnf transformation 182]
378. ~room(X0) | predz(X0) | predm(X0) [cnf transformation 184]
381. ~predm(X0) | predp(X0) | ~room(X0) [cnf transformation 186]
387. ~predr(X0) | ~predd(X0) | ~room(X0) [cnf transformation 189]
391. room(sK14) | ~there_is_a_room [cnf transformation 232]
392. predd(sK14) | ~there_is_a_room [cnf transformation 232]
625. predd(sK14) [subsumption resolution 392,314]
626. room(sK14) [subsumption resolution 391,314]
638. predz(sK14) | predm(sK14) [resolution 378,626]
694. 61 <=> predm(sK14) [avatar definition]
696. predm(sK14) <- (61) [avatar component clause 694]
698. 62 <=> predz(sK14) [avatar definition]
700. predz(sK14) <- (62) [avatar component clause 698]
701. 61 | 62 [avatar split clause 638,698,694]
753. predp(sK14) | ~room(sK14) <- (61) [resolution 696,381]
756. predp(sK14) <- (61) [subsumption resolution 753,626]
860. 83 <=> predr(sK14) [avatar definition]
862. predr(sK14) <- (83) [avatar component clause 860]
928. predr(sK14) | ~room(sK14) <- (61) [resolution 756,376]
932. predr(sK14) <- (61) [subsumption resolution 928,626]
933. 83 | ~61 [avatar split clause 932,694,860]
934. predr(sK14) | ~room(sK14) <- (62) [resolution 700,377]
935. predr(sK14) <- (62) [subsumption resolution 934,626]
936. 83 | ~62 [avatar split clause 935,698,860]
937. ~predd(sK14) | ~room(sK14) <- (83) [resolution 862,387]
938. ~room(sK14) <- (83) [subsumption resolution 937,625]
939. $false <- (83) [subsumption resolution 938,626]
940. ~83 [avatar contradiction clause 939]
941. $false [avatar sat refutation 701,933,936,940]
% SZS output end Proof for 6193082823675222320503665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0.632958 |
There is a room.
'Everyone outside the room is kind only if they is happy' if 'at least one person in the room is humble'.
Someone who is creative is richer than someone who either is kind or is quiet but not both.
Someone in the room is not a humble old person.
Everyone in the room is calm only if they is not a creative quiet person.
More than one person in the room is calm.
No one in the room is brave or is kind or both only if they is not a old funny person, is not a tall person or is not a old brave quiet person.
Everyone in the room neither is humble nor is funny only if they is not a calm person. | Not everyone in the room is humble. | entailment | (there_is_a_room)&
((((?[X]:(room(X)&humble(X)))))=>(![X]:(~room(X)=>(((happy(X))<=(kind(X)))))))&
(?[X,Y]:((creative(X))&(((kind(Y))<~>(quiet(Y))))&(richer(X,Y))))&
(?[X]:(room(X)&(~(humble(X)&old(X)&person(X)))))&
(![X]:(room(X)=>(((~(creative(X)&quiet(X)&person(X)))<=(calm(X))))))&
((?[X,Y]:(room(X)&room(Y)&(calm(X)&calm(Y))&(X!=Y))))&
(~?[X]:(room(X)=>(((((~(old(X)&funny(X)&person(X)))|(~(tall(X)&person(X)))|(~(old(X)&brave(X)&quiet(X)&person(X)))))<=(((brave(X))|(kind(X))))))))&
(![X]:(room(X)=>(((~(calm(X)&person(X)))<=(~((humble(X))|(funny(X)))))))) | (there_is_a_room)&
~![X]:(room(X)=>(humble(X))) | [
"p0",
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8572498516382457807452225
% SZS output start Proof for 8572498516382457807452225
44. there_is_a_room [input p0]
47. ? [X0] : (~(person(X0) & old(X0) & humble(X0)) & room(X0)) [input p3]
50. ~? [X0] : (room(X0) => ((kind(X0) | brave(X0)) => (~(person(X0) & quiet(X0) & brave(X0) & old(X0)) | ~(person(X0) & tall(X0)) | ~(person(X0) & funny(X0) & old(X0))))) [input p6]
52. ~(~! [X0] : (room(X0) => humble(X0)) & there_is_a_room) [input hypothesis]
54. ~? [X0] : (room(X0) => (~(person(X0) & quiet(X0) & old(X0)) | ~(person(X0) & tall(X0)) | ~(person(X0) & funny(X0) & old(X0)))) [pure predicate removal 50]
55. ~? [X0] : (room(X0) => (~(person(X0) & quiet(X0) & old(X0)) | ~person(X0) | ~(person(X0) & funny(X0) & old(X0)))) [pure predicate removal 54]
57. ~? [X0] : (room(X0) => (~(person(X0) & quiet(X0) & old(X0)) | ~person(X0) | ~(person(X0) & old(X0)))) [pure predicate removal 55]
131. ? [X0] : ((~person(X0) | ~old(X0) | ~humble(X0)) & room(X0)) [ennf transformation 47]
134. ! [X0] : (((person(X0) & quiet(X0) & old(X0)) & person(X0) & (person(X0) & old(X0))) & room(X0)) [ennf transformation 57]
135. ! [X0] : (person(X0) & quiet(X0) & old(X0) & person(X0) & person(X0) & old(X0) & room(X0)) [flattening 134]
136. ! [X0] : (humble(X0) | ~room(X0)) | ~there_is_a_room [ennf transformation 52]
142. ? [X0] : ((~person(X0) | ~old(X0) | ~humble(X0)) & room(X0)) => ((~person(sK2) | ~old(sK2) | ~humble(sK2)) & room(sK2)) [choice axiom]
143. (~person(sK2) | ~old(sK2) | ~humble(sK2)) & room(sK2) [skolemisation 131,142]
226. there_is_a_room [cnf transformation 44]
232. ~person(sK2) | ~old(sK2) | ~humble(sK2) [cnf transformation 143]
239. room(X0) [cnf transformation 135]
243. old(X0) [cnf transformation 135]
245. person(X0) [cnf transformation 135]
246. humble(X0) | ~room(X0) | ~there_is_a_room [cnf transformation 136]
258. 3 <=> humble(sK2) [avatar definition]
260. ~humble(sK2) <- (~3) [avatar component clause 258]
262. 4 <=> old(sK2) [avatar definition]
264. ~old(sK2) <- (~4) [avatar component clause 262]
266. 5 <=> person(sK2) [avatar definition]
268. ~person(sK2) <- (~5) [avatar component clause 266]
269. ~3 | ~4 | ~5 [avatar split clause 232,266,262,258]
270. humble(X0) | ~there_is_a_room [subsumption resolution 246,239]
271. humble(X0) [subsumption resolution 270,226]
272. $false <- (~5) [subsumption resolution 268,245]
273. 5 [avatar contradiction clause 272]
274. $false <- (~3) [subsumption resolution 260,271]
275. 3 [avatar contradiction clause 274]
276. $false <- (~4) [subsumption resolution 264,243]
277. 4 [avatar contradiction clause 276]
278. $false [avatar sat refutation 269,273,275,277]
% SZS output end Proof for 8572498516382457807452225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.364303 |
No one in the room who does not enjoy cross-country skiing, is an enthusiastic bird watcher who travels for rare sightings and plays video games enjoys cross-country skiing.
Everyone in the room enjoys cross-country skiing if they is a Linux enthusiast. | Everyone in the room is a Linux enthusiast. | contradiction | (there_is_a_room)&
(((![X]:(~room(X)=>(((owns_a_microscope(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_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))&((~(![X]:(~room(X)=>(((owns_a_microscope(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))))=>(![X]:(~room(X)=>(((does_enjoy_trail_running(X))<=(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))))&
((![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(collects_first_edition_books(X))))))=>(![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=(makes_homemade_pastries(X)))))))&
((![X]:(room(X)=>(((does_not_own_a_smartwatch(X))|(owns_a_microscope(X))))))<=>(![X]:(room(X)=>(((plays_video_games(X))|(does_not_play_video_games(X)))))))&
((![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))=>(![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(((does_not_enjoy_cross-country_skiing(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(plays_video_games(X)))))))))&
(~?[X]:(room(X)=>(((((does_not_enjoy_cross-country_skiing(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(plays_video_games(X))))=>(enjoys_cross-country_skiing(X))))))&
(((?[X]:(room(X)&enjoys_wildlife_photography(X)))))&
(~![X]:(room(X)=>(((((plays_video_games(X))|(is_a_Linux_enthusiast(X))|(practices_digital_art(X))))=>(practices_digital_art(X))))))&
(![X]:(~room(X)=>(((practices_digital_art(X))=>(does_not_enjoy_cross-country_skiing(X))))))&
((![X]:((((is_a_Linux_enthusiast(X))&(mentors_a_youth_basketball_team_on_weekends(X))))<=>(((collects_first_edition_books(X))&(enjoys_cross-country_skiing(X)))))))&
(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(room(X)=>(((does_not_own_a_microscope(X))|(owns_a_smartwatch(X))))))&
(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(owns_a_smartwatch(X))))))&
(![X]:(room(X)=>(((owns_a_smartwatch(X))=>(((is_a_Linux_enthusiast(X))|(owns_a_microscope(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))))&
(![X]:(~room(X)=>(((owns_a_microscope(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(is_a_Linux_enthusiast(X))) | [
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5791415053705427710997990
% SZS output start Proof for 5791415053705427710997990
49. ~? [X0] : (room(X0) => ((predg(X0) & predm(X0) & ~predd(X0)) => predd(X0))) [input p5]
54. ! [X0] : (room(X0) => (predc(X0) => predd(X0))) [input p10]
59. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis]
69. ~? [X0] : (room(X0) => ((predg(X0) & ~predd(X0)) => predd(X0))) [pure predicate removal 49]
71. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 59]
147. ! [X0] : ((~predd(X0) & (predg(X0) & ~predd(X0))) & room(X0)) [ennf transformation 69]
148. ! [X0] : (~predd(X0) & predg(X0) & ~predd(X0) & room(X0)) [flattening 147]
153. ! [X0] : ((predd(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 54]
154. ! [X0] : (predd(X0) | ~predc(X0) | ~room(X0)) [flattening 153]
161. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 71]
260. room(X0) [cnf transformation 148]
263. ~predd(X0) [cnf transformation 148]
273. predd(X0) | ~predc(X0) | ~room(X0) [cnf transformation 154]
277. predc(X0) | ~room(X0) [cnf transformation 161]
293. ~predc(X0) | ~room(X0) [subsumption resolution 273,263]
294. ~predc(X0) [subsumption resolution 293,260]
296. ~room(X0) [subsumption resolution 277,294]
297. $false [subsumption resolution 296,260]
% SZS output end Proof for 5791415053705427710997990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.05576 |
Chris, Barry, Sandra are the only persons in the room. Everyone in the room is not an avid hiker or creates YouTube content. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings if and only if they trains for and competes in international triathlons, designs and sews custom cosplay costumes for conventions or is an enthusiastic bird watcher who travels for rare sightings. If someone designs and sews custom cosplay costumes for conventions then he/she either is an enthusiastic bird watcher who travels for rare sightings or creates YouTube content but not both and vice versa. Everyone in the room does not have a pet dog or is not an enthusiastic bird watcher who travels for rare sightings. If someone practices calligraphy then he/she designs and sews custom cosplay costumes for conventions. Everyone anywhere is an avid hiker or has a pet dog or both. | Chris practices calligraphy. | contradiction | room(chris)&room(barry)&room(sandra)&(![X]:(room(X)=>(X='chris'|X='barry'|X='sandra')))&
((![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(is_not_allergic_to_anything(X))))))=>(![X]:(~room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X)))))&
((?[X]:(room(X)&(does_not_play_the_violin(X))))=>(?[X]:(anywhere(X)&(((bakes_bread_at_home(X))&(does_enjoy_mountain_biking(X)))))))&
((![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(does_not_collect_modern_art(X))))))=>((chris_dream=>(~![X]:(room(X)=>(((does_not_collect_modern_art(X))=>(((does_not_play_the_drums(X))|(collects_classic_novels(X)))))))))))&
((![X]:(room(X)=>(((does_enjoy_mountain_biking(X))|(does_not_play_the_violin(X))))))=>(~?[X]:(room(X)=>(((does_not_play_the_violin(X))=>(is_an_avid_hiker(X)))))))&
((![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(is_not_right-handed(X))))))<=>(![X]:(room(X)=>(((is_right-handed(X))|(collects_rare_and_antique_scientific_instruments(X)))))))&
((~![X]:(~room(X)=>(((does_not_enjoy_mountain_biking(X))|(does_not_work_on_fridays(X))))))<=>(~(?[X]:(room(X)&(can_play_the_harmonica(X))))))&
((![X]:(room(X)=>(((does_not_play_the_violin(X))|(does_not_have_a_pet_dog(X))))))=>(![X]:(anywhere(X)=>(((is_an_avid_hiker(X))|(has_a_pet_dog(X)))))))&
(~(![X]:(room(X)=>(((creates_YouTube_content(X))|(does_not_have_a_pet_dog(X))))))=>(![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(is_not_an_avid_hiker(X)))))))&
((![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(?[X]:(room(X)&(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(plays_the_drums(X))|(is_a_craft_beer_aficionado(X)))))))&
(![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(creates_YouTube_content(X))))))&
(![X]:(room(X)=>(((creates_YouTube_content(X))|(is_not_an_avid_hiker(X))))))&
((?[X,Y]:(room(X)&room(Y)&(bakes_bread_at_home(X)&bakes_bread_at_home(Y))&(X!=Y))))&
(![X]:(~room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X))))&
(![X]:(room(X)=>(((((reads_mystery_novels(X))&(collects_classic_novels(X))))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=>(((trains_for_and_competes_in_international_triathlons(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))&
((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(creates_YouTube_content(X)))))))&
(![X]:(~room(X)=>(((collects_modern_art(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_not_have_a_pet_dog(X))))))&
(?[X]:(room(X)&(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(plays_the_drums(X))|(is_a_craft_beer_aficionado(X))))))&
((![X]:((practices_calligraphy(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))&
(![X]:(~room(X)=>(((does_not_create_YouTube_content(X))<=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(collects_classic_novels(X))))))))&
(?[X]:(room(X)&(is_right-handed(X))))&
(![X]:(anywhere(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(creates_YouTube_content(X))|(is_allergic_to_anything(X))))=>(can_play_the_harmonica(X))))))&
((((is_not_a_craft_beer_aficionado(barry))&(develops_open-source_software_projects_in_their_free_time(barry))))&(((plays_the_violin(barry))|(is_a_certified_yoga_instructor_teaching_classes_weekly(barry))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(barry)))))&
((![X]:((((has_a_pet_dog(X))|(does_not_play_the_violin(X))|(collects_modern_art(X))))=>(((plays_the_violin(X))|(collects_modern_art(X))|(has_a_pet_dog(X)))))))&
(![X]:(anywhere(X)=>(((is_an_avid_hiker(X))|(has_a_pet_dog(X))))))&
((![X]:((((develops_open-source_software_projects_in_their_free_time(X))&(does_not_enjoy_mountain_biking(X))&(is_right-handed(X))))=>(does_not_play_the_drums(X))))) | room(chris)&room(barry)&room(sandra)&(![X]:(room(X)=>(X='chris'|X='barry'|X='sandra')))&
practices_calligraphy(chris) | [
"b4",
"p0",
"p11",
"p15",
"p16",
"p18",
"p20",
"p26",
"hypothesis"
] | % SZS status Unsatisfiable for 8837776930836293156711627
% SZS output start Proof for 8837776930836293156711627
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
55. ! [X0] : (room(X0) => (~predu(X0) | predr(X0))) [input p11]
59. ! [X0] : (room(X0) => (predh(X0) <=> (predh(X0) | predj(X0) | prede(X0)))) [input p15]
60. ! [X0] : (predj(X0) <=> (predh(X0) <~> predr(X0))) [input p16]
62. ! [X0] : (room(X0) => (~predq(X0) | ~predh(X0))) [input p18]
64. ! [X0] : (predi(X0) => predj(X0)) [input p20]
70. ! [X0] : (anywhere(X0) => (predq(X0) | predu(X0))) [input p26]
72. predi(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
162. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
163. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 162]
181. ! [X0] : ((~predu(X0) | predr(X0)) | ~room(X0)) [ennf transformation 55]
182. ! [X0] : (~predu(X0) | predr(X0) | ~room(X0)) [flattening 181]
184. ! [X0] : ((predh(X0) <=> (predh(X0) | predj(X0) | prede(X0))) | ~room(X0)) [ennf transformation 59]
187. ! [X0] : ((~predq(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 62]
188. ! [X0] : (~predq(X0) | ~predh(X0) | ~room(X0)) [flattening 187]
189. ! [X0] : (predj(X0) | ~predi(X0)) [ennf transformation 64]
195. ! [X0] : ((predq(X0) | predu(X0)) | ~anywhere(X0)) [ennf transformation 70]
196. ! [X0] : (predq(X0) | predu(X0) | ~anywhere(X0)) [flattening 195]
197. predi(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 72]
198. predi(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 197]
232. ! [X0] : (((predh(X0) | (~predh(X0) & ~predj(X0) & ~prede(X0))) & ((predh(X0) | predj(X0) | prede(X0)) | ~predh(X0))) | ~room(X0)) [nnf transformation 184]
233. ! [X0] : (((predh(X0) | (~predh(X0) & ~predj(X0) & ~prede(X0))) & (predh(X0) | predj(X0) | prede(X0) | ~predh(X0))) | ~room(X0)) [flattening 232]
234. ! [X0] : ((predj(X0) | ((predh(X0) | ~predr(X0)) & (predr(X0) | ~predh(X0)))) & (((~predr(X0) | ~predh(X0)) & (predr(X0) | predh(X0))) | ~predj(X0))) [nnf transformation 60]
241. anywhere(X0) [cnf transformation 5]
322. room(mary) [cnf transformation 163]
358. ~predu(X0) | predr(X0) | ~room(X0) [cnf transformation 182]
365. ~predj(X0) | predh(X0) | ~room(X0) [cnf transformation 233]
368. ~predj(X0) | ~predh(X0) | ~predr(X0) [cnf transformation 234]
372. ~predh(X0) | ~predq(X0) | ~room(X0) [cnf transformation 188]
374. ~predi(X0) | predj(X0) [cnf transformation 189]
387. predq(X0) | predu(X0) | ~anywhere(X0) [cnf transformation 196]
392. predi(mary) [cnf transformation 198]
526. 30 <=> ! [X0] : (predq(X0) | predu(X0)) [avatar definition]
527. predq(X0) | predu(X0) <- (30) [avatar component clause 526]
584. predq(X0) | predu(X0) [subsumption resolution 387,241]
585. 30 [avatar split clause 584,526]
586. predj(mary) [resolution 374,392]
609. 42 <=> predr(mary) [avatar definition]
610. ~predr(mary) <- (~42) [avatar component clause 609]
705. predh(mary) | ~room(mary) [resolution 365,586]
706. predh(mary) [subsumption resolution 705,322]
710. ~predh(mary) | ~predr(mary) [resolution 368,586]
711. ~predr(mary) [subsumption resolution 710,706]
714. ~42 [avatar split clause 711,609]
921. ~predq(mary) | ~room(mary) [resolution 706,372]
924. ~predq(mary) [subsumption resolution 921,322]
941. predu(mary) <- (30) [resolution 924,527]
999. predr(mary) | ~room(mary) <- (30) [resolution 941,358]
1358. ~room(mary) <- (30, ~42) [subsumption resolution 999,610]
1359. $false <- (30, ~42) [subsumption resolution 1358,322]
1360. ~30 | 42 [avatar contradiction clause 1359]
1361. $false [avatar sat refutation 585,714,1360]
% SZS output end Proof for 8837776930836293156711627
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5756
% Time elapsed: 0.042 s
% ------------------------------
% ------------------------------
| 0.006216 |
Thomas, Mathew are the only persons in the room. Everyone outside the room who is not quiet is not quiet, not old, not tall, not kind. Everyone in the room is richer than Erick. Mathew is a kind tall quiet old person. Everyone in the room is kind if they is older than Ruby. Mathew is a tall person. Mathew who is richer than Ruby, is older than Raymond or is older than Erick is older than Ruby. If someone is richer than Ruby then he/she is a tall person and vice versa. Everyone in the room is quieter than Erick only if they is quieter than Ruby. No one anywhere is not a tall person if they is quieter than Ruby. Raymond is older than Mathew. More than one person outside the room is not not kind. All quiet persons are old. Someone who is quieter than Ruby is older than someone who is older than Erick. Thomas and Mathew are tall. Everyone in the room is a quiet kind old person. Thomas and Mathew are quiet persons. Someone who is older than Erick is older than someone who is a tall person. Mathew is a old person. Thomas is old. Mathew is older than Ruby. Everyone in the room who is quieter than Erick, is not a kind old tall person or is not a quiet person is not a tall person. All old persons are kind. Erick is older than Mathew. Mathew is richer than Raymond. | Mathew is quieter than Ruby. | entailment | room(thomas)&room(mathew)&(![X]:(room(X)=>(X='thomas'|X='mathew')))&
(![X]:(~room(X)=>(((~quiet(X))=>(~quiet(X)&~old(X)&~tall(X)&~kind(X))))))&
(![X]:(room(X)=>(richer(erick,X))))&
(kind(mathew)&tall(mathew)&quiet(mathew)&old(mathew)&person(mathew))&
(![X]:(room(X)=>(((older(ruby,X))=>(kind(X))))))&
(tall(mathew)&person(mathew))&
((((richer(ruby,mathew))|(older(raymond,mathew))|(older(erick,mathew))))&(older(ruby,mathew)))&
((![X]:((richer(ruby,X))<=>(tall(X)&person(X)))))&
(![X]:(room(X)=>(((quieter(ruby,X))<=(quieter(erick,X))))))&
(~?[X]:(anywhere(X)=>(((quieter(ruby,X))=>(~(tall(X)&person(X)))))))&
(older(mathew,raymond))&
((?[X,Y]:(~room(X)&~room(Y)&(~~kind(X)&~~kind(Y))&(X!=Y))))&
(![X]:(quiet(X)=>old(X)))&
(?[X,Y]:((quieter(ruby,X))&(older(erick,Y))&(older(X,Y))))&
(tall(thomas)&tall(mathew))&
(![X]:(room(X)=>(quiet(X)&kind(X)&old(X)&person(X))))&
(quiet(thomas)&person(thomas)&quiet(mathew)&person(mathew))&
(?[X,Y]:((older(erick,X))&(tall(Y)&person(Y))&(older(X,Y))))&
(old(mathew)&person(mathew))&
(old(thomas))&
(older(ruby,mathew))&
(![X]:(room(X)=>(((((quieter(erick,X))|(~(kind(X)&old(X)&tall(X)&person(X)))|(~(quiet(X)&person(X)))))=>(~(tall(X)&person(X)))))))&
(![X]:(old(X)=>kind(X)))&
(older(mathew,erick))&
(richer(raymond,mathew)) | room(thomas)&room(mathew)&(![X]:(room(X)=>(X='thomas'|X='mathew')))&
quieter(ruby,mathew) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 384116803063534935261892
% SZS output start Proof for 384116803063534935261892
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
53. ~? [X0] : (anywhere(X0) => (quieter(john,X0) => ~(person(X0) & tall(X0)))) [input p9]
69. ~(quieter(john,paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
70. ~? [X0] : (quieter(john,X0) => ~(person(X0) & tall(X0))) [pure predicate removal 53]
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]
152. ! [X0] : ((person(X0) & tall(X0)) & quieter(john,X0)) [ennf transformation 70]
153. ! [X0] : (person(X0) & tall(X0) & quieter(john,X0)) [flattening 152]
159. ~quieter(john,paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 69]
160. ~quieter(john,paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 159]
170. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom]
171. ~quieter(john,paul) | (paul != sK6 & mary != sK6 & room(sK6)) | ~room(paul) | ~room(mary) [skolemisation 160,170]
252. room(mary) [cnf transformation 144]
253. room(paul) [cnf transformation 144]
254. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 144]
274. quieter(john,X0) [cnf transformation 153]
315. ~quieter(john,paul) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 171]
316. ~quieter(john,paul) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 171]
317. ~quieter(john,paul) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 171]
333. paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 317,274]
334. paul != sK6 | ~room(mary) [subsumption resolution 333,253]
335. paul != sK6 [subsumption resolution 334,252]
336. mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 316,274]
337. mary != sK6 | ~room(mary) [subsumption resolution 336,253]
338. mary != sK6 [subsumption resolution 337,252]
339. room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 315,274]
340. room(sK6) | ~room(mary) [subsumption resolution 339,253]
341. room(sK6) [subsumption resolution 340,252]
377. mary = sK6 | paul = sK6 [resolution 254,341]
378. paul = sK6 [subsumption resolution 377,338]
379. $false [subsumption resolution 378,335]
% SZS output end Proof for 384116803063534935261892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.23499 |
Flora, David, Helen, Shawn are the only persons in the room. Helen is an enthusiastic bird watcher who travels for rare sightings if everyone in the room collects luxury watches or does not enjoy wildlife photography and vice versa. If David collects luxury watches then everyone anywhere who enjoys wildlife photography collects antique clocks. If everyone in the room enjoys wildlife photography or does not have completed a triathlon then Helen is an enthusiastic bird watcher who travels for rare sightings. If David works as a freelance web developer specializing in e-commerce sites then everyone in the room who collects luxury watches has completed a triathlon. If Helen collects antique clocks then everyone anywhere who collects antique clocks makes intricate hand-cut paper art for exhibitions. If at least one person anywhere makes intricate hand-cut paper art for exhibitions then Helen collects antique clocks. If not everyone in the room is a skilled home brewer experimenting with craft beer recipes or does not make intricate hand-cut paper art for exhibitions then Helen enjoys wildlife photography. If Flora works as a freelance web developer specializing in e-commerce sites then if someone has completed a triathlon then he/she is a skilled home brewer experimenting with craft beer recipes and vice versa. If everyone in the room makes intricate hand-cut paper art for exhibitions or does not own an Android phone then Flora enjoys wildlife photography. David owns an Android phone if everyone in the room is an enthusiastic bird watcher who travels for rare sightings or does not own an Android phone and vice versa. If Helen is an enthusiastic bird watcher who travels for rare sightings then Helen collects luxury watches. If someone enjoys wildlife photography or creates large-scale murals for public art installations or both then he/she works as a freelance web developer specializing in e-commerce sites and vice versa. David works as a freelance web developer specializing in e-commerce sites. Helen is a member of a local theater group specializing in improv. David owns an Android phone. Helen collects antique clocks. At least one person in the room works as a freelance web developer specializing in e-commerce sites. | Everyone anywhere collects luxury watches. | neutral | room(flora)&room(david)&room(helen)&room(shawn)&(![X]:(room(X)=>(X='flora'|X='david'|X='helen'|X='shawn')))&
((![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))|(collects_luxury_watches(X))))))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(helen)))&
((collects_luxury_watches(david))=>(![X]:(anywhere(X)=>(((enjoys_wildlife_photography(X))=>(collects_antique_clocks(X)))))))&
((![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(enjoys_wildlife_photography(X))))))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(helen)))&
((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(david))=>(![X]:(room(X)=>(((collects_luxury_watches(X))=>(has_completed_a_triathlon(X)))))))&
((collects_antique_clocks(helen))=>(![X]:(anywhere(X)=>(((collects_antique_clocks(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))))&
((((?[X]:(anywhere(X)&makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))=>(collects_antique_clocks(helen)))&
((~![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(enjoys_wildlife_photography(helen)))&
((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(flora))=>((![X]:((has_completed_a_triathlon(X))<=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))&
((![X]:(room(X)=>(((does_not_own_an_Android_phone(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))=>(enjoys_wildlife_photography(flora)))&
((![X]:(room(X)=>(((does_not_own_an_Android_phone(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))<=>(owns_an_Android_phone(david)))&
((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(helen))=>(collects_luxury_watches(helen)))&
((![X]:((((enjoys_wildlife_photography(X))|(creates_large-scale_murals_for_public_art_installations(X))))<=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))&
(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(david))&
(is_a_member_of_a_local_theater_group_specializing_in_improv(helen))&
(owns_an_Android_phone(david))&
(collects_antique_clocks(helen))&
(((?[X]:(room(X)&works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))&
(![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(enjoys_wildlife_photography(helen))&
(creates_large-scale_murals_for_public_art_installations(flora))&
(collects_luxury_watches(david))&
(![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))&
((![X]:((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(has_completed_a_triathlon(X)))))&
(collects_luxury_watches(helen))&
((?[X,Y]:(anywhere(X)&anywhere(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))))&
(~(collects_antique_clocks(david)))&
(![X]:(anywhere(X)=>(((collects_antique_clocks(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))) | room(flora)&room(david)&room(helen)&room(shawn)&(![X]:(room(X)=>(X='flora'|X='david'|X='helen'|X='shawn')))&
![X]:(anywhere(X)=>(collects_luxury_watches(X))) | [] | null | 0.255505 |
Linda is the only person in the room.
If 'Linda is old' then 'Gary is older than Linda'.
Either 'Lenora is quieter than Linda' or 'Linda is quieter than Gary' but not both.
If 'Lenora is quieter than Linda' then 'if someone is quieter than Lenora then he/she is quiet and vice versa'.
If 'Linda is older than Gary' then 'Linda is not not not quiet'.
If 'Linda is richer than Gary' then 'all old person is quiet'.
All old person is quiet.
Linda is the oldest outside the room.
Everyone outside the room who is quieter than Gary is richer than Lenora.
All quiet person is old.
If someone is quieter than Lenora then he/she is not not not not not not quiet.
Gary is richer than Linda.
Lenora is richer than Linda.
Linda is not not not quiet.
Everyone in the room is quieter than Gary if they is not not not not not quiet.
Everyone in the room who is not not not old is quieter than Gary.
Linda is not a quiet old person. | Lenora is older than Linda. | contradiction | room(linda)&(![X]:(room(X)=>(X='linda')))&
((old(linda))=>(older(linda,gary)))&
((quieter(linda,lenora))<~>(quieter(gary,linda)))&
((quieter(linda,lenora))=>((![X]:((quieter(lenora,X))<=>(quiet(X))))))&
((older(gary,linda))=>(~~~quiet(linda)))&
((richer(gary,linda))=>(![X]:(old(X)=>quiet(X))))&
(![X]:(old(X)=>quiet(X)))&
(![X]:((~room(X)&(X!=linda))=>older(X,linda)))&
(![X]:(~room(X)=>(((quieter(gary,X))=>(richer(lenora,X))))))&
(![X]:(quiet(X)=>old(X)))&
((![X]:((quieter(lenora,X))=>(~~~~~~quiet(X)))))&
(richer(linda,gary))&
(richer(linda,lenora))&
(~~~quiet(linda))&
(![X]:(room(X)=>(((~~~~~quiet(X))=>(quieter(gary,X))))))&
(![X]:(room(X)=>(((~~~old(X))=>(quieter(gary,X))))))&
(~(quiet(linda)&old(linda)&person(linda))) | room(linda)&(![X]:(room(X)=>(X='linda')))&
older(linda,lenora) | [
"b19",
"b42",
"p0",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7313276390586747124529967
% SZS output start Proof for 7313276390586747124529967
20. ! [X0,X1] : (X0 != X1 => (older(X0,X1) => ~older(X1,X0))) [input b19]
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]
51. ! [X0] : ((mary != X0 & ~room(X0)) => older(X0,mary)) [input p7]
61. older(mary,fred) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
93. ! [X0,X1] : ((~older(X1,X0) | ~older(X0,X1)) | X0 = X1) [ennf transformation 20]
94. ! [X0,X1] : (~older(X1,X0) | ~older(X0,X1) | X0 = X1) [flattening 93]
135. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
141. ! [X0] : (older(X0,mary) | (mary = X0 | room(X0))) [ennf transformation 51]
142. ! [X0] : (older(X0,mary) | mary = X0 | room(X0)) [flattening 141]
151. older(mary,fred) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 61]
170. ~older(X1,X0) | ~older(X0,X1) | X0 = X1 [cnf transformation 94]
205. mary != fred [cnf transformation 43]
236. ~room(X0) | mary = X0 [cnf transformation 135]
245. older(X0,mary) | mary = X0 | room(X0) [cnf transformation 142]
256. older(mary,fred) [cnf transformation 151]
302. older(X0,mary) | mary = X0 [subsumption resolution 245,236]
326. ~older(fred,mary) | mary = fred [resolution 170,256]
329. ~older(fred,mary) [subsumption resolution 326,205]
338. mary = fred [resolution 329,302]
339. $false [subsumption resolution 338,205]
% SZS output end Proof for 7313276390586747124529967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.570034 |
Linda, Leslie are the only persons in the room.
If “Linda is not a old person” then “Leslie either is a tall person or is not a tall old quiet person but not both”.
“If someone is richer than Jean then he/she is quieter than Thomas” if “Linda is quieter than Thomas”.
No old person is tall.
Linda is older than Jessica.
Leslie is richer than Jean.
Linda is richer than Jean.
Leslie is not a old tall person.
If someone is quieter than Thomas then he/she neither is a quiet tall person nor is not a quiet tall person.
Jessica is quieter than Linda.
Linda is not a quiet old person.
Thomas is richer than Leslie. | Linda is quiet. | neutral | room(linda)&room(leslie)&(![X]:(room(X)=>(X='linda'|X='leslie')))&
((~(old(linda)&person(linda)))=>(((tall(leslie)&person(leslie))<~>(~(tall(leslie)&old(leslie)&quiet(leslie)&person(leslie))))))&
((quieter(thomas,linda))=>((![X]:((richer(jean,X))=>(quieter(thomas,X))))))&
(~?[X]:(old(X)=>tall(X)))&
(older(jessica,linda))&
(richer(jean,leslie))&
(richer(jean,linda))&
(~(old(leslie)&tall(leslie)&person(leslie)))&
((![X]:((quieter(thomas,X))=>(~((quiet(X)&tall(X)&person(X))|(~(quiet(X)&tall(X)&person(X))))))))&
(quieter(linda,jessica))&
(~(quiet(linda)&old(linda)&person(linda)))&
(richer(leslie,thomas)) | room(linda)&room(leslie)&(![X]:(room(X)=>(X='linda'|X='leslie')))&
quiet(linda) | [] | null | 0.402887 |
There is a room. Either everyone outside the room is a chess master who participates in national tournaments or is not a chess master who participates in national tournaments or everyone in the room is a chess master who participates in national tournaments or is not passionate about collecting and restoring classic cars but not both. Everyone in the room is not a cybersecurity expert or is passionate about collecting and restoring classic cars if it is true that at least one person in the room is a chess master who participates in national tournaments and vice versa. Everyone in the room is not passionate about collecting and restoring classic cars or practices pilates only if someone in the room neither is passionate about collecting and restoring classic cars nor creates bespoke furniture pieces from reclaimed wood. If at least one person in the room practices pilates then everyone in the room who neither is passionate about collecting and restoring classic cars nor creates bespoke furniture pieces from reclaimed wood practices pilates. Everyone in the room is not passionate about collecting and restoring classic cars if they practices pilates. | Everyone outside the room does not create bespoke furniture pieces from reclaimed wood. | neutral | (there_is_a_room)&
((![X]:(~room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))))<~>(![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(is_a_chess_master_who_participates_in_national_tournaments(X)))))))&
((((?[X]:(room(X)&is_a_chess_master_who_participates_in_national_tournaments(X)))))<=>(![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(is_not_a_cybersecurity_expert(X)))))))&
((![X]:(room(X)=>(((practices_pilates(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))=>(?[X]:(room(X)&(~((is_passionate_about_collecting_and_restoring_classic_cars(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))&
((((?[X]:(room(X)&practices_pilates(X)))))=>(![X]:(room(X)=>(((~((is_passionate_about_collecting_and_restoring_classic_cars(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(practices_pilates(X)))))))&
(![X]:(room(X)=>(((practices_pilates(X))=>(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))&
(![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))=>(practices_pilates(X))))))&
(![X]:(room(X)=>(((practices_pilates(X))=>(is_a_cybersecurity_expert(X))))))&
(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(~((is_a_cybersecurity_expert(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))))&
(((?[X]:(room(X)&creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))&
(![X]:(room(X)=>(((~((is_passionate_about_collecting_and_restoring_classic_cars(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(practices_pilates(X))))))&
(![X]:(room(X)=>(((((does_not_practice_pilates(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))&
(?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X)))) | (there_is_a_room)&
![X]:(~room(X)=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))) | [] | null | 0 |
Cecil, Lorraine are the only persons in the room.
If “at least one person in the room streams on Twitch” then “everyone in the room knows morse code if they is allergic to anything and vice versa”.
If “it is not the case that “someone in the room practices tai chi”” then “someone in the room has a specialized collection of handmade artisan pottery”.
“Someone outside the room collects first edition books” if “Cecil has a pet dog” and vice versa.
If “at least one person in the room does not know morse code” then “no one in the room is not a culinary enthusiast who experiments with international cuisines if they enjoys stand-up paddleboarding” otherwise “someone in the room is allergic to anything”.
Lorraine enjoys coding in Python.
If someone is a culinary enthusiast who experiments with international cuisines then he/she is allergic to anything.
Lorraine is a culinary enthusiast who experiments with international cuisines.
Everyone in the room who collects first edition books streams on Twitch.
At least one person in the room is a scotch connoisseur.
Cecil who is allergic to anything enjoys coding in Python.
Cecil enjoys stand-up paddleboarding.
Lorraine has a pet dog, is a culinary enthusiast who experiments with international cuisines or does not have a pet dog.
At least one person in the room is a culinary enthusiast who experiments with international cuisines, practices tai chi or has a specialized collection of handmade artisan pottery.
Lorraine has a pet dog.
Someone outside the room is allergic to anything.
If someone enjoys stand-up paddleboarding then he/she has a pet dog. | Only one person in the room is a culinary enthusiast who experiments with international cuisines. | neutral | room(cecil)&room(lorraine)&(![X]:(room(X)=>(X='cecil'|X='lorraine')))&
((((?[X]:(room(X)&streams_on_Twitch(X)))))=>(![X]:(room(X)=>(((knows_morse_code(X))<=>(is_allergic_to_anything(X)))))))&
((~(?[X]:(room(X)&(practices_tai_chi(X)))))=>(?[X]:(room(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))&
((has_a_pet_dog(cecil))<=>(?[X]:(~room(X)&(collects_first_edition_books(X)))))&
(((((?[X]:(room(X)&does_not_know_morse_code(X)))))=>(~?[X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))&((~(((?[X]:(room(X)&does_not_know_morse_code(X))))))=>(?[X]:(room(X)&(is_allergic_to_anything(X))))))&
(enjoys_coding_in_Python(lorraine))&
((![X]:((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(is_allergic_to_anything(X)))))&
(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(lorraine))&
(![X]:(room(X)=>(((collects_first_edition_books(X))=>(streams_on_Twitch(X))))))&
(((?[X]:(room(X)&is_a_scotch_connoisseur(X)))))&
((is_allergic_to_anything(cecil))&(enjoys_coding_in_Python(cecil)))&
(enjoys_stand-up_paddleboarding(cecil))&
(((has_a_pet_dog(lorraine))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(lorraine))|(does_not_have_a_pet_dog(lorraine))))&
(((?[X]:(room(X)&((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(practices_tai_chi(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))&
(has_a_pet_dog(lorraine))&
(?[X]:(~room(X)&(is_allergic_to_anything(X))))&
((![X]:((enjoys_stand-up_paddleboarding(X))=>(has_a_pet_dog(X)))))&
(?[X]:(room(X)&(is_a_scotch_connoisseur(X))))&
(knows_morse_code(cecil))&
(practices_tai_chi(cecil))&
(((has_a_specialized_collection_of_handmade_artisan_pottery(lorraine))|(knows_morse_code(lorraine))|(is_allergic_to_anything(lorraine))))&
(![X]:(anywhere(X)=>(((collects_first_edition_books(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(((?[X]:(room(X)&is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))) | room(cecil)&room(lorraine)&(![X]:(room(X)=>(X='cecil'|X='lorraine')))&
((?[X]:(room(X)&is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(Y)))=>(X=Y)))) | [] | null | 0.090254 |
Corey, David, Henry are the only persons in the room.
If “someone outside the room works on fridays” then “if someone works as a freelance web developer specializing in e-commerce sites, plays eSports competitively and enjoys windsurfing then he/she frequently participates in hackathons and coding competitions”.
If “everyone in the room does not work as a freelance web developer specializing in e-commerce sites or frequently participates in hackathons and coding competitions” then “it is not the case that “someone in the room does not work on fridays””.
If “someone in the room enjoys bird watching” then “at least one person in the room plays eSports competitively”.
“Everyone outside the room enjoys windsurfing if they has a curated collection of mid-century modern furniture” unless “everyone outside the room does not frequently participates in hackathons and coding competitions or works on fridays”.
If “everyone in the room plays eSports competitively or does not enjoy bird watching” then “if someone frequently participates in hackathons and coding competitions then he/she travels domestically frequently and vice versa”. | It is not the case that “David has a saltwater aquarium”. | neutral | room(corey)&room(david)&room(henry)&(![X]:(room(X)=>(X='corey'|X='david'|X='henry')))&
((?[X]:(~room(X)&(works_on_fridays(X))))=>((![X]:((((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(plays_eSports_competitively(X))&(enjoys_windsurfing(X))))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))&
((![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))=>(~(?[X]:(room(X)&(does_not_work_on_fridays(X))))))&
((?[X]:(room(X)&(enjoys_bird_watching(X))))=>(((?[X]:(room(X)&plays_eSports_competitively(X))))))&
(~(![X]:(~room(X)=>(((works_on_fridays(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(enjoys_windsurfing(X)))))))&
((![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))|(plays_eSports_competitively(X))))))=>((![X]:((frequently_participates_in_hackathons_and_coding_competitions(X))<=>(travels_domestically_frequently(X))))))&
((![X]:(~room(X)=>(((enjoys_windsurfing(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(?[X]:(room(X)&(frequently_participates_in_hackathons_and_coding_competitions(X)))))&
((?[X]:(room(X)&(enjoys_windsurfing(X))))=>(![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))))&
((((?[X]:(room(X)&enjoys_windsurfing(X)))))=>(?[X]:(~room(X)&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))&
((?[X]:(room(X)&(enjoys_windsurfing(X))))=>(![X]:(room(X)=>(((works_on_fridays(X))=>(does_not_have_a_saltwater_aquarium(X)))))))&
((![X]:((enjoys_windsurfing(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))&
(?[X]:(~room(X)&(has_a_curated_collection_of_mid-century_modern_furniture(X))))&
(((?[X]:(room(X)&frequently_participates_in_hackathons_and_coding_competitions(X)))))&
((![X]:((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(has_a_saltwater_aquarium(X)))))&
(![X]:(room(X)=>(((plays_eSports_competitively(X))=>(enjoys_windsurfing(X))))))&
(![X]:(room(X)=>(((enjoys_bird_watching(X))=>(travels_domestically_frequently(X))))))&
(![X]:(room(X)=>(((travels_domestically_frequently(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))&
(?[X]:(room(X)&(enjoys_windsurfing(X))))&
((![X]:((enjoys_windsurfing(X))=>(is_allergic_to_anything(X)))))&
(((?[X]:(room(X)&is_allergic_to_anything(X)))))&
((![X]:((enjoys_windsurfing(X))=>(has_a_saltwater_aquarium(X)))))&
((![X]:((has_a_saltwater_aquarium(X))=>(enjoys_bird_watching(X))))) | room(corey)&room(david)&room(henry)&(![X]:(room(X)=>(X='corey'|X='david'|X='henry')))&
~(has_a_saltwater_aquarium(david)) | [] | null | 0.640751 |
There is a room. If “everyone in the room maintains a large, organic vegetable garden year-round or does not maintain a large, organic vegetable garden year-round” then “if someone practices pilates then he/she does not maintain a large, organic vegetable garden year-round”. If “everyone anywhere does not host themed dinner parties featuring gourmet home-cooked meals or cannot play the guitar” then “not everyone in the room maintains a large, organic vegetable garden year-round”. “Everyone in the room who does not practice pilates does not host themed dinner parties featuring gourmet home-cooked meals” unless “no one in the room does not maintain a large, organic vegetable garden year-round or hosts themed dinner parties featuring gourmet home-cooked meals”. “Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or enjoys bird watching” if “everyone anywhere does not maintain a large, organic vegetable garden year-round or enjoys bird watching” and vice versa. “Someone in the room can play the guitar” if “everyone anywhere can play the guitar or does not host themed dinner parties featuring gourmet home-cooked meals” and vice versa. If “no one in the room enjoys bird watching” then “everyone outside the room who either hosts themed dinner parties featuring gourmet home-cooked meals or does not host themed dinner parties featuring gourmet home-cooked meals but not both neither maintains a large, organic vegetable garden year-round nor practices pilates”. Everyone in the room neither maintains a large, organic vegetable garden year-round nor practices pilates only if they can play the guitar. Everyone in the room either cannot play the guitar or can play the guitar but not both if they can play the guitar. Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or cannot play the guitar. Everyone in the room enjoys bird watching. Everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals if they hosts themed dinner parties featuring gourmet home-cooked meals or can play the guitar or both. Everyone in the room who maintains a large, organic vegetable garden year-round does not host themed dinner parties featuring gourmet home-cooked meals. No one outside the room who practices pilates does not host themed dinner parties featuring gourmet home-cooked meals. | Everyone in the room practices pilates. | entailment | (there_is_a_room)&
((![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))=>((![X]:((practices_pilates(X))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))&
((![X]:(anywhere(X)=>(((cannot_play_the_guitar(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))=>(~![X]:(room(X)=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))&
(~(~?[X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))=>(![X]:(room(X)=>(((does_not_practice_pilates(X))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))&
((![X]:(anywhere(X)=>(((enjoys_bird_watching(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))<=>(![X]:(room(X)=>(((enjoys_bird_watching(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))&
((![X]:(anywhere(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(can_play_the_guitar(X))))))<=>(?[X]:(room(X)&(can_play_the_guitar(X)))))&
((~?[X]:(room(X)=>(enjoys_bird_watching(X))))=>(![X]:(~room(X)=>(((((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<~>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))=>(~((maintains_a_large,_organic_vegetable_garden_year-round(X))|(practices_pilates(X)))))))))&
(![X]:(room(X)=>(((can_play_the_guitar(X))<=(~((maintains_a_large,_organic_vegetable_garden_year-round(X))|(practices_pilates(X))))))))&
(![X]:(room(X)=>(((can_play_the_guitar(X))=>(((cannot_play_the_guitar(X))<~>(can_play_the_guitar(X))))))))&
(![X]:(room(X)=>(((cannot_play_the_guitar(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(![X]:(room(X)=>(enjoys_bird_watching(X))))&
(![X]:(room(X)=>(((((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(can_play_the_guitar(X))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(~?[X]:(~room(X)=>(((practices_pilates(X))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(practices_pilates(X))) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8518665070750333441300985
% SZS output start Proof for 8518665070750333441300985
44. there_is_a_room [input p0]
57. ~? [X0] : (~room(X0) => (predc(X0) => ~prede(X0))) [input p13]
58. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis]
160. ! [X0] : ((prede(X0) & predc(X0)) & ~room(X0)) [ennf transformation 57]
161. ! [X0] : (prede(X0) & predc(X0) & ~room(X0)) [flattening 160]
162. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 58]
187. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK8) & room(sK8)) [choice axiom]
188. (~predc(sK8) & room(sK8)) | ~there_is_a_room [skolemisation 162,187]
270. there_is_a_room [cnf transformation 44]
309. predc(X0) [cnf transformation 161]
312. ~predc(sK8) | ~there_is_a_room [cnf transformation 188]
456. ~there_is_a_room [subsumption resolution 312,309]
457. $false [subsumption resolution 456,270]
% SZS output end Proof for 8518665070750333441300985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.001348 |
There is a room.
If “no one in the room enjoys deep-sea diving and exploring underwater caves or is not a tea enthusiast” then “everyone outside the room is a tea enthusiast”.
If “everyone in the room is a tea enthusiast or does not play the drums” then “everyone in the room is not a tea enthusiast if they enjoys deep-sea diving and exploring underwater caves”.
Everyone in the room who enjoys deep-sea diving and exploring underwater caves, is a tea enthusiast and enjoys logic puzzles plays the drums.
Not everyone in the room enjoys deep-sea diving and exploring underwater caves if they plays the drums.
Everyone anywhere enjoys logic puzzles if they plays the drums.
Everyone in the room who works as a freelance web developer specializing in e-commerce sites is a tea enthusiast.
Everyone in the room enjoys logic puzzles.
Everyone in the room does not work as a freelance web developer specializing in e-commerce sites or enjoys logic puzzles. | Everyone outside the room is a tea enthusiast. | neutral | (there_is_a_room)&
((~?[X]:(room(X)=>(((is_not_a_tea_enthusiast(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(![X]:(~room(X)=>(is_a_tea_enthusiast(X)))))&
((![X]:(room(X)=>(((does_not_play_the_drums(X))|(is_a_tea_enthusiast(X))))))=>(![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(is_not_a_tea_enthusiast(X)))))))&
(![X]:(room(X)=>(((((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(is_a_tea_enthusiast(X))&(enjoys_logic_puzzles(X))))=>(plays_the_drums(X))))))&
(~![X]:(room(X)=>(((plays_the_drums(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))&
(![X]:(anywhere(X)=>(((plays_the_drums(X))=>(enjoys_logic_puzzles(X))))))&
(![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(is_a_tea_enthusiast(X))))))&
(![X]:(room(X)=>(enjoys_logic_puzzles(X))))&
(![X]:(room(X)=>(((enjoys_logic_puzzles(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))&
(![X]:(anywhere(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(is_a_tea_enthusiast(X))) | [] | null | 0.312075 |
Anthony is the only person in the room. Everyone in the room enjoys bird watching if and only if they is a culinary enthusiast who experiments with international cuisines. Everyone in the room is a culinary enthusiast who experiments with international cuisines only if they enjoys bird watching. Everyone in the room collects first edition books if and only if they enjoys wildlife photography. Everyone in the room maintains a personal blog focused on cybersecurity tips, regularly goes on multi-day backpacking trips in national parks or has a saltwater aquarium if they enjoys wildlife photography. Anthony regularly goes on multi-day backpacking trips in national parks. Everyone in the room collects first edition books. | Anthony enjoys wildlife photography. | entailment | room(anthony)&(![X]:(room(X)=>(X='anthony')))&
(![X]:(room(X)=>(((enjoys_bird_watching(X))<=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(![X]:(room(X)=>(((enjoys_bird_watching(X))<=(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(![X]:(room(X)=>(((collects_first_edition_books(X))<=>(enjoys_wildlife_photography(X))))))&
(![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(has_a_saltwater_aquarium(X))))))))&
(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(anthony))&
(![X]:(room(X)=>(((owns_a_smart_tv(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))&
(![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))&
(![X]:(room(X)=>(((collect_rare_sneakers(X))=>(enjoys_fishing(X))))))&
(((?[X]:(room(X)&is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))&
(is_an_avid_hiker(anthony))&
(![X]:(room(X)=>(((((uses_a_Windows_laptop(X))&(plays_the_drums(X))))<=(plays_the_drums(X))))))&
(collect_rare_sneakers(anthony))&
(![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))|(enjoys_making_ceramics(X))))))&
(enjoys_fishing(anthony))&
((![X]:((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))&
(participates_in_citizen_science_projects_related_to_wildlife_monitoring(anthony))&
(![X]:(room(X)=>(collects_first_edition_books(X))))&
(uses_a_Windows_laptop(anthony))&
((![X]:((collect_rare_sneakers(X))<=>(enjoys_fishing(X))))) | room(anthony)&(![X]:(room(X)=>(X='anthony')))&
enjoys_wildlife_photography(anthony) | [
"p0",
"p3",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6028244808746929977798044
% SZS output start Proof for 6028244808746929977798044
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
47. ! [X0] : (room(X0) => (predq(X0) <=> predb(X0))) [input p3]
61. ! [X0] : (room(X0) => predq(X0)) [input p17]
64. ~(predb(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
146. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
150. ! [X0] : ((predq(X0) <=> predb(X0)) | ~room(X0)) [ennf transformation 47]
155. ! [X0] : (predq(X0) | ~room(X0)) [ennf transformation 61]
156. ~predb(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 64]
159. ! [X0] : (((predq(X0) | ~predb(X0)) & (predb(X0) | ~predq(X0))) | ~room(X0)) [nnf transformation 150]
163. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom]
164. ~predb(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 156,163]
245. room(mary) [cnf transformation 146]
246. ~room(X0) | mary = X0 [cnf transformation 146]
250. ~predq(X0) | predb(X0) | ~room(X0) [cnf transformation 159]
258. ~room(X0) | predq(X0) [cnf transformation 155]
261. ~predb(mary) | room(sK1) | ~room(mary) [cnf transformation 164]
262. ~predb(mary) | mary != sK1 | ~room(mary) [cnf transformation 164]
263. ~predb(mary) | mary != sK1 [subsumption resolution 262,245]
265. 1 <=> mary = sK1 [avatar definition]
267. mary != sK1 <- (~1) [avatar component clause 265]
269. 2 <=> predb(mary) [avatar definition]
272. ~1 | ~2 [avatar split clause 263,269,265]
273. ~predb(mary) | room(sK1) [subsumption resolution 261,245]
275. 3 <=> room(sK1) [avatar definition]
277. room(sK1) <- (3) [avatar component clause 275]
278. 3 | ~2 [avatar split clause 273,269,275]
279. predq(mary) [resolution 258,245]
291. predb(mary) | ~room(mary) [resolution 250,279]
295. predb(mary) [subsumption resolution 291,245]
296. 2 [avatar split clause 295,269]
297. mary = sK1 <- (3) [resolution 277,246]
299. $false <- (~1, 3) [subsumption resolution 297,267]
300. 1 | ~3 [avatar contradiction clause 299]
301. $false [avatar sat refutation 272,278,296,300]
% SZS output end Proof for 6028244808746929977798044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.101424 |