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Dylan, Yesenia, Donald are the only persons in the room. Yesenia does not enjoy rooftop gardening and enjoys making ceramics. Everyone anywhere who neither writes poetry nor collects luxury watches enjoys stargazing. Someone in the room neither own a television nor enjoys landscape photography. Only one person in the room hosts a YouTube channel dedicated to art tutorials. Only one person in the room either does not own a television or hosts a YouTube channel dedicated to art tutorials but not both. Yesenia either hosts regular workshops on creative writing or is not a night owl but not both. Dylan is a night owl. Donald does not enjoy making ceramics. Dylan does not own a television. Yesenia neither does not compose and performs experimental electronic music nor enjoys kayaking and exploring remote waterways. If someone neither does not own a smart tv nor mentors a youth basketball team on weekends then he/she is a night owl and vice versa. Donald enjoys rooftop gardening. Donald does not host a YouTube channel dedicated to art tutorials. More than one person in the room composes and performs experimental electronic music. Dylan either uses contact lenses or does not host regular workshops on creative writing but not both. Dylan owns a 3D printer.

Dylan owns a smart tv.

entailment

room(dylan)&room(yesenia)&room(donald)&(![X]:(room(X)=>(X='dylan'|X='yesenia'|X='donald')))& (((does_not_enjoy_rooftop_gardening(yesenia))&(enjoys_making_ceramics(yesenia))))& (![X]:(anywhere(X)=>(((~((writes_poetry(X))|(collects_luxury_watches(X))))=>(enjoys_stargazing(X))))))& (?[X]:(room(X)&(~((own_a_television(X))|(enjoys_landscape_photography(X))))))& (((?[X]:(room(X)&hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))&(![X,Y]:((room(X)&room(Y)&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(Y)))=>(X=Y)))))& (((?[X]:(room(X)&((does_not_own_a_television(X))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))&(![X,Y]:((room(X)&room(Y)&(((does_not_own_a_television(X))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))&(((does_not_own_a_television(Y))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(Y)))))=>(X=Y)))))& (((hosts_regular_workshops_on_creative_writing(yesenia))<~>(is_not_a_night_owl(yesenia))))& (is_a_night_owl(dylan))& (does_not_enjoy_making_ceramics(donald))& (does_not_own_a_television(dylan))& (~((does_not_compose_and_performs_experimental_electronic_music(yesenia))|(enjoys_kayaking_and_exploring_remote_waterways(yesenia))))& ((![X]:((~((does_not_own_a_smart_tv(X))|(mentors_a_youth_basketball_team_on_weekends(X))))<=>(is_a_night_owl(X)))))& (enjoys_rooftop_gardening(donald))& (does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(donald))& ((?[X,Y]:(room(X)&room(Y)&(composes_and_performs_experimental_electronic_music(X)&composes_and_performs_experimental_electronic_music(Y))&(X!=Y))))& (((uses_contact_lenses(dylan))<~>(does_not_host_regular_workshops_on_creative_writing(dylan))))& (owns_a_3D_printer(dylan))

room(dylan)&room(yesenia)&room(donald)&(![X]:(room(X)=>(X='dylan'|X='yesenia'|X='donald')))& owns_a_smart_tv(dylan)

% SZS status Unsatisfiable for 2627722657833727467389917 % SZS output start Proof for 2627722657833727467389917 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 51. predr(mary) [input p7] 55. ! [X0] : (~(predh(X0) | ~predq(X0)) <=> predr(X0)) [input p11] 61. ~(predq(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 142. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 142] 149. ! [X0] : ((~predh(X0) & predq(X0)) <=> predr(X0)) [ennf transformation 55] 150. ~predq(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 61] 151. ~predq(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 150] 162. ! [X0] : (((~predh(X0) & predq(X0)) | ~predr(X0)) & (predr(X0) | (predh(X0) | ~predq(X0)))) [nnf transformation 149] 163. ! [X0] : (((~predh(X0) & predq(X0)) | ~predr(X0)) & (predr(X0) | predh(X0) | ~predq(X0))) [flattening 162] 167. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 168. ~predq(mary) | (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 151,167] 249. room(mary) [cnf transformation 143] 250. room(paul) [cnf transformation 143] 251. room(fred) [cnf transformation 143] 252. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143] 269. predr(mary) [cnf transformation 51] 273. ~predr(X0) | predq(X0) [cnf transformation 163] 282. ~predq(mary) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 283. ~predq(mary) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 284. ~predq(mary) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 285. ~predq(mary) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 317. ~predq(mary) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 285,251] 318. ~predq(mary) | fred != sK5 | ~room(mary) [subsumption resolution 317,250] 319. ~predq(mary) | fred != sK5 [subsumption resolution 318,249] 321. 7 <=> fred = sK5 [avatar definition] 323. fred != sK5 <- (~7) [avatar component clause 321] 325. 8 <=> predq(mary) [avatar definition] 328. ~7 | ~8 [avatar split clause 319,325,321] 329. ~predq(mary) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 284,251] 330. ~predq(mary) | paul != sK5 | ~room(mary) [subsumption resolution 329,250] 331. ~predq(mary) | paul != sK5 [subsumption resolution 330,249] 333. 9 <=> paul = sK5 [avatar definition] 335. paul != sK5 <- (~9) [avatar component clause 333] 336. ~9 | ~8 [avatar split clause 331,325,333] 337. ~predq(mary) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 283,251] 338. ~predq(mary) | mary != sK5 | ~room(mary) [subsumption resolution 337,250] 339. ~predq(mary) | mary != sK5 [subsumption resolution 338,249] 341. 10 <=> mary = sK5 [avatar definition] 343. mary != sK5 <- (~10) [avatar component clause 341] 344. ~10 | ~8 [avatar split clause 339,325,341] 345. ~predq(mary) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 282,251] 346. ~predq(mary) | room(sK5) | ~room(mary) [subsumption resolution 345,250] 347. ~predq(mary) | room(sK5) [subsumption resolution 346,249] 349. 11 <=> room(sK5) [avatar definition] 351. room(sK5) <- (11) [avatar component clause 349] 352. 11 | ~8 [avatar split clause 347,325,349] 353. predq(mary) [resolution 273,269] 356. 8 [avatar split clause 353,325] 408. paul = sK5 | mary = sK5 | fred = sK5 <- (11) [resolution 252,351] 474. mary = sK5 | fred = sK5 <- (~9, 11) [subsumption resolution 408,335] 475. fred = sK5 <- (~9, ~10, 11) [subsumption resolution 474,343] 476. $false <- (~7, ~9, ~10, 11) [subsumption resolution 475,323] 477. 7 | 9 | 10 | ~11 [avatar contradiction clause 476] 478. $false [avatar sat refutation 328,336,344,352,356,477] % SZS output end Proof for 2627722657833727467389917 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Eugene is the only person in the room. If 'everyone in the room does not enjoy watercolor painting or is a dedicated volunteer for local community service projects' then 'Eugene does not compose and performs experimental electronic music'. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings if they does not enjoy watercolor painting. It is not the case that 'Eugene is a culinary enthusiast who experiments with international cuisines'. Everyone outside the room who enjoys landscape photography collects antique jewelry. Someone anywhere enjoys watercolor painting. Eugene can play the flute. Everyone in the room who creates large-scale murals for public art installations has a pet dog.

It is not the case that 'Eugene has a pet dog'.

neutral

room(eugene)&(![X]:(room(X)=>(X='eugene')))& ((![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(does_not_enjoy_watercolor_painting(X))))))=>(does_not_compose_and_performs_experimental_electronic_music(eugene)))& (![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (~(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(eugene)))& (![X]:(~room(X)=>(((enjoys_landscape_photography(X))=>(collects_antique_jewelry(X))))))& (?[X]:(anywhere(X)&(enjoys_watercolor_painting(X))))& (can_play_the_flute(eugene))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(has_a_pet_dog(X))))))

room(eugene)&(![X]:(room(X)=>(X='eugene')))& ~(has_a_pet_dog(eugene))

Debra, Jay, Marie are the only persons in the room. If “Debra is older than Kyle” then “Kyle is richer than Marie”. If “someone in the room is richer than Kyle” then “Marie is quieter than Kyle”. “It is not the case that “more than one person in the room is a tall old person”” if “Debra is quieter than Kyle”. If “Debra is richer than Kyle” then “Marie is a old person”. If “Kyle is older than Jay” then “Debra is a kind person and is quieter than Kyle”. If “Jay is not a old quiet person” then “Marie is quiet”. If “it is not the case that “Marie is a tall person”” then “it is not the case that “Jay is a kind tall old quiet person””. If “Debra is a old person” then “Debra is quieter than Kyle”. “It is not the case that “Marie is richer than Kyle”” if “someone in the room is a kind person and is not not kind” and vice versa. It is true that “someone in the room is a quiet person”. Marie is quieter than Kyle. Debra is older than Kyle. Jay is richer than Kyle. Debra is a quiet old person. Marie is not a kind person. Jay is a old quiet person. Marie is not quiet. Jay is quieter than Kyle. It is not the case that “Marie is richer than Kyle”. Debra is richer than Kyle. It is not the case that “Jay neither is a quiet person nor is richer than Kyle”. Marie is older than Kyle.

Kyle is quieter than Debra.

contradiction

room(debra)&room(jay)&room(marie)&(![X]:(room(X)=>(X='debra'|X='jay'|X='marie')))& ((older(kyle,debra))=>(richer(marie,kyle)))& ((?[X]:(room(X)&(richer(kyle,X))))=>(quieter(kyle,marie)))& ((quieter(kyle,debra))=>(~((?[X,Y]:(room(X)&room(Y)&(tall(X)&old(X)&person(X)&tall(Y)&old(Y)&person(Y))&(X!=Y))))))& ((richer(kyle,debra))=>(old(marie)&person(marie)))& ((older(jay,kyle))=>(((kind(debra)&person(debra))&(quieter(kyle,debra)))))& ((~(old(jay)&quiet(jay)&person(jay)))=>(quiet(marie)))& ((~(tall(marie)&person(marie)))=>(~(kind(jay)&tall(jay)&old(jay)&quiet(jay)&person(jay))))& ((old(debra)&person(debra))=>(quieter(kyle,debra)))& ((?[X]:(room(X)&(((kind(X)&person(X))&(~~kind(X))))))<=>(~(richer(kyle,marie))))& (?[X]:(room(X)&(quiet(X)&person(X))))& (quieter(kyle,marie))& (older(kyle,debra))& (richer(kyle,jay))& (quiet(debra)&old(debra)&person(debra))& (~(kind(marie)&person(marie)))& (old(jay)&quiet(jay)&person(jay))& (~quiet(marie))& (quieter(kyle,jay))& (~(richer(kyle,marie)))& (richer(kyle,debra))& (~(~((quiet(jay)&person(jay))|(richer(kyle,jay)))))& (older(kyle,marie))

room(debra)&room(jay)&room(marie)&(![X]:(room(X)=>(X='debra'|X='jay'|X='marie')))& quieter(debra,kyle)

% SZS status Unsatisfiable for 3785694041121902465749906 % SZS output start Proof for 3785694041121902465749906 14. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => ~quieter(X1,X0))) [input b13] 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] 52. (person(mary) & old(mary)) => quieter(alice,mary) [input p8] 58. person(mary) & old(mary) & quiet(mary) [input p14] 67. quieter(mary,alice) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 88. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14] 89. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 88] 151. quieter(alice,mary) | (~person(mary) | ~old(mary)) [ennf transformation 52] 152. quieter(alice,mary) | ~person(mary) | ~old(mary) [flattening 151] 154. quieter(mary,alice) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 67] 155. quieter(mary,alice) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 154] 172. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 89] 219. mary != alice [cnf transformation 43] 260. quieter(alice,mary) | ~person(mary) | ~old(mary) [cnf transformation 152] 273. old(mary) [cnf transformation 58] 274. person(mary) [cnf transformation 58] 290. quieter(mary,alice) [cnf transformation 155] 310. 5 <=> quieter(alice,mary) [avatar definition] 311. quieter(alice,mary) <- (5) [avatar component clause 310] 337. 11 <=> person(mary) [avatar definition] 380. 20 <=> old(mary) [avatar definition] 383. ~20 | ~11 | 5 [avatar split clause 260,310,337,380] 410. 11 [avatar split clause 274,337] 411. 20 [avatar split clause 273,380] 437. ~quieter(alice,mary) | mary = alice [resolution 172,290] 443. mary = alice <- (5) [subsumption resolution 437,311] 444. $false <- (5) [subsumption resolution 443,219] 445. ~5 [avatar contradiction clause 444] 446. $false [avatar sat refutation 383,410,411,445] % SZS output end Proof for 3785694041121902465749906 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Eric, Carol, Daniel are the only persons in the room. 'No one in the room is humble, is curious and is not quiet' if 'everyone in the room is creative' and vice versa. 'More than one person in the room either is a kind person or is patient but not both' if 'everyone anywhere is a wise person'. If 'someone in the room is not curious' then 'everyone in the room is a kind person'. If 'everyone in the room is a kind person' then 'all generous persons are happy'. 'No one in the room is a brave person' only if 'everyone in the room either is quiet or is wise but not both'. 'Everyone outside the room is humble, is not a calm person and is a creative person' if 'everyone in the room is a quiet person' and vice versa. Everyone anywhere is not calm. At least one person in the room is a humble person. Everyone in the room is funny. Someone in the room is happy. Everyone in the room is a humble person. Everyone in the room is patient.

Carol is funny.

entailment

room(eric)&room(carol)&room(daniel)&(![X]:(room(X)=>(X='eric'|X='carol'|X='daniel')))& ((![X]:(room(X)=>(creative(X))))<=>(~?[X]:(room(X)=>(((humble(X))&(curious(X))&(~quiet(X)))))))& ((![X]:(anywhere(X)=>(wise(X)&person(X))))=>((?[X,Y]:(room(X)&room(Y)&(((kind(X)&person(X))<~>(patient(X)))&((kind(Y)&person(Y))<~>(patient(Y))))&(X!=Y)))))& (((?[X]:(room(X)&(~curious(X))))=>(![X]:(room(X)=>(kind(X)&person(X)))))& ((![X]:(room(X)=>(kind(X)&person(X))))=>(![X]:(generous(X)=>happy(X)))))& ((~?[X]:(room(X)=>(brave(X)&person(X))))=>(![X]:(room(X)=>(((quiet(X))<~>(wise(X)))))))& ((![X]:(room(X)=>(quiet(X)&person(X))))<=>(![X]:(~room(X)=>(((humble(X))&(~(calm(X)&person(X)))&(creative(X)&person(X)))))))& (![X]:(anywhere(X)=>(~calm(X))))& (((?[X]:(room(X)&humble(X)&person(X)))))& (![X]:(room(X)=>(funny(X))))& (?[X]:(room(X)&(happy(X))))& (![X]:(room(X)=>(humble(X)&person(X))))& (![X]:(room(X)=>(patient(X))))

room(eric)&room(carol)&room(daniel)&(![X]:(room(X)=>(X='eric'|X='carol'|X='daniel')))& funny(carol)

% SZS status Unsatisfiable for 8890824496458757471743498 % SZS output start Proof for 8890824496458757471743498 44. ! [X0] : (room(X0) => patient(X0)) & ! [X0] : (room(X0) => (person(X0) & humble(X0))) & ? [X0] : (happy(X0) & room(X0)) & ! [X0] : (room(X0) => funny(X0)) & ? [X0] : (person(X0) & humble(X0) & room(X0)) & ! [X0] : (anywhere(X0) => ~calm(X0)) & (! [X0] : (room(X0) => (person(X0) & quiet(X0))) <=> ! [X0] : (~room(X0) => (person(X0) & creative(X0) & ~(person(X0) & calm(X0)) & humble(X0)))) & (~? [X0] : (room(X0) => (person(X0) & brave(X0))) => ! [X0] : (room(X0) => (quiet(X0) <~> wise(X0)))) & (! [X0] : (room(X0) => (person(X0) & kind(X0))) => ! [X0] : (generous(X0) => happy(X0))) & (? [X0] : (~curious(X0) & room(X0)) => ! [X0] : (room(X0) => (person(X0) & kind(X0)))) & (! [X0] : (anywhere(X0) => (person(X0) & wise(X0))) => ? [X0,X1] : (X0 != X1 & ((person(X1) & kind(X1)) <~> patient(X1)) & ((person(X0) & kind(X0)) <~> patient(X0)) & room(X1) & room(X0))) & (! [X0] : (room(X0) => creative(X0)) <=> ~? [X0] : (room(X0) => (~quiet(X0) & curious(X0) & humble(X0)))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(funny(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : (room(X0) => patient(X0)) & ! [X1] : (room(X1) => (person(X1) & humble(X1))) & ? [X2] : (happy(X2) & room(X2)) & ! [X3] : (room(X3) => funny(X3)) & ? [X4] : (person(X4) & humble(X4) & room(X4)) & ! [X5] : (anywhere(X5) => ~calm(X5)) & (! [X6] : (room(X6) => (person(X6) & quiet(X6))) <=> ! [X7] : (~room(X7) => (person(X7) & creative(X7) & ~(person(X7) & calm(X7)) & humble(X7)))) & (~? [X8] : (room(X8) => (person(X8) & brave(X8))) => ! [X9] : (room(X9) => (quiet(X9) <~> wise(X9)))) & (! [X10] : (room(X10) => (person(X10) & kind(X10))) => ! [X11] : (generous(X11) => happy(X11))) & (? [X12] : (~curious(X12) & room(X12)) => ! [X13] : (room(X13) => (person(X13) & kind(X13)))) & (! [X14] : (anywhere(X14) => (person(X14) & wise(X14))) => ? [X15,X16] : (X15 != X16 & ((person(X16) & kind(X16)) <~> patient(X16)) & ((person(X15) & kind(X15)) <~> patient(X15)) & room(X16) & room(X15))) & (! [X17] : (room(X17) => creative(X17)) <=> ~? [X18] : (room(X18) => (~quiet(X18) & curious(X18) & humble(X18)))) & ! [X19] : (room(X19) => (fred = X19 | paul = X19 | mary = X19)) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => patient(X0)) & ! [X1] : (room(X1) => (person(X1) & humble(X1))) & ? [X2] : (happy(X2) & room(X2)) & ! [X3] : (room(X3) => funny(X3)) & ? [X4] : (person(X4) & humble(X4) & room(X4)) & ! [X5] : (anywhere(X5) => ~calm(X5)) & (! [X6] : (room(X6) => (person(X6) & quiet(X6))) <=> ! [X7] : (~room(X7) => (person(X7) & creative(X7) & ~(person(X7) & calm(X7)) & humble(X7)))) & (~? [X8] : (room(X8) => person(X8)) => ! [X9] : (room(X9) => (quiet(X9) <~> wise(X9)))) & (! [X10] : (room(X10) => (person(X10) & kind(X10))) => ! [X11] : (generous(X11) => happy(X11))) & (? [X12] : (~curious(X12) & room(X12)) => ! [X13] : (room(X13) => (person(X13) & kind(X13)))) & (! [X14] : (anywhere(X14) => (person(X14) & wise(X14))) => ? [X15,X16] : (X15 != X16 & ((person(X16) & kind(X16)) <~> patient(X16)) & ((person(X15) & kind(X15)) <~> patient(X15)) & room(X16) & room(X15))) & (! [X17] : (room(X17) => creative(X17)) <=> ~? [X18] : (room(X18) => (~quiet(X18) & curious(X18) & humble(X18)))) & ! [X19] : (room(X19) => (fred = X19 | paul = X19 | mary = X19)) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (room(X0) => patient(X0)) & ! [X1] : (room(X1) => (person(X1) & humble(X1))) & ? [X2] : room(X2) & ! [X3] : (room(X3) => funny(X3)) & ? [X4] : (person(X4) & humble(X4) & room(X4)) & ! [X5] : (anywhere(X5) => ~calm(X5)) & (! [X6] : (room(X6) => (person(X6) & quiet(X6))) <=> ! [X7] : (~room(X7) => (person(X7) & creative(X7) & ~(person(X7) & calm(X7)) & humble(X7)))) & (~? [X8] : (room(X8) => person(X8)) => ! [X9] : (room(X9) => (quiet(X9) <~> wise(X9)))) & (? [X12] : (~curious(X12) & room(X12)) => ! [X13] : (room(X13) => (person(X13) & kind(X13)))) & (! [X14] : (anywhere(X14) => (person(X14) & wise(X14))) => ? [X15,X16] : (X15 != X16 & ((person(X16) & kind(X16)) <~> patient(X16)) & ((person(X15) & kind(X15)) <~> patient(X15)) & room(X16) & room(X15))) & (! [X17] : (room(X17) => creative(X17)) <=> ~? [X18] : (room(X18) => (~quiet(X18) & curious(X18) & humble(X18)))) & ! [X19] : (room(X19) => (fred = X19 | paul = X19 | mary = X19)) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 120. ! [X0] : (patient(X0) | ~room(X0)) & ! [X1] : ((person(X1) & humble(X1)) | ~room(X1)) & ? [X2] : room(X2) & ! [X3] : (funny(X3) | ~room(X3)) & ? [X4] : (person(X4) & humble(X4) & room(X4)) & ! [X5] : (~calm(X5) | ~anywhere(X5)) & (! [X6] : ((person(X6) & quiet(X6)) | ~room(X6)) <=> ! [X7] : ((person(X7) & creative(X7) & (~person(X7) | ~calm(X7)) & humble(X7)) | room(X7))) & (! [X9] : ((quiet(X9) <~> wise(X9)) | ~room(X9)) | ? [X8] : (person(X8) | ~room(X8))) & (! [X13] : ((person(X13) & kind(X13)) | ~room(X13)) | ! [X12] : (curious(X12) | ~room(X12))) & (? [X15,X16] : (X15 != X16 & ((person(X16) & kind(X16)) <~> patient(X16)) & ((person(X15) & kind(X15)) <~> patient(X15)) & room(X16) & room(X15)) | ? [X14] : ((~person(X14) | ~wise(X14)) & anywhere(X14))) & (! [X17] : (creative(X17) | ~room(X17)) <=> ! [X18] : ((quiet(X18) | ~curious(X18) | ~humble(X18)) & room(X18))) & ! [X19] : ((fred = X19 | paul = X19 | mary = X19) | ~room(X19)) & room(fred) & room(paul) & room(mary) [ennf transformation 48] 121. ! [X0] : (patient(X0) | ~room(X0)) & ! [X1] : ((person(X1) & humble(X1)) | ~room(X1)) & ? [X2] : room(X2) & ! [X3] : (funny(X3) | ~room(X3)) & ? [X4] : (person(X4) & humble(X4) & room(X4)) & ! [X5] : (~calm(X5) | ~anywhere(X5)) & (! [X6] : ((person(X6) & quiet(X6)) | ~room(X6)) <=> ! [X7] : ((person(X7) & creative(X7) & (~person(X7) | ~calm(X7)) & humble(X7)) | room(X7))) & (! [X9] : ((quiet(X9) <~> wise(X9)) | ~room(X9)) | ? [X8] : (person(X8) | ~room(X8))) & (! [X13] : ((person(X13) & kind(X13)) | ~room(X13)) | ! [X12] : (curious(X12) | ~room(X12))) & (? [X15,X16] : (X15 != X16 & ((person(X16) & kind(X16)) <~> patient(X16)) & ((person(X15) & kind(X15)) <~> patient(X15)) & room(X16) & room(X15)) | ? [X14] : ((~person(X14) | ~wise(X14)) & anywhere(X14))) & (! [X17] : (creative(X17) | ~room(X17)) <=> ! [X18] : ((quiet(X18) | ~curious(X18) | ~humble(X18)) & room(X18))) & ! [X19] : (fred = X19 | paul = X19 | mary = X19 | ~room(X19)) & room(fred) & room(paul) & room(mary) [flattening 120] 122. ~funny(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 123. ~funny(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 122] 124. ! [X15] : (((person(X15) & kind(X15)) <~> patient(X15)) | ~sP0(X15)) [predicate definition introduction] 125. ? [X15,X16] : (X15 != X16 & ((person(X16) & kind(X16)) <~> patient(X16)) & sP0(X15) & room(X16) & room(X15)) | ~sP1 [predicate definition introduction] 126. sP2 <=> ! [X7] : ((person(X7) & creative(X7) & (~person(X7) | ~calm(X7)) & humble(X7)) | room(X7)) [predicate definition introduction] 127. ! [X0] : (patient(X0) | ~room(X0)) & ! [X1] : ((person(X1) & humble(X1)) | ~room(X1)) & ? [X2] : room(X2) & ! [X3] : (funny(X3) | ~room(X3)) & ? [X4] : (person(X4) & humble(X4) & room(X4)) & ! [X5] : (~calm(X5) | ~anywhere(X5)) & (! [X6] : ((person(X6) & quiet(X6)) | ~room(X6)) <=> sP2) & (! [X9] : ((quiet(X9) <~> wise(X9)) | ~room(X9)) | ? [X8] : (person(X8) | ~room(X8))) & (! [X13] : ((person(X13) & kind(X13)) | ~room(X13)) | ! [X12] : (curious(X12) | ~room(X12))) & (sP1 | ? [X14] : ((~person(X14) | ~wise(X14)) & anywhere(X14))) & (! [X17] : (creative(X17) | ~room(X17)) <=> ! [X18] : ((quiet(X18) | ~curious(X18) | ~humble(X18)) & room(X18))) & ! [X19] : (fred = X19 | paul = X19 | mary = X19 | ~room(X19)) & room(fred) & room(paul) & room(mary) [definition folding 121,126,125,124] 141. ! [X0] : (patient(X0) | ~room(X0)) & ! [X1] : ((person(X1) & humble(X1)) | ~room(X1)) & ? [X2] : room(X2) & ! [X3] : (funny(X3) | ~room(X3)) & ? [X4] : (person(X4) & humble(X4) & room(X4)) & ! [X5] : (~calm(X5) | ~anywhere(X5)) & ((! [X6] : ((person(X6) & quiet(X6)) | ~room(X6)) | ~sP2) & (sP2 | ? [X6] : ((~person(X6) | ~quiet(X6)) & room(X6)))) & (! [X9] : (((~wise(X9) | ~quiet(X9)) & (wise(X9) | quiet(X9))) | ~room(X9)) | ? [X8] : (person(X8) | ~room(X8))) & (! [X13] : ((person(X13) & kind(X13)) | ~room(X13)) | ! [X12] : (curious(X12) | ~room(X12))) & (sP1 | ? [X14] : ((~person(X14) | ~wise(X14)) & anywhere(X14))) & ((! [X17] : (creative(X17) | ~room(X17)) | ? [X18] : ((~quiet(X18) & curious(X18) & humble(X18)) | ~room(X18))) & (! [X18] : ((quiet(X18) | ~curious(X18) | ~humble(X18)) & room(X18)) | ? [X17] : (~creative(X17) & room(X17)))) & ! [X19] : (fred = X19 | paul = X19 | mary = X19 | ~room(X19)) & room(fred) & room(paul) & room(mary) [nnf transformation 127] 142. ! [X0] : (patient(X0) | ~room(X0)) & ! [X1] : ((person(X1) & humble(X1)) | ~room(X1)) & ? [X2] : room(X2) & ! [X3] : (funny(X3) | ~room(X3)) & ? [X4] : (person(X4) & humble(X4) & room(X4)) & ! [X5] : (~calm(X5) | ~anywhere(X5)) & (! [X6] : ((person(X6) & quiet(X6)) | ~room(X6)) | ~sP2) & (sP2 | ? [X6] : ((~person(X6) | ~quiet(X6)) & room(X6))) & (! [X9] : (((~wise(X9) | ~quiet(X9)) & (wise(X9) | quiet(X9))) | ~room(X9)) | ? [X8] : (person(X8) | ~room(X8))) & (! [X13] : ((person(X13) & kind(X13)) | ~room(X13)) | ! [X12] : (curious(X12) | ~room(X12))) & (sP1 | ? [X14] : ((~person(X14) | ~wise(X14)) & anywhere(X14))) & (! [X17] : (creative(X17) | ~room(X17)) | ? [X18] : ((~quiet(X18) & curious(X18) & humble(X18)) | ~room(X18))) & (! [X18] : ((quiet(X18) | ~curious(X18) | ~humble(X18)) & room(X18)) | ? [X17] : (~creative(X17) & room(X17))) & ! [X19] : (fred = X19 | paul = X19 | mary = X19 | ~room(X19)) & room(fred) & room(paul) & room(mary) [flattening 141] 143. ! [X0] : (patient(X0) | ~room(X0)) & ! [X1] : ((person(X1) & humble(X1)) | ~room(X1)) & ? [X2] : room(X2) & ! [X3] : (funny(X3) | ~room(X3)) & ? [X4] : (person(X4) & humble(X4) & room(X4)) & ! [X5] : (~calm(X5) | ~anywhere(X5)) & (! [X6] : ((person(X6) & quiet(X6)) | ~room(X6)) | ~sP2) & (sP2 | ? [X7] : ((~person(X7) | ~quiet(X7)) & room(X7))) & (! [X8] : (((~wise(X8) | ~quiet(X8)) & (wise(X8) | quiet(X8))) | ~room(X8)) | ? [X9] : (person(X9) | ~room(X9))) & (! [X10] : ((person(X10) & kind(X10)) | ~room(X10)) | ! [X11] : (curious(X11) | ~room(X11))) & (sP1 | ? [X12] : ((~person(X12) | ~wise(X12)) & anywhere(X12))) & (! [X13] : (creative(X13) | ~room(X13)) | ? [X14] : ((~quiet(X14) & curious(X14) & humble(X14)) | ~room(X14))) & (! [X15] : ((quiet(X15) | ~curious(X15) | ~humble(X15)) & room(X15)) | ? [X16] : (~creative(X16) & room(X16))) & ! [X17] : (fred = X17 | paul = X17 | mary = X17 | ~room(X17)) & room(fred) & room(paul) & room(mary) [rectify 142] 144. ? [X2] : room(X2) => room(sK6) [choice axiom] 145. ? [X4] : (person(X4) & humble(X4) & room(X4)) => (person(sK7) & humble(sK7) & room(sK7)) [choice axiom] 146. ? [X7] : ((~person(X7) | ~quiet(X7)) & room(X7)) => ((~person(sK8) | ~quiet(sK8)) & room(sK8)) [choice axiom] 147. ? [X9] : (person(X9) | ~room(X9)) => (person(sK9) | ~room(sK9)) [choice axiom] 148. ? [X12] : ((~person(X12) | ~wise(X12)) & anywhere(X12)) => ((~person(sK10) | ~wise(sK10)) & anywhere(sK10)) [choice axiom] 149. ? [X14] : ((~quiet(X14) & curious(X14) & humble(X14)) | ~room(X14)) => ((~quiet(sK11) & curious(sK11) & humble(sK11)) | ~room(sK11)) [choice axiom] 150. ? [X16] : (~creative(X16) & room(X16)) => (~creative(sK12) & room(sK12)) [choice axiom] 151. ! [X0] : (patient(X0) | ~room(X0)) & ! [X1] : ((person(X1) & humble(X1)) | ~room(X1)) & room(sK6) & ! [X3] : (funny(X3) | ~room(X3)) & (person(sK7) & humble(sK7) & room(sK7)) & ! [X5] : (~calm(X5) | ~anywhere(X5)) & (! [X6] : ((person(X6) & quiet(X6)) | ~room(X6)) | ~sP2) & (sP2 | ((~person(sK8) | ~quiet(sK8)) & room(sK8))) & (! [X8] : (((~wise(X8) | ~quiet(X8)) & (wise(X8) | quiet(X8))) | ~room(X8)) | (person(sK9) | ~room(sK9))) & (! [X10] : ((person(X10) & kind(X10)) | ~room(X10)) | ! [X11] : (curious(X11) | ~room(X11))) & (sP1 | ((~person(sK10) | ~wise(sK10)) & anywhere(sK10))) & (! [X13] : (creative(X13) | ~room(X13)) | ((~quiet(sK11) & curious(sK11) & humble(sK11)) | ~room(sK11))) & (! [X15] : ((quiet(X15) | ~curious(X15) | ~humble(X15)) & room(X15)) | (~creative(sK12) & room(sK12))) & ! [X17] : (fred = X17 | paul = X17 | mary = X17 | ~room(X17)) & room(fred) & room(paul) & room(mary) [skolemisation 143,150,149,148,147,146,145,144] 152. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK13 & paul != sK13 & mary != sK13 & room(sK13)) [choice axiom] 153. ~funny(paul) | (fred != sK13 & paul != sK13 & mary != sK13 & room(sK13)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 123,152] 252. room(mary) [cnf transformation 151] 253. room(paul) [cnf transformation 151] 254. room(fred) [cnf transformation 151] 255. ~room(X17) | paul = X17 | mary = X17 | fred = X17 [cnf transformation 151] 277. ~room(X3) | funny(X3) [cnf transformation 151] 282. ~funny(paul) | room(sK13) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 283. ~funny(paul) | mary != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 284. ~funny(paul) | paul != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 285. ~funny(paul) | fred != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 437. ~funny(paul) | fred != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 285,254] 438. ~funny(paul) | fred != sK13 | ~room(mary) [subsumption resolution 437,253] 439. ~funny(paul) | fred != sK13 [subsumption resolution 438,252] 441. 35 <=> fred = sK13 [avatar definition] 443. fred != sK13 <- (~35) [avatar component clause 441] 445. 36 <=> funny(paul) [avatar definition] 448. ~35 | ~36 [avatar split clause 439,445,441] 449. ~funny(paul) | paul != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 284,254] 450. ~funny(paul) | paul != sK13 | ~room(mary) [subsumption resolution 449,253] 451. ~funny(paul) | paul != sK13 [subsumption resolution 450,252] 453. 37 <=> paul = sK13 [avatar definition] 455. paul != sK13 <- (~37) [avatar component clause 453] 456. ~37 | ~36 [avatar split clause 451,445,453] 457. ~funny(paul) | mary != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 283,254] 458. ~funny(paul) | mary != sK13 | ~room(mary) [subsumption resolution 457,253] 459. ~funny(paul) | mary != sK13 [subsumption resolution 458,252] 461. 38 <=> mary = sK13 [avatar definition] 463. mary != sK13 <- (~38) [avatar component clause 461] 464. ~38 | ~36 [avatar split clause 459,445,461] 465. ~funny(paul) | room(sK13) | ~room(paul) | ~room(mary) [subsumption resolution 282,254] 466. ~funny(paul) | room(sK13) | ~room(mary) [subsumption resolution 465,253] 467. ~funny(paul) | room(sK13) [subsumption resolution 466,252] 469. 39 <=> room(sK13) [avatar definition] 471. room(sK13) <- (39) [avatar component clause 469] 472. 39 | ~36 [avatar split clause 467,445,469] 476. funny(paul) [resolution 277,253] 483. 36 [avatar split clause 476,445] 563. paul = sK13 | mary = sK13 | fred = sK13 <- (39) [resolution 255,471] 603. mary = sK13 | fred = sK13 <- (~37, 39) [subsumption resolution 563,455] 604. fred = sK13 <- (~37, ~38, 39) [subsumption resolution 603,463] 605. $false <- (~35, ~37, ~38, 39) [subsumption resolution 604,443] 606. 35 | 37 | 38 | ~39 [avatar contradiction clause 605] 607. $false [avatar sat refutation 448,456,464,472,483,606] % SZS output end Proof for 8890824496458757471743498 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Juan, Crystal, Larhonda are the only persons in the room. If “Larhonda plays eSports competitively” then “Juan plays the violin”. If “it is not the case that “Juan either travels domestically frequently or owns an extensive assortment of vintage comic book memorabilia but not both”” then “Crystal trains for and competes in international triathlons”. If “no one in the room does not collect rare sneakers or does not have a tattoo” then “Crystal owns an extensive assortment of vintage comic book memorabilia”. If someone plays eSports competitively or has a specialized collection of handmade artisan pottery or both then he/she volunteers for local environmental conservation projects and vice versa. Larhonda has a specialized collection of handmade artisan pottery.

Larhonda volunteers for local environmental conservation projects.

entailment

room(juan)&room(crystal)&room(larhonda)&(![X]:(room(X)=>(X='juan'|X='crystal'|X='larhonda')))& ((plays_eSports_competitively(larhonda))=>(plays_the_violin(juan)))& ((~(((travels_domestically_frequently(juan))<~>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(juan)))))=>(trains_for_and_competes_in_international_triathlons(crystal)))& ((~?[X]:(room(X)=>(((does_not_have_a_tattoo(X))|(does_not_collect_rare_sneakers(X))))))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(crystal)))& ((collects_foreign_coins(larhonda))=>(![X]:(room(X)=>(((collects_foreign_coins(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))))& (((~((hosts_regular_game_nights_featuring_complex_strategy_games(larhonda))|(mentors_a_youth_basketball_team_on_weekends(larhonda))))=>((![X]:((volunteers_for_local_environmental_conservation_projects(X))<=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))&((~(~((hosts_regular_game_nights_featuring_complex_strategy_games(larhonda))|(mentors_a_youth_basketball_team_on_weekends(larhonda)))))=>(hosts_regular_game_nights_featuring_complex_strategy_games(juan))))& (collect_rare_sneakers(larhonda))& (~((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(larhonda))|(writes_a_travel_blog(larhonda))))& (~(~(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(larhonda))))& ((?[X,Y]:(~room(X)&~room(Y)&(has_a_specialized_collection_of_handmade_artisan_pottery(X)&has_a_specialized_collection_of_handmade_artisan_pottery(Y))&(X!=Y))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))=>(travels_domestically_frequently(X))))))& ((does_not_have_a_tattoo(juan))&(plays_eSports_competitively(juan)))& (writes_a_travel_blog(juan))& (has_a_tattoo(larhonda))& (writes_and_illustrates_their_own_graphic_novels(crystal))& (plays_eSports_competitively(crystal))& (hosts_regular_game_nights_featuring_complex_strategy_games(crystal))& (hosts_regular_game_nights_featuring_complex_strategy_games(juan))& ((![X]:((owns_a_3D_printer(X))<=>(collects_foreign_coins(X)))))& (plays_the_violin(juan))& (composes_and_performs_experimental_electronic_music(juan))& (plays_eSports_competitively(juan))& ((![X]:((((plays_eSports_competitively(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))<=>(volunteers_for_local_environmental_conservation_projects(X)))))& (has_a_specialized_collection_of_handmade_artisan_pottery(larhonda))& (does_not_have_a_specialized_collection_of_handmade_artisan_pottery(crystal))& (~(((travels_domestically_frequently(juan))<~>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(juan)))))

room(juan)&room(crystal)&room(larhonda)&(![X]:(room(X)=>(X='juan'|X='crystal'|X='larhonda')))& volunteers_for_local_environmental_conservation_projects(larhonda)

% SZS status Unsatisfiable for 7916015652314418303202625 % SZS output start Proof for 7916015652314418303202625 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 66. ! [X0] : ((predt(X0) | predf(X0)) <=> predn(X0)) [input p22] 67. predt(fred) [input p23] 70. ~(predn(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 151. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 152. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 151] 161. ~predn(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 162. ~predn(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 161] 169. ! [X0] : (((predt(X0) | predf(X0)) | ~predn(X0)) & (predn(X0) | (~predt(X0) & ~predf(X0)))) [nnf transformation 66] 170. ! [X0] : ((predt(X0) | predf(X0) | ~predn(X0)) & (predn(X0) | (~predt(X0) & ~predf(X0)))) [flattening 169] 172. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 173. ~predn(fred) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 162,172] 254. room(mary) [cnf transformation 152] 255. room(paul) [cnf transformation 152] 256. room(fred) [cnf transformation 152] 257. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 152] 281. ~predt(X0) | predn(X0) [cnf transformation 170] 283. predt(fred) [cnf transformation 67] 287. ~predn(fred) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 288. ~predn(fred) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 289. ~predn(fred) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 290. ~predn(fred) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 341. ~predn(fred) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 290,256] 342. ~predn(fred) | fred != sK3 | ~room(mary) [subsumption resolution 341,255] 343. ~predn(fred) | fred != sK3 [subsumption resolution 342,254] 345. 12 <=> fred = sK3 [avatar definition] 347. fred != sK3 <- (~12) [avatar component clause 345] 349. 13 <=> predn(fred) [avatar definition] 352. ~12 | ~13 [avatar split clause 343,349,345] 353. ~predn(fred) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 289,256] 354. ~predn(fred) | paul != sK3 | ~room(mary) [subsumption resolution 353,255] 355. ~predn(fred) | paul != sK3 [subsumption resolution 354,254] 357. 14 <=> paul = sK3 [avatar definition] 359. paul != sK3 <- (~14) [avatar component clause 357] 360. ~14 | ~13 [avatar split clause 355,349,357] 361. ~predn(fred) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 288,256] 362. ~predn(fred) | mary != sK3 | ~room(mary) [subsumption resolution 361,255] 363. ~predn(fred) | mary != sK3 [subsumption resolution 362,254] 365. 15 <=> mary = sK3 [avatar definition] 367. mary != sK3 <- (~15) [avatar component clause 365] 368. ~15 | ~13 [avatar split clause 363,349,365] 369. ~predn(fred) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 287,256] 370. ~predn(fred) | room(sK3) | ~room(mary) [subsumption resolution 369,255] 371. ~predn(fred) | room(sK3) [subsumption resolution 370,254] 373. 16 <=> room(sK3) [avatar definition] 375. room(sK3) <- (16) [avatar component clause 373] 376. 16 | ~13 [avatar split clause 371,349,373] 381. predn(fred) [resolution 281,283] 384. 13 [avatar split clause 381,349] 435. paul = sK3 | mary = sK3 | fred = sK3 <- (16) [resolution 257,375] 436. mary = sK3 | fred = sK3 <- (~14, 16) [subsumption resolution 435,359] 437. fred = sK3 <- (~14, ~15, 16) [subsumption resolution 436,367] 438. $false <- (~12, ~14, ~15, 16) [subsumption resolution 437,347] 439. 12 | 14 | 15 | ~16 [avatar contradiction clause 438] 440. $false [avatar sat refutation 352,360,368,376,384,439] % SZS output end Proof for 7916015652314418303202625 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Allison, Saul, Craig are the only persons in the room. “Allison is not a strong person” only if “no old person is creative”. “Allison is funny” if “Allison is not a quiet curious tall person”. “Allison neither is not a patient person nor is not a tall kind patient quiet person” if “Saul is curious”. Saul either is not a tall person or is not a brave funny person but not both. Saul is not a happy generous curious strong quiet person. Allison either is not a strong calm person or is not a quiet person but not both. Allison either is not a creative curious brave person or is not a kind person but not both. Saul is not a old person. Allison is not a curious person. Allison is not a patient generous person.

Saul and Allison are not a funny quiet tall generous wise persons.

neutral

room(allison)&room(saul)&room(craig)&(![X]:(room(X)=>(X='allison'|X='saul'|X='craig')))& ((~(strong(allison)&person(allison)))=>(~?[X]:(old(X)=>creative(X))))& ((~(quiet(allison)&curious(allison)&tall(allison)&person(allison)))=>(funny(allison)))& ((curious(saul))=>(~((~(patient(allison)&person(allison)))|(~(tall(allison)&kind(allison)&patient(allison)&quiet(allison)&person(allison))))))& (((~(tall(saul)&person(saul)))<~>(~(brave(saul)&funny(saul)&person(saul)))))& (~(happy(saul)&generous(saul)&curious(saul)&strong(saul)&quiet(saul)&person(saul)))& (((~(strong(allison)&calm(allison)&person(allison)))<~>(~(quiet(allison)&person(allison)))))& (((~(creative(allison)&curious(allison)&brave(allison)&person(allison)))<~>(~(kind(allison)&person(allison)))))& (~(old(saul)&person(saul)))& (~(curious(allison)&person(allison)))& (~(patient(allison)&generous(allison)&person(allison)))& (![X]:((room(X)&(X!=allison))=>quieter(X,allison)))& (~(wise(saul)&person(saul)))

room(allison)&room(saul)&room(craig)&(![X]:(room(X)=>(X='allison'|X='saul'|X='craig')))& ~(funny(saul)&quiet(saul)&tall(saul)&generous(saul)&wise(saul)&person(saul))&~(funny(allison)&quiet(allison)&tall(allison)&generous(allison)&wise(allison)&person(allison))

Barbara, Linda, Austin are the only persons in the room. No old person is strong. Someone in the room is not a calm quiet creative person. Linda is happy. More than one person in the room is quiet. Linda is the least old in the room. Barbara is happy. All quiet persons are old. Barbara is the richest in the room. All calm persons are quiet. Someone in the room is a funny patient kind wise generous person. All wise persons are tall. Linda is a creative old humble happy kind generous person. All happy persons are kind. All quiet persons are creative.

Linda and Barbara are not a funny quiet tall generous wise persons.

neutral

room(barbara)&room(linda)&room(austin)&(![X]:(room(X)=>(X='barbara'|X='linda'|X='austin')))& (~?[X]:(old(X)=>strong(X)))& (?[X]:(room(X)&(~(calm(X)&quiet(X)&creative(X)&person(X)))))& (happy(linda))& ((?[X,Y]:(room(X)&room(Y)&(quiet(X)&quiet(Y))&(X!=Y))))& (![X]:((room(X)&(X!=linda))=>older(linda,X)))& (happy(barbara))& (![X]:(quiet(X)=>old(X)))& (![X]:((room(X)&(X!=barbara))=>richer(X,barbara)))& (![X]:(calm(X)=>quiet(X)))& (?[X]:(room(X)&(funny(X)&patient(X)&kind(X)&wise(X)&generous(X)&person(X))))& (![X]:(wise(X)=>tall(X)))& (creative(linda)&old(linda)&humble(linda)&happy(linda)&kind(linda)&generous(linda)&person(linda))& (![X]:(happy(X)=>kind(X)))& (![X]:(quiet(X)=>creative(X)))

room(barbara)&room(linda)&room(austin)&(![X]:(room(X)=>(X='barbara'|X='linda'|X='austin')))& ~(funny(linda)&quiet(linda)&tall(linda)&generous(linda)&wise(linda)&person(linda))&~(funny(barbara)&quiet(barbara)&tall(barbara)&generous(barbara)&wise(barbara)&person(barbara))

Noelle, Jeffrey are the only persons in the room. If 'everyone anywhere does not host a popular podcast about emerging technologies or is a coffee connoisseur' then 'more than one person in the room is a coffee connoisseur'. 'Everyone in the room enjoys virtual reality gaming if they reads mystery novels and vice versa' if 'Noelle does not enjoy logic puzzles'. If someone enjoys logic puzzles, practices digital art or participates in long-distance cycling events across the country then he/she hosts a popular podcast about emerging technologies and vice versa. Noelle enjoys virtual reality gaming. Noelle does not host a popular podcast about emerging technologies.

Everyone in the room does not read mystery novels and does not host a popular podcast about emerging technologies.

contradiction

room(noelle)&room(jeffrey)&(![X]:(room(X)=>(X='noelle'|X='jeffrey')))& ((![X]:(anywhere(X)=>(((is_a_coffee_connoisseur(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))=>((?[X,Y]:(room(X)&room(Y)&(is_a_coffee_connoisseur(X)&is_a_coffee_connoisseur(Y))&(X!=Y)))))& ((enjoys_virtual_reality_gaming(noelle))<~>(![X]:(anywhere(X)=>(((enjoys_virtual_reality_gaming(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))& ((does_not_enjoy_logic_puzzles(noelle))=>(![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))<=>(reads_mystery_novels(X)))))))& ((![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(practices_urban_gardening(X))))))<~>(![X]:(room(X)=>(practices_digital_art(X)))))& ((![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(collects_action_figures(X))))))<~>(![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))& ((![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))<~>(![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_have_a_pet_dog(X)))))))& (((?[X]:(room(X)&does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))& (![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& ((((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(noelle))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(noelle))))&(((does_not_enjoy_bird_watching(noelle))<~>(is_an_avid_hiker(noelle)))))& (![X]:(room(X)=>(((((plays_video_games(X))<~>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(((enjoys_logic_puzzles(X))|(collects_action_figures(X))))))))& (?[X]:(room(X)&(plays_video_games(X))))& (has_a_tattoo(noelle))& (![X]:(room(X)=>(((practices_urban_gardening(X))|(does_not_read_mystery_novels(X))))))& (?[X]:(room(X)&(does_not_collect_action_figures(X))))& ((![X]:((((enjoys_logic_puzzles(X))|(practices_digital_art(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))<=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))& (practices_urban_gardening(noelle))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_have_a_pet_dog(X))))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<=>(reads_mystery_novels(X))))))& (enjoys_virtual_reality_gaming(noelle))& ((![X]:((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(does_not_enjoy_virtual_reality_gaming(X)))))& (does_not_have_lived_in_exactly_three_countries(noelle))& (![X]:(anywhere(X)=>(((collects_classic_novels(X))=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (does_not_host_a_popular_podcast_about_emerging_technologies(noelle))& (![X]:(room(X)=>(((practices_digital_art(X))|(does_not_enjoy_bird_watching(X))))))& (![X]:(anywhere(X)=>(((has_a_pet_dog(X))=>(practices_digital_art(X))))))& (((?[X]:(room(X)&is_a_coffee_connoisseur(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_coffee_connoisseur(X))&(is_a_coffee_connoisseur(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((plays_video_games(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))

room(noelle)&room(jeffrey)&(![X]:(room(X)=>(X='noelle'|X='jeffrey')))& ![X]:(room(X)=>(((does_not_read_mystery_novels(X))&(does_not_host_a_popular_podcast_about_emerging_technologies(X)))))

% SZS status Unsatisfiable for 2182166510839203448320277 % SZS output start Proof for 2182166510839203448320277 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ~predi(mary) => ! [X0] : (room(X0) => (predr(X0) <=> predd(X0))) [input p3] 60. ! [X0] : ((predt(X0) | predj(X0) | predi(X0)) <=> preda(X0)) [input p16] 64. predr(mary) [input p20] 68. ~preda(mary) [input p24] 73. ! [X0] : (room(X0) => (~preda(X0) & ~predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 79. ! [X0] : (room(X0) => (~preda(X0) & ~predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 73] 154. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 155. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 154] 160. ! [X0] : ((predr(X0) <=> predd(X0)) | ~room(X0)) | predi(mary) [ennf transformation 47] 187. ! [X0] : ((~preda(X0) & ~predd(X0)) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 79] 188. ! [X0] : ((~preda(X0) & ~predd(X0)) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 187] 202. ! [X0] : (((predr(X0) | ~predd(X0)) & (predd(X0) | ~predr(X0))) | ~room(X0)) | predi(mary) [nnf transformation 160] 227. ! [X0] : (((predt(X0) | predj(X0) | predi(X0)) | ~preda(X0)) & (preda(X0) | (~predt(X0) & ~predj(X0) & ~predi(X0)))) [nnf transformation 60] 228. ! [X0] : ((predt(X0) | predj(X0) | predi(X0) | ~preda(X0)) & (preda(X0) | (~predt(X0) & ~predj(X0) & ~predi(X0)))) [flattening 227] 313. room(mary) [cnf transformation 155] 328. predd(X0) | ~predr(X0) | ~room(X0) | predi(mary) [cnf transformation 202] 373. ~predi(X0) | preda(X0) [cnf transformation 228] 381. predr(mary) [cnf transformation 64] 383. ~preda(mary) [cnf transformation 68] 393. ~predd(X0) | ~room(X0) [cnf transformation 188] 437. 9 <=> predr(mary) [avatar definition] 438. predr(mary) <- (9) [avatar component clause 437] 456. 13 <=> predi(mary) [avatar definition] 458. predi(mary) <- (13) [avatar component clause 456] 464. 15 <=> ! [X0] : (predd(X0) | ~room(X0) | ~predr(X0)) [avatar definition] 465. predd(X0) | ~room(X0) | ~predr(X0) <- (15) [avatar component clause 464] 466. 13 | 15 [avatar split clause 328,464,456] 601. 9 [avatar split clause 381,437] 603. preda(mary) <- (13) [resolution 373,458] 604. $false <- (13) [subsumption resolution 603,383] 605. ~13 [avatar contradiction clause 604] 606. ~predr(X0) | ~room(X0) <- (15) [subsumption resolution 465,393] 616. ~room(mary) <- (9, 15) [resolution 606,438] 617. $false <- (9, 15) [subsumption resolution 616,313] 618. ~9 | ~15 [avatar contradiction clause 617] 619. $false [avatar sat refutation 466,601,605,618] % SZS output end Proof for 2182166510839203448320277 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Connie, Eileen, Frank, Margaret are the only persons in the room. If “no one in the room enjoys logic puzzles, is a night owl or can play the piano” then “everyone in the room practices urban gardening if they can play the piano”. If “everyone in the room enjoys cross-country skiing or does not have a piercing” then “someone outside the room is an enthusiastic bird watcher who travels for rare sightings”. If “someone outside the room is an enthusiastic bird watcher who travels for rare sightings” then “Joseph frequently participates in hackathons and coding competitions”. “Everyone in the room is not a night owl or enjoys cross-country skiing” only if “Eileen creates bespoke furniture pieces from reclaimed wood or enjoys cross-country skiing or both”. If “everyone in the room does not collect classic novels or does not have a piercing” then “Joseph can play the piano”. Frank is an enthusiastic bird watcher who travels for rare sightings. Frank who is a night owl enjoys logic puzzles. If someone collects classic novels then he/she enjoys cross-country skiing and vice versa. Everyone outside the room is a culinary enthusiast who experiments with international cuisines or enjoys logic puzzles or both if they collects classic novels.

Joseph frequently participates in hackathons and coding competitions.

neutral

room(joseph)&room(connie)&room(eileen)&room(frank)&room(margaret)&(![X]:(room(X)=>(X='joseph'|X='connie'|X='eileen'|X='frank'|X='margaret')))& ((~?[X]:(room(X)=>(((enjoys_logic_puzzles(X))|(is_a_night_owl(X))|(can_play_the_piano(X))))))=>(![X]:(room(X)=>(((can_play_the_piano(X))=>(practices_urban_gardening(X)))))))& (((![X]:(room(X)=>(((does_not_have_a_piercing(X))|(enjoys_cross-country_skiing(X))))))=>(?[X]:(~room(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))))=>(frequently_participates_in_hackathons_and_coding_competitions(joseph))))& ((![X]:(room(X)=>(((enjoys_cross-country_skiing(X))|(is_not_a_night_owl(X))))))=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(eileen))|(enjoys_cross-country_skiing(eileen)))))& ((![X]:(room(X)=>(((does_not_have_a_piercing(X))|(does_not_collect_classic_novels(X))))))=>(can_play_the_piano(joseph)))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(frank))& ((is_a_night_owl(frank))&(enjoys_logic_puzzles(frank)))& ((![X]:((collects_classic_novels(X))<=>(enjoys_cross-country_skiing(X)))))& (![X]:(~room(X)=>(((collects_classic_novels(X))=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(enjoys_logic_puzzles(X))))))))& (![X]:(~room(X)=>(((collects_classic_novels(X))=>(does_not_have_a_piercing(X))))))& (((enjoys_logic_puzzles(connie))&(collects_classic_novels(connie))&(is_a_night_owl(connie))))& (![X]:(~room(X)=>(((collects_classic_novels(X))=>(practices_urban_gardening(X))))))& (((?[X]:(room(X)&can_play_the_piano(X)))))& (![X]:(room(X)=>(((practices_urban_gardening(X))<=>(collects_classic_novels(X))))))& ((![X]:((has_a_piercing(X))<=>(enjoys_logic_puzzles(X)))))& ((?[X,Y]:(room(X)&room(Y)&(can_play_the_piano(X)&can_play_the_piano(Y))&(X!=Y))))

room(joseph)&room(connie)&room(eileen)&room(frank)&room(margaret)&(![X]:(room(X)=>(X='joseph'|X='connie'|X='eileen'|X='frank'|X='margaret')))& frequently_participates_in_hackathons_and_coding_competitions(joseph)

Henry, Judy, Nancy, Efren, Robin are the only persons in the room. Everyone in the room writes a travel blog, plays the drums and collects foreign coins if they owns a significant collection of rare gemstones and minerals. Everyone in the room who is not a cybersecurity expert or owns a significant collection of rare gemstones and minerals or both plays video games. Everyone in the room does not travel domestically frequently or plays video games. Everyone in the room practices pilates if they plays the violin. Everyone in the room has a curated collection of mid-century modern furniture and does enjoy mountain biking if they practices pilates. Everyone in the room collects rare and antique scientific instruments if they has a curated collection of mid-century modern furniture and does enjoy mountain biking. Everyone in the room does not collect rare and antique scientific instruments.

Judy plays the violin.

contradiction

room(henry)&room(judy)&room(nancy)&room(efren)&room(robin)&(![X]:(room(X)=>(X='henry'|X='judy'|X='nancy'|X='efren'|X='robin')))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(((writes_a_travel_blog(X))&(plays_the_drums(X))&(collects_foreign_coins(X))))))))& (![X]:(room(X)=>(((((is_not_a_cybersecurity_expert(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((plays_video_games(X))|(does_not_travel_domestically_frequently(X))))))& (~![X]:(room(X)=>(plays_the_violin(X))))& (![X]:(room(X)=>(collects_foreign_coins(X))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (![X]:(anywhere(X)=>(((collects_foreign_coins(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(((does_not_write_a_travel_blog(X))=>(does_not_collect_foreign_coins(X))))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(works_on_fridays(X))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(practices_pilates(X))))))& (![X]:(room(X)=>(((practices_pilates(X))=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))&(does_enjoy_mountain_biking(X))))))))& (![X]:(room(X)=>(((((has_a_curated_collection_of_mid-century_modern_furniture(X))&(does_enjoy_mountain_biking(X))))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(anywhere(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X))))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(practices_pilates(X))))))

room(henry)&room(judy)&room(nancy)&room(efren)&room(robin)&(![X]:(room(X)=>(X='henry'|X='judy'|X='nancy'|X='efren'|X='robin')))& plays_the_violin(judy)

% SZS status Unsatisfiable for 8883992202180019564692712 % SZS output start Proof for 8883992202180019564692712 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] 55. ! [X0] : (room(X0) => (predc(X0) => predp(X0))) [input p11] 56. ! [X0] : (room(X0) => (predp(X0) => (prede(X0) & predd(X0)))) [input p12] 57. ! [X0] : (room(X0) => ((prede(X0) & predd(X0)) => predn(X0))) [input p13] 59. ! [X0] : (room(X0) => ~predn(X0)) [input p15] 61. predc(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] 147. ! [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] 148. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147] 150. ! [X0] : ((predp(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 55] 151. ! [X0] : (predp(X0) | ~predc(X0) | ~room(X0)) [flattening 150] 152. ! [X0] : (((prede(X0) & predd(X0)) | ~predp(X0)) | ~room(X0)) [ennf transformation 56] 153. ! [X0] : ((prede(X0) & predd(X0)) | ~predp(X0) | ~room(X0)) [flattening 152] 154. ! [X0] : ((predn(X0) | (~prede(X0) | ~predd(X0))) | ~room(X0)) [ennf transformation 57] 155. ! [X0] : (predn(X0) | ~prede(X0) | ~predd(X0) | ~room(X0)) [flattening 154] 156. ! [X0] : (~predn(X0) | ~room(X0)) [ennf transformation 59] 157. predc(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 61] 158. predc(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 157] 243. room(paul) [cnf transformation 148] 250. ~predc(X0) | predp(X0) | ~room(X0) [cnf transformation 151] 251. ~predp(X0) | predd(X0) | ~room(X0) [cnf transformation 153] 252. ~predp(X0) | prede(X0) | ~room(X0) [cnf transformation 153] 253. ~prede(X0) | predn(X0) | ~predd(X0) | ~room(X0) [cnf transformation 155] 254. ~predn(X0) | ~room(X0) [cnf transformation 156] 261. predc(paul) [cnf transformation 158] 262. predp(paul) | ~room(paul) [resolution 250,261] 263. predp(paul) [subsumption resolution 262,243] 264. predd(paul) | ~room(paul) [resolution 251,263] 265. predd(paul) [subsumption resolution 264,243] 266. prede(paul) | ~room(paul) [resolution 252,263] 267. prede(paul) [subsumption resolution 266,243] 268. predn(paul) | ~predd(paul) | ~room(paul) [resolution 253,267] 269. predn(paul) | ~room(paul) [subsumption resolution 268,265] 270. predn(paul) [subsumption resolution 269,243] 271. ~room(paul) [resolution 270,254] 272. $false [subsumption resolution 271,243] % SZS output end Proof for 8883992202180019564692712 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Michelle is the only person in the room. If “Tesha is quieter than Michelle” then “if someone is older than Tesha then he/she is quieter than Kenneth and vice versa”. If “Kenneth is quieter than Michelle” then “no quiet person is old”. “If someone is older than Sara then he/she is older than June and is older than Kenneth and vice versa” unless “June is older than Michelle”. If “Tesha is richer than Michelle” then “someone who is quieter than Sara is quieter than someone who either is quieter than Tesha or is richer than Tesha but not both”. If “Sara is older than Michelle” then “Kenneth is older than Michelle”. Tesha is richer than Michelle.

Michelle is richer than Tesha.

contradiction

room(michelle)&(![X]:(room(X)=>(X='michelle')))& ((quieter(michelle,tesha))=>((![X]:((older(tesha,X))<=>(quieter(kenneth,X))))))& ((quieter(michelle,kenneth))=>(~?[X]:(quiet(X)=>old(X))))& (~(older(michelle,june))=>((![X]:((older(sara,X))<=>(((older(june,X))&(older(kenneth,X))))))))& ((richer(michelle,tesha))=>(?[X,Y]:((quieter(sara,X))&(((quieter(tesha,Y))<~>(richer(tesha,Y))))&(quieter(X,Y)))))& ((older(michelle,sara))=>(older(michelle,kenneth)))& ((richer(michelle,kenneth))=>(quieter(michelle,tesha)))& (~(older(michelle,kenneth))=>(?[X,Y]:((richer(tesha,X))&(richer(june,Y))&(older(X,Y)))))& (~(richer(michelle,tesha))=>((![X]:((older(june,X))<=>(older(sara,X))))))& (~(quieter(michelle,kenneth))=>(richer(michelle,june)))& (quieter(michelle,sara))& (?[X,Y]:((richer(kenneth,X))&(richer(tesha,Y))&(quieter(X,Y))))& ((![X]:((older(kenneth,X))<=>(quieter(sara,X)))))& (quieter(michelle,kenneth))& ((![X]:((richer(kenneth,X))<=>(quieter(sara,X)))))& (older(michelle,kenneth))& (older(michelle,june))& (richer(michelle,tesha))& ((![X]:((quieter(kenneth,X))<=>(older(kenneth,X)))))& ((![X]:((quieter(kenneth,X))<=>(((quieter(kenneth,X))<~>(older(tesha,X)))))))& (?[X,Y]:((((richer(sara,X))<~>(older(tesha,X))))&(quieter(tesha,Y))&(quieter(X,Y))))& (richer(michelle,sara))& (~?[X]:(quiet(X)=>old(X)))& (older(michelle,sara))& (?[X,Y]:((richer(kenneth,X))&(richer(tesha,Y))&(older(X,Y))))& ((![X]:((richer(june,X))<=>(quieter(june,X)))))& ((![X]:((quieter(tesha,X))<=>(quieter(kenneth,X)))))& (?[X,Y]:((richer(tesha,X))&(older(kenneth,Y))&(quieter(X,Y))))

room(michelle)&(![X]:(room(X)=>(X='michelle')))& richer(tesha,michelle)

% SZS status Unsatisfiable for 8962662163615562204323697 % SZS output start Proof for 8962662163615562204323697 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] 61. richer(mary,john) [input p17] 72. richer(john,mary) & ! [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] 156. richer(john,mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 72] 187. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 82] 246. mary != john [cnf transformation 43] 296. richer(mary,john) [cnf transformation 61] 323. richer(john,mary) [cnf transformation 156] 367. 11 <=> richer(mary,john) [avatar definition] 368. richer(mary,john) <- (11) [avatar component clause 367] 432. 11 [avatar split clause 296,367] 484. ~richer(mary,john) | mary = john [resolution 187,323] 537. mary = john <- (11) [subsumption resolution 484,368] 538. $false <- (11) [subsumption resolution 537,246] 539. ~11 [avatar contradiction clause 538] 567. $false [avatar sat refutation 432,539] % SZS output end Proof for 8962662163615562204323697 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Janice is the only person in the room. 'Only one person in the room is a sibling of Willie' if 'everyone in the room does not create YouTube content or is a quiet european'. 'Everyone in the room who is a calm european is quieter than Carl' if 'everyone in the room does not own a significant collection of rare gemstones and minerals or is poorer than Carl'. If 'at least one person in the room is calm' then 'Janice and Sharon like each other'. 'Everyone in the room is not patient, not tall or cannot play the guitar' if 'everyone in the room is not a happy humble quiet person or does not own a significant collection of rare gemstones and minerals' and vice versa. 'Janice neither does not practice and performs acrobatic dance routines nor is not brave' only if 'A desert does not bloom with snowdrops every year.'. ''Glass rain falls on a distant planet.' and 'A desert blooms with snowdrops every year.'' if 'Janice is poorer than Shannon'. 'Janice is a tall tourist' if 'everyone in the room is a calm european' and vice versa. If 'Janice is a generous person' then 'Janice and Louise like each other'.

Janice is happy.

entailment

room(janice)&(![X]:(room(X)=>(X='janice')))& ((![X]:(room(X)=>(((quiet(X)&european(X))|(does_not_create_YouTube_content(X))))))=>(((?[X]:(room(X)&sibling(willie,X)))&(![X,Y]:((room(X)&room(Y)&(sibling(willie,X))&(sibling(willie,Y)))=>(X=Y))))))& ((![X]:(room(X)=>(((poorer(carl,X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))=>(![X]:(room(X)=>(((calm(X)&european(X))=>(quieter(carl,X)))))))& ((((?[X]:(room(X)&calm(X)))))=>((like(janice,sharon) & like(sharon,janice))))& ((![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(~(happy(X)&humble(X)&quiet(X)&person(X)))))))<=>(![X]:(room(X)=>(((cannot_play_the_guitar(X))|(~patient(X)&~tall(X)))))))& ((~((does_not_practice_and_performs_acrobatic_dance_routines(janice))|(~brave(janice))))=>(A_desert_does_not_bloom_with_snowdrops_every_year.))& ((poorer(shannon,janice))=>(((Glass_rain_falls_on_a_distant_planet.)&(A_desert_blooms_with_snowdrops_every_year.))))& ((![X]:(room(X)=>(calm(X)&european(X))))<=>(tall(janice)&tourist(janice)))& ((generous(janice)&person(janice))=>((like(janice,louise) & like(louise,janice))))& ((~(((Glass_rain_does_not_fall_on_a_distant_planet.)<~>(A_clock_measures_time_in_various_colors.))))<=>(?[X]:(room(X)&(client(willie,X)))))& (((hate(susie,janice) & hate(janice,susie)))=>(![X]:(room(X)=>(((humble(X))<=(client(louise,X)))))))& ((((A_book_can_be_opened_only_at_midnight.)<~>(Glass_rain_falls_on_a_distant_planet.)))<~>(~![X]:(room(X)=>(((~(wise(X)&curious(X)&funny(X)&tourist(X)))|(cannot_play_the_guitar(X)))))))& (((~(wise(janice)&tourist(janice)))=>(happy(janice)&person(janice)))& ((happy(janice)&person(janice))=>(client(janice,louise))))& ((![X]:(~room(X)=>(((strong(X)&european(X))|(does_not_have_a_tattoo(X))))))=>(![X]:(anywhere(X)=>(((~like(carl,X))=>(patient(X)&european(X)))))))& (?[X]:(anywhere(X)&(sibling(shannon,X))))& (![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))=>(~(curious(X)&tourist(X)))))))& (~(happy(janice)&european(janice)))& (((A_desert_blooms_with_snowdrops_every_year.)&(A_clock_does_not_measure_time_in_various_colors.)))& (![X]:(funny(X)=>quiet(X)))& (~(~(curious(janice)&person(janice))))& (((A_car_does_not_run_solely_on_saltwater.)<~>(A_clock_does_not_measure_time_in_various_colors.)))& (~(wise(janice)&tourist(janice)))& (![X]:((anywhere(X)&(X!=janice))=>younger(X,janice)))& (poorer(janice,sharon))& (is_not_a_craft_beer_aficionado(janice))& (![X]:(room(X)=>(((does_not_enjoy_fishing(X))=>(quiet(X)&brave(X)&european(X))))))& (?[X]:(room(X)&(like(susie,X))))& (~![X]:(room(X)=>(((louder(susie,X))=>(((like(X,willie))&(patient(X)&person(X))))))))& (![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(sibling(sharon,X))))))& (creative(janice)&person(janice))

room(janice)&(![X]:(room(X)=>(X='janice')))& happy(janice)

% SZS status Unsatisfiable for 8730541512245773890930578 % SZS output start Proof for 8730541512245773890930578 44. person(mary) & creative(mary) & ! [X0] : (room(X0) => (sibling(alice,X0) | ~predf(X0))) & ~! [X0] : (room(X0) => (louder(lucy,X0) => (person(X0) & patient(X0) & like(X0,fred)))) & ? [X0] : (like(lucy,X0) & room(X0)) & ! [X0] : (room(X0) => (~preds(X0) => (european(X0) & brave(X0) & quiet(X0)))) & ~predu(mary) & poorer(mary,alice) & ! [X0] : ((mary != X0 & anywhere(X0)) => younger(X0,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ~~(person(mary) & curious(mary)) & ! [X0] : (funny(X0) => quiet(X0)) & ~propositione & propositionc & ~(european(mary) & happy(mary)) & ! [X0] : (room(X0) => (~predu(X0) => ~(tourist(X0) & curious(X0)))) & ? [X0] : (sibling(susan,X0) & anywhere(X0)) & (! [X0] : (~room(X0) => (~predk(X0) | (european(X0) & strong(X0)))) => ! [X0] : (anywhere(X0) => (~like(john,X0) => (european(X0) & patient(X0))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X0] : (room(X0) => (~predd(X0) | ~(tourist(X0) & funny(X0) & curious(X0) & wise(X0))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X0] : (room(X0) => (client(paul,X0) => humble(X0)))) & (~(~propositionb <~> propositione) <=> ? [X0] : (client(fred,X0) & room(X0))) & ((person(mary) & generous(mary)) => (like(paul,mary) & like(mary,paul))) & (! [X0] : (room(X0) => (european(X0) & calm(X0))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => (propositionc & propositionb)) & (~(~brave(mary) | ~predi(mary)) => ~propositionc) & (! [X0] : (room(X0) => (~(person(X0) & quiet(X0) & humble(X0) & happy(X0)) | ~predv(X0))) <=> ! [X0] : (room(X0) => ((~tall(X0) & ~patient(X0)) | ~predd(X0)))) & (? [X0] : (calm(X0) & room(X0)) => (like(alice,mary) & like(mary,alice))) & (! [X0] : (room(X0) => (~predv(X0) | poorer(john,X0))) => ! [X0] : (room(X0) => ((european(X0) & calm(X0)) => quieter(john,X0)))) & (! [X0] : (room(X0) => (~prede(X0) | (european(X0) & quiet(X0)))) => (! [X0,X1] : ((sibling(fred,X1) & sibling(fred,X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (sibling(fred,X0) & room(X0)))) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ~(happy(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 46. person(mary) & creative(mary) & ! [X0] : (room(X0) => (sibling(alice,X0) | ~predf(X0))) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ! [X3] : (room(X3) => (~preds(X3) => (european(X3) & brave(X3) & quiet(X3)))) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ~~(person(mary) & curious(mary)) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & propositionc & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : (~room(X8) => (~predk(X8) | (european(X8) & strong(X8)))) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & ((person(mary) & generous(mary)) => (like(paul,mary) & like(mary,paul))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => (propositionc & propositionb)) & (~(~brave(mary) | ~predi(mary)) => ~propositionc) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (~prede(X19) | (european(X19) & quiet(X19)))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [rectify 44] 47. person(mary) & creative(mary) & ! [X0] : (room(X0) => (sibling(alice,X0) | ~predf(X0))) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ! [X3] : (room(X3) => (~preds(X3) => (european(X3) & brave(X3) & quiet(X3)))) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & (person(mary) & curious(mary)) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & propositionc & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : (~room(X8) => (~predk(X8) | (european(X8) & strong(X8)))) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & ((person(mary) & generous(mary)) => (like(paul,mary) & like(mary,paul))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => (propositionc & propositionb)) & (~(~brave(mary) | ~predi(mary)) => ~propositionc) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (~prede(X19) | (european(X19) & quiet(X19)))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [flattening 46] 48. person(mary) & curious(mary) & person(mary) & ! [X0] : (room(X0) => (sibling(alice,X0) | ~predf(X0))) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ! [X3] : (room(X3) => (~preds(X3) => (european(X3) & brave(X3) & quiet(X3)))) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & propositionc & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : (~room(X8) => (~predk(X8) | (european(X8) & strong(X8)))) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & ((person(mary) & generous(mary)) => (like(paul,mary) & like(mary,paul))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => (propositionc & propositionb)) & (~(~brave(mary) | ~predi(mary)) => ~propositionc) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (~prede(X19) | (european(X19) & quiet(X19)))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [pure predicate removal 47] 49. person(mary) & curious(mary) & person(mary) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ! [X3] : (room(X3) => (~preds(X3) => (european(X3) & brave(X3) & quiet(X3)))) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & propositionc & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : (~room(X8) => (~predk(X8) | (european(X8) & strong(X8)))) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & ((person(mary) & generous(mary)) => (like(paul,mary) & like(mary,paul))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => (propositionc & propositionb)) & (~(~brave(mary) | ~predi(mary)) => ~propositionc) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (~prede(X19) | (european(X19) & quiet(X19)))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [pure predicate removal 48] 50. person(mary) & curious(mary) & person(mary) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & propositionc & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : (~room(X8) => (~predk(X8) | (european(X8) & strong(X8)))) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & ((person(mary) & generous(mary)) => (like(paul,mary) & like(mary,paul))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => (propositionc & propositionb)) & (~(~brave(mary) | ~predi(mary)) => ~propositionc) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (~prede(X19) | (european(X19) & quiet(X19)))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [pure predicate removal 49] 51. person(mary) & curious(mary) & person(mary) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & propositionc & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : (~room(X8) => (~predk(X8) | (european(X8) & strong(X8)))) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & ((person(mary) & generous(mary)) => (like(paul,mary) & like(mary,paul))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => (propositionc & propositionb)) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (~prede(X19) | (european(X19) & quiet(X19)))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [pure predicate removal 50] 52. person(mary) & curious(mary) & person(mary) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : (~room(X8) => (~predk(X8) | (european(X8) & strong(X8)))) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & ((person(mary) & generous(mary)) => (like(paul,mary) & like(mary,paul))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => propositionb) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (~prede(X19) | (european(X19) & quiet(X19)))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [pure predicate removal 51] 53. person(mary) & curious(mary) & person(mary) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : (~room(X8) => (european(X8) & strong(X8))) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & ((person(mary) & generous(mary)) => (like(paul,mary) & like(mary,paul))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => propositionb) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (~prede(X19) | (european(X19) & quiet(X19)))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [pure predicate removal 52] 54. person(mary) & curious(mary) & person(mary) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : ~~room(X8) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & ((person(mary) & generous(mary)) => (like(paul,mary) & like(mary,paul))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => propositionb) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (~prede(X19) | (european(X19) & quiet(X19)))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [pure predicate removal 53] 55. person(mary) & curious(mary) & person(mary) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : ~~room(X8) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => propositionb) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (~prede(X19) | (european(X19) & quiet(X19)))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [pure predicate removal 54] 56. person(mary) & curious(mary) & person(mary) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : ~~room(X8) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & ((hate(mary,lucy) & hate(lucy,mary)) => ! [X11] : (room(X11) => (client(paul,X11) => humble(X11)))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => propositionb) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (european(X19) & quiet(X19))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [pure predicate removal 55] 59. person(mary) & curious(mary) & person(mary) & ~! [X1] : (room(X1) => (louder(lucy,X1) => (person(X1) & patient(X1) & like(X1,fred)))) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : ((mary != X4 & anywhere(X4)) => younger(X4,mary)) & ~(tourist(mary) & wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (funny(X5) => quiet(X5)) & ~propositione & ~(european(mary) & happy(mary)) & ! [X6] : (room(X6) => (~predu(X6) => ~(tourist(X6) & curious(X6)))) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X8] : ~~room(X8) => ! [X9] : (anywhere(X9) => (~like(john,X9) => (european(X9) & patient(X9))))) & ((person(mary) & happy(mary)) => client(mary,paul)) & (~(tourist(mary) & wise(mary)) => (person(mary) & happy(mary))) & ((propositiond <~> propositionb) <~> ~! [X10] : (room(X10) => (~predd(X10) | ~(tourist(X10) & funny(X10) & curious(X10) & wise(X10))))) & (~(~propositionb <~> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & (! [X13] : (room(X13) => (european(X13) & calm(X13))) <=> (tourist(mary) & tall(mary))) & (poorer(susan,mary) => propositionb) & (! [X14] : (room(X14) => (~(person(X14) & quiet(X14) & humble(X14) & happy(X14)) | ~predv(X14))) <=> ! [X15] : (room(X15) => ((~tall(X15) & ~patient(X15)) | ~predd(X15)))) & (? [X16] : (calm(X16) & room(X16)) => (like(alice,mary) & like(mary,alice))) & (! [X17] : (room(X17) => (~predv(X17) | poorer(john,X17))) => ! [X18] : (room(X18) => ((european(X18) & calm(X18)) => quieter(john,X18)))) & (! [X19] : (room(X19) => (european(X19) & quiet(X19))) => (! [X20,X21] : ((sibling(fred,X21) & sibling(fred,X20) & room(X21) & room(X20)) => X20 = X21) & ? [X22] : (sibling(fred,X22) & room(X22)))) & ! [X23] : (room(X23) => mary = X23) & room(mary) [pure predicate removal 56] 129. person(mary) & curious(mary) & person(mary) & ? [X1] : (((~person(X1) | ~patient(X1) | ~like(X1,fred)) & louder(lucy,X1)) & room(X1)) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : (younger(X4,mary) | (mary = X4 | ~anywhere(X4))) & (~tourist(mary) | ~wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (quiet(X5) | ~funny(X5)) & ~propositione & (~european(mary) | ~happy(mary)) & ! [X6] : (((~tourist(X6) | ~curious(X6)) | predu(X6)) | ~room(X6)) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X9] : (((european(X9) & patient(X9)) | like(john,X9)) | ~anywhere(X9)) | ? [X8] : ~room(X8)) & (client(mary,paul) | (~person(mary) | ~happy(mary))) & ((person(mary) & happy(mary)) | (tourist(mary) & wise(mary))) & ((propositiond <~> propositionb) <~> ? [X10] : ((predd(X10) & (tourist(X10) & funny(X10) & curious(X10) & wise(X10))) & room(X10))) & ((~propositionb <=> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & (! [X13] : ((european(X13) & calm(X13)) | ~room(X13)) <=> (tourist(mary) & tall(mary))) & (propositionb | ~poorer(susan,mary)) & (! [X14] : (((~person(X14) | ~quiet(X14) | ~humble(X14) | ~happy(X14)) | ~predv(X14)) | ~room(X14)) <=> ! [X15] : (((~tall(X15) & ~patient(X15)) | ~predd(X15)) | ~room(X15))) & ((like(alice,mary) & like(mary,alice)) | ! [X16] : (~calm(X16) | ~room(X16))) & (! [X18] : ((quieter(john,X18) | (~european(X18) | ~calm(X18))) | ~room(X18)) | ? [X17] : ((predv(X17) & ~poorer(john,X17)) & room(X17))) & ((! [X20,X21] : (X20 = X21 | (~sibling(fred,X21) | ~sibling(fred,X20) | ~room(X21) | ~room(X20))) & ? [X22] : (sibling(fred,X22) & room(X22))) | ? [X19] : ((~european(X19) | ~quiet(X19)) & room(X19))) & ! [X23] : (mary = X23 | ~room(X23)) & room(mary) [ennf transformation 59] 130. person(mary) & curious(mary) & person(mary) & ? [X1] : ((~person(X1) | ~patient(X1) | ~like(X1,fred)) & louder(lucy,X1) & room(X1)) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : (younger(X4,mary) | mary = X4 | ~anywhere(X4)) & (~tourist(mary) | ~wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (quiet(X5) | ~funny(X5)) & ~propositione & (~european(mary) | ~happy(mary)) & ! [X6] : (~tourist(X6) | ~curious(X6) | predu(X6) | ~room(X6)) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X9] : ((european(X9) & patient(X9)) | like(john,X9) | ~anywhere(X9)) | ? [X8] : ~room(X8)) & (client(mary,paul) | ~person(mary) | ~happy(mary)) & ((person(mary) & happy(mary)) | (tourist(mary) & wise(mary))) & ((propositiond <~> propositionb) <~> ? [X10] : (predd(X10) & tourist(X10) & funny(X10) & curious(X10) & wise(X10) & room(X10))) & ((~propositionb <=> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & (! [X13] : ((european(X13) & calm(X13)) | ~room(X13)) <=> (tourist(mary) & tall(mary))) & (propositionb | ~poorer(susan,mary)) & (! [X14] : (~person(X14) | ~quiet(X14) | ~humble(X14) | ~happy(X14) | ~predv(X14) | ~room(X14)) <=> ! [X15] : ((~tall(X15) & ~patient(X15)) | ~predd(X15) | ~room(X15))) & ((like(alice,mary) & like(mary,alice)) | ! [X16] : (~calm(X16) | ~room(X16))) & (! [X18] : (quieter(john,X18) | ~european(X18) | ~calm(X18) | ~room(X18)) | ? [X17] : (predv(X17) & ~poorer(john,X17) & room(X17))) & ((! [X20,X21] : (X20 = X21 | ~sibling(fred,X21) | ~sibling(fred,X20) | ~room(X21) | ~room(X20)) & ? [X22] : (sibling(fred,X22) & room(X22))) | ? [X19] : ((~european(X19) | ~quiet(X19)) & room(X19))) & ! [X23] : (mary = X23 | ~room(X23)) & room(mary) [flattening 129] 131. ~happy(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 45] 132. sP0 <=> ! [X14] : (~person(X14) | ~quiet(X14) | ~humble(X14) | ~happy(X14) | ~predv(X14) | ~room(X14)) [predicate definition introduction] 133. sP1 <=> ? [X10] : (predd(X10) & tourist(X10) & funny(X10) & curious(X10) & wise(X10) & room(X10)) [predicate definition introduction] 134. person(mary) & curious(mary) & person(mary) & ? [X1] : ((~person(X1) | ~patient(X1) | ~like(X1,fred)) & louder(lucy,X1) & room(X1)) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : (younger(X4,mary) | mary = X4 | ~anywhere(X4)) & (~tourist(mary) | ~wise(mary)) & (~propositiona <~> ~propositione) & ! [X5] : (quiet(X5) | ~funny(X5)) & ~propositione & (~european(mary) | ~happy(mary)) & ! [X6] : (~tourist(X6) | ~curious(X6) | predu(X6) | ~room(X6)) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X9] : ((european(X9) & patient(X9)) | like(john,X9) | ~anywhere(X9)) | ? [X8] : ~room(X8)) & (client(mary,paul) | ~person(mary) | ~happy(mary)) & ((person(mary) & happy(mary)) | (tourist(mary) & wise(mary))) & ((propositiond <~> propositionb) <~> sP1) & ((~propositionb <=> propositione) <=> ? [X12] : (client(fred,X12) & room(X12))) & (! [X13] : ((european(X13) & calm(X13)) | ~room(X13)) <=> (tourist(mary) & tall(mary))) & (propositionb | ~poorer(susan,mary)) & (sP0 <=> ! [X15] : ((~tall(X15) & ~patient(X15)) | ~predd(X15) | ~room(X15))) & ((like(alice,mary) & like(mary,alice)) | ! [X16] : (~calm(X16) | ~room(X16))) & (! [X18] : (quieter(john,X18) | ~european(X18) | ~calm(X18) | ~room(X18)) | ? [X17] : (predv(X17) & ~poorer(john,X17) & room(X17))) & ((! [X20,X21] : (X20 = X21 | ~sibling(fred,X21) | ~sibling(fred,X20) | ~room(X21) | ~room(X20)) & ? [X22] : (sibling(fred,X22) & room(X22))) | ? [X19] : ((~european(X19) | ~quiet(X19)) & room(X19))) & ! [X23] : (mary = X23 | ~room(X23)) & room(mary) [definition folding 130,133,132] 144. person(mary) & curious(mary) & person(mary) & ? [X1] : ((~person(X1) | ~patient(X1) | ~like(X1,fred)) & louder(lucy,X1) & room(X1)) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : (younger(X4,mary) | mary = X4 | ~anywhere(X4)) & (~tourist(mary) | ~wise(mary)) & ((propositione | propositiona) & (~propositione | ~propositiona)) & ! [X5] : (quiet(X5) | ~funny(X5)) & ~propositione & (~european(mary) | ~happy(mary)) & ! [X6] : (~tourist(X6) | ~curious(X6) | predu(X6) | ~room(X6)) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X9] : ((european(X9) & patient(X9)) | like(john,X9) | ~anywhere(X9)) | ? [X8] : ~room(X8)) & (client(mary,paul) | ~person(mary) | ~happy(mary)) & ((person(mary) & happy(mary)) | (tourist(mary) & wise(mary))) & ((~sP1 | ((propositiond | ~propositionb) & (propositionb | ~propositiond))) & (sP1 | ((~propositionb | ~propositiond) & (propositionb | propositiond)))) & ((((~propositionb | ~propositione) & (propositione | propositionb)) | ! [X12] : (~client(fred,X12) | ~room(X12))) & (? [X12] : (client(fred,X12) & room(X12)) | ((~propositione | propositionb) & (propositione | ~propositionb)))) & ((! [X13] : ((european(X13) & calm(X13)) | ~room(X13)) | (~tourist(mary) | ~tall(mary))) & ((tourist(mary) & tall(mary)) | ? [X13] : ((~european(X13) | ~calm(X13)) & room(X13)))) & (propositionb | ~poorer(susan,mary)) & ((sP0 | ? [X15] : ((tall(X15) | patient(X15)) & predd(X15) & room(X15))) & (! [X15] : ((~tall(X15) & ~patient(X15)) | ~predd(X15) | ~room(X15)) | ~sP0)) & ((like(alice,mary) & like(mary,alice)) | ! [X16] : (~calm(X16) | ~room(X16))) & (! [X18] : (quieter(john,X18) | ~european(X18) | ~calm(X18) | ~room(X18)) | ? [X17] : (predv(X17) & ~poorer(john,X17) & room(X17))) & ((! [X20,X21] : (X20 = X21 | ~sibling(fred,X21) | ~sibling(fred,X20) | ~room(X21) | ~room(X20)) & ? [X22] : (sibling(fred,X22) & room(X22))) | ? [X19] : ((~european(X19) | ~quiet(X19)) & room(X19))) & ! [X23] : (mary = X23 | ~room(X23)) & room(mary) [nnf transformation 134] 145. person(mary) & curious(mary) & person(mary) & ? [X1] : ((~person(X1) | ~patient(X1) | ~like(X1,fred)) & louder(lucy,X1) & room(X1)) & ? [X2] : (like(lucy,X2) & room(X2)) & ~predu(mary) & poorer(mary,alice) & ! [X4] : (younger(X4,mary) | mary = X4 | ~anywhere(X4)) & (~tourist(mary) | ~wise(mary)) & (propositione | propositiona) & (~propositione | ~propositiona) & ! [X5] : (quiet(X5) | ~funny(X5)) & ~propositione & (~european(mary) | ~happy(mary)) & ! [X6] : (~tourist(X6) | ~curious(X6) | predu(X6) | ~room(X6)) & ? [X7] : (sibling(susan,X7) & anywhere(X7)) & (! [X9] : ((european(X9) & patient(X9)) | like(john,X9) | ~anywhere(X9)) | ? [X8] : ~room(X8)) & (client(mary,paul) | ~person(mary) | ~happy(mary)) & ((person(mary) & happy(mary)) | (tourist(mary) & wise(mary))) & (~sP1 | ((propositiond | ~propositionb) & (propositionb | ~propositiond))) & (sP1 | ((~propositionb | ~propositiond) & (propositionb | propositiond))) & (((~propositionb | ~propositione) & (propositione | propositionb)) | ! [X12] : (~client(fred,X12) | ~room(X12))) & (? [X12] : (client(fred,X12) & room(X12)) | ((~propositione | propositionb) & (propositione | ~propositionb))) & (! [X13] : ((european(X13) & calm(X13)) | ~room(X13)) | ~tourist(mary) | ~tall(mary)) & ((tourist(mary) & tall(mary)) | ? [X13] : ((~european(X13) | ~calm(X13)) & room(X13))) & (propositionb | ~poorer(susan,mary)) & (sP0 | ? [X15] : ((tall(X15) | patient(X15)) & predd(X15) & room(X15))) & (! [X15] : ((~tall(X15) & ~patient(X15)) | ~predd(X15) | ~room(X15)) | ~sP0) & ((like(alice,mary) & like(mary,alice)) | ! [X16] : (~calm(X16) | ~room(X16))) & (! [X18] : (quieter(john,X18) | ~european(X18) | ~calm(X18) | ~room(X18)) | ? [X17] : (predv(X17) & ~poorer(john,X17) & room(X17))) & ((! [X20,X21] : (X20 = X21 | ~sibling(fred,X21) | ~sibling(fred,X20) | ~room(X21) | ~room(X20)) & ? [X22] : (sibling(fred,X22) & room(X22))) | ? [X19] : ((~european(X19) | ~quiet(X19)) & room(X19))) & ! [X23] : (mary = X23 | ~room(X23)) & room(mary) [flattening 144] 146. person(mary) & curious(mary) & person(mary) & ? [X0] : ((~person(X0) | ~patient(X0) | ~like(X0,fred)) & louder(lucy,X0) & room(X0)) & ? [X1] : (like(lucy,X1) & room(X1)) & ~predu(mary) & poorer(mary,alice) & ! [X2] : (younger(X2,mary) | mary = X2 | ~anywhere(X2)) & (~tourist(mary) | ~wise(mary)) & (propositione | propositiona) & (~propositione | ~propositiona) & ! [X3] : (quiet(X3) | ~funny(X3)) & ~propositione & (~european(mary) | ~happy(mary)) & ! [X4] : (~tourist(X4) | ~curious(X4) | predu(X4) | ~room(X4)) & ? [X5] : (sibling(susan,X5) & anywhere(X5)) & (! [X6] : ((european(X6) & patient(X6)) | like(john,X6) | ~anywhere(X6)) | ? [X7] : ~room(X7)) & (client(mary,paul) | ~person(mary) | ~happy(mary)) & ((person(mary) & happy(mary)) | (tourist(mary) & wise(mary))) & (~sP1 | ((propositiond | ~propositionb) & (propositionb | ~propositiond))) & (sP1 | ((~propositionb | ~propositiond) & (propositionb | propositiond))) & (((~propositionb | ~propositione) & (propositione | propositionb)) | ! [X8] : (~client(fred,X8) | ~room(X8))) & (? [X9] : (client(fred,X9) & room(X9)) | ((~propositione | propositionb) & (propositione | ~propositionb))) & (! [X10] : ((european(X10) & calm(X10)) | ~room(X10)) | ~tourist(mary) | ~tall(mary)) & ((tourist(mary) & tall(mary)) | ? [X11] : ((~european(X11) | ~calm(X11)) & room(X11))) & (propositionb | ~poorer(susan,mary)) & (sP0 | ? [X12] : ((tall(X12) | patient(X12)) & predd(X12) & room(X12))) & (! [X13] : ((~tall(X13) & ~patient(X13)) | ~predd(X13) | ~room(X13)) | ~sP0) & ((like(alice,mary) & like(mary,alice)) | ! [X14] : (~calm(X14) | ~room(X14))) & (! [X15] : (quieter(john,X15) | ~european(X15) | ~calm(X15) | ~room(X15)) | ? [X16] : (predv(X16) & ~poorer(john,X16) & room(X16))) & ((! [X17,X18] : (X17 = X18 | ~sibling(fred,X18) | ~sibling(fred,X17) | ~room(X18) | ~room(X17)) & ? [X19] : (sibling(fred,X19) & room(X19))) | ? [X20] : ((~european(X20) | ~quiet(X20)) & room(X20))) & ! [X21] : (mary = X21 | ~room(X21)) & room(mary) [rectify 145] 147. ? [X0] : ((~person(X0) | ~patient(X0) | ~like(X0,fred)) & louder(lucy,X0) & room(X0)) => ((~person(sK4) | ~patient(sK4) | ~like(sK4,fred)) & louder(lucy,sK4) & room(sK4)) [choice axiom] 148. ? [X1] : (like(lucy,X1) & room(X1)) => (like(lucy,sK5) & room(sK5)) [choice axiom] 149. ? [X5] : (sibling(susan,X5) & anywhere(X5)) => (sibling(susan,sK6) & anywhere(sK6)) [choice axiom] 150. ? [X7] : ~room(X7) => ~room(sK7) [choice axiom] 151. ? [X9] : (client(fred,X9) & room(X9)) => (client(fred,sK8) & room(sK8)) [choice axiom] 152. ? [X11] : ((~european(X11) | ~calm(X11)) & room(X11)) => ((~european(sK9) | ~calm(sK9)) & room(sK9)) [choice axiom] 153. ? [X12] : ((tall(X12) | patient(X12)) & predd(X12) & room(X12)) => ((tall(sK10) | patient(sK10)) & predd(sK10) & room(sK10)) [choice axiom] 154. ? [X16] : (predv(X16) & ~poorer(john,X16) & room(X16)) => (predv(sK11) & ~poorer(john,sK11) & room(sK11)) [choice axiom] 155. ? [X19] : (sibling(fred,X19) & room(X19)) => (sibling(fred,sK12) & room(sK12)) [choice axiom] 156. ? [X20] : ((~european(X20) | ~quiet(X20)) & room(X20)) => ((~european(sK13) | ~quiet(sK13)) & room(sK13)) [choice axiom] 157. person(mary) & curious(mary) & person(mary) & ((~person(sK4) | ~patient(sK4) | ~like(sK4,fred)) & louder(lucy,sK4) & room(sK4)) & (like(lucy,sK5) & room(sK5)) & ~predu(mary) & poorer(mary,alice) & ! [X2] : (younger(X2,mary) | mary = X2 | ~anywhere(X2)) & (~tourist(mary) | ~wise(mary)) & (propositione | propositiona) & (~propositione | ~propositiona) & ! [X3] : (quiet(X3) | ~funny(X3)) & ~propositione & (~european(mary) | ~happy(mary)) & ! [X4] : (~tourist(X4) | ~curious(X4) | predu(X4) | ~room(X4)) & (sibling(susan,sK6) & anywhere(sK6)) & (! [X6] : ((european(X6) & patient(X6)) | like(john,X6) | ~anywhere(X6)) | ~room(sK7)) & (client(mary,paul) | ~person(mary) | ~happy(mary)) & ((person(mary) & happy(mary)) | (tourist(mary) & wise(mary))) & (~sP1 | ((propositiond | ~propositionb) & (propositionb | ~propositiond))) & (sP1 | ((~propositionb | ~propositiond) & (propositionb | propositiond))) & (((~propositionb | ~propositione) & (propositione | propositionb)) | ! [X8] : (~client(fred,X8) | ~room(X8))) & ((client(fred,sK8) & room(sK8)) | ((~propositione | propositionb) & (propositione | ~propositionb))) & (! [X10] : ((european(X10) & calm(X10)) | ~room(X10)) | ~tourist(mary) | ~tall(mary)) & ((tourist(mary) & tall(mary)) | ((~european(sK9) | ~calm(sK9)) & room(sK9))) & (propositionb | ~poorer(susan,mary)) & (sP0 | ((tall(sK10) | patient(sK10)) & predd(sK10) & room(sK10))) & (! [X13] : ((~tall(X13) & ~patient(X13)) | ~predd(X13) | ~room(X13)) | ~sP0) & ((like(alice,mary) & like(mary,alice)) | ! [X14] : (~calm(X14) | ~room(X14))) & (! [X15] : (quieter(john,X15) | ~european(X15) | ~calm(X15) | ~room(X15)) | (predv(sK11) & ~poorer(john,sK11) & room(sK11))) & ((! [X17,X18] : (X17 = X18 | ~sibling(fred,X18) | ~sibling(fred,X17) | ~room(X18) | ~room(X17)) & (sibling(fred,sK12) & room(sK12))) | ((~european(sK13) | ~quiet(sK13)) & room(sK13))) & ! [X21] : (mary = X21 | ~room(X21)) & room(mary) [skolemisation 146,156,155,154,153,152,151,150,149,148,147] 158. ? [X0] : (mary != X0 & room(X0)) => (mary != sK14 & room(sK14)) [choice axiom] 159. ~happy(mary) | (mary != sK14 & room(sK14)) | ~room(mary) [skolemisation 131,158] 257. room(mary) [cnf transformation 157] 258. ~room(X21) | mary = X21 [cnf transformation 157] 292. happy(mary) | wise(mary) [cnf transformation 157] 293. happy(mary) | tourist(mary) [cnf transformation 157] 307. ~tourist(mary) | ~wise(mary) [cnf transformation 157] 319. ~happy(mary) | room(sK14) | ~room(mary) [cnf transformation 159] 320. ~happy(mary) | mary != sK14 | ~room(mary) [cnf transformation 159] 412. 20 <=> wise(mary) [avatar definition] 416. 21 <=> tourist(mary) [avatar definition] 419. ~20 | ~21 [avatar split clause 307,416,412] 432. 24 <=> happy(mary) [avatar definition] 460. 21 | 24 [avatar split clause 293,432,416] 461. 20 | 24 [avatar split clause 292,432,412] 611. ~happy(mary) | mary != sK14 [subsumption resolution 320,257] 613. 61 <=> mary = sK14 [avatar definition] 615. mary != sK14 <- (~61) [avatar component clause 613] 616. ~61 | ~24 [avatar split clause 611,432,613] 617. ~happy(mary) | room(sK14) [subsumption resolution 319,257] 619. 62 <=> room(sK14) [avatar definition] 621. room(sK14) <- (62) [avatar component clause 619] 622. 62 | ~24 [avatar split clause 617,432,619] 633. mary = sK14 <- (62) [resolution 258,621] 665. $false <- (~61, 62) [subsumption resolution 633,615] 666. 61 | ~62 [avatar contradiction clause 665] 667. $false [avatar sat refutation 419,460,461,616,622,666] % SZS output end Proof for 8730541512245773890930578 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If “everyone in the room is not a coffee connoisseur or enjoys fishing” then “everyone in the room is not a coffee connoisseur”. “At least one person anywhere is a tea enthusiast” if “everyone anywhere does not practice and performs acrobatic dance routines or practices and performs acrobatic dance routines”. If “at least one person in the room does not practice and performs acrobatic dance routines” then “everyone in the room creates augmented reality experiences for mobile applications if they is a tea enthusiast”. If “someone in the room practices and performs acrobatic dance routines” then “more than one person in the room enjoys watercolor painting”. If “everyone in the room does not own a high-end gaming PC with custom-built components or is a coffee connoisseur” then “everyone in the room does not volunteer for local environmental conservation projects or is a tea enthusiast”. If “everyone in the room does not volunteer for local environmental conservation projects or is a tea enthusiast” then “it is not the case that “someone outside the room enjoys fishing””. Everyone in the room who practices and performs acrobatic dance routines enjoys salsa dancing. Everyone in the room who regularly goes on multi-day backpacking trips in national parks hosts regular game nights featuring complex strategy games. Someone anywhere creates augmented reality experiences for mobile applications. Everyone anywhere is not a tea enthusiast if they volunteers for local environmental conservation projects and vice versa. Everyone in the room who volunteers for local environmental conservation projects regularly goes on multi-day backpacking trips in national parks. More than one person in the room enjoys salsa dancing. More than one person in the room enjoys watercolor painting. Everyone in the room who owns a high-end gaming PC with custom-built components enjoys salsa dancing. It is not the case that “someone in the room is a tea enthusiast”. If someone creates augmented reality experiences for mobile applications then he/she volunteers for local environmental conservation projects.

Everyone in the room does not host regular game nights featuring complex strategy games or practices and performs acrobatic dance routines.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((enjoys_fishing(X))|(is_not_a_coffee_connoisseur(X))))))=>(![X]:(room(X)=>(is_not_a_coffee_connoisseur(X)))))& ((![X]:(anywhere(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))=>(((?[X]:(anywhere(X)&is_a_tea_enthusiast(X))))))& ((((?[X]:(room(X)&does_not_practice_and_performs_acrobatic_dance_routines(X)))))=>(![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))))& ((?[X]:(room(X)&(practices_and_performs_acrobatic_dance_routines(X))))=>((?[X,Y]:(room(X)&room(Y)&(enjoys_watercolor_painting(X)&enjoys_watercolor_painting(Y))&(X!=Y)))))& (((![X]:(room(X)=>(((is_a_coffee_connoisseur(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(![X]:(room(X)=>(((is_a_tea_enthusiast(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X)))))))& ((![X]:(room(X)=>(((is_a_tea_enthusiast(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))=>(~(?[X]:(~room(X)&(enjoys_fishing(X)))))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (?[X]:(anywhere(X)&(creates_augmented_reality_experiences_for_mobile_applications(X))))& (![X]:(anywhere(X)=>(((is_not_a_tea_enthusiast(X))<=>(volunteers_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_salsa_dancing(X)&enjoys_salsa_dancing(Y))&(X!=Y))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_watercolor_painting(X)&enjoys_watercolor_painting(Y))&(X!=Y))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(enjoys_salsa_dancing(X))))))& (~(?[X]:(room(X)&(is_a_tea_enthusiast(X)))))& ((![X]:((creates_augmented_reality_experiences_for_mobile_applications(X))=>(volunteers_for_local_environmental_conservation_projects(X)))))

(there_is_a_room)& ![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X)))))

Nancy, Erin are the only persons in the room. If “Nancy participates in citizen science projects related to wildlife monitoring and hosts regular workshops on creative writing” then “more than one person in the room has a pet dog”. “No one in the room does not collect first edition books or enjoys watercolor painting” only if “Erin plays the violin”. “Erin has a pet dog, is an avid mountain climber who has scaled several peaks and is a client of Costco” if “Erin is dedicated to sustainable living and zero-waste practices”. Nancy practices kickboxing. Erin enjoys watercolor painting. Everyone in the room who uses contact lenses collect rare sneakers. Everyone in the room who participates in citizen science projects related to wildlife monitoring is an avid collector of autographed memorabilia from famous musicians or enjoys watercolor painting or both. If someone does not collect rare sneakers then he/she enjoys watercolor painting and vice versa. Nancy participates in citizen science projects related to wildlife monitoring. Nancy uses contact lenses.

Nancy is an avid collector of autographed memorabilia from famous musicians.

entailment

room(nancy)&room(erin)&(![X]:(room(X)=>(X='nancy'|X='erin')))& ((((participates_in_citizen_science_projects_related_to_wildlife_monitoring(nancy))&(hosts_regular_workshops_on_creative_writing(nancy))))=>((?[X,Y]:(room(X)&room(Y)&(has_a_pet_dog(X)&has_a_pet_dog(Y))&(X!=Y)))))& ((~?[X]:(room(X)=>(((enjoys_watercolor_painting(X))|(does_not_collect_first_edition_books(X))))))=>(plays_the_violin(erin)))& ((is_dedicated_to_sustainable_living_and_zero-waste_practices(erin))=>(((has_a_pet_dog(erin))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(erin))&(is_a_client_of_Costco(erin)))))& (practices_kickboxing(nancy))& (enjoys_watercolor_painting(erin))& (~![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(uses_contact_lenses(X))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(collect_rare_sneakers(X))))))& (collects_first_edition_books(nancy))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(enjoys_watercolor_painting(X))))))))& (((participates_in_citizen_science_projects_related_to_wildlife_monitoring(nancy))&(hosts_regular_workshops_on_creative_writing(nancy))))& ((![X]:((does_not_collect_rare_sneakers(X))<=>(enjoys_watercolor_painting(X)))))& (?[X]:(room(X)&(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(nancy))& (?[X]:(room(X)&(collects_rare_and_antique_scientific_instruments(X))))& (![X]:(~room(X)=>(((practices_kickboxing(X))<=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (uses_contact_lenses(nancy))& (?[X]:(room(X)&(hosts_regular_workshops_on_creative_writing(X))))& ((?[X,Y]:(room(X)&room(Y)&(((collects_first_edition_books(X))<~>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))&((collects_first_edition_books(Y))<~>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(Y))))&(X!=Y))))& (((writes_a_travel_blog(erin))&(does_not_host_regular_workshops_on_creative_writing(erin))&(collects_rare_and_antique_scientific_instruments(erin))))& ((![X]:((writes_a_travel_blog(X))=>(practices_kickboxing(X)))))& (works_on_fridays(nancy))& (is_a_client_of_Costco(nancy))& ((practices_kickboxing(erin))&(writes_a_travel_blog(erin)))& (plays_the_violin(nancy))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(nancy))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(practices_kickboxing(X))))))& (plays_the_violin(erin))

room(nancy)&room(erin)&(![X]:(room(X)=>(X='nancy'|X='erin')))& is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(nancy)

% SZS status Unsatisfiable for 1333375912146683749934051 % SZS output start Proof for 1333375912146683749934051 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 51. ! [X0] : (room(X0) => (preda(X0) => predp(X0))) [input p7] 53. ! [X0] : (room(X0) => (predk(X0) => (predl(X0) | predg(X0)))) [input p9] 55. ! [X0] : (~predp(X0) <=> predl(X0)) [input p11] 57. predk(mary) [input p13] 60. preda(mary) [input p16] 72. ~(predg(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 73. ! [X0] : (predl(X0) => ~predp(X0)) [unused predicate definition removal 55] 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] : ((predp(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 51] 166. ! [X0] : (predp(X0) | ~preda(X0) | ~room(X0)) [flattening 165] 167. ! [X0] : (((predl(X0) | predg(X0)) | ~predk(X0)) | ~room(X0)) [ennf transformation 53] 168. ! [X0] : (predl(X0) | predg(X0) | ~predk(X0) | ~room(X0)) [flattening 167] 169. ! [X0] : (~predp(X0) | ~predl(X0)) [ennf transformation 73] 174. ~predg(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 72] 175. ~predg(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 174] 192. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 193. ~predg(mary) | (paul != sK8 & mary != sK8 & room(sK8)) | ~room(paul) | ~room(mary) [skolemisation 175,192] 274. room(mary) [cnf transformation 160] 275. room(paul) [cnf transformation 160] 276. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 160] 285. ~preda(X0) | predp(X0) | ~room(X0) [cnf transformation 166] 287. ~predk(X0) | predg(X0) | predl(X0) | ~room(X0) [cnf transformation 168] 290. ~predp(X0) | ~predl(X0) [cnf transformation 169] 292. predk(mary) [cnf transformation 57] 296. preda(mary) [cnf transformation 60] 312. ~predg(mary) | room(sK8) | ~room(paul) | ~room(mary) [cnf transformation 193] 313. ~predg(mary) | mary != sK8 | ~room(paul) | ~room(mary) [cnf transformation 193] 314. ~predg(mary) | paul != sK8 | ~room(paul) | ~room(mary) [cnf transformation 193] 316. 1 <=> predk(mary) [avatar definition] 317. predk(mary) <- (1) [avatar component clause 316] 340. 1 [avatar split clause 292,316] 361. ~predg(mary) | paul != sK8 | ~room(mary) [subsumption resolution 314,275] 362. ~predg(mary) | paul != sK8 [subsumption resolution 361,274] 364. 10 <=> paul = sK8 [avatar definition] 366. paul != sK8 <- (~10) [avatar component clause 364] 368. 11 <=> predg(mary) [avatar definition] 371. ~10 | ~11 [avatar split clause 362,368,364] 372. ~predg(mary) | mary != sK8 | ~room(mary) [subsumption resolution 313,275] 373. ~predg(mary) | mary != sK8 [subsumption resolution 372,274] 375. 12 <=> mary = sK8 [avatar definition] 377. mary != sK8 <- (~12) [avatar component clause 375] 378. ~12 | ~11 [avatar split clause 373,368,375] 379. ~predg(mary) | room(sK8) | ~room(mary) [subsumption resolution 312,275] 380. ~predg(mary) | room(sK8) [subsumption resolution 379,274] 382. 13 <=> room(sK8) [avatar definition] 384. room(sK8) <- (13) [avatar component clause 382] 385. 13 | ~11 [avatar split clause 380,368,382] 387. predp(mary) | ~room(mary) [resolution 285,296] 388. predp(mary) [subsumption resolution 387,274] 389. ~predl(mary) [resolution 388,290] 511. predg(mary) | predl(mary) | ~room(mary) <- (1) [resolution 287,317] 516. predg(mary) | ~room(mary) <- (1) [subsumption resolution 511,389] 517. predg(mary) <- (1) [subsumption resolution 516,274] 518. 11 | ~1 [avatar split clause 517,316,368] 519. mary = sK8 | paul = sK8 <- (13) [resolution 384,276] 520. paul = sK8 <- (~12, 13) [subsumption resolution 519,377] 521. $false <- (~10, ~12, 13) [subsumption resolution 520,366] 522. 10 | 12 | ~13 [avatar contradiction clause 521] 523. $false [avatar sat refutation 340,371,378,385,518,522] % SZS output end Proof for 1333375912146683749934051 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Eileen is the only person in the room. If everyone in the room collects first edition books or does not collect first edition books then not everyone in the room who is a client of LVMH can play the piano. Everyone in the room who writes in-depth travel guides for off-the-beaten-path destinations knows morse code. Everyone in the room who collects antique clocks has a pet dog. Everyone in the room who is a client of LVMH writes in-depth travel guides for off-the-beaten-path destinations. If someone collects antique clocks then he/she knows morse code and vice versa.

It is not the case that Eileen has a pet dog.

contradiction

room(eileen)&(![X]:(room(X)=>(X='eileen')))& ((~?[X]:(anywhere(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))=>((![X]:((knows_morse_code(X))<=>(is_a_client_of_LVMH(X))))))& ((?[X]:(room(X)&(collects_first_edition_books(X))))=>((![X]:((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=>(is_a_client_of_LVMH(X))))))& ((![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(collects_modern_art(X))))))=>(![X]:(room(X)=>(((collects_modern_art(X))=>(knows_morse_code(X)))))))& ((![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_enjoy_mountain_biking(X))))))=>(![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(knows_morse_code(X)))))))& ((![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(collects_first_edition_books(X))))))=>(~![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(can_play_the_piano(X)))))))& ((![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(collects_modern_art(X))))))=>(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(enjoys_origami(X)))))))& ((~?[X]:(room(X)=>(((cannot_play_the_guitar(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))=>(?[X]:(room(X)&(is_a_client_of_LVMH(X)))))& ((![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(is_a_drone_photographer(X))))))=>(![X]:(anywhere(X)=>(((is_a_drone_photographer(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))))& ((![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(has_a_pet_dog(X))))))=>(![X]:(~room(X)=>(((has_a_pet_dog(X))<=>(does_enjoy_mountain_biking(X)))))))& (((?[X]:(room(X)&own_a_television(X)))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(knows_morse_code(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(has_a_pet_dog(X))))))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(~room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(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))=>(has_a_pet_dog(X))))))& (~![X]:(room(X)=>(((creates_YouTube_content(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))=>(is_a_tea_enthusiast(X))))))& (?[X]:(room(X)&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(own_a_television(X))))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=>(collects_first_edition_books(X))))))& ((![X]:((collects_antique_clocks(X))<=>(knows_morse_code(X)))))& (![X]:(anywhere(X)=>(((can_play_the_guitar(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))

room(eileen)&(![X]:(room(X)=>(X='eileen')))& ~(has_a_pet_dog(eileen))

% SZS status Unsatisfiable for 5909656821933188281575063 % SZS output start Proof for 5909656821933188281575063 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (predi(X0) | ~predi(X0))) => ~! [X0] : (room(X0) => (predv(X0) => predw(X0))) [input p5] 56. ! [X0] : (room(X0) => (predz(X0) => predy(X0))) [input p12] 58. ! [X0] : (room(X0) => (predl(X0) => preda(X0))) [input p14] 67. ! [X0] : (room(X0) => (predv(X0) => predz(X0))) [input p23] 70. ! [X0] : (predl(X0) <=> predy(X0)) [input p26] 72. ~preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 77. ! [X0] : (room(X0) => (predi(X0) | ~predi(X0))) => ~! [X1] : (room(X1) => (predv(X1) => predw(X1))) [rectify 49] 82. ! [X0] : (predy(X0) => predl(X0)) [unused predicate definition removal 70] 92. ! [X0] : (room(X0) => (predi(X0) | ~predi(X0))) => ~! [X1] : (room(X1) => ~predv(X1)) [pure predicate removal 77] 166. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 172. ? [X1] : (predv(X1) & room(X1)) | ? [X0] : ((~predi(X0) & predi(X0)) & room(X0)) [ennf transformation 92] 173. ? [X1] : (predv(X1) & room(X1)) | ? [X0] : (~predi(X0) & predi(X0) & room(X0)) [flattening 172] 178. ! [X0] : ((predy(X0) | ~predz(X0)) | ~room(X0)) [ennf transformation 56] 179. ! [X0] : (predy(X0) | ~predz(X0) | ~room(X0)) [flattening 178] 182. ! [X0] : ((preda(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 58] 183. ! [X0] : (preda(X0) | ~predl(X0) | ~room(X0)) [flattening 182] 191. ! [X0] : ((predz(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 67] 192. ! [X0] : (predz(X0) | ~predv(X0) | ~room(X0)) [flattening 191] 196. ! [X0] : (predl(X0) | ~predy(X0)) [ennf transformation 82] 197. ~preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 72] 208. ? [X0] : (predv(X0) & room(X0)) | ? [X1] : (~predi(X1) & predi(X1) & room(X1)) [rectify 173] 209. ? [X0] : (predv(X0) & room(X0)) => (predv(sK2) & room(sK2)) [choice axiom] 210. ? [X1] : (~predi(X1) & predi(X1) & room(X1)) => (~predi(sK3) & predi(sK3) & room(sK3)) [choice axiom] 211. (predv(sK2) & room(sK2)) | (~predi(sK3) & predi(sK3) & room(sK3)) [skolemisation 208,210,209] 304. room(mary) [cnf transformation 166] 305. ~room(X0) | mary = X0 [cnf transformation 166] 314. room(sK2) | predi(sK3) [cnf transformation 211] 315. room(sK2) | ~predi(sK3) [cnf transformation 211] 317. predv(sK2) | predi(sK3) [cnf transformation 211] 318. predv(sK2) | ~predi(sK3) [cnf transformation 211] 327. ~predz(X0) | predy(X0) | ~room(X0) [cnf transformation 179] 329. ~predl(X0) | preda(X0) | ~room(X0) [cnf transformation 183] 336. ~predv(X0) | predz(X0) | ~room(X0) [cnf transformation 192] 340. ~predy(X0) | predl(X0) [cnf transformation 196] 343. ~preda(mary) [cnf transformation 197] 392. 12 <=> predi(sK3) [avatar definition] 396. 13 <=> predv(sK2) [avatar definition] 398. predv(sK2) <- (13) [avatar component clause 396] 399. ~12 | 13 [avatar split clause 318,396,392] 400. 12 | 13 [avatar split clause 317,396,392] 407. 15 <=> room(sK2) [avatar definition] 409. room(sK2) <- (15) [avatar component clause 407] 410. ~12 | 15 [avatar split clause 315,407,392] 411. 12 | 15 [avatar split clause 314,407,392] 438. mary = sK2 <- (15) [resolution 305,409] 443. predv(mary) <- (13, 15) [backward demodulation 398,438] 452. predz(mary) | ~room(mary) <- (13, 15) [resolution 336,443] 453. predz(mary) <- (13, 15) [subsumption resolution 452,304] 454. predy(mary) | ~room(mary) <- (13, 15) [resolution 453,327] 455. predy(mary) <- (13, 15) [subsumption resolution 454,304] 459. predl(mary) <- (13, 15) [resolution 455,340] 464. preda(mary) | ~room(mary) <- (13, 15) [resolution 459,329] 465. ~room(mary) <- (13, 15) [subsumption resolution 464,343] 466. $false <- (13, 15) [subsumption resolution 465,304] 467. ~13 | ~15 [avatar contradiction clause 466] 468. $false [avatar sat refutation 399,400,410,411,467] % SZS output end Proof for 5909656821933188281575063 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------

Don is the only person in the room. “Everyone in the room does not enjoy wildlife photography or collects rare and antique scientific instruments” only if “no one outside the room who maintains a personal blog focused on cybersecurity tips hosts a popular podcast about emerging technologies”. If “everyone outside the room owns a smart tv or does not practice digital art” then “everyone anywhere who owns a smart tv is a coffee connoisseur”. Either “Don hosts a popular podcast about emerging technologies” or “Don plays eSports competitively” but not both. “Everyone outside the room is passionate about collecting and restoring classic cars or does not write a travel blog” only if “Don collects rare and antique scientific instruments”. If “everyone in the room does not use contact lenses or owns a high-end gaming PC with custom-built components” then “everyone in the room who does not use contact lenses neither is a professional photographer specializing in portrait photography nor can play the piano”. “Everyone in the room cannot play the piano or owns a smart tv” only if “Don is a tea enthusiast”. If “everyone anywhere does not collect antique clocks or collects antique clocks” then “Don creates bespoke furniture pieces from reclaimed wood”. If “Don own a television” then “someone in the room is passionate about collecting and restoring classic cars”. Everyone in the room who does enjoy mountain biking hosts regular game nights featuring complex strategy games. Everyone in the room does not collect antique clocks or hosts regular game nights featuring complex strategy games. Everyone outside the room who is a tea enthusiast collects rare and antique scientific instruments.

Don own a television.

neutral

room(don)&(![X]:(room(X)=>(X='don')))& ((![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(does_not_enjoy_wildlife_photography(X))))))=>(~?[X]:(~room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))))& ((![X]:(~room(X)=>(((does_not_practice_digital_art(X))|(owns_a_smart_tv(X))))))=>(![X]:(anywhere(X)=>(((owns_a_smart_tv(X))=>(is_a_coffee_connoisseur(X)))))))& ((hosts_a_popular_podcast_about_emerging_technologies(don))<~>(plays_eSports_competitively(don)))& ((![X]:(~room(X)=>(((does_not_write_a_travel_blog(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))=>(collects_rare_and_antique_scientific_instruments(don)))& ((![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_use_contact_lenses(X))))))=>(![X]:(room(X)=>(((does_not_use_contact_lenses(X))=>(~((is_a_professional_photographer_specializing_in_portrait_photography(X))|(can_play_the_piano(X)))))))))& ((![X]:(room(X)=>(((owns_a_smart_tv(X))|(cannot_play_the_piano(X))))))=>(is_a_tea_enthusiast(don)))& ((![X]:(anywhere(X)=>(((collects_antique_clocks(X))|(does_not_collect_antique_clocks(X))))))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(don)))& ((own_a_television(don))=>(?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X)))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(does_not_collect_antique_clocks(X))))))& (![X]:(~room(X)=>(((is_a_tea_enthusiast(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(anywhere(X)=>(((writes_a_travel_blog(X))=>(can_play_the_piano(X))))))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(don))& (![X]:(room(X)=>(((~((plays_video_games(X))|(collects_antique_clocks(X))))=>(is_a_tea_enthusiast(X))))))& (?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(~((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(plays_eSports_competitively(X))))))))& (?[X]:(room(X)&(does_enjoy_mountain_biking(X))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(collects_antique_clocks(X))))))

room(don)&(![X]:(room(X)=>(X='don')))& own_a_television(don)

Sue, Marcus, Angel, Richard are the only persons in the room. Richard is a client of Charlene. "Mirrors do not fog permanently in one particular house." or "A tower does not lean significantly without falling." but not both. Everyone in the room is not a client of LVMH or has a curated collection of mid-century modern furniture. Not everyone in the room is a client of LVMH if they has a curated collection of mid-century modern furniture. Sue is a client of LVMH. "Mirrors do not fog permanently in one particular house." and "A door does not randomly teleport those who pass through it.". "A car runs solely on saltwater." and "A door does not randomly teleport those who pass through it.". Richard who is a client of LVMH is a client of Charlene. Richard has a curated collection of mid-century modern furniture. Sue is a client of Charlene. Everyone in the room has a curated collection of mid-century modern furniture if they is a client of Charlene. Everyone in the room is richer than Charlene if they has a curated collection of mid-century modern furniture. Sue is the richest anywhere. Angel is a client of LVMH. Everyone outside the room who has a curated collection of mid-century modern furniture is richer than Charlene. Richard is a client of LVMH.

Charlene is richer than Richard.

contradiction

room(sue)&room(marcus)&room(angel)&room(richard)&(![X]:(room(X)=>(X='sue'|X='marcus'|X='angel'|X='richard')))& (client(charlene,richard))& (((Mirrors_do_not_fog_permanently_in_one_particular_house.)<~>(A_tower_does_not_lean_significantly_without_falling.)))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(is_not_a_client_of_LVMH(X))))))& (~![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(is_a_client_of_LVMH(X))))))& (is_a_client_of_LVMH(sue))& (((Mirrors_do_not_fog_permanently_in_one_particular_house.)&(A_door_does_not_randomly_teleport_those_who_pass_through_it.)))& (((A_car_runs_solely_on_saltwater.)&(A_door_does_not_randomly_teleport_those_who_pass_through_it.)))& ((is_a_client_of_LVMH(richard))&(client(charlene,richard)))& (has_a_curated_collection_of_mid-century_modern_furniture(richard))& (client(charlene,sue))& (![X]:(room(X)=>(((client(charlene,X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(richer(charlene,X))))))& (![X]:((anywhere(X)&(X!=sue))=>richer(X,sue)))& (is_a_client_of_LVMH(angel))& (![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(richer(charlene,X))))))& (is_a_client_of_LVMH(richard))

room(sue)&room(marcus)&room(angel)&room(richard)&(![X]:(room(X)=>(X='sue'|X='marcus'|X='angel'|X='richard')))& richer(richard,charlene)

% SZS status Unsatisfiable for 1321292598740907116685281 % SZS output start Proof for 1321292598740907116685281 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] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 53. predn(alice) [input p9] 56. ! [X0] : (room(X0) => (predn(X0) => richer(john,X0))) [input p12] 61. richer(alice,john) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 72. ! [X0,X1] : ((~richer(X1,X0) | ~richer(X0,X1)) | X0 = X1) [ennf transformation 8] 73. ! [X0,X1] : (~richer(X1,X0) | ~richer(X0,X1) | X0 = X1) [flattening 72] 136. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 136] 144. ! [X0] : ((richer(john,X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 56] 145. ! [X0] : (richer(john,X0) | ~predn(X0) | ~room(X0)) [flattening 144] 150. richer(alice,john) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 61] 151. richer(alice,john) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 150] 160. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 73] 222. alice != john [cnf transformation 43] 240. room(alice) [cnf transformation 137] 253. predn(alice) [cnf transformation 53] 256. richer(john,X0) | ~predn(X0) | ~room(X0) [cnf transformation 145] 266. richer(alice,john) [cnf transformation 151] 287. ~richer(john,alice) | alice = john [resolution 160,266] 292. ~richer(john,alice) [subsumption resolution 287,222] 293. ~predn(alice) | ~room(alice) [resolution 292,256] 295. ~room(alice) [subsumption resolution 293,253] 296. $false [subsumption resolution 295,240] % SZS output end Proof for 1321292598740907116685281 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Everyone outside the room neither creates augmented reality experiences for mobile applications nor collects historical artifacts related to ancient civilizations only if they is a Linux enthusiast. Everyone in the room collects historical artifacts related to ancient civilizations or is not a client of Meta. Everyone in the room who collects historical artifacts related to ancient civilizations collects antique clocks. Everyone outside the room enjoys landscape photography. Everyone in the room is a Linux enthusiast if they is passionate about collecting and restoring classic cars. Everyone in the room is a Linux enthusiast only if they collects historical artifacts related to ancient civilizations. Someone outside the room either is a client of Meta or makes homemade pastries but not both. If someone makes homemade pastries then he/she collects historical artifacts related to ancient civilizations and vice versa.

Everyone in the room creates augmented reality experiences for mobile applications.

neutral

(there_is_a_room)& (![X]:(~room(X)=>(((is_a_Linux_enthusiast(X))<=(~((creates_augmented_reality_experiences_for_mobile_applications(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))))& (![X]:(room(X)=>(((is_not_a_client_of_Meta(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(collects_antique_clocks(X))))))& (![X]:(~room(X)=>(enjoys_landscape_photography(X))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(is_a_Linux_enthusiast(X))))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))<=(is_a_Linux_enthusiast(X))))))& (?[X]:(~room(X)&(((is_a_client_of_Meta(X))<~>(makes_homemade_pastries(X))))))& ((![X]:((makes_homemade_pastries(X))<=>(collects_historical_artifacts_related_to_ancient_civilizations(X)))))

(there_is_a_room)& ![X]:(room(X)=>(creates_augmented_reality_experiences_for_mobile_applications(X)))

There is a room. Not everyone anywhere is a dedicated advocate for digital privacy and encryption if they designs and sews custom cosplay costumes for conventions and vice versa. Everyone in the room designs and sews custom cosplay costumes for conventions if and only if they hosts themed dinner parties featuring gourmet home-cooked meals. Roberteric dreamt that “everyone outside the room either enjoys writing detailed reviews of new and classic board games or designs and sews custom cosplay costumes for conventions but not both if and only if they participates in citizen science projects related to wildlife monitoring and enjoys macrame”.

Everyone in the room does not practice graffiti art or is allergic to anything.

neutral

(there_is_a_room)& (~![X]:(anywhere(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& ((roberteric_dream=>(![X]:(~room(X)=>(((((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<~>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))<=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(enjoys_macrame(X))))))))))& ((![X]:((practices_archery(X))=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(writes_poetry(X)))))))& (~![X]:(room(X)=>(((((writes_poetry(X))&(enjoys_making_ceramics(X))))=>(does_not_practice_archery(X))))))& (![X]:(room(X)=>(((~((has_lived_in_exactly_three_countries(X))|(does_not_have_lived_in_exactly_three_countries(X))))<=(does_not_practice_archery(X))))))& ((![X]:((((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<~>(has_lived_in_exactly_three_countries(X))))=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<~>(can_play_the_guitar(X)))))))& (?[X]:(room(X)&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))& (?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))& (![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))|(enjoys_landscape_photography(X))))))& (~![X]:(room(X)=>(((enjoys_landscape_photography(X))<=>(practices_graffiti_art(X))))))& (![X]:(anywhere(X)=>(((((enjoys_macrame(X))&(practices_and_performs_acrobatic_dance_routines(X))&(does_not_have_a_pet_dog(X))))<=(practices_graffiti_art(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))<=>(((is_a_drone_photographer(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))))& (![X]:(room(X)=>(((((is_a_drone_photographer(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))=>(((is_allergic_to_anything(X))&(enjoys_rooftop_gardening(X))))))))& (![X]:(room(X)=>(((((is_allergic_to_anything(X))&(enjoys_rooftop_gardening(X))))=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<~>(has_a_pet_dog(X))))))))& (![X]:(~room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(((collects_vintage_vinyl_records(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))|(collects_vintage_vinyl_records(X))))))& (?[X]:(room(X)&(((enjoys_landscape_photography(X))&(can_play_the_guitar(X))))))& (?[X]:(room(X)&(~((has_a_pet_dog(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (~![X]:(room(X)=>(((practices_archery(X))<=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((is_allergic_to_anything(X))|(does_not_practice_graffiti_art(X)))))

Jean is the only person in the room. “Jean who does not compete in national level swimming championships enjoys kayaking and exploring remote waterways” unless “someone outside the room has completed a triathlon, does not have completed a triathlon or hosts a YouTube channel dedicated to art tutorials”. If “everyone in the room does not collect vintage vinyl records or competes in national level swimming championships” then “everyone in the room is not an expert in identifying and foraging wild edible plants and composes and performs experimental electronic music if they does not collect vintage vinyl records”. Jean enjoys origami. Jean who enjoys kayaking and exploring remote waterways watches fantasy movies, enjoys kayaking and exploring remote waterways and is a professional photographer specializing in portrait photography. Jean enjoys virtual reality gaming. Everyone in the room is not an expert in identifying and foraging wild edible plants and composes and performs experimental electronic music if they does not collect vintage vinyl records. Everyone in the room practices tai chi or is not an expert in identifying and foraging wild edible plants. Everyone in the room who practices tai chi has completed a triathlon. Not everyone in the room who enjoys kayaking and exploring remote waterways bakes bread at home. Everyone in the room who composes and performs experimental electronic music is an expert in identifying and foraging wild edible plants. It is not the case that “Jean owns a significant collection of rare gemstones and minerals”.

Jean collects vintage vinyl records.

entailment

room(jean)&(![X]:(room(X)=>(X='jean')))& (~(?[X]:(~room(X)&(((has_completed_a_triathlon(X))|(does_not_have_completed_a_triathlon(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))=>((does_not_compete_in_national_level_swimming_championships(jean))&(enjoys_kayaking_and_exploring_remote_waterways(jean))))& ((![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))|(does_not_collect_vintage_vinyl_records(X))))))=>(![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(composes_and_performs_experimental_electronic_music(X)))))))))& (enjoys_origami(jean))& ((enjoys_kayaking_and_exploring_remote_waterways(jean))&(((watches_fantasy_movies(jean))&(enjoys_kayaking_and_exploring_remote_waterways(jean))&(is_a_professional_photographer_specializing_in_portrait_photography(jean)))))& (enjoys_virtual_reality_gaming(jean))& (![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(composes_and_performs_experimental_electronic_music(X))))))))& (![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(practices_tai_chi(X))))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(has_completed_a_triathlon(X))))))& (~![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (~(owns_a_significant_collection_of_rare_gemstones_and_minerals(jean)))

room(jean)&(![X]:(room(X)=>(X='jean')))& collects_vintage_vinyl_records(jean)

% SZS status Unsatisfiable for 972639163397159820408208 % SZS output start Proof for 972639163397159820408208 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 50. ! [X0] : (room(X0) => (~predk(X0) => (predj(X0) & ~predi(X0)))) [input p6] 54. ! [X0] : (room(X0) => (predj(X0) => predi(X0))) [input p10] 56. ~(predk(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 143. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 146. ! [X0] : (((predj(X0) & ~predi(X0)) | predk(X0)) | ~room(X0)) [ennf transformation 50] 147. ! [X0] : ((predj(X0) & ~predi(X0)) | predk(X0) | ~room(X0)) [flattening 146] 149. ! [X0] : ((predi(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 54] 150. ! [X0] : (predi(X0) | ~predj(X0) | ~room(X0)) [flattening 149] 151. ~predk(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 56] 158. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom] 159. ~predk(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 151,158] 240. room(mary) [cnf transformation 143] 241. ~room(X0) | mary = X0 [cnf transformation 143] 246. ~predi(X0) | predk(X0) | ~room(X0) [cnf transformation 147] 247. predj(X0) | predk(X0) | ~room(X0) [cnf transformation 147] 249. ~predj(X0) | predi(X0) | ~room(X0) [cnf transformation 150] 250. ~predk(mary) | room(sK2) | ~room(mary) [cnf transformation 159] 251. ~predk(mary) | mary != sK2 | ~room(mary) [cnf transformation 159] 257. 2 <=> ! [X0] : (predj(X0) | ~room(X0) | predk(X0)) [avatar definition] 258. ~room(X0) | predj(X0) | predk(X0) <- (2) [avatar component clause 257] 266. 4 <=> ! [X0] : (~predi(X0) | ~room(X0) | predk(X0)) [avatar definition] 267. ~predi(X0) | ~room(X0) | predk(X0) <- (4) [avatar component clause 266] 270. 2 [avatar split clause 247,257] 271. 4 [avatar split clause 246,266] 272. ~predk(mary) | mary != sK2 [subsumption resolution 251,240] 274. 5 <=> mary = sK2 [avatar definition] 276. mary != sK2 <- (~5) [avatar component clause 274] 278. 6 <=> predk(mary) [avatar definition] 280. ~predk(mary) <- (~6) [avatar component clause 278] 281. ~5 | ~6 [avatar split clause 272,278,274] 282. ~predk(mary) | room(sK2) [subsumption resolution 250,240] 284. 7 <=> room(sK2) [avatar definition] 286. room(sK2) <- (7) [avatar component clause 284] 287. 7 | ~6 [avatar split clause 282,278,284] 291. predj(mary) | predk(mary) <- (2) [resolution 258,240] 292. predj(mary) <- (2, ~6) [subsumption resolution 291,280] 293. predi(mary) | ~room(mary) <- (2, ~6) [resolution 292,249] 294. predi(mary) <- (2, ~6) [subsumption resolution 293,240] 295. ~room(mary) | predk(mary) <- (2, 4, ~6) [resolution 294,267] 296. predk(mary) <- (2, 4, ~6) [subsumption resolution 295,240] 297. $false <- (2, 4, ~6) [subsumption resolution 296,280] 298. ~2 | ~4 | 6 [avatar contradiction clause 297] 305. mary = sK2 <- (7) [resolution 286,241] 315. $false <- (~5, 7) [subsumption resolution 305,276] 316. 5 | ~7 [avatar contradiction clause 315] 317. $false [avatar sat refutation 270,271,281,287,298,316] % SZS output end Proof for 972639163397159820408208 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Lorenzo, Miranda, Steven, Donald, Randy are the only persons in the room. If Lorenzo practices digital art then no one in the room who is a client of Costco travels domestically frequently otherwise only one person in the room collects antique clocks and collects comic books. If not everyone in the room plays video games or does not mentor a youth basketball team on weekends then no one outside the room plays video games if they mentors a youth basketball team on weekends and vice versa otherwise if someone collects comic books, is a coffee connoisseur or enjoys cross-country skiing then he/she practices digital art and vice versa. Lorenzo frequently participates in hackathons and coding competitions if everyone in the room is a client of Costco or does not play video games and vice versa. If Lorenzo collects comic books then Lorenzo does not play video games. Either everyone in the room does not practice digital art or mentors a youth basketball team on weekends or everyone in the room does not enjoy virtual reality gaming or does not play video games but not both. Everyone in the room who does not enjoy virtual reality gaming competes in national level swimming championships. Only one person anywhere travels domestically frequently. If someone regularly goes on multi-day backpacking trips in national parks then he/she enjoys writing detailed reviews of new and classic board games and vice versa. Lorenzo frequently participates in hackathons and coding competitions. Lorenzo is a client of Costco. Everyone anywhere who enjoys origami collects antique clocks. Not everyone outside the room collects antique clocks if and only if they competes in national level swimming championships. Everyone in the room is a coffee connoisseur or does not enjoy writing detailed reviews of new and classic board games. Everyone outside the room who is a coffee connoisseur mentors a youth basketball team on weekends. If someone enjoys origami then he/she plays video games. Lorenzo collects antique clocks.

Lorenzo regularly goes on multi-day backpacking trips in national parks.

contradiction

room(lorenzo)&room(miranda)&room(steven)&room(donald)&room(randy)&(![X]:(room(X)=>(X='lorenzo'|X='miranda'|X='steven'|X='donald'|X='randy')))& (((practices_digital_art(lorenzo))=>(~?[X]:(room(X)=>(((is_a_client_of_Costco(X))=>(travels_domestically_frequently(X)))))))&((~(practices_digital_art(lorenzo)))=>(((?[X]:(room(X)&((collects_antique_clocks(X))&(collects_comic_books(X)))))&(![X,Y]:((room(X)&room(Y)&(((collects_antique_clocks(X))&(collects_comic_books(X))))&(((collects_antique_clocks(Y))&(collects_comic_books(Y)))))=>(X=Y)))))))& (((~![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(plays_video_games(X))))))=>(~?[X]:(~room(X)=>(((plays_video_games(X))<=>(mentors_a_youth_basketball_team_on_weekends(X)))))))&((~(~![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(plays_video_games(X)))))))=>((![X]:((((collects_comic_books(X))|(is_a_coffee_connoisseur(X))|(enjoys_cross-country_skiing(X))))<=>(practices_digital_art(X)))))))& ((![X]:(room(X)=>(((does_not_play_video_games(X))|(is_a_client_of_Costco(X))))))<=>(frequently_participates_in_hackathons_and_coding_competitions(lorenzo)))& ((collects_comic_books(lorenzo))=>(does_not_play_video_games(lorenzo)))& ((![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(does_not_practice_digital_art(X))))))<~>(![X]:(room(X)=>(((does_not_play_video_games(X))|(does_not_enjoy_virtual_reality_gaming(X)))))))& (![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))=>(competes_in_national_level_swimming_championships(X))))))& (((?[X]:(anywhere(X)&travels_domestically_frequently(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(travels_domestically_frequently(X))&(travels_domestically_frequently(Y)))=>(X=Y)))))& ((![X]:((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))& (frequently_participates_in_hackathons_and_coding_competitions(lorenzo))& (is_a_client_of_Costco(lorenzo))& (![X]:(anywhere(X)=>(((enjoys_origami(X))=>(collects_antique_clocks(X))))))& (~![X]:(~room(X)=>(((collects_antique_clocks(X))<=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(is_a_coffee_connoisseur(X))))))& (![X]:(~room(X)=>(((is_a_coffee_connoisseur(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& ((![X]:((enjoys_origami(X))=>(plays_video_games(X)))))& (collects_antique_clocks(lorenzo))

room(lorenzo)&room(miranda)&room(steven)&room(donald)&room(randy)&(![X]:(room(X)=>(X='lorenzo'|X='miranda'|X='steven'|X='donald'|X='randy')))& regularly_goes_on_multi-day_backpacking_trips_in_national_parks(lorenzo)

% SZS status Unsatisfiable for 3226476373716353552626024 % SZS output start Proof for 3226476373716353552626024 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. (~predj(mary) => (! [X0,X1] : ((preda(X1) & predo(X1) & preda(X0) & predo(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (preda(X0) & predo(X0) & room(X0)))) & (predj(mary) => ~? [X0] : (room(X0) => (predh(X0) => predf(X0)))) [input p1] 46. (~~! [X0] : (room(X0) => (predp(X0) | ~predl(X0))) => ! [X0] : ((predn(X0) | predk(X0) | preda(X0)) <=> predj(X0))) & (~! [X0] : (room(X0) => (predp(X0) | ~predl(X0))) => ~? [X0] : (~room(X0) => (predp(X0) <=> predl(X0)))) [input p2] 51. ! [X0,X1] : ((predf(X1) & predf(X0) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X0] : (predf(X0) & anywhere(X0)) [input p7] 52. ! [X0] : (predd(X0) <=> predi(X0)) [input p8] 57. ! [X0] : (room(X0) => (predk(X0) | ~predi(X0))) [input p13] 61. 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] 62. (~predj(mary) => (! [X0,X1] : ((preda(X1) & predo(X1) & preda(X0) & predo(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (preda(X2) & predo(X2) & room(X2)))) & (predj(mary) => ~? [X3] : (room(X3) => (predh(X3) => predf(X3)))) [rectify 45] 63. (~~! [X0] : (room(X0) => (predp(X0) | ~predl(X0))) => ! [X1] : ((predn(X1) | predk(X1) | preda(X1)) <=> predj(X1))) & (~! [X2] : (room(X2) => (predp(X2) | ~predl(X2))) => ~? [X3] : (~room(X3) => (predp(X3) <=> predl(X3)))) [rectify 46] 64. (! [X0] : (room(X0) => (predp(X0) | ~predl(X0))) => ! [X1] : ((predn(X1) | predk(X1) | preda(X1)) <=> predj(X1))) & (~! [X2] : (room(X2) => (predp(X2) | ~predl(X2))) => ~? [X3] : (~room(X3) => (predp(X3) <=> predl(X3)))) [flattening 63] 66. ! [X0,X1] : ((predf(X1) & predf(X0) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (predf(X2) & anywhere(X2)) [rectify 51] 67. ! [X0] : (predd(X0) => predi(X0)) [unused predicate definition removal 52] 141. ! [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] 142. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 141] 143. ((! [X0,X1] : (X0 = X1 | (~preda(X1) | ~predo(X1) | ~preda(X0) | ~predo(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (preda(X2) & predo(X2) & room(X2))) | predj(mary)) & (! [X3] : ((~predf(X3) & predh(X3)) & room(X3)) | ~predj(mary)) [ennf transformation 62] 144. ((! [X0,X1] : (X0 = X1 | ~preda(X1) | ~predo(X1) | ~preda(X0) | ~predo(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (preda(X2) & predo(X2) & room(X2))) | predj(mary)) & (! [X3] : (~predf(X3) & predh(X3) & room(X3)) | ~predj(mary)) [flattening 143] 145. (! [X1] : ((predn(X1) | predk(X1) | preda(X1)) <=> predj(X1)) | ? [X0] : ((~predp(X0) & predl(X0)) & room(X0))) & (! [X3] : ((predp(X3) <~> predl(X3)) & ~room(X3)) | ! [X2] : ((predp(X2) | ~predl(X2)) | ~room(X2))) [ennf transformation 64] 146. (! [X1] : ((predn(X1) | predk(X1) | preda(X1)) <=> predj(X1)) | ? [X0] : (~predp(X0) & predl(X0) & room(X0))) & (! [X3] : ((predp(X3) <~> predl(X3)) & ~room(X3)) | ! [X2] : (predp(X2) | ~predl(X2) | ~room(X2))) [flattening 145] 154. ! [X0,X1] : (X0 = X1 | (~predf(X1) | ~predf(X0) | ~anywhere(X1) | ~anywhere(X0))) & ? [X2] : (predf(X2) & anywhere(X2)) [ennf transformation 66] 155. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~anywhere(X1) | ~anywhere(X0)) & ? [X2] : (predf(X2) & anywhere(X2)) [flattening 154] 156. ! [X0] : (predi(X0) | ~predd(X0)) [ennf transformation 67] 158. ! [X0] : ((predk(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 57] 159. ! [X0] : (predk(X0) | ~predi(X0) | ~room(X0)) [flattening 158] 162. 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 61] 163. 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 162] 164. ! [X1] : ((predn(X1) | predk(X1) | preda(X1)) <=> predj(X1)) | ~sP0 [predicate definition introduction] 165. (sP0 | ? [X0] : (~predp(X0) & predl(X0) & room(X0))) & (! [X3] : ((predp(X3) <~> predl(X3)) & ~room(X3)) | ! [X2] : (predp(X2) | ~predl(X2) | ~room(X2))) [definition folding 146,164] 167. ? [X2] : (preda(X2) & predo(X2) & room(X2)) => (preda(sK1) & predo(sK1) & room(sK1)) [choice axiom] 168. ((! [X0,X1] : (X0 = X1 | ~preda(X1) | ~predo(X1) | ~preda(X0) | ~predo(X0) | ~room(X1) | ~room(X0)) & (preda(sK1) & predo(sK1) & room(sK1))) | predj(mary)) & (! [X3] : (~predf(X3) & predh(X3) & room(X3)) | ~predj(mary)) [skolemisation 144,167] 169. ! [X1] : (((predn(X1) | predk(X1) | preda(X1)) | ~predj(X1)) & (predj(X1) | (~predn(X1) & ~predk(X1) & ~preda(X1)))) | ~sP0 [nnf transformation 164] 170. ! [X1] : ((predn(X1) | predk(X1) | preda(X1) | ~predj(X1)) & (predj(X1) | (~predn(X1) & ~predk(X1) & ~preda(X1)))) | ~sP0 [flattening 169] 171. ! [X0] : ((predn(X0) | predk(X0) | preda(X0) | ~predj(X0)) & (predj(X0) | (~predn(X0) & ~predk(X0) & ~preda(X0)))) | ~sP0 [rectify 170] 172. (sP0 | ? [X0] : (~predp(X0) & predl(X0) & room(X0))) & (! [X3] : (((~predl(X3) | ~predp(X3)) & (predl(X3) | predp(X3))) & ~room(X3)) | ! [X2] : (predp(X2) | ~predl(X2) | ~room(X2))) [nnf transformation 165] 173. (sP0 | ? [X0] : (~predp(X0) & predl(X0) & room(X0))) & (! [X3] : ((~predl(X3) | ~predp(X3)) & (predl(X3) | predp(X3)) & ~room(X3)) | ! [X2] : (predp(X2) | ~predl(X2) | ~room(X2))) [flattening 172] 174. (sP0 | ? [X0] : (~predp(X0) & predl(X0) & room(X0))) & (! [X1] : ((~predl(X1) | ~predp(X1)) & (predl(X1) | predp(X1)) & ~room(X1)) | ! [X2] : (predp(X2) | ~predl(X2) | ~room(X2))) [rectify 173] 175. ? [X0] : (~predp(X0) & predl(X0) & room(X0)) => (~predp(sK2) & predl(sK2) & room(sK2)) [choice axiom] 176. (sP0 | (~predp(sK2) & predl(sK2) & room(sK2))) & (! [X1] : ((~predl(X1) | ~predp(X1)) & (predl(X1) | predp(X1)) & ~room(X1)) | ! [X2] : (predp(X2) | ~predl(X2) | ~room(X2))) [skolemisation 174,175] 186. ? [X2] : (predf(X2) & anywhere(X2)) => (predf(sK6) & anywhere(sK6)) [choice axiom] 187. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~anywhere(X1) | ~anywhere(X0)) & (predf(sK6) & anywhere(sK6)) [skolemisation 155,186] 273. room(mary) [cnf transformation 142] 281. ~predf(X3) | ~predj(mary) [cnf transformation 168] 287. predj(X0) | ~predk(X0) | ~sP0 [cnf transformation 171] 290. ~room(X1) | predp(X2) | ~predl(X2) | ~room(X2) [cnf transformation 176] 293. sP0 | room(sK2) [cnf transformation 176] 294. sP0 | predl(sK2) [cnf transformation 176] 295. sP0 | ~predp(sK2) [cnf transformation 176] 313. predf(sK6) [cnf transformation 187] 315. ~predd(X0) | predi(X0) [cnf transformation 156] 321. ~predi(X0) | predk(X0) | ~room(X0) [cnf transformation 159] 330. predd(mary) [cnf transformation 163] 332. 1 <=> predj(mary) [avatar definition] 355. 6 <=> ! [X3] : ~predf(X3) [avatar definition] 356. ~predf(X3) <- (6) [avatar component clause 355] 357. ~1 | 6 [avatar split clause 281,355,332] 367. 9 <=> sP0 [avatar definition] 379. 12 <=> ! [X0] : (predj(X0) | ~predk(X0)) [avatar definition] 380. ~predk(X0) | predj(X0) <- (12) [avatar component clause 379] 381. ~9 | 12 [avatar split clause 287,379,367] 387. 14 <=> predp(sK2) [avatar definition] 389. ~predp(sK2) <- (~14) [avatar component clause 387] 390. ~14 | 9 [avatar split clause 295,367,387] 392. 15 <=> predl(sK2) [avatar definition] 394. predl(sK2) <- (15) [avatar component clause 392] 395. 15 | 9 [avatar split clause 294,367,392] 397. 16 <=> room(sK2) [avatar definition] 399. room(sK2) <- (16) [avatar component clause 397] 400. 16 | 9 [avatar split clause 293,367,397] 402. 17 <=> ! [X2] : (predp(X2) | ~room(X2) | ~predl(X2)) [avatar definition] 403. ~predl(X2) | ~room(X2) | predp(X2) <- (17) [avatar component clause 402] 413. 20 <=> ! [X1] : ~room(X1) [avatar definition] 414. ~room(X1) <- (20) [avatar component clause 413] 415. 17 | 20 [avatar split clause 290,413,402] 501. predi(mary) [resolution 315,330] 574. predk(mary) | ~room(mary) [resolution 321,501] 575. predk(mary) [subsumption resolution 574,273] 597. ~room(sK2) | predp(sK2) <- (15, 17) [resolution 394,403] 598. predp(sK2) <- (15, 16, 17) [subsumption resolution 597,399] 599. $false <- (~14, 15, 16, 17) [subsumption resolution 598,389] 600. 14 | ~15 | ~16 | ~17 [avatar contradiction clause 599] 611. $false <- (20) [resolution 414,273] 624. ~20 [avatar contradiction clause 611] 627. predj(mary) <- (12) [resolution 575,380] 630. 1 | ~12 [avatar split clause 627,379,332] 633. $false <- (6) [resolution 356,313] 634. ~6 [avatar contradiction clause 633] 635. $false [avatar sat refutation 357,381,390,395,400,415,600,624,630,634] % SZS output end Proof for 3226476373716353552626024 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------

Patricia is the only person in the room. If “it is not the case that “someone in the room is not a tall funny brave person”” then “everyone in the room is a old calm person if they is tall”. If “Patricia is humble” then “it is not the case that “Patricia is a brave person””. “It is not the case that “Patricia is quieter than Ronald”” if “Patricia is kind”. If “Patricia is richer than Ronald” then “everyone in the room is quieter than Ronald if they is not a tall person”. “Patricia is richer than Ronald” unless “Ronald is quieter than Patricia”. Everyone outside the room is not a funny person if and only if they neither is older than Ronald nor is not a patient generous person. Everyone anywhere who is older than Ronald is not a patient person. Everyone in the room who is a patient funny calm person is richer than Ronald. Everyone in the room either is richer than Ronald or is creative but not both if they is a old quiet person. Everyone in the room who is quieter than Ronald is not a curious person. Someone in the room is not a brave humble curious kind person. It is not the case that “more than one person in the room is curious”. Everyone in the room is richer than Ronald and is humble if they is richer than Ronald. Patricia is the oldest anywhere.

Patricia is humble.

neutral

room(patricia)&(![X]:(room(X)=>(X='patricia')))& ((~(?[X]:(room(X)&(~(tall(X)&funny(X)&brave(X)&person(X))))))=>(![X]:(room(X)=>(((tall(X))=>(old(X)&calm(X)&person(X)))))))& ((humble(patricia))=>(~(brave(patricia)&person(patricia))))& ((kind(patricia))=>(~(quieter(ronald,patricia))))& ((richer(ronald,patricia))=>(![X]:(room(X)=>(((~(tall(X)&person(X)))=>(quieter(ronald,X)))))))& (~(quieter(patricia,ronald))=>(richer(ronald,patricia)))& (![X]:(~room(X)=>(((~(funny(X)&person(X)))<=>(~((older(ronald,X))|(~(patient(X)&generous(X)&person(X)))))))))& (![X]:(anywhere(X)=>(((older(ronald,X))=>(~(patient(X)&person(X)))))))& (![X]:(room(X)=>(((patient(X)&funny(X)&calm(X)&person(X))=>(richer(ronald,X))))))& (![X]:(room(X)=>(((old(X)&quiet(X)&person(X))=>(((richer(ronald,X))<~>(creative(X))))))))& (![X]:(room(X)=>(((quieter(ronald,X))=>(~(curious(X)&person(X)))))))& (?[X]:(room(X)&(~(brave(X)&humble(X)&curious(X)&kind(X)&person(X)))))& (~((?[X,Y]:(room(X)&room(Y)&(curious(X)&curious(Y))&(X!=Y)))))& (![X]:(room(X)=>(((richer(ronald,X))=>(((richer(ronald,X))&(humble(X))))))))& (![X]:((anywhere(X)&(X!=patricia))=>older(X,patricia)))

room(patricia)&(![X]:(room(X)=>(X='patricia')))& humble(patricia)

Linda is the only person in the room. Either 'everyone in the room is quieter than Jonathan or does not play eSports competitively' or 'everyone in the room is quieter than Elizabeth or does not play eSports competitively' but not both. Everyone in the room is quieter than Elizabeth. Everyone in the room is quieter than Kenneth only if they is quieter than Jonathan.

Linda is quieter than Kenneth.

contradiction

room(linda)&(![X]:(room(X)=>(X='linda')))& ((![X]:(room(X)=>(((~quiet(X)&~happy(X))|(does_not_play_eSports_competitively(X))))))=>((~~~happy(linda))&(((quiet(linda)&person(linda))<~>(does_not_play_eSports_competitively(linda))))))& ((((does_not_play_eSports_competitively(linda))&(~(quiet(linda)&person(linda)))))<=>(![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(~happy(X)&~quiet(X)))))))& ((![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(~(quiet(X)&happy(X)&person(X)))))))=>(![X]:(room(X)=>(((~(quiet(X)&happy(X)&person(X)))<=(quieter(elizabeth,X)))))))& ((![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(quieter(jonathan,X))))))<~>(![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(quieter(elizabeth,X)))))))& (![X]:(room(X)=>(quieter(elizabeth,X))))& (~(quieter(linda,christopher)))& (![X]:((room(X)&(X!=linda))=>quieter(X,linda)))& ((![X]:((quieter(elizabeth,X))<=>(quieter(christopher,X)))))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(quieter(elizabeth,X))))))& (![X]:(room(X)=>(((quieter(jonathan,X))<=(quieter(kenneth,X))))))& (![X]:(~room(X)=>(((does_not_play_eSports_competitively(X))<=(quieter(christopher,X))))))& (![X]:(room(X)=>(((quieter(elizabeth,X))<=(does_not_play_eSports_competitively(X))))))& (![X]:(room(X)=>(((quieter(kenneth,X))<=(does_not_play_eSports_competitively(X))))))

room(linda)&(![X]:(room(X)=>(X='linda')))& quieter(kenneth,linda)

% SZS status Unsatisfiable for 1247994190041786633644043 % SZS output start Proof for 1247994190041786633644043 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (quieter(john,X0) | ~predq(X0))) <~> ! [X0] : (room(X0) => (quieter(paul,X0) | ~predq(X0))) [input p4] 49. ! [X0] : (room(X0) => quieter(paul,X0)) [input p5] 54. ! [X0] : (room(X0) => (quieter(fred,X0) => quieter(john,X0))) [input p10] 58. quieter(fred,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 60. ! [X0] : (room(X0) => (quieter(john,X0) | ~predq(X0))) <~> ! [X1] : (room(X1) => (quieter(paul,X1) | ~predq(X1))) [rectify 48] 133. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 140. ! [X0] : ((quieter(john,X0) | ~predq(X0)) | ~room(X0)) <~> ! [X1] : ((quieter(paul,X1) | ~predq(X1)) | ~room(X1)) [ennf transformation 60] 141. ! [X0] : (quieter(john,X0) | ~predq(X0) | ~room(X0)) <~> ! [X1] : (quieter(paul,X1) | ~predq(X1) | ~room(X1)) [flattening 140] 142. ! [X0] : (quieter(paul,X0) | ~room(X0)) [ennf transformation 49] 147. ! [X0] : ((quieter(john,X0) | ~quieter(fred,X0)) | ~room(X0)) [ennf transformation 54] 148. ! [X0] : (quieter(john,X0) | ~quieter(fred,X0) | ~room(X0)) [flattening 147] 155. quieter(fred,mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 58] 174. (? [X1] : (~quieter(paul,X1) & predq(X1) & room(X1)) | ? [X0] : (~quieter(john,X0) & predq(X0) & room(X0))) & (! [X1] : (quieter(paul,X1) | ~predq(X1) | ~room(X1)) | ! [X0] : (quieter(john,X0) | ~predq(X0) | ~room(X0))) [nnf transformation 141] 175. (? [X0] : (~quieter(paul,X0) & predq(X0) & room(X0)) | ? [X1] : (~quieter(john,X1) & predq(X1) & room(X1))) & (! [X2] : (quieter(paul,X2) | ~predq(X2) | ~room(X2)) | ! [X3] : (quieter(john,X3) | ~predq(X3) | ~room(X3))) [rectify 174] 176. ? [X0] : (~quieter(paul,X0) & predq(X0) & room(X0)) => (~quieter(paul,sK5) & predq(sK5) & room(sK5)) [choice axiom] 177. ? [X1] : (~quieter(john,X1) & predq(X1) & room(X1)) => (~quieter(john,sK6) & predq(sK6) & room(sK6)) [choice axiom] 178. ((~quieter(paul,sK5) & predq(sK5) & room(sK5)) | (~quieter(john,sK6) & predq(sK6) & room(sK6))) & (! [X2] : (quieter(paul,X2) | ~predq(X2) | ~room(X2)) | ! [X3] : (quieter(john,X3) | ~predq(X3) | ~room(X3))) [skolemisation 175,177,176] 260. room(mary) [cnf transformation 133] 261. ~room(X0) | mary = X0 [cnf transformation 133] 284. room(sK5) | room(sK6) [cnf transformation 178] 286. room(sK5) | ~quieter(john,sK6) [cnf transformation 178] 290. ~quieter(paul,sK5) | room(sK6) [cnf transformation 178] 292. ~quieter(paul,sK5) | ~quieter(john,sK6) [cnf transformation 178] 293. quieter(paul,X0) | ~room(X0) [cnf transformation 142] 299. ~quieter(fred,X0) | quieter(john,X0) | ~room(X0) [cnf transformation 148] 305. quieter(fred,mary) [cnf transformation 155] 413. 23 <=> quieter(john,sK6) [avatar definition] 415. ~quieter(john,sK6) <- (~23) [avatar component clause 413] 417. 24 <=> quieter(paul,sK5) [avatar definition] 419. ~quieter(paul,sK5) <- (~24) [avatar component clause 417] 420. ~23 | ~24 [avatar split clause 292,417,413] 427. 26 <=> room(sK6) [avatar definition] 429. room(sK6) <- (26) [avatar component clause 427] 430. 26 | ~24 [avatar split clause 290,417,427] 439. 28 <=> room(sK5) [avatar definition] 441. room(sK5) <- (28) [avatar component clause 439] 442. ~23 | 28 [avatar split clause 286,439,413] 444. 26 | 28 [avatar split clause 284,439,427] 456. mary = sK6 <- (26) [resolution 261,429] 478. mary = sK5 <- (28) [resolution 441,261] 479. ~quieter(paul,mary) <- (~24, 28) [backward demodulation 419,478] 482. ~room(mary) <- (~24, 28) [resolution 479,293] 483. $false <- (~24, 28) [subsumption resolution 482,260] 484. 24 | ~28 [avatar contradiction clause 483] 486. ~quieter(john,mary) <- (~23, 26) [forward demodulation 415,456] 488. quieter(john,mary) | ~room(mary) [resolution 299,305] 491. ~room(mary) <- (~23, 26) [subsumption resolution 488,486] 492. $false <- (~23, 26) [subsumption resolution 491,260] 493. 23 | ~26 [avatar contradiction clause 492] 494. $false [avatar sat refutation 420,430,442,444,484,493] % SZS output end Proof for 1247994190041786633644043 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Vanessa, Raphael are the only persons in the room. If everyone in the room plays the violin or does not watche fantasy movies then everyone in the room who is not a client of Costco is not a dedicated advocate for digital privacy and encryption or is a Linux enthusiast or both. Everyone in the room is not a dedicated advocate for digital privacy and encryption or is a Linux enthusiast or both if and only if they is a dedicated advocate for digital privacy and encryption. Not everyone in the room does not enjoy salsa dancing if they is a dedicated advocate for digital privacy and encryption. Everyone in the room creates large-scale murals for public art installations if they does not enjoy salsa dancing. Everyone in the room who is not a client of Costco is not a dedicated advocate for digital privacy and encryption or is a Linux enthusiast or both. Someone in the room composes and performs experimental electronic music. Raphael is a client of Costco. If someone neither is a scotch connoisseur nor builds model airplanes then he/she is a dedicated advocate for digital privacy and encryption, plays the violin or practices digital art. Everyone in the room creates large-scale murals for public art installations and plays the violin if they composes and performs experimental electronic music. Everyone in the room volunteers for local environmental conservation projects if and only if they is a client of Costco. Someone in the room is a dedicated advocate for digital privacy and encryption. Everyone in the room who enjoys salsa dancing is a client of Costco and plays the violin. It is not the case that someone in the room plays the violin and practices digital art. Raphael composes and performs experimental electronic music. Raphael watches fantasy movies.

It is true that Vanessa volunteers for local environmental conservation projects.

neutral

room(vanessa)&room(raphael)&(![X]:(room(X)=>(X='vanessa'|X='raphael')))& ((![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(plays_the_violin(X))))))=>(![X]:(room(X)=>(((is_not_a_client_of_Costco(X))=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_a_Linux_enthusiast(X)))))))))& (![X]:(room(X)=>(((((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_a_Linux_enthusiast(X))))<=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (~![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(does_not_enjoy_salsa_dancing(X))))))& (![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((is_not_a_client_of_Costco(X))=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_a_Linux_enthusiast(X))))))))& (?[X]:(room(X)&(composes_and_performs_experimental_electronic_music(X))))& (is_a_client_of_Costco(raphael))& ((![X]:((~((is_a_scotch_connoisseur(X))|(builds_model_airplanes(X))))=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(plays_the_violin(X))|(practices_digital_art(X)))))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(((creates_large-scale_murals_for_public_art_installations(X))&(plays_the_violin(X))))))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))<=>(is_a_client_of_Costco(X))))))& (?[X]:(room(X)&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(((is_a_client_of_Costco(X))&(plays_the_violin(X))))))))& (~(?[X]:(room(X)&(((plays_the_violin(X))&(practices_digital_art(X)))))))& (composes_and_performs_experimental_electronic_music(raphael))& (watches_fantasy_movies(raphael))& (![X]:(~room(X)=>(((does_not_practice_digital_art(X))|(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (?[X]:(anywhere(X)&(is_a_drone_photographer(X))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_practice_digital_art(X))))))& (?[X]:(room(X)&(~((enjoys_windsurfing(X))|(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))=>(((does_not_practice_digital_art(X))|(is_a_drone_photographer(X))))))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(is_a_scotch_connoisseur(X))))))

room(vanessa)&room(raphael)&(![X]:(room(X)=>(X='vanessa'|X='raphael')))& volunteers_for_local_environmental_conservation_projects(vanessa)

Everyone in the room creates large-scale murals for public art installations if they practices archery and vice versa. Everyone in the room practices archery if they does not train for and competes in international triathlons and vice versa. Everyone in the room trains for and competes in international triathlons if they is a client of Costco. More than one person in the room is a client of Costco.

Everyone in the room creates large-scale murals for public art installations.

contradiction

(there_is_a_room)& (?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))<=>(practices_archery(X))))))& (![X]:(room(X)=>(((practices_archery(X))<=>(does_not_train_for_and_competes_in_international_triathlons(X))))))& (![X]:(~room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))=>(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))<=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(((can_play_the_harmonica(X))|(uses_contact_lenses(X))|(plays_eSports_competitively(X))))))))& ((barbara_dream=>(?[X]:(room(X)&(((composes_and_performs_experimental_electronic_music(X))&(does_not_compose_and_performs_experimental_electronic_music(X))))))))& (![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((is_not_allergic_to_anything(X))=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(uses_contact_lenses(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_a_client_of_Costco(X)&is_a_client_of_Costco(Y))&(X!=Y))))& ((?[X,Y]:(room(X)&room(Y)&(practices_archery(X)&practices_archery(Y))&(X!=Y))))& ((?[X,Y]:(room(X)&room(Y)&(is_allergic_to_anything(X)&is_allergic_to_anything(Y))&(X!=Y))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(enjoys_snowboarding(X))))))

(there_is_a_room)& ![X]:(room(X)=>(creates_large-scale_murals_for_public_art_installations(X)))

% SZS status Unsatisfiable for 1447927208858174381682993 % SZS output start Proof for 1447927208858174381682993 46. ! [X0] : (room(X0) => (predc(X0) <=> predo(X0))) [input p2] 47. ! [X0] : (room(X0) => (predo(X0) <=> ~predj(X0))) [input p3] 49. ! [X0] : (room(X0) => (predn(X0) => predj(X0))) [input p5] 57. ? [X0,X1] : (X0 != X1 & predn(X1) & predn(X0) & room(X1) & room(X0)) [input p13] 61. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 66. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 61] 139. ! [X0] : ((predc(X0) <=> predo(X0)) | ~room(X0)) [ennf transformation 46] 140. ! [X0] : ((predo(X0) <=> ~predj(X0)) | ~room(X0)) [ennf transformation 47] 143. ! [X0] : ((predj(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 49] 144. ! [X0] : (predj(X0) | ~predn(X0) | ~room(X0)) [flattening 143] 154. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 66] 158. ! [X0] : (((predc(X0) | ~predo(X0)) & (predo(X0) | ~predc(X0))) | ~room(X0)) [nnf transformation 139] 159. ! [X0] : (((predo(X0) | predj(X0)) & (~predj(X0) | ~predo(X0))) | ~room(X0)) [nnf transformation 140] 161. ? [X0,X1] : (X0 != X1 & predn(X1) & predn(X0) & room(X1) & room(X0)) => (sK1 != sK2 & predn(sK2) & predn(sK1) & room(sK2) & room(sK1)) [choice axiom] 162. sK1 != sK2 & predn(sK2) & predn(sK1) & room(sK2) & room(sK1) [skolemisation 57,161] 249. ~predc(X0) | predo(X0) | ~room(X0) [cnf transformation 158] 251. ~predj(X0) | ~predo(X0) | ~room(X0) [cnf transformation 159] 254. ~predn(X0) | predj(X0) | ~room(X0) [cnf transformation 144] 260. room(sK1) [cnf transformation 162] 262. predn(sK1) [cnf transformation 162] 276. ~room(X0) | predc(X0) [cnf transformation 154] 282. predc(sK1) [resolution 276,260] 317. predo(sK1) | ~room(sK1) [resolution 249,282] 322. predo(sK1) [subsumption resolution 317,260] 337. predj(sK1) | ~room(sK1) [resolution 254,262] 341. predj(sK1) [subsumption resolution 337,260] 375. ~predo(sK1) | ~room(sK1) [resolution 341,251] 376. ~room(sK1) [subsumption resolution 375,322] 377. $false [subsumption resolution 376,260] % SZS output end Proof for 1447927208858174381682993 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If "everyone in the room collect rare sneakers or does not watche fantasy movies" then "someone in the room practices calligraphy". If "everyone in the room hosts regular workshops on creative writing or does not know morse code" then "everyone in the room hosts regular workshops on creative writing only if they enjoys skydiving". It is true that "someone in the room does not host regular workshops on creative writing". Everyone in the room who does not collect rare and antique scientific instruments enjoys wildlife photography. Not everyone in the room practices calligraphy if they enjoys wildlife photography. Not everyone in the room practices calligraphy if they is a drone photographer and vice versa. Everyone in the room is a drone photographer if and only if they watches fantasy movies. Everyone in the room hosts regular workshops on creative writing or does not know morse code. Everyone in the room has a curated collection of mid-century modern furniture, uses an ios phone or uses a Windows laptop if they is a drone photographer. Everyone outside the room collects foreign coins if they practices pilates and vice versa. Everyone in the room is not an active member of a local robotics club or plays as a goalkeeper for a local amateur soccer team. If someone practices calligraphy then he/she does not collect rare sneakers. Everyone in the room who writes in-depth travel guides for off-the-beaten-path destinations and plays as a goalkeeper for a local amateur soccer team knows morse code. It is not the case that "at least one person in the room collect rare sneakers". Everyone in the room knows morse code if they collects vintage vinyl records and does enjoy trail running and vice versa. If someone practices tai chi then he/she enjoys wildlife photography and vice versa.

Everyone in the room does not collect rare and antique scientific instruments or collects foreign coins.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(collect_rare_sneakers(X))))))=>(?[X]:(room(X)&(practices_calligraphy(X)))))& ((![X]:(room(X)=>(((does_not_know_morse_code(X))|(hosts_regular_workshops_on_creative_writing(X))))))=>(![X]:(room(X)=>(((enjoys_skydiving(X))<=(hosts_regular_workshops_on_creative_writing(X)))))))& (?[X]:(room(X)&(does_not_host_regular_workshops_on_creative_writing(X))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))=>(enjoys_wildlife_photography(X))))))& (~![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(practices_calligraphy(X))))))& (~![X]:(room(X)=>(((practices_calligraphy(X))<=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))<=>(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((does_not_know_morse_code(X))|(hosts_regular_workshops_on_creative_writing(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(uses_an_ios_phone(X))|(uses_a_Windows_laptop(X))))))))& (![X]:(~room(X)=>(((collects_foreign_coins(X))<=>(practices_pilates(X))))))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))))& ((![X]:((practices_calligraphy(X))=>(does_not_collect_rare_sneakers(X)))))& (![X]:(room(X)=>(((((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))=>(knows_morse_code(X))))))& (~(((?[X]:(room(X)&collect_rare_sneakers(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))<=>(((collects_vintage_vinyl_records(X))&(does_enjoy_trail_running(X))))))))& ((![X]:((practices_tai_chi(X))<=>(enjoys_wildlife_photography(X)))))& (![X]:(room(X)=>(((does_not_host_regular_workshops_on_creative_writing(X))=>(collects_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(((collects_foreign_coins(X))|(enjoys_wildlife_photography(X))|(does_not_practice_calligraphy(X))))))))& ((![X]:((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(practices_tai_chi(X)))))& (![X]:(~room(X)=>(((enjoys_wildlife_photography(X))=>(does_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((reads_mystery_novels(X))=>(~((does_not_enjoy_trail_running(X))|(is_a_drone_photographer(X))))))))& (![X]:(anywhere(X)=>(((((collects_foreign_coins(X))<~>(collects_modern_art(X))))=>(can_play_the_flute(X))))))& (![X]:(room(X)=>(((can_play_the_flute(X))=>(collects_vintage_vinyl_records(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((collects_foreign_coins(X))|(does_not_collect_rare_and_antique_scientific_instruments(X)))))

Dorothy, Stewart are the only persons in the room. Either “everyone in the room does not train for and competes in international triathlons or is a drone photographer” or “Stewart bakes bread at home” but not both. If “everyone in the room does enjoy trail running or does not own a telescope” then “everyone in the room does not train for and competes in international triathlons or does enjoy trail running”. If “everyone in the room can play the flute or does not own a telescope” then “Stewart who does not own a telescope has a piercing”. “Everyone in the room practices tai chi” unless “everyone in the room collects historical artifacts related to ancient civilizations or is not a client of LVMH”.

Stewart either does not enjoy trail running or does not have a specialized collection of handmade artisan pottery but not both.

neutral

room(dorothy)&room(stewart)&(![X]:(room(X)=>(X='dorothy'|X='stewart')))& ((![X]:(room(X)=>(((is_a_drone_photographer(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))<~>(bakes_bread_at_home(stewart)))& ((![X]:(room(X)=>(((does_not_own_a_telescope(X))|(does_enjoy_trail_running(X))))))=>(![X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_train_for_and_competes_in_international_triathlons(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_telescope(X))|(can_play_the_flute(X))))))=>((does_not_own_a_telescope(stewart))&(has_a_piercing(stewart))))& (~(![X]:(room(X)=>(((is_not_a_client_of_LVMH(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))=>(![X]:(room(X)=>(practices_tai_chi(X)))))& ((![X]:(room(X)=>(((is_a_client_of_LVMH(X))|(is_not_a_drone_photographer(X))))))=>(does_not_enjoy_trail_running(dorothy)))& ((~![X]:(room(X)=>(((is_not_a_client_of_LVMH(X))|(enjoys_origami(X))))))=>(![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(is_not_a_client_of_LVMH(X)))))))& ((~![X]:(room(X)=>(((owns_a_telescope(X))|(does_not_own_a_telescope(X))))))<=>(is_a_client_of_LVMH(dorothy)))& ((![X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))=>(![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))=>(enjoys_origami(X)))))))& ((~![X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))=>(![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(does_not_enjoy_kayaking(X)))))))& ((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(dorothy))=>(?[X]:(room(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))& (does_not_own_a_telescope(stewart))& (![X]:(~room(X)=>(((does_not_own_a_telescope(X))|(enjoys_kayaking(X))))))& (![X]:(anywhere(X)=>(((enjoys_kayaking(X))<=>(is_a_drone_photographer(X))))))& (?[X]:(room(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))& (~![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(can_play_the_flute(X))))))& (![X]:(room(X)=>(((can_play_the_flute(X))=>(does_not_own_a_telescope(X))))))& (is_not_a_client_of_LVMH(stewart))& (bakes_bread_at_home(stewart))& (((has_a_piercing(stewart))&(volunteers_for_local_environmental_conservation_projects(stewart))&(enjoys_origami(stewart))))& (practices_tai_chi(dorothy))& (![X]:(~room(X)=>(((((enjoys_rooftop_gardening(X))&(can_play_the_flute(X))&(does_not_train_for_and_competes_in_international_triathlons(X))))<=>(does_enjoy_trail_running(X))))))

room(dorothy)&room(stewart)&(![X]:(room(X)=>(X='dorothy'|X='stewart')))& ((does_not_enjoy_trail_running(stewart))<~>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(stewart)))

Ron is the only person in the room. Either “it is not the case that “someone in the room is dedicated to sustainable living and zero-waste practices”” or “someone in the room uses contact lenses” but not both. If “Ron is not a night owl” then “Ron practices archery”. If “Ron is dedicated to sustainable living and zero-waste practices, enjoys coding in Python or owns a smartwatch” then “Ron develops open-source software projects in their free time”. If “Ron enjoys windsurfing” then “Ron enjoys coding in Python”.

Ron enjoys coding in Python.

neutral

room(ron)&(![X]:(room(X)=>(X='ron')))& ((~(?[X]:(room(X)&(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))<~>(?[X]:(room(X)&(uses_contact_lenses(X)))))& ((is_not_a_night_owl(ron))=>(practices_archery(ron)))& ((((is_dedicated_to_sustainable_living_and_zero-waste_practices(ron))|(enjoys_coding_in_Python(ron))|(owns_a_smartwatch(ron))))=>(develops_open-source_software_projects_in_their_free_time(ron)))& ((enjoys_windsurfing(ron))=>(enjoys_coding_in_Python(ron)))& ((((?[X]:(room(X)&enjoys_windsurfing(X)))))<~>(practices_archery(ron)))& (uses_contact_lenses(ron))& (is_a_Linux_enthusiast(ron))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(ron))& (((?[X]:(room(X)&does_not_stream_on_Twitch(X)))))& ((![X]:((uses_contact_lenses(X))<=>(enjoys_virtual_reality_gaming(X)))))& (enjoys_watercolor_painting(ron))& (collects_antique_jewelry(ron))

room(ron)&(![X]:(room(X)=>(X='ron')))& enjoys_coding_in_Python(ron)

Barbara, Jane, Elizabeth, Jeanette, Jennifer are the only persons in the room. “Everyone anywhere does not maintain a large, organic vegetable garden year-round” only if “everyone anywhere does not enjoy snowboarding”. Everyone in the room is not a chess master who participates in national tournaments and does not collect first edition books. Everyone in the room either does not enjoy virtual reality gaming or does not practice yoga but not both. Everyone in the room does not enjoy writing detailed reviews of new and classic board games. Only one person in the room does not enjoy wildlife photography. Not everyone in the room is not a Linux enthusiast. Everyone in the room does not maintain a large, organic vegetable garden year-round. Jane who does not collect antique clocks and does not collect action figures does not maintain a large, organic vegetable garden year-round. Someone in the room does not practice yoga. Everyone in the room does not collect first edition books or is not a drone photographer or both. Everyone in the room does not own a 3D printer. At least one person in the room either does not practice calligraphy or does not watche fantasy movies but not both. Not everyone in the room either does not own a 3D printer or does not practice yoga but not both. Everyone in the room does not collect rare minerals. Everyone anywhere does not maintain a large, organic vegetable garden year-round. Everyone outside the room does not maintain a large, organic vegetable garden year-round. Everyone in the room does not enjoy landscape photography.

Barbara maintains a large, organic vegetable garden year-round.

contradiction

room(barbara)&room(jane)&room(elizabeth)&room(jeanette)&room(jennifer)&(![X]:(room(X)=>(X='barbara'|X='jane'|X='elizabeth'|X='jeanette'|X='jennifer')))& ((![X]:(anywhere(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))=>(![X]:(anywhere(X)=>(does_not_enjoy_snowboarding(X)))))& (![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))&(does_not_collect_first_edition_books(X))))))& (![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))<~>(does_not_practice_yoga(X))))))& (![X]:(room(X)=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (((?[X]:(room(X)&does_not_enjoy_wildlife_photography(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_enjoy_wildlife_photography(X))&(does_not_enjoy_wildlife_photography(Y)))=>(X=Y)))))& (~![X]:(room(X)=>(is_not_a_Linux_enthusiast(X))))& (![X]:(room(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))& ((((does_not_collect_antique_clocks(jane))&(does_not_collect_action_figures(jane))))&(does_not_maintain_a_large,_organic_vegetable_garden_year-round(jane)))& (?[X]:(room(X)&(does_not_practice_yoga(X))))& (![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(is_not_a_drone_photographer(X))))))& (![X]:(room(X)=>(does_not_own_a_3D_printer(X))))& (((?[X]:(room(X)&((does_not_practice_calligraphy(X))<~>(does_not_watche_fantasy_movies(X)))))))& (~![X]:(room(X)=>(((does_not_own_a_3D_printer(X))<~>(does_not_practice_yoga(X))))))& (![X]:(room(X)=>(does_not_collect_rare_minerals(X))))& (![X]:(anywhere(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))& (![X]:(~room(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))& (![X]:(room(X)=>(does_not_enjoy_landscape_photography(X))))

room(barbara)&room(jane)&room(elizabeth)&room(jeanette)&room(jennifer)&(![X]:(room(X)=>(X='barbara'|X='jane'|X='elizabeth'|X='jeanette'|X='jennifer')))& maintains_a_large,_organic_vegetable_garden_year-round(barbara)

% SZS status Unsatisfiable for 5268035683107780624304959 % SZS output start Proof for 5268035683107780624304959 5. ! [X0] : anywhere(X0) [input b4] 59. ! [X0] : (anywhere(X0) => ~predl(X0)) [input p15] 62. predl(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 155. ! [X0] : (~predl(X0) | ~anywhere(X0)) [ennf transformation 59] 157. predl(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 158. predl(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 157] 175. anywhere(X0) [cnf transformation 5] 279. ~predl(X0) | ~anywhere(X0) [cnf transformation 155] 287. predl(mary) [cnf transformation 158] 308. ~predl(X0) [subsumption resolution 279,175] 309. $false [subsumption resolution 287,308] % SZS output end Proof for 5268035683107780624304959 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Violet, James, Lucille, Martha are the only persons in the room. James neither does not practice urban gardening nor does not stream on Twitch. Violet is not allergic to anything. Lucille neither does not make homemade pastries nor does not maintain a personal blog focused on cybersecurity tips. Lucille is not a cybersecurity expert. Violet does not make homemade pastries. If someone neither is not a skilled home brewer experimenting with craft beer recipes nor does not collect modern art then he/she does not collect limited-edition art prints from contemporary artists. More than one person in the room does not use a Windows laptop. James is not a skilled home brewer experimenting with craft beer recipes. Violet does not host a YouTube channel dedicated to art tutorials. Violet streams on Twitch.

Lucille maintains a personal blog focused on cybersecurity tips.

entailment

room(violet)&room(james)&room(lucille)&room(martha)&(![X]:(room(X)=>(X='violet'|X='james'|X='lucille'|X='martha')))& (~((does_not_practice_urban_gardening(james))|(does_not_stream_on_Twitch(james))))& (is_not_allergic_to_anything(violet))& (~((does_not_make_homemade_pastries(lucille))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(lucille))))& (is_not_a_cybersecurity_expert(lucille))& (does_not_make_homemade_pastries(violet))& ((![X]:((~((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_collect_modern_art(X))))=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X)))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_use_a_Windows_laptop(X)&does_not_use_a_Windows_laptop(Y))&(X!=Y))))& (is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(james))& (does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(violet))& (streams_on_Twitch(violet))& (((?[X]:(room(X)&does_not_own_a_television(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_own_a_television(X))&(does_not_own_a_television(Y)))=>(X=Y)))))& (((?[X]:(room(X)&is_not_right-handed(X)))))& (does_not_make_homemade_pastries(james))& (?[X]:(room(X)&(is_not_a_cybersecurity_expert(X))))& (does_not_own_a_microscope(violet))& (((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(violet))&(is_not_a_cybersecurity_expert(violet))))& (((?[X]:(~room(X)&is_not_a_dedicated_volunteer_for_local_community_service_projects(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))&(is_not_a_dedicated_volunteer_for_local_community_service_projects(Y)))=>(X=Y)))))& (~((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(james))|(does_not_use_a_Windows_laptop(james))))& (((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(james))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(james))|(does_not_practice_urban_gardening(james))))& (is_not_right-handed(lucille))& (?[X]:(room(X)&(~((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_enjoy_snowboarding(X))))))& (is_not_a_cybersecurity_expert(james))& (?[X]:(~room(X)&(does_not_stream_on_Twitch(X))))& (((is_not_a_dedicated_volunteer_for_local_community_service_projects(lucille))&(does_not_collect_limited-edition_art_prints_from_contemporary_artists(lucille))))& (does_not_own_a_television(james))

room(violet)&room(james)&room(lucille)&room(martha)&(![X]:(room(X)=>(X='violet'|X='james'|X='lucille'|X='martha')))& maintains_a_personal_blog_focused_on_cybersecurity_tips(lucille)

% SZS status Unsatisfiable for 4851969680652222110941431 % SZS output start Proof for 4851969680652222110941431 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. ~(~predl(fred) | ~predi(fred)) [input p3] 70. ~(predl(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 159. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 160. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 159] 162. predl(fred) & predi(fred) [ennf transformation 47] 169. ~predl(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 170. ~predl(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 169] 186. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 187. ~predl(fred) | (alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 170,186] 268. room(mary) [cnf transformation 160] 269. room(paul) [cnf transformation 160] 270. room(fred) [cnf transformation 160] 271. room(alice) [cnf transformation 160] 272. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 160] 275. predl(fred) [cnf transformation 162] 302. ~predl(fred) | room(sK8) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 303. ~predl(fred) | mary != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 304. ~predl(fred) | paul != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 305. ~predl(fred) | fred != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 306. ~predl(fred) | alice != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 307. alice != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,275] 308. alice != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,271] 309. alice != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 308,270] 310. alice != sK8 | ~room(mary) [subsumption resolution 309,269] 311. alice != sK8 [subsumption resolution 310,268] 312. fred != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,275] 313. fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,271] 314. fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 313,270] 315. fred != sK8 | ~room(mary) [subsumption resolution 314,269] 316. fred != sK8 [subsumption resolution 315,268] 317. paul != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,275] 318. paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,271] 319. paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 318,270] 320. paul != sK8 | ~room(mary) [subsumption resolution 319,269] 321. paul != sK8 [subsumption resolution 320,268] 322. mary != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,275] 323. mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,271] 324. mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 323,270] 325. mary != sK8 | ~room(mary) [subsumption resolution 324,269] 326. mary != sK8 [subsumption resolution 325,268] 327. room(sK8) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,275] 328. room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,271] 329. room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 328,270] 330. room(sK8) | ~room(mary) [subsumption resolution 329,269] 331. room(sK8) [subsumption resolution 330,268] 515. fred = sK8 | paul = sK8 | mary = sK8 | alice = sK8 [resolution 272,331] 581. paul = sK8 | mary = sK8 | alice = sK8 [subsumption resolution 515,316] 582. mary = sK8 | alice = sK8 [subsumption resolution 581,321] 583. alice = sK8 [subsumption resolution 582,326] 584. $false [subsumption resolution 583,311] % SZS output end Proof for 4851969680652222110941431 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Chuck, Rebecca, Cassandra are the only persons in the room. "Everyone in the room does not stream on Twitch or enjoys origami" if "at least one person in the room either has completed a triathlon or collects antique jewelry but not both" and vice versa. Everyone in the room hosts a popular podcast about emerging technologies or does not stream on Twitch. Everyone in the room is not a chess master who participates in national tournaments or hosts a popular podcast about emerging technologies. Chuck neither owns a 3D printer nor enjoys macrame. If someone streams on Twitch, enjoys logic puzzles or bakes bread at home then he/she either enjoys macrame or does enjoy mountain biking but not both. Everyone in the room does not practice pilates or is passionate about collecting and restoring classic cars. Everyone in the room does not practice pilates only if they streams on Twitch, bakes bread at home and plays the violin. Chuck either does enjoy mountain biking or enjoys cross-country skiing but not both. Everyone outside the room neither can play the flute nor practices zumba only if they hosts a popular podcast about emerging technologies. Rebecca either bakes bread at home or is an avid collector of autographed memorabilia from famous musicians but not both. Rebecca who either can play the flute or hosts a popular podcast about emerging technologies but not both enjoys macrame. Everyone in the room cannot play the flute or does not play the violin. Chuck dreamt that "everyone in the room does not host a popular podcast about emerging technologies or cannot play the flute". Everyone in the room travels domestically frequently or does not own a telescope. Rebecca enjoys cross-country skiing. Rebecca is a chess master who participates in national tournaments. Everyone in the room owns a telescope, plays the violin and enjoys logic puzzles only if they does not collect antique jewelry, plays the violin and enjoys macrame.

Rebecca can play the flute.

contradiction

room(chuck)&room(rebecca)&room(cassandra)&(![X]:(room(X)=>(X='chuck'|X='rebecca'|X='cassandra')))& ((((?[X]:(room(X)&((has_completed_a_triathlon(X))<~>(collects_antique_jewelry(X)))))))<=>(![X]:(room(X)=>(((enjoys_origami(X))|(does_not_stream_on_Twitch(X)))))))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))|(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))& (~((owns_a_3D_printer(chuck))|(enjoys_macrame(chuck))))& ((![X]:((((streams_on_Twitch(X))|(enjoys_logic_puzzles(X))|(bakes_bread_at_home(X))))=>(((enjoys_macrame(X))<~>(does_enjoy_mountain_biking(X)))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_practice_pilates(X))))))& (![X]:(room(X)=>(((((streams_on_Twitch(X))&(bakes_bread_at_home(X))&(plays_the_violin(X))))<=(does_not_practice_pilates(X))))))& (((does_enjoy_mountain_biking(chuck))<~>(enjoys_cross-country_skiing(chuck))))& (![X]:(~room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))<=(~((can_play_the_flute(X))|(practices_zumba(X))))))))& (((bakes_bread_at_home(rebecca))<~>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(rebecca))))& ((((can_play_the_flute(rebecca))<~>(hosts_a_popular_podcast_about_emerging_technologies(rebecca))))&(enjoys_macrame(rebecca)))& (![X]:(room(X)=>(((does_not_play_the_violin(X))|(cannot_play_the_flute(X))))))& ((chuck_dream=>(![X]:(room(X)=>(((cannot_play_the_flute(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))))& (![X]:(room(X)=>(((does_not_own_a_telescope(X))|(travels_domestically_frequently(X))))))& (enjoys_cross-country_skiing(rebecca))& (is_a_chess_master_who_participates_in_national_tournaments(rebecca))& (![X]:(room(X)=>(((((does_not_collect_antique_jewelry(X))&(plays_the_violin(X))&(enjoys_macrame(X))))<=(((owns_a_telescope(X))&(plays_the_violin(X))&(enjoys_logic_puzzles(X))))))))

room(chuck)&room(rebecca)&room(cassandra)&(![X]:(room(X)=>(X='chuck'|X='rebecca'|X='cassandra')))& can_play_the_flute(rebecca)

% SZS status Unsatisfiable for 8122277155077896010962224 % SZS output start Proof for 8122277155077896010962224 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (~predj(X0) | predu(X0))) [input p3] 55. predo(paul) & (predm(paul) <~> predu(paul)) [input p11] 60. predj(paul) [input p16] 62. predm(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 145. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 146. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 145] 151. ! [X0] : ((~predj(X0) | predu(X0)) | ~room(X0)) [ennf transformation 47] 152. ! [X0] : (~predj(X0) | predu(X0) | ~room(X0)) [flattening 151] 155. predm(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 156. predm(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 155] 172. predo(paul) & ((~predu(paul) | ~predm(paul)) & (predu(paul) | predm(paul))) [nnf transformation 55] 173. predo(paul) & (~predu(paul) | ~predm(paul)) & (predu(paul) | predm(paul)) [flattening 172] 255. room(paul) [cnf transformation 146] 268. ~predj(X0) | predu(X0) | ~room(X0) [cnf transformation 152] 279. ~predu(paul) | ~predm(paul) [cnf transformation 173] 282. predj(paul) [cnf transformation 60] 287. predm(paul) [cnf transformation 156] 355. 15 <=> predm(paul) [avatar definition] 359. 16 <=> predu(paul) [avatar definition] 361. ~predu(paul) <- (~16) [avatar component clause 359] 362. ~15 | ~16 [avatar split clause 279,359,355] 364. 15 [avatar split clause 287,355] 365. predu(paul) | ~room(paul) [resolution 268,282] 366. ~room(paul) <- (~16) [subsumption resolution 365,361] 367. $false <- (~16) [subsumption resolution 366,255] 368. 16 [avatar contradiction clause 367] 369. $false [avatar sat refutation 362,364,368] % SZS output end Proof for 8122277155077896010962224 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Patsy, David, Edna, Margaret are the only persons in the room. If 'not everyone in the room is not a wine connoisseur or volunteers for local environmental conservation projects' then 'not everyone outside the room who is not a wine connoisseur is an enthusiastic bird watcher who travels for rare sightings'. 'Everyone in the room who hosts themed dinner parties featuring gourmet home-cooked meals does enjoy mountain biking' unless 'everyone in the room does not practice tai chi or plays video games'. If 'not everyone anywhere does not regularly goes on multi-day backpacking trips in national parks or enjoys snowboarding' then 'not everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or does not regularly goes on multi-day backpacking trips in national parks'. 'Everyone anywhere who own a television creates bespoke furniture pieces from reclaimed wood' unless 'at least one person in the room enjoys snowboarding'. Someone in the room owns a 3D printer, works on fridays and hosts themed dinner parties featuring gourmet home-cooked meals. Margaret who creates bespoke furniture pieces from reclaimed wood volunteers for local environmental conservation projects, enjoys fishing and own a television. If someone is allergic to anything and regularly contributes to tech forums and online communities then he/she enjoys stargazing. If someone own a television then he/she is allergic to anything. Everyone in the room does not enjoy cross-country skiing or regularly goes on multi-day backpacking trips in national parks. Everyone outside the room who is an enthusiastic bird watcher who travels for rare sightings plays video games. It is not the case that 'more than one person in the room is a coffee connoisseur, is an active member of a local robotics club or makes intricate hand-cut paper art for exhibitions'. Everyone in the room who reads mystery novels, works on fridays and regularly goes on multi-day backpacking trips in national parks creates large-scale murals for public art installations or mentors a youth basketball team on weekends or both. Everyone outside the room enjoys cross-country skiing if they enjoys fishing, own a television and reads mystery novels and vice versa. David who enjoys snowboarding volunteers for local environmental conservation projects. Everyone in the room enjoys fishing only if they creates large-scale murals for public art installations.

Everyone in the room enjoys fishing or does not enjoy fishing.

entailment

room(patsy)&room(david)&room(edna)&room(margaret)&(![X]:(room(X)=>(X='patsy'|X='david'|X='edna'|X='margaret')))& ((~![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))|(is_not_a_wine_connoisseur(X))))))=>(~![X]:(~room(X)=>(((is_not_a_wine_connoisseur(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))& (~(![X]:(room(X)=>(((plays_video_games(X))|(does_not_practice_tai_chi(X))))))=>(![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(does_enjoy_mountain_biking(X)))))))& ((~![X]:(anywhere(X)=>(((enjoys_snowboarding(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))=>(~![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))& (~(((?[X]:(room(X)&enjoys_snowboarding(X)))))=>(![X]:(anywhere(X)=>(((own_a_television(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))& (?[X]:(room(X)&(((owns_a_3D_printer(X))&(works_on_fridays(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& ((creates_bespoke_furniture_pieces_from_reclaimed_wood(margaret))&(((volunteers_for_local_environmental_conservation_projects(margaret))&(enjoys_fishing(margaret))&(own_a_television(margaret)))))& ((![X]:((((is_allergic_to_anything(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(enjoys_stargazing(X)))))& ((![X]:((own_a_television(X))=>(is_allergic_to_anything(X)))))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(does_not_enjoy_cross-country_skiing(X))))))& (![X]:(~room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(plays_video_games(X))))))& (~((?[X,Y]:(room(X)&room(Y)&(((is_a_coffee_connoisseur(X))|(is_an_active_member_of_a_local_robotics_club(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))&((is_a_coffee_connoisseur(Y))|(is_an_active_member_of_a_local_robotics_club(Y))|(makes_intricate_hand-cut_paper_art_for_exhibitions(Y))))&(X!=Y)))))& (![X]:(room(X)=>(((((reads_mystery_novels(X))&(works_on_fridays(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(((creates_large-scale_murals_for_public_art_installations(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))))& (![X]:(~room(X)=>(((enjoys_cross-country_skiing(X))<=>(((enjoys_fishing(X))&(own_a_television(X))&(reads_mystery_novels(X))))))))& ((enjoys_snowboarding(david))&(volunteers_for_local_environmental_conservation_projects(david)))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))<=(enjoys_fishing(X))))))& (((?[X]:(anywhere(X)&mentors_a_youth_basketball_team_on_weekends(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(mentors_a_youth_basketball_team_on_weekends(X))&(mentors_a_youth_basketball_team_on_weekends(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((can_play_the_guitar(X))<=(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(owns_a_3D_printer(X))))))))& (![X]:(~room(X)=>(((can_play_the_guitar(X))=>(((can_play_the_guitar(X))|(enjoys_snowboarding(X))))))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(reads_mystery_novels(X))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))<=>(plays_video_games(X))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(can_play_the_flute(X))))))

room(patsy)&room(david)&room(edna)&room(margaret)&(![X]:(room(X)=>(X='patsy'|X='david'|X='edna'|X='margaret')))& ![X]:(room(X)=>(((does_not_enjoy_fishing(X))|(enjoys_fishing(X)))))

% SZS status Unsatisfiable for 2966459380427229678307456 % SZS output start Proof for 2966459380427229678307456 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 67. ~(! [X0] : (room(X0) => (predw(X0) | ~predw(X0))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 73. ~(! [X0] : (room(X0) => (predw(X0) | ~predw(X0))) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 67] 168. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 169. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 168] 179. ? [X0] : ((~predw(X0) & predw(X0)) & room(X0)) | ? [X1] : ((alice != X1 & fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 73] 180. ? [X0] : (~predw(X0) & predw(X0) & room(X0)) | ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 179] 181. ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 182. ? [X0] : (~predw(X0) & predw(X0) & room(X0)) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 180,181] 194. ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 181] 195. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 194] 196. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 197. (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~sP0 [skolemisation 195,196] 198. ? [X0] : (~predw(X0) & predw(X0) & room(X0)) => (~predw(sK5) & predw(sK5) & room(sK5)) [choice axiom] 199. (~predw(sK5) & predw(sK5) & room(sK5)) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 182,198] 281. room(mary) [cnf transformation 169] 282. room(paul) [cnf transformation 169] 283. room(fred) [cnf transformation 169] 284. room(alice) [cnf transformation 169] 285. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 169] 302. room(sK4) | ~sP0 [cnf transformation 197] 303. mary != sK4 | ~sP0 [cnf transformation 197] 304. paul != sK4 | ~sP0 [cnf transformation 197] 305. fred != sK4 | ~sP0 [cnf transformation 197] 306. alice != sK4 | ~sP0 [cnf transformation 197] 308. predw(sK5) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 199] 309. ~predw(sK5) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 199] 322. 3 <=> sP0 [avatar definition] 326. 4 <=> alice = sK4 [avatar definition] 328. alice != sK4 <- (~4) [avatar component clause 326] 329. ~3 | ~4 [avatar split clause 306,326,322] 331. 5 <=> fred = sK4 [avatar definition] 333. fred != sK4 <- (~5) [avatar component clause 331] 334. ~3 | ~5 [avatar split clause 305,331,322] 336. 6 <=> paul = sK4 [avatar definition] 338. paul != sK4 <- (~6) [avatar component clause 336] 339. ~3 | ~6 [avatar split clause 304,336,322] 341. 7 <=> mary = sK4 [avatar definition] 343. mary != sK4 <- (~7) [avatar component clause 341] 344. ~3 | ~7 [avatar split clause 303,341,322] 346. 8 <=> room(sK4) [avatar definition] 348. room(sK4) <- (8) [avatar component clause 346] 349. ~3 | 8 [avatar split clause 302,346,322] 350. ~predw(sK5) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,284] 351. ~predw(sK5) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 350,283] 352. ~predw(sK5) | sP0 | ~room(mary) [subsumption resolution 351,282] 353. ~predw(sK5) | sP0 [subsumption resolution 352,281] 355. 9 <=> predw(sK5) [avatar definition] 358. 3 | ~9 [avatar split clause 353,355,322] 359. predw(sK5) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,284] 360. predw(sK5) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 359,283] 361. predw(sK5) | sP0 | ~room(mary) [subsumption resolution 360,282] 362. predw(sK5) | sP0 [subsumption resolution 361,281] 363. 3 | 9 [avatar split clause 362,355,322] 424. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 <- (8) [resolution 285,348] 442. paul = sK4 | mary = sK4 | alice = sK4 <- (~5, 8) [subsumption resolution 424,333] 443. mary = sK4 | alice = sK4 <- (~5, ~6, 8) [subsumption resolution 442,338] 444. alice = sK4 <- (~5, ~6, ~7, 8) [subsumption resolution 443,343] 445. $false <- (~4, ~5, ~6, ~7, 8) [subsumption resolution 444,328] 446. 4 | 5 | 6 | 7 | ~8 [avatar contradiction clause 445] 447. $false [avatar sat refutation 329,334,339,344,349,358,363,446] % SZS output end Proof for 2966459380427229678307456 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Joyce, Lawrence, Jason are the only persons in the room. Lawrence and Joyce are respectively calm and old. If someone is happy, is not a quiet person or is quieter than Guadalupe then he/she is not a funny person. Jason and Joyce are quieter than Guadalupe. Guadalupe is older than Joyce. Everyone outside the room who is quieter than Guadalupe, is a creative person and is a patient person is creative. Lawrence is quieter than Guadalupe. Everyone anywhere is richer than Guadalupe only if they is quiet. Everyone outside the room is a kind wise person if they is wise. Everyone in the room is happy, is a wise generous person or is older than Guadalupe if they is not patient, not creative. Jason is a generous person. Not everyone in the room is not a creative person if they is older than Guadalupe. Not everyone anywhere who is not a creative person is older than Guadalupe. Lawrence and Joyce are respectively creative and brave. If someone is tall, is not a quiet person and is quieter than Guadalupe then he/she is quieter than Guadalupe and vice versa. Jason who neither is a creative tall person nor is a strong happy brave generous curious humble person is wise. If someone is strong then he/she is a calm person. Lawrence is not a quiet happy person, is not a patient brave happy calm funny person or is not a kind person. Everyone in the room is quieter than Guadalupe. If someone is a curious person then he/she is not brave.

Lawrence is older than Guadalupe.

entailment

room(joyce)&room(lawrence)&room(jason)&(![X]:(room(X)=>(X='joyce'|X='lawrence'|X='jason')))& ((calm(lawrence))&(old(joyce)))& ((![X]:((((happy(X))|(~(quiet(X)&person(X)))|(quieter(guadalupe,X))))=>(~(funny(X)&person(X))))))& (quieter(guadalupe,jason)&quieter(guadalupe,joyce))& (older(joyce,guadalupe))& (![X]:(~room(X)=>(((((quieter(guadalupe,X))&(creative(X)&person(X))&(patient(X)&person(X))))=>(creative(X))))))& (quieter(guadalupe,lawrence))& (![X]:(anywhere(X)=>(((quiet(X))<=(richer(guadalupe,X))))))& (![X]:(~room(X)=>(((wise(X))=>(kind(X)&wise(X)&person(X))))))& (![X]:(room(X)=>(((~patient(X)&~creative(X))=>(((happy(X))|(wise(X)&generous(X)&person(X))|(older(guadalupe,X))))))))& (generous(jason)&person(jason))& (~![X]:(room(X)=>(((older(guadalupe,X))=>(~(creative(X)&person(X)))))))& (~![X]:(anywhere(X)=>(((~(creative(X)&person(X)))=>(older(guadalupe,X))))))& ((creative(lawrence))&(brave(joyce)))& ((![X]:((((tall(X))&(~(quiet(X)&person(X)))&(quieter(guadalupe,X))))<=>(quieter(guadalupe,X)))))& ((~((creative(jason)&tall(jason)&person(jason))|(strong(jason)&happy(jason)&brave(jason)&generous(jason)&curious(jason)&humble(jason)&person(jason))))&(wise(jason)))& ((![X]:((strong(X))=>(calm(X)&person(X)))))& (((~(quiet(lawrence)&happy(lawrence)&person(lawrence)))|(~(patient(lawrence)&brave(lawrence)&happy(lawrence)&calm(lawrence)&funny(lawrence)&person(lawrence)))|(~(kind(lawrence)&person(lawrence)))))& (![X]:(room(X)=>(quieter(guadalupe,X))))& ((![X]:((curious(X)&person(X))=>(~brave(X)))))

room(joyce)&room(lawrence)&room(jason)&(![X]:(room(X)=>(X='joyce'|X='lawrence'|X='jason')))& older(guadalupe,lawrence)

% SZS status Unsatisfiable for 3266421734437366412230860 % SZS output start Proof for 3266421734437366412230860 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) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. quieter(alice,mary) & quieter(alice,fred) [input p3] 48. older(mary,alice) [input p4] 54. person(fred) & generous(fred) [input p10] 55. ~! [X0] : (room(X0) => (older(alice,X0) => ~(person(X0) & creative(X0)))) [input p11] 58. ! [X0] : ((quieter(alice,X0) & ~(person(X0) & quiet(X0)) & tall(X0)) <=> quieter(alice,X0)) [input p14] 59. wise(fred) & ~((person(fred) & humble(fred) & curious(fred) & generous(fred) & brave(fred) & happy(fred) & strong(fred)) | (person(fred) & tall(fred) & creative(fred))) [input p15] 64. ~(older(alice,paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 65. wise(fred) & ~(person(fred) & tall(fred) & creative(fred)) [pure predicate removal 59] 66. person(fred) [pure predicate removal 54] 106. ! [X0,X1] : ((~older(X1,X0) | ~older(X0,X1)) | X0 = X1) [ennf transformation 20] 107. ! [X0,X1] : (~older(X1,X0) | ~older(X0,X1) | X0 = X1) [flattening 106] 148. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 148] 154. ? [X0] : (((person(X0) & creative(X0)) & older(alice,X0)) & room(X0)) [ennf transformation 55] 155. ? [X0] : (person(X0) & creative(X0) & older(alice,X0) & room(X0)) [flattening 154] 158. ! [X0] : ((quieter(alice,X0) & (~person(X0) | ~quiet(X0)) & tall(X0)) <=> quieter(alice,X0)) [ennf transformation 58] 159. wise(fred) & (~person(fred) | ~tall(fred) | ~creative(fred)) [ennf transformation 65] 161. ~older(alice,paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 64] 162. ~older(alice,paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 161] 164. ? [X0] : (person(X0) & creative(X0) & older(alice,X0) & room(X0)) => (person(sK0) & creative(sK0) & older(alice,sK0) & room(sK0)) [choice axiom] 165. person(sK0) & creative(sK0) & older(alice,sK0) & room(sK0) [skolemisation 155,164] 168. ! [X0] : (((quieter(alice,X0) & (~person(X0) | ~quiet(X0)) & tall(X0)) | ~quieter(alice,X0)) & (quieter(alice,X0) | (~quieter(alice,X0) | (person(X0) & quiet(X0)) | ~tall(X0)))) [nnf transformation 158] 169. ! [X0] : (((quieter(alice,X0) & (~person(X0) | ~quiet(X0)) & tall(X0)) | ~quieter(alice,X0)) & (quieter(alice,X0) | ~quieter(alice,X0) | (person(X0) & quiet(X0)) | ~tall(X0))) [flattening 168] 170. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 171. ~older(alice,paul) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 162,170] 188. ~older(X1,X0) | ~older(X0,X1) | X0 = X1 [cnf transformation 107] 229. mary != alice [cnf transformation 43] 253. room(mary) [cnf transformation 149] 254. room(paul) [cnf transformation 149] 255. room(fred) [cnf transformation 149] 256. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 149] 258. quieter(alice,fred) [cnf transformation 47] 260. older(mary,alice) [cnf transformation 48] 265. person(fred) [cnf transformation 66] 266. room(sK0) [cnf transformation 165] 267. older(alice,sK0) [cnf transformation 165] 268. creative(sK0) [cnf transformation 165] 276. ~quieter(alice,X0) | tall(X0) [cnf transformation 169] 279. ~person(fred) | ~tall(fred) | ~creative(fred) [cnf transformation 159] 282. ~older(alice,paul) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 283. ~older(alice,paul) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 284. ~older(alice,paul) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 285. ~older(alice,paul) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 296. ~tall(fred) | ~creative(fred) [subsumption resolution 279,265] 298. 3 <=> creative(fred) [avatar definition] 300. ~creative(fred) <- (~3) [avatar component clause 298] 302. 4 <=> tall(fred) [avatar definition] 305. ~3 | ~4 [avatar split clause 296,302,298] 306. ~older(alice,paul) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 285,255] 307. ~older(alice,paul) | fred != sK2 | ~room(mary) [subsumption resolution 306,254] 308. ~older(alice,paul) | fred != sK2 [subsumption resolution 307,253] 310. 5 <=> fred = sK2 [avatar definition] 312. fred != sK2 <- (~5) [avatar component clause 310] 314. 6 <=> older(alice,paul) [avatar definition] 317. ~5 | ~6 [avatar split clause 308,314,310] 318. ~older(alice,paul) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 284,255] 319. ~older(alice,paul) | paul != sK2 | ~room(mary) [subsumption resolution 318,254] 320. ~older(alice,paul) | paul != sK2 [subsumption resolution 319,253] 322. 7 <=> paul = sK2 [avatar definition] 324. paul != sK2 <- (~7) [avatar component clause 322] 325. ~7 | ~6 [avatar split clause 320,314,322] 326. ~older(alice,paul) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 283,255] 327. ~older(alice,paul) | mary != sK2 | ~room(mary) [subsumption resolution 326,254] 328. ~older(alice,paul) | mary != sK2 [subsumption resolution 327,253] 330. 8 <=> mary = sK2 [avatar definition] 332. mary != sK2 <- (~8) [avatar component clause 330] 333. ~8 | ~6 [avatar split clause 328,314,330] 334. ~older(alice,paul) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 282,255] 335. ~older(alice,paul) | room(sK2) | ~room(mary) [subsumption resolution 334,254] 336. ~older(alice,paul) | room(sK2) [subsumption resolution 335,253] 338. 9 <=> room(sK2) [avatar definition] 340. room(sK2) <- (9) [avatar component clause 338] 341. 9 | ~6 [avatar split clause 336,314,338] 342. tall(fred) [resolution 276,258] 347. 4 [avatar split clause 342,302] 391. ~older(alice,mary) | mary = alice [resolution 188,260] 393. ~older(alice,mary) [subsumption resolution 391,229] 567. paul = sK0 | mary = sK0 | fred = sK0 [resolution 266,256] 571. 27 <=> fred = sK0 [avatar definition] 573. fred = sK0 <- (27) [avatar component clause 571] 575. 28 <=> mary = sK0 [avatar definition] 577. mary = sK0 <- (28) [avatar component clause 575] 579. 29 <=> paul = sK0 [avatar definition] 581. paul = sK0 <- (29) [avatar component clause 579] 582. 27 | 28 | 29 [avatar split clause 567,579,575,571] 586. creative(fred) <- (27) [backward demodulation 268,573] 593. $false <- (~3, 27) [subsumption resolution 586,300] 594. 3 | ~27 [avatar contradiction clause 593] 596. older(alice,mary) <- (28) [backward demodulation 267,577] 604. $false <- (28) [subsumption resolution 596,393] 605. ~28 [avatar contradiction clause 604] 615. older(alice,paul) <- (29) [backward demodulation 267,581] 627. 6 | ~29 [avatar split clause 615,579,314] 628. paul = sK2 | mary = sK2 | fred = sK2 <- (9) [resolution 340,256] 631. mary = sK2 | fred = sK2 <- (~7, 9) [subsumption resolution 628,324] 632. fred = sK2 <- (~7, ~8, 9) [subsumption resolution 631,332] 633. $false <- (~5, ~7, ~8, 9) [subsumption resolution 632,312] 634. 5 | 7 | 8 | ~9 [avatar contradiction clause 633] 644. $false [avatar sat refutation 305,317,325,333,341,347,582,594,605,627,634] % SZS output end Proof for 3266421734437366412230860 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. If “someone in the room is dedicated to sustainable living and zero-waste practices” then “everyone in the room who hosts regular workshops on creative writing is dedicated to sustainable living and zero-waste practices”. “At least one person anywhere practices calligraphy” if “everyone outside the room is a client of Costco or does not enjoy trail running”. Everyone in the room is dedicated to sustainable living and zero-waste practices if they practices calligraphy. Not everyone in the room who is dedicated to sustainable living and zero-waste practices is a client of Costco. Everyone in the room does not collect rare and antique scientific instruments. Everyone in the room practices calligraphy. Everyone in the room who does not practice calligraphy is dedicated to sustainable living and zero-waste practices. Everyone anywhere who is dedicated to sustainable living and zero-waste practices is not a client of Costco. Everyone in the room is not a client of Costco if they does not collect rare and antique scientific instruments. Everyone outside the room is dedicated to sustainable living and zero-waste practices if they is not a client of Costco. If someone does enjoy trail running then he/she is a client of Costco and vice versa. Everyone in the room who hosts regular workshops on creative writing or is a client of Costco or both does enjoy trail running. Someone anywhere collects rare and antique scientific instruments.

Everyone outside the room does not host regular workshops on creative writing.

neutral

(there_is_a_room)& ((?[X]:(room(X)&(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))=>(![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))& ((![X]:(~room(X)=>(((does_not_enjoy_trail_running(X))|(is_a_client_of_Costco(X))))))=>(((?[X]:(anywhere(X)&practices_calligraphy(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (~![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X))))& (![X]:(room(X)=>(practices_calligraphy(X))))& (![X]:(room(X)=>(((does_not_practice_calligraphy(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(anywhere(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(is_not_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))=>(is_not_a_client_of_Costco(X))))))& (![X]:(~room(X)=>(((is_not_a_client_of_Costco(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& ((![X]:((does_enjoy_trail_running(X))<=>(is_a_client_of_Costco(X)))))& (![X]:(room(X)=>(((((hosts_regular_workshops_on_creative_writing(X))|(is_a_client_of_Costco(X))))=>(does_enjoy_trail_running(X))))))& (?[X]:(anywhere(X)&(collects_rare_and_antique_scientific_instruments(X))))

(there_is_a_room)& ![X]:(~room(X)=>(does_not_host_regular_workshops_on_creative_writing(X)))

Nancy, Mattie, Enda, Patricia, Enda are the only persons in the room. If “everyone in the room does not enjoy spelunking or enjoys kayaking” then “everyone in the room who does not enjoy spelunking participates in citizen science projects related to wildlife monitoring”. Either “it is not the case that “someone in the room collects vintage vinyl records”” or “Nancy collects antique jewelry” but not both. Someone in the room is an active member of a local robotics club. Everyone in the room who neither collects antique jewelry nor does enjoy mountain biking makes intricate hand-cut paper art for exhibitions. Everyone in the room who makes intricate hand-cut paper art for exhibitions enjoys spelunking. Everyone in the room has completed a triathlon only if they makes intricate hand-cut paper art for exhibitions. Everyone in the room who mentors a youth basketball team on weekends participates in citizen science projects related to wildlife monitoring. If someone collects antique jewelry then he/she enjoys spelunking. Nancy who collects antique jewelry is an avid mountain climber who has scaled several peaks. Everyone outside the room who collects antique clocks and writes and illustrates their own graphic novels makes intricate hand-cut paper art for exhibitions, works on fridays and collects antique jewelry. Everyone outside the room who makes intricate hand-cut paper art for exhibitions, works on fridays and collects antique jewelry collects antique jewelry. Everyone in the room who collects antique jewelry can play the piano, works on fridays or has completed a triathlon. More than one person outside the room owns a microscope. Everyone in the room who mentors a youth basketball team on weekends enjoys kayaking. Not everyone in the room enjoys kayaking if and only if they participates in citizen science projects related to wildlife monitoring. It is not the case that “Mattie owns a microscope”. If someone collects antique clocks then he/she does enjoy mountain biking and vice versa. If someone collects antique jewelry then he/she does enjoy mountain biking and vice versa. Everyone in the room who neither participates in citizen science projects related to wildlife monitoring nor collects comic books works on fridays. Nancy maintains a large, organic vegetable garden year-round. Everyone anywhere does enjoy mountain biking or does not know morse code. Everyone anywhere who does enjoy mountain biking knows morse code. Mattie neither knows morse code nor mentors a youth basketball team on weekends.

Mattie makes intricate hand-cut paper art for exhibitions.

entailment

room(nancy)&room(mattie)&room(enda)&room(patricia)&room(enda)&(![X]:(room(X)=>(X='nancy'|X='mattie'|X='enda'|X='patricia'|X='enda')))& ((![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_enjoy_spelunking(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_spelunking(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))))& ((~(?[X]:(room(X)&(collects_vintage_vinyl_records(X)))))<~>(collects_antique_jewelry(nancy)))& (?[X]:(room(X)&(is_an_active_member_of_a_local_robotics_club(X))))& (![X]:(room(X)=>(((~((collects_antique_jewelry(X))|(does_enjoy_mountain_biking(X))))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(enjoys_spelunking(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& ((![X]:((collects_antique_jewelry(X))=>(enjoys_spelunking(X)))))& ((collects_antique_jewelry(nancy))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(nancy)))& (![X]:(~room(X)=>(((((collects_antique_clocks(X))&(writes_and_illustrates_their_own_graphic_novels(X))))=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(works_on_fridays(X))&(collects_antique_jewelry(X))))))))& (![X]:(~room(X)=>(((((makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(works_on_fridays(X))&(collects_antique_jewelry(X))))=>(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(((can_play_the_piano(X))|(works_on_fridays(X))|(has_completed_a_triathlon(X))))))))& ((?[X,Y]:(~room(X)&~room(Y)&(owns_a_microscope(X)&owns_a_microscope(Y))&(X!=Y))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(enjoys_kayaking(X))))))& (~![X]:(room(X)=>(((enjoys_kayaking(X))<=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (~(owns_a_microscope(mattie)))& ((![X]:((collects_antique_clocks(X))<=>(does_enjoy_mountain_biking(X)))))& ((![X]:((collects_antique_jewelry(X))<=>(does_enjoy_mountain_biking(X)))))& (![X]:(room(X)=>(((~((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(collects_comic_books(X))))=>(works_on_fridays(X))))))& (maintains_a_large,_organic_vegetable_garden_year-round(nancy))& (![X]:(anywhere(X)=>(((does_not_know_morse_code(X))|(does_enjoy_mountain_biking(X))))))& (![X]:(anywhere(X)=>(((does_enjoy_mountain_biking(X))=>(knows_morse_code(X))))))& (~((knows_morse_code(mattie))|(mentors_a_youth_basketball_team_on_weekends(mattie))))& (practices_graffiti_art(mattie))& (enjoys_salsa_dancing(nancy))

room(nancy)&room(mattie)&room(enda)&room(patricia)&room(enda)&(![X]:(room(X)=>(X='nancy'|X='mattie'|X='enda'|X='patricia'|X='enda')))& makes_intricate_hand-cut_paper_art_for_exhibitions(mattie)

% SZS status Unsatisfiable for 3398759893574439062402777 % SZS output start Proof for 3398759893574439062402777 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] 48. ! [X0] : (room(X0) => (~(predj(X0) | predl(X0)) => preds(X0))) [input p4] 62. ! [X0] : (predl(X0) <=> predj(X0)) [input p18] 66. ! [X0] : (anywhere(X0) => (predj(X0) => predh(X0))) [input p22] 67. ~(predt(paul) | predh(paul)) [input p23] 70. ~(preds(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] 85. ~predh(paul) [pure predicate removal 67] 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] 164. ! [X0] : ((preds(X0) | (predj(X0) | predl(X0))) | ~room(X0)) [ennf transformation 48] 165. ! [X0] : (preds(X0) | predj(X0) | predl(X0) | ~room(X0)) [flattening 164] 169. ! [X0] : ((predh(X0) | ~predj(X0)) | ~anywhere(X0)) [ennf transformation 66] 170. ! [X0] : (predh(X0) | ~predj(X0) | ~anywhere(X0)) [flattening 169] 171. ~predh(paul) [ennf transformation 85] 172. ~preds(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 70] 173. ~preds(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 172] 187. ! [X0] : ((predl(X0) | ~predj(X0)) & (predj(X0) | ~predl(X0))) [nnf transformation 62] 188. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 189. ~preds(paul) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,188] 190. anywhere(X0) [cnf transformation 5] 271. room(mary) [cnf transformation 162] 272. room(paul) [cnf transformation 162] 273. room(fred) [cnf transformation 162] 274. room(alice) [cnf transformation 162] 275. room(john) [cnf transformation 162] 276. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 162] 281. ~room(X0) | predj(X0) | predl(X0) | preds(X0) [cnf transformation 165] 292. ~predl(X0) | predj(X0) [cnf transformation 187] 293. ~predj(X0) | predl(X0) [cnf transformation 187] 295. predh(X0) | ~predj(X0) | ~anywhere(X0) [cnf transformation 170] 296. ~predh(paul) [cnf transformation 171] 297. ~preds(paul) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 298. ~preds(paul) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 299. ~preds(paul) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 300. ~preds(paul) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 301. ~preds(paul) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 302. ~preds(paul) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 333. ~predj(X0) | predh(X0) [subsumption resolution 295,190] 334. ~preds(paul) | john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,275] 335. ~preds(paul) | john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 334,274] 336. ~preds(paul) | john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 335,273] 337. ~preds(paul) | john != sK5 | ~room(mary) [subsumption resolution 336,272] 338. ~preds(paul) | john != sK5 [subsumption resolution 337,271] 340. 7 <=> john = sK5 [avatar definition] 342. john != sK5 <- (~7) [avatar component clause 340] 344. 8 <=> preds(paul) [avatar definition] 346. ~preds(paul) <- (~8) [avatar component clause 344] 347. ~7 | ~8 [avatar split clause 338,344,340] 348. ~preds(paul) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,275] 349. ~preds(paul) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 348,274] 350. ~preds(paul) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 349,273] 351. ~preds(paul) | alice != sK5 | ~room(mary) [subsumption resolution 350,272] 352. ~preds(paul) | alice != sK5 [subsumption resolution 351,271] 354. 9 <=> alice = sK5 [avatar definition] 356. alice != sK5 <- (~9) [avatar component clause 354] 357. ~9 | ~8 [avatar split clause 352,344,354] 358. ~preds(paul) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 300,275] 359. ~preds(paul) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 358,274] 360. ~preds(paul) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 359,273] 361. ~preds(paul) | fred != sK5 | ~room(mary) [subsumption resolution 360,272] 362. ~preds(paul) | fred != sK5 [subsumption resolution 361,271] 364. 10 <=> fred = sK5 [avatar definition] 366. fred != sK5 <- (~10) [avatar component clause 364] 367. ~10 | ~8 [avatar split clause 362,344,364] 368. ~preds(paul) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 299,275] 369. ~preds(paul) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 368,274] 370. ~preds(paul) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 369,273] 371. ~preds(paul) | paul != sK5 | ~room(mary) [subsumption resolution 370,272] 372. ~preds(paul) | paul != sK5 [subsumption resolution 371,271] 374. 11 <=> paul = sK5 [avatar definition] 376. paul != sK5 <- (~11) [avatar component clause 374] 377. ~11 | ~8 [avatar split clause 372,344,374] 378. ~preds(paul) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 298,275] 379. ~preds(paul) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 378,274] 380. ~preds(paul) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 379,273] 381. ~preds(paul) | mary != sK5 | ~room(mary) [subsumption resolution 380,272] 382. ~preds(paul) | mary != sK5 [subsumption resolution 381,271] 384. 12 <=> mary = sK5 [avatar definition] 386. mary != sK5 <- (~12) [avatar component clause 384] 387. ~12 | ~8 [avatar split clause 382,344,384] 388. ~preds(paul) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 297,275] 389. ~preds(paul) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 388,274] 390. ~preds(paul) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 389,273] 391. ~preds(paul) | room(sK5) | ~room(mary) [subsumption resolution 390,272] 392. ~preds(paul) | room(sK5) [subsumption resolution 391,271] 394. 13 <=> room(sK5) [avatar definition] 396. room(sK5) <- (13) [avatar component clause 394] 397. 13 | ~8 [avatar split clause 392,344,394] 403. predj(paul) | predl(paul) | preds(paul) [resolution 281,272] 410. predj(paul) | predl(paul) <- (~8) [subsumption resolution 403,346] 411. predl(paul) <- (~8) [subsumption resolution 410,293] 472. predj(paul) <- (~8) [resolution 411,292] 473. predh(paul) <- (~8) [resolution 472,333] 475. $false <- (~8) [subsumption resolution 473,296] 476. 8 [avatar contradiction clause 475] 538. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (13) [resolution 276,396] 602. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~9, 13) [subsumption resolution 538,356] 603. paul = sK5 | mary = sK5 | john = sK5 <- (~9, ~10, 13) [subsumption resolution 602,366] 604. mary = sK5 | john = sK5 <- (~9, ~10, ~11, 13) [subsumption resolution 603,376] 605. john = sK5 <- (~9, ~10, ~11, ~12, 13) [subsumption resolution 604,386] 606. $false <- (~7, ~9, ~10, ~11, ~12, 13) [subsumption resolution 605,342] 607. 7 | 9 | 10 | 11 | 12 | ~13 [avatar contradiction clause 606] 608. $false [avatar sat refutation 347,357,367,377,387,397,476,607] % SZS output end Proof for 3398759893574439062402777 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Francis, Sandra, David, Gary are the only persons in the room. If "someone anywhere enjoys spelunking" then "David has a tattoo". If "David has a tattoo" then "David owns a high-end gaming PC with custom-built components". Everyone in the room enjoys rooftop gardening only if they neither collects antique jewelry nor is a certified scuba diver with advanced underwater photography skills. Francis frequently participates in hackathons and coding competitions. Sandra practices urban gardening. Francis has a vast collection of first-edition science fiction novels. Sandra has a vast collection of first-edition science fiction novels or collects first edition books or both. More than one person in the room watches fantasy movies. Not everyone outside the room who designs and sews custom cosplay costumes for conventions has a tattoo and does not enjoy kayaking. Everyone anywhere who does not play as a goalkeeper for a local amateur soccer team does not collect first edition books. Everyone in the room enjoys rooftop gardening if they enjoys spelunking, collects antique jewelry and is an avid mountain climber who has scaled several peaks and vice versa. Gary designs and sews custom cosplay costumes for conventions. Gary collects rare minerals. Gary is an avid mountain climber who has scaled several peaks. Everyone in the room frequently participates in hackathons and coding competitions if they enjoys kayaking. David who has a vast collection of first-edition science fiction novels collects first edition books. Sandra owns a high-end gaming PC with custom-built components. Francis who does not enjoy spelunking enjoys kayaking. Sandra collects first edition books. Not everyone in the room who does not enjoy cross-country skiing is an amateur astronomer who builds and uses custom telescopes. Sandra has a tattoo and designs and sews custom cosplay costumes for conventions.

Francis enjoys spelunking.

contradiction

room(francis)&room(sandra)&room(david)&room(gary)&(![X]:(room(X)=>(X='francis'|X='sandra'|X='david'|X='gary')))& (((?[X]:(anywhere(X)&(enjoys_spelunking(X))))=>(has_a_tattoo(david)))& ((has_a_tattoo(david))=>(owns_a_high-end_gaming_PC_with_custom-built_components(david))))& (![X]:(room(X)=>(((~((collects_antique_jewelry(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))<=(enjoys_rooftop_gardening(X))))))& (frequently_participates_in_hackathons_and_coding_competitions(francis))& (practices_urban_gardening(sandra))& (has_a_vast_collection_of_first-edition_science_fiction_novels(francis))& (((has_a_vast_collection_of_first-edition_science_fiction_novels(sandra))|(collects_first_edition_books(sandra))))& ((?[X,Y]:(room(X)&room(Y)&(watches_fantasy_movies(X)&watches_fantasy_movies(Y))&(X!=Y))))& (~![X]:(~room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(((has_a_tattoo(X))&(does_not_enjoy_kayaking(X))))))))& (![X]:(anywhere(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(does_not_collect_first_edition_books(X))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))<=>(((enjoys_spelunking(X))&(collects_antique_jewelry(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(gary))& (collects_rare_minerals(gary))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(gary))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& ((has_a_vast_collection_of_first-edition_science_fiction_novels(david))&(collects_first_edition_books(david)))& (owns_a_high-end_gaming_PC_with_custom-built_components(sandra))& ((does_not_enjoy_spelunking(francis))&(enjoys_kayaking(francis)))& (collects_first_edition_books(sandra))& (~![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (((has_a_tattoo(sandra))&(designs_and_sews_custom_cosplay_costumes_for_conventions(sandra))))

room(francis)&room(sandra)&room(david)&room(gary)&(![X]:(room(X)=>(X='francis'|X='sandra'|X='david'|X='gary')))& enjoys_spelunking(francis)

% SZS status Unsatisfiable for 2765899709098782083872867 % SZS output start Proof for 2765899709098782083872867 44. predw(paul) & prede(paul) & ~! [X0] : (room(X0) => (~predh(X0) => predd(X0))) & predr(paul) & predk(mary) & ~predn(mary) & predg(paul) & predr(fred) & predj(fred) & ! [X0] : (room(X0) => (predk(X0) => preda(X0))) & predf(alice) & predt(alice) & predw(alice) & ! [X0] : (room(X0) => (predq(X0) <=> (predf(X0) & predc(X0) & predn(X0)))) & ! [X0] : (anywhere(X0) => (~predp(X0) => ~predr(X0))) & ~! [X0] : (~room(X0) => (predw(X0) => (~predk(X0) & prede(X0)))) & ? [X0,X1] : (X0 != X1 & predb(X1) & predb(X0) & room(X1) & room(X0)) & (predr(paul) | predj(paul)) & predj(mary) & predo(paul) & preda(mary) & ! [X0] : (room(X0) => (predq(X0) => ~(preds(X0) | predc(X0)))) & (prede(fred) => predg(fred)) & (? [X0] : (predn(X0) & anywhere(X0)) => prede(fred)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. predn(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 46. predw(paul) & prede(paul) & ~! [X0] : (room(X0) => (~predh(X0) => predd(X0))) & predr(paul) & predk(mary) & ~predn(mary) & predg(paul) & predr(fred) & predj(fred) & ! [X1] : (room(X1) => (predk(X1) => preda(X1))) & predf(alice) & predt(alice) & predw(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ! [X3] : (anywhere(X3) => (~predp(X3) => ~predr(X3))) & ~! [X4] : (~room(X4) => (predw(X4) => (~predk(X4) & prede(X4)))) & ? [X5,X6] : (X5 != X6 & predb(X6) & predb(X5) & room(X6) & room(X5)) & (predr(paul) | predj(paul)) & predj(mary) & predo(paul) & preda(mary) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. predw(paul) & prede(paul) & ~! [X0] : (room(X0) => ~~predh(X0)) & predr(paul) & predk(mary) & ~predn(mary) & predg(paul) & predr(fred) & predj(fred) & ! [X1] : (room(X1) => (predk(X1) => preda(X1))) & predf(alice) & predt(alice) & predw(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ! [X3] : (anywhere(X3) => (~predp(X3) => ~predr(X3))) & ~! [X4] : (~room(X4) => (predw(X4) => (~predk(X4) & prede(X4)))) & ? [X5,X6] : (X5 != X6 & predb(X6) & predb(X5) & room(X6) & room(X5)) & (predr(paul) | predj(paul)) & predj(mary) & predo(paul) & preda(mary) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. predw(paul) & prede(paul) & ~! [X0] : ~room(X0) & predr(paul) & predk(mary) & ~predn(mary) & predg(paul) & predr(fred) & predj(fred) & ! [X1] : (room(X1) => (predk(X1) => preda(X1))) & predf(alice) & predt(alice) & predw(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ! [X3] : (anywhere(X3) => (~predp(X3) => ~predr(X3))) & ~! [X4] : (~room(X4) => (predw(X4) => (~predk(X4) & prede(X4)))) & ? [X5,X6] : (X5 != X6 & predb(X6) & predb(X5) & room(X6) & room(X5)) & (predr(paul) | predj(paul)) & predj(mary) & predo(paul) & preda(mary) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. predw(paul) & prede(paul) & ~! [X0] : ~room(X0) & predr(paul) & predk(mary) & ~predn(mary) & predg(paul) & predr(fred) & predj(fred) & ! [X1] : (room(X1) => (predk(X1) => preda(X1))) & predf(alice) & predw(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ! [X3] : (anywhere(X3) => (~predp(X3) => ~predr(X3))) & ~! [X4] : (~room(X4) => (predw(X4) => (~predk(X4) & prede(X4)))) & ? [X5,X6] : (X5 != X6 & predb(X6) & predb(X5) & room(X6) & room(X5)) & (predr(paul) | predj(paul)) & predj(mary) & predo(paul) & preda(mary) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. predw(paul) & prede(paul) & ~! [X0] : ~room(X0) & predr(paul) & predk(mary) & ~predn(mary) & predg(paul) & predr(fred) & predj(fred) & ! [X1] : (room(X1) => (predk(X1) => preda(X1))) & predf(alice) & predw(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : (~room(X4) => (predw(X4) => (~predk(X4) & prede(X4)))) & ? [X5,X6] : (X5 != X6 & predb(X6) & predb(X5) & room(X6) & room(X5)) & (predr(paul) | predj(paul)) & predj(mary) & predo(paul) & preda(mary) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. predw(paul) & prede(paul) & ~! [X0] : ~room(X0) & predk(mary) & ~predn(mary) & predg(paul) & predj(fred) & ! [X1] : (room(X1) => (predk(X1) => preda(X1))) & predf(alice) & predw(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : (~room(X4) => (predw(X4) => (~predk(X4) & prede(X4)))) & ? [X5,X6] : (X5 != X6 & predb(X6) & predb(X5) & room(X6) & room(X5)) & predj(mary) & predo(paul) & preda(mary) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. prede(paul) & ~! [X0] : ~room(X0) & predk(mary) & ~predn(mary) & predg(paul) & predj(fred) & ! [X1] : (room(X1) => (predk(X1) => preda(X1))) & predf(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : (~room(X4) => (~predk(X4) & prede(X4))) & ? [X5,X6] : (X5 != X6 & predb(X6) & predb(X5) & room(X6) & room(X5)) & predj(mary) & predo(paul) & preda(mary) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. prede(paul) & ~! [X0] : ~room(X0) & predk(mary) & ~predn(mary) & predg(paul) & predj(fred) & ! [X1] : (room(X1) => (predk(X1) => preda(X1))) & predf(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : (~room(X4) => (~predk(X4) & prede(X4))) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & predj(mary) & predo(paul) & preda(mary) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. prede(paul) & ~! [X0] : ~room(X0) & predk(mary) & ~predn(mary) & predg(paul) & ! [X1] : (room(X1) => (predk(X1) => preda(X1))) & predf(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : (~room(X4) => (~predk(X4) & prede(X4))) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & predo(paul) & preda(mary) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. prede(paul) & ~! [X0] : ~room(X0) & predk(mary) & ~predn(mary) & predg(paul) & ! [X1] : (room(X1) => (predk(X1) => preda(X1))) & predf(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : (~room(X4) => (~predk(X4) & prede(X4))) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & preda(mary) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 56. prede(paul) & ~! [X0] : ~room(X0) & predk(mary) & ~predn(mary) & predg(paul) & predf(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : (~room(X4) => (~predk(X4) & prede(X4))) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 55] 57. prede(paul) & ~! [X0] : ~room(X0) & ~predn(mary) & predg(paul) & predf(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : ~~room(X4) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (room(X7) => (predq(X7) => ~(preds(X7) | predc(X7)))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 56] 58. prede(paul) & ~! [X0] : ~room(X0) & ~predn(mary) & predg(paul) & predf(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : ~~room(X4) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (room(X7) => (predq(X7) => ~predc(X7))) & (prede(fred) => predg(fred)) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 57] 59. prede(paul) & ~! [X0] : ~room(X0) & ~predn(mary) & predf(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : ~~room(X4) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (room(X7) => (predq(X7) => ~predc(X7))) & (? [X8] : (predn(X8) & anywhere(X8)) => prede(fred)) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 58] 60. ~! [X0] : ~room(X0) & ~predn(mary) & predf(alice) & ! [X2] : (room(X2) => (predq(X2) <=> (predf(X2) & predc(X2) & predn(X2)))) & ~! [X4] : ~~room(X4) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (room(X7) => (predq(X7) => ~predc(X7))) & ! [X9] : (room(X9) => (alice = X9 | fred = X9 | paul = X9 | mary = X9)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 59] 133. ? [X0] : room(X0) & ~predn(mary) & predf(alice) & ! [X2] : ((predq(X2) <=> (predf(X2) & predc(X2) & predn(X2))) | ~room(X2)) & ? [X4] : ~room(X4) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : ((~predc(X7) | ~predq(X7)) | ~room(X7)) & ! [X9] : ((alice = X9 | fred = X9 | paul = X9 | mary = X9) | ~room(X9)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 134. ? [X0] : room(X0) & ~predn(mary) & predf(alice) & ! [X2] : ((predq(X2) <=> (predf(X2) & predc(X2) & predn(X2))) | ~room(X2)) & ? [X4] : ~room(X4) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (~predc(X7) | ~predq(X7) | ~room(X7)) & ! [X9] : (alice = X9 | fred = X9 | paul = X9 | mary = X9 | ~room(X9)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133] 135. predn(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 45] 136. predn(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 135] 138. ? [X0] : room(X0) & ~predn(mary) & predf(alice) & ! [X2] : (((predq(X2) | (~predf(X2) | ~predc(X2) | ~predn(X2))) & ((predf(X2) & predc(X2) & predn(X2)) | ~predq(X2))) | ~room(X2)) & ? [X4] : ~room(X4) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (~predc(X7) | ~predq(X7) | ~room(X7)) & ! [X9] : (alice = X9 | fred = X9 | paul = X9 | mary = X9 | ~room(X9)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 134] 139. ? [X0] : room(X0) & ~predn(mary) & predf(alice) & ! [X2] : (((predq(X2) | ~predf(X2) | ~predc(X2) | ~predn(X2)) & ((predf(X2) & predc(X2) & predn(X2)) | ~predq(X2))) | ~room(X2)) & ? [X4] : ~room(X4) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (~predc(X7) | ~predq(X7) | ~room(X7)) & ! [X9] : (alice = X9 | fred = X9 | paul = X9 | mary = X9 | ~room(X9)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 138] 140. ? [X0] : room(X0) & ~predn(mary) & predf(alice) & ! [X1] : (((predq(X1) | ~predf(X1) | ~predc(X1) | ~predn(X1)) & ((predf(X1) & predc(X1) & predn(X1)) | ~predq(X1))) | ~room(X1)) & ? [X2] : ~room(X2) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5] : (~predc(X5) | ~predq(X5) | ~room(X5)) & ! [X6] : (alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 139] 141. ? [X0] : room(X0) => room(sK0) [choice axiom] 142. ? [X2] : ~room(X2) => ~room(sK1) [choice axiom] 143. ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) => (sK2 != sK3 & room(sK3) & room(sK2)) [choice axiom] 144. room(sK0) & ~predn(mary) & predf(alice) & ! [X1] : (((predq(X1) | ~predf(X1) | ~predc(X1) | ~predn(X1)) & ((predf(X1) & predc(X1) & predn(X1)) | ~predq(X1))) | ~room(X1)) & ~room(sK1) & (sK2 != sK3 & room(sK3) & room(sK2)) & ! [X5] : (~predc(X5) | ~predq(X5) | ~room(X5)) & ! [X6] : (alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 140,143,142,141] 240. ~predn(mary) [cnf transformation 144] 247. predn(mary) [cnf transformation 136] 249. $false [subsumption resolution 247,240] % SZS output end Proof for 2765899709098782083872867 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Delores, Jose, Emmy are the only persons in the room. Emmy is the least quiet in the room. Jose is not a tall generous calm kind person. Emmy is not a brave person. If someone is not a tall calm person then he/she is not a tall person. Delores is not a patient strong tall person. Delores is not a generous person. Jose neither is not a brave person nor is not a generous person. Jose is not a funny person. Jose neither is not a brave person nor is not a old person. Delores is not a old person. Delores is not a funny person. Delores is not a happy person. At least one person in the room is not a quiet funny person.

Jose is tall, is old or is quiet.

entailment

room(delores)&room(jose)&room(emmy)&(![X]:(room(X)=>(X='delores'|X='jose'|X='emmy')))& (![X]:((room(X)&(X!=emmy))=>quieter(emmy,X)))& (~(tall(jose)&generous(jose)&calm(jose)&kind(jose)&person(jose)))& (~(brave(emmy)&person(emmy)))& ((![X]:((~(tall(X)&calm(X)&person(X)))=>(~(tall(X)&person(X))))))& (~(patient(delores)&strong(delores)&tall(delores)&person(delores)))& (~(generous(delores)&person(delores)))& (~((~(brave(jose)&person(jose)))|(~(generous(jose)&person(jose)))))& (~(funny(jose)&person(jose)))& (~((~(brave(jose)&person(jose)))|(~(old(jose)&person(jose)))))& (~(old(delores)&person(delores)))& (~(funny(delores)&person(delores)))& (~(happy(delores)&person(delores)))& (((?[X]:(room(X)&~(quiet(X)&funny(X)&person(X))))))

room(delores)&room(jose)&room(emmy)&(![X]:(room(X)=>(X='delores'|X='jose'|X='emmy')))& ((tall(jose))|(old(jose))|(quiet(jose)))

% SZS status Unsatisfiable for 2447157232719903300267128 % SZS output start Proof for 2447157232719903300267128 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 53. ~(~(person(paul) & old(paul)) | ~(person(paul) & brave(paul))) [input p9] 58. ~((quiet(paul) | old(paul) | tall(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 138. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 138] 148. (person(paul) & old(paul)) & (person(paul) & brave(paul)) [ennf transformation 53] 149. person(paul) & old(paul) & person(paul) & brave(paul) [flattening 148] 151. (~quiet(paul) & ~old(paul) & ~tall(paul)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58] 152. (~quiet(paul) & ~old(paul) & ~tall(paul)) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 151] 153. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [predicate definition introduction] 154. (~quiet(paul) & ~old(paul) & ~tall(paul)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 152,153] 158. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [nnf transformation 153] 159. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 160. (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~sP0 [skolemisation 158,159] 241. room(mary) [cnf transformation 139] 242. room(paul) [cnf transformation 139] 243. room(fred) [cnf transformation 139] 244. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 139] 256. old(paul) [cnf transformation 149] 260. room(sK2) | ~sP0 [cnf transformation 160] 261. mary != sK2 | ~sP0 [cnf transformation 160] 262. paul != sK2 | ~sP0 [cnf transformation 160] 263. fred != sK2 | ~sP0 [cnf transformation 160] 265. ~old(paul) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154] 291. 6 <=> sP0 [avatar definition] 295. 7 <=> fred = sK2 [avatar definition] 297. fred != sK2 <- (~7) [avatar component clause 295] 298. ~6 | ~7 [avatar split clause 263,295,291] 300. 8 <=> paul = sK2 [avatar definition] 302. paul != sK2 <- (~8) [avatar component clause 300] 303. ~6 | ~8 [avatar split clause 262,300,291] 305. 9 <=> mary = sK2 [avatar definition] 307. mary != sK2 <- (~9) [avatar component clause 305] 308. ~6 | ~9 [avatar split clause 261,305,291] 310. 10 <=> room(sK2) [avatar definition] 312. room(sK2) <- (10) [avatar component clause 310] 313. ~6 | 10 [avatar split clause 260,310,291] 322. sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,256] 323. sP0 | ~room(paul) | ~room(mary) [subsumption resolution 322,243] 324. sP0 | ~room(mary) [subsumption resolution 323,242] 325. sP0 [subsumption resolution 324,241] 326. 6 [avatar split clause 325,291] 418. paul = sK2 | mary = sK2 | fred = sK2 <- (10) [resolution 244,312] 432. mary = sK2 | fred = sK2 <- (~8, 10) [subsumption resolution 418,302] 433. fred = sK2 <- (~8, ~9, 10) [subsumption resolution 432,307] 434. $false <- (~7, ~8, ~9, 10) [subsumption resolution 433,297] 435. 7 | 8 | 9 | ~10 [avatar contradiction clause 434] 436. $false [avatar sat refutation 298,303,308,313,326,435] % SZS output end Proof for 2447157232719903300267128 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Jesse is the only person in the room. If “everyone in the room does not collect luxury watches or is not a drone photographer” then “no one in the room who is a sibling of Patricia is not a drone photographer”. If “Jesse is a client of Patricia, is a drone photographer and is a sibling of Patricia” then “not everyone in the room who neither is a drone photographer nor is curious is a drone photographer”. Everyone in the room who collects luxury watches is a sibling of Lillie. If someone is a wine connoisseur with a private cellar of vintage wines then he/she either is a sibling of Lillie or collects rare and antique scientific instruments but not both and vice versa. Everyone in the room does not collect luxury watches and is curious if they does not collect luxury watches. Everyone in the room is a client of Vernon or does not collect luxury watches. Everyone in the room who neither is a sibling of Patricia nor is a client of Vernon is a sibling of Vernon. Everyone in the room who collects rare and antique scientific instruments does not collect luxury watches.

Jesse is a drone photographer.

entailment

room(jesse)&(![X]:(room(X)=>(X='jesse')))& ((![X]:(room(X)=>(((is_not_a_drone_photographer(X))|(does_not_collect_luxury_watches(X))))))=>(~?[X]:(room(X)=>(((sibling(patricia,X))=>(is_not_a_drone_photographer(X)))))))& ((((client(patricia,jesse))&(is_a_drone_photographer(jesse))&(sibling(patricia,jesse))))=>(~![X]:(room(X)=>(((~((is_a_drone_photographer(X))|(curious(X))))=>(is_a_drone_photographer(X)))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(sibling(lillie,X))))))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(((sibling(lillie,X))<~>(collects_rare_and_antique_scientific_instruments(X)))))))& (![X]:(room(X)=>(((does_not_collect_luxury_watches(X))=>(((does_not_collect_luxury_watches(X))&(curious(X))))))))& (![X]:(room(X)=>(((does_not_collect_luxury_watches(X))|(client(vernon,X))))))& (![X]:(room(X)=>(((~((sibling(patricia,X))|(client(vernon,X))))=>(sibling(vernon,X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(does_not_collect_luxury_watches(X))))))

room(jesse)&(![X]:(room(X)=>(X='jesse')))& is_a_drone_photographer(jesse)

% SZS status Unsatisfiable for 2167620113923673987192926 % SZS output start Proof for 2167620113923673987192926 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (~predw(X0) | ~predt(X0))) => ~? [X0] : (room(X0) => (sibling(alice,X0) => ~predt(X0))) [input p1] 53. ~(predt(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 54. ! [X0] : (room(X0) => (~predw(X0) | ~predt(X0))) => ~? [X1] : (room(X1) => (sibling(alice,X1) => ~predt(X1))) [rectify 45] 128. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 129. ! [X1] : ((predt(X1) & sibling(alice,X1)) & room(X1)) | ? [X0] : ((predw(X0) & predt(X0)) & room(X0)) [ennf transformation 54] 130. ! [X1] : (predt(X1) & sibling(alice,X1) & room(X1)) | ? [X0] : (predw(X0) & predt(X0) & room(X0)) [flattening 129] 141. ~predt(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 53] 142. ? [X0] : (predw(X0) & predt(X0) & room(X0)) | ~sP0 [predicate definition introduction] 143. ! [X1] : (predt(X1) & sibling(alice,X1) & room(X1)) | sP0 [definition folding 130,142] 145. ? [X0] : (predw(X0) & predt(X0) & room(X0)) | ~sP0 [nnf transformation 142] 146. ? [X0] : (predw(X0) & predt(X0) & room(X0)) => (predw(sK1) & predt(sK1) & room(sK1)) [choice axiom] 147. (predw(sK1) & predt(sK1) & room(sK1)) | ~sP0 [skolemisation 145,146] 148. ! [X0] : (predt(X0) & sibling(alice,X0) & room(X0)) | sP0 [rectify 143] 151. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 152. ~predt(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 141,151] 197. mary != paul [cnf transformation 43] 233. room(mary) [cnf transformation 128] 234. ~room(X0) | mary = X0 [cnf transformation 128] 235. room(sK1) | ~sP0 [cnf transformation 147] 236. predt(sK1) | ~sP0 [cnf transformation 147] 238. room(X0) | sP0 [cnf transformation 148] 250. ~predt(mary) | room(sK3) | ~room(mary) [cnf transformation 152] 251. ~predt(mary) | mary != sK3 | ~room(mary) [cnf transformation 152] 253. 1 <=> sP0 [avatar definition] 262. 3 <=> predt(sK1) [avatar definition] 264. predt(sK1) <- (3) [avatar component clause 262] 265. ~1 | 3 [avatar split clause 236,262,253] 267. 4 <=> room(sK1) [avatar definition] 269. room(sK1) <- (4) [avatar component clause 267] 270. ~1 | 4 [avatar split clause 235,267,253] 280. 7 <=> ! [X0] : room(X0) [avatar definition] 281. room(X0) <- (7) [avatar component clause 280] 282. 1 | 7 [avatar split clause 238,280,253] 288. 9 <=> predt(mary) [avatar definition] 311. ~predt(mary) | mary != sK3 [subsumption resolution 251,233] 313. 14 <=> mary = sK3 [avatar definition] 316. ~14 | ~9 [avatar split clause 311,288,313] 317. ~predt(mary) | room(sK3) [subsumption resolution 250,233] 319. 15 <=> room(sK3) [avatar definition] 321. room(sK3) <- (15) [avatar component clause 319] 322. 15 | ~9 [avatar split clause 317,288,319] 326. mary = X0 <- (7) [resolution 234,281] 361. mary != mary <- (7) [superposition 197,326] 380. $false <- (7) [trivial inequality removal 361] 381. ~7 [avatar contradiction clause 380] 382. mary = sK1 <- (4) [resolution 269,234] 385. mary = sK3 <- (15) [resolution 321,234] 388. predt(mary) <- (3, 4) [forward demodulation 264,382] 389. 9 | ~3 | ~4 [avatar split clause 388,267,262,288] 390. 14 | ~15 [avatar split clause 385,319,313] 392. $false [avatar sat refutation 265,270,282,316,322,381,389,390] % SZS output end Proof for 2167620113923673987192926 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

If someone is an avid hiker then he/she bakes bread at home, creates YouTube content or enjoys camping and organizing outdoor survival workshops and vice versa. Everyone in the room does not enjoy coding in Python if they bakes bread at home or does not collect historical artifacts related to ancient civilizations or both. Everyone in the room drives a hybrid car only if they collects classic novels and is not an avid hiker. Everyone in the room creates YouTube content if they does not enjoy coding in Python. Someone in the room bakes bread at home.

Everyone in the room does not create YouTube content or drives a hybrid car.

contradiction

(there_is_a_room)& ((![X]:(~room(X)=>(((does_not_practice_urban_gardening(X))|(collects_classic_novels(X))))))=>(![X]:(room(X)=>(((collects_classic_novels(X))=>(is_an_avid_hiker(X)))))))& ((![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))<=>(![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(drives_a_hybrid_car(X)))))))& ((~?[X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(enjoys_coding_in_Python(X))))))=>(![X]:(~room(X)=>(((((collects_historical_artifacts_related_to_ancient_civilizations(X))|(is_not_an_avid_hiker(X))|(is_allergic_to_anything(X))))=>(drives_a_hybrid_car(X)))))))& ((![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(creates_YouTube_content(X))))))<=>(![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X)))))))& ((![X]:(~room(X)=>(enjoys_coding_in_Python(X))))=>(![X]:(room(X)=>(((enjoys_coding_in_Python(X))<=>(((does_not_practice_urban_gardening(X))|(is_allergic_to_anything(X)))))))))& ((![X]:(room(X)=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))<=>(![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(is_not_allergic_to_anything(X)))))))& ((![X]:((is_an_avid_hiker(X))<=>(((bakes_bread_at_home(X))|(creates_YouTube_content(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))& (~?[X]:(anywhere(X)=>(((does_not_enjoy_cross-country_skiing(X))=>(enjoys_cross-country_skiing(X))))))& (((?[X]:(anywhere(X)&does_not_practice_urban_gardening(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(does_not_practice_urban_gardening(X))&(does_not_practice_urban_gardening(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((((bakes_bread_at_home(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))=>(does_not_enjoy_coding_in_Python(X))))))& (![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))=>(does_not_drive_a_hybrid_car(X))))))& (![X]:(anywhere(X)=>(((is_not_allergic_to_anything(X))|(is_an_avid_hiker(X))))))& (~![X]:(room(X)=>(((is_an_avid_hiker(X))=>(enjoys_cross-country_skiing(X))))))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(practices_urban_gardening(X))))))& (~![X]:(room(X)=>(((practices_urban_gardening(X))=>(creates_YouTube_content(X))))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(collects_classic_novels(X))))))& ((?[X,Y]:(room(X)&room(Y)&(((is_allergic_to_anything(X))|(does_not_collect_classic_novels(X)))&((is_allergic_to_anything(Y))|(does_not_collect_classic_novels(Y))))&(X!=Y))))& (![X]:(room(X)=>(((((collects_classic_novels(X))&(is_not_an_avid_hiker(X))))<=(drives_a_hybrid_car(X))))))& (![X]:(~room(X)=>(((((collects_classic_novels(X))&(is_not_an_avid_hiker(X))))<=>(((enjoys_coding_in_Python(X))&(practices_urban_gardening(X))))))))& (((?[X]:(~room(X)&is_an_avid_hiker(X)))))& (![X]:(~room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))=>(does_not_enjoy_coding_in_Python(X))))))& (![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))=>(creates_YouTube_content(X))))))& (?[X]:(room(X)&(bakes_bread_at_home(X))))

(there_is_a_room)& ![X]:(room(X)=>(((drives_a_hybrid_car(X))|(does_not_create_YouTube_content(X)))))

% SZS status Unsatisfiable for 6454397801439992474707378 % SZS output start Proof for 6454397801439992474707378 51. ! [X0] : (predf(X0) <=> (predk(X0) | predd(X0) | predh(X0))) [input p7] 54. ! [X0] : (room(X0) => ((~predc(X0) | predh(X0)) => ~preda(X0))) [input p10] 62. ! [X0] : (room(X0) => (predj(X0) => (~predf(X0) & predi(X0)))) [input p18] 66. ! [X0] : (room(X0) => (~preda(X0) => predd(X0))) [input p22] 67. ? [X0] : (predh(X0) & room(X0)) [input p23] 68. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room [input hypothesis] 79. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [pure predicate removal 68] 166. ! [X0] : ((~preda(X0) | (predc(X0) & ~predh(X0))) | ~room(X0)) [ennf transformation 54] 167. ! [X0] : (~preda(X0) | (predc(X0) & ~predh(X0)) | ~room(X0)) [flattening 166] 177. ! [X0] : (((~predf(X0) & predi(X0)) | ~predj(X0)) | ~room(X0)) [ennf transformation 62] 178. ! [X0] : ((~predf(X0) & predi(X0)) | ~predj(X0) | ~room(X0)) [flattening 177] 182. ! [X0] : ((predd(X0) | preda(X0)) | ~room(X0)) [ennf transformation 66] 183. ! [X0] : (predd(X0) | preda(X0) | ~room(X0)) [flattening 182] 184. ! [X0] : ((~predd(X0) | predj(X0)) | ~room(X0)) [ennf transformation 79] 185. ! [X0] : (~predd(X0) | predj(X0) | ~room(X0)) [flattening 184] 213. ! [X0] : ((predf(X0) | (~predk(X0) & ~predd(X0) & ~predh(X0))) & ((predk(X0) | predd(X0) | predh(X0)) | ~predf(X0))) [nnf transformation 51] 214. ! [X0] : ((predf(X0) | (~predk(X0) & ~predd(X0) & ~predh(X0))) & (predk(X0) | predd(X0) | predh(X0) | ~predf(X0))) [flattening 213] 227. ? [X0] : (predh(X0) & room(X0)) => (predh(sK15) & room(sK15)) [choice axiom] 228. predh(sK15) & room(sK15) [skolemisation 67,227] 340. ~predh(X0) | predf(X0) [cnf transformation 214] 347. ~predh(X0) | ~preda(X0) | ~room(X0) [cnf transformation 167] 363. ~predj(X0) | ~predf(X0) | ~room(X0) [cnf transformation 178] 371. ~room(X0) | preda(X0) | predd(X0) [cnf transformation 183] 372. room(sK15) [cnf transformation 228] 373. predh(sK15) [cnf transformation 228] 374. ~predd(X0) | predj(X0) | ~room(X0) [cnf transformation 185] 566. predf(sK15) [resolution 340,373] 581. ~preda(sK15) | ~room(sK15) [resolution 347,373] 582. ~preda(sK15) [subsumption resolution 581,372] 618. preda(sK15) | predd(sK15) [resolution 371,372] 665. predd(sK15) [subsumption resolution 618,582] 733. predj(sK15) | ~room(sK15) [resolution 665,374] 735. predj(sK15) [subsumption resolution 733,372] 902. ~predf(sK15) | ~room(sK15) [resolution 735,363] 905. ~room(sK15) [subsumption resolution 902,566] 906. $false [subsumption resolution 905,372] % SZS output end Proof for 6454397801439992474707378 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s % ------------------------------ % ------------------------------

There is a room. “Everyone in the room enjoys deep-sea diving and exploring underwater caves if they builds model airplanes” unless “no one outside the room is not a night owl or builds model airplanes”. If “everyone in the room does not host regular game nights featuring complex strategy games or is a client of LVMH” then “no one in the room is not an avid mountain climber who has scaled several peaks or hosts regular game nights featuring complex strategy games”. If “no one in the room is not an avid mountain climber who has scaled several peaks or hosts regular game nights featuring complex strategy games” then “everyone in the room who plays video games enjoys deep-sea diving and exploring underwater caves”. If “everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or hosts regular game nights featuring complex strategy games” then “everyone anywhere is an enthusiastic bird watcher who travels for rare sightings if they is not an enthusiastic bird watcher who travels for rare sightings”. If “everyone outside the room is not an enthusiastic bird watcher who travels for rare sightings or enjoys deep-sea diving and exploring underwater caves” then “everyone in the room who is not an enthusiastic bird watcher who travels for rare sightings enjoys deep-sea diving and exploring underwater caves”. Everyone in the room who enjoys deep-sea diving and exploring underwater caves builds model airplanes. Everyone in the room who builds model airplanes collects vintage vinyl records. Everyone in the room enjoys deep-sea diving and exploring underwater caves if they is an enthusiastic bird watcher who travels for rare sightings and vice versa. At least one person anywhere creates large-scale murals for public art installations. Everyone outside the room hosts regular game nights featuring complex strategy games if they plays video games. Everyone in the room who is a client of LVMH collects vintage vinyl records. Everyone outside the room hosts regular game nights featuring complex strategy games if they collects vintage vinyl records. Everyone anywhere does not create large-scale murals for public art installations or hosts regular game nights featuring complex strategy games.

Everyone in the room does not collect vintage vinyl records or creates large-scale murals for public art installations.

neutral

(there_is_a_room)& (~(~?[X]:(~room(X)=>(((builds_model_airplanes(X))|(is_not_a_night_owl(X))))))=>(![X]:(room(X)=>(((builds_model_airplanes(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))& (((![X]:(room(X)=>(((is_a_client_of_LVMH(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))=>(~?[X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& ((~?[X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(![X]:(room(X)=>(((plays_video_games(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))))& ((![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>(![X]:(anywhere(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))& ((![X]:(~room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(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))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(builds_model_airplanes(X))))))& (![X]:(room(X)=>(((builds_model_airplanes(X))=>(collects_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (((?[X]:(anywhere(X)&creates_large-scale_murals_for_public_art_installations(X)))))& (![X]:(~room(X)=>(((plays_video_games(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(collects_vintage_vinyl_records(X))))))& (![X]:(~room(X)=>(((collects_vintage_vinyl_records(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(anywhere(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(does_not_collect_vintage_vinyl_records(X)))))

There is a room. Either not everyone in the room does not collect classic novels or everyone in the room is not a certified scuba diver with advanced underwater photography skills but not both. Everyone in the room does not mentor a youth basketball team on weekends, does not collect classic novels or does not practice graffiti art only if not everyone outside the room does not own a smart tv or does not practice graffiti art or both. Everyone outside the room either does not enjoy kayaking or is not an active member of a local robotics club but not both. Everyone in the room does not enjoy kayaking and exploring remote waterways. Everyone in the room either does not mentor a youth basketball team on weekends or does not own a smart tv but not both. Not everyone in the room does not practice urban gardening or does not write poetry or both. Everyone in the room either does not enjoy kayaking or does not practice pilates but not both. Everyone in the room does not own a smart tv. Everyone anywhere is not a certified scuba diver with advanced underwater photography skills. Everyone in the room does not enjoy virtual reality gaming or is not a chess master who participates in national tournaments or both. Not everyone outside the room does not own a smart tv or does not practice graffiti art or both. Everyone in the room either does not practice pilates or does not write poetry but not both.

Everyone in the room does not enjoy kayaking or enjoys kayaking and exploring remote waterways.

contradiction

(there_is_a_room)& ((~![X]:(room(X)=>(does_not_collect_classic_novels(X))))<~>(![X]:(room(X)=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& ((![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(does_not_collect_classic_novels(X))|(does_not_practice_graffiti_art(X))))))=>(~![X]:(~room(X)=>(((does_not_own_a_smart_tv(X))|(does_not_practice_graffiti_art(X)))))))& (![X]:(~room(X)=>(((does_not_enjoy_kayaking(X))<~>(is_not_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))& (![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))<~>(does_not_own_a_smart_tv(X))))))& (~![X]:(room(X)=>(((does_not_practice_urban_gardening(X))|(does_not_write_poetry(X))))))& (![X]:(room(X)=>(((does_not_enjoy_kayaking(X))<~>(does_not_practice_pilates(X))))))& (![X]:(room(X)=>(does_not_own_a_smart_tv(X))))& (![X]:(anywhere(X)=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))& (![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))& (~![X]:(~room(X)=>(((does_not_own_a_smart_tv(X))|(does_not_practice_graffiti_art(X))))))& (![X]:(room(X)=>(((does_not_practice_pilates(X))<~>(does_not_write_poetry(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(does_not_enjoy_kayaking(X)))))

% SZS status Unsatisfiable for 4403983307089009483726470 % SZS output start Proof for 4403983307089009483726470 48. ! [X0] : (room(X0) => ~predj(X0)) [input p4] 50. ~! [X0] : (room(X0) => (~predp(X0) | ~preda(X0))) [input p6] 51. ! [X0] : (room(X0) => (~predd(X0) <~> ~predh(X0))) [input p7] 56. ! [X0] : (room(X0) => (~predh(X0) <~> ~predp(X0))) [input p12] 57. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room [input hypothesis] 61. ~! [X0] : (room(X0) => ~predp(X0)) [pure predicate removal 50] 65. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [pure predicate removal 57] 141. ! [X0] : (~predj(X0) | ~room(X0)) [ennf transformation 48] 143. ? [X0] : (predp(X0) & room(X0)) [ennf transformation 61] 144. ! [X0] : ((~predd(X0) <~> ~predh(X0)) | ~room(X0)) [ennf transformation 51] 148. ! [X0] : ((~predh(X0) <~> ~predp(X0)) | ~room(X0)) [ennf transformation 56] 149. ! [X0] : ((~predd(X0) | predj(X0)) | ~room(X0)) [ennf transformation 65] 150. ! [X0] : (~predd(X0) | predj(X0) | ~room(X0)) [flattening 149] 163. ? [X0] : (predp(X0) & room(X0)) => (predp(sK4) & room(sK4)) [choice axiom] 164. predp(sK4) & room(sK4) [skolemisation 143,163] 165. ! [X0] : (((predh(X0) | predd(X0)) & (~predh(X0) | ~predd(X0))) | ~room(X0)) [nnf transformation 144] 168. ! [X0] : (((predp(X0) | predh(X0)) & (~predp(X0) | ~predh(X0))) | ~room(X0)) [nnf transformation 148] 262. ~predj(X0) | ~room(X0) [cnf transformation 141] 265. room(sK4) [cnf transformation 164] 266. predp(sK4) [cnf transformation 164] 268. ~room(X0) | predd(X0) | predh(X0) [cnf transformation 165] 273. ~predh(X0) | ~predp(X0) | ~room(X0) [cnf transformation 168] 275. ~predd(X0) | predj(X0) | ~room(X0) [cnf transformation 150] 329. ~predd(X0) | ~room(X0) [subsumption resolution 275,262] 364. predd(sK4) | predh(sK4) [resolution 268,265] 367. 16 <=> predh(sK4) [avatar definition] 369. predh(sK4) <- (16) [avatar component clause 367] 371. 17 <=> predd(sK4) [avatar definition] 373. predd(sK4) <- (17) [avatar component clause 371] 374. 16 | 17 [avatar split clause 364,371,367] 392. ~predp(sK4) | ~room(sK4) <- (16) [resolution 369,273] 394. ~room(sK4) <- (16) [subsumption resolution 392,266] 395. $false <- (16) [subsumption resolution 394,265] 396. ~16 [avatar contradiction clause 395] 397. ~room(sK4) <- (17) [resolution 373,329] 398. $false <- (17) [subsumption resolution 397,265] 399. ~17 [avatar contradiction clause 398] 400. $false [avatar sat refutation 374,396,399] % SZS output end Proof for 4403983307089009483726470 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If "everyone outside the room is not hated by Sarah and is not liked by Sarah" then "everyone in the room is not liked by Debra" otherwise "if someone either is not hated by Stephen or is not liked by Stephen but not both then he/she either is not liked by Debra or is not hated by Stephen but not both and vice versa". "Everyone in the room is not liked by Sarah" only if "everyone in the room is not hated by Guy". "Everyone in the room either is not liked by Debra or is not liked by Stephen but not both" only if "everyone in the room neither is not liked by Stephen nor is not liked by Sarah". Everyone in the room is not hated by Stephen. Everyone in the room is not hated by Debra and is not liked by Debra. If someone is not hated by Stephen and is not hated by Debra then he/she neither is not hated by Debra nor is not liked by Guy and vice versa.

Everyone in the room hates Guy.

entailment

(there_is_a_room)& (((![X]:(~room(X)=>(((~hate(X,sarah))&(~like(X,sarah))))))=>(![X]:(room(X)=>(~like(X,debra)))))&((~(![X]:(~room(X)=>(((~hate(X,sarah))&(~like(X,sarah)))))))=>((![X]:((((~hate(X,stephen))<~>(~like(X,stephen))))<=>(((~like(X,debra))<~>(~hate(X,stephen)))))))))& ((![X]:(room(X)=>(~like(X,sarah))))=>(![X]:(room(X)=>(~hate(X,guy)))))& ((![X]:(room(X)=>(((~like(X,debra))<~>(~like(X,stephen))))))=>(![X]:(room(X)=>(~((~like(X,stephen))|(~like(X,sarah)))))))& (~(![X]:(room(X)=>(~((~hate(X,debra))|(~hate(X,guy))))))=>(![X]:(anywhere(X)=>(((~like(X,debra))&(~hate(X,guy)))))))& (![X]:(room(X)=>(((~hate(X,guy))|(~like(X,stephen))))))& (![X]:(room(X)=>(~hate(X,stephen))))& (![X]:(room(X)=>(((~hate(X,debra))&(~like(X,debra))))))& ((![X]:((((~hate(X,stephen))&(~hate(X,debra))))<=>(~((~hate(X,debra))|(~like(X,guy)))))))& (![X]:(room(X)=>(~like(X,debra))))& ((![X]:((((~hate(X,debra))|(~hate(X,stephen))))<=>(~((~like(X,sarah))|(~hate(X,sarah)))))))

(there_is_a_room)& ![X]:(room(X)=>(hate(guy,X)))

% SZS status Unsatisfiable for 1155602920867582194316124 % SZS output start Proof for 1155602920867582194316124 44. there_is_a_room [input p0] 50. ! [X0] : (room(X0) => ~hate(X0,fred)) [input p6] 51. ! [X0] : (room(X0) => (~like(X0,mary) & ~hate(X0,mary))) [input p7] 52. ! [X0] : ((~hate(X0,mary) & ~hate(X0,fred)) <=> ~(~like(X0,paul) | ~hate(X0,mary))) [input p8] 55. ~(! [X0] : (room(X0) => hate(paul,X0)) & there_is_a_room) [input hypothesis] 139. ! [X0] : (~hate(X0,fred) | ~room(X0)) [ennf transformation 50] 140. ! [X0] : ((~like(X0,mary) & ~hate(X0,mary)) | ~room(X0)) [ennf transformation 51] 141. ! [X0] : ((~hate(X0,mary) & ~hate(X0,fred)) <=> (like(X0,paul) & hate(X0,mary))) [ennf transformation 52] 144. ? [X0] : (~hate(paul,X0) & room(X0)) | ~there_is_a_room [ennf transformation 55] 162. ! [X0] : (((~hate(X0,mary) & ~hate(X0,fred)) | (~like(X0,paul) | ~hate(X0,mary))) & ((like(X0,paul) & hate(X0,mary)) | (hate(X0,mary) | hate(X0,fred)))) [nnf transformation 141] 163. ! [X0] : (((~hate(X0,mary) & ~hate(X0,fred)) | ~like(X0,paul) | ~hate(X0,mary)) & ((like(X0,paul) & hate(X0,mary)) | hate(X0,mary) | hate(X0,fred))) [flattening 162] 166. ? [X0] : (~hate(paul,X0) & room(X0)) => (~hate(paul,sK4) & room(sK4)) [choice axiom] 167. (~hate(paul,sK4) & room(sK4)) | ~there_is_a_room [skolemisation 144,166] 251. there_is_a_room [cnf transformation 44] 277. ~hate(X0,fred) | ~room(X0) [cnf transformation 139] 278. ~hate(X0,mary) | ~room(X0) [cnf transformation 140] 280. hate(X0,mary) | hate(X0,mary) | hate(X0,fred) [cnf transformation 163] 290. room(sK4) | ~there_is_a_room [cnf transformation 167] 292. hate(X0,fred) | hate(X0,mary) [duplicate literal removal 280] 403. room(sK4) [subsumption resolution 290,251] 426. hate(X0,mary) | ~room(X0) [resolution 292,277] 436. ~room(X0) [subsumption resolution 426,278] 440. $false [resolution 436,403] % SZS output end Proof for 1155602920867582194316124 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Solomon, Yolanda, Louis, Marion, Ruby are the only persons in the room. Yolanda knows morse code. Someone in the room has a curated collection of mid-century modern furniture. If someone does not own a telescope then he/she travels domestically frequently and vice versa. Everyone in the room is a client of Meta if they is not a client of Meta and watches fantasy movies and vice versa. Louis knows morse code.

Solomon watches fantasy movies.

contradiction

room(solomon)&room(yolanda)&room(louis)&room(marion)&room(ruby)&(![X]:(room(X)=>(X='solomon'|X='yolanda'|X='louis'|X='marion'|X='ruby')))& (knows_morse_code(yolanda))& (?[X]:(room(X)&(has_a_curated_collection_of_mid-century_modern_furniture(X))))& ((![X]:((does_not_own_a_telescope(X))<=>(travels_domestically_frequently(X)))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))<=>(((is_not_a_client_of_Meta(X))&(watches_fantasy_movies(X))))))))& (knows_morse_code(louis))& ((![X]:((has_completed_a_triathlon(X))=>(travels_domestically_frequently(X)))))& ((![X]:((is_a_craft_beer_aficionado(X))<=>(is_allergic_to_anything(X)))))& (((does_not_use_contact_lenses(louis))|(is_a_client_of_LVMH(louis))))& (![X]:(room(X)=>(((uses_contact_lenses(X))<=>(is_a_client_of_LVMH(X))))))& ((![X]:((is_a_craft_beer_aficionado(X))=>(owns_a_telescope(X)))))& (~((creates_augmented_reality_experiences_for_mobile_applications(solomon))|(has_a_curated_collection_of_mid-century_modern_furniture(solomon))))& (![X]:(room(X)=>(((((has_a_curated_collection_of_mid-century_modern_furniture(X))|(collects_antique_clocks(X))))=>(practices_urban_gardening(X))))))& (owns_a_telescope(solomon))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X)&makes_intricate_hand-cut_paper_art_for_exhibitions(Y))&(X!=Y))))& (~![X]:(room(X)=>(((owns_a_telescope(X))=>(watches_fantasy_movies(X))))))

room(solomon)&room(yolanda)&room(louis)&room(marion)&room(ruby)&(![X]:(room(X)=>(X='solomon'|X='yolanda'|X='louis'|X='marion'|X='ruby')))& watches_fantasy_movies(solomon)

% SZS status Unsatisfiable for 2502281607963165835337770 % SZS output start Proof for 2502281607963165835337770 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (predw(X0) <=> (predc(X0) & ~predw(X0)))) [input p4] 60. predc(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 147. ! [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] 148. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147] 149. ! [X0] : ((predw(X0) <=> (predc(X0) & ~predw(X0))) | ~room(X0)) [ennf transformation 48] 153. predc(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 154. predc(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 153] 158. ! [X0] : (((predw(X0) | (~predc(X0) | predw(X0))) & ((predc(X0) & ~predw(X0)) | ~predw(X0))) | ~room(X0)) [nnf transformation 149] 159. ! [X0] : (((predw(X0) | ~predc(X0) | predw(X0)) & ((predc(X0) & ~predw(X0)) | ~predw(X0))) | ~room(X0)) [flattening 158] 245. room(mary) [cnf transformation 148] 253. ~predw(X0) | ~predw(X0) | ~room(X0) [cnf transformation 159] 255. predw(X0) | ~predc(X0) | predw(X0) | ~room(X0) [cnf transformation 159] 269. predc(mary) [cnf transformation 154] 270. ~predw(X0) | ~room(X0) [duplicate literal removal 253] 271. ~predc(X0) | predw(X0) | ~room(X0) [duplicate literal removal 255] 281. predw(mary) | ~room(mary) [resolution 271,269] 282. predw(mary) [subsumption resolution 281,245] 284. ~room(mary) [resolution 282,270] 285. $false [subsumption resolution 284,245] % SZS output end Proof for 2502281607963165835337770 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Richard is the only person in the room. If Richard writes in-depth travel guides for off-the-beaten-path destinations then Richard participates in citizen science projects related to wildlife monitoring. If someone enjoys spelunking, participates in citizen science projects related to wildlife monitoring and enjoys deep-sea diving and exploring underwater caves then he/she participates in citizen science projects related to wildlife monitoring unless Richard hosts a popular podcast about emerging technologies. If it is not the case that Richard writes in-depth travel guides for off-the-beaten-path destinations then Richard enjoys spelunking or is a Linux enthusiast or both. Richard regularly contributes to tech forums and online communities if at least one person in the room enjoys stand-up paddleboarding. Richard either regularly contributes to tech forums and online communities or writes in-depth travel guides for off-the-beaten-path destinations but not both. Richard enjoys stand-up paddleboarding. Someone outside the room enjoys stand-up paddleboarding. If someone collects first edition books then he/she enjoys deep-sea diving and exploring underwater caves and vice versa. Richard hosts a popular podcast about emerging technologies.

Richard enjoys spelunking.

neutral

room(richard)&(![X]:(room(X)=>(X='richard')))& ((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(richard))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(richard)))& (~(hosts_a_popular_podcast_about_emerging_technologies(richard))=>((![X]:((((enjoys_spelunking(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& ((~(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(richard)))=>(((enjoys_spelunking(richard))|(is_a_Linux_enthusiast(richard)))))& ((((?[X]:(room(X)&enjoys_stand-up_paddleboarding(X)))))=>(regularly_contributes_to_tech_forums_and_online_communities(richard)))& (((regularly_contributes_to_tech_forums_and_online_communities(richard))<~>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(richard))))& (enjoys_stand-up_paddleboarding(richard))& (?[X]:(~room(X)&(enjoys_stand-up_paddleboarding(X))))& ((![X]:((collects_first_edition_books(X))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))& (hosts_a_popular_podcast_about_emerging_technologies(richard))& (~(owns_a_significant_collection_of_rare_gemstones_and_minerals(richard)))& (((enjoys_deep-sea_diving_and_exploring_underwater_caves(richard))<~>(composes_and_performs_experimental_electronic_music(richard))))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(richard))& (~((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(richard))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(richard))))& ((is_a_scotch_connoisseur(richard))&(regularly_contributes_to_tech_forums_and_online_communities(richard)))& (((?[X]:(room(X)&collects_first_edition_books(X)))))& (collects_first_edition_books(richard))& (is_a_Linux_enthusiast(richard))& ((![X]:((collects_rare_minerals(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))

room(richard)&(![X]:(room(X)=>(X='richard')))& enjoys_spelunking(richard)

Mike, Linda, Oma are the only persons in the room. It is true that someone in the room is not a generous creative curious quiet tourist if it is true that at least one person in the room is not a kind tourist. More than one person anywhere is not a strong happy quiet creative european if at least one person outside the room neither is not a patient tourist nor is not a wise european. Only one person outside the room is not a patient tourist if someone in the room is not calm. Someone in the room neither is tall nor is not a tall happy patient quiet person if someone outside the room is not a humble tourist.

Linda and Mike are not a funny quiet tall generous wise persons.

neutral

room(mike)&room(linda)&room(oma)&(![X]:(room(X)=>(X='mike'|X='linda'|X='oma')))& ((((?[X]:(room(X)&~(kind(X)&tourist(X))))))=>(?[X]:(room(X)&(~(generous(X)&creative(X)&curious(X)&quiet(X)&tourist(X))))))& ((((?[X]:(~room(X)&~((~(patient(X)&tourist(X)))|(~(wise(X)&european(X))))))))=>((?[X,Y]:(anywhere(X)&anywhere(Y)&(~(strong(X)&happy(X)&quiet(X)&creative(X)&european(X))&~(strong(Y)&happy(Y)&quiet(Y)&creative(Y)&european(Y)))&(X!=Y)))))& ((?[X]:(room(X)&(~calm(X))))=>(((?[X]:(~room(X)&~(patient(X)&tourist(X))))&(![X,Y]:((~room(X)&~room(Y)&(~(patient(X)&tourist(X)))&(~(patient(Y)&tourist(Y))))=>(X=Y))))))& ((?[X]:(~room(X)&(~(humble(X)&tourist(X)))))=>(?[X]:(room(X)&(~((tall(X))|(~(tall(X)&happy(X)&patient(X)&quiet(X)&person(X))))))))& ((?[X]:(room(X)&(~(wise(X)&european(X)))))=>(((?[X]:(room(X)&~(wise(X)&tourist(X))))&(![X,Y]:((room(X)&room(Y)&(~(wise(X)&tourist(X)))&(~(wise(Y)&tourist(Y))))=>(X=Y))))))& ((?[X]:(room(X)&(~(generous(X)&european(X)))))=>(?[X]:(room(X)&(~~curious(X)))))& ((((?[X]:(room(X)&~~~patient(X)))))=>(((?[X]:(room(X)&~(strong(X)&patient(X)&european(X)))))))& ((((?[X]:(anywhere(X)&~((~(tall(X)&person(X)))|(~(funny(X)&tourist(X))))))))=>(((?[X]:(anywhere(X)&~(kind(X)&european(X))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(~(kind(X)&european(X)))&(~(kind(Y)&european(Y))))=>(X=Y))))))& (((?[X]:(anywhere(X)&~(kind(X)&european(X))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(~(kind(X)&european(X)))&(~(kind(Y)&european(Y))))=>(X=Y)))))& (((?[X]:(room(X)&~(wise(X)&humble(X)&generous(X)&european(X))))&(![X,Y]:((room(X)&room(Y)&(~(wise(X)&humble(X)&generous(X)&european(X)))&(~(wise(Y)&humble(Y)&generous(Y)&european(Y))))=>(X=Y)))))& (((?[X]:(anywhere(X)&~(strong(X)&tourist(X))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(~(strong(X)&tourist(X)))&(~(strong(Y)&tourist(Y))))=>(X=Y)))))& (((?[X]:(~room(X)&~((~(patient(X)&tourist(X)))|(~(wise(X)&european(X))))))))& (((?[X]:(~room(X)&~(curious(X)&generous(X)&happy(X)&person(X))))))& (((?[X]:(room(X)&~old(X)))&(![X,Y]:((room(X)&room(Y)&(~old(X))&(~old(Y)))=>(X=Y)))))& (?[X]:(anywhere(X)&(strong(X))))& (((?[X]:(room(X)&creative(X)))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(~(wise(X)&creative(X)&strong(X)&happy(X)&person(X))&~(wise(Y)&creative(Y)&strong(Y)&happy(Y)&person(Y)))&(X!=Y))))& (?[X]:(room(X)&(~humble(X))))& ((?[X,Y]:(~room(X)&~room(Y)&(~(quiet(X)&european(X))&~(quiet(Y)&european(Y)))&(X!=Y))))& (((?[X]:(room(X)&tall(X)))&(![X,Y]:((room(X)&room(Y)&(tall(X))&(tall(Y)))=>(X=Y)))))& (?[X]:(room(X)&(~(patient(X)&tourist(X)))))& (?[X]:(room(X)&(old(X))))& (((?[X]:(room(X)&~(calm(X)&european(X))))))& (((?[X]:(room(X)&~(patient(X)&european(X))))))& (((?[X]:(room(X)&~(curious(X)&funny(X)&humble(X)&tourist(X))))&(![X,Y]:((room(X)&room(Y)&(~(curious(X)&funny(X)&humble(X)&tourist(X)))&(~(curious(Y)&funny(Y)&humble(Y)&tourist(Y))))=>(X=Y)))))& (((?[X]:(room(X)&~quiet(X)))&(![X,Y]:((room(X)&room(Y)&(~quiet(X))&(~quiet(Y)))=>(X=Y)))))& (((?[X]:(room(X)&~(brave(X)&european(X))))&(![X,Y]:((room(X)&room(Y)&(~(brave(X)&european(X)))&(~(brave(Y)&european(Y))))=>(X=Y)))))& (((?[X]:(anywhere(X)&~(tall(X)&humble(X)&tourist(X))))))& (?[X]:(room(X)&(~(creative(X)&european(X)))))

room(mike)&room(linda)&room(oma)&(![X]:(room(X)=>(X='mike'|X='linda'|X='oma')))& ~(funny(linda)&quiet(linda)&tall(linda)&generous(linda)&wise(linda)&person(linda))&~(funny(mike)&quiet(mike)&tall(mike)&generous(mike)&wise(mike)&person(mike))

Joseph is the only person in the room. If “Joseph enjoys writing detailed reviews of new and classic board games” then “Joseph is passionate about collecting and restoring classic cars”. If “Joseph streams on Twitch” then “Joseph works on fridays”. If “Joseph owns an Android phone” then “it is not the case that “Joseph practices zumba””. If “it is not the case that “it is not the case that “Joseph has a tattoo””” then “only one person in the room enjoys kayaking and exploring remote waterways”. If “Joseph regularly goes on multi-day backpacking trips in national parks” then “Joseph has a tattoo”. If “Joseph uses contact lenses” then “Joseph can play the guitar”. If “Joseph enjoys writing detailed reviews of new and classic board games” then “Joseph has a tattoo”. “Joseph practices digital art” only if “Joseph enjoys bird watching”. If “at least one person in the room can play the guitar” then “Joseph is a certified yoga instructor teaching classes weekly”. Either “Joseph plays as a goalkeeper for a local amateur soccer team” or “Joseph practices zumba” but not both. Joseph enjoys writing detailed reviews of new and classic board games.

Joseph is passionate about collecting and restoring classic cars.

entailment

room(joseph)&(![X]:(room(X)=>(X='joseph')))& ((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(joseph))=>(is_passionate_about_collecting_and_restoring_classic_cars(joseph)))& ((streams_on_Twitch(joseph))=>(works_on_fridays(joseph)))& ((owns_an_Android_phone(joseph))=>(~(practices_zumba(joseph))))& ((~(~(has_a_tattoo(joseph))))=>(((?[X]:(room(X)&enjoys_kayaking_and_exploring_remote_waterways(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_kayaking_and_exploring_remote_waterways(X))&(enjoys_kayaking_and_exploring_remote_waterways(Y)))=>(X=Y))))))& ((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(joseph))=>(has_a_tattoo(joseph)))& ((uses_contact_lenses(joseph))=>(can_play_the_guitar(joseph)))& ((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(joseph))=>(has_a_tattoo(joseph)))& ((practices_digital_art(joseph))=>(enjoys_bird_watching(joseph)))& ((((?[X]:(room(X)&can_play_the_guitar(X)))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(joseph)))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(joseph))<~>(practices_zumba(joseph)))& (can_play_the_guitar(joseph))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(joseph))& (is_a_certified_yoga_instructor_teaching_classes_weekly(joseph))& (enjoys_bird_watching(joseph))& (((?[X]:(anywhere(X)&enjoys_logic_puzzles(X)))))& (streams_on_Twitch(joseph))& (practices_zumba(joseph))& (has_a_tattoo(joseph))& (owns_a_3D_printer(joseph))& (competes_in_national_level_swimming_championships(joseph))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(joseph))& ((![X]:((is_passionate_about_collecting_and_restoring_classic_cars(X))<=>(owns_a_3D_printer(X)))))& (uses_contact_lenses(joseph))& (~(owns_an_Android_phone(joseph)))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(joseph))

room(joseph)&(![X]:(room(X)=>(X='joseph')))& is_passionate_about_collecting_and_restoring_classic_cars(joseph)

% SZS status Unsatisfiable for 3403172500393955221329758 % SZS output start Proof for 3403172500393955221329758 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. predy(mary) => predn(mary) [input p1] 56. predy(mary) [input p12] 70. ~(predn(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 159. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 160. predn(mary) | ~predy(mary) [ennf transformation 45] 165. ~predn(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 70] 171. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 172. ~predn(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 165,171] 253. room(mary) [cnf transformation 159] 254. ~room(X0) | mary = X0 [cnf transformation 159] 255. predn(mary) | ~predy(mary) [cnf transformation 160] 263. predy(mary) [cnf transformation 56] 270. ~predn(mary) | room(sK1) | ~room(mary) [cnf transformation 172] 271. ~predn(mary) | mary != sK1 | ~room(mary) [cnf transformation 172] 273. 1 <=> predy(mary) [avatar definition] 277. 2 <=> predn(mary) [avatar definition] 280. ~1 | 2 [avatar split clause 255,277,273] 315. 1 [avatar split clause 263,273] 319. ~predn(mary) | mary != sK1 [subsumption resolution 271,253] 321. 10 <=> mary = sK1 [avatar definition] 323. mary != sK1 <- (~10) [avatar component clause 321] 324. ~10 | ~2 [avatar split clause 319,277,321] 325. ~predn(mary) | room(sK1) [subsumption resolution 270,253] 327. 11 <=> room(sK1) [avatar definition] 329. room(sK1) <- (11) [avatar component clause 327] 330. 11 | ~2 [avatar split clause 325,277,327] 335. mary = sK1 <- (11) [resolution 254,329] 338. $false <- (~10, 11) [subsumption resolution 335,323] 339. 10 | ~11 [avatar contradiction clause 338] 340. $false [avatar sat refutation 280,315,324,330,339] % SZS output end Proof for 3403172500393955221329758 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s % ------------------------------ % ------------------------------

Janice is the only person in the room. Everyone in the room who writes and illustrates their own graphic novels collects limited-edition art prints from contemporary artists and collects luxury watches. Everyone in the room frequently participates in hackathons and coding competitions. Janice has a specialized collection of handmade artisan pottery. Not everyone in the room who does not practice pilates has a tattoo. Everyone in the room does not enjoy wildlife photography or has a tattoo. Everyone in the room has a specialized collection of handmade artisan pottery if they does not enjoy wildlife photography. At least one person in the room owns an extensive assortment of vintage comic book memorabilia and designs and sews custom cosplay costumes for conventions. Everyone in the room who owns an Android phone does enjoy mountain biking. Everyone in the room who owns an extensive assortment of vintage comic book memorabilia writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room who writes in-depth travel guides for off-the-beaten-path destinations collects rare and antique scientific instruments. Everyone in the room does not collect rare and antique scientific instruments or collects rare and antique scientific instruments. Everyone anywhere does not collect luxury watches or does not collect rare and antique scientific instruments. Everyone in the room frequently participates in hackathons and coding competitions if they does not collect luxury watches.

Janice collects rare and antique scientific instruments.

entailment

room(janice)&(![X]:(room(X)=>(X='janice')))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))&(collects_luxury_watches(X))))))))& (![X]:(room(X)=>(frequently_participates_in_hackathons_and_coding_competitions(X))))& (has_a_specialized_collection_of_handmade_artisan_pottery(janice))& (~![X]:(room(X)=>(((does_not_practice_pilates(X))=>(has_a_tattoo(X))))))& (![X]:(room(X)=>(((has_a_tattoo(X))|(does_not_enjoy_wildlife_photography(X))))))& (![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (((?[X]:(room(X)&((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))))& (![X]:(room(X)=>(((owns_an_Android_phone(X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (![X]:(anywhere(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(does_not_collect_luxury_watches(X))))))& (![X]:(room(X)=>(((does_not_collect_luxury_watches(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))

room(janice)&(![X]:(room(X)=>(X='janice')))& collects_rare_and_antique_scientific_instruments(janice)

% SZS status Unsatisfiable for 143385074666498296572443 % SZS output start Proof for 143385074666498296572443 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 51. ? [X0] : (predt(X0) & predk(X0) & room(X0)) [input p7] 53. ! [X0] : (room(X0) => (predk(X0) => predf(X0))) [input p9] 54. ! [X0] : (room(X0) => (predf(X0) => predn(X0))) [input p10] 58. ~(predn(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 60. ? [X0] : (predk(X0) & room(X0)) [pure predicate removal 51] 143. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 145. ! [X0] : ((predf(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 53] 146. ! [X0] : (predf(X0) | ~predk(X0) | ~room(X0)) [flattening 145] 147. ! [X0] : ((predn(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 54] 148. ! [X0] : (predn(X0) | ~predf(X0) | ~room(X0)) [flattening 147] 151. ~predn(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 58] 155. ? [X0] : (predk(X0) & room(X0)) => (predk(sK1) & room(sK1)) [choice axiom] 156. predk(sK1) & room(sK1) [skolemisation 60,155] 157. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom] 158. ~predn(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 151,157] 239. room(mary) [cnf transformation 143] 240. ~room(X0) | mary = X0 [cnf transformation 143] 242. room(sK1) [cnf transformation 156] 243. predk(sK1) [cnf transformation 156] 244. ~predk(X0) | predf(X0) | ~room(X0) [cnf transformation 146] 245. ~predf(X0) | predn(X0) | ~room(X0) [cnf transformation 148] 247. ~predn(mary) | room(sK2) | ~room(mary) [cnf transformation 158] 248. ~predn(mary) | mary != sK2 | ~room(mary) [cnf transformation 158] 249. ~predn(mary) | mary != sK2 [subsumption resolution 248,239] 251. 1 <=> mary = sK2 [avatar definition] 253. mary != sK2 <- (~1) [avatar component clause 251] 255. 2 <=> predn(mary) [avatar definition] 258. ~1 | ~2 [avatar split clause 249,255,251] 259. ~predn(mary) | room(sK2) [subsumption resolution 247,239] 261. 3 <=> room(sK2) [avatar definition] 263. room(sK2) <- (3) [avatar component clause 261] 264. 3 | ~2 [avatar split clause 259,255,261] 267. mary = sK1 [resolution 240,242] 270. predk(mary) [backward demodulation 243,267] 271. predf(mary) | ~room(mary) [resolution 244,270] 272. predf(mary) [subsumption resolution 271,239] 273. predn(mary) | ~room(mary) [resolution 245,272] 277. predn(mary) [subsumption resolution 273,239] 278. 2 [avatar split clause 277,255] 279. mary = sK2 <- (3) [resolution 263,240] 280. $false <- (~1, 3) [subsumption resolution 279,253] 281. 1 | ~3 [avatar contradiction clause 280] 282. $false [avatar sat refutation 258,264,278,281] % SZS output end Proof for 143385074666498296572443 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.029 s % ------------------------------ % ------------------------------

There is a room. If “everyone anywhere is not a cybersecurity expert or is not a drone photographer” then “everyone in the room is a cybersecurity expert, does not enjoy spelunking or frequently participates in hackathons and coding competitions if they is not a cybersecurity expert”. Everyone in the room travels domestically frequently. No one in the room enjoys virtual reality gaming if they does not enjoy virtual reality gaming. No one anywhere frequently participates in hackathons and coding competitions if they is a drone photographer, has lived in exactly three countries or does not enjoy stand-up paddleboarding.

Everyone in the room frequently participates in hackathons and coding competitions.

contradiction

(there_is_a_room)& ((![X]:(anywhere(X)=>(((is_not_a_drone_photographer(X))|(is_not_a_cybersecurity_expert(X))))))=>(![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))=>(((is_a_cybersecurity_expert(X))|(does_not_enjoy_spelunking(X))|(frequently_participates_in_hackathons_and_coding_competitions(X)))))))))& (![X]:(room(X)=>(travels_domestically_frequently(X))))& (~?[X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(participates_in_long-distance_cycling_events_across_the_country(X))))& (![X]:(anywhere(X)=>(((is_not_a_drone_photographer(X))|(is_not_a_cybersecurity_expert(X))))))& (((?[X]:(room(X)&does_not_enjoy_wildlife_photography(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_enjoy_wildlife_photography(X))&(does_not_enjoy_wildlife_photography(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((does_not_make_homemade_pastries(X))|(cannot_play_the_harmonica(X))))))& (![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))=>(enjoys_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(collects_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((((collects_rare_minerals(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))=>(is_not_a_drone_photographer(X))))))& (?[X]:(room(X)&(collects_vintage_vinyl_records(X))))& (![X]:(room(X)=>(((((does_enjoy_trail_running(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(has_lived_in_exactly_three_countries(X))))=>(enjoys_stand-up_paddleboarding(X))))))& (((?[X]:(room(X)&is_not_a_drone_photographer(X)))&(![X,Y]:((room(X)&room(Y)&(is_not_a_drone_photographer(X))&(is_not_a_drone_photographer(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((makes_homemade_pastries(X))=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& ((![X]:((does_not_enjoy_mountain_biking(X))<=>(does_not_have_lived_in_exactly_three_countries(X)))))& (~?[X]:(anywhere(X)=>(((((is_a_drone_photographer(X))|(has_lived_in_exactly_three_countries(X))|(does_not_enjoy_stand-up_paddleboarding(X))))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(does_not_enjoy_spelunking(X))))))

(there_is_a_room)& ![X]:(room(X)=>(frequently_participates_in_hackathons_and_coding_competitions(X)))

% SZS status Unsatisfiable for 3838342803343030064905917 % SZS output start Proof for 3838342803343030064905917 47. ~? [X0] : (room(X0) => (~predp(X0) => predp(X0))) [input p3] 61. ~? [X0] : (anywhere(X0) => ((~predn(X0) | predm(X0) | predh(X0)) => predc(X0))) [input p17] 63. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 77. ~? [X0] : ~room(X0) [pure predicate removal 47] 84. ~? [X0] : ((~predn(X0) | predm(X0) | predh(X0)) => predc(X0)) [pure predicate removal 61] 86. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 63] 158. ! [X0] : room(X0) [ennf transformation 77] 167. ! [X0] : (~predc(X0) & (~predn(X0) | predm(X0) | predh(X0))) [ennf transformation 84] 168. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 86] 256. room(X0) [cnf transformation 158] 267. ~predc(X0) [cnf transformation 167] 268. predc(X0) | ~room(X0) [cnf transformation 168] 276. ~room(X0) [subsumption resolution 268,267] 277. $false [subsumption resolution 276,256] % SZS output end Proof for 3838342803343030064905917 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Lisa is the only person in the room. If “everyone in the room does not have a curated collection of mid-century modern furniture or does not stream on Twitch” then “everyone in the room practices archery”. “Everyone outside the room does not have a pet dog only if they volunteers for local environmental conservation projects” if “no one anywhere does not have a pet dog or enjoys spelunking”. Either “everyone in the room practices archery or does not compete in national level swimming championships” or “Lisa enjoys skydiving” but not both. If “Lisa does not travel domestically frequently” then “everyone in the room is a client of Costco, owns a 3D printer or enjoys spelunking if they competes in national level swimming championships”. “Lisa streams on Twitch” unless “everyone in the room reads mystery novels or is not an expert in identifying and foraging wild edible plants”. If “Lisa does not work as a freelance web developer specializing in e-commerce sites” then “no one in the room enjoys watercolor painting if they works as a freelance web developer specializing in e-commerce sites” otherwise “Lisa does not stream on Twitch”. If “everyone in the room owns a 3D printer or does not practice yoga” then “Lisa does not practice yoga”. If “Lisa does not practice yoga” then “everyone anywhere is a client of Costco only if they reads mystery novels”. If “everyone in the room does not collect antique clocks or is not a client of Costco” then “Lisa who works as a freelance web developer specializing in e-commerce sites has a curated collection of mid-century modern furniture”. If someone does not enjoy kayaking, is a client of Costco or regularly contributes to tech forums and online communities then he/she neither is a client of Costco nor enjoys watercolor painting and vice versa. Lisa enjoys spelunking. Lisa practices archery. Everyone anywhere neither practices archery nor competes in national level swimming championships if they is a client of Meta. If someone collects antique clocks and does practice yoga then he/she travels domestically frequently and vice versa. It is true that “someone outside the room collects antique clocks”. Everyone in the room who builds model airplanes enjoys origami. Lisa enjoys kayaking. Lisa does not stream on Twitch.

Not everyone in the room enjoys kayaking.

contradiction

room(lisa)&(![X]:(room(X)=>(X='lisa')))& ((![X]:(room(X)=>(((does_not_stream_on_Twitch(X))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))=>(![X]:(room(X)=>(practices_archery(X)))))& ((~?[X]:(anywhere(X)=>(((enjoys_spelunking(X))|(does_not_have_a_pet_dog(X))))))=>(![X]:(~room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))<=(does_not_have_a_pet_dog(X)))))))& ((![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))|(practices_archery(X))))))<~>(enjoys_skydiving(lisa)))& ((does_not_travel_domestically_frequently(lisa))=>(![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(((is_a_client_of_Costco(X))|(owns_a_3D_printer(X))|(enjoys_spelunking(X)))))))))& (~(![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(reads_mystery_novels(X))))))=>(streams_on_Twitch(lisa)))& (((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(lisa))=>(~?[X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(enjoys_watercolor_painting(X)))))))&((~(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(lisa)))=>(does_not_stream_on_Twitch(lisa))))& (((![X]:(room(X)=>(((does_not_practice_yoga(X))|(owns_a_3D_printer(X))))))=>(does_not_practice_yoga(lisa)))& ((does_not_practice_yoga(lisa))=>(![X]:(anywhere(X)=>(((reads_mystery_novels(X))<=(is_a_client_of_Costco(X))))))))& ((![X]:(room(X)=>(((is_not_a_client_of_Costco(X))|(does_not_collect_antique_clocks(X))))))=>((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(lisa))&(has_a_curated_collection_of_mid-century_modern_furniture(lisa))))& ((![X]:((((does_not_enjoy_kayaking(X))|(is_a_client_of_Costco(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))<=>(~((is_a_client_of_Costco(X))|(enjoys_watercolor_painting(X)))))))& (enjoys_spelunking(lisa))& (practices_archery(lisa))& (![X]:(anywhere(X)=>(((is_a_client_of_Meta(X))=>(~((practices_archery(X))|(competes_in_national_level_swimming_championships(X))))))))& ((![X]:((((collects_antique_clocks(X))&(does_practice_yoga(X))))<=>(travels_domestically_frequently(X)))))& (?[X]:(~room(X)&(collects_antique_clocks(X))))& (![X]:(room(X)=>(((builds_model_airplanes(X))=>(enjoys_origami(X))))))& (enjoys_kayaking(lisa))& (does_not_stream_on_Twitch(lisa))

room(lisa)&(![X]:(room(X)=>(X='lisa')))& ~![X]:(room(X)=>(enjoys_kayaking(X)))

% SZS status Unsatisfiable for 5622569878903639791140014 % SZS output start Proof for 5622569878903639791140014 44. ~predo(mary) & predd(mary) & ! [X0] : (room(X0) => (preda(X0) => predg(X0))) & ? [X0] : (predu(X0) & ~room(X0)) & ! [X0] : ((predv(X0) & predu(X0)) <=> predw(X0)) & ! [X0] : (anywhere(X0) => (predt(X0) => ~(predk(X0) | predn(X0)))) & predn(mary) & predr(mary) & ! [X0] : ((predx(X0) | predp(X0) | ~predd(X0)) <=> ~(predl(X0) | predp(X0))) & (! [X0] : (room(X0) => (~predu(X0) | ~predp(X0))) => (predh(mary) & predf(mary))) & (~predv(mary) => ! [X0] : (anywhere(X0) => (predp(X0) => prede(X0)))) & (! [X0] : (room(X0) => (predb(X0) | ~predv(X0))) => ~predv(mary)) & (predf(mary) => ~predo(mary)) & (~predf(mary) => ~? [X0] : (room(X0) => (predf(X0) => predl(X0)))) & (~! [X0] : (room(X0) => (prede(X0) | ~preds(X0))) => predo(mary)) & (~predw(mary) => ! [X0] : (room(X0) => (predk(X0) => (predr(X0) | predb(X0) | predp(X0))))) & (! [X0] : (room(X0) => (predn(X0) | ~predk(X0))) <~> predz(mary)) & (~? [X0] : (anywhere(X0) => (~predj(X0) | predr(X0))) => ! [X0] : (~room(X0) => (~predj(X0) => predy(X0)))) & (! [X0] : (room(X0) => (~predh(X0) | ~predo(X0))) => ! [X0] : (room(X0) => predn(X0))) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ~! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 46. ~predo(mary) & predd(mary) & ! [X0] : (room(X0) => (preda(X0) => predg(X0))) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : ((predv(X2) & predu(X2)) <=> predw(X2)) & ! [X3] : (anywhere(X3) => (predt(X3) => ~(predk(X3) | predn(X3)))) & predn(mary) & predr(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4)) <=> ~(predl(X4) | predp(X4))) & (! [X5] : (room(X5) => (~predu(X5) | ~predp(X5))) => (predh(mary) & predf(mary))) & (~predv(mary) => ! [X6] : (anywhere(X6) => (predp(X6) => prede(X6)))) & (! [X7] : (room(X7) => (predb(X7) | ~predv(X7))) => ~predv(mary)) & (predf(mary) => ~predo(mary)) & (~predf(mary) => ~? [X8] : (room(X8) => (predf(X8) => predl(X8)))) & (~! [X9] : (room(X9) => (prede(X9) | ~preds(X9))) => predo(mary)) & (~predw(mary) => ! [X10] : (room(X10) => (predk(X10) => (predr(X10) | predb(X10) | predp(X10))))) & (! [X11] : (room(X11) => (predn(X11) | ~predk(X11))) <~> predz(mary)) & (~? [X12] : (anywhere(X12) => (~predj(X12) | predr(X12))) => ! [X13] : (~room(X13) => (~predj(X13) => predy(X13)))) & (! [X14] : (room(X14) => (~predh(X14) | ~predo(X14))) => ! [X15] : (room(X15) => predn(X15))) & ! [X16] : (room(X16) => mary = X16) & room(mary) [rectify 44] 47. ~! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => mary = X1) & room(mary) [rectify 45] 48. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : ((predv(X2) & predu(X2)) <=> predw(X2)) & ! [X3] : (anywhere(X3) => (predt(X3) => ~(predk(X3) | predn(X3)))) & predn(mary) & predr(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4)) <=> ~(predl(X4) | predp(X4))) & (! [X5] : (room(X5) => (~predu(X5) | ~predp(X5))) => (predh(mary) & predf(mary))) & (~predv(mary) => ! [X6] : (anywhere(X6) => (predp(X6) => prede(X6)))) & (! [X7] : (room(X7) => (predb(X7) | ~predv(X7))) => ~predv(mary)) & (predf(mary) => ~predo(mary)) & (~predf(mary) => ~? [X8] : (room(X8) => (predf(X8) => predl(X8)))) & (~! [X9] : (room(X9) => (prede(X9) | ~preds(X9))) => predo(mary)) & (~predw(mary) => ! [X10] : (room(X10) => (predk(X10) => (predr(X10) | predb(X10) | predp(X10))))) & (! [X11] : (room(X11) => (predn(X11) | ~predk(X11))) <~> predz(mary)) & (~? [X12] : (anywhere(X12) => (~predj(X12) | predr(X12))) => ! [X13] : (~room(X13) => (~predj(X13) => predy(X13)))) & (! [X14] : (room(X14) => (~predh(X14) | ~predo(X14))) => ! [X15] : (room(X15) => predn(X15))) & ! [X16] : (room(X16) => mary = X16) & room(mary) [pure predicate removal 46] 49. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : ((predv(X2) & predu(X2)) <=> predw(X2)) & predn(mary) & predr(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4)) <=> ~(predl(X4) | predp(X4))) & (! [X5] : (room(X5) => (~predu(X5) | ~predp(X5))) => (predh(mary) & predf(mary))) & (~predv(mary) => ! [X6] : (anywhere(X6) => (predp(X6) => prede(X6)))) & (! [X7] : (room(X7) => (predb(X7) | ~predv(X7))) => ~predv(mary)) & (predf(mary) => ~predo(mary)) & (~predf(mary) => ~? [X8] : (room(X8) => (predf(X8) => predl(X8)))) & (~! [X9] : (room(X9) => (prede(X9) | ~preds(X9))) => predo(mary)) & (~predw(mary) => ! [X10] : (room(X10) => (predk(X10) => (predr(X10) | predb(X10) | predp(X10))))) & (! [X11] : (room(X11) => (predn(X11) | ~predk(X11))) <~> predz(mary)) & (~? [X12] : (anywhere(X12) => (~predj(X12) | predr(X12))) => ! [X13] : (~room(X13) => (~predj(X13) => predy(X13)))) & (! [X14] : (room(X14) => (~predh(X14) | ~predo(X14))) => ! [X15] : (room(X15) => predn(X15))) & ! [X16] : (room(X16) => mary = X16) & room(mary) [pure predicate removal 48] 50. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : ((predv(X2) & predu(X2)) <=> predw(X2)) & predn(mary) & predr(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4)) <=> ~(predl(X4) | predp(X4))) & (! [X5] : (room(X5) => (~predu(X5) | ~predp(X5))) => (predh(mary) & predf(mary))) & (! [X7] : (room(X7) => (predb(X7) | ~predv(X7))) => ~predv(mary)) & (predf(mary) => ~predo(mary)) & (~predf(mary) => ~? [X8] : (room(X8) => (predf(X8) => predl(X8)))) & (~predw(mary) => ! [X10] : (room(X10) => (predk(X10) => (predr(X10) | predb(X10) | predp(X10))))) & (! [X11] : (room(X11) => (predn(X11) | ~predk(X11))) <~> predz(mary)) & (~? [X12] : (anywhere(X12) => (~predj(X12) | predr(X12))) => ! [X13] : (~room(X13) => (~predj(X13) => predy(X13)))) & (! [X14] : (room(X14) => (~predh(X14) | ~predo(X14))) => ! [X15] : (room(X15) => predn(X15))) & ! [X16] : (room(X16) => mary = X16) & room(mary) [pure predicate removal 49] 51. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : ((predv(X2) & predu(X2)) <=> predw(X2)) & predn(mary) & predr(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4)) <=> ~(predl(X4) | predp(X4))) & (! [X5] : (room(X5) => (~predu(X5) | ~predp(X5))) => (predh(mary) & predf(mary))) & (! [X7] : (room(X7) => (predb(X7) | ~predv(X7))) => ~predv(mary)) & (predf(mary) => ~predo(mary)) & (~predf(mary) => ~? [X8] : (room(X8) => (predf(X8) => predl(X8)))) & (~predw(mary) => ! [X10] : (room(X10) => (predk(X10) => (predr(X10) | predb(X10) | predp(X10))))) & (! [X11] : (room(X11) => (predn(X11) | ~predk(X11))) <~> predz(mary)) & (! [X14] : (room(X14) => (~predh(X14) | ~predo(X14))) => ! [X15] : (room(X15) => predn(X15))) & ! [X16] : (room(X16) => mary = X16) & room(mary) [pure predicate removal 50] 53. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : ((predv(X2) & predu(X2)) <=> predw(X2)) & predn(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4)) <=> ~(predl(X4) | predp(X4))) & (! [X5] : (room(X5) => (~predu(X5) | ~predp(X5))) => (predh(mary) & predf(mary))) & (! [X7] : (room(X7) => (predb(X7) | ~predv(X7))) => ~predv(mary)) & (predf(mary) => ~predo(mary)) & (~predf(mary) => ~? [X8] : (room(X8) => (predf(X8) => predl(X8)))) & (! [X11] : (room(X11) => (predn(X11) | ~predk(X11))) <~> predz(mary)) & (! [X14] : (room(X14) => (~predh(X14) | ~predo(X14))) => ! [X15] : (room(X15) => predn(X15))) & ! [X16] : (room(X16) => mary = X16) & room(mary) [pure predicate removal 51] 54. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : ((predv(X2) & predu(X2)) <=> predw(X2)) & predn(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4)) <=> ~(predl(X4) | predp(X4))) & (! [X5] : (room(X5) => (~predu(X5) | ~predp(X5))) => (predh(mary) & predf(mary))) & (! [X7] : (room(X7) => ~predv(X7)) => ~predv(mary)) & (predf(mary) => ~predo(mary)) & (~predf(mary) => ~? [X8] : (room(X8) => (predf(X8) => predl(X8)))) & (! [X11] : (room(X11) => (predn(X11) | ~predk(X11))) <~> predz(mary)) & (! [X14] : (room(X14) => (~predh(X14) | ~predo(X14))) => ! [X15] : (room(X15) => predn(X15))) & ! [X16] : (room(X16) => mary = X16) & room(mary) [pure predicate removal 53] 55. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : ((predv(X2) & predu(X2)) <=> predw(X2)) & predn(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4)) <=> ~(predl(X4) | predp(X4))) & (! [X5] : (room(X5) => (~predu(X5) | ~predp(X5))) => predf(mary)) & (! [X7] : (room(X7) => ~predv(X7)) => ~predv(mary)) & (predf(mary) => ~predo(mary)) & (~predf(mary) => ~? [X8] : (room(X8) => (predf(X8) => predl(X8)))) & (! [X11] : (room(X11) => (predn(X11) | ~predk(X11))) <~> predz(mary)) & (! [X14] : (room(X14) => ~predo(X14)) => ! [X15] : (room(X15) => predn(X15))) & ! [X16] : (room(X16) => mary = X16) & room(mary) [pure predicate removal 54] 127. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : ((predv(X2) & predu(X2)) <=> predw(X2)) & predn(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4)) <=> (~predl(X4) & ~predp(X4))) & (predf(mary) | ? [X5] : ((predu(X5) & predp(X5)) & room(X5))) & (~predv(mary) | ? [X7] : (predv(X7) & room(X7))) & (~predo(mary) | ~predf(mary)) & (! [X8] : ((~predl(X8) & predf(X8)) & room(X8)) | predf(mary)) & (! [X11] : ((predn(X11) | ~predk(X11)) | ~room(X11)) <~> predz(mary)) & (! [X15] : (predn(X15) | ~room(X15)) | ? [X14] : (predo(X14) & room(X14))) & ! [X16] : (mary = X16 | ~room(X16)) & room(mary) [ennf transformation 55] 128. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : ((predv(X2) & predu(X2)) <=> predw(X2)) & predn(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4)) <=> (~predl(X4) & ~predp(X4))) & (predf(mary) | ? [X5] : (predu(X5) & predp(X5) & room(X5))) & (~predv(mary) | ? [X7] : (predv(X7) & room(X7))) & (~predo(mary) | ~predf(mary)) & (! [X8] : (~predl(X8) & predf(X8) & room(X8)) | predf(mary)) & (! [X11] : (predn(X11) | ~predk(X11) | ~room(X11)) <~> predz(mary)) & (! [X15] : (predn(X15) | ~room(X15)) | ? [X14] : (predo(X14) & room(X14))) & ! [X16] : (mary = X16 | ~room(X16)) & room(mary) [flattening 127] 129. ? [X0] : (~predd(X0) & room(X0)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [ennf transformation 47] 131. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : (((predv(X2) & predu(X2)) | ~predw(X2)) & (predw(X2) | (~predv(X2) | ~predu(X2)))) & predn(mary) & ! [X4] : (((predx(X4) | predp(X4) | ~predd(X4)) | (predl(X4) | predp(X4))) & ((~predl(X4) & ~predp(X4)) | (~predx(X4) & ~predp(X4) & predd(X4)))) & (predf(mary) | ? [X5] : (predu(X5) & predp(X5) & room(X5))) & (~predv(mary) | ? [X7] : (predv(X7) & room(X7))) & (~predo(mary) | ~predf(mary)) & (! [X8] : (~predl(X8) & predf(X8) & room(X8)) | predf(mary)) & ((~predz(mary) | ? [X11] : (~predn(X11) & predk(X11) & room(X11))) & (predz(mary) | ! [X11] : (predn(X11) | ~predk(X11) | ~room(X11)))) & (! [X15] : (predn(X15) | ~room(X15)) | ? [X14] : (predo(X14) & room(X14))) & ! [X16] : (mary = X16 | ~room(X16)) & room(mary) [nnf transformation 128] 132. ~predo(mary) & predd(mary) & ? [X1] : (predu(X1) & ~room(X1)) & ! [X2] : (((predv(X2) & predu(X2)) | ~predw(X2)) & (predw(X2) | ~predv(X2) | ~predu(X2))) & predn(mary) & ! [X4] : ((predx(X4) | predp(X4) | ~predd(X4) | predl(X4) | predp(X4)) & ((~predl(X4) & ~predp(X4)) | (~predx(X4) & ~predp(X4) & predd(X4)))) & (predf(mary) | ? [X5] : (predu(X5) & predp(X5) & room(X5))) & (~predv(mary) | ? [X7] : (predv(X7) & room(X7))) & (~predo(mary) | ~predf(mary)) & (! [X8] : (~predl(X8) & predf(X8) & room(X8)) | predf(mary)) & (~predz(mary) | ? [X11] : (~predn(X11) & predk(X11) & room(X11))) & (predz(mary) | ! [X11] : (predn(X11) | ~predk(X11) | ~room(X11))) & (! [X15] : (predn(X15) | ~room(X15)) | ? [X14] : (predo(X14) & room(X14))) & ! [X16] : (mary = X16 | ~room(X16)) & room(mary) [flattening 131] 133. ~predo(mary) & predd(mary) & ? [X0] : (predu(X0) & ~room(X0)) & ! [X1] : (((predv(X1) & predu(X1)) | ~predw(X1)) & (predw(X1) | ~predv(X1) | ~predu(X1))) & predn(mary) & ! [X2] : ((predx(X2) | predp(X2) | ~predd(X2) | predl(X2) | predp(X2)) & ((~predl(X2) & ~predp(X2)) | (~predx(X2) & ~predp(X2) & predd(X2)))) & (predf(mary) | ? [X3] : (predu(X3) & predp(X3) & room(X3))) & (~predv(mary) | ? [X4] : (predv(X4) & room(X4))) & (~predo(mary) | ~predf(mary)) & (! [X5] : (~predl(X5) & predf(X5) & room(X5)) | predf(mary)) & (~predz(mary) | ? [X6] : (~predn(X6) & predk(X6) & room(X6))) & (predz(mary) | ! [X7] : (predn(X7) | ~predk(X7) | ~room(X7))) & (! [X8] : (predn(X8) | ~room(X8)) | ? [X9] : (predo(X9) & room(X9))) & ! [X10] : (mary = X10 | ~room(X10)) & room(mary) [rectify 132] 134. ? [X0] : (predu(X0) & ~room(X0)) => (predu(sK0) & ~room(sK0)) [choice axiom] 135. ? [X3] : (predu(X3) & predp(X3) & room(X3)) => (predu(sK1) & predp(sK1) & room(sK1)) [choice axiom] 136. ? [X4] : (predv(X4) & room(X4)) => (predv(sK2) & room(sK2)) [choice axiom] 137. ? [X6] : (~predn(X6) & predk(X6) & room(X6)) => (~predn(sK3) & predk(sK3) & room(sK3)) [choice axiom] 138. ? [X9] : (predo(X9) & room(X9)) => (predo(sK4) & room(sK4)) [choice axiom] 139. ~predo(mary) & predd(mary) & (predu(sK0) & ~room(sK0)) & ! [X1] : (((predv(X1) & predu(X1)) | ~predw(X1)) & (predw(X1) | ~predv(X1) | ~predu(X1))) & predn(mary) & ! [X2] : ((predx(X2) | predp(X2) | ~predd(X2) | predl(X2) | predp(X2)) & ((~predl(X2) & ~predp(X2)) | (~predx(X2) & ~predp(X2) & predd(X2)))) & (predf(mary) | (predu(sK1) & predp(sK1) & room(sK1))) & (~predv(mary) | (predv(sK2) & room(sK2))) & (~predo(mary) | ~predf(mary)) & (! [X5] : (~predl(X5) & predf(X5) & room(X5)) | predf(mary)) & (~predz(mary) | (~predn(sK3) & predk(sK3) & room(sK3))) & (predz(mary) | ! [X7] : (predn(X7) | ~predk(X7) | ~room(X7))) & (! [X8] : (predn(X8) | ~room(X8)) | (predo(sK4) & room(sK4))) & ! [X10] : (mary = X10 | ~room(X10)) & room(mary) [skolemisation 133,138,137,136,135,134] 140. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK5) & room(sK5)) [choice axiom] 141. (~predd(sK5) & room(sK5)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [skolemisation 129,140] 223. ~room(X10) | mary = X10 [cnf transformation 139] 252. predd(mary) [cnf transformation 139] 256. room(sK5) [cnf transformation 141] 257. ~predd(sK5) [cnf transformation 141] 345. mary = sK5 [resolution 223,256] 349. ~predd(mary) [backward demodulation 257,345] 350. $false [subsumption resolution 349,252] % SZS output end Proof for 5622569878903639791140014 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Chris, Sandra, Kenneth, Anthony are the only persons in the room. If “everyone in the room does not enjoy kayaking and exploring remote waterways or owns an Android phone” then “Sandra is a certified yoga instructor teaching classes weekly”. If someone does not collect modern art then he/she hosts regular workshops on creative writing. Everyone in the room does not enjoy kayaking and exploring remote waterways or owns an Android phone. Everyone in the room can play the harmonica. Everyone in the room who enjoys kayaking and exploring remote waterways does not maintain a large, organic vegetable garden year-round. Everyone in the room who plays video games or plays the violin or both enjoys macrame and is a drone photographer. Everyone outside the room is a coffee connoisseur if they enjoys macrame and is a drone photographer. Everyone in the room does not enjoy mountain biking. Someone in the room enjoys writing detailed reviews of new and classic board games. Everyone in the room who develops open-source software projects in their free time cannot play the harmonica. Everyone anywhere does not create bespoke furniture pieces from reclaimed wood. Everyone in the room plays the violin if they does not create bespoke furniture pieces from reclaimed wood.

Kenneth enjoys macrame.

entailment

room(chris)&room(sandra)&room(kenneth)&room(anthony)&(![X]:(room(X)=>(X='chris'|X='sandra'|X='kenneth'|X='anthony')))& ((![X]:(room(X)=>(((owns_an_Android_phone(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(sandra)))& ((![X]:((does_not_collect_modern_art(X))=>(hosts_regular_workshops_on_creative_writing(X)))))& (![X]:(room(X)=>(((owns_an_Android_phone(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(can_play_the_harmonica(X))))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(((((plays_video_games(X))|(plays_the_violin(X))))=>(((enjoys_macrame(X))&(is_a_drone_photographer(X))))))))& (![X]:(~room(X)=>(((((enjoys_macrame(X))&(is_a_drone_photographer(X))))=>(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(does_not_enjoy_mountain_biking(X))))& (?[X]:(room(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(cannot_play_the_harmonica(X))))))& ((((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(kenneth))|(hosts_regular_workshops_on_creative_writing(kenneth))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(kenneth))))&(enjoys_kayaking_and_exploring_remote_waterways(kenneth)))& (?[X]:(room(X)&(is_a_coffee_connoisseur(X))))& (enjoys_kayaking_and_exploring_remote_waterways(sandra))& ((((creates_large-scale_murals_for_public_art_installations(kenneth))|(practices_kickboxing(kenneth))))&(does_not_play_video_games(kenneth)))& (![X]:(~room(X)=>(((travels_domestically_frequently(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (?[X]:(~room(X)&(((is_a_drone_photographer(X))&(hosts_regular_workshops_on_creative_writing(X))))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(streams_on_Twitch(X))))))& (does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(sandra))& (![X]:(anywhere(X)=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))& (![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(enjoys_salsa_dancing(X))))& (![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(((does_not_play_the_violin(X))|(practices_kickboxing(X))))))))& (![X]:(~room(X)=>(((((does_not_play_the_violin(X))|(practices_kickboxing(X))))=>(streams_on_Twitch(X))))))

room(chris)&room(sandra)&room(kenneth)&room(anthony)&(![X]:(room(X)=>(X='chris'|X='sandra'|X='kenneth'|X='anthony')))& enjoys_macrame(kenneth)

% SZS status Unsatisfiable for 6391819307015002522416192 % SZS output start Proof for 6391819307015002522416192 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] 50. ! [X0] : (room(X0) => ((predk(X0) | predf(X0)) => (predq(X0) & preda(X0)))) [input p6] 63. ! [X0] : (anywhere(X0) => ~preds(X0)) [input p19] 64. ! [X0] : (room(X0) => (~preds(X0) => predk(X0))) [input p20] 68. ~(preda(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 85. ! [X0] : (room(X0) => ((predk(X0) | predf(X0)) => preda(X0))) [pure predicate removal 50] 88. ! [X0] : (room(X0) => (predk(X0) => preda(X0))) [pure predicate removal 85] 165. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 166. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 165] 167. ! [X0] : ((preda(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 88] 168. ! [X0] : (preda(X0) | ~predk(X0) | ~room(X0)) [flattening 167] 169. ! [X0] : (~preds(X0) | ~anywhere(X0)) [ennf transformation 63] 170. ! [X0] : ((predk(X0) | preds(X0)) | ~room(X0)) [ennf transformation 64] 171. ! [X0] : (predk(X0) | preds(X0) | ~room(X0)) [flattening 170] 172. ~preda(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 68] 173. ~preda(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 172] 181. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 182. ~preda(fred) | (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,181] 183. anywhere(X0) [cnf transformation 5] 264. room(mary) [cnf transformation 166] 265. room(paul) [cnf transformation 166] 266. room(fred) [cnf transformation 166] 267. room(alice) [cnf transformation 166] 268. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 166] 269. ~predk(X0) | preda(X0) | ~room(X0) [cnf transformation 168] 273. ~preds(X0) | ~anywhere(X0) [cnf transformation 169] 274. predk(X0) | preds(X0) | ~room(X0) [cnf transformation 171] 275. ~preda(fred) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 182] 276. ~preda(fred) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 182] 277. ~preda(fred) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 182] 278. ~preda(fred) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 182] 279. ~preda(fred) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 182] 280. ~preds(X0) [subsumption resolution 273,183] 281. ~room(X0) | predk(X0) [subsumption resolution 274,280] 282. ~preda(fred) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,267] 283. ~preda(fred) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 282,266] 284. ~preda(fred) | alice != sK3 | ~room(mary) [subsumption resolution 283,265] 285. ~preda(fred) | alice != sK3 [subsumption resolution 284,264] 287. 1 <=> alice = sK3 [avatar definition] 289. alice != sK3 <- (~1) [avatar component clause 287] 291. 2 <=> preda(fred) [avatar definition] 294. ~1 | ~2 [avatar split clause 285,291,287] 295. ~preda(fred) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,267] 296. ~preda(fred) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 295,266] 297. ~preda(fred) | fred != sK3 | ~room(mary) [subsumption resolution 296,265] 298. ~preda(fred) | fred != sK3 [subsumption resolution 297,264] 300. 3 <=> fred = sK3 [avatar definition] 302. fred != sK3 <- (~3) [avatar component clause 300] 303. ~3 | ~2 [avatar split clause 298,291,300] 304. ~preda(fred) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,267] 305. ~preda(fred) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 304,266] 306. ~preda(fred) | paul != sK3 | ~room(mary) [subsumption resolution 305,265] 307. ~preda(fred) | paul != sK3 [subsumption resolution 306,264] 309. 4 <=> paul = sK3 [avatar definition] 311. paul != sK3 <- (~4) [avatar component clause 309] 312. ~4 | ~2 [avatar split clause 307,291,309] 313. ~preda(fred) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,267] 314. ~preda(fred) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 313,266] 315. ~preda(fred) | mary != sK3 | ~room(mary) [subsumption resolution 314,265] 316. ~preda(fred) | mary != sK3 [subsumption resolution 315,264] 318. 5 <=> mary = sK3 [avatar definition] 320. mary != sK3 <- (~5) [avatar component clause 318] 321. ~5 | ~2 [avatar split clause 316,291,318] 322. ~preda(fred) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,267] 323. ~preda(fred) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 322,266] 324. ~preda(fred) | room(sK3) | ~room(mary) [subsumption resolution 323,265] 325. ~preda(fred) | room(sK3) [subsumption resolution 324,264] 327. 6 <=> room(sK3) [avatar definition] 329. room(sK3) <- (6) [avatar component clause 327] 330. 6 | ~2 [avatar split clause 325,291,327] 333. predk(fred) [resolution 281,266] 341. preda(fred) | ~room(fred) [resolution 333,269] 345. preda(fred) [subsumption resolution 341,266] 346. 2 [avatar split clause 345,291] 404. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (6) [resolution 268,329] 439. paul = sK3 | mary = sK3 | alice = sK3 <- (~3, 6) [subsumption resolution 404,302] 440. mary = sK3 | alice = sK3 <- (~3, ~4, 6) [subsumption resolution 439,311] 441. alice = sK3 <- (~3, ~4, ~5, 6) [subsumption resolution 440,320] 442. $false <- (~1, ~3, ~4, ~5, 6) [subsumption resolution 441,289] 443. 1 | 3 | 4 | 5 | ~6 [avatar contradiction clause 442] 444. $false [avatar sat refutation 294,303,312,321,330,346,443] % SZS output end Proof for 6391819307015002522416192 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Edith, Deloise, Thomas, Teresa, Judith are the only persons in the room. Everyone in the room who collects historical artifacts related to ancient civilizations cannot play the flute. Everyone anywhere cannot play the flute only if they enjoys salsa dancing or own a television or both. Teresa owns a telescope. Everyone in the room either is a craft beer aficionado or can play the piano but not both if they is not a Linux enthusiast. Teresa has a specialized collection of handmade artisan pottery or does not own a television or both. If someone does not collect rare minerals then he/she is a craft beer aficionado and vice versa. Everyone in the room enjoys making ceramics only if they knows morse code. It is not the case that Edith does not enjoy making ceramics. Everyone outside the room does not travel domestically frequently if they plays eSports competitively. Only one person in the room collects historical artifacts related to ancient civilizations. Everyone in the room who can play the piano and knows morse code collects historical artifacts related to ancient civilizations. Teresa cannot play the flute. If someone does not have a specialized collection of handmade artisan pottery then he/she travels domestically frequently and vice versa. Judith cannot play the flute. If someone enjoys salsa dancing then he/she can play the flute and vice versa. Teresa does enjoy mountain biking. Thomas plays eSports competitively. Everyone in the room who is not a craft beer aficionado can play the flute, travels domestically frequently and does enjoy trail running. Thomas collects comic books and has a specialized collection of handmade artisan pottery. Everyone outside the room who does enjoy mountain biking does enjoy trail running. Thomas cannot play the flute. If someone enjoys stand-up paddleboarding then he/she has completed a triathlon. If someone is a Linux enthusiast then he/she can play the piano.

Edith collects rare minerals.

contradiction

room(edith)&room(deloise)&room(thomas)&room(teresa)&room(judith)&(![X]:(room(X)=>(X='edith'|X='deloise'|X='thomas'|X='teresa'|X='judith')))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(cannot_play_the_flute(X))))))& (![X]:(anywhere(X)=>(((((enjoys_salsa_dancing(X))|(own_a_television(X))))<=(cannot_play_the_flute(X))))))& (owns_a_telescope(teresa))& (![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))=>(((is_a_craft_beer_aficionado(X))<~>(can_play_the_piano(X))))))))& (((has_a_specialized_collection_of_handmade_artisan_pottery(teresa))|(does_not_own_a_television(teresa))))& ((![X]:((does_not_collect_rare_minerals(X))<=>(is_a_craft_beer_aficionado(X)))))& (![X]:(room(X)=>(((knows_morse_code(X))<=(enjoys_making_ceramics(X))))))& (~(does_not_enjoy_making_ceramics(edith)))& (![X]:(~room(X)=>(((plays_eSports_competitively(X))=>(does_not_travel_domestically_frequently(X))))))& (((?[X]:(room(X)&collects_historical_artifacts_related_to_ancient_civilizations(X)))&(![X,Y]:((room(X)&room(Y)&(collects_historical_artifacts_related_to_ancient_civilizations(X))&(collects_historical_artifacts_related_to_ancient_civilizations(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((((can_play_the_piano(X))&(knows_morse_code(X))))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (cannot_play_the_flute(teresa))& ((![X]:((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))<=>(travels_domestically_frequently(X)))))& (cannot_play_the_flute(judith))& ((![X]:((enjoys_salsa_dancing(X))<=>(can_play_the_flute(X)))))& (does_enjoy_mountain_biking(teresa))& (plays_eSports_competitively(thomas))& (![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))=>(((can_play_the_flute(X))&(travels_domestically_frequently(X))&(does_enjoy_trail_running(X))))))))& (((collects_comic_books(thomas))&(has_a_specialized_collection_of_handmade_artisan_pottery(thomas))))& (![X]:(~room(X)=>(((does_enjoy_mountain_biking(X))=>(does_enjoy_trail_running(X))))))& (cannot_play_the_flute(thomas))& ((![X]:((enjoys_stand-up_paddleboarding(X))=>(has_completed_a_triathlon(X)))))& ((![X]:((is_a_Linux_enthusiast(X))=>(can_play_the_piano(X)))))

room(edith)&room(deloise)&room(thomas)&room(teresa)&room(judith)&(![X]:(room(X)=>(X='edith'|X='deloise'|X='thomas'|X='teresa'|X='judith')))& collects_rare_minerals(edith)

% SZS status Unsatisfiable for 1858239351697903015293336 % SZS output start Proof for 1858239351697903015293336 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (predd(X0) => ~predz(X0))) [input p1] 48. ! [X0] : (room(X0) => (~predg(X0) => (predu(X0) <~> predn(X0)))) [input p4] 50. ! [X0] : (~predh(X0) <=> predu(X0)) [input p6] 51. ! [X0] : (room(X0) => (preds(X0) => predb(X0))) [input p7] 52. preds(mary) [input p8] 55. ! [X0] : (room(X0) => ((predb(X0) & predn(X0)) => predd(X0))) [input p11] 62. ! [X0] : (room(X0) => (~predu(X0) => (predq(X0) & prede(X0) & predz(X0)))) [input p18] 67. ! [X0] : (predg(X0) => predn(X0)) [input p23] 68. predh(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] 70. ! [X0] : (predu(X0) => ~predh(X0)) [unused predicate definition removal 50] 75. ! [X0] : (room(X0) => (~predu(X0) => (prede(X0) & predz(X0)))) [pure predicate removal 62] 150. ! [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] 151. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 150] 152. ! [X0] : ((~predz(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 45] 153. ! [X0] : (~predz(X0) | ~predd(X0) | ~room(X0)) [flattening 152] 156. ! [X0] : (((predu(X0) <~> predn(X0)) | predg(X0)) | ~room(X0)) [ennf transformation 48] 157. ! [X0] : ((predu(X0) <~> predn(X0)) | predg(X0) | ~room(X0)) [flattening 156] 158. ! [X0] : (~predh(X0) | ~predu(X0)) [ennf transformation 70] 159. ! [X0] : ((predb(X0) | ~preds(X0)) | ~room(X0)) [ennf transformation 51] 160. ! [X0] : (predb(X0) | ~preds(X0) | ~room(X0)) [flattening 159] 165. ! [X0] : ((predd(X0) | (~predb(X0) | ~predn(X0))) | ~room(X0)) [ennf transformation 55] 166. ! [X0] : (predd(X0) | ~predb(X0) | ~predn(X0) | ~room(X0)) [flattening 165] 169. ! [X0] : (((prede(X0) & predz(X0)) | predu(X0)) | ~room(X0)) [ennf transformation 75] 170. ! [X0] : ((prede(X0) & predz(X0)) | predu(X0) | ~room(X0)) [flattening 169] 171. ! [X0] : (predn(X0) | ~predg(X0)) [ennf transformation 67] 172. predh(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 68] 173. predh(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 172] 175. ! [X0] : (((~predn(X0) | ~predu(X0)) & (predn(X0) | predu(X0))) | predg(X0) | ~room(X0)) [nnf transformation 157] 259. room(mary) [cnf transformation 151] 265. ~predz(X0) | ~predd(X0) | ~room(X0) [cnf transformation 153] 267. ~room(X0) | predu(X0) | predg(X0) | predn(X0) [cnf transformation 175] 270. ~predh(X0) | ~predu(X0) [cnf transformation 158] 271. ~preds(X0) | predb(X0) | ~room(X0) [cnf transformation 160] 272. preds(mary) [cnf transformation 52] 277. ~predb(X0) | predd(X0) | ~predn(X0) | ~room(X0) [cnf transformation 166] 283. ~room(X0) | predu(X0) | predz(X0) [cnf transformation 170] 287. ~predg(X0) | predn(X0) [cnf transformation 171] 294. predh(mary) [cnf transformation 173] 305. ~predu(mary) [resolution 270,294] 306. predb(mary) | ~room(mary) [resolution 271,272] 307. predb(mary) [subsumption resolution 306,259] 308. predu(mary) | predz(mary) [resolution 283,259] 314. predz(mary) [subsumption resolution 308,305] 336. ~predd(mary) | ~room(mary) [resolution 314,265] 337. ~predd(mary) [subsumption resolution 336,259] 359. predu(mary) | predg(mary) | predn(mary) [resolution 267,259] 365. predg(mary) | predn(mary) [subsumption resolution 359,305] 366. predn(mary) [subsumption resolution 365,287] 367. predd(mary) | ~predn(mary) | ~room(mary) [resolution 277,307] 368. ~predn(mary) | ~room(mary) [subsumption resolution 367,337] 369. ~room(mary) [subsumption resolution 368,366] 370. $false [subsumption resolution 369,259] % SZS output end Proof for 1858239351697903015293336 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Henry is the only person in the room. Henry has a vast collection of first-edition science fiction novels. Henry is a chess master who participates in national tournaments. Henry collects action figures, practices urban gardening and reads mystery novels. Henry enjoys writing detailed reviews of new and classic board games. It is not the case that “Henry is an avid hiker”. Henry who is a scotch connoisseur or has a specialized collection of handmade artisan pottery or both frequently participates in hackathons and coding competitions. Henry volunteers for local environmental conservation projects. Henry practices urban gardening. Henry owns a 3D printer. Henry either owns a microscope or enjoys kayaking and exploring remote waterways but not both. Henry owns a microscope. Only one person in the room frequently participates in hackathons and coding competitions or reads mystery novels or both. Henry enjoys windsurfing. It is not the case that “Henry writes poetry”. Everyone in the room reads mystery novels or is not a skilled home brewer experimenting with craft beer recipes. If someone enjoys kayaking and exploring remote waterways then he/she neither is a chess master who participates in national tournaments nor has a vast collection of first-edition science fiction novels. Henry either has a vast collection of first-edition science fiction novels or enjoys kayaking and exploring remote waterways but not both. Henry either enjoys kayaking and exploring remote waterways or enjoys rooftop gardening but not both. Henry does enjoy mountain biking. Henry who does enjoy mountain biking practices urban gardening. Henry enjoys coding in Python. Henry has a specialized collection of handmade artisan pottery. Henry plays as a goalkeeper for a local amateur soccer team.

It is not the case that “it is not the case that “Henry is a scotch connoisseur””.

neutral

room(henry)&(![X]:(room(X)=>(X='henry')))& (has_a_vast_collection_of_first-edition_science_fiction_novels(henry))& (is_a_chess_master_who_participates_in_national_tournaments(henry))& (((collects_action_figures(henry))&(practices_urban_gardening(henry))&(reads_mystery_novels(henry))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(henry))& (~(is_an_avid_hiker(henry)))& ((((is_a_scotch_connoisseur(henry))|(has_a_specialized_collection_of_handmade_artisan_pottery(henry))))&(frequently_participates_in_hackathons_and_coding_competitions(henry)))& (volunteers_for_local_environmental_conservation_projects(henry))& (practices_urban_gardening(henry))& (owns_a_3D_printer(henry))& (((owns_a_microscope(henry))<~>(enjoys_kayaking_and_exploring_remote_waterways(henry))))& (owns_a_microscope(henry))& (((?[X]:(room(X)&((frequently_participates_in_hackathons_and_coding_competitions(X))|(reads_mystery_novels(X)))))&(![X,Y]:((room(X)&room(Y)&(((frequently_participates_in_hackathons_and_coding_competitions(X))|(reads_mystery_novels(X))))&(((frequently_participates_in_hackathons_and_coding_competitions(Y))|(reads_mystery_novels(Y)))))=>(X=Y)))))& (enjoys_windsurfing(henry))& (~(writes_poetry(henry)))& (![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(reads_mystery_novels(X))))))& ((![X]:((enjoys_kayaking_and_exploring_remote_waterways(X))=>(~((is_a_chess_master_who_participates_in_national_tournaments(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))& (((has_a_vast_collection_of_first-edition_science_fiction_novels(henry))<~>(enjoys_kayaking_and_exploring_remote_waterways(henry))))& (((enjoys_kayaking_and_exploring_remote_waterways(henry))<~>(enjoys_rooftop_gardening(henry))))& (does_enjoy_mountain_biking(henry))& ((does_enjoy_mountain_biking(henry))&(practices_urban_gardening(henry)))& (enjoys_coding_in_Python(henry))& (has_a_specialized_collection_of_handmade_artisan_pottery(henry))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(henry))

room(henry)&(![X]:(room(X)=>(X='henry')))& ~(~(is_a_scotch_connoisseur(henry)))

Daniel is the only person in the room. “Daniel does not write a travel blog” if “everyone in the room does not own a significant collection of rare gemstones and minerals or enjoys watercolor painting”. If “someone in the room watches fantasy movies” then “everyone outside the room who does not own a significant collection of rare gemstones and minerals does not watche fantasy movies” otherwise “Daniel who designs and sews custom cosplay costumes for conventions is not a cybersecurity expert”. If “Daniel enjoys coding in Python” then “Daniel bakes bread at home” otherwise “everyone in the room watches fantasy movies”. If “everyone in the room collects comic books or does not bake bread at home” then “everyone in the room who collects comic books does not write a travel blog, is allergic to anything or is a cybersecurity expert” otherwise “more than one person anywhere is a client of Costco”. If “no one anywhere is allergic to anything” then “everyone in the room does not bake bread at home if they is an amateur astronomer who builds and uses custom telescopes”. If “everyone anywhere enjoys writing detailed reviews of new and classic board games or does not enjoy deep-sea diving and exploring underwater caves” then “not everyone outside the room does not play the violin”. If “someone in the room is a cybersecurity expert and hosts themed dinner parties featuring gourmet home-cooked meals” then “Daniel creates YouTube content” otherwise “Daniel collects comic books”. Daniel enjoys spelunking. Everyone anywhere is allergic to anything if they is a client of Costco. Daniel does not bake bread at home. If someone is an active member of a local robotics club then he/she is not a dedicated volunteer for local community service projects and vice versa. Daniel either enjoys writing detailed reviews of new and classic board games or is an amateur astronomer who builds and uses custom telescopes but not both. Everyone in the room who is allergic to anything bakes bread at home. Everyone in the room who plays the violin is a dedicated volunteer for local community service projects.

Daniel enjoys writing detailed reviews of new and classic board games.

neutral

room(daniel)&(![X]:(room(X)=>(X='daniel')))& ((![X]:(room(X)=>(((enjoys_watercolor_painting(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))=>(does_not_write_a_travel_blog(daniel)))& (((?[X]:(room(X)&(watches_fantasy_movies(X))))=>(![X]:(~room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(does_not_watche_fantasy_movies(X)))))))&((~(?[X]:(room(X)&(watches_fantasy_movies(X)))))=>((designs_and_sews_custom_cosplay_costumes_for_conventions(daniel))&(is_not_a_cybersecurity_expert(daniel)))))& (((enjoys_coding_in_Python(daniel))=>(bakes_bread_at_home(daniel)))&((~(enjoys_coding_in_Python(daniel)))=>(![X]:(room(X)=>(watches_fantasy_movies(X))))))& (((![X]:(room(X)=>(((does_not_bake_bread_at_home(X))|(collects_comic_books(X))))))=>(![X]:(room(X)=>(((collects_comic_books(X))=>(((does_not_write_a_travel_blog(X))|(is_allergic_to_anything(X))|(is_a_cybersecurity_expert(X)))))))))&((~(![X]:(room(X)=>(((does_not_bake_bread_at_home(X))|(collects_comic_books(X)))))))=>((?[X,Y]:(anywhere(X)&anywhere(Y)&(is_a_client_of_Costco(X)&is_a_client_of_Costco(Y))&(X!=Y))))))& ((~?[X]:(anywhere(X)=>(is_allergic_to_anything(X))))=>(![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(does_not_bake_bread_at_home(X)))))))& ((![X]:(anywhere(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))=>(~![X]:(~room(X)=>(does_not_play_the_violin(X)))))& (((?[X]:(room(X)&(((is_a_cybersecurity_expert(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))=>(creates_YouTube_content(daniel)))&((~(?[X]:(room(X)&(((is_a_cybersecurity_expert(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))=>(collects_comic_books(daniel))))& (enjoys_spelunking(daniel))& (![X]:(anywhere(X)=>(((is_a_client_of_Costco(X))=>(is_allergic_to_anything(X))))))& (does_not_bake_bread_at_home(daniel))& ((![X]:((is_an_active_member_of_a_local_robotics_club(X))<=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X)))))& (((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(daniel))<~>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(daniel))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(daniel))& (enjoys_rooftop_gardening(daniel))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(creates_YouTube_content(X))))))& (((plays_the_violin(daniel))|(collects_comic_books(daniel))|(enjoys_spelunking(daniel))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(does_not_watche_fantasy_movies(X))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(writes_a_travel_blog(X))))))& (![X]:(~room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))=>(enjoys_coding_in_Python(X))))))

room(daniel)&(![X]:(room(X)=>(X='daniel')))& enjoys_writing_detailed_reviews_of_new_and_classic_board_games(daniel)

Ethan is the only person in the room. “Ethan collects rare and antique scientific instruments” if “everyone in the room is not an avid hiker or owns a smartwatch”. If someone does not have a saltwater aquarium then he/she owns a smartwatch. Everyone in the room who designs and sews custom cosplay costumes for conventions owns a 3D printer. Everyone in the room enjoys camping and organizing outdoor survival workshops if they collects antique clocks. Not everyone in the room does not own a telescope or enjoys camping and organizing outdoor survival workshops. Ethan regularly contributes to tech forums and online communities. Everyone outside the room owns an Android phone or enjoys watercolor painting or both. Everyone in the room who enjoys windsurfing has a saltwater aquarium, does not enjoy windsurfing or owns a smartwatch. Ethan who writes in-depth travel guides for off-the-beaten-path destinations is a cybersecurity expert. Ethan owns a significant collection of rare gemstones and minerals. Ethan is a dedicated volunteer for local community service projects. If someone is an avid hiker then he/she enjoys windsurfing and vice versa. Everyone in the room who creates YouTube content or is an amateur astronomer who builds and uses custom telescopes or both is a tea enthusiast. Everyone in the room enjoys watercolor painting or does not write in-depth travel guides for off-the-beaten-path destinations.

Ethan enjoys watercolor painting.

entailment

room(ethan)&(![X]:(room(X)=>(X='ethan')))& ((![X]:(room(X)=>(((owns_a_smartwatch(X))|(is_not_an_avid_hiker(X))))))=>(collects_rare_and_antique_scientific_instruments(ethan)))& ((![X]:((does_not_have_a_saltwater_aquarium(X))=>(owns_a_smartwatch(X)))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (~![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_own_a_telescope(X))))))& (regularly_contributes_to_tech_forums_and_online_communities(ethan))& (![X]:(~room(X)=>(((owns_an_Android_phone(X))|(enjoys_watercolor_painting(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(((has_a_saltwater_aquarium(X))|(does_not_enjoy_windsurfing(X))|(owns_a_smartwatch(X))))))))& ((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(ethan))&(is_a_cybersecurity_expert(ethan)))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(ethan))& (is_a_dedicated_volunteer_for_local_community_service_projects(ethan))& ((![X]:((is_an_avid_hiker(X))<=>(enjoys_windsurfing(X)))))& (![X]:(room(X)=>(((((creates_YouTube_content(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(enjoys_watercolor_painting(X))))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(enjoys_landscape_photography(X))))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(has_a_saltwater_aquarium(X))))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))<=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))

room(ethan)&(![X]:(room(X)=>(X='ethan')))& enjoys_watercolor_painting(ethan)

% SZS status Unsatisfiable for 8914954612331926411457840 % SZS output start Proof for 8914954612331926411457840 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 53. predz(mary) & predi(mary) [input p9] 58. ! [X0] : (room(X0) => (predj(X0) | ~predi(X0))) [input p14] 62. ~(predj(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 68. predi(mary) [pure predicate removal 53] 154. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 156. ! [X0] : ((predj(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 58] 157. ! [X0] : (predj(X0) | ~predi(X0) | ~room(X0)) [flattening 156] 159. ~predj(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 62] 164. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 165. ~predj(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 159,164] 246. room(mary) [cnf transformation 154] 247. ~room(X0) | mary = X0 [cnf transformation 154] 249. predi(mary) [cnf transformation 68] 250. ~predi(X0) | predj(X0) | ~room(X0) [cnf transformation 157] 253. ~predj(mary) | room(sK1) | ~room(mary) [cnf transformation 165] 254. ~predj(mary) | mary != sK1 | ~room(mary) [cnf transformation 165] 255. ~predj(mary) | mary != sK1 [subsumption resolution 254,246] 257. 1 <=> mary = sK1 [avatar definition] 259. mary != sK1 <- (~1) [avatar component clause 257] 261. 2 <=> predj(mary) [avatar definition] 264. ~1 | ~2 [avatar split clause 255,261,257] 265. ~predj(mary) | room(sK1) [subsumption resolution 253,246] 267. 3 <=> room(sK1) [avatar definition] 269. room(sK1) <- (3) [avatar component clause 267] 270. 3 | ~2 [avatar split clause 265,261,267] 274. predj(mary) | ~room(mary) [resolution 250,249] 278. predj(mary) [subsumption resolution 274,246] 279. 2 [avatar split clause 278,261] 280. mary = sK1 <- (3) [resolution 269,247] 281. $false <- (~1, 3) [subsumption resolution 280,259] 282. 1 | ~3 [avatar contradiction clause 281] 283. $false [avatar sat refutation 264,270,279,282] % SZS output end Proof for 8914954612331926411457840 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s % ------------------------------ % ------------------------------

Sean, Elaine are the only persons in the room. “Everyone in the room does not own a smart tv or uses a Windows laptop” if “everyone in the room is not a certified yoga instructor teaching classes weekly or owns a significant collection of rare gemstones and minerals” and vice versa. If “everyone anywhere does not enjoy writing detailed reviews of new and classic board games or does not enjoy skydiving” then “if someone practices and performs acrobatic dance routines then he/she has a saltwater aquarium and vice versa” otherwise “not everyone in the room hosts regular game nights featuring complex strategy games or drives a hybrid car or both if they is a coffee connoisseur”. If “everyone in the room does not practice and performs acrobatic dance routines or enjoys stargazing” then “everyone in the room plays as a goalkeeper for a local amateur soccer team if they does not practice and performs acrobatic dance routines”. “Everyone in the room is a coffee connoisseur or does not play as a goalkeeper for a local amateur soccer team” if “everyone outside the room does not stream on Twitch or is a culinary enthusiast who experiments with international cuisines” and vice versa. If “everyone in the room enjoys landscape photography or does not enjoy landscape photography” then “everyone in the room owns an extensive assortment of vintage comic book memorabilia if they drives a hybrid car”. If “everyone in the room streams on Twitch” then “everyone outside the room who enjoys coding in Python owns a significant collection of rare gemstones and minerals” otherwise “no one outside the room owns a significant collection of rare gemstones and minerals if they regularly goes on multi-day backpacking trips in national parks”. If “no one in the room does not drive a hybrid car or enjoys skydiving” then “only one person in the room owns a significant collection of rare gemstones and minerals”. Everyone in the room who does not drive a hybrid car does not stream on Twitch. Everyone in the room does not use a Windows laptop if they does not stream on Twitch. Everyone in the room enjoys origami or owns a smart tv or both if they streams on Twitch or does enjoy mountain biking or both. Everyone in the room enjoys origami or owns a smart tv or both if they does not host regular game nights featuring complex strategy games and vice versa. Everyone in the room enjoys landscape photography if they does not host regular game nights featuring complex strategy games.

Elaine enjoys landscape photography.

entailment

room(sean)&room(elaine)&(![X]:(room(X)=>(X='sean'|X='elaine')))& ((![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))<=>(![X]:(room(X)=>(((uses_a_Windows_laptop(X))|(does_not_own_a_smart_tv(X)))))))& (((![X]:(anywhere(X)=>(((does_not_enjoy_skydiving(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))=>((![X]:((practices_and_performs_acrobatic_dance_routines(X))<=>(has_a_saltwater_aquarium(X))))))&((~(![X]:(anywhere(X)=>(((does_not_enjoy_skydiving(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))=>(~![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(drives_a_hybrid_car(X))))))))))& ((![X]:(room(X)=>(((enjoys_stargazing(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))=>(![X]:(room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))& ((![X]:(~room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_stream_on_Twitch(X))))))<=>(![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_a_coffee_connoisseur(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_landscape_photography(X))|(enjoys_landscape_photography(X))))))=>(![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))))& (((![X]:(room(X)=>(streams_on_Twitch(X))))=>(![X]:(~room(X)=>(((enjoys_coding_in_Python(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))))&((~(![X]:(room(X)=>(streams_on_Twitch(X)))))=>(~?[X]:(~room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))))& ((~?[X]:(room(X)=>(((enjoys_skydiving(X))|(does_not_drive_a_hybrid_car(X))))))=>(((?[X]:(room(X)&owns_a_significant_collection_of_rare_gemstones_and_minerals(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)=>(((does_not_drive_a_hybrid_car(X))=>(does_not_stream_on_Twitch(X))))))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(does_not_use_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((((streams_on_Twitch(X))|(does_enjoy_mountain_biking(X))))=>(((enjoys_origami(X))|(owns_a_smart_tv(X))))))))& (![X]:(room(X)=>(((((enjoys_origami(X))|(owns_a_smart_tv(X))))<=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))=>(enjoys_landscape_photography(X))))))

room(sean)&room(elaine)&(![X]:(room(X)=>(X='sean'|X='elaine')))& enjoys_landscape_photography(elaine)

% SZS status Unsatisfiable for 2808998689438495828452538 % SZS output start Proof for 2808998689438495828452538 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 50. (~! [X0] : (room(X0) => predc(X0)) => ~? [X0] : (~room(X0) => (predn(X0) => preds(X0)))) & (! [X0] : (room(X0) => predc(X0)) => ! [X0] : (~room(X0) => (predt(X0) => preds(X0)))) [input p6] 54. ! [X0] : (room(X0) => ((preda(X0) | predc(X0)) => (predh(X0) | predd(X0)))) [input p10] 55. ! [X0] : (room(X0) => ((predh(X0) | predd(X0)) <=> ~predx(X0))) [input p11] 56. ! [X0] : (room(X0) => (~predx(X0) => predv(X0))) [input p12] 57. ~(predv(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 63. (~! [X0] : (room(X0) => predc(X0)) => ~? [X1] : (~room(X1) => (predn(X1) => preds(X1)))) & (! [X2] : (room(X2) => predc(X2)) => ! [X3] : (~room(X3) => (predt(X3) => preds(X3)))) [rectify 50] 65. ! [X0] : (room(X0) => (predc(X0) => (predh(X0) | predd(X0)))) [pure predicate removal 54] 66. (~! [X0] : (room(X0) => predc(X0)) => ~? [X1] : (~room(X1) => preds(X1))) & (! [X2] : (room(X2) => predc(X2)) => ! [X3] : (~room(X3) => (predt(X3) => preds(X3)))) [pure predicate removal 63] 67. ~! [X0] : (room(X0) => predc(X0)) => ~? [X1] : (~room(X1) => preds(X1)) [pure predicate removal 66] 141. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 142. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 141] 151. ! [X1] : (~preds(X1) & ~room(X1)) | ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 67] 158. ! [X0] : (((predh(X0) | predd(X0)) | ~predc(X0)) | ~room(X0)) [ennf transformation 65] 159. ! [X0] : (predh(X0) | predd(X0) | ~predc(X0) | ~room(X0)) [flattening 158] 160. ! [X0] : (((predh(X0) | predd(X0)) <=> ~predx(X0)) | ~room(X0)) [ennf transformation 55] 161. ! [X0] : ((predv(X0) | predx(X0)) | ~room(X0)) [ennf transformation 56] 162. ! [X0] : (predv(X0) | predx(X0) | ~room(X0)) [flattening 161] 163. ~predv(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 57] 164. ~predv(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 163] 184. ! [X0] : (~preds(X0) & ~room(X0)) | ! [X1] : (predc(X1) | ~room(X1)) [rectify 151] 189. ! [X0] : ((((predh(X0) | predd(X0)) | predx(X0)) & (~predx(X0) | (~predh(X0) & ~predd(X0)))) | ~room(X0)) [nnf transformation 160] 190. ! [X0] : (((predh(X0) | predd(X0) | predx(X0)) & (~predx(X0) | (~predh(X0) & ~predd(X0)))) | ~room(X0)) [flattening 189] 191. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK9 & mary != sK9 & room(sK9)) [choice axiom] 192. ~predv(paul) | (paul != sK9 & mary != sK9 & room(sK9)) | ~room(paul) | ~room(mary) [skolemisation 164,191] 274. room(mary) [cnf transformation 142] 275. room(paul) [cnf transformation 142] 276. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 142] 301. ~room(X0) | predc(X1) | ~room(X1) [cnf transformation 184] 308. ~predc(X0) | predd(X0) | predh(X0) | ~room(X0) [cnf transformation 159] 309. ~predd(X0) | ~predx(X0) | ~room(X0) [cnf transformation 190] 310. ~predx(X0) | ~predh(X0) | ~room(X0) [cnf transformation 190] 312. ~room(X0) | predx(X0) | predv(X0) [cnf transformation 162] 313. ~predv(paul) | room(sK9) | ~room(paul) | ~room(mary) [cnf transformation 192] 314. ~predv(paul) | mary != sK9 | ~room(paul) | ~room(mary) [cnf transformation 192] 315. ~predv(paul) | paul != sK9 | ~room(paul) | ~room(mary) [cnf transformation 192] 447. 29 <=> ! [X1] : (predc(X1) | ~room(X1)) [avatar definition] 448. ~room(X1) | predc(X1) <- (29) [avatar component clause 447] 454. 31 <=> ! [X0] : ~room(X0) [avatar definition] 455. ~room(X0) <- (31) [avatar component clause 454] 456. 29 | 31 [avatar split clause 301,454,447] 483. ~predv(paul) | paul != sK9 | ~room(mary) [subsumption resolution 315,275] 484. ~predv(paul) | paul != sK9 [subsumption resolution 483,274] 486. 38 <=> paul = sK9 [avatar definition] 488. paul != sK9 <- (~38) [avatar component clause 486] 490. 39 <=> predv(paul) [avatar definition] 492. ~predv(paul) <- (~39) [avatar component clause 490] 493. ~38 | ~39 [avatar split clause 484,490,486] 494. ~predv(paul) | mary != sK9 | ~room(mary) [subsumption resolution 314,275] 495. ~predv(paul) | mary != sK9 [subsumption resolution 494,274] 497. 40 <=> mary = sK9 [avatar definition] 499. mary != sK9 <- (~40) [avatar component clause 497] 500. ~40 | ~39 [avatar split clause 495,490,497] 501. ~predv(paul) | room(sK9) | ~room(mary) [subsumption resolution 313,275] 502. ~predv(paul) | room(sK9) [subsumption resolution 501,274] 504. 41 <=> room(sK9) [avatar definition] 506. room(sK9) <- (41) [avatar component clause 504] 507. 41 | ~39 [avatar split clause 502,490,504] 512. predc(paul) <- (29) [resolution 448,275] 526. predx(paul) | predv(paul) [resolution 312,275] 537. predx(paul) <- (~39) [subsumption resolution 526,492] 539. ~predh(paul) | ~room(paul) <- (~39) [resolution 537,310] 540. ~predh(paul) <- (~39) [subsumption resolution 539,275] 605. predd(paul) | predh(paul) | ~room(paul) <- (29) [resolution 308,512] 616. predd(paul) | ~room(paul) <- (29, ~39) [subsumption resolution 605,540] 617. predd(paul) <- (29, ~39) [subsumption resolution 616,275] 624. ~predx(paul) | ~room(paul) <- (29, ~39) [resolution 617,309] 625. ~room(paul) <- (29, ~39) [subsumption resolution 624,537] 626. $false <- (29, ~39) [subsumption resolution 625,275] 627. ~29 | 39 [avatar contradiction clause 626] 648. mary = sK9 | paul = sK9 <- (41) [resolution 506,276] 665. paul = sK9 <- (~40, 41) [subsumption resolution 648,499] 666. $false <- (~38, ~40, 41) [subsumption resolution 665,488] 667. 38 | 40 | ~41 [avatar contradiction clause 666] 682. $false <- (31) [resolution 455,274] 685. ~31 [avatar contradiction clause 682] 686. $false [avatar sat refutation 456,493,500,507,627,667,685] % SZS output end Proof for 2808998689438495828452538 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.042 s % ------------------------------ % ------------------------------

Irene, Teresa, Lona, Geraldine are the only persons in the room. All calm persons are quiet. All old persons are quiet.

Irene and Lona are respectively old and quiet.

neutral

room(irene)&room(teresa)&room(lona)&room(geraldine)&(![X]:(room(X)=>(X='irene'|X='teresa'|X='lona'|X='geraldine')))& (![X]:(calm(X)=>quiet(X)))& (![X]:(old(X)=>quiet(X)))& (![X]:(room(X)=>(((old(X)&calm(X)&person(X))<=>(quiet(X)&calm(X)&person(X))))))& (((owns_a_smartwatch(teresa))|(old(teresa))|(quiet(teresa)&person(teresa))))& (![X]:(room(X)=>(((((old(X))&(calm(X))))=>(((frequently_participates_in_hackathons_and_coding_competitions(X))&(quiet(X)&old(X)&person(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))))))))& (![X]:(room(X)=>(((~((frequently_participates_in_hackathons_and_coding_competitions(X))|(~~calm(X))))=>(~(old(X)&quiet(X)&calm(X)&person(X)))))))& (![X]:(anywhere(X)=>(((~(old(X)&quiet(X)&calm(X)&person(X)))=>(((frequently_participates_in_hackathons_and_coding_competitions(X))<~>(does_not_own_a_smartwatch(X))))))))& (?[X]:(room(X)&(quiet(X)&person(X))))& (frequently_participates_in_hackathons_and_coding_competitions(teresa))& ((quiet(teresa))&(old(irene)))& (![X]:(room(X)=>(((creates_YouTube_content(X))=>(~(quiet(X)&old(X)&person(X)))))))& (![X]:(~room(X)=>(((~old(X))=>(old(X))))))& (![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(quiet(X)=>calm(X)))& (~(does_not_own_a_smartwatch(teresa)))& (![X]:(room(X)=>(((owns_a_smartwatch(X))<=(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(old(X)&person(X))))))& (?[X,Y]:((creates_augmented_reality_experiences_for_mobile_applications(X))&(calm(Y))&(quieter(X,Y))))

room(irene)&room(teresa)&room(lona)&room(geraldine)&(![X]:(room(X)=>(X='irene'|X='teresa'|X='lona'|X='geraldine')))& (old(irene))&(quiet(lona))

Pete is the only person in the room. If 'everyone anywhere does not play video games or collects vintage stamps' then 'Pete who collects rare and antique scientific instruments creates augmented reality experiences for mobile applications'. If 'no one in the room plays video games or is not a wine connoisseur with a private cellar of vintage wines' then 'Pete who creates augmented reality experiences for mobile applications does not use a Windows laptop'. 'It is true that 'Pete collects limited-edition art prints from contemporary artists'' only if 'Pete dreamt that 'everyone in the room uses a Windows laptop if and only if they creates augmented reality experiences for mobile applications''. If 'everyone in the room does not use a Windows laptop or plays video games' then 'everyone outside the room who does not use a Windows laptop collects limited-edition art prints from contemporary artists'. Pete collects limited-edition art prints from contemporary artists. Pete collects rare and antique scientific instruments. Pete is a wine connoisseur with a private cellar of vintage wines, plays video games or bakes bread at home. Everyone in the room does not collect vintage stamps if they practices tai chi. Everyone in the room practices tai chi, uses a Windows laptop and writes and illustrates their own graphic novels if they does not collect vintage stamps. Everyone anywhere who practices tai chi, uses a Windows laptop and writes and illustrates their own graphic novels collects limited-edition art prints from contemporary artists.

Pete is a wine connoisseur with a private cellar of vintage wines.

neutral

room(pete)&(![X]:(room(X)=>(X='pete')))& ((![X]:(anywhere(X)=>(((collects_vintage_stamps(X))|(does_not_play_video_games(X))))))=>((collects_rare_and_antique_scientific_instruments(pete))&(creates_augmented_reality_experiences_for_mobile_applications(pete))))& ((~?[X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(plays_video_games(X))))))=>((creates_augmented_reality_experiences_for_mobile_applications(pete))&(does_not_use_a_Windows_laptop(pete))))& ((collects_limited-edition_art_prints_from_contemporary_artists(pete))=>((pete_dream=>(![X]:(room(X)=>(((uses_a_Windows_laptop(X))<=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))))))& ((![X]:(room(X)=>(((plays_video_games(X))|(does_not_use_a_Windows_laptop(X))))))=>(![X]:(~room(X)=>(((does_not_use_a_Windows_laptop(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X)))))))& (collects_limited-edition_art_prints_from_contemporary_artists(pete))& (collects_rare_and_antique_scientific_instruments(pete))& (((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(pete))|(plays_video_games(pete))|(bakes_bread_at_home(pete))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(does_not_collect_vintage_stamps(X))))))& (![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))=>(((practices_tai_chi(X))&(uses_a_Windows_laptop(X))&(writes_and_illustrates_their_own_graphic_novels(X))))))))& (![X]:(anywhere(X)=>(((((practices_tai_chi(X))&(uses_a_Windows_laptop(X))&(writes_and_illustrates_their_own_graphic_novels(X))))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))

room(pete)&(![X]:(room(X)=>(X='pete')))& is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(pete)

Diane, Guillermo, Rosemarie are the only persons in the room. Either “Rosemarie is a curious person” or “someone in the room is a old person” but not both. If “Diane is funny” then “someone in the room is calm”. If “someone in the room is calm” then “Diane and Guillermo are wise persons”. Either “Diane is a humble person” or “Diane is brave” but not both. Guillermo is generous. Diane and Guillermo are not a strong persons. Guillermo and Diane are respectively brave and quiet. Diane is kind.

Guillermo is tall, is old or is quiet.

entailment

room(diane)&room(guillermo)&room(rosemarie)&(![X]:(room(X)=>(X='diane'|X='guillermo'|X='rosemarie')))& ((curious(rosemarie)&person(rosemarie))<~>(?[X]:(room(X)&(old(X)&person(X)))))& (((funny(diane))=>(?[X]:(room(X)&(calm(X)))))& ((?[X]:(room(X)&(calm(X))))=>(wise(diane)&person(diane)&wise(guillermo)&person(guillermo))))& ((humble(diane)&person(diane))<~>(brave(diane)))& (generous(guillermo))& (~(strong(diane)&person(diane))&~(strong(guillermo)&person(guillermo)))& ((brave(guillermo))&(quiet(diane)))& (kind(diane))& (?[X,Y]:((calm(X)&person(X))&(funny(Y)&person(Y))&(older(X,Y))))& ((![X]:((happy(X)&person(X))=>(((~(strong(X)&person(X)))|(calm(X))|(~(curious(X)&person(X))))))))& (![X]:((room(X)&(X!=guillermo))=>quieter(X,guillermo)))& (~(strong(rosemarie)&person(rosemarie)))& (![X]:(brave(X)=>funny(X)))& (((funny(guillermo)&person(guillermo))|(~(strong(guillermo)&person(guillermo))))&((funny(rosemarie)&person(rosemarie))|(~(strong(rosemarie)&person(rosemarie)))))& ((![X]:((((calm(X))&(funny(X))&(humble(X)&person(X))))=>(((brave(X)&person(X))&(kind(X)&person(X)))))))& (~(creative(diane)&person(diane)))& (tall(guillermo)&person(guillermo))& (creative(guillermo))& ((?[X,Y]:(room(X)&room(Y)&(happy(X)&person(X)&happy(Y)&person(Y))&(X!=Y))))& (((wise(diane)&person(diane))|(generous(diane))|(calm(diane)&person(diane))))& (patient(diane))& ((?[X,Y]:(room(X)&room(Y)&(generous(X)&generous(Y))&(X!=Y))))& (![X]:(humble(X)=>generous(X)))& ((?[X,Y]:(room(X)&room(Y)&(kind(X)&kind(Y))&(X!=Y))))& (~(old(diane)&person(diane)))& (?[X]:(room(X)&(~humble(X))))& ((![X]:((((~(curious(X)&person(X)))&(quiet(X)&person(X))))<=>(wise(X)&person(X)))))& ((~(old(diane)&person(diane)))&(((humble(diane)&person(diane))|(~(old(diane)&person(diane)))|(~(tall(diane)&person(diane))))))& (~funny(rosemarie))& (calm(rosemarie)&person(rosemarie))& (((?[X]:(room(X)&creative(X)&person(X)))&(![X,Y]:((room(X)&room(Y)&(creative(X)&person(X))&(creative(Y)&person(Y)))=>(X=Y)))))

room(diane)&room(guillermo)&room(rosemarie)&(![X]:(room(X)=>(X='diane'|X='guillermo'|X='rosemarie')))& ((tall(guillermo))|(old(guillermo))|(quiet(guillermo)))

% SZS status Unsatisfiable for 5694070274185370080399929 % SZS output start Proof for 5694070274185370080399929 44. ! [X0,X1] : ((person(X1) & creative(X1) & person(X0) & creative(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (person(X0) & creative(X0) & room(X0)) & person(fred) & calm(fred) & ~funny(fred) & (~(person(mary) & tall(mary)) | ~(person(mary) & old(mary)) | (person(mary) & humble(mary))) & ~(person(mary) & old(mary)) & ! [X0] : ((person(X0) & quiet(X0) & ~(person(X0) & curious(X0))) <=> (person(X0) & wise(X0))) & ? [X0] : (~humble(X0) & room(X0)) & ~(person(mary) & old(mary)) & ? [X0,X1] : (X0 != X1 & kind(X1) & kind(X0) & room(X1) & room(X0)) & ! [X0] : (humble(X0) => generous(X0)) & ? [X0,X1] : (X0 != X1 & generous(X1) & generous(X0) & room(X1) & room(X0)) & patient(mary) & ((person(mary) & calm(mary)) | generous(mary) | (person(mary) & wise(mary))) & ? [X0,X1] : (X0 != X1 & person(X1) & happy(X1) & person(X0) & happy(X0) & room(X1) & room(X0)) & creative(paul) & person(paul) & tall(paul) & ~(person(mary) & creative(mary)) & ! [X0] : ((person(X0) & humble(X0) & funny(X0) & calm(X0)) => (person(X0) & kind(X0) & person(X0) & brave(X0))) & (~(person(fred) & strong(fred)) | (person(fred) & funny(fred))) & (~(person(paul) & strong(paul)) | (person(paul) & funny(paul))) & ! [X0] : (brave(X0) => funny(X0)) & ~(person(fred) & strong(fred)) & ! [X0] : ((paul != X0 & room(X0)) => quieter(X0,paul)) & ! [X0] : ((person(X0) & happy(X0)) => (~(person(X0) & curious(X0)) | calm(X0) | ~(person(X0) & strong(X0)))) & ? [X0,X1] : (older(X0,X1) & person(X1) & funny(X1) & person(X0) & calm(X0)) & kind(mary) & quiet(mary) & brave(paul) & ~(person(paul) & strong(paul)) & ~(person(mary) & strong(mary)) & generous(paul) & ((person(mary) & humble(mary)) <~> brave(mary)) & (? [X0] : (calm(X0) & room(X0)) => (person(paul) & wise(paul) & person(mary) & wise(mary))) & (funny(mary) => ? [X0] : (calm(X0) & room(X0))) & ((person(fred) & curious(fred)) <~> ? [X0] : (person(X0) & old(X0) & room(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~((quiet(paul) | old(paul) | tall(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0,X1] : ((person(X1) & creative(X1) & person(X0) & creative(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & (~(person(mary) & tall(mary)) | ~(person(mary) & old(mary)) | (person(mary) & humble(mary))) & ~(person(mary) & old(mary)) & ! [X3] : ((person(X3) & quiet(X3) & ~(person(X3) & curious(X3))) <=> (person(X3) & wise(X3))) & ? [X4] : (~humble(X4) & room(X4)) & ~(person(mary) & old(mary)) & ? [X5,X6] : (X5 != X6 & kind(X6) & kind(X5) & room(X6) & room(X5)) & ! [X7] : (humble(X7) => generous(X7)) & ? [X8,X9] : (X8 != X9 & generous(X9) & generous(X8) & room(X9) & room(X8)) & patient(mary) & ((person(mary) & calm(mary)) | generous(mary) | (person(mary) & wise(mary))) & ? [X10,X11] : (X10 != X11 & person(X11) & happy(X11) & person(X10) & happy(X10) & room(X11) & room(X10)) & creative(paul) & person(paul) & tall(paul) & ~(person(mary) & creative(mary)) & ! [X12] : ((person(X12) & humble(X12) & funny(X12) & calm(X12)) => (person(X12) & kind(X12) & person(X12) & brave(X12))) & (~(person(fred) & strong(fred)) | (person(fred) & funny(fred))) & (~(person(paul) & strong(paul)) | (person(paul) & funny(paul))) & ! [X13] : (brave(X13) => funny(X13)) & ~(person(fred) & strong(fred)) & ! [X14] : ((paul != X14 & room(X14)) => quieter(X14,paul)) & ! [X15] : ((person(X15) & happy(X15)) => (~(person(X15) & curious(X15)) | calm(X15) | ~(person(X15) & strong(X15)))) & ? [X16,X17] : (older(X16,X17) & person(X17) & funny(X17) & person(X16) & calm(X16)) & kind(mary) & quiet(mary) & brave(paul) & ~(person(paul) & strong(paul)) & ~(person(mary) & strong(mary)) & generous(paul) & ((person(mary) & humble(mary)) <~> brave(mary)) & (? [X18] : (calm(X18) & room(X18)) => (person(paul) & wise(paul) & person(mary) & wise(mary))) & (funny(mary) => ? [X19] : (calm(X19) & room(X19))) & ((person(fred) & curious(fred)) <~> ? [X20] : (person(X20) & old(X20) & room(X20))) & ! [X21] : (room(X21) => (fred = X21 | paul = X21 | mary = X21)) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0,X1] : ((person(X1) & creative(X1) & person(X0) & creative(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & (~(person(mary) & tall(mary)) | ~(person(mary) & old(mary)) | (person(mary) & humble(mary))) & ~(person(mary) & old(mary)) & ! [X3] : ((person(X3) & quiet(X3) & ~(person(X3) & curious(X3))) <=> (person(X3) & wise(X3))) & ? [X4] : (~humble(X4) & room(X4)) & ~(person(mary) & old(mary)) & ? [X5,X6] : (X5 != X6 & kind(X6) & kind(X5) & room(X6) & room(X5)) & ! [X7] : (humble(X7) => generous(X7)) & ? [X8,X9] : (X8 != X9 & generous(X9) & generous(X8) & room(X9) & room(X8)) & ((person(mary) & calm(mary)) | generous(mary) | (person(mary) & wise(mary))) & ? [X10,X11] : (X10 != X11 & person(X11) & happy(X11) & person(X10) & happy(X10) & room(X11) & room(X10)) & creative(paul) & person(paul) & tall(paul) & ~(person(mary) & creative(mary)) & ! [X12] : ((person(X12) & humble(X12) & funny(X12) & calm(X12)) => (person(X12) & kind(X12) & person(X12) & brave(X12))) & (~(person(fred) & strong(fred)) | (person(fred) & funny(fred))) & (~(person(paul) & strong(paul)) | (person(paul) & funny(paul))) & ! [X13] : (brave(X13) => funny(X13)) & ~(person(fred) & strong(fred)) & ! [X14] : ((paul != X14 & room(X14)) => quieter(X14,paul)) & ! [X15] : ((person(X15) & happy(X15)) => (~(person(X15) & curious(X15)) | calm(X15) | ~(person(X15) & strong(X15)))) & ? [X16,X17] : (older(X16,X17) & person(X17) & funny(X17) & person(X16) & calm(X16)) & kind(mary) & quiet(mary) & brave(paul) & ~(person(paul) & strong(paul)) & ~(person(mary) & strong(mary)) & generous(paul) & ((person(mary) & humble(mary)) <~> brave(mary)) & (? [X18] : (calm(X18) & room(X18)) => (person(paul) & wise(paul) & person(mary) & wise(mary))) & (funny(mary) => ? [X19] : (calm(X19) & room(X19))) & ((person(fred) & curious(fred)) <~> ? [X20] : (person(X20) & old(X20) & room(X20))) & ! [X21] : (room(X21) => (fred = X21 | paul = X21 | mary = X21)) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0,X1] : ((person(X1) & creative(X1) & person(X0) & creative(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & (~(person(mary) & tall(mary)) | ~(person(mary) & old(mary)) | (person(mary) & humble(mary))) & ~(person(mary) & old(mary)) & ! [X3] : ((person(X3) & quiet(X3) & ~(person(X3) & curious(X3))) <=> (person(X3) & wise(X3))) & ? [X4] : (~humble(X4) & room(X4)) & ~(person(mary) & old(mary)) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (humble(X7) => generous(X7)) & ? [X8,X9] : (X8 != X9 & generous(X9) & generous(X8) & room(X9) & room(X8)) & ((person(mary) & calm(mary)) | generous(mary) | (person(mary) & wise(mary))) & ? [X10,X11] : (X10 != X11 & person(X11) & happy(X11) & person(X10) & happy(X10) & room(X11) & room(X10)) & creative(paul) & person(paul) & tall(paul) & ~(person(mary) & creative(mary)) & ! [X12] : ((person(X12) & humble(X12) & funny(X12) & calm(X12)) => (person(X12) & person(X12) & brave(X12))) & (~(person(fred) & strong(fred)) | (person(fred) & funny(fred))) & (~(person(paul) & strong(paul)) | (person(paul) & funny(paul))) & ! [X13] : (brave(X13) => funny(X13)) & ~(person(fred) & strong(fred)) & ! [X14] : ((paul != X14 & room(X14)) => quieter(X14,paul)) & ! [X15] : ((person(X15) & happy(X15)) => (~(person(X15) & curious(X15)) | calm(X15) | ~(person(X15) & strong(X15)))) & ? [X16,X17] : (older(X16,X17) & person(X17) & funny(X17) & person(X16) & calm(X16)) & quiet(mary) & brave(paul) & ~(person(paul) & strong(paul)) & ~(person(mary) & strong(mary)) & generous(paul) & ((person(mary) & humble(mary)) <~> brave(mary)) & (? [X18] : (calm(X18) & room(X18)) => (person(paul) & wise(paul) & person(mary) & wise(mary))) & (funny(mary) => ? [X19] : (calm(X19) & room(X19))) & ((person(fred) & curious(fred)) <~> ? [X20] : (person(X20) & old(X20) & room(X20))) & ! [X21] : (room(X21) => (fred = X21 | paul = X21 | mary = X21)) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0,X1] : ((person(X1) & creative(X1) & person(X0) & creative(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & (~(person(mary) & tall(mary)) | ~(person(mary) & old(mary)) | (person(mary) & humble(mary))) & ~(person(mary) & old(mary)) & ! [X3] : ((person(X3) & quiet(X3) & ~(person(X3) & curious(X3))) <=> (person(X3) & wise(X3))) & ? [X4] : (~humble(X4) & room(X4)) & ~(person(mary) & old(mary)) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (humble(X7) => generous(X7)) & ? [X8,X9] : (X8 != X9 & generous(X9) & generous(X8) & room(X9) & room(X8)) & ((person(mary) & calm(mary)) | generous(mary) | (person(mary) & wise(mary))) & ? [X10,X11] : (X10 != X11 & person(X11) & happy(X11) & person(X10) & happy(X10) & room(X11) & room(X10)) & creative(paul) & person(paul) & tall(paul) & ~(person(mary) & creative(mary)) & ! [X12] : ((person(X12) & humble(X12) & funny(X12) & calm(X12)) => (person(X12) & person(X12) & brave(X12))) & ! [X13] : (brave(X13) => funny(X13)) & ! [X14] : ((paul != X14 & room(X14)) => quieter(X14,paul)) & ? [X16,X17] : (older(X16,X17) & person(X17) & funny(X17) & person(X16) & calm(X16)) & quiet(mary) & brave(paul) & generous(paul) & ((person(mary) & humble(mary)) <~> brave(mary)) & (? [X18] : (calm(X18) & room(X18)) => (person(paul) & wise(paul) & person(mary) & wise(mary))) & (funny(mary) => ? [X19] : (calm(X19) & room(X19))) & ((person(fred) & curious(fred)) <~> ? [X20] : (person(X20) & old(X20) & room(X20))) & ! [X21] : (room(X21) => (fred = X21 | paul = X21 | mary = X21)) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0,X1] : ((person(X1) & creative(X1) & person(X0) & creative(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & (~(person(mary) & tall(mary)) | ~(person(mary) & old(mary)) | (person(mary) & humble(mary))) & ~(person(mary) & old(mary)) & ! [X3] : ((person(X3) & quiet(X3) & ~(person(X3) & curious(X3))) <=> (person(X3) & wise(X3))) & ? [X4] : (~humble(X4) & room(X4)) & ~(person(mary) & old(mary)) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ! [X7] : (humble(X7) => generous(X7)) & ? [X8,X9] : (X8 != X9 & generous(X9) & generous(X8) & room(X9) & room(X8)) & ((person(mary) & calm(mary)) | generous(mary) | (person(mary) & wise(mary))) & ? [X10,X11] : (X10 != X11 & person(X11) & person(X10) & room(X11) & room(X10)) & creative(paul) & person(paul) & tall(paul) & ~(person(mary) & creative(mary)) & ! [X12] : ((person(X12) & humble(X12) & funny(X12) & calm(X12)) => (person(X12) & person(X12) & brave(X12))) & ! [X13] : (brave(X13) => funny(X13)) & ! [X14] : ((paul != X14 & room(X14)) => quieter(X14,paul)) & ? [X16,X17] : (older(X16,X17) & person(X17) & funny(X17) & person(X16) & calm(X16)) & quiet(mary) & brave(paul) & generous(paul) & ((person(mary) & humble(mary)) <~> brave(mary)) & (? [X18] : (calm(X18) & room(X18)) => (person(paul) & wise(paul) & person(mary) & wise(mary))) & (funny(mary) => ? [X19] : (calm(X19) & room(X19))) & ((person(fred) & curious(fred)) <~> ? [X20] : (person(X20) & old(X20) & room(X20))) & ! [X21] : (room(X21) => (fred = X21 | paul = X21 | mary = X21)) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0,X1] : ((person(X1) & creative(X1) & person(X0) & creative(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & (~(person(mary) & tall(mary)) | ~(person(mary) & old(mary)) | (person(mary) & humble(mary))) & ~(person(mary) & old(mary)) & ! [X3] : ((person(X3) & quiet(X3) & ~(person(X3) & curious(X3))) <=> (person(X3) & wise(X3))) & ? [X4] : (~humble(X4) & room(X4)) & ~(person(mary) & old(mary)) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ? [X8,X9] : (X8 != X9 & room(X9) & room(X8)) & ? [X10,X11] : (X10 != X11 & person(X11) & person(X10) & room(X11) & room(X10)) & creative(paul) & person(paul) & tall(paul) & ~(person(mary) & creative(mary)) & ! [X12] : ((person(X12) & humble(X12) & funny(X12) & calm(X12)) => (person(X12) & person(X12) & brave(X12))) & ! [X13] : (brave(X13) => funny(X13)) & ! [X14] : ((paul != X14 & room(X14)) => quieter(X14,paul)) & ? [X16,X17] : (older(X16,X17) & person(X17) & funny(X17) & person(X16) & calm(X16)) & quiet(mary) & brave(paul) & ((person(mary) & humble(mary)) <~> brave(mary)) & (? [X18] : (calm(X18) & room(X18)) => (person(paul) & wise(paul) & person(mary) & wise(mary))) & (funny(mary) => ? [X19] : (calm(X19) & room(X19))) & ((person(fred) & curious(fred)) <~> ? [X20] : (person(X20) & old(X20) & room(X20))) & ! [X21] : (room(X21) => (fred = X21 | paul = X21 | mary = X21)) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 124. ! [X0,X1] : (X0 = X1 | (~person(X1) | ~creative(X1) | ~person(X0) | ~creative(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & ((~person(mary) | ~tall(mary)) | (~person(mary) | ~old(mary)) | (person(mary) & humble(mary))) & (~person(mary) | ~old(mary)) & ! [X3] : ((person(X3) & quiet(X3) & (~person(X3) | ~curious(X3))) <=> (person(X3) & wise(X3))) & ? [X4] : (~humble(X4) & room(X4)) & (~person(mary) | ~old(mary)) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ? [X8,X9] : (X8 != X9 & room(X9) & room(X8)) & ? [X10,X11] : (X10 != X11 & person(X11) & person(X10) & room(X11) & room(X10)) & creative(paul) & person(paul) & tall(paul) & (~person(mary) | ~creative(mary)) & ! [X12] : ((person(X12) & person(X12) & brave(X12)) | (~person(X12) | ~humble(X12) | ~funny(X12) | ~calm(X12))) & ! [X13] : (funny(X13) | ~brave(X13)) & ! [X14] : (quieter(X14,paul) | (paul = X14 | ~room(X14))) & ? [X16,X17] : (older(X16,X17) & person(X17) & funny(X17) & person(X16) & calm(X16)) & quiet(mary) & brave(paul) & ((person(mary) & humble(mary)) <~> brave(mary)) & ((person(paul) & wise(paul) & person(mary) & wise(mary)) | ! [X18] : (~calm(X18) | ~room(X18))) & (? [X19] : (calm(X19) & room(X19)) | ~funny(mary)) & ((person(fred) & curious(fred)) <~> ? [X20] : (person(X20) & old(X20) & room(X20))) & ! [X21] : ((fred = X21 | paul = X21 | mary = X21) | ~room(X21)) & room(fred) & room(paul) & room(mary) [ennf transformation 51] 125. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~creative(X1) | ~person(X0) | ~creative(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & (~person(mary) | ~tall(mary) | ~person(mary) | ~old(mary) | (person(mary) & humble(mary))) & (~person(mary) | ~old(mary)) & ! [X3] : ((person(X3) & quiet(X3) & (~person(X3) | ~curious(X3))) <=> (person(X3) & wise(X3))) & ? [X4] : (~humble(X4) & room(X4)) & (~person(mary) | ~old(mary)) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ? [X8,X9] : (X8 != X9 & room(X9) & room(X8)) & ? [X10,X11] : (X10 != X11 & person(X11) & person(X10) & room(X11) & room(X10)) & creative(paul) & person(paul) & tall(paul) & (~person(mary) | ~creative(mary)) & ! [X12] : ((person(X12) & person(X12) & brave(X12)) | ~person(X12) | ~humble(X12) | ~funny(X12) | ~calm(X12)) & ! [X13] : (funny(X13) | ~brave(X13)) & ! [X14] : (quieter(X14,paul) | paul = X14 | ~room(X14)) & ? [X16,X17] : (older(X16,X17) & person(X17) & funny(X17) & person(X16) & calm(X16)) & quiet(mary) & brave(paul) & ((person(mary) & humble(mary)) <~> brave(mary)) & ((person(paul) & wise(paul) & person(mary) & wise(mary)) | ! [X18] : (~calm(X18) | ~room(X18))) & (? [X19] : (calm(X19) & room(X19)) | ~funny(mary)) & ((person(fred) & curious(fred)) <~> ? [X20] : (person(X20) & old(X20) & room(X20))) & ! [X21] : (fred = X21 | paul = X21 | mary = X21 | ~room(X21)) & room(fred) & room(paul) & room(mary) [flattening 124] 126. (~quiet(paul) & ~old(paul) & ~tall(paul)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 127. (~quiet(paul) & ~old(paul) & ~tall(paul)) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 126] 128. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [predicate definition introduction] 129. (~quiet(paul) & ~old(paul) & ~tall(paul)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 127,128] 131. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~creative(X1) | ~person(X0) | ~creative(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & (~person(mary) | ~tall(mary) | ~person(mary) | ~old(mary) | (person(mary) & humble(mary))) & (~person(mary) | ~old(mary)) & ! [X3] : (((person(X3) & quiet(X3) & (~person(X3) | ~curious(X3))) | (~person(X3) | ~wise(X3))) & ((person(X3) & wise(X3)) | (~person(X3) | ~quiet(X3) | (person(X3) & curious(X3))))) & ? [X4] : (~humble(X4) & room(X4)) & (~person(mary) | ~old(mary)) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ? [X8,X9] : (X8 != X9 & room(X9) & room(X8)) & ? [X10,X11] : (X10 != X11 & person(X11) & person(X10) & room(X11) & room(X10)) & creative(paul) & person(paul) & tall(paul) & (~person(mary) | ~creative(mary)) & ! [X12] : ((person(X12) & person(X12) & brave(X12)) | ~person(X12) | ~humble(X12) | ~funny(X12) | ~calm(X12)) & ! [X13] : (funny(X13) | ~brave(X13)) & ! [X14] : (quieter(X14,paul) | paul = X14 | ~room(X14)) & ? [X16,X17] : (older(X16,X17) & person(X17) & funny(X17) & person(X16) & calm(X16)) & quiet(mary) & brave(paul) & ((~brave(mary) | (~person(mary) | ~humble(mary))) & (brave(mary) | (person(mary) & humble(mary)))) & ((person(paul) & wise(paul) & person(mary) & wise(mary)) | ! [X18] : (~calm(X18) | ~room(X18))) & (? [X19] : (calm(X19) & room(X19)) | ~funny(mary)) & ((! [X20] : (~person(X20) | ~old(X20) | ~room(X20)) | (~person(fred) | ~curious(fred))) & (? [X20] : (person(X20) & old(X20) & room(X20)) | (person(fred) & curious(fred)))) & ! [X21] : (fred = X21 | paul = X21 | mary = X21 | ~room(X21)) & room(fred) & room(paul) & room(mary) [nnf transformation 125] 132. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~creative(X1) | ~person(X0) | ~creative(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & (~person(mary) | ~tall(mary) | ~person(mary) | ~old(mary) | (person(mary) & humble(mary))) & (~person(mary) | ~old(mary)) & ! [X3] : (((person(X3) & quiet(X3) & (~person(X3) | ~curious(X3))) | ~person(X3) | ~wise(X3)) & ((person(X3) & wise(X3)) | ~person(X3) | ~quiet(X3) | (person(X3) & curious(X3)))) & ? [X4] : (~humble(X4) & room(X4)) & (~person(mary) | ~old(mary)) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ? [X8,X9] : (X8 != X9 & room(X9) & room(X8)) & ? [X10,X11] : (X10 != X11 & person(X11) & person(X10) & room(X11) & room(X10)) & creative(paul) & person(paul) & tall(paul) & (~person(mary) | ~creative(mary)) & ! [X12] : ((person(X12) & person(X12) & brave(X12)) | ~person(X12) | ~humble(X12) | ~funny(X12) | ~calm(X12)) & ! [X13] : (funny(X13) | ~brave(X13)) & ! [X14] : (quieter(X14,paul) | paul = X14 | ~room(X14)) & ? [X16,X17] : (older(X16,X17) & person(X17) & funny(X17) & person(X16) & calm(X16)) & quiet(mary) & brave(paul) & (~brave(mary) | ~person(mary) | ~humble(mary)) & (brave(mary) | (person(mary) & humble(mary))) & ((person(paul) & wise(paul) & person(mary) & wise(mary)) | ! [X18] : (~calm(X18) | ~room(X18))) & (? [X19] : (calm(X19) & room(X19)) | ~funny(mary)) & (! [X20] : (~person(X20) | ~old(X20) | ~room(X20)) | ~person(fred) | ~curious(fred)) & (? [X20] : (person(X20) & old(X20) & room(X20)) | (person(fred) & curious(fred))) & ! [X21] : (fred = X21 | paul = X21 | mary = X21 | ~room(X21)) & room(fred) & room(paul) & room(mary) [flattening 131] 133. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~creative(X1) | ~person(X0) | ~creative(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (person(X2) & creative(X2) & room(X2)) & person(fred) & calm(fred) & ~funny(fred) & (~person(mary) | ~tall(mary) | ~person(mary) | ~old(mary) | (person(mary) & humble(mary))) & (~person(mary) | ~old(mary)) & ! [X3] : (((person(X3) & quiet(X3) & (~person(X3) | ~curious(X3))) | ~person(X3) | ~wise(X3)) & ((person(X3) & wise(X3)) | ~person(X3) | ~quiet(X3) | (person(X3) & curious(X3)))) & ? [X4] : (~humble(X4) & room(X4)) & (~person(mary) | ~old(mary)) & ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) & ? [X7,X8] : (X7 != X8 & room(X8) & room(X7)) & ? [X9,X10] : (X9 != X10 & person(X10) & person(X9) & room(X10) & room(X9)) & creative(paul) & person(paul) & tall(paul) & (~person(mary) | ~creative(mary)) & ! [X11] : ((person(X11) & person(X11) & brave(X11)) | ~person(X11) | ~humble(X11) | ~funny(X11) | ~calm(X11)) & ! [X12] : (funny(X12) | ~brave(X12)) & ! [X13] : (quieter(X13,paul) | paul = X13 | ~room(X13)) & ? [X14,X15] : (older(X14,X15) & person(X15) & funny(X15) & person(X14) & calm(X14)) & quiet(mary) & brave(paul) & (~brave(mary) | ~person(mary) | ~humble(mary)) & (brave(mary) | (person(mary) & humble(mary))) & ((person(paul) & wise(paul) & person(mary) & wise(mary)) | ! [X16] : (~calm(X16) | ~room(X16))) & (? [X17] : (calm(X17) & room(X17)) | ~funny(mary)) & (! [X18] : (~person(X18) | ~old(X18) | ~room(X18)) | ~person(fred) | ~curious(fred)) & (? [X19] : (person(X19) & old(X19) & room(X19)) | (person(fred) & curious(fred))) & ! [X20] : (fred = X20 | paul = X20 | mary = X20 | ~room(X20)) & room(fred) & room(paul) & room(mary) [rectify 132] 134. ? [X2] : (person(X2) & creative(X2) & room(X2)) => (person(sK1) & creative(sK1) & room(sK1)) [choice axiom] 135. ? [X4] : (~humble(X4) & room(X4)) => (~humble(sK2) & room(sK2)) [choice axiom] 136. ? [X5,X6] : (X5 != X6 & room(X6) & room(X5)) => (sK3 != sK4 & room(sK4) & room(sK3)) [choice axiom] 137. ? [X7,X8] : (X7 != X8 & room(X8) & room(X7)) => (sK5 != sK6 & room(sK6) & room(sK5)) [choice axiom] 138. ? [X9,X10] : (X9 != X10 & person(X10) & person(X9) & room(X10) & room(X9)) => (sK7 != sK8 & person(sK8) & person(sK7) & room(sK8) & room(sK7)) [choice axiom] 139. ? [X14,X15] : (older(X14,X15) & person(X15) & funny(X15) & person(X14) & calm(X14)) => (older(sK9,sK10) & person(sK10) & funny(sK10) & person(sK9) & calm(sK9)) [choice axiom] 140. ? [X17] : (calm(X17) & room(X17)) => (calm(sK11) & room(sK11)) [choice axiom] 141. ? [X19] : (person(X19) & old(X19) & room(X19)) => (person(sK12) & old(sK12) & room(sK12)) [choice axiom] 142. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~creative(X1) | ~person(X0) | ~creative(X0) | ~room(X1) | ~room(X0)) & (person(sK1) & creative(sK1) & room(sK1)) & person(fred) & calm(fred) & ~funny(fred) & (~person(mary) | ~tall(mary) | ~person(mary) | ~old(mary) | (person(mary) & humble(mary))) & (~person(mary) | ~old(mary)) & ! [X3] : (((person(X3) & quiet(X3) & (~person(X3) | ~curious(X3))) | ~person(X3) | ~wise(X3)) & ((person(X3) & wise(X3)) | ~person(X3) | ~quiet(X3) | (person(X3) & curious(X3)))) & (~humble(sK2) & room(sK2)) & (~person(mary) | ~old(mary)) & (sK3 != sK4 & room(sK4) & room(sK3)) & (sK5 != sK6 & room(sK6) & room(sK5)) & (sK7 != sK8 & person(sK8) & person(sK7) & room(sK8) & room(sK7)) & creative(paul) & person(paul) & tall(paul) & (~person(mary) | ~creative(mary)) & ! [X11] : ((person(X11) & person(X11) & brave(X11)) | ~person(X11) | ~humble(X11) | ~funny(X11) | ~calm(X11)) & ! [X12] : (funny(X12) | ~brave(X12)) & ! [X13] : (quieter(X13,paul) | paul = X13 | ~room(X13)) & (older(sK9,sK10) & person(sK10) & funny(sK10) & person(sK9) & calm(sK9)) & quiet(mary) & brave(paul) & (~brave(mary) | ~person(mary) | ~humble(mary)) & (brave(mary) | (person(mary) & humble(mary))) & ((person(paul) & wise(paul) & person(mary) & wise(mary)) | ! [X16] : (~calm(X16) | ~room(X16))) & ((calm(sK11) & room(sK11)) | ~funny(mary)) & (! [X18] : (~person(X18) | ~old(X18) | ~room(X18)) | ~person(fred) | ~curious(fred)) & ((person(sK12) & old(sK12) & room(sK12)) | (person(fred) & curious(fred))) & ! [X20] : (fred = X20 | paul = X20 | mary = X20 | ~room(X20)) & room(fred) & room(paul) & room(mary) [skolemisation 133,141,140,139,138,137,136,135,134] 143. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [nnf transformation 128] 144. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK13 & paul != sK13 & mary != sK13 & room(sK13)) [choice axiom] 145. (fred != sK13 & paul != sK13 & mary != sK13 & room(sK13)) | ~sP0 [skolemisation 143,144] 226. room(mary) [cnf transformation 142] 227. room(paul) [cnf transformation 142] 228. room(fred) [cnf transformation 142] 229. ~room(X20) | paul = X20 | mary = X20 | fred = X20 [cnf transformation 142] 259. tall(paul) [cnf transformation 142] 293. room(sK13) | ~sP0 [cnf transformation 145] 294. mary != sK13 | ~sP0 [cnf transformation 145] 295. paul != sK13 | ~sP0 [cnf transformation 145] 296. fred != sK13 | ~sP0 [cnf transformation 145] 297. ~tall(paul) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 129] 388. 18 <=> sP0 [avatar definition] 392. 19 <=> fred = sK13 [avatar definition] 394. fred != sK13 <- (~19) [avatar component clause 392] 395. ~18 | ~19 [avatar split clause 296,392,388] 397. 20 <=> paul = sK13 [avatar definition] 399. paul != sK13 <- (~20) [avatar component clause 397] 400. ~18 | ~20 [avatar split clause 295,397,388] 402. 21 <=> mary = sK13 [avatar definition] 404. mary != sK13 <- (~21) [avatar component clause 402] 405. ~18 | ~21 [avatar split clause 294,402,388] 407. 22 <=> room(sK13) [avatar definition] 409. room(sK13) <- (22) [avatar component clause 407] 410. ~18 | 22 [avatar split clause 293,407,388] 427. sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 297,259] 428. sP0 | ~room(paul) | ~room(mary) [subsumption resolution 427,228] 429. sP0 | ~room(mary) [subsumption resolution 428,227] 430. sP0 [subsumption resolution 429,226] 431. 18 [avatar split clause 430,388] 644. paul = sK13 | mary = sK13 | fred = sK13 <- (22) [resolution 229,409] 762. mary = sK13 | fred = sK13 <- (~20, 22) [subsumption resolution 644,399] 763. fred = sK13 <- (~20, ~21, 22) [subsumption resolution 762,404] 764. $false <- (~19, ~20, ~21, 22) [subsumption resolution 763,394] 765. 19 | 20 | 21 | ~22 [avatar contradiction clause 764] 766. $false [avatar sat refutation 395,400,405,410,431,765] % SZS output end Proof for 5694070274185370080399929 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s % ------------------------------ % ------------------------------

Gary, Nicholas are the only persons in the room. “Gary does not collect luxury watches” if “everyone outside the room does not host regular workshops on creative writing or is not a wine connoisseur”. “Everyone in the room owns a microscope” only if “Gary either does not work on fridays or does not enjoy cross-country skiing but not both”. “Everyone in the room does not enjoy camping and organizing outdoor survival workshops or does not have lived in exactly three countries or both” if “Gary is not a night owl and does not practice yoga”. Only one person in the room is not a night owl. Everyone in the room can play the guitar. Everyone in the room is not a drone photographer. Everyone outside the room does not host regular workshops on creative writing or is not a wine connoisseur. Gary does not practice yoga. Everyone in the room neither cannot play the flute nor is a culinary enthusiast who experiments with international cuisines. Gary is not a wine connoisseur. Gary neither is a certified yoga instructor teaching classes weekly nor is not a member of a local theater group specializing in improv. Everyone in the room is not a culinary enthusiast who experiments with international cuisines.

Nicholas can play the guitar.

entailment

room(gary)&room(nicholas)&(![X]:(room(X)=>(X='gary'|X='nicholas')))& ((![X]:(~room(X)=>(((is_not_a_wine_connoisseur(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))=>(does_not_collect_luxury_watches(gary)))& ((![X]:(room(X)=>(owns_a_microscope(X))))=>(((does_not_work_on_fridays(gary))<~>(does_not_enjoy_cross-country_skiing(gary)))))& ((((is_not_a_night_owl(gary))&(does_not_practice_yoga(gary))))=>(![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_have_lived_in_exactly_three_countries(X)))))))& (((?[X]:(room(X)&is_not_a_night_owl(X)))&(![X,Y]:((room(X)&room(Y)&(is_not_a_night_owl(X))&(is_not_a_night_owl(Y)))=>(X=Y)))))& (![X]:(room(X)=>(can_play_the_guitar(X))))& (![X]:(room(X)=>(is_not_a_drone_photographer(X))))& (![X]:(~room(X)=>(((is_not_a_wine_connoisseur(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))& (does_not_practice_yoga(gary))& (![X]:(room(X)=>(~((cannot_play_the_flute(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (is_not_a_wine_connoisseur(gary))& (~((is_a_certified_yoga_instructor_teaching_classes_weekly(gary))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(gary))))& (![X]:(room(X)=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))

room(gary)&room(nicholas)&(![X]:(room(X)=>(X='gary'|X='nicholas')))& can_play_the_guitar(nicholas)

% SZS status Unsatisfiable for 217449312253277005910086 % SZS output start Proof for 217449312253277005910086 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => predd(X0)) [input p5] 57. ~(predd(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 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] 148. ! [X0] : (predd(X0) | ~room(X0)) [ennf transformation 49] 149. ~predd(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 57] 150. ~predd(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 149] 157. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 158. ~predd(paul) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 150,157] 239. room(mary) [cnf transformation 144] 240. room(paul) [cnf transformation 144] 241. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 144] 247. ~room(X0) | predd(X0) [cnf transformation 148] 248. ~predd(paul) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 158] 249. ~predd(paul) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 158] 250. ~predd(paul) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 158] 265. ~predd(paul) | paul != sK2 | ~room(mary) [subsumption resolution 250,240] 266. ~predd(paul) | paul != sK2 [subsumption resolution 265,239] 268. 4 <=> paul = sK2 [avatar definition] 270. paul != sK2 <- (~4) [avatar component clause 268] 272. 5 <=> predd(paul) [avatar definition] 275. ~4 | ~5 [avatar split clause 266,272,268] 276. ~predd(paul) | mary != sK2 | ~room(mary) [subsumption resolution 249,240] 277. ~predd(paul) | mary != sK2 [subsumption resolution 276,239] 279. 6 <=> mary = sK2 [avatar definition] 281. mary != sK2 <- (~6) [avatar component clause 279] 282. ~6 | ~5 [avatar split clause 277,272,279] 283. ~predd(paul) | room(sK2) | ~room(mary) [subsumption resolution 248,240] 284. ~predd(paul) | room(sK2) [subsumption resolution 283,239] 286. 7 <=> room(sK2) [avatar definition] 288. room(sK2) <- (7) [avatar component clause 286] 289. 7 | ~5 [avatar split clause 284,272,286] 291. predd(paul) [resolution 247,240] 295. 5 [avatar split clause 291,272] 300. mary = sK2 | paul = sK2 <- (7) [resolution 241,288] 310. paul = sK2 <- (~6, 7) [subsumption resolution 300,281] 311. $false <- (~4, ~6, 7) [subsumption resolution 310,270] 312. 4 | 6 | ~7 [avatar contradiction clause 311] 313. $false [avatar sat refutation 275,282,289,295,312] % SZS output end Proof for 217449312253277005910086 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.019 s % ------------------------------ % ------------------------------

Gary, Miguel, Glenda are the only persons in the room. If someone is tall then he/she is quiet and vice versa. All old persons are quiet. More than one person in the room is not a old person. Everyone in the room is quiet. Everyone anywhere is tall. Everyone in the room is not a quiet person.

Gary is quiet.

entailment

room(gary)&room(miguel)&room(glenda)&(![X]:(room(X)=>(X='gary'|X='miguel'|X='glenda')))& ((![X]:((tall(X))<=>(quiet(X)))))& (![X]:(old(X)=>quiet(X)))& ((?[X,Y]:(room(X)&room(Y)&(~(old(X)&person(X))&~(old(Y)&person(Y)))&(X!=Y))))& (![X]:(room(X)=>(quiet(X))))& (![X]:(anywhere(X)=>(tall(X))))& (![X]:(room(X)=>(~(quiet(X)&person(X)))))

room(gary)&room(miguel)&room(glenda)&(![X]:(room(X)=>(X='gary'|X='miguel'|X='glenda')))& quiet(gary)

% SZS status Unsatisfiable for 256974972532358688156973 % SZS output start Proof for 256974972532358688156973 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (tall(X0) <=> quiet(X0)) [input p1] 49. ! [X0] : (anywhere(X0) => tall(X0)) [input p5] 51. ~(quiet(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 52. ! [X0] : (tall(X0) => quiet(X0)) [unused predicate definition removal 45] 126. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 127. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 126] 128. ! [X0] : (quiet(X0) | ~tall(X0)) [ennf transformation 52] 131. ! [X0] : (tall(X0) | ~anywhere(X0)) [ennf transformation 49] 132. ~quiet(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 51] 133. ~quiet(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 132] 137. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 138. ~quiet(mary) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 133,137] 139. anywhere(X0) [cnf transformation 5] 220. room(mary) [cnf transformation 127] 221. room(paul) [cnf transformation 127] 222. room(fred) [cnf transformation 127] 223. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 127] 224. ~tall(X0) | quiet(X0) [cnf transformation 128] 230. tall(X0) | ~anywhere(X0) [cnf transformation 131] 231. ~quiet(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 232. ~quiet(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 233. ~quiet(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 234. ~quiet(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 235. tall(X0) [subsumption resolution 230,139] 236. ~quiet(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 234,222] 237. ~quiet(mary) | fred != sK2 | ~room(mary) [subsumption resolution 236,221] 238. ~quiet(mary) | fred != sK2 [subsumption resolution 237,220] 240. 1 <=> fred = sK2 [avatar definition] 242. fred != sK2 <- (~1) [avatar component clause 240] 244. 2 <=> quiet(mary) [avatar definition] 246. ~quiet(mary) <- (~2) [avatar component clause 244] 247. ~1 | ~2 [avatar split clause 238,244,240] 248. ~quiet(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 233,222] 249. ~quiet(mary) | paul != sK2 | ~room(mary) [subsumption resolution 248,221] 250. ~quiet(mary) | paul != sK2 [subsumption resolution 249,220] 252. 3 <=> paul = sK2 [avatar definition] 254. paul != sK2 <- (~3) [avatar component clause 252] 255. ~3 | ~2 [avatar split clause 250,244,252] 256. ~quiet(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 232,222] 257. ~quiet(mary) | mary != sK2 | ~room(mary) [subsumption resolution 256,221] 258. ~quiet(mary) | mary != sK2 [subsumption resolution 257,220] 260. 4 <=> mary = sK2 [avatar definition] 262. mary != sK2 <- (~4) [avatar component clause 260] 263. ~4 | ~2 [avatar split clause 258,244,260] 264. ~quiet(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 231,222] 265. ~quiet(mary) | room(sK2) | ~room(mary) [subsumption resolution 264,221] 266. ~quiet(mary) | room(sK2) [subsumption resolution 265,220] 268. 5 <=> room(sK2) [avatar definition] 270. room(sK2) <- (5) [avatar component clause 268] 271. 5 | ~2 [avatar split clause 266,244,268] 272. quiet(X0) [resolution 224,235] 273. $false <- (~2) [resolution 272,246] 274. 2 [avatar contradiction clause 273] 328. paul = sK2 | mary = sK2 | fred = sK2 <- (5) [resolution 223,270] 355. mary = sK2 | fred = sK2 <- (~3, 5) [subsumption resolution 328,254] 356. fred = sK2 <- (~3, ~4, 5) [subsumption resolution 355,262] 357. $false <- (~1, ~3, ~4, 5) [subsumption resolution 356,242] 358. 1 | 3 | 4 | ~5 [avatar contradiction clause 357] 359. $false [avatar sat refutation 247,255,263,271,274,358] % SZS output end Proof for 256974972532358688156973 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Everyone in the room who works on fridays owns a microscope. Everyone in the room who maintains a personal blog focused on cybersecurity tips mentors a youth basketball team on weekends. Everyone in the room who maintains a personal blog focused on cybersecurity tips collects modern art. Everyone anywhere who collects modern art, enjoys virtual reality gaming or can play the piano either owns a smart tv or can play the piano but not both. Not everyone in the room does practice yoga if they owns a significant collection of rare gemstones and minerals. Everyone in the room who enjoys spelunking owns a smart tv. Everyone anywhere who owns a smart tv works as a freelance web developer specializing in e-commerce sites.

Everyone in the room plays as a goalkeeper for a local amateur soccer team.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((works_on_fridays(X))=>(owns_a_microscope(X))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(collects_modern_art(X))))))& (![X]:(anywhere(X)=>(((((collects_modern_art(X))|(enjoys_virtual_reality_gaming(X))|(can_play_the_piano(X))))=>(((owns_a_smart_tv(X))<~>(can_play_the_piano(X))))))))& (~![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(owns_a_smart_tv(X))))))& (![X]:(anywhere(X)=>(((owns_a_smart_tv(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))<=(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((does_practice_yoga(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))=>(((collects_modern_art(X))&(mentors_a_youth_basketball_team_on_weekends(X))&(works_on_fridays(X))))))))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(is_a_drone_photographer(X))))))& (![X]:(~room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(owns_a_smart_tv(X))))))& (~![X]:(~room(X)=>(((owns_a_smart_tv(X))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(owns_a_smart_tv(X))))))& (![X]:(anywhere(X)=>(((owns_a_smart_tv(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(~room(X)=>(((collects_modern_art(X))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(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))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))<=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((((can_play_the_flute(X))&(is_a_client_of_Meta(X))&(is_a_drone_photographer(X))))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(~room(X)=>(can_play_the_flute(X))))& (![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))=>(owns_a_smart_tv(X))))))& (![X]:(anywhere(X)=>(is_a_client_of_Meta(X))))& (![X]:(anywhere(X)=>(((does_practice_yoga(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((owns_a_microscope(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))

(there_is_a_room)& ![X]:(room(X)=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))

Eric, Margaret, Cynthia, Armando, Clara are the only persons in the room. “Everyone in the room is not an expert in identifying and foraging wild edible plants and is not a chess master who participates in national tournaments” only if “only one person in the room does not write a travel blog”. Everyone in the room does not collect comic books, does not write a travel blog and is not a client of Meta. Everyone in the room does not enjoy kayaking, does not compete in national level swimming championships and is not a chess master who participates in national tournaments. Everyone outside the room is not allergic to anything. Everyone in the room does not bake bread at home. Everyone outside the room does not enjoy fishing. Everyone outside the room does not enjoy making ceramics. Everyone in the room is not a client of Meta. Everyone anywhere does not practice archery, does not enjoy making ceramics or does not have a curated collection of mid-century modern furniture. Everyone in the room does not enjoy making ceramics.

Everyone in the room is not allergic to anything or bakes bread at home.

neutral

room(eric)&room(margaret)&room(cynthia)&room(armando)&room(clara)&(![X]:(room(X)=>(X='eric'|X='margaret'|X='cynthia'|X='armando'|X='clara')))& ((![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))=>(((?[X]:(room(X)&does_not_write_a_travel_blog(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_write_a_travel_blog(X))&(does_not_write_a_travel_blog(Y)))=>(X=Y))))))& (![X]:(room(X)=>(((does_not_collect_comic_books(X))&(does_not_write_a_travel_blog(X))&(is_not_a_client_of_Meta(X))))))& (![X]:(room(X)=>(((does_not_enjoy_kayaking(X))&(does_not_compete_in_national_level_swimming_championships(X))&(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(~room(X)=>(is_not_allergic_to_anything(X))))& (![X]:(room(X)=>(does_not_bake_bread_at_home(X))))& (![X]:(~room(X)=>(does_not_enjoy_fishing(X))))& (![X]:(~room(X)=>(does_not_enjoy_making_ceramics(X))))& (![X]:(room(X)=>(is_not_a_client_of_Meta(X))))& (![X]:(anywhere(X)=>(((does_not_practice_archery(X))|(does_not_enjoy_making_ceramics(X))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(does_not_enjoy_making_ceramics(X))))

room(eric)&room(margaret)&room(cynthia)&room(armando)&room(clara)&(![X]:(room(X)=>(X='eric'|X='margaret'|X='cynthia'|X='armando'|X='clara')))& ![X]:(room(X)=>(((bakes_bread_at_home(X))|(is_not_allergic_to_anything(X)))))

Laura is the only person in the room. It is not the case that “Patricia is older than Laura”.

Patricia is older than Laura.

contradiction

room(laura)&(![X]:(room(X)=>(X='laura')))& (~(older(laura,patricia)))& (![X]:(room(X)=>(((kind(X)&person(X))=>(((~(tall(X)&quiet(X)&old(X)&person(X)))&(older(patricia,X))))))))& (![X]:(room(X)=>(((((~(tall(X)&quiet(X)&old(X)&person(X)))&(older(patricia,X))))=>(tall(X)&person(X))))))& (![X]:(old(X)=>quiet(X)))& (![X]:(room(X)=>(((~(quiet(X)&person(X)))=>(older(patricia,X))))))& (![X]:(room(X)=>(((older(patricia,X))=>(tall(X)&old(X)&person(X))))))& (![X]:(room(X)=>(((tall(X)&old(X)&person(X))=>(kind(X)&old(X)&quiet(X)&person(X))))))& (quieter(laura,patricia))& (![X]:(room(X)=>(((quieter(patricia,X))=>(richer(patricia,X))))))& (![X]:(room(X)=>(((richer(patricia,X))=>(old(X)&person(X))))))& (~?[X]:(anywhere(X)=>(((old(X)&person(X))=>(quiet(X)&kind(X)&person(X))))))& (![X]:(room(X)=>(((richer(patricia,X))=>(quieter(patricia,X))))))

room(laura)&(![X]:(room(X)=>(X='laura')))& older(laura,patricia)

% SZS status Unsatisfiable for 975096630767853919104656 % SZS output start Proof for 975096630767853919104656 45. ~older(mary,paul) [input p1] 57. older(mary,paul) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 151. older(mary,paul) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 57] 235. ~older(mary,paul) [cnf transformation 45] 266. older(mary,paul) [cnf transformation 151] 272. $false [subsumption resolution 266,235] % SZS output end Proof for 975096630767853919104656 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Kenneth, Thomas, Fred, Lidia are the only persons in the room. Fred is a certified yoga instructor teaching classes weekly. Fred is a skilled home brewer experimenting with craft beer recipes. If someone is a certified yoga instructor teaching classes weekly then he/she is a skilled home brewer experimenting with craft beer recipes. Only one person in the room is a dedicated advocate for digital privacy and encryption. Thomas is a dedicated advocate for digital privacy and encryption or is a skilled home brewer experimenting with craft beer recipes or both. Kenneth is a skilled home brewer experimenting with craft beer recipes. Thomas either is a skilled home brewer experimenting with craft beer recipes or is a dedicated advocate for digital privacy and encryption but not both. Thomas is a dedicated advocate for digital privacy and encryption. Fred can play the harmonica.

It is true that “Thomas is a certified yoga instructor teaching classes weekly”.

contradiction

room(kenneth)&room(thomas)&room(fred)&room(lidia)&(![X]:(room(X)=>(X='kenneth'|X='thomas'|X='fred'|X='lidia')))& (is_a_certified_yoga_instructor_teaching_classes_weekly(fred))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(fred))& ((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))& (((?[X]:(room(X)&is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(Y)))=>(X=Y)))))& (((is_a_dedicated_advocate_for_digital_privacy_and_encryption(thomas))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(thomas))))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(kenneth))& (((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(thomas))<~>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(thomas))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(thomas))& (can_play_the_harmonica(fred))

room(kenneth)&room(thomas)&room(fred)&room(lidia)&(![X]:(room(X)=>(X='kenneth'|X='thomas'|X='fred'|X='lidia')))& is_a_certified_yoga_instructor_teaching_classes_weekly(thomas)

% SZS status Unsatisfiable for 6008949138235158475500830 % SZS output start Proof for 6008949138235158475500830 47. ! [X0] : (predd(X0) => predc(X0)) [input p3] 51. predc(paul) <~> preda(paul) [input p7] 52. preda(paul) [input p8] 54. predd(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 131. ! [X0] : (predc(X0) | ~predd(X0)) [ennf transformation 47] 134. predd(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 135. predd(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134] 139. (~preda(paul) | ~predc(paul)) & (preda(paul) | predc(paul)) [nnf transformation 51] 227. ~predd(X0) | predc(X0) [cnf transformation 131] 234. ~preda(paul) | ~predc(paul) [cnf transformation 139] 235. preda(paul) [cnf transformation 52] 241. predd(paul) [cnf transformation 135] 243. 1 <=> preda(paul) [avatar definition] 247. 2 <=> predc(paul) [avatar definition] 248. ~predc(paul) <- (~2) [avatar component clause 247] 251. ~2 | ~1 [avatar split clause 234,243,247] 253. 1 [avatar split clause 235,243] 255. predc(paul) [resolution 227,241] 256. $false <- (~2) [subsumption resolution 255,248] 257. 2 [avatar contradiction clause 256] 258. $false [avatar sat refutation 251,253,257] % SZS output end Proof for 6008949138235158475500830 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ronda, Jonathan are the only persons in the room. If “Ronda either creates bespoke furniture pieces from reclaimed wood or practices urban gardening but not both” then “it is not the case that “Ronda does not enjoy stargazing”” otherwise “Jonathan makes intricate hand-cut paper art for exhibitions, works on fridays and enjoys kayaking and exploring remote waterways”. “Not everyone in the room collects action figures or does not enjoy kayaking and exploring remote waterways” if “Ronda does not collect comic books” and vice versa. “Everyone outside the room does not compete in national level swimming championships or does not have a tattoo” if “Jonathan collects historical artifacts related to ancient civilizations” and vice versa. Jonathan creates bespoke furniture pieces from reclaimed wood. Everyone anywhere is a professional photographer specializing in portrait photography only if they does not collect action figures. Everyone in the room competes in national level swimming championships if they can play the harmonica, creates YouTube content and collects limited-edition art prints from contemporary artists. Ronda does not participate in long-distance cycling events across the country. Ronda who practices urban gardening, competes in national level swimming championships or collects historical artifacts related to ancient civilizations does not compete in national level swimming championships. Jonathan is not a dedicated advocate for digital privacy and encryption or hosts a YouTube channel dedicated to art tutorials or both. Ronda either creates bespoke furniture pieces from reclaimed wood or practices urban gardening but not both. Everyone in the room is a client of Costco if they does not collect action figures. Not everyone anywhere who is a client of Costco collects historical artifacts related to ancient civilizations. Ronda enjoys stargazing. Everyone in the room has a tattoo if they is a dedicated advocate for digital privacy and encryption. Jonathan does not practice urban gardening. If someone is not a client of Costco then he/she enjoys macrame. Jonathan can play the harmonica. Ronda who is an avid collector of autographed memorabilia from famous musicians collects limited-edition art prints from contemporary artists. If someone is a professional photographer specializing in portrait photography then he/she participates in long-distance cycling events across the country.

Ronda is an avid collector of autographed memorabilia from famous musicians.

entailment

room(ronda)&room(jonathan)&(![X]:(room(X)=>(X='ronda'|X='jonathan')))& (((((creates_bespoke_furniture_pieces_from_reclaimed_wood(ronda))<~>(practices_urban_gardening(ronda))))=>(~(does_not_enjoy_stargazing(ronda))))&((~(((creates_bespoke_furniture_pieces_from_reclaimed_wood(ronda))<~>(practices_urban_gardening(ronda)))))=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(jonathan))&(works_on_fridays(jonathan))&(enjoys_kayaking_and_exploring_remote_waterways(jonathan))))))& ((does_not_collect_comic_books(ronda))<=>(~![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(collects_action_figures(X)))))))& ((collects_historical_artifacts_related_to_ancient_civilizations(jonathan))<=>(![X]:(~room(X)=>(((does_not_have_a_tattoo(X))|(does_not_compete_in_national_level_swimming_championships(X)))))))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(jonathan))& (![X]:(anywhere(X)=>(((does_not_collect_action_figures(X))<=(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((((can_play_the_harmonica(X))&(creates_YouTube_content(X))&(collects_limited-edition_art_prints_from_contemporary_artists(X))))=>(competes_in_national_level_swimming_championships(X))))))& (does_not_participate_in_long-distance_cycling_events_across_the_country(ronda))& ((((practices_urban_gardening(ronda))|(competes_in_national_level_swimming_championships(ronda))|(collects_historical_artifacts_related_to_ancient_civilizations(ronda))))&(does_not_compete_in_national_level_swimming_championships(ronda)))& (((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(jonathan))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(jonathan))))& (((creates_bespoke_furniture_pieces_from_reclaimed_wood(ronda))<~>(practices_urban_gardening(ronda))))& (![X]:(room(X)=>(((does_not_collect_action_figures(X))=>(is_a_client_of_Costco(X))))))& (~![X]:(anywhere(X)=>(((is_a_client_of_Costco(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (enjoys_stargazing(ronda))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(has_a_tattoo(X))))))& (does_not_practice_urban_gardening(jonathan))& ((![X]:((is_not_a_client_of_Costco(X))=>(enjoys_macrame(X)))))& (can_play_the_harmonica(jonathan))& ((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(ronda))&(collects_limited-edition_art_prints_from_contemporary_artists(ronda)))& ((![X]:((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(participates_in_long-distance_cycling_events_across_the_country(X)))))

room(ronda)&room(jonathan)&(![X]:(room(X)=>(X='ronda'|X='jonathan')))& is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(ronda)

% SZS status Unsatisfiable for 6036335596205118895940957 % SZS output start Proof for 6036335596205118895940957 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 62. preds(mary) & predc(mary) [input p18] 64. ~(predc(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 71. predc(mary) [pure predicate removal 62] 153. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 154. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 153] 161. ~predc(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 64] 162. ~predc(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 161] 176. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 177. ~predc(mary) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 162,176] 258. room(mary) [cnf transformation 154] 259. room(paul) [cnf transformation 154] 260. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 154] 278. predc(mary) [cnf transformation 71] 279. ~predc(mary) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 177] 280. ~predc(mary) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 177] 281. ~predc(mary) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 177] 350. paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 281,278] 351. paul != sK3 | ~room(mary) [subsumption resolution 350,259] 352. paul != sK3 [subsumption resolution 351,258] 353. mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 280,278] 354. mary != sK3 | ~room(mary) [subsumption resolution 353,259] 355. mary != sK3 [subsumption resolution 354,258] 356. room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 279,278] 357. room(sK3) | ~room(mary) [subsumption resolution 356,259] 358. room(sK3) [subsumption resolution 357,258] 361. mary = sK3 | paul = sK3 [resolution 260,358] 362. paul = sK3 [subsumption resolution 361,355] 363. $false [subsumption resolution 362,352] % SZS output end Proof for 6036335596205118895940957 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Stewart is the only person in the room. If “Stewart is not generous, not creative, not happy, not funny, not patient” then “Stewart is a calm creative person”. If “Stewart is patient” then “Stewart is quieter than Thomas”. If “Stewart is a quiet creative person” then “everyone in the room is quieter than Anne”. Either “Stewart is not humble, not curious, is not funny, not strong and is not funny” or “Stewart neither is not creative nor is richer than Thomas” but not both. If “Stewart neither is quieter than Anne nor is richer than Jay” then “Stewart is richer than Jay”. If “Stewart is richer than Anne” then “someone in the room is curious”. “No one outside the room is older than Anne” if “Stewart is brave” and vice versa. If “Stewart is not tall” then “Stewart is a happy tall strong funny person and is not tall, not wise, not strong”. If “Stewart is not wise” then “Stewart who is not strong, is not old, not generous, not patient, not curious, not quiet and is older than Janene neither is quieter than Janene nor is tall”.

Stewart is old.

neutral

room(stewart)&(![X]:(room(X)=>(X='stewart')))& ((~generous(stewart)&~creative(stewart)&~happy(stewart)&~funny(stewart)&~patient(stewart))=>(calm(stewart)&creative(stewart)&person(stewart)))& ((patient(stewart))=>(quieter(thomas,stewart)))& ((quiet(stewart)&creative(stewart)&person(stewart))=>(![X]:(room(X)=>(quieter(anne,X)))))& ((((~humble(stewart)&~curious(stewart))&(~funny(stewart)&~strong(stewart))&(~funny(stewart))))<~>(~((~creative(stewart))|(richer(thomas,stewart)))))& ((~((quieter(anne,stewart))|(richer(jay,stewart))))=>(richer(jay,stewart)))& ((richer(anne,stewart))=>(?[X]:(room(X)&(curious(X)))))& ((brave(stewart))<=>(~?[X]:(~room(X)=>(older(anne,X)))))& ((~tall(stewart))=>(((happy(stewart)&tall(stewart)&strong(stewart)&funny(stewart)&person(stewart))&(~tall(stewart)&~wise(stewart)&~strong(stewart)))))& ((~wise(stewart))=>((((~strong(stewart))&(~old(stewart)&~generous(stewart)&~patient(stewart)&~curious(stewart)&~quiet(stewart))&(older(janene,stewart))))&(~((quieter(janene,stewart))|(tall(stewart))))))& ((~tall(stewart)&~happy(stewart)&~generous(stewart))<=>(~((older(thomas,stewart))|(~generous(stewart)))))& ((((~tall(stewart)&~strong(stewart))&(~patient(stewart)&~curious(stewart)&~strong(stewart)&~quiet(stewart))))=>(quieter(thomas,stewart)))& ((~((quieter(anne,stewart))|(~quiet(stewart)&~kind(stewart)&~humble(stewart)&~patient(stewart))))=>(?[X,Y]:((~((older(thomas,X))|(~old(X)&~strong(X)&~kind(X))))&(~funny(Y)&~happy(Y)&~quiet(Y))&(quieter(X,Y)))))& (older(thomas,stewart))& (![X]:(room(X)=>(((older(anne,X))<=>(quieter(anne,X))))))& (older(jay,stewart))& (~((~funny(stewart)&~wise(stewart))|(quieter(janene,stewart))))& (richer(jay,stewart))& (~((strong(stewart))|(~generous(stewart)&~creative(stewart))))& (?[X,Y]:((older(janene,X))&(~quiet(Y)&~kind(Y))&(older(X,Y))))& (~creative(stewart)&~brave(stewart))& (quieter(anne,stewart))& (![X]:(room(X)=>(((older(thomas,X))=>(~~tall(X))))))

room(stewart)&(![X]:(room(X)=>(X='stewart')))& old(stewart)

Tracy, Sonya are the only persons in the room. If “someone in the room is a professional photographer specializing in portrait photography” then “at least one person in the room is not a professional photographer specializing in portrait photography”. Only one person in the room bakes bread at home. Someone in the room is not a culinary enthusiast who experiments with international cuisines. Tracy owns an Android phone. Someone in the room does enjoy mountain biking. Everyone in the room is a craft beer aficionado. If someone does not enjoy deep-sea diving and exploring underwater caves then he/she develops open-source software projects in their free time. At least one person in the room is not a professional photographer specializing in portrait photography. Someone anywhere enjoys deep-sea diving and exploring underwater caves. At least one person in the room is not dedicated to sustainable living and zero-waste practices. More than one person in the room is an avid collector of autographed memorabilia from famous musicians. More than one person in the room regularly goes on multi-day backpacking trips in national parks. Someone in the room is not a member of a local theater group specializing in improv. Someone in the room does not have a vast collection of first-edition science fiction novels. Someone in the room does not enjoy mountain biking. Someone in the room develops open-source software projects in their free time. Everyone in the room is not a member of a local theater group specializing in improv if they regularly goes on multi-day backpacking trips in national parks or is not a member of a local theater group specializing in improv or both. Everyone in the room does not bake bread at home if they does not own a smartwatch. Tracy regularly goes on multi-day backpacking trips in national parks or is not a member of a local theater group specializing in improv or both.

Only one person in the room enjoys deep-sea diving and exploring underwater caves.

neutral

room(tracy)&room(sonya)&(![X]:(room(X)=>(X='tracy'|X='sonya')))& ((?[X]:(room(X)&(is_a_professional_photographer_specializing_in_portrait_photography(X))))=>(((?[X]:(room(X)&is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& (((?[X]:(room(X)&bakes_bread_at_home(X)))&(![X,Y]:((room(X)&room(Y)&(bakes_bread_at_home(X))&(bakes_bread_at_home(Y)))=>(X=Y)))))& (?[X]:(room(X)&(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))& (owns_an_Android_phone(tracy))& (?[X]:(room(X)&(does_enjoy_mountain_biking(X))))& (![X]:(room(X)=>(is_a_craft_beer_aficionado(X))))& ((![X]:((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))=>(develops_open-source_software_projects_in_their_free_time(X)))))& (((?[X]:(room(X)&is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))& (?[X]:(anywhere(X)&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))& (((?[X]:(room(X)&is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& ((?[X,Y]:(room(X)&room(Y)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)&is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(Y))&(X!=Y))))& ((?[X,Y]:(room(X)&room(Y)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)&regularly_goes_on_multi-day_backpacking_trips_in_national_parks(Y))&(X!=Y))))& (?[X]:(room(X)&(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))& (?[X]:(room(X)&(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))& (?[X]:(room(X)&(does_not_enjoy_mountain_biking(X))))& (?[X]:(room(X)&(develops_open-source_software_projects_in_their_free_time(X))))& (![X]:(room(X)=>(((((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(((does_not_own_a_smartwatch(X))=>(does_not_bake_bread_at_home(X))))))& (((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(tracy))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(tracy))))

room(tracy)&room(sonya)&(![X]:(room(X)=>(X='tracy'|X='sonya')))& ((?[X]:(room(X)&enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(Y)))=>(X=Y))))

There is a room. Everyone outside the room who is a skilled home brewer experimenting with craft beer recipes is a client of Meta. Everyone in the room is not a certified yoga instructor teaching classes weekly only if they is a client of Meta and does enjoy mountain biking. Everyone in the room is a client of Meta and does enjoy mountain biking only if they is not a certified yoga instructor teaching classes weekly. Everyone outside the room is a certified yoga instructor teaching classes weekly if they does enjoy mountain biking. If someone is a certified yoga instructor teaching classes weekly then he/she does enjoy mountain biking. Everyone in the room is a skilled home brewer experimenting with craft beer recipes if they is a certified yoga instructor teaching classes weekly and does enjoy mountain biking. Everyone in the room does enjoy mountain biking if they is a client of Meta. Everyone in the room who does enjoy mountain biking is a certified yoga instructor teaching classes weekly.

Everyone outside the room is a skilled home brewer experimenting with craft beer recipes.

neutral

(there_is_a_room)& (![X]:(~room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(is_a_client_of_Meta(X))))))& (![X]:(room(X)=>(((((is_a_client_of_Meta(X))&(does_enjoy_mountain_biking(X))))<=(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))<=(((is_a_client_of_Meta(X))&(does_enjoy_mountain_biking(X))))))))& (![X]:(~room(X)=>(((does_enjoy_mountain_biking(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& ((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(does_enjoy_mountain_biking(X)))))& (![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(does_enjoy_mountain_biking(X))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))

(there_is_a_room)& ![X]:(~room(X)=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))

Joseph, David, Avril are the only persons in the room. “Someone in the room works on fridays” unless “Joseph and Erin hate each other”. If “it is true that “it is true that “someone in the room practices kickboxing””” then “Avril and Erik like each other”. Joseph and Erin hate each other. If someone is a client of Erik then he/she is a client of Erinny. Someone in the room is a sibling of Erik. If someone is a client of Erik then he/she own a television. No brave person is generous. All funny persons are humble. Someone who is an avid hiker like someone who owns a smartwatch. If someone is a client of Erinny then he/she collects rare and antique scientific instruments. No calm person is humble. Joseph and Avril are respectively brave and happy. All old persons are humble. All strong persons are generous. Someone who is a sibling of Erinny hate someone who is not liked by Erik. Avril is quieter than Joseph. David is the poorest in the room. Avril and Joseph hate each other. David and Avril are respectively patient and kind. Only one person in the room collects antique jewelry.

All brave persons are funny.

contradiction

room(joseph)&room(david)&room(avril)&(![X]:(room(X)=>(X='joseph'|X='david'|X='avril')))& (~((hate(joseph,erin) & hate(erin,joseph)))=>(?[X]:(room(X)&(works_on_fridays(X)))))& ((?[X]:(room(X)&(practices_kickboxing(X))))=>((like(avril,erik) & like(erik,avril))))& ((hate(joseph,erin) & hate(erin,joseph)))& ((![X]:((client(erik,X))=>(client(erinny,X)))))& (?[X]:(room(X)&(sibling(erik,X))))& ((![X]:((client(erik,X))=>(own_a_television(X)))))& (~?[X]:(brave(X)=>generous(X)))& (![X]:(funny(X)=>humble(X)))& (?[X,Y]:((is_an_avid_hiker(X))&(owns_a_smartwatch(Y))&(like(X,Y))))& ((![X]:((client(erinny,X))=>(collects_rare_and_antique_scientific_instruments(X)))))& (~?[X]:(calm(X)=>humble(X)))& ((brave(joseph))&(happy(avril)))& (![X]:(old(X)=>humble(X)))& (![X]:(strong(X)=>generous(X)))& (?[X,Y]:((sibling(erinny,X))&(~like(Y,erik))&(hate(X,Y))))& (quieter(joseph,avril))& (![X]:((room(X)&(X!=david))=>poorer(X,david)))& ((hate(avril,joseph) & hate(joseph,avril)))& ((patient(david))&(kind(avril)))& (((?[X]:(room(X)&collects_antique_jewelry(X)))&(![X,Y]:((room(X)&room(Y)&(collects_antique_jewelry(X))&(collects_antique_jewelry(Y)))=>(X=Y)))))& ((like(avril,erik) & like(erik,avril)))& (louder(david,avril))& ((![X]:((collects_vintage_stamps(X))=>(poorer(erin,X)))))& (?[X]:(room(X)&(works_on_fridays(X))))& (![X]:(tall(X)=>creative(X)))

room(joseph)&room(david)&room(avril)&(![X]:(room(X)=>(X='joseph'|X='david'|X='avril')))& ![X]:(brave(X)=>funny(X))

% SZS status Unsatisfiable for 79457266587399639296864 % SZS output start Proof for 79457266587399639296864 51. ~? [X0] : (brave(X0) => generous(X0)) [input p7] 52. ! [X0] : (funny(X0) => humble(X0)) [input p8] 55. ~? [X0] : (calm(X0) => humble(X0)) [input p11] 70. ! [X0] : (brave(X0) => funny(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 72. ! [X0] : (brave(X0) => funny(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 70] 78. ~? [X0] : ~brave(X0) [pure predicate removal 51] 80. ~? [X0] : humble(X0) [pure predicate removal 55] 166. ! [X0] : brave(X0) [ennf transformation 78] 167. ! [X0] : (humble(X0) | ~funny(X0)) [ennf transformation 52] 168. ! [X0] : ~humble(X0) [ennf transformation 80] 174. ! [X0] : (funny(X0) | ~brave(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 72] 175. ! [X0] : (funny(X0) | ~brave(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 174] 282. brave(X0) [cnf transformation 166] 283. ~funny(X0) | humble(X0) [cnf transformation 167] 285. ~humble(X0) [cnf transformation 168] 306. funny(X0) | ~brave(X0) [cnf transformation 175] 324. funny(X0) [subsumption resolution 306,282] 325. humble(X0) [resolution 283,324] 326. $false [subsumption resolution 325,285] % SZS output end Proof for 79457266587399639296864 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. If 'everyone in the room is not an avid collector of autographed memorabilia from famous musicians or collects historical artifacts related to ancient civilizations' then 'not everyone in the room does not enjoy origami or is not an avid collector of autographed memorabilia from famous musicians'. 'Everyone in the room drives a hybrid car only if they does not own a telescope, enjoys virtual reality gaming or has a saltwater aquarium' unless 'everyone anywhere does not enjoy logic puzzles or enjoys virtual reality gaming'. 'Sarah dreamt that 'everyone in the room does not have a saltwater aquarium if they does not have a pet dog and vice versa'' unless 'everyone anywhere bakes bread at home, does practice yoga and is a tea enthusiast'. 'Everyone anywhere does not participate in citizen science projects related to wildlife monitoring or does not host themed dinner parties featuring gourmet home-cooked meals' only if 'everyone in the room does not collect historical artifacts related to ancient civilizations if they collects historical artifacts related to ancient civilizations'. 'No one in the room who does not bake bread at home collects modern art' if 'everyone outside the room does not bake bread at home or plays video games'. Everyone in the room collects modern art only if they collects first edition books. Not everyone in the room collects historical artifacts related to ancient civilizations if they collects first edition books.

Everyone in the room collects historical artifacts related to ancient civilizations.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))=>(~![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_enjoy_origami(X)))))))& (~(![X]:(anywhere(X)=>(((enjoys_virtual_reality_gaming(X))|(does_not_enjoy_logic_puzzles(X))))))=>(![X]:(room(X)=>(((((does_not_own_a_telescope(X))|(enjoys_virtual_reality_gaming(X))|(has_a_saltwater_aquarium(X))))<=(drives_a_hybrid_car(X)))))))& (~(![X]:(anywhere(X)=>(((bakes_bread_at_home(X))&(does_practice_yoga(X))&(is_a_tea_enthusiast(X))))))=>((sarah_dream=>(![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))<=>(does_not_have_a_pet_dog(X)))))))))& ((![X]:(anywhere(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>(![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X)))))))& ((![X]:(~room(X)=>(((plays_video_games(X))|(does_not_bake_bread_at_home(X))))))=>(~?[X]:(room(X)=>(((does_not_bake_bread_at_home(X))=>(collects_modern_art(X)))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))<=(collects_modern_art(X))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(owns_a_microscope(X))))))))& (![X]:(room(X)=>(((((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(owns_a_microscope(X))))=>(writes_poetry(X))))))& (~![X]:(room(X)=>(((collects_first_edition_books(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (~![X]:(anywhere(X)=>(((does_not_enjoy_origami(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(has_a_pet_dog(X))))=>(((does_practice_yoga(X))|(collects_modern_art(X))|(collects_first_edition_books(X))))))))& (![X]:(room(X)=>(((((does_practice_yoga(X))|(collects_modern_art(X))|(collects_first_edition_books(X))))<=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (~?[X]:(room(X)=>(((does_not_bake_bread_at_home(X))=>(collects_modern_art(X))))))& (![X]:(anywhere(X)=>(((writes_poetry(X))|(does_not_use_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((does_not_have_a_pet_dog(X))<=(does_not_collect_modern_art(X))))))& (![X]:(anywhere(X)=>(((does_not_have_a_pet_dog(X))=>(does_not_use_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((does_not_use_a_Windows_laptop(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (~![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))<~>(does_not_enjoy_logic_puzzles(X))))))& (![X]:(room(X)=>(((((has_a_pet_dog(X))|(has_a_saltwater_aquarium(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))<=(has_a_pet_dog(X))))))& ((![X]:((is_a_tea_enthusiast(X))=>(plays_the_violin(X)))))& (![X]:(room(X)=>(((owns_a_telescope(X))<=>(((enjoys_logic_puzzles(X))|(does_not_collect_modern_art(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))))& (![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))=>(((does_not_enjoy_virtual_reality_gaming(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_write_poetry(X))))))))& (![X]:(room(X)=>(((((does_not_enjoy_virtual_reality_gaming(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_write_poetry(X))))=>(has_a_saltwater_aquarium(X))))))& (![X]:(anywhere(X)=>(((has_a_saltwater_aquarium(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))<~>(owns_a_telescope(X))))))& (![X]:(~room(X)=>(((has_a_pet_dog(X))=>(((does_practice_yoga(X))|(is_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((does_not_have_a_pet_dog(X))<=(((does_practice_yoga(X))|(is_a_tea_enthusiast(X))))))))& ((![X]:((((writes_poetry(X))|(has_a_saltwater_aquarium(X))|(is_a_tea_enthusiast(X))))=>(owns_a_telescope(X)))))

(there_is_a_room)& ![X]:(room(X)=>(collects_historical_artifacts_related_to_ancient_civilizations(X)))

% SZS status Unsatisfiable for 7545634456790919489731812 % SZS output start Proof for 7545634456790919489731812 53. ~! [X0] : (room(X0) => (predd(X0) => predk(X0))) [input p9] 73. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 84. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 73] 169. ? [X0] : ((~predk(X0) & predd(X0)) & room(X0)) [ennf transformation 53] 170. ? [X0] : (~predk(X0) & predd(X0) & room(X0)) [flattening 169] 202. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 84] 218. ? [X0] : (~predk(X0) & predd(X0) & room(X0)) => (~predk(sK5) & predd(sK5) & room(sK5)) [choice axiom] 219. ~predk(sK5) & predd(sK5) & room(sK5) [skolemisation 170,218] 330. room(sK5) [cnf transformation 219] 332. ~predk(sK5) [cnf transformation 219] 369. ~room(X0) | predk(X0) [cnf transformation 202] 455. predk(sK5) [resolution 369,330] 458. $false [subsumption resolution 455,332] % SZS output end Proof for 7545634456790919489731812 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Carolina, Stephanie, Robert, Wade, Stephanie are the only persons in the room. "Someone in the room does enjoy trail running" unless "Stephanie either practices pilates or does not enjoy cross-country skiing but not both". "Everyone anywhere is calm if they does not enjoy fishing or owns a microscope or both" unless "everyone in the room is a client of Samuel or does not collect rare and antique scientific instruments". If "Stephanie is not old, not calm, makes homemade pastries or is richer than Samuel" then "everyone in the room who does not hate Samuel and is old uses contact lenses". "Stephanie and Samuel like each other" only if "not everyone in the room is not an avid mountain climber who has scaled several peaks". If "someone in the room is older than Kristen" then "A car runs solely on saltwater.". "Everyone in the room is not an avid mountain climber who has scaled several peaks or is not tall" only if "Samuel is older than Wade". Stephanie is not old, not calm, makes homemade pastries or is richer than Samuel.

Not everyone in the room is not a old person, is quiet and is not quiet.

entailment

room(carolina)&room(stephanie)&room(robert)&room(wade)&room(stephanie)&(![X]:(room(X)=>(X='carolina'|X='stephanie'|X='robert'|X='wade'|X='stephanie')))& (~(((practices_pilates(stephanie))<~>(does_not_enjoy_cross-country_skiing(stephanie))))=>(?[X]:(room(X)&(does_enjoy_trail_running(X)))))& (~(![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(client(samuel,X))))))=>(![X]:(anywhere(X)=>(((((does_not_enjoy_fishing(X))|(owns_a_microscope(X))))=>(calm(X)))))))& ((((~old(stephanie)&~calm(stephanie))|(makes_homemade_pastries(stephanie))|(richer(samuel,stephanie))))=>(![X]:(room(X)=>(((((~hate(samuel,X))&(old(X))))=>(uses_contact_lenses(X)))))))& (((like(stephanie,samuel) & like(samuel,stephanie)))=>(~![X]:(room(X)=>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))& ((?[X]:(room(X)&(older(kristen,X))))=>(A_car_runs_solely_on_saltwater.))& ((![X]:(room(X)=>(((~tall(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(older(wade,samuel)))& (((~old(stephanie)&~calm(stephanie))|(makes_homemade_pastries(stephanie))|(richer(samuel,stephanie))))& (((does_not_collect_rare_and_antique_scientific_instruments(stephanie))&(makes_homemade_pastries(stephanie))))& (![X]:(room(X)=>(sibling(samuel,X))))& (older(wade,samuel))& (~(?[X]:(room(X)&(quiet(X)&person(X)))))& (calm(stephanie)&european(stephanie)&calm(wade)&european(wade))& (?[X]:(~room(X)&(~(curious(X)&tourist(X)))))& (![X]:(old(X)=>humble(X)))& (sibling(samuel,stephanie))& (((~hate(samuel,stephanie))&(old(stephanie))))& (![X]:(anywhere(X)=>(((((~quiet(X))&(~(humble(X)&person(X)))))=>(owns_a_microscope(X))))))& (![X]:(room(X)=>(((owns_a_microscope(X))=>(humble(X)&funny(X)&tourist(X))))))& (![X]:((anywhere(X)&(X!=carolina))=>quieter(carolina,X)))& ((hate(kristen,wade) & hate(wade,kristen)))& (![X]:(room(X)=>(((strong(X)&person(X))=>(does_practice_yoga(X))))))& (![X]:(funny(X)=>patient(X)))& (~((A_car_runs_solely_on_saltwater.)|(A_river_does_not_flow_uphill_on_Tuesdays.)))& (?[X,Y]:((((~hate(samuel,X))&(old(X))))&(~~wise(Y))&(richer(X,Y))))

room(carolina)&room(stephanie)&room(robert)&room(wade)&room(stephanie)&(![X]:(room(X)=>(X='carolina'|X='stephanie'|X='robert'|X='wade'|X='stephanie')))& ~![X]:(room(X)=>(((~(old(X)&person(X)))&(quiet(X))&(~quiet(X)))))

% SZS status Unsatisfiable for 2586594313926840805127765 % SZS output start Proof for 2586594313926840805127765 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] 69. ~(~! [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] 71. ~(~! [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 69] 163. ! [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] 164. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 163] 177. ! [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 71] 178. ! [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 177] 179. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 180. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 178,179] 191. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 179] 192. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 191] 193. ? [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] 194. (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~sP0 [skolemisation 192,193] 278. room(mary) [cnf transformation 164] 279. room(paul) [cnf transformation 164] 280. room(fred) [cnf transformation 164] 281. room(alice) [cnf transformation 164] 282. room(john) [cnf transformation 164] 283. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 164] 306. room(sK6) | ~sP0 [cnf transformation 194] 307. mary != sK6 | ~sP0 [cnf transformation 194] 308. paul != sK6 | ~sP0 [cnf transformation 194] 309. fred != sK6 | ~sP0 [cnf transformation 194] 310. alice != sK6 | ~sP0 [cnf transformation 194] 311. john != sK6 | ~sP0 [cnf transformation 194] 313. quiet(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180] 314. ~quiet(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180] 351. 8 <=> sP0 [avatar definition] 355. 9 <=> john = sK6 [avatar definition] 357. john != sK6 <- (~9) [avatar component clause 355] 358. ~8 | ~9 [avatar split clause 311,355,351] 360. 10 <=> alice = sK6 [avatar definition] 362. alice != sK6 <- (~10) [avatar component clause 360] 363. ~8 | ~10 [avatar split clause 310,360,351] 365. 11 <=> fred = sK6 [avatar definition] 368. ~8 | ~11 [avatar split clause 309,365,351] 370. 12 <=> paul = sK6 [avatar definition] 372. paul != sK6 <- (~12) [avatar component clause 370] 373. ~8 | ~12 [avatar split clause 308,370,351] 375. 13 <=> mary = sK6 [avatar definition] 377. mary != sK6 <- (~13) [avatar component clause 375] 378. ~8 | ~13 [avatar split clause 307,375,351] 380. 14 <=> room(sK6) [avatar definition] 382. room(sK6) <- (14) [avatar component clause 380] 383. ~8 | 14 [avatar split clause 306,380,351] 384. ~quiet(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 314,282] 385. ~quiet(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 384,281] 386. ~quiet(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 385,280] 387. ~quiet(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 386,279] 388. ~quiet(X0) | ~room(X0) | sP0 [subsumption resolution 387,278] 390. 15 <=> ! [X0] : (~quiet(X0) | ~room(X0)) [avatar definition] 391. ~quiet(X0) | ~room(X0) <- (15) [avatar component clause 390] 392. 8 | 15 [avatar split clause 388,390,351] 393. quiet(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,282] 394. quiet(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 393,281] 395. quiet(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 394,280] 396. quiet(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 395,279] 397. quiet(X0) | ~room(X0) | sP0 [subsumption resolution 396,278] 399. 16 <=> ! [X0] : (quiet(X0) | ~room(X0)) [avatar definition] 400. quiet(X0) | ~room(X0) <- (16) [avatar component clause 399] 401. 8 | 16 [avatar split clause 397,399,351] 614. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (14) [resolution 283,382] 615. fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (~10, 14) [subsumption resolution 614,362] 621. fred = sK6 | mary = sK6 | john = sK6 <- (~10, ~12, 14) [subsumption resolution 615,372] 622. fred = sK6 | john = sK6 <- (~10, ~12, ~13, 14) [subsumption resolution 621,377] 623. fred = sK6 <- (~9, ~10, ~12, ~13, 14) [subsumption resolution 622,357] 624. 11 | 9 | 10 | 12 | 13 | ~14 [avatar split clause 623,380,375,370,360,355,365] 625. ~room(X0) <- (15, 16) [subsumption resolution 391,400] 631. $false <- (15, 16) [resolution 625,278] 640. ~15 | ~16 [avatar contradiction clause 631] 641. $false [avatar sat refutation 358,363,368,373,378,383,392,401,624,640] % SZS output end Proof for 2586594313926840805127765 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------

There is a room. If “everyone in the room cannot play the flute or works on fridays” then “everyone in the room is a chess master who participates in national tournaments if they cannot play the flute”. “No one in the room is not an enthusiastic bird watcher who travels for rare sightings” unless “everyone in the room does not have a saltwater aquarium or is an expert in identifying and foraging wild edible plants”. If someone has a tattoo and practices and performs acrobatic dance routines then he/she has a curated collection of mid-century modern furniture and vice versa. No one in the room who practices tai chi has a saltwater aquarium. Everyone in the room is an expert in identifying and foraging wild edible plants, works on fridays or practices urban gardening if they has a saltwater aquarium. Everyone in the room who is an expert in identifying and foraging wild edible plants, works on fridays or practices urban gardening is not a tea enthusiast. Everyone in the room does not practice yoga if they enjoys windsurfing. Everyone in the room practices and performs acrobatic dance routines and enjoys windsurfing if they does not practice yoga. Everyone in the room does not work on fridays, is an expert in identifying and foraging wild edible plants or enjoys windsurfing. No one in the room has a saltwater aquarium if they does not work as a freelance web developer specializing in e-commerce sites and has a tattoo. Someone in the room does not practice yoga. Everyone outside the room is not a tea enthusiast if they is a certified yoga instructor teaching classes weekly. Everyone in the room who is not a tea enthusiast practices archery. Everyone in the room neither is a certified yoga instructor teaching classes weekly nor collects historical artifacts related to ancient civilizations. Everyone in the room maintains a large, organic vegetable garden year-round if they has a tattoo. Everyone anywhere does not collect historical artifacts related to ancient civilizations, can play the flute or does not practice yoga if they maintains a large, organic vegetable garden year-round. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room who does not practice archery has a curated collection of mid-century modern furniture.

Everyone in the room hosts a YouTube channel dedicated to art tutorials.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((works_on_fridays(X))|(cannot_play_the_flute(X))))))=>(![X]:(room(X)=>(((cannot_play_the_flute(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X)))))))& (~(![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_have_a_saltwater_aquarium(X))))))=>(~?[X]:(room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& ((![X]:((((has_a_tattoo(X))&(practices_and_performs_acrobatic_dance_routines(X))))<=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))& (~?[X]:(room(X)=>(((practices_tai_chi(X))=>(has_a_saltwater_aquarium(X))))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(works_on_fridays(X))|(practices_urban_gardening(X))))))))& (![X]:(room(X)=>(((((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(works_on_fridays(X))|(practices_urban_gardening(X))))=>(is_not_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(does_not_practice_yoga(X))))))& (![X]:(room(X)=>(((does_not_practice_yoga(X))=>(((practices_and_performs_acrobatic_dance_routines(X))&(enjoys_windsurfing(X))))))))& (![X]:(room(X)=>(((does_not_work_on_fridays(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(enjoys_windsurfing(X))))))& (~?[X]:(room(X)=>(((((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(has_a_tattoo(X))))=>(has_a_saltwater_aquarium(X))))))& (?[X]:(room(X)&(does_not_practice_yoga(X))))& (![X]:(~room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_not_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))=>(practices_archery(X))))))& (![X]:(room(X)=>(~((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(anywhere(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(can_play_the_flute(X))|(does_not_practice_yoga(X))))))))& (![X]:(room(X)=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (![X]:(room(X)=>(((does_not_practice_archery(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((owns_a_smartwatch(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(has_a_piercing(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))|(practices_tai_chi(X))|(does_not_own_a_smartwatch(X))))))& (![X]:(room(X)=>(((can_play_the_flute(X))=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (?[X]:(room(X)&(does_practice_yoga(X))))

(there_is_a_room)& ![X]:(room(X)=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))

Michelle, Vera are the only persons in the room. Either “Vera volunteers for local environmental conservation projects” or “Michelle neither collects luxury watches nor cannot play the guitar” but not both. Either “Michelle collects historical artifacts related to ancient civilizations” or “Michelle does not collect historical artifacts related to ancient civilizations” but not both. Vera does not enjoy stand-up paddleboarding. Only one person in the room bakes bread at home. Michelle can play the guitar. Michelle is a client of Meta. Michelle has a pet dog. Michelle collects luxury watches. Michelle collects historical artifacts related to ancient civilizations. Vera bakes bread at home. Vera collects historical artifacts related to ancient civilizations. Michelle enjoys making ceramics. Only one person in the room enjoys stand-up paddleboarding. If someone can play the guitar then he/she is a client of Meta and vice versa. If someone collects historical artifacts related to ancient civilizations then he/she has a pet dog and vice versa. Only one person in the room collects luxury watches. Only one person anywhere bakes bread at home. Michelle volunteers for local environmental conservation projects. If someone can play the guitar then he/she enjoys stand-up paddleboarding and vice versa. If someone neither collects luxury watches nor is a client of Meta then he/she has a pet dog. Michelle is a Linux enthusiast. Michelle enjoys stand-up paddleboarding. Only one person in the room enjoys making ceramics. Vera is a Linux enthusiast.

Michelle bakes bread at home.

contradiction

room(michelle)&room(vera)&(![X]:(room(X)=>(X='michelle'|X='vera')))& ((volunteers_for_local_environmental_conservation_projects(vera))<~>(~((collects_luxury_watches(michelle))|(cannot_play_the_guitar(michelle)))))& ((collects_historical_artifacts_related_to_ancient_civilizations(michelle))<~>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(michelle)))& (does_not_enjoy_stand-up_paddleboarding(vera))& (((?[X]:(room(X)&bakes_bread_at_home(X)))&(![X,Y]:((room(X)&room(Y)&(bakes_bread_at_home(X))&(bakes_bread_at_home(Y)))=>(X=Y)))))& (can_play_the_guitar(michelle))& (is_a_client_of_Meta(michelle))& (has_a_pet_dog(michelle))& (collects_luxury_watches(michelle))& (collects_historical_artifacts_related_to_ancient_civilizations(michelle))& (bakes_bread_at_home(vera))& (collects_historical_artifacts_related_to_ancient_civilizations(vera))& (enjoys_making_ceramics(michelle))& (((?[X]:(room(X)&enjoys_stand-up_paddleboarding(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_stand-up_paddleboarding(X))&(enjoys_stand-up_paddleboarding(Y)))=>(X=Y)))))& ((![X]:((can_play_the_guitar(X))<=>(is_a_client_of_Meta(X)))))& ((![X]:((collects_historical_artifacts_related_to_ancient_civilizations(X))<=>(has_a_pet_dog(X)))))& (((?[X]:(room(X)&collects_luxury_watches(X)))&(![X,Y]:((room(X)&room(Y)&(collects_luxury_watches(X))&(collects_luxury_watches(Y)))=>(X=Y)))))& (((?[X]:(anywhere(X)&bakes_bread_at_home(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(bakes_bread_at_home(X))&(bakes_bread_at_home(Y)))=>(X=Y)))))& (volunteers_for_local_environmental_conservation_projects(michelle))& ((![X]:((can_play_the_guitar(X))<=>(enjoys_stand-up_paddleboarding(X)))))& ((![X]:((~((collects_luxury_watches(X))|(is_a_client_of_Meta(X))))=>(has_a_pet_dog(X)))))& (is_a_Linux_enthusiast(michelle))& (enjoys_stand-up_paddleboarding(michelle))& (((?[X]:(room(X)&enjoys_making_ceramics(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_making_ceramics(X))&(enjoys_making_ceramics(Y)))=>(X=Y)))))& (is_a_Linux_enthusiast(vera))

room(michelle)&room(vera)&(![X]:(room(X)=>(X='michelle'|X='vera')))& bakes_bread_at_home(michelle)

% SZS status Unsatisfiable for 82270686161084555269032 % SZS output start Proof for 82270686161084555269032 5. ! [X0] : anywhere(X0) [input b4] 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] 54. predf(paul) [input p10] 61. ! [X0,X1] : ((predf(X1) & predf(X0) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X0] : (predf(X0) & anywhere(X0)) [input p17] 69. predf(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 73. ! [X0,X1] : ((predf(X1) & predf(X0) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (predf(X2) & anywhere(X2)) [rectify 61] 157. ! [X0,X1] : (X0 = X1 | (~predf(X1) | ~predf(X0) | ~anywhere(X1) | ~anywhere(X0))) & ? [X2] : (predf(X2) & anywhere(X2)) [ennf transformation 73] 158. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~anywhere(X1) | ~anywhere(X0)) & ? [X2] : (predf(X2) & anywhere(X2)) [flattening 157] 163. predf(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 69] 164. predf(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 163] 177. ? [X2] : (predf(X2) & anywhere(X2)) => (predf(sK3) & anywhere(sK3)) [choice axiom] 178. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~anywhere(X1) | ~anywhere(X0)) & (predf(sK3) & anywhere(sK3)) [skolemisation 158,177] 182. anywhere(X0) [cnf transformation 5] 227. mary != paul [cnf transformation 43] 280. predf(paul) [cnf transformation 54] 295. X0 = X1 | ~predf(X1) | ~predf(X0) | ~anywhere(X1) | ~anywhere(X0) [cnf transformation 178] 307. predf(mary) [cnf transformation 164] 325. X0 = X1 | ~predf(X1) | ~predf(X0) | ~anywhere(X0) [subsumption resolution 295,182] 326. ~predf(X1) | X0 = X1 | ~predf(X0) [subsumption resolution 325,182] 340. ~predf(X0) | mary = X0 [resolution 326,307] 345. mary = paul [resolution 340,280] 348. $false [subsumption resolution 345,227] % SZS output end Proof for 82270686161084555269032 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Leola, Gwen, Mae, Diana, Jason are the only persons in the room. Either “Gwen collects historical artifacts related to ancient civilizations” or “Mae is a client of LVMH” but not both.

Everyone in the room is not a wine connoisseur.

neutral

room(leola)&room(gwen)&room(mae)&room(diana)&room(jason)&(![X]:(room(X)=>(X='leola'|X='gwen'|X='mae'|X='diana'|X='jason')))& ((collects_historical_artifacts_related_to_ancient_civilizations(gwen))<~>(is_a_client_of_LVMH(mae)))& ((?[X]:(room(X)&(owns_a_telescope(X))))=>((![X]:((creates_augmented_reality_experiences_for_mobile_applications(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& ((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(mae))=>(~(is_dedicated_to_sustainable_living_and_zero-waste_practices(leola))))& ((is_a_client_of_LVMH(mae))=>(![X]:(room(X)=>(((((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_a_wine_connoisseur(X))))=>(competes_in_national_level_swimming_championships(X)))))))& ((trains_for_and_competes_in_international_triathlons(gwen))=>(![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))& (is_a_client_of_LVMH(gwen))& (~?[X]:(anywhere(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(does_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((((does_enjoy_trail_running(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (creates_augmented_reality_experiences_for_mobile_applications(gwen))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (~![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(competes_in_national_level_swimming_championships(X))))))& ((![X]:((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(trains_for_and_competes_in_international_triathlons(X)))))& ((![X]:((owns_a_telescope(X))=>(watches_fantasy_movies(X)))))& ((![X]:((is_a_client_of_LVMH(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))

room(leola)&room(gwen)&room(mae)&room(diana)&room(jason)&(![X]:(room(X)=>(X='leola'|X='gwen'|X='mae'|X='diana'|X='jason')))& ![X]:(room(X)=>(is_not_a_wine_connoisseur(X)))

David is the only person in the room. “David streams on Twitch” unless “everyone in the room does not collect action figures or does not host regular game nights featuring complex strategy games”. “Everyone in the room is not a scotch connoisseur if they collects action figures” if “everyone in the room collects action figures or does not host regular game nights featuring complex strategy games”. If “David plays eSports competitively” then “everyone in the room bakes bread at home if they works on fridays”. If “everyone in the room enjoys skydiving” then “if someone does not create large-scale murals for public art installations then he/she is not a scotch connoisseur and vice versa”. If “no one in the room enjoys stargazing or does not own a high-end gaming PC with custom-built components” then “everyone in the room competes in national level swimming championships”. “Everyone in the room does practice yoga, mentors a youth basketball team on weekends or enjoys landscape photography if they hosts a YouTube channel dedicated to art tutorials” unless “everyone in the room does not create large-scale murals for public art installations or does not own a 3D printer”. If “everyone in the room owns a high-end gaming PC with custom-built components or does not enjoy landscape photography” then “no one in the room owns a high-end gaming PC with custom-built components if they collects action figures” otherwise “if someone hosts a YouTube channel dedicated to art tutorials then he/she hosts regular game nights featuring complex strategy games and vice versa”. If “everyone in the room is a scotch connoisseur” then “not everyone in the room who is a wine connoisseur neither does practice yoga nor enjoys cross-country skiing” otherwise “everyone in the room who neither does practice yoga nor enjoys cross-country skiing either enjoys landscape photography or collects action figures but not both”. Someone in the room collects action figures. David hosts regular game nights featuring complex strategy games.

David streams on Twitch.

entailment

room(david)&(![X]:(room(X)=>(X='david')))& (~(![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(does_not_collect_action_figures(X))))))=>(streams_on_Twitch(david)))& ((![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(collects_action_figures(X))))))=>(![X]:(room(X)=>(((collects_action_figures(X))=>(is_not_a_scotch_connoisseur(X)))))))& ((plays_eSports_competitively(david))=>(![X]:(room(X)=>(((works_on_fridays(X))=>(bakes_bread_at_home(X)))))))& ((![X]:(room(X)=>(enjoys_skydiving(X))))=>((![X]:((does_not_create_large-scale_murals_for_public_art_installations(X))<=>(is_not_a_scotch_connoisseur(X))))))& ((~?[X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(enjoys_stargazing(X))))))=>(![X]:(room(X)=>(competes_in_national_level_swimming_championships(X)))))& (~(![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))=>(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(((does_practice_yoga(X))|(mentors_a_youth_basketball_team_on_weekends(X))|(enjoys_landscape_photography(X)))))))))& (((![X]:(room(X)=>(((does_not_enjoy_landscape_photography(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(~?[X]:(room(X)=>(((collects_action_figures(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))&((~(![X]:(room(X)=>(((does_not_enjoy_landscape_photography(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))=>((![X]:((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))<=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))& (((![X]:(room(X)=>(is_a_scotch_connoisseur(X))))=>(~![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(~((does_practice_yoga(X))|(enjoys_cross-country_skiing(X)))))))))&((~(![X]:(room(X)=>(is_a_scotch_connoisseur(X)))))=>(![X]:(room(X)=>(((~((does_practice_yoga(X))|(enjoys_cross-country_skiing(X))))=>(((enjoys_landscape_photography(X))<~>(collects_action_figures(X))))))))))& ((?[X]:(room(X)&(((owns_a_3D_printer(X))|(collects_action_figures(X))))))=>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(david)))& (~(~![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(creates_large-scale_murals_for_public_art_installations(X))))))=>(![X]:(room(X)=>(((does_not_collect_luxury_watches(X))=>(owns_a_3D_printer(X)))))))& ((?[X]:(room(X)&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))=>((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(david))&(collects_first_edition_books(david))))& ((~(does_practice_yoga(david)))=>(works_on_fridays(david)))& ((collects_luxury_watches(david))<~>(~![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(is_not_a_wine_connoisseur(X)))))))& (![X]:(room(X)=>(does_not_collect_classic_novels(X))))& (competes_in_national_level_swimming_championships(david))& (![X]:(anywhere(X)=>(((enjoys_landscape_photography(X))=>(((enjoys_landscape_photography(X))&(does_practice_yoga(X))&(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))))& (![X]:(room(X)=>(((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_stream_on_Twitch(X))))=>(collects_action_figures(X))))))& (?[X]:(room(X)&(collects_action_figures(X))))& (![X]:(room(X)=>(((does_not_work_on_fridays(X))|(collects_luxury_watches(X))))))& (hosts_regular_game_nights_featuring_complex_strategy_games(david))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(anywhere(X)=>(((creates_large-scale_murals_for_public_art_installations(X))<=>(~((is_a_client_of_Costco(X))|(owns_a_3D_printer(X))))))))& (does_not_collect_luxury_watches(david))& (![X]:(~room(X)=>(((competes_in_national_level_swimming_championships(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(mentors_a_youth_basketball_team_on_weekends(X))))))))& (![X]:(room(X)=>(((does_not_collect_luxury_watches(X))|(is_not_a_scotch_connoisseur(X))))))

room(david)&(![X]:(room(X)=>(X='david')))& streams_on_Twitch(david)

% SZS status Unsatisfiable for 4787033230000660443260976 % SZS output start Proof for 4787033230000660443260976 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ~! [X0] : (room(X0) => (~predq(X0) | ~predh(X0))) => predv(mary) [input p1] 62. ? [X0] : (predq(X0) & room(X0)) [input p18] 64. predh(mary) [input p20] 72. ~(predv(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 166. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 167. predv(mary) | ! [X0] : ((~predq(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 45] 168. predv(mary) | ! [X0] : (~predq(X0) | ~predh(X0) | ~room(X0)) [flattening 167] 190. ~predv(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 72] 218. ? [X0] : (predq(X0) & room(X0)) => (predq(sK8) & room(sK8)) [choice axiom] 219. predq(sK8) & room(sK8) [skolemisation 62,218] 222. ? [X0] : (mary != X0 & room(X0)) => (mary != sK9 & room(sK9)) [choice axiom] 223. ~predv(mary) | (mary != sK9 & room(sK9)) | ~room(mary) [skolemisation 190,222] 305. room(mary) [cnf transformation 166] 306. ~room(X0) | mary = X0 [cnf transformation 166] 307. predv(mary) | ~predq(X0) | ~predh(X0) | ~room(X0) [cnf transformation 168] 340. room(sK8) [cnf transformation 219] 341. predq(sK8) [cnf transformation 219] 342. predh(mary) [cnf transformation 64] 349. ~predv(mary) | room(sK9) | ~room(mary) [cnf transformation 223] 350. ~predv(mary) | mary != sK9 | ~room(mary) [cnf transformation 223] 352. 1 <=> ! [X0] : (~predq(X0) | ~room(X0) | ~predh(X0)) [avatar definition] 353. ~predq(X0) | ~room(X0) | ~predh(X0) <- (1) [avatar component clause 352] 355. 2 <=> predv(mary) [avatar definition] 358. 1 | 2 [avatar split clause 307,355,352] 517. ~predv(mary) | mary != sK9 [subsumption resolution 350,305] 519. 38 <=> mary = sK9 [avatar definition] 521. mary != sK9 <- (~38) [avatar component clause 519] 522. ~38 | ~2 [avatar split clause 517,355,519] 523. ~predv(mary) | room(sK9) [subsumption resolution 349,305] 525. 39 <=> room(sK9) [avatar definition] 527. room(sK9) <- (39) [avatar component clause 525] 528. 39 | ~2 [avatar split clause 523,355,525] 540. mary = sK8 [resolution 306,340] 541. mary = sK9 <- (39) [resolution 306,527] 552. predq(mary) [backward demodulation 341,540] 553. $false <- (~38, 39) [subsumption resolution 541,521] 554. 38 | ~39 [avatar contradiction clause 553] 558. ~room(mary) | ~predh(mary) <- (1) [resolution 353,552] 559. ~predh(mary) <- (1) [subsumption resolution 558,305] 560. $false <- (1) [subsumption resolution 559,342] 561. ~1 [avatar contradiction clause 560] 562. $false [avatar sat refutation 358,522,528,554,561] % SZS output end Proof for 4787033230000660443260976 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. “No one in the room is not a old person” if “everyone in the room is a kind person” and vice versa. “Everyone in the room is not a tall person, is not a kind person or is not a old person” if “everyone in the room is not a old person”. “Everyone in the room is not a kind person” if “everyone anywhere is not a old person” and vice versa. “Everyone outside the room is not a tall person” if “everyone anywhere is not a kind person”. “No one in the room is not a old person” if “no one in the room is not old”. Everyone in the room is not a kind person only if they is not a old person. Everyone in the room is not a tall person. Everyone in the room is not a quiet person. Everyone in the room is not a kind person only if they is not tall. Everyone in the room is not tall. Everyone anywhere is not a tall person. No one in the room is not old. Not everyone in the room is not a kind person. If someone is not a tall person, is a old person or is not old then he/she either is not a quiet person or is not kind but not both.

All tall persons are quiet.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(kind(X)&person(X))))<=>(~?[X]:(room(X)=>(~(old(X)&person(X))))))& ((![X]:(room(X)=>(~(old(X)&person(X)))))=>(![X]:(room(X)=>(((~(tall(X)&person(X)))|(~(kind(X)&person(X)))|(~(old(X)&person(X))))))))& ((![X]:(anywhere(X)=>(~(old(X)&person(X)))))<=>(![X]:(room(X)=>(~(kind(X)&person(X))))))& ((![X]:(anywhere(X)=>(~(kind(X)&person(X)))))=>(![X]:(~room(X)=>(~(tall(X)&person(X))))))& ((~?[X]:(room(X)=>(~old(X))))=>(~?[X]:(room(X)=>(~(old(X)&person(X))))))& (![X]:(room(X)=>(((~(old(X)&person(X)))<=(~(kind(X)&person(X)))))))& (![X]:(room(X)=>(~(tall(X)&person(X)))))& (![X]:(room(X)=>(~(quiet(X)&person(X)))))& (![X]:(room(X)=>(((~tall(X))<=(~(kind(X)&person(X)))))))& (![X]:(room(X)=>(~tall(X))))& (![X]:(anywhere(X)=>(~(tall(X)&person(X)))))& (~?[X]:(room(X)=>(~old(X))))& (~![X]:(room(X)=>(~(kind(X)&person(X)))))& ((![X]:((((~(tall(X)&person(X)))|(old(X)&person(X))|(~old(X))))=>(((~(quiet(X)&person(X)))<~>(~kind(X)))))))

(there_is_a_room)& ![X]:(tall(X)=>quiet(X))

% SZS status Unsatisfiable for 8072549280731869371204564 % SZS output start Proof for 8072549280731869371204564 44. there_is_a_room [input p0] 51. ! [X0] : (room(X0) => ~(person(X0) & tall(X0))) [input p7] 53. ! [X0] : (room(X0) => (~(person(X0) & kind(X0)) => ~tall(X0))) [input p9] 56. ~? [X0] : (room(X0) => ~old(X0)) [input p12] 59. ~(! [X0] : (tall(X0) => quiet(X0)) & there_is_a_room) [input hypothesis] 148. ! [X0] : ((~person(X0) | ~tall(X0)) | ~room(X0)) [ennf transformation 51] 149. ! [X0] : (~person(X0) | ~tall(X0) | ~room(X0)) [flattening 148] 152. ! [X0] : ((~tall(X0) | (person(X0) & kind(X0))) | ~room(X0)) [ennf transformation 53] 153. ! [X0] : (~tall(X0) | (person(X0) & kind(X0)) | ~room(X0)) [flattening 152] 157. ! [X0] : (old(X0) & room(X0)) [ennf transformation 56] 162. ? [X0] : (~quiet(X0) & tall(X0)) | ~there_is_a_room [ennf transformation 59] 190. ? [X0] : (~quiet(X0) & tall(X0)) => (~quiet(sK9) & tall(sK9)) [choice axiom] 191. (~quiet(sK9) & tall(sK9)) | ~there_is_a_room [skolemisation 162,190] 273. there_is_a_room [cnf transformation 44] 299. ~person(X0) | ~tall(X0) | ~room(X0) [cnf transformation 149] 302. ~tall(X0) | person(X0) | ~room(X0) [cnf transformation 153] 305. room(X0) [cnf transformation 157] 317. tall(sK9) | ~there_is_a_room [cnf transformation 191] 365. 11 <=> ! [X2] : room(X2) [avatar definition] 366. room(X2) <- (11) [avatar component clause 365] 445. ~tall(X0) | ~room(X0) [subsumption resolution 302,299] 448. 11 [avatar split clause 305,365] 455. tall(sK9) [subsumption resolution 317,273] 472. ~room(sK9) [resolution 445,455] 473. $false <- (11) [subsumption resolution 472,366] 474. ~11 [avatar contradiction clause 473] 475. $false [avatar sat refutation 448,474] % SZS output end Proof for 8072549280731869371204564 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Melanie is the only person in the room. If “Melanie participates in citizen science projects related to wildlife monitoring” then “Melanie does practice yoga”. If “someone in the room owns an extensive assortment of vintage comic book memorabilia” then “everyone in the room who owns an extensive assortment of vintage comic book memorabilia has a tattoo”. If “everyone in the room is dedicated to sustainable living and zero-waste practices or does not participate in citizen science projects related to wildlife monitoring” then “Melanie who is dedicated to sustainable living and zero-waste practices participates in citizen science projects related to wildlife monitoring”. If “not everyone outside the room does not use a Windows laptop or owns an extensive assortment of vintage comic book memorabilia” then “someone in the room has a tattoo”. Melanie has a tattoo. If someone uses a Windows laptop then he/she does practice yoga and vice versa. Everyone in the room who uses a Windows laptop is dedicated to sustainable living and zero-waste practices. Melanie uses a Windows laptop. If someone does practice yoga then he/she plays the drums.

Melanie does practice yoga, plays the drums and is dedicated to sustainable living and zero-waste practices.

entailment

room(melanie)&(![X]:(room(X)=>(X='melanie')))& ((participates_in_citizen_science_projects_related_to_wildlife_monitoring(melanie))=>(does_practice_yoga(melanie)))& ((?[X]:(room(X)&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))=>(![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(has_a_tattoo(X)))))))& ((![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))=>((is_dedicated_to_sustainable_living_and_zero-waste_practices(melanie))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(melanie))))& ((~![X]:(~room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_use_a_Windows_laptop(X))))))=>(?[X]:(room(X)&(has_a_tattoo(X)))))& (has_a_tattoo(melanie))& ((![X]:((uses_a_Windows_laptop(X))<=>(does_practice_yoga(X)))))& ((![X]:((plays_the_drums(X))<=>(practices_and_performs_acrobatic_dance_routines(X)))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(melanie))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(does_practice_yoga(X))))))& ((![X]:((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=>(uses_a_Windows_laptop(X)))))& (uses_a_Windows_laptop(melanie))& ((![X]:((does_practice_yoga(X))=>(plays_the_drums(X)))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))|(does_not_play_the_drums(X))))))& (?[X]:(room(X)&(has_a_tattoo(X))))& (~((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(melanie))|(travels_domestically_frequently(melanie))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(is_an_avid_hiker(X))))))& ((![X]:((uses_a_Windows_laptop(X))=>(does_practice_yoga(X)))))& (~((?[X,Y]:(room(X)&room(Y)&(is_an_avid_hiker(X)&is_an_avid_hiker(Y))&(X!=Y)))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(uses_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(plays_the_drums(X))))))

room(melanie)&(![X]:(room(X)=>(X='melanie')))& ((does_practice_yoga(melanie))&(plays_the_drums(melanie))&(is_dedicated_to_sustainable_living_and_zero-waste_practices(melanie)))

% SZS status Unsatisfiable for 3358039139292355153646483 % SZS output start Proof for 3358039139292355153646483 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 50. ! [X0] : (predd(X0) <=> prede(X0)) [input p6] 53. ! [X0] : (room(X0) => (predd(X0) => predb(X0))) [input p9] 56. predd(mary) [input p12] 57. ! [X0] : (prede(X0) => preda(X0)) [input p13] 67. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 144. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 152. ! [X0] : ((predb(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 53] 153. ! [X0] : (predb(X0) | ~predd(X0) | ~room(X0)) [flattening 152] 156. ! [X0] : (preda(X0) | ~prede(X0)) [ennf transformation 57] 170. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 67] 178. ! [X0] : ((predd(X0) | ~prede(X0)) & (prede(X0) | ~predd(X0))) [nnf transformation 50] 183. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 184. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 170,183] 265. room(mary) [cnf transformation 144] 266. ~room(X0) | mary = X0 [cnf transformation 144] 278. ~predd(X0) | prede(X0) [cnf transformation 178] 282. ~predd(X0) | predb(X0) | ~room(X0) [cnf transformation 153] 286. predd(mary) [cnf transformation 56] 287. ~prede(X0) | preda(X0) [cnf transformation 156] 298. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK3) | ~room(mary) [cnf transformation 184] 299. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK3 | ~room(mary) [cnf transformation 184] 305. 2 <=> prede(mary) [avatar definition] 332. 8 <=> predb(mary) [avatar definition] 351. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK3 [subsumption resolution 299,265] 352. ~predb(mary) | ~prede(mary) | mary != sK3 [subsumption resolution 351,287] 354. 12 <=> mary = sK3 [avatar definition] 356. mary != sK3 <- (~12) [avatar component clause 354] 357. ~12 | ~2 | ~8 [avatar split clause 352,332,305,354] 358. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK3) [subsumption resolution 298,265] 359. ~predb(mary) | ~prede(mary) | room(sK3) [subsumption resolution 358,287] 361. 13 <=> room(sK3) [avatar definition] 363. room(sK3) <- (13) [avatar component clause 361] 364. 13 | ~2 | ~8 [avatar split clause 359,332,305,361] 365. prede(mary) [resolution 278,286] 368. 2 [avatar split clause 365,305] 394. predb(mary) | ~room(mary) [resolution 282,286] 398. predb(mary) [subsumption resolution 394,265] 399. 8 [avatar split clause 398,332] 402. mary = sK3 <- (13) [resolution 363,266] 403. $false <- (~12, 13) [subsumption resolution 402,356] 404. 12 | ~13 [avatar contradiction clause 403] 405. $false [avatar sat refutation 357,364,368,399,404] % SZS output end Proof for 3358039139292355153646483 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If “everyone anywhere is not a wine connoisseur with a private cellar of vintage wines or is a certified scuba diver with advanced underwater photography skills” then “if someone enjoys salsa dancing then he/she enjoys skydiving and vice versa”. “Everyone in the room participates in citizen science projects related to wildlife monitoring” if “everyone in the room enjoys rooftop gardening” and vice versa. If “everyone in the room is not a wine connoisseur with a private cellar of vintage wines or collects rare and antique scientific instruments” then “everyone in the room collects rare and antique scientific instruments”. “Everyone in the room does not host a popular podcast about emerging technologies or is right-handed” if “everyone in the room does not own an extensive assortment of vintage comic book memorabilia or is a skilled home brewer experimenting with craft beer recipes” and vice versa.

Everyone in the room does not host a popular podcast about emerging technologies.

neutral

(there_is_a_room)& ((![X]:(anywhere(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))=>((![X]:((enjoys_salsa_dancing(X))<=>(enjoys_skydiving(X))))))& ((![X]:(room(X)=>(enjoys_rooftop_gardening(X))))<=>(![X]:(room(X)=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))& ((![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))=>(![X]:(room(X)=>(collects_rare_and_antique_scientific_instruments(X)))))& ((![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))<=>(![X]:(room(X)=>(((is_right-handed(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X)))))))& (~(![X]:(anywhere(X)=>(((collect_rare_sneakers(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>((![X]:((collects_foreign_coins(X))<=>(enjoys_rooftop_gardening(X))))))& ((![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_enjoy_salsa_dancing(X))))))=>(![X]:(~room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(does_not_enjoy_rooftop_gardening(X))))))& (~![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_enjoy_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_enjoy_virtual_reality_gaming(X))|(enjoys_skydiving(X))))))))& (![X]:(room(X)=>(((((collects_first_edition_books(X))|(collects_rare_and_antique_scientific_instruments(X))))=>(does_not_collect_foreign_coins(X))))))& ((![X]:((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (?[X]:(room(X)&(is_right-handed(X))))& ((![X]:((enjoys_salsa_dancing(X))<=>(enjoys_skydiving(X)))))& (![X]:(~room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((is_right-handed(X))<=(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (?[X]:(room(X)&(((does_not_collect_rare_and_antique_scientific_instruments(X))<~>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((practices_zumba(X))<=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& ((![X]:((does_not_enjoy_origami(X))<=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))

(there_is_a_room)& ![X]:(room(X)=>(does_not_host_a_popular_podcast_about_emerging_technologies(X)))

There is a room. Everyone in the room is an active member of a local robotics club. Everyone outside the room who neither does not watche fantasy movies nor watches fantasy movies plays as a goalkeeper for a local amateur soccer team. Everyone in the room is not an active member of a local robotics club. Everyone in the room is an active member of a local robotics club or does not watche fantasy movies.

Everyone outside the room is an active member of a local robotics club.

neutral

(there_is_a_room)& (![X]:(room(X)=>(is_an_active_member_of_a_local_robotics_club(X))))& (![X]:(~room(X)=>(((~((does_not_watche_fantasy_movies(X))|(watches_fantasy_movies(X))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(is_not_an_active_member_of_a_local_robotics_club(X))))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(((is_an_active_member_of_a_local_robotics_club(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(does_not_watche_fantasy_movies(X))))))))& (![X]:(room(X)=>(((((is_an_active_member_of_a_local_robotics_club(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(does_not_watche_fantasy_movies(X))))|(is_not_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(does_not_watche_fantasy_movies(X))))))& (~![X]:(~room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))

(there_is_a_room)& ![X]:(~room(X)=>(is_an_active_member_of_a_local_robotics_club(X)))

There is a room. Everyone in the room is quieter than Mark only if they is not a quiet person. Not everyone in the room is older than Mark if they is not a quiet person. Everyone in the room who is quieter than Mark is richer than Mark. Someone who is not a old quiet person is older than someone who is not a quiet old person. Someone who is quiet is older than someone who either is quieter than Mark or is a quiet person but not both. Everyone in the room who is a quiet person is quieter than Mark. Someone who is not a old quiet person is older than someone who is a quiet old person. Everyone anywhere is a quiet person or is older than Mark or both if they is a old person. Someone who is a quiet person is older than someone who is not a quiet old person. Everyone anywhere is a old person if they is not old. Everyone anywhere is richer than Mark if they is a quiet old person. If someone is richer than Mark then he/she is quieter than Mark and vice versa.

Everyone in the room is a old person or is quieter than Mark or both.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((~(quiet(X)&person(X)))<=(quieter(mark,X))))))& (~![X]:(room(X)=>(((~(quiet(X)&person(X)))=>(older(mark,X))))))& (![X]:(room(X)=>(((quieter(mark,X))=>(richer(mark,X))))))& (?[X,Y]:((~(old(X)&quiet(X)&person(X)))&(~(quiet(Y)&old(Y)&person(Y)))&(older(X,Y))))& (?[X,Y]:((quiet(X))&(((quieter(mark,Y))<~>(quiet(Y)&person(Y))))&(older(X,Y))))& (![X]:(room(X)=>(((quiet(X)&person(X))=>(quieter(mark,X))))))& (?[X,Y]:((~(old(X)&quiet(X)&person(X)))&(quiet(Y)&old(Y)&person(Y))&(older(X,Y))))& (![X]:(anywhere(X)=>(((old(X)&person(X))=>(((quiet(X)&person(X))|(older(mark,X))))))))& (?[X,Y]:((quiet(X)&person(X))&(~(quiet(Y)&old(Y)&person(Y)))&(older(X,Y))))& (![X]:(anywhere(X)=>(((~old(X))=>(old(X)&person(X))))))& (![X]:(anywhere(X)=>(((quiet(X)&old(X)&person(X))=>(richer(mark,X))))))& ((![X]:((richer(mark,X))<=>(quieter(mark,X)))))

(there_is_a_room)& ![X]:(room(X)=>(((old(X)&person(X))|(quieter(mark,X)))))

Bernice, Jamie, Dixie are the only persons in the room. Either “everyone in the room participates in long-distance cycling events across the country or does not collect limited-edition art prints from contemporary artists” or “Bernice either practices and performs acrobatic dance routines or maintains a large, organic vegetable garden year-round but not both” but not both. If “Bernice neither does not collect limited-edition art prints from contemporary artists nor collects historical artifacts related to ancient civilizations” then “everyone in the room does not participate in long-distance cycling events across the country”. If “everyone in the room does not participate in long-distance cycling events across the country” then “Bernice does not drive a hybrid car”. If “Bernice enjoys logic puzzles or collects limited-edition art prints from contemporary artists or both” then “at least one person in the room is not a dedicated volunteer for local community service projects”.

Bernice is a night owl.

entailment

room(bernice)&room(jamie)&room(dixie)&(![X]:(room(X)=>(X='bernice'|X='jamie'|X='dixie')))& ((![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))))<~>(((practices_and_performs_acrobatic_dance_routines(bernice))<~>(maintains_a_large,_organic_vegetable_garden_year-round(bernice)))))& (((~((does_not_collect_limited-edition_art_prints_from_contemporary_artists(bernice))|(collects_historical_artifacts_related_to_ancient_civilizations(bernice))))=>(![X]:(room(X)=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X)))))& ((![X]:(room(X)=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))=>(does_not_drive_a_hybrid_car(bernice))))& (((((enjoys_logic_puzzles(bernice))|(collects_limited-edition_art_prints_from_contemporary_artists(bernice))))=>(((?[X]:(room(X)&is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))& ((((?[X]:(room(X)&is_not_a_dedicated_volunteer_for_local_community_service_projects(X)))))=>(does_not_mentor_a_youth_basketball_team_on_weekends(bernice))))& (((![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(bakes_bread_at_home(X))))))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(bernice)))& ((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(bernice))=>(((does_not_bake_bread_at_home(bernice))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(bernice))))))& (((![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))))=>(((owns_a_smart_tv(bernice))<~>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(bernice)))))& ((((owns_a_smart_tv(bernice))<~>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(bernice))))=>(is_a_night_owl(bernice))))& (enjoys_windsurfing(bernice))& (((practices_tai_chi(bernice))<~>(does_not_mentor_a_youth_basketball_team_on_weekends(bernice))))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(bernice))& ((?[X,Y]:(room(X)&room(Y)&(drives_a_hybrid_car(X)&drives_a_hybrid_car(Y))&(X!=Y))))& (bakes_bread_at_home(bernice))& (~((does_not_enjoy_skydiving(bernice))|(collects_limited-edition_art_prints_from_contemporary_artists(bernice))))& (![X]:(anywhere(X)=>(((~((does_not_collect_vintage_vinyl_records(X))|(collects_limited-edition_art_prints_from_contemporary_artists(X))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(does_not_practice_tai_chi(X))))))))& (is_a_tea_enthusiast(bernice))& (is_a_night_owl(bernice))& (((collects_vintage_vinyl_records(bernice))|(is_not_a_tea_enthusiast(bernice))|(does_not_enjoy_windsurfing(bernice))))& (collects_historical_artifacts_related_to_ancient_civilizations(bernice))& (![X]:(room(X)=>(((((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(maintains_a_large,_organic_vegetable_garden_year-round(X))))<=(mentors_a_youth_basketball_team_on_weekends(X))))))& (enjoys_logic_puzzles(bernice))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(bernice))

room(bernice)&room(jamie)&room(dixie)&(![X]:(room(X)=>(X='bernice'|X='jamie'|X='dixie')))& is_a_night_owl(bernice)

% SZS status Unsatisfiable for 3808456655488081727308093 % SZS output start Proof for 3808456655488081727308093 44. predr(mary) & predv(mary) & ! [X0] : (room(X0) => (prede(X0) => (predm(X0) & preds(X0) & ~predm(X0)))) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X0] : (room(X0) => (~predv(X0) => (~predw(X0) | ~predu(X0)))) & ! [X0] : (anywhere(X0) => (~(predb(X0) | ~predq(X0)) => preds(X0))) & ~(predb(mary) | ~predh(mary)) & predo(mary) & ? [X0,X1] : (X0 != X1 & predi(X1) & predi(X0) & room(X1) & room(X0)) & preds(mary) & (predw(mary) <~> ~prede(mary)) & predf(mary) & ((predj(mary) <~> ~predg(mary)) => preda(mary)) & (! [X0] : (room(X0) => (predx(X0) | ~predd(X0))) => (predj(mary) <~> ~predg(mary))) & (~preds(mary) => (~predg(mary) | ~predo(mary))) & (! [X0] : (room(X0) => (predo(X0) | ~predp(X0))) => ~preds(mary)) & (? [X0] : (~predu(X0) & room(X0)) => ~prede(mary)) & ((predb(mary) | predv(mary)) => ? [X0] : (~predu(X0) & room(X0))) & (! [X0] : (room(X0) => ~predx(X0)) => ~predi(mary)) & (~(predg(mary) | ~predb(mary)) => ! [X0] : (room(X0) => ~predx(X0))) & (! [X0] : (room(X0) => (predx(X0) | ~predb(X0))) <~> (predt(mary) <~> predm(mary))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(preda(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. predr(mary) & predv(mary) & ! [X0] : (room(X0) => (prede(X0) => (predm(X0) & preds(X0) & ~predm(X0)))) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (room(X1) => (~predv(X1) => (~predw(X1) | ~predu(X1)))) & ! [X2] : (anywhere(X2) => (~(predb(X2) | ~predq(X2)) => preds(X2))) & ~(predb(mary) | ~predh(mary)) & predo(mary) & ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) & preds(mary) & (predw(mary) <~> ~prede(mary)) & predf(mary) & ((predj(mary) <~> ~predg(mary)) => preda(mary)) & (! [X5] : (room(X5) => (predx(X5) | ~predd(X5))) => (predj(mary) <~> ~predg(mary))) & (~preds(mary) => (~predg(mary) | ~predo(mary))) & (! [X6] : (room(X6) => (predo(X6) | ~predp(X6))) => ~preds(mary)) & (? [X7] : (~predu(X7) & room(X7)) => ~prede(mary)) & ((predb(mary) | predv(mary)) => ? [X8] : (~predu(X8) & room(X8))) & (! [X9] : (room(X9) => ~predx(X9)) => ~predi(mary)) & (~(predg(mary) | ~predb(mary)) => ! [X10] : (room(X10) => ~predx(X10))) & (! [X11] : (room(X11) => (predx(X11) | ~predb(X11))) <~> (predt(mary) <~> predm(mary))) & ! [X12] : (room(X12) => (fred = X12 | paul = X12 | mary = X12)) & room(fred) & room(paul) & room(mary) [rectify 44] 47. predv(mary) & ! [X0] : (room(X0) => (prede(X0) => (predm(X0) & preds(X0) & ~predm(X0)))) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (room(X1) => (~predv(X1) => (~predw(X1) | ~predu(X1)))) & ! [X2] : (anywhere(X2) => (~(predb(X2) | ~predq(X2)) => preds(X2))) & ~(predb(mary) | ~predh(mary)) & predo(mary) & ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) & preds(mary) & (predw(mary) <~> ~prede(mary)) & predf(mary) & ((predj(mary) <~> ~predg(mary)) => preda(mary)) & (! [X5] : (room(X5) => (predx(X5) | ~predd(X5))) => (predj(mary) <~> ~predg(mary))) & (~preds(mary) => (~predg(mary) | ~predo(mary))) & (! [X6] : (room(X6) => (predo(X6) | ~predp(X6))) => ~preds(mary)) & (? [X7] : (~predu(X7) & room(X7)) => ~prede(mary)) & ((predb(mary) | predv(mary)) => ? [X8] : (~predu(X8) & room(X8))) & (! [X9] : (room(X9) => ~predx(X9)) => ~predi(mary)) & (~(predg(mary) | ~predb(mary)) => ! [X10] : (room(X10) => ~predx(X10))) & (! [X11] : (room(X11) => (predx(X11) | ~predb(X11))) <~> (predt(mary) <~> predm(mary))) & ! [X12] : (room(X12) => (fred = X12 | paul = X12 | mary = X12)) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. predv(mary) & ! [X0] : (room(X0) => (prede(X0) => (predm(X0) & preds(X0) & ~predm(X0)))) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (room(X1) => (~predv(X1) => (~predw(X1) | ~predu(X1)))) & ! [X2] : (anywhere(X2) => (~(predb(X2) | ~predq(X2)) => preds(X2))) & ~predb(mary) & predo(mary) & ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) & preds(mary) & (predw(mary) <~> ~prede(mary)) & predf(mary) & ((predj(mary) <~> ~predg(mary)) => preda(mary)) & (! [X5] : (room(X5) => (predx(X5) | ~predd(X5))) => (predj(mary) <~> ~predg(mary))) & (~preds(mary) => (~predg(mary) | ~predo(mary))) & (! [X6] : (room(X6) => (predo(X6) | ~predp(X6))) => ~preds(mary)) & (? [X7] : (~predu(X7) & room(X7)) => ~prede(mary)) & ((predb(mary) | predv(mary)) => ? [X8] : (~predu(X8) & room(X8))) & (! [X9] : (room(X9) => ~predx(X9)) => ~predi(mary)) & (~(predg(mary) | ~predb(mary)) => ! [X10] : (room(X10) => ~predx(X10))) & (! [X11] : (room(X11) => (predx(X11) | ~predb(X11))) <~> (predt(mary) <~> predm(mary))) & ! [X12] : (room(X12) => (fred = X12 | paul = X12 | mary = X12)) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. predv(mary) & ! [X0] : (room(X0) => (prede(X0) => (predm(X0) & preds(X0) & ~predm(X0)))) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (room(X1) => (~predv(X1) => (~predw(X1) | ~predu(X1)))) & ! [X2] : (anywhere(X2) => (~(predb(X2) | ~predq(X2)) => preds(X2))) & ~predb(mary) & predo(mary) & ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) & preds(mary) & (predw(mary) <~> ~prede(mary)) & predf(mary) & ((predj(mary) <~> ~predg(mary)) => preda(mary)) & (! [X5] : (room(X5) => predx(X5)) => (predj(mary) <~> ~predg(mary))) & (~preds(mary) => (~predg(mary) | ~predo(mary))) & (! [X6] : (room(X6) => (predo(X6) | ~predp(X6))) => ~preds(mary)) & (? [X7] : (~predu(X7) & room(X7)) => ~prede(mary)) & ((predb(mary) | predv(mary)) => ? [X8] : (~predu(X8) & room(X8))) & (! [X9] : (room(X9) => ~predx(X9)) => ~predi(mary)) & (~(predg(mary) | ~predb(mary)) => ! [X10] : (room(X10) => ~predx(X10))) & (! [X11] : (room(X11) => (predx(X11) | ~predb(X11))) <~> (predt(mary) <~> predm(mary))) & ! [X12] : (room(X12) => (fred = X12 | paul = X12 | mary = X12)) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. predv(mary) & ! [X0] : (room(X0) => (prede(X0) => (predm(X0) & preds(X0) & ~predm(X0)))) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (room(X1) => (~predv(X1) => (~predw(X1) | ~predu(X1)))) & ! [X2] : (anywhere(X2) => (~(predb(X2) | ~predq(X2)) => preds(X2))) & ~predb(mary) & predo(mary) & ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) & preds(mary) & (predw(mary) <~> ~prede(mary)) & predf(mary) & ((predj(mary) <~> ~predg(mary)) => preda(mary)) & (! [X5] : (room(X5) => predx(X5)) => (predj(mary) <~> ~predg(mary))) & (~preds(mary) => (~predg(mary) | ~predo(mary))) & (! [X6] : (room(X6) => predo(X6)) => ~preds(mary)) & (? [X7] : (~predu(X7) & room(X7)) => ~prede(mary)) & ((predb(mary) | predv(mary)) => ? [X8] : (~predu(X8) & room(X8))) & (! [X9] : (room(X9) => ~predx(X9)) => ~predi(mary)) & (~(predg(mary) | ~predb(mary)) => ! [X10] : (room(X10) => ~predx(X10))) & (! [X11] : (room(X11) => (predx(X11) | ~predb(X11))) <~> (predt(mary) <~> predm(mary))) & ! [X12] : (room(X12) => (fred = X12 | paul = X12 | mary = X12)) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 122. predv(mary) & ! [X0] : (((predm(X0) & preds(X0) & ~predm(X0)) | ~prede(X0)) | ~room(X0)) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (((~predw(X1) | ~predu(X1)) | predv(X1)) | ~room(X1)) & ! [X2] : ((preds(X2) | (predb(X2) | ~predq(X2))) | ~anywhere(X2)) & ~predb(mary) & predo(mary) & ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) & preds(mary) & (predw(mary) <~> ~prede(mary)) & predf(mary) & (preda(mary) | (predj(mary) <=> ~predg(mary))) & ((predj(mary) <~> ~predg(mary)) | ? [X5] : (~predx(X5) & room(X5))) & ((~predg(mary) | ~predo(mary)) | preds(mary)) & (~preds(mary) | ? [X6] : (~predo(X6) & room(X6))) & (~prede(mary) | ! [X7] : (predu(X7) | ~room(X7))) & (? [X8] : (~predu(X8) & room(X8)) | (~predb(mary) & ~predv(mary))) & (~predi(mary) | ? [X9] : (predx(X9) & room(X9))) & (! [X10] : (~predx(X10) | ~room(X10)) | (predg(mary) | ~predb(mary))) & (! [X11] : ((predx(X11) | ~predb(X11)) | ~room(X11)) <~> (predt(mary) <~> predm(mary))) & ! [X12] : ((fred = X12 | paul = X12 | mary = X12) | ~room(X12)) & room(fred) & room(paul) & room(mary) [ennf transformation 50] 123. predv(mary) & ! [X0] : ((predm(X0) & preds(X0) & ~predm(X0)) | ~prede(X0) | ~room(X0)) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (~predw(X1) | ~predu(X1) | predv(X1) | ~room(X1)) & ! [X2] : (preds(X2) | predb(X2) | ~predq(X2) | ~anywhere(X2)) & ~predb(mary) & predo(mary) & ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) & preds(mary) & (predw(mary) <~> ~prede(mary)) & predf(mary) & (preda(mary) | (predj(mary) <=> ~predg(mary))) & ((predj(mary) <~> ~predg(mary)) | ? [X5] : (~predx(X5) & room(X5))) & (~predg(mary) | ~predo(mary) | preds(mary)) & (~preds(mary) | ? [X6] : (~predo(X6) & room(X6))) & (~prede(mary) | ! [X7] : (predu(X7) | ~room(X7))) & (? [X8] : (~predu(X8) & room(X8)) | (~predb(mary) & ~predv(mary))) & (~predi(mary) | ? [X9] : (predx(X9) & room(X9))) & (! [X10] : (~predx(X10) | ~room(X10)) | predg(mary) | ~predb(mary)) & (! [X11] : (predx(X11) | ~predb(X11) | ~room(X11)) <~> (predt(mary) <~> predm(mary))) & ! [X12] : (fred = X12 | paul = X12 | mary = X12 | ~room(X12)) & room(fred) & room(paul) & room(mary) [flattening 122] 124. ~preda(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 125. ~preda(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 124] 127. predv(mary) & ! [X0] : ((predm(X0) & preds(X0) & ~predm(X0)) | ~prede(X0) | ~room(X0)) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (~predw(X1) | ~predu(X1) | predv(X1) | ~room(X1)) & ! [X2] : (preds(X2) | predb(X2) | ~predq(X2) | ~anywhere(X2)) & ~predb(mary) & predo(mary) & ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) & preds(mary) & ((prede(mary) | ~predw(mary)) & (~prede(mary) | predw(mary))) & predf(mary) & (preda(mary) | ((predj(mary) | predg(mary)) & (~predg(mary) | ~predj(mary)))) & (((predg(mary) | ~predj(mary)) & (~predg(mary) | predj(mary))) | ? [X5] : (~predx(X5) & room(X5))) & (~predg(mary) | ~predo(mary) | preds(mary)) & (~preds(mary) | ? [X6] : (~predo(X6) & room(X6))) & (~prede(mary) | ! [X7] : (predu(X7) | ~room(X7))) & (? [X8] : (~predu(X8) & room(X8)) | (~predb(mary) & ~predv(mary))) & (~predi(mary) | ? [X9] : (predx(X9) & room(X9))) & (! [X10] : (~predx(X10) | ~room(X10)) | predg(mary) | ~predb(mary)) & ((((predt(mary) | ~predm(mary)) & (predm(mary) | ~predt(mary))) | ? [X11] : (~predx(X11) & predb(X11) & room(X11))) & (((~predm(mary) | ~predt(mary)) & (predm(mary) | predt(mary))) | ! [X11] : (predx(X11) | ~predb(X11) | ~room(X11)))) & ! [X12] : (fred = X12 | paul = X12 | mary = X12 | ~room(X12)) & room(fred) & room(paul) & room(mary) [nnf transformation 123] 128. predv(mary) & ! [X0] : ((predm(X0) & preds(X0) & ~predm(X0)) | ~prede(X0) | ~room(X0)) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (~predw(X1) | ~predu(X1) | predv(X1) | ~room(X1)) & ! [X2] : (preds(X2) | predb(X2) | ~predq(X2) | ~anywhere(X2)) & ~predb(mary) & predo(mary) & ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) & preds(mary) & (prede(mary) | ~predw(mary)) & (~prede(mary) | predw(mary)) & predf(mary) & (preda(mary) | ((predj(mary) | predg(mary)) & (~predg(mary) | ~predj(mary)))) & (((predg(mary) | ~predj(mary)) & (~predg(mary) | predj(mary))) | ? [X5] : (~predx(X5) & room(X5))) & (~predg(mary) | ~predo(mary) | preds(mary)) & (~preds(mary) | ? [X6] : (~predo(X6) & room(X6))) & (~prede(mary) | ! [X7] : (predu(X7) | ~room(X7))) & (? [X8] : (~predu(X8) & room(X8)) | (~predb(mary) & ~predv(mary))) & (~predi(mary) | ? [X9] : (predx(X9) & room(X9))) & (! [X10] : (~predx(X10) | ~room(X10)) | predg(mary) | ~predb(mary)) & (((predt(mary) | ~predm(mary)) & (predm(mary) | ~predt(mary))) | ? [X11] : (~predx(X11) & predb(X11) & room(X11))) & (((~predm(mary) | ~predt(mary)) & (predm(mary) | predt(mary))) | ! [X11] : (predx(X11) | ~predb(X11) | ~room(X11))) & ! [X12] : (fred = X12 | paul = X12 | mary = X12 | ~room(X12)) & room(fred) & room(paul) & room(mary) [flattening 127] 129. predv(mary) & ! [X0] : ((predm(X0) & preds(X0) & ~predm(X0)) | ~prede(X0) | ~room(X0)) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (~predw(X1) | ~predu(X1) | predv(X1) | ~room(X1)) & ! [X2] : (preds(X2) | predb(X2) | ~predq(X2) | ~anywhere(X2)) & ~predb(mary) & predo(mary) & ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) & preds(mary) & (prede(mary) | ~predw(mary)) & (~prede(mary) | predw(mary)) & predf(mary) & (preda(mary) | ((predj(mary) | predg(mary)) & (~predg(mary) | ~predj(mary)))) & (((predg(mary) | ~predj(mary)) & (~predg(mary) | predj(mary))) | ? [X5] : (~predx(X5) & room(X5))) & (~predg(mary) | ~predo(mary) | preds(mary)) & (~preds(mary) | ? [X6] : (~predo(X6) & room(X6))) & (~prede(mary) | ! [X7] : (predu(X7) | ~room(X7))) & (? [X8] : (~predu(X8) & room(X8)) | (~predb(mary) & ~predv(mary))) & (~predi(mary) | ? [X9] : (predx(X9) & room(X9))) & (! [X10] : (~predx(X10) | ~room(X10)) | predg(mary) | ~predb(mary)) & (((predt(mary) | ~predm(mary)) & (predm(mary) | ~predt(mary))) | ? [X11] : (~predx(X11) & predb(X11) & room(X11))) & (((~predm(mary) | ~predt(mary)) & (predm(mary) | predt(mary))) | ! [X12] : (predx(X12) | ~predb(X12) | ~room(X12))) & ! [X13] : (fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(fred) & room(paul) & room(mary) [rectify 128] 130. ? [X3,X4] : (X3 != X4 & predi(X4) & predi(X3) & room(X4) & room(X3)) => (sK0 != sK1 & predi(sK1) & predi(sK0) & room(sK1) & room(sK0)) [choice axiom] 131. ? [X5] : (~predx(X5) & room(X5)) => (~predx(sK2) & room(sK2)) [choice axiom] 132. ? [X6] : (~predo(X6) & room(X6)) => (~predo(sK3) & room(sK3)) [choice axiom] 133. ? [X8] : (~predu(X8) & room(X8)) => (~predu(sK4) & room(sK4)) [choice axiom] 134. ? [X9] : (predx(X9) & room(X9)) => (predx(sK5) & room(sK5)) [choice axiom] 135. ? [X11] : (~predx(X11) & predb(X11) & room(X11)) => (~predx(sK6) & predb(sK6) & room(sK6)) [choice axiom] 136. predv(mary) & ! [X0] : ((predm(X0) & preds(X0) & ~predm(X0)) | ~prede(X0) | ~room(X0)) & predg(mary) & (~predf(mary) | ~predn(mary) | predq(mary)) & preda(mary) & predn(mary) & ! [X1] : (~predw(X1) | ~predu(X1) | predv(X1) | ~room(X1)) & ! [X2] : (preds(X2) | predb(X2) | ~predq(X2) | ~anywhere(X2)) & ~predb(mary) & predo(mary) & (sK0 != sK1 & predi(sK1) & predi(sK0) & room(sK1) & room(sK0)) & preds(mary) & (prede(mary) | ~predw(mary)) & (~prede(mary) | predw(mary)) & predf(mary) & (preda(mary) | ((predj(mary) | predg(mary)) & (~predg(mary) | ~predj(mary)))) & (((predg(mary) | ~predj(mary)) & (~predg(mary) | predj(mary))) | (~predx(sK2) & room(sK2))) & (~predg(mary) | ~predo(mary) | preds(mary)) & (~preds(mary) | (~predo(sK3) & room(sK3))) & (~prede(mary) | ! [X7] : (predu(X7) | ~room(X7))) & ((~predu(sK4) & room(sK4)) | (~predb(mary) & ~predv(mary))) & (~predi(mary) | (predx(sK5) & room(sK5))) & (! [X10] : (~predx(X10) | ~room(X10)) | predg(mary) | ~predb(mary)) & (((predt(mary) | ~predm(mary)) & (predm(mary) | ~predt(mary))) | (~predx(sK6) & predb(sK6) & room(sK6))) & (((~predm(mary) | ~predt(mary)) & (predm(mary) | predt(mary))) | ! [X12] : (predx(X12) | ~predb(X12) | ~room(X12))) & ! [X13] : (fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(fred) & room(paul) & room(mary) [skolemisation 129,135,134,133,132,131,130] 137. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 138. ~preda(mary) | (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 125,137] 220. room(mary) [cnf transformation 136] 221. room(paul) [cnf transformation 136] 222. room(fred) [cnf transformation 136] 223. ~room(X13) | paul = X13 | mary = X13 | fred = X13 [cnf transformation 136] 263. preda(mary) [cnf transformation 136] 270. ~preda(mary) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 271. ~preda(mary) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 272. ~preda(mary) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 273. ~preda(mary) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 370. fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,263] 371. fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 370,222] 372. fred != sK7 | ~room(mary) [subsumption resolution 371,221] 373. fred != sK7 [subsumption resolution 372,220] 374. paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,263] 375. paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 374,222] 376. paul != sK7 | ~room(mary) [subsumption resolution 375,221] 377. paul != sK7 [subsumption resolution 376,220] 378. mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,263] 379. mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 378,222] 380. mary != sK7 | ~room(mary) [subsumption resolution 379,221] 381. mary != sK7 [subsumption resolution 380,220] 382. room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,263] 383. room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 382,222] 384. room(sK7) | ~room(mary) [subsumption resolution 383,221] 385. room(sK7) [subsumption resolution 384,220] 431. paul = sK7 | mary = sK7 | fred = sK7 [resolution 223,385] 497. mary = sK7 | fred = sK7 [subsumption resolution 431,377] 498. fred = sK7 [subsumption resolution 497,381] 499. $false [subsumption resolution 498,373] % SZS output end Proof for 3808456655488081727308093 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. “Everyone in the room is a calm person” if “someone in the room is strong” and vice versa. Someone who is not a creative person is older than someone who is patient. Everyone in the room is a calm person. Everyone in the room is not a curious person. Everyone in the room is a strong person. If someone is not a tall person or is a generous person or both then he/she is a tall person and vice versa. If someone is calm then he/she is not a wise person. Someone who is old is older than someone who is old, is not patient and is a creative person.

Not everyone in the room is a curious person.

entailment

(there_is_a_room)& ((?[X]:(room(X)&(strong(X))))<=>(![X]:(room(X)=>(calm(X)&person(X)))))& (?[X,Y]:((~(creative(X)&person(X)))&(patient(Y))&(older(X,Y))))& (![X]:(room(X)=>(calm(X)&person(X))))& (![X]:(room(X)=>(~(curious(X)&person(X)))))& (![X]:(room(X)=>(strong(X)&person(X))))& ((![X]:((((~(tall(X)&person(X)))|(generous(X)&person(X))))<=>(tall(X)&person(X)))))& ((![X]:((calm(X))=>(~(wise(X)&person(X))))))& (?[X,Y]:((old(X))&(((old(Y))&(~patient(Y))&(creative(Y)&person(Y))))&(older(X,Y))))

(there_is_a_room)& ~![X]:(room(X)=>(curious(X)&person(X)))

% SZS status Unsatisfiable for 4292138532530622594861280 % SZS output start Proof for 4292138532530622594861280 44. there_is_a_room [input p0] 45. ? [X0] : (strong(X0) & room(X0)) <=> ! [X0] : (room(X0) => (person(X0) & calm(X0))) [input p1] 47. ! [X0] : (room(X0) => (person(X0) & calm(X0))) [input p3] 48. ! [X0] : (room(X0) => ~(person(X0) & curious(X0))) [input p4] 50. ! [X0] : (((person(X0) & generous(X0)) | ~(person(X0) & tall(X0))) <=> (person(X0) & tall(X0))) [input p6] 53. ~(~! [X0] : (room(X0) => (person(X0) & curious(X0))) & there_is_a_room) [input hypothesis] 54. ? [X0] : (strong(X0) & room(X0)) <=> ! [X1] : (room(X1) => (person(X1) & calm(X1))) [rectify 45] 128. ? [X0] : (strong(X0) & room(X0)) <=> ! [X1] : ((person(X1) & calm(X1)) | ~room(X1)) [ennf transformation 54] 130. ! [X0] : ((person(X0) & calm(X0)) | ~room(X0)) [ennf transformation 47] 131. ! [X0] : ((~person(X0) | ~curious(X0)) | ~room(X0)) [ennf transformation 48] 132. ! [X0] : (~person(X0) | ~curious(X0) | ~room(X0)) [flattening 131] 134. ! [X0] : (((person(X0) & generous(X0)) | (~person(X0) | ~tall(X0))) <=> (person(X0) & tall(X0))) [ennf transformation 50] 135. ! [X0] : (((person(X0) & generous(X0)) | ~person(X0) | ~tall(X0)) <=> (person(X0) & tall(X0))) [flattening 134] 136. ! [X0] : ((person(X0) & curious(X0)) | ~room(X0)) | ~there_is_a_room [ennf transformation 53] 138. (? [X0] : (strong(X0) & room(X0)) | ? [X1] : ((~person(X1) | ~calm(X1)) & room(X1))) & (! [X1] : ((person(X1) & calm(X1)) | ~room(X1)) | ! [X0] : (~strong(X0) | ~room(X0))) [nnf transformation 128] 139. (? [X0] : (strong(X0) & room(X0)) | ? [X1] : ((~person(X1) | ~calm(X1)) & room(X1))) & (! [X2] : ((person(X2) & calm(X2)) | ~room(X2)) | ! [X3] : (~strong(X3) | ~room(X3))) [rectify 138] 140. ? [X0] : (strong(X0) & room(X0)) => (strong(sK0) & room(sK0)) [choice axiom] 141. ? [X1] : ((~person(X1) | ~calm(X1)) & room(X1)) => ((~person(sK1) | ~calm(sK1)) & room(sK1)) [choice axiom] 142. ((strong(sK0) & room(sK0)) | ((~person(sK1) | ~calm(sK1)) & room(sK1))) & (! [X2] : ((person(X2) & calm(X2)) | ~room(X2)) | ! [X3] : (~strong(X3) | ~room(X3))) [skolemisation 139,141,140] 145. ! [X0] : ((((person(X0) & generous(X0)) | ~person(X0) | ~tall(X0)) | (~person(X0) | ~tall(X0))) & ((person(X0) & tall(X0)) | ((~person(X0) | ~generous(X0)) & person(X0) & tall(X0)))) [nnf transformation 135] 146. ! [X0] : (((person(X0) & generous(X0)) | ~person(X0) | ~tall(X0) | ~person(X0) | ~tall(X0)) & ((person(X0) & tall(X0)) | ((~person(X0) | ~generous(X0)) & person(X0) & tall(X0)))) [flattening 145] 229. there_is_a_room [cnf transformation 44] 232. room(sK0) | room(sK1) [cnf transformation 142] 233. room(sK0) | ~person(sK1) | ~calm(sK1) [cnf transformation 142] 239. calm(X0) | ~room(X0) [cnf transformation 130] 241. ~curious(X0) | ~person(X0) | ~room(X0) [cnf transformation 132] 248. person(X0) | person(X0) [cnf transformation 146] 258. curious(X0) | ~room(X0) | ~there_is_a_room [cnf transformation 136] 261. person(X0) [duplicate literal removal 248] 265. 1 <=> calm(sK1) [avatar definition] 267. ~calm(sK1) <- (~1) [avatar component clause 265] 269. 2 <=> person(sK1) [avatar definition] 271. ~person(sK1) <- (~2) [avatar component clause 269] 278. 4 <=> room(sK1) [avatar definition] 280. room(sK1) <- (4) [avatar component clause 278] 283. 5 <=> room(sK0) [avatar definition] 285. room(sK0) <- (5) [avatar component clause 283] 286. ~1 | ~2 | 5 [avatar split clause 233,283,269,265] 287. 4 | 5 [avatar split clause 232,283,278] 296. 8 <=> ! [X2] : (calm(X2) | ~room(X2)) [avatar definition] 297. ~room(X2) | calm(X2) <- (8) [avatar component clause 296] 309. 8 [avatar split clause 239,296] 312. ~room(X0) | curious(X0) [subsumption resolution 258,229] 314. calm(sK1) <- (4, 8) [resolution 297,280] 315. $false <- (~1, 4, 8) [subsumption resolution 314,267] 316. 1 | ~4 | ~8 [avatar contradiction clause 315] 319. curious(sK0) <- (5) [resolution 312,285] 320. ~person(sK0) | ~room(sK0) <- (5) [resolution 241,319] 321. ~room(sK0) <- (5) [subsumption resolution 320,261] 322. $false <- (5) [subsumption resolution 321,285] 323. ~5 [avatar contradiction clause 322] 324. $false <- (~2) [subsumption resolution 271,261] 325. 2 [avatar contradiction clause 324] 326. $false [avatar sat refutation 286,287,309,316,323,325] % SZS output end Proof for 4292138532530622594861280 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. No one in the room does not enjoy deep-sea diving and exploring underwater caves. No one in the room does not enjoy fishing if they does not collect historical artifacts related to ancient civilizations. Everyone in the room who does not enjoy fishing practices digital art. Everyone in the room who does not maintain a large, organic vegetable garden year-round collects rare and antique scientific instruments. Everyone anywhere has a tattoo only if they practices kickboxing. No one in the room designs and sews custom cosplay costumes for conventions if they practices kickboxing. Everyone in the room collects rare and antique scientific instruments if they designs and sews custom cosplay costumes for conventions. Everyone in the room enjoys making ceramics if they collects rare and antique scientific instruments. Everyone in the room does not practice zumba. Everyone in the room maintains a personal blog focused on cybersecurity tips if they collects rare and antique scientific instruments. Everyone anywhere does not maintain a large, organic vegetable garden year-round or practices zumba. No one in the room does not maintain a large, organic vegetable garden year-round if they does not enjoy deep-sea diving and exploring underwater caves or plays video games or both and vice versa. If someone enjoys making ceramics then he/she does not play video games.

Everyone in the room does not maintain a personal blog focused on cybersecurity tips.

contradiction

(there_is_a_room)& (~?[X]:(room(X)=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))& (~?[X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))=>(does_not_enjoy_fishing(X))))))& (![X]:(room(X)=>(((does_not_enjoy_fishing(X))=>(practices_digital_art(X))))))& (![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(anywhere(X)=>(((practices_kickboxing(X))<=(has_a_tattoo(X))))))& (~?[X]:(room(X)=>(((practices_kickboxing(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(does_not_practice_zumba(X))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(anywhere(X)=>(((practices_zumba(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& (~?[X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))<=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(plays_video_games(X))))))))& ((![X]:((enjoys_making_ceramics(X))=>(does_not_play_video_games(X)))))

(there_is_a_room)& ![X]:(room(X)=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X)))

% SZS status Unsatisfiable for 7439899983863189059124102 % SZS output start Proof for 7439899983863189059124102 5. ! [X0] : anywhere(X0) [input b4] 45. ~? [X0] : (room(X0) => ~predc(X0)) [input p1] 48. ! [X0] : (room(X0) => (~predk(X0) => predd(X0))) [input p4] 53. ! [X0] : (room(X0) => ~predl(X0)) [input p9] 54. ! [X0] : (room(X0) => (predd(X0) => predm(X0))) [input p10] 55. ! [X0] : (anywhere(X0) => (~predk(X0) | predl(X0))) [input p11] 58. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 66. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 58] 139. ! [X0] : (predc(X0) & room(X0)) [ennf transformation 45] 141. ! [X0] : ((predd(X0) | predk(X0)) | ~room(X0)) [ennf transformation 48] 142. ! [X0] : (predd(X0) | predk(X0) | ~room(X0)) [flattening 141] 146. ! [X0] : (~predl(X0) | ~room(X0)) [ennf transformation 53] 147. ! [X0] : ((predm(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 54] 148. ! [X0] : (predm(X0) | ~predd(X0) | ~room(X0)) [flattening 147] 149. ! [X0] : ((~predk(X0) | predl(X0)) | ~anywhere(X0)) [ennf transformation 55] 150. ! [X0] : (~predk(X0) | predl(X0) | ~anywhere(X0)) [flattening 149] 153. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 66] 157. anywhere(X0) [cnf transformation 5] 238. room(X0) [cnf transformation 139] 241. predd(X0) | predk(X0) | ~room(X0) [cnf transformation 142] 244. ~predl(X0) | ~room(X0) [cnf transformation 146] 245. predm(X0) | ~predd(X0) | ~room(X0) [cnf transformation 148] 246. ~predk(X0) | predl(X0) | ~anywhere(X0) [cnf transformation 150] 252. ~predm(X0) | ~room(X0) [cnf transformation 153] 253. predd(X0) | predk(X0) [subsumption resolution 241,238] 255. ~predl(X0) [subsumption resolution 244,238] 256. ~predd(X0) | predm(X0) [subsumption resolution 245,238] 257. ~predk(X0) | ~anywhere(X0) [subsumption resolution 246,255] 258. ~predk(X0) [subsumption resolution 257,157] 260. ~predm(X0) [subsumption resolution 252,238] 263. predm(X0) | predk(X0) [resolution 256,253] 264. predk(X0) [subsumption resolution 263,260] 265. $false [subsumption resolution 264,258] % SZS output end Proof for 7439899983863189059124102 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Everyone in the room is not hated by Jesse and does not hate Jesse if and only if they either is not liked by Jesse or is hated by Jesse but not both. Everyone in the room is not liked by Jesse if they either is not liked by Jesse or is hated by Jesse but not both. Everyone outside the room is liked by Jesse or is not liked by Jean or both if they is not liked by Jesse. Everyone outside the room who is liked by Jesse or is not liked by Jean or both does not like Jean and is hated by Jean. Everyone in the room is not hated by Jean, is not hated by Jesse and is liked by Jean if they does not like Jean and is hated by Jean. Someone in the room either is not hated by Jean or is liked by Jesse but not both. Everyone in the room does not like Jean if they is liked by Jean and vice versa. Everyone anywhere is hated by Jesse, is hated by Jean or is not hated by Jean if they is liked by Jean.

More than one person in the room is liked by Jean.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((((~hate(X,jesse))&(~hate(jesse,X))))<=>(((~like(X,jesse))<~>(hate(X,jesse))))))))& (![X]:(room(X)=>(((((~like(X,jesse))<~>(hate(X,jesse))))=>(~like(X,jesse))))))& (![X]:(~room(X)=>(((~like(X,jesse))=>(((like(X,jesse))|(~like(X,jean))))))))& (![X]:(~room(X)=>(((((like(X,jesse))|(~like(X,jean))))=>(((~like(jean,X))&(hate(X,jean))))))))& (![X]:(room(X)=>(((((~like(jean,X))&(hate(X,jean))))=>(((~hate(X,jean))&(~hate(X,jesse))&(like(X,jean))))))))& (?[X]:(room(X)&(((~hate(X,jean))<~>(like(X,jesse))))))& (![X]:(room(X)=>(((~like(jean,X))<=>(like(X,jean))))))& (![X]:(anywhere(X)=>(((like(X,jean))=>(((hate(X,jesse))|(hate(X,jean))|(~hate(X,jean))))))))

(there_is_a_room)& (?[X,Y]:(room(X)&room(Y)&(like(X,jean)&like(Y,jean))&(X!=Y)))

Karl is the only person in the room. Karl enjoys virtual reality gaming. Karl develops open-source software projects in their free time. Karl hosts themed dinner parties featuring gourmet home-cooked meals. Everyone in the room who develops open-source software projects in their free time does not write and illustrates their own graphic novels and collects action figures. Everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals if and only if they either writes and illustrates their own graphic novels or enjoys watercolor painting but not both.

Karl enjoys watercolor painting.

entailment

room(karl)&(![X]:(room(X)=>(X='karl')))& (enjoys_virtual_reality_gaming(karl))& ((![X]:((does_not_enjoy_cross-country_skiing(X))=>(knows_morse_code(X)))))& ((![X]:((collects_foreign_coins(X))=>(does_practice_yoga(X)))))& ((![X]:((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(can_play_the_guitar(X)))))& (![X]:(~room(X)=>(is_an_active_member_of_a_local_robotics_club(X))))& (((trains_for_and_competes_in_international_triathlons(karl))&(collects_foreign_coins(karl))&(does_practice_yoga(karl))))& (![X]:(~room(X)=>(((enjoys_virtual_reality_gaming(X))=>(knows_morse_code(X))))))& (can_play_the_guitar(karl))& (develops_open-source_software_projects_in_their_free_time(karl))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(karl))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))&(collects_action_figures(X))))))))& (((is_an_active_member_of_a_local_robotics_club(karl))&(does_not_know_morse_code(karl))))& (((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(karl))<~>(develops_open-source_software_projects_in_their_free_time(karl))))& (![X]:(~room(X)=>(((enjoys_virtual_reality_gaming(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=>(((writes_and_illustrates_their_own_graphic_novels(X))<~>(enjoys_watercolor_painting(X))))))))& (is_an_active_member_of_a_local_robotics_club(karl))& (~![X]:(room(X)=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))

room(karl)&(![X]:(room(X)=>(X='karl')))& enjoys_watercolor_painting(karl)

% SZS status Unsatisfiable for 3776142032548676405614694 % SZS output start Proof for 3776142032548676405614694 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 53. predd(mary) [input p9] 54. predf(mary) [input p10] 55. ! [X0] : (room(X0) => (predd(X0) => (predn(X0) & ~predh(X0)))) [input p11] 59. ! [X0] : (room(X0) => (predf(X0) <=> (predh(X0) <~> predp(X0)))) [input p15] 62. ~(predp(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 64. ! [X0] : (room(X0) => (predd(X0) => ~predh(X0))) [pure predicate removal 55] 147. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 150. ! [X0] : ((~predh(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 64] 151. ! [X0] : (~predh(X0) | ~predd(X0) | ~room(X0)) [flattening 150] 154. ! [X0] : ((predf(X0) <=> (predh(X0) <~> predp(X0))) | ~room(X0)) [ennf transformation 59] 156. ~predp(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 62] 159. ! [X0] : (((predf(X0) | ((predh(X0) | ~predp(X0)) & (predp(X0) | ~predh(X0)))) & (((~predp(X0) | ~predh(X0)) & (predp(X0) | predh(X0))) | ~predf(X0))) | ~room(X0)) [nnf transformation 154] 162. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 163. ~predp(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 156,162] 244. room(mary) [cnf transformation 147] 245. ~room(X0) | mary = X0 [cnf transformation 147] 248. predd(mary) [cnf transformation 53] 249. predf(mary) [cnf transformation 54] 250. ~predh(X0) | ~predd(X0) | ~room(X0) [cnf transformation 151] 255. ~predf(X0) | predh(X0) | predp(X0) | ~room(X0) [cnf transformation 159] 260. ~predp(mary) | room(sK1) | ~room(mary) [cnf transformation 163] 261. ~predp(mary) | mary != sK1 | ~room(mary) [cnf transformation 163] 263. ~predp(mary) | mary != sK1 [subsumption resolution 261,244] 265. 1 <=> mary = sK1 [avatar definition] 267. mary != sK1 <- (~1) [avatar component clause 265] 269. 2 <=> predp(mary) [avatar definition] 271. ~predp(mary) <- (~2) [avatar component clause 269] 272. ~1 | ~2 [avatar split clause 263,269,265] 273. ~predp(mary) | room(sK1) [subsumption resolution 260,244] 275. 3 <=> room(sK1) [avatar definition] 277. room(sK1) <- (3) [avatar component clause 275] 278. 3 | ~2 [avatar split clause 273,269,275] 284. predh(mary) | predp(mary) | ~room(mary) [resolution 255,249] 285. predh(mary) | ~room(mary) <- (~2) [subsumption resolution 284,271] 286. predh(mary) <- (~2) [subsumption resolution 285,244] 287. ~predd(mary) | ~room(mary) <- (~2) [resolution 286,250] 288. ~room(mary) <- (~2) [subsumption resolution 287,248] 289. $false <- (~2) [subsumption resolution 288,244] 290. 2 [avatar contradiction clause 289] 297. mary = sK1 <- (3) [resolution 277,245] 298. $false <- (~1, 3) [subsumption resolution 297,267] 299. 1 | ~3 [avatar contradiction clause 298] 300. $false [avatar sat refutation 272,278,290,299] % SZS output end Proof for 3776142032548676405614694 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry, Mark are the only persons in the room. Someone who is not a old person is richer than someone who is quiet. If someone is quiet then he/she is a quiet person. It is not the case that “Larry is a quiet person or is a old person or both”. Mark is not a old person. Everyone outside the room is not a quiet person. If someone is a old person then he/she is a old person, is a quiet person and is old and vice versa.

Mark is quiet.

entailment

room(larry)&room(mark)&(![X]:(room(X)=>(X='larry'|X='mark')))& (?[X,Y]:((~(old(X)&person(X)))&(quiet(Y))&(richer(X,Y))))& ((![X]:((quiet(X))=>(quiet(X)&person(X)))))& (~(((quiet(larry)&person(larry))|(old(larry)&person(larry)))))& (~(old(mark)&person(mark)))& (![X]:(~room(X)=>(~(quiet(X)&person(X)))))& ((![X]:((old(X)&person(X))<=>(((old(X)&person(X))&(quiet(X)&person(X))&(old(X)))))))

room(larry)&room(mark)&(![X]:(room(X)=>(X='larry'|X='mark')))& quiet(mark)

% SZS status Unsatisfiable for 7709235485534103006369390 % SZS output start Proof for 7709235485534103006369390 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ? [X0,X1] : (richer(X0,X1) & quiet(X1) & ~(person(X0) & old(X0))) [input p1] 46. ! [X0] : (quiet(X0) => (person(X0) & quiet(X0))) [input p2] 47. ~((person(mary) & old(mary)) | (person(mary) & quiet(mary))) [input p3] 49. ! [X0] : (~room(X0) => ~(person(X0) & quiet(X0))) [input p5] 51. ~(quiet(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 124. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 125. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 124] 126. ? [X0,X1] : (richer(X0,X1) & quiet(X1) & (~person(X0) | ~old(X0))) [ennf transformation 45] 127. ! [X0] : ((person(X0) & quiet(X0)) | ~quiet(X0)) [ennf transformation 46] 128. (~person(mary) | ~old(mary)) & (~person(mary) | ~quiet(mary)) [ennf transformation 47] 130. ! [X0] : ((~person(X0) | ~quiet(X0)) | room(X0)) [ennf transformation 49] 131. ! [X0] : (~person(X0) | ~quiet(X0) | room(X0)) [flattening 130] 132. ~quiet(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 51] 133. ~quiet(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 132] 135. ? [X0,X1] : (richer(X0,X1) & quiet(X1) & (~person(X0) | ~old(X0))) => (richer(sK0,sK1) & quiet(sK1) & (~person(sK0) | ~old(sK0))) [choice axiom] 136. richer(sK0,sK1) & quiet(sK1) & (~person(sK0) | ~old(sK0)) [skolemisation 126,135] 139. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 140. ~quiet(paul) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 133,139] 221. room(mary) [cnf transformation 125] 222. room(paul) [cnf transformation 125] 223. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 125] 225. quiet(sK1) [cnf transformation 136] 228. ~quiet(X0) | person(X0) [cnf transformation 127] 229. ~person(mary) | ~quiet(mary) [cnf transformation 128] 232. ~person(X0) | ~quiet(X0) | room(X0) [cnf transformation 131] 240. ~quiet(paul) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 140] 241. ~quiet(paul) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 140] 242. ~quiet(paul) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 140] 263. ~quiet(mary) [subsumption resolution 229,228] 273. ~quiet(X0) | room(X0) [subsumption resolution 232,228] 274. ~quiet(paul) | paul != sK2 | ~room(mary) [subsumption resolution 242,222] 275. ~quiet(paul) | paul != sK2 [subsumption resolution 274,221] 277. 7 <=> paul = sK2 [avatar definition] 281. 8 <=> quiet(paul) [avatar definition] 284. ~7 | ~8 [avatar split clause 275,281,277] 285. ~quiet(paul) | mary != sK2 | ~room(mary) [subsumption resolution 241,222] 286. ~quiet(paul) | mary != sK2 [subsumption resolution 285,221] 288. 9 <=> mary = sK2 [avatar definition] 290. mary != sK2 <- (~9) [avatar component clause 288] 291. ~9 | ~8 [avatar split clause 286,281,288] 292. ~quiet(paul) | room(sK2) | ~room(mary) [subsumption resolution 240,222] 293. ~quiet(paul) | room(sK2) [subsumption resolution 292,221] 295. 10 <=> room(sK2) [avatar definition] 297. room(sK2) <- (10) [avatar component clause 295] 298. 10 | ~8 [avatar split clause 293,281,295] 300. room(sK1) [resolution 273,225] 303. mary = sK1 | paul = sK1 [resolution 223,300] 305. 11 <=> paul = sK1 [avatar definition] 307. paul = sK1 <- (11) [avatar component clause 305] 309. 12 <=> mary = sK1 [avatar definition] 311. mary = sK1 <- (12) [avatar component clause 309] 312. 11 | 12 [avatar split clause 303,309,305] 315. quiet(paul) <- (11) [backward demodulation 225,307] 320. 8 | ~11 [avatar split clause 315,305,281] 323. mary = sK2 | paul = sK2 <- (10) [resolution 297,223] 324. paul = sK2 <- (~9, 10) [subsumption resolution 323,290] 327. 7 | 9 | ~10 [avatar split clause 324,295,288,277] 330. quiet(mary) <- (12) [backward demodulation 225,311] 334. $false <- (12) [subsumption resolution 330,263] 335. ~12 [avatar contradiction clause 334] 338. $false [avatar sat refutation 284,291,298,312,320,327,335] % SZS output end Proof for 7709235485534103006369390 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Vicente, Teresa are the only persons in the room. Everyone in the room does not have a curated collection of mid-century modern furniture. Everyone in the room either does not practice yoga or does not enjoy stand-up paddleboarding but not both. Everyone in the room is not a wine connoisseur. Everyone in the room either does not practice kickboxing or does not practice yoga but not both. Everyone in the room either does not make intricate hand-cut paper art for exhibitions or does not bake bread at home but not both. Everyone in the room either is not an avid collector of autographed memorabilia from famous musicians or does not read mystery novels but not both. Everyone in the room is not an avid collector of autographed memorabilia from famous musicians. At least one person in the room does not practice digital art. Everyone in the room does not practice graffiti art and does not have a curated collection of mid-century modern furniture. Not everyone in the room does not collect antique clocks. Not everyone anywhere does not practice graffiti art. Everyone in the room does not practice digital art and does not have a pet dog. Everyone outside the room does not use a Windows laptop. Not everyone in the room does not bake bread at home. Everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations. Everyone outside the room does not create augmented reality experiences for mobile applications. Everyone in the room does not practice graffiti art. Everyone in the room is not an avid collector of autographed memorabilia from famous musicians and does not practice graffiti art. Everyone outside the room cannot play the flute. Everyone outside the room does not make intricate hand-cut paper art for exhibitions. Everyone in the room does not own a significant collection of rare gemstones and minerals and does not have a pet dog. It is true that “everyone anywhere does not write and illustrates their own graphic novels”.

Only one person in the room enjoys stand-up paddleboarding.

neutral

room(vicente)&room(teresa)&(![X]:(room(X)=>(X='vicente'|X='teresa')))& (![X]:(room(X)=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))& (![X]:(room(X)=>(((does_not_practice_yoga(X))<~>(does_not_enjoy_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(is_not_a_wine_connoisseur(X))))& (![X]:(room(X)=>(((does_not_practice_kickboxing(X))<~>(does_not_practice_yoga(X))))))& (![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))<~>(does_not_bake_bread_at_home(X))))))& (![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))<~>(does_not_read_mystery_novels(X))))))& (![X]:(room(X)=>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& (((?[X]:(room(X)&does_not_practice_digital_art(X)))))& (![X]:(room(X)=>(((does_not_practice_graffiti_art(X))&(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))& (~![X]:(room(X)=>(does_not_collect_antique_clocks(X))))& (~![X]:(anywhere(X)=>(does_not_practice_graffiti_art(X))))& (![X]:(room(X)=>(((does_not_practice_digital_art(X))&(does_not_have_a_pet_dog(X))))))& (![X]:(~room(X)=>(does_not_use_a_Windows_laptop(X))))& (~![X]:(room(X)=>(does_not_bake_bread_at_home(X))))& (![X]:(room(X)=>(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))& (![X]:(~room(X)=>(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))& (![X]:(room(X)=>(does_not_practice_graffiti_art(X))))& (![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(does_not_practice_graffiti_art(X))))))& (![X]:(~room(X)=>(cannot_play_the_flute(X))))& (![X]:(~room(X)=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))& (![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))&(does_not_have_a_pet_dog(X))))))& (![X]:(anywhere(X)=>(does_not_write_and_illustrates_their_own_graphic_novels(X))))

room(vicente)&room(teresa)&(![X]:(room(X)=>(X='vicente'|X='teresa')))& ((?[X]:(room(X)&enjoys_stand-up_paddleboarding(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_stand-up_paddleboarding(X))&(enjoys_stand-up_paddleboarding(Y)))=>(X=Y))))

Ma, Dennis, Lynda are the only persons in the room. Everyone anywhere who is older than Virginia is not a creative person. All humble persons are old. Everyone in the room who is a calm quiet person either is a brave happy curious quiet person or is a strong person but not both. Everyone in the room is a wise old person if they is older than Virginia. If someone is a wise creative brave tall person then he/she is not kind. If someone is old then he/she is quiet. Everyone in the room is not a kind person if they is a kind person. Not everyone in the room who neither is happy nor is older than Virginia is generous. Everyone in the room who is older than Virginia is richer than Virginia. Everyone anywhere is a funny calm person.

Dennis is funny.

entailment

room(ma)&room(dennis)&room(lynda)&(![X]:(room(X)=>(X='ma'|X='dennis'|X='lynda')))& (![X]:(anywhere(X)=>(((older(virginia,X))=>(~(creative(X)&person(X)))))))& (![X]:(humble(X)=>old(X)))& (![X]:(room(X)=>(((calm(X)&quiet(X)&person(X))=>(((brave(X)&happy(X)&curious(X)&quiet(X)&person(X))<~>(strong(X)&person(X))))))))& (![X]:(room(X)=>(((older(virginia,X))=>(wise(X)&old(X)&person(X))))))& ((![X]:((wise(X)&creative(X)&brave(X)&tall(X)&person(X))=>(~kind(X)))))& ((![X]:((old(X))=>(quiet(X)))))& (![X]:(room(X)=>(((kind(X)&person(X))=>(~(kind(X)&person(X)))))))& (~![X]:(room(X)=>(((~((happy(X))|(older(virginia,X))))=>(generous(X))))))& (![X]:(room(X)=>(((older(virginia,X))=>(richer(virginia,X))))))& (![X]:(anywhere(X)=>(funny(X)&calm(X)&person(X))))& (![X]:(room(X)=>(calm(X))))& (![X]:(room(X)=>(((quieter(virginia,X))<=(~wise(X))))))& (![X]:(room(X)=>(((generous(X)&person(X))=>(~((old(X)&person(X))|(happy(X)&person(X))))))))& (![X]:(room(X)=>(richer(virginia,X))))

room(ma)&room(dennis)&room(lynda)&(![X]:(room(X)=>(X='ma'|X='dennis'|X='lynda')))& funny(dennis)

% SZS status Unsatisfiable for 4448840883469386471333855 % SZS output start Proof for 4448840883469386471333855 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 54. ! [X0] : (anywhere(X0) => (person(X0) & calm(X0) & funny(X0))) [input p10] 59. ~(funny(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 139. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 140. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 139] 150. ! [X0] : ((person(X0) & calm(X0) & funny(X0)) | ~anywhere(X0)) [ennf transformation 54] 153. ~funny(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 154. ~funny(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 153] 160. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 161. ~funny(paul) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 154,160] 162. anywhere(X0) [cnf transformation 5] 243. room(mary) [cnf transformation 140] 244. room(paul) [cnf transformation 140] 245. room(fred) [cnf transformation 140] 246. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 140] 265. funny(X0) | ~anywhere(X0) [cnf transformation 150] 270. ~funny(paul) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 271. ~funny(paul) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 272. ~funny(paul) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 273. ~funny(paul) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 278. funny(X0) [subsumption resolution 265,162] 279. fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,278] 280. fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 279,245] 281. fred != sK1 | ~room(mary) [subsumption resolution 280,244] 282. fred != sK1 [subsumption resolution 281,243] 283. paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,278] 284. paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 283,245] 285. paul != sK1 | ~room(mary) [subsumption resolution 284,244] 286. paul != sK1 [subsumption resolution 285,243] 287. mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,278] 288. mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 287,245] 289. mary != sK1 | ~room(mary) [subsumption resolution 288,244] 290. mary != sK1 [subsumption resolution 289,243] 291. room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,278] 292. room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 291,245] 293. room(sK1) | ~room(mary) [subsumption resolution 292,244] 294. room(sK1) [subsumption resolution 293,243] 394. paul = sK1 | mary = sK1 | fred = sK1 [resolution 246,294] 408. mary = sK1 | fred = sK1 [subsumption resolution 394,286] 409. fred = sK1 [subsumption resolution 408,290] 410. $false [subsumption resolution 409,282] % SZS output end Proof for 4448840883469386471333855 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jane is the only person in the room. If “Jane has a tattoo” then “if someone enjoys making ceramics then he/she does not play eSports competitively”. Everyone in the room is not an active member of a local robotics club if and only if they is an avid mountain climber who has scaled several peaks. Jane is an active member of a local robotics club. If someone can play the piano and collects antique clocks then he/she writes poetry. Everyone in the room practices and performs acrobatic dance routines and plays eSports competitively. Jane collects rare minerals, is an amateur astronomer who builds and uses custom telescopes and plays the drums. Only one person in the room collects rare minerals. Everyone in the room who owns an extensive assortment of vintage comic book memorabilia is a dedicated advocate for digital privacy and encryption. Everyone in the room plays the violin. Everyone outside the room who plays the drums is an enthusiastic bird watcher who travels for rare sightings. Jane can play the piano. Everyone in the room enjoys making ceramics only if they does not have completed a triathlon. Everyone in the room plays the violin if they does not have completed a triathlon. Jane is a client of Costco. Everyone in the room builds model airplanes if they collects rare minerals. Jane owns an extensive assortment of vintage comic book memorabilia. If someone is an amateur astronomer who builds and uses custom telescopes then he/she can play the piano. Someone in the room is a dedicated advocate for digital privacy and encryption. Everyone outside the room practices and performs acrobatic dance routines if they is not an active member of a local robotics club and vice versa. Jane hosts regular game nights featuring complex strategy games. Jane plays the drums. Jane plays the violin. Everyone in the room either has completed a triathlon or does not write poetry but not both if and only if they collects vintage stamps. Jane does not have completed a triathlon. Everyone in the room does not practice and performs acrobatic dance routines if and only if they collects antique clocks. Jane collects rare minerals.

Jane collects vintage stamps.

neutral

room(jane)&(![X]:(room(X)=>(X='jane')))& ((has_a_tattoo(jane))=>((![X]:((enjoys_making_ceramics(X))=>(does_not_play_eSports_competitively(X))))))& (![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))<=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (is_an_active_member_of_a_local_robotics_club(jane))& ((![X]:((((can_play_the_piano(X))&(collects_antique_clocks(X))))=>(writes_poetry(X)))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))&(plays_eSports_competitively(X))))))& (((collects_rare_minerals(jane))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(jane))&(plays_the_drums(jane))))& (((?[X]:(room(X)&collects_rare_minerals(X)))&(![X,Y]:((room(X)&room(Y)&(collects_rare_minerals(X))&(collects_rare_minerals(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(plays_the_violin(X))))& (![X]:(~room(X)=>(((plays_the_drums(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (can_play_the_piano(jane))& (![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))<=(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))=>(plays_the_violin(X))))))& (is_a_client_of_Costco(jane))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(builds_model_airplanes(X))))))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(jane))& ((![X]:((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(can_play_the_piano(X)))))& (?[X]:(room(X)&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))& (![X]:(~room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))<=>(is_not_an_active_member_of_a_local_robotics_club(X))))))& (hosts_regular_game_nights_featuring_complex_strategy_games(jane))& (plays_the_drums(jane))& (plays_the_violin(jane))& (![X]:(room(X)=>(((((has_completed_a_triathlon(X))<~>(does_not_write_poetry(X))))<=>(collects_vintage_stamps(X))))))& (does_not_have_completed_a_triathlon(jane))& (![X]:(room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))<=>(collects_antique_clocks(X))))))& (collects_rare_minerals(jane))

room(jane)&(![X]:(room(X)=>(X='jane')))& collects_vintage_stamps(jane)

Jesse, Steven, Karen are the only persons in the room. “At least one person in the room is not a kind person” only if “at least one person in the room neither is a tall person nor is not a patient person”. “Steven is kind or is a generous calm person or both” unless “Karen is a generous person”. Jesse and Karen are not a funny persons. Karen and Steven are strong. It is not the case that “Jesse is a wise person or is a patient person or both”. Steven is a funny person. If someone either is a strong person or is a tall brave person but not both then he/she is not a kind person. Everyone in the room who is a funny person is not a calm person.

Karen is not funny.

entailment

room(jesse)&room(steven)&room(karen)&(![X]:(room(X)=>(X='jesse'|X='steven'|X='karen')))& ((((?[X]:(room(X)&~(kind(X)&person(X))))))=>(((?[X]:(room(X)&~((tall(X)&person(X))|(~(patient(X)&person(X)))))))))& ((curious(steven)&person(steven))=>(~(generous(jesse)&calm(jesse)&person(jesse))))& ((quiet(karen)&person(karen))=>(~?[X]:(quiet(X)=>humble(X))))& (~(generous(karen)&person(karen))=>(((kind(steven))|(generous(steven)&calm(steven)&person(steven)))))& ((((quiet(jesse)&person(jesse))&(tall(jesse))&(brave(jesse)))&((quiet(steven)&person(steven))&(tall(steven))&(brave(steven))))=>(~?[X]:(humble(X)=>brave(X))))& (((strong(steven))&(wise(jesse)))=>(~(funny(steven)&quiet(steven)&person(steven))))& (~(funny(jesse)&person(jesse))&~(funny(karen)&person(karen)))& (~(funny(steven)&quiet(steven)&person(steven)))& (![X]:(~room(X)=>(((((wise(X)&old(X)&person(X))<~>(~(curious(X)&wise(X)&person(X)))))=>(kind(X))))))& (~(~humble(steven)))& (kind(jesse))& (strong(karen)&strong(steven))& (((?[X]:(anywhere(X)&~(strong(X)&person(X))))))& (~(((wise(jesse)&person(jesse))|(patient(jesse)&person(jesse)))))& (~calm(karen))& (((?[X]:(anywhere(X)&curious(X)&person(X)))))& (funny(steven)&person(steven))& ((((wise(karen)&old(karen)&person(karen))<~>(~(curious(karen)&wise(karen)&person(karen)))))&(happy(karen)))& ((![X]:((((strong(X)&person(X))<~>(tall(X)&brave(X)&person(X))))=>(~(kind(X)&person(X))))))& (~~old(steven))& (~(strong(steven)&wise(steven)&person(steven)))& (~(((curious(karen)&person(karen))|(calm(karen))|(~~~~calm(karen)))&((curious(jesse)&person(jesse))|(calm(jesse))|(~~~~calm(jesse)))))& (~(~(((~(creative(jesse)&patient(jesse)&person(jesse)))|(kind(jesse)&funny(jesse)&person(jesse))))))& (![X]:(room(X)=>(((funny(X)&person(X))=>(~(calm(X)&person(X)))))))

room(jesse)&room(steven)&room(karen)&(![X]:(room(X)=>(X='jesse'|X='steven'|X='karen')))& ~funny(karen)

% SZS status Unsatisfiable for 9016406411375993806453736 % SZS output start Proof for 9016406411375993806453736 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ? [X0] : (~(person(X0) & kind(X0)) & room(X0)) => ? [X0] : (~(~(person(X0) & patient(X0)) | (person(X0) & tall(X0))) & room(X0)) [input p1] 48. ~(person(fred) & generous(fred)) => ((person(paul) & calm(paul) & generous(paul)) | kind(paul)) [input p4] 51. ~(person(fred) & funny(fred)) & ~(person(mary) & funny(mary)) [input p7] 56. strong(paul) & strong(fred) [input p12] 58. ~((person(mary) & patient(mary)) | (person(mary) & wise(mary))) [input p14] 61. person(paul) & funny(paul) [input p17] 63. ! [X0] : (((person(X0) & strong(X0)) <~> (person(X0) & brave(X0) & tall(X0))) => ~(person(X0) & kind(X0))) [input p19] 68. ! [X0] : (room(X0) => ((person(X0) & funny(X0)) => ~(person(X0) & calm(X0)))) [input p24] 69. ~(~funny(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 70. ? [X0] : (~(person(X0) & kind(X0)) & room(X0)) => ? [X1] : (~(~(person(X1) & patient(X1)) | (person(X1) & tall(X1))) & room(X1)) [rectify 45] 148. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 148] 150. ? [X1] : (((person(X1) & patient(X1)) & (~person(X1) | ~tall(X1))) & room(X1)) | ! [X0] : ((person(X0) & kind(X0)) | ~room(X0)) [ennf transformation 70] 151. ? [X1] : (person(X1) & patient(X1) & (~person(X1) | ~tall(X1)) & room(X1)) | ! [X0] : ((person(X0) & kind(X0)) | ~room(X0)) [flattening 150] 156. ((person(paul) & calm(paul) & generous(paul)) | kind(paul)) | (person(fred) & generous(fred)) [ennf transformation 48] 157. (person(paul) & calm(paul) & generous(paul)) | kind(paul) | (person(fred) & generous(fred)) [flattening 156] 162. (~person(fred) | ~funny(fred)) & (~person(mary) | ~funny(mary)) [ennf transformation 51] 167. (~person(mary) | ~patient(mary)) & (~person(mary) | ~wise(mary)) [ennf transformation 58] 169. ! [X0] : ((~person(X0) | ~kind(X0)) | ((person(X0) & strong(X0)) <=> (person(X0) & brave(X0) & tall(X0)))) [ennf transformation 63] 170. ! [X0] : (~person(X0) | ~kind(X0) | ((person(X0) & strong(X0)) <=> (person(X0) & brave(X0) & tall(X0)))) [flattening 169] 173. ! [X0] : (((~person(X0) | ~calm(X0)) | (~person(X0) | ~funny(X0))) | ~room(X0)) [ennf transformation 68] 174. ! [X0] : (~person(X0) | ~calm(X0) | ~person(X0) | ~funny(X0) | ~room(X0)) [flattening 173] 175. funny(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 69] 176. funny(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 175] 184. ? [X0] : (person(X0) & patient(X0) & (~person(X0) | ~tall(X0)) & room(X0)) | ! [X1] : ((person(X1) & kind(X1)) | ~room(X1)) [rectify 151] 185. ? [X0] : (person(X0) & patient(X0) & (~person(X0) | ~tall(X0)) & room(X0)) => (person(sK3) & patient(sK3) & (~person(sK3) | ~tall(sK3)) & room(sK3)) [choice axiom] 186. (person(sK3) & patient(sK3) & (~person(sK3) | ~tall(sK3)) & room(sK3)) | ! [X1] : ((person(X1) & kind(X1)) | ~room(X1)) [skolemisation 184,185] 199. ! [X0] : (~person(X0) | ~kind(X0) | (((person(X0) & strong(X0)) | (~person(X0) | ~brave(X0) | ~tall(X0))) & ((person(X0) & brave(X0) & tall(X0)) | (~person(X0) | ~strong(X0))))) [nnf transformation 170] 200. ! [X0] : (~person(X0) | ~kind(X0) | (((person(X0) & strong(X0)) | ~person(X0) | ~brave(X0) | ~tall(X0)) & ((person(X0) & brave(X0) & tall(X0)) | ~person(X0) | ~strong(X0)))) [flattening 199] 202. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 203. funny(fred) | (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 176,202] 284. room(mary) [cnf transformation 149] 285. room(paul) [cnf transformation 149] 286. room(fred) [cnf transformation 149] 287. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 149] 289. room(sK3) | person(X1) | ~room(X1) [cnf transformation 186] 291. ~person(sK3) | ~tall(sK3) | person(X1) | ~room(X1) [cnf transformation 186] 293. patient(sK3) | person(X1) | ~room(X1) [cnf transformation 186] 295. person(sK3) | person(X1) | ~room(X1) [cnf transformation 186] 302. calm(paul) | kind(paul) | person(fred) [cnf transformation 157] 309. ~person(fred) | ~funny(fred) [cnf transformation 162] 322. strong(paul) [cnf transformation 56] 325. ~person(mary) | ~patient(mary) [cnf transformation 167] 329. funny(paul) [cnf transformation 61] 330. person(paul) [cnf transformation 61] 339. ~person(X0) | ~kind(X0) | tall(X0) | ~person(X0) | ~strong(X0) [cnf transformation 200] 352. ~person(X0) | ~calm(X0) | ~person(X0) | ~funny(X0) | ~room(X0) [cnf transformation 174] 353. funny(fred) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 354. funny(fred) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 355. funny(fred) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 356. funny(fred) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 357. ~funny(X0) | ~calm(X0) | ~person(X0) | ~room(X0) [duplicate literal removal 352] 358. ~strong(X0) | ~kind(X0) | tall(X0) | ~person(X0) [duplicate literal removal 339] 364. 1 <=> ! [X1] : (person(X1) | ~room(X1)) [avatar definition] 365. ~room(X1) | person(X1) <- (1) [avatar component clause 364] 367. 2 <=> person(sK3) [avatar definition] 369. person(sK3) <- (2) [avatar component clause 367] 370. 1 | 2 [avatar split clause 295,367,364] 376. 4 <=> patient(sK3) [avatar definition] 378. patient(sK3) <- (4) [avatar component clause 376] 379. 1 | 4 [avatar split clause 293,376,364] 382. 5 <=> tall(sK3) [avatar definition] 384. ~tall(sK3) <- (~5) [avatar component clause 382] 385. 1 | ~5 | ~2 [avatar split clause 291,367,382,364] 388. 6 <=> room(sK3) [avatar definition] 390. room(sK3) <- (6) [avatar component clause 388] 391. 1 | 6 [avatar split clause 289,388,364] 398. 8 <=> person(paul) [avatar definition] 399. person(paul) <- (8) [avatar component clause 398] 410. 11 <=> person(mary) [avatar definition] 412. ~person(mary) <- (~11) [avatar component clause 410] 419. 13 <=> person(fred) [avatar definition] 421. ~person(fred) <- (~13) [avatar component clause 419] 431. 16 <=> kind(paul) [avatar definition] 433. kind(paul) <- (16) [avatar component clause 431] 441. 18 <=> calm(paul) [avatar definition] 444. 13 | 16 | 18 [avatar split clause 302,441,431,419] 469. 24 <=> tall(paul) [avatar definition] 470. tall(paul) <- (24) [avatar component clause 469] 485. 28 <=> strong(paul) [avatar definition] 486. strong(paul) <- (28) [avatar component clause 485] 493. 30 <=> funny(paul) [avatar definition] 494. funny(paul) <- (30) [avatar component clause 493] 498. 31 <=> funny(fred) [avatar definition] 501. ~31 | ~13 [avatar split clause 309,419,498] 512. 28 [avatar split clause 322,485] 523. 35 <=> patient(mary) [avatar definition] 526. ~35 | ~11 [avatar split clause 325,410,523] 528. 8 [avatar split clause 330,398] 529. 30 [avatar split clause 329,493] 571. funny(fred) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 356,286] 572. funny(fred) | fred != sK6 | ~room(mary) [subsumption resolution 571,285] 573. funny(fred) | fred != sK6 [subsumption resolution 572,284] 575. 43 <=> fred = sK6 [avatar definition] 578. ~43 | 31 [avatar split clause 573,498,575] 579. funny(fred) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 355,286] 580. funny(fred) | paul != sK6 | ~room(mary) [subsumption resolution 579,285] 581. funny(fred) | paul != sK6 [subsumption resolution 580,284] 583. 44 <=> paul = sK6 [avatar definition] 585. paul != sK6 <- (~44) [avatar component clause 583] 586. ~44 | 31 [avatar split clause 581,498,583] 587. funny(fred) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 354,286] 588. funny(fred) | mary != sK6 | ~room(mary) [subsumption resolution 587,285] 589. funny(fred) | mary != sK6 [subsumption resolution 588,284] 591. 45 <=> mary = sK6 [avatar definition] 593. mary != sK6 <- (~45) [avatar component clause 591] 594. ~45 | 31 [avatar split clause 589,498,591] 595. funny(fred) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 353,286] 596. funny(fred) | room(sK6) | ~room(mary) [subsumption resolution 595,285] 597. funny(fred) | room(sK6) [subsumption resolution 596,284] 599. 46 <=> room(sK6) [avatar definition] 601. room(sK6) <- (46) [avatar component clause 599] 602. 46 | 31 [avatar split clause 597,498,599] 609. ~calm(paul) | ~person(paul) | ~room(paul) <- (30) [resolution 357,494] 611. ~calm(paul) | ~room(paul) <- (8, 30) [subsumption resolution 609,399] 612. ~calm(paul) <- (8, 30) [subsumption resolution 611,285] 613. ~18 | ~8 | ~30 [avatar split clause 612,493,398,441] 615. ~kind(paul) | tall(paul) | ~person(paul) <- (28) [resolution 358,486] 616. tall(paul) | ~person(paul) <- (16, 28) [subsumption resolution 615,433] 617. tall(paul) <- (8, 16, 28) [subsumption resolution 616,399] 618. 24 | ~8 | ~16 | ~28 [avatar split clause 617,485,431,398,469] 673. paul = sK3 | mary = sK3 | fred = sK3 <- (6) [resolution 287,390] 675. 47 <=> fred = sK3 [avatar definition] 677. fred = sK3 <- (47) [avatar component clause 675] 679. 48 <=> mary = sK3 [avatar definition] 681. mary = sK3 <- (48) [avatar component clause 679] 683. 49 <=> paul = sK3 [avatar definition] 685. paul = sK3 <- (49) [avatar component clause 683] 686. 47 | 48 | 49 | ~6 [avatar split clause 673,388,683,679,675] 687. person(fred) <- (2, 47) [backward demodulation 369,677] 693. 13 | ~2 | ~47 [avatar split clause 687,675,367,419] 707. paul = sK6 | mary = sK6 | fred = sK6 <- (46) [resolution 601,287] 708. mary = sK6 | fred = sK6 <- (~44, 46) [subsumption resolution 707,585] 709. fred = sK6 <- (~44, ~45, 46) [subsumption resolution 708,593] 712. 43 | 44 | 45 | ~46 [avatar split clause 709,599,591,583,575] 721. person(fred) <- (1) [resolution 365,286] 724. $false <- (1, ~13) [subsumption resolution 721,421] 725. ~1 | 13 [avatar contradiction clause 724] 727. ~tall(paul) <- (~5, 49) [backward demodulation 384,685] 729. $false <- (~5, 24, 49) [subsumption resolution 727,470] 730. 5 | ~24 | ~49 [avatar contradiction clause 729] 734. patient(mary) <- (4, 48) [backward demodulation 378,681] 738. person(mary) <- (2, 48) [backward demodulation 369,681] 739. 35 | ~4 | ~48 [avatar split clause 734,679,376,523] 741. $false <- (2, ~11, 48) [subsumption resolution 738,412] 742. ~2 | 11 | ~48 [avatar contradiction clause 741] 743. $false [avatar sat refutation 370,379,385,391,444,501,512,526,528,529,578,586,594,602,613,618,686,693,712,725,730,739,742] % SZS output end Proof for 9016406411375993806453736 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Marco, Kelsey, Christopher are the only persons in the room. If “everyone in the room is not a old person, is not a quiet person or is not quiet” then “everyone in the room is not quiet” otherwise “everyone in the room is a quiet person”. Everyone in the room is not quiet.

Christopher and Kelsey are quiet.

contradiction

room(marco)&room(kelsey)&room(christopher)&(![X]:(room(X)=>(X='marco'|X='kelsey'|X='christopher')))& (((![X]:(room(X)=>(((~(old(X)&person(X)))|(~(quiet(X)&person(X)))|(~quiet(X))))))=>(![X]:(room(X)=>(~quiet(X)))))&((~(![X]:(room(X)=>(((~(old(X)&person(X)))|(~(quiet(X)&person(X)))|(~quiet(X)))))))=>(![X]:(room(X)=>(quiet(X)&person(X))))))& ((![X]:(room(X)=>(old(X)&person(X))))<=>(![X]:(room(X)=>(quiet(X)&person(X)))))& ((![X]:(room(X)=>(quiet(X)&person(X))))=>(~?[X]:(anywhere(X)=>(~old(X)))))& ((![X]:(room(X)=>(old(X)&person(X))))=>(![X]:(room(X)=>(quiet(X)&person(X)))))& (![X]:(room(X)=>(~old(X))))& (![X]:(room(X)=>(~quiet(X))))

room(marco)&room(kelsey)&room(christopher)&(![X]:(room(X)=>(X='marco'|X='kelsey'|X='christopher')))& quiet(christopher)&quiet(kelsey)

% SZS status Unsatisfiable for 8443660315920737388631081 % SZS output start Proof for 8443660315920737388631081 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 50. ! [X0] : (room(X0) => ~quiet(X0)) [input p6] 51. quiet(paul) & quiet(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 129. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 130. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 129] 137. ! [X0] : (~quiet(X0) | ~room(X0)) [ennf transformation 50] 138. quiet(paul) & quiet(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 51] 139. quiet(paul) & quiet(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 138] 237. room(fred) [cnf transformation 130] 262. ~quiet(X0) | ~room(X0) [cnf transformation 137] 267. quiet(fred) [cnf transformation 139] 287. 5 <=> ! [X2] : (~quiet(X2) | ~room(X2)) [avatar definition] 288. ~room(X2) | ~quiet(X2) <- (5) [avatar component clause 287] 375. 5 [avatar split clause 262,287] 427. ~quiet(fred) <- (5) [resolution 288,237] 434. $false <- (5) [subsumption resolution 427,267] 435. ~5 [avatar contradiction clause 434] 436. $false [avatar sat refutation 375,435] % SZS output end Proof for 8443660315920737388631081 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Robert, Theresa are the only persons in the room. If “everyone in the room is an active member of a local robotics club or does not write in-depth travel guides for off-the-beaten-path destinations” then “Theresa does enjoy mountain biking”. “Not everyone in the room is an active member of a local robotics club or does not enjoy mountain biking” only if “someone in the room enjoys origami”. If “Robert creates bespoke furniture pieces from reclaimed wood” then “someone anywhere does not host themed dinner parties featuring gourmet home-cooked meals”. If “Robert enjoys origami” then “everyone in the room is a culinary enthusiast who experiments with international cuisines”. Everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals if they plays video games. Everyone anywhere hosts themed dinner parties featuring gourmet home-cooked meals only if they plays video games.

Robert enjoys origami.

neutral

room(robert)&room(theresa)&(![X]:(room(X)=>(X='robert'|X='theresa')))& ((![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(is_an_active_member_of_a_local_robotics_club(X))))))=>(does_enjoy_mountain_biking(theresa)))& ((~![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))|(is_an_active_member_of_a_local_robotics_club(X))))))=>(?[X]:(room(X)&(enjoys_origami(X)))))& ((creates_bespoke_furniture_pieces_from_reclaimed_wood(robert))=>(?[X]:(anywhere(X)&(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& ((enjoys_origami(robert))=>(![X]:(room(X)=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))& (![X]:(room(X)=>(((plays_video_games(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(anywhere(X)=>(((plays_video_games(X))<=(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(theresa))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(anywhere(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(anywhere(X)=>(((uses_contact_lenses(X))<=(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))<=(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))

room(robert)&room(theresa)&(![X]:(room(X)=>(X='robert'|X='theresa')))& enjoys_origami(robert)

Daniel, Keith, Esther, Oma are the only persons in the room. Either “Keith does not collect foreign coins” or “Oma is not a wise tall tourist” but not both. If “everyone outside the room is a old person or is not a chess master who participates in national tournaments” then “Esther is not a calm strong wise european”. “Oma is not a brave person” if “Oma is not creative, not funny” and vice versa. “At least one person in the room is not a night owl” if “William and Keith like each other”. If “Oma does not regularly goes on multi-day backpacking trips in national parks, is not a creative calm old humble person and is a sibling of William” then “Oma either is not a creative patient tourist or is generous but not both”. If someone does not use an ios phone then he/she does not regularly goes on multi-day backpacking trips in national parks. More than one person in the room is not a quiet creative european. Daniel is hated by Carol. Daniel who is not a patient person, is not a funny tourist and is not a calm tourist is wise. Ryan and Daniel like each other. Esther is not a funny brave european. Esther is the least rich in the room. At least one person in the room has completed a triathlon. Everyone in the room is not liked by Carol if they does not own a high-end gaming PC with custom-built components and vice versa. Esther is a client of William. Esther neither is quiet nor is not a tall person. Esther who is not old, not humble, not generous, not happy does not participate in citizen science projects related to wildlife monitoring.

Esther is old.

contradiction

room(daniel)&room(keith)&room(esther)&room(oma)&(![X]:(room(X)=>(X='daniel'|X='keith'|X='esther'|X='oma')))& ((does_not_collect_foreign_coins(keith))<~>(~(wise(oma)&tall(oma)&tourist(oma))))& ((![X]:(~room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(old(X)&person(X))))))=>(~(calm(esther)&strong(esther)&wise(esther)&european(esther))))& ((~creative(oma)&~funny(oma))<=>(~(brave(oma)&person(oma))))& (((like(william,keith) & like(keith,william)))=>(((?[X]:(room(X)&is_not_a_night_owl(X))))))& ((((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(oma))&(~(creative(oma)&calm(oma)&old(oma)&humble(oma)&person(oma)))&(sibling(william,oma))))=>(((~(creative(oma)&patient(oma)&tourist(oma)))<~>(generous(oma)))))& ((![X]:((does_not_use_an_ios_phone(X))=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))& ((?[X,Y]:(room(X)&room(Y)&(~(quiet(X)&creative(X)&european(X))&~(quiet(Y)&creative(Y)&european(Y)))&(X!=Y))))& (hate(daniel,carol))& ((((~(patient(daniel)&person(daniel)))&(~(funny(daniel)&tourist(daniel)))&(~(calm(daniel)&tourist(daniel)))))&(wise(daniel)))& ((like(ryan,daniel) & like(daniel,ryan)))& (~(funny(esther)&brave(esther)&european(esther)))& (![X]:((room(X)&(X!=esther))=>richer(esther,X)))& (((?[X]:(room(X)&has_completed_a_triathlon(X)))))& (![X]:(room(X)=>(((~like(X,carol))<=>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))& (client(william,esther))& (~((quiet(esther))|(~(tall(esther)&person(esther)))))& (((?[X]:(room(X)&is_not_a_client_of_Meta(X)))))& (~(happy(daniel)&strong(daniel)&funny(daniel)&tourist(daniel)))& (![X]:(room(X)=>(((hate(X,william))<=(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& ((sibling(ryan,keith))&(((~(generous(keith)&person(keith)))&(client(carol,keith))&(kind(keith)))))& (is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(esther))& ((~old(esther)&~humble(esther)&~generous(esther)&~happy(esther))&(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(esther)))& (like(oma,carol))& ((~like(esther,carol))&(((practices_and_performs_acrobatic_dance_routines(esther))<~>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(esther)))))& (~(tall(keith)&happy(keith)&humble(keith)&generous(keith)&tourist(keith)))

room(daniel)&room(keith)&room(esther)&room(oma)&(![X]:(room(X)=>(X='daniel'|X='keith'|X='esther'|X='oma')))& old(esther)

% SZS status Unsatisfiable for 389582269924609001144403 % SZS output start Proof for 389582269924609001144403 66. ~predx(fred) & ~happy(fred) & ~generous(fred) & ~humble(fred) & ~old(fred) [input p22] 70. old(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 71. ~happy(fred) & ~generous(fred) & ~humble(fred) & ~old(fred) [pure predicate removal 66] 74. ~generous(fred) & ~humble(fred) & ~old(fred) [pure predicate removal 71] 177. old(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 70] 178. old(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 177] 328. ~old(fred) [cnf transformation 74] 340. old(fred) [cnf transformation 178] 478. $false [subsumption resolution 340,328] % SZS output end Proof for 389582269924609001144403 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

There is a room. All happy persons are curious. Everyone in the room is a funny person. Everyone in the room is a humble person.

All creative persons are generous.

neutral

(there_is_a_room)& (![X]:(happy(X)=>curious(X)))& (![X]:(room(X)=>(funny(X)&person(X))))& (![X]:(room(X)=>(humble(X)&person(X))))& (![X]:(room(X)=>(~curious(X))))& (![X]:(~room(X)=>(~(patient(X)&person(X)))))& (![X]:(room(X)=>(strong(X))))& (![X]:(wise(X)=>kind(X)))& (![X]:(room(X)=>(~strong(X))))& (~![X]:(anywhere(X)=>(patient(X))))& (![X]:(room(X)=>(~(strong(X)&person(X)))))& (![X]:(room(X)=>(creative(X)&person(X))))& (![X]:(room(X)=>(~(patient(X)&person(X)))))& ((![X]:((patient(X))<=>(~kind(X)))))& (![X]:(room(X)=>(~(quiet(X)&person(X)))))& (![X]:(funny(X)=>humble(X)))& (~?[X]:(quiet(X)=>generous(X)))& (![X]:(room(X)=>(~(humble(X)&person(X)))))& (?[X,Y]:((kind(X))&(~(curious(Y)&person(Y)))&(older(X,Y))))& (![X]:(room(X)=>(patient(X))))

(there_is_a_room)& ![X]:(creative(X)=>generous(X))

David, Maria, Irene, Lynsey are the only persons in the room. “Irene builds model airplanes, is a cybersecurity expert and enjoys watercolor painting” unless “Lynsey enjoys rooftop gardening”.

Irene builds model airplanes.

neutral

room(david)&room(maria)&room(irene)&room(lynsey)&(![X]:(room(X)=>(X='david'|X='maria'|X='irene'|X='lynsey')))& (~(enjoys_rooftop_gardening(lynsey))=>(((builds_model_airplanes(irene))&(is_a_cybersecurity_expert(irene))&(enjoys_watercolor_painting(irene)))))& ((((enjoys_rooftop_gardening(maria))|(is_a_cybersecurity_expert(maria))))=>(enjoys_stargazing(david)))& ((((is_a_client_of_LVMH(david))<~>(is_dedicated_to_sustainable_living_and_zero-waste_practices(david))))&(enjoys_rooftop_gardening(david)))& ((?[X,Y]:(room(X)&room(Y)&(((builds_model_airplanes(X))<~>(enjoys_windsurfing(X)))&((builds_model_airplanes(Y))<~>(enjoys_windsurfing(Y))))&(X!=Y))))& (enjoys_stargazing(david))& (is_a_cybersecurity_expert(lynsey))& (((can_play_the_piano(david))|(enjoys_windsurfing(david))|(enjoys_stargazing(david))))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(lynsey))& (is_a_client_of_LVMH(david))& (enjoys_rooftop_gardening(maria))& ((![X]:((((is_a_cybersecurity_expert(X))|(can_play_the_piano(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(builds_model_airplanes(X)))))& (regularly_contributes_to_tech_forums_and_online_communities(david))

room(david)&room(maria)&room(irene)&room(lynsey)&(![X]:(room(X)=>(X='david'|X='maria'|X='irene'|X='lynsey')))& builds_model_airplanes(irene)

Linda, Lisa are the only persons in the room. If 'at least one person in the room is quieter than Daniel' then 'Daniel is quieter than Linda'. 'It is not the case that 'Daniel is older than Lisa'' only if 'more than one person anywhere is older than Daniel'. More than one person anywhere is older than Daniel. It is not the case that 'it is not the case that 'more than one person in the room is richer than Daniel''. More than one person in the room is older than Daniel. At least one person in the room is richer than Daniel. Lisa is the richest in the room. Someone anywhere is a humble person. Daniel is quieter than Lisa. It is not the case that 'someone in the room is a old person'. It is not the case that 'Daniel is richer than Lisa'. It is not the case that 'it is not the case that 'it is not the case that 'Daniel is richer than Linda'''. Linda is the oldest anywhere. At least one person outside the room is a wise person. Someone in the room is a patient funny person. Someone outside the room is a generous quiet person. More than one person outside the room is a kind humble person. At least one person in the room is older than Daniel.

Lisa is older than Daniel.

entailment

room(linda)&room(lisa)&(![X]:(room(X)=>(X='linda'|X='lisa')))& ((((?[X]:(room(X)&quieter(daniel,X)))))=>(quieter(linda,daniel)))& ((~(older(lisa,daniel)))=>((?[X,Y]:(anywhere(X)&anywhere(Y)&(older(daniel,X)&older(daniel,Y))&(X!=Y)))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(older(daniel,X)&older(daniel,Y))&(X!=Y))))& (~(~((?[X,Y]:(room(X)&room(Y)&(richer(daniel,X)&richer(daniel,Y))&(X!=Y))))))& ((?[X,Y]:(room(X)&room(Y)&(older(daniel,X)&older(daniel,Y))&(X!=Y))))& (((?[X]:(room(X)&richer(daniel,X)))))& (![X]:((room(X)&(X!=lisa))=>richer(X,lisa)))& (?[X]:(anywhere(X)&(humble(X)&person(X))))& (quieter(lisa,daniel))& (~(?[X]:(room(X)&(old(X)&person(X)))))& (~(richer(lisa,daniel)))& (~(~(~(richer(linda,daniel)))))& (![X]:((anywhere(X)&(X!=linda))=>older(X,linda)))& (((?[X]:(~room(X)&wise(X)&person(X)))))& (?[X]:(room(X)&(patient(X)&funny(X)&person(X))))& (?[X]:(~room(X)&(generous(X)&quiet(X)&person(X))))& ((?[X,Y]:(~room(X)&~room(Y)&(kind(X)&humble(X)&person(X)&kind(Y)&humble(Y)&person(Y))&(X!=Y))))& (((?[X]:(room(X)&older(daniel,X)))))

room(linda)&room(lisa)&(![X]:(room(X)=>(X='linda'|X='lisa')))& older(daniel,lisa)

% SZS status Unsatisfiable for 2471034809317352025586758 % SZS output start Proof for 2471034809317352025586758 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. ? [X0,X1] : (X0 != X1 & older(fred,X1) & older(fred,X0) & room(X1) & room(X0)) [input p5] 63. ~(older(fred,paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 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. ~older(fred,paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 63] 153. ~older(fred,paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 152] 161. ? [X0,X1] : (X0 != X1 & older(fred,X1) & older(fred,X0) & room(X1) & room(X0)) => (sK6 != sK7 & older(fred,sK7) & older(fred,sK6) & room(sK7) & room(sK6)) [choice axiom] 162. sK6 != sK7 & older(fred,sK7) & older(fred,sK6) & room(sK7) & room(sK6) [skolemisation 49,161] 177. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK16 & mary != sK16 & room(sK16)) [choice axiom] 178. ~older(fred,paul) | (paul != sK16 & mary != sK16 & room(sK16)) | ~room(paul) | ~room(mary) [skolemisation 153,177] 260. room(mary) [cnf transformation 144] 261. room(paul) [cnf transformation 144] 262. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 144] 279. room(sK6) [cnf transformation 162] 280. room(sK7) [cnf transformation 162] 281. older(fred,sK6) [cnf transformation 162] 282. older(fred,sK7) [cnf transformation 162] 283. sK6 != sK7 [cnf transformation 162] 308. ~older(fred,paul) | room(sK16) | ~room(paul) | ~room(mary) [cnf transformation 178] 309. ~older(fred,paul) | mary != sK16 | ~room(paul) | ~room(mary) [cnf transformation 178] 310. ~older(fred,paul) | paul != sK16 | ~room(paul) | ~room(mary) [cnf transformation 178] 339. ~older(fred,paul) | paul != sK16 | ~room(mary) [subsumption resolution 310,261] 340. ~older(fred,paul) | paul != sK16 [subsumption resolution 339,260] 342. 7 <=> paul = sK16 [avatar definition] 346. 8 <=> older(fred,paul) [avatar definition] 348. ~older(fred,paul) <- (~8) [avatar component clause 346] 349. ~7 | ~8 [avatar split clause 340,346,342] 350. ~older(fred,paul) | mary != sK16 | ~room(mary) [subsumption resolution 309,261] 351. ~older(fred,paul) | mary != sK16 [subsumption resolution 350,260] 353. 9 <=> mary = sK16 [avatar definition] 355. mary != sK16 <- (~9) [avatar component clause 353] 356. ~9 | ~8 [avatar split clause 351,346,353] 357. ~older(fred,paul) | room(sK16) | ~room(mary) [subsumption resolution 308,261] 358. ~older(fred,paul) | room(sK16) [subsumption resolution 357,260] 360. 10 <=> room(sK16) [avatar definition] 362. room(sK16) <- (10) [avatar component clause 360] 363. 10 | ~8 [avatar split clause 358,346,360] 450. mary = sK6 | paul = sK6 [resolution 262,279] 451. mary = sK7 | paul = sK7 [resolution 262,280] 474. 31 <=> paul = sK6 [avatar definition] 476. paul = sK6 <- (31) [avatar component clause 474] 478. 32 <=> mary = sK6 [avatar definition] 480. mary = sK6 <- (32) [avatar component clause 478] 481. 31 | 32 [avatar split clause 450,478,474] 483. 33 <=> paul = sK7 [avatar definition] 485. paul = sK7 <- (33) [avatar component clause 483] 487. 34 <=> mary = sK7 [avatar definition] 490. 33 | 34 [avatar split clause 451,487,483] 532. older(fred,paul) <- (33) [backward demodulation 282,485] 540. older(fred,paul) <- (31) [backward demodulation 281,476] 542. $false <- (~8, 31) [subsumption resolution 540,348] 543. 8 | ~31 [avatar contradiction clause 542] 553. 8 | ~33 [avatar split clause 532,483,346] 566. mary = sK16 | paul = sK16 <- (10) [resolution 362,262] 568. paul = sK16 <- (~9, 10) [subsumption resolution 566,355] 580. 7 | 9 | ~10 [avatar split clause 568,360,353,342] 581. mary != sK7 <- (32) [forward demodulation 283,480] 582. ~34 | ~32 [avatar split clause 581,478,487] 598. $false [avatar sat refutation 349,356,363,481,490,543,553,580,582] % SZS output end Proof for 2471034809317352025586758 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Elizabeth, Marian, Bobbie are the only persons in the room. Bobbie and Marian are not quiet, not brave unless Bobbie and Marian are respectively strong and creative. Marian and Elizabeth are strong. Elizabeth is the richest in the room. Marian is the least old in the room. Bruce is richer than Elizabeth. Someone in the room is not a tall strong person. It is not the case that Bobbie is quieter than Bruce. Everyone in the room is not strong if they is not a old person. All happy persons are old. Only one person anywhere is not a old person. More than one person outside the room is quiet.

Everyone anywhere is not a brave person.

neutral

room(elizabeth)&room(marian)&room(bobbie)&(![X]:(room(X)=>(X='elizabeth'|X='marian'|X='bobbie')))& (~((strong(bobbie))&(creative(marian)))=>(~quiet(bobbie)&~brave(bobbie)&~quiet(marian)&~brave(marian)))& (strong(marian)&strong(elizabeth))& (![X]:((room(X)&(X!=elizabeth))=>richer(X,elizabeth)))& (![X]:((room(X)&(X!=marian))=>older(marian,X)))& (richer(elizabeth,bruce))& (?[X]:(room(X)&(~(tall(X)&strong(X)&person(X)))))& (~(quieter(bruce,bobbie)))& (![X]:(room(X)=>(((~(old(X)&person(X)))=>(~strong(X))))))& (![X]:(happy(X)=>old(X)))& (((?[X]:(anywhere(X)&~(old(X)&person(X))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(~(old(X)&person(X)))&(~(old(Y)&person(Y))))=>(X=Y)))))& ((?[X,Y]:(~room(X)&~room(Y)&(quiet(X)&quiet(Y))&(X!=Y))))& (![X]:(room(X)=>(((quieter(bruce,X))=>(older(bruce,X))))))& (![X]:(room(X)=>(((tall(X)&person(X))<=(older(bruce,X))))))& (~![X]:(room(X)=>(((older(bruce,X))=>(~(patient(X)&person(X)))))))& (((brave(elizabeth)&person(elizabeth))|(strong(elizabeth))|(richer(bruce,elizabeth))))& (![X]:(wise(X)=>kind(X)))& (quieter(bruce,elizabeth))& (~((?[X,Y]:(room(X)&room(Y)&(kind(X)&person(X)&kind(Y)&person(Y))&(X!=Y)))))& (quieter(bruce,bobbie))& ((![X]:((patient(X))=>(~(quiet(X)&person(X))))))

room(elizabeth)&room(marian)&room(bobbie)&(![X]:(room(X)=>(X='elizabeth'|X='marian'|X='bobbie')))& ![X]:(anywhere(X)=>(~(brave(X)&person(X))))

Billy is the only person in the room. Everyone in the room who enjoys camping and organizing outdoor survival workshops is wise. Everyone outside the room practices kickboxing, is quieter than Robert and is a quiet person if they practices tai chi. Everyone in the room practices tai chi or does not practice tai chi. Everyone in the room who enjoys camping and organizing outdoor survival workshops is not a wise quiet person. Billy practices tai chi. Billy develops open-source software projects in their free time. Everyone in the room practices tai chi if they practices kickboxing and vice versa. If someone practices tai chi then he/she is quiet. Billy enjoys camping and organizing outdoor survival workshops. Everyone in the room who is quieter than Isabel does not enjoy writing detailed reviews of new and classic board games.

Billy practices kickboxing.

entailment

room(billy)&(![X]:(room(X)=>(X='billy')))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(wise(X))))))& (![X]:(~room(X)=>(((practices_tai_chi(X))=>(((practices_kickboxing(X))&(quieter(robert,X))&(quiet(X)&person(X))))))))& (![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(practices_tai_chi(X))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(~(wise(X)&quiet(X)&person(X)))))))& (practices_tai_chi(billy))& (develops_open-source_software_projects_in_their_free_time(billy))& (![X]:(room(X)=>(((practices_tai_chi(X))<=>(practices_kickboxing(X))))))& ((![X]:((practices_tai_chi(X))=>(quiet(X)))))& (enjoys_camping_and_organizing_outdoor_survival_workshops(billy))& (![X]:(room(X)=>(((quieter(isabel,X))=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))

room(billy)&(![X]:(room(X)=>(X='billy')))& practices_kickboxing(billy)

% SZS status Unsatisfiable for 8068616971049424709614033 % SZS output start Proof for 8068616971049424709614033 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (~room(X0) => (predu(X0) => (person(X0) & quiet(X0) & quieter(fred,X0) & predc(X0)))) [input p2] 49. predu(mary) [input p5] 51. ! [X0] : (room(X0) => (predu(X0) <=> predc(X0))) [input p7] 55. ~(predc(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 130. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 133. ! [X0] : (((person(X0) & quiet(X0) & quieter(fred,X0) & predc(X0)) | ~predu(X0)) | room(X0)) [ennf transformation 46] 134. ! [X0] : ((person(X0) & quiet(X0) & quieter(fred,X0) & predc(X0)) | ~predu(X0) | room(X0)) [flattening 133] 139. ! [X0] : ((predu(X0) <=> predc(X0)) | ~room(X0)) [ennf transformation 51] 141. ~predc(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 55] 143. ! [X0] : (((predu(X0) | ~predc(X0)) & (predc(X0) | ~predu(X0))) | ~room(X0)) [nnf transformation 139] 144. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom] 145. ~predc(mary) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 141,144] 226. room(mary) [cnf transformation 130] 227. ~room(X0) | mary = X0 [cnf transformation 130] 229. predc(X0) | ~predu(X0) | room(X0) [cnf transformation 134] 235. predu(mary) [cnf transformation 49] 236. predc(X0) | ~predu(X0) | ~room(X0) [cnf transformation 143] 240. ~predc(mary) | room(sK0) | ~room(mary) [cnf transformation 145] 241. ~predc(mary) | mary != sK0 | ~room(mary) [cnf transformation 145] 243. ~predu(X0) | predc(X0) [subsumption resolution 236,229] 244. ~predc(mary) | mary != sK0 [subsumption resolution 241,226] 246. 1 <=> mary = sK0 [avatar definition] 248. mary != sK0 <- (~1) [avatar component clause 246] 250. 2 <=> predc(mary) [avatar definition] 253. ~1 | ~2 [avatar split clause 244,250,246] 254. ~predc(mary) | room(sK0) [subsumption resolution 240,226] 256. 3 <=> room(sK0) [avatar definition] 258. room(sK0) <- (3) [avatar component clause 256] 259. 3 | ~2 [avatar split clause 254,250,256] 261. predc(mary) [resolution 243,235] 264. 2 [avatar split clause 261,250] 266. mary = sK0 <- (3) [resolution 227,258] 267. $false <- (~1, 3) [subsumption resolution 266,248] 268. 1 | ~3 [avatar contradiction clause 267] 269. $false [avatar sat refutation 253,259,264,268] % SZS output end Proof for 8068616971049424709614033 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Juan, Eli, Christopher are the only persons in the room. Juan who is a funny tall humble generous person is richer than Frank. Eli who is not a quiet person is older than Shirley. Everyone in the room is older than Shirley if they is a happy person. Someone in the room is not a tall person.

Juan is tall.

entailment

room(juan)&room(eli)&room(christopher)&(![X]:(room(X)=>(X='juan'|X='eli'|X='christopher')))& ((funny(juan)&tall(juan)&humble(juan)&generous(juan)&person(juan))&(richer(frank,juan)))& ((~(quiet(eli)&person(eli)))&(older(shirley,eli)))& (![X]:(room(X)=>(((happy(X)&person(X))=>(older(shirley,X))))))& (?[X]:(room(X)&(~(tall(X)&person(X)))))

room(juan)&room(eli)&room(christopher)&(![X]:(room(X)=>(X='juan'|X='eli'|X='christopher')))& tall(juan)

% SZS status Unsatisfiable for 7615545068470657750243569 % SZS output start Proof for 7615545068470657750243569 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. richer(alice,mary) & person(mary) & generous(mary) & humble(mary) & tall(mary) & funny(mary) [input p1] 49. ~(tall(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 51. richer(alice,mary) & person(mary) & humble(mary) & tall(mary) & funny(mary) [pure predicate removal 45] 52. richer(alice,mary) & person(mary) & tall(mary) & funny(mary) [pure predicate removal 51] 53. richer(alice,mary) & person(mary) & tall(mary) [pure predicate removal 52] 126. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 127. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 126] 130. ~tall(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 49] 131. ~tall(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 130] 135. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 136. ~tall(mary) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 131,135] 217. room(mary) [cnf transformation 127] 218. room(paul) [cnf transformation 127] 219. room(fred) [cnf transformation 127] 220. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 127] 221. tall(mary) [cnf transformation 53] 228. ~tall(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 136] 229. ~tall(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 136] 230. ~tall(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 136] 231. ~tall(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 136] 250. fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 231,221] 251. fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 250,219] 252. fred != sK1 | ~room(mary) [subsumption resolution 251,218] 253. fred != sK1 [subsumption resolution 252,217] 254. paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 230,221] 255. paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 254,219] 256. paul != sK1 | ~room(mary) [subsumption resolution 255,218] 257. paul != sK1 [subsumption resolution 256,217] 258. mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 229,221] 259. mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 258,219] 260. mary != sK1 | ~room(mary) [subsumption resolution 259,218] 261. mary != sK1 [subsumption resolution 260,217] 262. room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 228,221] 263. room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 262,219] 264. room(sK1) | ~room(mary) [subsumption resolution 263,218] 265. room(sK1) [subsumption resolution 264,217] 368. paul = sK1 | mary = sK1 | fred = sK1 [resolution 220,265] 382. mary = sK1 | fred = sK1 [subsumption resolution 368,257] 383. fred = sK1 [subsumption resolution 382,261] 384. $false [subsumption resolution 383,253] % SZS output end Proof for 7615545068470657750243569 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Lisa, Joseph, Ivan, Jason, Roseann are the only persons in the room. If “Lisa collects antique clocks” then “Joseph has a pet dog, drives a hybrid car or enjoys deep-sea diving and exploring underwater caves” otherwise “everyone in the room neither enjoys deep-sea diving and exploring underwater caves nor has a specialized collection of handmade artisan pottery if they can play the piano, has a pet dog and streams on Twitch”. If “Lisa practices tai chi” then “everyone in the room collects foreign coins”. If someone is a client of Costco or collects foreign coins or both then he/she is a client of Costco. Everyone in the room collects foreign coins.

Joseph is a client of Costco.

entailment

room(lisa)&room(joseph)&room(ivan)&room(jason)&room(roseann)&(![X]:(room(X)=>(X='lisa'|X='joseph'|X='ivan'|X='jason'|X='roseann')))& (((collects_antique_clocks(lisa))=>(((has_a_pet_dog(joseph))|(drives_a_hybrid_car(joseph))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(joseph)))))&((~(collects_antique_clocks(lisa)))=>(![X]:(room(X)=>(((((can_play_the_piano(X))&(has_a_pet_dog(X))&(streams_on_Twitch(X))))=>(~((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))))& ((practices_tai_chi(lisa))=>(![X]:(room(X)=>(collects_foreign_coins(X)))))& ((~?[X]:(~room(X)=>(practices_urban_gardening(X))))=>(((can_play_the_piano(jason))&(has_a_pet_dog(jason))&(streams_on_Twitch(jason)))))& (~(practices_kickboxing(lisa))=>(~?[X]:(anywhere(X)=>(((works_on_fridays(X))|(does_not_own_a_smartwatch(X)))))))& ((![X]:(room(X)=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))=>(((can_play_the_piano(joseph))&(has_a_pet_dog(joseph))&(streams_on_Twitch(joseph)))))& (?[X]:(room(X)&(is_a_drone_photographer(X))))& (enjoys_watercolor_painting(lisa))& (![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& ((![X]:((((is_a_client_of_Costco(X))|(collects_foreign_coins(X))))=>(is_a_client_of_Costco(X)))))& (![X]:(room(X)=>(((is_not_a_client_of_Costco(X))=>(practices_tai_chi(X))))))& (works_on_fridays(ivan))& (((practices_urban_gardening(jason))<~>(enjoys_deep-sea_diving_and_exploring_underwater_caves(jason))))& (![X]:(room(X)=>(collects_foreign_coins(X))))& (works_on_fridays(lisa))& (?[X]:(room(X)&(owns_a_3D_printer(X))))& (writes_and_illustrates_their_own_graphic_novels(ivan))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(lisa))& (practices_tai_chi(lisa))

room(lisa)&room(joseph)&room(ivan)&room(jason)&room(roseann)&(![X]:(room(X)=>(X='lisa'|X='joseph'|X='ivan'|X='jason'|X='roseann')))& is_a_client_of_Costco(joseph)

% SZS status Unsatisfiable for 723090777313834085490085 % SZS output start Proof for 723090777313834085490085 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] 53. ! [X0] : ((predb(X0) | predc(X0)) => predc(X0)) [input p9] 57. ! [X0] : (room(X0) => predb(X0)) [input p13] 63. ~(predc(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] 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] 158. ! [X0] : (predc(X0) | (~predb(X0) & ~predc(X0))) [ennf transformation 53] 161. ! [X0] : (predb(X0) | ~room(X0)) [ennf transformation 57] 162. ~predc(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 63] 163. ~predc(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 162] 170. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 171. ~predc(paul) | (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 163,170] 252. room(mary) [cnf transformation 156] 253. room(paul) [cnf transformation 156] 254. room(fred) [cnf transformation 156] 255. room(alice) [cnf transformation 156] 256. room(john) [cnf transformation 156] 257. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 156] 261. ~predb(X0) | predc(X0) [cnf transformation 158] 265. predb(X0) | ~room(X0) [cnf transformation 161] 268. ~predc(paul) | room(sK2) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 269. ~predc(paul) | mary != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 270. ~predc(paul) | paul != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 271. ~predc(paul) | fred != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 272. ~predc(paul) | alice != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 273. ~predc(paul) | john != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 279. 2 <=> ! [X0] : (predb(X0) | ~room(X0)) [avatar definition] 280. ~room(X0) | predb(X0) <- (2) [avatar component clause 279] 292. 2 [avatar split clause 265,279] 294. ~predc(paul) | john != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,256] 295. ~predc(paul) | john != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,255] 296. ~predc(paul) | john != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 295,254] 297. ~predc(paul) | john != sK2 | ~room(mary) [subsumption resolution 296,253] 298. ~predc(paul) | john != sK2 [subsumption resolution 297,252] 300. 5 <=> john = sK2 [avatar definition] 302. john != sK2 <- (~5) [avatar component clause 300] 304. 6 <=> predc(paul) [avatar definition] 307. ~5 | ~6 [avatar split clause 298,304,300] 308. ~predc(paul) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,256] 309. ~predc(paul) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,255] 310. ~predc(paul) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 309,254] 311. ~predc(paul) | alice != sK2 | ~room(mary) [subsumption resolution 310,253] 312. ~predc(paul) | alice != sK2 [subsumption resolution 311,252] 314. 7 <=> alice = sK2 [avatar definition] 316. alice != sK2 <- (~7) [avatar component clause 314] 317. ~7 | ~6 [avatar split clause 312,304,314] 318. ~predc(paul) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,256] 319. ~predc(paul) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,255] 320. ~predc(paul) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 319,254] 321. ~predc(paul) | fred != sK2 | ~room(mary) [subsumption resolution 320,253] 322. ~predc(paul) | fred != sK2 [subsumption resolution 321,252] 324. 8 <=> fred = sK2 [avatar definition] 326. fred != sK2 <- (~8) [avatar component clause 324] 327. ~8 | ~6 [avatar split clause 322,304,324] 328. ~predc(paul) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,256] 329. ~predc(paul) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,255] 330. ~predc(paul) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 329,254] 331. ~predc(paul) | paul != sK2 | ~room(mary) [subsumption resolution 330,253] 332. ~predc(paul) | paul != sK2 [subsumption resolution 331,252] 334. 9 <=> paul = sK2 [avatar definition] 336. paul != sK2 <- (~9) [avatar component clause 334] 337. ~9 | ~6 [avatar split clause 332,304,334] 338. ~predc(paul) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,256] 339. ~predc(paul) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 338,255] 340. ~predc(paul) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 339,254] 341. ~predc(paul) | mary != sK2 | ~room(mary) [subsumption resolution 340,253] 342. ~predc(paul) | mary != sK2 [subsumption resolution 341,252] 344. 10 <=> mary = sK2 [avatar definition] 346. mary != sK2 <- (~10) [avatar component clause 344] 347. ~10 | ~6 [avatar split clause 342,304,344] 348. ~predc(paul) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,256] 349. ~predc(paul) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 348,255] 350. ~predc(paul) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 349,254] 351. ~predc(paul) | room(sK2) | ~room(mary) [subsumption resolution 350,253] 352. ~predc(paul) | room(sK2) [subsumption resolution 351,252] 354. 11 <=> room(sK2) [avatar definition] 356. room(sK2) <- (11) [avatar component clause 354] 357. 11 | ~6 [avatar split clause 352,304,354] 359. predb(paul) <- (2) [resolution 280,253] 419. predc(paul) <- (2) [resolution 359,261] 422. 6 | ~2 [avatar split clause 419,279,304] 494. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (11) [resolution 257,356] 537. fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (~7, 11) [subsumption resolution 494,316] 538. paul = sK2 | mary = sK2 | john = sK2 <- (~7, ~8, 11) [subsumption resolution 537,326] 539. mary = sK2 | john = sK2 <- (~7, ~8, ~9, 11) [subsumption resolution 538,336] 540. john = sK2 <- (~7, ~8, ~9, ~10, 11) [subsumption resolution 539,346] 541. $false <- (~5, ~7, ~8, ~9, ~10, 11) [subsumption resolution 540,302] 542. 5 | 7 | 8 | 9 | 10 | ~11 [avatar contradiction clause 541] 543. $false [avatar sat refutation 292,307,317,327,337,347,357,422,542] % SZS output end Proof for 723090777313834085490085 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------