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0.72
Kristy, Earl, Carol, Kerri are the only persons in the room. If “everyone in the room has completed a triathlon or does not have completed a triathlon” then “everyone in the room does not have completed a triathlon or has completed a triathlon”. If “everyone in the room does not use an ios phone or owns a smart tv” then “everyone in the room does not use an ios phone if and only if they neither has completed a triathlon nor uses an ios phone”. Either “not everyone in the room owns a smart tv or does not own a smart tv” or “everyone in the room owns a smart tv or does not have completed a triathlon” but not both. “Everyone in the room who uses an ios phone, has completed a triathlon and owns a smart tv owns a smart tv” unless “Kristy uses an ios phone”. Either “Kristy has a piercing, uses an ios phone and has completed a triathlon” or “everyone in the room owns a smart tv or does not have a piercing” but not both. “Everyone in the room does not have a piercing only if they has a piercing and owns a smart tv” if “everyone outside the room does not have a piercing or has completed a triathlon”. “Kerri owns a smart tv” if “everyone in the room has completed a triathlon or does not own a smart tv”. Everyone in the room who either has completed a triathlon or owns a smart tv but not both owns a smart tv. Carol has a piercing. Kerri owns a smart tv. Everyone outside the room does not have completed a triathlon only if they does not have a piercing. Everyone in the room uses an ios phone. Kristy dreamt that “everyone in the room who has completed a triathlon does not have a piercing, has completed a triathlon and does not have completed a triathlon”. Kerri owns a smart tv and does not have completed a triathlon. Everyone in the room does not own a smart tv only if they has completed a triathlon. Kristy uses an ios phone. Everyone outside the room who has completed a triathlon and does not have completed a triathlon does not have completed a triathlon. Everyone in the room does not have a piercing or has a piercing. Everyone in the room has completed a triathlon and has a piercing if they does not have a piercing. Kristy has a piercing. Kristy owns a smart tv. Carol uses an ios phone and owns a smart tv. Carol uses an ios phone.
Kristy has completed a triathlon.
contradiction
room(kristy)&room(earl)&room(carol)&room(kerri)&(![X]:(room(X)=>(X='kristy'|X='earl'|X='carol'|X='kerri')))& ((![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(has_completed_a_triathlon(X))))))=>(![X]:(room(X)=>(((has_completed_a_triathlon(X))|(does_not_have_completed_a_triathlon(X)))))))& ((![X]:(room(X)=>(((owns_a_smart_tv(X))|(does_not_use_an_ios_phone(X))))))=>(![X]:(room(X)=>(((does_not_use_an_ios_phone(X))<=>(~((has_completed_a_triathlon(X))|(uses_an_ios_phone(X)))))))))& ((~![X]:(room(X)=>(((does_not_own_a_smart_tv(X))|(owns_a_smart_tv(X))))))<~>(![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(owns_a_smart_tv(X)))))))& (~(uses_an_ios_phone(kristy))=>(![X]:(room(X)=>(((((uses_an_ios_phone(X))&(has_completed_a_triathlon(X))&(owns_a_smart_tv(X))))=>(owns_a_smart_tv(X)))))))& ((((has_a_piercing(kristy))&(uses_an_ios_phone(kristy))&(has_completed_a_triathlon(kristy))))<~>(![X]:(room(X)=>(((does_not_have_a_piercing(X))|(owns_a_smart_tv(X)))))))& ((![X]:(~room(X)=>(((has_completed_a_triathlon(X))|(does_not_have_a_piercing(X))))))=>(![X]:(room(X)=>(((((has_a_piercing(X))&(owns_a_smart_tv(X))))<=(does_not_have_a_piercing(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_smart_tv(X))|(has_completed_a_triathlon(X))))))=>(owns_a_smart_tv(kerri)))& (![X]:(room(X)=>(((((has_completed_a_triathlon(X))<~>(owns_a_smart_tv(X))))=>(owns_a_smart_tv(X))))))& (has_a_piercing(carol))& (owns_a_smart_tv(kerri))& (![X]:(~room(X)=>(((does_not_have_a_piercing(X))<=(does_not_have_completed_a_triathlon(X))))))& (![X]:(room(X)=>(uses_an_ios_phone(X))))& ((kristy_dream=>(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(((does_not_have_a_piercing(X))&(has_completed_a_triathlon(X))&(does_not_have_completed_a_triathlon(X))))))))))& (((owns_a_smart_tv(kerri))&(does_not_have_completed_a_triathlon(kerri))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))<=(does_not_own_a_smart_tv(X))))))& (uses_an_ios_phone(kristy))& (![X]:(~room(X)=>(((((has_completed_a_triathlon(X))&(does_not_have_completed_a_triathlon(X))))=>(does_not_have_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((has_a_piercing(X))|(does_not_have_a_piercing(X))))))& (![X]:(room(X)=>(((does_not_have_a_piercing(X))=>(((has_completed_a_triathlon(X))&(has_a_piercing(X))))))))& (has_a_piercing(kristy))& (owns_a_smart_tv(kristy))& (((uses_an_ios_phone(carol))&(owns_a_smart_tv(carol))))& (uses_an_ios_phone(carol))
room(kristy)&room(earl)&room(carol)&room(kerri)&(![X]:(room(X)=>(X='kristy'|X='earl'|X='carol'|X='kerri')))& has_completed_a_triathlon(kristy)
[ "p5", "p8", "p15", "p16", "p20", "hypothesis" ]
% SZS status Unsatisfiable for 2661528959958601982719568 % SZS output start Proof for 2661528959958601982719568 49. (predd(mary) & predb(mary) & predc(mary)) <~> ! [X0] : (room(X0) => (preda(X0) | ~predc(X0))) [input p5] 52. ! [X0] : (room(X0) => ((predd(X0) <~> preda(X0)) => preda(X0))) [input p8] 59. ! [X0] : (room(X0) => (~preda(X0) => predd(X0))) [input p15] 60. predb(mary) [input p16] 64. predc(mary) [input p20] 68. predd(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 156. (predd(mary) & predb(mary) & predc(mary)) <~> ! [X0] : ((preda(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 49] 157. (predd(mary) & predb(mary) & predc(mary)) <~> ! [X0] : (preda(X0) | ~predc(X0) | ~room(X0)) [flattening 156] 162. ! [X0] : ((preda(X0) | (predd(X0) <=> preda(X0))) | ~room(X0)) [ennf transformation 52] 163. ! [X0] : (preda(X0) | (predd(X0) <=> preda(X0)) | ~room(X0)) [flattening 162] 167. ! [X0] : ((predd(X0) | preda(X0)) | ~room(X0)) [ennf transformation 59] 168. ! [X0] : (predd(X0) | preda(X0) | ~room(X0)) [flattening 167] 175. predd(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 68] 176. predd(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 175] 181. sP2 <=> (predd(mary) & predb(mary) & predc(mary)) [predicate definition introduction] 182. sP2 <~> ! [X0] : (preda(X0) | ~predc(X0) | ~room(X0)) [definition folding 157,181] 201. (sP2 | (~predd(mary) | ~predb(mary) | ~predc(mary))) & ((predd(mary) & predb(mary) & predc(mary)) | ~sP2) [nnf transformation 181] 202. (sP2 | ~predd(mary) | ~predb(mary) | ~predc(mary)) & ((predd(mary) & predb(mary) & predc(mary)) | ~sP2) [flattening 201] 203. (? [X0] : (~preda(X0) & predc(X0) & room(X0)) | ~sP2) & (! [X0] : (preda(X0) | ~predc(X0) | ~room(X0)) | sP2) [nnf transformation 182] 204. (? [X0] : (~preda(X0) & predc(X0) & room(X0)) | ~sP2) & (! [X1] : (preda(X1) | ~predc(X1) | ~room(X1)) | sP2) [rectify 203] 205. ? [X0] : (~preda(X0) & predc(X0) & room(X0)) => (~preda(sK7) & predc(sK7) & room(sK7)) [choice axiom] 206. ((~preda(sK7) & predc(sK7) & room(sK7)) | ~sP2) & (! [X1] : (preda(X1) | ~predc(X1) | ~room(X1)) | sP2) [skolemisation 204,205] 212. ! [X0] : (preda(X0) | ((predd(X0) | ~preda(X0)) & (preda(X0) | ~predd(X0))) | ~room(X0)) [nnf transformation 163] 319. sP2 | ~predd(mary) | ~predb(mary) | ~predc(mary) [cnf transformation 202] 321. room(sK7) | ~sP2 [cnf transformation 206] 323. ~preda(sK7) | ~sP2 [cnf transformation 206] 333. preda(X0) | preda(X0) | ~predd(X0) | ~room(X0) [cnf transformation 212] 341. predd(X0) | preda(X0) | ~room(X0) [cnf transformation 168] 342. predb(mary) [cnf transformation 60] 347. predc(mary) [cnf transformation 64] 357. predd(mary) [cnf transformation 176] 360. preda(X0) | ~predd(X0) | ~room(X0) [duplicate literal removal 333] 418. 12 <=> ! [X1] : (preda(X1) | ~room(X1) | ~predd(X1)) [avatar definition] 419. preda(X1) | ~room(X1) | ~predd(X1) <- (12) [avatar component clause 418] 422. 13 <=> predc(mary) [avatar definition] 426. 14 <=> predb(mary) [avatar definition] 430. 15 <=> predd(mary) [avatar definition] 434. 16 <=> sP2 [avatar definition] 437. ~13 | ~14 | ~15 | 16 [avatar split clause 319,434,430,426,422] 442. 17 <=> preda(sK7) [avatar definition] 444. ~preda(sK7) <- (~17) [avatar component clause 442] 445. ~16 | ~17 [avatar split clause 323,442,434] 452. 19 <=> room(sK7) [avatar definition] 454. room(sK7) <- (19) [avatar component clause 452] 455. ~16 | 19 [avatar split clause 321,452,434] 503. 12 [avatar split clause 360,418] 506. 14 [avatar split clause 342,426] 508. 13 [avatar split clause 347,422] 509. 15 [avatar split clause 357,430] 510. ~room(X1) | preda(X1) <- (12) [subsumption resolution 419,341] 525. preda(sK7) <- (12, 19) [resolution 510,454] 526. $false <- (12, ~17, 19) [subsumption resolution 525,444] 527. ~12 | 17 | ~19 [avatar contradiction clause 526] 528. $false [avatar sat refutation 437,445,455,503,506,508,509,527] % SZS output end Proof for 2661528959958601982719568 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------
0.206495
There is a room. Everyone anywhere does not hate Antoine, is liked by Casey or is not liked by Antoine if they is hated by Melanie, is not hated by John and does not like Melanie. Everyone in the room does not hate Antoine, is liked by Casey or is not liked by Antoine only if they does not like Antoine, does not hate Antoine and is not liked by Melanie. Someone who either is not liked by Antoine or hates Earnest but not both like someone who does not hate Melanie. Everyone outside the room does not like Melanie and is not hated by John if they hates Melanie or is not liked by Casey or both. Everyone outside the room who does not like Melanie and is not hated by John either does not hate Earnest or is liked by Melanie but not both. Everyone anywhere either does not hate Earnest or is liked by Melanie but not both only if they is liked by Casey. Everyone in the room who is liked by Earnest and is not liked by Casey either does not like Earnest or is liked by John but not both. Someone who does not hate Antoine, is liked by Casey or is not liked by Antoine hate someone who hates John, is hated by Antoine or likes John. Someone who either does not like Casey or is not liked by Casey but not both like someone who neither is not hated by Earnest nor does not hate Melanie. Someone in the room neither hates Earnest nor is not liked by John. Everyone in the room is not hated by Antoine if they hates John.
Everyone in the room hates Melanie.
neutral
(there_is_a_room)& (![X]:(anywhere(X)=>(((((hate(X,melanie))&(~hate(X,john))&(~like(melanie,X))))=>(((~hate(antoine,X))|(like(X,casey))|(~like(X,antoine))))))))& (![X]:(room(X)=>(((((~like(antoine,X))&(~hate(antoine,X))&(~like(X,melanie))))<=(((~hate(antoine,X))|(like(X,casey))|(~like(X,antoine))))))))& (?[X,Y]:((((~like(X,antoine))<~>(hate(earnest,X))))&(~hate(melanie,Y))&(like(X,Y))))& (![X]:(~room(X)=>(((((hate(melanie,X))|(~like(X,casey))))=>(((~like(melanie,X))&(~hate(X,john))))))))& (![X]:(~room(X)=>(((((~like(melanie,X))&(~hate(X,john))))=>(((~hate(earnest,X))<~>(like(X,melanie))))))))& (![X]:(anywhere(X)=>(((like(X,casey))<=(((~hate(earnest,X))<~>(like(X,melanie))))))))& (![X]:(room(X)=>(((((like(X,earnest))&(~like(X,casey))))=>(((~like(earnest,X))<~>(like(X,john))))))))& (?[X,Y]:((((~hate(antoine,X))|(like(X,casey))|(~like(X,antoine))))&(((hate(john,Y))|(hate(Y,antoine))|(like(john,Y))))&(hate(X,Y))))& (?[X,Y]:((((~like(casey,X))<~>(~like(X,casey))))&(~((~hate(Y,earnest))|(~hate(melanie,Y))))&(like(X,Y))))& (?[X]:(room(X)&(~((hate(earnest,X))|(~like(X,john))))))& (![X]:(room(X)=>(((hate(john,X))=>(~hate(X,antoine))))))
(there_is_a_room)& ![X]:(room(X)=>(hate(melanie,X)))
[]
null
0.023363
Tracey is the only person in the room. Everyone in the room who maintains a large, organic vegetable garden year-round neither plays the violin nor collects antique jewelry. Tracey plays the violin.
Tracey maintains a large, organic vegetable garden year-round.
contradiction
room(tracey)&(![X]:(room(X)=>(X='tracey')))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(~((plays_the_violin(X))|(collects_antique_jewelry(X))))))))& (![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(is_a_night_owl(X))))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(~room(X)=>(((collects_rare_minerals(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (is_a_night_owl(tracey))& (collects_antique_jewelry(tracey))& (![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))=>(does_not_practice_archery(X))))))& (enjoys_spelunking(tracey))& (![X]:(anywhere(X)=>(((enjoys_spelunking(X))=>(((collects_luxury_watches(X))<~>(enjoys_spelunking(X))))))))& (~![X]:(room(X)=>(((plays_the_violin(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (enjoys_macrame(tracey))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(does_not_practice_and_performs_acrobatic_dance_routines(X))))))& (plays_the_violin(tracey))& (![X]:(anywhere(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(tracey))& (reads_mystery_novels(tracey))& (![X]:(room(X)=>(((((practices_and_performs_acrobatic_dance_routines(X))<~>(collects_luxury_watches(X))))=>(is_a_night_owl(X))))))& (![X]:(~room(X)=>(((does_not_have_a_tattoo(X))|(does_not_collect_action_figures(X))))))
room(tracey)&(![X]:(room(X)=>(X='tracey')))& maintains_a_large,_organic_vegetable_garden_year-round(tracey)
[ "p0", "p2", "p14", "hypothesis" ]
% SZS status Unsatisfiable for 8817009297523703548947072 % SZS output start Proof for 8817009297523703548947072 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (preds(X0) => ~(predb(X0) | predk(X0)))) [input p2] 58. predk(mary) [input p14] 64. preds(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 150. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 151. ! [X0] : (((~predb(X0) & ~predk(X0)) | ~preds(X0)) | ~room(X0)) [ennf transformation 46] 152. ! [X0] : ((~predb(X0) & ~predk(X0)) | ~preds(X0) | ~room(X0)) [flattening 151] 156. preds(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 64] 242. room(mary) [cnf transformation 150] 244. ~predk(X0) | ~preds(X0) | ~room(X0) [cnf transformation 152] 252. predk(mary) [cnf transformation 58] 255. preds(mary) [cnf transformation 156] 262. ~preds(mary) | ~room(mary) [resolution 244,252] 263. ~room(mary) [subsumption resolution 262,255] 264. $false [subsumption resolution 263,242] % SZS output end Proof for 8817009297523703548947072 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0.27416
Linda is the only person in the room. 'Linda enjoys deep-sea diving and exploring underwater caves' if 'Linda creates bespoke furniture pieces from reclaimed wood' and vice versa. Linda does not enjoy logic puzzles. Linda is right-handed. Linda plays the violin. Linda creates bespoke furniture pieces from reclaimed wood. Linda hosts a YouTube channel dedicated to art tutorials.
Linda plays the violin, enjoys making ceramics and enjoys logic puzzles.
contradiction
room(linda)&(![X]:(room(X)=>(X='linda')))& ((creates_bespoke_furniture_pieces_from_reclaimed_wood(linda))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(linda)))& (does_not_enjoy_logic_puzzles(linda))& (is_right-handed(linda))& (plays_the_violin(linda))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(linda))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(linda))& (![X]:(anywhere(X)=>(((does_not_enjoy_logic_puzzles(X))=>(plays_the_violin(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(does_not_enjoy_logic_puzzles(X)&does_not_enjoy_logic_puzzles(Y))&(X!=Y))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(hosts_regular_game_nights_featuring_complex_strategy_games(X)&hosts_regular_game_nights_featuring_complex_strategy_games(Y))&(X!=Y))))
room(linda)&(![X]:(room(X)=>(X='linda')))& ((plays_the_violin(linda))&(enjoys_making_ceramics(linda))&(enjoys_logic_puzzles(linda)))
[ "p2", "hypothesis" ]
% SZS status Unsatisfiable for 2644561760680544030369152 % SZS output start Proof for 2644561760680544030369152 46. ~predb(mary) [input p2] 56. predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 60. predb(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [pure predicate removal 56] 64. predb(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [pure predicate removal 60] 140. predb(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 64] 231. ~predb(mary) [cnf transformation 46] 241. predb(mary) [cnf transformation 140] 253. $false [subsumption resolution 241,231] % SZS output end Proof for 2644561760680544030369152 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------
0.20765
Eric, Mercedes are the only persons in the room. If “Eric is a old wise humble patient person or is richer than Gwen or both” then “Mercedes is the least old outside the room”. “Mercedes and Eric are calm tall persons” unless “Mercedes is a old humble kind creative person”. “Eric is creative” only if “Mercedes is quieter than Cecil”. If “Cecil is older than Mercedes” then “Eric is richer than Cecil”. Eric is not old or is richer than Cecil or both. Not everyone in the room is a generous person if they is richer than Gwen. Someone in the room is quieter than Cecil. Eric who is older than Gwen is quieter than Gwen. Mercedes is a old humble kind creative person.
Mercedes is old.
entailment
room(eric)&room(mercedes)&(![X]:(room(X)=>(X='eric'|X='mercedes')))& ((((old(eric)&wise(eric)&humble(eric)&patient(eric)&person(eric))|(richer(gwen,eric))))=>(![X]:((~room(X)&(X!=mercedes))=>older(mercedes,X))))& (~(old(mercedes)&humble(mercedes)&kind(mercedes)&creative(mercedes)&person(mercedes))=>(calm(mercedes)&tall(mercedes)&person(mercedes)&calm(eric)&tall(eric)&person(eric)))& ((creative(eric))=>(quieter(cecil,mercedes)))& ((older(mercedes,cecil))=>(richer(cecil,eric)))& (((~old(eric))|(richer(cecil,eric))))& (~![X]:(room(X)=>(((richer(gwen,X))=>(generous(X)&person(X))))))& (?[X]:(room(X)&(quieter(cecil,X))))& ((older(gwen,eric))&(quieter(gwen,eric)))& (old(mercedes)&humble(mercedes)&kind(mercedes)&creative(mercedes)&person(mercedes))
room(eric)&room(mercedes)&(![X]:(room(X)=>(X='eric'|X='mercedes')))& old(mercedes)
[ "p0", "p9", "hypothesis" ]
% SZS status Unsatisfiable for 150515503902850902655687 % SZS output start Proof for 150515503902850902655687 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 53. person(paul) & creative(paul) & kind(paul) & humble(paul) & old(paul) [input p9] 54. ~(old(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 59. person(paul) & creative(paul) & humble(paul) & old(paul) [pure predicate removal 53] 63. creative(paul) & humble(paul) & old(paul) [pure predicate removal 59] 65. creative(paul) & old(paul) [pure predicate removal 63] 136. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 136] 143. ~old(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 54] 144. ~old(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 143] 150. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 151. ~old(paul) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 144,150] 232. room(mary) [cnf transformation 137] 233. room(paul) [cnf transformation 137] 234. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 137] 245. old(paul) [cnf transformation 65] 247. ~old(paul) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 151] 248. ~old(paul) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 151] 249. ~old(paul) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 151] 281. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 249,245] 282. paul != sK2 | ~room(mary) [subsumption resolution 281,233] 283. paul != sK2 [subsumption resolution 282,232] 284. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 248,245] 285. mary != sK2 | ~room(mary) [subsumption resolution 284,233] 286. mary != sK2 [subsumption resolution 285,232] 287. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 247,245] 288. room(sK2) | ~room(mary) [subsumption resolution 287,233] 289. room(sK2) [subsumption resolution 288,232] 294. mary = sK2 | paul = sK2 [resolution 234,289] 313. paul = sK2 [subsumption resolution 294,286] 314. $false [subsumption resolution 313,283] % SZS output end Proof for 150515503902850902655687 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------
0.062145
Ashlee is the only person in the room. If “Ashlee does not own a smartwatch” then “at least one person in the room own a television”. Either “Ashlee watches fantasy movies” or “Ashlee creates large-scale murals for public art installations” but not both. Ashlee collects comic books. Ashlee has a piercing. Only one person in the room enjoys kayaking.
Ashlee collects comic books, has a piercing and enjoys kayaking.
entailment
room(ashlee)&(![X]:(room(X)=>(X='ashlee')))& ((does_not_own_a_smartwatch(ashlee))=>(((?[X]:(room(X)&own_a_television(X))))))& ((watches_fantasy_movies(ashlee))<~>(creates_large-scale_murals_for_public_art_installations(ashlee)))& (~(?[X]:(room(X)&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))=>((![X]:((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<~>(enjoys_wildlife_photography(X))))))))& ((trains_for_and_competes_in_international_triathlons(ashlee))<~>(enjoys_wildlife_photography(ashlee)))& ((~(((has_a_specialized_collection_of_handmade_artisan_pottery(ashlee))|(is_passionate_about_collecting_and_restoring_classic_cars(ashlee)))))=>(~(enjoys_deep-sea_diving_and_exploring_underwater_caves(ashlee))))& ((~(((?[X]:(room(X)&collects_comic_books(X))))))=>(is_passionate_about_collecting_and_restoring_classic_cars(ashlee)))& ((?[X]:(room(X)&(watches_fantasy_movies(X))))=>(does_not_train_for_and_competes_in_international_triathlons(ashlee)))& ((collects_luxury_watches(ashlee))=>(((?[X]:(room(X)&watches_fantasy_movies(X))))))& ((enjoys_deep-sea_diving_and_exploring_underwater_caves(ashlee))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(ashlee)))& (trains_for_and_competes_in_international_triathlons(ashlee))& (collects_comic_books(ashlee))& ((ashlee_dream=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(ashlee))))& (own_a_television(ashlee))& (?[X]:(room(X)&(((enjoys_skydiving(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(enjoys_origami(X))))))& (has_a_piercing(ashlee))& (enjoys_deep-sea_diving_and_exploring_underwater_caves(ashlee))& (((?[X]:(room(X)&own_a_television(X)))))& ((![X]:((~((enjoys_origami(X))|(collects_comic_books(X))))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))& (((?[X]:(room(X)&enjoys_kayaking(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_kayaking(X))&(enjoys_kayaking(Y)))=>(X=Y)))))& ((![X]:((creates_large-scale_murals_for_public_art_installations(X))<=>(trains_for_and_competes_in_international_triathlons(X)))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(ashlee))& (is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(ashlee))
room(ashlee)&(![X]:(room(X)=>(X='ashlee')))& ((collects_comic_books(ashlee))&(has_a_piercing(ashlee))&(enjoys_kayaking(ashlee)))
[ "p0", "p11", "p15", "p19", "hypothesis" ]
% SZS status Unsatisfiable for 465373718611957411236383 % SZS output start Proof for 465373718611957411236383 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 55. prede(mary) [input p11] 59. preda(mary) [input p15] 63. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predb(X0) & room(X0)) [input p19] 67. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 69. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) [rectify 63] 157. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 160. ! [X0,X1] : (X0 = X1 | (~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predb(X2) & room(X2)) [ennf transformation 69] 161. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predb(X2) & room(X2)) [flattening 160] 162. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 67] 174. ? [X2] : (predb(X2) & room(X2)) => (predb(sK3) & room(sK3)) [choice axiom] 175. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & (predb(sK3) & room(sK3)) [skolemisation 161,174] 177. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom] 178. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 162,177] 259. room(mary) [cnf transformation 157] 260. ~room(X0) | mary = X0 [cnf transformation 157] 271. prede(mary) [cnf transformation 55] 273. preda(mary) [cnf transformation 59] 276. room(sK3) [cnf transformation 175] 277. predb(sK3) [cnf transformation 175] 281. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK4) | ~room(mary) [cnf transformation 178] 282. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK4 | ~room(mary) [cnf transformation 178] 323. ~predb(mary) | ~prede(mary) | mary != sK4 | ~room(mary) [subsumption resolution 282,273] 324. ~predb(mary) | mary != sK4 | ~room(mary) [subsumption resolution 323,271] 325. ~predb(mary) | mary != sK4 [subsumption resolution 324,259] 327. 9 <=> mary = sK4 [avatar definition] 329. mary != sK4 <- (~9) [avatar component clause 327] 331. 10 <=> predb(mary) [avatar definition] 334. ~9 | ~10 [avatar split clause 325,331,327] 335. ~predb(mary) | ~prede(mary) | room(sK4) | ~room(mary) [subsumption resolution 281,273] 336. ~predb(mary) | room(sK4) | ~room(mary) [subsumption resolution 335,271] 337. ~predb(mary) | room(sK4) [subsumption resolution 336,259] 339. 11 <=> room(sK4) [avatar definition] 341. room(sK4) <- (11) [avatar component clause 339] 342. 11 | ~10 [avatar split clause 337,331,339] 348. mary = sK3 [resolution 260,276] 352. predb(mary) [backward demodulation 277,348] 355. 10 [avatar split clause 352,331] 356. mary = sK4 <- (11) [resolution 341,260] 357. $false <- (~9, 11) [subsumption resolution 356,329] 358. 9 | ~11 [avatar contradiction clause 357] 359. $false [avatar sat refutation 334,342,355,358] % SZS output end Proof for 465373718611957411236383 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------
0.047442
Joseph, Elisha are the only persons in the room. Not everyone in the room collects rare minerals if they is a dedicated advocate for digital privacy and encryption. Elisha collects rare minerals. Joseph either enjoys rooftop gardening or is a client of Costco but not both. It is not the case that “Joseph neither does not enjoy rooftop gardening nor collects rare minerals”.
Joseph is a client of Costco.
entailment
room(joseph)&room(elisha)&(![X]:(room(X)=>(X='joseph'|X='elisha')))& ((![X]:(room(X)=>(((is_not_a_client_of_Costco(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))=>(enjoys_kayaking_and_exploring_remote_waterways(elisha)))& (![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))=>(enjoys_watercolor_painting(X))))))& (~![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (~![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(can_play_the_guitar(X))))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(joseph))& (plays_the_violin(joseph))& (?[X]:(room(X)&(enjoys_rooftop_gardening(X))))& (collects_rare_minerals(elisha))& (((enjoys_rooftop_gardening(joseph))<~>(is_a_client_of_Costco(joseph))))& (practices_digital_art(elisha))& (is_a_tea_enthusiast(joseph))& (((?[X]:(room(X)&enjoys_bird_watching(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_bird_watching(X))&(enjoys_bird_watching(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (~(~((does_not_enjoy_rooftop_gardening(joseph))|(collects_rare_minerals(joseph)))))& (![X]:(room(X)=>(plays_the_violin(X))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(can_play_the_flute(X))))))& (is_a_tea_enthusiast(elisha))& (can_play_the_flute(joseph))& (![X]:(room(X)=>(((is_not_a_night_owl(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(anywhere(X)=>(((is_a_tea_enthusiast(X))=>(enjoys_virtual_reality_gaming(X))))))& (is_a_night_owl(joseph))
room(joseph)&room(elisha)&(![X]:(room(X)=>(X='joseph'|X='elisha')))& is_a_client_of_Costco(joseph)
[ "p0", "p4", "p9", "p10", "p15", "hypothesis" ]
% SZS status Unsatisfiable for 6575917730956186207510364 % SZS output start Proof for 6575917730956186207510364 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. ~! [X0] : (room(X0) => (predo(X0) => predb(X0))) [input p4] 53. predb(paul) [input p9] 54. predk(mary) <~> predq(mary) [input p10] 59. ~~(predb(mary) | ~predk(mary)) [input p15] 68. ~(predq(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 70. predb(mary) | ~predk(mary) [flattening 59] 156. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 157. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 156] 159. ? [X0] : ((~predb(X0) & predo(X0)) & room(X0)) [ennf transformation 48] 160. ? [X0] : (~predb(X0) & predo(X0) & room(X0)) [flattening 159] 167. ~predq(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 68] 168. ~predq(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 167] 172. ? [X0] : (~predb(X0) & predo(X0) & room(X0)) => (~predb(sK1) & predo(sK1) & room(sK1)) [choice axiom] 173. ~predb(sK1) & predo(sK1) & room(sK1) [skolemisation 160,172] 176. (~predq(mary) | ~predk(mary)) & (predq(mary) | predk(mary)) [nnf transformation 54] 179. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 180. ~predq(mary) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 168,179] 262. room(mary) [cnf transformation 157] 263. room(paul) [cnf transformation 157] 264. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 157] 267. room(sK1) [cnf transformation 173] 269. ~predb(sK1) [cnf transformation 173] 272. predb(paul) [cnf transformation 53] 273. predq(mary) | predk(mary) [cnf transformation 176] 279. predb(mary) | ~predk(mary) [cnf transformation 70] 283. ~predq(mary) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 180] 284. ~predq(mary) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 180] 285. ~predq(mary) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 180] 287. 1 <=> predk(mary) [avatar definition] 291. 2 <=> predq(mary) [avatar definition] 295. 1 | 2 [avatar split clause 273,291,287] 297. 3 <=> predb(mary) [avatar definition] 299. predb(mary) <- (3) [avatar component clause 297] 300. ~1 | 3 [avatar split clause 279,297,287] 302. ~predq(mary) | paul != sK4 | ~room(mary) [subsumption resolution 285,263] 303. ~predq(mary) | paul != sK4 [subsumption resolution 302,262] 305. 4 <=> paul = sK4 [avatar definition] 307. paul != sK4 <- (~4) [avatar component clause 305] 308. ~4 | ~2 [avatar split clause 303,291,305] 309. ~predq(mary) | mary != sK4 | ~room(mary) [subsumption resolution 284,263] 310. ~predq(mary) | mary != sK4 [subsumption resolution 309,262] 312. 5 <=> mary = sK4 [avatar definition] 314. mary != sK4 <- (~5) [avatar component clause 312] 315. ~5 | ~2 [avatar split clause 310,291,312] 316. ~predq(mary) | room(sK4) | ~room(mary) [subsumption resolution 283,263] 317. ~predq(mary) | room(sK4) [subsumption resolution 316,262] 319. 6 <=> room(sK4) [avatar definition] 321. room(sK4) <- (6) [avatar component clause 319] 322. 6 | ~2 [avatar split clause 317,291,319] 329. mary = sK1 | paul = sK1 [resolution 264,267] 332. mary = sK4 | paul = sK4 <- (6) [resolution 264,321] 343. 9 <=> paul = sK1 [avatar definition] 345. paul = sK1 <- (9) [avatar component clause 343] 347. 10 <=> mary = sK1 [avatar definition] 349. mary = sK1 <- (10) [avatar component clause 347] 350. 9 | 10 [avatar split clause 329,347,343] 369. paul = sK4 <- (~5, 6) [subsumption resolution 332,314] 370. $false <- (~4, ~5, 6) [subsumption resolution 369,307] 371. 4 | 5 | ~6 [avatar contradiction clause 370] 378. ~predb(paul) <- (9) [backward demodulation 269,345] 379. $false <- (9) [subsumption resolution 378,272] 380. ~9 [avatar contradiction clause 379] 387. ~predb(mary) <- (10) [backward demodulation 269,349] 388. $false <- (3, 10) [subsumption resolution 387,299] 389. ~3 | ~10 [avatar contradiction clause 388] 391. $false [avatar sat refutation 295,300,308,315,322,350,371,380,389] % SZS output end Proof for 6575917730956186207510364 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0.310328
Rhonda, Keith, Sadie, William, Frederick are the only persons in the room. If “everyone anywhere collects vintage vinyl records or does not make intricate hand-cut paper art for exhibitions” then “Rhonda is a drone photographer”. If “Rhonda is a client of LVMH” then “no one anywhere is not a humble person only if they is a humble person” otherwise “everyone anywhere makes intricate hand-cut paper art for exhibitions only if they is a humble person”. If “everyone in the room is not a client of LVMH or does not make intricate hand-cut paper art for exhibitions” then “everyone anywhere is a client of LVMH if they is not a client of LVMH”. Everyone in the room is not a drone photographer or is a client of LVMH. Everyone in the room who collects vintage vinyl records is not a humble person. Not everyone in the room is a drone photographer. Rhonda collects vintage vinyl records. Everyone anywhere is humble.
Rhonda is a drone photographer.
neutral
room(rhonda)&room(keith)&room(sadie)&room(william)&room(frederick)&(![X]:(room(X)=>(X='rhonda'|X='keith'|X='sadie'|X='william'|X='frederick')))& ((![X]:(anywhere(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(collects_vintage_vinyl_records(X))))))=>(is_a_drone_photographer(rhonda)))& (((is_a_client_of_LVMH(rhonda))=>(~?[X]:(anywhere(X)=>(((humble(X)&person(X))<=(~(humble(X)&person(X))))))))&((~(is_a_client_of_LVMH(rhonda)))=>(![X]:(anywhere(X)=>(((humble(X)&person(X))<=(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))))& ((![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(is_not_a_client_of_LVMH(X))))))=>(![X]:(anywhere(X)=>(((is_not_a_client_of_LVMH(X))=>(is_a_client_of_LVMH(X)))))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))|(is_not_a_drone_photographer(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(~(humble(X)&person(X)))))))& (~![X]:(room(X)=>(is_a_drone_photographer(X))))& (collects_vintage_vinyl_records(rhonda))& (![X]:(anywhere(X)=>(humble(X))))
room(rhonda)&room(keith)&room(sadie)&room(william)&room(frederick)&(![X]:(room(X)=>(X='rhonda'|X='keith'|X='sadie'|X='william'|X='frederick')))& is_a_drone_photographer(rhonda)
[]
null
0
Bernice is the only person in the room. “Bernice is the richest anywhere” if “no one in the room does not create large-scale murals for public art installations or is a strong happy person”. If “Bernice is louder than Marilyn” then “all creative person is generous”. If “everyone in the room is a sibling of Carmen or does not collect foreign coins” then “everyone anywhere who is a client of Carmen does not enjoy kayaking and exploring remote waterways”. If “Bernice practices urban gardening” then “everyone in the room collects foreign coins if they collects rare and antique scientific instruments”. If “no one in the room enjoys kayaking and exploring remote waterways or does not read mystery novels” then “no one outside the room who is not hated by Julia hosts regular game nights featuring complex strategy games”. All quiet person is calm. Everyone outside the room is a old curious happy european if they enjoys deep-sea diving and exploring underwater caves. Everyone in the room practices urban gardening. Someone who is a sibling of Carmen like someone who enjoys kayaking and exploring remote waterways.
Bernice collects foreign coins.
neutral
room(bernice)&(![X]:(room(X)=>(X='bernice')))& ((~?[X]:(room(X)=>(((strong(X)&happy(X)&person(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))=>(![X]:((anywhere(X)&(X!=bernice))=>richer(X,bernice))))& ((louder(marilyn,bernice))=>(![X]:(creative(X)=>generous(X))))& ((![X]:(room(X)=>(((does_not_collect_foreign_coins(X))|(sibling(carmen,X))))))=>(![X]:(anywhere(X)=>(((client(carmen,X))=>(does_not_enjoy_kayaking_and_exploring_remote_waterways(X)))))))& ((practices_urban_gardening(bernice))=>(![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(collects_foreign_coins(X)))))))& ((~?[X]:(room(X)=>(((does_not_read_mystery_novels(X))|(enjoys_kayaking_and_exploring_remote_waterways(X))))))=>(~?[X]:(~room(X)=>(((~hate(X,julia))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))& (![X]:(quiet(X)=>calm(X)))& (![X]:(~room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(old(X)&curious(X)&happy(X)&european(X))))))& (![X]:(room(X)=>(practices_urban_gardening(X))))& (?[X,Y]:((sibling(carmen,X))&(enjoys_kayaking_and_exploring_remote_waterways(Y))&(like(X,Y))))& (![X]:(anywhere(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(enjoys_macrame(X))))))& (generous(bernice)&strong(bernice)&european(bernice))& (louder(nicholas,bernice))& (reads_mystery_novels(bernice))& (![X]:(room(X)=>(((~like(X,marilyn))=>(funny(X))))))& (![X]:(room(X)=>(((~(creative(X)&european(X)))=>(collects_rare_and_antique_scientific_instruments(X))))))& ((enjoys_kayaking_and_exploring_remote_waterways(bernice))&(~(funny(bernice)&european(bernice))))& (is_a_professional_photographer_specializing_in_portrait_photography(bernice))& (![X]:(room(X)=>(((((practices_urban_gardening(X))<~>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))=>(tall(X))))))& ((hate(nicholas,bernice) & hate(bernice,nicholas)))& (![X]:(calm(X)=>creative(X)))& (![X]:(anywhere(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(like(julia,X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(has_completed_a_triathlon(X))))))
room(bernice)&(![X]:(room(X)=>(X='bernice')))& collects_foreign_coins(bernice)
[]
null
0.469299
Henry, Damon, Terry are the only persons in the room. “Henry likes Gertrude” only if “Henry neither likes Andy nor hates Gertrude”. If “Henry and Gertrude hate each other” then “Damon does not hate Gertrude” otherwise “Damon either is hated by Andy or is hated by Gertrude but not both”. “Terry does not like Andy” if “Damon either does not like Gertrude or does not hate Andy but not both” and vice versa. If “Damon does not like Gertrude” then “Henry does not hate Andy” otherwise “Terry neither hates Gertrude nor does not hate Andy”. If “Henry hates Gertrude” then “Henry does not hate Andy”. “Henry does not hate Gertrude” if “Henry either does not hate Gertrude or is liked by Andy but not both” and vice versa. Terry hates Gertrude.
Terry is liked by Gertrude.
neutral
room(henry)&room(damon)&room(terry)&(![X]:(room(X)=>(X='henry'|X='damon'|X='terry')))& ((like(gertrude,henry))=>(~((like(andy,henry))|(hate(gertrude,henry)))))& ((((hate(henry,gertrude) & hate(gertrude,henry)))=>(~hate(gertrude,damon)))&((~((hate(henry,gertrude) & hate(gertrude,henry))))=>(((hate(damon,andy))<~>(hate(damon,gertrude))))))& ((((~like(gertrude,damon))<~>(~hate(andy,damon))))<=>(~like(andy,terry)))& (((~like(gertrude,damon))=>(~hate(andy,henry)))&((~(~like(gertrude,damon)))=>(~((hate(gertrude,terry))|(~hate(andy,terry))))))& ((hate(gertrude,henry))=>(~hate(andy,henry)))& ((((~hate(gertrude,henry))<~>(like(henry,andy))))<=>(~hate(gertrude,henry)))& (hate(gertrude,terry))& ((hate(henry,gertrude) & hate(gertrude,henry)))& ((like(damon,andy) & like(andy,damon)))& (((?[X]:(room(X)&~like(gertrude,X)))))& (like(andy,henry))& (~like(gertrude,henry))& ((![X]:((((hate(andy,X))<~>(like(X,andy))))=>(((~hate(gertrude,X))<~>(~like(andy,X)))))))
room(henry)&room(damon)&room(terry)&(![X]:(room(X)=>(X='henry'|X='damon'|X='terry')))& like(terry,gertrude)
[]
null
0.637886
Dorothy, Kimberley are the only persons in the room. Everyone in the room who does not create large-scale murals for public art installations enjoys stargazing. If someone is an enthusiastic bird watcher who travels for rare sightings, is passionate about collecting and restoring classic cars or plays eSports competitively then he/she practices urban gardening and vice versa. Dorothy has a specialized collection of handmade artisan pottery, does enjoy trail running or trains for and competes in international triathlons. Kimberley enjoys stargazing. Everyone in the room collects luxury watches if they is an enthusiastic bird watcher who travels for rare sightings and vice versa. Kimberley collects luxury watches. If someone can play the guitar then he/she practices urban gardening and vice versa.
Kimberley can play the guitar.
entailment
room(dorothy)&room(kimberley)&(![X]:(room(X)=>(X='dorothy'|X='kimberley')))& (![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))=>(enjoys_stargazing(X))))))& ((![X]:((((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))|(plays_eSports_competitively(X))))<=>(practices_urban_gardening(X)))))& (((has_a_specialized_collection_of_handmade_artisan_pottery(dorothy))|(does_enjoy_trail_running(dorothy))|(trains_for_and_competes_in_international_triathlons(dorothy))))& (enjoys_stargazing(kimberley))& (![X]:(room(X)=>(((collects_luxury_watches(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& ((![X]:((((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))&(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))=>(creates_large-scale_murals_for_public_art_installations(X)))))& (![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(plays_the_violin(X))))))& (~(~(trains_for_and_competes_in_international_triathlons(kimberley))))& ((![X]:((((has_lived_in_exactly_three_countries(X))<~>(does_not_play_the_violin(X))))<=>(plays_the_violin(X)))))& (![X]:(room(X)=>(((can_play_the_piano(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(room(X)=>(((((collects_first_edition_books(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(~room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(collects_luxury_watches(X))))))& (?[X]:(room(X)&(((is_passionate_about_collecting_and_restoring_classic_cars(X))<~>(plays_the_violin(X))))))& (?[X]:(room(X)&(((can_play_the_piano(X))|(collects_first_edition_books(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(anywhere(X)=>(((enjoys_stargazing(X))=>(has_lived_in_exactly_three_countries(X))))))& (?[X]:(room(X)&(own_a_television(X))))& (can_play_the_guitar(dorothy))& (![X]:(room(X)=>(((((does_not_train_for_and_competes_in_international_triathlons(X))|(collects_luxury_watches(X))|(hosts_regular_workshops_on_creative_writing(X))))=>(((can_play_the_piano(X))|(does_not_collect_first_edition_books(X))))))))& (?[X]:(room(X)&(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))& (collects_luxury_watches(kimberley))& (has_lived_in_exactly_three_countries(dorothy))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(own_a_television(X))|(enjoys_stargazing(X))))))))& ((![X]:((can_play_the_guitar(X))<=>(practices_urban_gardening(X)))))& (?[X]:(anywhere(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X))))
room(dorothy)&room(kimberley)&(![X]:(room(X)=>(X='dorothy'|X='kimberley')))& can_play_the_guitar(kimberley)
[ "p0", "p2", "p5", "p20", "p23", "hypothesis" ]
% SZS status Unsatisfiable for 7358891617310100397666716 % SZS output start Proof for 7358891617310100397666716 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. ! [X0] : ((predl(X0) | predt(X0) | predi(X0)) <=> predk(X0)) [input p2] 49. ! [X0] : (room(X0) => (predr(X0) <=> predi(X0))) [input p5] 64. predr(paul) [input p20] 67. ! [X0] : (predc(X0) <=> predk(X0)) [input p23] 69. ~(predc(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 155. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 156. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 155] 157. ! [X0] : ((predr(X0) <=> predi(X0)) | ~room(X0)) [ennf transformation 49] 160. ~predc(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 69] 161. ~predc(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 160] 163. ! [X0] : (((predl(X0) | predt(X0) | predi(X0)) | ~predk(X0)) & (predk(X0) | (~predl(X0) & ~predt(X0) & ~predi(X0)))) [nnf transformation 46] 164. ! [X0] : ((predl(X0) | predt(X0) | predi(X0) | ~predk(X0)) & (predk(X0) | (~predl(X0) & ~predt(X0) & ~predi(X0)))) [flattening 163] 165. ! [X0] : (((predr(X0) | ~predi(X0)) & (predi(X0) | ~predr(X0))) | ~room(X0)) [nnf transformation 157] 177. ! [X0] : ((predc(X0) | ~predk(X0)) & (predk(X0) | ~predc(X0))) [nnf transformation 67] 180. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 181. ~predc(paul) | (paul != sK5 & mary != sK5 & room(sK5)) | ~room(paul) | ~room(mary) [skolemisation 161,180] 263. room(mary) [cnf transformation 156] 264. room(paul) [cnf transformation 156] 265. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 156] 266. ~predi(X0) | predk(X0) [cnf transformation 164] 271. ~predr(X0) | predi(X0) | ~room(X0) [cnf transformation 165] 285. predr(paul) [cnf transformation 64] 288. ~predk(X0) | predc(X0) [cnf transformation 177] 291. ~predc(paul) | room(sK5) | ~room(paul) | ~room(mary) [cnf transformation 181] 292. ~predc(paul) | mary != sK5 | ~room(paul) | ~room(mary) [cnf transformation 181] 293. ~predc(paul) | paul != sK5 | ~room(paul) | ~room(mary) [cnf transformation 181] 307. ~predc(paul) | paul != sK5 | ~room(mary) [subsumption resolution 293,264] 308. ~predc(paul) | paul != sK5 [subsumption resolution 307,263] 310. 3 <=> paul = sK5 [avatar definition] 312. paul != sK5 <- (~3) [avatar component clause 310] 314. 4 <=> predc(paul) [avatar definition] 317. ~3 | ~4 [avatar split clause 308,314,310] 318. ~predc(paul) | mary != sK5 | ~room(mary) [subsumption resolution 292,264] 319. ~predc(paul) | mary != sK5 [subsumption resolution 318,263] 321. 5 <=> mary = sK5 [avatar definition] 323. mary != sK5 <- (~5) [avatar component clause 321] 324. ~5 | ~4 [avatar split clause 319,314,321] 325. ~predc(paul) | room(sK5) | ~room(mary) [subsumption resolution 291,264] 326. ~predc(paul) | room(sK5) [subsumption resolution 325,263] 328. 6 <=> room(sK5) [avatar definition] 330. room(sK5) <- (6) [avatar component clause 328] 331. 6 | ~4 [avatar split clause 326,314,328] 338. predi(paul) | ~room(paul) [resolution 271,285] 339. predi(paul) [subsumption resolution 338,264] 341. predk(paul) [resolution 339,266] 391. predc(paul) [resolution 341,288] 394. 4 [avatar split clause 391,314] 396. mary = sK5 | paul = sK5 <- (6) [resolution 330,265] 397. paul = sK5 <- (~5, 6) [subsumption resolution 396,323] 398. $false <- (~3, ~5, 6) [subsumption resolution 397,312] 399. 3 | 5 | ~6 [avatar contradiction clause 398] 400. $false [avatar sat refutation 317,324,331,394,399] % SZS output end Proof for 7358891617310100397666716 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s % ------------------------------ % ------------------------------
0
Linda, Warren are the only persons in the room. “It is not the case that “it is not the case that “someone in the room neither collects historical artifacts related to ancient civilizations nor drives a hybrid car””” if “Warren is a craft beer aficionado”. “Warren collects antique clocks” unless “Linda can play the piano”. If “it is not the case that “Linda enjoys deep-sea diving and exploring underwater caves”” then “Linda enjoys camping and organizing outdoor survival workshops”. “At least one person in the room collects antique clocks” unless “someone in the room is not a dedicated volunteer for local community service projects or collects action figures or both”. If “it is not the case that “Warren enjoys camping and organizing outdoor survival workshops”” then “Linda collects foreign coins”. If “Warren collect rare sneakers” then “it is not the case that “Linda does not practice zumba””. If “Linda drives a hybrid car” then “Linda does enjoy trail running”.
Linda collects foreign coins.
neutral
room(linda)&room(warren)&(![X]:(room(X)=>(X='linda'|X='warren')))& ((is_a_craft_beer_aficionado(warren))=>(~(~(?[X]:(room(X)&(~((collects_historical_artifacts_related_to_ancient_civilizations(X))|(drives_a_hybrid_car(X)))))))))& (~(can_play_the_piano(linda))=>(collects_antique_clocks(warren)))& ((~(enjoys_deep-sea_diving_and_exploring_underwater_caves(linda)))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(linda)))& (~(?[X]:(room(X)&(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(collects_action_figures(X))))))=>(((?[X]:(room(X)&collects_antique_clocks(X))))))& ((~(enjoys_camping_and_organizing_outdoor_survival_workshops(warren)))=>(collects_foreign_coins(linda)))& ((collect_rare_sneakers(warren))=>(~(does_not_practice_zumba(linda))))& ((drives_a_hybrid_car(linda))=>(does_enjoy_trail_running(linda)))& (collects_antique_clocks(linda))& ((linda_dream=>(drives_a_hybrid_car(warren))))& (is_a_dedicated_volunteer_for_local_community_service_projects(warren))& (~(enjoys_kayaking_and_exploring_remote_waterways(warren)))& (is_a_craft_beer_aficionado(warren))& (does_enjoy_trail_running(linda))& (practices_zumba(linda))& (enjoys_kayaking_and_exploring_remote_waterways(linda))& (?[X]:(room(X)&(can_play_the_piano(X))))
room(linda)&room(warren)&(![X]:(room(X)=>(X='linda'|X='warren')))& collects_foreign_coins(linda)
[]
null
0.072142
Laura, Patricia, Katheryn, Deborah, Deborah are the only persons in the room. 'Everyone in the room makes homemade pastries or is not a wine connoisseur with a private cellar of vintage wines' only if 'more than one person in the room is not a wine connoisseur with a private cellar of vintage wines'. 'Everyone anywhere is not a tall person or is not a wine connoisseur with a private cellar of vintage wines' only if 'everyone in the room is a wine connoisseur with a private cellar of vintage wines if they is not a tall person'. If 'Patricia makes homemade pastries, does not make homemade pastries and is a wine connoisseur with a private cellar of vintage wines' then 'everyone in the room makes homemade pastries if they is a wine connoisseur with a private cellar of vintage wines'. If 'everyone in the room does not make homemade pastries or is tall' then 'Patricia is not a wine connoisseur with a private cellar of vintage wines'. 'Laura is tall' if 'everyone in the room does not make homemade pastries or is a tall person' and vice versa. Laura either is a wine connoisseur with a private cellar of vintage wines or is tall but not both. Not everyone in the room neither is a wine connoisseur with a private cellar of vintage wines nor is a tall person if and only if they is a tall person. Laura makes homemade pastries. Patricia is tall. Not everyone outside the room who is tall makes homemade pastries. Everyone in the room makes homemade pastries only if they is a wine connoisseur with a private cellar of vintage wines. Everyone in the room is a tall person only if they is not tall.
Laura is tall.
contradiction
room(laura)&room(patricia)&room(katheryn)&room(deborah)&room(deborah)&(![X]:(room(X)=>(X='laura'|X='patricia'|X='katheryn'|X='deborah'|X='deborah')))& ((![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(makes_homemade_pastries(X))))))=>((?[X,Y]:(room(X)&room(Y)&(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)&is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(Y))&(X!=Y)))))& ((![X]:(anywhere(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(~(tall(X)&person(X)))))))=>(![X]:(room(X)=>(((~(tall(X)&person(X)))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& ((((makes_homemade_pastries(patricia))&(does_not_make_homemade_pastries(patricia))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(patricia))))=>(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(makes_homemade_pastries(X)))))))& ((![X]:(room(X)=>(((tall(X))|(does_not_make_homemade_pastries(X))))))=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(patricia)))& ((![X]:(room(X)=>(((tall(X)&person(X))|(does_not_make_homemade_pastries(X))))))<=>(tall(laura)))& (((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(laura))<~>(tall(laura))))& (~![X]:(room(X)=>(((~((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(tall(X)&person(X))))<=>(tall(X)&person(X))))))& (makes_homemade_pastries(laura))& (tall(patricia))& (~![X]:(~room(X)=>(((tall(X))=>(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((~tall(X))<=(tall(X)&person(X))))))
room(laura)&room(patricia)&room(katheryn)&room(deborah)&room(deborah)&(![X]:(room(X)=>(X='laura'|X='patricia'|X='katheryn'|X='deborah'|X='deborah')))& tall(laura)
[ "p0", "p6", "p8", "p11", "hypothesis" ]
% SZS status Unsatisfiable for 3336196665611466983185466 % SZS output start Proof for 3336196665611466983185466 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. predz(mary) <~> tall(mary) [input p6] 52. predr(mary) [input p8] 55. ! [X0] : (room(X0) => (predr(X0) => predz(X0))) [input p11] 57. tall(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 133. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 134. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133] 148. ! [X0] : ((predz(X0) | ~predr(X0)) | ~room(X0)) [ennf transformation 55] 149. ! [X0] : (predz(X0) | ~predr(X0) | ~room(X0)) [flattening 148] 152. tall(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 153. tall(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 152] 172. (~tall(mary) | ~predz(mary)) & (tall(mary) | predz(mary)) [nnf transformation 50] 259. room(mary) [cnf transformation 134] 289. ~tall(mary) | ~predz(mary) [cnf transformation 172] 297. predr(mary) [cnf transformation 52] 302. ~predr(X0) | predz(X0) | ~room(X0) [cnf transformation 149] 310. tall(mary) [cnf transformation 153] 400. 19 <=> tall(mary) [avatar definition] 431. 26 <=> predz(mary) [avatar definition] 433. ~predz(mary) <- (~26) [avatar component clause 431] 434. ~26 | ~19 [avatar split clause 289,400,431] 450. 19 [avatar split clause 310,400] 451. predz(mary) | ~room(mary) [resolution 302,297] 452. ~room(mary) <- (~26) [subsumption resolution 451,433] 453. $false <- (~26) [subsumption resolution 452,259] 454. 26 [avatar contradiction clause 453] 455. $false [avatar sat refutation 434,450,454] % SZS output end Proof for 3336196665611466983185466 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0
There is a room. If “everyone in the room is not a night owl or is a night owl” then “everyone in the room is a night owl if they is not a night owl”. It is true that “someone in the room collects luxury watches or is a night owl or both”. Everyone in the room is not a night owl or is a night owl. Everyone in the room is a night owl if they collects luxury watches. Everyone in the room who enjoys deep-sea diving and exploring underwater caves collects luxury watches. Everyone in the room is not a night owl or enjoys deep-sea diving and exploring underwater caves. It is true that “someone in the room collects luxury watches”. Everyone in the room enjoys deep-sea diving and exploring underwater caves if they is a night owl. At least one person anywhere enjoys deep-sea diving and exploring underwater caves.
Everyone outside the room is a night owl.
neutral
(there_is_a_room)& ((![X]:(room(X)=>(((is_a_night_owl(X))|(is_not_a_night_owl(X))))))=>(![X]:(room(X)=>(((is_not_a_night_owl(X))=>(is_a_night_owl(X)))))))& (?[X]:(room(X)&(((collects_luxury_watches(X))|(is_a_night_owl(X))))))& (![X]:(room(X)=>(((is_a_night_owl(X))|(is_not_a_night_owl(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(is_a_night_owl(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(collects_luxury_watches(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(is_not_a_night_owl(X))))))& (?[X]:(room(X)&(collects_luxury_watches(X))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (((?[X]:(anywhere(X)&enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))
(there_is_a_room)& ![X]:(~room(X)=>(is_a_night_owl(X)))
[]
null
0.006048
Carmelita, Ollie, Kristina, Hazel are the only persons in the room. If “it is not the case that “at least one person in the room is a skilled home brewer experimenting with craft beer recipes”” then “not everyone anywhere is a skilled home brewer experimenting with craft beer recipes or is not a tea enthusiast”. If “not everyone anywhere is a skilled home brewer experimenting with craft beer recipes or is not a tea enthusiast” then “everyone outside the room is not a night owl or is a skilled home brewer experimenting with craft beer recipes”. “Everyone in the room who enjoys making ceramics is a tea enthusiast” unless “it is not the case that “it is true that “Ollie is an enthusiastic bird watcher who travels for rare sightings, reads mystery novels or enjoys making ceramics”””. Everyone in the room is a tea enthusiast if they is a cybersecurity expert or collects vintage vinyl records or both and vice versa. Everyone anywhere has a vast collection of first-edition science fiction novels. It is not the case that “Ollie either collects limited-edition art prints from contemporary artists or plays as a goalkeeper for a local amateur soccer team but not both”. Kristina plays as a goalkeeper for a local amateur soccer team and has completed a triathlon. Everyone anywhere travels domestically frequently if they is a skilled home brewer experimenting with craft beer recipes. Carmelita reads mystery novels. Kristina who owns an Android phone, is a cybersecurity expert or does not frequently participates in hackathons and coding competitions collects vintage vinyl records.
Carmelita is a skilled home brewer experimenting with craft beer recipes.
entailment
room(carmelita)&room(ollie)&room(kristina)&room(hazel)&(![X]:(room(X)=>(X='carmelita'|X='ollie'|X='kristina'|X='hazel')))& (((~(((?[X]:(room(X)&is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(~![X]:(anywhere(X)=>(((is_not_a_tea_enthusiast(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))& ((~![X]:(anywhere(X)=>(((is_not_a_tea_enthusiast(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))|(is_not_a_night_owl(X))))))))& (~(~(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(ollie))|(reads_mystery_novels(ollie))|(enjoys_making_ceramics(ollie)))))=>(![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(is_a_tea_enthusiast(X)))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))<=>(((is_a_cybersecurity_expert(X))|(collects_vintage_vinyl_records(X))))))))& (![X]:(anywhere(X)=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))& (~(((collects_limited-edition_art_prints_from_contemporary_artists(ollie))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(ollie)))))& (((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(kristina))&(has_completed_a_triathlon(kristina))))& (![X]:(anywhere(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(travels_domestically_frequently(X))))))& (reads_mystery_novels(carmelita))& ((((owns_an_Android_phone(kristina))|(is_a_cybersecurity_expert(kristina))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(kristina))))&(collects_vintage_vinyl_records(kristina)))& (does_not_frequently_participates_in_hackathons_and_coding_competitions(kristina))& ((![X]:((is_a_client_of_Meta(X))=>(~((is_a_tea_enthusiast(X))|(is_a_night_owl(X)))))))& (![X]:(room(X)=>(((reads_mystery_novels(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(enjoys_making_ceramics(X))))))
room(carmelita)&room(ollie)&room(kristina)&room(hazel)&(![X]:(room(X)=>(X='carmelita'|X='ollie'|X='kristina'|X='hazel')))& is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(carmelita)
[ "p0", "hypothesis" ]
% SZS status Unsatisfiable for 851812279355469469120003 % SZS output start Proof for 851812279355469469120003 44. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X0] : (room(X0) => (predd(X0) => predk(X0))) & ! [X0] : (predr(X0) => ~(predf(X0) | predn(X0))) & ~predc(fred) & predm(fred) & (~predc(fred) | prede(fred) | predu(fred)) & predd(mary) & ! [X0] : (anywhere(X0) => (predk(X0) => preda(X0))) & preds(fred) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X0] : (anywhere(X0) => predp(X0)) & ! [X0] : (room(X0) => (predn(X0) <=> (predm(X0) | prede(X0)))) & (~~(predh(paul) | predd(paul) | predi(paul)) => ! [X0] : (room(X0) => (predh(X0) => predn(X0)))) & (~! [X0] : (anywhere(X0) => (predk(X0) | ~predn(X0))) => ! [X0] : (~room(X0) => (~predf(X0) | predk(X0)))) & (~? [X0] : (predk(X0) & room(X0)) => ~! [X0] : (anywhere(X0) => (predk(X0) | ~predn(X0)))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(predk(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X1] : (room(X1) => (predd(X1) => predk(X1))) & ! [X2] : (predr(X2) => ~(predf(X2) | predn(X2))) & ~predc(fred) & predm(fred) & (~predc(fred) | prede(fred) | predu(fred)) & predd(mary) & ! [X3] : (anywhere(X3) => (predk(X3) => preda(X3))) & preds(fred) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X4] : (anywhere(X4) => predp(X4)) & ! [X5] : (room(X5) => (predn(X5) <=> (predm(X5) | prede(X5)))) & (~~(predh(paul) | predd(paul) | predi(paul)) => ! [X6] : (room(X6) => (predh(X6) => predn(X6)))) & (~! [X7] : (anywhere(X7) => (predk(X7) | ~predn(X7))) => ! [X8] : (~room(X8) => (~predf(X8) | predk(X8)))) & (~? [X9] : (predk(X9) & room(X9)) => ~! [X10] : (anywhere(X10) => (predk(X10) | ~predn(X10)))) & ! [X11] : (room(X11) => (alice = X11 | fred = X11 | paul = X11 | mary = X11)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X1] : (room(X1) => (predd(X1) => predk(X1))) & ! [X2] : (predr(X2) => ~(predf(X2) | predn(X2))) & ~predc(fred) & predm(fred) & (~predc(fred) | prede(fred) | predu(fred)) & predd(mary) & ! [X3] : (anywhere(X3) => (predk(X3) => preda(X3))) & preds(fred) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X4] : (anywhere(X4) => predp(X4)) & ! [X5] : (room(X5) => (predn(X5) <=> (predm(X5) | prede(X5)))) & ((predh(paul) | predd(paul) | predi(paul)) => ! [X6] : (room(X6) => (predh(X6) => predn(X6)))) & (~! [X7] : (anywhere(X7) => (predk(X7) | ~predn(X7))) => ! [X8] : (~room(X8) => (~predf(X8) | predk(X8)))) & (~? [X9] : (predk(X9) & room(X9)) => ~! [X10] : (anywhere(X10) => (predk(X10) | ~predn(X10)))) & ! [X11] : (room(X11) => (alice = X11 | fred = X11 | paul = X11 | mary = X11)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 46] 48. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X1] : (room(X1) => (predd(X1) => predk(X1))) & ~predc(fred) & predm(fred) & (~predc(fred) | prede(fred) | predu(fred)) & predd(mary) & ! [X3] : (anywhere(X3) => (predk(X3) => preda(X3))) & preds(fred) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X4] : (anywhere(X4) => predp(X4)) & ! [X5] : (room(X5) => (predn(X5) <=> (predm(X5) | prede(X5)))) & ((predh(paul) | predd(paul) | predi(paul)) => ! [X6] : (room(X6) => (predh(X6) => predn(X6)))) & (~! [X7] : (anywhere(X7) => (predk(X7) | ~predn(X7))) => ! [X8] : (~room(X8) => (~predf(X8) | predk(X8)))) & (~? [X9] : (predk(X9) & room(X9)) => ~! [X10] : (anywhere(X10) => (predk(X10) | ~predn(X10)))) & ! [X11] : (room(X11) => (alice = X11 | fred = X11 | paul = X11 | mary = X11)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X1] : (room(X1) => (predd(X1) => predk(X1))) & predm(fred) & predd(mary) & ! [X3] : (anywhere(X3) => (predk(X3) => preda(X3))) & preds(fred) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X4] : (anywhere(X4) => predp(X4)) & ! [X5] : (room(X5) => (predn(X5) <=> (predm(X5) | prede(X5)))) & ((predh(paul) | predd(paul) | predi(paul)) => ! [X6] : (room(X6) => (predh(X6) => predn(X6)))) & (~! [X7] : (anywhere(X7) => (predk(X7) | ~predn(X7))) => ! [X8] : (~room(X8) => (~predf(X8) | predk(X8)))) & (~? [X9] : (predk(X9) & room(X9)) => ~! [X10] : (anywhere(X10) => (predk(X10) | ~predn(X10)))) & ! [X11] : (room(X11) => (alice = X11 | fred = X11 | paul = X11 | mary = X11)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X1] : (room(X1) => (predd(X1) => predk(X1))) & predm(fred) & predd(mary) & preds(fred) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X4] : (anywhere(X4) => predp(X4)) & ! [X5] : (room(X5) => (predn(X5) <=> (predm(X5) | prede(X5)))) & ((predh(paul) | predd(paul) | predi(paul)) => ! [X6] : (room(X6) => (predh(X6) => predn(X6)))) & (~! [X7] : (anywhere(X7) => (predk(X7) | ~predn(X7))) => ! [X8] : (~room(X8) => (~predf(X8) | predk(X8)))) & (~? [X9] : (predk(X9) & room(X9)) => ~! [X10] : (anywhere(X10) => (predk(X10) | ~predn(X10)))) & ! [X11] : (room(X11) => (alice = X11 | fred = X11 | paul = X11 | mary = X11)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X1] : (room(X1) => (predd(X1) => predk(X1))) & predm(fred) & predd(mary) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X4] : (anywhere(X4) => predp(X4)) & ! [X5] : (room(X5) => (predn(X5) <=> (predm(X5) | prede(X5)))) & ((predh(paul) | predd(paul) | predi(paul)) => ! [X6] : (room(X6) => (predh(X6) => predn(X6)))) & (~! [X7] : (anywhere(X7) => (predk(X7) | ~predn(X7))) => ! [X8] : (~room(X8) => (~predf(X8) | predk(X8)))) & (~? [X9] : (predk(X9) & room(X9)) => ~! [X10] : (anywhere(X10) => (predk(X10) | ~predn(X10)))) & ! [X11] : (room(X11) => (alice = X11 | fred = X11 | paul = X11 | mary = X11)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X1] : (room(X1) => (predd(X1) => predk(X1))) & predm(fred) & predd(mary) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X5] : (room(X5) => (predn(X5) <=> (predm(X5) | prede(X5)))) & ((predh(paul) | predd(paul) | predi(paul)) => ! [X6] : (room(X6) => (predh(X6) => predn(X6)))) & (~! [X7] : (anywhere(X7) => (predk(X7) | ~predn(X7))) => ! [X8] : (~room(X8) => (~predf(X8) | predk(X8)))) & (~? [X9] : (predk(X9) & room(X9)) => ~! [X10] : (anywhere(X10) => (predk(X10) | ~predn(X10)))) & ! [X11] : (room(X11) => (alice = X11 | fred = X11 | paul = X11 | mary = X11)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X1] : (room(X1) => (predd(X1) => predk(X1))) & predm(fred) & predd(mary) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X5] : (room(X5) => (predn(X5) <=> (predm(X5) | prede(X5)))) & ((predh(paul) | predd(paul)) => ! [X6] : (room(X6) => (predh(X6) => predn(X6)))) & (~! [X7] : (anywhere(X7) => (predk(X7) | ~predn(X7))) => ! [X8] : (~room(X8) => (~predf(X8) | predk(X8)))) & (~? [X9] : (predk(X9) & room(X9)) => ~! [X10] : (anywhere(X10) => (predk(X10) | ~predn(X10)))) & ! [X11] : (room(X11) => (alice = X11 | fred = X11 | paul = X11 | mary = X11)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X1] : (room(X1) => (predd(X1) => predk(X1))) & predm(fred) & predd(mary) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X5] : (room(X5) => (predn(X5) <=> (predm(X5) | prede(X5)))) & ((predh(paul) | predd(paul)) => ! [X6] : (room(X6) => (predh(X6) => predn(X6)))) & (~? [X9] : (predk(X9) & room(X9)) => ~! [X10] : (anywhere(X10) => (predk(X10) | ~predn(X10)))) & ! [X11] : (room(X11) => (alice = X11 | fred = X11 | paul = X11 | mary = X11)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ! [X1] : (room(X1) => (predd(X1) => predk(X1))) & predm(fred) & predd(mary) & predo(fred) & ~(predq(paul) <~> predo(paul)) & ! [X5] : (room(X5) => (predn(X5) <=> (predm(X5) | prede(X5)))) & ((predh(paul) | predd(paul)) => ! [X6] : (room(X6) => (predh(X6) => predn(X6)))) & (~? [X9] : (predk(X9) & room(X9)) => ~! [X10] : (predk(X10) | ~predn(X10))) & ! [X11] : (room(X11) => (alice = X11 | fred = X11 | paul = X11 | mary = X11)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 128. ! [X0] : ((predh(X0) | ~predn(X0)) | ~room(X0)) & ! [X1] : ((predk(X1) | ~predd(X1)) | ~room(X1)) & predm(fred) & predd(mary) & predo(fred) & (predq(paul) <=> predo(paul)) & ! [X5] : ((predn(X5) <=> (predm(X5) | prede(X5))) | ~room(X5)) & (! [X6] : ((predn(X6) | ~predh(X6)) | ~room(X6)) | (~predh(paul) & ~predd(paul))) & (? [X10] : (~predk(X10) & predn(X10)) | ? [X9] : (predk(X9) & room(X9))) & ! [X11] : ((alice = X11 | fred = X11 | paul = X11 | mary = X11) | ~room(X11)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 55] 129. ! [X0] : (predh(X0) | ~predn(X0) | ~room(X0)) & ! [X1] : (predk(X1) | ~predd(X1) | ~room(X1)) & predm(fred) & predd(mary) & predo(fred) & (predq(paul) <=> predo(paul)) & ! [X5] : ((predn(X5) <=> (predm(X5) | prede(X5))) | ~room(X5)) & (! [X6] : (predn(X6) | ~predh(X6) | ~room(X6)) | (~predh(paul) & ~predd(paul))) & (? [X10] : (~predk(X10) & predn(X10)) | ? [X9] : (predk(X9) & room(X9))) & ! [X11] : (alice = X11 | fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 128] 130. ~predk(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 131. ~predk(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 130] 133. ! [X0] : (predh(X0) | ~predn(X0) | ~room(X0)) & ! [X1] : (predk(X1) | ~predd(X1) | ~room(X1)) & predm(fred) & predd(mary) & predo(fred) & ((predq(paul) | ~predo(paul)) & (predo(paul) | ~predq(paul))) & ! [X5] : (((predn(X5) | (~predm(X5) & ~prede(X5))) & ((predm(X5) | prede(X5)) | ~predn(X5))) | ~room(X5)) & (! [X6] : (predn(X6) | ~predh(X6) | ~room(X6)) | (~predh(paul) & ~predd(paul))) & (? [X10] : (~predk(X10) & predn(X10)) | ? [X9] : (predk(X9) & room(X9))) & ! [X11] : (alice = X11 | fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 129] 134. ! [X0] : (predh(X0) | ~predn(X0) | ~room(X0)) & ! [X1] : (predk(X1) | ~predd(X1) | ~room(X1)) & predm(fred) & predd(mary) & predo(fred) & (predq(paul) | ~predo(paul)) & (predo(paul) | ~predq(paul)) & ! [X5] : (((predn(X5) | (~predm(X5) & ~prede(X5))) & (predm(X5) | prede(X5) | ~predn(X5))) | ~room(X5)) & (! [X6] : (predn(X6) | ~predh(X6) | ~room(X6)) | (~predh(paul) & ~predd(paul))) & (? [X10] : (~predk(X10) & predn(X10)) | ? [X9] : (predk(X9) & room(X9))) & ! [X11] : (alice = X11 | fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133] 135. ! [X0] : (predh(X0) | ~predn(X0) | ~room(X0)) & ! [X1] : (predk(X1) | ~predd(X1) | ~room(X1)) & predm(fred) & predd(mary) & predo(fred) & (predq(paul) | ~predo(paul)) & (predo(paul) | ~predq(paul)) & ! [X2] : (((predn(X2) | (~predm(X2) & ~prede(X2))) & (predm(X2) | prede(X2) | ~predn(X2))) | ~room(X2)) & (! [X3] : (predn(X3) | ~predh(X3) | ~room(X3)) | (~predh(paul) & ~predd(paul))) & (? [X4] : (~predk(X4) & predn(X4)) | ? [X5] : (predk(X5) & room(X5))) & ! [X6] : (alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 134] 136. ? [X4] : (~predk(X4) & predn(X4)) => (~predk(sK0) & predn(sK0)) [choice axiom] 137. ? [X5] : (predk(X5) & room(X5)) => (predk(sK1) & room(sK1)) [choice axiom] 138. ! [X0] : (predh(X0) | ~predn(X0) | ~room(X0)) & ! [X1] : (predk(X1) | ~predd(X1) | ~room(X1)) & predm(fred) & predd(mary) & predo(fred) & (predq(paul) | ~predo(paul)) & (predo(paul) | ~predq(paul)) & ! [X2] : (((predn(X2) | (~predm(X2) & ~prede(X2))) & (predm(X2) | prede(X2) | ~predn(X2))) | ~room(X2)) & (! [X3] : (predn(X3) | ~predh(X3) | ~room(X3)) | (~predh(paul) & ~predd(paul))) & ((~predk(sK0) & predn(sK0)) | (predk(sK1) & room(sK1))) & ! [X6] : (alice = X6 | fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 135,137,136] 139. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 140. ~predk(mary) | (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 131,139] 221. room(mary) [cnf transformation 138] 222. room(paul) [cnf transformation 138] 223. room(fred) [cnf transformation 138] 224. room(alice) [cnf transformation 138] 225. ~room(X6) | fred = X6 | paul = X6 | mary = X6 | alice = X6 [cnf transformation 138] 238. predd(mary) [cnf transformation 138] 240. ~predd(X1) | predk(X1) | ~room(X1) [cnf transformation 138] 242. ~predk(mary) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 140] 243. ~predk(mary) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 140] 244. ~predk(mary) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 140] 245. ~predk(mary) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 140] 246. ~predk(mary) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 140] 290. ~predk(mary) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 246,224] 291. ~predk(mary) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 290,223] 292. ~predk(mary) | alice != sK2 | ~room(mary) [subsumption resolution 291,222] 293. ~predk(mary) | alice != sK2 [subsumption resolution 292,221] 295. 10 <=> alice = sK2 [avatar definition] 297. alice != sK2 <- (~10) [avatar component clause 295] 299. 11 <=> predk(mary) [avatar definition] 302. ~10 | ~11 [avatar split clause 293,299,295] 303. ~predk(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 245,224] 304. ~predk(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 303,223] 305. ~predk(mary) | fred != sK2 | ~room(mary) [subsumption resolution 304,222] 306. ~predk(mary) | fred != sK2 [subsumption resolution 305,221] 308. 12 <=> fred = sK2 [avatar definition] 310. fred != sK2 <- (~12) [avatar component clause 308] 311. ~12 | ~11 [avatar split clause 306,299,308] 312. ~predk(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 244,224] 313. ~predk(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 312,223] 314. ~predk(mary) | paul != sK2 | ~room(mary) [subsumption resolution 313,222] 315. ~predk(mary) | paul != sK2 [subsumption resolution 314,221] 317. 13 <=> paul = sK2 [avatar definition] 319. paul != sK2 <- (~13) [avatar component clause 317] 320. ~13 | ~11 [avatar split clause 315,299,317] 321. ~predk(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 243,224] 322. ~predk(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 321,223] 323. ~predk(mary) | mary != sK2 | ~room(mary) [subsumption resolution 322,222] 324. ~predk(mary) | mary != sK2 [subsumption resolution 323,221] 326. 14 <=> mary = sK2 [avatar definition] 328. mary != sK2 <- (~14) [avatar component clause 326] 329. ~14 | ~11 [avatar split clause 324,299,326] 330. ~predk(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 242,224] 331. ~predk(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 330,223] 332. ~predk(mary) | room(sK2) | ~room(mary) [subsumption resolution 331,222] 333. ~predk(mary) | room(sK2) [subsumption resolution 332,221] 335. 15 <=> room(sK2) [avatar definition] 337. room(sK2) <- (15) [avatar component clause 335] 338. 15 | ~11 [avatar split clause 333,299,335] 341. predk(mary) | ~room(mary) [resolution 240,238] 345. predk(mary) [subsumption resolution 341,221] 346. 11 [avatar split clause 345,299] 397. fred = sK2 | paul = sK2 | mary = sK2 | alice = sK2 <- (15) [resolution 225,337] 415. paul = sK2 | mary = sK2 | alice = sK2 <- (~12, 15) [subsumption resolution 397,310] 416. mary = sK2 | alice = sK2 <- (~12, ~13, 15) [subsumption resolution 415,319] 417. alice = sK2 <- (~12, ~13, ~14, 15) [subsumption resolution 416,328] 418. $false <- (~10, ~12, ~13, ~14, 15) [subsumption resolution 417,297] 419. 10 | 12 | 13 | 14 | ~15 [avatar contradiction clause 418] 420. $false [avatar sat refutation 302,311,320,329,338,346,419] % SZS output end Proof for 851812279355469469120003 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------
0
Orlando, Ronald, Donald, Richard, Machelle are the only persons in the room. Orlando is quiet. Everyone anywhere is kind if they is not a tall person and vice versa. All kind persons are old. Everyone in the room is not a old person only if they is a kind person. All quiet persons are tall. Everyone in the room who is a old person and is not tall is a quiet person and is not quiet. Orlando is the richest in the room. All old persons are tall.
Orlando is kind.
contradiction
room(orlando)&room(ronald)&room(donald)&room(richard)&room(machelle)&(![X]:(room(X)=>(X='orlando'|X='ronald'|X='donald'|X='richard'|X='machelle')))& (quiet(orlando))& (![X]:(anywhere(X)=>(((kind(X))<=>(~(tall(X)&person(X)))))))& (![X]:(kind(X)=>old(X)))& (![X]:(room(X)=>(((kind(X)&person(X))<=(~(old(X)&person(X)))))))& (![X]:(quiet(X)=>tall(X)))& (![X]:(room(X)=>(((((old(X)&person(X))&(~tall(X))))=>(((quiet(X)&person(X))&(~quiet(X))))))))& (![X]:((room(X)&(X!=orlando))=>richer(X,orlando)))& (![X]:(old(X)=>tall(X)))
room(orlando)&room(ronald)&room(donald)&room(richard)&room(machelle)&(![X]:(room(X)=>(X='orlando'|X='ronald'|X='donald'|X='richard'|X='machelle')))& kind(orlando)
[ "b4", "p0", "p1", "p2", "p4", "p5", "hypothesis" ]
% SZS status Unsatisfiable for 8593191795947404023836756 % SZS output start Proof for 8593191795947404023836756 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. quiet(mary) [input p1] 46. ! [X0] : (anywhere(X0) => (kind(X0) <=> ~(person(X0) & tall(X0)))) [input p2] 48. ! [X0] : (room(X0) => (~(person(X0) & old(X0)) => (person(X0) & kind(X0)))) [input p4] 49. ! [X0] : (quiet(X0) => tall(X0)) [input p5] 53. kind(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] 125. ! [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] 126. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 125] 127. ! [X0] : ((kind(X0) <=> (~person(X0) | ~tall(X0))) | ~anywhere(X0)) [ennf transformation 46] 129. ! [X0] : (((person(X0) & kind(X0)) | (person(X0) & old(X0))) | ~room(X0)) [ennf transformation 48] 130. ! [X0] : ((person(X0) & kind(X0)) | (person(X0) & old(X0)) | ~room(X0)) [flattening 129] 131. ! [X0] : (tall(X0) | ~quiet(X0)) [ennf transformation 49] 137. kind(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 53] 138. kind(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 137] 140. ! [X0] : (((kind(X0) | (person(X0) & tall(X0))) & ((~person(X0) | ~tall(X0)) | ~kind(X0))) | ~anywhere(X0)) [nnf transformation 127] 141. ! [X0] : (((kind(X0) | (person(X0) & tall(X0))) & (~person(X0) | ~tall(X0) | ~kind(X0))) | ~anywhere(X0)) [flattening 140] 142. anywhere(X0) [cnf transformation 5] 223. room(mary) [cnf transformation 126] 229. quiet(mary) [cnf transformation 45] 230. ~person(X0) | ~tall(X0) | ~kind(X0) | ~anywhere(X0) [cnf transformation 141] 237. person(X0) | person(X0) | ~room(X0) [cnf transformation 130] 238. ~quiet(X0) | tall(X0) [cnf transformation 131] 250. kind(mary) [cnf transformation 138] 251. ~room(X0) | person(X0) [duplicate literal removal 237] 254. ~tall(X0) | ~person(X0) | ~kind(X0) [subsumption resolution 230,142] 260. tall(mary) [resolution 238,229] 262. person(mary) [resolution 251,223] 278. ~person(mary) | ~kind(mary) [resolution 254,260] 280. ~kind(mary) [subsumption resolution 278,262] 281. $false [subsumption resolution 280,250] % SZS output end Proof for 8593191795947404023836756 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------
0
Brad, Joan, Melissa, Roger, Thomas are the only persons in the room. It is not the case that 'it is not the case that 'Brad is right-handed''. If someone is right-handed then he/she writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations if they does not own a high-end gaming PC with custom-built components. Everyone in the room practices digital art if they writes in-depth travel guides for off-the-beaten-path destinations. Not everyone in the room is right-handed if they writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room owns a high-end gaming PC with custom-built components, writes in-depth travel guides for off-the-beaten-path destinations and practices digital art if they is not right-handed.
Roger practices digital art.
entailment
room(brad)&room(joan)&room(melissa)&room(roger)&room(thomas)&(![X]:(room(X)=>(X='brad'|X='joan'|X='melissa'|X='roger'|X='thomas')))& (~(~(is_right-handed(brad))))& ((![X]:((is_right-handed(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))& (![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(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))=>(practices_digital_art(X))))))& (~![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(is_right-handed(X))))))& (![X]:(room(X)=>(((is_not_right-handed(X))=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(practices_digital_art(X))))))))& (((?[X]:(room(X)&does_not_own_a_high-end_gaming_PC_with_custom-built_components(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(Y)))=>(X=Y)))))& (does_not_own_a_high-end_gaming_PC_with_custom-built_components(melissa))
room(brad)&room(joan)&room(melissa)&room(roger)&room(thomas)&(![X]:(room(X)=>(X='brad'|X='joan'|X='melissa'|X='roger'|X='thomas')))& practices_digital_art(roger)
[ "p0", "p2", "p4", "p6", "hypothesis" ]
% SZS status Unsatisfiable for 1321026157660834986442679 % SZS output start Proof for 1321026157660834986442679 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (predc(X0) => predb(X0)) [input p2] 48. ! [X0] : (room(X0) => (predb(X0) => prede(X0))) [input p4] 50. ! [X0] : (room(X0) => (~predc(X0) => (prede(X0) & predb(X0) & preda(X0)))) [input p6] 53. ~(prede(alice) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 127. ! [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] 128. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 127] 129. ! [X0] : (predb(X0) | ~predc(X0)) [ennf transformation 46] 132. ! [X0] : ((prede(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 48] 133. ! [X0] : (prede(X0) | ~predb(X0) | ~room(X0)) [flattening 132] 136. ! [X0] : (((prede(X0) & predb(X0) & preda(X0)) | predc(X0)) | ~room(X0)) [ennf transformation 50] 137. ! [X0] : ((prede(X0) & predb(X0) & preda(X0)) | predc(X0) | ~room(X0)) [flattening 136] 140. ~prede(alice) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 53] 141. ~prede(alice) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 140] 147. ? [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] 148. ~prede(alice) | (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 141,147] 229. room(mary) [cnf transformation 128] 230. room(paul) [cnf transformation 128] 231. room(fred) [cnf transformation 128] 232. room(alice) [cnf transformation 128] 233. room(john) [cnf transformation 128] 234. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 128] 236. ~predc(X0) | predb(X0) [cnf transformation 129] 238. ~predb(X0) | prede(X0) | ~room(X0) [cnf transformation 133] 243. predb(X0) | predc(X0) | ~room(X0) [cnf transformation 137] 249. ~prede(alice) | room(sK2) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 250. ~prede(alice) | mary != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 251. ~prede(alice) | paul != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 252. ~prede(alice) | fred != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 253. ~prede(alice) | alice != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 254. ~prede(alice) | john != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 148] 255. ~room(X0) | predb(X0) [subsumption resolution 243,236] 256. ~prede(alice) | john != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 254,233] 257. ~prede(alice) | john != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 256,232] 258. ~prede(alice) | john != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 257,231] 259. ~prede(alice) | john != sK2 | ~room(mary) [subsumption resolution 258,230] 260. ~prede(alice) | john != sK2 [subsumption resolution 259,229] 262. 1 <=> john = sK2 [avatar definition] 264. john != sK2 <- (~1) [avatar component clause 262] 266. 2 <=> prede(alice) [avatar definition] 269. ~1 | ~2 [avatar split clause 260,266,262] 270. ~prede(alice) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 253,233] 271. ~prede(alice) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,232] 272. ~prede(alice) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 271,231] 273. ~prede(alice) | alice != sK2 | ~room(mary) [subsumption resolution 272,230] 274. ~prede(alice) | alice != sK2 [subsumption resolution 273,229] 276. 3 <=> alice = sK2 [avatar definition] 278. alice != sK2 <- (~3) [avatar component clause 276] 279. ~3 | ~2 [avatar split clause 274,266,276] 280. ~prede(alice) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 252,233] 281. ~prede(alice) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,232] 282. ~prede(alice) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 281,231] 283. ~prede(alice) | fred != sK2 | ~room(mary) [subsumption resolution 282,230] 284. ~prede(alice) | fred != sK2 [subsumption resolution 283,229] 286. 4 <=> fred = sK2 [avatar definition] 288. fred != sK2 <- (~4) [avatar component clause 286] 289. ~4 | ~2 [avatar split clause 284,266,286] 290. ~prede(alice) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 251,233] 291. ~prede(alice) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,232] 292. ~prede(alice) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 291,231] 293. ~prede(alice) | paul != sK2 | ~room(mary) [subsumption resolution 292,230] 294. ~prede(alice) | paul != sK2 [subsumption resolution 293,229] 296. 5 <=> paul = sK2 [avatar definition] 298. paul != sK2 <- (~5) [avatar component clause 296] 299. ~5 | ~2 [avatar split clause 294,266,296] 300. ~prede(alice) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 250,233] 301. ~prede(alice) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 300,232] 302. ~prede(alice) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 301,231] 303. ~prede(alice) | mary != sK2 | ~room(mary) [subsumption resolution 302,230] 304. ~prede(alice) | mary != sK2 [subsumption resolution 303,229] 306. 6 <=> mary = sK2 [avatar definition] 308. mary != sK2 <- (~6) [avatar component clause 306] 309. ~6 | ~2 [avatar split clause 304,266,306] 310. ~prede(alice) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 249,233] 311. ~prede(alice) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 310,232] 312. ~prede(alice) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 311,231] 313. ~prede(alice) | room(sK2) | ~room(mary) [subsumption resolution 312,230] 314. ~prede(alice) | room(sK2) [subsumption resolution 313,229] 316. 7 <=> room(sK2) [avatar definition] 318. room(sK2) <- (7) [avatar component clause 316] 319. 7 | ~2 [avatar split clause 314,266,316] 324. predb(alice) [resolution 255,232] 343. prede(alice) | ~room(alice) [resolution 324,238] 347. prede(alice) [subsumption resolution 343,232] 348. 2 [avatar split clause 347,266] 492. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (7) [resolution 234,318] 535. fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (~3, 7) [subsumption resolution 492,278] 536. paul = sK2 | mary = sK2 | john = sK2 <- (~3, ~4, 7) [subsumption resolution 535,288] 537. mary = sK2 | john = sK2 <- (~3, ~4, ~5, 7) [subsumption resolution 536,298] 538. john = sK2 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 537,308] 539. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 538,264] 540. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 539] 541. $false [avatar sat refutation 269,279,289,299,309,319,348,540] % SZS output end Proof for 1321026157660834986442679 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------
0
Doris is the only person in the room. Doris is an avid collector of autographed memorabilia from famous musicians. Doris who practices urban gardening enjoys snowboarding. Doris volunteers for local environmental conservation projects. Everyone in the room mentors a youth basketball team on weekends. Doris mentors a youth basketball team on weekends. Everyone in the room enjoys virtual reality gaming, hosts a popular podcast about emerging technologies and can play the guitar if and only if they is a dedicated advocate for digital privacy and encryption. Doris develops open-source software projects in their free time. Doris enjoys virtual reality gaming, hosts a popular podcast about emerging technologies and can play the guitar.
It is not the case that “Doris plays the violin”.
neutral
room(doris)&(![X]:(room(X)=>(X='doris')))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(doris))& ((practices_urban_gardening(doris))&(enjoys_snowboarding(doris)))& (volunteers_for_local_environmental_conservation_projects(doris))& (![X]:(room(X)=>(mentors_a_youth_basketball_team_on_weekends(X))))& (mentors_a_youth_basketball_team_on_weekends(doris))& (![X]:(room(X)=>(((((enjoys_virtual_reality_gaming(X))&(hosts_a_popular_podcast_about_emerging_technologies(X))&(can_play_the_guitar(X))))<=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (develops_open-source_software_projects_in_their_free_time(doris))& (((enjoys_virtual_reality_gaming(doris))&(hosts_a_popular_podcast_about_emerging_technologies(doris))&(can_play_the_guitar(doris))))& ((![X]:((is_a_night_owl(X))<=>(enjoys_logic_puzzles(X)))))& (is_a_cybersecurity_expert(doris))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(doris))& (?[X]:(room(X)&(can_play_the_guitar(X))))& (practices_digital_art(doris))& (~![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(((plays_the_violin(X))&(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))))
room(doris)&(![X]:(room(X)=>(X='doris')))& ~(plays_the_violin(doris))
[]
null
0.020128
Eric is the only person in the room. If “A river does not flow uphill on Tuesdays.” then “no humble person is funny”. If “Eric does not collect rare minerals” then “Eric is a brave european, does not build model airplanes or is a sibling of Carl”. If “Carl is louder than Eric” then “Chad is younger than Eric”. “Everyone in the room is a sibling of Alvin or does not have lived in exactly three countries” only if “Eric is louder than Cornelia”. Everyone outside the room who is a client of Alvin cannot play the flute, does not enjoy skydiving or is poorer than Alvin. Eric is older than Alvin. Everyone in the room who is a brave wise curious tourist is a client of Cornelia. Eric is not liked by Carl. Cornelia and Eric hate each other. Eric does not enjoy making ceramics. Eric is a client of Alvin. Eric is a client of Chad. Chad is younger than Eric. Everyone in the room is patient if they is a client of Vickie. Eric is a sibling of Chad. Eric neither is younger than Charles nor does not collect rare minerals. Eric is not liked by Vickie. All curious person is tall. Chad and Eric like each other. At least one person in the room is a quiet curious tall person. All wise person is strong. Eric is quiet. Eric neither is a tall tourist nor is a sibling of Cornelia. Everyone in the room is a funny patient calm curious european or cannot play the flute. Someone who is a wise creative generous kind person like someone who is a brave european. Everyone in the room is funny if they is tall.
Eric is humble.
neutral
room(eric)&(![X]:(room(X)=>(X='eric')))& ((A_river_does_not_flow_uphill_on_Tuesdays.)=>(~?[X]:(humble(X)=>funny(X))))& ((does_not_collect_rare_minerals(eric))=>(((brave(eric)&european(eric))|(does_not_build_model_airplanes(eric))|(sibling(carl,eric)))))& ((louder(eric,carl))=>(younger(eric,chad)))& ((![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(sibling(alvin,X))))))=>(louder(cornelia,eric)))& (![X]:(~room(X)=>(((client(alvin,X))=>(((cannot_play_the_flute(X))|(does_not_enjoy_skydiving(X))|(poorer(alvin,X))))))))& (older(alvin,eric))& (![X]:(room(X)=>(((brave(X)&wise(X)&curious(X)&tourist(X))=>(client(cornelia,X))))))& (~like(eric,carl))& ((hate(cornelia,eric) & hate(eric,cornelia)))& (does_not_enjoy_making_ceramics(eric))& (client(alvin,eric))& (client(chad,eric))& (younger(eric,chad))& (![X]:(room(X)=>(((client(vickie,X))=>(patient(X))))))& (sibling(chad,eric))& (~((younger(charles,eric))|(does_not_collect_rare_minerals(eric))))& (~like(eric,vickie))& (![X]:(curious(X)=>tall(X)))& ((like(chad,eric) & like(eric,chad)))& (((?[X]:(room(X)&quiet(X)&curious(X)&tall(X)&person(X)))))& (![X]:(wise(X)=>strong(X)))& (quiet(eric))& (~((tall(eric)&tourist(eric))|(sibling(cornelia,eric))))& (![X]:(room(X)=>(((cannot_play_the_flute(X))|(funny(X)&patient(X)&calm(X)&curious(X)&european(X))))))& (?[X,Y]:((wise(X)&creative(X)&generous(X)&kind(X)&person(X))&(brave(Y)&european(Y))&(like(X,Y))))& (![X]:(room(X)=>(((tall(X))=>(funny(X))))))
room(eric)&(![X]:(room(X)=>(X='eric')))& humble(eric)
[]
null
0.386629
Jesse, Jeffry, Elaine, Stacy are the only persons in the room. Either "everyone in the room regularly goes on multi-day backpacking trips in national parks" or "everyone in the room does not regularly goes on multi-day backpacking trips in national parks and is not an avid hiker" but not both. Not everyone anywhere does not build model airplanes or collect rare sneakers or both. Not everyone in the room works on fridays if they is not an avid mountain climber who has scaled several peaks and vice versa. Everyone in the room who is not an avid mountain climber who has scaled several peaks is not a dedicated advocate for digital privacy and encryption. Everyone in the room is not a dedicated advocate for digital privacy and encryption if and only if they does not have completed a triathlon and does not have a curated collection of mid-century modern furniture. Everyone in the room does not regularly goes on multi-day backpacking trips in national parks and is not an avid hiker. Everyone in the room is an avid mountain climber who has scaled several peaks or is an avid hiker or both if they works on fridays or does not regularly goes on multi-day backpacking trips in national parks or both.
Jeffry is an avid mountain climber who has scaled several peaks.
entailment
room(jesse)&room(jeffry)&room(elaine)&room(stacy)&(![X]:(room(X)=>(X='jesse'|X='jeffry'|X='elaine'|X='stacy')))& ((![X]:(room(X)=>(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))&(is_not_an_avid_hiker(X)))))))& (~![X]:(anywhere(X)=>(((does_not_build_model_airplanes(X))|(collect_rare_sneakers(X))))))& (~![X]:(room(X)=>(((works_on_fridays(X))<=>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(((does_not_have_completed_a_triathlon(X))&(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))))& (?[X]:(room(X)&(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))& (![X]:(~room(X)=>(((((creates_augmented_reality_experiences_for_mobile_applications(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(owns_an_Android_phone(X))))))& (((creates_augmented_reality_experiences_for_mobile_applications(jesse))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(jesse))))& (![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(is_not_an_avid_hiker(X))))))& ((![X]:((is_not_a_chess_master_who_participates_in_national_tournaments(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))& (![X]:(room(X)=>(((((reads_mystery_novels(X))&(does_enjoy_trail_running(X))))=>(can_play_the_flute(X))))))& (![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((((works_on_fridays(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_an_avid_hiker(X))))))))
room(jesse)&room(jeffry)&room(elaine)&room(stacy)&(![X]:(room(X)=>(X='jesse'|X='jeffry'|X='elaine'|X='stacy')))& is_an_avid_mountain_climber_who_has_scaled_several_peaks(jeffry)
[ "p0", "p10", "p14", "hypothesis" ]
% SZS status Unsatisfiable for 610328299771211073187527 % SZS output start Proof for 610328299771211073187527 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 54. ! [X0] : (room(X0) => (~predn(X0) & ~prede(X0))) [input p10] 58. ! [X0] : (room(X0) => ((~prede(X0) | predx(X0)) => (predn(X0) | predj(X0)))) [input p14] 59. ~(predj(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 139. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 140. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 139] 148. ! [X0] : ((~predn(X0) & ~prede(X0)) | ~room(X0)) [ennf transformation 54] 151. ! [X0] : (((predn(X0) | predj(X0)) | (prede(X0) & ~predx(X0))) | ~room(X0)) [ennf transformation 58] 152. ! [X0] : (predn(X0) | predj(X0) | (prede(X0) & ~predx(X0)) | ~room(X0)) [flattening 151] 153. ~predj(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 154. ~predj(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 153] 169. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 170. ~predj(paul) | (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 154,169] 251. room(mary) [cnf transformation 140] 252. room(paul) [cnf transformation 140] 253. room(fred) [cnf transformation 140] 254. room(alice) [cnf transformation 140] 255. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 140] 274. ~prede(X0) | ~room(X0) [cnf transformation 148] 275. ~predn(X0) | ~room(X0) [cnf transformation 148] 278. ~room(X0) | predj(X0) | prede(X0) | predn(X0) [cnf transformation 152] 279. ~predj(paul) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 280. ~predj(paul) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 281. ~predj(paul) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 282. ~predj(paul) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 283. ~predj(paul) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 312. 7 <=> ! [X2] : (~predn(X2) | ~room(X2)) [avatar definition] 313. ~predn(X2) | ~room(X2) <- (7) [avatar component clause 312] 316. 8 <=> ! [X2] : (~prede(X2) | ~room(X2)) [avatar definition] 317. ~prede(X2) | ~room(X2) <- (8) [avatar component clause 316] 338. 7 [avatar split clause 275,312] 339. 8 [avatar split clause 274,316] 340. ~predj(paul) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,254] 341. ~predj(paul) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 340,253] 342. ~predj(paul) | alice != sK4 | ~room(mary) [subsumption resolution 341,252] 343. ~predj(paul) | alice != sK4 [subsumption resolution 342,251] 345. 13 <=> alice = sK4 [avatar definition] 347. alice != sK4 <- (~13) [avatar component clause 345] 349. 14 <=> predj(paul) [avatar definition] 352. ~13 | ~14 [avatar split clause 343,349,345] 353. ~predj(paul) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,254] 354. ~predj(paul) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 353,253] 355. ~predj(paul) | fred != sK4 | ~room(mary) [subsumption resolution 354,252] 356. ~predj(paul) | fred != sK4 [subsumption resolution 355,251] 358. 15 <=> fred = sK4 [avatar definition] 360. fred != sK4 <- (~15) [avatar component clause 358] 361. ~15 | ~14 [avatar split clause 356,349,358] 362. ~predj(paul) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 281,254] 363. ~predj(paul) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 362,253] 364. ~predj(paul) | paul != sK4 | ~room(mary) [subsumption resolution 363,252] 365. ~predj(paul) | paul != sK4 [subsumption resolution 364,251] 367. 16 <=> paul = sK4 [avatar definition] 370. ~16 | ~14 [avatar split clause 365,349,367] 371. ~predj(paul) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,254] 372. ~predj(paul) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 371,253] 373. ~predj(paul) | mary != sK4 | ~room(mary) [subsumption resolution 372,252] 374. ~predj(paul) | mary != sK4 [subsumption resolution 373,251] 376. 17 <=> mary = sK4 [avatar definition] 378. mary != sK4 <- (~17) [avatar component clause 376] 379. ~17 | ~14 [avatar split clause 374,349,376] 380. ~predj(paul) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,254] 381. ~predj(paul) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 380,253] 382. ~predj(paul) | room(sK4) | ~room(mary) [subsumption resolution 381,252] 383. ~predj(paul) | room(sK4) [subsumption resolution 382,251] 385. 18 <=> room(sK4) [avatar definition] 387. room(sK4) <- (18) [avatar component clause 385] 388. 18 | ~14 [avatar split clause 383,349,385] 391. predj(paul) | prede(paul) | predn(paul) [resolution 278,252] 408. 21 <=> predn(paul) [avatar definition] 410. predn(paul) <- (21) [avatar component clause 408] 412. 22 <=> prede(paul) [avatar definition] 414. prede(paul) <- (22) [avatar component clause 412] 476. 21 | 22 | 14 [avatar split clause 391,349,412,408] 577. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 <- (18) [resolution 255,387] 629. paul = sK4 | mary = sK4 | alice = sK4 <- (~15, 18) [subsumption resolution 577,360] 634. paul = sK4 | alice = sK4 <- (~15, ~17, 18) [subsumption resolution 629,378] 635. paul = sK4 <- (~13, ~15, ~17, 18) [subsumption resolution 634,347] 636. 16 | 13 | 15 | 17 | ~18 [avatar split clause 635,385,376,358,345,367] 668. ~room(paul) <- (7, 21) [resolution 410,313] 669. $false <- (7, 21) [subsumption resolution 668,252] 670. ~7 | ~21 [avatar contradiction clause 669] 681. ~room(paul) <- (8, 22) [resolution 414,317] 682. $false <- (8, 22) [subsumption resolution 681,252] 683. ~8 | ~22 [avatar contradiction clause 682] 684. $false [avatar sat refutation 338,339,352,361,370,379,388,476,636,670,683] % SZS output end Proof for 610328299771211073187527 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.026 s % ------------------------------ % ------------------------------
0.382292
Thomas is the only person in the room. If “everyone in the room does not participate in long-distance cycling events across the country or is a chess master who participates in national tournaments” then “it is not the case that “Thomas collects classic novels””. If “everyone in the room drives a hybrid car or does not read mystery novels” then “everyone in the room who participates in long-distance cycling events across the country drives a hybrid car”. If “someone anywhere can play the piano” then “Thomas who enjoys stargazing drives a hybrid car”. “Thomas is a certified scuba diver with advanced underwater photography skills and collects rare and antique scientific instruments” only if “it is not the case that “someone outside the room is not a certified scuba diver with advanced underwater photography skills””. If “everyone in the room develops open-source software projects in their free time or does not participate in long-distance cycling events across the country” then “more than one person in the room develops open-source software projects in their free time”. If “everyone anywhere does not participate in long-distance cycling events across the country or is a certified scuba diver with advanced underwater photography skills” then “Thomas uses a Windows laptop”. If “everyone in the room does not drive a hybrid car or collects rare and antique scientific instruments” then “everyone in the room who does not drive a hybrid car does not enjoy landscape photography”. Everyone in the room who drives a hybrid car can play the piano. Everyone in the room who does not drive a hybrid car does not enjoy landscape photography. Everyone anywhere does not participate in long-distance cycling events across the country or is a certified scuba diver with advanced underwater photography skills. Thomas who does not write poetry, does not read mystery novels and enjoys stargazing is passionate about collecting and restoring classic cars. Not everyone in the room who reads mystery novels or is a certified scuba diver with advanced underwater photography skills or both is not a Linux enthusiast. Everyone in the room does not participate in long-distance cycling events across the country if they is not a certified scuba diver with advanced underwater photography skills.
Thomas develops open-source software projects in their free time.
contradiction
room(thomas)&(![X]:(room(X)=>(X='thomas')))& ((![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))=>(~(collects_classic_novels(thomas))))& ((![X]:(room(X)=>(((does_not_read_mystery_novels(X))|(drives_a_hybrid_car(X))))))=>(![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(drives_a_hybrid_car(X)))))))& ((?[X]:(anywhere(X)&(can_play_the_piano(X))))=>((enjoys_stargazing(thomas))&(drives_a_hybrid_car(thomas))))& ((((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(thomas))&(collects_rare_and_antique_scientific_instruments(thomas))))=>(~(?[X]:(~room(X)&(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& ((![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(develops_open-source_software_projects_in_their_free_time(X))))))=>((?[X,Y]:(room(X)&room(Y)&(develops_open-source_software_projects_in_their_free_time(X)&develops_open-source_software_projects_in_their_free_time(Y))&(X!=Y)))))& ((![X]:(anywhere(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))=>(uses_a_Windows_laptop(thomas)))& ((![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(does_not_drive_a_hybrid_car(X))))))=>(![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))=>(does_not_enjoy_landscape_photography(X)))))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(can_play_the_piano(X))))))& (![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))=>(does_not_enjoy_landscape_photography(X))))))& (![X]:(anywhere(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))& ((((does_not_write_poetry(thomas))&(does_not_read_mystery_novels(thomas))&(enjoys_stargazing(thomas))))&(is_passionate_about_collecting_and_restoring_classic_cars(thomas)))& (~![X]:(room(X)=>(((((reads_mystery_novels(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(is_not_a_Linux_enthusiast(X))))))& (![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))& (~(~(?[X]:(room(X)&(is_a_wine_connoisseur(X))))))& (~(~(?[X]:(room(X)&(participates_in_long-distance_cycling_events_across_the_country(X))))))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(thomas))& (![X]:(room(X)=>(((writes_poetry(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (uses_a_Windows_laptop(thomas))
room(thomas)&(![X]:(room(X)=>(X='thomas')))& develops_open-source_software_projects_in_their_free_time(thomas)
[ "p0", "p5", "hypothesis" ]
% SZS status Unsatisfiable for 3064802494385108743389872 % SZS output start Proof for 3064802494385108743389872 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (predc(X0) | ~predp(X0))) => ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) [input p5] 63. predc(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 65. ! [X0] : (room(X0) => (predc(X0) | ~predp(X0))) => ? [X1,X2] : (X1 != X2 & predc(X2) & predc(X1) & room(X2) & room(X1)) [rectify 49] 158. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 162. ? [X1,X2] : (X1 != X2 & predc(X2) & predc(X1) & room(X2) & room(X1)) | ? [X0] : ((~predc(X0) & predp(X0)) & room(X0)) [ennf transformation 65] 163. ? [X1,X2] : (X1 != X2 & predc(X2) & predc(X1) & room(X2) & room(X1)) | ? [X0] : (~predc(X0) & predp(X0) & room(X0)) [flattening 162] 167. predc(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 63] 168. ? [X1,X2] : (X1 != X2 & predc(X2) & predc(X1) & room(X2) & room(X1)) | ~sP0 [predicate definition introduction] 169. sP0 | ? [X0] : (~predc(X0) & predp(X0) & room(X0)) [definition folding 163,168] 174. ? [X1,X2] : (X1 != X2 & predc(X2) & predc(X1) & room(X2) & room(X1)) | ~sP0 [nnf transformation 168] 175. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) | ~sP0 [rectify 174] 176. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) => (sK2 != sK3 & predc(sK3) & predc(sK2) & room(sK3) & room(sK2)) [choice axiom] 177. (sK2 != sK3 & predc(sK3) & predc(sK2) & room(sK3) & room(sK2)) | ~sP0 [skolemisation 175,176] 178. ? [X0] : (~predc(X0) & predp(X0) & room(X0)) => (~predc(sK4) & predp(sK4) & room(sK4)) [choice axiom] 179. sP0 | (~predc(sK4) & predp(sK4) & room(sK4)) [skolemisation 169,178] 268. ~room(X0) | mary = X0 [cnf transformation 158] 273. room(sK2) | ~sP0 [cnf transformation 177] 274. room(sK3) | ~sP0 [cnf transformation 177] 277. sK2 != sK3 | ~sP0 [cnf transformation 177] 278. sP0 | room(sK4) [cnf transformation 179] 280. sP0 | ~predc(sK4) [cnf transformation 179] 289. predc(mary) [cnf transformation 167] 318. 7 <=> sP0 [avatar definition] 322. 8 <=> sK2 = sK3 [avatar definition] 324. sK2 != sK3 <- (~8) [avatar component clause 322] 325. ~7 | ~8 [avatar split clause 277,322,318] 337. 11 <=> room(sK3) [avatar definition] 339. room(sK3) <- (11) [avatar component clause 337] 340. ~7 | 11 [avatar split clause 274,337,318] 342. 12 <=> room(sK2) [avatar definition] 344. room(sK2) <- (12) [avatar component clause 342] 345. ~7 | 12 [avatar split clause 273,342,318] 347. 13 <=> predc(sK4) [avatar definition] 349. ~predc(sK4) <- (~13) [avatar component clause 347] 350. ~13 | 7 [avatar split clause 280,318,347] 357. 15 <=> room(sK4) [avatar definition] 359. room(sK4) <- (15) [avatar component clause 357] 360. 15 | 7 [avatar split clause 278,318,357] 362. mary = sK2 <- (12) [resolution 268,344] 363. mary = sK3 <- (11) [resolution 268,339] 367. mary != sK3 <- (~8, 12) [backward demodulation 324,362] 370. $false <- (~8, 11, 12) [subsumption resolution 363,367] 371. 8 | ~11 | ~12 [avatar contradiction clause 370] 379. mary = sK4 <- (15) [resolution 359,268] 380. ~predc(mary) <- (~13, 15) [backward demodulation 349,379] 383. $false <- (~13, 15) [subsumption resolution 380,289] 384. 13 | ~15 [avatar contradiction clause 383] 385. $false [avatar sat refutation 325,340,345,350,360,371,384] % SZS output end Proof for 3064802494385108743389872 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------
0.255255
David, Carol are the only persons in the room. Everyone in the room does not have a piercing or does not write in-depth travel guides for off-the-beaten-path destinations. David does not write in-depth travel guides for off-the-beaten-path destinations. Everyone outside the room who composes and performs experimental electronic music has a piercing or writes in-depth travel guides for off-the-beaten-path destinations or both. At least one person anywhere neither enjoys camping and organizing outdoor survival workshops nor works on fridays. David has a tattoo, can play the flute and enjoys bird watching. Everyone in the room has a piercing if they owns an extensive assortment of vintage comic book memorabilia. David collects vintage vinyl records. At least one person in the room owns a significant collection of rare gemstones and minerals.
It is true that “David does not write in-depth travel guides for off-the-beaten-path destinations”.
entailment
room(david)&room(carol)&(![X]:(room(X)=>(X='david'|X='carol')))& (![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(does_not_have_a_piercing(X))))))& (does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(david))& (![X]:(~room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(((has_a_piercing(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))))& (((?[X]:(anywhere(X)&~((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(works_on_fridays(X)))))))& (((has_a_tattoo(david))&(can_play_the_flute(david))&(enjoys_bird_watching(david))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(has_a_piercing(X))))))& (collects_vintage_vinyl_records(david))& (((?[X]:(room(X)&owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))& (?[X]:(room(X)&(((plays_the_violin(X))|(does_not_collect_comic_books(X))|(uses_a_Windows_laptop(X))))))& (![X]:(anywhere(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(((frequently_participates_in_hackathons_and_coding_competitions(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(practices_calligraphy(X))))))))& (((?[X]:(anywhere(X)&((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(collects_first_edition_books(X)))))))& (((does_not_enjoy_kayaking_and_exploring_remote_waterways(david))<~>(enjoys_kayaking_and_exploring_remote_waterways(david))))& (((?[X]:(room(X)&collects_first_edition_books(X)))))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(david))& (![X]:(room(X)=>(((((does_not_play_the_violin(X))&(plays_video_games(X))))=>(~((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(has_a_tattoo(X))))))))& (~![X]:(room(X)=>(((((practices_calligraphy(X))&(uses_a_Windows_laptop(X))))=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(has_a_piercing(X))))))))& (![X]:(room(X)=>(((((is_a_professional_photographer_specializing_in_portrait_photography(X))|(has_a_piercing(X))))=>(~((is_right-handed(X))|(collects_comic_books(X))))))))& (((?[X]:(room(X)&uses_a_Windows_laptop(X)))&(![X,Y]:((room(X)&room(Y)&(uses_a_Windows_laptop(X))&(uses_a_Windows_laptop(Y)))=>(X=Y)))))
room(david)&room(carol)&(![X]:(room(X)=>(X='david'|X='carol')))& does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(david)
[ "p0", "p2", "hypothesis" ]
% SZS status Unsatisfiable for 1431416280088445680867383 % SZS output start Proof for 1431416280088445680867383 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. ~predk(mary) [input p2] 64. ~(~predk(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 156. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 157. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 156] 168. predk(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 64] 169. predk(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 168] 185. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 186. predk(mary) | (paul != sK6 & mary != sK6 & room(sK6)) | ~room(paul) | ~room(mary) [skolemisation 169,185] 267. room(mary) [cnf transformation 157] 268. room(paul) [cnf transformation 157] 269. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 157] 271. ~predk(mary) [cnf transformation 46] 291. predk(mary) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 186] 292. predk(mary) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 186] 293. predk(mary) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 186] 304. paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 293,271] 305. paul != sK6 | ~room(mary) [subsumption resolution 304,268] 306. paul != sK6 [subsumption resolution 305,267] 307. mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 292,271] 308. mary != sK6 | ~room(mary) [subsumption resolution 307,268] 309. mary != sK6 [subsumption resolution 308,267] 310. room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 291,271] 311. room(sK6) | ~room(mary) [subsumption resolution 310,268] 312. room(sK6) [subsumption resolution 311,267] 325. mary = sK6 | paul = sK6 [resolution 269,312] 371. paul = sK6 [subsumption resolution 325,309] 372. $false [subsumption resolution 371,306] % SZS output end Proof for 1431416280088445680867383 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------
0.030069
Edith is the only person in the room. If “everyone in the room enjoys origami or is not a dedicated advocate for digital privacy and encryption” then “Edith does practice yoga”. “Edith owns a telescope” only if “everyone in the room is a wine connoisseur with a private cellar of vintage wines and is not a wine connoisseur with a private cellar of vintage wines”. If “Edith does not stream on Twitch” then “everyone in the room who is not a dedicated advocate for digital privacy and encryption enjoys origami”. Edith works on fridays. Everyone in the room does not enjoy watercolor painting if and only if they owns a telescope. Edith does not practice yoga. Everyone in the room has a saltwater aquarium only if they collects rare minerals. Everyone in the room either collects vintage vinyl records or is a dedicated advocate for digital privacy and encryption but not both. Everyone in the room owns a telescope if and only if they streams on Twitch. Everyone in the room streams on Twitch only if they either is a dedicated advocate for digital privacy and encryption or can play the harmonica but not both. Edith collects action figures. Everyone in the room who streams on Twitch is not a culinary enthusiast who experiments with international cuisines.
Edith owns a telescope.
contradiction
room(edith)&(![X]:(room(X)=>(X='edith')))& ((![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(enjoys_origami(X))))))=>(does_practice_yoga(edith)))& ((owns_a_telescope(edith))=>(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& ((does_not_stream_on_Twitch(edith))=>(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(enjoys_origami(X)))))))& (works_on_fridays(edith))& (![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))<=>(owns_a_telescope(X))))))& (does_not_practice_yoga(edith))& (![X]:(room(X)=>(((collects_rare_minerals(X))<=(has_a_saltwater_aquarium(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))<~>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((owns_a_telescope(X))<=>(streams_on_Twitch(X))))))& (![X]:(room(X)=>(((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<~>(can_play_the_harmonica(X))))<=(streams_on_Twitch(X))))))& (collects_action_figures(edith))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))
room(edith)&(![X]:(room(X)=>(X='edith')))& owns_a_telescope(edith)
[ "p1", "p2", "p6", "hypothesis" ]
% SZS status Unsatisfiable for 7900822308135526097748414 % SZS output start Proof for 7900822308135526097748414 45. ! [X0] : (room(X0) => (predp(X0) | ~predm(X0))) => preds(mary) [input p1] 46. predw(mary) => ! [X0] : (room(X0) => (~predi(X0) & predi(X0))) [input p2] 50. ~preds(mary) [input p6] 57. predw(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 135. preds(mary) | ? [X0] : ((~predp(X0) & predm(X0)) & room(X0)) [ennf transformation 45] 136. preds(mary) | ? [X0] : (~predp(X0) & predm(X0) & room(X0)) [flattening 135] 137. ! [X0] : ((~predi(X0) & predi(X0)) | ~room(X0)) | ~predw(mary) [ennf transformation 46] 145. predw(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 57] 147. ? [X0] : (~predp(X0) & predm(X0) & room(X0)) => (~predp(sK0) & predm(sK0) & room(sK0)) [choice axiom] 148. preds(mary) | (~predp(sK0) & predm(sK0) & room(sK0)) [skolemisation 136,147] 235. preds(mary) | room(sK0) [cnf transformation 148] 238. predi(X0) | ~room(X0) | ~predw(mary) [cnf transformation 137] 239. ~predi(X0) | ~room(X0) | ~predw(mary) [cnf transformation 137] 243. ~preds(mary) [cnf transformation 50] 252. predw(mary) [cnf transformation 145] 258. 2 <=> preds(mary) [avatar definition] 268. 4 <=> room(sK0) [avatar definition] 270. room(sK0) <- (4) [avatar component clause 268] 271. 4 | 2 [avatar split clause 235,258,268] 273. 5 <=> predw(mary) [avatar definition] 277. 6 <=> ! [X0] : (~predi(X0) | ~room(X0)) [avatar definition] 278. ~predi(X0) | ~room(X0) <- (6) [avatar component clause 277] 279. ~5 | 6 [avatar split clause 239,277,273] 281. 7 <=> ! [X0] : (predi(X0) | ~room(X0)) [avatar definition] 282. predi(X0) | ~room(X0) <- (7) [avatar component clause 281] 283. ~5 | 7 [avatar split clause 238,281,273] 292. ~2 [avatar split clause 243,258] 293. 5 [avatar split clause 252,273] 294. ~room(X0) <- (6, 7) [subsumption resolution 278,282] 295. $false <- (4, 6, 7) [subsumption resolution 270,294] 296. ~4 | ~6 | ~7 [avatar contradiction clause 295] 297. $false [avatar sat refutation 271,279,283,292,293,296] % SZS output end Proof for 7900822308135526097748414 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------
0.316146
David is the only person in the room. Everyone in the room who does not host regular game nights featuring complex strategy games and mentors a youth basketball team on weekends neither enjoys snowboarding nor has a specialized collection of handmade artisan pottery unless everyone in the room knows morse code or does not practice yoga. Everyone in the room does not know morse code or collects first edition books only if David collects first edition books. Everyone in the room collects limited-edition art prints from contemporary artists. David does not host regular game nights featuring complex strategy games and mentors a youth basketball team on weekends. Not everyone in the room enjoys kayaking and exploring remote waterways if and only if they has completed a triathlon. If someone collects antique jewelry then he/she does not have lived in exactly three countries, practices archery and does not have completed a triathlon. Everyone in the room competes in national level swimming championships if they practices archery. Everyone in the room who competes in national level swimming championships enjoys kayaking and exploring remote waterways. At least one person in the room has completed a triathlon. Everyone in the room is not a scotch connoisseur if they has a saltwater aquarium, enjoys kayaking and exploring remote waterways and collects first edition books. Everyone in the room who is not a scotch connoisseur has lived in exactly three countries. David who has completed a triathlon enjoys skydiving, cannot play the piano or can play the piano. Everyone in the room who has a saltwater aquarium mentors a youth basketball team on weekends. David either has lived in exactly three countries or is a dedicated advocate for digital privacy and encryption but not both. David neither does practice yoga nor enjoys making ceramics. Everyone in the room who has a specialized collection of handmade artisan pottery enjoys skydiving. David is a scotch connoisseur. David is a cybersecurity expert. David who collects first edition books can play the piano. If someone hosts regular game nights featuring complex strategy games then he/she is a scotch connoisseur.
David has lived in exactly three countries.
neutral
room(david)&(![X]:(room(X)=>(X='david')))& (~(![X]:(room(X)=>(((does_not_practice_yoga(X))|(knows_morse_code(X))))))=>(![X]:(room(X)=>(((((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))&(mentors_a_youth_basketball_team_on_weekends(X))))=>(~((enjoys_snowboarding(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))))& ((![X]:(room(X)=>(((collects_first_edition_books(X))|(does_not_know_morse_code(X))))))=>(collects_first_edition_books(david)))& (![X]:(room(X)=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))& (((does_not_host_regular_game_nights_featuring_complex_strategy_games(david))&(mentors_a_youth_basketball_team_on_weekends(david))))& (~![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))<=>(has_completed_a_triathlon(X))))))& ((![X]:((collects_antique_jewelry(X))=>(((does_not_have_lived_in_exactly_three_countries(X))&(practices_archery(X))&(does_not_have_completed_a_triathlon(X)))))))& (![X]:(room(X)=>(((practices_archery(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (((?[X]:(room(X)&has_completed_a_triathlon(X)))))& (![X]:(room(X)=>(((((has_a_saltwater_aquarium(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))&(collects_first_edition_books(X))))=>(is_not_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))=>(has_lived_in_exactly_three_countries(X))))))& ((has_completed_a_triathlon(david))&(((enjoys_skydiving(david))|(cannot_play_the_piano(david))|(can_play_the_piano(david)))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (((has_lived_in_exactly_three_countries(david))<~>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(david))))& (~((does_practice_yoga(david))|(enjoys_making_ceramics(david))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(enjoys_skydiving(X))))))& (is_a_scotch_connoisseur(david))& (is_a_cybersecurity_expert(david))& ((collects_first_edition_books(david))&(can_play_the_piano(david)))& ((![X]:((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(is_a_scotch_connoisseur(X)))))& (![X]:(room(X)=>(((((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))&(mentors_a_youth_basketball_team_on_weekends(X))))=>(~((enjoys_snowboarding(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (collects_first_edition_books(david))& (![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))=>(does_not_enjoy_snowboarding(X))))))& (((?[X]:(room(X)&has_completed_a_triathlon(X)))&(![X,Y]:((room(X)&room(Y)&(has_completed_a_triathlon(X))&(has_completed_a_triathlon(Y)))=>(X=Y)))))& ((![X]:((enjoys_skydiving(X))<=>(((is_an_active_member_of_a_local_robotics_club(X))&(practices_archery(X))&(is_a_scotch_connoisseur(X)))))))
room(david)&(![X]:(room(X)=>(X='david')))& has_lived_in_exactly_three_countries(david)
[]
null
0
Lisa, Holly, Allen, Wesley, John are the only persons in the room. Everyone in the room does not own a high-end gaming PC with custom-built components or is dedicated to sustainable living and zero-waste practices. Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or does not own a high-end gaming PC with custom-built components. Everyone anywhere does not enjoy macrame or is not an enthusiastic bird watcher who travels for rare sightings. Everyone in the room who does not enjoy macrame is an avid mountain climber who has scaled several peaks. Everyone in the room who is an avid mountain climber who has scaled several peaks enjoys macrame. Everyone in the room is an amateur astronomer who builds and uses custom telescopes only if they enjoys making ceramics. At least one person in the room is dedicated to sustainable living and zero-waste practices. Lisa who uses a Windows laptop is an avid mountain climber who has scaled several peaks. It is not the case that "more than one person in the room uses a Windows laptop".
Holly uses a Windows laptop.
contradiction
room(lisa)&room(holly)&room(allen)&room(wesley)&room(john)&(![X]:(room(X)=>(X='lisa'|X='holly'|X='allen'|X='wesley'|X='john')))& (![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(is_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))|(does_not_enjoy_macrame(X))))))& (![X]:(room(X)=>(((does_not_enjoy_macrame(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(enjoys_macrame(X))))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))<=(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (((?[X]:(room(X)&is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& (![X]:(~room(X)=>(((enjoys_skydiving(X))<=(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(~room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& ((uses_a_Windows_laptop(lisa))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(lisa)))& (![X]:(room(X)=>(((((creates_augmented_reality_experiences_for_mobile_applications(X))<~>(is_an_avid_hiker(X))))<=(((collects_antique_clocks(X))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))& (~![X]:(room(X)=>(((((is_an_avid_hiker(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(owns_an_Android_phone(X))))=>(uses_a_Windows_laptop(X))))))& ((![X]:((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=>(uses_a_Windows_laptop(X)))))& (![X]:(anywhere(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (?[X]:(room(X)&(creates_augmented_reality_experiences_for_mobile_applications(X))))& (![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (~((?[X,Y]:(room(X)&room(Y)&(uses_a_Windows_laptop(X)&uses_a_Windows_laptop(Y))&(X!=Y)))))& ((lisa_dream=>(![X]:(~room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<=>(((uses_a_Windows_laptop(X))&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))))& ((is_passionate_about_collecting_and_restoring_classic_cars(lisa))&(((enjoys_skydiving(lisa))|(does_practice_yoga(lisa))|(enjoys_stand-up_paddleboarding(lisa)))))& (~![X]:(room(X)=>(((does_practice_yoga(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))=>(collects_antique_clocks(X))))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=(((collects_vintage_vinyl_records(X))|(enjoys_virtual_reality_gaming(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))<=(((is_right-handed(X))<~>(enjoys_making_ceramics(X))))))))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_use_a_Windows_laptop(X))))))& (((?[X]:(room(X)&is_right-handed(X)))&(![X,Y]:((room(X)&room(Y)&(is_right-handed(X))&(is_right-handed(Y)))=>(X=Y)))))
room(lisa)&room(holly)&room(allen)&room(wesley)&room(john)&(![X]:(room(X)=>(X='lisa'|X='holly'|X='allen'|X='wesley'|X='john')))& uses_a_Windows_laptop(holly)
[ "b42", "p0", "p11", "p18", "hypothesis" ]
% SZS status Unsatisfiable for 6405293783912059971355841 % SZS output start Proof for 6405293783912059971355841 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 55. predl(mary) & predf(mary) [input p11] 62. ~? [X0,X1] : (X0 != X1 & predf(X1) & predf(X0) & room(X1) & room(X0)) [input p18] 71. predf(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] 154. ! [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] 155. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 154] 176. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0)) [ennf transformation 62] 188. predf(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 71] 189. predf(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 188] 248. mary != paul [cnf transformation 43] 284. room(mary) [cnf transformation 155] 285. room(paul) [cnf transformation 155] 299. predf(mary) [cnf transformation 55] 311. ~predf(X1) | X0 = X1 | ~predf(X0) | ~room(X1) | ~room(X0) [cnf transformation 176] 329. predf(paul) [cnf transformation 189] 454. mary = X0 | ~predf(X0) | ~room(mary) | ~room(X0) [resolution 311,299] 456. ~predf(X0) | mary = X0 | ~room(X0) [subsumption resolution 454,284] 459. mary = paul | ~room(paul) [resolution 456,329] 460. ~room(paul) [subsumption resolution 459,248] 461. $false [subsumption resolution 460,285] % SZS output end Proof for 6405293783912059971355841 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------
0.190964
There is a room. Everyone in the room plays eSports competitively if they does not collect first edition books.
Everyone in the room collects luxury watches.
neutral
(there_is_a_room)& (![X]:(room(X)=>(((does_not_collect_first_edition_books(X))=>(plays_eSports_competitively(X))))))& (((?[X]:(room(X)&does_not_collect_first_edition_books(X)))))& (![X]:(room(X)=>(((practices_calligraphy(X))<=>(does_not_collect_rare_sneakers(X))))))& ((![X]:((plays_eSports_competitively(X))=>(collects_luxury_watches(X)))))& (~?[X]:(room(X)=>(((has_a_piercing(X))=>(is_a_wine_connoisseur(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (?[X]:(room(X)&(((does_not_practice_calligraphy(X))|(practices_calligraphy(X))|(is_a_wine_connoisseur(X))))))& (~![X]:(room(X)=>(((does_not_have_a_piercing(X))|(enjoys_stargazing(X))))))& (![X]:(~room(X)=>(((((practices_calligraphy(X))|(is_a_wine_connoisseur(X))|(collects_luxury_watches(X))))=>(((has_a_piercing(X))|(collect_rare_sneakers(X))))))))& (?[X]:(room(X)&(((creates_large-scale_murals_for_public_art_installations(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((has_a_piercing(X))=>(is_not_a_coffee_connoisseur(X))))))& ((![X]:((is_a_wine_connoisseur(X))=>(((enjoys_stargazing(X))|(is_a_coffee_connoisseur(X))|(does_not_play_eSports_competitively(X)))))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(plays_eSports_competitively(X))))))& (~![X]:(room(X)=>(((collect_rare_sneakers(X))&(practices_calligraphy(X))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(((is_a_wine_connoisseur(X))&(plays_eSports_competitively(X))))))))& (![X]:(room(X)=>(((((is_a_wine_connoisseur(X))&(plays_eSports_competitively(X))))=>(practices_calligraphy(X))))))
(there_is_a_room)& ![X]:(room(X)=>(collects_luxury_watches(X)))
[]
null
0.118465
Matilde is the only person in the room. If 'someone in the room uses an ios phone, enjoys windsurfing and enjoys wildlife photography' then 'Matilde who owns a significant collection of rare gemstones and minerals practices kickboxing'. Matilde who enjoys kayaking and exploring remote waterways, enjoys origami and makes intricate hand-cut paper art for exhibitions uses an ios phone. Matilde who owns a smartwatch owns a smart tv. Matilde who makes intricate hand-cut paper art for exhibitions owns a significant collection of rare gemstones and minerals.
Matilde owns a significant collection of rare gemstones and minerals, uses an ios phone and owns a smart tv.
entailment
room(matilde)&(![X]:(room(X)=>(X='matilde')))& ((?[X]:(room(X)&(((uses_an_ios_phone(X))&(enjoys_windsurfing(X))&(enjoys_wildlife_photography(X))))))=>((owns_a_significant_collection_of_rare_gemstones_and_minerals(matilde))&(practices_kickboxing(matilde))))& (~(~(?[X]:(room(X)&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))=>(((?[X]:(room(X)&is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(Y)))=>(X=Y))))))& ((~(~(?[X]:(room(X)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(?[X]:(room(X)&(((enjoys_origami(X))&(collects_foreign_coins(X))&(enjoys_rooftop_gardening(X)))))))& ((~(?[X]:(room(X)&(enjoys_rooftop_gardening(X)))))=>(?[X]:(room(X)&(enjoys_macrame(X)))))& ((enjoys_wildlife_photography(matilde))&(makes_intricate_hand-cut_paper_art_for_exhibitions(matilde)))& (?[X]:(room(X)&(owns_a_smart_tv(X))))& ((enjoys_stargazing(matilde))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(matilde)))& ((![X]:((uses_an_ios_phone(X))=>(enjoys_wildlife_photography(X)))))& (((?[X]:(room(X)&enjoys_macrame(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_macrame(X))&(enjoys_macrame(Y)))=>(X=Y)))))& ((((enjoys_kayaking_and_exploring_remote_waterways(matilde))&(enjoys_origami(matilde))&(makes_intricate_hand-cut_paper_art_for_exhibitions(matilde))))&(uses_an_ios_phone(matilde)))& (~((?[X,Y]:(room(X)&room(Y)&(enjoys_rooftop_gardening(X)&enjoys_rooftop_gardening(Y))&(X!=Y)))))& (?[X]:(room(X)&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))& ((owns_a_smartwatch(matilde))&(owns_a_smart_tv(matilde)))& (?[X]:(anywhere(X)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))& (((?[X]:(room(X)&is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(Y)))=>(X=Y)))))& ((![X]:((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(enjoys_stargazing(X)))))& ((![X]:((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(uses_an_ios_phone(X)))))& ((makes_intricate_hand-cut_paper_art_for_exhibitions(matilde))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(matilde)))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(collects_comic_books(X)))))
room(matilde)&(![X]:(room(X)=>(X='matilde')))& ((owns_a_significant_collection_of_rare_gemstones_and_minerals(matilde))&(uses_an_ios_phone(matilde))&(owns_a_smart_tv(matilde)))
[ "p0", "p10", "p13", "p18", "hypothesis" ]
% SZS status Unsatisfiable for 7986470571161557516903013 % SZS output start Proof for 7986470571161557516903013 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 54. preda(mary) & predh(mary) & predf(mary) & predy(mary) [input p10] 57. predb(mary) & predd(mary) [input p13] 62. prede(mary) & predh(mary) [input p18] 64. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 73. predb(mary) [pure predicate removal 57] 74. preda(mary) & predh(mary) & predf(mary) [pure predicate removal 54] 79. prede(mary) [pure predicate removal 62] 80. preda(mary) & predf(mary) [pure predicate removal 74] 82. preda(mary) [pure predicate removal 80] 161. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 172. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 64] 192. ? [X0] : (mary != X0 & room(X0)) => (mary != sK8 & room(sK8)) [choice axiom] 193. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK8 & room(sK8)) | ~room(mary) [skolemisation 172,192] 274. room(mary) [cnf transformation 161] 275. ~room(X0) | mary = X0 [cnf transformation 161] 291. preda(mary) [cnf transformation 82] 295. predb(mary) [cnf transformation 73] 300. prede(mary) [cnf transformation 79] 301. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK8) | ~room(mary) [cnf transformation 193] 302. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK8 | ~room(mary) [cnf transformation 193] 354. ~preda(mary) | ~prede(mary) | mary != sK8 | ~room(mary) [subsumption resolution 302,295] 355. ~prede(mary) | mary != sK8 | ~room(mary) [subsumption resolution 354,291] 356. mary != sK8 | ~room(mary) [subsumption resolution 355,300] 357. mary != sK8 [subsumption resolution 356,274] 358. ~preda(mary) | ~prede(mary) | room(sK8) | ~room(mary) [subsumption resolution 301,295] 359. ~prede(mary) | room(sK8) | ~room(mary) [subsumption resolution 358,291] 360. room(sK8) | ~room(mary) [subsumption resolution 359,300] 361. room(sK8) [subsumption resolution 360,274] 378. mary = sK8 [resolution 275,361] 394. $false [subsumption resolution 378,357] % SZS output end Proof for 7986470571161557516903013 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0.561909
Allyson, Gavin, Evelyn are the only persons in the room. If not everyone in the room participates in long-distance cycling events across the country then everyone in the room works as a freelance web developer specializing in e-commerce sites if they collects vintage stamps. Everyone in the room works as a freelance web developer specializing in e-commerce sites only if they either does not read mystery novels or reads mystery novels but not both. Allyson dreamt that everyone in the room is not a dedicated advocate for digital privacy and encryption if they collects action figures. Only one person anywhere owns an Android phone. Everyone in the room who either is a client of Costco or creates bespoke furniture pieces from reclaimed wood but not both plays eSports competitively. Everyone outside the room creates bespoke furniture pieces from reclaimed wood if they plays eSports competitively. Everyone in the room who participates in long-distance cycling events across the country is a certified scuba diver with advanced underwater photography skills. Everyone in the room who is a certified scuba diver with advanced underwater photography skills creates bespoke furniture pieces from reclaimed wood. Everyone in the room is passionate about collecting and restoring classic cars if they creates bespoke furniture pieces from reclaimed wood. Everyone in the room is passionate about collecting and restoring classic cars only if they is not a Linux enthusiast. Everyone anywhere who enjoys spelunking mentors a youth basketball team on weekends. Everyone anywhere who mentors a youth basketball team on weekends owns a smart tv. Everyone outside the room is not a client of Costco if they plays the violin. Everyone in the room who is not a client of Costco does not have a specialized collection of handmade artisan pottery. Everyone in the room can play the piano if they does not have a specialized collection of handmade artisan pottery. Not everyone in the room is a coffee connoisseur only if they enjoys spelunking. Everyone in the room who enjoys spelunking enjoys rooftop gardening. Everyone in the room is a certified scuba diver with advanced underwater photography skills only if they enjoys rooftop gardening. Everyone in the room enjoys rooftop gardening only if they owns a smart tv. It is true that everyone in the room is not a client of Costco if they owns a smart tv. Not everyone anywhere is a Linux enthusiast if they is not a client of Costco. Everyone in the room creates bespoke furniture pieces from reclaimed wood if they is a Linux enthusiast. If someone is a tea enthusiast then he/she is a coffee connoisseur and vice versa. Everyone anywhere does not enjoy rooftop gardening only if they is a Linux enthusiast.
Allyson can play the piano.
entailment
room(allyson)&room(gavin)&room(evelyn)&(![X]:(room(X)=>(X='allyson'|X='gavin'|X='evelyn')))& ((~![X]:(room(X)=>(participates_in_long-distance_cycling_events_across_the_country(X))))=>(![X]:(room(X)=>(((collects_vintage_stamps(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))& (![X]:(room(X)=>(((((does_not_read_mystery_novels(X))<~>(reads_mystery_novels(X))))<=(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& ((allyson_dream=>(![X]:(room(X)=>(((collects_action_figures(X))=>(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))))& (((?[X]:(anywhere(X)&owns_an_Android_phone(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(owns_an_Android_phone(X))&(owns_an_Android_phone(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((((is_a_client_of_Costco(X))<~>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(plays_eSports_competitively(X))))))& (![X]:(~room(X)=>(((plays_eSports_competitively(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(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))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))<=(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(anywhere(X)=>(((enjoys_spelunking(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (![X]:(anywhere(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(owns_a_smart_tv(X))))))& (![X]:(~room(X)=>(((plays_the_violin(X))=>(is_not_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((is_not_a_client_of_Costco(X))=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))=>(can_play_the_piano(X))))))& (~![X]:(room(X)=>(((enjoys_spelunking(X))<=(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))<=(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))<=(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))=>(is_not_a_client_of_Costco(X))))))& (~![X]:(anywhere(X)=>(((is_not_a_client_of_Costco(X))=>(is_a_Linux_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& ((![X]:((is_a_tea_enthusiast(X))<=>(is_a_coffee_connoisseur(X)))))& (![X]:(~room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(does_not_regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))=>(enjoys_spelunking(X))))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(enjoys_bird_watching(X))))))& (![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))<=(collects_action_figures(X))))))& (![X]:(anywhere(X)=>(((is_a_Linux_enthusiast(X))<=(does_not_enjoy_rooftop_gardening(X))))))
room(allyson)&room(gavin)&room(evelyn)&(![X]:(room(X)=>(X='allyson'|X='gavin'|X='evelyn')))& can_play_the_piano(allyson)
[ "b4", "p0", "p9", "p10", "p14", "p15", "p19", "p20", "p22", "p28", "hypothesis" ]
% SZS status Unsatisfiable for 8024709814567636678812917 % SZS output start Proof for 8024709814567636678812917 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 53. ! [X0] : (room(X0) => (predq(X0) => predm(X0))) [input p9] 54. ! [X0] : (room(X0) => (predm(X0) => ~predv(X0))) [input p10] 58. ! [X0] : (room(X0) => (~predn(X0) => ~predt(X0))) [input p14] 59. ! [X0] : (room(X0) => (~predt(X0) => predr(X0))) [input p15] 63. ! [X0] : (room(X0) => (preds(X0) => predi(X0))) [input p19] 64. ! [X0] : (room(X0) => (predi(X0) => ~predn(X0))) [input p20] 66. ! [X0] : (room(X0) => (predv(X0) => predq(X0))) [input p22] 72. ! [X0] : (anywhere(X0) => (~preds(X0) => predv(X0))) [input p28] 73. ~(predr(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 163. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 164. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 163] 171. ! [X0] : ((predm(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 53] 172. ! [X0] : (predm(X0) | ~predq(X0) | ~room(X0)) [flattening 171] 173. ! [X0] : ((~predv(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 54] 174. ! [X0] : (~predv(X0) | ~predm(X0) | ~room(X0)) [flattening 173] 175. ! [X0] : ((~predt(X0) | predn(X0)) | ~room(X0)) [ennf transformation 58] 176. ! [X0] : (~predt(X0) | predn(X0) | ~room(X0)) [flattening 175] 177. ! [X0] : ((predr(X0) | predt(X0)) | ~room(X0)) [ennf transformation 59] 178. ! [X0] : (predr(X0) | predt(X0) | ~room(X0)) [flattening 177] 180. ! [X0] : ((predi(X0) | ~preds(X0)) | ~room(X0)) [ennf transformation 63] 181. ! [X0] : (predi(X0) | ~preds(X0) | ~room(X0)) [flattening 180] 182. ! [X0] : ((~predn(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 64] 183. ! [X0] : (~predn(X0) | ~predi(X0) | ~room(X0)) [flattening 182] 186. ! [X0] : ((predq(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 66] 187. ! [X0] : (predq(X0) | ~predv(X0) | ~room(X0)) [flattening 186] 188. ! [X0] : ((predv(X0) | preds(X0)) | ~anywhere(X0)) [ennf transformation 72] 189. ! [X0] : (predv(X0) | preds(X0) | ~anywhere(X0)) [flattening 188] 190. ~predr(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 73] 191. ~predr(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 190] 200. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 201. ~predr(mary) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 191,200] 202. anywhere(X0) [cnf transformation 5] 283. room(mary) [cnf transformation 164] 284. room(paul) [cnf transformation 164] 285. room(fred) [cnf transformation 164] 286. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 164] 293. ~predq(X0) | predm(X0) | ~room(X0) [cnf transformation 172] 294. ~predv(X0) | ~predm(X0) | ~room(X0) [cnf transformation 174] 295. ~predt(X0) | predn(X0) | ~room(X0) [cnf transformation 176] 296. ~room(X0) | predt(X0) | predr(X0) [cnf transformation 178] 298. ~preds(X0) | predi(X0) | ~room(X0) [cnf transformation 181] 299. ~predi(X0) | ~predn(X0) | ~room(X0) [cnf transformation 183] 303. ~predv(X0) | predq(X0) | ~room(X0) [cnf transformation 187] 304. predv(X0) | preds(X0) | ~anywhere(X0) [cnf transformation 189] 305. ~predr(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 201] 306. ~predr(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 201] 307. ~predr(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 201] 308. ~predr(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 201] 311. preds(X0) | predv(X0) [subsumption resolution 304,202] 312. ~predr(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 308,285] 313. ~predr(mary) | fred != sK3 | ~room(mary) [subsumption resolution 312,284] 314. ~predr(mary) | fred != sK3 [subsumption resolution 313,283] 316. 1 <=> fred = sK3 [avatar definition] 318. fred != sK3 <- (~1) [avatar component clause 316] 320. 2 <=> predr(mary) [avatar definition] 323. ~1 | ~2 [avatar split clause 314,320,316] 324. ~predr(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 307,285] 325. ~predr(mary) | paul != sK3 | ~room(mary) [subsumption resolution 324,284] 326. ~predr(mary) | paul != sK3 [subsumption resolution 325,283] 328. 3 <=> paul = sK3 [avatar definition] 330. paul != sK3 <- (~3) [avatar component clause 328] 331. ~3 | ~2 [avatar split clause 326,320,328] 332. ~predr(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 306,285] 333. ~predr(mary) | mary != sK3 | ~room(mary) [subsumption resolution 332,284] 334. ~predr(mary) | mary != sK3 [subsumption resolution 333,283] 336. 4 <=> mary = sK3 [avatar definition] 338. mary != sK3 <- (~4) [avatar component clause 336] 339. ~4 | ~2 [avatar split clause 334,320,336] 340. ~predr(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 305,285] 341. ~predr(mary) | room(sK3) | ~room(mary) [subsumption resolution 340,284] 342. ~predr(mary) | room(sK3) [subsumption resolution 341,283] 344. 5 <=> room(sK3) [avatar definition] 346. room(sK3) <- (5) [avatar component clause 344] 347. 5 | ~2 [avatar split clause 342,320,344] 348. predt(mary) | predr(mary) [resolution 296,283] 380. ~room(X0) | predi(X0) | predv(X0) [resolution 298,311] 391. 13 <=> predq(mary) [avatar definition] 393. predq(mary) <- (13) [avatar component clause 391] 396. 14 <=> predt(mary) [avatar definition] 398. predt(mary) <- (14) [avatar component clause 396] 399. 2 | 14 [avatar split clause 348,396,320] 410. predn(mary) | ~room(mary) <- (14) [resolution 398,295] 411. predn(mary) <- (14) [subsumption resolution 410,283] 415. predi(mary) | predv(mary) [resolution 380,283] 420. 17 <=> predv(mary) [avatar definition] 422. predv(mary) <- (17) [avatar component clause 420] 424. 18 <=> predi(mary) [avatar definition] 426. predi(mary) <- (18) [avatar component clause 424] 427. 17 | 18 [avatar split clause 415,424,420] 455. predq(mary) | ~room(mary) <- (17) [resolution 422,303] 456. ~predm(mary) | ~room(mary) <- (17) [resolution 422,294] 457. predq(mary) <- (17) [subsumption resolution 455,283] 458. 13 | ~17 [avatar split clause 457,420,391] 459. ~predm(mary) <- (17) [subsumption resolution 456,283] 473. predm(mary) | ~room(mary) <- (13) [resolution 393,293] 474. ~room(mary) <- (13, 17) [subsumption resolution 473,459] 475. $false <- (13, 17) [subsumption resolution 474,283] 476. ~13 | ~17 [avatar contradiction clause 475] 478. ~predn(mary) | ~room(mary) <- (18) [resolution 426,299] 479. ~room(mary) <- (14, 18) [subsumption resolution 478,411] 480. $false <- (14, 18) [subsumption resolution 479,283] 481. ~14 | ~18 [avatar contradiction clause 480] 610. paul = sK3 | mary = sK3 | fred = sK3 <- (5) [resolution 286,346] 624. mary = sK3 | fred = sK3 <- (~3, 5) [subsumption resolution 610,330] 625. fred = sK3 <- (~3, ~4, 5) [subsumption resolution 624,338] 626. $false <- (~1, ~3, ~4, 5) [subsumption resolution 625,318] 627. 1 | 3 | 4 | ~5 [avatar contradiction clause 626] 628. $false [avatar sat refutation 323,331,339,347,399,427,458,476,481,627] % SZS output end Proof for 8024709814567636678812917 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s % ------------------------------ % ------------------------------
0.293306
There is a room. Everyone in the room either enjoys writing detailed reviews of new and classic board games or is a happy person but not both. Everyone in the room is a funny person. No one in the room has lived in exactly three countries. Everyone in the room is a funny person if they has a piercing or is a happy person or both. All happy persons are generous. All generous persons are funny. Everyone outside the room is a happy person. Everyone in the room enjoys writing detailed reviews of new and classic board games only if they is a generous funny person.
Not everyone in the room is a generous person.
contradiction
(there_is_a_room)& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<~>(happy(X)&person(X))))))& (![X]:(room(X)=>(funny(X)&person(X))))& (~?[X]:(room(X)=>(has_lived_in_exactly_three_countries(X))))& (![X]:(room(X)=>(((((has_a_piercing(X))|(happy(X)&person(X))))=>(funny(X)&person(X))))))& (![X]:(happy(X)=>generous(X)))& (![X]:(generous(X)=>funny(X)))& (![X]:(~room(X)=>(happy(X)&person(X))))& (![X]:(room(X)=>(((generous(X)&funny(X)&person(X))<=(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))
(there_is_a_room)& ~![X]:(room(X)=>(generous(X)&person(X)))
[ "p1", "p2", "p3", "p5", "p8", "hypothesis" ]
% SZS status Unsatisfiable for 7217756398489823200631125 % SZS output start Proof for 7217756398489823200631125 45. ! [X0] : (room(X0) => (predz(X0) <~> (person(X0) & happy(X0)))) [input p1] 46. ! [X0] : (room(X0) => (person(X0) & funny(X0))) [input p2] 47. ~? [X0] : (room(X0) => predr(X0)) [input p3] 49. ! [X0] : (happy(X0) => generous(X0)) [input p5] 52. ! [X0] : (room(X0) => (predz(X0) => (person(X0) & funny(X0) & generous(X0)))) [input p8] 53. ~! [X0] : (room(X0) => (person(X0) & generous(X0))) & there_is_a_room [input hypothesis] 55. ~? [X0] : ~room(X0) [pure predicate removal 47] 57. ! [X0] : (room(X0) => person(X0)) [pure predicate removal 46] 59. ! [X0] : (room(X0) => (predz(X0) => (person(X0) & generous(X0)))) [pure predicate removal 52] 61. ~! [X0] : (room(X0) => (person(X0) & generous(X0))) [pure predicate removal 53] 134. ! [X0] : ((predz(X0) <~> (person(X0) & happy(X0))) | ~room(X0)) [ennf transformation 45] 135. ! [X0] : (person(X0) | ~room(X0)) [ennf transformation 57] 136. ! [X0] : room(X0) [ennf transformation 55] 139. ! [X0] : (generous(X0) | ~happy(X0)) [ennf transformation 49] 141. ! [X0] : (((person(X0) & generous(X0)) | ~predz(X0)) | ~room(X0)) [ennf transformation 59] 142. ! [X0] : ((person(X0) & generous(X0)) | ~predz(X0) | ~room(X0)) [flattening 141] 143. ? [X0] : ((~person(X0) | ~generous(X0)) & room(X0)) [ennf transformation 61] 145. ! [X0] : ((((~person(X0) | ~happy(X0)) | ~predz(X0)) & ((person(X0) & happy(X0)) | predz(X0))) | ~room(X0)) [nnf transformation 134] 146. ! [X0] : (((~person(X0) | ~happy(X0) | ~predz(X0)) & ((person(X0) & happy(X0)) | predz(X0))) | ~room(X0)) [flattening 145] 147. ? [X0] : ((~person(X0) | ~generous(X0)) & room(X0)) => ((~person(sK0) | ~generous(sK0)) & room(sK0)) [choice axiom] 148. (~person(sK0) | ~generous(sK0)) & room(sK0) [skolemisation 143,147] 229. ~room(X0) | predz(X0) | happy(X0) [cnf transformation 146] 232. ~room(X0) | person(X0) [cnf transformation 135] 233. room(X0) [cnf transformation 136] 235. ~happy(X0) | generous(X0) [cnf transformation 139] 238. generous(X0) | ~predz(X0) | ~room(X0) [cnf transformation 142] 241. ~person(sK0) | ~generous(sK0) [cnf transformation 148] 242. ~predz(X0) | generous(X0) [subsumption resolution 238,233] 244. 1 <=> generous(sK0) [avatar definition] 246. ~generous(sK0) <- (~1) [avatar component clause 244] 248. 2 <=> person(sK0) [avatar definition] 250. ~person(sK0) <- (~2) [avatar component clause 248] 251. ~1 | ~2 [avatar split clause 241,248,244] 252. person(X0) [resolution 232,233] 253. happy(X0) | predz(X0) [resolution 229,233] 255. predz(X0) | generous(X0) [resolution 253,235] 256. generous(X0) [subsumption resolution 255,242] 258. $false <- (~1) [resolution 256,246] 259. 1 [avatar contradiction clause 258] 260. $false <- (~2) [subsumption resolution 250,252] 261. 2 [avatar contradiction clause 260] 262. $false [avatar sat refutation 251,259,261] % SZS output end Proof for 7217756398489823200631125 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------
0.156739
Sidney, Ruben, Christopher are the only persons in the room. If 'everyone in the room does not enjoy skydiving or owns a smartwatch' then 'everyone in the room who does not enjoy skydiving is a skilled home brewer experimenting with craft beer recipes'. If 'everyone in the room is not a skilled home brewer experimenting with craft beer recipes or owns a 3D printer' then 'everyone outside the room who is not a skilled home brewer experimenting with craft beer recipes practices tai chi'.
Everyone anywhere owns a smartwatch.
neutral
room(sidney)&room(ruben)&room(christopher)&(![X]:(room(X)=>(X='sidney'|X='ruben'|X='christopher')))& ((![X]:(room(X)=>(((owns_a_smartwatch(X))|(does_not_enjoy_skydiving(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_skydiving(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))& ((![X]:(room(X)=>(((owns_a_3D_printer(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(![X]:(~room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(practices_tai_chi(X)))))))& ((![X]:(room(X)=>(((owns_a_smartwatch(X))|(does_not_own_a_3D_printer(X))))))=>((![X]:((practices_tai_chi(X))=>(owns_a_smartwatch(X))))))& (~(![X]:(anywhere(X)=>(((owns_a_3D_printer(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(![X]:(~room(X)=>(((((uses_a_Windows_laptop(X))|(practices_tai_chi(X))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))& (~(?[X]:(room(X)&(practices_tai_chi(X))))=>(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(knows_morse_code(X)))))))& ((![X]:(room(X)=>(((practices_tai_chi(X))|(does_not_own_a_3D_printer(X))))))=>(~![X]:(~room(X)=>(((does_not_own_a_3D_printer(X))=>(is_allergic_to_anything(X)))))))& ((![X]:(room(X)=>(((enjoys_skydiving(X))|(cannot_play_the_piano(X))))))=>(![X]:(anywhere(X)=>(((knows_morse_code(X))=>(owns_a_smartwatch(X)))))))& ((![X]:(room(X)=>(((owns_a_3D_printer(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(((can_play_the_piano(X))<~>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))))& ((![X]:(room(X)=>(((knows_morse_code(X))|(cannot_play_the_piano(X))))))=>(![X]:(~room(X)=>(((enjoys_skydiving(X))<=>(can_play_the_piano(X)))))))& ((![X]:(room(X)=>(((is_allergic_to_anything(X))|(is_not_allergic_to_anything(X))))))=>((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(ruben))&(owns_a_3D_printer(ruben))))& (![X]:(anywhere(X)=>(((is_not_allergic_to_anything(X))=>(((can_play_the_piano(X))<~>(is_allergic_to_anything(X))))))))& ((![X]:((practices_tai_chi(X))=>(can_play_the_piano(X)))))& (![X]:(~room(X)=>(((((knows_morse_code(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))=>(practices_tai_chi(X))))))& (![X]:(room(X)=>(((practices_tai_chi(X))<=>(uses_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(knows_morse_code(X))))))& ((uses_a_Windows_laptop(sidney))&(is_allergic_to_anything(sidney)))& ((knows_morse_code(sidney))&(((owns_a_3D_printer(sidney))|(knows_morse_code(sidney)))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(is_allergic_to_anything(X))))))& ((![X]:((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))& (?[X]:(room(X)&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))& ((![X]:((is_allergic_to_anything(X))=>(knows_morse_code(X)))))
room(sidney)&room(ruben)&room(christopher)&(![X]:(room(X)=>(X='sidney'|X='ruben'|X='christopher')))& ![X]:(anywhere(X)=>(owns_a_smartwatch(X)))
[]
null
0.355521
Darren, Jay, Daniel, Jennifer are the only persons in the room. If 'someone in the room has a curated collection of mid-century modern furniture' then 'if someone works as a freelance web developer specializing in e-commerce sites then he/she collects vintage vinyl records'. Either 'everyone in the room does not work as a freelance web developer specializing in e-commerce sites or collects vintage vinyl records' or 'Darren enjoys making ceramics or enjoys logic puzzles or both' but not both. Darren who enjoys making ceramics enjoys landscape photography.
Jay has a curated collection of mid-century modern furniture.
contradiction
room(darren)&room(jay)&room(daniel)&room(jennifer)&(![X]:(room(X)=>(X='darren'|X='jay'|X='daniel'|X='jennifer')))& ((?[X]:(room(X)&(has_a_curated_collection_of_mid-century_modern_furniture(X))))=>((![X]:((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(collects_vintage_vinyl_records(X))))))& ((![X]:(room(X)=>(((collects_vintage_vinyl_records(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))<~>(((enjoys_making_ceramics(darren))|(enjoys_logic_puzzles(darren)))))& ((![X]:(room(X)=>(((can_play_the_guitar(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))=>(~(~(~(enjoys_landscape_photography(darren))))))& (((enjoys_making_ceramics(darren))|(enjoys_logic_puzzles(darren))))& ((![X]:((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(~((is_a_Linux_enthusiast(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(collects_vintage_vinyl_records(X))))))& ((enjoys_making_ceramics(darren))&(enjoys_landscape_photography(darren)))& (?[X]:(room(X)&(collects_rare_minerals(X))))& (collects_vintage_vinyl_records(darren))& (can_play_the_guitar(darren))& ((![X]:((collects_rare_minerals(X))=>(trains_for_and_competes_in_international_triathlons(X)))))& (enjoys_macrame(darren))& (((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(darren))&(enjoys_logic_puzzles(darren))&(practices_kickboxing(darren))))& ((collects_rare_minerals(darren))&(can_play_the_guitar(darren)))& ((can_play_the_guitar(darren))&(does_not_have_a_curated_collection_of_mid-century_modern_furniture(darren)))& (enjoys_coding_in_Python(darren))& ((![X]:((enjoys_landscape_photography(X))=>(enjoys_making_ceramics(X)))))& ((![X]:((trains_for_and_competes_in_international_triathlons(X))=>(practices_kickboxing(X)))))& (practices_pilates(darren))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(darren))& (collects_rare_minerals(darren))
room(darren)&room(jay)&room(daniel)&room(jennifer)&(![X]:(room(X)=>(X='darren'|X='jay'|X='daniel'|X='jennifer')))& has_a_curated_collection_of_mid-century_modern_furniture(jay)
[ "p0", "p1", "p2", "p7", "hypothesis" ]
% SZS status Unsatisfiable for 3380000925187245184349162 % SZS output start Proof for 3380000925187245184349162 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ? [X0] : (predh(X0) & room(X0)) => ! [X0] : (predm(X0) => predl(X0)) [input p1] 46. ! [X0] : (room(X0) => (~predm(X0) | predl(X0))) <~> (predo(mary) | predk(mary)) [input p2] 51. preda(mary) & predk(mary) [input p7] 66. predh(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 67. ? [X0] : (predh(X0) & room(X0)) => ! [X1] : (predm(X1) => predl(X1)) [rectify 45] 150. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 151. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 150] 152. ! [X1] : (predl(X1) | ~predm(X1)) | ! [X0] : (~predh(X0) | ~room(X0)) [ennf transformation 67] 153. ! [X0] : ((~predm(X0) | predl(X0)) | ~room(X0)) <~> (predo(mary) | predk(mary)) [ennf transformation 46] 154. ! [X0] : (~predm(X0) | predl(X0) | ~room(X0)) <~> (predo(mary) | predk(mary)) [flattening 153] 160. predh(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 66] 161. predh(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 160] 163. ! [X0] : (predl(X0) | ~predm(X0)) | ! [X1] : (~predh(X1) | ~room(X1)) [rectify 152] 164. ((~predo(mary) & ~predk(mary)) | ? [X0] : (predm(X0) & ~predl(X0) & room(X0))) & ((predo(mary) | predk(mary)) | ! [X0] : (~predm(X0) | predl(X0) | ~room(X0))) [nnf transformation 154] 165. ((~predo(mary) & ~predk(mary)) | ? [X0] : (predm(X0) & ~predl(X0) & room(X0))) & (predo(mary) | predk(mary) | ! [X0] : (~predm(X0) | predl(X0) | ~room(X0))) [flattening 164] 166. ((~predo(mary) & ~predk(mary)) | ? [X0] : (predm(X0) & ~predl(X0) & room(X0))) & (predo(mary) | predk(mary) | ! [X1] : (~predm(X1) | predl(X1) | ~room(X1))) [rectify 165] 167. ? [X0] : (predm(X0) & ~predl(X0) & room(X0)) => (predm(sK0) & ~predl(sK0) & room(sK0)) [choice axiom] 168. ((~predo(mary) & ~predk(mary)) | (predm(sK0) & ~predl(sK0) & room(sK0))) & (predo(mary) | predk(mary) | ! [X1] : (~predm(X1) | predl(X1) | ~room(X1))) [skolemisation 166,167] 254. room(paul) [cnf transformation 151] 258. predl(X0) | ~predm(X0) | ~predh(X1) | ~room(X1) [cnf transformation 163] 261. ~predk(mary) | ~predl(sK0) [cnf transformation 168] 262. ~predk(mary) | predm(sK0) [cnf transformation 168] 271. predk(mary) [cnf transformation 51] 289. predh(paul) [cnf transformation 161] 291. 1 <=> ! [X1] : (~predh(X1) | ~room(X1)) [avatar definition] 292. ~predh(X1) | ~room(X1) <- (1) [avatar component clause 291] 294. 2 <=> ! [X0] : (predl(X0) | ~predm(X0)) [avatar definition] 295. ~predm(X0) | predl(X0) <- (2) [avatar component clause 294] 296. 1 | 2 [avatar split clause 258,294,291] 298. 3 <=> predm(sK0) [avatar definition] 300. predm(sK0) <- (3) [avatar component clause 298] 307. 5 <=> predl(sK0) [avatar definition] 309. ~predl(sK0) <- (~5) [avatar component clause 307] 317. 7 <=> predk(mary) [avatar definition] 320. 3 | ~7 [avatar split clause 262,317,298] 321. ~5 | ~7 [avatar split clause 261,317,307] 343. 7 [avatar split clause 271,317] 349. predl(sK0) <- (2, 3) [resolution 295,300] 350. $false <- (2, 3, ~5) [subsumption resolution 349,309] 351. ~2 | ~3 | 5 [avatar contradiction clause 350] 352. ~room(paul) <- (1) [resolution 292,289] 353. $false <- (1) [subsumption resolution 352,254] 354. ~1 [avatar contradiction clause 353] 355. $false [avatar sat refutation 296,320,321,343,351,354] % SZS output end Proof for 3380000925187245184349162 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------
0.321716
Cody, Linette are the only persons in the room. Cody is the oldest in the room. Cody is not a tall person. It is not the case that “Linette is a old person”. If someone is a tall person then he/she is not a tall person or is a tall person or both. Cody is not a quiet person. Cody neither is a old person nor is a tall person. Linette is a quiet person. Linette is the richest in the room. Only one person anywhere is a quiet person and is a old person. Cody is not a tall person or is a old person or both. Linette is not a tall person. Someone who neither is not a old person nor is a quiet person is older than someone who is not a old person.
Cody is quiet.
neutral
room(cody)&room(linette)&(![X]:(room(X)=>(X='cody'|X='linette')))& (![X]:((room(X)&(X!=cody))=>older(X,cody)))& (~(tall(cody)&person(cody)))& (~(old(linette)&person(linette)))& ((![X]:((tall(X)&person(X))=>(((~(tall(X)&person(X)))|(tall(X)&person(X)))))))& (~(quiet(cody)&person(cody)))& (~((old(cody)&person(cody))|(tall(cody)&person(cody))))& (quiet(linette)&person(linette))& (![X]:((room(X)&(X!=linette))=>richer(X,linette)))& (((?[X]:(anywhere(X)&((quiet(X)&person(X))&(old(X)&person(X)))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(((quiet(X)&person(X))&(old(X)&person(X))))&(((quiet(Y)&person(Y))&(old(Y)&person(Y)))))=>(X=Y)))))& (((~(tall(cody)&person(cody)))|(old(cody)&person(cody))))& (~(tall(linette)&person(linette)))& (?[X,Y]:((~((~(old(X)&person(X)))|(quiet(X)&person(X))))&(~(old(Y)&person(Y)))&(older(X,Y))))
room(cody)&room(linette)&(![X]:(room(X)=>(X='cody'|X='linette')))& quiet(cody)
[]
null
0.38314
Elizabeth is the only person in the room. No funny person is happy. Everyone in the room who is calm is not old, not happy. Everyone outside the room is not old, not happy only if they is humble. No one anywhere is a curious funny person if they is a creative person. Someone who is not a patient tall old person is older than someone who is calm. Everyone anywhere who neither is not a happy person nor is not a funny person is not a brave old humble person.
All curious person is tall.
entailment
room(elizabeth)&(![X]:(room(X)=>(X='elizabeth')))& (~?[X]:(funny(X)=>happy(X)))& (![X]:(room(X)=>(((calm(X))=>(~old(X)&~happy(X))))))& (![X]:(~room(X)=>(((humble(X))<=(~old(X)&~happy(X))))))& (~?[X]:(anywhere(X)=>(((creative(X)&person(X))=>(curious(X)&funny(X)&person(X))))))& (?[X,Y]:((~(patient(X)&tall(X)&old(X)&person(X)))&(calm(Y))&(older(X,Y))))& (![X]:(anywhere(X)=>(((~((~(happy(X)&person(X)))|(~(funny(X)&person(X)))))=>(~(brave(X)&old(X)&humble(X)&person(X)))))))& (![X]:(room(X)=>(((~(brave(X)&old(X)&humble(X)&person(X)))=>(~~calm(X))))))& (![X]:(strong(X)=>wise(X)))
room(elizabeth)&(![X]:(room(X)=>(X='elizabeth')))& ![X]:(curious(X)=>tall(X))
[ "p0", "p1", "p4", "hypothesis" ]
% SZS status Unsatisfiable for 6285570479363064828258263 % SZS output start Proof for 6285570479363064828258263 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ~? [X0] : (funny(X0) => happy(X0)) [input p1] 48. ~? [X0] : (anywhere(X0) => ((person(X0) & creative(X0)) => (person(X0) & funny(X0) & curious(X0)))) [input p4] 53. ~(! [X0] : (curious(X0) => tall(X0)) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 54. ~(! [X0] : (curious(X0) => tall(X0)) & ! [X1] : (room(X1) => mary = X1) & room(mary)) [rectify 53] 57. ~(! [X0] : ~curious(X0) & ! [X1] : (room(X1) => mary = X1) & room(mary)) [pure predicate removal 54] 58. ~? [X0] : (anywhere(X0) => (person(X0) => (person(X0) & funny(X0) & curious(X0)))) [pure predicate removal 48] 130. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 131. ! [X0] : (~happy(X0) & funny(X0)) [ennf transformation 45] 136. ! [X0] : (((~person(X0) | ~funny(X0) | ~curious(X0)) & person(X0)) & anywhere(X0)) [ennf transformation 58] 137. ! [X0] : ((~person(X0) | ~funny(X0) | ~curious(X0)) & person(X0) & anywhere(X0)) [flattening 136] 142. ? [X0] : curious(X0) | ? [X1] : (mary != X1 & room(X1)) | ~room(mary) [ennf transformation 57] 146. ? [X0] : curious(X0) => curious(sK2) [choice axiom] 147. ? [X1] : (mary != X1 & room(X1)) => (mary != sK3 & room(sK3)) [choice axiom] 148. curious(sK2) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 142,147,146] 230. room(mary) [cnf transformation 130] 231. ~room(X0) | mary = X0 [cnf transformation 130] 232. funny(X0) [cnf transformation 131] 238. person(X0) [cnf transformation 137] 239. ~person(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 137] 247. curious(sK2) | room(sK3) | ~room(mary) [cnf transformation 148] 248. curious(sK2) | mary != sK3 | ~room(mary) [cnf transformation 148] 251. ~curious(X0) | ~person(X0) [subsumption resolution 239,232] 252. curious(sK2) | mary != sK3 [subsumption resolution 248,230] 254. 1 <=> mary = sK3 [avatar definition] 256. mary != sK3 <- (~1) [avatar component clause 254] 258. 2 <=> curious(sK2) [avatar definition] 260. curious(sK2) <- (2) [avatar component clause 258] 261. ~1 | 2 [avatar split clause 252,258,254] 262. curious(sK2) | room(sK3) [subsumption resolution 247,230] 264. 3 <=> room(sK3) [avatar definition] 266. room(sK3) <- (3) [avatar component clause 264] 267. 3 | 2 [avatar split clause 262,258,264] 268. ~person(sK2) <- (2) [resolution 251,260] 269. $false <- (2) [subsumption resolution 268,238] 270. ~2 [avatar contradiction clause 269] 272. mary = sK3 <- (3) [resolution 231,266] 273. $false <- (~1, 3) [subsumption resolution 272,256] 274. 1 | ~3 [avatar contradiction clause 273] 275. $false [avatar sat refutation 261,267,270,274] % SZS output end Proof for 6285570479363064828258263 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0.000061
There is a room. “If someone mentors a youth basketball team on weekends, enjoys origami and can play the guitar then he/she frequently participates in hackathons and coding competitions and vice versa” if “everyone anywhere frequently participates in hackathons and coding competitions”. “Everyone in the room does not frequently participates in hackathons and coding competitions or does not mentor a youth basketball team on weekends” only if “everyone in the room who does not frequently participates in hackathons and coding competitions does not frequently participates in hackathons and coding competitions, can play the guitar and does not enjoy origami”. “Everyone in the room can play the guitar or cannot play the guitar” only if “everyone in the room mentors a youth basketball team on weekends and does not stream on Twitch if they frequently participates in hackathons and coding competitions”. “Everyone in the room frequently participates in hackathons and coding competitions if and only if they streams on Twitch” if “everyone in the room frequently participates in hackathons and coding competitions or cannot play the guitar”. Everyone in the room enjoys origami. If someone neither can play the guitar nor does not mentor a youth basketball team on weekends then he/she streams on Twitch, mentors a youth basketball team on weekends or frequently participates in hackathons and coding competitions. If someone mentors a youth basketball team on weekends then he/she does not enjoy origami and frequently participates in hackathons and coding competitions and vice versa. Everyone in the room who streams on Twitch can play the guitar. Everyone in the room who can play the guitar enjoys origami. If someone neither frequently participates in hackathons and coding competitions nor streams on Twitch then he/she can play the guitar.
Everyone outside the room mentors a youth basketball team on weekends.
contradiction
(there_is_a_room)& ((![X]:(anywhere(X)=>(frequently_participates_in_hackathons_and_coding_competitions(X))))=>((![X]:((((mentors_a_youth_basketball_team_on_weekends(X))&(enjoys_origami(X))&(can_play_the_guitar(X))))<=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& ((![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))&(can_play_the_guitar(X))&(does_not_enjoy_origami(X)))))))))& ((![X]:(room(X)=>(((cannot_play_the_guitar(X))|(can_play_the_guitar(X))))))=>(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(((mentors_a_youth_basketball_team_on_weekends(X))&(does_not_stream_on_Twitch(X)))))))))& ((![X]:(room(X)=>(((cannot_play_the_guitar(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))<=>(streams_on_Twitch(X)))))))& (![X]:(room(X)=>(enjoys_origami(X))))& ((![X]:((~((can_play_the_guitar(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))=>(((streams_on_Twitch(X))|(mentors_a_youth_basketball_team_on_weekends(X))|(frequently_participates_in_hackathons_and_coding_competitions(X)))))))& ((![X]:((mentors_a_youth_basketball_team_on_weekends(X))<=>(((does_not_enjoy_origami(X))&(frequently_participates_in_hackathons_and_coding_competitions(X)))))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(enjoys_origami(X))))))& ((![X]:((~((frequently_participates_in_hackathons_and_coding_competitions(X))|(streams_on_Twitch(X))))=>(can_play_the_guitar(X)))))
(there_is_a_room)& ![X]:(~room(X)=>(mentors_a_youth_basketball_team_on_weekends(X)))
[ "p1", "p2", "p3", "p4", "p5", "p7", "hypothesis" ]
% SZS status Unsatisfiable for 1593137530111068170332891 % SZS output start Proof for 1593137530111068170332891 45. ! [X0] : (anywhere(X0) => preda(X0)) => ! [X0] : ((predd(X0) & prede(X0) & predc(X0)) <=> preda(X0)) [input p1] 46. ! [X0] : (room(X0) => (~preda(X0) | ~predc(X0))) => ! [X0] : (room(X0) => (~preda(X0) => (~prede(X0) & predd(X0) & ~preda(X0)))) [input p2] 47. ! [X0] : (room(X0) => (predd(X0) | ~predd(X0))) => ! [X0] : (room(X0) => (preda(X0) => (~predb(X0) & predc(X0)))) [input p3] 48. ! [X0] : (room(X0) => (preda(X0) | ~predd(X0))) => ! [X0] : (room(X0) => (preda(X0) <=> predb(X0))) [input p4] 49. ! [X0] : (room(X0) => prede(X0)) [input p5] 51. ! [X0] : (predc(X0) <=> (preda(X0) & ~prede(X0))) [input p7] 55. ! [X0] : (~room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 56. ! [X0] : (anywhere(X0) => preda(X0)) => ! [X1] : ((predd(X1) & prede(X1) & predc(X1)) <=> preda(X1)) [rectify 45] 57. ! [X0] : (room(X0) => (~preda(X0) | ~predc(X0))) => ! [X1] : (room(X1) => (~preda(X1) => (~prede(X1) & predd(X1) & ~preda(X1)))) [rectify 46] 58. ! [X0] : (room(X0) => (predd(X0) | ~predd(X0))) => ! [X1] : (room(X1) => (preda(X1) => (~predb(X1) & predc(X1)))) [rectify 47] 59. ! [X0] : (room(X0) => (preda(X0) | ~predd(X0))) => ! [X1] : (room(X1) => (preda(X1) <=> predb(X1))) [rectify 48] 61. ! [X0] : (~room(X0) => predc(X0)) [pure predicate removal 55] 62. ! [X0] : preda(X0) => ! [X1] : ((predd(X1) & prede(X1) & predc(X1)) <=> preda(X1)) [pure predicate removal 56] 135. ! [X1] : ((predd(X1) & prede(X1) & predc(X1)) <=> preda(X1)) | ? [X0] : ~preda(X0) [ennf transformation 62] 136. ! [X1] : (((~prede(X1) & predd(X1) & ~preda(X1)) | preda(X1)) | ~room(X1)) | ? [X0] : ((preda(X0) & predc(X0)) & room(X0)) [ennf transformation 57] 137. ! [X1] : ((~prede(X1) & predd(X1) & ~preda(X1)) | preda(X1) | ~room(X1)) | ? [X0] : (preda(X0) & predc(X0) & room(X0)) [flattening 136] 138. ! [X1] : (((~predb(X1) & predc(X1)) | ~preda(X1)) | ~room(X1)) | ? [X0] : ((~predd(X0) & predd(X0)) & room(X0)) [ennf transformation 58] 139. ! [X1] : ((~predb(X1) & predc(X1)) | ~preda(X1) | ~room(X1)) | ? [X0] : (~predd(X0) & predd(X0) & room(X0)) [flattening 138] 140. ! [X1] : ((preda(X1) <=> predb(X1)) | ~room(X1)) | ? [X0] : ((~preda(X0) & predd(X0)) & room(X0)) [ennf transformation 59] 141. ! [X1] : ((preda(X1) <=> predb(X1)) | ~room(X1)) | ? [X0] : (~preda(X0) & predd(X0) & room(X0)) [flattening 140] 142. ! [X0] : (prede(X0) | ~room(X0)) [ennf transformation 49] 151. ! [X0] : (predc(X0) | room(X0)) [ennf transformation 61] 152. ? [X0] : (preda(X0) & predc(X0) & room(X0)) | ~sP0 [predicate definition introduction] 153. ! [X1] : ((~prede(X1) & predd(X1) & ~preda(X1)) | preda(X1) | ~room(X1)) | sP0 [definition folding 137,152] 155. ! [X1] : (((predd(X1) & prede(X1) & predc(X1)) | ~preda(X1)) & (preda(X1) | (~predd(X1) | ~prede(X1) | ~predc(X1)))) | ? [X0] : ~preda(X0) [nnf transformation 135] 156. ! [X1] : (((predd(X1) & prede(X1) & predc(X1)) | ~preda(X1)) & (preda(X1) | ~predd(X1) | ~prede(X1) | ~predc(X1))) | ? [X0] : ~preda(X0) [flattening 155] 157. ! [X0] : (((predd(X0) & prede(X0) & predc(X0)) | ~preda(X0)) & (preda(X0) | ~predd(X0) | ~prede(X0) | ~predc(X0))) | ? [X1] : ~preda(X1) [rectify 156] 158. ? [X1] : ~preda(X1) => ~preda(sK1) [choice axiom] 159. ! [X0] : (((predd(X0) & prede(X0) & predc(X0)) | ~preda(X0)) & (preda(X0) | ~predd(X0) | ~prede(X0) | ~predc(X0))) | ~preda(sK1) [skolemisation 157,158] 160. ? [X0] : (preda(X0) & predc(X0) & room(X0)) | ~sP0 [nnf transformation 152] 161. ? [X0] : (preda(X0) & predc(X0) & room(X0)) => (preda(sK2) & predc(sK2) & room(sK2)) [choice axiom] 162. (preda(sK2) & predc(sK2) & room(sK2)) | ~sP0 [skolemisation 160,161] 163. ! [X0] : ((~prede(X0) & predd(X0) & ~preda(X0)) | preda(X0) | ~room(X0)) | sP0 [rectify 153] 164. ! [X0] : ((~predb(X0) & predc(X0)) | ~preda(X0) | ~room(X0)) | ? [X1] : (~predd(X1) & predd(X1) & room(X1)) [rectify 139] 165. ? [X1] : (~predd(X1) & predd(X1) & room(X1)) => (~predd(sK3) & predd(sK3) & room(sK3)) [choice axiom] 166. ! [X0] : ((~predb(X0) & predc(X0)) | ~preda(X0) | ~room(X0)) | (~predd(sK3) & predd(sK3) & room(sK3)) [skolemisation 164,165] 167. ! [X1] : (((preda(X1) | ~predb(X1)) & (predb(X1) | ~preda(X1))) | ~room(X1)) | ? [X0] : (~preda(X0) & predd(X0) & room(X0)) [nnf transformation 141] 168. ! [X0] : (((preda(X0) | ~predb(X0)) & (predb(X0) | ~preda(X0))) | ~room(X0)) | ? [X1] : (~preda(X1) & predd(X1) & room(X1)) [rectify 167] 169. ? [X1] : (~preda(X1) & predd(X1) & room(X1)) => (~preda(sK4) & predd(sK4) & room(sK4)) [choice axiom] 170. ! [X0] : (((preda(X0) | ~predb(X0)) & (predb(X0) | ~preda(X0))) | ~room(X0)) | (~preda(sK4) & predd(sK4) & room(sK4)) [skolemisation 168,169] 171. ! [X0] : ((predc(X0) | (~preda(X0) | prede(X0))) & ((preda(X0) & ~prede(X0)) | ~predc(X0))) [nnf transformation 51] 172. ! [X0] : ((predc(X0) | ~preda(X0) | prede(X0)) & ((preda(X0) & ~prede(X0)) | ~predc(X0))) [flattening 171] 255. prede(X0) | ~preda(X0) | ~preda(sK1) [cnf transformation 159] 257. room(sK2) | ~sP0 [cnf transformation 162] 258. predc(sK2) | ~sP0 [cnf transformation 162] 262. ~prede(X0) | preda(X0) | ~room(X0) | sP0 [cnf transformation 163] 267. ~predb(X0) | ~preda(X0) | ~room(X0) | predd(sK3) [cnf transformation 166] 268. ~predb(X0) | ~preda(X0) | ~room(X0) | ~predd(sK3) [cnf transformation 166] 269. predb(X0) | ~preda(X0) | ~room(X0) | room(sK4) [cnf transformation 170] 271. predb(X0) | ~preda(X0) | ~room(X0) | ~preda(sK4) [cnf transformation 170] 275. ~room(X0) | prede(X0) [cnf transformation 142] 277. ~prede(X0) | ~predc(X0) [cnf transformation 172] 278. ~predc(X0) | preda(X0) [cnf transformation 172] 283. room(X0) | predc(X0) [cnf transformation 151] 285. 1 <=> preda(sK1) [avatar definition] 287. ~preda(sK1) <- (~1) [avatar component clause 285] 293. 3 <=> ! [X0] : (prede(X0) | ~preda(X0)) [avatar definition] 294. prede(X0) | ~preda(X0) <- (3) [avatar component clause 293] 295. ~1 | 3 [avatar split clause 255,293,285] 305. 6 <=> sP0 [avatar definition] 314. 8 <=> predc(sK2) [avatar definition] 316. predc(sK2) <- (8) [avatar component clause 314] 317. ~6 | 8 [avatar split clause 258,314,305] 319. 9 <=> room(sK2) [avatar definition] 321. room(sK2) <- (9) [avatar component clause 319] 322. ~6 | 9 [avatar split clause 257,319,305] 324. 10 <=> ! [X0] : (~prede(X0) | ~room(X0) | preda(X0)) [avatar definition] 325. ~prede(X0) | ~room(X0) | preda(X0) <- (10) [avatar component clause 324] 326. 6 | 10 [avatar split clause 262,324,305] 332. 12 <=> predd(sK3) [avatar definition] 336. 13 <=> ! [X0] : (~predb(X0) | ~room(X0) | ~preda(X0)) [avatar definition] 337. ~predb(X0) | ~room(X0) | ~preda(X0) <- (13) [avatar component clause 336] 338. ~12 | 13 [avatar split clause 268,336,332] 339. 12 | 13 [avatar split clause 267,336,332] 352. 16 <=> preda(sK4) [avatar definition] 354. ~preda(sK4) <- (~16) [avatar component clause 352] 365. 19 <=> room(sK4) [avatar definition] 367. room(sK4) <- (19) [avatar component clause 365] 370. 20 <=> ! [X0] : (predb(X0) | ~room(X0) | ~preda(X0)) [avatar definition] 371. predb(X0) | ~room(X0) | ~preda(X0) <- (20) [avatar component clause 370] 372. ~16 | 20 [avatar split clause 271,370,352] 374. 19 | 20 [avatar split clause 269,370,365] 377. ~room(X0) | preda(X0) <- (10) [subsumption resolution 325,275] 381. preda(sK4) <- (10, 19) [resolution 377,367] 383. $false <- (10, ~16, 19) [subsumption resolution 381,354] 384. ~10 | 16 | ~19 [avatar contradiction clause 383] 388. prede(sK2) <- (9) [resolution 321,275] 390. ~predc(sK2) <- (9) [resolution 388,277] 391. $false <- (8, 9) [subsumption resolution 390,316] 392. ~8 | ~9 [avatar contradiction clause 391] 393. ~room(X0) | ~preda(X0) <- (13, 20) [subsumption resolution 371,337] 395. ~room(X0) | preda(X0) <- (10) [subsumption resolution 325,275] 396. ~room(X0) <- (10, 13, 20) [subsumption resolution 395,393] 401. predc(X0) <- (10, 13, 20) [resolution 396,283] 404. preda(X0) <- (10, 13, 20) [resolution 401,278] 405. $false <- (~1, 10, 13, 20) [resolution 404,287] 408. 1 | ~10 | ~13 | ~20 [avatar contradiction clause 405] 409. prede(X0) <- (3, 10, 13, 20) [subsumption resolution 294,404] 411. ~predc(X0) <- (3, 10, 13, 20) [resolution 409,277] 412. $false <- (3, 10, 13, 20) [subsumption resolution 411,401] 413. ~3 | ~10 | ~13 | ~20 [avatar contradiction clause 412] 414. $false [avatar sat refutation 295,317,322,326,338,339,372,374,384,392,408,413] % SZS output end Proof for 1593137530111068170332891 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------
0
Viva, Deborah, Jose, Christina, Julie are the only persons in the room. “Viva uses an ios phone” if “it is true that “neither “A tower does not lean significantly without falling.” nor “A bird tweets using morse code.””” and vice versa. No calm person is quiet. All quiet persons are brave. Viva uses an ios phone. Everyone in the room who collects limited-edition art prints from contemporary artists designs and sews custom cosplay costumes for conventions. If someone is a wise calm happy patient curious tourist then he/she collects limited-edition art prints from contemporary artists and vice versa. “A shadow appears only at noon.” or “A tower leans significantly but never falls.” but not both. Christina is not a generous person. Deborah who collects limited-edition art prints from contemporary artists develops open-source software projects in their free time. Everyone in the room who is creative is not not quiet. Everyone in the room is not hated by Madonna, does not practice zumba or enjoys watercolor painting if they is not not quiet.
Everyone in the room is not a curious person.
contradiction
room(viva)&room(deborah)&room(jose)&room(christina)&room(julie)&(![X]:(room(X)=>(X='viva'|X='deborah'|X='jose'|X='christina'|X='julie')))& ((~((A_tower_does_not_lean_significantly_without_falling.)|(A_bird_tweets_using_morse_code.)))<=>(uses_an_ios_phone(viva)))& (~?[X]:(calm(X)=>quiet(X)))& (![X]:(quiet(X)=>brave(X)))& (uses_an_ios_phone(viva))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& ((![X]:((wise(X)&calm(X)&happy(X)&patient(X)&curious(X)&tourist(X))<=>(collects_limited-edition_art_prints_from_contemporary_artists(X)))))& (((A_shadow_appears_only_at_noon.)<~>(A_tower_leans_significantly_but_never_falls.)))& (~(generous(christina)&person(christina)))& ((collects_limited-edition_art_prints_from_contemporary_artists(deborah))&(develops_open-source_software_projects_in_their_free_time(deborah)))& (![X]:(room(X)=>(((creative(X))=>(~~quiet(X))))))& (![X]:(room(X)=>(((~~quiet(X))=>(((~hate(X,madonna))|(does_not_practice_zumba(X))|(enjoys_watercolor_painting(X))))))))& (![X]:(creative(X)=>kind(X)))& (![X]:(room(X)=>(((practices_kickboxing(X))|(does_not_practice_digital_art(X))))))
room(viva)&room(deborah)&room(jose)&room(christina)&room(julie)&(![X]:(room(X)=>(X='viva'|X='deborah'|X='jose'|X='christina'|X='julie')))& ![X]:(room(X)=>(~(curious(X)&person(X))))
[ "b3", "p0", "p6", "p9", "hypothesis" ]
% SZS status Unsatisfiable for 2834893686966011732773966 % SZS output start Proof for 2834893686966011732773966 4. ! [X0] : (tourist(X0) => person(X0)) [input b3] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. ! [X0] : ((tourist(X0) & curious(X0) & patient(X0) & happy(X0) & calm(X0) & wise(X0)) <=> predk(X0)) [input p6] 53. preds(paul) & predk(paul) [input p9] 58. ! [X0] : (room(X0) => ~(person(X0) & curious(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] 59. ! [X0] : (room(X0) => ~(person(X0) & curious(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 58] 64. predk(paul) [pure predicate removal 53] 72. ! [X0] : (predk(X0) => (tourist(X0) & curious(X0) & patient(X0) & happy(X0) & calm(X0) & wise(X0))) [unused predicate definition removal 50] 73. ! [X0] : (predk(X0) => (tourist(X0) & curious(X0) & happy(X0) & calm(X0) & wise(X0))) [pure predicate removal 72] 74. ! [X0] : (predk(X0) => (tourist(X0) & curious(X0) & calm(X0) & wise(X0))) [pure predicate removal 73] 76. ! [X0] : (predk(X0) => (tourist(X0) & curious(X0) & wise(X0))) [pure predicate removal 74] 77. ! [X0] : (predk(X0) => (tourist(X0) & curious(X0))) [pure predicate removal 76] 78. ! [X0] : (person(X0) | ~tourist(X0)) [ennf transformation 4] 146. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 147. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 146] 150. ! [X0] : ((tourist(X0) & curious(X0)) | ~predk(X0)) [ennf transformation 77] 151. ! [X0] : ((~person(X0) | ~curious(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 59] 152. ! [X0] : (~person(X0) | ~curious(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 151] 157. ~tourist(X0) | person(X0) [cnf transformation 78] 239. room(paul) [cnf transformation 147] 249. ~predk(X0) | curious(X0) [cnf transformation 150] 250. ~predk(X0) | tourist(X0) [cnf transformation 150] 253. predk(paul) [cnf transformation 64] 260. ~curious(X0) | ~person(X0) | ~room(X0) [cnf transformation 152] 283. curious(paul) [resolution 249,253] 284. tourist(paul) [resolution 250,253] 285. ~person(paul) | ~room(paul) [resolution 260,283] 286. ~person(paul) [subsumption resolution 285,239] 287. person(paul) [resolution 284,157] 288. $false [subsumption resolution 287,286] % SZS output end Proof for 2834893686966011732773966 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.030 s % ------------------------------ % ------------------------------
0
Sean is the only person in the room. If “Sean owns a 3D printer” then “if someone does not enjoy macrame then he/she is an avid mountain climber who has scaled several peaks or owns a 3D printer or both”. If “Sean either does not practice digital art or enjoys stand-up paddleboarding but not both” then “if someone does not enjoy macrame then he/she collects modern art”. If “Sean enjoys cross-country skiing” then “only one person in the room enjoys landscape photography”. If “Sean enjoys macrame” then “if someone is a cybersecurity expert then he/she creates large-scale murals for public art installations”.
Sean collects modern art.
neutral
room(sean)&(![X]:(room(X)=>(X='sean')))& ((owns_a_3D_printer(sean))=>((![X]:((does_not_enjoy_macrame(X))=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(owns_a_3D_printer(X))))))))& ((((does_not_practice_digital_art(sean))<~>(enjoys_stand-up_paddleboarding(sean))))=>((![X]:((does_not_enjoy_macrame(X))=>(collects_modern_art(X))))))& ((enjoys_cross-country_skiing(sean))=>(((?[X]:(room(X)&enjoys_landscape_photography(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_landscape_photography(X))&(enjoys_landscape_photography(Y)))=>(X=Y))))))& ((enjoys_macrame(sean))=>((![X]:((is_a_cybersecurity_expert(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (?[X]:(~room(X)&(owns_a_3D_printer(X))))& (trains_for_and_competes_in_international_triathlons(sean))& ((![X]:((creates_large-scale_murals_for_public_art_installations(X))<=>(enjoys_stand-up_paddleboarding(X)))))& (enjoys_snowboarding(sean))& ((![X]:((enjoys_landscape_photography(X))=>(does_not_enjoy_stand-up_paddleboarding(X)))))& ((![X]:((((enjoys_snowboarding(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))<=>(((enjoys_salsa_dancing(X))&(trains_for_and_competes_in_international_triathlons(X)))))))& ((![X]:((enjoys_landscape_photography(X))=>(does_not_enjoy_cross-country_skiing(X)))))& (((enjoys_landscape_photography(sean))|(does_not_enjoy_cross-country_skiing(sean))))& ((![X]:((enjoys_salsa_dancing(X))=>(enjoys_landscape_photography(X)))))& (enjoys_macrame(sean))& (((enjoys_salsa_dancing(sean))<~>(enjoys_snowboarding(sean))))& (is_right-handed(sean))& (((?[X]:(anywhere(X)&enjoys_virtual_reality_gaming(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(enjoys_virtual_reality_gaming(X))&(enjoys_virtual_reality_gaming(Y)))=>(X=Y)))))& ((![X]:((does_enjoy_trail_running(X))<=>(((collects_modern_art(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& (owns_a_3D_printer(sean))& (?[X]:(room(X)&(enjoys_stand-up_paddleboarding(X))))& (enjoys_virtual_reality_gaming(sean))& (practices_digital_art(sean))
room(sean)&(![X]:(room(X)=>(X='sean')))& collects_modern_art(sean)
[]
null
0.264245
There is a room. Everyone in the room who collects antique jewelry and is an avid collector of autographed memorabilia from famous musicians is an avid collector of autographed memorabilia from famous musicians. Everyone in the room who collects luxury watches either collects antique jewelry or is an avid collector of autographed memorabilia from famous musicians but not both. Everyone in the room is an avid collector of autographed memorabilia from famous musicians if they either collects antique jewelry or is an avid collector of autographed memorabilia from famous musicians but not both. Everyone in the room does not enjoy stand-up paddleboarding if they is an avid collector of autographed memorabilia from famous musicians. It is true that “not everyone in the room practices tai chi if they does not enjoy stand-up paddleboarding”. Everyone in the room bakes bread at home. If someone bakes bread at home then he/she is a certified scuba diver with advanced underwater photography skills and vice versa. Someone outside the room is an avid collector of autographed memorabilia from famous musicians. Only one person in the room collects action figures. Everyone in the room who collects rare and antique scientific instruments collects antique clocks. If someone enjoys snowboarding or enjoys deep-sea diving and exploring underwater caves or both then he/she neither creates YouTube content nor is a certified scuba diver with advanced underwater photography skills.
Everyone in the room enjoys deep-sea diving and exploring underwater caves.
contradiction
(there_is_a_room)& (![X]:(room(X)=>(((((collects_antique_jewelry(X))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(((collects_antique_jewelry(X))<~>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))& (![X]:(room(X)=>(((((collects_antique_jewelry(X))<~>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(does_not_enjoy_stand-up_paddleboarding(X))))))& (~![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))=>(practices_tai_chi(X))))))& (![X]:(room(X)=>(bakes_bread_at_home(X))))& ((![X]:((bakes_bread_at_home(X))<=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& (?[X]:(~room(X)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& (((?[X]:(room(X)&collects_action_figures(X)))&(![X,Y]:((room(X)&room(Y)&(collects_action_figures(X))&(collects_action_figures(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(collects_antique_clocks(X))))))& ((![X]:((((enjoys_snowboarding(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))=>(~((creates_YouTube_content(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))
(there_is_a_room)& ![X]:(room(X)=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))
[ "p5", "p6", "p7", "p11", "hypothesis" ]
% SZS status Unsatisfiable for 6298400216216573277219920 % SZS output start Proof for 6298400216216573277219920 49. ~! [X0] : (room(X0) => (~predm(X0) => predi(X0))) [input p5] 50. ! [X0] : (room(X0) => predp(X0)) [input p6] 51. ! [X0] : (predp(X0) <=> predq(X0)) [input p7] 55. ! [X0] : ((predc(X0) | predk(X0)) => ~(predq(X0) | predd(X0))) [input p11] 56. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 58. ! [X0] : (predp(X0) => predq(X0)) [unused predicate definition removal 51] 59. ! [X0] : ((predc(X0) | predk(X0)) => ~predq(X0)) [pure predicate removal 55] 60. ! [X0] : (predc(X0) => ~predq(X0)) [pure predicate removal 59] 62. ~! [X0] : (room(X0) => ~~predm(X0)) [pure predicate removal 49] 64. ~! [X0] : ~room(X0) [pure predicate removal 62] 66. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 56] 144. ? [X0] : room(X0) [ennf transformation 64] 145. ! [X0] : (predp(X0) | ~room(X0)) [ennf transformation 50] 146. ! [X0] : (predq(X0) | ~predp(X0)) [ennf transformation 58] 149. ! [X0] : (~predq(X0) | ~predc(X0)) [ennf transformation 60] 150. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 66] 153. ? [X0] : room(X0) => room(sK0) [choice axiom] 154. room(sK0) [skolemisation 144,153] 242. room(sK0) [cnf transformation 154] 243. ~room(X0) | predp(X0) [cnf transformation 145] 244. ~predp(X0) | predq(X0) [cnf transformation 146] 250. ~predc(X0) | ~predq(X0) [cnf transformation 149] 251. ~room(X0) | predc(X0) [cnf transformation 150] 253. predp(sK0) [resolution 243,242] 255. predq(sK0) [resolution 244,253] 257. predc(sK0) [resolution 251,242] 259. ~predq(sK0) [resolution 257,250] 260. $false [subsumption resolution 259,255] % SZS output end Proof for 6298400216216573277219920 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.033 s % ------------------------------ % ------------------------------
0.00445
Gwen, Linda, Keith, Rose are the only persons in the room. Rose enjoys spelunking or practices and performs acrobatic dance routines or both. Everyone anywhere does not enjoy spelunking if they builds model airplanes. Everyone in the room owns an Android phone or does not enjoy spelunking. Rose practices and performs acrobatic dance routines. Linda does not enjoy spelunking. It is not the case that “Gwen practices and performs acrobatic dance routines”. Everyone in the room practices and performs acrobatic dance routines if they does not create YouTube content and creates YouTube content. Gwen enjoys spelunking. Keith builds model airplanes. Linda practices and performs acrobatic dance routines. Keith does not build model airplanes or builds model airplanes or both.
Rose enjoys spelunking.
neutral
room(gwen)&room(linda)&room(keith)&room(rose)&(![X]:(room(X)=>(X='gwen'|X='linda'|X='keith'|X='rose')))& (((enjoys_spelunking(rose))|(practices_and_performs_acrobatic_dance_routines(rose))))& (![X]:(anywhere(X)=>(((builds_model_airplanes(X))=>(does_not_enjoy_spelunking(X))))))& (![X]:(room(X)=>(((does_not_enjoy_spelunking(X))|(owns_an_Android_phone(X))))))& (practices_and_performs_acrobatic_dance_routines(rose))& (does_not_enjoy_spelunking(linda))& (~(practices_and_performs_acrobatic_dance_routines(gwen)))& (![X]:(room(X)=>(((((does_not_create_YouTube_content(X))&(creates_YouTube_content(X))))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (enjoys_spelunking(gwen))& (builds_model_airplanes(keith))& (practices_and_performs_acrobatic_dance_routines(linda))& (((does_not_build_model_airplanes(keith))|(builds_model_airplanes(keith))))
room(gwen)&room(linda)&room(keith)&room(rose)&(![X]:(room(X)=>(X='gwen'|X='linda'|X='keith'|X='rose')))& enjoys_spelunking(rose)
[]
null
0.025177
Marcus, Robby are the only persons in the room. Everyone in the room does not enjoy skydiving if they knows morse code. Everyone outside the room enjoys skydiving if they does enjoy mountain biking. Marcus is not a skilled home brewer experimenting with craft beer recipes. Marcus collects foreign coins. Marcus collects action figures. Robby knows morse code. Everyone in the room enjoys rooftop gardening if they writes poetry, is a tea enthusiast and is a chess master who participates in national tournaments. Everyone in the room who knows morse code enjoys rooftop gardening. Everyone in the room who practices archery collects vintage stamps. Everyone in the room who collects vintage stamps neither practices calligraphy nor does not write poetry. Everyone in the room who collects first edition books is not an active member of a local robotics club, is a culinary enthusiast who experiments with international cuisines or writes poetry. Marcus owns a significant collection of rare gemstones and minerals. Everyone in the room does not collect vintage stamps if they hosts a YouTube channel dedicated to art tutorials and vice versa. If someone collects vintage stamps then he/she collects rare minerals. Everyone in the room is a member of a local theater group specializing in improv if they does enjoy mountain biking. Marcus knows morse code. Not everyone in the room is not a dedicated volunteer for local community service projects or reads mystery novels or both if they is a skilled home brewer experimenting with craft beer recipes. Everyone anywhere collects rare minerals if they is not a dedicated volunteer for local community service projects or reads mystery novels or both. Everyone in the room who is a skilled home brewer experimenting with craft beer recipes collects action figures. Marcus is an active member of a local robotics club.
Robby enjoys rooftop gardening.
entailment
room(marcus)&room(robby)&(![X]:(room(X)=>(X='marcus'|X='robby')))& (![X]:(room(X)=>(((knows_morse_code(X))=>(does_not_enjoy_skydiving(X))))))& (![X]:(~room(X)=>(((does_enjoy_mountain_biking(X))=>(enjoys_skydiving(X))))))& (is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(marcus))& (collects_foreign_coins(marcus))& (collects_action_figures(marcus))& (knows_morse_code(robby))& (![X]:(room(X)=>(((((writes_poetry(X))&(is_a_tea_enthusiast(X))&(is_a_chess_master_who_participates_in_national_tournaments(X))))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((practices_archery(X))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(~((practices_calligraphy(X))|(does_not_write_poetry(X))))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))=>(((is_not_an_active_member_of_a_local_robotics_club(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(writes_poetry(X))))))))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(marcus))& (![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))<=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& ((![X]:((collects_vintage_stamps(X))=>(collects_rare_minerals(X)))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (knows_morse_code(marcus))& (~![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(reads_mystery_novels(X))))))))& (![X]:(anywhere(X)=>(((((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(reads_mystery_novels(X))))=>(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(collects_action_figures(X))))))& (is_an_active_member_of_a_local_robotics_club(marcus))& (![X]:(~room(X)=>(((((collects_foreign_coins(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))=>(does_not_read_mystery_novels(X))))))& (![X]:(room(X)=>(((does_not_know_morse_code(X))=>(collects_vintage_stamps(X))))))& (collects_vintage_stamps(robby))
room(marcus)&room(robby)&(![X]:(room(X)=>(X='marcus'|X='robby')))& enjoys_rooftop_gardening(robby)
[ "p0", "p6", "p8", "hypothesis" ]
% SZS status Unsatisfiable for 4249195146452770879867190 % SZS output start Proof for 4249195146452770879867190 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 50. predk(paul) [input p6] 52. ! [X0] : (room(X0) => (predk(X0) => predb(X0))) [input p8] 68. ~(predb(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 160. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 161. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 160] 162. ! [X0] : ((predb(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 52] 163. ! [X0] : (predb(X0) | ~predk(X0) | ~room(X0)) [flattening 162] 168. ~predb(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 68] 169. ~predb(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 168] 174. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 175. ~predb(paul) | (paul != sK1 & mary != sK1 & room(sK1)) | ~room(paul) | ~room(mary) [skolemisation 169,174] 256. room(mary) [cnf transformation 161] 257. room(paul) [cnf transformation 161] 258. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 161] 260. predk(paul) [cnf transformation 50] 261. ~predk(X0) | predb(X0) | ~room(X0) [cnf transformation 163] 269. ~predb(paul) | room(sK1) | ~room(paul) | ~room(mary) [cnf transformation 175] 270. ~predb(paul) | mary != sK1 | ~room(paul) | ~room(mary) [cnf transformation 175] 271. ~predb(paul) | paul != sK1 | ~room(paul) | ~room(mary) [cnf transformation 175] 272. ~predb(paul) | paul != sK1 | ~room(mary) [subsumption resolution 271,257] 273. ~predb(paul) | paul != sK1 [subsumption resolution 272,256] 275. 1 <=> paul = sK1 [avatar definition] 277. paul != sK1 <- (~1) [avatar component clause 275] 279. 2 <=> predb(paul) [avatar definition] 282. ~1 | ~2 [avatar split clause 273,279,275] 283. ~predb(paul) | mary != sK1 | ~room(mary) [subsumption resolution 270,257] 284. ~predb(paul) | mary != sK1 [subsumption resolution 283,256] 286. 3 <=> mary = sK1 [avatar definition] 288. mary != sK1 <- (~3) [avatar component clause 286] 289. ~3 | ~2 [avatar split clause 284,279,286] 290. ~predb(paul) | room(sK1) | ~room(mary) [subsumption resolution 269,257] 291. ~predb(paul) | room(sK1) [subsumption resolution 290,256] 293. 4 <=> room(sK1) [avatar definition] 295. room(sK1) <- (4) [avatar component clause 293] 296. 4 | ~2 [avatar split clause 291,279,293] 297. predb(paul) | ~room(paul) [resolution 261,260] 303. predb(paul) [subsumption resolution 297,257] 304. 2 [avatar split clause 303,279] 352. mary = sK1 | paul = sK1 <- (4) [resolution 258,295] 362. paul = sK1 <- (~3, 4) [subsumption resolution 352,288] 363. $false <- (~1, ~3, 4) [subsumption resolution 362,277] 364. 1 | 3 | ~4 [avatar contradiction clause 363] 365. $false [avatar sat refutation 282,289,296,304,364] % SZS output end Proof for 4249195146452770879867190 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0.224196
Joseph, Gloria, Virgilio are the only persons in the room. 'Everyone anywhere who enjoys logic puzzles enjoys writing detailed reviews of new and classic board games' unless 'Joseph collects classic novels or does not write and illustrates their own graphic novels or both'. Either 'Joseph enjoys writing detailed reviews of new and classic board games' or 'everyone in the room does not enjoy writing detailed reviews of new and classic board games or does not write and illustrates their own graphic novels' but not both. If 'Joseph is a tea enthusiast' then 'everyone in the room does not have a vast collection of first-edition science fiction novels if they collects vintage stamps'. If 'Joseph does not own an Android phone' then 'Joseph does not enjoy kayaking'. Either 'no one in the room does not host themed dinner parties featuring gourmet home-cooked meals or can play the piano' or 'Joseph is a tea enthusiast' but not both. Either 'Joseph does not collect vintage stamps, enjoys logic puzzles and collects classic novels' or 'Joseph does not own an Android phone' but not both. If 'Joseph can play the piano' then 'Joseph neither hosts themed dinner parties featuring gourmet home-cooked meals nor is a tea enthusiast'. Joseph is not a skilled home brewer experimenting with craft beer recipes. Everyone in the room writes and illustrates their own graphic novels if they enjoys writing detailed reviews of new and classic board games. If someone enjoys writing detailed reviews of new and classic board games, does not enjoy logic puzzles or has a tattoo then he/she is a skilled home brewer experimenting with craft beer recipes.
Virgilio enjoys writing detailed reviews of new and classic board games.
contradiction
room(joseph)&room(gloria)&room(virgilio)&(![X]:(room(X)=>(X='joseph'|X='gloria'|X='virgilio')))& (~(((collects_classic_novels(joseph))|(does_not_write_and_illustrates_their_own_graphic_novels(joseph))))=>(![X]:(anywhere(X)=>(((enjoys_logic_puzzles(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))& ((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(joseph))<~>(![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))& ((is_a_tea_enthusiast(joseph))=>(![X]:(room(X)=>(((collects_vintage_stamps(X))=>(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))& ((does_not_own_an_Android_phone(joseph))=>(does_not_enjoy_kayaking(joseph)))& ((~?[X]:(room(X)=>(((can_play_the_piano(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))<~>(is_a_tea_enthusiast(joseph)))& ((((does_not_collect_vintage_stamps(joseph))&(enjoys_logic_puzzles(joseph))&(collects_classic_novels(joseph))))<~>(does_not_own_an_Android_phone(joseph)))& ((can_play_the_piano(joseph))=>(~((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(joseph))|(is_a_tea_enthusiast(joseph)))))& (![X]:(room(X)=>(((~((collects_vintage_stamps(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))=>(has_a_tattoo(X))))))& (is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(joseph))& ((![X]:((does_not_enjoy_logic_puzzles(X))=>(does_not_collect_vintage_stamps(X)))))& (((?[X]:(~room(X)&((does_not_enjoy_landscape_photography(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))&(![X,Y]:((~room(X)&~room(Y)&(((does_not_enjoy_landscape_photography(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))&(((does_not_enjoy_landscape_photography(Y))|(has_a_vast_collection_of_first-edition_science_fiction_novels(Y))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(Y)))))=>(X=Y)))))& (((?[X]:(room(X)&collects_modern_art(X)))))& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(((can_play_the_piano(X))|(has_a_tattoo(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))))& (((collects_vintage_stamps(joseph))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(joseph))|(enjoys_logic_puzzles(joseph))))& (has_a_vast_collection_of_first-edition_science_fiction_novels(joseph))& ((![X]:((((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_enjoy_logic_puzzles(X))|(has_a_tattoo(X))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))& (![X]:(room(X)=>(((does_not_collect_modern_art(X))=>(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))
room(joseph)&room(gloria)&room(virgilio)&(![X]:(room(X)=>(X='joseph'|X='gloria'|X='virgilio')))& enjoys_writing_detailed_reviews_of_new_and_classic_board_games(virgilio)
[ "p0", "p2", "p9", "p13", "p18", "hypothesis" ]
% SZS status Unsatisfiable for 9196852255791373037735127 % SZS output start Proof for 9196852255791373037735127 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. predl(mary) <~> ! [X0] : (room(X0) => (~predl(X0) | ~preda(X0))) [input p2] 53. ~predp(mary) [input p9] 57. ! [X0] : (room(X0) => (predl(X0) => preda(X0))) [input p13] 62. ! [X0] : ((predj(X0) | ~predk(X0) | predl(X0)) => predp(X0)) [input p18] 64. predl(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 140. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 141. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 140] 144. predl(mary) <~> ! [X0] : ((~predl(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 46] 145. predl(mary) <~> ! [X0] : (~predl(X0) | ~preda(X0) | ~room(X0)) [flattening 144] 156. ! [X0] : ((preda(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 57] 157. ! [X0] : (preda(X0) | ~predl(X0) | ~room(X0)) [flattening 156] 162. ! [X0] : (predp(X0) | (~predj(X0) & predk(X0) & ~predl(X0))) [ennf transformation 62] 163. predl(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 64] 164. predl(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 163] 168. (? [X0] : (predl(X0) & preda(X0) & room(X0)) | ~predl(mary)) & (! [X0] : (~predl(X0) | ~preda(X0) | ~room(X0)) | predl(mary)) [nnf transformation 145] 169. (? [X0] : (predl(X0) & preda(X0) & room(X0)) | ~predl(mary)) & (! [X1] : (~predl(X1) | ~preda(X1) | ~room(X1)) | predl(mary)) [rectify 168] 170. ? [X0] : (predl(X0) & preda(X0) & room(X0)) => (predl(sK1) & preda(sK1) & room(sK1)) [choice axiom] 171. ((predl(sK1) & preda(sK1) & room(sK1)) | ~predl(mary)) & (! [X1] : (~predl(X1) | ~preda(X1) | ~room(X1)) | predl(mary)) [skolemisation 169,170] 266. room(fred) [cnf transformation 141] 269. ~predl(X1) | ~preda(X1) | ~room(X1) | predl(mary) [cnf transformation 171] 285. ~predp(mary) [cnf transformation 53] 296. preda(X0) | ~predl(X0) | ~room(X0) [cnf transformation 157] 301. ~predl(X0) | predp(X0) [cnf transformation 162] 308. predl(fred) [cnf transformation 164] 323. 4 <=> predl(mary) [avatar definition] 324. predl(mary) <- (4) [avatar component clause 323] 342. 8 <=> ! [X1] : (~predl(X1) | ~room(X1) | ~preda(X1)) [avatar definition] 343. ~predl(X1) | ~room(X1) | ~preda(X1) <- (8) [avatar component clause 342] 344. 4 | 8 [avatar split clause 269,342,323] 418. predp(mary) <- (4) [resolution 301,324] 420. $false <- (4) [subsumption resolution 418,285] 421. ~4 [avatar contradiction clause 420] 422. ~predl(X1) | ~room(X1) <- (8) [subsumption resolution 343,296] 425. ~room(fred) <- (8) [resolution 422,308] 427. $false <- (8) [subsumption resolution 425,266] 428. ~8 [avatar contradiction clause 427] 431. $false [avatar sat refutation 344,421,428] % SZS output end Proof for 9196852255791373037735127 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------
0.269954
Latonya is the only person in the room. “It is true that “someone in the room either is a client of Costco or does enjoy trail running but not both”” if “everyone in the room enjoys deep-sea diving and exploring underwater caves or does not play eSports competitively”. Everyone in the room who enjoys deep-sea diving and exploring underwater caves plays eSports competitively. Everyone in the room collects antique jewelry if they plays eSports competitively. Everyone anywhere who enjoys deep-sea diving and exploring underwater caves knows morse code. Everyone in the room is a client of Meta if they is a professional photographer specializing in portrait photography. Latonya is a professional photographer specializing in portrait photography. Everyone in the room enjoys deep-sea diving and exploring underwater caves or does not play eSports competitively. No one anywhere plays as a goalkeeper for a local amateur soccer team if they own a television.
Latonya own a television.
entailment
room(latonya)&(![X]:(room(X)=>(X='latonya')))& ((![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(?[X]:(room(X)&(((is_a_client_of_Costco(X))<~>(does_enjoy_trail_running(X)))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(collects_antique_jewelry(X))))))& (![X]:(anywhere(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(knows_morse_code(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(is_a_client_of_Meta(X))))))& (is_a_professional_photographer_specializing_in_portrait_photography(latonya))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(~room(X)=>(((competes_in_national_level_swimming_championships(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (does_enjoy_trail_running(latonya))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(enjoys_kayaking(X))))))& (plays_eSports_competitively(latonya))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(is_a_client_of_Costco(X))))))& ((![X]:((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(does_not_use_an_ios_phone(X)))))))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(latonya))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((((enjoys_kayaking(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(anywhere(X)=>(((plays_eSports_competitively(X))=>(collects_antique_jewelry(X))))))& (competes_in_national_level_swimming_championships(latonya))& (owns_a_high-end_gaming_PC_with_custom-built_components(latonya))& (~?[X]:(anywhere(X)=>(((own_a_television(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(anywhere(X)=>(((creates_large-scale_murals_for_public_art_installations(X))<=(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((((is_a_client_of_Meta(X))<~>(does_not_compete_in_national_level_swimming_championships(X))))=>(((does_not_know_morse_code(X))|(enjoys_coding_in_Python(X))))))))
room(latonya)&(![X]:(room(X)=>(X='latonya')))& own_a_television(latonya)
[ "p0", "p21", "hypothesis" ]
% SZS status Unsatisfiable for 3931607575506839335845541 % SZS output start Proof for 3931607575506839335845541 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 65. ~? [X0] : (anywhere(X0) => (predm(X0) => predb(X0))) [input p21] 68. ~(predm(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 83. ~? [X0] : (predm(X0) => predb(X0)) [pure predicate removal 65] 156. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 167. ! [X0] : (~predb(X0) & predm(X0)) [ennf transformation 83] 168. ~predm(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 68] 182. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 183. ~predm(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 168,182] 264. room(mary) [cnf transformation 156] 265. ~room(X0) | mary = X0 [cnf transformation 156] 282. predm(X0) [cnf transformation 167] 284. ~predm(mary) | room(sK3) | ~room(mary) [cnf transformation 183] 285. ~predm(mary) | mary != sK3 | ~room(mary) [cnf transformation 183] 320. mary != sK3 | ~room(mary) [subsumption resolution 285,282] 321. mary != sK3 [subsumption resolution 320,264] 322. room(sK3) | ~room(mary) [subsumption resolution 284,282] 323. room(sK3) [subsumption resolution 322,264] 326. mary = sK3 [resolution 265,323] 332. $false [subsumption resolution 326,321] % SZS output end Proof for 3931607575506839335845541 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------
0.265822
Tim, Mathew, Devon, James are the only persons in the room. James hosts themed dinner parties featuring gourmet home-cooked meals. Mathew cannot play the piano. Tim hosts themed dinner parties featuring gourmet home-cooked meals. Only one person in the room participates in long-distance cycling events across the country, does not host themed dinner parties featuring gourmet home-cooked meals and can play the piano.
Devon participates in long-distance cycling events across the country.
entailment
room(tim)&room(mathew)&room(devon)&room(james)&(![X]:(room(X)=>(X='tim'|X='mathew'|X='devon'|X='james')))& (?[X]:(room(X)&(can_play_the_piano(X))))& (is_a_certified_yoga_instructor_teaching_classes_weekly(james))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(james))& (is_a_certified_yoga_instructor_teaching_classes_weekly(devon))& ((participates_in_long-distance_cycling_events_across_the_country(tim))&(can_play_the_piano(tim)))& (enjoys_stargazing(devon))& (participates_in_long-distance_cycling_events_across_the_country(james))& (cannot_play_the_piano(mathew))& (enjoys_stargazing(james))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(mathew))& (?[X]:(room(X)&(~((does_not_enjoy_stargazing(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(tim))& ((enjoys_stargazing(james))&(can_play_the_piano(james)))& (participates_in_long-distance_cycling_events_across_the_country(tim))& (((can_play_the_piano(mathew))|(participates_in_long-distance_cycling_events_across_the_country(mathew))))& (can_play_the_piano(devon))& (((does_not_participate_in_long-distance_cycling_events_across_the_country(mathew))|(participates_in_long-distance_cycling_events_across_the_country(mathew))|(is_a_certified_yoga_instructor_teaching_classes_weekly(mathew))))& (can_play_the_piano(tim))& (?[X]:(room(X)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))& (((?[X]:(room(X)&((participates_in_long-distance_cycling_events_across_the_country(X))&(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(can_play_the_piano(X)))))&(![X,Y]:((room(X)&room(Y)&(((participates_in_long-distance_cycling_events_across_the_country(X))&(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(can_play_the_piano(X))))&(((participates_in_long-distance_cycling_events_across_the_country(Y))&(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(Y))&(can_play_the_piano(Y)))))=>(X=Y)))))& (is_a_certified_yoga_instructor_teaching_classes_weekly(mathew))& (does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(devon))& (((enjoys_stargazing(mathew))|(is_a_certified_yoga_instructor_teaching_classes_weekly(mathew))|(can_play_the_piano(mathew))))& (((?[X]:(anywhere(X)&does_not_enjoy_stargazing(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(does_not_enjoy_stargazing(X))&(does_not_enjoy_stargazing(Y)))=>(X=Y)))))& (can_play_the_piano(james))
room(tim)&room(mathew)&room(devon)&room(james)&(![X]:(room(X)=>(X='tim'|X='mathew'|X='devon'|X='james')))& participates_in_long-distance_cycling_events_across_the_country(devon)
[ "p0", "p3", "p8", "p12", "p20", "hypothesis" ]
% SZS status Unsatisfiable for 1849185893985196122183766 % SZS output start Proof for 1849185893985196122183766 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. preda(alice) [input p3] 52. ~prede(paul) [input p8] 56. preda(mary) [input p12] 64. ! [X0,X1] : ((prede(X1) & ~preda(X1) & predb(X1) & prede(X0) & ~preda(X0) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (prede(X0) & ~preda(X0) & predb(X0) & room(X0)) [input p20] 70. ~(predb(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 71. ! [X0,X1] : ((prede(X1) & ~preda(X1) & predb(X1) & prede(X0) & ~preda(X0) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (prede(X2) & ~preda(X2) & predb(X2) & room(X2)) [rectify 64] 150. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 151. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 150] 154. ! [X0,X1] : (X0 = X1 | (~prede(X1) | preda(X1) | ~predb(X1) | ~prede(X0) | preda(X0) | ~predb(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (prede(X2) & ~preda(X2) & predb(X2) & room(X2)) [ennf transformation 71] 155. ! [X0,X1] : (X0 = X1 | ~prede(X1) | preda(X1) | ~predb(X1) | ~prede(X0) | preda(X0) | ~predb(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (prede(X2) & ~preda(X2) & predb(X2) & room(X2)) [flattening 154] 158. ~predb(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 159. ~predb(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 158] 167. ? [X2] : (prede(X2) & ~preda(X2) & predb(X2) & room(X2)) => (prede(sK3) & ~preda(sK3) & predb(sK3) & room(sK3)) [choice axiom] 168. ! [X0,X1] : (X0 = X1 | ~prede(X1) | preda(X1) | ~predb(X1) | ~prede(X0) | preda(X0) | ~predb(X0) | ~room(X1) | ~room(X0)) & (prede(sK3) & ~preda(sK3) & predb(sK3) & room(sK3)) [skolemisation 155,167] 171. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 172. ~predb(fred) | (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 159,171] 254. room(mary) [cnf transformation 151] 255. room(paul) [cnf transformation 151] 256. room(fred) [cnf transformation 151] 257. room(alice) [cnf transformation 151] 258. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 151] 261. preda(alice) [cnf transformation 47] 266. ~prede(paul) [cnf transformation 52] 272. preda(mary) [cnf transformation 56] 280. room(sK3) [cnf transformation 168] 281. predb(sK3) [cnf transformation 168] 282. ~preda(sK3) [cnf transformation 168] 283. prede(sK3) [cnf transformation 168] 290. ~predb(fred) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 291. ~predb(fred) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 292. ~predb(fred) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 293. ~predb(fred) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 294. ~predb(fred) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 298. ~predb(fred) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,257] 299. ~predb(fred) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 298,256] 300. ~predb(fred) | alice != sK5 | ~room(mary) [subsumption resolution 299,255] 301. ~predb(fred) | alice != sK5 [subsumption resolution 300,254] 303. 1 <=> alice = sK5 [avatar definition] 305. alice != sK5 <- (~1) [avatar component clause 303] 307. 2 <=> predb(fred) [avatar definition] 310. ~1 | ~2 [avatar split clause 301,307,303] 311. ~predb(fred) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 293,257] 312. ~predb(fred) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 311,256] 313. ~predb(fred) | fred != sK5 | ~room(mary) [subsumption resolution 312,255] 314. ~predb(fred) | fred != sK5 [subsumption resolution 313,254] 316. 3 <=> fred = sK5 [avatar definition] 318. fred != sK5 <- (~3) [avatar component clause 316] 319. ~3 | ~2 [avatar split clause 314,307,316] 320. ~predb(fred) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,257] 321. ~predb(fred) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 320,256] 322. ~predb(fred) | paul != sK5 | ~room(mary) [subsumption resolution 321,255] 323. ~predb(fred) | paul != sK5 [subsumption resolution 322,254] 325. 4 <=> paul = sK5 [avatar definition] 327. paul != sK5 <- (~4) [avatar component clause 325] 328. ~4 | ~2 [avatar split clause 323,307,325] 329. ~predb(fred) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,257] 330. ~predb(fred) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 329,256] 331. ~predb(fred) | mary != sK5 | ~room(mary) [subsumption resolution 330,255] 332. ~predb(fred) | mary != sK5 [subsumption resolution 331,254] 334. 5 <=> mary = sK5 [avatar definition] 336. mary != sK5 <- (~5) [avatar component clause 334] 337. ~5 | ~2 [avatar split clause 332,307,334] 338. ~predb(fred) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,257] 339. ~predb(fred) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 338,256] 340. ~predb(fred) | room(sK5) | ~room(mary) [subsumption resolution 339,255] 341. ~predb(fred) | room(sK5) [subsumption resolution 340,254] 343. 6 <=> room(sK5) [avatar definition] 345. room(sK5) <- (6) [avatar component clause 343] 346. 6 | ~2 [avatar split clause 341,307,343] 394. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 [resolution 258,280] 447. 19 <=> alice = sK3 [avatar definition] 449. alice = sK3 <- (19) [avatar component clause 447] 451. 20 <=> mary = sK3 [avatar definition] 453. mary = sK3 <- (20) [avatar component clause 451] 455. 21 <=> paul = sK3 [avatar definition] 457. paul = sK3 <- (21) [avatar component clause 455] 459. 22 <=> fred = sK3 [avatar definition] 461. fred = sK3 <- (22) [avatar component clause 459] 462. 19 | 20 | 21 | 22 [avatar split clause 394,459,455,451,447] 465. ~preda(alice) <- (19) [backward demodulation 282,449] 467. $false <- (19) [subsumption resolution 465,261] 468. ~19 [avatar contradiction clause 467] 479. ~preda(mary) <- (20) [backward demodulation 282,453] 481. $false <- (20) [subsumption resolution 479,272] 482. ~20 [avatar contradiction clause 481] 493. prede(paul) <- (21) [backward demodulation 283,457] 497. $false <- (21) [subsumption resolution 493,266] 498. ~21 [avatar contradiction clause 497] 506. predb(fred) <- (22) [backward demodulation 281,461] 516. 2 | ~22 [avatar split clause 506,459,307] 517. fred = sK5 | paul = sK5 | mary = sK5 | alice = sK5 <- (6) [resolution 345,258] 518. paul = sK5 | mary = sK5 | alice = sK5 <- (~3, 6) [subsumption resolution 517,318] 519. mary = sK5 | alice = sK5 <- (~3, ~4, 6) [subsumption resolution 518,327] 520. alice = sK5 <- (~3, ~4, ~5, 6) [subsumption resolution 519,336] 521. $false <- (~1, ~3, ~4, ~5, 6) [subsumption resolution 520,305] 522. 1 | 3 | 4 | 5 | ~6 [avatar contradiction clause 521] 523. $false [avatar sat refutation 310,319,328,337,346,462,468,482,498,516,522] % SZS output end Proof for 1849185893985196122183766 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------
0.278761
Leonel is the only person in the room. All old person is kind. Everyone in the room who is not a old kind person is a tall person. Everyone in the room is a kind person. Everyone in the room either is not a tall person or is a kind person but not both only if they is not a quiet old kind person. Everyone anywhere who is not a quiet old kind person is kind. All old person is tall. Everyone in the room is old if they is a tall person. Everyone in the room who is a tall kind person is older than Linda or is a tall quiet person or both.
Leonel is older than Linda.
entailment
room(leonel)&(![X]:(room(X)=>(X='leonel')))& (![X]:(old(X)=>kind(X)))& ((((richer(blanca,leonel))|(quiet(leonel))|(~(old(leonel)&person(leonel)))))&(quieter(blanca,leonel)))& (![X]:(room(X)=>(((~(old(X)&kind(X)&person(X)))=>(tall(X)&person(X))))))& (![X]:(room(X)=>(kind(X)&person(X))))& (![X]:(room(X)=>(((~(quiet(X)&old(X)&kind(X)&person(X)))<=(((~(tall(X)&person(X)))<~>(kind(X)&person(X))))))))& (![X]:(anywhere(X)=>(((~(quiet(X)&old(X)&kind(X)&person(X)))=>(kind(X))))))& (![X]:(old(X)=>tall(X)))& (![X]:(room(X)=>(((tall(X)&old(X)&kind(X)&person(X))=>(~(quiet(X)&person(X)))))))& (![X]:(~room(X)=>(((~(quiet(X)&person(X)))=>(older(blanca,X))))))& (richer(leonel,linda))& ((![X]:((((kind(X)&person(X))&(~(old(X)&person(X)))&(~(quiet(X)&old(X)&person(X)))))=>(richer(linda,X)))))& (![X]:(room(X)=>(((tall(X)&person(X))=>(old(X))))))& (![X]:(~room(X)=>(richer(blanca,X))))& (![X]:(tall(X)=>old(X)))& (?[X]:(anywhere(X)&(quiet(X)&kind(X)&old(X)&tall(X)&person(X))))& (![X]:(room(X)=>(((tall(X)&kind(X)&person(X))=>(((older(linda,X))|(tall(X)&quiet(X)&person(X))))))))
room(leonel)&(![X]:(room(X)=>(X='leonel')))& older(linda,leonel)
[ "b4", "p0", "p3", "p4", "p5", "p6", "p7", "p12", "p16", "hypothesis" ]
% SZS status Unsatisfiable for 5749891439414354279994587 % SZS output start Proof for 5749891439414354279994587 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (~(person(X0) & kind(X0) & old(X0)) => (person(X0) & tall(X0)))) [input p3] 48. ! [X0] : (room(X0) => (person(X0) & kind(X0))) [input p4] 49. ! [X0] : (room(X0) => ((~(person(X0) & tall(X0)) <~> (person(X0) & kind(X0))) => ~(person(X0) & kind(X0) & old(X0) & quiet(X0)))) [input p5] 50. ! [X0] : (anywhere(X0) => (~(person(X0) & kind(X0) & old(X0) & quiet(X0)) => kind(X0))) [input p6] 51. ! [X0] : (old(X0) => tall(X0)) [input p7] 56. ! [X0] : (room(X0) => ((person(X0) & tall(X0)) => old(X0))) [input p12] 60. ! [X0] : (room(X0) => ((person(X0) & kind(X0) & tall(X0)) => ((person(X0) & quiet(X0) & tall(X0)) | older(paul,X0)))) [input p16] 61. ~(older(paul,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 133. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 137. ! [X0] : (((person(X0) & tall(X0)) | (person(X0) & kind(X0) & old(X0))) | ~room(X0)) [ennf transformation 47] 138. ! [X0] : ((person(X0) & tall(X0)) | (person(X0) & kind(X0) & old(X0)) | ~room(X0)) [flattening 137] 139. ! [X0] : ((person(X0) & kind(X0)) | ~room(X0)) [ennf transformation 48] 140. ! [X0] : (((~person(X0) | ~kind(X0) | ~old(X0) | ~quiet(X0)) | ((~person(X0) | ~tall(X0)) <=> (person(X0) & kind(X0)))) | ~room(X0)) [ennf transformation 49] 141. ! [X0] : (~person(X0) | ~kind(X0) | ~old(X0) | ~quiet(X0) | ((~person(X0) | ~tall(X0)) <=> (person(X0) & kind(X0))) | ~room(X0)) [flattening 140] 142. ! [X0] : ((kind(X0) | (person(X0) & kind(X0) & old(X0) & quiet(X0))) | ~anywhere(X0)) [ennf transformation 50] 143. ! [X0] : (kind(X0) | (person(X0) & kind(X0) & old(X0) & quiet(X0)) | ~anywhere(X0)) [flattening 142] 144. ! [X0] : (tall(X0) | ~old(X0)) [ennf transformation 51] 151. ! [X0] : ((old(X0) | (~person(X0) | ~tall(X0))) | ~room(X0)) [ennf transformation 56] 152. ! [X0] : (old(X0) | ~person(X0) | ~tall(X0) | ~room(X0)) [flattening 151] 155. ! [X0] : ((((person(X0) & quiet(X0) & tall(X0)) | older(paul,X0)) | (~person(X0) | ~kind(X0) | ~tall(X0))) | ~room(X0)) [ennf transformation 60] 156. ! [X0] : ((person(X0) & quiet(X0) & tall(X0)) | older(paul,X0) | ~person(X0) | ~kind(X0) | ~tall(X0) | ~room(X0)) [flattening 155] 157. ~older(paul,mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 61] 159. ! [X0] : (~person(X0) | ~kind(X0) | ~old(X0) | ~quiet(X0) | (((~person(X0) | ~tall(X0)) | (~person(X0) | ~kind(X0))) & ((person(X0) & kind(X0)) | (person(X0) & tall(X0)))) | ~room(X0)) [nnf transformation 141] 160. ! [X0] : (~person(X0) | ~kind(X0) | ~old(X0) | ~quiet(X0) | ((~person(X0) | ~tall(X0) | ~person(X0) | ~kind(X0)) & ((person(X0) & kind(X0)) | (person(X0) & tall(X0)))) | ~room(X0)) [flattening 159] 163. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 164. ~older(paul,mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 157,163] 165. anywhere(X0) [cnf transformation 5] 246. room(mary) [cnf transformation 133] 247. ~room(X0) | mary = X0 [cnf transformation 133] 251. ~room(X0) | old(X0) | tall(X0) [cnf transformation 138] 256. person(X0) | person(X0) | ~room(X0) [cnf transformation 138] 257. ~room(X0) | kind(X0) [cnf transformation 139] 263. ~person(X0) | ~kind(X0) | ~old(X0) | ~quiet(X0) | ~person(X0) | ~tall(X0) | ~person(X0) | ~kind(X0) | ~room(X0) [cnf transformation 160] 266. kind(X0) | kind(X0) | ~anywhere(X0) [cnf transformation 143] 268. ~old(X0) | tall(X0) [cnf transformation 144] 279. old(X0) | ~person(X0) | ~tall(X0) | ~room(X0) [cnf transformation 152] 289. quiet(X0) | older(paul,X0) | ~person(X0) | ~kind(X0) | ~tall(X0) | ~room(X0) [cnf transformation 156] 291. ~older(paul,mary) | room(sK1) | ~room(mary) [cnf transformation 164] 292. ~older(paul,mary) | mary != sK1 | ~room(mary) [cnf transformation 164] 296. kind(X0) | ~anywhere(X0) [duplicate literal removal 266] 298. ~person(X0) | ~kind(X0) | ~old(X0) | ~quiet(X0) | ~tall(X0) | ~room(X0) [duplicate literal removal 263] 299. ~room(X0) | person(X0) [duplicate literal removal 256] 305. 2 <=> quiet(mary) [avatar definition] 306. ~quiet(mary) <- (~2) [avatar component clause 305] 309. 3 <=> old(mary) [avatar definition] 310. old(mary) <- (3) [avatar component clause 309] 317. ~kind(X0) | ~old(X0) | ~quiet(X0) | ~tall(X0) | ~room(X0) [subsumption resolution 298,299] 318. ~tall(X0) | ~quiet(X0) | ~old(X0) | ~room(X0) [subsumption resolution 317,257] 320. kind(X0) [subsumption resolution 296,165] 323. old(X0) | ~tall(X0) | ~room(X0) [subsumption resolution 279,299] 324. ~room(X0) | old(X0) [subsumption resolution 323,251] 325. quiet(X0) | older(paul,X0) | ~person(X0) | ~tall(X0) | ~room(X0) [subsumption resolution 289,320] 326. older(paul,X0) | quiet(X0) | ~tall(X0) | ~room(X0) [subsumption resolution 325,299] 327. ~older(paul,mary) | mary != sK1 [subsumption resolution 292,246] 329. 5 <=> mary = sK1 [avatar definition] 331. mary != sK1 <- (~5) [avatar component clause 329] 333. 6 <=> older(paul,mary) [avatar definition] 335. ~older(paul,mary) <- (~6) [avatar component clause 333] 336. ~5 | ~6 [avatar split clause 327,333,329] 337. ~older(paul,mary) | room(sK1) [subsumption resolution 291,246] 339. 7 <=> room(sK1) [avatar definition] 341. room(sK1) <- (7) [avatar component clause 339] 342. 7 | ~6 [avatar split clause 337,333,339] 351. old(mary) [resolution 324,246] 354. 3 [avatar split clause 351,309] 355. tall(mary) <- (3) [resolution 310,268] 362. ~quiet(mary) | ~old(mary) | ~room(mary) <- (3) [resolution 318,355] 369. ~quiet(mary) | ~room(mary) <- (3) [subsumption resolution 362,310] 370. ~quiet(mary) <- (3) [subsumption resolution 369,246] 371. ~2 | ~3 [avatar split clause 370,309,305] 423. quiet(mary) | ~tall(mary) | ~room(mary) <- (~6) [resolution 326,335] 426. ~tall(mary) | ~room(mary) <- (~2, ~6) [subsumption resolution 423,306] 427. ~room(mary) <- (~2, 3, ~6) [subsumption resolution 426,355] 428. $false <- (~2, 3, ~6) [subsumption resolution 427,246] 429. 2 | ~3 | 6 [avatar contradiction clause 428] 432. mary = sK1 <- (7) [resolution 341,247] 437. $false <- (~5, 7) [subsumption resolution 432,331] 438. 5 | ~7 [avatar contradiction clause 437] 439. $false [avatar sat refutation 336,342,354,371,429,438] % SZS output end Proof for 5749891439414354279994587 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0.304343
Tabitha is the only person in the room. Everyone anywhere is a quiet person if everyone in the room is tall and vice versa. Everyone in the room is a tall person only if only one person in the room is a old person. If everyone in the room either is not old or is not kind but not both then everyone in the room is a quiet person. Either at least one person in the room is a kind person or Tabitha is not quiet but not both. Everyone in the room is a quiet person. Everyone in the room either is a old person or is kind but not both. Tabitha is quiet.
Tabitha is tall.
contradiction
room(tabitha)&(![X]:(room(X)=>(X='tabitha')))& ((![X]:(room(X)=>(tall(X))))<=>(![X]:(anywhere(X)=>(quiet(X)&person(X)))))& ((![X]:(room(X)=>(tall(X)&person(X))))=>(((?[X]:(room(X)&old(X)&person(X)))&(![X,Y]:((room(X)&room(Y)&(old(X)&person(X))&(old(Y)&person(Y)))=>(X=Y))))))& ((![X]:(room(X)=>(((~old(X))<~>(~kind(X))))))=>(![X]:(room(X)=>(quiet(X)&person(X)))))& (((![X]:(anywhere(X)=>(quiet(X)&person(X))))=>(![X]:(room(X)=>(quiet(X)&person(X)))))&((~(![X]:(anywhere(X)=>(quiet(X)&person(X)))))=>(![X]:(room(X)=>(((quieter(christopher,X))|(quiet(X))))))))& ((((?[X]:(room(X)&kind(X)&person(X)))))<~>(~quiet(tabitha)))& (((?[X]:(room(X)&kind(X)&person(X)))))& (![X]:(room(X)=>(quiet(X)&person(X))))& (![X]:(room(X)=>(((quiet(X))=>(kind(X)&person(X))))))& (![X]:(room(X)=>(((old(X)&person(X))<~>(kind(X))))))& (quiet(tabitha))& (![X]:(room(X)=>(((quieter(debra,X))|(quieter(william,X))|(tall(X))))))
room(tabitha)&(![X]:(room(X)=>(X='tabitha')))& tall(tabitha)
[ "p0", "p2", "p5", "p7", "p9", "p10", "hypothesis" ]
% SZS status Unsatisfiable for 6693223170418443497888624 % SZS output start Proof for 6693223170418443497888624 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (person(X0) & tall(X0))) => (! [X0,X1] : ((person(X1) & old(X1) & person(X0) & old(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (person(X0) & old(X0) & room(X0))) [input p2] 49. ? [X0] : (person(X0) & kind(X0) & room(X0)) <~> ~quiet(mary) [input p5] 51. ! [X0] : (room(X0) => (person(X0) & quiet(X0))) [input p7] 53. ! [X0] : (room(X0) => ((person(X0) & old(X0)) <~> kind(X0))) [input p9] 54. quiet(mary) [input p10] 56. tall(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 58. ! [X0] : (room(X0) => (person(X0) & tall(X0))) => (! [X1,X2] : ((person(X2) & old(X2) & person(X1) & old(X1) & room(X2) & room(X1)) => X1 = X2) & ? [X3] : (person(X3) & old(X3) & room(X3))) [rectify 46] 132. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 134. (! [X1,X2] : (X1 = X2 | (~person(X2) | ~old(X2) | ~person(X1) | ~old(X1) | ~room(X2) | ~room(X1))) & ? [X3] : (person(X3) & old(X3) & room(X3))) | ? [X0] : ((~person(X0) | ~tall(X0)) & room(X0)) [ennf transformation 58] 135. (! [X1,X2] : (X1 = X2 | ~person(X2) | ~old(X2) | ~person(X1) | ~old(X1) | ~room(X2) | ~room(X1)) & ? [X3] : (person(X3) & old(X3) & room(X3))) | ? [X0] : ((~person(X0) | ~tall(X0)) & room(X0)) [flattening 134] 139. ! [X0] : ((person(X0) & quiet(X0)) | ~room(X0)) [ennf transformation 51] 142. ! [X0] : (((person(X0) & old(X0)) <~> kind(X0)) | ~room(X0)) [ennf transformation 53] 145. tall(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56] 152. (! [X0,X1] : (X0 = X1 | ~person(X1) | ~old(X1) | ~person(X0) | ~old(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (person(X2) & old(X2) & room(X2))) | ? [X3] : ((~person(X3) | ~tall(X3)) & room(X3)) [rectify 135] 153. ? [X2] : (person(X2) & old(X2) & room(X2)) => (person(sK2) & old(sK2) & room(sK2)) [choice axiom] 154. ? [X3] : ((~person(X3) | ~tall(X3)) & room(X3)) => ((~person(sK3) | ~tall(sK3)) & room(sK3)) [choice axiom] 155. (! [X0,X1] : (X0 = X1 | ~person(X1) | ~old(X1) | ~person(X0) | ~old(X0) | ~room(X1) | ~room(X0)) & (person(sK2) & old(sK2) & room(sK2))) | ((~person(sK3) | ~tall(sK3)) & room(sK3)) [skolemisation 152,154,153] 164. (quiet(mary) | ! [X0] : (~person(X0) | ~kind(X0) | ~room(X0))) & (~quiet(mary) | ? [X0] : (person(X0) & kind(X0) & room(X0))) [nnf transformation 49] 165. (quiet(mary) | ! [X0] : (~person(X0) | ~kind(X0) | ~room(X0))) & (~quiet(mary) | ? [X1] : (person(X1) & kind(X1) & room(X1))) [rectify 164] 166. ? [X1] : (person(X1) & kind(X1) & room(X1)) => (person(sK6) & kind(sK6) & room(sK6)) [choice axiom] 167. (quiet(mary) | ! [X0] : (~person(X0) | ~kind(X0) | ~room(X0))) & (~quiet(mary) | (person(sK6) & kind(sK6) & room(sK6))) [skolemisation 165,166] 170. ! [X0] : (((~kind(X0) | (~person(X0) | ~old(X0))) & (kind(X0) | (person(X0) & old(X0)))) | ~room(X0)) [nnf transformation 142] 171. ! [X0] : (((~kind(X0) | ~person(X0) | ~old(X0)) & (kind(X0) | (person(X0) & old(X0)))) | ~room(X0)) [flattening 170] 253. room(mary) [cnf transformation 132] 254. ~room(X0) | mary = X0 [cnf transformation 132] 261. room(sK2) | room(sK3) [cnf transformation 155] 262. room(sK2) | ~person(sK3) | ~tall(sK3) [cnf transformation 155] 263. old(sK2) | room(sK3) [cnf transformation 155] 264. old(sK2) | ~person(sK3) | ~tall(sK3) [cnf transformation 155] 281. ~quiet(mary) | room(sK6) [cnf transformation 167] 282. ~quiet(mary) | kind(sK6) [cnf transformation 167] 289. person(X0) | ~room(X0) [cnf transformation 139] 294. ~kind(X0) | ~person(X0) | ~old(X0) | ~room(X0) [cnf transformation 171] 295. quiet(mary) [cnf transformation 54] 299. tall(mary) [cnf transformation 145] 335. 8 <=> tall(sK3) [avatar definition] 337. ~tall(sK3) <- (~8) [avatar component clause 335] 339. 9 <=> person(sK3) [avatar definition] 347. 11 <=> room(sK3) [avatar definition] 349. room(sK3) <- (11) [avatar component clause 347] 358. 13 <=> old(sK2) [avatar definition] 360. old(sK2) <- (13) [avatar component clause 358] 361. ~8 | ~9 | 13 [avatar split clause 264,358,339,335] 362. 11 | 13 [avatar split clause 263,358,347] 364. 14 <=> room(sK2) [avatar definition] 366. room(sK2) <- (14) [avatar component clause 364] 367. ~8 | ~9 | 14 [avatar split clause 262,364,339,335] 368. 11 | 14 [avatar split clause 261,364,347] 378. 17 <=> ! [X0] : (person(X0) | ~room(X0)) [avatar definition] 379. ~room(X0) | person(X0) <- (17) [avatar component clause 378] 414. 24 <=> quiet(mary) [avatar definition] 424. 26 <=> kind(sK6) [avatar definition] 426. kind(sK6) <- (26) [avatar component clause 424] 427. 26 | ~24 [avatar split clause 282,414,424] 429. 27 <=> room(sK6) [avatar definition] 431. room(sK6) <- (27) [avatar component clause 429] 432. 27 | ~24 [avatar split clause 281,414,429] 433. 17 [avatar split clause 289,378] 435. 24 [avatar split clause 295,414] 438. person(mary) <- (17) [resolution 379,253] 440. person(sK3) <- (11, 17) [resolution 379,349] 443. 9 | ~11 | ~17 [avatar split clause 440,378,347,339] 451. mary = sK3 <- (11) [resolution 254,349] 452. mary = sK6 <- (27) [resolution 254,431] 460. ~tall(mary) <- (~8, 11) [backward demodulation 337,451] 462. $false <- (~8, 11) [subsumption resolution 460,299] 463. 8 | ~11 [avatar contradiction clause 462] 465. kind(mary) <- (26, 27) [backward demodulation 426,452] 476. mary = sK2 <- (14) [resolution 366,254] 480. old(mary) <- (13, 14) [backward demodulation 360,476] 487. ~person(mary) | ~old(mary) | ~room(mary) <- (26, 27) [resolution 294,465] 488. ~old(mary) | ~room(mary) <- (17, 26, 27) [subsumption resolution 487,438] 489. ~room(mary) <- (13, 14, 17, 26, 27) [subsumption resolution 488,480] 490. $false <- (13, 14, 17, 26, 27) [subsumption resolution 489,253] 491. ~13 | ~14 | ~17 | ~26 | ~27 [avatar contradiction clause 490] 492. $false [avatar sat refutation 361,362,367,368,427,432,433,435,443,463,491] % SZS output end Proof for 6693223170418443497888624 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------
0.590395
There is a room. If “someone in the room is an expert in identifying and foraging wild edible plants” then “at least one person in the room creates large-scale murals for public art installations”. If “it is not the case that “at least one person anywhere does not mentor a youth basketball team on weekends”” then “someone in the room maintains a large, organic vegetable garden year-round”. If someone hosts themed dinner parties featuring gourmet home-cooked meals, collect rare sneakers and does not create large-scale murals for public art installations then he/she plays the drums and is passionate about collecting and restoring classic cars and vice versa. Only one person in the room volunteers for local environmental conservation projects. Someone in the room uses contact lenses. Someone in the room mentors a youth basketball team on weekends. At least one person in the room is a coffee connoisseur. It is not the case that “more than one person anywhere own a television”. It is not the case that “it is not the case that “it is not the case that “more than one person in the room is a dedicated volunteer for local community service projects”””. Someone in the room enjoys watercolor painting. Someone in the room does not practice tai chi. If someone is a client of LVMH then he/she hosts regular workshops on creative writing and vice versa. More than one person in the room uses contact lenses. It is not the case that “it is not the case that “more than one person in the room collects luxury watches””. It is not the case that “it is not the case that “more than one person in the room is a client of LVMH””. If someone collects comic books, volunteers for local environmental conservation projects and enjoys skydiving then he/she does not host themed dinner parties featuring gourmet home-cooked meals and vice versa. It is not the case that “it is not the case that “it is true that “someone in the room hosts themed dinner parties featuring gourmet home-cooked meals”””. It is not the case that “someone in the room is an expert in identifying and foraging wild edible plants”. If someone is not an amateur astronomer who builds and uses custom telescopes then he/she enjoys watercolor painting and vice versa.
Everyone in the room is not a coffee connoisseur.
contradiction
(there_is_a_room)& ((?[X]:(room(X)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))=>(((?[X]:(room(X)&creates_large-scale_murals_for_public_art_installations(X))))))& ((~(((?[X]:(anywhere(X)&does_not_mentor_a_youth_basketball_team_on_weekends(X))))))=>(?[X]:(room(X)&(maintains_a_large,_organic_vegetable_garden_year-round(X)))))& ((![X]:((((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(collect_rare_sneakers(X))&(does_not_create_large-scale_murals_for_public_art_installations(X))))<=>(((plays_the_drums(X))&(is_passionate_about_collecting_and_restoring_classic_cars(X)))))))& (((?[X]:(room(X)&volunteers_for_local_environmental_conservation_projects(X)))&(![X,Y]:((room(X)&room(Y)&(volunteers_for_local_environmental_conservation_projects(X))&(volunteers_for_local_environmental_conservation_projects(Y)))=>(X=Y)))))& (?[X]:(room(X)&(uses_contact_lenses(X))))& (?[X]:(room(X)&(mentors_a_youth_basketball_team_on_weekends(X))))& (((?[X]:(room(X)&is_a_coffee_connoisseur(X)))))& (~((?[X,Y]:(anywhere(X)&anywhere(Y)&(own_a_television(X)&own_a_television(Y))&(X!=Y)))))& (~(~(~((?[X,Y]:(room(X)&room(Y)&(is_a_dedicated_volunteer_for_local_community_service_projects(X)&is_a_dedicated_volunteer_for_local_community_service_projects(Y))&(X!=Y)))))))& (?[X]:(room(X)&(enjoys_watercolor_painting(X))))& (?[X]:(room(X)&(does_not_practice_tai_chi(X))))& ((![X]:((is_a_client_of_LVMH(X))<=>(hosts_regular_workshops_on_creative_writing(X)))))& ((?[X,Y]:(room(X)&room(Y)&(uses_contact_lenses(X)&uses_contact_lenses(Y))&(X!=Y))))& (~(~((?[X,Y]:(room(X)&room(Y)&(collects_luxury_watches(X)&collects_luxury_watches(Y))&(X!=Y))))))& (~(~((?[X,Y]:(room(X)&room(Y)&(is_a_client_of_LVMH(X)&is_a_client_of_LVMH(Y))&(X!=Y))))))& ((![X]:((((collects_comic_books(X))&(volunteers_for_local_environmental_conservation_projects(X))&(enjoys_skydiving(X))))<=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& (~(~(?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (~(?[X]:(room(X)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))& ((![X]:((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=>(enjoys_watercolor_painting(X)))))& (~(?[X]:(room(X)&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))& (((?[X]:(room(X)&works_on_fridays(X)))))& (((?[X]:(room(X)&works_on_fridays(X)))&(![X,Y]:((room(X)&room(Y)&(works_on_fridays(X))&(works_on_fridays(Y)))=>(X=Y)))))& (~(~(?[X]:(anywhere(X)&(does_not_work_on_fridays(X))))))& (?[X]:(room(X)&(does_not_use_contact_lenses(X))))& (((?[X]:(room(X)&collect_rare_sneakers(X)))&(![X,Y]:((room(X)&room(Y)&(collect_rare_sneakers(X))&(collect_rare_sneakers(Y)))=>(X=Y)))))& ((![X]:((plays_the_drums(X))<=>(does_not_use_contact_lenses(X)))))& (?[X]:(room(X)&(plays_the_drums(X))))
(there_is_a_room)& ![X]:(room(X)=>(is_not_a_coffee_connoisseur(X)))
[ "p7", "hypothesis" ]
% SZS status Unsatisfiable for 998590909661087945342829 % SZS output start Proof for 998590909661087945342829 51. ? [X0] : (predm(X0) & room(X0)) [input p7] 72. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 100. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 72] 180. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 100] 194. ? [X0] : (predm(X0) & room(X0)) => (predm(sK5) & room(sK5)) [choice axiom] 195. predm(sK5) & room(sK5) [skolemisation 51,194] 316. room(sK5) [cnf transformation 195] 317. predm(sK5) [cnf transformation 195] 352. ~predm(X0) | ~room(X0) [cnf transformation 180] 367. ~room(sK5) [resolution 352,317] 368. $false [subsumption resolution 367,316] % SZS output end Proof for 998590909661087945342829 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------
0.488669
Marcia, Angelica, Timothy, Nancy, William are the only persons in the room. If “it is not the case that “Marcia practices pilates”” then “Marcia is an expert in identifying and foraging wild edible plants”. If “Marcia is an amateur astronomer who builds and uses custom telescopes” then “Marcia has a piercing”. If “Marcia practices pilates” then “Marcia writes and illustrates their own graphic novels”. “Marcia has a piercing” only if “Marcia is a scotch connoisseur”. If “Marcia practices kickboxing” then “Marcia collects foreign coins”. If “Marcia has a piercing” then “Marcia participates in long-distance cycling events across the country” otherwise “Marcia is a scotch connoisseur”. Either “it is not the case that “Marcia owns a 3D printer”” or “Marcia collects foreign coins” but not both. If someone is a scotch connoisseur then he/she works on fridays and vice versa. Marcia is a scotch connoisseur. At least one person in the room writes and illustrates their own graphic novels. It is not the case that “Marcia plays video games”. Marcia makes homemade pastries. Marcia is an amateur astronomer who builds and uses custom telescopes. If someone writes a travel blog and is an amateur astronomer who builds and uses custom telescopes then he/she has a piercing, plays video games or is a chess master who participates in national tournaments and vice versa. If someone participates in long-distance cycling events across the country then he/she practices pilates and vice versa. Marcia is a chess master who participates in national tournaments. Someone in the room does practice yoga. Marcia practices pilates, has a piercing or is an expert in identifying and foraging wild edible plants. Marcia bakes bread at home. Marcia travels domestically frequently. Marcia is a drone photographer.
Marcia writes a travel blog.
entailment
room(marcia)&room(angelica)&room(timothy)&room(nancy)&room(william)&(![X]:(room(X)=>(X='marcia'|X='angelica'|X='timothy'|X='nancy'|X='william')))& ((~(practices_pilates(marcia)))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(marcia)))& ((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(marcia))=>(has_a_piercing(marcia)))& ((practices_pilates(marcia))=>(writes_and_illustrates_their_own_graphic_novels(marcia)))& ((has_a_piercing(marcia))=>(is_a_scotch_connoisseur(marcia)))& ((practices_kickboxing(marcia))=>(collects_foreign_coins(marcia)))& (((has_a_piercing(marcia))=>(participates_in_long-distance_cycling_events_across_the_country(marcia)))&((~(has_a_piercing(marcia)))=>(is_a_scotch_connoisseur(marcia))))& ((~(owns_a_3D_printer(marcia)))<~>(collects_foreign_coins(marcia)))& ((![X]:((is_a_scotch_connoisseur(X))<=>(works_on_fridays(X)))))& (is_a_scotch_connoisseur(marcia))& (((?[X]:(room(X)&writes_and_illustrates_their_own_graphic_novels(X)))))& (~(plays_video_games(marcia)))& (makes_homemade_pastries(marcia))& (is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(marcia))& ((![X]:((((writes_a_travel_blog(X))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))<=>(((has_a_piercing(X))|(plays_video_games(X))|(is_a_chess_master_who_participates_in_national_tournaments(X)))))))& ((![X]:((participates_in_long-distance_cycling_events_across_the_country(X))<=>(practices_pilates(X)))))& (is_a_chess_master_who_participates_in_national_tournaments(marcia))& (?[X]:(room(X)&(does_practice_yoga(X))))& (((practices_pilates(marcia))|(has_a_piercing(marcia))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(marcia))))& (bakes_bread_at_home(marcia))& (travels_domestically_frequently(marcia))& (is_a_drone_photographer(marcia))
room(marcia)&room(angelica)&room(timothy)&room(nancy)&room(william)&(![X]:(room(X)=>(X='marcia'|X='angelica'|X='timothy'|X='nancy'|X='william')))& writes_a_travel_blog(marcia)
[ "p0", "p2", "p13", "p14", "hypothesis" ]
% SZS status Unsatisfiable for 2290752587537126033977908 % SZS output start Proof for 2290752587537126033977908 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. predz(mary) => predp(mary) [input p2] 57. predz(mary) [input p13] 58. ! [X0] : ((predz(X0) & predb(X0)) <=> (predt(X0) | predi(X0) | predp(X0))) [input p14] 66. ~(predb(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] 157. ! [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] 158. ! [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] 159. predp(mary) | ~predz(mary) [ennf transformation 46] 160. ~predb(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 66] 161. ~predb(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 160] 166. ! [X0] : (((predz(X0) & predb(X0)) | (~predt(X0) & ~predi(X0) & ~predp(X0))) & ((predt(X0) | predi(X0) | predp(X0)) | (~predz(X0) | ~predb(X0)))) [nnf transformation 58] 167. ! [X0] : (((predz(X0) & predb(X0)) | (~predt(X0) & ~predi(X0) & ~predp(X0))) & (predt(X0) | predi(X0) | predp(X0) | ~predz(X0) | ~predb(X0))) [flattening 166] 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. ~predb(mary) | (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 161,170] 252. room(mary) [cnf transformation 158] 253. room(paul) [cnf transformation 158] 254. room(fred) [cnf transformation 158] 255. room(alice) [cnf transformation 158] 256. room(john) [cnf transformation 158] 257. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 158] 258. predp(mary) | ~predz(mary) [cnf transformation 159] 263. predz(mary) [cnf transformation 57] 265. ~predp(X0) | predb(X0) [cnf transformation 167] 273. ~predb(mary) | room(sK2) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 274. ~predb(mary) | mary != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 275. ~predb(mary) | paul != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 276. ~predb(mary) | fred != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 277. ~predb(mary) | alice != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 278. ~predb(mary) | john != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 280. 1 <=> predz(mary) [avatar definition] 284. 2 <=> predp(mary) [avatar definition] 286. predp(mary) <- (2) [avatar component clause 284] 287. ~1 | 2 [avatar split clause 258,284,280] 298. 1 [avatar split clause 263,280] 299. ~predb(mary) | john != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,256] 300. ~predb(mary) | john != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 299,255] 301. ~predb(mary) | john != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 300,254] 302. ~predb(mary) | john != sK2 | ~room(mary) [subsumption resolution 301,253] 303. ~predb(mary) | john != sK2 [subsumption resolution 302,252] 305. 5 <=> john = sK2 [avatar definition] 307. john != sK2 <- (~5) [avatar component clause 305] 309. 6 <=> predb(mary) [avatar definition] 312. ~5 | ~6 [avatar split clause 303,309,305] 313. ~predb(mary) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,256] 314. ~predb(mary) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,255] 315. ~predb(mary) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 314,254] 316. ~predb(mary) | alice != sK2 | ~room(mary) [subsumption resolution 315,253] 317. ~predb(mary) | alice != sK2 [subsumption resolution 316,252] 319. 7 <=> alice = sK2 [avatar definition] 321. alice != sK2 <- (~7) [avatar component clause 319] 322. ~7 | ~6 [avatar split clause 317,309,319] 323. ~predb(mary) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,256] 324. ~predb(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 323,255] 325. ~predb(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 324,254] 326. ~predb(mary) | fred != sK2 | ~room(mary) [subsumption resolution 325,253] 327. ~predb(mary) | fred != sK2 [subsumption resolution 326,252] 329. 8 <=> fred = sK2 [avatar definition] 331. fred != sK2 <- (~8) [avatar component clause 329] 332. ~8 | ~6 [avatar split clause 327,309,329] 333. ~predb(mary) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,256] 334. ~predb(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 333,255] 335. ~predb(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 334,254] 336. ~predb(mary) | paul != sK2 | ~room(mary) [subsumption resolution 335,253] 337. ~predb(mary) | paul != sK2 [subsumption resolution 336,252] 339. 9 <=> paul = sK2 [avatar definition] 341. paul != sK2 <- (~9) [avatar component clause 339] 342. ~9 | ~6 [avatar split clause 337,309,339] 343. ~predb(mary) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,256] 344. ~predb(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 343,255] 345. ~predb(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 344,254] 346. ~predb(mary) | mary != sK2 | ~room(mary) [subsumption resolution 345,253] 347. ~predb(mary) | mary != sK2 [subsumption resolution 346,252] 349. 10 <=> mary = sK2 [avatar definition] 351. mary != sK2 <- (~10) [avatar component clause 349] 352. ~10 | ~6 [avatar split clause 347,309,349] 353. ~predb(mary) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,256] 354. ~predb(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 353,255] 355. ~predb(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 354,254] 356. ~predb(mary) | room(sK2) | ~room(mary) [subsumption resolution 355,253] 357. ~predb(mary) | room(sK2) [subsumption resolution 356,252] 359. 11 <=> room(sK2) [avatar definition] 361. room(sK2) <- (11) [avatar component clause 359] 362. 11 | ~6 [avatar split clause 357,309,359] 363. predb(mary) <- (2) [resolution 265,286] 366. 6 | ~2 [avatar split clause 363,284,309] 414. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (11) [resolution 257,361] 457. fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (~7, 11) [subsumption resolution 414,321] 458. paul = sK2 | mary = sK2 | john = sK2 <- (~7, ~8, 11) [subsumption resolution 457,331] 459. mary = sK2 | john = sK2 <- (~7, ~8, ~9, 11) [subsumption resolution 458,341] 460. john = sK2 <- (~7, ~8, ~9, ~10, 11) [subsumption resolution 459,351] 461. $false <- (~5, ~7, ~8, ~9, ~10, 11) [subsumption resolution 460,307] 462. 5 | 7 | 8 | 9 | 10 | ~11 [avatar contradiction clause 461] 463. $false [avatar sat refutation 287,298,312,322,332,342,352,362,366,462] % SZS output end Proof for 2290752587537126033977908 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------
0.424127
Mark, Jean, Russell are the only persons in the room. “Everyone in the room frequently participates in hackathons and coding competitions or does not practice digital art” unless “Mark is passionate about collecting and restoring classic cars”. Jean does not have a piercing or is an avid mountain climber who has scaled several peaks or both. Everyone in the room frequently participates in hackathons and coding competitions or does not practice digital art. It is not the case that “Mark does not collect vintage vinyl records”. Jean neither enjoys deep-sea diving and exploring underwater caves nor collects first edition books. If someone practices digital art then he/she enjoys kayaking and exploring remote waterways and does not travel domestically frequently and vice versa. Everyone in the room has a piercing. At least one person in the room hosts regular game nights featuring complex strategy games. At least one person in the room own a television. Mark does not enjoy landscape photography. Everyone in the room enjoys landscape photography if they enjoys deep-sea diving and exploring underwater caves.
More than one person in the room enjoys deep-sea diving and exploring underwater caves.
contradiction
room(mark)&room(jean)&room(russell)&(![X]:(room(X)=>(X='mark'|X='jean'|X='russell')))& (~(is_passionate_about_collecting_and_restoring_classic_cars(mark))=>(![X]:(room(X)=>(((does_not_practice_digital_art(X))|(frequently_participates_in_hackathons_and_coding_competitions(X)))))))& (((does_not_have_a_piercing(jean))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(jean))))& (![X]:(room(X)=>(((does_not_practice_digital_art(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (~(does_not_collect_vintage_vinyl_records(mark)))& (~((enjoys_deep-sea_diving_and_exploring_underwater_caves(jean))|(collects_first_edition_books(jean))))& ((![X]:((practices_digital_art(X))<=>(((enjoys_kayaking_and_exploring_remote_waterways(X))&(does_not_travel_domestically_frequently(X)))))))& (![X]:(room(X)=>(has_a_piercing(X))))& (((?[X]:(room(X)&hosts_regular_game_nights_featuring_complex_strategy_games(X)))))& (((?[X]:(room(X)&own_a_television(X)))))& (does_not_enjoy_landscape_photography(mark))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(enjoys_landscape_photography(X))))))
room(mark)&room(jean)&room(russell)&(![X]:(room(X)=>(X='mark'|X='jean'|X='russell')))& (?[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)))
[ "p0", "p5", "p10", "p11", "hypothesis" ]
% SZS status Unsatisfiable for 7349774576035708104380877 % SZS output start Proof for 7349774576035708104380877 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ~(predc(paul) | predr(paul)) [input p5] 54. ~predj(mary) [input p10] 55. ! [X0] : (room(X0) => (predr(X0) => predj(X0))) [input p11] 56. ? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 57. ? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (fred = X2 | paul = X2 | mary = X2)) & room(fred) & room(paul) & room(mary) [rectify 56] 64. ~predr(paul) [pure predicate removal 49] 140. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 141. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 140] 142. ~predr(paul) [ennf transformation 64] 143. ! [X0] : ((predj(X0) | ~predr(X0)) | ~room(X0)) [ennf transformation 55] 144. ! [X0] : (predj(X0) | ~predr(X0) | ~room(X0)) [flattening 143] 145. ? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) & ! [X2] : ((fred = X2 | paul = X2 | mary = X2) | ~room(X2)) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 146. ? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [flattening 145] 152. ? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) => (sK2 != sK3 & predr(sK3) & predr(sK2) & room(sK3) & room(sK2)) [choice axiom] 153. (sK2 != sK3 & predr(sK3) & predr(sK2) & room(sK3) & room(sK2)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [skolemisation 146,152] 237. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 141] 238. ~predr(paul) [cnf transformation 142] 241. ~predj(mary) [cnf transformation 54] 242. ~predr(X0) | predj(X0) | ~room(X0) [cnf transformation 144] 247. room(sK2) [cnf transformation 153] 248. room(sK3) [cnf transformation 153] 249. predr(sK2) [cnf transformation 153] 250. predr(sK3) [cnf transformation 153] 251. sK2 != sK3 [cnf transformation 153] 252. predj(sK2) | ~room(sK2) [resolution 242,249] 253. predj(sK3) | ~room(sK3) [resolution 242,250] 254. predj(sK2) [subsumption resolution 252,247] 255. predj(sK3) [subsumption resolution 253,248] 303. paul = sK2 | mary = sK2 | fred = sK2 [resolution 237,247] 304. paul = sK3 | mary = sK3 | fred = sK3 [resolution 237,248] 332. 7 <=> fred = sK2 [avatar definition] 336. 8 <=> mary = sK2 [avatar definition] 338. mary = sK2 <- (8) [avatar component clause 336] 340. 9 <=> paul = sK2 [avatar definition] 342. paul = sK2 <- (9) [avatar component clause 340] 343. 7 | 8 | 9 [avatar split clause 303,340,336,332] 345. 10 <=> fred = sK3 [avatar definition] 347. fred = sK3 <- (10) [avatar component clause 345] 349. 11 <=> mary = sK3 [avatar definition] 351. mary = sK3 <- (11) [avatar component clause 349] 353. 12 <=> paul = sK3 [avatar definition] 355. paul = sK3 <- (12) [avatar component clause 353] 356. 10 | 11 | 12 [avatar split clause 304,353,349,345] 360. fred != sK2 <- (10) [backward demodulation 251,347] 361. ~7 | ~10 [avatar split clause 360,345,332] 367. predj(mary) <- (8) [backward demodulation 254,338] 370. $false <- (8) [subsumption resolution 367,241] 371. ~8 [avatar contradiction clause 370] 375. predr(paul) <- (9) [backward demodulation 249,342] 377. $false <- (9) [subsumption resolution 375,238] 378. ~9 [avatar contradiction clause 377] 379. predj(mary) <- (11) [backward demodulation 255,351] 383. $false <- (11) [subsumption resolution 379,241] 384. ~11 [avatar contradiction clause 383] 392. predr(paul) <- (12) [backward demodulation 250,355] 394. $false <- (12) [subsumption resolution 392,238] 395. ~12 [avatar contradiction clause 394] 396. $false [avatar sat refutation 343,356,361,371,378,384,395] % SZS output end Proof for 7349774576035708104380877 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------
0.067102
There is a room. Everyone in the room makes homemade pastries only if they is a tea enthusiast. Everyone in the room makes homemade pastries. Everyone in the room does not make homemade pastries or makes homemade pastries. Everyone in the room enjoys skydiving. Everyone in the room makes homemade pastries if they is a tea enthusiast. Everyone in the room who makes homemade pastries enjoys skydiving. Everyone in the room who enjoys skydiving does not enjoy skydiving. Everyone outside the room enjoys skydiving if they does not enjoy skydiving.
Everyone outside the room does not enjoy skydiving.
contradiction
(there_is_a_room)& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))<=(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(makes_homemade_pastries(X))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))|(does_not_make_homemade_pastries(X))))))& (![X]:(room(X)=>(enjoys_skydiving(X))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))=>(enjoys_skydiving(X))))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(does_not_enjoy_skydiving(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_skydiving(X))=>(enjoys_skydiving(X))))))
(there_is_a_room)& ![X]:(~room(X)=>(does_not_enjoy_skydiving(X)))
[ "p4", "p7", "p8", "hypothesis" ]
% SZS status Unsatisfiable for 468737750615551212559277 % SZS output start Proof for 468737750615551212559277 48. ! [X0] : (room(X0) => preda(X0)) [input p4] 51. ! [X0] : (room(X0) => (preda(X0) => ~preda(X0))) [input p7] 52. ! [X0] : (~room(X0) => (~preda(X0) => preda(X0))) [input p8] 53. ! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room [input hypothesis] 55. ! [X0] : (~room(X0) => ~preda(X0)) [pure predicate removal 53] 133. ! [X0] : (preda(X0) | ~room(X0)) [ennf transformation 48] 138. ! [X0] : ((~preda(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 51] 139. ! [X0] : (~preda(X0) | ~preda(X0) | ~room(X0)) [flattening 138] 140. ! [X0] : ((preda(X0) | preda(X0)) | room(X0)) [ennf transformation 52] 141. ! [X0] : (preda(X0) | preda(X0) | room(X0)) [flattening 140] 142. ! [X0] : (~preda(X0) | room(X0)) [ennf transformation 55] 227. preda(X0) | ~room(X0) [cnf transformation 133] 230. ~preda(X0) | ~preda(X0) | ~room(X0) [cnf transformation 139] 231. preda(X0) | preda(X0) | room(X0) [cnf transformation 141] 232. ~preda(X0) | room(X0) [cnf transformation 142] 233. preda(X0) | room(X0) [duplicate literal removal 231] 234. ~preda(X0) | ~room(X0) [duplicate literal removal 230] 235. ~room(X0) [subsumption resolution 234,227] 236. preda(X0) [subsumption resolution 233,235] 237. room(X0) [subsumption resolution 232,236] 238. $false [subsumption resolution 237,235] % SZS output end Proof for 468737750615551212559277 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.033 s % ------------------------------ % ------------------------------
0.120967
Juan, Joseph, Oleta are the only persons in the room. “Everyone outside the room practices archery or is not a night owl” only if “at least one person in the room has a piercing”. “Oleta practices archery” if “Juan neither has a piercing nor owns a high-end gaming PC with custom-built components” and vice versa. Not everyone in the room who does not enjoy snowboarding creates augmented reality experiences for mobile applications. Juan enjoys virtual reality gaming. Joseph is not a night owl. Everyone in the room who practices graffiti art practices tai chi. Someone anywhere is a drone photographer. If someone enjoys bird watching then he/she does not enjoy virtual reality gaming, practices tai chi and creates augmented reality experiences for mobile applications. More than one person in the room does not enjoy snowboarding. Not everyone in the room who collects rare minerals practices archery. Everyone in the room either creates augmented reality experiences for mobile applications or owns a significant collection of rare gemstones and minerals but not both if they practices archery. Not everyone in the room who either creates augmented reality experiences for mobile applications or owns a significant collection of rare gemstones and minerals but not both enjoys snowboarding. If someone creates augmented reality experiences for mobile applications then he/she hosts themed dinner parties featuring gourmet home-cooked meals and practices graffiti art. Everyone in the room owns a significant collection of rare gemstones and minerals if they neither practices tai chi nor has a piercing and vice versa. Everyone in the room who neither practices tai chi nor has a piercing is not a craft beer aficionado. Joseph enjoys snowboarding. Joseph does not collect rare minerals. Everyone outside the room practices graffiti art if they practices tai chi. If someone collects rare minerals then he/she practices graffiti art. Everyone outside the room practices archery or is not a night owl. Everyone in the room who collects rare minerals does not host themed dinner parties featuring gourmet home-cooked meals. Everyone in the room enjoys virtual reality gaming if they does not host themed dinner parties featuring gourmet home-cooked meals. Oleta practices archery. Everyone in the room collects rare minerals if they either enjoys virtual reality gaming or is a craft beer aficionado but not both.
Juan creates augmented reality experiences for mobile applications.
contradiction
room(juan)&room(joseph)&room(oleta)&(![X]:(room(X)=>(X='juan'|X='joseph'|X='oleta')))& ((![X]:(~room(X)=>(((is_not_a_night_owl(X))|(practices_archery(X))))))=>(((?[X]:(room(X)&has_a_piercing(X))))))& ((~((has_a_piercing(juan))|(owns_a_high-end_gaming_PC_with_custom-built_components(juan))))<=>(practices_archery(oleta)))& (~![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (enjoys_virtual_reality_gaming(juan))& (is_not_a_night_owl(joseph))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(practices_tai_chi(X))))))& (?[X]:(anywhere(X)&(is_a_drone_photographer(X))))& ((![X]:((enjoys_bird_watching(X))=>(((does_not_enjoy_virtual_reality_gaming(X))&(practices_tai_chi(X))&(creates_augmented_reality_experiences_for_mobile_applications(X)))))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_enjoy_snowboarding(X)&does_not_enjoy_snowboarding(Y))&(X!=Y))))& (~![X]:(room(X)=>(((collects_rare_minerals(X))=>(practices_archery(X))))))& (![X]:(room(X)=>(((practices_archery(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))<~>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))))& (~![X]:(room(X)=>(((((creates_augmented_reality_experiences_for_mobile_applications(X))<~>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(enjoys_snowboarding(X))))))& ((![X]:((creates_augmented_reality_experiences_for_mobile_applications(X))=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(practices_graffiti_art(X)))))))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<=>(~((practices_tai_chi(X))|(has_a_piercing(X))))))))& (![X]:(room(X)=>(((~((practices_tai_chi(X))|(has_a_piercing(X))))=>(is_not_a_craft_beer_aficionado(X))))))& (enjoys_snowboarding(joseph))& (does_not_collect_rare_minerals(joseph))& (![X]:(~room(X)=>(((practices_tai_chi(X))=>(practices_graffiti_art(X))))))& ((![X]:((collects_rare_minerals(X))=>(practices_graffiti_art(X)))))& (![X]:(~room(X)=>(((is_not_a_night_owl(X))|(practices_archery(X))))))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(enjoys_virtual_reality_gaming(X))))))& (practices_archery(oleta))& (![X]:(room(X)=>(((((enjoys_virtual_reality_gaming(X))<~>(is_a_craft_beer_aficionado(X))))=>(collects_rare_minerals(X))))))
room(juan)&room(joseph)&room(oleta)&(![X]:(room(X)=>(X='juan'|X='joseph'|X='oleta')))& creates_augmented_reality_experiences_for_mobile_applications(juan)
[ "p0", "p10", "p13", "p17", "p21", "p23", "hypothesis" ]
% SZS status Unsatisfiable for 1340653665770218074122349 % SZS output start Proof for 1340653665770218074122349 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 54. ~! [X0] : (room(X0) => (predb(X0) => predf(X0))) [input p10] 57. ! [X0] : (preda(X0) => (predg(X0) & predi(X0))) [input p13] 61. ~predb(paul) [input p17] 65. ! [X0] : (room(X0) => (predb(X0) => ~predi(X0))) [input p21] 67. predf(fred) [input p23] 69. preda(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 146. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 147. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 146] 155. ? [X0] : ((~predf(X0) & predb(X0)) & room(X0)) [ennf transformation 54] 156. ? [X0] : (~predf(X0) & predb(X0) & room(X0)) [flattening 155] 161. ! [X0] : ((predg(X0) & predi(X0)) | ~preda(X0)) [ennf transformation 57] 170. ! [X0] : ((~predi(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 65] 171. ! [X0] : (~predi(X0) | ~predb(X0) | ~room(X0)) [flattening 170] 176. preda(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 69] 177. preda(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 176] 189. ? [X0] : (~predf(X0) & predb(X0) & room(X0)) => (~predf(sK5) & predb(sK5) & room(sK5)) [choice axiom] 190. ~predf(sK5) & predb(sK5) & room(sK5) [skolemisation 156,189] 279. room(mary) [cnf transformation 147] 282. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 147] 303. room(sK5) [cnf transformation 190] 304. predb(sK5) [cnf transformation 190] 305. ~predf(sK5) [cnf transformation 190] 312. ~preda(X0) | predi(X0) [cnf transformation 161] 319. ~predb(paul) [cnf transformation 61] 323. ~predi(X0) | ~predb(X0) | ~room(X0) [cnf transformation 171] 325. predf(fred) [cnf transformation 67] 332. preda(mary) [cnf transformation 177] 360. 6 <=> predf(fred) [avatar definition] 361. predf(fred) <- (6) [avatar component clause 360] 384. 6 [avatar split clause 325,360] 385. predi(mary) [resolution 312,332] 404. ~predb(mary) | ~room(mary) [resolution 323,385] 406. ~predb(mary) [subsumption resolution 404,279] 730. paul = sK5 | mary = sK5 | fred = sK5 [resolution 282,303] 785. 65 <=> fred = sK5 [avatar definition] 787. fred = sK5 <- (65) [avatar component clause 785] 789. 66 <=> mary = sK5 [avatar definition] 791. mary = sK5 <- (66) [avatar component clause 789] 793. 67 <=> paul = sK5 [avatar definition] 795. paul = sK5 <- (67) [avatar component clause 793] 796. 65 | 66 | 67 [avatar split clause 730,793,789,785] 820. ~predf(fred) <- (65) [backward demodulation 305,787] 827. $false <- (6, 65) [subsumption resolution 820,361] 828. ~6 | ~65 [avatar contradiction clause 827] 891. predb(mary) <- (66) [backward demodulation 304,791] 897. $false <- (66) [subsumption resolution 891,406] 898. ~66 [avatar contradiction clause 897] 927. predb(paul) <- (67) [backward demodulation 304,795] 934. $false <- (67) [subsumption resolution 927,319] 935. ~67 [avatar contradiction clause 934] 976. $false [avatar sat refutation 384,796,828,898,935] % SZS output end Proof for 1340653665770218074122349 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.042 s % ------------------------------ % ------------------------------
0.026663
Barbara, Mildred are the only persons in the room. If “not everyone in the room does not enjoy making ceramics or enjoys making ceramics” then “everyone in the room who has a specialized collection of handmade artisan pottery enjoys kayaking”. If “at least one person in the room owns a significant collection of rare gemstones and minerals” then “everyone in the room does not design and sews custom cosplay costumes for conventions or enjoys kayaking”. If “everyone in the room does not design and sews custom cosplay costumes for conventions or enjoys kayaking” then “not everyone in the room practices calligraphy if they does not design and sews custom cosplay costumes for conventions”. If “everyone in the room is not a scotch connoisseur or has lived in exactly three countries” then “no one anywhere enjoys virtual reality gaming if they is not a scotch connoisseur”. “Everyone in the room who has lived in exactly three countries either plays the drums or has a vast collection of first-edition science fiction novels but not both” if “everyone in the room has a vast collection of first-edition science fiction novels”. Barbara who practices calligraphy drives a hybrid car. Everyone in the room designs and sews custom cosplay costumes for conventions only if they is a night owl. Everyone in the room does not have a vast collection of first-edition science fiction novels, makes homemade pastries or has a curated collection of mid-century modern furniture if they is a night owl. Everyone outside the room who does not have a vast collection of first-edition science fiction novels, makes homemade pastries or has a curated collection of mid-century modern furniture owns a significant collection of rare gemstones and minerals. Someone in the room does not have a specialized collection of handmade artisan pottery. Everyone in the room who has a vast collection of first-edition science fiction novels has lived in exactly three countries, does not enjoy fishing and practices calligraphy.
Everyone in the room does not enjoy fishing.
entailment
room(barbara)&room(mildred)&(![X]:(room(X)=>(X='barbara'|X='mildred')))& ((~![X]:(room(X)=>(((enjoys_making_ceramics(X))|(does_not_enjoy_making_ceramics(X))))))=>(![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(enjoys_kayaking(X)))))))& (((((?[X]:(room(X)&owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))=>(![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))))& ((![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(~![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))=>(practices_calligraphy(X))))))))& ((![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))|(is_not_a_scotch_connoisseur(X))))))=>(~?[X]:(anywhere(X)=>(((is_not_a_scotch_connoisseur(X))=>(enjoys_virtual_reality_gaming(X)))))))& ((![X]:(room(X)=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))=>(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(((plays_the_drums(X))<~>(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))))& ((practices_calligraphy(barbara))&(drives_a_hybrid_car(barbara)))& (![X]:(room(X)=>(((is_a_night_owl(X))<=(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(makes_homemade_pastries(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))))& (![X]:(~room(X)=>(((((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(makes_homemade_pastries(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (?[X]:(room(X)&(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(((has_lived_in_exactly_three_countries(X))&(does_not_enjoy_fishing(X))&(practices_calligraphy(X))))))))& ((![X]:((has_a_curated_collection_of_mid-century_modern_furniture(X))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(does_not_make_homemade_pastries(X))))))& (![X]:(room(X)=>(((does_not_make_homemade_pastries(X))=>(is_an_avid_hiker(X))))))& (?[X]:(room(X)&(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))& (((?[X]:(room(X)&enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))& (![X]:(room(X)=>(((enjoys_fishing(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))
room(barbara)&room(mildred)&(![X]:(room(X)=>(X='barbara'|X='mildred')))& ![X]:(room(X)=>(does_not_enjoy_fishing(X)))
[ "p0", "hypothesis" ]
% SZS status Unsatisfiable for 853090798887359347323164 % SZS output start Proof for 853090798887359347323164 44. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ? [X0] : (predt(X0) & room(X0)) & ? [X0] : (~predh(X0) & room(X0)) & ! [X0] : (room(X0) => (~predo(X0) => predc(X0))) & ! [X0] : (room(X0) => (predg(X0) => ~predo(X0))) & ! [X0] : (predy(X0) <=> predt(X0)) & ! [X0] : (room(X0) => (predh(X0) => (predg(X0) & ~predn(X0) & preda(X0)))) & ? [X0] : (~predv(X0) & room(X0)) & ! [X0] : (~room(X0) => ((predy(X0) | predo(X0) | ~predh(X0)) => predr(X0))) & ! [X0] : (room(X0) => (predj(X0) => (predy(X0) | predo(X0) | ~predh(X0)))) & ! [X0] : (room(X0) => (predm(X0) => predj(X0))) & predd(mary) & predg(mary) & (! [X0] : (room(X0) => predh(X0)) => ! [X0] : (room(X0) => (preda(X0) => (prede(X0) <~> predh(X0))))) & (! [X0] : (room(X0) => (~predp(X0) | preda(X0))) => ~? [X0] : (anywhere(X0) => (~predp(X0) => predb(X0)))) & (! [X0] : (room(X0) => (~predm(X0) | predl(X0))) => ~! [X0] : (room(X0) => (~predm(X0) => predg(X0)))) & (? [X0] : (predr(X0) & room(X0)) => ! [X0] : (room(X0) => (~predm(X0) | predl(X0)))) & (~! [X0] : (room(X0) => (~predx(X0) | predx(X0))) => ! [X0] : (room(X0) => (predv(X0) => predl(X0)))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~(! [X0] : (room(X0) => ~predn(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X3] : (room(X3) => (~predo(X3) => predc(X3))) & ! [X4] : (room(X4) => (predg(X4) => ~predo(X4))) & ! [X5] : (predy(X5) <=> predt(X5)) & ! [X6] : (room(X6) => (predh(X6) => (predg(X6) & ~predn(X6) & preda(X6)))) & ? [X7] : (~predv(X7) & room(X7)) & ! [X8] : (~room(X8) => ((predy(X8) | predo(X8) | ~predh(X8)) => predr(X8))) & ! [X9] : (room(X9) => (predj(X9) => (predy(X9) | predo(X9) | ~predh(X9)))) & ! [X10] : (room(X10) => (predm(X10) => predj(X10))) & predd(mary) & predg(mary) & (! [X11] : (room(X11) => predh(X11)) => ! [X12] : (room(X12) => (preda(X12) => (prede(X12) <~> predh(X12))))) & (! [X13] : (room(X13) => (~predp(X13) | preda(X13))) => ~? [X14] : (anywhere(X14) => (~predp(X14) => predb(X14)))) & (! [X15] : (room(X15) => (~predm(X15) | predl(X15))) => ~! [X16] : (room(X16) => (~predm(X16) => predg(X16)))) & (? [X17] : (predr(X17) & room(X17)) => ! [X18] : (room(X18) => (~predm(X18) | predl(X18)))) & (~! [X19] : (room(X19) => (~predx(X19) | predx(X19))) => ! [X20] : (room(X20) => (predv(X20) => predl(X20)))) & ! [X21] : (room(X21) => (paul = X21 | mary = X21)) & room(paul) & room(mary) [rectify 44] 47. ~(! [X0] : (room(X0) => ~predn(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary)) [rectify 45] 48. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X4] : (room(X4) => (predg(X4) => ~predo(X4))) & ! [X5] : (predy(X5) <=> predt(X5)) & ! [X6] : (room(X6) => (predh(X6) => (predg(X6) & ~predn(X6) & preda(X6)))) & ? [X7] : (~predv(X7) & room(X7)) & ! [X8] : (~room(X8) => ((predy(X8) | predo(X8) | ~predh(X8)) => predr(X8))) & ! [X9] : (room(X9) => (predj(X9) => (predy(X9) | predo(X9) | ~predh(X9)))) & ! [X10] : (room(X10) => (predm(X10) => predj(X10))) & predd(mary) & predg(mary) & (! [X11] : (room(X11) => predh(X11)) => ! [X12] : (room(X12) => (preda(X12) => (prede(X12) <~> predh(X12))))) & (! [X13] : (room(X13) => (~predp(X13) | preda(X13))) => ~? [X14] : (anywhere(X14) => (~predp(X14) => predb(X14)))) & (! [X15] : (room(X15) => (~predm(X15) | predl(X15))) => ~! [X16] : (room(X16) => (~predm(X16) => predg(X16)))) & (? [X17] : (predr(X17) & room(X17)) => ! [X18] : (room(X18) => (~predm(X18) | predl(X18)))) & (~! [X19] : (room(X19) => (~predx(X19) | predx(X19))) => ! [X20] : (room(X20) => (predv(X20) => predl(X20)))) & ! [X21] : (room(X21) => (paul = X21 | mary = X21)) & room(paul) & room(mary) [pure predicate removal 46] 49. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X4] : (room(X4) => (predg(X4) => ~predo(X4))) & ! [X5] : (predy(X5) <=> predt(X5)) & ! [X6] : (room(X6) => (predh(X6) => (predg(X6) & ~predn(X6) & preda(X6)))) & ? [X7] : (~predv(X7) & room(X7)) & ! [X8] : (~room(X8) => ((predy(X8) | predo(X8) | ~predh(X8)) => predr(X8))) & ! [X9] : (room(X9) => (predj(X9) => (predy(X9) | predo(X9) | ~predh(X9)))) & ! [X10] : (room(X10) => (predm(X10) => predj(X10))) & predg(mary) & (! [X11] : (room(X11) => predh(X11)) => ! [X12] : (room(X12) => (preda(X12) => (prede(X12) <~> predh(X12))))) & (! [X13] : (room(X13) => (~predp(X13) | preda(X13))) => ~? [X14] : (anywhere(X14) => (~predp(X14) => predb(X14)))) & (! [X15] : (room(X15) => (~predm(X15) | predl(X15))) => ~! [X16] : (room(X16) => (~predm(X16) => predg(X16)))) & (? [X17] : (predr(X17) & room(X17)) => ! [X18] : (room(X18) => (~predm(X18) | predl(X18)))) & (~! [X19] : (room(X19) => (~predx(X19) | predx(X19))) => ! [X20] : (room(X20) => (predv(X20) => predl(X20)))) & ! [X21] : (room(X21) => (paul = X21 | mary = X21)) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X4] : (room(X4) => (predg(X4) => ~predo(X4))) & ! [X5] : (predy(X5) <=> predt(X5)) & ! [X6] : (room(X6) => (predh(X6) => (predg(X6) & ~predn(X6) & preda(X6)))) & ? [X7] : (~predv(X7) & room(X7)) & ! [X8] : (~room(X8) => ((predy(X8) | predo(X8) | ~predh(X8)) => predr(X8))) & ! [X9] : (room(X9) => (predj(X9) => (predy(X9) | predo(X9) | ~predh(X9)))) & ! [X10] : (room(X10) => (predm(X10) => predj(X10))) & predg(mary) & (! [X11] : (room(X11) => predh(X11)) => ! [X12] : (room(X12) => (preda(X12) => (prede(X12) <~> predh(X12))))) & (! [X13] : (room(X13) => (~predp(X13) | preda(X13))) => ~? [X14] : (anywhere(X14) => ~~predp(X14))) & (! [X15] : (room(X15) => (~predm(X15) | predl(X15))) => ~! [X16] : (room(X16) => (~predm(X16) => predg(X16)))) & (? [X17] : (predr(X17) & room(X17)) => ! [X18] : (room(X18) => (~predm(X18) | predl(X18)))) & (~! [X19] : (room(X19) => (~predx(X19) | predx(X19))) => ! [X20] : (room(X20) => (predv(X20) => predl(X20)))) & ! [X21] : (room(X21) => (paul = X21 | mary = X21)) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X4] : (room(X4) => (predg(X4) => ~predo(X4))) & ! [X5] : (predy(X5) <=> predt(X5)) & ! [X6] : (room(X6) => (predh(X6) => (predg(X6) & ~predn(X6) & preda(X6)))) & ? [X7] : room(X7) & ! [X8] : (~room(X8) => ((predy(X8) | predo(X8) | ~predh(X8)) => predr(X8))) & ! [X9] : (room(X9) => (predj(X9) => (predy(X9) | predo(X9) | ~predh(X9)))) & ! [X10] : (room(X10) => (predm(X10) => predj(X10))) & predg(mary) & (! [X11] : (room(X11) => predh(X11)) => ! [X12] : (room(X12) => (preda(X12) => (prede(X12) <~> predh(X12))))) & (! [X13] : (room(X13) => (~predp(X13) | preda(X13))) => ~? [X14] : (anywhere(X14) => ~~predp(X14))) & (! [X15] : (room(X15) => (~predm(X15) | predl(X15))) => ~! [X16] : (room(X16) => (~predm(X16) => predg(X16)))) & (? [X17] : (predr(X17) & room(X17)) => ! [X18] : (room(X18) => (~predm(X18) | predl(X18)))) & ! [X21] : (room(X21) => (paul = X21 | mary = X21)) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (room(X0) => (predn(X0) => predh(X0))) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X4] : (room(X4) => (predg(X4) => ~predo(X4))) & ! [X5] : (predy(X5) <=> predt(X5)) & ! [X6] : (room(X6) => (predh(X6) => (predg(X6) & ~predn(X6) & preda(X6)))) & ? [X7] : room(X7) & ! [X8] : (~room(X8) => ((predy(X8) | predo(X8) | ~predh(X8)) => predr(X8))) & ! [X9] : (room(X9) => (predj(X9) => (predy(X9) | predo(X9) | ~predh(X9)))) & ! [X10] : (room(X10) => (predm(X10) => predj(X10))) & predg(mary) & (! [X11] : (room(X11) => predh(X11)) => ! [X12] : (room(X12) => (preda(X12) => (prede(X12) <~> predh(X12))))) & (! [X13] : (room(X13) => (~predp(X13) | preda(X13))) => ~? [X14] : ~~predp(X14)) & (! [X15] : (room(X15) => (~predm(X15) | predl(X15))) => ~! [X16] : (room(X16) => (~predm(X16) => predg(X16)))) & (? [X17] : (predr(X17) & room(X17)) => ! [X18] : (room(X18) => (~predm(X18) | predl(X18)))) & ! [X21] : (room(X21) => (paul = X21 | mary = X21)) & room(paul) & room(mary) [pure predicate removal 51] 125. ! [X0] : ((predh(X0) | ~predn(X0)) | ~room(X0)) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X4] : ((~predo(X4) | ~predg(X4)) | ~room(X4)) & ! [X5] : (predy(X5) <=> predt(X5)) & ! [X6] : (((predg(X6) & ~predn(X6) & preda(X6)) | ~predh(X6)) | ~room(X6)) & ? [X7] : room(X7) & ! [X8] : ((predr(X8) | (~predy(X8) & ~predo(X8) & predh(X8))) | room(X8)) & ! [X9] : (((predy(X9) | predo(X9) | ~predh(X9)) | ~predj(X9)) | ~room(X9)) & ! [X10] : ((predj(X10) | ~predm(X10)) | ~room(X10)) & predg(mary) & (! [X12] : (((prede(X12) <~> predh(X12)) | ~preda(X12)) | ~room(X12)) | ? [X11] : (~predh(X11) & room(X11))) & (! [X14] : ~predp(X14) | ? [X13] : ((predp(X13) & ~preda(X13)) & room(X13))) & (? [X16] : ((~predg(X16) & ~predm(X16)) & room(X16)) | ? [X15] : ((predm(X15) & ~predl(X15)) & room(X15))) & (! [X18] : ((~predm(X18) | predl(X18)) | ~room(X18)) | ! [X17] : (~predr(X17) | ~room(X17))) & ! [X21] : ((paul = X21 | mary = X21) | ~room(X21)) & room(paul) & room(mary) [ennf transformation 52] 126. ! [X0] : (predh(X0) | ~predn(X0) | ~room(X0)) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X4] : (~predo(X4) | ~predg(X4) | ~room(X4)) & ! [X5] : (predy(X5) <=> predt(X5)) & ! [X6] : ((predg(X6) & ~predn(X6) & preda(X6)) | ~predh(X6) | ~room(X6)) & ? [X7] : room(X7) & ! [X8] : (predr(X8) | (~predy(X8) & ~predo(X8) & predh(X8)) | room(X8)) & ! [X9] : (predy(X9) | predo(X9) | ~predh(X9) | ~predj(X9) | ~room(X9)) & ! [X10] : (predj(X10) | ~predm(X10) | ~room(X10)) & predg(mary) & (! [X12] : ((prede(X12) <~> predh(X12)) | ~preda(X12) | ~room(X12)) | ? [X11] : (~predh(X11) & room(X11))) & (! [X14] : ~predp(X14) | ? [X13] : (predp(X13) & ~preda(X13) & room(X13))) & (? [X16] : (~predg(X16) & ~predm(X16) & room(X16)) | ? [X15] : (predm(X15) & ~predl(X15) & room(X15))) & (! [X18] : (~predm(X18) | predl(X18) | ~room(X18)) | ! [X17] : (~predr(X17) | ~room(X17))) & ! [X21] : (paul = X21 | mary = X21 | ~room(X21)) & room(paul) & room(mary) [flattening 125] 127. ? [X0] : (predn(X0) & room(X0)) | ? [X1] : ((paul != X1 & mary != X1) & room(X1)) | ~room(paul) | ~room(mary) [ennf transformation 47] 128. ? [X0] : (predn(X0) & room(X0)) | ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~room(paul) | ~room(mary) [flattening 127] 129. ? [X15] : (predm(X15) & ~predl(X15) & room(X15)) | ~sP0 [predicate definition introduction] 130. ! [X0] : (predh(X0) | ~predn(X0) | ~room(X0)) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X4] : (~predo(X4) | ~predg(X4) | ~room(X4)) & ! [X5] : (predy(X5) <=> predt(X5)) & ! [X6] : ((predg(X6) & ~predn(X6) & preda(X6)) | ~predh(X6) | ~room(X6)) & ? [X7] : room(X7) & ! [X8] : (predr(X8) | (~predy(X8) & ~predo(X8) & predh(X8)) | room(X8)) & ! [X9] : (predy(X9) | predo(X9) | ~predh(X9) | ~predj(X9) | ~room(X9)) & ! [X10] : (predj(X10) | ~predm(X10) | ~room(X10)) & predg(mary) & (! [X12] : ((prede(X12) <~> predh(X12)) | ~preda(X12) | ~room(X12)) | ? [X11] : (~predh(X11) & room(X11))) & (! [X14] : ~predp(X14) | ? [X13] : (predp(X13) & ~preda(X13) & room(X13))) & (? [X16] : (~predg(X16) & ~predm(X16) & room(X16)) | sP0) & (! [X18] : (~predm(X18) | predl(X18) | ~room(X18)) | ! [X17] : (~predr(X17) | ~room(X17))) & ! [X21] : (paul = X21 | mary = X21 | ~room(X21)) & room(paul) & room(mary) [definition folding 126,129] 136. ! [X0] : (predh(X0) | ~predn(X0) | ~room(X0)) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X4] : (~predo(X4) | ~predg(X4) | ~room(X4)) & ! [X5] : ((predy(X5) | ~predt(X5)) & (predt(X5) | ~predy(X5))) & ! [X6] : ((predg(X6) & ~predn(X6) & preda(X6)) | ~predh(X6) | ~room(X6)) & ? [X7] : room(X7) & ! [X8] : (predr(X8) | (~predy(X8) & ~predo(X8) & predh(X8)) | room(X8)) & ! [X9] : (predy(X9) | predo(X9) | ~predh(X9) | ~predj(X9) | ~room(X9)) & ! [X10] : (predj(X10) | ~predm(X10) | ~room(X10)) & predg(mary) & (! [X12] : (((~predh(X12) | ~prede(X12)) & (predh(X12) | prede(X12))) | ~preda(X12) | ~room(X12)) | ? [X11] : (~predh(X11) & room(X11))) & (! [X14] : ~predp(X14) | ? [X13] : (predp(X13) & ~preda(X13) & room(X13))) & (? [X16] : (~predg(X16) & ~predm(X16) & room(X16)) | sP0) & (! [X18] : (~predm(X18) | predl(X18) | ~room(X18)) | ! [X17] : (~predr(X17) | ~room(X17))) & ! [X21] : (paul = X21 | mary = X21 | ~room(X21)) & room(paul) & room(mary) [nnf transformation 130] 137. ! [X0] : (predh(X0) | ~predn(X0) | ~room(X0)) & ? [X1] : (predt(X1) & room(X1)) & ? [X2] : (~predh(X2) & room(X2)) & ! [X3] : (~predo(X3) | ~predg(X3) | ~room(X3)) & ! [X4] : ((predy(X4) | ~predt(X4)) & (predt(X4) | ~predy(X4))) & ! [X5] : ((predg(X5) & ~predn(X5) & preda(X5)) | ~predh(X5) | ~room(X5)) & ? [X6] : room(X6) & ! [X7] : (predr(X7) | (~predy(X7) & ~predo(X7) & predh(X7)) | room(X7)) & ! [X8] : (predy(X8) | predo(X8) | ~predh(X8) | ~predj(X8) | ~room(X8)) & ! [X9] : (predj(X9) | ~predm(X9) | ~room(X9)) & predg(mary) & (! [X10] : (((~predh(X10) | ~prede(X10)) & (predh(X10) | prede(X10))) | ~preda(X10) | ~room(X10)) | ? [X11] : (~predh(X11) & room(X11))) & (! [X12] : ~predp(X12) | ? [X13] : (predp(X13) & ~preda(X13) & room(X13))) & (? [X14] : (~predg(X14) & ~predm(X14) & room(X14)) | sP0) & (! [X15] : (~predm(X15) | predl(X15) | ~room(X15)) | ! [X16] : (~predr(X16) | ~room(X16))) & ! [X17] : (paul = X17 | mary = X17 | ~room(X17)) & room(paul) & room(mary) [rectify 136] 138. ? [X1] : (predt(X1) & room(X1)) => (predt(sK2) & room(sK2)) [choice axiom] 139. ? [X2] : (~predh(X2) & room(X2)) => (~predh(sK3) & room(sK3)) [choice axiom] 140. ? [X6] : room(X6) => room(sK4) [choice axiom] 141. ? [X11] : (~predh(X11) & room(X11)) => (~predh(sK5) & room(sK5)) [choice axiom] 142. ? [X13] : (predp(X13) & ~preda(X13) & room(X13)) => (predp(sK6) & ~preda(sK6) & room(sK6)) [choice axiom] 143. ? [X14] : (~predg(X14) & ~predm(X14) & room(X14)) => (~predg(sK7) & ~predm(sK7) & room(sK7)) [choice axiom] 144. ! [X0] : (predh(X0) | ~predn(X0) | ~room(X0)) & (predt(sK2) & room(sK2)) & (~predh(sK3) & room(sK3)) & ! [X3] : (~predo(X3) | ~predg(X3) | ~room(X3)) & ! [X4] : ((predy(X4) | ~predt(X4)) & (predt(X4) | ~predy(X4))) & ! [X5] : ((predg(X5) & ~predn(X5) & preda(X5)) | ~predh(X5) | ~room(X5)) & room(sK4) & ! [X7] : (predr(X7) | (~predy(X7) & ~predo(X7) & predh(X7)) | room(X7)) & ! [X8] : (predy(X8) | predo(X8) | ~predh(X8) | ~predj(X8) | ~room(X8)) & ! [X9] : (predj(X9) | ~predm(X9) | ~room(X9)) & predg(mary) & (! [X10] : (((~predh(X10) | ~prede(X10)) & (predh(X10) | prede(X10))) | ~preda(X10) | ~room(X10)) | (~predh(sK5) & room(sK5))) & (! [X12] : ~predp(X12) | (predp(sK6) & ~preda(sK6) & room(sK6))) & ((~predg(sK7) & ~predm(sK7) & room(sK7)) | sP0) & (! [X15] : (~predm(X15) | predl(X15) | ~room(X15)) | ! [X16] : (~predr(X16) | ~room(X16))) & ! [X17] : (paul = X17 | mary = X17 | ~room(X17)) & room(paul) & room(mary) [skolemisation 137,143,142,141,140,139,138] 145. ? [X0] : (predn(X0) & room(X0)) => (predn(sK8) & room(sK8)) [choice axiom] 146. ? [X1] : (paul != X1 & mary != X1 & room(X1)) => (paul != sK9 & mary != sK9 & room(sK9)) [choice axiom] 147. (predn(sK8) & room(sK8)) | (paul != sK9 & mary != sK9 & room(sK9)) | ~room(paul) | ~room(mary) [skolemisation 128,146,145] 231. room(mary) [cnf transformation 144] 232. room(paul) [cnf transformation 144] 233. ~room(X17) | mary = X17 | paul = X17 [cnf transformation 144] 253. ~predn(X5) | ~predh(X5) | ~room(X5) [cnf transformation 144] 262. ~predn(X0) | predh(X0) | ~room(X0) [cnf transformation 144] 263. room(sK8) | room(sK9) | ~room(paul) | ~room(mary) [cnf transformation 147] 264. room(sK8) | mary != sK9 | ~room(paul) | ~room(mary) [cnf transformation 147] 265. room(sK8) | paul != sK9 | ~room(paul) | ~room(mary) [cnf transformation 147] 266. predn(sK8) | room(sK9) | ~room(paul) | ~room(mary) [cnf transformation 147] 267. predn(sK8) | mary != sK9 | ~room(paul) | ~room(mary) [cnf transformation 147] 268. predn(sK8) | paul != sK9 | ~room(paul) | ~room(mary) [cnf transformation 147] 288. ~predn(X5) | ~room(X5) [subsumption resolution 253,262] 349. predn(sK8) | paul != sK9 | ~room(mary) [subsumption resolution 268,232] 350. predn(sK8) | paul != sK9 [subsumption resolution 349,231] 352. 18 <=> paul = sK9 [avatar definition] 354. paul != sK9 <- (~18) [avatar component clause 352] 356. 19 <=> predn(sK8) [avatar definition] 358. predn(sK8) <- (19) [avatar component clause 356] 359. ~18 | 19 [avatar split clause 350,356,352] 360. predn(sK8) | mary != sK9 | ~room(mary) [subsumption resolution 267,232] 361. predn(sK8) | mary != sK9 [subsumption resolution 360,231] 363. 20 <=> mary = sK9 [avatar definition] 365. mary != sK9 <- (~20) [avatar component clause 363] 366. ~20 | 19 [avatar split clause 361,356,363] 367. predn(sK8) | room(sK9) | ~room(mary) [subsumption resolution 266,232] 368. predn(sK8) | room(sK9) [subsumption resolution 367,231] 370. 21 <=> room(sK9) [avatar definition] 372. room(sK9) <- (21) [avatar component clause 370] 373. 21 | 19 [avatar split clause 368,356,370] 374. room(sK8) | paul != sK9 | ~room(mary) [subsumption resolution 265,232] 375. room(sK8) | paul != sK9 [subsumption resolution 374,231] 377. 22 <=> room(sK8) [avatar definition] 379. room(sK8) <- (22) [avatar component clause 377] 380. ~18 | 22 [avatar split clause 375,377,352] 381. room(sK8) | mary != sK9 | ~room(mary) [subsumption resolution 264,232] 382. room(sK8) | mary != sK9 [subsumption resolution 381,231] 383. ~20 | 22 [avatar split clause 382,377,363] 384. room(sK8) | room(sK9) | ~room(mary) [subsumption resolution 263,232] 385. room(sK8) | room(sK9) [subsumption resolution 384,231] 386. 21 | 22 [avatar split clause 385,377,370] 401. mary = sK9 | paul = sK9 <- (21) [resolution 233,372] 447. paul = sK9 <- (~20, 21) [subsumption resolution 401,365] 448. $false <- (~18, ~20, 21) [subsumption resolution 447,354] 449. 18 | 20 | ~21 [avatar contradiction clause 448] 465. ~room(sK8) <- (19) [resolution 358,288] 467. $false <- (19, 22) [subsumption resolution 465,379] 468. ~19 | ~22 [avatar contradiction clause 467] 469. $false [avatar sat refutation 359,366,373,380,383,386,449,468] % SZS output end Proof for 853090798887359347323164 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------
0.180667
Oscar, David, Janice, Suzanne are the only persons in the room. If “Oscar bakes bread at home” then “David is a professional photographer specializing in portrait photography” otherwise “if someone is a dedicated advocate for digital privacy and encryption then he/she can play the harmonica”. If “at least one person in the room regularly goes on multi-day backpacking trips in national parks” then “Janice is a dedicated advocate for digital privacy and encryption”. It is not the case that “David bakes bread at home”.
David bakes bread at home.
contradiction
room(oscar)&room(david)&room(janice)&room(suzanne)&(![X]:(room(X)=>(X='oscar'|X='david'|X='janice'|X='suzanne')))& (((bakes_bread_at_home(oscar))=>(is_a_professional_photographer_specializing_in_portrait_photography(david)))&((~(bakes_bread_at_home(oscar)))=>((![X]:((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(can_play_the_harmonica(X)))))))& ((((?[X]:(room(X)&regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(janice)))& (((?[X]:(room(X)&((owns_a_telescope(X))|(enjoys_stargazing(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))&(![X,Y]:((room(X)&room(Y)&(((owns_a_telescope(X))|(enjoys_stargazing(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))&(((owns_a_telescope(Y))|(enjoys_stargazing(Y))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(Y)))))=>(X=Y)))))& (is_a_professional_photographer_specializing_in_portrait_photography(david))& (enjoys_origami(janice))& (designs_and_sews_custom_cosplay_costumes_for_conventions(oscar))& ((![X]:((is_a_cybersecurity_expert(X))=>(owns_an_Android_phone(X)))))& (collects_modern_art(oscar))& (does_not_own_a_smartwatch(david))& (has_a_curated_collection_of_mid-century_modern_furniture(oscar))& (enjoys_wildlife_photography(oscar))& ((![X]:((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(is_not_a_cybersecurity_expert(X)))))& (~(bakes_bread_at_home(david)))& (owns_a_smartwatch(janice))& ((![X]:((bakes_bread_at_home(X))=>(((is_a_cybersecurity_expert(X))&(is_a_wine_connoisseur(X)))))))& (can_play_the_harmonica(oscar))& ((((is_a_professional_photographer_specializing_in_portrait_photography(david))&(is_a_wine_connoisseur(david))&(owns_an_Android_phone(david))))&(((enjoys_wildlife_photography(david))<~>(does_not_own_a_smartwatch(david)))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(janice))& ((enjoys_windsurfing(david))&(does_not_own_a_telescope(david)))
room(oscar)&room(david)&room(janice)&room(suzanne)&(![X]:(room(X)=>(X='oscar'|X='david'|X='janice'|X='suzanne')))& bakes_bread_at_home(david)
[ "p13", "hypothesis" ]
% SZS status Unsatisfiable for 54310526084068795351883 % SZS output start Proof for 54310526084068795351883 57. ~predl(paul) [input p13] 64. predl(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 160. predl(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 64] 161. predl(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 160] 266. ~predl(paul) [cnf transformation 57] 278. predl(paul) [cnf transformation 161] 302. $false [subsumption resolution 278,266] % SZS output end Proof for 54310526084068795351883 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------
0.229903
Tammy is the only person in the room. If “someone in the room is quieter than Ronald, is quieter than Virginia and is older than Virginia” then “Tammy is quieter than Ronald”. If “Tammy is richer than Virginia” then “Tammy is richer than Ronald”. If “Ronald is richer than Tammy” then “Tammy is the oldest in the room”. If “someone in the room is older than Daniel” then “someone who is richer than Virginia is older than someone who is not not not not not not funny”. If “it is not the case that “Virginia is richer than Tammy”” then “Tammy who is quieter than Virginia is richer than Daniel”. If “Ronald is richer than Tammy” then “if someone is older than Virginia then he/she is older than Daniel”. If “Daniel is older than Tammy” then “Ronald is quieter than Tammy”. If “Daniel is quieter than Tammy” then “Tammy is the least old in the room”. If “Tammy is quieter than Ronald and is richer than Ronald” then “Virginia is quieter than Tammy”. If “Daniel is quieter than Tammy” then “only one person anywhere is older than Ronald”. If “Virginia is richer than Tammy” then “Tammy is a old tall person”. Someone who is richer than Daniel is richer than someone who is richer than Ronald. Tammy is a wise humble funny curious brave happy person. It is true that “if someone is older than Ronald and is not not not old then he/she is quieter than Ronald”. It is not the case that “someone in the room is older than Daniel”. Tammy is a old tall person. Someone who is not not not old or is older than Daniel or both is richer than someone who is richer than Virginia. Someone in the room is quieter than Daniel. No creative person is quiet. If someone is quieter than Virginia then he/she is a generous person and vice versa. Virginia is quieter than Tammy. Someone in the room is older than Ronald. If someone is quieter than Daniel then he/she is richer than Ronald.
Daniel is older than Tammy.
neutral
room(tammy)&(![X]:(room(X)=>(X='tammy')))& ((?[X]:(room(X)&(((quieter(ronald,X))&(quieter(virginia,X))&(older(virginia,X))))))=>(quieter(ronald,tammy)))& ((richer(virginia,tammy))=>(richer(ronald,tammy)))& ((richer(tammy,ronald))=>(![X]:((room(X)&(X!=tammy))=>older(X,tammy))))& ((?[X]:(room(X)&(older(daniel,X))))=>(?[X,Y]:((richer(virginia,X))&(~~~~~~funny(Y))&(older(X,Y)))))& ((~(richer(tammy,virginia)))=>((quieter(virginia,tammy))&(richer(daniel,tammy))))& ((richer(tammy,ronald))=>((![X]:((older(virginia,X))=>(older(daniel,X))))))& ((older(tammy,daniel))=>(quieter(tammy,ronald)))& ((quieter(tammy,daniel))=>(![X]:((room(X)&(X!=tammy))=>older(tammy,X))))& ((((quieter(ronald,tammy))&(richer(ronald,tammy))))=>(quieter(tammy,virginia)))& ((quieter(tammy,daniel))=>(((?[X]:(anywhere(X)&older(ronald,X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(older(ronald,X))&(older(ronald,Y)))=>(X=Y))))))& ((richer(tammy,virginia))=>(old(tammy)&tall(tammy)&person(tammy)))& (?[X,Y]:((richer(daniel,X))&(richer(ronald,Y))&(richer(X,Y))))& (wise(tammy)&humble(tammy)&funny(tammy)&curious(tammy)&brave(tammy)&happy(tammy)&person(tammy))& ((![X]:((((older(ronald,X))&(~~~old(X))))=>(quieter(ronald,X)))))& (~(?[X]:(room(X)&(older(daniel,X)))))& (old(tammy)&tall(tammy)&person(tammy))& (?[X,Y]:((((~~~old(X))|(older(daniel,X))))&(richer(virginia,Y))&(richer(X,Y))))& (?[X]:(room(X)&(quieter(daniel,X))))& (~?[X]:(creative(X)=>quiet(X)))& ((![X]:((quieter(virginia,X))<=>(generous(X)&person(X)))))& (quieter(tammy,virginia))& (?[X]:(room(X)&(older(ronald,X))))& ((![X]:((quieter(daniel,X))=>(richer(ronald,X)))))
room(tammy)&(![X]:(room(X)=>(X='tammy')))& older(tammy,daniel)
[]
null
0.008371
Stephen, Meagan are the only persons in the room. “Stephen enjoys making ceramics” if “Meagan neither plays eSports competitively nor is an amateur astronomer who builds and uses custom telescopes” and vice versa. Everyone in the room composes and performs experimental electronic music if they owns a smartwatch and vice versa. Meagan who does not compose and performs experimental electronic music does not enjoy writing detailed reviews of new and classic board games. Everyone in the room who neither is an active member of a local robotics club nor drives a hybrid car plays eSports competitively. Everyone in the room plays eSports competitively if they is an amateur astronomer who builds and uses custom telescopes and vice versa. Everyone in the room owns a high-end gaming PC with custom-built components if they does not compose and performs experimental electronic music. Everyone in the room practices calligraphy and collects vintage vinyl records if they enjoys writing detailed reviews of new and classic board games and vice versa. Everyone in the room who enjoys making ceramics enjoys bird watching. Stephen enjoys logic puzzles. Everyone in the room who owns a high-end gaming PC with custom-built components enjoys making ceramics. It is true that “everyone in the room who enjoys making ceramics does not enjoy windsurfing”. If someone plays eSports competitively then he/she creates large-scale murals for public art installations and vice versa. Everyone in the room who plays eSports competitively designs and sews custom cosplay costumes for conventions. If someone enjoys bird watching or collects vintage vinyl records or both then he/she practices calligraphy and vice versa. Everyone in the room who does not practice kickboxing practices calligraphy. Everyone in the room enjoys logic puzzles or enjoys windsurfing or both.
Meagan enjoys bird watching.
entailment
room(stephen)&room(meagan)&(![X]:(room(X)=>(X='stephen'|X='meagan')))& ((~((plays_eSports_competitively(meagan))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(meagan))))<=>(enjoys_making_ceramics(stephen)))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))<=>(owns_a_smartwatch(X))))))& ((does_not_compose_and_performs_experimental_electronic_music(meagan))&(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(meagan)))& (![X]:(room(X)=>(((~((is_an_active_member_of_a_local_robotics_club(X))|(drives_a_hybrid_car(X))))=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))<=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((((practices_calligraphy(X))&(collects_vintage_vinyl_records(X))))<=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(enjoys_bird_watching(X))))))& (enjoys_logic_puzzles(stephen))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(does_not_enjoy_windsurfing(X))))))& ((![X]:((plays_eSports_competitively(X))<=>(creates_large-scale_murals_for_public_art_installations(X)))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& ((![X]:((((enjoys_bird_watching(X))|(collects_vintage_vinyl_records(X))))<=>(practices_calligraphy(X)))))& (![X]:(room(X)=>(((does_not_practice_kickboxing(X))=>(practices_calligraphy(X))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))|(enjoys_windsurfing(X))))))
room(stephen)&room(meagan)&(![X]:(room(X)=>(X='stephen'|X='meagan')))& enjoys_bird_watching(meagan)
[ "p0", "p3", "p6", "p8", "p10", "hypothesis" ]
% SZS status Unsatisfiable for 2799083165063884813909912 % SZS output start Proof for 2799083165063884813909912 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ~predo(paul) & ~predx(paul) [input p3] 50. ! [X0] : (room(X0) => (~predx(X0) => predy(X0))) [input p6] 52. ! [X0] : (room(X0) => (predq(X0) => preds(X0))) [input p8] 54. ! [X0] : (room(X0) => (predy(X0) => predq(X0))) [input p10] 61. ~(preds(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 140. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 141. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 140] 145. ! [X0] : ((predy(X0) | predx(X0)) | ~room(X0)) [ennf transformation 50] 146. ! [X0] : (predy(X0) | predx(X0) | ~room(X0)) [flattening 145] 148. ! [X0] : ((preds(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 52] 149. ! [X0] : (preds(X0) | ~predq(X0) | ~room(X0)) [flattening 148] 150. ! [X0] : ((predq(X0) | ~predy(X0)) | ~room(X0)) [ennf transformation 54] 151. ! [X0] : (predq(X0) | ~predy(X0) | ~room(X0)) [flattening 150] 152. ~preds(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 61] 153. ~preds(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 152] 164. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 165. ~preds(paul) | (paul != sK0 & mary != sK0 & room(sK0)) | ~room(paul) | ~room(mary) [skolemisation 153,164] 246. room(mary) [cnf transformation 141] 247. room(paul) [cnf transformation 141] 248. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 141] 254. ~predx(paul) [cnf transformation 47] 258. ~room(X0) | predx(X0) | predy(X0) [cnf transformation 146] 262. ~predq(X0) | preds(X0) | ~room(X0) [cnf transformation 149] 263. ~predy(X0) | predq(X0) | ~room(X0) [cnf transformation 151] 269. ~preds(paul) | room(sK0) | ~room(paul) | ~room(mary) [cnf transformation 165] 270. ~preds(paul) | mary != sK0 | ~room(paul) | ~room(mary) [cnf transformation 165] 271. ~preds(paul) | paul != sK0 | ~room(paul) | ~room(mary) [cnf transformation 165] 287. ~preds(paul) | paul != sK0 | ~room(mary) [subsumption resolution 271,247] 288. ~preds(paul) | paul != sK0 [subsumption resolution 287,246] 290. 4 <=> paul = sK0 [avatar definition] 292. paul != sK0 <- (~4) [avatar component clause 290] 294. 5 <=> preds(paul) [avatar definition] 297. ~4 | ~5 [avatar split clause 288,294,290] 298. ~preds(paul) | mary != sK0 | ~room(mary) [subsumption resolution 270,247] 299. ~preds(paul) | mary != sK0 [subsumption resolution 298,246] 301. 6 <=> mary = sK0 [avatar definition] 303. mary != sK0 <- (~6) [avatar component clause 301] 304. ~6 | ~5 [avatar split clause 299,294,301] 305. ~preds(paul) | room(sK0) | ~room(mary) [subsumption resolution 269,247] 306. ~preds(paul) | room(sK0) [subsumption resolution 305,246] 308. 7 <=> room(sK0) [avatar definition] 310. room(sK0) <- (7) [avatar component clause 308] 311. 7 | ~5 [avatar split clause 306,294,308] 319. predx(paul) | predy(paul) [resolution 258,247] 329. predy(paul) [subsumption resolution 319,254] 331. predq(paul) | ~room(paul) [resolution 263,329] 335. predq(paul) [subsumption resolution 331,247] 343. preds(paul) | ~room(paul) [resolution 335,262] 347. preds(paul) [subsumption resolution 343,247] 348. 5 [avatar split clause 347,294] 350. mary = sK0 | paul = sK0 <- (7) [resolution 310,248] 352. paul = sK0 <- (~6, 7) [subsumption resolution 350,303] 353. $false <- (~4, ~6, 7) [subsumption resolution 352,292] 354. 4 | 6 | ~7 [avatar contradiction clause 353] 364. $false [avatar sat refutation 297,304,311,348,354] % SZS output end Proof for 2799083165063884813909912 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0.293208
There is a room. Someone in the room owns a telescope. Everyone in the room enjoys bird watching, is not a wine connoisseur with a private cellar of vintage wines and does not collect rare sneakers only if they has a specialized collection of handmade artisan pottery and does not collect vintage vinyl records. Everyone in the room has a specialized collection of handmade artisan pottery and does not collect vintage vinyl records only if they does not collect vintage vinyl records, enjoys origami and regularly contributes to tech forums and online communities. Everyone in the room does not play the violin, owns an extensive assortment of vintage comic book memorabilia or does not collect foreign coins. Everyone in the room does not practice digital art or collects vintage vinyl records. No one in the room does not enjoy stand-up paddleboarding or does not build model airplanes or both. Someone in the room regularly contributes to tech forums and online communities, enjoys stand-up paddleboarding or builds model airplanes. Everyone in the room collects vintage vinyl records if they does not enjoy bird watching and regularly contributes to tech forums and online communities. No one anywhere either does not enjoy spelunking or knows morse code but not both only if they collects vintage vinyl records. Everyone anywhere owns an extensive assortment of vintage comic book memorabilia if they does not collect rare sneakers. Everyone in the room owns an extensive assortment of vintage comic book memorabilia if they enjoys spelunking and vice versa. Everyone in the room collects vintage vinyl records, regularly contributes to tech forums and online communities and is a tea enthusiast if they enjoys spelunking. Everyone anywhere is a wine connoisseur with a private cellar of vintage wines or does not collect foreign coins. Not everyone in the room who is a wine connoisseur with a private cellar of vintage wines either is allergic to anything or enjoys bird watching but not both.
Everyone in the room does not collect rare sneakers.
contradiction
(there_is_a_room)& (?[X]:(room(X)&(owns_a_telescope(X))))& (![X]:(room(X)=>(((((has_a_specialized_collection_of_handmade_artisan_pottery(X))&(does_not_collect_vintage_vinyl_records(X))))<=(((enjoys_bird_watching(X))&(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(does_not_collect_rare_sneakers(X))))))))& (![X]:(room(X)=>(((((does_not_collect_vintage_vinyl_records(X))&(enjoys_origami(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))<=(((has_a_specialized_collection_of_handmade_artisan_pottery(X))&(does_not_collect_vintage_vinyl_records(X))))))))& (![X]:(room(X)=>(((does_not_play_the_violin(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_collect_foreign_coins(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))|(does_not_practice_digital_art(X))))))& (~?[X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(does_not_build_model_airplanes(X))))))& (?[X]:(room(X)&(((regularly_contributes_to_tech_forums_and_online_communities(X))|(enjoys_stand-up_paddleboarding(X))|(builds_model_airplanes(X))))))& (![X]:(room(X)=>(((((does_not_enjoy_bird_watching(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(collects_vintage_vinyl_records(X))))))& (~?[X]:(anywhere(X)=>(((collects_vintage_vinyl_records(X))<=(((does_not_enjoy_spelunking(X))<~>(knows_morse_code(X))))))))& (![X]:(anywhere(X)=>(((does_not_collect_rare_sneakers(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=>(enjoys_spelunking(X))))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(((collects_vintage_vinyl_records(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))&(is_a_tea_enthusiast(X))))))))& (![X]:(anywhere(X)=>(((does_not_collect_foreign_coins(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (~![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(((is_allergic_to_anything(X))<~>(enjoys_bird_watching(X))))))))
(there_is_a_room)& ![X]:(room(X)=>(does_not_collect_rare_sneakers(X)))
[ "b4", "p6", "p9", "p10", "p11", "p12", "hypothesis" ]
% SZS status Unsatisfiable for 6844604948736602667349750 % SZS output start Proof for 6844604948736602667349750 5. ! [X0] : anywhere(X0) [input b4] 50. ~? [X0] : (room(X0) => (~preda(X0) | ~predt(X0))) [input p6] 53. ~? [X0] : (anywhere(X0) => ((~preds(X0) <~> predk(X0)) => predj(X0))) [input p9] 54. ! [X0] : (anywhere(X0) => (~predm(X0) => predr(X0))) [input p10] 55. ! [X0] : (room(X0) => (predr(X0) <=> preds(X0))) [input p11] 56. ! [X0] : (room(X0) => (preds(X0) => (predl(X0) & predg(X0) & predj(X0)))) [input p12] 59. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 60. ! [X0] : (room(X0) => (preds(X0) => (predg(X0) & predj(X0)))) [pure predicate removal 56] 61. ~? [X0] : (room(X0) => ~predt(X0)) [pure predicate removal 50] 63. ~? [X0] : ~room(X0) [pure predicate removal 61] 72. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 59] 145. ! [X0] : room(X0) [ennf transformation 63] 148. ! [X0] : ((~predj(X0) & (~preds(X0) <~> predk(X0))) & anywhere(X0)) [ennf transformation 53] 149. ! [X0] : (~predj(X0) & (~preds(X0) <~> predk(X0)) & anywhere(X0)) [flattening 148] 150. ! [X0] : ((predr(X0) | predm(X0)) | ~anywhere(X0)) [ennf transformation 54] 151. ! [X0] : (predr(X0) | predm(X0) | ~anywhere(X0)) [flattening 150] 152. ! [X0] : ((predr(X0) <=> preds(X0)) | ~room(X0)) [ennf transformation 55] 153. ! [X0] : (((predg(X0) & predj(X0)) | ~preds(X0)) | ~room(X0)) [ennf transformation 60] 154. ! [X0] : ((predg(X0) & predj(X0)) | ~preds(X0) | ~room(X0)) [flattening 153] 156. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 72] 162. ! [X0] : (~predj(X0) & ((~predk(X0) | preds(X0)) & (predk(X0) | ~preds(X0))) & anywhere(X0)) [nnf transformation 149] 163. ! [X0] : (~predj(X0) & (~predk(X0) | preds(X0)) & (predk(X0) | ~preds(X0)) & anywhere(X0)) [flattening 162] 164. ! [X0] : (((predr(X0) | ~preds(X0)) & (preds(X0) | ~predr(X0))) | ~room(X0)) [nnf transformation 152] 169. anywhere(X0) [cnf transformation 5] 251. room(X0) [cnf transformation 145] 257. ~predj(X0) [cnf transformation 163] 258. predr(X0) | predm(X0) | ~anywhere(X0) [cnf transformation 151] 259. preds(X0) | ~predr(X0) | ~room(X0) [cnf transformation 164] 261. predj(X0) | ~preds(X0) | ~room(X0) [cnf transformation 154] 266. ~predm(X0) | ~room(X0) [cnf transformation 156] 268. predr(X0) | predm(X0) [subsumption resolution 258,169] 270. ~predr(X0) | preds(X0) [subsumption resolution 259,251] 272. ~preds(X0) | ~room(X0) [subsumption resolution 261,257] 273. ~preds(X0) [subsumption resolution 272,251] 284. ~predm(X0) [subsumption resolution 266,251] 285. preds(X0) | predm(X0) [resolution 270,268] 286. predm(X0) [subsumption resolution 285,273] 287. $false [subsumption resolution 286,284] % SZS output end Proof for 6844604948736602667349750 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------
0.003019
Juan is the only person in the room. Juan is older than Ronald. Juan is older than Robert. All quiet person is tall. Juan is richer than Ronald. All tall person is quiet. All old person is quiet. Juan neither is richer than Robert nor is quieter than Robert. Juan is older than Ronnie. Someone who is older than Ronald is richer than someone who is older than Ronnie. Juan is richer than Ronnie. All tall person is kind. Juan is older than Robert and is old. All old person is kind. All quiet person is old.
Juan is kind.
entailment
room(juan)&(![X]:(room(X)=>(X='juan')))& (older(ronald,juan))& (older(robert,juan))& (![X]:(quiet(X)=>tall(X)))& (richer(ronald,juan))& (![X]:(tall(X)=>quiet(X)))& (![X]:(old(X)=>quiet(X)))& (~((richer(robert,juan))|(quieter(robert,juan))))& (older(ronnie,juan))& (?[X,Y]:((older(ronald,X))&(older(ronnie,Y))&(richer(X,Y))))& (richer(ronnie,juan))& (![X]:(tall(X)=>kind(X)))& (((older(robert,juan))&(old(juan))))& (![X]:(old(X)=>kind(X)))& (![X]:(quiet(X)=>old(X)))
room(juan)&(![X]:(room(X)=>(X='juan')))& kind(juan)
[ "p0", "p3", "p6", "p11", "p12", "hypothesis" ]
% SZS status Unsatisfiable for 4832758628398555670973826 % SZS output start Proof for 4832758628398555670973826 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0] : (quiet(X0) => tall(X0)) [input p3] 50. ! [X0] : (old(X0) => quiet(X0)) [input p6] 55. ! [X0] : (tall(X0) => kind(X0)) [input p11] 56. old(mary) & older(alice,mary) [input p12] 59. ~(kind(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 132. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 133. ! [X0] : (tall(X0) | ~quiet(X0)) [ennf transformation 47] 135. ! [X0] : (quiet(X0) | ~old(X0)) [ennf transformation 50] 137. ! [X0] : (kind(X0) | ~tall(X0)) [ennf transformation 55] 140. ~kind(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 59] 144. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom] 145. ~kind(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 140,144] 226. room(mary) [cnf transformation 132] 227. ~room(X0) | mary = X0 [cnf transformation 132] 230. ~quiet(X0) | tall(X0) [cnf transformation 133] 233. ~old(X0) | quiet(X0) [cnf transformation 135] 241. ~tall(X0) | kind(X0) [cnf transformation 137] 243. old(mary) [cnf transformation 56] 246. ~kind(mary) | room(sK2) | ~room(mary) [cnf transformation 145] 247. ~kind(mary) | mary != sK2 | ~room(mary) [cnf transformation 145] 248. ~kind(mary) | mary != sK2 [subsumption resolution 247,226] 250. 1 <=> mary = sK2 [avatar definition] 252. mary != sK2 <- (~1) [avatar component clause 250] 254. 2 <=> kind(mary) [avatar definition] 257. ~1 | ~2 [avatar split clause 248,254,250] 258. ~kind(mary) | room(sK2) [subsumption resolution 246,226] 260. 3 <=> room(sK2) [avatar definition] 262. room(sK2) <- (3) [avatar component clause 260] 263. 3 | ~2 [avatar split clause 258,254,260] 264. quiet(mary) [resolution 233,243] 265. tall(mary) [resolution 264,230] 266. kind(mary) [resolution 265,241] 270. 2 [avatar split clause 266,254] 274. mary = sK2 <- (3) [resolution 227,262] 275. $false <- (~1, 3) [subsumption resolution 274,252] 276. 1 | ~3 [avatar contradiction clause 275] 277. $false [avatar sat refutation 257,263,270,276] % SZS output end Proof for 4832758628398555670973826 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------
0.71148
Dylan, Stephen are the only persons in the room. Either “Dylan maintains a personal blog focused on cybersecurity tips” or “Dylan is a professional photographer specializing in portrait photography” but not both. If “Stephen enjoys cross-country skiing” then “everyone in the room who writes and illustrates their own graphic novels trains for and competes in international triathlons”. If someone is not a professional photographer specializing in portrait photography then he/she maintains a personal blog focused on cybersecurity tips and vice versa. Stephen neither maintains a personal blog focused on cybersecurity tips nor trains for and competes in international triathlons.
Stephen is a professional photographer specializing in portrait photography.
entailment
room(dylan)&room(stephen)&(![X]:(room(X)=>(X='dylan'|X='stephen')))& ((maintains_a_personal_blog_focused_on_cybersecurity_tips(dylan))<~>(is_a_professional_photographer_specializing_in_portrait_photography(dylan)))& ((enjoys_cross-country_skiing(stephen))=>(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(trains_for_and_competes_in_international_triathlons(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))|(does_enjoy_mountain_biking(X))))))=>(has_a_tattoo(stephen)))& ((![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>((does_enjoy_mountain_biking(dylan))&(collects_action_figures(dylan))))& ((can_play_the_flute(stephen))=>(![X]:(room(X)=>(((((is_a_client_of_LVMH(X))<~>(is_a_drone_photographer(X))))=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))& ((~?[X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(writes_and_illustrates_their_own_graphic_novels(X))))))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(stephen)))& ((![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(writes_and_illustrates_their_own_graphic_novels(dylan)))& (~(is_a_drone_photographer(stephen)))& (![X]:(room(X)=>(((can_play_the_flute(X))=>(~((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))))& (writes_and_illustrates_their_own_graphic_novels(dylan))& ((![X]:((collects_action_figures(X))=>(makes_homemade_pastries(X)))))& (((?[X]:(room(X)&does_not_enjoy_mountain_biking(X)))))& (![X]:(anywhere(X)=>(((has_a_tattoo(X))|(does_not_travel_domestically_frequently(X))))))& ((![X]:((is_not_a_professional_photographer_specializing_in_portrait_photography(X))<=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))& (can_play_the_flute(dylan))& (owns_a_smart_tv(stephen))& (![X]:(room(X)=>(((((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<~>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))=>(~((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))))& (![X]:(room(X)=>(((~((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (((enjoys_cross-country_skiing(dylan))<~>(maintains_a_personal_blog_focused_on_cybersecurity_tips(dylan))))& (~((maintains_a_personal_blog_focused_on_cybersecurity_tips(stephen))|(trains_for_and_competes_in_international_triathlons(stephen))))
room(dylan)&room(stephen)&(![X]:(room(X)=>(X='dylan'|X='stephen')))& is_a_professional_photographer_specializing_in_portrait_photography(stephen)
[ "p0", "p14", "p20", "hypothesis" ]
% SZS status Unsatisfiable for 3453553001300219586379011 % SZS output start Proof for 3453553001300219586379011 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 58. ! [X0] : (~preds(X0) <=> predo(X0)) [input p14] 64. ~(predq(paul) | predo(paul)) [input p20] 65. ~(preds(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 150. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 151. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 150] 159. ~predq(paul) & ~predo(paul) [ennf transformation 64] 160. ~preds(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 65] 161. ~preds(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 160] 171. ! [X0] : ((~preds(X0) | ~predo(X0)) & (predo(X0) | preds(X0))) [nnf transformation 58] 173. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 174. ~preds(paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 161,173] 255. room(mary) [cnf transformation 151] 256. room(paul) [cnf transformation 151] 257. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 151] 272. preds(X0) | predo(X0) [cnf transformation 171] 277. ~predo(paul) [cnf transformation 159] 279. ~preds(paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 174] 280. ~preds(paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 174] 281. ~preds(paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 174] 352. ~preds(paul) | paul != sK3 | ~room(mary) [subsumption resolution 281,256] 353. ~preds(paul) | paul != sK3 [subsumption resolution 352,255] 355. 16 <=> paul = sK3 [avatar definition] 357. paul != sK3 <- (~16) [avatar component clause 355] 359. 17 <=> preds(paul) [avatar definition] 361. ~preds(paul) <- (~17) [avatar component clause 359] 362. ~16 | ~17 [avatar split clause 353,359,355] 363. ~preds(paul) | mary != sK3 | ~room(mary) [subsumption resolution 280,256] 364. ~preds(paul) | mary != sK3 [subsumption resolution 363,255] 366. 18 <=> mary = sK3 [avatar definition] 368. mary != sK3 <- (~18) [avatar component clause 366] 369. ~18 | ~17 [avatar split clause 364,359,366] 370. ~preds(paul) | room(sK3) | ~room(mary) [subsumption resolution 279,256] 371. ~preds(paul) | room(sK3) [subsumption resolution 370,255] 373. 19 <=> room(sK3) [avatar definition] 375. room(sK3) <- (19) [avatar component clause 373] 376. 19 | ~17 [avatar split clause 371,359,373] 377. predo(paul) <- (~17) [resolution 272,361] 378. $false <- (~17) [subsumption resolution 377,277] 379. 17 [avatar contradiction clause 378] 386. mary = sK3 | paul = sK3 <- (19) [resolution 257,375] 396. paul = sK3 <- (~18, 19) [subsumption resolution 386,368] 397. $false <- (~16, ~18, 19) [subsumption resolution 396,357] 398. 16 | 18 | ~19 [avatar contradiction clause 397] 399. $false [avatar sat refutation 362,369,376,379,398] % SZS output end Proof for 3453553001300219586379011 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------
0.307998
Jerry, Sandra, Daniel are the only persons in the room. If “Jerry enjoys logic puzzles” then “Sandra does not drive a hybrid car”. If “Sandra does not drive a hybrid car” then “Sandra who is a client of Lourdes either is not a humble european or is a sibling of Anne but not both”. If “Jerry is not a wine connoisseur” then “Daniel owns a microscope” otherwise “Sandra is not a kind european”.
Sandra and Jerry are not a funny quiet tall generous wise persons.
neutral
room(jerry)&room(sandra)&room(daniel)&(![X]:(room(X)=>(X='jerry'|X='sandra'|X='daniel')))& (((enjoys_logic_puzzles(jerry))=>(does_not_drive_a_hybrid_car(sandra)))& ((does_not_drive_a_hybrid_car(sandra))=>((client(lourdes,sandra))&(((~(humble(sandra)&european(sandra)))<~>(sibling(anne,sandra)))))))& (((is_not_a_wine_connoisseur(jerry))=>(owns_a_microscope(daniel)))&((~(is_not_a_wine_connoisseur(jerry)))=>(~(kind(sandra)&european(sandra)))))& ((((hosts_regular_game_nights_featuring_complex_strategy_games(jerry))|(does_not_enjoy_logic_puzzles(jerry))))=>(~(creative(jerry)&humble(jerry)&brave(jerry)&funny(jerry)&happy(jerry)&person(jerry))))& ((is_not_right-handed(jerry))=>(client(anne,sandra)))& ((~(happy(daniel)&kind(daniel)&strong(daniel)&calm(daniel)&person(daniel)))=>(does_not_drive_a_hybrid_car(sandra)))& ((~(brave(daniel)&kind(daniel)&european(daniel)))=>(~(brave(daniel)&european(daniel))))& ((does_not_build_model_airplanes(daniel))=>(~hate(sandra,patricia)))& ((owns_a_significant_collection_of_rare_gemstones_and_minerals(jerry))=>(~(humble(daniel)&quiet(daniel)&patient(daniel)&strong(daniel)&happy(daniel)&european(daniel))))& ((knows_morse_code(jerry))<=>(~like(sandra,lourdes)))& ((((~(calm(sandra)&brave(sandra)&european(sandra)))|(~(brave(sandra)&tourist(sandra)))|(~(patient(sandra)&quiet(sandra)&strong(sandra)&old(sandra)&tourist(sandra)))))=>(?[X,Y]:((enjoys_logic_puzzles(X))&(~(old(Y)&wise(Y)&person(Y)))&(sibling(X,Y)))))& ((sibling(lourdes,daniel))=>((hate(sandra,anne))&(client(anne,sandra))))& (((client(jerry,anne))=>(does_not_enjoy_windsurfing(sandra)))& ((does_not_enjoy_windsurfing(sandra))=>((![X]:((~(brave(X)&tourist(X)))=>(does_not_build_model_airplanes(X)))))))& ((~(kind(jerry)&tourist(jerry)))&(((client(patricia,jerry))<~>(~(generous(jerry)&person(jerry))))))& ((hate(shawna,daniel) & hate(daniel,shawna)))& ((![X]:((~(funny(X)&wise(X)&old(X)&person(X)))=>(((~(strong(X)&old(X)&humble(X)&patient(X)&european(X)))|(client(shawna,X))|(~(creative(X)&tall(X)&european(X))))))))& (is_a_wine_connoisseur(jerry))& (~(humble(daniel)&person(daniel)))& ((![X]:((sibling(shawna,X))=>(hate(X,shawna)))))& (~(old(jerry)&humble(jerry)&generous(jerry)&european(jerry)))& (funny(daniel)&creative(daniel)&happy(daniel)&european(daniel))& (sibling(anne,sandra))& (~(happy(daniel)&kind(daniel)&curious(daniel)&person(daniel)))& (~(wise(jerry)&tourist(jerry)))& (((does_not_enjoy_logic_puzzles(jerry))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(jerry))|(~(curious(jerry)&person(jerry)))))& (is_not_right-handed(sandra))& (sibling(jerry,lourdes))& (client(jerry,shawna))& (((client(anne,jerry))&(~(calm(jerry)&strong(jerry)&person(jerry)))&(does_not_practice_kickboxing(jerry))))
room(jerry)&room(sandra)&room(daniel)&(![X]:(room(X)=>(X='jerry'|X='sandra'|X='daniel')))& ~(funny(sandra)&quiet(sandra)&tall(sandra)&generous(sandra)&wise(sandra)&person(sandra))&~(funny(jerry)&quiet(jerry)&tall(jerry)&generous(jerry)&wise(jerry)&person(jerry))
[]
null
0.043171
There is a room. Everyone in the room who hosts themed dinner parties featuring gourmet home-cooked meals owns a 3D printer. Everyone in the room who does enjoy trail running writes and illustrates their own graphic novels. Everyone in the room who writes and illustrates their own graphic novels owns a 3D printer. Everyone anywhere does not collect vintage stamps or owns a 3D printer. Everyone in the room who does not collect vintage stamps does enjoy trail running, practices kickboxing or makes homemade pastries. Not everyone in the room who owns a high-end gaming PC with custom-built components enjoys stand-up paddleboarding. Not everyone in the room who is an active member of a local robotics club does enjoy trail running. Everyone in the room who does enjoy trail running practices tai chi. Everyone anywhere who practices tai chi mentors a youth basketball team on weekends. Everyone in the room who is a chess master who participates in national tournaments practices kickboxing. Everyone outside the room who practices kickboxing is a chess master who participates in national tournaments. Everyone in the room who is a chess master who participates in national tournaments owns a high-end gaming PC with custom-built components. Everyone in the room owns a high-end gaming PC with custom-built components if they regularly contributes to tech forums and online communities and vice versa. Someone outside the room neither is an enthusiastic bird watcher who travels for rare sightings nor composes and performs experimental electronic music. Everyone in the room who makes homemade pastries does not collect vintage stamps. Everyone in the room owns a telescope if they does not collect vintage stamps. Everyone in the room who collects vintage stamps regularly contributes to tech forums and online communities, creates YouTube content or makes homemade pastries. Everyone in the room who frequently participates in hackathons and coding competitions collects vintage stamps. Everyone in the room writes a travel blog, mentors a youth basketball team on weekends and does not mentor a youth basketball team on weekends only if they owns a high-end gaming PC with custom-built components. Everyone in the room who is an active member of a local robotics club enjoys stand-up paddleboarding. Everyone in the room who makes homemade pastries has a pet dog. Everyone outside the room uses an ios phone.
Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or writes and illustrates their own graphic novels.
neutral
(there_is_a_room)& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(owns_a_3D_printer(X))))))& (![X]:(anywhere(X)=>(((owns_a_3D_printer(X))|(does_not_collect_vintage_stamps(X))))))& (![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))=>(((does_enjoy_trail_running(X))|(practices_kickboxing(X))|(makes_homemade_pastries(X))))))))& (~![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(enjoys_stand-up_paddleboarding(X))))))& (~![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(does_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(practices_tai_chi(X))))))& (![X]:(anywhere(X)=>(((practices_tai_chi(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(practices_kickboxing(X))))))& (![X]:(~room(X)=>(((practices_kickboxing(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (?[X]:(~room(X)&(~((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))=>(does_not_collect_vintage_stamps(X))))))& (![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))=>(owns_a_telescope(X))))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(((regularly_contributes_to_tech_forums_and_online_communities(X))|(creates_YouTube_content(X))|(makes_homemade_pastries(X))))))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=(((writes_a_travel_blog(X))&(mentors_a_youth_basketball_team_on_weekends(X))&(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(enjoys_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))=>(has_a_pet_dog(X))))))& (![X]:(~room(X)=>(uses_an_ios_phone(X))))
(there_is_a_room)& ![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))
[]
null
0.588031
There is a room. More than one person in the room does enjoy mountain biking, collects historical artifacts related to ancient civilizations or enjoys stand-up paddleboarding. Everyone anywhere does enjoy mountain biking or practices graffiti art or both if they writes in-depth travel guides for off-the-beaten-path destinations. More than one person anywhere writes a travel blog. Everyone in the room who owns a telescope neither practices urban gardening nor writes a travel blog. Everyone outside the room who neither practices urban gardening nor writes a travel blog enjoys wildlife photography or is a certified scuba diver with advanced underwater photography skills or both. Everyone in the room collects classic novels or does enjoy mountain biking or both if they enjoys wildlife photography or is a certified scuba diver with advanced underwater photography skills or both. Everyone in the room who owns a significant collection of rare gemstones and minerals practices graffiti art. Everyone anywhere collects vintage stamps if they practices graffiti art. Everyone in the room hosts regular game nights featuring complex strategy games or does not write in-depth travel guides for off-the-beaten-path destinations. Someone in the room practices urban gardening. At least one person in the room owns a telescope. Everyone in the room who practices urban gardening enjoys deep-sea diving and exploring underwater caves. Only one person in the room collects historical artifacts related to ancient civilizations, practices graffiti art or enjoys stand-up paddleboarding. Everyone in the room neither enjoys salsa dancing nor collects vintage stamps if they collect rare sneakers. If someone owns a telescope then he/she writes in-depth travel guides for off-the-beaten-path destinations. Everyone anywhere writes a travel blog only if they owns a telescope. Everyone in the room who hosts regular game nights featuring complex strategy games owns a significant collection of rare gemstones and minerals, does not collect rare sneakers and develops open-source software projects in their free time. Everyone in the room streams on Twitch if they owns a significant collection of rare gemstones and minerals, does not collect rare sneakers and develops open-source software projects in their free time. Everyone outside the room owns a telescope only if they owns a significant collection of rare gemstones and minerals. If someone does enjoy mountain biking then he/she does not own a significant collection of rare gemstones and minerals.
Everyone outside the room does enjoy mountain biking.
contradiction
(there_is_a_room)& ((?[X,Y]:(room(X)&room(Y)&(((does_enjoy_mountain_biking(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))|(enjoys_stand-up_paddleboarding(X)))&((does_enjoy_mountain_biking(Y))|(collects_historical_artifacts_related_to_ancient_civilizations(Y))|(enjoys_stand-up_paddleboarding(Y))))&(X!=Y))))& (![X]:(anywhere(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(((does_enjoy_mountain_biking(X))|(practices_graffiti_art(X))))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(writes_a_travel_blog(X)&writes_a_travel_blog(Y))&(X!=Y))))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(~((practices_urban_gardening(X))|(writes_a_travel_blog(X))))))))& (![X]:(~room(X)=>(((~((practices_urban_gardening(X))|(writes_a_travel_blog(X))))=>(((enjoys_wildlife_photography(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))))& (![X]:(room(X)=>(((((enjoys_wildlife_photography(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(((collects_classic_novels(X))|(does_enjoy_mountain_biking(X))))))))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(practices_graffiti_art(X))))))& (![X]:(anywhere(X)=>(((practices_graffiti_art(X))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (?[X]:(room(X)&(practices_urban_gardening(X))))& (((?[X]:(room(X)&owns_a_telescope(X)))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (((?[X]:(room(X)&((collects_historical_artifacts_related_to_ancient_civilizations(X))|(practices_graffiti_art(X))|(enjoys_stand-up_paddleboarding(X)))))&(![X,Y]:((room(X)&room(Y)&(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(practices_graffiti_art(X))|(enjoys_stand-up_paddleboarding(X))))&(((collects_historical_artifacts_related_to_ancient_civilizations(Y))|(practices_graffiti_art(Y))|(enjoys_stand-up_paddleboarding(Y)))))=>(X=Y)))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))=>(~((enjoys_salsa_dancing(X))|(collects_vintage_stamps(X))))))))& ((![X]:((owns_a_telescope(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))& (![X]:(anywhere(X)=>(((owns_a_telescope(X))<=(writes_a_travel_blog(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(does_not_collect_rare_sneakers(X))&(develops_open-source_software_projects_in_their_free_time(X))))))))& (![X]:(room(X)=>(((((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(does_not_collect_rare_sneakers(X))&(develops_open-source_software_projects_in_their_free_time(X))))=>(streams_on_Twitch(X))))))& (![X]:(~room(X)=>(streams_on_Twitch(X))))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_wildlife_photography(X)&enjoys_wildlife_photography(Y))&(X!=Y))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& ((![X]:((plays_the_violin(X))<=>(competes_in_national_level_swimming_championships(X)))))& (![X]:(room(X)=>(((((practices_graffiti_art(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(((collects_vintage_stamps(X))|(plays_the_violin(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))& (![X]:(~room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<=(owns_a_telescope(X))))))& ((![X]:((does_enjoy_mountain_biking(X))=>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X)))))& (![X]:(room(X)=>(((((plays_the_violin(X))|(enjoys_watercolor_painting(X))))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (((?[X]:(room(X)&plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))& (![X]:(~room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))
(there_is_a_room)& ![X]:(~room(X)=>(does_enjoy_mountain_biking(X)))
[ "b4", "p3", "p4", "p16", "p25", "p26", "hypothesis" ]
% SZS status Unsatisfiable for 7545217222442986490867760 % SZS output start Proof for 7545217222442986490867760 5. ! [X0] : anywhere(X0) [input b4] 47. ? [X0,X1] : (X0 != X1 & predg(X1) & predg(X0) & anywhere(X1) & anywhere(X0)) [input p3] 48. ! [X0] : (room(X0) => (predf(X0) => ~(predg(X0) | predi(X0)))) [input p4] 60. ! [X0] : (anywhere(X0) => (predg(X0) => predf(X0))) [input p16] 69. ! [X0] : (~room(X0) => (predf(X0) => predd(X0))) [input p25] 70. ! [X0] : (predc(X0) => ~predd(X0)) [input p26] 74. ! [X0] : (~room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 93. ! [X0] : (~room(X0) => predc(X0)) [pure predicate removal 74] 170. ! [X0] : (((~predg(X0) & ~predi(X0)) | ~predf(X0)) | ~room(X0)) [ennf transformation 48] 171. ! [X0] : ((~predg(X0) & ~predi(X0)) | ~predf(X0) | ~room(X0)) [flattening 170] 179. ! [X0] : ((predf(X0) | ~predg(X0)) | ~anywhere(X0)) [ennf transformation 60] 180. ! [X0] : (predf(X0) | ~predg(X0) | ~anywhere(X0)) [flattening 179] 183. ! [X0] : ((predd(X0) | ~predf(X0)) | room(X0)) [ennf transformation 69] 184. ! [X0] : (predd(X0) | ~predf(X0) | room(X0)) [flattening 183] 185. ! [X0] : (~predd(X0) | ~predc(X0)) [ennf transformation 70] 186. ! [X0] : (predc(X0) | room(X0)) [ennf transformation 93] 192. ? [X0,X1] : (X0 != X1 & predg(X1) & predg(X0) & anywhere(X1) & anywhere(X0)) => (sK3 != sK4 & predg(sK4) & predg(sK3) & anywhere(sK4) & anywhere(sK3)) [choice axiom] 193. sK3 != sK4 & predg(sK4) & predg(sK3) & anywhere(sK4) & anywhere(sK3) [skolemisation 47,192] 205. anywhere(X0) [cnf transformation 5] 294. predg(sK3) [cnf transformation 193] 298. ~predf(X0) | ~predg(X0) | ~room(X0) [cnf transformation 171] 314. predf(X0) | ~predg(X0) | ~anywhere(X0) [cnf transformation 180] 319. ~predf(X0) | predd(X0) | room(X0) [cnf transformation 184] 320. ~predd(X0) | ~predc(X0) [cnf transformation 185] 322. predc(X0) | room(X0) [cnf transformation 186] 363. ~predg(X0) | predf(X0) [subsumption resolution 314,205] 365. predf(sK3) [resolution 363,294] 371. ~predg(sK3) | ~room(sK3) [resolution 298,365] 373. ~room(sK3) [subsumption resolution 371,294] 381. predd(sK3) | room(sK3) [resolution 319,365] 383. predd(sK3) [subsumption resolution 381,373] 401. 13 <=> predc(sK3) [avatar definition] 402. ~predc(sK3) <- (~13) [avatar component clause 401] 419. ~predc(sK3) [resolution 383,320] 420. ~13 [avatar split clause 419,401] 424. room(sK3) <- (~13) [resolution 402,322] 425. $false <- (~13) [subsumption resolution 424,373] 426. 13 [avatar contradiction clause 425] 427. $false [avatar sat refutation 420,426] % SZS output end Proof for 7545217222442986490867760 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------
0.151333
Hannelore, Nathaniel, Ivy, Jason are the only persons in the room. Either “Hannelore enjoys camping and organizing outdoor survival workshops” or “Hannelore practices kickboxing” but not both. If “it is not the case that “Hannelore writes and illustrates their own graphic novels”” then “Hannelore is a Linux enthusiast”. “Hannelore is a night owl” only if “Hannelore collects limited-edition art prints from contemporary artists”. Hannelore enjoys writing detailed reviews of new and classic board games. Hannelore is a night owl. Hannelore practices kickboxing or enjoys virtual reality gaming or both. Hannelore trains for and competes in international triathlons. Hannelore is an amateur astronomer who builds and uses custom telescopes. Hannelore who practices tai chi enjoys writing detailed reviews of new and classic board games. If someone enjoys camping and organizing outdoor survival workshops or enjoys watercolor painting or both then he/she is dedicated to sustainable living and zero-waste practices. If someone enjoys writing detailed reviews of new and classic board games then he/she owns an extensive assortment of vintage comic book memorabilia and vice versa. Hannelore neither is dedicated to sustainable living and zero-waste practices nor collects rare minerals. If someone writes and illustrates their own graphic novels then he/she is a Linux enthusiast, can play the piano and enjoys writing detailed reviews of new and classic board games. Hannelore collects limited-edition art prints from contemporary artists. Hannelore is a Linux enthusiast. Hannelore is a cybersecurity expert. Hannelore enjoys writing detailed reviews of new and classic board games or is dedicated to sustainable living and zero-waste practices or both. It is not the case that “Hannelore writes and illustrates their own graphic novels”. Hannelore can play the piano. More than one person outside the room trains for and competes in international triathlons. If someone practices kickboxing then he/she builds model airplanes. Hannelore hosts regular workshops on creative writing. Hannelore enjoys kayaking.
Hannelore enjoys watercolor painting.
contradiction
room(hannelore)&room(nathaniel)&room(ivy)&room(jason)&(![X]:(room(X)=>(X='hannelore'|X='nathaniel'|X='ivy'|X='jason')))& ((enjoys_camping_and_organizing_outdoor_survival_workshops(hannelore))<~>(practices_kickboxing(hannelore)))& ((~(writes_and_illustrates_their_own_graphic_novels(hannelore)))=>(is_a_Linux_enthusiast(hannelore)))& ((is_a_night_owl(hannelore))=>(collects_limited-edition_art_prints_from_contemporary_artists(hannelore)))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(hannelore))& (is_a_night_owl(hannelore))& (((practices_kickboxing(hannelore))|(enjoys_virtual_reality_gaming(hannelore))))& (trains_for_and_competes_in_international_triathlons(hannelore))& (is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(hannelore))& ((practices_tai_chi(hannelore))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(hannelore)))& ((![X]:((((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(enjoys_watercolor_painting(X))))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& ((![X]:((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))& (~((is_dedicated_to_sustainable_living_and_zero-waste_practices(hannelore))|(collects_rare_minerals(hannelore))))& ((![X]:((writes_and_illustrates_their_own_graphic_novels(X))=>(((is_a_Linux_enthusiast(X))&(can_play_the_piano(X))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))& (collects_limited-edition_art_prints_from_contemporary_artists(hannelore))& (is_a_Linux_enthusiast(hannelore))& (is_a_cybersecurity_expert(hannelore))& (((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(hannelore))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(hannelore))))& (~(writes_and_illustrates_their_own_graphic_novels(hannelore)))& (can_play_the_piano(hannelore))& ((?[X,Y]:(~room(X)&~room(Y)&(trains_for_and_competes_in_international_triathlons(X)&trains_for_and_competes_in_international_triathlons(Y))&(X!=Y))))& ((![X]:((practices_kickboxing(X))=>(builds_model_airplanes(X)))))& (hosts_regular_workshops_on_creative_writing(hannelore))& (enjoys_kayaking(hannelore))
room(hannelore)&room(nathaniel)&room(ivy)&room(jason)&(![X]:(room(X)=>(X='hannelore'|X='nathaniel'|X='ivy'|X='jason')))& enjoys_watercolor_painting(hannelore)
[ "p10", "p12", "hypothesis" ]
% SZS status Unsatisfiable for 7003278471301867955871394 % SZS output start Proof for 7003278471301867955871394 54. ! [X0] : ((predy(X0) | predt(X0)) => predo(X0)) [input p10] 56. ~(predm(mary) | predo(mary)) [input p12] 68. predy(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 81. ~predo(mary) [pure predicate removal 56] 168. ! [X0] : (predo(X0) | (~predy(X0) & ~predt(X0))) [ennf transformation 54] 169. ~predo(mary) [ennf transformation 81] 170. predy(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 68] 171. predy(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 170] 264. ~predy(X0) | predo(X0) [cnf transformation 168] 265. ~predo(mary) [cnf transformation 169] 274. predy(mary) [cnf transformation 171] 285. predo(mary) [resolution 264,274] 286. $false [subsumption resolution 285,265] % SZS output end Proof for 7003278471301867955871394 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------
0.300682
Megan, Margaret, Thomas are the only persons in the room. If Thomas is liked by Leo then everyone in the room likes German or is liked by German or both only if they likes German, is liked by Leo and does not like Leo otherwise Thomas likes German or is liked by German or both. If German and Megan like each other then if someone is liked by German then he/she neither likes German nor is liked by Leo. Margaret likes German or is liked by German or both. At least one person in the room is liked by Leo or is liked by German or both. At least one person in the room does not like German. Thomas likes German or likes Leo or both. Someone in the room neither is liked by Leo nor is liked by German. Thomas likes German or is liked by German or both.
Thomas likes German.
neutral
room(megan)&room(margaret)&room(thomas)&(![X]:(room(X)=>(X='megan'|X='margaret'|X='thomas')))& (((like(thomas,leo))=>(![X]:(room(X)=>(((((like(german,X))&(like(X,leo))&(~like(leo,X))))<=(((like(german,X))|(like(X,german)))))))))&((~(like(thomas,leo)))=>(((like(german,thomas))|(like(thomas,german))))))& (((like(german,megan) & like(megan,german)))=>((![X]:((like(X,german))=>(~((like(german,X))|(like(X,leo))))))))& (((like(german,margaret))|(like(margaret,german))))& (((?[X]:(room(X)&((like(X,leo))|(like(X,german)))))))& (((?[X]:(room(X)&~like(german,X)))))& (((like(german,thomas))|(like(leo,thomas))))& (?[X]:(room(X)&(~((like(X,leo))|(like(X,german))))))& (((like(german,thomas))|(like(thomas,german))))
room(megan)&room(margaret)&room(thomas)&(![X]:(room(X)=>(X='megan'|X='margaret'|X='thomas')))& like(german,thomas)
[]
null
0.327613
Margaret, Annette, Jennifer are the only persons in the room. Either "Jennifer owns a microscope" or "everyone in the room is not dedicated to sustainable living and zero-waste practices or is a dedicated volunteer for local community service projects" but not both. If "someone in the room cannot play the harmonica" then "no one anywhere does not enjoy spelunking or uses an ios phone". If "no one anywhere does not enjoy spelunking or uses an ios phone" then "everyone outside the room who does not enjoy spelunking is an enthusiastic bird watcher who travels for rare sightings or creates bespoke furniture pieces from reclaimed wood or both". "Margaret owns a 3D printer" unless "everyone in the room cannot play the harmonica or does not own an Android phone". Someone in the room neither own a television nor does not enjoy spelunking. Jennifer owns a 3D printer. Everyone in the room maintains a personal blog focused on cybersecurity tips or does not own a microscope. If someone collects rare minerals then he/she own a television and vice versa. Margaret who enjoys watercolor painting is not dedicated to sustainable living and zero-waste practices. Everyone outside the room who collects first edition books enjoys camping and organizing outdoor survival workshops. Everyone in the room can play the harmonica if they enjoys camping and organizing outdoor survival workshops. If someone maintains a personal blog focused on cybersecurity tips then he/she enjoys watercolor painting. If someone streams on Twitch then he/she maintains a personal blog focused on cybersecurity tips or owns a microscope or both and vice versa. Everyone in the room owns a 3D printer if and only if they is an enthusiastic bird watcher who travels for rare sightings.
Margaret is dedicated to sustainable living and zero-waste practices.
contradiction
room(margaret)&room(annette)&room(jennifer)&(![X]:(room(X)=>(X='margaret'|X='annette'|X='jennifer')))& ((owns_a_microscope(jennifer))<~>(![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))& (((?[X]:(room(X)&(cannot_play_the_harmonica(X))))=>(~?[X]:(anywhere(X)=>(((uses_an_ios_phone(X))|(does_not_enjoy_spelunking(X)))))))& ((~?[X]:(anywhere(X)=>(((uses_an_ios_phone(X))|(does_not_enjoy_spelunking(X))))))=>(![X]:(~room(X)=>(((does_not_enjoy_spelunking(X))=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))))& (~(![X]:(room(X)=>(((does_not_own_an_Android_phone(X))|(cannot_play_the_harmonica(X))))))=>(owns_a_3D_printer(margaret)))& (?[X]:(room(X)&(~((own_a_television(X))|(does_not_enjoy_spelunking(X))))))& (owns_a_3D_printer(jennifer))& (![X]:(room(X)=>(((does_not_own_a_microscope(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& ((![X]:((collects_rare_minerals(X))<=>(own_a_television(X)))))& ((enjoys_watercolor_painting(margaret))&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(margaret)))& (![X]:(~room(X)=>(((collects_first_edition_books(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(can_play_the_harmonica(X))))))& ((![X]:((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(enjoys_watercolor_painting(X)))))& ((![X]:((streams_on_Twitch(X))<=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(owns_a_microscope(X)))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))
room(margaret)&room(annette)&room(jennifer)&(![X]:(room(X)=>(X='margaret'|X='annette'|X='jennifer')))& is_dedicated_to_sustainable_living_and_zero-waste_practices(margaret)
[ "p0", "hypothesis" ]
% SZS status Unsatisfiable for 5789263241503443448798257 % SZS output start Proof for 5789263241503443448798257 44. ! [X0] : (room(X0) => (predl(X0) <=> predi(X0))) & ! [X0] : (predf(X0) <=> (predp(X0) | predc(X0))) & ! [X0] : (predc(X0) => predr(X0)) & ! [X0] : (room(X0) => (predg(X0) => predm(X0))) & ! [X0] : (~room(X0) => (predj(X0) => predg(X0))) & ~predn(mary) & predr(mary) & ! [X0] : (predq(X0) <=> preda(X0)) & ! [X0] : (room(X0) => (predc(X0) | ~predp(X0))) & predl(fred) & ? [X0] : (~(~predb(X0) | preda(X0)) & room(X0)) & (~! [X0] : (room(X0) => (~predm(X0) | ~predu(X0))) => predl(mary)) & (~? [X0] : (anywhere(X0) => (~predb(X0) | predh(X0))) => ! [X0] : (~room(X0) => (~predb(X0) => (predk(X0) | predi(X0))))) & (? [X0] : (~predm(X0) & room(X0)) => ~? [X0] : (anywhere(X0) => (~predb(X0) | predh(X0)))) & (predp(fred) <~> ! [X0] : (room(X0) => (~predn(X0) | predt(X0)))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. predn(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 46. ! [X0] : (room(X0) => (predl(X0) <=> predi(X0))) & ! [X1] : (predf(X1) <=> (predp(X1) | predc(X1))) & ! [X2] : (predc(X2) => predr(X2)) & ! [X3] : (room(X3) => (predg(X3) => predm(X3))) & ! [X4] : (~room(X4) => (predj(X4) => predg(X4))) & ~predn(mary) & predr(mary) & ! [X5] : (predq(X5) <=> preda(X5)) & ! [X6] : (room(X6) => (predc(X6) | ~predp(X6))) & predl(fred) & ? [X7] : (~(~predb(X7) | preda(X7)) & room(X7)) & (~! [X8] : (room(X8) => (~predm(X8) | ~predu(X8))) => predl(mary)) & (~? [X9] : (anywhere(X9) => (~predb(X9) | predh(X9))) => ! [X10] : (~room(X10) => (~predb(X10) => (predk(X10) | predi(X10))))) & (? [X11] : (~predm(X11) & room(X11)) => ~? [X12] : (anywhere(X12) => (~predb(X12) | predh(X12)))) & (predp(fred) <~> ! [X13] : (room(X13) => (~predn(X13) | predt(X13)))) & ! [X14] : (room(X14) => (fred = X14 | paul = X14 | mary = X14)) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => (predl(X0) <=> predi(X0))) & ! [X1] : (predf(X1) <=> (predp(X1) | predc(X1))) & ! [X2] : (predc(X2) => predr(X2)) & ! [X3] : (room(X3) => (predg(X3) => predm(X3))) & ~predn(mary) & predr(mary) & ! [X5] : (predq(X5) <=> preda(X5)) & ! [X6] : (room(X6) => (predc(X6) | ~predp(X6))) & predl(fred) & ? [X7] : (~(~predb(X7) | preda(X7)) & room(X7)) & (~! [X8] : (room(X8) => (~predm(X8) | ~predu(X8))) => predl(mary)) & (~? [X9] : (anywhere(X9) => (~predb(X9) | predh(X9))) => ! [X10] : (~room(X10) => (~predb(X10) => (predk(X10) | predi(X10))))) & (? [X11] : (~predm(X11) & room(X11)) => ~? [X12] : (anywhere(X12) => (~predb(X12) | predh(X12)))) & (predp(fred) <~> ! [X13] : (room(X13) => (~predn(X13) | predt(X13)))) & ! [X14] : (room(X14) => (fred = X14 | paul = X14 | mary = X14)) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (room(X0) => (predl(X0) <=> predi(X0))) & ! [X1] : (predf(X1) <=> (predp(X1) | predc(X1))) & ! [X2] : (predc(X2) => predr(X2)) & ~predn(mary) & predr(mary) & ! [X5] : (predq(X5) <=> preda(X5)) & ! [X6] : (room(X6) => (predc(X6) | ~predp(X6))) & predl(fred) & ? [X7] : (~(~predb(X7) | preda(X7)) & room(X7)) & (~! [X8] : (room(X8) => (~predm(X8) | ~predu(X8))) => predl(mary)) & (~? [X9] : (anywhere(X9) => (~predb(X9) | predh(X9))) => ! [X10] : (~room(X10) => (~predb(X10) => (predk(X10) | predi(X10))))) & (? [X11] : (~predm(X11) & room(X11)) => ~? [X12] : (anywhere(X12) => (~predb(X12) | predh(X12)))) & (predp(fred) <~> ! [X13] : (room(X13) => (~predn(X13) | predt(X13)))) & ! [X14] : (room(X14) => (fred = X14 | paul = X14 | mary = X14)) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (room(X0) => (predl(X0) <=> predi(X0))) & ! [X1] : (predf(X1) <=> (predp(X1) | predc(X1))) & ~predn(mary) & ! [X5] : (predq(X5) <=> preda(X5)) & ! [X6] : (room(X6) => (predc(X6) | ~predp(X6))) & predl(fred) & ? [X7] : (~(~predb(X7) | preda(X7)) & room(X7)) & (~! [X8] : (room(X8) => (~predm(X8) | ~predu(X8))) => predl(mary)) & (~? [X9] : (anywhere(X9) => (~predb(X9) | predh(X9))) => ! [X10] : (~room(X10) => (~predb(X10) => (predk(X10) | predi(X10))))) & (? [X11] : (~predm(X11) & room(X11)) => ~? [X12] : (anywhere(X12) => (~predb(X12) | predh(X12)))) & (predp(fred) <~> ! [X13] : (room(X13) => (~predn(X13) | predt(X13)))) & ! [X14] : (room(X14) => (fred = X14 | paul = X14 | mary = X14)) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (room(X0) => (predl(X0) <=> predi(X0))) & ! [X1] : (predf(X1) <=> (predp(X1) | predc(X1))) & ~predn(mary) & ! [X5] : (predq(X5) <=> preda(X5)) & ! [X6] : (room(X6) => (predc(X6) | ~predp(X6))) & predl(fred) & ? [X7] : (~(~predb(X7) | preda(X7)) & room(X7)) & (~? [X9] : (anywhere(X9) => (~predb(X9) | predh(X9))) => ! [X10] : (~room(X10) => (~predb(X10) => (predk(X10) | predi(X10))))) & (? [X11] : (~predm(X11) & room(X11)) => ~? [X12] : (anywhere(X12) => (~predb(X12) | predh(X12)))) & (predp(fred) <~> ! [X13] : (room(X13) => (~predn(X13) | predt(X13)))) & ! [X14] : (room(X14) => (fred = X14 | paul = X14 | mary = X14)) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (room(X0) => (predl(X0) <=> predi(X0))) & ! [X1] : (predf(X1) <=> (predp(X1) | predc(X1))) & ~predn(mary) & ! [X5] : (predq(X5) <=> preda(X5)) & ! [X6] : (room(X6) => (predc(X6) | ~predp(X6))) & predl(fred) & ? [X7] : (~(~predb(X7) | preda(X7)) & room(X7)) & (~? [X9] : (anywhere(X9) => (~predb(X9) | predh(X9))) => ! [X10] : (~room(X10) => (~predb(X10) => (predk(X10) | predi(X10))))) & (predp(fred) <~> ! [X13] : (room(X13) => (~predn(X13) | predt(X13)))) & ! [X14] : (room(X14) => (fred = X14 | paul = X14 | mary = X14)) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (room(X0) => (predl(X0) <=> predi(X0))) & ! [X1] : (predf(X1) <=> (predp(X1) | predc(X1))) & ~predn(mary) & ! [X5] : (predq(X5) <=> preda(X5)) & ! [X6] : (room(X6) => (predc(X6) | ~predp(X6))) & predl(fred) & ? [X7] : (~(~predb(X7) | preda(X7)) & room(X7)) & (predp(fred) <~> ! [X13] : (room(X13) => (~predn(X13) | predt(X13)))) & ! [X14] : (room(X14) => (fred = X14 | paul = X14 | mary = X14)) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0] : (room(X0) => (predl(X0) <=> predi(X0))) & ! [X1] : (predf(X1) <=> (predp(X1) | predc(X1))) & ~predn(mary) & ! [X5] : (predq(X5) <=> preda(X5)) & ! [X6] : (room(X6) => (predc(X6) | ~predp(X6))) & predl(fred) & ? [X7] : (~preda(X7) & room(X7)) & (predp(fred) <~> ! [X13] : (room(X13) => (~predn(X13) | predt(X13)))) & ! [X14] : (room(X14) => (fred = X14 | paul = X14 | mary = X14)) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 126. ! [X0] : ((predl(X0) <=> predi(X0)) | ~room(X0)) & ! [X1] : (predf(X1) <=> (predp(X1) | predc(X1))) & ~predn(mary) & ! [X5] : (predq(X5) <=> preda(X5)) & ! [X6] : ((predc(X6) | ~predp(X6)) | ~room(X6)) & predl(fred) & ? [X7] : (~preda(X7) & room(X7)) & (predp(fred) <~> ! [X13] : ((~predn(X13) | predt(X13)) | ~room(X13))) & ! [X14] : ((fred = X14 | paul = X14 | mary = X14) | ~room(X14)) & room(fred) & room(paul) & room(mary) [ennf transformation 53] 127. ! [X0] : ((predl(X0) <=> predi(X0)) | ~room(X0)) & ! [X1] : (predf(X1) <=> (predp(X1) | predc(X1))) & ~predn(mary) & ! [X5] : (predq(X5) <=> preda(X5)) & ! [X6] : (predc(X6) | ~predp(X6) | ~room(X6)) & predl(fred) & ? [X7] : (~preda(X7) & room(X7)) & (predp(fred) <~> ! [X13] : (~predn(X13) | predt(X13) | ~room(X13))) & ! [X14] : (fred = X14 | paul = X14 | mary = X14 | ~room(X14)) & room(fred) & room(paul) & room(mary) [flattening 126] 128. predn(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 45] 129. predn(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 128] 131. ! [X0] : (((predl(X0) | ~predi(X0)) & (predi(X0) | ~predl(X0))) | ~room(X0)) & ! [X1] : ((predf(X1) | (~predp(X1) & ~predc(X1))) & ((predp(X1) | predc(X1)) | ~predf(X1))) & ~predn(mary) & ! [X5] : ((predq(X5) | ~preda(X5)) & (preda(X5) | ~predq(X5))) & ! [X6] : (predc(X6) | ~predp(X6) | ~room(X6)) & predl(fred) & ? [X7] : (~preda(X7) & room(X7)) & ((? [X13] : (predn(X13) & ~predt(X13) & room(X13)) | ~predp(fred)) & (! [X13] : (~predn(X13) | predt(X13) | ~room(X13)) | predp(fred))) & ! [X14] : (fred = X14 | paul = X14 | mary = X14 | ~room(X14)) & room(fred) & room(paul) & room(mary) [nnf transformation 127] 132. ! [X0] : (((predl(X0) | ~predi(X0)) & (predi(X0) | ~predl(X0))) | ~room(X0)) & ! [X1] : ((predf(X1) | (~predp(X1) & ~predc(X1))) & (predp(X1) | predc(X1) | ~predf(X1))) & ~predn(mary) & ! [X5] : ((predq(X5) | ~preda(X5)) & (preda(X5) | ~predq(X5))) & ! [X6] : (predc(X6) | ~predp(X6) | ~room(X6)) & predl(fred) & ? [X7] : (~preda(X7) & room(X7)) & (? [X13] : (predn(X13) & ~predt(X13) & room(X13)) | ~predp(fred)) & (! [X13] : (~predn(X13) | predt(X13) | ~room(X13)) | predp(fred)) & ! [X14] : (fred = X14 | paul = X14 | mary = X14 | ~room(X14)) & room(fred) & room(paul) & room(mary) [flattening 131] 133. ! [X0] : (((predl(X0) | ~predi(X0)) & (predi(X0) | ~predl(X0))) | ~room(X0)) & ! [X1] : ((predf(X1) | (~predp(X1) & ~predc(X1))) & (predp(X1) | predc(X1) | ~predf(X1))) & ~predn(mary) & ! [X2] : ((predq(X2) | ~preda(X2)) & (preda(X2) | ~predq(X2))) & ! [X3] : (predc(X3) | ~predp(X3) | ~room(X3)) & predl(fred) & ? [X4] : (~preda(X4) & room(X4)) & (? [X5] : (predn(X5) & ~predt(X5) & room(X5)) | ~predp(fred)) & (! [X6] : (~predn(X6) | predt(X6) | ~room(X6)) | predp(fred)) & ! [X7] : (fred = X7 | paul = X7 | mary = X7 | ~room(X7)) & room(fred) & room(paul) & room(mary) [rectify 132] 134. ? [X4] : (~preda(X4) & room(X4)) => (~preda(sK0) & room(sK0)) [choice axiom] 135. ? [X5] : (predn(X5) & ~predt(X5) & room(X5)) => (predn(sK1) & ~predt(sK1) & room(sK1)) [choice axiom] 136. ! [X0] : (((predl(X0) | ~predi(X0)) & (predi(X0) | ~predl(X0))) | ~room(X0)) & ! [X1] : ((predf(X1) | (~predp(X1) & ~predc(X1))) & (predp(X1) | predc(X1) | ~predf(X1))) & ~predn(mary) & ! [X2] : ((predq(X2) | ~preda(X2)) & (preda(X2) | ~predq(X2))) & ! [X3] : (predc(X3) | ~predp(X3) | ~room(X3)) & predl(fred) & (~preda(sK0) & room(sK0)) & ((predn(sK1) & ~predt(sK1) & room(sK1)) | ~predp(fred)) & (! [X6] : (~predn(X6) | predt(X6) | ~room(X6)) | predp(fred)) & ! [X7] : (fred = X7 | paul = X7 | mary = X7 | ~room(X7)) & room(fred) & room(paul) & room(mary) [skolemisation 133,135,134] 231. ~predn(mary) [cnf transformation 136] 241. predn(mary) [cnf transformation 129] 265. $false [subsumption resolution 241,231] % SZS output end Proof for 5789263241503443448798257 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s % ------------------------------ % ------------------------------
0
Natalie, Lou, Robert are the only persons in the room. Lou enjoys macrame. Everyone outside the room owns a 3D printer only if they enjoys macrame. If someone owns a 3D printer then he/she either owns a 3D printer or collects vintage vinyl records but not both. Natalie owns a 3D printer. Lou who collects vintage vinyl records enjoys macrame. Everyone in the room who owns a 3D printer enjoys macrame. Natalie who owns a 3D printer enjoys macrame. Someone in the room enjoys macrame. Everyone in the room who owns a 3D printer is a client of LVMH. Lou either collects vintage vinyl records or owns a 3D printer but not both.
Everyone in the room enjoys macrame.
neutral
room(natalie)&room(lou)&room(robert)&(![X]:(room(X)=>(X='natalie'|X='lou'|X='robert')))& (enjoys_macrame(lou))& (![X]:(~room(X)=>(((enjoys_macrame(X))<=(owns_a_3D_printer(X))))))& ((![X]:((owns_a_3D_printer(X))=>(((owns_a_3D_printer(X))<~>(collects_vintage_vinyl_records(X)))))))& (owns_a_3D_printer(natalie))& ((collects_vintage_vinyl_records(lou))&(enjoys_macrame(lou)))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(enjoys_macrame(X))))))& ((owns_a_3D_printer(natalie))&(enjoys_macrame(natalie)))& (?[X]:(room(X)&(enjoys_macrame(X))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(is_a_client_of_LVMH(X))))))& (((collects_vintage_vinyl_records(lou))<~>(owns_a_3D_printer(lou))))
room(natalie)&room(lou)&room(robert)&(![X]:(room(X)=>(X='natalie'|X='lou'|X='robert')))& ![X]:(room(X)=>(enjoys_macrame(X)))
[]
null
0.485492
Marcus, Keith, Brett, Bobbie are the only persons in the room. Keith is old. Marcus and Bobbie are old. Keith is not quiet. Not everyone in the room either is not old or is not a quiet old person but not both if and only if they either is not old, not quiet or is not old but not both. Everyone in the room either is not old, not quiet or is not old but not both if and only if they is not old.
Marcus and Brett are respectively old and quiet.
neutral
room(marcus)&room(keith)&room(brett)&room(bobbie)&(![X]:(room(X)=>(X='marcus'|X='keith'|X='brett'|X='bobbie')))& (old(keith))& (old(marcus)&old(bobbie))& (~quiet(keith))& (~![X]:(room(X)=>(((((~old(X))<~>(~(quiet(X)&old(X)&person(X)))))<=>(((~old(X)&~quiet(X))<~>(~old(X))))))))& (![X]:(room(X)=>(((((~old(X)&~quiet(X))<~>(~old(X))))<=>(~old(X))))))& (?[X]:(room(X)&(~(old(X)&person(X)))))& (((~old(bobbie))<~>(~(quiet(bobbie)&old(bobbie)&person(bobbie))))&((~old(keith))<~>(~(quiet(keith)&old(keith)&person(keith)))))& (quiet(bobbie))& (![X]:(room(X)=>(((((old(X))<~>(quiet(X)&person(X))))=>(old(X))))))
room(marcus)&room(keith)&room(brett)&room(bobbie)&(![X]:(room(X)=>(X='marcus'|X='keith'|X='brett'|X='bobbie')))& (old(marcus))&(quiet(brett))
[]
null
0.01206
Sylvia, Kenneth are the only persons in the room. If someone does not enjoy stand-up paddleboarding then he/she has lived in exactly three countries. Sylvia enjoys logic puzzles. Everyone in the room is a cybersecurity expert if they can play the guitar. More than one person in the room enjoys stand-up paddleboarding. It is true that "everyone in the room collects rare and antique scientific instruments only if they is a cybersecurity expert". Kenneth enjoys logic puzzles. Everyone anywhere who is a cybersecurity expert is an avid hiker. Everyone in the room has lived in exactly three countries if they can play the guitar. Everyone in the room who is a cybersecurity expert cannot play the guitar. Everyone in the room does not practice kickboxing if they enjoys logic puzzles. Everyone in the room who does not practice kickboxing is a cybersecurity expert. Everyone in the room who is a cybersecurity expert enjoys stand-up paddleboarding. More than one person in the room is a member of a local theater group specializing in improv. If someone is not an avid hiker then he/she enjoys stand-up paddleboarding.
Sylvia practices kickboxing.
contradiction
room(sylvia)&room(kenneth)&(![X]:(room(X)=>(X='sylvia'|X='kenneth')))& ((![X]:((does_not_enjoy_stand-up_paddleboarding(X))=>(has_lived_in_exactly_three_countries(X)))))& (enjoys_logic_puzzles(sylvia))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(is_a_cybersecurity_expert(X))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_stand-up_paddleboarding(X)&enjoys_stand-up_paddleboarding(Y))&(X!=Y))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))<=(collects_rare_and_antique_scientific_instruments(X))))))& (enjoys_logic_puzzles(kenneth))& (![X]:(anywhere(X)=>(((is_a_cybersecurity_expert(X))=>(is_an_avid_hiker(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(has_lived_in_exactly_three_countries(X))))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(cannot_play_the_guitar(X))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(does_not_practice_kickboxing(X))))))& (![X]:(room(X)=>(((does_not_practice_kickboxing(X))=>(is_a_cybersecurity_expert(X))))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(enjoys_stand-up_paddleboarding(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_a_member_of_a_local_theater_group_specializing_in_improv(X)&is_a_member_of_a_local_theater_group_specializing_in_improv(Y))&(X!=Y))))& ((![X]:((is_not_an_avid_hiker(X))=>(enjoys_stand-up_paddleboarding(X)))))
room(sylvia)&room(kenneth)&(![X]:(room(X)=>(X='sylvia'|X='kenneth')))& practices_kickboxing(sylvia)
[ "p0", "p2", "p10", "hypothesis" ]
% SZS status Unsatisfiable for 6704784818472714540278369 % SZS output start Proof for 6704784818472714540278369 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. prede(mary) [input p2] 54. ! [X0] : (room(X0) => (prede(X0) => ~predh(X0))) [input p10] 59. predh(mary) & ! [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] 145. ! [X0] : ((~predh(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 54] 146. ! [X0] : (~predh(X0) | ~prede(X0) | ~room(X0)) [flattening 145] 147. predh(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 59] 148. predh(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 147] 234. room(mary) [cnf transformation 144] 237. prede(mary) [cnf transformation 46] 242. ~predh(X0) | ~prede(X0) | ~room(X0) [cnf transformation 146] 249. predh(mary) [cnf transformation 148] 250. ~prede(mary) | ~room(mary) [resolution 242,249] 251. ~room(mary) [subsumption resolution 250,237] 252. $false [subsumption resolution 251,234] % SZS output end Proof for 6704784818472714540278369 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------
0.183377
Jose is the only person in the room. If “everyone in the room is not old” then “everyone in the room is not quiet, is a old person and is old”. “Not everyone in the room is a old person if they either is not a quiet person or is a quiet old person but not both” unless “everyone in the room is a quiet old person”.
Jose is quiet.
neutral
room(jose)&(![X]:(room(X)=>(X='jose')))& ((![X]:(room(X)=>(~old(X))))=>(![X]:(room(X)=>(((~quiet(X))&(old(X)&person(X))&(old(X)))))))& (~(![X]:(room(X)=>(quiet(X)&old(X)&person(X))))=>(~![X]:(room(X)=>(((((~(quiet(X)&person(X)))<~>(quiet(X)&old(X)&person(X))))=>(old(X)&person(X)))))))& (![X]:(~room(X)=>(((quiet(X))&(old(X)&person(X))))))& (![X]:(room(X)=>(((old(X)&person(X))=>(~quiet(X)&~old(X))))))& ((![X]:((((~old(X))|(quiet(X)&person(X))))<=>(old(X)&person(X)))))& (![X]:(room(X)=>(((quiet(X)&person(X))=>(old(X)&person(X))))))
room(jose)&(![X]:(room(X)=>(X='jose')))& quiet(jose)
[]
null
0.026934
There is a room. 'Everyone in the room does not play the drums or enjoys stand-up paddleboarding' if 'no one anywhere composes and performs experimental electronic music or does not create large-scale murals for public art installations' and vice versa. 'Not everyone in the room is a skilled home brewer experimenting with craft beer recipes or does not create large-scale murals for public art installations' only if 'everyone anywhere does not enjoy stand-up paddleboarding or is a skilled home brewer experimenting with craft beer recipes'.
Everyone in the room is a skilled home brewer experimenting with craft beer recipes.
neutral
(there_is_a_room)& ((~?[X]:(anywhere(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))|(composes_and_performs_experimental_electronic_music(X))))))<=>(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))|(does_not_play_the_drums(X)))))))& ((~![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(![X]:(anywhere(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_enjoy_stand-up_paddleboarding(X)))))))& ((![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))|(enjoys_stand-up_paddleboarding(X))))))=>(~![X]:(room(X)=>(((((composes_and_performs_experimental_electronic_music(X))|(enjoys_stand-up_paddleboarding(X))))=>(creates_large-scale_murals_for_public_art_installations(X)))))))& ((![X]:(anywhere(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(does_not_play_the_drums(X))))))=>(((?[X]:(~room(X)&composes_and_performs_experimental_electronic_music(X))))))& (?[X]:(room(X)&(creates_large-scale_murals_for_public_art_installations(X))))& (~(?[X]:(~room(X)&(plays_the_drums(X)))))& (((?[X]:(~room(X)&composes_and_performs_experimental_electronic_music(X)))))& (![X]:(anywhere(X)=>(((enjoys_stand-up_paddleboarding(X))=>(composes_and_performs_experimental_electronic_music(X))))))& (?[X]:(anywhere(X)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))& (![X]:(room(X)=>(((((composes_and_performs_experimental_electronic_music(X))|(enjoys_stand-up_paddleboarding(X))|(plays_the_drums(X))))=>(((creates_large-scale_murals_for_public_art_installations(X))&(enjoys_coding_in_Python(X))&(plays_the_drums(X))))))))& ((amy_dream=>((![X]:((enjoys_stand-up_paddleboarding(X))<=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(composes_and_performs_experimental_electronic_music(X))&(plays_the_drums(X)))))))))
(there_is_a_room)& ![X]:(room(X)=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))
[]
null
0
Adrienne, Erica, Patricia, George are the only persons in the room. No tall person is quiet.
Adrienne and Patricia are respectively old and quiet.
contradiction
room(adrienne)&room(erica)&room(patricia)&room(george)&(![X]:(room(X)=>(X='adrienne'|X='erica'|X='patricia'|X='george')))& (((quiet(george))&(old(adrienne)))=>(~?[X]:(quiet(X)=>old(X))))& (~(?[X]:(room(X)&(tall(X))))=>(~?[X]:(old(X)=>tall(X))))& ((((?[X]:(anywhere(X)&richer(danny,X)))))=>(![X]:((~room(X)&(X!=adrienne))=>quieter(adrienne,X))))& (quieter(erica,danny))& (~![X]:(room(X)=>(((richer(danny,X))=>(quieter(danny,X))))))& (![X]:(room(X)=>(((older(danny,X))=>(~quiet(X))))))& (~?[X]:(tall(X)=>quiet(X)))
room(adrienne)&room(erica)&room(patricia)&room(george)&(![X]:(room(X)=>(X='adrienne'|X='erica'|X='patricia'|X='george')))& (old(adrienne))&(quiet(patricia))
[ "p7", "hypothesis" ]
% SZS status Unsatisfiable for 4588341083368039712842069 % SZS output start Proof for 4588341083368039712842069 51. ~? [X0] : (tall(X0) => quiet(X0)) [input p7] 52. quiet(fred) & old(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 137. ! [X0] : (~quiet(X0) & tall(X0)) [ennf transformation 51] 138. quiet(fred) & old(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 52] 139. quiet(fred) & old(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 138] 246. ~quiet(X0) [cnf transformation 137] 253. quiet(fred) [cnf transformation 139] 296. $false [subsumption resolution 253,246] % SZS output end Proof for 4588341083368039712842069 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------
0.083975
Tom, Lorena, Monique are the only persons in the room. If “everyone in the room does not host regular workshops on creative writing or owns a smartwatch” then “Tom owns a smartwatch”. Everyone outside the room who does not host regular workshops on creative writing does not compete in national level swimming championships or enjoys windsurfing or both. Everyone anywhere does not host regular workshops on creative writing. Tom owns a smartwatch. If someone enjoys windsurfing then he/she does enjoy mountain biking. Lorena owns a smartwatch. Someone in the room owns a smartwatch, competes in national level swimming championships or does enjoy mountain biking. Lorena who competes in national level swimming championships enjoys stargazing.
Tom does enjoy mountain biking.
neutral
room(tom)&room(lorena)&room(monique)&(![X]:(room(X)=>(X='tom'|X='lorena'|X='monique')))& ((![X]:(room(X)=>(((owns_a_smartwatch(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))=>(owns_a_smartwatch(tom)))& (![X]:(~room(X)=>(((does_not_host_regular_workshops_on_creative_writing(X))=>(((does_not_compete_in_national_level_swimming_championships(X))|(enjoys_windsurfing(X))))))))& (![X]:(anywhere(X)=>(does_not_host_regular_workshops_on_creative_writing(X))))& (owns_a_smartwatch(tom))& ((![X]:((enjoys_windsurfing(X))=>(does_enjoy_mountain_biking(X)))))& (owns_a_smartwatch(lorena))& (?[X]:(room(X)&(((owns_a_smartwatch(X))|(competes_in_national_level_swimming_championships(X))|(does_enjoy_mountain_biking(X))))))& ((competes_in_national_level_swimming_championships(lorena))&(enjoys_stargazing(lorena)))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(~room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(enjoys_windsurfing(X))))))& (((does_enjoy_mountain_biking(tom))|(does_not_enjoy_windsurfing(tom))))
room(tom)&room(lorena)&room(monique)&(![X]:(room(X)=>(X='tom'|X='lorena'|X='monique')))& does_enjoy_mountain_biking(tom)
[]
null
0
Callie, David, Ronald, Josefina, Paul are the only persons in the room. “Everyone anywhere hosts regular game nights featuring complex strategy games or does not enjoy virtual reality gaming” only if “Callie is a client of LVMH”. “Callie writes in-depth travel guides for off-the-beaten-path destinations” only if “Callie enjoys stand-up paddleboarding”. Either “Callie practices and performs acrobatic dance routines or hosts themed dinner parties featuring gourmet home-cooked meals or both” or “everyone outside the room enjoys windsurfing or does not train for and competes in international triathlons” but not both. Callie makes intricate hand-cut paper art for exhibitions or practices and performs acrobatic dance routines or both. Callie can play the piano. Callie is a dedicated volunteer for local community service projects or practices tai chi or both. Callie writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room who makes intricate hand-cut paper art for exhibitions neither enjoys stand-up paddleboarding nor is an enthusiastic bird watcher who travels for rare sightings. Callie participates in citizen science projects related to wildlife monitoring. Callie enjoys coding in Python.
Callie makes intricate hand-cut paper art for exhibitions.
contradiction
room(callie)&room(david)&room(ronald)&room(josefina)&room(paul)&(![X]:(room(X)=>(X='callie'|X='david'|X='ronald'|X='josefina'|X='paul')))& ((![X]:(anywhere(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))=>(is_a_client_of_LVMH(callie)))& ((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(callie))=>(enjoys_stand-up_paddleboarding(callie)))& ((((practices_and_performs_acrobatic_dance_routines(callie))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(callie))))<~>(![X]:(~room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(enjoys_windsurfing(X)))))))& (((makes_intricate_hand-cut_paper_art_for_exhibitions(callie))|(practices_and_performs_acrobatic_dance_routines(callie))))& (can_play_the_piano(callie))& (((is_a_dedicated_volunteer_for_local_community_service_projects(callie))|(practices_tai_chi(callie))))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(callie))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(~((enjoys_stand-up_paddleboarding(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(callie))& (enjoys_coding_in_Python(callie))
room(callie)&room(david)&room(ronald)&room(josefina)&room(paul)&(![X]:(room(X)=>(X='callie'|X='david'|X='ronald'|X='josefina'|X='paul')))& makes_intricate_hand-cut_paper_art_for_exhibitions(callie)
[ "p0", "p2", "p7", "p8", "hypothesis" ]
% SZS status Unsatisfiable for 1041348414584356603360748 % SZS output start Proof for 1041348414584356603360748 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. prede(mary) => preds(mary) [input p2] 51. prede(mary) [input p7] 52. ! [X0] : (room(X0) => (predu(X0) => ~(predz(X0) | preds(X0)))) [input p8] 55. predu(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] 58. ! [X0] : (room(X0) => (predu(X0) => ~preds(X0))) [pure predicate removal 52] 134. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 135. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134] 136. preds(mary) | ~prede(mary) [ennf transformation 46] 139. ! [X0] : ((~preds(X0) | ~predu(X0)) | ~room(X0)) [ennf transformation 58] 140. ! [X0] : (~preds(X0) | ~predu(X0) | ~room(X0)) [flattening 139] 141. predu(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 55] 142. predu(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 141] 229. room(mary) [cnf transformation 135] 235. preds(mary) | ~prede(mary) [cnf transformation 136] 244. prede(mary) [cnf transformation 51] 245. ~predu(X0) | ~preds(X0) | ~room(X0) [cnf transformation 140] 252. predu(mary) [cnf transformation 142] 254. 1 <=> prede(mary) [avatar definition] 258. 2 <=> preds(mary) [avatar definition] 260. preds(mary) <- (2) [avatar component clause 258] 261. ~1 | 2 [avatar split clause 235,258,254] 293. 9 <=> predu(mary) [avatar definition] 295. predu(mary) <- (9) [avatar component clause 293] 297. 1 [avatar split clause 244,254] 298. 9 [avatar split clause 252,293] 299. ~preds(mary) | ~room(mary) <- (9) [resolution 245,295] 300. ~room(mary) <- (2, 9) [subsumption resolution 299,260] 301. $false <- (2, 9) [subsumption resolution 300,229] 302. ~2 | ~9 [avatar contradiction clause 301] 303. $false [avatar sat refutation 261,297,298,302] % SZS output end Proof for 1041348414584356603360748 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------
0.275234
Mark, Sylvia are the only persons in the room. Sylvia is not a quiet person unless everyone in the room is not a old person. Everyone in the room is not old. Everyone in the room is a tall person. Someone who is not tall is quieter than someone who is not a tall person. Someone who is not tall is richer than someone who is not a quiet person. Mark is the richest in the room.
Mark is quiet.
neutral
room(mark)&room(sylvia)&(![X]:(room(X)=>(X='mark'|X='sylvia')))& (~(![X]:(room(X)=>(~(old(X)&person(X)))))=>(~(quiet(sylvia)&person(sylvia))))& (![X]:(room(X)=>(~old(X))))& (![X]:(room(X)=>(tall(X)&person(X))))& (?[X,Y]:((~tall(X))&(~(tall(Y)&person(Y)))&(quieter(X,Y))))& (?[X,Y]:((~tall(X))&(~(quiet(Y)&person(Y)))&(richer(X,Y))))& (![X]:((room(X)&(X!=mark))=>richer(X,mark)))
room(mark)&room(sylvia)&(![X]:(room(X)=>(X='mark'|X='sylvia')))& quiet(mark)
[]
null
0.312346
There is a room. If "everyone outside the room does not own a high-end gaming PC with custom-built components or makes homemade pastries" then "someone in the room plays the violin". If "everyone in the room does enjoy mountain biking" then "someone in the room does not read mystery novels" otherwise "everyone anywhere does not design and sews custom cosplay costumes for conventions only if they collects rare minerals". Everyone in the room is a chess master who participates in national tournaments. Everyone in the room collects vintage stamps only if they does not enjoy camping and organizing outdoor survival workshops. No one anywhere either owns an extensive assortment of vintage comic book memorabilia or enjoys deep-sea diving and exploring underwater caves but not both if they is a cybersecurity expert. If someone is a cybersecurity expert then he/she enjoys camping and organizing outdoor survival workshops.
Everyone in the room does not collect vintage stamps.
entailment
(there_is_a_room)& ((![X]:(~room(X)=>(((makes_homemade_pastries(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(?[X]:(room(X)&(plays_the_violin(X)))))& (((![X]:(room(X)=>(does_enjoy_mountain_biking(X))))=>(?[X]:(room(X)&(does_not_read_mystery_novels(X)))))&((~(![X]:(room(X)=>(does_enjoy_mountain_biking(X)))))=>(![X]:(anywhere(X)=>(((collects_rare_minerals(X))<=(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))))& (![X]:(room(X)=>(is_a_chess_master_who_participates_in_national_tournaments(X))))& (?[X]:(room(X)&(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))<~>(plays_the_violin(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(practices_tai_chi(X))))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(does_practice_yoga(X))))))& (~![X]:(room(X)=>(((does_practice_yoga(X))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))<=(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(is_a_cybersecurity_expert(X))))))& (~?[X]:(anywhere(X)=>(((is_a_cybersecurity_expert(X))=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<~>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(builds_model_airplanes(X))&(practices_and_performs_acrobatic_dance_routines(X))))))))& (![X]:(room(X)=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(((does_not_collect_rare_minerals(X))<~>(is_a_chess_master_who_participates_in_national_tournaments(X))))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<=(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))& ((![X]:((is_a_cybersecurity_expert(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (![X]:(room(X)=>(((((enjoys_stargazing(X))|(reads_mystery_novels(X))))=>(practices_pilates(X))))))& (![X]:(anywhere(X)=>(((plays_eSports_competitively(X))<=(practices_pilates(X))))))& ((![X]:((practices_pilates(X))=>(plays_eSports_competitively(X)))))
(there_is_a_room)& ![X]:(room(X)=>(does_not_collect_vintage_stamps(X)))
[ "p0", "p8", "p11", "p17", "hypothesis" ]
% SZS status Unsatisfiable for 7521787428998391509307302 % SZS output start Proof for 7521787428998391509307302 44. there_is_a_room [input p0] 52. ! [X0] : (room(X0) => (predm(X0) => ~predc(X0))) [input p8] 55. ~? [X0] : (anywhere(X0) => (predi(X0) => (predw(X0) <~> predu(X0)))) [input p11] 61. ! [X0] : (predi(X0) => predc(X0)) [input p17] 65. ~(! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room) [input hypothesis] 82. ~? [X0] : (predi(X0) => (predw(X0) <~> predu(X0))) [pure predicate removal 55] 160. ! [X0] : ((~predc(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 52] 161. ! [X0] : (~predc(X0) | ~predm(X0) | ~room(X0)) [flattening 160] 166. ! [X0] : ((predw(X0) <=> predu(X0)) & predi(X0)) [ennf transformation 82] 171. ! [X0] : (predc(X0) | ~predi(X0)) [ennf transformation 61] 172. ? [X0] : (predm(X0) & room(X0)) | ~there_is_a_room [ennf transformation 65] 188. ! [X0] : (((predw(X0) | ~predu(X0)) & (predu(X0) | ~predw(X0))) & predi(X0)) [nnf transformation 166] 189. ! [X0] : ((predw(X0) | ~predu(X0)) & (predu(X0) | ~predw(X0)) & predi(X0)) [flattening 188] 191. ? [X0] : (predm(X0) & room(X0)) => (predm(sK6) & room(sK6)) [choice axiom] 192. (predm(sK6) & room(sK6)) | ~there_is_a_room [skolemisation 172,191] 273. there_is_a_room [cnf transformation 44] 285. ~predc(X0) | ~predm(X0) | ~room(X0) [cnf transformation 161] 288. predi(X0) [cnf transformation 189] 295. predc(X0) | ~predi(X0) [cnf transformation 171] 296. room(sK6) | ~there_is_a_room [cnf transformation 192] 297. predm(sK6) | ~there_is_a_room [cnf transformation 192] 339. predc(X0) [subsumption resolution 295,288] 340. predm(sK6) [subsumption resolution 297,273] 341. room(sK6) [subsumption resolution 296,273] 358. ~predm(X0) | ~room(X0) [resolution 285,339] 368. ~room(sK6) [resolution 358,340] 369. $false [subsumption resolution 368,341] % SZS output end Proof for 7521787428998391509307302 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------
0.098689
Gladys, Anthony are the only persons in the room. Everyone in the room enjoys windsurfing if they is not an enthusiastic bird watcher who travels for rare sightings. If someone is a dedicated advocate for digital privacy and encryption then he/she collects antique jewelry and vice versa. Gladys is a dedicated advocate for digital privacy and encryption. Gladys does not enjoy windsurfing. Everyone in the room does not enjoy windsurfing. Anthony is a dedicated advocate for digital privacy and encryption. If someone does not collect antique jewelry then he/she is not an enthusiastic bird watcher who travels for rare sightings and vice versa.
Anthony either is not a dedicated advocate for digital privacy and encryption or does not collect antique jewelry but not both.
contradiction
room(gladys)&room(anthony)&(![X]:(room(X)=>(X='gladys'|X='anthony')))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(enjoys_windsurfing(X))))))& ((![X]:((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(collects_antique_jewelry(X)))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(gladys))& (does_not_enjoy_windsurfing(gladys))& (![X]:(room(X)=>(does_not_enjoy_windsurfing(X))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(anthony))& ((![X]:((does_not_collect_antique_jewelry(X))<=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))
room(gladys)&room(anthony)&(![X]:(room(X)=>(X='gladys'|X='anthony')))& ((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(anthony))<~>(does_not_collect_antique_jewelry(anthony)))
[ "p2", "p6", "hypothesis" ]
% SZS status Unsatisfiable for 3541949589976527634767059 % SZS output start Proof for 3541949589976527634767059 46. ! [X0] : (predb(X0) <=> predd(X0)) [input p2] 50. predb(paul) [input p6] 52. (~predb(paul) <~> ~predd(paul)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 130. (~predb(paul) <~> ~predd(paul)) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 52] 131. (~predb(paul) <~> ~predd(paul)) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 130] 133. ! [X0] : ((predb(X0) | ~predd(X0)) & (predd(X0) | ~predb(X0))) [nnf transformation 46] 135. ((predd(paul) | predb(paul)) & (~predd(paul) | ~predb(paul))) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [nnf transformation 131] 136. (predd(paul) | predb(paul)) & (~predd(paul) | ~predb(paul)) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 135] 221. ~predb(X0) | predd(X0) [cnf transformation 133] 226. predb(paul) [cnf transformation 50] 232. ~predd(paul) | ~predb(paul) [cnf transformation 136] 234. ~predd(paul) [subsumption resolution 232,226] 236. predd(paul) [resolution 221,226] 237. $false [subsumption resolution 236,234] % SZS output end Proof for 3541949589976527634767059 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------
0.084032
Betty is the only person in the room. If "Betty is a coffee connoisseur" then "everyone in the room is a coffee connoisseur only if they is older than William". If "Betty collects limited-edition art prints from contemporary artists" then "Betty collects limited-edition art prints from contemporary artists and is a old kind european". "Everyone in the room does not create large-scale murals for public art installations or regularly goes on multi-day backpacking trips in national parks" only if "everyone anywhere is a kind european if they is older than William". Betty who is a kind european is older than Henry. Everyone in the room is older than William or does not write poetry. Everyone in the room is a coffee connoisseur only if they is older than William. Betty does not regularly goes on multi-day backpacking trips in national parks and is older than Henry. Betty is a kind old european. Not everyone in the room is not old. Someone in the room is older than William. Everyone in the room who is old is older than Henry. Betty is older than William. Someone in the room creates large-scale murals for public art installations.
William is older than Betty.
contradiction
room(betty)&(![X]:(room(X)=>(X='betty')))& ((is_a_coffee_connoisseur(betty))=>(![X]:(room(X)=>(((older(william,X))<=(is_a_coffee_connoisseur(X)))))))& ((collects_limited-edition_art_prints_from_contemporary_artists(betty))=>(((collects_limited-edition_art_prints_from_contemporary_artists(betty))&(old(betty)&kind(betty)&european(betty)))))& ((![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))=>(![X]:(anywhere(X)=>(((older(william,X))=>(kind(X)&european(X)))))))& ((kind(betty)&european(betty))&(older(henry,betty)))& (![X]:(room(X)=>(((does_not_write_poetry(X))|(older(william,X))))))& (![X]:(room(X)=>(((older(william,X))<=(is_a_coffee_connoisseur(X))))))& (((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(betty))&(older(henry,betty))))& (kind(betty)&old(betty)&european(betty))& (~![X]:(room(X)=>(~old(X))))& (?[X]:(room(X)&(older(william,X))))& (![X]:(room(X)=>(((old(X))=>(older(henry,X))))))& (older(william,betty))& (?[X]:(room(X)&(creates_large-scale_murals_for_public_art_installations(X))))
room(betty)&(![X]:(room(X)=>(X='betty')))& older(betty,william)
[ "b19", "b42", "p12", "hypothesis" ]
% SZS status Unsatisfiable for 2861601722323089039169557 % SZS output start Proof for 2861601722323089039169557 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] 56. older(fred,mary) [input p12] 58. older(mary,fred) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 105. ! [X0,X1] : ((~older(X1,X0) | ~older(X0,X1)) | X0 = X1) [ennf transformation 20] 106. ! [X0,X1] : (~older(X1,X0) | ~older(X0,X1) | X0 = X1) [flattening 105] 152. older(mary,fred) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 58] 175. ~older(X1,X0) | ~older(X0,X1) | X0 = X1 [cnf transformation 106] 210. mary != fred [cnf transformation 43] 252. older(fred,mary) [cnf transformation 56] 256. older(mary,fred) [cnf transformation 152] 278. ~older(mary,fred) | mary = fred [resolution 175,252] 281. mary = fred [subsumption resolution 278,256] 282. $false [subsumption resolution 281,210] % SZS output end Proof for 2861601722323089039169557 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s % ------------------------------ % ------------------------------
0.008849
Melissa, Angelica, Victoria, Arturo, Albert are the only persons in the room. Melissa is an expert in identifying and foraging wild edible plants. Someone outside the room writes and illustrates their own graphic novels. Everyone anywhere is an active member of a local robotics club if they is a wine connoisseur with a private cellar of vintage wines. Everyone in the room writes and illustrates their own graphic novels if they is an active member of a local robotics club. Everyone in the room is a cybersecurity expert if they writes and illustrates their own graphic novels. If someone practices digital art then he/she is a wine connoisseur with a private cellar of vintage wines. Angelica practices digital art.
Angelica is a cybersecurity expert.
entailment
room(melissa)&room(angelica)&room(victoria)&room(arturo)&room(albert)&(![X]:(room(X)=>(X='melissa'|X='angelica'|X='victoria'|X='arturo'|X='albert')))& (is_an_expert_in_identifying_and_foraging_wild_edible_plants(melissa))& (?[X]:(~room(X)&(writes_and_illustrates_their_own_graphic_novels(X))))& (enjoys_macrame(victoria))& (?[X]:(room(X)&(makes_homemade_pastries(X))))& (![X]:(anywhere(X)=>(((~((makes_homemade_pastries(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(anywhere(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (~(((is_passionate_about_collecting_and_restoring_classic_cars(melissa))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(melissa))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(melissa)))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(is_a_cybersecurity_expert(X))))))& (~![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(practices_calligraphy(X))))))& (is_a_client_of_Costco(melissa))& ((?[X,Y]:(room(X)&room(Y)&(drives_a_hybrid_car(X)&drives_a_hybrid_car(Y))&(X!=Y))))& (![X]:(anywhere(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(does_not_work_on_fridays(X))))))& ((![X]:((practices_digital_art(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))& (makes_homemade_pastries(angelica))& (![X]:(anywhere(X)=>(((is_a_coffee_connoisseur(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (is_an_active_member_of_a_local_robotics_club(victoria))& (practices_digital_art(angelica))& (does_not_drive_a_hybrid_car(melissa))& (~![X]:(anywhere(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& ((![X]:((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& (enjoys_spelunking(melissa))& (designs_and_sews_custom_cosplay_costumes_for_conventions(melissa))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(((is_a_coffee_connoisseur(X))|(is_a_client_of_Costco(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))))
room(melissa)&room(angelica)&room(victoria)&room(arturo)&room(albert)&(![X]:(room(X)=>(X='melissa'|X='angelica'|X='victoria'|X='arturo'|X='albert')))& is_a_cybersecurity_expert(angelica)
[ "b4", "p0", "p6", "p7", "p9", "p14", "p18", "hypothesis" ]
% SZS status Unsatisfiable for 503516168799363074733467 % SZS output start Proof for 503516168799363074733467 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. ! [X0] : (anywhere(X0) => (predq(X0) => preda(X0))) [input p6] 51. ! [X0] : (room(X0) => (preda(X0) => predu(X0))) [input p7] 53. ! [X0] : (room(X0) => (predu(X0) => preds(X0))) [input p9] 58. ! [X0] : (predl(X0) => predq(X0)) [input p14] 62. predl(paul) [input p18] 69. ~(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] 157. ! [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] 158. ! [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] 159. ! [X0] : ((preda(X0) | ~predq(X0)) | ~anywhere(X0)) [ennf transformation 50] 160. ! [X0] : (preda(X0) | ~predq(X0) | ~anywhere(X0)) [flattening 159] 161. ! [X0] : ((predu(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 51] 162. ! [X0] : (predu(X0) | ~preda(X0) | ~room(X0)) [flattening 161] 164. ! [X0] : ((preds(X0) | ~predu(X0)) | ~room(X0)) [ennf transformation 53] 165. ! [X0] : (preds(X0) | ~predu(X0) | ~room(X0)) [flattening 164] 167. ! [X0] : (predq(X0) | ~predl(X0)) [ennf transformation 58] 169. ~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 69] 170. ~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 169] 182. ? [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] 183. ~preds(paul) | (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 170,182] 184. anywhere(X0) [cnf transformation 5] 265. room(mary) [cnf transformation 158] 266. room(paul) [cnf transformation 158] 267. room(fred) [cnf transformation 158] 268. room(alice) [cnf transformation 158] 269. room(john) [cnf transformation 158] 270. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 158] 274. preda(X0) | ~predq(X0) | ~anywhere(X0) [cnf transformation 160] 275. ~preda(X0) | predu(X0) | ~room(X0) [cnf transformation 162] 277. ~predu(X0) | preds(X0) | ~room(X0) [cnf transformation 165] 285. ~predl(X0) | predq(X0) [cnf transformation 167] 287. predl(paul) [cnf transformation 62] 291. ~preds(paul) | room(sK6) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 292. ~preds(paul) | mary != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 293. ~preds(paul) | paul != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 294. ~preds(paul) | fred != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 295. ~preds(paul) | alice != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 296. ~preds(paul) | john != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 297. ~predq(X0) | preda(X0) [subsumption resolution 274,184] 298. ~preds(paul) | john != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,269] 299. ~preds(paul) | john != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 298,268] 300. ~preds(paul) | john != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 299,267] 301. ~preds(paul) | john != sK6 | ~room(mary) [subsumption resolution 300,266] 302. ~preds(paul) | john != sK6 [subsumption resolution 301,265] 304. 1 <=> john = sK6 [avatar definition] 306. john != sK6 <- (~1) [avatar component clause 304] 308. 2 <=> preds(paul) [avatar definition] 311. ~1 | ~2 [avatar split clause 302,308,304] 312. ~preds(paul) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,269] 313. ~preds(paul) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,268] 314. ~preds(paul) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 313,267] 315. ~preds(paul) | alice != sK6 | ~room(mary) [subsumption resolution 314,266] 316. ~preds(paul) | alice != sK6 [subsumption resolution 315,265] 318. 3 <=> alice = sK6 [avatar definition] 320. alice != sK6 <- (~3) [avatar component clause 318] 321. ~3 | ~2 [avatar split clause 316,308,318] 322. ~preds(paul) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,269] 323. ~preds(paul) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,268] 324. ~preds(paul) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 323,267] 325. ~preds(paul) | fred != sK6 | ~room(mary) [subsumption resolution 324,266] 326. ~preds(paul) | fred != sK6 [subsumption resolution 325,265] 328. 4 <=> fred = sK6 [avatar definition] 330. fred != sK6 <- (~4) [avatar component clause 328] 331. ~4 | ~2 [avatar split clause 326,308,328] 332. ~preds(paul) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 293,269] 333. ~preds(paul) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 332,268] 334. ~preds(paul) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 333,267] 335. ~preds(paul) | paul != sK6 | ~room(mary) [subsumption resolution 334,266] 336. ~preds(paul) | paul != sK6 [subsumption resolution 335,265] 338. 5 <=> paul = sK6 [avatar definition] 340. paul != sK6 <- (~5) [avatar component clause 338] 341. ~5 | ~2 [avatar split clause 336,308,338] 342. ~preds(paul) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,269] 343. ~preds(paul) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 342,268] 344. ~preds(paul) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 343,267] 345. ~preds(paul) | mary != sK6 | ~room(mary) [subsumption resolution 344,266] 346. ~preds(paul) | mary != sK6 [subsumption resolution 345,265] 348. 6 <=> mary = sK6 [avatar definition] 350. mary != sK6 <- (~6) [avatar component clause 348] 351. ~6 | ~2 [avatar split clause 346,308,348] 352. ~preds(paul) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,269] 353. ~preds(paul) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 352,268] 354. ~preds(paul) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 353,267] 355. ~preds(paul) | room(sK6) | ~room(mary) [subsumption resolution 354,266] 356. ~preds(paul) | room(sK6) [subsumption resolution 355,265] 358. 7 <=> room(sK6) [avatar definition] 360. room(sK6) <- (7) [avatar component clause 358] 361. 7 | ~2 [avatar split clause 356,308,358] 362. predq(paul) [resolution 285,287] 363. preda(paul) [resolution 362,297] 369. predu(paul) | ~room(paul) [resolution 363,275] 370. predu(paul) [subsumption resolution 369,266] 371. preds(paul) | ~room(paul) [resolution 370,277] 375. preds(paul) [subsumption resolution 371,266] 376. 2 [avatar split clause 375,308] 422. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (7) [resolution 270,360] 507. fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (~3, 7) [subsumption resolution 422,320] 508. paul = sK6 | mary = sK6 | john = sK6 <- (~3, ~4, 7) [subsumption resolution 507,330] 509. mary = sK6 | john = sK6 <- (~3, ~4, ~5, 7) [subsumption resolution 508,340] 510. john = sK6 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 509,350] 511. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 510,306] 512. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 511] 513. $false [avatar sat refutation 311,321,331,341,351,361,376,512] % SZS output end Proof for 503516168799363074733467 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------
0.412768
Joshua, Patrick, Robert, George are the only persons in the room. If “Joshua is not tall, not humble, not calm” then “Patrick and Robert are respectively happy and curious” otherwise “Patrick is kind”. “Joshua and Robert are respectively creative and curious” if “Patrick is not a funny person” and vice versa. “Patrick and Joshua are respectively brave and kind” if “Patrick is tall or is generous or both” and vice versa. “Robert is not a tall person” if “Robert is not tall, not kind”. If “Joshua is not old” then “Joshua and Robert are respectively kind and wise”. All brave persons are quiet. All patient persons are funny. Everyone outside the room who is not funny is a old person. More than one person in the room is not a wise funny person. If someone is curious then he/she is not a calm creative wise person. Robert is kind. Someone who is old is richer than someone who is a brave happy creative wise kind person. All humble persons are generous. If someone is not brave or is patient or both then he/she is a humble creative person. Robert is kind or is not patient, not wise or both. Robert is not calm, not creative, not old, not tall. Joshua is not a happy person. If someone is not a wise person then he/she is not funny, not calm, not tall or is humble or both and vice versa. More than one person in the room is not a funny person. Joshua is not a calm tall person. Robert is strong. Joshua and Robert are respectively kind and wise. Not everyone in the room is not a strong generous wise person if they is happy. Joshua dreamt that “Joshua is not a happy person”. Joshua is not a generous quiet curious strong kind person.
Patrick is quiet.
entailment
room(joshua)&room(patrick)&room(robert)&room(george)&(![X]:(room(X)=>(X='joshua'|X='patrick'|X='robert'|X='george')))& (((~tall(joshua)&~humble(joshua)&~calm(joshua))=>((happy(patrick))&(curious(robert))))&((~(~tall(joshua)&~humble(joshua)&~calm(joshua)))=>(kind(patrick))))& ((~(funny(patrick)&person(patrick)))<=>((creative(joshua))&(curious(robert))))& ((((tall(patrick))|(generous(patrick))))<=>((brave(patrick))&(kind(joshua))))& ((~tall(robert)&~kind(robert))=>(~(tall(robert)&person(robert))))& ((~old(joshua))=>((kind(joshua))&(wise(robert))))& (![X]:(brave(X)=>quiet(X)))& (![X]:(patient(X)=>funny(X)))& (![X]:(~room(X)=>(((~funny(X))=>(old(X)&person(X))))))& ((?[X,Y]:(room(X)&room(Y)&(~(wise(X)&funny(X)&person(X))&~(wise(Y)&funny(Y)&person(Y)))&(X!=Y))))& ((![X]:((curious(X))=>(~(calm(X)&creative(X)&wise(X)&person(X))))))& (kind(robert))& (?[X,Y]:((old(X))&(brave(Y)&happy(Y)&creative(Y)&wise(Y)&kind(Y)&person(Y))&(richer(X,Y))))& (![X]:(humble(X)=>generous(X)))& ((![X]:((((~brave(X))|(patient(X))))=>(humble(X)&creative(X)&person(X)))))& (((kind(robert))|(~patient(robert)&~wise(robert))))& (~calm(robert)&~creative(robert)&~old(robert)&~tall(robert))& (~(happy(joshua)&person(joshua)))& ((![X]:((~(wise(X)&person(X)))<=>(((~funny(X)&~calm(X)&~tall(X))|(humble(X)))))))& ((?[X,Y]:(room(X)&room(Y)&(~(funny(X)&person(X))&~(funny(Y)&person(Y)))&(X!=Y))))& (~(calm(joshua)&tall(joshua)&person(joshua)))& (strong(robert))& ((kind(joshua))&(wise(robert)))& (~![X]:(room(X)=>(((happy(X))=>(~(strong(X)&generous(X)&wise(X)&person(X)))))))& ((joshua_dream=>(~(happy(joshua)&person(joshua)))))& (~(generous(joshua)&quiet(joshua)&curious(joshua)&strong(joshua)&kind(joshua)&person(joshua)))& (~(tall(robert)&strong(robert)&person(robert)))
room(joshua)&room(patrick)&room(robert)&room(george)&(![X]:(room(X)=>(X='joshua'|X='patrick'|X='robert'|X='george')))& quiet(patrick)
[ "p0", "p3", "p6", "p13", "p14", "hypothesis" ]
% SZS status Unsatisfiable for 290518505035171008825424 % SZS output start Proof for 290518505035171008825424 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. (generous(paul) | tall(paul)) <=> (kind(mary) & brave(paul)) [input p3] 50. ! [X0] : (brave(X0) => quiet(X0)) [input p6] 57. ! [X0] : (humble(X0) => generous(X0)) [input p13] 58. ! [X0] : ((patient(X0) | ~brave(X0)) => (person(X0) & creative(X0) & humble(X0))) [input p14] 71. ~(quiet(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 74. ! [X0] : (~brave(X0) => (person(X0) & creative(X0) & humble(X0))) [pure predicate removal 58] 148. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 148] 156. ! [X0] : (quiet(X0) | ~brave(X0)) [ennf transformation 50] 162. ! [X0] : (generous(X0) | ~humble(X0)) [ennf transformation 57] 163. ! [X0] : ((person(X0) & creative(X0) & humble(X0)) | brave(X0)) [ennf transformation 74] 172. ~quiet(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 71] 173. ~quiet(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 172] 177. ((generous(paul) | tall(paul)) | (~kind(mary) | ~brave(paul))) & ((kind(mary) & brave(paul)) | (~generous(paul) & ~tall(paul))) [nnf transformation 47] 178. (generous(paul) | tall(paul) | ~kind(mary) | ~brave(paul)) & ((kind(mary) & brave(paul)) | (~generous(paul) & ~tall(paul))) [flattening 177] 189. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 190. ~quiet(paul) | (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,189] 271. room(mary) [cnf transformation 149] 272. room(paul) [cnf transformation 149] 273. room(fred) [cnf transformation 149] 274. room(alice) [cnf transformation 149] 275. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 149] 287. brave(paul) | ~generous(paul) [cnf transformation 178] 294. ~brave(X0) | quiet(X0) [cnf transformation 156] 312. ~humble(X0) | generous(X0) [cnf transformation 162] 313. brave(X0) | humble(X0) [cnf transformation 163] 347. ~quiet(paul) | room(sK7) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 348. ~quiet(paul) | mary != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 349. ~quiet(paul) | paul != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 350. ~quiet(paul) | fred != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 351. ~quiet(paul) | alice != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 399. 10 <=> brave(paul) [avatar definition] 400. brave(paul) <- (10) [avatar component clause 399] 401. ~brave(paul) <- (~10) [avatar component clause 399] 411. 13 <=> generous(paul) [avatar definition] 412. ~generous(paul) <- (~13) [avatar component clause 411] 417. ~13 | 10 [avatar split clause 287,399,411] 502. ~quiet(paul) | alice != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 351,274] 503. ~quiet(paul) | alice != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 502,273] 504. ~quiet(paul) | alice != sK7 | ~room(mary) [subsumption resolution 503,272] 505. ~quiet(paul) | alice != sK7 [subsumption resolution 504,271] 507. 32 <=> alice = sK7 [avatar definition] 509. alice != sK7 <- (~32) [avatar component clause 507] 511. 33 <=> quiet(paul) [avatar definition] 514. ~32 | ~33 [avatar split clause 505,511,507] 515. ~quiet(paul) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 350,274] 516. ~quiet(paul) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 515,273] 517. ~quiet(paul) | fred != sK7 | ~room(mary) [subsumption resolution 516,272] 518. ~quiet(paul) | fred != sK7 [subsumption resolution 517,271] 520. 34 <=> fred = sK7 [avatar definition] 522. fred != sK7 <- (~34) [avatar component clause 520] 523. ~34 | ~33 [avatar split clause 518,511,520] 524. ~quiet(paul) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 349,274] 525. ~quiet(paul) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 524,273] 526. ~quiet(paul) | paul != sK7 | ~room(mary) [subsumption resolution 525,272] 527. ~quiet(paul) | paul != sK7 [subsumption resolution 526,271] 529. 35 <=> paul = sK7 [avatar definition] 531. paul != sK7 <- (~35) [avatar component clause 529] 532. ~35 | ~33 [avatar split clause 527,511,529] 533. ~quiet(paul) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 348,274] 534. ~quiet(paul) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 533,273] 535. ~quiet(paul) | mary != sK7 | ~room(mary) [subsumption resolution 534,272] 536. ~quiet(paul) | mary != sK7 [subsumption resolution 535,271] 538. 36 <=> mary = sK7 [avatar definition] 540. mary != sK7 <- (~36) [avatar component clause 538] 541. ~36 | ~33 [avatar split clause 536,511,538] 542. ~quiet(paul) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 347,274] 543. ~quiet(paul) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 542,273] 544. ~quiet(paul) | room(sK7) | ~room(mary) [subsumption resolution 543,272] 545. ~quiet(paul) | room(sK7) [subsumption resolution 544,271] 547. 37 <=> room(sK7) [avatar definition] 549. room(sK7) <- (37) [avatar component clause 547] 550. 37 | ~33 [avatar split clause 545,511,547] 554. humble(paul) <- (~10) [resolution 313,401] 556. generous(paul) <- (~10) [resolution 554,312] 557. $false <- (~10, ~13) [subsumption resolution 556,412] 558. 10 | 13 [avatar contradiction clause 557] 559. quiet(paul) <- (10) [resolution 400,294] 562. 33 | ~10 [avatar split clause 559,399,511] 819. fred = sK7 | paul = sK7 | mary = sK7 | alice = sK7 <- (37) [resolution 275,549] 905. paul = sK7 | mary = sK7 | alice = sK7 <- (~34, 37) [subsumption resolution 819,522] 906. mary = sK7 | alice = sK7 <- (~34, ~35, 37) [subsumption resolution 905,531] 907. alice = sK7 <- (~34, ~35, ~36, 37) [subsumption resolution 906,540] 908. $false <- (~32, ~34, ~35, ~36, 37) [subsumption resolution 907,509] 909. 32 | 34 | 35 | 36 | ~37 [avatar contradiction clause 908] 910. $false [avatar sat refutation 417,514,523,532,541,550,558,562,909] % SZS output end Proof for 290518505035171008825424 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5500 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------
0.326293
Gladys, Dustin are the only persons in the room. Everyone in the room does not make intricate hand-cut paper art for exhibitions or has a specialized collection of handmade artisan pottery. Only one person in the room has a specialized collection of handmade artisan pottery. Gladys who designs and sews custom cosplay costumes for conventions makes intricate hand-cut paper art for exhibitions.
Dustin has a specialized collection of handmade artisan pottery.
contradiction
room(gladys)&room(dustin)&(![X]:(room(X)=>(X='gladys'|X='dustin')))& ((?[X]:(room(X)&(can_play_the_piano(X))))=>((enjoys_watercolor_painting(dustin))&(((does_not_collect_vintage_stamps(dustin))&(collects_action_figures(dustin))))))& ((![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(dustin)))& (~(![X]:(~room(X)=>(((plays_the_violin(X))|(does_not_collect_antique_jewelry(X))))))=>(![X]:(room(X)=>(((enjoys_bird_watching(X))=>(plays_the_violin(X)))))))& ((![X]:((can_play_the_piano(X))=>(((enjoys_coding_in_Python(X))<~>(collects_vintage_stamps(X)))))))& (((?[X]:(anywhere(X)&can_play_the_piano(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(can_play_the_piano(X))&(can_play_the_piano(Y)))=>(X=Y)))))& (![X]:(room(X)=>(enjoys_watercolor_painting(X))))& ((enjoys_watercolor_painting(dustin))&(((does_not_collect_vintage_stamps(dustin))&(collects_action_figures(dustin)))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=(((writes_and_illustrates_their_own_graphic_novels(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))& ((has_a_tattoo(gladys))&(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(gladys)))& (![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(enjoys_stargazing(X))))))& ((![X]:((does_not_collect_rare_minerals(X))<=>(plays_the_violin(X)))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(does_not_enjoy_fishing(X))))))& (?[X]:(room(X)&(enjoys_stargazing(X))))& (((?[X]:(room(X)&((does_not_train_for_and_competes_in_international_triathlons(X))&(has_a_tattoo(X)))))&(![X,Y]:((room(X)&room(Y)&(((does_not_train_for_and_competes_in_international_triathlons(X))&(has_a_tattoo(X))))&(((does_not_train_for_and_competes_in_international_triathlons(Y))&(has_a_tattoo(Y)))))=>(X=Y)))))& (((?[X]:(room(X)&has_a_specialized_collection_of_handmade_artisan_pottery(X)))&(![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]:((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))<=(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(does_enjoy_mountain_biking(X))))& ((gladys_dream=>((((enjoys_watercolor_painting(gladys))<~>(enjoys_fishing(gladys))))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(gladys)))))& ((designs_and_sews_custom_cosplay_costumes_for_conventions(gladys))&(makes_intricate_hand-cut_paper_art_for_exhibitions(gladys)))& (((?[X]:(room(X)&can_play_the_piano(X)))&(![X,Y]:((room(X)&room(Y)&(can_play_the_piano(X))&(can_play_the_piano(Y)))=>(X=Y)))))
room(gladys)&room(dustin)&(![X]:(room(X)=>(X='gladys'|X='dustin')))& has_a_specialized_collection_of_handmade_artisan_pottery(dustin)
[ "b42", "p0", "p9", "p17", "p22", "hypothesis" ]
% SZS status Unsatisfiable for 8912654291075352614995797 % SZS output start Proof for 8912654291075352614995797 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 53. ! [X0] : (room(X0) => (~preds(X0) | preda(X0))) [input p9] 61. ! [X0,X1] : ((preda(X1) & preda(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (preda(X0) & room(X0)) [input p17] 66. preds(mary) & predj(mary) [input p22] 68. preda(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 72. ! [X0,X1] : ((preda(X1) & preda(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (preda(X2) & room(X2)) [rectify 61] 84. preds(mary) [pure predicate removal 66] 163. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 164. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 163] 169. ! [X0] : ((~preds(X0) | preda(X0)) | ~room(X0)) [ennf transformation 53] 170. ! [X0] : (~preds(X0) | preda(X0) | ~room(X0)) [flattening 169] 173. ! [X0,X1] : (X0 = X1 | (~preda(X1) | ~preda(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (preda(X2) & room(X2)) [ennf transformation 72] 174. ! [X0,X1] : (X0 = X1 | ~preda(X1) | ~preda(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (preda(X2) & room(X2)) [flattening 173] 177. preda(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 68] 178. preda(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 177] 187. ? [X2] : (preda(X2) & room(X2)) => (preda(sK3) & room(sK3)) [choice axiom] 188. ! [X0,X1] : (X0 = X1 | ~preda(X1) | ~preda(X0) | ~room(X1) | ~room(X0)) & (preda(sK3) & room(sK3)) [skolemisation 174,187] 236. mary != paul [cnf transformation 43] 272. room(mary) [cnf transformation 164] 273. room(paul) [cnf transformation 164] 282. ~preds(X0) | preda(X0) | ~room(X0) [cnf transformation 170] 291. ~preda(X1) | X0 = X1 | ~preda(X0) | ~room(X1) | ~room(X0) [cnf transformation 188] 292. preds(mary) [cnf transformation 84] 299. preda(paul) [cnf transformation 178] 331. preda(mary) | ~room(mary) [resolution 282,292] 332. preda(mary) [subsumption resolution 331,272] 462. paul = X1 | ~preda(X1) | ~room(paul) | ~room(X1) [resolution 291,299] 464. ~preda(X1) | paul = X1 | ~room(X1) [subsumption resolution 462,273] 465. mary = paul | ~room(mary) [resolution 464,332] 467. ~room(mary) [subsumption resolution 465,236] 468. $false [subsumption resolution 467,272] % SZS output end Proof for 8912654291075352614995797 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------
0.018413
Diann is the only person in the room. Either 'Diann either is a craft beer aficionado or is a client of Costco but not both' or 'at least one person in the room collects foreign coins' but not both. If 'Diann hosts regular game nights featuring complex strategy games' then 'it is not the case that 'Diann is a client of Costco''. If 'Diann competes in national level swimming championships' then 'Diann hosts regular game nights featuring complex strategy games'. 'Diann competes in national level swimming championships' if 'Diann either collects foreign coins or hosts regular game nights featuring complex strategy games but not both'. 'Diann hosts regular game nights featuring complex strategy games or streams on Twitch or both' if 'Diann enjoys camping and organizing outdoor survival workshops' and vice versa. If 'Diann competes in national level swimming championships' then 'Diann collects first edition books'. If 'Diann is a craft beer aficionado' then 'Diann neither collects foreign coins nor practices tai chi'. If 'Diann has a piercing' then 'Diann collects first edition books'. 'Diann collects modern art' if 'it is not the case that 'it is not the case that 'Diann practices kickboxing''' and vice versa. Either 'Diann is a craft beer aficionado' or 'Diann streams on Twitch' but not both. Diann streams on Twitch.
It is not the case that 'Diann streams on Twitch'.
contradiction
room(diann)&(![X]:(room(X)=>(X='diann')))& ((((is_a_craft_beer_aficionado(diann))<~>(is_a_client_of_Costco(diann))))<~>(((?[X]:(room(X)&collects_foreign_coins(X))))))& ((hosts_regular_game_nights_featuring_complex_strategy_games(diann))=>(~(is_a_client_of_Costco(diann))))& ((competes_in_national_level_swimming_championships(diann))=>(hosts_regular_game_nights_featuring_complex_strategy_games(diann)))& ((((collects_foreign_coins(diann))<~>(hosts_regular_game_nights_featuring_complex_strategy_games(diann))))=>(competes_in_national_level_swimming_championships(diann)))& ((enjoys_camping_and_organizing_outdoor_survival_workshops(diann))<=>(((hosts_regular_game_nights_featuring_complex_strategy_games(diann))|(streams_on_Twitch(diann)))))& ((competes_in_national_level_swimming_championships(diann))=>(collects_first_edition_books(diann)))& ((is_a_craft_beer_aficionado(diann))=>(~((collects_foreign_coins(diann))|(practices_tai_chi(diann)))))& ((has_a_piercing(diann))=>(collects_first_edition_books(diann)))& ((~(~(practices_kickboxing(diann))))<=>(collects_modern_art(diann)))& ((is_a_craft_beer_aficionado(diann))<~>(streams_on_Twitch(diann)))& ((streams_on_Twitch(diann))<=>(enjoys_virtual_reality_gaming(diann)))& ((writes_and_illustrates_their_own_graphic_novels(diann))=>(streams_on_Twitch(diann)))& (streams_on_Twitch(diann))& (practices_kickboxing(diann))& (((is_a_craft_beer_aficionado(diann))<~>(is_a_client_of_Costco(diann))))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(diann))& (enjoys_bird_watching(diann))& (practices_tai_chi(diann))& ((![X]:((has_a_piercing(X))=>(is_a_craft_beer_aficionado(X)))))& (collects_first_edition_books(diann))& (enjoys_virtual_reality_gaming(diann))& (enjoys_camping_and_organizing_outdoor_survival_workshops(diann))& ((diann_dream=>(collects_first_edition_books(diann))))& (((?[X]:(room(X)&enjoys_virtual_reality_gaming(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_virtual_reality_gaming(X))&(enjoys_virtual_reality_gaming(Y)))=>(X=Y)))))& (collects_modern_art(diann))
room(diann)&(![X]:(room(X)=>(X='diann')))& ~(streams_on_Twitch(diann))
[ "p13", "hypothesis" ]
% SZS status Unsatisfiable for 2713045716665571604199452 % SZS output start Proof for 2713045716665571604199452 57. preda(mary) [input p13] 70. ~preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 159. ~preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 70] 277. preda(mary) [cnf transformation 57] 290. ~preda(mary) [cnf transformation 159] 333. 9 <=> preda(mary) [avatar definition] 367. 9 [avatar split clause 277,333] 375. ~9 [avatar split clause 290,333] 376. $false [avatar sat refutation 367,375] % SZS output end Proof for 2713045716665571604199452 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------
0.328861
Leslie, Debra are the only persons in the room. “Everyone in the room plays the violin” if “everyone in the room plays video games or cannot play the guitar”. Leslie is a wine connoisseur. More than one person in the room cannot play the guitar. Leslie does not develop open-source software projects in their free time. If someone streams on Twitch then he/she practices calligraphy. Debra cannot play the guitar. Everyone in the room plays the violin. Leslie owns an extensive assortment of vintage comic book memorabilia. Everyone in the room is allergic to anything only if they plays the violin. It is not the case that “Leslie practices calligraphy or is allergic to anything or both”. If someone owns an extensive assortment of vintage comic book memorabilia then he/she either collects historical artifacts related to ancient civilizations or owns a telescope but not both and vice versa. If someone enjoys stand-up paddleboarding then he/she either streams on Twitch or is a wine connoisseur but not both and vice versa.
Leslie enjoys stand-up paddleboarding.
entailment
room(leslie)&room(debra)&(![X]:(room(X)=>(X='leslie'|X='debra')))& ((![X]:(room(X)=>(((cannot_play_the_guitar(X))|(plays_video_games(X))))))=>(![X]:(room(X)=>(plays_the_violin(X)))))& (is_a_wine_connoisseur(leslie))& ((?[X,Y]:(room(X)&room(Y)&(cannot_play_the_guitar(X)&cannot_play_the_guitar(Y))&(X!=Y))))& (does_not_develop_open-source_software_projects_in_their_free_time(leslie))& ((![X]:((streams_on_Twitch(X))=>(practices_calligraphy(X)))))& (cannot_play_the_guitar(debra))& (![X]:(room(X)=>(plays_the_violin(X))))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(leslie))& (![X]:(room(X)=>(((plays_the_violin(X))<=(is_allergic_to_anything(X))))))& (~(((practices_calligraphy(leslie))|(is_allergic_to_anything(leslie)))))& ((![X]:((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))<~>(owns_a_telescope(X)))))))& ((![X]:((enjoys_stand-up_paddleboarding(X))<=>(((streams_on_Twitch(X))<~>(is_a_wine_connoisseur(X)))))))& (owns_an_Android_phone(leslie))& (![X]:(room(X)=>(enjoys_windsurfing(X))))& (plays_the_violin(debra))& (![X]:(room(X)=>(((is_allergic_to_anything(X))|(cannot_play_the_guitar(X))))))& ((?[X,Y]:(room(X)&room(Y)&(owns_a_telescope(X)&owns_a_telescope(Y))&(X!=Y))))
room(leslie)&room(debra)&(![X]:(room(X)=>(X='leslie'|X='debra')))& enjoys_stand-up_paddleboarding(leslie)
[ "p0", "p2", "p5", "p10", "p12", "hypothesis" ]
% SZS status Unsatisfiable for 3205075485261470019191405 % SZS output start Proof for 3205075485261470019191405 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. predj(mary) [input p2] 49. ! [X0] : (predf(X0) => predu(X0)) [input p5] 54. ~(predp(mary) | predu(mary)) [input p10] 56. ! [X0] : (predd(X0) <=> (predf(X0) <~> predj(X0))) [input p12] 62. ~(predd(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 64. ! [X0] : ((predf(X0) <~> predj(X0)) => predd(X0)) [unused predicate definition removal 56] 76. ~predu(mary) [pure predicate removal 54] 149. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 150. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 149] 151. ! [X0] : (predu(X0) | ~predf(X0)) [ennf transformation 49] 152. ~predu(mary) [ennf transformation 76] 154. ! [X0] : (predd(X0) | (predf(X0) <=> predj(X0))) [ennf transformation 64] 155. ~predd(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 62] 156. ~predd(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 155] 161. ! [X0] : (predd(X0) | ((predf(X0) | ~predj(X0)) & (predj(X0) | ~predf(X0)))) [nnf transformation 154] 164. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 165. ~predd(mary) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 156,164] 246. room(mary) [cnf transformation 150] 247. room(paul) [cnf transformation 150] 248. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 150] 249. predj(mary) [cnf transformation 46] 253. ~predf(X0) | predu(X0) [cnf transformation 151] 255. ~predu(mary) [cnf transformation 152] 259. ~predj(X0) | predf(X0) | predd(X0) [cnf transformation 161] 265. ~predd(mary) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 165] 266. ~predd(mary) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 165] 267. ~predd(mary) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 165] 268. ~predd(mary) | paul != sK4 | ~room(mary) [subsumption resolution 267,247] 269. ~predd(mary) | paul != sK4 [subsumption resolution 268,246] 271. 1 <=> paul = sK4 [avatar definition] 273. paul != sK4 <- (~1) [avatar component clause 271] 275. 2 <=> predd(mary) [avatar definition] 277. ~predd(mary) <- (~2) [avatar component clause 275] 278. ~1 | ~2 [avatar split clause 269,275,271] 279. ~predd(mary) | mary != sK4 | ~room(mary) [subsumption resolution 266,247] 280. ~predd(mary) | mary != sK4 [subsumption resolution 279,246] 282. 3 <=> mary = sK4 [avatar definition] 284. mary != sK4 <- (~3) [avatar component clause 282] 285. ~3 | ~2 [avatar split clause 280,275,282] 286. ~predd(mary) | room(sK4) | ~room(mary) [subsumption resolution 265,247] 287. ~predd(mary) | room(sK4) [subsumption resolution 286,246] 289. 4 <=> room(sK4) [avatar definition] 291. room(sK4) <- (4) [avatar component clause 289] 292. 4 | ~2 [avatar split clause 287,275,289] 326. predf(mary) | predd(mary) [resolution 259,249] 327. predf(mary) <- (~2) [subsumption resolution 326,277] 394. predu(mary) <- (~2) [resolution 327,253] 395. $false <- (~2) [subsumption resolution 394,255] 396. 2 [avatar contradiction clause 395] 402. mary = sK4 | paul = sK4 <- (4) [resolution 291,248] 403. paul = sK4 <- (~3, 4) [subsumption resolution 402,284] 404. $false <- (~1, ~3, 4) [subsumption resolution 403,273] 405. 1 | 3 | ~4 [avatar contradiction clause 404] 406. $false [avatar sat refutation 278,285,292,396,405] % SZS output end Proof for 3205075485261470019191405 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------
0.04558
Lisa, Leanne, Robert are the only persons in the room. Lisa dreamt that 'if someone trains for and competes in international triathlons then he/she maintains a personal blog focused on cybersecurity tips, creates augmented reality experiences for mobile applications or can play the harmonica and vice versa'. Lisa who neither writes in-depth travel guides for off-the-beaten-path destinations nor makes intricate hand-cut paper art for exhibitions writes in-depth travel guides for off-the-beaten-path destinations, trains for and competes in international triathlons or works as a freelance web developer specializing in e-commerce sites.
Lisa makes intricate hand-cut paper art for exhibitions.
contradiction
room(lisa)&room(leanne)&room(robert)&(![X]:(room(X)=>(X='lisa'|X='leanne'|X='robert')))& ((lisa_dream=>((![X]:((trains_for_and_competes_in_international_triathlons(X))<=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))|(can_play_the_harmonica(X)))))))))& (?[X]:(room(X)&(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(is_a_tea_enthusiast(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))& (?[X]:(room(X)&(enjoys_macrame(X))))& (?[X]:(room(X)&(((collects_classic_novels(X))|(can_play_the_harmonica(X))|(enjoys_salsa_dancing(X))))))& (?[X]:(room(X)&(builds_model_airplanes(X))))& (?[X]:(room(X)&(((builds_model_airplanes(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))&(mentors_a_youth_basketball_team_on_weekends(X))))))& ((?[X,Y]:(room(X)&room(Y)&(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(mentors_a_youth_basketball_team_on_weekends(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))&((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(Y))|(mentors_a_youth_basketball_team_on_weekends(Y))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(Y))))&(X!=Y))))& (((?[X]:(room(X)&is_a_wine_connoisseur(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_wine_connoisseur(X))&(is_a_wine_connoisseur(Y)))=>(X=Y)))))& ((builds_model_airplanes(lisa))&(enjoys_macrame(lisa)))& ((~((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(lisa))|(makes_intricate_hand-cut_paper_art_for_exhibitions(lisa))))&(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(lisa))|(trains_for_and_competes_in_international_triathlons(lisa))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(lisa)))))& (?[X]:(room(X)&(enjoys_snowboarding(X))))
room(lisa)&room(leanne)&room(robert)&(![X]:(room(X)=>(X='lisa'|X='leanne'|X='robert')))& makes_intricate_hand-cut_paper_art_for_exhibitions(lisa)
[ "p10", "hypothesis" ]
% SZS status Unsatisfiable for 6233172955394916242444146 % SZS output start Proof for 6233172955394916242444146 54. (predx(mary) | predp(mary) | predm(mary)) & ~(predd(mary) | predm(mary)) [input p10] 56. predd(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 59. ~(predd(mary) | predm(mary)) [pure predicate removal 54] 69. ~predd(mary) [pure predicate removal 59] 148. ~predd(mary) [ennf transformation 69] 149. predd(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 56] 150. predd(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 149] 263. ~predd(mary) [cnf transformation 148] 269. predd(mary) [cnf transformation 150] 270. $false [subsumption resolution 269,263] % SZS output end Proof for 6233172955394916242444146 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0.315754
Corey is the only person in the room. Not everyone in the room who maintains a personal blog focused on cybersecurity tips owns a 3D printer. Everyone outside the room who enjoys writing detailed reviews of new and classic board games neither writes in-depth travel guides for off-the-beaten-path destinations nor owns a 3D printer. Corey is not a scotch connoisseur. Corey maintains a personal blog focused on cybersecurity tips. Someone outside the room writes in-depth travel guides for off-the-beaten-path destinations. Corey writes in-depth travel guides for off-the-beaten-path destinations. Corey collects modern art. Everyone in the room who owns a 3D printer is a scotch connoisseur. Everyone in the room practices zumba or does not write in-depth travel guides for off-the-beaten-path destinations.
Corey enjoys writing detailed reviews of new and classic board games.
neutral
room(corey)&(![X]:(room(X)=>(X='corey')))& (~![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(owns_a_3D_printer(X))))))& (![X]:(~room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(~((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(owns_a_3D_printer(X))))))))& (is_not_a_scotch_connoisseur(corey))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(corey))& (?[X]:(~room(X)&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(corey))& (collects_modern_art(corey))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(practices_zumba(X))))))
room(corey)&(![X]:(room(X)=>(X='corey')))& enjoys_writing_detailed_reviews_of_new_and_classic_board_games(corey)
[]
null
0.042946
Melissa, Timothy, Nana, Richard, Gabriella are the only persons in the room. If “everyone in the room does not practice archery or collects classic novels” then “if someone knows morse code and is a dedicated volunteer for local community service projects then he/she knows morse code”. Everyone in the room does not practice archery if and only if they is a dedicated volunteer for local community service projects. Melissa practices archery. Everyone in the room practices archery if they knows morse code. Everyone in the room plays video games if they does not play video games. Everyone in the room who collects classic novels plays video games, is a dedicated volunteer for local community service projects and practices archery. Everyone in the room knows morse code if they plays video games.
Nana collects classic novels.
contradiction
room(melissa)&room(timothy)&room(nana)&room(richard)&room(gabriella)&(![X]:(room(X)=>(X='melissa'|X='timothy'|X='nana'|X='richard'|X='gabriella')))& ((![X]:(room(X)=>(((collects_classic_novels(X))|(does_not_practice_archery(X))))))=>((![X]:((((knows_morse_code(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))=>(knows_morse_code(X))))))& (![X]:(room(X)=>(((does_not_practice_archery(X))<=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (practices_archery(melissa))& (![X]:(room(X)=>(((knows_morse_code(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))& ((does_not_collect_classic_novels(melissa))&(practices_archery(melissa)))& (![X]:(room(X)=>(((knows_morse_code(X))=>(practices_archery(X))))))& (((?[X]:(room(X)&practices_archery(X)))))& (![X]:(room(X)=>(((practices_archery(X))=>(knows_morse_code(X))))))& (knows_morse_code(melissa))& (![X]:(room(X)=>(((does_not_know_morse_code(X))=>(plays_video_games(X))))))& (![X]:(anywhere(X)=>(((plays_video_games(X))|(does_not_collect_classic_novels(X))))))& (plays_video_games(melissa))& (![X]:(room(X)=>(((does_not_play_video_games(X))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(((plays_video_games(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))&(practices_archery(X))))))))& ((![X]:((practices_archery(X))=>(knows_morse_code(X)))))& (![X]:(~room(X)=>(((collects_classic_novels(X))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(knows_morse_code(X))))))
room(melissa)&room(timothy)&room(nana)&room(richard)&room(gabriella)&(![X]:(room(X)=>(X='melissa'|X='timothy'|X='nana'|X='richard'|X='gabriella')))& collects_classic_novels(nana)
[ "p0", "p2", "p6", "p13", "p14", "p18", "hypothesis" ]
% SZS status Unsatisfiable for 386944608911865093022397 % SZS output start Proof for 386944608911865093022397 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (~preda(X0) <=> predb(X0))) [input p2] 50. ! [X0] : (room(X0) => (predc(X0) => preda(X0))) [input p6] 57. ! [X0] : (room(X0) => (~prede(X0) => prede(X0))) [input p13] 58. ! [X0] : (room(X0) => (predd(X0) => (preda(X0) & predb(X0) & prede(X0)))) [input p14] 62. ! [X0] : (room(X0) => (prede(X0) => predc(X0))) [input p18] 63. predd(fred) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 136. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 136] 140. ! [X0] : ((~preda(X0) <=> predb(X0)) | ~room(X0)) [ennf transformation 46] 143. ! [X0] : ((preda(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 50] 144. ! [X0] : (preda(X0) | ~predc(X0) | ~room(X0)) [flattening 143] 151. ! [X0] : ((prede(X0) | prede(X0)) | ~room(X0)) [ennf transformation 57] 152. ! [X0] : (prede(X0) | prede(X0) | ~room(X0)) [flattening 151] 153. ! [X0] : (((preda(X0) & predb(X0) & prede(X0)) | ~predd(X0)) | ~room(X0)) [ennf transformation 58] 154. ! [X0] : ((preda(X0) & predb(X0) & prede(X0)) | ~predd(X0) | ~room(X0)) [flattening 153] 160. ! [X0] : ((predc(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 62] 161. ! [X0] : (predc(X0) | ~prede(X0) | ~room(X0)) [flattening 160] 162. predd(fred) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 63] 163. predd(fred) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 162] 168. ! [X0] : (((~preda(X0) | ~predb(X0)) & (predb(X0) | preda(X0))) | ~room(X0)) [nnf transformation 140] 254. room(fred) [cnf transformation 137] 262. ~predb(X0) | ~preda(X0) | ~room(X0) [cnf transformation 168] 267. ~predc(X0) | preda(X0) | ~room(X0) [cnf transformation 144] 275. prede(X0) | prede(X0) | ~room(X0) [cnf transformation 152] 277. ~predd(X0) | predb(X0) | ~room(X0) [cnf transformation 154] 282. predc(X0) | ~prede(X0) | ~room(X0) [cnf transformation 161] 289. predd(fred) [cnf transformation 163] 290. ~room(X0) | prede(X0) [duplicate literal removal 275] 292. ~room(X0) | predc(X0) [subsumption resolution 282,290] 304. predc(fred) [resolution 292,254] 324. 3 <=> predb(fred) [avatar definition] 326. predb(fred) <- (3) [avatar component clause 324] 328. 4 <=> preda(fred) [avatar definition] 330. preda(fred) <- (4) [avatar component clause 328] 353. preda(fred) | ~room(fred) [resolution 304,267] 354. preda(fred) [subsumption resolution 353,254] 355. 4 [avatar split clause 354,328] 370. predb(fred) | ~room(fred) [resolution 277,289] 375. ~preda(fred) | ~room(fred) <- (3) [resolution 326,262] 376. ~room(fred) <- (3, 4) [subsumption resolution 375,330] 377. $false <- (3, 4) [subsumption resolution 376,254] 378. ~3 | ~4 [avatar contradiction clause 377] 379. predb(fred) [subsumption resolution 370,254] 380. 3 [avatar split clause 379,324] 381. $false [avatar sat refutation 355,378,380] % SZS output end Proof for 386944608911865093022397 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------
0.156669
Linda is the only person in the room. If “everyone outside the room enjoys bird watching or does not create YouTube content” then “everyone in the room who enjoys bird watching can play the flute”. Everyone in the room can play the flute or does not enjoy coding in Python. Everyone in the room who can play the flute neither is a professional photographer specializing in portrait photography nor is a certified yoga instructor teaching classes weekly. Linda collects action figures. Linda maintains a personal blog focused on cybersecurity tips.
Linda hosts regular workshops on creative writing.
neutral
room(linda)&(![X]:(room(X)=>(X='linda')))& ((![X]:(~room(X)=>(((does_not_create_YouTube_content(X))|(enjoys_bird_watching(X))))))=>(![X]:(room(X)=>(((enjoys_bird_watching(X))=>(can_play_the_flute(X)))))))& (![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))|(can_play_the_flute(X))))))& (![X]:(room(X)=>(((can_play_the_flute(X))=>(~((is_a_professional_photographer_specializing_in_portrait_photography(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))& (collects_action_figures(linda))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(linda))& ((![X]:((enjoys_bird_watching(X))=>(collects_first_edition_books(X)))))& (hosts_a_popular_podcast_about_emerging_technologies(linda))& (collects_first_edition_books(linda))& ((![X]:((bakes_bread_at_home(X))=>(is_a_client_of_Meta(X)))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& ((![X]:((collects_first_edition_books(X))=>(is_a_client_of_Meta(X)))))& (![X]:(anywhere(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(hosts_regular_workshops_on_creative_writing(X))))))& (has_a_pet_dog(linda))& (uses_an_ios_phone(linda))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(enjoys_coding_in_Python(X))))))& (can_play_the_flute(linda))& (![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(plays_eSports_competitively(X))))))& (~![X]:(room(X)=>(((uses_an_ios_phone(X))=>(creates_YouTube_content(X))))))& (![X]:(~room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(uses_an_ios_phone(X))))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (enjoys_coding_in_Python(linda))
room(linda)&(![X]:(room(X)=>(X='linda')))& hosts_regular_workshops_on_creative_writing(linda)
[]
null
0.610123
Dorla, Dollie, Gordon are the only persons in the room. If “Gordon is richer than Harold” then “Dorla is a humble creative person and is a humble person” otherwise “someone in the room is curious”. “Everyone in the room who is curious is quieter than Harold” if “Dorla and Dollie are quieter than Harold”. If “everyone in the room is a kind old person” then “someone in the room is a old kind wise creative person”. “Gordon is older than Harold” only if “Dollie and Gordon are not a funny persons”. “Only one person anywhere is not happy” unless “Dollie is wise”. Dollie and Gordon are not a humble persons. Everyone in the room is richer than Harold.
Dollie is richer than Harold.
entailment
room(dorla)&room(dollie)&room(gordon)&(![X]:(room(X)=>(X='dorla'|X='dollie'|X='gordon')))& (((richer(harold,gordon))=>(((humble(dorla)&creative(dorla)&person(dorla))&(humble(dorla)&person(dorla)))))&((~(richer(harold,gordon)))=>(?[X]:(room(X)&(curious(X))))))& ((quieter(harold,dorla)&quieter(harold,dollie))=>(![X]:(room(X)=>(((curious(X))=>(quieter(harold,X)))))))& ((![X]:(room(X)=>(kind(X)&old(X)&person(X))))=>(?[X]:(room(X)&(old(X)&kind(X)&wise(X)&creative(X)&person(X)))))& ((older(harold,gordon))=>(~(funny(dollie)&person(dollie))&~(funny(gordon)&person(gordon))))& (~(wise(dollie))=>(((?[X]:(anywhere(X)&~happy(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(~happy(X))&(~happy(Y)))=>(X=Y))))))& (~(humble(dollie)&person(dollie))&~(humble(gordon)&person(gordon)))& (![X]:(room(X)=>(((strong(X)&wise(X)&generous(X)&person(X))<=>(~(quiet(X)&brave(X)&humble(X)&old(X)&person(X)))))))& (![X]:(room(X)=>(((curious(X)&tall(X)&strong(X)&person(X))=>(calm(X)&person(X))))))& (((~generous(gordon))|(quieter(harold,gordon))|(~(patient(gordon)&curious(gordon)&humble(gordon)&person(gordon)))))& (![X]:(room(X)=>(((kind(X))=>(curious(X)&person(X))))))& (~![X]:(anywhere(X)=>(((tall(X)&person(X))<=>(~((~(strong(X)&person(X)))|(older(harold,X))))))))& (~![X]:(room(X)=>(((~((~(strong(X)&person(X)))|(older(harold,X))))=>(((old(X)&happy(X)&person(X))|(old(X))|(tall(X)&person(X))))))))& (wise(dorla))& (((?[X]:(~room(X)&~brave(X)))&(![X,Y]:((~room(X)&~room(Y)&(~brave(X))&(~brave(Y)))=>(X=Y)))))& (quieter(gordon,harold))& (![X]:(room(X)=>(((~patient(X))<=>(curious(X)&person(X))))))& (![X]:(generous(X)=>strong(X)))& (((?[X]:(room(X)&((quieter(harold,X))&(richer(harold,X)))))&(![X,Y]:((room(X)&room(Y)&(((quieter(harold,X))&(richer(harold,X))))&(((quieter(harold,Y))&(richer(harold,Y)))))=>(X=Y)))))& (![X]:(~room(X)=>(~~quiet(X))))& (![X]:(room(X)=>(((quieter(harold,X))=>(kind(X)&funny(X)&person(X))))))& (![X]:(room(X)=>(richer(harold,X))))& (![X]:(room(X)=>(((~((happy(X)&person(X))|(old(X))))=>(older(harold,X))))))& (![X]:(room(X)=>(((~(strong(X)&curious(X)&person(X)))=>(calm(X)&person(X))))))& (![X]:(room(X)=>(((~(generous(X)&calm(X)&person(X)))=>(((old(X))&(generous(X)&creative(X)&person(X))&(~(patient(X)&person(X)))))))))& (![X]:(room(X)=>(((((old(X))&(generous(X)&creative(X)&person(X))&(~(patient(X)&person(X)))))=>(tall(X))))))& (![X]:(tall(X)=>strong(X)))& (?[X]:(anywhere(X)&(wise(X))))& (![X]:(room(X)=>(((patient(X)&person(X))=>(older(harold,X))))))& (![X]:(room(X)=>(((older(harold,X))=>(((funny(X)&curious(X)&happy(X)&patient(X)&person(X))|(older(harold,X))|(richer(harold,X))))))))
room(dorla)&room(dollie)&room(gordon)&(![X]:(room(X)=>(X='dorla'|X='dollie'|X='gordon')))& richer(harold,dollie)
[ "p0", "p21", "hypothesis" ]
% SZS status Unsatisfiable for 8421812779983426973603229 % SZS output start Proof for 8421812779983426973603229 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 65. ! [X0] : (room(X0) => richer(alice,X0)) [input p21] 74. ~(richer(alice,paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 153. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 154. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 153] 183. ! [X0] : (richer(alice,X0) | ~room(X0)) [ennf transformation 65] 197. ~richer(alice,paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 74] 198. ~richer(alice,paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 197] 236. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK13 & paul != sK13 & mary != sK13 & room(sK13)) [choice axiom] 237. ~richer(alice,paul) | (fred != sK13 & paul != sK13 & mary != sK13 & room(sK13)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 198,236] 319. room(mary) [cnf transformation 154] 320. room(paul) [cnf transformation 154] 321. room(fred) [cnf transformation 154] 322. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 154] 394. richer(alice,X0) | ~room(X0) [cnf transformation 183] 418. ~richer(alice,paul) | room(sK13) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 237] 419. ~richer(alice,paul) | mary != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 237] 420. ~richer(alice,paul) | paul != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 237] 421. ~richer(alice,paul) | fred != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 237] 621. ~richer(alice,paul) | fred != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 421,321] 622. ~richer(alice,paul) | fred != sK13 | ~room(mary) [subsumption resolution 621,320] 623. ~richer(alice,paul) | fred != sK13 [subsumption resolution 622,319] 625. 41 <=> fred = sK13 [avatar definition] 627. fred != sK13 <- (~41) [avatar component clause 625] 629. 42 <=> richer(alice,paul) [avatar definition] 631. ~richer(alice,paul) <- (~42) [avatar component clause 629] 632. ~41 | ~42 [avatar split clause 623,629,625] 633. ~richer(alice,paul) | paul != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 420,321] 634. ~richer(alice,paul) | paul != sK13 | ~room(mary) [subsumption resolution 633,320] 635. ~richer(alice,paul) | paul != sK13 [subsumption resolution 634,319] 637. 43 <=> paul = sK13 [avatar definition] 639. paul != sK13 <- (~43) [avatar component clause 637] 640. ~43 | ~42 [avatar split clause 635,629,637] 641. ~richer(alice,paul) | mary != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 419,321] 642. ~richer(alice,paul) | mary != sK13 | ~room(mary) [subsumption resolution 641,320] 643. ~richer(alice,paul) | mary != sK13 [subsumption resolution 642,319] 645. 44 <=> mary = sK13 [avatar definition] 647. mary != sK13 <- (~44) [avatar component clause 645] 648. ~44 | ~42 [avatar split clause 643,629,645] 649. ~richer(alice,paul) | room(sK13) | ~room(paul) | ~room(mary) [subsumption resolution 418,321] 650. ~richer(alice,paul) | room(sK13) | ~room(mary) [subsumption resolution 649,320] 651. ~richer(alice,paul) | room(sK13) [subsumption resolution 650,319] 653. 45 <=> room(sK13) [avatar definition] 655. room(sK13) <- (45) [avatar component clause 653] 656. 45 | ~42 [avatar split clause 651,629,653] 696. ~room(paul) <- (~42) [resolution 394,631] 699. $false <- (~42) [subsumption resolution 696,320] 700. 42 [avatar contradiction clause 699] 1203. paul = sK13 | mary = sK13 | fred = sK13 <- (45) [resolution 322,655] 1256. mary = sK13 | fred = sK13 <- (~43, 45) [subsumption resolution 1203,639] 1257. fred = sK13 <- (~43, ~44, 45) [subsumption resolution 1256,647] 1258. $false <- (~41, ~43, ~44, 45) [subsumption resolution 1257,627] 1259. 41 | 43 | 44 | ~45 [avatar contradiction clause 1258] 1260. $false [avatar sat refutation 632,640,648,656,700,1259] % SZS output end Proof for 8421812779983426973603229 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5628 % Time elapsed: 0.045 s % ------------------------------ % ------------------------------
0.000002
There is a room. If someone owns a 3D printer then he/she does not build model airplanes, does not collect vintage vinyl records and does not enjoy kayaking. Everyone in the room does not enjoy kayaking. Everyone outside the room who neither does not collect limited-edition art prints from contemporary artists nor collects vintage vinyl records owns an Android phone. At least one person in the room neither does not own an Android phone nor owns a 3D printer. Everyone in the room does not design and sews custom cosplay costumes for conventions. If someone collects comic books, is not a skilled home brewer experimenting with craft beer recipes or does not practice yoga then he/she neither does not compete in national level swimming championships nor does not enjoy kayaking. Everyone in the room collects vintage vinyl records if they collects vintage vinyl records, does not enjoy snowboarding or competes in national level swimming championships. Everyone in the room who collects vintage vinyl records builds model airplanes. If someone is not a client of LVMH then he/she either does not own an extensive assortment of vintage comic book memorabilia or does not build model airplanes but not both. Everyone in the room is not a skilled home brewer experimenting with craft beer recipes, does not collect vintage vinyl records or owns a 3D printer. Everyone in the room neither is a skilled home brewer experimenting with craft beer recipes nor does not practice yoga if they neither does not collect limited-edition art prints from contemporary artists nor does not build model airplanes. Only one person in the room does not own an Android phone. If someone is a client of LVMH then he/she can play the flute. Everyone outside the room who collects limited-edition art prints from contemporary artists does not own an Android phone.
Everyone in the room does not enjoy snowboarding.
contradiction
(there_is_a_room)& ((![X]:((owns_a_3D_printer(X))=>(((does_not_build_model_airplanes(X))&(does_not_collect_vintage_vinyl_records(X))&(does_not_enjoy_kayaking(X)))))))& (![X]:(room(X)=>(does_not_enjoy_kayaking(X))))& (![X]:(~room(X)=>(((~((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(collects_vintage_vinyl_records(X))))=>(owns_an_Android_phone(X))))))& (((?[X]:(room(X)&~((does_not_own_an_Android_phone(X))|(owns_a_3D_printer(X)))))))& (![X]:(room(X)=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))& ((![X]:((((collects_comic_books(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_practice_yoga(X))))=>(~((does_not_compete_in_national_level_swimming_championships(X))|(does_not_enjoy_kayaking(X)))))))& (![X]:(room(X)=>(((((collects_vintage_vinyl_records(X))|(does_not_enjoy_snowboarding(X))|(competes_in_national_level_swimming_championships(X))))=>(collects_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(builds_model_airplanes(X))))))& ((![X]:((is_not_a_client_of_LVMH(X))=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<~>(does_not_build_model_airplanes(X)))))))& (![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_collect_vintage_vinyl_records(X))|(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(((~((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_build_model_airplanes(X))))=>(~((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_practice_yoga(X))))))))& (((?[X]:(room(X)&does_not_own_an_Android_phone(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_own_an_Android_phone(X))&(does_not_own_an_Android_phone(Y)))=>(X=Y)))))& ((![X]:((is_a_client_of_LVMH(X))=>(can_play_the_flute(X)))))& (![X]:(~room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(does_not_own_an_Android_phone(X))))))
(there_is_a_room)& ![X]:(room(X)=>(does_not_enjoy_snowboarding(X)))
[ "p1", "p2", "p4", "p6", "p7", "p10", "hypothesis" ]
% SZS status Unsatisfiable for 3247155405311873414571303 % SZS output start Proof for 3247155405311873414571303 45. ! [X0] : (predk(X0) => (~predc(X0) & ~preda(X0) & ~prede(X0))) [input p1] 46. ! [X0] : (room(X0) => ~predc(X0)) [input p2] 48. ? [X0] : (~(predk(X0) | ~predi(X0)) & room(X0)) [input p4] 50. ! [X0] : ((~predf(X0) | ~predd(X0) | predb(X0)) => ~(~predc(X0) | ~predj(X0))) [input p6] 51. ! [X0] : (room(X0) => ((predj(X0) | ~predm(X0) | preda(X0)) => preda(X0))) [input p7] 54. ! [X0] : (room(X0) => (predk(X0) | ~preda(X0) | ~predd(X0))) [input p10] 59. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 63. ! [X0] : ((~predd(X0) | predb(X0)) => ~(~predc(X0) | ~predj(X0))) [pure predicate removal 50] 65. ! [X0] : (~predd(X0) => ~(~predc(X0) | ~predj(X0))) [pure predicate removal 63] 70. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 59] 144. ! [X0] : ((~predc(X0) & ~preda(X0) & ~prede(X0)) | ~predk(X0)) [ennf transformation 45] 145. ! [X0] : (~predc(X0) | ~room(X0)) [ennf transformation 46] 146. ? [X0] : ((~predk(X0) & predi(X0)) & room(X0)) [ennf transformation 48] 147. ? [X0] : (~predk(X0) & predi(X0) & room(X0)) [flattening 146] 148. ! [X0] : ((predc(X0) & predj(X0)) | predd(X0)) [ennf transformation 65] 149. ! [X0] : ((preda(X0) | (~predj(X0) & predm(X0) & ~preda(X0))) | ~room(X0)) [ennf transformation 51] 150. ! [X0] : (preda(X0) | (~predj(X0) & predm(X0) & ~preda(X0)) | ~room(X0)) [flattening 149] 153. ! [X0] : ((predk(X0) | ~preda(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 54] 154. ! [X0] : (predk(X0) | ~preda(X0) | ~predd(X0) | ~room(X0)) [flattening 153] 157. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 70] 159. ? [X0] : (~predk(X0) & predi(X0) & room(X0)) => (~predk(sK0) & predi(sK0) & room(sK0)) [choice axiom] 160. ~predk(sK0) & predi(sK0) & room(sK0) [skolemisation 147,159] 244. ~preda(X0) | ~predk(X0) [cnf transformation 144] 246. ~room(X0) | ~predc(X0) [cnf transformation 145] 247. room(sK0) [cnf transformation 160] 251. predd(X0) | predc(X0) [cnf transformation 148] 253. ~room(X0) | predm(X0) | preda(X0) [cnf transformation 150] 256. predk(X0) | ~preda(X0) | ~predd(X0) | ~room(X0) [cnf transformation 154] 260. ~predm(X0) | ~room(X0) [cnf transformation 157] 261. ~predd(X0) | ~preda(X0) | ~room(X0) [subsumption resolution 256,244] 264. predm(sK0) | preda(sK0) [resolution 253,247] 267. 1 <=> preda(sK0) [avatar definition] 269. preda(sK0) <- (1) [avatar component clause 267] 271. 2 <=> predm(sK0) [avatar definition] 273. predm(sK0) <- (2) [avatar component clause 271] 274. 1 | 2 [avatar split clause 264,271,267] 285. ~room(sK0) <- (2) [resolution 273,260] 286. $false <- (2) [subsumption resolution 285,247] 287. ~2 [avatar contradiction clause 286] 293. ~preda(X0) | ~room(X0) | predc(X0) [resolution 261,251] 294. ~room(X0) | ~preda(X0) [subsumption resolution 293,246] 298. ~preda(sK0) [resolution 294,247] 300. $false <- (1) [subsumption resolution 298,269] 301. ~1 [avatar contradiction clause 300] 304. $false [avatar sat refutation 274,287,301] % SZS output end Proof for 3247155405311873414571303 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.030 s % ------------------------------ % ------------------------------
0.348018
Melissa, Luis are the only persons in the room. If “everyone anywhere does not practice tai chi or does not enjoy skydiving” then “no one in the room does not practice tai chi only if they does not enjoy skydiving”. If “Luis enjoys skydiving” then “Luis owns a significant collection of rare gemstones and minerals”. Luis either does not own a significant collection of rare gemstones and minerals or enjoys bird watching but not both. Luis practices tai chi. Everyone anywhere enjoys bird watching if they neither enjoys skydiving nor does not own a significant collection of rare gemstones and minerals. Only one person anywhere neither enjoys skydiving nor does not own a significant collection of rare gemstones and minerals. Melissa enjoys skydiving. Luis either enjoys bird watching or practices tai chi but not both. Melissa practices tai chi. Everyone outside the room enjoys skydiving only if they practices tai chi. Everyone in the room enjoys skydiving if they enjoys bird watching.
Melissa enjoys bird watching.
neutral
room(melissa)&room(luis)&(![X]:(room(X)=>(X='melissa'|X='luis')))& ((![X]:(anywhere(X)=>(((does_not_enjoy_skydiving(X))|(does_not_practice_tai_chi(X))))))=>(~?[X]:(room(X)=>(((does_not_enjoy_skydiving(X))<=(does_not_practice_tai_chi(X)))))))& ((enjoys_skydiving(luis))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(luis)))& (((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(luis))<~>(enjoys_bird_watching(luis))))& (practices_tai_chi(luis))& (![X]:(anywhere(X)=>(((~((enjoys_skydiving(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(enjoys_bird_watching(X))))))& (((?[X]:(anywhere(X)&~((enjoys_skydiving(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X)))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(~((enjoys_skydiving(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))&(~((enjoys_skydiving(Y))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(Y)))))=>(X=Y)))))& (enjoys_skydiving(melissa))& (((enjoys_bird_watching(luis))<~>(practices_tai_chi(luis))))& (practices_tai_chi(melissa))& (![X]:(~room(X)=>(((practices_tai_chi(X))<=(enjoys_skydiving(X))))))& (![X]:(room(X)=>(((enjoys_bird_watching(X))=>(enjoys_skydiving(X))))))
room(melissa)&room(luis)&(![X]:(room(X)=>(X='melissa'|X='luis')))& enjoys_bird_watching(melissa)
[]
null
0.005708
Rebecca, Fletcher, Howard are the only persons in the room. Everyone outside the room does not host a popular podcast about emerging technologies only if everyone in the room does not use contact lenses. Everyone in the room does not use contact lenses. Everyone in the room does not use contact lenses, does not frequently participates in hackathons and coding competitions and does not host a popular podcast about emerging technologies. Everyone in the room does not frequently participates in hackathons and coding competitions, does not use contact lenses and does not own a telescope. At least one person in the room does not own a telescope. Everyone in the room does not frequently participates in hackathons and coding competitions. If someone either does not own a telescope or does not frequently participates in hackathons and coding competitions but not both then he/she does not frequently participates in hackathons and coding competitions. Everyone outside the room either does not own a telescope or does not host a popular podcast about emerging technologies but not both. Fletcher does not host a popular podcast about emerging technologies, does not use contact lenses and does not own a telescope. Everyone in the room does not own a telescope, does not use contact lenses and does not frequently participates in hackathons and coding competitions.
Everyone in the room owns a telescope.
contradiction
room(rebecca)&room(fletcher)&room(howard)&(![X]:(room(X)=>(X='rebecca'|X='fletcher'|X='howard')))& ((![X]:(~room(X)=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))=>(![X]:(room(X)=>(does_not_use_contact_lenses(X)))))& (![X]:(room(X)=>(does_not_use_contact_lenses(X))))& (![X]:(room(X)=>(((does_not_use_contact_lenses(X))&(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))&(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))&(does_not_use_contact_lenses(X))&(does_not_own_a_telescope(X))))))& (((?[X]:(room(X)&does_not_own_a_telescope(X)))))& (![X]:(room(X)=>(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))& ((![X]:((((does_not_own_a_telescope(X))<~>(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))=>(does_not_frequently_participates_in_hackathons_and_coding_competitions(X)))))& (![X]:(~room(X)=>(((does_not_own_a_telescope(X))<~>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))& (((does_not_host_a_popular_podcast_about_emerging_technologies(fletcher))&(does_not_use_contact_lenses(fletcher))&(does_not_own_a_telescope(fletcher))))& (![X]:(room(X)=>(((does_not_own_a_telescope(X))&(does_not_use_contact_lenses(X))&(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))
room(rebecca)&room(fletcher)&room(howard)&(![X]:(room(X)=>(X='rebecca'|X='fletcher'|X='howard')))& ![X]:(room(X)=>(owns_a_telescope(X)))
[ "p4", "p5", "hypothesis" ]
% SZS status Unsatisfiable for 6440335073483348881487158 % SZS output start Proof for 6440335073483348881487158 48. ! [X0] : (room(X0) => (~preda(X0) & ~predc(X0) & ~predb(X0))) [input p4] 49. ? [X0] : (~preda(X0) & room(X0)) [input p5] 55. ! [X0] : (room(X0) => preda(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 57. ! [X0] : (room(X0) => preda(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 55] 58. ! [X0] : (room(X0) => (~preda(X0) & ~predb(X0))) [pure predicate removal 48] 139. ! [X0] : ((~preda(X0) & ~predb(X0)) | ~room(X0)) [ennf transformation 58] 144. ! [X0] : (preda(X0) | ~room(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 145. ! [X0] : (preda(X0) | ~room(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 144] 147. ? [X0] : (~preda(X0) & room(X0)) => (~preda(sK0) & room(sK0)) [choice axiom] 148. ~preda(sK0) & room(sK0) [skolemisation 49,147] 238. ~preda(X0) | ~room(X0) [cnf transformation 139] 239. room(sK0) [cnf transformation 148] 254. preda(X0) | ~room(X0) [cnf transformation 145] 257. ~room(X0) [subsumption resolution 254,238] 261. $false [resolution 257,239] % SZS output end Proof for 6440335073483348881487158 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------
0.097522
Maurice, Reyna, Rebecca, Gilbert, Brian are the only persons in the room. Rebecca neither is not old nor is a tall person. Rebecca who is a quiet person is not kind. All old persons are quiet. Someone who neither is old nor is a tall person is older than someone who is a tall person. Reyna is old. Reyna is the least quiet in the room. Rebecca is not kind. Someone who is a quiet person is older than someone who either is a kind person or is not quiet but not both. Someone in the room is a quiet person. Reyna is a kind person. All kind persons are old. Reyna is the richest in the room.
Maurice is quiet.
entailment
room(maurice)&room(reyna)&room(rebecca)&room(gilbert)&room(brian)&(![X]:(room(X)=>(X='maurice'|X='reyna'|X='rebecca'|X='gilbert'|X='brian')))& (~((~old(rebecca))|(tall(rebecca)&person(rebecca))))& ((quiet(rebecca)&person(rebecca))&(~kind(rebecca)))& (![X]:(old(X)=>quiet(X)))& (?[X,Y]:((~((old(X))|(tall(X)&person(X))))&(tall(Y)&person(Y))&(older(X,Y))))& (old(reyna))& (![X]:((room(X)&(X!=reyna))=>quieter(reyna,X)))& (~kind(rebecca))& (?[X,Y]:((quiet(X)&person(X))&(((kind(Y)&person(Y))<~>(~quiet(Y))))&(older(X,Y))))& (?[X]:(room(X)&(quiet(X)&person(X))))& (kind(reyna)&person(reyna))& (![X]:(kind(X)=>old(X)))& (![X]:((room(X)&(X!=reyna))=>richer(X,reyna)))
room(maurice)&room(reyna)&room(rebecca)&room(gilbert)&room(brian)&(![X]:(room(X)=>(X='maurice'|X='reyna'|X='rebecca'|X='gilbert'|X='brian')))& quiet(maurice)
[ "b14", "b42", "p0", "p3", "p5", "p6", "hypothesis" ]
% SZS status Unsatisfiable for 7037112934216619014491474 % SZS output start Proof for 7037112934216619014491474 15. ! [X0,X1] : (X0 != X1 => ((quiet(X0) & quieter(X0,X1)) => quiet(X1))) [input b14] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : (old(X0) => quiet(X0)) [input p3] 49. old(paul) [input p5] 50. ! [X0] : ((paul != X0 & room(X0)) => quieter(paul,X0)) [input p6] 57. ~(quiet(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] 79. ! [X0,X1] : ((quiet(X1) | (~quiet(X0) | ~quieter(X0,X1))) | X0 = X1) [ennf transformation 15] 80. ! [X0,X1] : (quiet(X1) | ~quiet(X0) | ~quieter(X0,X1) | X0 = X1) [flattening 79] 130. ! [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] 131. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 130] 133. ! [X0] : (quiet(X0) | ~old(X0)) [ennf transformation 47] 136. ! [X0] : (quieter(paul,X0) | (paul = X0 | ~room(X0))) [ennf transformation 50] 137. ! [X0] : (quieter(paul,X0) | paul = X0 | ~room(X0)) [flattening 136] 141. ~quiet(mary) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57] 142. ~quiet(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 141] 152. ? [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] 153. ~quiet(mary) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 142,152] 164. ~quieter(X0,X1) | ~quiet(X0) | quiet(X1) | X0 = X1 [cnf transformation 80] 198. mary != paul [cnf transformation 43] 234. room(mary) [cnf transformation 131] 235. room(paul) [cnf transformation 131] 236. room(fred) [cnf transformation 131] 237. room(alice) [cnf transformation 131] 238. room(john) [cnf transformation 131] 239. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 131] 245. ~old(X0) | quiet(X0) [cnf transformation 133] 251. old(paul) [cnf transformation 49] 252. quieter(paul,X0) | paul = X0 | ~room(X0) [cnf transformation 137] 267. ~quiet(mary) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 268. ~quiet(mary) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 269. ~quiet(mary) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 270. ~quiet(mary) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 271. ~quiet(mary) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 272. ~quiet(mary) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 307. ~quiet(mary) | john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,238] 308. ~quiet(mary) | john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,237] 309. ~quiet(mary) | john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 308,236] 310. ~quiet(mary) | john != sK5 | ~room(mary) [subsumption resolution 309,235] 311. ~quiet(mary) | john != sK5 [subsumption resolution 310,234] 313. 8 <=> john = sK5 [avatar definition] 315. john != sK5 <- (~8) [avatar component clause 313] 317. 9 <=> quiet(mary) [avatar definition] 320. ~8 | ~9 [avatar split clause 311,317,313] 321. ~quiet(mary) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,238] 322. ~quiet(mary) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,237] 323. ~quiet(mary) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 322,236] 324. ~quiet(mary) | alice != sK5 | ~room(mary) [subsumption resolution 323,235] 325. ~quiet(mary) | alice != sK5 [subsumption resolution 324,234] 327. 10 <=> alice = sK5 [avatar definition] 329. alice != sK5 <- (~10) [avatar component clause 327] 330. ~10 | ~9 [avatar split clause 325,317,327] 331. ~quiet(mary) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,238] 332. ~quiet(mary) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 331,237] 333. ~quiet(mary) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 332,236] 334. ~quiet(mary) | fred != sK5 | ~room(mary) [subsumption resolution 333,235] 335. ~quiet(mary) | fred != sK5 [subsumption resolution 334,234] 337. 11 <=> fred = sK5 [avatar definition] 339. fred != sK5 <- (~11) [avatar component clause 337] 340. ~11 | ~9 [avatar split clause 335,317,337] 341. ~quiet(mary) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,238] 342. ~quiet(mary) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 341,237] 343. ~quiet(mary) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 342,236] 344. ~quiet(mary) | paul != sK5 | ~room(mary) [subsumption resolution 343,235] 345. ~quiet(mary) | paul != sK5 [subsumption resolution 344,234] 347. 12 <=> paul = sK5 [avatar definition] 349. paul != sK5 <- (~12) [avatar component clause 347] 350. ~12 | ~9 [avatar split clause 345,317,347] 351. ~quiet(mary) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,238] 352. ~quiet(mary) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 351,237] 353. ~quiet(mary) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 352,236] 354. ~quiet(mary) | mary != sK5 | ~room(mary) [subsumption resolution 353,235] 355. ~quiet(mary) | mary != sK5 [subsumption resolution 354,234] 357. 13 <=> mary = sK5 [avatar definition] 359. mary != sK5 <- (~13) [avatar component clause 357] 360. ~13 | ~9 [avatar split clause 355,317,357] 361. ~quiet(mary) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 267,238] 362. ~quiet(mary) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 361,237] 363. ~quiet(mary) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 362,236] 364. ~quiet(mary) | room(sK5) | ~room(mary) [subsumption resolution 363,235] 365. ~quiet(mary) | room(sK5) [subsumption resolution 364,234] 367. 14 <=> room(sK5) [avatar definition] 369. room(sK5) <- (14) [avatar component clause 367] 370. 14 | ~9 [avatar split clause 365,317,367] 372. quiet(paul) [resolution 245,251] 492. ~quiet(paul) | quiet(X0) | paul = X0 | paul = X0 | ~room(X0) [resolution 164,252] 493. ~quiet(paul) | quiet(X0) | paul = X0 | ~room(X0) [duplicate literal removal 492] 494. ~room(X0) | paul = X0 | quiet(X0) [subsumption resolution 493,372] 555. mary = paul | quiet(mary) [resolution 494,234] 561. quiet(mary) [subsumption resolution 555,198] 566. 9 [avatar split clause 561,317] 624. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (14) [resolution 239,369] 642. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~10, 14) [subsumption resolution 624,329] 643. paul = sK5 | mary = sK5 | john = sK5 <- (~10, ~11, 14) [subsumption resolution 642,339] 644. mary = sK5 | john = sK5 <- (~10, ~11, ~12, 14) [subsumption resolution 643,349] 645. john = sK5 <- (~10, ~11, ~12, ~13, 14) [subsumption resolution 644,359] 646. $false <- (~8, ~10, ~11, ~12, ~13, 14) [subsumption resolution 645,315] 647. 8 | 10 | 11 | 12 | 13 | ~14 [avatar contradiction clause 646] 648. $false [avatar sat refutation 320,330,340,350,360,370,566,647] % SZS output end Proof for 7037112934216619014491474 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------
0.084943
Erica, Kenneth, Thomas are the only persons in the room. Erica is kind. Thomas is strong. Erica is calm. Everyone in the room is generous only if they is happy. Everyone outside the room is happy only if they is quiet or is kind or both. Everyone outside the room is quiet or is kind or both only if they is not a tall person. Kenneth is funny. Thomas is not a wise person. Everyone anywhere is not a calm person only if they is not a generous person or is tall or both. Erica is funny. Erica is brave. Erica is not a calm happy humble person or is not a patient person or both. Kenneth neither is not a creative person nor is not a calm person. Everyone in the room is not a funny generous person.
Kenneth and Erica are not a funny quiet tall generous wise persons.
entailment
room(erica)&room(kenneth)&room(thomas)&(![X]:(room(X)=>(X='erica'|X='kenneth'|X='thomas')))& (kind(erica))& (strong(thomas))& (calm(erica))& (![X]:(room(X)=>(((happy(X))<=(generous(X))))))& (![X]:(~room(X)=>(((((quiet(X))|(kind(X))))<=(happy(X))))))& (![X]:(~room(X)=>(((~(tall(X)&person(X)))<=(((quiet(X))|(kind(X))))))))& (funny(kenneth))& (~(wise(thomas)&person(thomas)))& (![X]:(anywhere(X)=>(((((~(generous(X)&person(X)))|(tall(X))))<=(~(calm(X)&person(X)))))))& (funny(erica))& (brave(erica))& (((~(calm(erica)&happy(erica)&humble(erica)&person(erica)))|(~(patient(erica)&person(erica)))))& (?[X,Y]:((~(kind(X)&patient(X)&person(X)))&(~((~(generous(Y)&humble(Y)&person(Y)))|(~(quiet(Y)&humble(Y)&brave(Y)&old(Y)&creative(Y)&person(Y)))))&(richer(X,Y))))& (~(happy(thomas)&generous(thomas)&brave(thomas)&person(thomas)))& ((old(thomas))&(tall(erica)))& (~((~(creative(kenneth)&person(kenneth)))|(~(calm(kenneth)&person(kenneth)))))& (![X]:(room(X)=>(((((~(curious(X)&calm(X)&brave(X)&person(X)))|(kind(X))))<=(~(brave(X)&curious(X)&person(X)))))))& (patient(erica))& (tall(thomas))& (~(old(thomas)&person(thomas)))& (![X]:(room(X)=>(~(funny(X)&generous(X)&person(X)))))& (![X]:(room(X)=>(((~((~(patient(X)&tall(X)&calm(X)&person(X)))|(strong(X))))<=(((kind(X))&(~(calm(X)&wise(X)&strong(X)&person(X)))&(~(strong(X)&funny(X)&calm(X)&person(X)))))))))& (![X]:(room(X)=>(((brave(X))<=(~((~(generous(X)&person(X)))|(~(happy(X)&person(X)))))))))& (~![X]:(room(X)=>(((~(funny(X)&person(X)))<=(brave(X))))))& (quiet(kenneth))
room(erica)&room(kenneth)&room(thomas)&(![X]:(room(X)=>(X='erica'|X='kenneth'|X='thomas')))& ~(funny(kenneth)&quiet(kenneth)&tall(kenneth)&generous(kenneth)&wise(kenneth)&person(kenneth))&~(funny(erica)&quiet(erica)&tall(erica)&generous(erica)&wise(erica)&person(erica))
[ "p0", "p7", "p10", "p16", "p21", "hypothesis" ]
% SZS status Unsatisfiable for 7056720107237951118133181 % SZS output start Proof for 7056720107237951118133181 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 51. funny(paul) [input p7] 54. funny(mary) [input p10] 60. ~(~(person(paul) & calm(paul)) | ~(person(paul) & creative(paul))) [input p16] 65. ! [X0] : (room(X0) => ~(person(X0) & generous(X0) & funny(X0))) [input p21] 70. ~(~(person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) & ~(person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 72. ~(~(person(paul) & calm(paul)) | ~person(paul)) [pure predicate removal 60] 144. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 144] 160. (person(paul) & calm(paul)) & person(paul) [ennf transformation 72] 161. person(paul) & calm(paul) & person(paul) [flattening 160] 165. ! [X0] : ((~person(X0) | ~generous(X0) | ~funny(X0)) | ~room(X0)) [ennf transformation 65] 166. ! [X0] : (~person(X0) | ~generous(X0) | ~funny(X0) | ~room(X0)) [flattening 165] 173. (person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) | (person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 174. (person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) | (person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 173] 178. (person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) | ~sP2 [predicate definition introduction] 179. (person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) | ~sP3 [predicate definition introduction] 180. sP3 | sP2 | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 174,179,178] 188. (person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) | ~sP3 [nnf transformation 179] 189. (person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) | ~sP2 [nnf transformation 178] 190. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 191. sP3 | sP2 | (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 180,190] 273. room(mary) [cnf transformation 145] 274. room(paul) [cnf transformation 145] 275. room(fred) [cnf transformation 145] 276. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 145] 284. funny(paul) [cnf transformation 51] 288. funny(mary) [cnf transformation 54] 306. person(paul) [cnf transformation 161] 313. ~funny(X0) | ~generous(X0) | ~person(X0) | ~room(X0) [cnf transformation 166] 336. generous(mary) | ~sP3 [cnf transformation 188] 338. person(mary) | ~sP3 [cnf transformation 188] 342. generous(paul) | ~sP2 [cnf transformation 189] 345. sP3 | sP2 | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 346. sP3 | sP2 | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 347. sP3 | sP2 | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 348. sP3 | sP2 | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 375. 6 <=> person(mary) [avatar definition] 376. person(mary) <- (6) [avatar component clause 375] 415. 13 <=> sP3 [avatar definition] 418. ~13 | 6 [avatar split clause 338,375,415] 425. 15 <=> generous(mary) [avatar definition] 428. ~13 | 15 [avatar split clause 336,425,415] 435. 17 <=> sP2 [avatar definition] 444. 19 <=> generous(paul) [avatar definition] 447. ~17 | 19 [avatar split clause 342,444,435] 453. sP3 | sP2 | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 348,275] 454. sP3 | sP2 | fred != sK7 | ~room(mary) [subsumption resolution 453,274] 455. sP3 | sP2 | fred != sK7 [subsumption resolution 454,273] 457. 21 <=> fred = sK7 [avatar definition] 459. fred != sK7 <- (~21) [avatar component clause 457] 460. ~21 | 17 | 13 [avatar split clause 455,415,435,457] 461. sP3 | sP2 | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 347,275] 462. sP3 | sP2 | paul != sK7 | ~room(mary) [subsumption resolution 461,274] 463. sP3 | sP2 | paul != sK7 [subsumption resolution 462,273] 465. 22 <=> paul = sK7 [avatar definition] 467. paul != sK7 <- (~22) [avatar component clause 465] 468. ~22 | 17 | 13 [avatar split clause 463,415,435,465] 469. sP3 | sP2 | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 346,275] 470. sP3 | sP2 | mary != sK7 | ~room(mary) [subsumption resolution 469,274] 471. sP3 | sP2 | mary != sK7 [subsumption resolution 470,273] 473. 23 <=> mary = sK7 [avatar definition] 475. mary != sK7 <- (~23) [avatar component clause 473] 476. ~23 | 17 | 13 [avatar split clause 471,415,435,473] 477. sP3 | sP2 | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 345,275] 478. sP3 | sP2 | room(sK7) | ~room(mary) [subsumption resolution 477,274] 479. sP3 | sP2 | room(sK7) [subsumption resolution 478,273] 481. 24 <=> room(sK7) [avatar definition] 483. room(sK7) <- (24) [avatar component clause 481] 484. 24 | 17 | 13 [avatar split clause 479,415,435,481] 509. ~generous(paul) | ~person(paul) | ~room(paul) [resolution 313,284] 510. ~generous(mary) | ~person(mary) | ~room(mary) [resolution 313,288] 518. ~generous(mary) | ~room(mary) <- (6) [subsumption resolution 510,376] 519. ~generous(mary) <- (6) [subsumption resolution 518,273] 520. ~15 | ~6 [avatar split clause 519,375,425] 521. ~generous(paul) | ~room(paul) [subsumption resolution 509,306] 522. ~generous(paul) [subsumption resolution 521,274] 523. ~19 [avatar split clause 522,444] 650. paul = sK7 | mary = sK7 | fred = sK7 <- (24) [resolution 276,483] 677. mary = sK7 | fred = sK7 <- (~22, 24) [subsumption resolution 650,467] 678. fred = sK7 <- (~22, ~23, 24) [subsumption resolution 677,475] 679. $false <- (~21, ~22, ~23, 24) [subsumption resolution 678,459] 680. 21 | 22 | 23 | ~24 [avatar contradiction clause 679] 681. $false [avatar sat refutation 418,428,447,460,468,476,484,520,523,680] % SZS output end Proof for 7056720107237951118133181 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------
0.455242
Dolores is the only person in the room. Everyone in the room who enjoys skydiving creates large-scale murals for public art installations. Everyone in the room who creates large-scale murals for public art installations is not a wine connoisseur. Everyone in the room who does not enjoy mountain biking has completed a triathlon. Everyone in the room is a wine connoisseur. Everyone in the room does not own a smartwatch if they enjoys camping and organizing outdoor survival workshops. Everyone in the room who does not own a smartwatch is a cybersecurity expert. Everyone in the room does not enjoy mountain biking. If someone enjoys deep-sea diving and exploring underwater caves then he/she can play the piano.
Dolores creates large-scale murals for public art installations.
contradiction
room(dolores)&(![X]:(room(X)=>(X='dolores')))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(is_not_a_wine_connoisseur(X))))))& (![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))=>(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(is_a_wine_connoisseur(X))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(does_not_own_a_smartwatch(X))))))& (![X]:(room(X)=>(((does_not_own_a_smartwatch(X))=>(is_a_cybersecurity_expert(X))))))& (![X]:(room(X)=>(does_not_enjoy_mountain_biking(X))))& ((![X]:((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(can_play_the_piano(X)))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(cannot_play_the_piano(X))))))
room(dolores)&(![X]:(room(X)=>(X='dolores')))& creates_large-scale_murals_for_public_art_installations(dolores)
[ "p0", "p2", "p4", "hypothesis" ]
% SZS status Unsatisfiable for 3701151112101134083905999 % SZS output start Proof for 3701151112101134083905999 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (predk(X0) => ~predl(X0))) [input p2] 48. ! [X0] : (room(X0) => predl(X0)) [input p4] 56. predk(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 138. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 139. ! [X0] : ((~predl(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 46] 140. ! [X0] : (~predl(X0) | ~predk(X0) | ~room(X0)) [flattening 139] 141. ! [X0] : (predl(X0) | ~room(X0)) [ennf transformation 48] 142. predk(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56] 224. room(mary) [cnf transformation 138] 226. ~predl(X0) | ~predk(X0) | ~room(X0) [cnf transformation 140] 227. ~room(X0) | predl(X0) [cnf transformation 141] 230. predk(mary) [cnf transformation 142] 231. predl(mary) [resolution 227,224] 233. ~predk(mary) | ~room(mary) [resolution 226,231] 234. ~room(mary) [subsumption resolution 233,230] 235. $false [subsumption resolution 234,224] % SZS output end Proof for 3701151112101134083905999 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0.645604
Daniel, Clyde, Lillian are the only persons in the room. At least one person outside the room has a curated collection of mid-century modern furniture. Only one person in the room is an expert in identifying and foraging wild edible plants. Everyone in the room enjoys skydiving. Everyone anywhere composes and performs experimental electronic music only if they enjoys skydiving. Everyone in the room who enjoys skydiving works on fridays. Everyone in the room enjoys snowboarding if they writes and illustrates their own graphic novels. Everyone anywhere writes and illustrates their own graphic novels. Everyone in the room who is a scotch connoisseur practices kickboxing. Everyone in the room who enjoys snowboarding practices kickboxing. Everyone in the room who practices kickboxing enjoys making ceramics. Everyone in the room is right-handed if they enjoys making ceramics. Daniel is a scotch connoisseur. Everyone in the room who travels domestically frequently practices pilates. Daniel dreamt that 'everyone in the room who practices pilates is a Linux enthusiast'.
More than one person in the room does not enjoy making ceramics.
contradiction
room(daniel)&room(clyde)&room(lillian)&(![X]:(room(X)=>(X='daniel'|X='clyde'|X='lillian')))& (((?[X]:(~room(X)&has_a_curated_collection_of_mid-century_modern_furniture(X)))))& (((?[X]:(room(X)&is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))&(![X,Y]:((room(X)&room(Y)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(Y)))=>(X=Y)))))& (![X]:(room(X)=>(enjoys_skydiving(X))))& (![X]:(anywhere(X)=>(((enjoys_skydiving(X))<=(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(works_on_fridays(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(enjoys_snowboarding(X))))))& (![X]:(anywhere(X)=>(writes_and_illustrates_their_own_graphic_novels(X))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(practices_kickboxing(X))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))=>(practices_kickboxing(X))))))& (![X]:(room(X)=>(((practices_kickboxing(X))=>(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(is_right-handed(X))))))& (is_a_scotch_connoisseur(daniel))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(practices_pilates(X))))))& ((daniel_dream=>(![X]:(room(X)=>(((practices_pilates(X))=>(is_a_Linux_enthusiast(X))))))))
room(daniel)&room(clyde)&room(lillian)&(![X]:(room(X)=>(X='daniel'|X='clyde'|X='lillian')))& (?[X,Y]:(room(X)&room(Y)&(does_not_enjoy_making_ceramics(X)&does_not_enjoy_making_ceramics(Y))&(X!=Y)))
[ "b4", "p6", "p7", "p9", "p10", "hypothesis" ]
% SZS status Unsatisfiable for 4540673811718692406362128 % SZS output start Proof for 4540673811718692406362128 5. ! [X0] : anywhere(X0) [input b4] 50. ! [X0] : (room(X0) => (predt(X0) => predn(X0))) [input p6] 51. ! [X0] : (anywhere(X0) => predt(X0)) [input p7] 53. ! [X0] : (room(X0) => (predn(X0) => preda(X0))) [input p9] 54. ! [X0] : (room(X0) => (preda(X0) => prede(X0))) [input p10] 59. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 61. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (fred = X2 | paul = X2 | mary = X2)) & room(fred) & room(paul) & room(mary) [rectify 59] 144. ! [X0] : ((predn(X0) | ~predt(X0)) | ~room(X0)) [ennf transformation 50] 145. ! [X0] : (predn(X0) | ~predt(X0) | ~room(X0)) [flattening 144] 146. ! [X0] : (predt(X0) | ~anywhere(X0)) [ennf transformation 51] 149. ! [X0] : ((preda(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 53] 150. ! [X0] : (preda(X0) | ~predn(X0) | ~room(X0)) [flattening 149] 151. ! [X0] : ((prede(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 54] 152. ! [X0] : (prede(X0) | ~preda(X0) | ~room(X0)) [flattening 151] 153. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : ((fred = X2 | paul = X2 | mary = X2) | ~room(X2)) & room(fred) & room(paul) & room(mary) [ennf transformation 61] 154. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [flattening 153] 160. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) => (sK2 != sK3 & ~prede(sK3) & ~prede(sK2) & room(sK3) & room(sK2)) [choice axiom] 161. (sK2 != sK3 & ~prede(sK3) & ~prede(sK2) & room(sK3) & room(sK2)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [skolemisation 154,160] 162. anywhere(X0) [cnf transformation 5] 251. ~predt(X0) | predn(X0) | ~room(X0) [cnf transformation 145] 252. predt(X0) | ~anywhere(X0) [cnf transformation 146] 254. ~predn(X0) | preda(X0) | ~room(X0) [cnf transformation 150] 255. ~preda(X0) | prede(X0) | ~room(X0) [cnf transformation 152] 261. room(sK2) [cnf transformation 161] 263. ~prede(sK2) [cnf transformation 161] 266. predt(X0) [subsumption resolution 252,162] 267. ~room(X0) | predn(X0) [resolution 251,266] 274. predn(sK2) [resolution 267,261] 285. preda(sK2) | ~room(sK2) [resolution 274,254] 286. preda(sK2) [subsumption resolution 285,261] 295. prede(sK2) | ~room(sK2) [resolution 286,255] 296. ~room(sK2) [subsumption resolution 295,263] 297. $false [subsumption resolution 296,261] % SZS output end Proof for 4540673811718692406362128 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------
0.384836
Barbara, Keith are the only persons in the room. Everyone in the room who plays as a goalkeeper for a local amateur soccer team either is a drone photographer or is a chess master who participates in national tournaments but not both. Barbara creates bespoke furniture pieces from reclaimed wood. Barbara who enjoys skydiving is not a wine connoisseur. Everyone in the room plays as a goalkeeper for a local amateur soccer team if they neither is a chess master who participates in national tournaments nor plays as a goalkeeper for a local amateur soccer team. Barbara creates bespoke furniture pieces from reclaimed wood and collects action figures. Everyone in the room is a drone photographer if they owns a high-end gaming PC with custom-built components, has lived in exactly three countries and does not host regular workshops on creative writing. Everyone anywhere does not host regular workshops on creative writing if they is a drone photographer. It is not the case that “Barbara is a client of LVMH”. Everyone in the room neither plays as a goalkeeper for a local amateur soccer team nor does not host regular workshops on creative writing.
Everyone in the room is not a drone photographer or creates bespoke furniture pieces from reclaimed wood.
entailment
room(barbara)&room(keith)&(![X]:(room(X)=>(X='barbara'|X='keith')))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(((is_a_drone_photographer(X))<~>(is_a_chess_master_who_participates_in_national_tournaments(X))))))))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(barbara))& ((enjoys_skydiving(barbara))&(is_not_a_wine_connoisseur(barbara)))& (![X]:(room(X)=>(((~((is_a_chess_master_who_participates_in_national_tournaments(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (((creates_bespoke_furniture_pieces_from_reclaimed_wood(barbara))&(collects_action_figures(barbara))))& (![X]:(room(X)=>(((((owns_a_high-end_gaming_PC_with_custom-built_components(X))&(has_lived_in_exactly_three_countries(X))&(does_not_host_regular_workshops_on_creative_writing(X))))=>(is_a_drone_photographer(X))))))& (![X]:(anywhere(X)=>(((is_a_drone_photographer(X))=>(does_not_host_regular_workshops_on_creative_writing(X))))))& (~(is_a_client_of_LVMH(barbara)))& (![X]:(room(X)=>(~((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))& (does_not_have_lived_in_exactly_three_countries(barbara))& (![X]:(~room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_not_a_wine_connoisseur(X))))))& (![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(collects_action_figures(X))))))))& (![X]:(room(X)=>(((is_not_a_client_of_LVMH(X))<=(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (~(is_a_wine_connoisseur(barbara)))
room(barbara)&room(keith)&(![X]:(room(X)=>(X='barbara'|X='keith')))& ![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(is_not_a_drone_photographer(X)))))
[ "b4", "p0", "p2", "p7", "p9", "hypothesis" ]
% SZS status Unsatisfiable for 2970291334195471237552021 % SZS output start Proof for 2970291334195471237552021 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. predd(mary) [input p2] 51. ! [X0] : (anywhere(X0) => (predg(X0) => ~predc(X0))) [input p7] 53. ! [X0] : (room(X0) => ~(~predc(X0) | predb(X0))) [input p9] 59. ~(! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 60. ~(! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary)) [rectify 59] 142. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 142] 148. ! [X0] : ((~predc(X0) | ~predg(X0)) | ~anywhere(X0)) [ennf transformation 51] 149. ! [X0] : (~predc(X0) | ~predg(X0) | ~anywhere(X0)) [flattening 148] 150. ! [X0] : ((predc(X0) & ~predb(X0)) | ~room(X0)) [ennf transformation 53] 151. ? [X0] : ((predg(X0) & ~predd(X0)) & room(X0)) | ? [X1] : ((paul != X1 & mary != X1) & room(X1)) | ~room(paul) | ~room(mary) [ennf transformation 60] 152. ? [X0] : (predg(X0) & ~predd(X0) & room(X0)) | ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~room(paul) | ~room(mary) [flattening 151] 153. ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 154. ? [X0] : (predg(X0) & ~predd(X0) & room(X0)) | sP0 | ~room(paul) | ~room(mary) [definition folding 152,153] 157. ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 153] 158. ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 157] 159. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 160. (paul != sK1 & mary != sK1 & room(sK1)) | ~sP0 [skolemisation 158,159] 161. ? [X0] : (predg(X0) & ~predd(X0) & room(X0)) => (predg(sK2) & ~predd(sK2) & room(sK2)) [choice axiom] 162. (predg(sK2) & ~predd(sK2) & room(sK2)) | sP0 | ~room(paul) | ~room(mary) [skolemisation 154,161] 163. anywhere(X0) [cnf transformation 5] 244. room(mary) [cnf transformation 143] 245. room(paul) [cnf transformation 143] 246. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 143] 249. predd(mary) [cnf transformation 46] 252. ~predc(X0) | ~predg(X0) | ~anywhere(X0) [cnf transformation 149] 254. ~room(X0) | predc(X0) [cnf transformation 150] 255. room(sK1) | ~sP0 [cnf transformation 160] 256. mary != sK1 | ~sP0 [cnf transformation 160] 257. paul != sK1 | ~sP0 [cnf transformation 160] 258. room(sK2) | sP0 | ~room(paul) | ~room(mary) [cnf transformation 162] 259. ~predd(sK2) | sP0 | ~room(paul) | ~room(mary) [cnf transformation 162] 260. predg(sK2) | sP0 | ~room(paul) | ~room(mary) [cnf transformation 162] 262. ~predc(X0) | ~predg(X0) [subsumption resolution 252,163] 264. 1 <=> sP0 [avatar definition] 268. 2 <=> paul = sK1 [avatar definition] 270. paul != sK1 <- (~2) [avatar component clause 268] 271. ~1 | ~2 [avatar split clause 257,268,264] 273. 3 <=> mary = sK1 [avatar definition] 276. ~1 | ~3 [avatar split clause 256,273,264] 278. 4 <=> room(sK1) [avatar definition] 280. room(sK1) <- (4) [avatar component clause 278] 281. ~1 | 4 [avatar split clause 255,278,264] 282. predg(sK2) | sP0 | ~room(mary) [subsumption resolution 260,245] 283. predg(sK2) | sP0 [subsumption resolution 282,244] 285. 5 <=> predg(sK2) [avatar definition] 287. predg(sK2) <- (5) [avatar component clause 285] 288. 1 | 5 [avatar split clause 283,285,264] 289. ~predd(sK2) | sP0 | ~room(mary) [subsumption resolution 259,245] 290. ~predd(sK2) | sP0 [subsumption resolution 289,244] 292. 6 <=> predd(sK2) [avatar definition] 294. ~predd(sK2) <- (~6) [avatar component clause 292] 295. 1 | ~6 [avatar split clause 290,292,264] 296. room(sK2) | sP0 | ~room(mary) [subsumption resolution 258,245] 297. room(sK2) | sP0 [subsumption resolution 296,244] 299. 7 <=> room(sK2) [avatar definition] 301. room(sK2) <- (7) [avatar component clause 299] 302. 1 | 7 [avatar split clause 297,299,264] 304. predc(paul) [resolution 254,245] 307. ~predg(paul) [resolution 304,262] 356. mary = sK2 | paul = sK2 <- (7) [resolution 246,301] 358. 16 <=> paul = sK2 [avatar definition] 360. paul = sK2 <- (16) [avatar component clause 358] 362. 17 <=> mary = sK2 [avatar definition] 364. mary = sK2 <- (17) [avatar component clause 362] 365. 16 | 17 | ~7 [avatar split clause 356,299,362,358] 366. mary = sK1 | paul = sK1 <- (4) [resolution 280,246] 372. mary = sK1 <- (~2, 4) [subsumption resolution 366,270] 373. 3 | 2 | ~4 [avatar split clause 372,278,268,273] 375. predg(paul) <- (5, 16) [backward demodulation 287,360] 377. $false <- (5, 16) [subsumption resolution 375,307] 378. ~5 | ~16 [avatar contradiction clause 377] 389. ~predd(mary) <- (~6, 17) [backward demodulation 294,364] 395. $false <- (~6, 17) [subsumption resolution 389,249] 396. 6 | ~17 [avatar contradiction clause 395] 400. $false [avatar sat refutation 271,276,281,288,295,302,365,373,378,396] % SZS output end Proof for 2970291334195471237552021 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s % ------------------------------ % ------------------------------
0.163762
David is the only person in the room. If “David is a curious happy person” then “David is not a brave person” otherwise “David is a client of Harry”. “David is creative” if “it is not the case that “David is a generous tourist”” and vice versa. If “David does not enjoy wildlife photography, does not collect first edition books and is a curious european” then “David is patient”. If “David is a wise curious tourist” then “David does not maintain a personal blog focused on cybersecurity tips”. If “David does not maintain a personal blog focused on cybersecurity tips” then “David is kind”. If “David is a calm kind person” then “if someone is not a client of Meta then he/she does not enjoy cross-country skiing and vice versa” otherwise “David is not a tea enthusiast”. If “David is a brave european” then “David is a sibling of James”. If “David is a curious european” then “David is a client of James”. If “David is a client of James” then “William and David like each other”. If “Eddie and David like each other” then “everyone in the room is a patient curious tall generous person”. If “everyone in the room is a patient curious tall generous person” then “James is a client of David”. Everyone in the room is a client of Eddie if they is not a wine connoisseur with a private cellar of vintage wines. David is a tall tourist. David is a curious tourist. David does not enjoy bird watching. David is not a wine connoisseur with a private cellar of vintage wines. David is patient. All funny person is happy. Everyone in the room is a client of James if they is patient or is a happy tourist or both. David is a wise tourist. Not everyone anywhere writes and illustrates their own graphic novels if they is a brave tourist. David does not enjoy wildlife photography, does not collect first edition books and is a curious european. David is a creative european.
David enjoys bird watching.
contradiction
room(david)&(![X]:(room(X)=>(X='david')))& (((curious(david)&happy(david)&person(david))=>(~(brave(david)&person(david))))&((~(curious(david)&happy(david)&person(david)))=>(client(harry,david))))& ((~(generous(david)&tourist(david)))<=>(creative(david)))& ((((does_not_enjoy_wildlife_photography(david))&(does_not_collect_first_edition_books(david))&(curious(david)&european(david))))=>(patient(david)))& (((wise(david)&curious(david)&tourist(david))=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(david)))& ((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(david))=>(kind(david))))& (((calm(david)&kind(david)&person(david))=>((![X]:((is_not_a_client_of_Meta(X))<=>(does_not_enjoy_cross-country_skiing(X))))))&((~(calm(david)&kind(david)&person(david)))=>(is_not_a_tea_enthusiast(david))))& ((brave(david)&european(david))=>(sibling(james,david)))& (((curious(david)&european(david))=>(client(james,david)))& ((client(james,david))=>((like(william,david) & like(david,william)))))& ((((like(eddie,david) & like(david,eddie)))=>(![X]:(room(X)=>(patient(X)&curious(X)&tall(X)&generous(X)&person(X)))))& ((![X]:(room(X)=>(patient(X)&curious(X)&tall(X)&generous(X)&person(X))))=>(client(david,james))))& (![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(client(eddie,X))))))& (tall(david)&tourist(david))& (curious(david)&tourist(david))& (does_not_enjoy_bird_watching(david))& (is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(david))& (patient(david))& (![X]:(funny(X)=>happy(X)))& (![X]:(room(X)=>(((((patient(X))|(happy(X)&tourist(X))))=>(client(james,X))))))& (wise(david)&tourist(david))& (~![X]:(anywhere(X)=>(((brave(X)&tourist(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (((does_not_enjoy_wildlife_photography(david))&(does_not_collect_first_edition_books(david))&(curious(david)&european(david))))& (creative(david)&european(david))
room(david)&(![X]:(room(X)=>(X='david')))& enjoys_bird_watching(david)
[ "p0", "hypothesis" ]
% SZS status Unsatisfiable for 5467823218994063979606709 % SZS output start Proof for 5467823218994063979606709 44. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ~! [X0] : (anywhere(X0) => ((tourist(X0) & brave(X0)) => predi(X0))) & tourist(mary) & wise(mary) & ! [X0] : (room(X0) => (((tourist(X0) & happy(X0)) | patient(X0)) => client(susan,X0))) & ! [X0] : (funny(X0) => happy(X0)) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X0] : (room(X0) => (~predk(X0) => client(lucy,X0))) & (! [X0] : (room(X0) => (person(X0) & generous(X0) & tall(X0) & curious(X0) & patient(X0))) => client(mary,susan)) & ((like(mary,lucy) & like(lucy,mary)) => ! [X0] : (room(X0) => (person(X0) & generous(X0) & tall(X0) & curious(X0) & patient(X0)))) & (client(susan,mary) => (like(mary,john) & like(john,mary))) & ((european(mary) & curious(mary)) => client(susan,mary)) & ((european(mary) & brave(mary)) => sibling(alice,mary)) & (~(person(mary) & kind(mary) & calm(mary)) => ~predl(mary)) & ((person(mary) & kind(mary) & calm(mary)) => ! [X0] : (~predm(X0) <=> ~preds(X0))) & (~predz(mary) => kind(mary)) & ((tourist(mary) & curious(mary) & wise(mary)) => ~predz(mary)) & ((european(mary) & curious(mary) & ~predw(mary) & ~predb(mary)) => patient(mary)) & (~(tourist(mary) & generous(mary)) <=> creative(mary)) & (~(person(mary) & happy(mary) & curious(mary)) => client(fred,mary)) & ((person(mary) & happy(mary) & curious(mary)) => ~(person(mary) & brave(mary))) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. predj(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 46. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ~! [X0] : (anywhere(X0) => ((tourist(X0) & brave(X0)) => predi(X0))) & tourist(mary) & wise(mary) & ! [X1] : (room(X1) => (((tourist(X1) & happy(X1)) | patient(X1)) => client(susan,X1))) & ! [X2] : (funny(X2) => happy(X2)) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (room(X3) => (~predk(X3) => client(lucy,X3))) & (! [X4] : (room(X4) => (person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4))) => client(mary,susan)) & ((like(mary,lucy) & like(lucy,mary)) => ! [X5] : (room(X5) => (person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)))) & (client(susan,mary) => (like(mary,john) & like(john,mary))) & ((european(mary) & curious(mary)) => client(susan,mary)) & ((european(mary) & brave(mary)) => sibling(alice,mary)) & (~(person(mary) & kind(mary) & calm(mary)) => ~predl(mary)) & ((person(mary) & kind(mary) & calm(mary)) => ! [X6] : (~predm(X6) <=> ~preds(X6))) & (~predz(mary) => kind(mary)) & ((tourist(mary) & curious(mary) & wise(mary)) => ~predz(mary)) & ((european(mary) & curious(mary) & ~predw(mary) & ~predb(mary)) => patient(mary)) & (~(tourist(mary) & generous(mary)) <=> creative(mary)) & (~(person(mary) & happy(mary) & curious(mary)) => client(fred,mary)) & ((person(mary) & happy(mary) & curious(mary)) => ~(person(mary) & brave(mary))) & ! [X7] : (room(X7) => mary = X7) & room(mary) [rectify 44] 47. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ~! [X0] : (anywhere(X0) => ~(tourist(X0) & brave(X0))) & tourist(mary) & wise(mary) & ! [X1] : (room(X1) => (((tourist(X1) & happy(X1)) | patient(X1)) => client(susan,X1))) & ! [X2] : (funny(X2) => happy(X2)) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (room(X3) => (~predk(X3) => client(lucy,X3))) & (! [X4] : (room(X4) => (person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4))) => client(mary,susan)) & ((like(mary,lucy) & like(lucy,mary)) => ! [X5] : (room(X5) => (person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)))) & (client(susan,mary) => (like(mary,john) & like(john,mary))) & ((european(mary) & curious(mary)) => client(susan,mary)) & ((european(mary) & brave(mary)) => sibling(alice,mary)) & (~(person(mary) & kind(mary) & calm(mary)) => ~predl(mary)) & ((person(mary) & kind(mary) & calm(mary)) => ! [X6] : (~predm(X6) <=> ~preds(X6))) & (~predz(mary) => kind(mary)) & ((tourist(mary) & curious(mary) & wise(mary)) => ~predz(mary)) & ((european(mary) & curious(mary) & ~predw(mary) & ~predb(mary)) => patient(mary)) & (~(tourist(mary) & generous(mary)) <=> creative(mary)) & (~(person(mary) & happy(mary) & curious(mary)) => client(fred,mary)) & ((person(mary) & happy(mary) & curious(mary)) => ~(person(mary) & brave(mary))) & ! [X7] : (room(X7) => mary = X7) & room(mary) [pure predicate removal 46] 48. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ~! [X0] : (anywhere(X0) => ~(tourist(X0) & brave(X0))) & tourist(mary) & wise(mary) & ! [X1] : (room(X1) => (((tourist(X1) & happy(X1)) | patient(X1)) => client(susan,X1))) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (room(X3) => (~predk(X3) => client(lucy,X3))) & (! [X4] : (room(X4) => (person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4))) => client(mary,susan)) & ((like(mary,lucy) & like(lucy,mary)) => ! [X5] : (room(X5) => (person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)))) & (client(susan,mary) => (like(mary,john) & like(john,mary))) & ((european(mary) & curious(mary)) => client(susan,mary)) & ((european(mary) & brave(mary)) => sibling(alice,mary)) & (~(person(mary) & kind(mary) & calm(mary)) => ~predl(mary)) & ((person(mary) & kind(mary) & calm(mary)) => ! [X6] : (~predm(X6) <=> ~preds(X6))) & (~predz(mary) => kind(mary)) & ((tourist(mary) & curious(mary) & wise(mary)) => ~predz(mary)) & ((european(mary) & curious(mary) & ~predw(mary) & ~predb(mary)) => patient(mary)) & (~(tourist(mary) & generous(mary)) <=> creative(mary)) & (~(person(mary) & happy(mary) & curious(mary)) => client(fred,mary)) & ((person(mary) & happy(mary) & curious(mary)) => ~(person(mary) & brave(mary))) & ! [X7] : (room(X7) => mary = X7) & room(mary) [pure predicate removal 47] 49. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ~! [X0] : (anywhere(X0) => ~(tourist(X0) & brave(X0))) & tourist(mary) & wise(mary) & ! [X1] : (room(X1) => (((tourist(X1) & happy(X1)) | patient(X1)) => client(susan,X1))) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (room(X3) => (~predk(X3) => client(lucy,X3))) & (! [X4] : (room(X4) => (person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4))) => client(mary,susan)) & ((like(mary,lucy) & like(lucy,mary)) => ! [X5] : (room(X5) => (person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)))) & (client(susan,mary) => (like(mary,john) & like(john,mary))) & ((european(mary) & curious(mary)) => client(susan,mary)) & ((european(mary) & brave(mary)) => sibling(alice,mary)) & ((person(mary) & kind(mary) & calm(mary)) => ! [X6] : (~predm(X6) <=> ~preds(X6))) & (~predz(mary) => kind(mary)) & ((tourist(mary) & curious(mary) & wise(mary)) => ~predz(mary)) & ((european(mary) & curious(mary) & ~predw(mary) & ~predb(mary)) => patient(mary)) & (~(tourist(mary) & generous(mary)) <=> creative(mary)) & (~(person(mary) & happy(mary) & curious(mary)) => client(fred,mary)) & ((person(mary) & happy(mary) & curious(mary)) => ~(person(mary) & brave(mary))) & ! [X7] : (room(X7) => mary = X7) & room(mary) [pure predicate removal 48] 50. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ~! [X0] : (anywhere(X0) => ~(tourist(X0) & brave(X0))) & tourist(mary) & wise(mary) & ! [X1] : (room(X1) => (((tourist(X1) & happy(X1)) | patient(X1)) => client(susan,X1))) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (room(X3) => (~predk(X3) => client(lucy,X3))) & (! [X4] : (room(X4) => (person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4))) => client(mary,susan)) & ((like(mary,lucy) & like(lucy,mary)) => ! [X5] : (room(X5) => (person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)))) & (client(susan,mary) => (like(mary,john) & like(john,mary))) & ((european(mary) & curious(mary)) => client(susan,mary)) & ((european(mary) & brave(mary)) => sibling(alice,mary)) & (~predz(mary) => kind(mary)) & ((tourist(mary) & curious(mary) & wise(mary)) => ~predz(mary)) & ((european(mary) & curious(mary) & ~predw(mary) & ~predb(mary)) => patient(mary)) & (~(tourist(mary) & generous(mary)) <=> creative(mary)) & (~(person(mary) & happy(mary) & curious(mary)) => client(fred,mary)) & ((person(mary) & happy(mary) & curious(mary)) => ~(person(mary) & brave(mary))) & ! [X7] : (room(X7) => mary = X7) & room(mary) [pure predicate removal 49] 51. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ~! [X0] : (anywhere(X0) => ~(tourist(X0) & brave(X0))) & tourist(mary) & wise(mary) & ! [X1] : (room(X1) => (((tourist(X1) & happy(X1)) | patient(X1)) => client(susan,X1))) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (room(X3) => (~predk(X3) => client(lucy,X3))) & (! [X4] : (room(X4) => (person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4))) => client(mary,susan)) & ((like(mary,lucy) & like(lucy,mary)) => ! [X5] : (room(X5) => (person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)))) & (client(susan,mary) => (like(mary,john) & like(john,mary))) & ((european(mary) & curious(mary)) => client(susan,mary)) & ((european(mary) & brave(mary)) => sibling(alice,mary)) & ((tourist(mary) & curious(mary) & wise(mary)) => ~predz(mary)) & ((european(mary) & curious(mary) & ~predw(mary) & ~predb(mary)) => patient(mary)) & (~(tourist(mary) & generous(mary)) <=> creative(mary)) & (~(person(mary) & happy(mary) & curious(mary)) => client(fred,mary)) & ((person(mary) & happy(mary) & curious(mary)) => ~(person(mary) & brave(mary))) & ! [X7] : (room(X7) => mary = X7) & room(mary) [pure predicate removal 50] 52. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ~! [X0] : (anywhere(X0) => ~(tourist(X0) & brave(X0))) & tourist(mary) & wise(mary) & ! [X1] : (room(X1) => (((tourist(X1) & happy(X1)) | patient(X1)) => client(susan,X1))) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (room(X3) => (~predk(X3) => client(lucy,X3))) & (! [X4] : (room(X4) => (person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4))) => client(mary,susan)) & ((like(mary,lucy) & like(lucy,mary)) => ! [X5] : (room(X5) => (person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)))) & (client(susan,mary) => (like(mary,john) & like(john,mary))) & ((european(mary) & curious(mary)) => client(susan,mary)) & ((european(mary) & brave(mary)) => sibling(alice,mary)) & ((european(mary) & curious(mary) & ~predw(mary) & ~predb(mary)) => patient(mary)) & (~(tourist(mary) & generous(mary)) <=> creative(mary)) & (~(person(mary) & happy(mary) & curious(mary)) => client(fred,mary)) & ((person(mary) & happy(mary) & curious(mary)) => ~(person(mary) & brave(mary))) & ! [X7] : (room(X7) => mary = X7) & room(mary) [pure predicate removal 51] 53. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ~! [X0] : (anywhere(X0) => ~(tourist(X0) & brave(X0))) & tourist(mary) & ! [X1] : (room(X1) => (((tourist(X1) & happy(X1)) | patient(X1)) => client(susan,X1))) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (room(X3) => (~predk(X3) => client(lucy,X3))) & (! [X4] : (room(X4) => (person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4))) => client(mary,susan)) & ((like(mary,lucy) & like(lucy,mary)) => ! [X5] : (room(X5) => (person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)))) & (client(susan,mary) => (like(mary,john) & like(john,mary))) & ((european(mary) & curious(mary)) => client(susan,mary)) & ((european(mary) & brave(mary)) => sibling(alice,mary)) & ((european(mary) & curious(mary) & ~predw(mary) & ~predb(mary)) => patient(mary)) & (~(tourist(mary) & generous(mary)) <=> creative(mary)) & (~(person(mary) & happy(mary) & curious(mary)) => client(fred,mary)) & ((person(mary) & happy(mary) & curious(mary)) => ~(person(mary) & brave(mary))) & ! [X7] : (room(X7) => mary = X7) & room(mary) [pure predicate removal 52] 54. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ~! [X0] : ~(tourist(X0) & brave(X0)) & tourist(mary) & ! [X1] : (room(X1) => (((tourist(X1) & happy(X1)) | patient(X1)) => client(susan,X1))) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (room(X3) => (~predk(X3) => client(lucy,X3))) & (! [X4] : (room(X4) => (person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4))) => client(mary,susan)) & ((like(mary,lucy) & like(lucy,mary)) => ! [X5] : (room(X5) => (person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)))) & (client(susan,mary) => (like(mary,john) & like(john,mary))) & ((european(mary) & curious(mary)) => client(susan,mary)) & ((european(mary) & brave(mary)) => sibling(alice,mary)) & ((european(mary) & curious(mary) & ~predw(mary) & ~predb(mary)) => patient(mary)) & (~(tourist(mary) & generous(mary)) <=> creative(mary)) & (~(person(mary) & happy(mary) & curious(mary)) => client(fred,mary)) & ((person(mary) & happy(mary) & curious(mary)) => ~(person(mary) & brave(mary))) & ! [X7] : (room(X7) => mary = X7) & room(mary) [pure predicate removal 53] 127. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ? [X0] : (tourist(X0) & brave(X0)) & tourist(mary) & ! [X1] : ((client(susan,X1) | ((~tourist(X1) | ~happy(X1)) & ~patient(X1))) | ~room(X1)) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : ((client(lucy,X3) | predk(X3)) | ~room(X3)) & (client(mary,susan) | ? [X4] : ((~person(X4) | ~generous(X4) | ~tall(X4) | ~curious(X4) | ~patient(X4)) & room(X4))) & (! [X5] : ((person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)) | ~room(X5)) | (~like(mary,lucy) | ~like(lucy,mary))) & ((like(mary,john) & like(john,mary)) | ~client(susan,mary)) & (client(susan,mary) | (~european(mary) | ~curious(mary))) & (sibling(alice,mary) | (~european(mary) | ~brave(mary))) & (patient(mary) | (~european(mary) | ~curious(mary) | predw(mary) | predb(mary))) & ((~tourist(mary) | ~generous(mary)) <=> creative(mary)) & (client(fred,mary) | (person(mary) & happy(mary) & curious(mary))) & ((~person(mary) | ~brave(mary)) | (~person(mary) | ~happy(mary) | ~curious(mary))) & ! [X7] : (mary = X7 | ~room(X7)) & room(mary) [ennf transformation 54] 128. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ? [X0] : (tourist(X0) & brave(X0)) & tourist(mary) & ! [X1] : (client(susan,X1) | ((~tourist(X1) | ~happy(X1)) & ~patient(X1)) | ~room(X1)) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (client(lucy,X3) | predk(X3) | ~room(X3)) & (client(mary,susan) | ? [X4] : ((~person(X4) | ~generous(X4) | ~tall(X4) | ~curious(X4) | ~patient(X4)) & room(X4))) & (! [X5] : ((person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)) | ~room(X5)) | ~like(mary,lucy) | ~like(lucy,mary)) & ((like(mary,john) & like(john,mary)) | ~client(susan,mary)) & (client(susan,mary) | ~european(mary) | ~curious(mary)) & (sibling(alice,mary) | ~european(mary) | ~brave(mary)) & (patient(mary) | ~european(mary) | ~curious(mary) | predw(mary) | predb(mary)) & ((~tourist(mary) | ~generous(mary)) <=> creative(mary)) & (client(fred,mary) | (person(mary) & happy(mary) & curious(mary))) & (~person(mary) | ~brave(mary) | ~person(mary) | ~happy(mary) | ~curious(mary)) & ! [X7] : (mary = X7 | ~room(X7)) & room(mary) [flattening 127] 129. predj(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 45] 131. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ? [X0] : (tourist(X0) & brave(X0)) & tourist(mary) & ! [X1] : (client(susan,X1) | ((~tourist(X1) | ~happy(X1)) & ~patient(X1)) | ~room(X1)) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (client(lucy,X3) | predk(X3) | ~room(X3)) & (client(mary,susan) | ? [X4] : ((~person(X4) | ~generous(X4) | ~tall(X4) | ~curious(X4) | ~patient(X4)) & room(X4))) & (! [X5] : ((person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)) | ~room(X5)) | ~like(mary,lucy) | ~like(lucy,mary)) & ((like(mary,john) & like(john,mary)) | ~client(susan,mary)) & (client(susan,mary) | ~european(mary) | ~curious(mary)) & (sibling(alice,mary) | ~european(mary) | ~brave(mary)) & (patient(mary) | ~european(mary) | ~curious(mary) | predw(mary) | predb(mary)) & (((~tourist(mary) | ~generous(mary)) | ~creative(mary)) & (creative(mary) | (tourist(mary) & generous(mary)))) & (client(fred,mary) | (person(mary) & happy(mary) & curious(mary))) & (~person(mary) | ~brave(mary) | ~person(mary) | ~happy(mary) | ~curious(mary)) & ! [X7] : (mary = X7 | ~room(X7)) & room(mary) [nnf transformation 128] 132. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ? [X0] : (tourist(X0) & brave(X0)) & tourist(mary) & ! [X1] : (client(susan,X1) | ((~tourist(X1) | ~happy(X1)) & ~patient(X1)) | ~room(X1)) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X3] : (client(lucy,X3) | predk(X3) | ~room(X3)) & (client(mary,susan) | ? [X4] : ((~person(X4) | ~generous(X4) | ~tall(X4) | ~curious(X4) | ~patient(X4)) & room(X4))) & (! [X5] : ((person(X5) & generous(X5) & tall(X5) & curious(X5) & patient(X5)) | ~room(X5)) | ~like(mary,lucy) | ~like(lucy,mary)) & ((like(mary,john) & like(john,mary)) | ~client(susan,mary)) & (client(susan,mary) | ~european(mary) | ~curious(mary)) & (sibling(alice,mary) | ~european(mary) | ~brave(mary)) & (patient(mary) | ~european(mary) | ~curious(mary) | predw(mary) | predb(mary)) & (~tourist(mary) | ~generous(mary) | ~creative(mary)) & (creative(mary) | (tourist(mary) & generous(mary))) & (client(fred,mary) | (person(mary) & happy(mary) & curious(mary))) & (~person(mary) | ~brave(mary) | ~person(mary) | ~happy(mary) | ~curious(mary)) & ! [X7] : (mary = X7 | ~room(X7)) & room(mary) [flattening 131] 133. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & ? [X0] : (tourist(X0) & brave(X0)) & tourist(mary) & ! [X1] : (client(susan,X1) | ((~tourist(X1) | ~happy(X1)) & ~patient(X1)) | ~room(X1)) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X2] : (client(lucy,X2) | predk(X2) | ~room(X2)) & (client(mary,susan) | ? [X3] : ((~person(X3) | ~generous(X3) | ~tall(X3) | ~curious(X3) | ~patient(X3)) & room(X3))) & (! [X4] : ((person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4)) | ~room(X4)) | ~like(mary,lucy) | ~like(lucy,mary)) & ((like(mary,john) & like(john,mary)) | ~client(susan,mary)) & (client(susan,mary) | ~european(mary) | ~curious(mary)) & (sibling(alice,mary) | ~european(mary) | ~brave(mary)) & (patient(mary) | ~european(mary) | ~curious(mary) | predw(mary) | predb(mary)) & (~tourist(mary) | ~generous(mary) | ~creative(mary)) & (creative(mary) | (tourist(mary) & generous(mary))) & (client(fred,mary) | (person(mary) & happy(mary) & curious(mary))) & (~person(mary) | ~brave(mary) | ~person(mary) | ~happy(mary) | ~curious(mary)) & ! [X5] : (mary = X5 | ~room(X5)) & room(mary) [rectify 132] 134. ? [X0] : (tourist(X0) & brave(X0)) => (tourist(sK0) & brave(sK0)) [choice axiom] 135. ? [X3] : ((~person(X3) | ~generous(X3) | ~tall(X3) | ~curious(X3) | ~patient(X3)) & room(X3)) => ((~person(sK1) | ~generous(sK1) | ~tall(sK1) | ~curious(sK1) | ~patient(sK1)) & room(sK1)) [choice axiom] 136. european(mary) & creative(mary) & european(mary) & curious(mary) & ~predw(mary) & ~predb(mary) & (tourist(sK0) & brave(sK0)) & tourist(mary) & ! [X1] : (client(susan,X1) | ((~tourist(X1) | ~happy(X1)) & ~patient(X1)) | ~room(X1)) & patient(mary) & ~predk(mary) & ~predj(mary) & tourist(mary) & curious(mary) & tourist(mary) & tall(mary) & ! [X2] : (client(lucy,X2) | predk(X2) | ~room(X2)) & (client(mary,susan) | ((~person(sK1) | ~generous(sK1) | ~tall(sK1) | ~curious(sK1) | ~patient(sK1)) & room(sK1))) & (! [X4] : ((person(X4) & generous(X4) & tall(X4) & curious(X4) & patient(X4)) | ~room(X4)) | ~like(mary,lucy) | ~like(lucy,mary)) & ((like(mary,john) & like(john,mary)) | ~client(susan,mary)) & (client(susan,mary) | ~european(mary) | ~curious(mary)) & (sibling(alice,mary) | ~european(mary) | ~brave(mary)) & (patient(mary) | ~european(mary) | ~curious(mary) | predw(mary) | predb(mary)) & (~tourist(mary) | ~generous(mary) | ~creative(mary)) & (creative(mary) | (tourist(mary) & generous(mary))) & (client(fred,mary) | (person(mary) & happy(mary) & curious(mary))) & (~person(mary) | ~brave(mary) | ~person(mary) | ~happy(mary) | ~curious(mary)) & ! [X5] : (mary = X5 | ~room(X5)) & room(mary) [skolemisation 133,135,134] 245. ~predj(mary) [cnf transformation 136] 261. predj(mary) [cnf transformation 129] 366. $false [subsumption resolution 261,245] % SZS output end Proof for 5467823218994063979606709 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------
0.084036
Eunice, Martha, Adela, Michael, Michael are the only persons in the room. More than one person in the room is a quiet person. Martha is the least old in the room. No quiet person is kind. Martha is the richest in the room. At least one person anywhere is not a tall person. No tall person is kind. Someone in the room is not a quiet person. If someone is a tall person then he/she is a old person and vice versa. At least one person outside the room is not a old person.
Eunice is kind.
contradiction
room(eunice)&room(martha)&room(adela)&room(michael)&room(michael)&(![X]:(room(X)=>(X='eunice'|X='martha'|X='adela'|X='michael'|X='michael')))& ((?[X,Y]:(room(X)&room(Y)&(quiet(X)&person(X)&quiet(Y)&person(Y))&(X!=Y))))& (![X]:((room(X)&(X!=martha))=>older(martha,X)))& (~?[X]:(quiet(X)=>kind(X)))& (![X]:((room(X)&(X!=martha))=>richer(X,martha)))& (((?[X]:(anywhere(X)&~(tall(X)&person(X))))))& (~?[X]:(tall(X)=>kind(X)))& (?[X]:(room(X)&(~(quiet(X)&person(X)))))& ((![X]:((tall(X)&person(X))<=>(old(X)&person(X)))))& (((?[X]:(~room(X)&~(old(X)&person(X))))))
room(eunice)&room(martha)&room(adela)&room(michael)&room(michael)&(![X]:(room(X)=>(X='eunice'|X='martha'|X='adela'|X='michael'|X='michael')))& kind(eunice)
[ "p3", "hypothesis" ]
% SZS status Unsatisfiable for 7483781755545709077600831 % SZS output start Proof for 7483781755545709077600831 47. ~? [X0] : (quiet(X0) => kind(X0)) [input p3] 54. kind(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] 132. ! [X0] : (~kind(X0) & quiet(X0)) [ennf transformation 47] 139. kind(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 140. kind(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 139] 247. ~kind(X0) [cnf transformation 132] 266. kind(mary) [cnf transformation 140] 279. $false [subsumption resolution 266,247] % SZS output end Proof for 7483781755545709077600831 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------
0.573372
Victor, Maria, Sarah, Denny are the only persons in the room. If Sarah plays as a goalkeeper for a local amateur soccer team then Maria does not enjoy windsurfing. If Denny has a saltwater aquarium then more than one person in the room enjoys camping and organizing outdoor survival workshops or does not enjoy macrame or both. If at least one person in the room enjoys windsurfing or does not enjoy camping and organizing outdoor survival workshops or both then Denny enjoys salsa dancing. If someone does not practice urban gardening then he/she practices tai chi and vice versa. Maria enjoys salsa dancing. If someone does not practice tai chi then he/she has a saltwater aquarium, enjoys macrame or plays video games. It is true that Victor plays as a goalkeeper for a local amateur soccer team. Victor enjoys windsurfing. More than one person in the room enjoys salsa dancing, practices tai chi and enjoys rooftop gardening. Maria practices urban gardening. Maria does not enjoy windsurfing. Victor neither plays video games nor enjoys salsa dancing. It is true that if someone enjoys skydiving then he/she enjoys salsa dancing or enjoys windsurfing or both and vice versa. More than one person in the room practices tai chi. Someone in the room has a saltwater aquarium. Maria enjoys camping and organizing outdoor survival workshops.
Denny has a saltwater aquarium.
neutral
room(victor)&room(maria)&room(sarah)&room(denny)&(![X]:(room(X)=>(X='victor'|X='maria'|X='sarah'|X='denny')))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(sarah))=>(does_not_enjoy_windsurfing(maria)))& ((has_a_saltwater_aquarium(denny))=>((?[X,Y]:(room(X)&room(Y)&(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_enjoy_macrame(X)))&((enjoys_camping_and_organizing_outdoor_survival_workshops(Y))|(does_not_enjoy_macrame(Y))))&(X!=Y)))))& ((((?[X]:(room(X)&((enjoys_windsurfing(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X)))))))=>(enjoys_salsa_dancing(denny)))& ((![X]:((does_not_practice_urban_gardening(X))<=>(practices_tai_chi(X)))))& (enjoys_salsa_dancing(maria))& ((![X]:((does_not_practice_tai_chi(X))=>(((has_a_saltwater_aquarium(X))|(enjoys_macrame(X))|(plays_video_games(X)))))))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(victor))& (enjoys_windsurfing(victor))& ((?[X,Y]:(room(X)&room(Y)&(((enjoys_salsa_dancing(X))&(practices_tai_chi(X))&(enjoys_rooftop_gardening(X)))&((enjoys_salsa_dancing(Y))&(practices_tai_chi(Y))&(enjoys_rooftop_gardening(Y))))&(X!=Y))))& (practices_urban_gardening(maria))& (does_not_enjoy_windsurfing(maria))& (~((plays_video_games(victor))|(enjoys_salsa_dancing(victor))))& ((![X]:((enjoys_skydiving(X))<=>(((enjoys_salsa_dancing(X))|(enjoys_windsurfing(X)))))))& ((?[X,Y]:(room(X)&room(Y)&(practices_tai_chi(X)&practices_tai_chi(Y))&(X!=Y))))& (?[X]:(room(X)&(has_a_saltwater_aquarium(X))))& (enjoys_camping_and_organizing_outdoor_survival_workshops(maria))
room(victor)&room(maria)&room(sarah)&room(denny)&(![X]:(room(X)=>(X='victor'|X='maria'|X='sarah'|X='denny')))& has_a_saltwater_aquarium(denny)
[]
null
0.184482
There is a room. Either “at least one person in the room neither bakes bread at home nor enjoys virtual reality gaming” or “everyone in the room writes and illustrates their own graphic novels or does not host a YouTube channel dedicated to art tutorials” but not both. “No one outside the room writes and illustrates their own graphic novels or does not enjoy stargazing” if “everyone anywhere enjoys landscape photography or does not own a high-end gaming PC with custom-built components” and vice versa. Everyone in the room owns a high-end gaming PC with custom-built components or does not maintain a large, organic vegetable garden year-round. Everyone in the room owns a high-end gaming PC with custom-built components if they enjoys virtual reality gaming and vice versa. Everyone in the room who bakes bread at home enjoys stargazing and enjoys virtual reality gaming. Everyone in the room enjoys stargazing only if they uses contact lenses. Not everyone in the room enjoys stargazing or bakes bread at home or both if and only if they neither enjoys virtual reality gaming nor uses contact lenses. Everyone in the room neither enjoys virtual reality gaming nor uses contact lenses if they hosts a YouTube channel dedicated to art tutorials and vice versa. Everyone in the room hosts a YouTube channel dedicated to art tutorials if they maintains a large, organic vegetable garden year-round or enjoys stand-up paddleboarding or both and vice versa.
Everyone in the room maintains a large, organic vegetable garden year-round.
contradiction
(there_is_a_room)& ((((?[X]:(room(X)&~((bakes_bread_at_home(X))|(enjoys_virtual_reality_gaming(X)))))))<~>(![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(writes_and_illustrates_their_own_graphic_novels(X)))))))& ((![X]:(anywhere(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(enjoys_landscape_photography(X))))))<=>(~?[X]:(~room(X)=>(((does_not_enjoy_stargazing(X))|(writes_and_illustrates_their_own_graphic_novels(X)))))))& (((![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(~![X]:(room(X)=>(((enjoys_stargazing(X))=>(plays_video_games(X)))))))&((~(![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))=>(![X]:(~room(X)=>(((plays_video_games(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))))& (((![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))=>(![X]:(~room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(writes_and_illustrates_their_own_graphic_novels(X)))))))&((~(![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))))=>(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))<=>(enjoys_landscape_photography(X))))))))& ((![X]:(room(X)=>(((does_not_enjoy_landscape_photography(X))|(enjoys_stand-up_paddleboarding(X))))))=>(((?[X]:(room(X)&owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(~room(X)=>(((plays_video_games(X))=>(~((enjoys_stargazing(X))|(enjoys_virtual_reality_gaming(X))))))))& (![X]:(room(X)=>(((~((enjoys_stargazing(X))|(enjoys_virtual_reality_gaming(X))))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(plays_video_games(X))))))))& (![X]:(room(X)=>(((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(plays_video_games(X))))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (((?[X]:(room(X)&owns_a_high-end_gaming_PC_with_custom-built_components(X)))))& (![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))<=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((bakes_bread_at_home(X))=>(((enjoys_stargazing(X))&(enjoys_virtual_reality_gaming(X))))))))& (((?[X]:(room(X)&((enjoys_landscape_photography(X))|(enjoys_stand-up_paddleboarding(X)))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))<=(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((does_not_play_video_games(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=>(((enjoys_stargazing(X))|(bakes_bread_at_home(X))))))))& (~![X]:(room(X)=>(((((enjoys_stargazing(X))|(bakes_bread_at_home(X))))<=>(~((enjoys_virtual_reality_gaming(X))|(uses_contact_lenses(X))))))))& (![X]:(room(X)=>(((~((enjoys_virtual_reality_gaming(X))|(uses_contact_lenses(X))))<=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))<=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(enjoys_stand-up_paddleboarding(X))))))))& (![X]:(room(X)=>(((((maintains_a_large,_organic_vegetable_garden_year-round(X))|(enjoys_stand-up_paddleboarding(X))))=>(((uses_contact_lenses(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(bakes_bread_at_home(X))))))))& (![X]:(room(X)=>(((((uses_contact_lenses(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(bakes_bread_at_home(X))))=>(((plays_video_games(X))|(writes_and_illustrates_their_own_graphic_novels(X))))))))
(there_is_a_room)& ![X]:(room(X)=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))
[ "p11", "p12", "p14", "p16", "p19", "p20", "p21", "hypothesis" ]
% SZS status Unsatisfiable for 3743331454343702235272471 % SZS output start Proof for 3743331454343702235272471 55. ! [X0] : (room(X0) => (predg(X0) | ~predc(X0))) [input p11] 56. ! [X0] : (room(X0) => (predg(X0) <=> predh(X0))) [input p12] 58. ! [X0] : (room(X0) => (predd(X0) => (predh(X0) & prede(X0)))) [input p14] 60. ! [X0] : (room(X0) => (prede(X0) => predi(X0))) [input p16] 63. ~! [X0] : (room(X0) => ((predd(X0) | prede(X0)) <=> ~(predi(X0) | predh(X0)))) [input p19] 64. ! [X0] : (room(X0) => (~(predi(X0) | predh(X0)) <=> preda(X0))) [input p20] 65. ! [X0] : (room(X0) => (preda(X0) <=> (predk(X0) | predc(X0)))) [input p21] 68. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 74. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 68] 165. ! [X0] : ((predg(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 55] 166. ! [X0] : (predg(X0) | ~predc(X0) | ~room(X0)) [flattening 165] 167. ! [X0] : ((predg(X0) <=> predh(X0)) | ~room(X0)) [ennf transformation 56] 169. ! [X0] : (((predh(X0) & prede(X0)) | ~predd(X0)) | ~room(X0)) [ennf transformation 58] 170. ! [X0] : ((predh(X0) & prede(X0)) | ~predd(X0) | ~room(X0)) [flattening 169] 171. ! [X0] : ((predi(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 60] 172. ! [X0] : (predi(X0) | ~prede(X0) | ~room(X0)) [flattening 171] 176. ? [X0] : (((predd(X0) | prede(X0)) <~> (~predi(X0) & ~predh(X0))) & room(X0)) [ennf transformation 63] 177. ! [X0] : (((~predi(X0) & ~predh(X0)) <=> preda(X0)) | ~room(X0)) [ennf transformation 64] 178. ! [X0] : ((preda(X0) <=> (predk(X0) | predc(X0))) | ~room(X0)) [ennf transformation 65] 183. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 74] 184. sP0 <=> ? [X0] : (~predh(X0) & ~predd(X0) & room(X0)) [predicate definition introduction] 191. (sP0 | ! [X0] : (predh(X0) | predd(X0) | ~room(X0))) & (? [X0] : (~predh(X0) & ~predd(X0) & room(X0)) | ~sP0) [nnf transformation 184] 192. (sP0 | ! [X0] : (predh(X0) | predd(X0) | ~room(X0))) & (? [X1] : (~predh(X1) & ~predd(X1) & room(X1)) | ~sP0) [rectify 191] 193. ? [X1] : (~predh(X1) & ~predd(X1) & room(X1)) => (~predh(sK3) & ~predd(sK3) & room(sK3)) [choice axiom] 194. (sP0 | ! [X0] : (predh(X0) | predd(X0) | ~room(X0))) & ((~predh(sK3) & ~predd(sK3) & room(sK3)) | ~sP0) [skolemisation 192,193] 224. ! [X0] : (((predg(X0) | ~predh(X0)) & (predh(X0) | ~predg(X0))) | ~room(X0)) [nnf transformation 167] 230. ? [X0] : ((((predi(X0) | predh(X0)) | (~predd(X0) & ~prede(X0))) & ((~predi(X0) & ~predh(X0)) | (predd(X0) | prede(X0)))) & room(X0)) [nnf transformation 176] 231. ? [X0] : ((predi(X0) | predh(X0) | (~predd(X0) & ~prede(X0))) & ((~predi(X0) & ~predh(X0)) | predd(X0) | prede(X0)) & room(X0)) [flattening 230] 232. ? [X0] : ((predi(X0) | predh(X0) | (~predd(X0) & ~prede(X0))) & ((~predi(X0) & ~predh(X0)) | predd(X0) | prede(X0)) & room(X0)) => ((predi(sK14) | predh(sK14) | (~predd(sK14) & ~prede(sK14))) & ((~predi(sK14) & ~predh(sK14)) | predd(sK14) | prede(sK14)) & room(sK14)) [choice axiom] 233. (predi(sK14) | predh(sK14) | (~predd(sK14) & ~prede(sK14))) & ((~predi(sK14) & ~predh(sK14)) | predd(sK14) | prede(sK14)) & room(sK14) [skolemisation 231,232] 234. ! [X0] : ((((~predi(X0) & ~predh(X0)) | ~preda(X0)) & (preda(X0) | (predi(X0) | predh(X0)))) | ~room(X0)) [nnf transformation 177] 235. ! [X0] : ((((~predi(X0) & ~predh(X0)) | ~preda(X0)) & (preda(X0) | predi(X0) | predh(X0))) | ~room(X0)) [flattening 234] 236. ! [X0] : (((preda(X0) | (~predk(X0) & ~predc(X0))) & ((predk(X0) | predc(X0)) | ~preda(X0))) | ~room(X0)) [nnf transformation 178] 237. ! [X0] : (((preda(X0) | (~predk(X0) & ~predc(X0))) & (predk(X0) | predc(X0) | ~preda(X0))) | ~room(X0)) [flattening 236] 319. room(sK3) | ~sP0 [cnf transformation 194] 321. ~predh(sK3) | ~sP0 [cnf transformation 194] 322. sP0 | predh(X0) | predd(X0) | ~room(X0) [cnf transformation 194] 361. ~predc(X0) | predg(X0) | ~room(X0) [cnf transformation 166] 362. ~predg(X0) | predh(X0) | ~room(X0) [cnf transformation 224] 366. ~predd(X0) | prede(X0) | ~room(X0) [cnf transformation 170] 367. ~predd(X0) | predh(X0) | ~room(X0) [cnf transformation 170] 370. ~prede(X0) | predi(X0) | ~room(X0) [cnf transformation 172] 375. room(sK14) [cnf transformation 233] 376. ~predh(sK14) | predd(sK14) | prede(sK14) [cnf transformation 233] 382. ~predi(X0) | ~preda(X0) | ~room(X0) [cnf transformation 235] 384. ~predc(X0) | preda(X0) | ~room(X0) [cnf transformation 237] 393. ~room(X0) | predc(X0) [cnf transformation 183] 395. 1 <=> ! [X0] : (predh(X0) | ~room(X0) | predd(X0)) [avatar definition] 396. predh(X0) | ~room(X0) | predd(X0) <- (1) [avatar component clause 395] 398. 2 <=> sP0 [avatar definition] 401. 1 | 2 [avatar split clause 322,398,395] 403. 3 <=> predh(sK3) [avatar definition] 405. ~predh(sK3) <- (~3) [avatar component clause 403] 406. ~2 | ~3 [avatar split clause 321,403,398] 413. 5 <=> room(sK3) [avatar definition] 415. room(sK3) <- (5) [avatar component clause 413] 416. ~2 | 5 [avatar split clause 319,413,398] 572. 39 <=> predd(sK14) [avatar definition] 573. predd(sK14) <- (39) [avatar component clause 572] 576. 40 <=> predh(sK14) [avatar definition] 580. 41 <=> predi(sK14) [avatar definition] 581. ~predi(sK14) <- (~41) [avatar component clause 580] 582. predi(sK14) <- (41) [avatar component clause 580] 585. 42 <=> prede(sK14) [avatar definition] 586. prede(sK14) <- (42) [avatar component clause 585] 590. 42 | 39 | ~40 [avatar split clause 376,576,572,585] 591. predc(sK3) <- (5) [resolution 393,415] 597. predc(sK14) [resolution 393,375] 598. predg(sK3) | ~room(sK3) <- (5) [resolution 361,591] 601. predg(sK3) <- (5) [subsumption resolution 598,415] 648. predh(sK3) | ~room(sK3) <- (5) [resolution 601,362] 649. ~room(sK3) <- (~3, 5) [subsumption resolution 648,405] 650. $false <- (~3, 5) [subsumption resolution 649,415] 651. 3 | ~5 [avatar contradiction clause 650] 653. ~room(X0) | predh(X0) <- (1) [subsumption resolution 396,367] 663. predh(sK14) <- (1) [resolution 653,375] 666. 40 | ~1 [avatar split clause 663,395,576] 669. predi(sK14) | ~room(sK14) <- (42) [resolution 586,370] 670. ~room(sK14) <- (~41, 42) [subsumption resolution 669,581] 671. $false <- (~41, 42) [subsumption resolution 670,375] 672. 41 | ~42 [avatar contradiction clause 671] 675. prede(sK14) | ~room(sK14) <- (39) [resolution 573,366] 681. prede(sK14) <- (39) [subsumption resolution 675,375] 682. 42 | ~39 [avatar split clause 681,572,585] 683. ~preda(sK14) | ~room(sK14) <- (41) [resolution 582,382] 684. ~preda(sK14) <- (41) [subsumption resolution 683,375] 693. preda(sK14) | ~room(sK14) [resolution 384,597] 704. ~room(sK14) <- (41) [subsumption resolution 693,684] 705. $false <- (41) [subsumption resolution 704,375] 706. ~41 [avatar contradiction clause 705] 707. $false [avatar sat refutation 401,406,416,590,651,666,672,682,706] % SZS output end Proof for 3743331454343702235272471 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------
0.057871
Nancy, Jon, Bennie are the only persons in the room. “Everyone outside the room either is not old, not quiet or is old but not both” if “Jon is a tall person”. Everyone in the room is older than Vesta if they is a tall person. If someone is not a tall person then he/she is quieter than Winfred or is not a old person or both. Someone in the room is richer than Winfred. Everyone in the room who is a tall person is a old tall person. Everyone in the room is old if they is a tall person. Nancy who is a quiet person is quieter than Vesta. Jon and Bennie are respectively tall and old. Bennie is older than Winfred. Jon is a quiet person, is a tall person or is a old tall person.
Jon is old.
entailment
room(nancy)&room(jon)&room(bennie)&(![X]:(room(X)=>(X='nancy'|X='jon'|X='bennie')))& ((tall(jon)&person(jon))=>(![X]:(~room(X)=>(((~old(X)&~quiet(X))<~>(old(X)))))))& (![X]:(room(X)=>(((tall(X)&person(X))=>(older(vesta,X))))))& ((![X]:((~(tall(X)&person(X)))=>(((quieter(winfred,X))|(~(old(X)&person(X))))))))& (?[X]:(room(X)&(richer(winfred,X))))& (![X]:(room(X)=>(((tall(X)&person(X))=>(old(X)&tall(X)&person(X))))))& (![X]:(room(X)=>(((tall(X)&person(X))=>(old(X))))))& ((quiet(nancy)&person(nancy))&(quieter(vesta,nancy)))& ((tall(jon))&(old(bennie)))& (older(winfred,bennie))& (((quiet(jon)&person(jon))|(tall(jon)&person(jon))|(old(jon)&tall(jon)&person(jon))))
room(nancy)&room(jon)&room(bennie)&(![X]:(room(X)=>(X='nancy'|X='jon'|X='bennie')))& old(jon)
[ "p0", "p5", "p8", "p10", "hypothesis" ]
% SZS status Unsatisfiable for 1700175557271582105842360 % SZS output start Proof for 1700175557271582105842360 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => ((person(X0) & tall(X0)) => (person(X0) & tall(X0) & old(X0)))) [input p5] 52. old(fred) & tall(paul) [input p8] 54. (person(paul) & tall(paul) & old(paul)) | (person(paul) & tall(paul)) | (person(paul) & quiet(paul)) [input p10] 55. ~(old(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 128. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 129. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 128] 136. ! [X0] : (((person(X0) & tall(X0) & old(X0)) | (~person(X0) | ~tall(X0))) | ~room(X0)) [ennf transformation 49] 137. ! [X0] : ((person(X0) & tall(X0) & old(X0)) | ~person(X0) | ~tall(X0) | ~room(X0)) [flattening 136] 140. ~old(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 55] 141. ~old(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 140] 142. (person(paul) & tall(paul) & old(paul)) | ~sP0 [predicate definition introduction] 143. sP0 | (person(paul) & tall(paul)) | (person(paul) & quiet(paul)) [definition folding 54,142] 149. (person(paul) & tall(paul) & old(paul)) | ~sP0 [nnf transformation 142] 150. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 151. ~old(paul) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 141,150] 232. room(mary) [cnf transformation 129] 233. room(paul) [cnf transformation 129] 234. room(fred) [cnf transformation 129] 235. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 129] 244. ~tall(X0) | ~person(X0) | old(X0) | ~room(X0) [cnf transformation 137] 251. tall(paul) [cnf transformation 52] 254. old(paul) | ~sP0 [cnf transformation 149] 260. sP0 | person(paul) | person(paul) [cnf transformation 143] 261. ~old(paul) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 151] 262. ~old(paul) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 151] 263. ~old(paul) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 151] 264. ~old(paul) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 151] 265. sP0 | person(paul) [duplicate literal removal 260] 267. 1 <=> tall(paul) [avatar definition] 268. tall(paul) <- (1) [avatar component clause 267] 271. 2 <=> person(paul) [avatar definition] 272. person(paul) <- (2) [avatar component clause 271] 278. 1 [avatar split clause 251,267] 280. 4 <=> sP0 [avatar definition] 286. 5 <=> old(paul) [avatar definition] 289. ~4 | 5 [avatar split clause 254,286,280] 290. 2 | 4 [avatar split clause 265,280,271] 298. ~old(paul) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 264,234] 299. ~old(paul) | fred != sK2 | ~room(mary) [subsumption resolution 298,233] 300. ~old(paul) | fred != sK2 [subsumption resolution 299,232] 302. 7 <=> fred = sK2 [avatar definition] 304. fred != sK2 <- (~7) [avatar component clause 302] 305. ~7 | ~5 [avatar split clause 300,286,302] 306. ~old(paul) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 263,234] 307. ~old(paul) | paul != sK2 | ~room(mary) [subsumption resolution 306,233] 308. ~old(paul) | paul != sK2 [subsumption resolution 307,232] 310. 8 <=> paul = sK2 [avatar definition] 312. paul != sK2 <- (~8) [avatar component clause 310] 313. ~8 | ~5 [avatar split clause 308,286,310] 314. ~old(paul) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 262,234] 315. ~old(paul) | mary != sK2 | ~room(mary) [subsumption resolution 314,233] 316. ~old(paul) | mary != sK2 [subsumption resolution 315,232] 318. 9 <=> mary = sK2 [avatar definition] 320. mary != sK2 <- (~9) [avatar component clause 318] 321. ~9 | ~5 [avatar split clause 316,286,318] 322. ~old(paul) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 261,234] 323. ~old(paul) | room(sK2) | ~room(mary) [subsumption resolution 322,233] 324. ~old(paul) | room(sK2) [subsumption resolution 323,232] 326. 10 <=> room(sK2) [avatar definition] 328. room(sK2) <- (10) [avatar component clause 326] 329. 10 | ~5 [avatar split clause 324,286,326] 331. ~person(paul) | old(paul) | ~room(paul) <- (1) [resolution 244,268] 332. old(paul) | ~room(paul) <- (1, 2) [subsumption resolution 331,272] 336. old(paul) <- (1, 2) [subsumption resolution 332,233] 337. 5 | ~1 | ~2 [avatar split clause 336,271,267,286] 484. paul = sK2 | mary = sK2 | fred = sK2 <- (10) [resolution 235,328] 498. mary = sK2 | fred = sK2 <- (~8, 10) [subsumption resolution 484,312] 499. fred = sK2 <- (~8, ~9, 10) [subsumption resolution 498,320] 500. $false <- (~7, ~8, ~9, 10) [subsumption resolution 499,304] 501. 7 | 8 | 9 | ~10 [avatar contradiction clause 500] 502. $false [avatar sat refutation 278,289,290,305,313,321,329,337,501] % SZS output end Proof for 1700175557271582105842360 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------
0
Wallace is the only person in the room. "At least one person in the room is a certified scuba diver with advanced underwater photography skills" if "Wallace enjoys macrame or creates augmented reality experiences for mobile applications or both". "It is true that "Wallace practices tai chi"" only if "everyone in the room owns a smart tv and reads mystery novels if they enjoys virtual reality gaming and vice versa". "Wallace enjoys windsurfing" only if "everyone in the room enjoys deep-sea diving and exploring underwater caves if they knows morse code and vice versa". If "Wallace enjoys macrame" then "Wallace neither enjoys macrame nor does not create YouTube content". "Wallace is a tea enthusiast" if "Wallace drives a hybrid car" and vice versa. "Wallace is not a tea enthusiast" only if "only one person outside the room creates YouTube content". Wallace who does not maintain a large, organic vegetable garden year-round, is a tea enthusiast and is not a wine connoisseur with a private cellar of vintage wines enjoys virtual reality gaming. Everyone in the room enjoys macrame and enjoys virtual reality gaming if they does not enjoy deep-sea diving and exploring underwater caves. Wallace who reads mystery novels, is a tea enthusiast and does not own a smartwatch does not build model airplanes. Wallace does not practice tai chi. Everyone in the room does not drive a hybrid car or does not build model airplanes. Everyone outside the room maintains a large, organic vegetable garden year-round if they does not drive a hybrid car. Wallace is a certified scuba diver with advanced underwater photography skills. Wallace enjoys bird watching or is a certified scuba diver with advanced underwater photography skills or both. Wallace enjoys deep-sea diving and exploring underwater caves. Wallace collects historical artifacts related to ancient civilizations. Wallace owns a smart tv and reads mystery novels. Wallace who is dedicated to sustainable living and zero-waste practices, owns a smart tv and collects first edition books is not dedicated to sustainable living and zero-waste practices or creates augmented reality experiences for mobile applications or both. No one anywhere who enjoys macrame or works on fridays or both does not drive a hybrid car. Everyone in the room who either makes homemade pastries or creates augmented reality experiences for mobile applications but not both makes homemade pastries, does not know morse code and is a wine connoisseur with a private cellar of vintage wines. Wallace enjoys bird watching, uses a Windows laptop and enjoys virtual reality gaming. Wallace creates augmented reality experiences for mobile applications.
Wallace practices tai chi.
contradiction
room(wallace)&(![X]:(room(X)=>(X='wallace')))& ((((enjoys_macrame(wallace))|(creates_augmented_reality_experiences_for_mobile_applications(wallace))))=>(((?[X]:(room(X)&is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& ((practices_tai_chi(wallace))=>(![X]:(room(X)=>(((((owns_a_smart_tv(X))&(reads_mystery_novels(X))))<=>(enjoys_virtual_reality_gaming(X)))))))& ((enjoys_windsurfing(wallace))=>(![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<=>(knows_morse_code(X)))))))& ((enjoys_macrame(wallace))=>(~((enjoys_macrame(wallace))|(does_not_create_YouTube_content(wallace)))))& ((drives_a_hybrid_car(wallace))<=>(is_a_tea_enthusiast(wallace)))& ((is_not_a_tea_enthusiast(wallace))=>(((?[X]:(~room(X)&creates_YouTube_content(X)))&(![X,Y]:((~room(X)&~room(Y)&(creates_YouTube_content(X))&(creates_YouTube_content(Y)))=>(X=Y))))))& ((((does_not_maintain_a_large,_organic_vegetable_garden_year-round(wallace))&(is_a_tea_enthusiast(wallace))&(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(wallace))))&(enjoys_virtual_reality_gaming(wallace)))& (![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))=>(((enjoys_macrame(X))&(enjoys_virtual_reality_gaming(X))))))))& ((((reads_mystery_novels(wallace))&(is_a_tea_enthusiast(wallace))&(does_not_own_a_smartwatch(wallace))))&(does_not_build_model_airplanes(wallace)))& (does_not_practice_tai_chi(wallace))& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))|(does_not_drive_a_hybrid_car(X))))))& (![X]:(~room(X)=>(((does_not_drive_a_hybrid_car(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(wallace))& (((enjoys_bird_watching(wallace))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(wallace))))& (enjoys_deep-sea_diving_and_exploring_underwater_caves(wallace))& (collects_historical_artifacts_related_to_ancient_civilizations(wallace))& (((owns_a_smart_tv(wallace))&(reads_mystery_novels(wallace))))& ((((is_dedicated_to_sustainable_living_and_zero-waste_practices(wallace))&(owns_a_smart_tv(wallace))&(collects_first_edition_books(wallace))))&(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(wallace))|(creates_augmented_reality_experiences_for_mobile_applications(wallace)))))& (~?[X]:(anywhere(X)=>(((((enjoys_macrame(X))|(works_on_fridays(X))))=>(does_not_drive_a_hybrid_car(X))))))& (![X]:(room(X)=>(((((makes_homemade_pastries(X))<~>(creates_augmented_reality_experiences_for_mobile_applications(X))))=>(((makes_homemade_pastries(X))&(does_not_know_morse_code(X))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))))& (((enjoys_bird_watching(wallace))&(uses_a_Windows_laptop(wallace))&(enjoys_virtual_reality_gaming(wallace))))& (creates_augmented_reality_experiences_for_mobile_applications(wallace))
room(wallace)&(![X]:(room(X)=>(X='wallace')))& practices_tai_chi(wallace)
[ "p10", "hypothesis" ]
% SZS status Unsatisfiable for 197630081244421958316751 % SZS output start Proof for 197630081244421958316751 54. ~predn(mary) [input p10] 67. predn(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 169. predn(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 67] 276. ~predn(mary) [cnf transformation 54] 292. predn(mary) [cnf transformation 169] 304. 3 <=> predn(mary) [avatar definition] 345. ~3 [avatar split clause 276,304] 353. 3 [avatar split clause 292,304] 354. $false [avatar sat refutation 345,353] % SZS output end Proof for 197630081244421958316751 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------
0.517435
Lisa, Jacinda, Christopher are the only persons in the room. Lisa who has a saltwater aquarium maintains a large, organic vegetable garden year-round and does not enjoy making ceramics. Everyone in the room practices urban gardening.
Christopher practices urban gardening.
entailment
room(lisa)&room(jacinda)&room(christopher)&(![X]:(room(X)=>(X='lisa'|X='jacinda'|X='christopher')))& ((has_a_saltwater_aquarium(lisa))&(((maintains_a_large,_organic_vegetable_garden_year-round(lisa))&(does_not_enjoy_making_ceramics(lisa)))))& (?[X]:(room(X)&(enjoys_bird_watching(X))))& (is_a_craft_beer_aficionado(jacinda))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))<=(((hosts_a_popular_podcast_about_emerging_technologies(X))&(uses_contact_lenses(X))))))))& (((?[X]:(room(X)&is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& (![X]:(room(X)=>(practices_urban_gardening(X))))& (![X]:(room(X)=>(((cannot_play_the_guitar(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(is_an_avid_hiker(X))))& (does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(lisa))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(lisa))& ((does_not_host_a_popular_podcast_about_emerging_technologies(lisa))&(does_not_use_contact_lenses(lisa)))& (own_a_television(jacinda))& ((enjoys_kayaking_and_exploring_remote_waterways(jacinda))&(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jacinda))<~>(makes_intricate_hand-cut_paper_art_for_exhibitions(jacinda)))))& (((hosts_a_popular_podcast_about_emerging_technologies(jacinda))&(uses_contact_lenses(jacinda))))
room(lisa)&room(jacinda)&room(christopher)&(![X]:(room(X)=>(X='lisa'|X='jacinda'|X='christopher')))& practices_urban_gardening(christopher)
[ "p0", "p6", "hypothesis" ]
% SZS status Unsatisfiable for 2386767609236754528303117 % SZS output start Proof for 2386767609236754528303117 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 50. ! [X0] : (room(X0) => predh(X0)) [input p6] 59. ~(predh(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 144. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 144] 146. ! [X0] : (predh(X0) | ~room(X0)) [ennf transformation 50] 147. ~predh(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 148. ~predh(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 147] 155. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 156. ~predh(fred) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 148,155] 237. room(mary) [cnf transformation 145] 238. room(paul) [cnf transformation 145] 239. room(fred) [cnf transformation 145] 240. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 145] 244. ~room(X0) | predh(X0) [cnf transformation 146] 251. ~predh(fred) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 252. ~predh(fred) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 253. ~predh(fred) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 254. ~predh(fred) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 265. ~predh(fred) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 254,239] 266. ~predh(fred) | fred != sK2 | ~room(mary) [subsumption resolution 265,238] 267. ~predh(fred) | fred != sK2 [subsumption resolution 266,237] 269. 3 <=> fred = sK2 [avatar definition] 271. fred != sK2 <- (~3) [avatar component clause 269] 273. 4 <=> predh(fred) [avatar definition] 276. ~3 | ~4 [avatar split clause 267,273,269] 277. ~predh(fred) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 253,239] 278. ~predh(fred) | paul != sK2 | ~room(mary) [subsumption resolution 277,238] 279. ~predh(fred) | paul != sK2 [subsumption resolution 278,237] 281. 5 <=> paul = sK2 [avatar definition] 283. paul != sK2 <- (~5) [avatar component clause 281] 284. ~5 | ~4 [avatar split clause 279,273,281] 285. ~predh(fred) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 252,239] 286. ~predh(fred) | mary != sK2 | ~room(mary) [subsumption resolution 285,238] 287. ~predh(fred) | mary != sK2 [subsumption resolution 286,237] 289. 6 <=> mary = sK2 [avatar definition] 291. mary != sK2 <- (~6) [avatar component clause 289] 292. ~6 | ~4 [avatar split clause 287,273,289] 293. ~predh(fred) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 251,239] 294. ~predh(fred) | room(sK2) | ~room(mary) [subsumption resolution 293,238] 295. ~predh(fred) | room(sK2) [subsumption resolution 294,237] 297. 7 <=> room(sK2) [avatar definition] 299. room(sK2) <- (7) [avatar component clause 297] 300. 7 | ~4 [avatar split clause 295,273,297] 303. predh(fred) [resolution 244,239] 308. 4 [avatar split clause 303,273] 351. paul = sK2 | mary = sK2 | fred = sK2 <- (7) [resolution 240,299] 378. mary = sK2 | fred = sK2 <- (~5, 7) [subsumption resolution 351,283] 379. fred = sK2 <- (~5, ~6, 7) [subsumption resolution 378,291] 380. $false <- (~3, ~5, ~6, 7) [subsumption resolution 379,271] 381. 3 | 5 | 6 | ~7 [avatar contradiction clause 380] 382. $false [avatar sat refutation 276,284,292,300,308,381] % SZS output end Proof for 2386767609236754528303117 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------
0.00386
Joseph, Jose, Russell, Louis are the only persons in the room. 'Jose collects antique clocks' if 'everyone in the room does not own a significant collection of rare gemstones and minerals or enjoys fishing'. 'No one in the room does not enjoy fishing or is a night owl' only if 'only one person anywhere writes a travel blog'. If 'everyone in the room enjoys salsa dancing or is not a dedicated volunteer for local community service projects' then 'Russell is a dedicated volunteer for local community service projects, does not collect comic books and creates YouTube content'. 'Everyone in the room does not enjoy stargazing or enjoys coding in Python' if 'everyone in the room does not enjoy camping and organizing outdoor survival workshops or uses a Windows laptop' and vice versa. If 'not everyone anywhere creates YouTube content' then 'Joseph collects antique clocks'. If 'Joseph collects antique clocks' then 'Jose who is an expert in identifying and foraging wild edible plants and collects classic novels plays video games'. Jose who is an expert in identifying and foraging wild edible plants and collects classic novels plays video games. Russell does not enjoy stargazing. Joseph collects comic books. Not everyone in the room who is not a night owl is an enthusiastic bird watcher who travels for rare sightings, is not a certified yoga instructor teaching classes weekly and writes a travel blog. Everyone in the room who is an enthusiastic bird watcher who travels for rare sightings, is not a certified yoga instructor teaching classes weekly and writes a travel blog is an expert in identifying and foraging wild edible plants. Jose is a night owl. Someone in the room collects comic books. Only one person in the room either collects comic books or enjoys coding in Python but not both. More than one person anywhere plays the drums. Everyone in the room who does not play the drums is a dedicated volunteer for local community service projects.
Jose plays video games.
entailment
room(joseph)&room(jose)&room(russell)&room(louis)&(![X]:(room(X)=>(X='joseph'|X='jose'|X='russell'|X='louis')))& ((![X]:(room(X)=>(((enjoys_fishing(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))=>(collects_antique_clocks(jose)))& ((~?[X]:(room(X)=>(((is_a_night_owl(X))|(does_not_enjoy_fishing(X))))))=>(((?[X]:(anywhere(X)&writes_a_travel_blog(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(writes_a_travel_blog(X))&(writes_a_travel_blog(Y)))=>(X=Y))))))& ((![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(enjoys_salsa_dancing(X))))))=>(((is_a_dedicated_volunteer_for_local_community_service_projects(russell))&(does_not_collect_comic_books(russell))&(creates_YouTube_content(russell)))))& ((![X]:(room(X)=>(((uses_a_Windows_laptop(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))<=>(![X]:(room(X)=>(((enjoys_coding_in_Python(X))|(does_not_enjoy_stargazing(X)))))))& (((~![X]:(anywhere(X)=>(creates_YouTube_content(X))))=>(collects_antique_clocks(joseph)))& ((collects_antique_clocks(joseph))=>((((is_an_expert_in_identifying_and_foraging_wild_edible_plants(jose))&(collects_classic_novels(jose))))&(plays_video_games(jose)))))& ((((is_an_expert_in_identifying_and_foraging_wild_edible_plants(jose))&(collects_classic_novels(jose))))&(plays_video_games(jose)))& (does_not_enjoy_stargazing(russell))& (collects_comic_books(joseph))& (~![X]:(room(X)=>(((is_not_a_night_owl(X))=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))&(writes_a_travel_blog(X))))))))& (![X]:(room(X)=>(((((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))&(writes_a_travel_blog(X))))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (is_a_night_owl(jose))& (?[X]:(room(X)&(collects_comic_books(X))))& (((?[X]:(room(X)&((collects_comic_books(X))<~>(enjoys_coding_in_Python(X)))))&(![X,Y]:((room(X)&room(Y)&(((collects_comic_books(X))<~>(enjoys_coding_in_Python(X))))&(((collects_comic_books(Y))<~>(enjoys_coding_in_Python(Y)))))=>(X=Y)))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(plays_the_drums(X)&plays_the_drums(Y))&(X!=Y))))& (![X]:(room(X)=>(((does_not_play_the_drums(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))
room(joseph)&room(jose)&room(russell)&room(louis)&(![X]:(room(X)=>(X='joseph'|X='jose'|X='russell'|X='louis')))& plays_video_games(jose)
[ "p0", "hypothesis" ]
% SZS status Unsatisfiable for 9182611586873005167494151 % SZS output start Proof for 9182611586873005167494151 44. ! [X0] : (room(X0) => (~predt(X0) => predk(X0))) & ? [X0,X1] : (X0 != X1 & predt(X1) & predt(X0) & anywhere(X1) & anywhere(X0)) & ! [X0,X1] : (((predc(X1) <~> predp(X1)) & (predc(X0) <~> predp(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : ((predc(X0) <~> predp(X0)) & room(X0)) & ? [X0] : (predc(X0) & room(X0)) & predj(paul) & ! [X0] : (room(X0) => ((predw(X0) & ~predz(X0) & predb(X0)) => predl(X0))) & ~! [X0] : (room(X0) => (~predj(X0) => (predw(X0) & ~predz(X0) & predb(X0)))) & predc(mary) & ~predg(fred) & predf(paul) & predv(paul) & predl(paul) & (predn(mary) => (predf(paul) & predv(paul) & predl(paul))) & (~! [X0] : (anywhere(X0) => predm(X0)) => predn(mary)) & (! [X0] : (room(X0) => (~preda(X0) | predq(X0))) <=> ! [X0] : (room(X0) => (~predg(X0) | predp(X0)))) & (! [X0] : (room(X0) => (predr(X0) | ~predk(X0))) => (predm(fred) & ~predc(fred) & predk(fred))) & (~? [X0] : (room(X0) => (~prede(X0) | predj(X0))) => (! [X0,X1] : ((predw(X1) & predw(X0) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X0] : (predw(X0) & anywhere(X0)))) & (! [X0] : (room(X0) => (~preds(X0) | prede(X0))) => predn(paul)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(predf(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : (room(X0) => (~predt(X0) => predk(X0))) & ? [X1,X2] : (X1 != X2 & predt(X2) & predt(X1) & anywhere(X2) & anywhere(X1)) & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ! [X7] : (room(X7) => ((predw(X7) & ~predz(X7) & predb(X7)) => predl(X7))) & ~! [X8] : (room(X8) => (~predj(X8) => (predw(X8) & ~predz(X8) & predb(X8)))) & predc(mary) & ~predg(fred) & predf(paul) & predv(paul) & predl(paul) & (predn(mary) => (predf(paul) & predv(paul) & predl(paul))) & (~! [X9] : (anywhere(X9) => predm(X9)) => predn(mary)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : (room(X12) => (predr(X12) | ~predk(X12))) => (predm(fred) & ~predc(fred) & predk(fred))) & (~? [X13] : (room(X13) => (~prede(X13) | predj(X13))) => (! [X14,X15] : ((predw(X15) & predw(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predw(X16) & anywhere(X16)))) & (! [X17] : (room(X17) => (~preds(X17) | prede(X17))) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ? [X1,X2] : (X1 != X2 & anywhere(X2) & anywhere(X1)) & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ! [X7] : (room(X7) => ((predw(X7) & ~predz(X7) & predb(X7)) => predl(X7))) & ~! [X8] : (room(X8) => (~predj(X8) => (predw(X8) & ~predz(X8) & predb(X8)))) & predc(mary) & ~predg(fred) & predf(paul) & predv(paul) & predl(paul) & (predn(mary) => (predf(paul) & predv(paul) & predl(paul))) & (~! [X9] : (anywhere(X9) => predm(X9)) => predn(mary)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : (room(X12) => (predr(X12) | ~predk(X12))) => (predm(fred) & ~predc(fred) & predk(fred))) & (~? [X13] : (room(X13) => (~prede(X13) | predj(X13))) => (! [X14,X15] : ((predw(X15) & predw(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predw(X16) & anywhere(X16)))) & (! [X17] : (room(X17) => (~preds(X17) | prede(X17))) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ? [X1,X2] : (X1 != X2 & anywhere(X2) & anywhere(X1)) & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ~! [X8] : (room(X8) => ~~predj(X8)) & predc(mary) & ~predg(fred) & predf(paul) & predv(paul) & predl(paul) & (predn(mary) => (predf(paul) & predv(paul) & predl(paul))) & (~! [X9] : (anywhere(X9) => predm(X9)) => predn(mary)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : (room(X12) => (predr(X12) | ~predk(X12))) => (predm(fred) & ~predc(fred) & predk(fred))) & (~? [X13] : (room(X13) => (~prede(X13) | predj(X13))) => (! [X14,X15] : ((predw(X15) & predw(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predw(X16) & anywhere(X16)))) & (! [X17] : (room(X17) => (~preds(X17) | prede(X17))) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ? [X1,X2] : (X1 != X2 & anywhere(X2) & anywhere(X1)) & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ~! [X8] : (room(X8) => ~~predj(X8)) & predc(mary) & ~predg(fred) & predf(paul) & predl(paul) & (predn(mary) => (predf(paul) & predl(paul))) & (~! [X9] : (anywhere(X9) => predm(X9)) => predn(mary)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : (room(X12) => (predr(X12) | ~predk(X12))) => (predm(fred) & ~predc(fred) & predk(fred))) & (~? [X13] : (room(X13) => (~prede(X13) | predj(X13))) => (! [X14,X15] : ((predw(X15) & predw(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predw(X16) & anywhere(X16)))) & (! [X17] : (room(X17) => (~preds(X17) | prede(X17))) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ? [X1,X2] : (X1 != X2 & anywhere(X2) & anywhere(X1)) & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ~! [X8] : (room(X8) => ~~predj(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predn(mary) => predf(paul)) & (~! [X9] : (anywhere(X9) => predm(X9)) => predn(mary)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : (room(X12) => (predr(X12) | ~predk(X12))) => (predm(fred) & ~predc(fred) & predk(fred))) & (~? [X13] : (room(X13) => (~prede(X13) | predj(X13))) => (! [X14,X15] : ((predw(X15) & predw(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predw(X16) & anywhere(X16)))) & (! [X17] : (room(X17) => (~preds(X17) | prede(X17))) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ? [X1,X2] : (X1 != X2 & anywhere(X2) & anywhere(X1)) & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ~! [X8] : (room(X8) => ~~predj(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predn(mary) => predf(paul)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : (room(X12) => (predr(X12) | ~predk(X12))) => (~predc(fred) & predk(fred))) & (~? [X13] : (room(X13) => (~prede(X13) | predj(X13))) => (! [X14,X15] : ((predw(X15) & predw(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predw(X16) & anywhere(X16)))) & (! [X17] : (room(X17) => (~preds(X17) | prede(X17))) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ? [X1,X2] : (X1 != X2 & anywhere(X2) & anywhere(X1)) & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ~! [X8] : (room(X8) => ~~predj(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predn(mary) => predf(paul)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : (room(X12) => ~predk(X12)) => (~predc(fred) & predk(fred))) & (~? [X13] : (room(X13) => (~prede(X13) | predj(X13))) => (! [X14,X15] : ((predw(X15) & predw(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predw(X16) & anywhere(X16)))) & (! [X17] : (room(X17) => (~preds(X17) | prede(X17))) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ? [X1,X2] : (X1 != X2 & anywhere(X2) & anywhere(X1)) & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ~! [X8] : (room(X8) => ~~predj(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predn(mary) => predf(paul)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : ~room(X12) => ~predc(fred)) & (~? [X13] : (room(X13) => (~prede(X13) | predj(X13))) => (! [X14,X15] : ((predw(X15) & predw(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predw(X16) & anywhere(X16)))) & (! [X17] : (room(X17) => (~preds(X17) | prede(X17))) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. ? [X1,X2] : (X1 != X2 & anywhere(X2) & anywhere(X1)) & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ~! [X8] : (room(X8) => ~~predj(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predn(mary) => predf(paul)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : ~room(X12) => ~predc(fred)) & (~? [X13] : (room(X13) => (~prede(X13) | predj(X13))) => (! [X14,X15] : ((predw(X15) & predw(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predw(X16) & anywhere(X16)))) & (! [X17] : (room(X17) => prede(X17)) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. ? [X1,X2] : (X1 != X2 & anywhere(X2) & anywhere(X1)) & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ~! [X8] : (room(X8) => ~~predj(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predn(mary) => predf(paul)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : ~room(X12) => ~predc(fred)) & (! [X17] : ~room(X17) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 56. ? [X1,X2] : X1 != X2 & ! [X3,X4] : (((predc(X4) <~> predp(X4)) & (predc(X3) <~> predp(X3)) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ~! [X8] : (room(X8) => ~~predj(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predn(mary) => predf(paul)) & (! [X10] : (room(X10) => (~preda(X10) | predq(X10))) <=> ! [X11] : (room(X11) => (~predg(X11) | predp(X11)))) & (! [X12] : ~room(X12) => ~predc(fred)) & (! [X17] : ~room(X17) => predn(paul)) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 55] 129. ? [X1,X2] : X1 != X2 & ! [X3,X4] : (X3 = X4 | ((predc(X4) <=> predp(X4)) | (predc(X3) <=> predp(X3)) | ~room(X4) | ~room(X3))) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ? [X8] : (~predj(X8) & room(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predf(paul) | ~predn(mary)) & (! [X10] : ((~preda(X10) | predq(X10)) | ~room(X10)) <=> ! [X11] : ((~predg(X11) | predp(X11)) | ~room(X11))) & (~predc(fred) | ? [X12] : room(X12)) & (predn(paul) | ? [X17] : room(X17)) & ! [X18] : ((alice = X18 | fred = X18 | paul = X18 | mary = X18) | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 56] 130. ? [X1,X2] : X1 != X2 & ! [X3,X4] : (X3 = X4 | (predc(X4) <=> predp(X4)) | (predc(X3) <=> predp(X3)) | ~room(X4) | ~room(X3)) & ? [X5] : ((predc(X5) <~> predp(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ? [X8] : (~predj(X8) & room(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predf(paul) | ~predn(mary)) & (! [X10] : (~preda(X10) | predq(X10) | ~room(X10)) <=> ! [X11] : (~predg(X11) | predp(X11) | ~room(X11))) & (~predc(fred) | ? [X12] : room(X12)) & (predn(paul) | ? [X17] : room(X17)) & ! [X18] : (alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 129] 131. ~predf(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 132. ~predf(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 131] 134. ? [X1,X2] : X1 != X2 & ! [X3,X4] : (X3 = X4 | ((predc(X4) | ~predp(X4)) & (predp(X4) | ~predc(X4))) | ((predc(X3) | ~predp(X3)) & (predp(X3) | ~predc(X3))) | ~room(X4) | ~room(X3)) & ? [X5] : (((~predp(X5) | ~predc(X5)) & (predp(X5) | predc(X5))) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ? [X8] : (~predj(X8) & room(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predf(paul) | ~predn(mary)) & ((! [X10] : (~preda(X10) | predq(X10) | ~room(X10)) | ? [X11] : (predg(X11) & ~predp(X11) & room(X11))) & (! [X11] : (~predg(X11) | predp(X11) | ~room(X11)) | ? [X10] : (preda(X10) & ~predq(X10) & room(X10)))) & (~predc(fred) | ? [X12] : room(X12)) & (predn(paul) | ? [X17] : room(X17)) & ! [X18] : (alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 130] 135. ? [X1,X2] : X1 != X2 & ! [X3,X4] : (X3 = X4 | ((predc(X4) | ~predp(X4)) & (predp(X4) | ~predc(X4))) | ((predc(X3) | ~predp(X3)) & (predp(X3) | ~predc(X3))) | ~room(X4) | ~room(X3)) & ? [X5] : ((~predp(X5) | ~predc(X5)) & (predp(X5) | predc(X5)) & room(X5)) & ? [X6] : (predc(X6) & room(X6)) & predj(paul) & ? [X8] : (~predj(X8) & room(X8)) & predc(mary) & ~predg(fred) & predf(paul) & (predf(paul) | ~predn(mary)) & (! [X10] : (~preda(X10) | predq(X10) | ~room(X10)) | ? [X11] : (predg(X11) & ~predp(X11) & room(X11))) & (! [X11] : (~predg(X11) | predp(X11) | ~room(X11)) | ? [X10] : (preda(X10) & ~predq(X10) & room(X10))) & (~predc(fred) | ? [X12] : room(X12)) & (predn(paul) | ? [X17] : room(X17)) & ! [X18] : (alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134] 136. ? [X0,X1] : X0 != X1 & ! [X2,X3] : (X2 = X3 | ((predc(X3) | ~predp(X3)) & (predp(X3) | ~predc(X3))) | ((predc(X2) | ~predp(X2)) & (predp(X2) | ~predc(X2))) | ~room(X3) | ~room(X2)) & ? [X4] : ((~predp(X4) | ~predc(X4)) & (predp(X4) | predc(X4)) & room(X4)) & ? [X5] : (predc(X5) & room(X5)) & predj(paul) & ? [X6] : (~predj(X6) & room(X6)) & predc(mary) & ~predg(fred) & predf(paul) & (predf(paul) | ~predn(mary)) & (! [X7] : (~preda(X7) | predq(X7) | ~room(X7)) | ? [X8] : (predg(X8) & ~predp(X8) & room(X8))) & (! [X9] : (~predg(X9) | predp(X9) | ~room(X9)) | ? [X10] : (preda(X10) & ~predq(X10) & room(X10))) & (~predc(fred) | ? [X11] : room(X11)) & (predn(paul) | ? [X12] : room(X12)) & ! [X13] : (alice = X13 | fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 135] 137. ? [X0,X1] : X0 != X1 => sK0 != sK1 [choice axiom] 138. ? [X4] : ((~predp(X4) | ~predc(X4)) & (predp(X4) | predc(X4)) & room(X4)) => ((~predp(sK2) | ~predc(sK2)) & (predp(sK2) | predc(sK2)) & room(sK2)) [choice axiom] 139. ? [X5] : (predc(X5) & room(X5)) => (predc(sK3) & room(sK3)) [choice axiom] 140. ? [X6] : (~predj(X6) & room(X6)) => (~predj(sK4) & room(sK4)) [choice axiom] 141. ? [X8] : (predg(X8) & ~predp(X8) & room(X8)) => (predg(sK5) & ~predp(sK5) & room(sK5)) [choice axiom] 142. ? [X10] : (preda(X10) & ~predq(X10) & room(X10)) => (preda(sK6) & ~predq(sK6) & room(sK6)) [choice axiom] 143. ? [X11] : room(X11) => room(sK7) [choice axiom] 144. ? [X12] : room(X12) => room(sK8) [choice axiom] 145. sK0 != sK1 & ! [X2,X3] : (X2 = X3 | ((predc(X3) | ~predp(X3)) & (predp(X3) | ~predc(X3))) | ((predc(X2) | ~predp(X2)) & (predp(X2) | ~predc(X2))) | ~room(X3) | ~room(X2)) & ((~predp(sK2) | ~predc(sK2)) & (predp(sK2) | predc(sK2)) & room(sK2)) & (predc(sK3) & room(sK3)) & predj(paul) & (~predj(sK4) & room(sK4)) & predc(mary) & ~predg(fred) & predf(paul) & (predf(paul) | ~predn(mary)) & (! [X7] : (~preda(X7) | predq(X7) | ~room(X7)) | (predg(sK5) & ~predp(sK5) & room(sK5))) & (! [X9] : (~predg(X9) | predp(X9) | ~room(X9)) | (preda(sK6) & ~predq(sK6) & room(sK6))) & (~predc(fred) | room(sK7)) & (predn(paul) | room(sK8)) & ! [X13] : (alice = X13 | fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 136,144,143,142,141,140,139,138,137] 146. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK9 & fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) [choice axiom] 147. ~predf(paul) | (alice != sK9 & fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 132,146] 228. room(mary) [cnf transformation 145] 229. room(paul) [cnf transformation 145] 230. room(fred) [cnf transformation 145] 231. room(alice) [cnf transformation 145] 232. ~room(X13) | fred = X13 | paul = X13 | mary = X13 | alice = X13 [cnf transformation 145] 242. predf(paul) [cnf transformation 145] 258. ~predf(paul) | room(sK9) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 259. ~predf(paul) | mary != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 260. ~predf(paul) | paul != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 261. ~predf(paul) | fred != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 262. ~predf(paul) | alice != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 327. alice != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,242] 328. alice != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,231] 329. alice != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 328,230] 330. alice != sK9 | ~room(mary) [subsumption resolution 329,229] 331. alice != sK9 [subsumption resolution 330,228] 332. fred != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,242] 333. fred != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 332,231] 334. fred != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 333,230] 335. fred != sK9 | ~room(mary) [subsumption resolution 334,229] 336. fred != sK9 [subsumption resolution 335,228] 337. paul != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,242] 338. paul != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 337,231] 339. paul != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 338,230] 340. paul != sK9 | ~room(mary) [subsumption resolution 339,229] 341. paul != sK9 [subsumption resolution 340,228] 342. mary != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 259,242] 343. mary != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 342,231] 344. mary != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 343,230] 345. mary != sK9 | ~room(mary) [subsumption resolution 344,229] 346. mary != sK9 [subsumption resolution 345,228] 347. room(sK9) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 258,242] 348. room(sK9) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 347,231] 349. room(sK9) | ~room(paul) | ~room(mary) [subsumption resolution 348,230] 350. room(sK9) | ~room(mary) [subsumption resolution 349,229] 351. room(sK9) [subsumption resolution 350,228] 402. fred = sK9 | paul = sK9 | mary = sK9 | alice = sK9 [resolution 232,351] 471. paul = sK9 | mary = sK9 | alice = sK9 [subsumption resolution 402,336] 472. mary = sK9 | alice = sK9 [subsumption resolution 471,341] 473. alice = sK9 [subsumption resolution 472,346] 474. $false [subsumption resolution 473,331] % SZS output end Proof for 9182611586873005167494151 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------
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