premise
stringlengths 12
3.12k
| hypothesis
stringlengths 10
236
| label
stringclasses 3
values | premise_tptp
stringlengths 51
8k
| hypothesis_tptp
stringlengths 41
352
| proof_inputs
sequencelengths 0
20
| proof
stringlengths 767
76.8k
⌀ | rule_concentration
float64 0
0.72
|
|---|---|---|---|---|---|---|---|
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 |
End of preview. Expand
in Dataset Viewer.
- Downloads last month
- 0