premise
stringlengths 17
1.33k
| hypothesis
stringlengths 15
140
| label
stringclasses 3
values | proof
stringlengths 1
237k
| premise_tptp
stringlengths 57
1.78k
| hypothesis_tptp
stringlengths 55
438
| deberta_pred
stringclasses 3
values | deberta_pred_r1_label
stringclasses 3
values |
|---|---|---|---|---|---|---|---|
Deborah, Nancy are the only persons in the room.
"Luciana is richer than Deborah" only if "more than one person in the room is not Deborah".
Deborah likes Luciana.
Only one person in the room enjoys landscape photography. | Luciana is richer than Deborah. | contradiction | - | room(deborah)&room(nancy)&(![X]:(room(X)=>(X='deborah'|X='nancy')))&
(((richer(deborah,luciana))=>((?[X,Y]:(room(X)&room(Y)&(X!=deborah&Y!=deborah)&(X!=Y)))))&
(like(luciana,deborah))&
(((?[X]:(room(X)&enjoys_landscape_photography(X)))&(![X,Y]:((enjoys_landscape_photography(X)&enjoys_landscape_photography(Y))=>(X=Y)))))) | room(deborah)&room(nancy)&(![X]:(room(X)=>(X='deborah'|X='nancy')))&
(richer(deborah,luciana)) | neutral | entailment |
Paulinea is the only person in the room. If Paulinea is the quietest in the room then Tamika and Paulinea like each other otherwise Paulinea does not enjoy pottery or hates Gertrude or both. Pauline is quieter than Paulinea. More than one person outside the room is a happy quiet person. Paulinea is the least quiet in the room. Paulinea does not enjoy pottery. Only one person outside the room hates Mary. Gertrude is quieter than Paulinea. Paulinea is not quiet, not happy or enjoys pottery or both. Paulinea who is not happy, does not enjoy pottery. | Paulinea is a tall brave rich quiet person or is not a quiet rich european or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(european_type, type, (
european: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(predc_type, type, (
predc: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(paul_type, type, (
paul: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(1,plain,
((~predc(mary)) <=> (~predc(mary))),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((((((((![X: $i] : quieter(X, mary) => (like(fred, mary) & like(mary, fred))) | ((~![X: $i] : quieter(X, mary)) => ((~predc(mary)) | hate(susan, mary)))) & quieter(mary, paul)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (((((happy(X) & quiet(X)) & person(X)) & happy(Y)) & quiet(Y)) & person(Y))) & (~(X = Y)))) & ![X: $i] : quieter(mary, X)) & (~predc(mary))) & (?[X: $i] : ((~room(X)) & hate(john, X)) & ![X: $i, Y: $i] : ((hate(john, X) & hate(john, Y)) => (X = Y)))) & quieter(mary, susan)) & (((~quiet(mary)) & (~happy(mary))) | predc(mary))) & ((~happy(mary)) & (~predc(mary))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((tall(mary) & brave(mary)) & rich(mary)) & quiet(mary)) & person(mary)) | (~((quiet(mary) & rich(mary)) & european(mary))))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & quieter(mary, paul) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & happy(X) & quiet(X) & person(X) & happy(Y) & quiet(Y) & person(Y) & (~(X = Y))) & ![X: $i] : quieter(mary, X) & (~predc(mary)) & ?[X: $i] : ((~room(X)) & hate(john, X)) & ![X: $i, Y: $i] : ((~(hate(john, X) & hate(john, Y))) | (X = Y)) & quieter(mary, susan) & (predc(mary) | ((~quiet(mary)) & (~happy(mary)))) & (~happy(mary)))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((((((((![X: $i] : quieter(X, mary) => (like(fred, mary) & like(mary, fred))) | ((~![X: $i] : quieter(X, mary)) => ((~predc(mary)) | hate(susan, mary)))) & quieter(mary, paul)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (((((happy(X) & quiet(X)) & person(X)) & happy(Y)) & quiet(Y)) & person(Y))) & (~(X = Y)))) & ![X: $i] : quieter(mary, X)) & (~predc(mary))) & (?[X: $i] : ((~room(X)) & hate(john, X)) & ![X: $i, Y: $i] : ((hate(john, X) & hate(john, Y)) => (X = Y)))) & quieter(mary, susan)) & (((~quiet(mary)) & (~happy(mary))) | predc(mary))) & ((~happy(mary)) & (~predc(mary))))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((tall(mary) & brave(mary)) & rich(mary)) & quiet(mary)) & person(mary)) | (~((quiet(mary) & rich(mary)) & european(mary))))))), file('/mnt/tmpfs//5046641616017787754589947.p','negated')).
tff(4,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & quieter(mary, paul) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & happy(X) & quiet(X) & person(X) & happy(Y) & quiet(Y) & person(Y) & (~(X = Y))) & ![X: $i] : quieter(mary, X) & (~predc(mary)) & ?[X: $i] : ((~room(X)) & hate(john, X)) & ![X: $i, Y: $i] : ((~(hate(john, X) & hate(john, Y))) | (X = Y)) & quieter(mary, susan) & (predc(mary) | ((~quiet(mary)) & (~happy(mary)))) & (~happy(mary)))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary))))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & quieter(mary, paul) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & happy(X) & quiet(X) & person(X) & happy(Y) & quiet(Y) & person(Y) & (~(X = Y))) & ![X: $i] : quieter(mary, X) & (~predc(mary)) & ?[X: $i] : ((~room(X)) & hate(john, X)) & ![X: $i, Y: $i] : ((~(hate(john, X) & hate(john, Y))) | (X = Y)) & quieter(mary, susan) & (predc(mary) | ((~quiet(mary)) & (~happy(mary)))) & (~happy(mary))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(~predc(mary)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(~predc(mary)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
((predc(mary) | ((~quiet(mary)) & (~happy(mary)))) <=> (predc(mary) | (~(quiet(mary) | happy(mary))))),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
((predc(mary) | ((~quiet(mary)) & (~happy(mary)))) <=> (predc(mary) | ((~quiet(mary)) & (~happy(mary))))),
inference(rewrite,[status(thm)],[])).
tff(10,plain,
(predc(mary) | ((~quiet(mary)) & (~happy(mary)))),
inference(and_elim,[status(thm)],[5])).
tff(11,plain,
(predc(mary) | ((~quiet(mary)) & (~happy(mary)))),
inference(modus_ponens,[status(thm)],[10, 9])).
tff(12,plain,
(predc(mary) | (~(quiet(mary) | happy(mary)))),
inference(modus_ponens,[status(thm)],[11, 8])).
tff(13,plain,
(~(quiet(mary) | happy(mary))),
inference(unit_resolution,[status(thm)],[12, 7])).
tff(14,plain,
((quiet(mary) | happy(mary)) | (~quiet(mary))),
inference(tautology,[status(thm)],[])).
tff(15,plain,
(~quiet(mary)),
inference(unit_resolution,[status(thm)],[14, 13])).
tff(16,plain,
(((~quiet(mary)) | (~rich(mary)) | (~((~quiet(mary)) | (~tall(mary)) | (~brave(mary)) | (~rich(mary)) | (~person(mary)))) | (~european(mary))) | quiet(mary)),
inference(tautology,[status(thm)],[])).
tff(17,plain,
((~quiet(mary)) | (~rich(mary)) | (~((~quiet(mary)) | (~tall(mary)) | (~brave(mary)) | (~rich(mary)) | (~person(mary)))) | (~european(mary))),
inference(unit_resolution,[status(thm)],[16, 15])).
tff(18,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(20,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(((~room(mary)) | (~((~room(X!3)) | (X!3 = |'mary'|))) | (~((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))) <=> ((~room(mary)) | (~((~room(X!3)) | (X!3 = |'mary'|))) | (~((~quiet(mary)) | (~rich(mary)) | (~((~quiet(mary)) | (~tall(mary)) | (~brave(mary)) | (~rich(mary)) | (~person(mary)))) | (~european(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
((~((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary))))) <=> (~((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(23,plain,
(((~room(mary)) | (~((~room(X!3)) | (X!3 = |'mary'|))) | (~((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))) <=> ((~room(mary)) | (~((~room(X!3)) | (X!3 = |'mary'|))) | (~((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary))))))),
inference(monotonicity,[status(thm)],[22])).
tff(24,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary))))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary))))))),
inference(monotonicity,[status(thm)],[24])).
tff(26,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(27,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))),
inference(or_elim,[status(thm)],[4])).
tff(28,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))),
inference(modus_ponens,[status(thm)],[27, 25])).
tff(29,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))),
inference(modus_ponens,[status(thm)],[28, 26])).
tff(30,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((tall(mary) & brave(mary) & rich(mary) & quiet(mary) & person(mary)) | (~(quiet(mary) & rich(mary) & european(mary)))))),
inference(modus_ponens,[status(thm)],[29, 25])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!3)) (= X!3 |'mary'|))))
(a!4 (or (and (tall mary)
(brave mary)
(rich mary)
(quiet mary)
(person mary))
(not (and (quiet mary) (rich mary) (european mary))))))
(let ((a!5 (~ (not (and (room mary) a!2 a!4))
(or (not (room mary)) a!3 (not a!4)))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ (not a!4) (not a!4))) a!5)))
| room(paulineinea)&(![X]:(room(X)=>(X='paulineinea')))&
((((![X]:(quieter(X,paulineinea)))=>((like(tamika,paulineinea) & like(paulineinea,tamika))))|((~(![X]:(quieter(X,paulineinea))))=>(((does_not_enjoy_pottery(paulineinea))|(hate(gertrude,paulineinea))))))&
(quieter(paulineinea,paulineine))&
((?[X,Y]:(~room(X)&~room(Y)&(happy(X)&quiet(X)&person(X)&happy(Y)&quiet(Y)&person(Y))&(X!=Y))))&
(![X]:(quieter(paulineinea,X)))&
(does_not_enjoy_pottery(paulineinea))&
(((?[X]:(~room(X)&hate(mary,X)))&(![X,Y]:((hate(mary,X)&hate(mary,Y))=>(X=Y)))))&
(quieter(paulineinea,gertrude))&
(((~quiet(paulineinea)&~happy(paulineinea))|(enjoys_pottery(paulineinea))))&
((~happy(paulineinea))&(does_not_enjoy_pottery(paulineinea)))) | room(paulineinea)&(![X]:(room(X)=>(X='paulineinea')))&
(((tall(paulineinea)&brave(paulineinea)&rich(paulineinea)&quiet(paulineinea)&person(paulineinea))|(~(quiet(paulineinea)&rich(paulineinea)&european(paulineinea))))) | neutral | neutral |
Rudy, Carol, Edna, Carla are the only persons in the room. Carol knows morse code and is a client of Harry. Only one person outside the room does not like Dolores. Carol is the tallest in the room. Carol is taller than Dolores and is hated by Harry. It is not the case that 'it is not the case that 'Carol who enjoys salsa dancing, does not hate Jeanne''. | Carol does not hate Jeanne and is a client of Harry. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(predc_type, type, (
predc: $i > $o)).
tff(susan_type, type, (
susan: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(client_type, type, (
client: ( $i * $i ) > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(alice_type, type, (
alice: $i)).
tff(fred_type, type, (
fred: $i)).
tff(mary_type, type, (
mary: $i)).
tff(1,plain,
((~hate(lucy, paul)) <=> (~hate(lucy, paul))),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((preda(paul) & client(susan, paul)) & (?[X: $i] : ((~room(X)) & (~like(john, X))) & ![X: $i, Y: $i] : (((~like(john, X)) & (~like(john, Y))) => (X = Y)))) & ![X: $i] : taller(X, paul)) & (taller(john, paul) & hate(paul, susan))) & (~(~(predc(paul) & (~hate(lucy, paul))))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~hate(lucy, paul)) & client(susan, paul))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & preda(paul) & client(susan, paul) & ?[X: $i] : ((~room(X)) & (~like(john, X))) & ![X: $i, Y: $i] : ((~((~like(john, X)) & (~like(john, Y)))) | (X = Y)) & ![X: $i] : taller(X, paul) & taller(john, paul) & hate(paul, susan) & predc(paul) & (~hate(lucy, paul)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((preda(paul) & client(susan, paul)) & (?[X: $i] : ((~room(X)) & (~like(john, X))) & ![X: $i, Y: $i] : (((~like(john, X)) & (~like(john, Y))) => (X = Y)))) & ![X: $i] : taller(X, paul)) & (taller(john, paul) & hate(paul, susan))) & (~(~(predc(paul) & (~hate(lucy, paul))))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~hate(lucy, paul)) & client(susan, paul))))), file('/mnt/tmpfs//861988591385622270771088.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & preda(paul) & client(susan, paul) & ?[X: $i] : ((~room(X)) & (~like(john, X))) & ![X: $i, Y: $i] : ((~((~like(john, X)) & (~like(john, Y)))) | (X = Y)) & ![X: $i] : taller(X, paul) & taller(john, paul) & hate(paul, susan) & predc(paul) & (~hate(lucy, paul)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul)))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & preda(paul) & client(susan, paul) & ?[X: $i] : ((~room(X)) & (~like(john, X))) & ![X: $i, Y: $i] : ((~((~like(john, X)) & (~like(john, Y)))) | (X = Y)) & ![X: $i] : taller(X, paul) & taller(john, paul) & hate(paul, susan) & predc(paul) & (~hate(lucy, paul))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(~hate(lucy, paul)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(~hate(lucy, paul)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(client(susan, paul) <=> client(susan, paul)),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
(client(susan, paul)),
inference(and_elim,[status(thm)],[5])).
tff(10,plain,
(client(susan, paul)),
inference(modus_ponens,[status(thm)],[9, 8])).
tff(11,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(12,plain,
(room(alice)),
inference(and_elim,[status(thm)],[5])).
tff(13,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
(room(fred)),
inference(and_elim,[status(thm)],[5])).
tff(16,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[15, 14])).
tff(17,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(18,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(19,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[18, 17])).
tff(20,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(22,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[21, 20])).
tff(23,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | hate(lucy, paul) | (~client(susan, paul))) <=> (hate(lucy, paul) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~client(susan, paul)))),
inference(rewrite,[status(thm)],[])).
tff(24,plain,
((~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | hate(lucy, paul) | (~client(susan, paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | hate(lucy, paul) | (~client(susan, paul)))),
inference(monotonicity,[status(thm)],[24])).
tff(26,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | hate(lucy, paul) | (~client(susan, paul))) <=> (hate(lucy, paul) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~client(susan, paul)))),
inference(transitivity,[status(thm)],[25, 23])).
tff(27,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul)) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul))),
inference(rewrite,[status(thm)],[])).
tff(28,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul)))),
inference(monotonicity,[status(thm)],[27])).
tff(29,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul)))),
inference(rewrite,[status(thm)],[])).
tff(30,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul))),
inference(or_elim,[status(thm)],[4])).
tff(31,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul))),
inference(modus_ponens,[status(thm)],[30, 28])).
tff(32,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul))),
inference(modus_ponens,[status(thm)],[31, 29])).
tff(33,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~hate(lucy, paul)) & client(susan, paul))),
inference(modus_ponens,[status(thm)],[32, 28])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!1 |'alice'|)
(= X!1 |'fred'|)
(= X!1 |'paul'|)
(= X!1 |'mary'|)
(not (room X!1)))))
(a!7 (refl (~ (not (client susan paul)) (not (client susan paul))))))
(let ((a!8 (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
(not (hate lucy paul))
(client susan paul)))))
(let ((a!9 (~ a!8
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
(hate lucy paul)
(not (client susan paul))))))
(nnf-neg a!1
a!2
a!3
a!4
(sk (~ (not a!5) a!6))
(refl (~ (hate lucy paul) (hate lucy paul)))
a!7
a!9))))
| room(rudy)&room(carol)&room(edna)&room(carla)&(![X]:(room(X)=>(X='rudy'|X='carol'|X='edna'|X='carla')))&
(((knows_morse_code(carol))&(client(harry,carol)))&
(((?[X]:(~room(X)&~like(dolores,X)))&(![X,Y]:((~like(dolores,X)&~like(dolores,Y))=>(X=Y)))))&
(![X]:(taller(X,carol)))&
((taller(dolores,carol))&(hate(carol,harry)))&
(~(~((enjoys_salsa_dancing(carol))&(~hate(jeanne,carol)))))) | room(rudy)&room(carol)&room(edna)&room(carla)&(![X]:(room(X)=>(X='rudy'|X='carol'|X='edna'|X='carla')))&
((~hate(jeanne,carol))&(client(harry,carol))) | contradiction | contradiction |
Elizabeth, Teresa, Jimmy are the only persons in the room. "No one in the room who is not Elizabeth is not a brave tourist" if "Elizabeth is the least quiet in the room". "Teresa is the richest in the room" if "Elizabeth and Erica hate each other". Jimmy and Elizabeth are not creative, not quiet. Elizabeth and Darrick hate each other. Jimmy and Elizabeth hate each other. Jimmy is a client of Erica or practices urban gardening or both. | Jimmy is a creative person or is a quiet tourist or both. | contradiction | - | room(elizabeth)&room(teresa)&room(jimmy)&(![X]:(room(X)=>(X='elizabeth'|X='teresa'|X='jimmy')))&
(((![X]:(quieter(elizabeth,X)))=>(~?[X]:(room(X)=>(((X!=elizabeth)=>(~(brave(X)&tourist(X))))))))&
(((hate(elizabeth,erica) & hate(erica,elizabeth)))=>(![X]:(richer(X,teresa))))&
(~creative(jimmy)&~quiet(jimmy)&~creative(elizabeth)&~quiet(elizabeth))&
((hate(elizabeth,darrick) & hate(darrick,elizabeth)))&
((hate(jimmy,elizabeth) & hate(elizabeth,jimmy)))&
(((client(erica,jimmy))|(practices_urban_gardening(jimmy))))) | room(elizabeth)&room(teresa)&room(jimmy)&(![X]:(room(X)=>(X='elizabeth'|X='teresa'|X='jimmy')))&
(((creative(jimmy)&person(jimmy))|(quiet(jimmy)&tourist(jimmy)))) | contradiction | entailment |
Martha, William, Robert are the only persons in the room.
William and Martha are not quiet, not happy.
William is the quietest in the room.
Everyone in the room who is not William does not like Stuart.
Martha neither is hated by Larry nor is liked by Larry. | Martha neither is liked by Stuart nor is not happy, not quiet. | contradiction | - | room(martha)&room(william)&room(robert)&(![X]:(room(X)=>(X='martha'|X='william'|X='robert')))&
((~quiet(william)&~happy(william)&~quiet(martha)&~happy(martha))&
(![X]:(quieter(X,william)))&
(![X]:(room(X)=>(((X!=william)=>(~like(stuart,X))))))&
(~((hate(martha,larry))|(like(martha,larry))))) | room(martha)&room(william)&room(robert)&(![X]:(room(X)=>(X='martha'|X='william'|X='robert')))&
(~((like(martha,stuart))|(~happy(martha)&~quiet(martha)))) | entailment | contradiction |
Daniel, Mark, Alfred are the only persons in the room. "Daniel and Mark are liked by Samuel" if "someone outside the room does not enjoy logic puzzles" and vice versa. Mark is the richest in the room. Mary is taller than Daniel. | It is not the case that 'Mark is richer than Samuel or likes Samuel or both'. | contradiction | - | room(daniel)&room(mark)&room(alalfred)&(![X]:(room(X)=>(X='daniel'|X='mark'|X='alalfred')))&
(((?[X]:(~room(X)=>(does_not_enjoy_logic_puzzles(X))))<=>(like(daniel,samuel)&like(mark,samuel)))&
(![X]:(richer(X,mark)))&
(taller(daniel,mary))) | room(daniel)&room(mark)&room(alalfred)&(![X]:(room(X)=>(X='daniel'|X='mark'|X='alalfred')))&
(~(((richer(samuel,mark))|(like(samuel,mark))))) | contradiction | entailment |
If "Francisca neither is not liked by Florence nor is not a tall person" then "Delia and Justin are respectively happy and creative".
Delia and Justin are respectively happy and creative.
Delia is a tall happy creative tourist and is not a happy creative tall brave person. | Delia is not a brave person and is not a tall tourist. | contradiction | - | room(claude)&room(francisca)&room(justin)&room(delia)&(![X]:(room(X)=>(X='claude'|X='francisca'|X='justin'|X='delia')))&
(((~((~like(francisca,florence))|(~(tall(francisca)&person(francisca)))))=>((happy(delia))&(creative(justin))))&
((happy(delia))&(creative(justin)))&
((tall(delia)&happy(delia)&creative(delia)&tourist(delia))&(~(happy(delia)&creative(delia)&tall(delia)&brave(delia)&person(delia))))) | room(claude)&room(francisca)&room(justin)&room(delia)&(![X]:(room(X)=>(X='claude'|X='francisca'|X='justin'|X='delia')))&
((~(brave(delia)&person(delia)))&(~(tall(delia)&tourist(delia)))) | contradiction | contradiction |
None of the following is true:.
-Ruby either can play the guitar or is not a night owl.
-Ruby does not make homemade pastries. | Ruby neither makes homemade pastries nor can play the guitar. | contradiction | - | room(ruby)&(![X]:(room(X)=>(X='ruby')))&
(~(((((can_play_the_guitar(ruby))|(is_not_a_night_owl(ruby)))&(~((can_play_the_guitar(ruby))|(is_not_a_night_owl(ruby))))))|(does_not_make_homemade_pastries(ruby)))) | room(ruby)&(![X]:(room(X)=>(X='ruby')))&
(~((makes_homemade_pastries(ruby))|(can_play_the_guitar(ruby)))) | entailment | neutral |
Christopher, Grace are the only persons in the room.
“Only one person outside the room is not a quiet tall rich european” if “Naomi is richer than Christopher”.
Grace is the richest in the room.
Everyone outside the room does not hate Naomi.
Christopher is a quiet european.
Christopher is the tallest in the room. | Christopher is not hated by Paul or is a happy tall quiet rich european or both. | neutral | % SZS status Satisfiable
| room(christopher)&room(grace)&(![X]:(room(X)=>(X='christopher'|X='grace')))&
(((richer(christopher,naomi))=>(((?[X]:(~room(X)&~(quiet(X)&tall(X)&rich(X)&european(X))))&(![X,Y]:((~(quiet(X)&tall(X)&rich(X)&european(X))&~(quiet(Y)&tall(Y)&rich(Y)&european(Y)))=>(X=Y))))))&
(![X]:(richer(X,grace)))&
(![X]:(~room(X)=>(~hate(naomi,X))))&
(quiet(christopher)&european(christopher))&
(![X]:(taller(X,christopher)))) | room(christopher)&room(grace)&(![X]:(room(X)=>(X='christopher'|X='grace')))&
(((~hate(christopher,paul))|(happy(christopher)&tall(christopher)&quiet(christopher)&rich(christopher)&european(christopher)))) | neutral | entailment |
Stephen is hated by Shaun if Stephen hates Donald and vice versa.
Gerald and Stephen do not like Donald.
Stephen is not hated by Shaun or is not a rich person or both. | Stephen neither is not hated by Donald nor does not like Shaun. | neutral | % SZS status Satisfiable
| room(gerald)&room(stephen)&(![X]:(room(X)=>(X='gerald'|X='stephen')))&
(((hate(donald,stephen))<=>(hate(stephen,shaun)))&
(~like(donald,gerald)&~like(donald,stephen))&
(((~hate(stephen,shaun))|(~(rich(stephen)&person(stephen)))))) | room(gerald)&room(stephen)&(![X]:(room(X)=>(X='gerald'|X='stephen')))&
(~((~hate(stephen,donald))|(~like(shaun,stephen)))) | contradiction | contradiction |
Barbara, Patricia, Rex are the only persons in the room.
Ashleigh is a sibling of Barbara only if Frances and Rex hate each other.
Barbara is the least tall in the room only if Patricia who is not hated by Ashleigh, hates Ashleigh.
Only one person in the room is not happy, not tall unless everyone in the room who is hated by Ashleigh is not hated by Ashleigh.
Barbara is the least tall in the room if Patricia is the least tall in the room and vice versa.
Patricia and Barbara are hated by Ashleigh.
Rex who is not a happy brave european, is hated by Marie.
Barbara is a happy european and is a sibling of Marie.
Patricia and Rex are respectively brave and happy.
Patricia and Rex do not hate Marie.
Patricia neither does not hate Ashleigh nor is a sibling of Ashleigh. | Someone who hates Ashleigh is a sibling of someone who does not hate Ashleigh. | neutral | % SZS status Satisfiable
| room(barbara)&room(patricia)&room(rex)&(![X]:(room(X)=>(X='barbara'|X='patricia'|X='rex')))&
(((sibling(barbara,ashleigh))=>((hate(frances,rex) & hate(rex,frances))))&
((![X]:(taller(barbara,X)))=>((~hate(patricia,ashleigh))&(hate(ashleigh,patricia))))&
(~(![X]:(room(X)=>(((hate(X,ashleigh))=>(~hate(X,ashleigh))))))=>(((?[X]:(room(X)&~happy(X)&~tall(X)))&(![X,Y]:((~happy(X)&~tall(X)&~happy(Y)&~tall(Y))=>(X=Y))))))&
((![X]:(taller(patricia,X)))<=>(![X]:(taller(barbara,X))))&
(hate(patricia,ashleigh)&hate(barbara,ashleigh))&
((~(happy(rex)&brave(rex)&european(rex)))&(hate(rex,marie)))&
((happy(barbara)&european(barbara))&(sibling(marie,barbara)))&
((brave(patricia))&(happy(rex)))&
(~hate(marie,patricia)&~hate(marie,rex))&
(~((~hate(ashleigh,patricia))|(sibling(ashleigh,patricia))))) | room(barbara)&room(patricia)&room(rex)&(![X]:(room(X)=>(X='barbara'|X='patricia'|X='rex')))&
(?[X,Y]:((hate(ashleigh,X))&(~hate(ashleigh,Y))&(sibling(X,Y)))) | entailment | entailment |
Connie, Ronnie are the only persons in the room.
If "someone outside the room is quieter than Tina" then "Connie and Ronnie are quiet tourist".
"Janet and Katherine hate each other" only if "Ronnie and Benjamin hate each other".
Someone outside the room does not hate Tina.
Ronnie who is not Connie, is quieter than Katherine.
Tina and Janet hate each other.
Connie who is not a happy tourist, hates Janet. | Connie is not hated by Janet and is not a quiet person. | contradiction | - | room(connie)&room(ronnie)&(![X]:(room(X)=>(X='connie'|X='ronnie')))&
(((?[X]:(~room(X)=>(quieter(tina,X))))=>(quiet(connie)&tourist(connie)&quiet(ronnie)&tourist(ronnie)))&
(((hate(janet,katherine) & hate(katherine,janet)))=>((hate(ronnie,benjamin) & hate(benjamin,ronnie))))&
(?[X]:(~room(X)=>(~hate(tina,X))))&
((ronnie!=connie)&(quieter(katherine,ronnie)))&
((hate(tina,janet) & hate(janet,tina)))&
((~(happy(connie)&tourist(connie)))&(hate(janet,connie)))) | room(connie)&room(ronnie)&(![X]:(room(X)=>(X='connie'|X='ronnie')))&
((~hate(connie,janet))&(~(quiet(connie)&person(connie)))) | entailment | contradiction |
William is the only person in the room. 'Lori is quieter than William' only if 'someone who is liked by Jessica like someone who is taller than Jessica'. 'Only one person outside the room is not liked by Lori' if 'William is the least rich in the room' and vice versa. 'Someone who is not William like someone who is not tall' only if 'William neither is not tall, not rich, not brave, not happy nor likes Carl'. It is not the case that 'William and Lori like each other'. Someone outside the room who does not like Jessica is not a creative tall european. Only one person outside the room is richer than Jessica. William neither is quieter than Jessica nor is not liked by Lori. William who is not a rich brave creative european, has a saltwater aquarium. | William is not a creative tall rich brave quiet european or is right-handed or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_8_type, type, (
tptp_fun_X_8: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(european_type, type, (
european: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(predc_type, type, (
predc: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(1,assumption,(~((~tall(mary)) | (~rich(mary)) | (~brave(mary)) | preda(mary) | (~creative(mary)) | (~european(mary)) | (~quiet(mary)))), introduced(assumption)).
tff(2,plain,
(((~tall(mary)) | (~rich(mary)) | (~brave(mary)) | preda(mary) | (~creative(mary)) | (~european(mary)) | (~quiet(mary))) | european(mary)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(european(mary)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((~tall(mary)) | (~rich(mary)) | (~brave(mary)) | preda(mary) | (~creative(mary)) | (~european(mary)) | (~quiet(mary))) | creative(mary)),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(creative(mary)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
(((~tall(mary)) | (~rich(mary)) | (~brave(mary)) | preda(mary) | (~creative(mary)) | (~european(mary)) | (~quiet(mary))) | rich(mary)),
inference(tautology,[status(thm)],[])).
tff(7,plain,
(rich(mary)),
inference(unit_resolution,[status(thm)],[6, 1])).
tff(8,plain,
(((~tall(mary)) | (~rich(mary)) | (~brave(mary)) | preda(mary) | (~creative(mary)) | (~european(mary)) | (~quiet(mary))) | brave(mary)),
inference(tautology,[status(thm)],[])).
tff(9,plain,
(brave(mary)),
inference(unit_resolution,[status(thm)],[8, 1])).
tff(10,plain,
((~(~((~rich(mary)) | (~brave(mary)) | (~creative(mary)) | (~european(mary))))) <=> ((~rich(mary)) | (~brave(mary)) | (~creative(mary)) | (~european(mary)))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
((rich(mary) & brave(mary) & creative(mary) & european(mary)) <=> (~((~rich(mary)) | (~brave(mary)) | (~creative(mary)) | (~european(mary))))),
inference(rewrite,[status(thm)],[])).
tff(12,plain,
((~(rich(mary) & brave(mary) & creative(mary) & european(mary))) <=> (~(~((~rich(mary)) | (~brave(mary)) | (~creative(mary)) | (~european(mary)))))),
inference(monotonicity,[status(thm)],[11])).
tff(13,plain,
((~(rich(mary) & brave(mary) & creative(mary) & european(mary))) <=> ((~rich(mary)) | (~brave(mary)) | (~creative(mary)) | (~european(mary)))),
inference(transitivity,[status(thm)],[12, 10])).
tff(14,plain,
((~(rich(mary) & brave(mary) & creative(mary) & european(mary))) <=> (~(rich(mary) & brave(mary) & creative(mary) & european(mary)))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((((((quieter(mary, fred) => ?[X: $i, Y: $i] : ((like(X, john) & taller(john, Y)) & like(X, Y))) & (![X: $i] : richer(mary, X) <=> (?[X: $i] : ((~room(X)) & (~like(X, fred))) & ![X: $i, Y: $i] : (((~like(X, fred)) & (~like(Y, fred))) => (X = Y))))) & (?[X: $i, Y: $i] : (((~(X = mary)) & (~tall(Y))) & like(X, Y)) => (~(((((~tall(mary)) & (~rich(mary))) & (~brave(mary))) & (~happy(mary))) | like(paul, mary))))) & (~(like(mary, fred) & like(fred, mary)))) & ?[X: $i] : ((~room(X)) => ((~like(john, X)) => (~((creative(X) & tall(X)) & european(X)))))) & (?[X: $i] : ((~room(X)) & richer(john, X)) & ![X: $i, Y: $i] : ((richer(john, X) & richer(john, Y)) => (X = Y)))) & (~(quieter(john, mary) | (~like(mary, fred))))) & ((~(((rich(mary) & brave(mary)) & creative(mary)) & european(mary))) & predc(mary)))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~(((((creative(mary) & tall(mary)) & rich(mary)) & brave(mary)) & quiet(mary)) & european(mary))) | preda(mary))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~quieter(mary, fred)) | ?[X: $i, Y: $i] : (like(X, john) & taller(john, Y) & like(X, Y))) & (![X: $i] : richer(mary, X) <=> (?[X: $i] : ((~room(X)) & (~like(X, fred))) & ![X: $i, Y: $i] : ((~((~like(X, fred)) & (~like(Y, fred)))) | (X = Y)))) & ((~?[X: $i, Y: $i] : ((~(X = mary)) & (~tall(Y)) & like(X, Y))) | (~(like(paul, mary) | ((~tall(mary)) & (~rich(mary)) & (~brave(mary)) & (~happy(mary)))))) & (~(like(mary, fred) & like(fred, mary))) & ?[X: $i] : (room(X) | like(john, X) | (~(creative(X) & tall(X) & european(X)))) & ?[X: $i] : ((~room(X)) & richer(john, X)) & ![X: $i, Y: $i] : ((~(richer(john, X) & richer(john, Y))) | (X = Y)) & (~((~like(mary, fred)) | quieter(john, mary))) & (~(rich(mary) & brave(mary) & creative(mary) & european(mary))) & predc(mary))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(16,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((((((quieter(mary, fred) => ?[X: $i, Y: $i] : ((like(X, john) & taller(john, Y)) & like(X, Y))) & (![X: $i] : richer(mary, X) <=> (?[X: $i] : ((~room(X)) & (~like(X, fred))) & ![X: $i, Y: $i] : (((~like(X, fred)) & (~like(Y, fred))) => (X = Y))))) & (?[X: $i, Y: $i] : (((~(X = mary)) & (~tall(Y))) & like(X, Y)) => (~(((((~tall(mary)) & (~rich(mary))) & (~brave(mary))) & (~happy(mary))) | like(paul, mary))))) & (~(like(mary, fred) & like(fred, mary)))) & ?[X: $i] : ((~room(X)) => ((~like(john, X)) => (~((creative(X) & tall(X)) & european(X)))))) & (?[X: $i] : ((~room(X)) & richer(john, X)) & ![X: $i, Y: $i] : ((richer(john, X) & richer(john, Y)) => (X = Y)))) & (~(quieter(john, mary) | (~like(mary, fred))))) & ((~(((rich(mary) & brave(mary)) & creative(mary)) & european(mary))) & predc(mary)))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~(((((creative(mary) & tall(mary)) & rich(mary)) & brave(mary)) & quiet(mary)) & european(mary))) | preda(mary))))), file('/mnt/tmpfs//1590258834225805198658451.p','negated')).
tff(17,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~quieter(mary, fred)) | ?[X: $i, Y: $i] : (like(X, john) & taller(john, Y) & like(X, Y))) & (![X: $i] : richer(mary, X) <=> (?[X: $i] : ((~room(X)) & (~like(X, fred))) & ![X: $i, Y: $i] : ((~((~like(X, fred)) & (~like(Y, fred)))) | (X = Y)))) & ((~?[X: $i, Y: $i] : ((~(X = mary)) & (~tall(Y)) & like(X, Y))) | (~(like(paul, mary) | ((~tall(mary)) & (~rich(mary)) & (~brave(mary)) & (~happy(mary)))))) & (~(like(mary, fred) & like(fred, mary))) & ?[X: $i] : (room(X) | like(john, X) | (~(creative(X) & tall(X) & european(X)))) & ?[X: $i] : ((~room(X)) & richer(john, X)) & ![X: $i, Y: $i] : ((~(richer(john, X) & richer(john, Y))) | (X = Y)) & (~((~like(mary, fred)) | quieter(john, mary))) & (~(rich(mary) & brave(mary) & creative(mary) & european(mary))) & predc(mary))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary))))))),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~quieter(mary, fred)) | ?[X: $i, Y: $i] : (like(X, john) & taller(john, Y) & like(X, Y))) & (![X: $i] : richer(mary, X) <=> (?[X: $i] : ((~room(X)) & (~like(X, fred))) & ![X: $i, Y: $i] : ((~((~like(X, fred)) & (~like(Y, fred)))) | (X = Y)))) & ((~?[X: $i, Y: $i] : ((~(X = mary)) & (~tall(Y)) & like(X, Y))) | (~(like(paul, mary) | ((~tall(mary)) & (~rich(mary)) & (~brave(mary)) & (~happy(mary)))))) & (~(like(mary, fred) & like(fred, mary))) & ?[X: $i] : (room(X) | like(john, X) | (~(creative(X) & tall(X) & european(X)))) & ?[X: $i] : ((~room(X)) & richer(john, X)) & ![X: $i, Y: $i] : ((~(richer(john, X) & richer(john, Y))) | (X = Y)) & (~((~like(mary, fred)) | quieter(john, mary))) & (~(rich(mary) & brave(mary) & creative(mary) & european(mary))) & predc(mary)),
inference(or_elim,[status(thm)],[17])).
tff(19,plain,
(~(rich(mary) & brave(mary) & creative(mary) & european(mary))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
(~(rich(mary) & brave(mary) & creative(mary) & european(mary))),
inference(modus_ponens,[status(thm)],[19, 14])).
tff(21,plain,
((~rich(mary)) | (~brave(mary)) | (~creative(mary)) | (~european(mary))),
inference(modus_ponens,[status(thm)],[20, 13])).
tff(22,plain,
($false),
inference(unit_resolution,[status(thm)],[21, 9, 7, 5, 3])).
tff(23,plain,((~tall(mary)) | (~rich(mary)) | (~brave(mary)) | preda(mary) | (~creative(mary)) | (~european(mary)) | (~quiet(mary))), inference(lemma,lemma(discharge,[]))).
tff(24,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
(room(mary)),
inference(and_elim,[status(thm)],[18])).
tff(26,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[25, 24])).
tff(27,plain,
(((~room(mary)) | (~((~room(X!8)) | (X!8 = |'mary'|))) | (~(preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary)))))) <=> ((~room(mary)) | (~((~room(X!8)) | (X!8 = |'mary'|))) | (~((~tall(mary)) | (~rich(mary)) | (~brave(mary)) | preda(mary) | (~creative(mary)) | (~european(mary)) | (~quiet(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(28,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary))))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(29,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary))))))),
inference(monotonicity,[status(thm)],[28])).
tff(30,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary)))))),
inference(or_elim,[status(thm)],[17])).
tff(32,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary)))))),
inference(modus_ponens,[status(thm)],[31, 29])).
tff(33,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary)))))),
inference(modus_ponens,[status(thm)],[32, 30])).
tff(34,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (preda(mary) | (~(creative(mary) & tall(mary) & rich(mary) & brave(mary) & quiet(mary) & european(mary)))))),
inference(modus_ponens,[status(thm)],[33, 29])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!8)) (= X!8 |'mary'|))))
(a!4 (or (preda mary)
(not (and (creative mary)
(tall mary)
(rich mary)
(brave mary)
(quiet mary)
(european mary))))))
(let ((a!5 (~ (not (and (room mary) a!2 a!4))
(or (not (room mary)) a!3 (not a!4)))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ (not a!4) (not a!4))) a!5)))
| room(william)&(![X]:(room(X)=>(X='william')))&
(((quieter(william,lori))=>(?[X,Y]:((like(X,jessica))&(taller(jessica,Y))&(like(X,Y)))))&
((![X]:(richer(william,X)))<=>(((?[X]:(~room(X)&~like(X,lori)))&(![X,Y]:((~like(X,lori)&~like(Y,lori))=>(X=Y))))))&
((?[X,Y]:((X!=william)&(~tall(Y))&(like(X,Y))))=>(~((~tall(william)&~rich(william)&~brave(william)&~happy(william))|(like(carl,william)))))&
(~((like(william,lori) & like(lori,william))))&
(?[X]:(~room(X)=>(((~like(jessica,X))=>(~(creative(X)&tall(X)&european(X)))))))&
(((?[X]:(~room(X)&richer(jessica,X)))&(![X,Y]:((richer(jessica,X)&richer(jessica,Y))=>(X=Y)))))&
(~((quieter(jessica,william))|(~like(william,lori))))&
((~(rich(william)&brave(william)&creative(william)&european(william)))&(has_a_saltwater_aquarium(william)))) | room(william)&(![X]:(room(X)=>(X='william')))&
(((~(creative(william)&tall(william)&rich(william)&brave(william)&quiet(william)&european(william)))|(is_right-handed(william)))) | contradiction | entailment |
Matthew is the only person in the room.
“William is quieter than Matthew” only if “someone who is not hated by William is quieter than someone who is a brave person”.
More than one person outside the room is quieter than William.
William is quieter than Matthew.
Someone who is not a happy person hate someone who is not hated by William. | Matthew is a quiet european or is not a happy quiet european or both. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_6_type, type, (
tptp_fun_X_6: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(european_type, type, (
european: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(1,assumption,(~((~quiet(mary)) | (~european(mary)) | (~((~quiet(mary)) | (~european(mary)))) | (~happy(mary)))), introduced(assumption)).
tff(2,plain,
(((~quiet(mary)) | (~european(mary)) | (~((~quiet(mary)) | (~european(mary)))) | (~happy(mary))) | ((~quiet(mary)) | (~european(mary)))),
inference(tautology,[status(thm)],[])).
tff(3,plain,
((~quiet(mary)) | (~european(mary))),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(((~quiet(mary)) | (~european(mary)) | (~((~quiet(mary)) | (~european(mary)))) | (~happy(mary))) | quiet(mary)),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(quiet(mary)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
(((~quiet(mary)) | (~european(mary)) | (~((~quiet(mary)) | (~european(mary)))) | (~happy(mary))) | european(mary)),
inference(tautology,[status(thm)],[])).
tff(7,plain,
(european(mary)),
inference(unit_resolution,[status(thm)],[6, 1])).
tff(8,plain,
((~((~quiet(mary)) | (~european(mary)))) | (~quiet(mary)) | (~european(mary))),
inference(tautology,[status(thm)],[])).
tff(9,plain,
($false),
inference(unit_resolution,[status(thm)],[8, 7, 5, 3])).
tff(10,plain,((~quiet(mary)) | (~european(mary)) | (~((~quiet(mary)) | (~european(mary)))) | (~happy(mary))), inference(lemma,lemma(discharge,[]))).
tff(11,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(12,plain,
((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((quieter(mary, paul) => ?[X: $i, Y: $i] : (((~hate(X, paul)) & (brave(Y) & person(Y))) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (quieter(paul, X) & quieter(paul, Y))) & (~(X = Y)))) & quieter(mary, paul)) & ?[X: $i, Y: $i] : (((~(happy(X) & person(X))) & (~hate(Y, paul))) & hate(X, Y)))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((quiet(mary) & european(mary)) | (~((happy(mary) & quiet(mary)) & european(mary))))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~quieter(mary, paul)) | ?[X: $i, Y: $i] : ((~hate(X, paul)) & brave(Y) & person(Y) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & quieter(paul, X) & quieter(paul, Y) & (~(X = Y))) & quieter(mary, paul) & ?[X: $i, Y: $i] : ((~(happy(X) & person(X))) & (~hate(Y, paul)) & hate(X, Y)))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))))),
inference(rewrite,[status(thm)],[])).
tff(13,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((((quieter(mary, paul) => ?[X: $i, Y: $i] : (((~hate(X, paul)) & (brave(Y) & person(Y))) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (quieter(paul, X) & quieter(paul, Y))) & (~(X = Y)))) & quieter(mary, paul)) & ?[X: $i, Y: $i] : (((~(happy(X) & person(X))) & (~hate(Y, paul))) & hate(X, Y)))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((quiet(mary) & european(mary)) | (~((happy(mary) & quiet(mary)) & european(mary))))))), file('/mnt/tmpfs//7602939589555169796264600.p','negated')).
tff(14,plain,
(~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~quieter(mary, paul)) | ?[X: $i, Y: $i] : ((~hate(X, paul)) & brave(Y) & person(Y) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & quieter(paul, X) & quieter(paul, Y) & (~(X = Y))) & quieter(mary, paul) & ?[X: $i, Y: $i] : ((~(happy(X) & person(X))) & (~hate(Y, paul)) & hate(X, Y)))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary))))))),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~quieter(mary, paul)) | ?[X: $i, Y: $i] : ((~hate(X, paul)) & brave(Y) & person(Y) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & quieter(paul, X) & quieter(paul, Y) & (~(X = Y))) & quieter(mary, paul) & ?[X: $i, Y: $i] : ((~(happy(X) & person(X))) & (~hate(Y, paul)) & hate(X, Y))),
inference(or_elim,[status(thm)],[14])).
tff(16,plain,
(room(mary)),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[16, 11])).
tff(18,plain,
(((~room(mary)) | (~((~room(X!6)) | (X!6 = |'mary'|))) | (~((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))) <=> ((~room(mary)) | (~((~room(X!6)) | (X!6 = |'mary'|))) | (~((~quiet(mary)) | (~european(mary)) | (~((~quiet(mary)) | (~european(mary)))) | (~happy(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary))))) <=> (~((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(20,plain,
(((~room(mary)) | (~((~room(X!6)) | (X!6 = |'mary'|))) | (~((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))) <=> ((~room(mary)) | (~((~room(X!6)) | (X!6 = |'mary'|))) | (~((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary))))))),
inference(monotonicity,[status(thm)],[19])).
tff(21,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary))))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary))))))),
inference(monotonicity,[status(thm)],[21])).
tff(23,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary))))))),
inference(rewrite,[status(thm)],[])).
tff(24,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))),
inference(or_elim,[status(thm)],[14])).
tff(25,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))),
inference(modus_ponens,[status(thm)],[24, 22])).
tff(26,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))),
inference(modus_ponens,[status(thm)],[25, 23])).
tff(27,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((quiet(mary) & european(mary)) | (~(happy(mary) & quiet(mary) & european(mary)))))),
inference(modus_ponens,[status(thm)],[26, 22])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!6)) (= X!6 |'mary'|))))
(a!4 (or (and (quiet mary) (european mary))
(not (and (happy mary) (quiet mary) (european mary))))))
(let ((a!5 (~ (not (and (room mary) a!2 a!4))
(or (not (room mary)) a!3 (not a!4)))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ (not a!4) (not a!4))) a!5)))
| room(matthew)&(![X]:(room(X)=>(X='matthew')))&
(((quieter(matthew,william))=>(?[X,Y]:((~hate(X,william))&(brave(Y)&person(Y))&(quieter(X,Y)))))&
((?[X,Y]:(~room(X)&~room(Y)&(quieter(william,X)&quieter(william,Y))&(X!=Y))))&
(quieter(matthew,william))&
(?[X,Y]:((~(happy(X)&person(X)))&(~hate(Y,william))&(hate(X,Y))))) | room(matthew)&(![X]:(room(X)=>(X='matthew')))&
(((quiet(matthew)&european(matthew))|(~(happy(matthew)&quiet(matthew)&european(matthew))))) | neutral | entailment |
Nancy, Kenneth are the only persons in the room.
If “no one outside the room is liked by Victor” then “someone outside the room who hates Victor is hated by Victor” otherwise “Nancy neither is not brave nor does not enjoy salsa dancing”.
“No one outside the room is not Nancy” unless “everyone outside the room is not creative”.
Someone who does not like Victor hate someone who hates Victor.
Nancy is the quietest in the room.
Kenneth and Victor like each other.
Victor is quieter than Kenneth. | Someone who likes Victor like someone who is not creative. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(mary_type, type, (
mary: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(paul_type, type, (
paul: $i)).
tff(alice_type, type, (
alice: $i)).
tff(john_type, type, (
john: $i)).
tff(susan_type, type, (
susan: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(predc_type, type, (
predc: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(1,plain,
((fred = mary) <=> (mary = fred)),
inference(commutativity,[status(thm)],[])).
tff(2,assumption,(room(fred)), introduced(assumption)).
tff(3,assumption,(paul = |'paul'|), introduced(assumption)).
tff(4,plain,
(|'paul'| = paul),
inference(symmetry,[status(thm)],[3])).
tff(5,plain,
((mary = |'paul'|) <=> (mary = paul)),
inference(monotonicity,[status(thm)],[4])).
tff(6,plain,
((mary = paul) <=> (mary = |'paul'|)),
inference(symmetry,[status(thm)],[5])).
tff(7,plain,
((~(mary = paul)) <=> (~(mary = |'paul'|))),
inference(monotonicity,[status(thm)],[6])).
tff(8,plain,
((~(mary = paul)) <=> (~(mary = paul))),
inference(rewrite,[status(thm)],[])).
tff(9,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//1046168352070741187219218.p','b14')).
tff(10,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[10])).
tff(12,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[11])).
tff(13,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[12])).
tff(14,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[13])).
tff(15,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[16])).
tff(18,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[17])).
tff(19,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[19])).
tff(21,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[20])).
tff(22,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[22])).
tff(24,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[23])).
tff(25,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[29])).
tff(31,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[30])).
tff(32,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[31])).
tff(33,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[32])).
tff(34,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[33])).
tff(35,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[34])).
tff(36,plain,
(((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))),
inference(and_elim,[status(thm)],[35])).
tff(37,plain,
((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))),
inference(and_elim,[status(thm)],[36])).
tff(38,plain,
(((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))),
inference(and_elim,[status(thm)],[37])).
tff(39,plain,
((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))),
inference(and_elim,[status(thm)],[38])).
tff(40,plain,
(((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))),
inference(and_elim,[status(thm)],[39])).
tff(41,plain,
((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))),
inference(and_elim,[status(thm)],[40])).
tff(42,plain,
(((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))),
inference(and_elim,[status(thm)],[41])).
tff(43,plain,
((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))),
inference(and_elim,[status(thm)],[42])).
tff(44,plain,
(((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))),
inference(and_elim,[status(thm)],[43])).
tff(45,plain,
((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))),
inference(and_elim,[status(thm)],[44])).
tff(46,plain,
(((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))),
inference(and_elim,[status(thm)],[45])).
tff(47,plain,
((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))),
inference(and_elim,[status(thm)],[46])).
tff(48,plain,
(((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))),
inference(and_elim,[status(thm)],[47])).
tff(49,plain,
((~(mary = paul)) & (~(mary = fred))),
inference(and_elim,[status(thm)],[48])).
tff(50,plain,
(~(mary = paul)),
inference(and_elim,[status(thm)],[49])).
tff(51,plain,
(~(mary = paul)),
inference(modus_ponens,[status(thm)],[50, 8])).
tff(52,plain,
(~(mary = |'paul'|)),
inference(modus_ponens,[status(thm)],[51, 7])).
tff(53,plain,
(^[X: $i] : refl(((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(54,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[53])).
tff(55,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(56,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((((~?[X: $i] : ((~room(X)) => like(X, fred))) => ?[X: $i] : ((~room(X)) => (hate(fred, X) => hate(X, fred)))) | ((~(~?[X: $i] : ((~room(X)) => like(X, fred)))) => (~((~brave(mary)) | (~predc(mary)))))) & ((~![X: $i] : ((~room(X)) => (~creative(X)))) => (~?[X: $i] : ((~room(X)) => (~(X = mary)))))) & ?[X: $i, Y: $i] : (((~like(fred, X)) & hate(fred, Y)) & hate(X, Y))) & ![X: $i] : quieter(X, mary)) & (like(paul, fred) & like(fred, paul))) & quieter(paul, fred))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : ((like(fred, X) & (~creative(Y))) & like(X, Y))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : (room(X) | (~creative(X))) | (~?[X: $i] : (room(X) | (~(X = mary))))) & ?[X: $i, Y: $i] : ((~like(fred, X)) & hate(fred, Y) & hate(X, Y)) & ![X: $i] : quieter(X, mary) & like(paul, fred) & like(fred, paul) & quieter(paul, fred))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y)))))),
inference(rewrite,[status(thm)],[])).
tff(57,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((((~?[X: $i] : ((~room(X)) => like(X, fred))) => ?[X: $i] : ((~room(X)) => (hate(fred, X) => hate(X, fred)))) | ((~(~?[X: $i] : ((~room(X)) => like(X, fred)))) => (~((~brave(mary)) | (~predc(mary)))))) & ((~![X: $i] : ((~room(X)) => (~creative(X)))) => (~?[X: $i] : ((~room(X)) => (~(X = mary)))))) & ?[X: $i, Y: $i] : (((~like(fred, X)) & hate(fred, Y)) & hate(X, Y))) & ![X: $i] : quieter(X, mary)) & (like(paul, fred) & like(fred, paul))) & quieter(paul, fred))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : ((like(fred, X) & (~creative(Y))) & like(X, Y))))), file('/mnt/tmpfs//1046168352070741187219218.p','negated')).
tff(58,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : (room(X) | (~creative(X))) | (~?[X: $i] : (room(X) | (~(X = mary))))) & ?[X: $i, Y: $i] : ((~like(fred, X)) & hate(fred, Y) & hate(X, Y)) & ![X: $i] : quieter(X, mary) & like(paul, fred) & like(fred, paul) & quieter(paul, fred))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y))))),
inference(modus_ponens,[status(thm)],[57, 56])).
tff(59,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (![X: $i] : (room(X) | (~creative(X))) | (~?[X: $i] : (room(X) | (~(X = mary))))) & ?[X: $i, Y: $i] : ((~like(fred, X)) & hate(fred, Y) & hate(X, Y)) & ![X: $i] : quieter(X, mary) & like(paul, fred) & like(fred, paul) & quieter(paul, fred)),
inference(or_elim,[status(thm)],[58])).
tff(60,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[59])).
tff(61,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[60, 55])).
tff(62,plain,(
![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[61])).
tff(63,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[62, 54])).
tff(64,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(65,plain,
(room(mary)),
inference(and_elim,[status(thm)],[59])).
tff(66,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[65, 64])).
tff(67,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(68,plain,
(((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary))) <=> ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(69,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|)))),
inference(monotonicity,[status(thm)],[68])).
tff(70,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(transitivity,[status(thm)],[69, 67])).
tff(71,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))),
inference(quant_inst,[status(thm)],[])).
tff(72,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[71, 70])).
tff(73,plain,
((mary = |'paul'|) | (mary = |'mary'|)),
inference(unit_resolution,[status(thm)],[72, 66, 63])).
tff(74,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[73, 52])).
tff(75,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[74])).
tff(76,plain,
((fred = |'mary'|) <=> (fred = mary)),
inference(monotonicity,[status(thm)],[75])).
tff(77,plain,
((fred = |'mary'|) <=> (mary = fred)),
inference(transitivity,[status(thm)],[76, 1])).
tff(78,plain,
((mary = fred) <=> (fred = |'mary'|)),
inference(symmetry,[status(thm)],[77])).
tff(79,plain,
((~(mary = fred)) <=> (~(fred = |'mary'|))),
inference(monotonicity,[status(thm)],[78])).
tff(80,plain,
((~(mary = fred)) <=> (~(mary = fred))),
inference(rewrite,[status(thm)],[])).
tff(81,plain,
(~(mary = fred)),
inference(and_elim,[status(thm)],[49])).
tff(82,plain,
(~(mary = fred)),
inference(modus_ponens,[status(thm)],[81, 80])).
tff(83,plain,
(~(fred = |'mary'|)),
inference(modus_ponens,[status(thm)],[82, 79])).
tff(84,plain,
((fred = paul) <=> (paul = fred)),
inference(commutativity,[status(thm)],[])).
tff(85,plain,
((fred = |'paul'|) <=> (fred = paul)),
inference(monotonicity,[status(thm)],[4])).
tff(86,plain,
((fred = |'paul'|) <=> (paul = fred)),
inference(transitivity,[status(thm)],[85, 84])).
tff(87,plain,
((paul = fred) <=> (fred = |'paul'|)),
inference(symmetry,[status(thm)],[86])).
tff(88,plain,
((~(paul = fred)) <=> (~(fred = |'paul'|))),
inference(monotonicity,[status(thm)],[87])).
tff(89,plain,
((~(paul = fred)) <=> (~(paul = fred))),
inference(rewrite,[status(thm)],[])).
tff(90,plain,
(~(paul = fred)),
inference(and_elim,[status(thm)],[43])).
tff(91,plain,
(~(paul = fred)),
inference(modus_ponens,[status(thm)],[90, 89])).
tff(92,plain,
(~(fred = |'paul'|)),
inference(modus_ponens,[status(thm)],[91, 88])).
tff(93,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((fred = |'paul'|) | (fred = |'mary'|) | (~room(fred)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (fred = |'paul'|) | (fred = |'mary'|) | (~room(fred)))),
inference(rewrite,[status(thm)],[])).
tff(94,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((fred = |'paul'|) | (fred = |'mary'|) | (~room(fred)))),
inference(quant_inst,[status(thm)],[])).
tff(95,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (fred = |'paul'|) | (fred = |'mary'|) | (~room(fred))),
inference(modus_ponens,[status(thm)],[94, 93])).
tff(96,plain,
((fred = |'paul'|) | (fred = |'mary'|)),
inference(unit_resolution,[status(thm)],[95, 63, 2])).
tff(97,plain,
(fred = |'mary'|),
inference(unit_resolution,[status(thm)],[96, 92])).
tff(98,plain,
($false),
inference(unit_resolution,[status(thm)],[97, 83])).
tff(99,plain,((~(paul = |'paul'|)) | (~room(fred))), inference(lemma,lemma(discharge,[]))).
tff(100,plain,
(~(paul = |'paul'|)),
inference(unit_resolution,[status(thm)],[99, 2])).
tff(101,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(102,plain,
(room(paul)),
inference(and_elim,[status(thm)],[59])).
tff(103,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[102, 101])).
tff(104,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(105,plain,
(((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul))) <=> ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(106,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|)))),
inference(monotonicity,[status(thm)],[105])).
tff(107,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(transitivity,[status(thm)],[106, 104])).
tff(108,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))),
inference(quant_inst,[status(thm)],[])).
tff(109,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|)),
inference(modus_ponens,[status(thm)],[108, 107])).
tff(110,plain,
((paul = |'paul'|) | (paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[109, 103, 63])).
tff(111,plain,
(paul = |'mary'|),
inference(unit_resolution,[status(thm)],[110, 100])).
tff(112,plain,
(|'mary'| = paul),
inference(symmetry,[status(thm)],[111])).
tff(113,plain,
((mary = |'mary'|) <=> (mary = paul)),
inference(monotonicity,[status(thm)],[112])).
tff(114,plain,
((mary = paul) <=> (mary = |'mary'|)),
inference(symmetry,[status(thm)],[113])).
tff(115,plain,
((~(mary = paul)) <=> (~(mary = |'mary'|))),
inference(monotonicity,[status(thm)],[114])).
tff(116,plain,
(~(mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[51, 115])).
tff(117,plain,
(mary = |'paul'|),
inference(unit_resolution,[status(thm)],[73, 116])).
tff(118,plain,
(|'paul'| = mary),
inference(symmetry,[status(thm)],[117])).
tff(119,plain,
((fred = |'paul'|) <=> (fred = mary)),
inference(monotonicity,[status(thm)],[118])).
tff(120,plain,
((fred = |'paul'|) <=> (mary = fred)),
inference(transitivity,[status(thm)],[119, 1])).
tff(121,plain,
((mary = fred) <=> (fred = |'paul'|)),
inference(symmetry,[status(thm)],[120])).
tff(122,plain,
((~(mary = fred)) <=> (~(fred = |'paul'|))),
inference(monotonicity,[status(thm)],[121])).
tff(123,plain,
(~(fred = |'paul'|)),
inference(modus_ponens,[status(thm)],[82, 122])).
tff(124,plain,
((fred = |'mary'|) <=> (fred = paul)),
inference(monotonicity,[status(thm)],[112])).
tff(125,plain,
((fred = |'mary'|) <=> (paul = fred)),
inference(transitivity,[status(thm)],[124, 84])).
tff(126,plain,
((paul = fred) <=> (fred = |'mary'|)),
inference(symmetry,[status(thm)],[125])).
tff(127,plain,
((~(paul = fred)) <=> (~(fred = |'mary'|))),
inference(monotonicity,[status(thm)],[126])).
tff(128,plain,
(~(fred = |'mary'|)),
inference(modus_ponens,[status(thm)],[91, 127])).
tff(129,plain,
(fred = |'paul'|),
inference(unit_resolution,[status(thm)],[96, 128])).
tff(130,plain,
($false),
inference(unit_resolution,[status(thm)],[129, 123])).
tff(131,plain,(~room(fred)), inference(lemma,lemma(discharge,[]))).
tff(132,assumption,(~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))), introduced(assumption)).
tff(133,plain,
(((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))) | room(X!2)),
inference(tautology,[status(thm)],[])).
tff(134,plain,
(room(X!2)),
inference(unit_resolution,[status(thm)],[133, 132])).
tff(135,plain,
(((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))) | (~(X!2 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(136,plain,
(~(X!2 = |'mary'|)),
inference(unit_resolution,[status(thm)],[135, 132])).
tff(137,plain,
(((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))) | (~(X!2 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(138,plain,
(~(X!2 = |'paul'|)),
inference(unit_resolution,[status(thm)],[137, 132])).
tff(139,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))),
inference(rewrite,[status(thm)],[])).
tff(140,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))),
inference(quant_inst,[status(thm)],[])).
tff(141,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))),
inference(modus_ponens,[status(thm)],[140, 139])).
tff(142,plain,
($false),
inference(unit_resolution,[status(thm)],[141, 63, 138, 136, 134])).
tff(143,plain,((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))), inference(lemma,lemma(discharge,[]))).
tff(144,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : ((~like(X, Y)) | creative(Y) | (~like(fred, X)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : ((~like(X, Y)) | creative(Y) | (~like(fred, X))))),
inference(rewrite,[status(thm)],[])).
tff(145,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(like(fred, X) & (~creative(Y)) & like(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : ((~like(X, Y)) | creative(Y) | (~like(fred, X))))),
inference(rewrite,[status(thm)],[])).
tff(146,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(like(fred, X) & (~creative(Y)) & like(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(like(fred, X) & (~creative(Y)) & like(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(147,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(148,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y))))),
inference(monotonicity,[status(thm)],[147])).
tff(149,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(150,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y)))),
inference(or_elim,[status(thm)],[58])).
tff(151,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y)))),
inference(modus_ponens,[status(thm)],[150, 148])).
tff(152,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y)))),
inference(modus_ponens,[status(thm)],[151, 149])).
tff(153,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (like(fred, X) & (~creative(Y)) & like(X, Y)))),
inference(modus_ponens,[status(thm)],[152, 148])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!2 |'paul'|) (= X!2 |'mary'|) (not (room X!2)))))
(a!5 (lambda ((X $i) (Y $i))
(let ((a!1 (and (like fred X) (not (creative Y)) (like X Y))))
(refl (~ (not a!1) (not a!1))))))
(a!6 (exists ((X $i) (Y $i))
(and (like fred X) (not (creative Y)) (like X Y))))
(a!7 (forall ((X $i) (Y $i))
(let ((a!1 (and (like fred X) (not (creative Y)) (like X Y))))
(not a!1)))))
(let ((a!8 (~ (not (and (room mary) (room paul) a!3 a!6))
(or (not (room mary)) (not (room paul)) a!4 a!7))))
(nnf-neg a!1
a!2
(sk (~ (not a!3) a!4))
(nnf-neg (proof-bind a!5) (~ (not a!6) a!7))
a!8)))
| room(nancy)&room(kenneth)&(![X]:(room(X)=>(X='nancy'|X='kenneth')))&
((((~?[X]:(~room(X)=>(like(X,victor))))=>(?[X]:(~room(X)=>(((hate(victor,X))=>(hate(X,victor)))))))|((~(~?[X]:(~room(X)=>(like(X,victor)))))=>(~((~brave(nancy))|(does_not_enjoy_salsa_dancing(nancy))))))&
(~(![X]:(~room(X)=>(~creative(X))))=>(~?[X]:(~room(X)=>(X!=nancy))))&
(?[X,Y]:((~like(victor,X))&(hate(victor,Y))&(hate(X,Y))))&
(![X]:(quieter(X,nancy)))&
((like(kenneth,victor) & like(victor,kenneth)))&
(quieter(kenneth,victor))) | room(nancy)&room(kenneth)&(![X]:(room(X)=>(X='nancy'|X='kenneth')))&
(?[X,Y]:((like(victor,X))&(~creative(Y))&(like(X,Y)))) | contradiction | neutral |
Michael, Crystal are the only persons in the room.
At least one of the following is true:.
-Crystal who is a client of Margaret, is not Michael.
-Michael is the richest in the room.
-Michael either does not play the violin or is not a happy european. | Michael is a happy rich european. | neutral | % SZS status Satisfiable
| room(michael)&room(crystal)&(![X]:(room(X)=>(X='michael'|X='crystal')))&
((((client(margaret,crystal))&(crystal!=michael))|
(![X]:(richer(X,michael)))|
((((does_not_play_the_violin(michael))|(~(happy(michael)&european(michael))))&(~((does_not_play_the_violin(michael))|(~(happy(michael)&european(michael))))))))) | room(michael)&room(crystal)&(![X]:(room(X)=>(X='michael'|X='crystal')))&
(happy(michael)&rich(michael)&european(michael)) | contradiction | contradiction |
Gregory, Beulah, Daniel are the only persons in the room.
If 'more than one person in the room is quieter than Jean' then 'Frank and Jean hate each other'.
It is not the case that 'more than one person outside the room is a rich happy tourist'.
Daniel neither is a tall tourist nor is quieter than Michelle.
Daniel is the tallest in the room.
Gregory and Beulah are not hated by Frank. | It is not the case that 'Daniel either is hated by Michelle or is a client of Jean'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(fred_type, type, (
fred: $i)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(john_type, type, (
john: $i)).
tff(paul_type, type, (
paul: $i)).
tff(mary_type, type, (
mary: $i)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(tourist_type, type, (
tourist: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(client_type, type, (
client: ( $i * $i ) > $o)).
tff(1,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((?[X: $i, Y: $i] : (((room(X) & room(Y)) & (quieter(lucy, X) & quieter(lucy, Y))) & (~(X = Y))) => (hate(john, lucy) & hate(lucy, john))) & (~?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (((((rich(X) & happy(X)) & tourist(X)) & rich(Y)) & happy(Y)) & tourist(Y))) & (~(X = Y))))) & (~((tall(fred) & tourist(fred)) | quieter(susan, fred)))) & ![X: $i] : taller(X, fred)) & ((~hate(mary, john)) & (~hate(paul, john))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~((hate(fred, susan) | client(lucy, fred)) & (~(hate(fred, susan) | client(lucy, fred)))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : (room(X) & room(Y) & quieter(lucy, X) & quieter(lucy, Y) & (~(X = Y)))) | (hate(john, lucy) & hate(lucy, john))) & (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & rich(X) & happy(X) & tourist(X) & rich(Y) & happy(Y) & tourist(Y) & (~(X = Y)))) & (~((tall(fred) & tourist(fred)) | quieter(susan, fred))) & ![X: $i] : taller(X, fred) & (~hate(mary, john)) & (~hate(paul, john)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((?[X: $i, Y: $i] : (((room(X) & room(Y)) & (quieter(lucy, X) & quieter(lucy, Y))) & (~(X = Y))) => (hate(john, lucy) & hate(lucy, john))) & (~?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (((((rich(X) & happy(X)) & tourist(X)) & rich(Y)) & happy(Y)) & tourist(Y))) & (~(X = Y))))) & (~((tall(fred) & tourist(fred)) | quieter(susan, fred)))) & ![X: $i] : taller(X, fred)) & ((~hate(mary, john)) & (~hate(paul, john))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~((hate(fred, susan) | client(lucy, fred)) & (~(hate(fred, susan) | client(lucy, fred)))))))), file('/mnt/tmpfs//6650870952862351164903457.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : (room(X) & room(Y) & quieter(lucy, X) & quieter(lucy, Y) & (~(X = Y)))) | (hate(john, lucy) & hate(lucy, john))) & (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & rich(X) & happy(X) & tourist(X) & rich(Y) & happy(Y) & tourist(Y) & (~(X = Y)))) & (~((tall(fred) & tourist(fred)) | quieter(susan, fred))) & ![X: $i] : taller(X, fred) & (~hate(mary, john)) & (~hate(paul, john)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : (room(X) & room(Y) & quieter(lucy, X) & quieter(lucy, Y) & (~(X = Y)))) | (hate(john, lucy) & hate(lucy, john))) & (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & rich(X) & happy(X) & tourist(X) & rich(Y) & happy(Y) & tourist(Y) & (~(X = Y)))) & (~((tall(fred) & tourist(fred)) | quieter(susan, fred))) & ![X: $i] : taller(X, fred) & (~hate(mary, john)) & (~hate(paul, john))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(room(fred)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(10,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[9, 8])).
tff(11,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(12,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(13,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
((~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))),
inference(monotonicity,[status(thm)],[15])).
tff(17,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))),
inference(transitivity,[status(thm)],[16, 14])).
tff(18,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(monotonicity,[status(thm)],[18])).
tff(20,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(or_elim,[status(thm)],[4])).
tff(22,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[21, 19])).
tff(23,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[22, 20])).
tff(24,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[23, 19])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!0 |'fred'|)
(= X!0 |'paul'|)
(= X!0 |'mary'|)
(not (room X!0))))))
(let ((a!6 (~ (not (and (room mary) (room paul) (room fred) a!4))
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5))))
(nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) a!6)))
| room(gregory)&room(beulah)&room(daniel)&(![X]:(room(X)=>(X='gregory'|X='beulah'|X='daniel')))&
((((?[X,Y]:(room(X)&room(Y)&(quieter(jean,X)&quieter(jean,Y))&(X!=Y))))=>((hate(frank,jean) & hate(jean,frank))))&
(~((?[X,Y]:(~room(X)&~room(Y)&(rich(X)&happy(X)&tourist(X)&rich(Y)&happy(Y)&tourist(Y))&(X!=Y)))))&
(~((tall(daniel)&tourist(daniel))|(quieter(michelle,daniel))))&
(![X]:(taller(X,daniel)))&
(~hate(gregory,frank)&~hate(beulah,frank))) | room(gregory)&room(beulah)&room(daniel)&(![X]:(room(X)=>(X='gregory'|X='beulah'|X='daniel')))&
(~((((hate(daniel,michelle))|(client(jean,daniel)))&(~((hate(daniel,michelle))|(client(jean,daniel))))))) | neutral | entailment |
Carey, Adriana, Marvin, Barbara are the only persons in the room.
If "Carey is a rich creative european and does not enjoy stand-up paddleboarding" then "more than one person outside the room is a creative tall european" otherwise "more than one person outside the room is richer than Lucille".
"It is not the case that 'Carey is not liked by Lucille and is not a tall rich european'" if "it is not the case that 'Carey does not enjoy stand-up paddleboarding and is a client of Lucille'" and vice versa.
Barbara is the tallest in the room.
It is not the case that 'Lucille is a client of Adriana'.
Barbara likes Lucille or collects action figures or both.
Adriana is not a creative european or does not travel domestically frequently or both.
Barbara is not tall.
Adriana is the richest in the room. | Someone who is a tall creative person like someone who is hated by Alicia. | contradiction | - | room(carey)&room(adriana)&room(marvin)&room(barbara)&(![X]:(room(X)=>(X='carey'|X='adriana'|X='marvin'|X='barbara')))&
(((((rich(carey)&creative(carey)&european(carey))&(does_not_enjoy_stand-up_paddleboarding(carey)))=>((?[X,Y]:(~room(X)&~room(Y)&(creative(X)&tall(X)&european(X)&creative(Y)&tall(Y)&european(Y))&(X!=Y)))))|((~((rich(carey)&creative(carey)&european(carey))&(does_not_enjoy_stand-up_paddleboarding(carey))))=>((?[X,Y]:(~room(X)&~room(Y)&(richer(lucille,X)&richer(lucille,Y))&(X!=Y))))))&
((~((does_not_enjoy_stand-up_paddleboarding(carey))&(client(lucille,carey))))<=>(~((~like(carey,lucille))&(~(tall(carey)&rich(carey)&european(carey))))))&
(![X]:(taller(X,barbara)))&
(~(client(adriana,lucille)))&
(((like(lucille,barbara))|(collects_action_figures(barbara))))&
(((~(creative(adriana)&european(adriana)))|(does_not_travel_domestically_frequently(adriana))))&
(~tall(barbara))&
(![X]:(richer(X,adriana)))) | room(carey)&room(adriana)&room(marvin)&room(barbara)&(![X]:(room(X)=>(X='carey'|X='adriana'|X='marvin'|X='barbara')))&
(?[X,Y]:((tall(X)&creative(X)&person(X))&(hate(Y,alicia))&(like(X,Y)))) | neutral | neutral |
Emma is the only person in the room. If Emma is the least quiet in the room then Emma either is not liked by Michele or does not like Michele otherwise Sabrina is a client of Emma. Emma is the least quiet in the room. Sabrina is a client of Emma. It is not the case that 'Emma either is not hated by Sabrina or is not liked by Michele'. Only one person outside the room is hated by Michele. | It is not the case that 'someone who is not liked by Sabrina is quieter than someone who is hated by Paul'. | neutral | % SZS status Satisfiable
| room(emma)&(![X]:(room(X)=>(X='emma')))&
((((![X]:(quieter(emma,X)))=>((((~like(emma,michele))|(~like(michele,emma)))&(~((~like(emma,michele))|(~like(michele,emma)))))))|((~(![X]:(quieter(emma,X))))=>(client(emma,sabrina))))&
(![X]:(quieter(emma,X)))&
(client(emma,sabrina))&
(~((((~hate(emma,sabrina))|(~like(emma,michele)))&(~((~hate(emma,sabrina))|(~like(emma,michele)))))))&
(((?[X]:(~room(X)&hate(X,michele)))&(![X,Y]:((hate(X,michele)&hate(Y,michele))=>(X=Y)))))) | room(emma)&(![X]:(room(X)=>(X='emma')))&
(~(?[X,Y]:((~like(X,sabrina))&(hate(Y,paul))&(quieter(X,Y))))) | entailment | entailment |
Charles, Diane are the only persons in the room. More than one person outside the room is not Charles. Only one person in the room is a tall tourist. Charles is the least tall in the room. Charles is not liked by Jeanette and does not hate Noah. | Someone who does not hate Noah is taller than someone who hates Jeanette. | neutral | % SZS status Satisfiable
| room(charles)&room(diane)&(![X]:(room(X)=>(X='charles'|X='diane')))&
(((?[X,Y]:(~room(X)&~room(Y)&(X!=charles&Y!=charles)&(X!=Y))))&
(((?[X]:(room(X)&tall(X)&tourist(X)))&(![X,Y]:((tall(X)&tourist(X)&tall(Y)&tourist(Y))=>(X=Y)))))&
(![X]:(taller(charles,X)))&
((~like(charles,jeanette))&(~hate(noah,charles)))) | room(charles)&room(diane)&(![X]:(room(X)=>(X='charles'|X='diane')))&
(?[X,Y]:((~hate(noah,X))&(hate(jeanette,Y))&(taller(X,Y)))) | neutral | neutral |
Raymond, Carlos, Patricia are the only persons in the room.
If "Patricia is the tallest in the room" then "Carlos neither plays video games nor is not tall, not creative, not happy" otherwise "Patricia who likes Darla, is liked by Darla".
"No one outside the room is a happy rich tall tourist" if "Carlos who enjoys stargazing, is taller than Darla".
Only one person outside the room is not a tall rich happy creative tourist.
Patricia does not play video games and likes Darla.
Carlos neither is richer than Matt nor does not like Angela.
Carlos neither is not a creative tall tourist nor is not a rich tall tourist. | Raymond neither is a rich tourist nor hates Angela. | contradiction | - | room(raymond)&room(carlos)&room(patricia)&(![X]:(room(X)=>(X='raymond'|X='carlos'|X='patricia')))&
((((![X]:(taller(X,patricia)))=>(~((plays_video_games(carlos))|(~tall(carlos)&~creative(carlos)&~happy(carlos)))))|((~(![X]:(taller(X,patricia))))=>((like(darla,patricia))&(like(patricia,darla)))))&
(((enjoys_stargazing(carlos))&(taller(darla,carlos)))=>(~?[X]:(~room(X)=>(happy(X)&rich(X)&tall(X)&tourist(X)))))&
(((?[X]:(~room(X)&~(tall(X)&rich(X)&happy(X)&creative(X)&tourist(X))))&(![X,Y]:((~(tall(X)&rich(X)&happy(X)&creative(X)&tourist(X))&~(tall(Y)&rich(Y)&happy(Y)&creative(Y)&tourist(Y)))=>(X=Y)))))&
((does_not_play_video_games(patricia))&(like(darla,patricia)))&
(~((richer(matt,carlos))|(~like(angela,carlos))))&
(~((~(creative(carlos)&tall(carlos)&tourist(carlos)))|(~(rich(carlos)&tall(carlos)&tourist(carlos)))))) | room(raymond)&room(carlos)&room(patricia)&(![X]:(room(X)=>(X='raymond'|X='carlos'|X='patricia')))&
(~((rich(raymond)&tourist(raymond))|(hate(angela,raymond)))) | neutral | neutral |
Nancy, Margaret, Adele are the only persons in the room. Margaret who is liked by Charles, is not Nancy. Nancy who enjoys landscape photography, does not hate Philip. Everyone outside the room is a sibling of Philip. More than one person outside the room is not Margaret. Margaret does not enjoy jogging or does not like Philip or both. Margaret is the least quiet in the room. Nancy is the least rich in the room. Someone who is a rich person like someone who is not liked by Philip. Everyone in the room who is not a quiet rich tall person likes Philip. | Someone who does not hate Philip is richer than someone who is a sibling of Philip. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(alice_type, type, (
alice: $i)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(paul_type, type, (
paul: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(mary_type, type, (
mary: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(susan_type, type, (
susan: $i)).
tff(john_type, type, (
john: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(predc_type, type, (
predc: $i > $o)).
tff(sibling_type, type, (
sibling: ( $i * $i ) > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(1,plain,
((alice = fred) <=> (fred = alice)),
inference(commutativity,[status(thm)],[])).
tff(2,plain,
((fred = paul) <=> (paul = fred)),
inference(commutativity,[status(thm)],[])).
tff(3,plain,
((fred = mary) <=> (mary = fred)),
inference(commutativity,[status(thm)],[])).
tff(4,assumption,(~(paul = |'mary'|)), introduced(assumption)).
tff(5,plain,
((paul = mary) <=> (mary = paul)),
inference(commutativity,[status(thm)],[])).
tff(6,assumption,(~(mary = |'fred'|)), introduced(assumption)).
tff(7,assumption,(fred = |'paul'|), introduced(assumption)).
tff(8,plain,
(|'paul'| = fred),
inference(symmetry,[status(thm)],[7])).
tff(9,plain,
((alice = |'paul'|) <=> (alice = fred)),
inference(monotonicity,[status(thm)],[8])).
tff(10,plain,
((alice = |'paul'|) <=> (fred = alice)),
inference(transitivity,[status(thm)],[9, 1])).
tff(11,plain,
((fred = alice) <=> (alice = |'paul'|)),
inference(symmetry,[status(thm)],[10])).
tff(12,plain,
((~(fred = alice)) <=> (~(alice = |'paul'|))),
inference(monotonicity,[status(thm)],[11])).
tff(13,plain,
((~(fred = alice)) <=> (~(fred = alice))),
inference(rewrite,[status(thm)],[])).
tff(14,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//415293252675742377897884.p','b14')).
tff(15,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[16])).
tff(18,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[17])).
tff(19,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[18])).
tff(20,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[19])).
tff(21,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[20])).
tff(22,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[22])).
tff(24,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[23])).
tff(25,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[29])).
tff(31,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[30])).
tff(32,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[31])).
tff(33,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[32])).
tff(34,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[33])).
tff(35,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[34])).
tff(36,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[35])).
tff(37,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[36])).
tff(38,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[37])).
tff(39,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[38])).
tff(40,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[39])).
tff(41,plain,
(((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))),
inference(and_elim,[status(thm)],[40])).
tff(42,plain,
(~(fred = alice)),
inference(and_elim,[status(thm)],[41])).
tff(43,plain,
(~(fred = alice)),
inference(modus_ponens,[status(thm)],[42, 13])).
tff(44,plain,
(~(alice = |'paul'|)),
inference(modus_ponens,[status(thm)],[43, 12])).
tff(45,plain,
((alice = mary) <=> (mary = alice)),
inference(commutativity,[status(thm)],[])).
tff(46,plain,
((mary = |'paul'|) <=> (mary = fred)),
inference(monotonicity,[status(thm)],[8])).
tff(47,plain,
((mary = fred) <=> (mary = |'paul'|)),
inference(symmetry,[status(thm)],[46])).
tff(48,plain,
((~(mary = fred)) <=> (~(mary = |'paul'|))),
inference(monotonicity,[status(thm)],[47])).
tff(49,plain,
((~(mary = fred)) <=> (~(mary = fred))),
inference(rewrite,[status(thm)],[])).
tff(50,plain,
((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))),
inference(and_elim,[status(thm)],[41])).
tff(51,plain,
(((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))),
inference(and_elim,[status(thm)],[50])).
tff(52,plain,
((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))),
inference(and_elim,[status(thm)],[51])).
tff(53,plain,
(((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))),
inference(and_elim,[status(thm)],[52])).
tff(54,plain,
((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))),
inference(and_elim,[status(thm)],[53])).
tff(55,plain,
(((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))),
inference(and_elim,[status(thm)],[54])).
tff(56,plain,
((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))),
inference(and_elim,[status(thm)],[55])).
tff(57,plain,
(((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))),
inference(and_elim,[status(thm)],[56])).
tff(58,plain,
((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))),
inference(and_elim,[status(thm)],[57])).
tff(59,plain,
(((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))),
inference(and_elim,[status(thm)],[58])).
tff(60,plain,
((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))),
inference(and_elim,[status(thm)],[59])).
tff(61,plain,
(((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))),
inference(and_elim,[status(thm)],[60])).
tff(62,plain,
((~(mary = paul)) & (~(mary = fred))),
inference(and_elim,[status(thm)],[61])).
tff(63,plain,
(~(mary = fred)),
inference(and_elim,[status(thm)],[62])).
tff(64,plain,
(~(mary = fred)),
inference(modus_ponens,[status(thm)],[63, 49])).
tff(65,plain,
(~(mary = |'paul'|)),
inference(modus_ponens,[status(thm)],[64, 48])).
tff(66,plain,
(^[X: $i] : refl(((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(67,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[66])).
tff(68,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(69,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((like(paul, john) & (~(paul = mary))) & (predb(mary) & (~hate(lucy, mary)))) & ![X: $i] : ((~room(X)) => sibling(lucy, X))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = paul)) & (~(Y = paul)))) & (~(X = Y)))) & ((~predc(paul)) | (~like(lucy, paul)))) & ![X: $i] : quieter(paul, X)) & ![X: $i] : richer(mary, X)) & ?[X: $i, Y: $i] : (((rich(X) & person(X)) & (~like(Y, lucy))) & like(X, Y))) & ![X: $i] : (room(X) => ((~(((quiet(X) & rich(X)) & tall(X)) & person(X))) => like(lucy, X))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ?[X: $i, Y: $i] : (((~hate(lucy, X)) & sibling(lucy, Y)) & richer(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(paul, john) & (~(paul = mary)) & predb(mary) & (~hate(lucy, mary)) & ![X: $i] : (room(X) | sibling(lucy, X)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = paul)) & (~(Y = paul)) & (~(X = Y))) & ((~predc(paul)) | (~like(lucy, paul))) & ![X: $i] : quieter(paul, X) & ![X: $i] : richer(mary, X) & ?[X: $i, Y: $i] : (rich(X) & person(X) & (~like(Y, lucy)) & like(X, Y)) & ![X: $i] : ((~room(X)) | like(lucy, X) | (quiet(X) & rich(X) & tall(X) & person(X))))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))))),
inference(rewrite,[status(thm)],[])).
tff(70,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((like(paul, john) & (~(paul = mary))) & (predb(mary) & (~hate(lucy, mary)))) & ![X: $i] : ((~room(X)) => sibling(lucy, X))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = paul)) & (~(Y = paul)))) & (~(X = Y)))) & ((~predc(paul)) | (~like(lucy, paul)))) & ![X: $i] : quieter(paul, X)) & ![X: $i] : richer(mary, X)) & ?[X: $i, Y: $i] : (((rich(X) & person(X)) & (~like(Y, lucy))) & like(X, Y))) & ![X: $i] : (room(X) => ((~(((quiet(X) & rich(X)) & tall(X)) & person(X))) => like(lucy, X))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ?[X: $i, Y: $i] : (((~hate(lucy, X)) & sibling(lucy, Y)) & richer(X, Y))))), file('/mnt/tmpfs//415293252675742377897884.p','negated')).
tff(71,plain,
(~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(paul, john) & (~(paul = mary)) & predb(mary) & (~hate(lucy, mary)) & ![X: $i] : (room(X) | sibling(lucy, X)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = paul)) & (~(Y = paul)) & (~(X = Y))) & ((~predc(paul)) | (~like(lucy, paul))) & ![X: $i] : quieter(paul, X) & ![X: $i] : richer(mary, X) & ?[X: $i, Y: $i] : (rich(X) & person(X) & (~like(Y, lucy)) & like(X, Y)) & ![X: $i] : ((~room(X)) | like(lucy, X) | (quiet(X) & rich(X) & tall(X) & person(X))))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y))))),
inference(modus_ponens,[status(thm)],[70, 69])).
tff(72,plain,
(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & like(paul, john) & (~(paul = mary)) & predb(mary) & (~hate(lucy, mary)) & ![X: $i] : (room(X) | sibling(lucy, X)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = paul)) & (~(Y = paul)) & (~(X = Y))) & ((~predc(paul)) | (~like(lucy, paul))) & ![X: $i] : quieter(paul, X) & ![X: $i] : richer(mary, X) & ?[X: $i, Y: $i] : (rich(X) & person(X) & (~like(Y, lucy)) & like(X, Y)) & ![X: $i] : ((~room(X)) | like(lucy, X) | (quiet(X) & rich(X) & tall(X) & person(X)))),
inference(or_elim,[status(thm)],[71])).
tff(73,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(and_elim,[status(thm)],[72])).
tff(74,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[73, 68])).
tff(75,plain,(
![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[74])).
tff(76,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[75, 67])).
tff(77,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(78,plain,
(room(mary)),
inference(and_elim,[status(thm)],[72])).
tff(79,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[78, 77])).
tff(80,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(mary)) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(81,plain,
(((mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|) | (~room(mary))) <=> ((~room(mary)) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(82,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(mary)) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|)))),
inference(monotonicity,[status(thm)],[81])).
tff(83,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(transitivity,[status(thm)],[82, 80])).
tff(84,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))),
inference(quant_inst,[status(thm)],[])).
tff(85,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[84, 83])).
tff(86,plain,
((mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|)),
inference(unit_resolution,[status(thm)],[85, 79, 76])).
tff(87,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[86, 65, 6])).
tff(88,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[87])).
tff(89,plain,
((alice = |'mary'|) <=> (alice = mary)),
inference(monotonicity,[status(thm)],[88])).
tff(90,plain,
((alice = |'mary'|) <=> (mary = alice)),
inference(transitivity,[status(thm)],[89, 45])).
tff(91,plain,
((mary = alice) <=> (alice = |'mary'|)),
inference(symmetry,[status(thm)],[90])).
tff(92,plain,
((~(mary = alice)) <=> (~(alice = |'mary'|))),
inference(monotonicity,[status(thm)],[91])).
tff(93,plain,
((~(mary = alice)) <=> (~(mary = alice))),
inference(rewrite,[status(thm)],[])).
tff(94,plain,
(~(mary = alice)),
inference(and_elim,[status(thm)],[61])).
tff(95,plain,
(~(mary = alice)),
inference(modus_ponens,[status(thm)],[94, 93])).
tff(96,plain,
(~(alice = |'mary'|)),
inference(modus_ponens,[status(thm)],[95, 92])).
tff(97,plain,
((alice = paul) <=> (paul = alice)),
inference(commutativity,[status(thm)],[])).
tff(98,plain,
((paul = |'paul'|) <=> (paul = fred)),
inference(monotonicity,[status(thm)],[8])).
tff(99,plain,
((paul = fred) <=> (paul = |'paul'|)),
inference(symmetry,[status(thm)],[98])).
tff(100,plain,
((~(paul = fred)) <=> (~(paul = |'paul'|))),
inference(monotonicity,[status(thm)],[99])).
tff(101,plain,
((~(paul = fred)) <=> (~(paul = fred))),
inference(rewrite,[status(thm)],[])).
tff(102,plain,
(~(paul = fred)),
inference(and_elim,[status(thm)],[56])).
tff(103,plain,
(~(paul = fred)),
inference(modus_ponens,[status(thm)],[102, 101])).
tff(104,plain,
(~(paul = |'paul'|)),
inference(modus_ponens,[status(thm)],[103, 100])).
tff(105,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(106,plain,
(room(paul)),
inference(and_elim,[status(thm)],[72])).
tff(107,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[106, 105])).
tff(108,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(paul)) | (paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(109,plain,
(((paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|) | (~room(paul))) <=> ((~room(paul)) | (paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(110,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(paul)) | (paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|)))),
inference(monotonicity,[status(thm)],[109])).
tff(111,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(transitivity,[status(thm)],[110, 108])).
tff(112,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))),
inference(quant_inst,[status(thm)],[])).
tff(113,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|)),
inference(modus_ponens,[status(thm)],[112, 111])).
tff(114,plain,
((paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[113, 107, 76])).
tff(115,plain,
(paul = |'fred'|),
inference(unit_resolution,[status(thm)],[114, 104, 4])).
tff(116,plain,
(|'fred'| = paul),
inference(symmetry,[status(thm)],[115])).
tff(117,plain,
((alice = |'fred'|) <=> (alice = paul)),
inference(monotonicity,[status(thm)],[116])).
tff(118,plain,
((alice = |'fred'|) <=> (paul = alice)),
inference(transitivity,[status(thm)],[117, 97])).
tff(119,plain,
((paul = alice) <=> (alice = |'fred'|)),
inference(symmetry,[status(thm)],[118])).
tff(120,plain,
((~(paul = alice)) <=> (~(alice = |'fred'|))),
inference(monotonicity,[status(thm)],[119])).
tff(121,plain,
((~(paul = alice)) <=> (~(paul = alice))),
inference(rewrite,[status(thm)],[])).
tff(122,plain,
(~(paul = alice)),
inference(and_elim,[status(thm)],[55])).
tff(123,plain,
(~(paul = alice)),
inference(modus_ponens,[status(thm)],[122, 121])).
tff(124,plain,
(~(alice = |'fred'|)),
inference(modus_ponens,[status(thm)],[123, 120])).
tff(125,plain,
(^[X: $i] : refl(richer(mary, X) <=> richer(mary, X))),
inference(bind,[status(th)],[])).
tff(126,plain,
(![X: $i] : richer(mary, X) <=> ![X: $i] : richer(mary, X)),
inference(quant_intro,[status(thm)],[125])).
tff(127,plain,
(![X: $i] : richer(mary, X) <=> ![X: $i] : richer(mary, X)),
inference(rewrite,[status(thm)],[])).
tff(128,plain,
(![X: $i] : richer(mary, X)),
inference(and_elim,[status(thm)],[72])).
tff(129,plain,
(![X: $i] : richer(mary, X)),
inference(modus_ponens,[status(thm)],[128, 127])).
tff(130,plain,(
![X: $i] : richer(mary, X)),
inference(skolemize,[status(sab)],[129])).
tff(131,plain,
(![X: $i] : richer(mary, X)),
inference(modus_ponens,[status(thm)],[130, 126])).
tff(132,plain,
((~![X: $i] : richer(mary, X)) | richer(mary, alice)),
inference(quant_inst,[status(thm)],[])).
tff(133,plain,
(richer(mary, alice)),
inference(unit_resolution,[status(thm)],[132, 131])).
tff(134,assumption,(~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))), introduced(assumption)).
tff(135,plain,
(((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | room(X!4)),
inference(tautology,[status(thm)],[])).
tff(136,plain,
(room(X!4)),
inference(unit_resolution,[status(thm)],[135, 134])).
tff(137,plain,
(((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(138,plain,
(~(X!4 = |'mary'|)),
inference(unit_resolution,[status(thm)],[137, 134])).
tff(139,plain,
(((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(140,plain,
(~(X!4 = |'paul'|)),
inference(unit_resolution,[status(thm)],[139, 134])).
tff(141,plain,
(((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'fred'|))),
inference(tautology,[status(thm)],[])).
tff(142,plain,
(~(X!4 = |'fred'|)),
inference(unit_resolution,[status(thm)],[141, 134])).
tff(143,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(rewrite,[status(thm)],[])).
tff(144,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(quant_inst,[status(thm)],[])).
tff(145,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))),
inference(modus_ponens,[status(thm)],[144, 143])).
tff(146,plain,
($false),
inference(unit_resolution,[status(thm)],[145, 76, 142, 140, 138, 136])).
tff(147,plain,((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))), inference(lemma,lemma(discharge,[]))).
tff(148,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(149,plain,
(room(fred)),
inference(and_elim,[status(thm)],[72])).
tff(150,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[149, 148])).
tff(151,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y))))),
inference(rewrite,[status(thm)],[])).
tff(152,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y))))),
inference(rewrite,[status(thm)],[])).
tff(153,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)) <=> (~(hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y))))), ((~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y))) <=> (~(~(hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y))))))), rewrite((~(~(hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y))))) <=> (hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y)))), ((~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y))) <=> (hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y)))))),
inference(bind,[status(th)],[])).
tff(154,plain,
(![X: $i, Y: $i] : (~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y))) <=> ![X: $i, Y: $i] : (hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y)))),
inference(quant_intro,[status(thm)],[153])).
tff(155,plain,
((~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))),
inference(rewrite,[status(thm)],[])).
tff(156,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y))))),
inference(monotonicity,[status(thm)],[155, 154])).
tff(157,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (hate(lucy, X) | (~richer(X, Y)) | (~sibling(lucy, Y))))),
inference(transitivity,[status(thm)],[156, 152])).
tff(158,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(159,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y))))),
inference(monotonicity,[status(thm)],[155])).
tff(160,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y))))),
inference(transitivity,[status(thm)],[159, 158])).
tff(161,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(162,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y))))),
inference(monotonicity,[status(thm)],[161])).
tff(163,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(164,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))),
inference(or_elim,[status(thm)],[71])).
tff(165,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))),
inference(modus_ponens,[status(thm)],[164, 162])).
tff(166,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))),
inference(modus_ponens,[status(thm)],[165, 163])).
tff(167,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~hate(lucy, X)) & sibling(lucy, Y) & richer(X, Y)))),
inference(modus_ponens,[status(thm)],[166, 162])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (forall ((X $i))
(or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!5 (not (or (= X!4 |'fred'|)
(= X!4 |'paul'|)
(= X!4 |'mary'|)
(not (room X!4)))))
(a!6 (lambda ((X $i) (Y $i))
(let ((a!1 (and (not (hate lucy X)) (sibling lucy Y) (richer X Y))))
(refl (~ (not a!1) (not a!1))))))
(a!7 (exists ((X $i) (Y $i))
(and (not (hate lucy X)) (sibling lucy Y) (richer X Y))))
(a!8 (forall ((X $i) (Y $i))
(let ((a!1 (and (not (hate lucy X)) (sibling lucy Y) (richer X Y))))
(not a!1)))))
(let ((a!9 (~ (not (and (room mary) (room paul) (room fred) a!4 a!7))
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!8))))
(nnf-neg a!1
a!2
a!3
(sk (~ (not a!4) a!5))
(nnf-neg (proof-bind a!6) (~ (not a!7) a!8))
a!9)))
| room(nancy)&room(margaret)&room(adele)&(![X]:(room(X)=>(X='nancy'|X='margaret'|X='adele')))&
(((like(margaret,charles))&(margaret!=nancy))&
((enjoys_landscape_photography(nancy))&(~hate(philip,nancy)))&
(![X]:(~room(X)=>(sibling(philip,X))))&
((?[X,Y]:(~room(X)&~room(Y)&(X!=margaret&Y!=margaret)&(X!=Y))))&
(((does_not_enjoy_jogging(margaret))|(~like(philip,margaret))))&
(![X]:(quieter(margaret,X)))&
(![X]:(richer(nancy,X)))&
(?[X,Y]:((rich(X)&person(X))&(~like(Y,philip))&(like(X,Y))))&
(![X]:(room(X)=>(((~(quiet(X)&rich(X)&tall(X)&person(X)))=>(like(philip,X))))))) | room(nancy)&room(margaret)&room(adele)&(![X]:(room(X)=>(X='nancy'|X='margaret'|X='adele')))&
(?[X,Y]:((~hate(philip,X))&(sibling(philip,Y))&(richer(X,Y)))) | neutral | contradiction |
Jaime, Leo, Crystal are the only persons in the room.
Kirk is a client of Leo.
Crystal is not liked by Norma and is a tall european.
Only one person in the room does not hate Whitney.
Someone who is not hated by Norma is taller than someone who is a brave european.
Everyone in the room is not happy, not brave, not creative. | Crystal neither is hated by Whitney nor is a client of Norma. | neutral | % SZS status Satisfiable
| room(jaime)&room(leo)&room(crystal)&(![X]:(room(X)=>(X='jaime'|X='leo'|X='crystal')))&
((client(leo,kirk))&
((~like(crystal,norma))&(tall(crystal)&european(crystal)))&
(((?[X]:(room(X)&~hate(whitney,X)))&(![X,Y]:((~hate(whitney,X)&~hate(whitney,Y))=>(X=Y)))))&
(?[X,Y]:((~hate(X,norma))&(brave(Y)&european(Y))&(taller(X,Y))))&
(![X]:(room(X)=>(~happy(X)&~brave(X)&~creative(X))))) | room(jaime)&room(leo)&room(crystal)&(![X]:(room(X)=>(X='jaime'|X='leo'|X='crystal')))&
(~((hate(crystal,whitney))|(client(norma,crystal)))) | contradiction | contradiction |
Kimberly, George are the only persons in the room. If “Kimberly and George like each other” then “George neither does not enjoy watercolor painting nor does not like Bessie”. “George and Kimberly are respectively rich and brave” if “George likes Jennette” and vice versa. “Farrah and George like each other” only if “it is not the case that 'everyone outside the room is liked by Bessie'”. George neither does not enjoy watercolor painting nor does not like Bessie. Someone outside the room does not like Farrah. | It is not the case that 'George either is richer than Bessie or is a brave person'. | entailment | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(paul_type, type, (
paul: $i)).
tff(like_type, type, (
like: ( $i * $i ) > $o)).
tff(susan_type, type, (
susan: $i)).
tff(john_type, type, (
john: $i)).
tff(predb_type, type, (
predb: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(rich_type, type, (
rich: $i > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(richer_type, type, (
richer: ( $i * $i ) > $o)).
tff(1,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((like(mary, paul) & like(paul, mary)) => (~((~predb(paul)) | (~like(john, paul))))) & (like(lucy, paul) <=> (rich(paul) & brave(mary)))) & ((like(susan, paul) & like(paul, susan)) => (~![X: $i] : ((~room(X)) => like(X, john))))) & (~((~predb(paul)) | (~like(john, paul))))) & ?[X: $i] : ((~room(X)) => (~like(susan, X))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((richer(john, paul) | (brave(paul) & person(paul))) & (~(richer(john, paul) | (brave(paul) & person(paul))))))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(like(mary, paul) & like(paul, mary))) | (~((~predb(paul)) | (~like(john, paul))))) & (like(lucy, paul) <=> (rich(paul) & brave(mary))) & ((~(like(susan, paul) & like(paul, susan))) | (~![X: $i] : (room(X) | like(X, john)))) & (~((~predb(paul)) | (~like(john, paul)))) & ?[X: $i] : (room(X) | (~like(susan, X))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))))),
inference(rewrite,[status(thm)],[])).
tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((like(mary, paul) & like(paul, mary)) => (~((~predb(paul)) | (~like(john, paul))))) & (like(lucy, paul) <=> (rich(paul) & brave(mary)))) & ((like(susan, paul) & like(paul, susan)) => (~![X: $i] : ((~room(X)) => like(X, john))))) & (~((~predb(paul)) | (~like(john, paul))))) & ?[X: $i] : ((~room(X)) => (~like(susan, X))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((richer(john, paul) | (brave(paul) & person(paul))) & (~(richer(john, paul) | (brave(paul) & person(paul))))))))), file('/mnt/tmpfs//8636957654566003246225591.p','negated')).
tff(4,plain,
(~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(like(mary, paul) & like(paul, mary))) | (~((~predb(paul)) | (~like(john, paul))))) & (like(lucy, paul) <=> (rich(paul) & brave(mary))) & ((~(like(susan, paul) & like(paul, susan))) | (~![X: $i] : (room(X) | like(X, john)))) & (~((~predb(paul)) | (~like(john, paul)))) & ?[X: $i] : (room(X) | (~like(susan, X))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(modus_ponens,[status(thm)],[3, 2])).
tff(5,plain,
(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(like(mary, paul) & like(paul, mary))) | (~((~predb(paul)) | (~like(john, paul))))) & (like(lucy, paul) <=> (rich(paul) & brave(mary))) & ((~(like(susan, paul) & like(paul, susan))) | (~![X: $i] : (room(X) | like(X, john)))) & (~((~predb(paul)) | (~like(john, paul)))) & ?[X: $i] : (room(X) | (~like(susan, X)))),
inference(or_elim,[status(thm)],[4])).
tff(6,plain,
(room(paul)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
(room(mary)),
inference(and_elim,[status(thm)],[5])).
tff(10,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[9, 8])).
tff(11,plain,
((~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))),
inference(rewrite,[status(thm)],[])).
tff(12,plain,
(((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))))),
inference(monotonicity,[status(thm)],[11])).
tff(13,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(14,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(monotonicity,[status(thm)],[13])).
tff(15,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(or_elim,[status(thm)],[4])).
tff(17,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[16, 14])).
tff(18,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[17, 15])).
tff(19,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(modus_ponens,[status(thm)],[18, 14])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!2 |'paul'|) (= X!2 |'mary'|) (not (room X!2))))))
(let ((a!5 (~ (not (and (room mary) (room paul) a!3))
(or (not (room mary)) (not (room paul)) a!4))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) a!5)))
| room(kimberly)&room(george)&(![X]:(room(X)=>(X='kimberly'|X='george')))&
((((like(kimberly,george) & like(george,kimberly)))=>(~((does_not_enjoy_watercolor_painting(george))|(~like(bessie,george)))))&
((like(jennette,george))<=>((rich(george))&(brave(kimberly))))&
(((like(farrah,george) & like(george,farrah)))=>(~(![X]:(~room(X)=>(like(X,bessie))))))&
(~((does_not_enjoy_watercolor_painting(george))|(~like(bessie,george))))&
(?[X]:(~room(X)=>(~like(farrah,X))))) | room(kimberly)&room(george)&(![X]:(room(X)=>(X='kimberly'|X='george')))&
(~((((richer(bessie,george))|(brave(george)&person(george)))&(~((richer(bessie,george))|(brave(george)&person(george))))))) | entailment | contradiction |
Rudy, Nancy, Earl, Frederick are the only persons in the room. If 'Nancy is the least rich in the room' then 'more than one person outside the room is a brave rich tall quiet person' otherwise 'Nancy either is a brave person or likes Louis'. If 'only one person outside the room is liked by Louis' then 'Frederick is the least quiet in the room'. Nancy is a brave quiet person. It is not the case that 'Nancy who does not like Louis, is quieter than Louis'. Only one person outside the room does not like Louis. Louis is richer than Nancy. More than one person outside the room is not a tall quiet brave person. | Someone who is not quiet, not creative is quieter than someone who is not liked by Louis. | neutral | % SZS status Satisfiable
| room(rudy)&room(nancy)&room(earl)&room(frederick)&(![X]:(room(X)=>(X='rudy'|X='nancy'|X='earl'|X='frederick')))&
((((![X]:(richer(nancy,X)))=>((?[X,Y]:(~room(X)&~room(Y)&(brave(X)&rich(X)&tall(X)&quiet(X)&person(X)&brave(Y)&rich(Y)&tall(Y)&quiet(Y)&person(Y))&(X!=Y)))))|((~(![X]:(richer(nancy,X))))=>((((brave(nancy)&person(nancy))|(like(louis,nancy)))&(~((brave(nancy)&person(nancy))|(like(louis,nancy))))))))&
((((?[X]:(~room(X)&like(X,louis)))&(![X,Y]:((like(X,louis)&like(Y,louis))=>(X=Y)))))=>(![X]:(quieter(frederick,X))))&
(brave(nancy)&quiet(nancy)&person(nancy))&
(~((~like(louis,nancy))&(quieter(louis,nancy))))&
(((?[X]:(~room(X)&~like(louis,X)))&(![X,Y]:((~like(louis,X)&~like(louis,Y))=>(X=Y)))))&
(richer(nancy,louis))&
((?[X,Y]:(~room(X)&~room(Y)&(~(tall(X)&quiet(X)&brave(X)&person(X))&~(tall(Y)&quiet(Y)&brave(Y)&person(Y)))&(X!=Y))))) | room(rudy)&room(nancy)&room(earl)&room(frederick)&(![X]:(room(X)=>(X='rudy'|X='nancy'|X='earl'|X='frederick')))&
(?[X,Y]:((~quiet(X)&~creative(X))&(~like(Y,louis))&(quieter(X,Y)))) | neutral | neutral |
Danny neither hates Glenn nor does not have scuba dived. | Danny who does not hate Glenn, does not have scuba dived. | contradiction | - | room(danny)&(![X]:(room(X)=>(X='danny')))&
(~((hate(glenn,danny))|(does_not_have_scuba_dived(danny)))) | room(danny)&(![X]:(room(X)=>(X='danny')))&
((~hate(glenn,danny))&(does_not_have_scuba_dived(danny))) | entailment | contradiction |
Mozelle is the only person in the room. Not all of the following is true:. -Mozelle is not happy, not quiet or collects classic novels or both. -Someone who does not like Deborah is quieter than someone who is not Mozelle. -Mozelle either does not collect classic novels or does not like Joanne. | Mozelle is a quiet european or is liked by Joanne or both. | neutral | % SZS status Satisfiable
| room(mozelle)&(![X]:(room(X)=>(X='mozelle')))&
(~(((~happy(mozelle)&~quiet(mozelle))|(collects_classic_novels(mozelle)))&?[X,Y]:((~like(deborah,X))&(Y!=mozelle)&(quieter(X,Y)))&(((does_not_collect_classic_novels(mozelle))|(~like(joanne,mozelle)))&(~((does_not_collect_classic_novels(mozelle))|(~like(joanne,mozelle))))))) | room(mozelle)&(![X]:(room(X)=>(X='mozelle')))&
(((quiet(mozelle)&european(mozelle))|(like(mozelle,joanne)))) | contradiction | neutral |
It is not the case that 'Pamela is not hated by Guadalupe or does not like Guadalupe or both'. | Pamela who is hated by Virginia, is liked by Guadalupe. | contradiction | - | room(josephine)&room(pamela)&(![X]:(room(X)=>(X='josephine'|X='pamela')))&
(~(((~hate(pamela,guadalupe))|(~like(guadalupe,pamela))))) | room(josephine)&room(pamela)&(![X]:(room(X)=>(X='josephine'|X='pamela')))&
((hate(pamela,virginia))&(like(pamela,guadalupe))) | neutral | neutral |
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