premise
stringlengths 18
2.39k
| hypothesis
stringlengths 17
200
| label
stringclasses 3
values | premise_tptp
stringlengths 62
2.43k
| hypothesis_tptp
stringlengths 56
356
| deberta_pred
stringclasses 3
values | proof_inputs
sequencelengths 0
13
| proof
stringlengths 782
1M
⌀ |
|---|---|---|---|---|---|---|---|
Josephine, Terrance, James, Cecil are the only persons in the room.
“Lisa is quieter than Cecil” if “Terrance is the oldest in the room”.
If “Cecil is the quietest in the room” then “James neither is taller than Lisa nor is a quiet person”.
Only one person outside the room is not wise.
Terrance is quieter than Lisa or is not creative or both.
Only one person in the room is not a tall person.
Terrance is the least tall in the room. | Terrance either is not quiet, not tall, not creative, not wise or is older than Lisa. | neutral | room(josephine)&room(terrance)&room(james)&room(cecil)&(![X]:(room(X)=>(X='josephine'|X='terrance'|X='james'|X='cecil')))&
(((![X]:(older(X,terrance)))=>(quieter(cecil,lisa)))&
((![X]:(quieter(X,cecil)))=>(~((taller(lisa,james))|(quiet(james)&person(james)))))&
(((?[X]:(~room(X)&~wise(X)))&(![X,Y]:((~wise(X)&~wise(Y))=>(X=Y)))))&
(((quieter(lisa,terrance))|(~creative(terrance))))&
(((?[X]:(room(X)&~(tall(X)&person(X))))&(![X,Y]:((~(tall(X)&person(X))&~(tall(Y)&person(Y)))=>(X=Y)))))&
(![X]:(taller(terrance,X)))) | room(josephine)&room(terrance)&room(james)&room(cecil)&(![X]:(room(X)=>(X='josephine'|X='terrance'|X='james'|X='cecil')))&
(((~quiet(terrance)&~tall(terrance)&~creative(terrance)&~wise(terrance))<~>(older(lisa,terrance)))) | entailment | [] | null |
Lupe, Janet are the only persons in the room.
“More than one person outside the room is older than Shane” unless “Lupe is the quietest in the room”.
“Lupe is richer than Robert” if “someone who is not a old brave person is quieter than someone who is not creative, not old”.
“Everyone in the room who is not creative is quieter than Bertha” unless “no one outside the room is not creative, not brave”.
Lupe who is a happy creative person, is a quiet creative person.
Lupe is richer than Robert.
Someone who is quieter than Bertha is quieter than someone who is quieter than Robert.
Lupe is the least quiet in the room.
Everyone in the room who is not happy, not creative, not tall, not wise, not rich is richer than Robert. | Someone who is a old wise creative person is older than someone who is not rich, not wise, not happy, not creative, not quiet. | contradiction | room(lupe)&room(janet)&(![X]:(room(X)=>(X='lupe'|X='janet')))&
((~(![X]:(quieter(X,lupe)))=>((?[X,Y]:(~room(X)&~room(Y)&(older(shane,X)&older(shane,Y))&(X!=Y)))))&
((?[X,Y]:((~(old(X)&brave(X)&person(X)))&(~creative(Y)&~old(Y))&(quieter(X,Y))))=>(richer(robert,lupe)))&
(~(~?[X]:(~room(X)=>(~creative(X)&~brave(X))))=>(![X]:(room(X)=>(((~creative(X))=>(quieter(bertha,X)))))))&
((happy(lupe)&creative(lupe)&person(lupe))&(quiet(lupe)&creative(lupe)&person(lupe)))&
(richer(robert,lupe))&
(?[X,Y]:((quieter(bertha,X))&(quieter(robert,Y))&(quieter(X,Y))))&
(![X]:(quieter(lupe,X)))&
(![X]:(room(X)=>(((~happy(X)&~creative(X)&~tall(X)&~wise(X)&~rich(X))=>(richer(robert,X))))))) | room(lupe)&room(janet)&(![X]:(room(X)=>(X='lupe'|X='janet')))&
(?[X,Y]:((old(X)&wise(X)&creative(X)&person(X))&(~rich(Y)&~wise(Y)&~happy(Y)&~creative(Y)&~quiet(Y))&(older(X,Y)))) | contradiction | [
"h7",
"hypothesis",
"h4",
"b12"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(happy_type, type, (
happy: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(tptp_fun_Y_4_type, type, (
tptp_fun_Y_4: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(older_type, type, (
older: ( $i * $i ) > $o)).
tff(tptp_fun_X_5_type, type, (
tptp_fun_X_5: $i)).
tff(creative_type, type, (
creative: $i > $o)).
tff(wise_type, type, (
wise: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(old_type, type, (
old: $i > $o)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(1,assumption,(~quieter(mary, Y!4)), introduced(assumption)).
tff(2,plain,
(^[X: $i] : refl(quieter(mary, X) <=> quieter(mary, X))),
inference(bind,[status(th)],[])).
tff(3,plain,
(![X: $i] : quieter(mary, X) <=> ![X: $i] : quieter(mary, X)),
inference(quant_intro,[status(thm)],[2])).
tff(4,plain,
(![X: $i] : quieter(mary, X) <=> ![X: $i] : quieter(mary, X)),
inference(rewrite,[status(thm)],[])).
tff(5,axiom,(![X: $i] : quieter(mary, X)), file('/mnt/tmpfs//887023209484039864511052.p','h7')).
tff(6,plain,
(![X: $i] : quieter(mary, X)),
inference(modus_ponens,[status(thm)],[5, 4])).
tff(7,plain,(
![X: $i] : quieter(mary, X)),
inference(skolemize,[status(sab)],[6])).
tff(8,plain,
(![X: $i] : quieter(mary, X)),
inference(modus_ponens,[status(thm)],[7, 3])).
tff(9,plain,
((~![X: $i] : quieter(mary, X)) | quieter(mary, Y!4)),
inference(quant_inst,[status(thm)],[])).
tff(10,plain,
($false),
inference(unit_resolution,[status(thm)],[9, 8, 1])).
tff(11,plain,(quieter(mary, Y!4)), inference(lemma,lemma(discharge,[]))).
tff(12,plain,
(?[X: $i, Y: $i] : (old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)) & older(X, Y)) <=> ?[X: $i, Y: $i] : (old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)) & older(X, Y))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((old(X) & wise(X)) & creative(X)) <=> (old(X) & wise(X) & creative(X))), ((((old(X) & wise(X)) & creative(X)) & person(X)) <=> ((old(X) & wise(X) & creative(X)) & person(X)))), rewrite(((old(X) & wise(X) & creative(X)) & person(X)) <=> (old(X) & wise(X) & creative(X) & person(X))), ((((old(X) & wise(X)) & creative(X)) & person(X)) <=> (old(X) & wise(X) & creative(X) & person(X)))), trans(monotonicity(trans(monotonicity(rewrite((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) <=> ((~rich(Y)) & (~wise(Y)) & (~happy(Y)))), (((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) <=> (((~rich(Y)) & (~wise(Y)) & (~happy(Y))) & (~creative(Y))))), rewrite((((~rich(Y)) & (~wise(Y)) & (~happy(Y))) & (~creative(Y))) <=> ((~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)))), (((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) <=> ((~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y))))), ((((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) & (~quiet(Y))) <=> (((~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y))) & (~quiet(Y))))), rewrite((((~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y))) & (~quiet(Y))) <=> ((~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)))), ((((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) & (~quiet(Y))) <=> ((~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y))))), (((((old(X) & wise(X)) & creative(X)) & person(X)) & (((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) & (~quiet(Y)))) <=> ((old(X) & wise(X) & creative(X) & person(X)) & ((~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)))))), rewrite(((old(X) & wise(X) & creative(X) & person(X)) & ((~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)))) <=> (old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)))), (((((old(X) & wise(X)) & creative(X)) & person(X)) & (((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) & (~quiet(Y)))) <=> (old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y))))), ((((((old(X) & wise(X)) & creative(X)) & person(X)) & (((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) & (~quiet(Y)))) & older(X, Y)) <=> ((old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y))) & older(X, Y)))), rewrite(((old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y))) & older(X, Y)) <=> (old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)) & older(X, Y))), ((((((old(X) & wise(X)) & creative(X)) & person(X)) & (((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) & (~quiet(Y)))) & older(X, Y)) <=> (old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)) & older(X, Y))))),
inference(bind,[status(th)],[])).
tff(14,plain,
(?[X: $i, Y: $i] : (((((old(X) & wise(X)) & creative(X)) & person(X)) & (((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) & (~quiet(Y)))) & older(X, Y)) <=> ?[X: $i, Y: $i] : (old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)) & older(X, Y))),
inference(quant_intro,[status(thm)],[13])).
tff(15,axiom,(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : (((((old(X) & wise(X)) & creative(X)) & person(X)) & (((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) & (~quiet(Y)))) & older(X, Y))), file('/mnt/tmpfs//887023209484039864511052.p','hypothesis')).
tff(16,plain,
(?[X: $i, Y: $i] : (((((old(X) & wise(X)) & creative(X)) & person(X)) & (((((~rich(Y)) & (~wise(Y))) & (~happy(Y))) & (~creative(Y))) & (~quiet(Y)))) & older(X, Y))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
(?[X: $i, Y: $i] : (old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)) & older(X, Y))),
inference(modus_ponens,[status(thm)],[16, 14])).
tff(18,plain,
(?[X: $i, Y: $i] : (old(X) & wise(X) & creative(X) & person(X) & (~rich(Y)) & (~wise(Y)) & (~happy(Y)) & (~creative(Y)) & (~quiet(Y)) & older(X, Y))),
inference(modus_ponens,[status(thm)],[17, 12])).
tff(19,plain,(
old(X!5) & wise(X!5) & creative(X!5) & person(X!5) & (~rich(Y!4)) & (~wise(Y!4)) & (~happy(Y!4)) & (~creative(Y!4)) & (~quiet(Y!4)) & older(X!5, Y!4)),
inference(skolemize,[status(sab)],[18])).
tff(20,plain,
(~quiet(Y!4)),
inference(and_elim,[status(thm)],[19])).
tff(21,plain,
(quiet(mary) <=> quiet(mary)),
inference(rewrite,[status(thm)],[])).
tff(22,axiom,(((happy(mary) & creative(mary)) & person(mary)) & ((quiet(mary) & creative(mary)) & person(mary))), file('/mnt/tmpfs//887023209484039864511052.p','h4')).
tff(23,plain,
((quiet(mary) & creative(mary)) & person(mary)),
inference(and_elim,[status(thm)],[22])).
tff(24,plain,
(quiet(mary) & creative(mary)),
inference(and_elim,[status(thm)],[23])).
tff(25,plain,
(quiet(mary)),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
(quiet(mary)),
inference(modus_ponens,[status(thm)],[25, 21])).
tff(27,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X))) <=> ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X))))),
inference(bind,[status(th)],[])).
tff(28,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))),
inference(quant_intro,[status(thm)],[27])).
tff(29,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((quieter(X, Y) & quiet(X)) <=> (~((~quieter(X, Y)) | (~quiet(X))))), ((~(quieter(X, Y) & quiet(X))) <=> (~(~((~quieter(X, Y)) | (~quiet(X))))))), rewrite((~(~((~quieter(X, Y)) | (~quiet(X))))) <=> ((~quieter(X, Y)) | (~quiet(X)))), ((~(quieter(X, Y) & quiet(X))) <=> ((~quieter(X, Y)) | (~quiet(X))))), (((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ((X = Y) | quiet(Y) | ((~quieter(X, Y)) | (~quiet(X)))))), rewrite(((X = Y) | quiet(Y) | ((~quieter(X, Y)) | (~quiet(X)))) <=> ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))), (((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))))),
inference(bind,[status(th)],[])).
tff(30,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))),
inference(quant_intro,[status(thm)],[29])).
tff(31,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(rewrite,[status(thm)],[])).
tff(32,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite(((quieter(X, Y) & quiet(X)) => quiet(Y)) <=> (quiet(Y) | (~(quieter(X, Y) & quiet(X))))), (((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ((~(X = Y)) => (quiet(Y) | (~(quieter(X, Y) & quiet(X))))))), rewrite(((~(X = Y)) => (quiet(Y) | (~(quieter(X, Y) & quiet(X))))) <=> ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))), (((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))))),
inference(bind,[status(th)],[])).
tff(33,plain,
(![X: $i, Y: $i] : ((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(quant_intro,[status(thm)],[32])).
tff(34,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y)))), file('/mnt/tmpfs//887023209484039864511052.p','b12')).
tff(35,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(modus_ponens,[status(thm)],[34, 33])).
tff(36,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(modus_ponens,[status(thm)],[35, 31])).
tff(37,plain,(
![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(skolemize,[status(sab)],[36])).
tff(38,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))),
inference(modus_ponens,[status(thm)],[37, 30])).
tff(39,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))),
inference(modus_ponens,[status(thm)],[38, 28])).
tff(40,plain,
(((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | (quiet(Y!4) | (~quiet(mary)) | (~quieter(mary, Y!4)) | (mary = Y!4))) <=> ((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | quiet(Y!4) | (~quiet(mary)) | (~quieter(mary, Y!4)) | (mary = Y!4))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
(((mary = Y!4) | quiet(Y!4) | (~quieter(mary, Y!4)) | (~quiet(mary))) <=> (quiet(Y!4) | (~quiet(mary)) | (~quieter(mary, Y!4)) | (mary = Y!4))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
(((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | ((mary = Y!4) | quiet(Y!4) | (~quieter(mary, Y!4)) | (~quiet(mary)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | (quiet(Y!4) | (~quiet(mary)) | (~quieter(mary, Y!4)) | (mary = Y!4)))),
inference(monotonicity,[status(thm)],[41])).
tff(43,plain,
(((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | ((mary = Y!4) | quiet(Y!4) | (~quieter(mary, Y!4)) | (~quiet(mary)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | quiet(Y!4) | (~quiet(mary)) | (~quieter(mary, Y!4)) | (mary = Y!4))),
inference(transitivity,[status(thm)],[42, 40])).
tff(44,plain,
((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | ((mary = Y!4) | quiet(Y!4) | (~quieter(mary, Y!4)) | (~quiet(mary)))),
inference(quant_inst,[status(thm)],[])).
tff(45,plain,
((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | quiet(Y!4) | (~quiet(mary)) | (~quieter(mary, Y!4)) | (mary = Y!4)),
inference(modus_ponens,[status(thm)],[44, 43])).
tff(46,plain,
((~quieter(mary, Y!4)) | (mary = Y!4)),
inference(unit_resolution,[status(thm)],[45, 39, 26, 20])).
tff(47,plain,
(mary = Y!4),
inference(unit_resolution,[status(thm)],[46, 11])).
tff(48,plain,
(happy(mary) <=> happy(Y!4)),
inference(monotonicity,[status(thm)],[47])).
tff(49,plain,
(happy(Y!4) <=> happy(mary)),
inference(symmetry,[status(thm)],[48])).
tff(50,plain,
((~happy(Y!4)) <=> (~happy(mary))),
inference(monotonicity,[status(thm)],[49])).
tff(51,plain,
(~happy(Y!4)),
inference(and_elim,[status(thm)],[19])).
tff(52,plain,
(~happy(mary)),
inference(modus_ponens,[status(thm)],[51, 50])).
tff(53,plain,
(happy(mary) <=> happy(mary)),
inference(rewrite,[status(thm)],[])).
tff(54,plain,
((happy(mary) & creative(mary)) & person(mary)),
inference(and_elim,[status(thm)],[22])).
tff(55,plain,
(happy(mary) & creative(mary)),
inference(and_elim,[status(thm)],[54])).
tff(56,plain,
(happy(mary)),
inference(and_elim,[status(thm)],[55])).
tff(57,plain,
(happy(mary)),
inference(modus_ponens,[status(thm)],[56, 53])).
tff(58,plain,
($false),
inference(unit_resolution,[status(thm)],[57, 52])).
% SZS output end Proof
|
Minnie, George are the only persons in the room. If "Deanna is richer than Minnie" then "Garrett is quieter than Minnie". If "Minnie and George are respectively brave and creative" then "no one in the room is not happy". Only one person in the room is a brave person. Minnie and George are not creative, not quiet. George either is not rich, not creative, not quiet or is not creative. George is not a brave creative person. George is the quietest in the room. | Someone who is not creative is quieter than someone who is not a happy quiet brave rich person. | entailment | room(minnie)&room(george)&(![X]:(room(X)=>(X='minnie'|X='george')))&
(((richer(minnie,deanna))=>(quieter(minnie,garrett)))&
(((brave(minnie))&(creative(george)))=>(~?[X]:(room(X)=>(~happy(X)))))&
(((?[X]:(room(X)&brave(X)&person(X)))&(![X,Y]:((brave(X)&person(X)&brave(Y)&person(Y))=>(X=Y)))))&
(~creative(minnie)&~quiet(minnie)&~creative(george)&~quiet(george))&
(((~rich(george)&~creative(george)&~quiet(george))<~>(~creative(george))))&
(~(brave(george)&creative(george)&person(george)))&
(![X]:(quieter(X,george)))) | room(minnie)&room(george)&(![X]:(room(X)=>(X='minnie'|X='george')))&
(?[X,Y]:((~creative(X))&(~(happy(Y)&quiet(Y)&brave(Y)&rich(Y)&person(Y)))&(quieter(X,Y)))) | neutral | [
"h7",
"h4",
"h0",
"hypothesis"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(paul_type, type, (
paul: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(mary_type, type, (
mary: $i)).
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(1,plain,
(^[X: $i] : refl(quieter(X, paul) <=> quieter(X, paul))),
inference(bind,[status(th)],[])).
tff(2,plain,
(![X: $i] : quieter(X, paul) <=> ![X: $i] : quieter(X, paul)),
inference(quant_intro,[status(thm)],[1])).
tff(3,plain,
(![X: $i] : quieter(X, paul) <=> ![X: $i] : quieter(X, paul)),
inference(rewrite,[status(thm)],[])).
tff(4,axiom,(![X: $i] : quieter(X, paul)), file('/mnt/tmpfs//3299788741774825635992814.p','h7')).
tff(5,plain,
(![X: $i] : quieter(X, paul)),
inference(modus_ponens,[status(thm)],[4, 3])).
tff(6,plain,(
![X: $i] : quieter(X, paul)),
inference(skolemize,[status(sab)],[5])).
tff(7,plain,
(![X: $i] : quieter(X, paul)),
inference(modus_ponens,[status(thm)],[6, 2])).
tff(8,plain,
((~![X: $i] : quieter(X, paul)) | quieter(paul, paul)),
inference(quant_inst,[status(thm)],[])).
tff(9,plain,
(quieter(paul, paul)),
inference(unit_resolution,[status(thm)],[8, 7])).
tff(10,plain,
((~quiet(paul)) <=> (~quiet(paul))),
inference(rewrite,[status(thm)],[])).
tff(11,axiom,((((~creative(mary)) & (~quiet(mary))) & (~creative(paul))) & (~quiet(paul))), file('/mnt/tmpfs//3299788741774825635992814.p','h4')).
tff(12,plain,
(~quiet(paul)),
inference(and_elim,[status(thm)],[11])).
tff(13,plain,
(~quiet(paul)),
inference(modus_ponens,[status(thm)],[12, 10])).
tff(14,plain,
(((~quiet(paul)) | (~rich(paul)) | (~brave(paul)) | (~person(paul)) | (~happy(paul))) | quiet(paul)),
inference(tautology,[status(thm)],[])).
tff(15,plain,
((~quiet(paul)) | (~rich(paul)) | (~brave(paul)) | (~person(paul)) | (~happy(paul))),
inference(unit_resolution,[status(thm)],[14, 13])).
tff(16,assumption,(~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))), introduced(assumption)).
tff(17,plain,
(((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | room(X!1)),
inference(tautology,[status(thm)],[])).
tff(18,plain,
(room(X!1)),
inference(unit_resolution,[status(thm)],[17, 16])).
tff(19,plain,
(((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(20,plain,
(~(X!1 = |'mary'|)),
inference(unit_resolution,[status(thm)],[19, 16])).
tff(21,plain,
(((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'paul'|))),
inference(tautology,[status(thm)],[])).
tff(22,plain,
(~(X!1 = |'paul'|)),
inference(unit_resolution,[status(thm)],[21, 16])).
tff(23,plain,
(^[X: $i] : refl(((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(24,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[23])).
tff(25,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(26,plain,
(^[X: $i] : rewrite((room(X) => ((X = |'mary'|) | (X = |'paul'|))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(27,plain,
(![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[26])).
tff(28,axiom,((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))), file('/mnt/tmpfs//3299788741774825635992814.p','h0')).
tff(29,plain,
(![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[29, 27])).
tff(31,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[30, 25])).
tff(32,plain,(
![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[31])).
tff(33,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[32, 24])).
tff(34,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))),
inference(quant_inst,[status(thm)],[])).
tff(36,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))),
inference(modus_ponens,[status(thm)],[35, 34])).
tff(37,plain,
($false),
inference(unit_resolution,[status(thm)],[36, 33, 22, 20, 18])).
tff(38,plain,((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))), inference(lemma,lemma(discharge,[]))).
tff(39,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
(room(mary) & room(paul)),
inference(and_elim,[status(thm)],[28])).
tff(41,plain,
(room(paul)),
inference(and_elim,[status(thm)],[40])).
tff(42,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[41, 39])).
tff(43,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
(room(mary)),
inference(and_elim,[status(thm)],[40])).
tff(45,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[44, 43])).
tff(46,plain,
(((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (creative(X) | (~quieter(X, Y)) | (~((~happy(Y)) | (~brave(Y)) | (~person(Y)) | (~quiet(Y)) | (~rich(Y)))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (creative(X) | (~quieter(X, Y)) | (~((~happy(Y)) | (~brave(Y)) | (~person(Y)) | (~quiet(Y)) | (~rich(Y))))))),
inference(rewrite,[status(thm)],[])).
tff(47,plain,
(((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (creative(X) | (~quieter(X, Y)) | (~((~happy(Y)) | (~brave(Y)) | (~person(Y)) | (~quiet(Y)) | (~rich(Y))))))),
inference(rewrite,[status(thm)],[])).
tff(48,plain,
(((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ![X: $i, Y: $i] : (~((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(50,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y))))),
inference(monotonicity,[status(thm)],[49])).
tff(51,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(52,plain,
((~(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : (((~creative(X)) & (~((((happy(Y) & quiet(Y)) & brave(Y)) & rich(Y)) & person(Y)))) & quieter(X, Y)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(53,axiom,(~(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : (((~creative(X)) & (~((((happy(Y) & quiet(Y)) & brave(Y)) & rich(Y)) & person(Y)))) & quieter(X, Y)))), file('/mnt/tmpfs//3299788741774825635992814.p','hypothesis')).
tff(54,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y)))),
inference(modus_ponens,[status(thm)],[53, 52])).
tff(55,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y)))),
inference(modus_ponens,[status(thm)],[54, 50])).
tff(56,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y)))),
inference(modus_ponens,[status(thm)],[55, 51])).
tff(57,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(happy(Y) & quiet(Y) & brave(Y) & rich(Y) & person(Y))) & quieter(X, Y)))),
inference(modus_ponens,[status(thm)],[56, 50])).
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!1 |'paul'|) (= X!1 |'mary'|) (not (room X!1)))))
(a!5 (lambda ((X $i) (Y $i))
(let ((a!1 (and (not (creative X))
(not (and (happy Y)
(quiet Y)
(brave Y)
(rich Y)
(person Y)))
(quieter X Y))))
(refl (~ (not a!1) (not a!1))))))
(a!6 (exists ((X $i) (Y $i))
(and (not (creative X))
(not (and (happy Y) (quiet Y) (brave Y) (rich Y) (person Y)))
(quieter X Y))))
(a!7 (forall ((X $i) (Y $i))
(let ((a!1 (and (not (creative X))
(not (and (happy Y)
(quiet Y)
(brave Y)
(rich Y)
(person Y)))
(quieter 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)))
|
Henry, Vonnie, Holley are the only persons in the room. Either Henry is not a brave person and is older than Alexander or Henry is the richest in the room or but not both. Only one person in the room is not tall unless only one person outside the room is not old. Only one person outside the room is not a rich old person. Only one person outside the room is not tall. | It is not the case that 'Henry is not a old tall rich person or is richer than Alexander or both'. | neutral | room(henry)&room(vonnie)&room(holley)&(![X]:(room(X)=>(X='henry'|X='vonnie'|X='holley')))&
((((~(brave(henry)&person(henry)))&(older(alexander,henry)))<~>(![X]:(richer(X,henry))))&
(~(((?[X]:(~room(X)&~old(X)))&(![X,Y]:((~old(X)&~old(Y))=>(X=Y)))))=>(((?[X]:(room(X)&~tall(X)))&(![X,Y]:((~tall(X)&~tall(Y))=>(X=Y))))))&
(((?[X]:(~room(X)&~(rich(X)&old(X)&person(X))))&(![X,Y]:((~(rich(X)&old(X)&person(X))&~(rich(Y)&old(Y)&person(Y)))=>(X=Y)))))&
(((?[X]:(~room(X)&~tall(X)))&(![X,Y]:((~tall(X)&~tall(Y))=>(X=Y)))))) | room(henry)&room(vonnie)&room(holley)&(![X]:(room(X)=>(X='henry'|X='vonnie'|X='holley')))&
(~(((~(old(henry)&tall(henry)&rich(henry)&person(henry)))|(richer(alexander,henry))))) | entailment | [] | null |
Melanie is the only person in the room. Everyone in the room is hated by Danielle. More than one person outside the room is hated by Patricia. Melanie is not hated by Patricia. | Melanie is not hated by Patricia or does not hate Danielle or both. | entailment | room(melanie)&(![X]:(room(X)=>(X='melanie')))&
((![X]:(room(X)=>(hate(X,danielle))))&
((?[X,Y]:(~room(X)&~room(Y)&(hate(X,patricia)&hate(Y,patricia))&(X!=Y))))&
(~hate(melanie,patricia))) | room(melanie)&(![X]:(room(X)=>(X='melanie')))&
(((~hate(melanie,patricia))|(~hate(danielle,melanie)))) | entailment | [
"h3",
"h0",
"hypothesis"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(hate_type, type, (
hate: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(paul_type, type, (
paul: $i)).
tff(susan_type, type, (
susan: $i)).
tff(1,plain,
((~hate(mary, susan)) <=> (~hate(mary, susan))),
inference(rewrite,[status(thm)],[])).
tff(2,axiom,(~hate(mary, susan)), file('/mnt/tmpfs//4808752014352467205268500.p','h3')).
tff(3,plain,
(~hate(mary, susan)),
inference(modus_ponens,[status(thm)],[2, 1])).
tff(4,plain,
(((~hate(mary, susan)) | (~hate(paul, mary))) | hate(mary, susan)),
inference(tautology,[status(thm)],[])).
tff(5,plain,
((~hate(mary, susan)) | (~hate(paul, mary))),
inference(unit_resolution,[status(thm)],[4, 3])).
tff(6,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(7,axiom,(room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))), file('/mnt/tmpfs//4808752014352467205268500.p','h0')).
tff(8,plain,
(room(mary)),
inference(and_elim,[status(thm)],[7])).
tff(9,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[8, 6])).
tff(10,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary)))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary))))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary)))))),
inference(monotonicity,[status(thm)],[10])).
tff(12,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary)))))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
((~((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~hate(mary, susan)) | (~hate(paul, mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary)))))),
inference(rewrite,[status(thm)],[])).
tff(14,axiom,(~((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~hate(mary, susan)) | (~hate(paul, mary))))), file('/mnt/tmpfs//4808752014352467205268500.p','hypothesis')).
tff(15,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary))))),
inference(modus_ponens,[status(thm)],[14, 13])).
tff(16,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary))))),
inference(modus_ponens,[status(thm)],[15, 11])).
tff(17,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary))))),
inference(modus_ponens,[status(thm)],[16, 12])).
tff(18,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ((~hate(mary, susan)) | (~hate(paul, mary))))),
inference(modus_ponens,[status(thm)],[17, 11])).
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!2)) (= X!2 |'mary'|))))
(a!4 (not (or (not (hate mary susan)) (not (hate paul mary))))))
(let ((a!5 (and (room mary)
a!2
(or (not (hate mary susan)) (not (hate paul mary))))))
(let ((a!6 (~ (not a!5) (or (not (room mary)) a!3 a!4))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) (refl (~ a!4 a!4)) a!6))))
|
Milton is the only person in the room.
Milton is not a rich old happy person.
Someone who is not a rich old person is richer than someone who is quieter than Athena.
Milton is the least old in the room.
Everyone outside the room who is not a quiet person is not a rich person.
Someone who is not old is older than someone who is not quiet, not rich, not old, not happy.
Milton is the richest in the room. | Milton who is a rich old person, is quieter than Athena. | contradiction | room(milton)&(![X]:(room(X)=>(X='milton')))&
((~(rich(milton)&old(milton)&happy(milton)&person(milton)))&
(?[X,Y]:((~(rich(X)&old(X)&person(X)))&(quieter(athena,Y))&(richer(X,Y))))&
(![X]:(older(milton,X)))&
(![X]:(~room(X)=>(((~(quiet(X)&person(X)))=>(~(rich(X)&person(X)))))))&
(?[X,Y]:((~old(X))&(~quiet(Y)&~rich(Y)&~old(Y)&~happy(Y))&(older(X,Y))))&
(![X]:(richer(X,milton)))) | room(milton)&(![X]:(room(X)=>(X='milton')))&
((rich(milton)&old(milton)&person(milton))&(quieter(athena,milton))) | contradiction | [
"h0",
"h3",
"hypothesis",
"h5",
"b15"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(rich_type, type, (
rich: $i > $o)).
tff(tptp_fun_Y_2_type, type, (
tptp_fun_Y_2: $i)).
tff(mary_type, type, (
mary: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(older_type, type, (
older: ( $i * $i ) > $o)).
tff(old_type, type, (
old: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(1,plain,
(^[X: $i] : refl(((~room(X)) | (X = |'mary'|)) <=> ((~room(X)) | (X = |'mary'|)))),
inference(bind,[status(th)],[])).
tff(2,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(quant_intro,[status(thm)],[1])).
tff(3,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(4,plain,
(^[X: $i] : rewrite((room(X) => (X = |'mary'|)) <=> ((~room(X)) | (X = |'mary'|)))),
inference(bind,[status(th)],[])).
tff(5,plain,
(![X: $i] : (room(X) => (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(quant_intro,[status(thm)],[4])).
tff(6,axiom,(room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))), file('/mnt/tmpfs//6477968205973781253966323.p','h0')).
tff(7,plain,
(![X: $i] : (room(X) => (X = |'mary'|))),
inference(and_elim,[status(thm)],[6])).
tff(8,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[7, 5])).
tff(9,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[8, 3])).
tff(10,plain,(
![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(skolemize,[status(sab)],[9])).
tff(11,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[10, 2])).
tff(12,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(room(mary)),
inference(and_elim,[status(thm)],[6])).
tff(14,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
(((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(mary)) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(17,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(mary)) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[17, 14, 11])).
tff(19,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[18])).
tff(20,plain,
(older(mary, Y!2) <=> older(|'mary'|, Y!2)),
inference(monotonicity,[status(thm)],[18])).
tff(21,plain,
(older(|'mary'|, Y!2) <=> older(mary, Y!2)),
inference(symmetry,[status(thm)],[20])).
tff(22,plain,
((~older(|'mary'|, Y!2)) <=> (~older(mary, Y!2))),
inference(monotonicity,[status(thm)],[21])).
tff(23,assumption,(~older(|'mary'|, Y!2)), introduced(assumption)).
tff(24,plain,
(~older(mary, Y!2)),
inference(modus_ponens,[status(thm)],[23, 22])).
tff(25,plain,
(^[X: $i] : refl(older(mary, X) <=> older(mary, X))),
inference(bind,[status(th)],[])).
tff(26,plain,
(![X: $i] : older(mary, X) <=> ![X: $i] : older(mary, X)),
inference(quant_intro,[status(thm)],[25])).
tff(27,plain,
(![X: $i] : older(mary, X) <=> ![X: $i] : older(mary, X)),
inference(rewrite,[status(thm)],[])).
tff(28,axiom,(![X: $i] : older(mary, X)), file('/mnt/tmpfs//6477968205973781253966323.p','h3')).
tff(29,plain,
(![X: $i] : older(mary, X)),
inference(modus_ponens,[status(thm)],[28, 27])).
tff(30,plain,(
![X: $i] : older(mary, X)),
inference(skolemize,[status(sab)],[29])).
tff(31,plain,
(![X: $i] : older(mary, X)),
inference(modus_ponens,[status(thm)],[30, 26])).
tff(32,plain,
((~![X: $i] : older(mary, X)) | older(mary, Y!2)),
inference(quant_inst,[status(thm)],[])).
tff(33,plain,
(older(mary, Y!2)),
inference(unit_resolution,[status(thm)],[32, 31])).
tff(34,plain,
($false),
inference(unit_resolution,[status(thm)],[33, 24])).
tff(35,plain,(older(|'mary'|, Y!2)), inference(lemma,lemma(discharge,[]))).
tff(36,plain,
(old(|'mary'|) <=> old(mary)),
inference(monotonicity,[status(thm)],[19])).
tff(37,plain,
(old(mary) <=> old(|'mary'|)),
inference(symmetry,[status(thm)],[36])).
tff(38,plain,
(old(mary) <=> old(mary)),
inference(rewrite,[status(thm)],[])).
tff(39,axiom,((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((rich(mary) & old(mary)) & person(mary)) & quieter(fred, mary))), file('/mnt/tmpfs//6477968205973781253966323.p','hypothesis')).
tff(40,plain,
(((rich(mary) & old(mary)) & person(mary)) & quieter(fred, mary)),
inference(and_elim,[status(thm)],[39])).
tff(41,plain,
((rich(mary) & old(mary)) & person(mary)),
inference(and_elim,[status(thm)],[40])).
tff(42,plain,
(rich(mary) & old(mary)),
inference(and_elim,[status(thm)],[41])).
tff(43,plain,
(old(mary)),
inference(and_elim,[status(thm)],[42])).
tff(44,plain,
(old(mary)),
inference(modus_ponens,[status(thm)],[43, 38])).
tff(45,plain,
(old(|'mary'|)),
inference(modus_ponens,[status(thm)],[44, 37])).
tff(46,plain,
(?[X: $i, Y: $i] : ((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)) & older(X, Y)) <=> ?[X: $i, Y: $i] : ((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)) & older(X, Y))),
inference(rewrite,[status(thm)],[])).
tff(47,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~quiet(Y)) & (~rich(Y))) & (~old(Y))) <=> ((~quiet(Y)) & (~rich(Y)) & (~old(Y)))), (((((~quiet(Y)) & (~rich(Y))) & (~old(Y))) & (~happy(Y))) <=> (((~quiet(Y)) & (~rich(Y)) & (~old(Y))) & (~happy(Y))))), rewrite((((~quiet(Y)) & (~rich(Y)) & (~old(Y))) & (~happy(Y))) <=> ((~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)))), (((((~quiet(Y)) & (~rich(Y))) & (~old(Y))) & (~happy(Y))) <=> ((~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y))))), (((~old(X)) & ((((~quiet(Y)) & (~rich(Y))) & (~old(Y))) & (~happy(Y)))) <=> ((~old(X)) & ((~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)))))), rewrite(((~old(X)) & ((~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)))) <=> ((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)))), (((~old(X)) & ((((~quiet(Y)) & (~rich(Y))) & (~old(Y))) & (~happy(Y)))) <=> ((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y))))), ((((~old(X)) & ((((~quiet(Y)) & (~rich(Y))) & (~old(Y))) & (~happy(Y)))) & older(X, Y)) <=> (((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y))) & older(X, Y)))), rewrite((((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y))) & older(X, Y)) <=> ((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)) & older(X, Y))), ((((~old(X)) & ((((~quiet(Y)) & (~rich(Y))) & (~old(Y))) & (~happy(Y)))) & older(X, Y)) <=> ((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)) & older(X, Y))))),
inference(bind,[status(th)],[])).
tff(48,plain,
(?[X: $i, Y: $i] : (((~old(X)) & ((((~quiet(Y)) & (~rich(Y))) & (~old(Y))) & (~happy(Y)))) & older(X, Y)) <=> ?[X: $i, Y: $i] : ((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)) & older(X, Y))),
inference(quant_intro,[status(thm)],[47])).
tff(49,axiom,(?[X: $i, Y: $i] : (((~old(X)) & ((((~quiet(Y)) & (~rich(Y))) & (~old(Y))) & (~happy(Y)))) & older(X, Y))), file('/mnt/tmpfs//6477968205973781253966323.p','h5')).
tff(50,plain,
(?[X: $i, Y: $i] : ((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)) & older(X, Y))),
inference(modus_ponens,[status(thm)],[49, 48])).
tff(51,plain,
(?[X: $i, Y: $i] : ((~old(X)) & (~quiet(Y)) & (~rich(Y)) & (~old(Y)) & (~happy(Y)) & older(X, Y))),
inference(modus_ponens,[status(thm)],[50, 46])).
tff(52,plain,(
(~old(X!3)) & (~quiet(Y!2)) & (~rich(Y!2)) & (~old(Y!2)) & (~happy(Y!2)) & older(X!3, Y!2)),
inference(skolemize,[status(sab)],[51])).
tff(53,plain,
(~old(Y!2)),
inference(and_elim,[status(thm)],[52])).
tff(54,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | old(Y) | (~old(X)) | (~older(X, Y))) <=> ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y))))),
inference(bind,[status(th)],[])).
tff(55,plain,
(![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))),
inference(quant_intro,[status(thm)],[54])).
tff(56,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((older(X, Y) & old(X)) <=> (~((~old(X)) | (~older(X, Y))))), ((~(older(X, Y) & old(X))) <=> (~(~((~old(X)) | (~older(X, Y))))))), rewrite((~(~((~old(X)) | (~older(X, Y))))) <=> ((~old(X)) | (~older(X, Y)))), ((~(older(X, Y) & old(X))) <=> ((~old(X)) | (~older(X, Y))))), (((X = Y) | old(Y) | (~(older(X, Y) & old(X)))) <=> ((X = Y) | old(Y) | ((~old(X)) | (~older(X, Y)))))), rewrite(((X = Y) | old(Y) | ((~old(X)) | (~older(X, Y)))) <=> ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))), (((X = Y) | old(Y) | (~(older(X, Y) & old(X)))) <=> ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))))),
inference(bind,[status(th)],[])).
tff(57,plain,
(![X: $i, Y: $i] : ((X = Y) | old(Y) | (~(older(X, Y) & old(X)))) <=> ![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))),
inference(quant_intro,[status(thm)],[56])).
tff(58,plain,
(![X: $i, Y: $i] : ((X = Y) | old(Y) | (~(older(X, Y) & old(X)))) <=> ![X: $i, Y: $i] : ((X = Y) | old(Y) | (~(older(X, Y) & old(X))))),
inference(rewrite,[status(thm)],[])).
tff(59,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite(((older(X, Y) & old(X)) => old(Y)) <=> (old(Y) | (~(older(X, Y) & old(X))))), (((~(X = Y)) => ((older(X, Y) & old(X)) => old(Y))) <=> ((~(X = Y)) => (old(Y) | (~(older(X, Y) & old(X))))))), rewrite(((~(X = Y)) => (old(Y) | (~(older(X, Y) & old(X))))) <=> ((X = Y) | old(Y) | (~(older(X, Y) & old(X))))), (((~(X = Y)) => ((older(X, Y) & old(X)) => old(Y))) <=> ((X = Y) | old(Y) | (~(older(X, Y) & old(X))))))),
inference(bind,[status(th)],[])).
tff(60,plain,
(![X: $i, Y: $i] : ((~(X = Y)) => ((older(X, Y) & old(X)) => old(Y))) <=> ![X: $i, Y: $i] : ((X = Y) | old(Y) | (~(older(X, Y) & old(X))))),
inference(quant_intro,[status(thm)],[59])).
tff(61,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => ((older(X, Y) & old(X)) => old(Y)))), file('/mnt/tmpfs//6477968205973781253966323.p','b15')).
tff(62,plain,
(![X: $i, Y: $i] : ((X = Y) | old(Y) | (~(older(X, Y) & old(X))))),
inference(modus_ponens,[status(thm)],[61, 60])).
tff(63,plain,
(![X: $i, Y: $i] : ((X = Y) | old(Y) | (~(older(X, Y) & old(X))))),
inference(modus_ponens,[status(thm)],[62, 58])).
tff(64,plain,(
![X: $i, Y: $i] : ((X = Y) | old(Y) | (~(older(X, Y) & old(X))))),
inference(skolemize,[status(sab)],[63])).
tff(65,plain,
(![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))),
inference(modus_ponens,[status(thm)],[64, 57])).
tff(66,plain,
(![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))),
inference(modus_ponens,[status(thm)],[65, 55])).
tff(67,plain,
(((~![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))) | (old(Y!2) | (~older(|'mary'|, Y!2)) | (~old(|'mary'|)) | (|'mary'| = Y!2))) <=> ((~![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))) | old(Y!2) | (~older(|'mary'|, Y!2)) | (~old(|'mary'|)) | (|'mary'| = Y!2))),
inference(rewrite,[status(thm)],[])).
tff(68,plain,
(((|'mary'| = Y!2) | old(Y!2) | (~old(|'mary'|)) | (~older(|'mary'|, Y!2))) <=> (old(Y!2) | (~older(|'mary'|, Y!2)) | (~old(|'mary'|)) | (|'mary'| = Y!2))),
inference(rewrite,[status(thm)],[])).
tff(69,plain,
(((~![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))) | ((|'mary'| = Y!2) | old(Y!2) | (~old(|'mary'|)) | (~older(|'mary'|, Y!2)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))) | (old(Y!2) | (~older(|'mary'|, Y!2)) | (~old(|'mary'|)) | (|'mary'| = Y!2)))),
inference(monotonicity,[status(thm)],[68])).
tff(70,plain,
(((~![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))) | ((|'mary'| = Y!2) | old(Y!2) | (~old(|'mary'|)) | (~older(|'mary'|, Y!2)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))) | old(Y!2) | (~older(|'mary'|, Y!2)) | (~old(|'mary'|)) | (|'mary'| = Y!2))),
inference(transitivity,[status(thm)],[69, 67])).
tff(71,plain,
((~![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))) | ((|'mary'| = Y!2) | old(Y!2) | (~old(|'mary'|)) | (~older(|'mary'|, Y!2)))),
inference(quant_inst,[status(thm)],[])).
tff(72,plain,
((~![X: $i, Y: $i] : ((X = Y) | old(Y) | (~old(X)) | (~older(X, Y)))) | old(Y!2) | (~older(|'mary'|, Y!2)) | (~old(|'mary'|)) | (|'mary'| = Y!2)),
inference(modus_ponens,[status(thm)],[71, 70])).
tff(73,plain,
((~older(|'mary'|, Y!2)) | (~old(|'mary'|)) | (|'mary'| = Y!2)),
inference(unit_resolution,[status(thm)],[72, 66, 53])).
tff(74,plain,
((~older(|'mary'|, Y!2)) | (|'mary'| = Y!2)),
inference(unit_resolution,[status(thm)],[73, 45])).
tff(75,plain,
(|'mary'| = Y!2),
inference(unit_resolution,[status(thm)],[74, 35])).
tff(76,plain,
(Y!2 = |'mary'|),
inference(symmetry,[status(thm)],[75])).
tff(77,plain,
(Y!2 = mary),
inference(transitivity,[status(thm)],[76, 19])).
tff(78,plain,
(rich(Y!2) <=> rich(mary)),
inference(monotonicity,[status(thm)],[77])).
tff(79,plain,
(rich(mary) <=> rich(Y!2)),
inference(symmetry,[status(thm)],[78])).
tff(80,plain,
(rich(mary) <=> rich(mary)),
inference(rewrite,[status(thm)],[])).
tff(81,plain,
(rich(mary)),
inference(and_elim,[status(thm)],[42])).
tff(82,plain,
(rich(mary)),
inference(modus_ponens,[status(thm)],[81, 80])).
tff(83,plain,
(rich(Y!2)),
inference(modus_ponens,[status(thm)],[82, 79])).
tff(84,plain,
(~rich(Y!2)),
inference(and_elim,[status(thm)],[52])).
tff(85,plain,
($false),
inference(unit_resolution,[status(thm)],[84, 83])).
% SZS output end Proof
|
Brian, Kenneth, Bobby are the only persons in the room. Kenneth neither is not a old brave person nor is a rich quiet person. Only one person in the room is not old. Bobby who is not a old person, is not creative. Kenneth is the quietest in the room. Bobby is not rich. Brian and Kenneth are not a brave quiet persons. Ray is quieter than Brian. Kenneth is the tallest in the room. | Brian neither is a brave creative tall person nor is not a creative rich brave quiet person. | contradiction | room(brian)&room(kenneth)&room(bobby)&(![X]:(room(X)=>(X='brian'|X='kenneth'|X='bobby')))&
((~((~(old(kenneth)&brave(kenneth)&person(kenneth)))|(rich(kenneth)&quiet(kenneth)&person(kenneth))))&
(((?[X]:(room(X)&~old(X)))&(![X,Y]:((~old(X)&~old(Y))=>(X=Y)))))&
((~(old(bobby)&person(bobby)))&(~creative(bobby)))&
(![X]:(quieter(X,kenneth)))&
(~rich(bobby))&
(~(brave(brian)&quiet(brian)&person(brian))&~(brave(kenneth)&quiet(kenneth)&person(kenneth)))&
(quieter(brian,ray))&
(![X]:(taller(X,kenneth)))) | room(brian)&room(kenneth)&room(bobby)&(![X]:(room(X)=>(X='brian'|X='kenneth'|X='bobby')))&
(~((brave(brian)&creative(brian)&tall(brian)&person(brian))|(~(creative(brian)&rich(brian)&brave(brian)&quiet(brian)&person(brian))))) | neutral | [
"hypothesis",
"h6"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(person_type, type, (
person: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(paul_type, type, (
paul: $i)).
tff(1,plain,
(person(mary) <=> person(mary)),
inference(rewrite,[status(thm)],[])).
tff(2,axiom,((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~((((brave(mary) & creative(mary)) & tall(mary)) & person(mary)) | (~((((creative(mary) & rich(mary)) & brave(mary)) & quiet(mary)) & person(mary)))))), file('/mnt/tmpfs//8205260459378652626534782.p','hypothesis')).
tff(3,plain,
(~((((brave(mary) & creative(mary)) & tall(mary)) & person(mary)) | (~((((creative(mary) & rich(mary)) & brave(mary)) & quiet(mary)) & person(mary))))),
inference(and_elim,[status(thm)],[2])).
tff(4,plain,
((((creative(mary) & rich(mary)) & brave(mary)) & quiet(mary)) & person(mary)),
inference(or_elim,[status(thm)],[3])).
tff(5,plain,
(person(mary)),
inference(and_elim,[status(thm)],[4])).
tff(6,plain,
(person(mary)),
inference(modus_ponens,[status(thm)],[5, 1])).
tff(7,plain,
(brave(mary) <=> brave(mary)),
inference(rewrite,[status(thm)],[])).
tff(8,plain,
(((creative(mary) & rich(mary)) & brave(mary)) & quiet(mary)),
inference(and_elim,[status(thm)],[4])).
tff(9,plain,
((creative(mary) & rich(mary)) & brave(mary)),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
(brave(mary)),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
(brave(mary)),
inference(modus_ponens,[status(thm)],[10, 7])).
tff(12,plain,
(quiet(mary) <=> quiet(mary)),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(quiet(mary)),
inference(and_elim,[status(thm)],[8])).
tff(14,plain,
(quiet(mary)),
inference(modus_ponens,[status(thm)],[13, 12])).
tff(15,plain,
((~(~((~brave(mary)) | (~quiet(mary)) | (~person(mary))))) <=> ((~brave(mary)) | (~quiet(mary)) | (~person(mary)))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
((brave(mary) & quiet(mary) & person(mary)) <=> (~((~brave(mary)) | (~quiet(mary)) | (~person(mary))))),
inference(rewrite,[status(thm)],[])).
tff(17,plain,
((~(brave(mary) & quiet(mary) & person(mary))) <=> (~(~((~brave(mary)) | (~quiet(mary)) | (~person(mary)))))),
inference(monotonicity,[status(thm)],[16])).
tff(18,plain,
((~(brave(mary) & quiet(mary) & person(mary))) <=> ((~brave(mary)) | (~quiet(mary)) | (~person(mary)))),
inference(transitivity,[status(thm)],[17, 15])).
tff(19,plain,
((~(brave(mary) & quiet(mary) & person(mary))) <=> (~(brave(mary) & quiet(mary) & person(mary)))),
inference(rewrite,[status(thm)],[])).
tff(20,plain,
((~((brave(mary) & quiet(mary)) & person(mary))) <=> (~(brave(mary) & quiet(mary) & person(mary)))),
inference(rewrite,[status(thm)],[])).
tff(21,axiom,((~((brave(mary) & quiet(mary)) & person(mary))) & (~((brave(paul) & quiet(paul)) & person(paul)))), file('/mnt/tmpfs//8205260459378652626534782.p','h6')).
tff(22,plain,
(~((brave(mary) & quiet(mary)) & person(mary))),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
(~(brave(mary) & quiet(mary) & person(mary))),
inference(modus_ponens,[status(thm)],[22, 20])).
tff(24,plain,
(~(brave(mary) & quiet(mary) & person(mary))),
inference(modus_ponens,[status(thm)],[23, 19])).
tff(25,plain,
((~brave(mary)) | (~quiet(mary)) | (~person(mary))),
inference(modus_ponens,[status(thm)],[24, 18])).
tff(26,plain,
($false),
inference(unit_resolution,[status(thm)],[25, 14, 11, 6])).
% SZS output end Proof
|
Molly, Ethan are the only persons in the room. If "Molly is not a creative brave person or is older than Ricardo or both" then "Molly is the least tall in the room" otherwise "more than one person outside the room is richer than Ricardo". "More than one person in the room is not a tall rich quiet brave person" unless "Molly who is not a rich tall person, is not a brave happy person". Only one person in the room is not tall, not quiet. Molly is the oldest in the room. Ethan is not a quiet old rich person or is not a old brave person or both. Everyone in the room who is not old is older than Ricardo. More than one person in the room is not a tall rich quiet brave person. Someone who is not a creative person is quieter than someone who is not a happy person. Molly is a creative brave quiet old rich person or is a creative person or both. | Molly is taller than Ricardo or is not a tall rich quiet creative brave person or both. | entailment | room(molly)&room(ethan)&(![X]:(room(X)=>(X='molly'|X='ethan')))&
((((((~(creative(molly)&brave(molly)&person(molly)))|(older(ricardo,molly))))=>(![X]:(taller(molly,X))))|((~(((~(creative(molly)&brave(molly)&person(molly)))|(older(ricardo,molly)))))=>((?[X,Y]:(~room(X)&~room(Y)&(richer(ricardo,X)&richer(ricardo,Y))&(X!=Y))))))&
(~((~(rich(molly)&tall(molly)&person(molly)))&(~(brave(molly)&happy(molly)&person(molly))))=>((?[X,Y]:(room(X)&room(Y)&(~(tall(X)&rich(X)&quiet(X)&brave(X)&person(X))&~(tall(Y)&rich(Y)&quiet(Y)&brave(Y)&person(Y)))&(X!=Y)))))&
(((?[X]:(room(X)&~tall(X)&~quiet(X)))&(![X,Y]:((~tall(X)&~quiet(X)&~tall(Y)&~quiet(Y))=>(X=Y)))))&
(![X]:(older(X,molly)))&
(((~(quiet(ethan)&old(ethan)&rich(ethan)&person(ethan)))|(~(old(ethan)&brave(ethan)&person(ethan)))))&
(![X]:(room(X)=>(((~old(X))=>(older(ricardo,X))))))&
((?[X,Y]:(room(X)&room(Y)&(~(tall(X)&rich(X)&quiet(X)&brave(X)&person(X))&~(tall(Y)&rich(Y)&quiet(Y)&brave(Y)&person(Y)))&(X!=Y))))&
(?[X,Y]:((~(creative(X)&person(X)))&(~(happy(Y)&person(Y)))&(quieter(X,Y))))&
(((creative(molly)&brave(molly)&quiet(molly)&old(molly)&rich(molly)&person(molly))|(creative(molly)&person(molly))))) | room(molly)&room(ethan)&(![X]:(room(X)=>(X='molly'|X='ethan')))&
(((taller(ricardo,molly))|(~(tall(molly)&rich(molly)&quiet(molly)&creative(molly)&brave(molly)&person(molly))))) | contradiction | [
"h2"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_5_type, type, (
tptp_fun_X_5: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(creative_type, type, (
creative: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(tptp_fun_Y_0_type, type, (
tptp_fun_Y_0: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(1,assumption,(~(taller(fred, mary) | (~rich(mary)) | (~tall(mary)) | (~person(mary)) | (~brave(mary)) | (~creative(mary)) | (~quiet(mary)))), introduced(assumption)).
tff(2,plain,
((taller(fred, mary) | (~rich(mary)) | (~tall(mary)) | (~person(mary)) | (~brave(mary)) | (~creative(mary)) | (~quiet(mary))) | rich(mary)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(rich(mary)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
((taller(fred, mary) | (~rich(mary)) | (~tall(mary)) | (~person(mary)) | (~brave(mary)) | (~creative(mary)) | (~quiet(mary))) | person(mary)),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(person(mary)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,plain,
((taller(fred, mary) | (~rich(mary)) | (~tall(mary)) | (~person(mary)) | (~brave(mary)) | (~creative(mary)) | (~quiet(mary))) | tall(mary)),
inference(tautology,[status(thm)],[])).
tff(7,plain,
(tall(mary)),
inference(unit_resolution,[status(thm)],[6, 1])).
tff(8,plain,
((~((~rich(mary)) | (~tall(mary)) | (~person(mary)))) | (~rich(mary)) | (~tall(mary)) | (~person(mary))),
inference(tautology,[status(thm)],[])).
tff(9,plain,
(~((~rich(mary)) | (~tall(mary)) | (~person(mary)))),
inference(unit_resolution,[status(thm)],[8, 7, 5, 3])).
tff(10,plain,
(((~((~rich(mary)) | (~tall(mary)) | (~person(mary)))) | (~((~brave(mary)) | (~happy(mary)) | (~person(mary))))) | ((~rich(mary)) | (~tall(mary)) | (~person(mary)))),
inference(tautology,[status(thm)],[])).
tff(11,plain,
((~((~rich(mary)) | (~tall(mary)) | (~person(mary)))) | (~((~brave(mary)) | (~happy(mary)) | (~person(mary))))),
inference(unit_resolution,[status(thm)],[10, 9])).
tff(12,plain,
((((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary)))) | (room(X!1) & room(Y!0) & (~(tall(X!1) & rich(X!1) & quiet(X!1) & brave(X!1) & person(X!1))) & (~(tall(Y!0) & rich(Y!0) & quiet(Y!0) & brave(Y!0) & person(Y!0))) & (~(X!1 = Y!0)))) <=> ((~((~((~rich(mary)) | (~tall(mary)) | (~person(mary)))) | (~((~brave(mary)) | (~happy(mary)) | (~person(mary)))))) | (~((~room(X!1)) | (~room(Y!0)) | (~((~tall(X!1)) | (~rich(X!1)) | (~quiet(X!1)) | (~brave(X!1)) | (~person(X!1)))) | (~((~tall(Y!0)) | (~rich(Y!0)) | (~quiet(Y!0)) | (~brave(Y!0)) | (~person(Y!0)))) | (X!1 = Y!0))))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
((((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary)))) | ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y)))) <=> (((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary)))) | ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y))))),
inference(rewrite,[status(thm)],[])).
tff(14,plain,
(((~((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary))))) => ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y)))) <=> (((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary)))) | ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y))))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~((((tall(Y) & rich(Y)) & quiet(Y)) & brave(Y)) & person(Y)))) <=> ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))))), (((room(X) & room(Y)) & ((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~((((tall(Y) & rich(Y)) & quiet(Y)) & brave(Y)) & person(Y))))) <=> ((room(X) & room(Y)) & ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))))))), rewrite(((room(X) & room(Y)) & ((~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))))) <=> (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))))), (((room(X) & room(Y)) & ((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~((((tall(Y) & rich(Y)) & quiet(Y)) & brave(Y)) & person(Y))))) <=> (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y)))))), ((((room(X) & room(Y)) & ((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~((((tall(Y) & rich(Y)) & quiet(Y)) & brave(Y)) & person(Y))))) & (~(X = Y))) <=> ((room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y)))) & (~(X = Y))))), rewrite(((room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y)))) & (~(X = Y))) <=> (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y)))), ((((room(X) & room(Y)) & ((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~((((tall(Y) & rich(Y)) & quiet(Y)) & brave(Y)) & person(Y))))) & (~(X = Y))) <=> (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y)))))),
inference(bind,[status(th)],[])).
tff(16,plain,
(?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~((((tall(Y) & rich(Y)) & quiet(Y)) & brave(Y)) & person(Y))))) & (~(X = Y))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y)))),
inference(quant_intro,[status(thm)],[15])).
tff(17,plain,
((~((~((rich(mary) & tall(mary)) & person(mary))) & (~((brave(mary) & happy(mary)) & person(mary))))) <=> (~((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(18,plain,
(((~((~((rich(mary) & tall(mary)) & person(mary))) & (~((brave(mary) & happy(mary)) & person(mary))))) => ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~((((tall(Y) & rich(Y)) & quiet(Y)) & brave(Y)) & person(Y))))) & (~(X = Y)))) <=> ((~((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary))))) => ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y))))),
inference(monotonicity,[status(thm)],[17, 16])).
tff(19,plain,
(((~((~((rich(mary) & tall(mary)) & person(mary))) & (~((brave(mary) & happy(mary)) & person(mary))))) => ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~((((tall(Y) & rich(Y)) & quiet(Y)) & brave(Y)) & person(Y))))) & (~(X = Y)))) <=> (((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary)))) | ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y))))),
inference(transitivity,[status(thm)],[18, 14])).
tff(20,axiom,((~((~((rich(mary) & tall(mary)) & person(mary))) & (~((brave(mary) & happy(mary)) & person(mary))))) => ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~((((tall(X) & rich(X)) & quiet(X)) & brave(X)) & person(X))) & (~((((tall(Y) & rich(Y)) & quiet(Y)) & brave(Y)) & person(Y))))) & (~(X = Y)))), file('/mnt/tmpfs//7884767495364015195578877.p','h2')).
tff(21,plain,
(((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary)))) | ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y)))),
inference(modus_ponens,[status(thm)],[20, 19])).
tff(22,plain,
(((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary)))) | ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y)))),
inference(modus_ponens,[status(thm)],[21, 13])).
tff(23,plain,
(((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary)))) | ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y)))),
inference(modus_ponens,[status(thm)],[22, 13])).
tff(24,plain,
(((~(rich(mary) & tall(mary) & person(mary))) & (~(brave(mary) & happy(mary) & person(mary)))) | ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(tall(X) & rich(X) & quiet(X) & brave(X) & person(X))) & (~(tall(Y) & rich(Y) & quiet(Y) & brave(Y) & person(Y))) & (~(X = Y)))),
inference(modus_ponens,[status(thm)],[23, 13])).
|
Deborah, Holly, Jerry are the only persons in the room.
'More than one person in the room enjoys pottery' unless 'Jerry neither does not enjoy pottery nor can play the piano'.
Jerry enjoys pottery.
Someone in the room who does not enjoy pottery cannot play the piano.
Everyone in the room who enjoys pottery can play the piano. | Jerry does not enjoy pottery or cannot play the piano or both. | contradiction | room(deborah)&room(holly)&room(jerry)&(![X]:(room(X)=>(X='deborah'|X='holly'|X='jerry')))&
((~(~((does_not_enjoy_pottery(jerry))|(can_play_the_piano(jerry))))=>((?[X,Y]:(room(X)&room(Y)&(enjoys_pottery(X)&enjoys_pottery(Y))&(X!=Y)))))&
(enjoys_pottery(jerry))&
(?[X]:(room(X)=>(((does_not_enjoy_pottery(X))=>(cannot_play_the_piano(X))))))&
(![X]:(room(X)=>(((enjoys_pottery(X))=>(can_play_the_piano(X))))))) | room(deborah)&room(holly)&room(jerry)&(![X]:(room(X)=>(X='deborah'|X='holly'|X='jerry')))&
(((does_not_enjoy_pottery(jerry))|(cannot_play_the_piano(jerry)))) | contradiction | [
"h4",
"h2",
"hypothesis",
"h0"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__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(mary_type, type, (
mary: $i)).
tff(1,plain,
(^[X: $i] : refl((preda(X) | (~predb(X)) | (~room(X))) <=> (preda(X) | (~predb(X)) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(2,plain,
(![X: $i] : (preda(X) | (~predb(X)) | (~room(X))) <=> ![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))),
inference(quant_intro,[status(thm)],[1])).
tff(3,plain,
(![X: $i] : (preda(X) | (~predb(X)) | (~room(X))) <=> ![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(4,plain,
(^[X: $i] : trans(monotonicity(rewrite((predb(X) => preda(X)) <=> (preda(X) | (~predb(X)))), ((room(X) => (predb(X) => preda(X))) <=> (room(X) => (preda(X) | (~predb(X)))))), rewrite((room(X) => (preda(X) | (~predb(X)))) <=> (preda(X) | (~predb(X)) | (~room(X)))), ((room(X) => (predb(X) => preda(X))) <=> (preda(X) | (~predb(X)) | (~room(X)))))),
inference(bind,[status(th)],[])).
tff(5,plain,
(![X: $i] : (room(X) => (predb(X) => preda(X))) <=> ![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))),
inference(quant_intro,[status(thm)],[4])).
tff(6,axiom,(![X: $i] : (room(X) => (predb(X) => preda(X)))), file('/mnt/tmpfs//5949580294531099436708480.p','h4')).
tff(7,plain,
(![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[6, 5])).
tff(8,plain,
(![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[7, 3])).
tff(9,plain,(
![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))),
inference(skolemize,[status(sab)],[8])).
tff(10,plain,
(![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[9, 2])).
tff(11,plain,
(predb(fred) <=> predb(fred)),
inference(rewrite,[status(thm)],[])).
tff(12,axiom,(predb(fred)), file('/mnt/tmpfs//5949580294531099436708480.p','h2')).
tff(13,plain,
(predb(fred)),
inference(modus_ponens,[status(thm)],[12, 11])).
tff(14,plain,
(((~predb(fred)) | (~preda(fred))) <=> ((~predb(fred)) | (~preda(fred)))),
inference(rewrite,[status(thm)],[])).
tff(15,axiom,((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((~predb(fred)) | (~preda(fred)))), file('/mnt/tmpfs//5949580294531099436708480.p','hypothesis')).
tff(16,plain,
((~predb(fred)) | (~preda(fred))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
((~predb(fred)) | (~preda(fred))),
inference(modus_ponens,[status(thm)],[16, 14])).
tff(18,plain,
((~predb(fred)) | (~preda(fred))),
inference(modus_ponens,[status(thm)],[17, 14])).
tff(19,plain,
((~predb(fred)) | (~preda(fred))),
inference(modus_ponens,[status(thm)],[18, 14])).
tff(20,plain,
((~predb(fred)) | (~preda(fred))),
inference(modus_ponens,[status(thm)],[19, 14])).
tff(21,plain,
((~predb(fred)) | (~preda(fred))),
inference(modus_ponens,[status(thm)],[20, 14])).
tff(22,plain,
(~preda(fred)),
inference(unit_resolution,[status(thm)],[21, 13])).
tff(23,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(24,axiom,(((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))), file('/mnt/tmpfs//5949580294531099436708480.p','h0')).
tff(25,plain,
((room(mary) & room(paul)) & room(fred)),
inference(and_elim,[status(thm)],[24])).
tff(26,plain,
(room(fred)),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[26, 23])).
tff(28,plain,
(((~![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))) | (preda(fred) | (~predb(fred)) | (~room(fred)))) <=> ((~![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))) | preda(fred) | (~predb(fred)) | (~room(fred)))),
inference(rewrite,[status(thm)],[])).
tff(29,plain,
((~![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))) | (preda(fred) | (~predb(fred)) | (~room(fred)))),
inference(quant_inst,[status(thm)],[])).
tff(30,plain,
((~![X: $i] : (preda(X) | (~predb(X)) | (~room(X)))) | preda(fred) | (~predb(fred)) | (~room(fred))),
inference(modus_ponens,[status(thm)],[29, 28])).
tff(31,plain,
($false),
inference(unit_resolution,[status(thm)],[30, 27, 13, 22, 10])).
% SZS output end Proof
|
April, Eddie are the only persons in the room.
Eddie who is a quiet person, is a rich tall quiet person.
Someone who is not a happy person is quieter than someone who is taller than James.
April who is older than James, is a tall old person.
Eddie neither is not quiet nor is not a wise happy person.
Only one person outside the room is not rich.
Eddie is not a brave quiet person and is not a tall creative old rich person. | Eddie neither is not wise, not rich, not quiet, not creative, not old nor is a wise brave tall person. | entailment | room(april)&room(eddie)&(![X]:(room(X)=>(X='april'|X='eddie')))&
(((quiet(eddie)&person(eddie))&(rich(eddie)&tall(eddie)&quiet(eddie)&person(eddie)))&
(?[X,Y]:((~(happy(X)&person(X)))&(taller(james,Y))&(quieter(X,Y))))&
((older(james,april))&(tall(april)&old(april)&person(april)))&
(~((~quiet(eddie))|(~(wise(eddie)&happy(eddie)&person(eddie)))))&
(((?[X]:(~room(X)&~rich(X)))&(![X,Y]:((~rich(X)&~rich(Y))=>(X=Y)))))&
((~(brave(eddie)&quiet(eddie)&person(eddie)))&(~(tall(eddie)&creative(eddie)&old(eddie)&rich(eddie)&person(eddie))))) | room(april)&room(eddie)&(![X]:(room(X)=>(X='april'|X='eddie')))&
(~((~wise(eddie)&~rich(eddie)&~quiet(eddie)&~creative(eddie)&~old(eddie))|(wise(eddie)&brave(eddie)&tall(eddie)&person(eddie)))) | contradiction | [
"h1",
"h6",
"h0",
"hypothesis"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tall_type, type, (
tall: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(wise_type, type, (
wise: $i > $o)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(old_type, type, (
old: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(1,plain,
(person(paul) <=> person(paul)),
inference(rewrite,[status(thm)],[])).
tff(2,axiom,((quiet(paul) & person(paul)) & (((rich(paul) & tall(paul)) & quiet(paul)) & person(paul))), file('/mnt/tmpfs//7885112753707158927241221.p','h1')).
tff(3,plain,
(quiet(paul) & person(paul)),
inference(and_elim,[status(thm)],[2])).
tff(4,plain,
(person(paul)),
inference(and_elim,[status(thm)],[3])).
tff(5,plain,
(person(paul)),
inference(modus_ponens,[status(thm)],[4, 1])).
tff(6,plain,
(quiet(paul) <=> quiet(paul)),
inference(rewrite,[status(thm)],[])).
tff(7,plain,
(quiet(paul)),
inference(and_elim,[status(thm)],[3])).
tff(8,plain,
(quiet(paul)),
inference(modus_ponens,[status(thm)],[7, 6])).
tff(9,plain,
((~(~((~quiet(paul)) | (~brave(paul)) | (~person(paul))))) <=> ((~quiet(paul)) | (~brave(paul)) | (~person(paul)))),
inference(rewrite,[status(thm)],[])).
tff(10,plain,
((brave(paul) & quiet(paul) & person(paul)) <=> (~((~quiet(paul)) | (~brave(paul)) | (~person(paul))))),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
((~(brave(paul) & quiet(paul) & person(paul))) <=> (~(~((~quiet(paul)) | (~brave(paul)) | (~person(paul)))))),
inference(monotonicity,[status(thm)],[10])).
tff(12,plain,
((~(brave(paul) & quiet(paul) & person(paul))) <=> ((~quiet(paul)) | (~brave(paul)) | (~person(paul)))),
inference(transitivity,[status(thm)],[11, 9])).
tff(13,plain,
((~(brave(paul) & quiet(paul) & person(paul))) <=> (~(brave(paul) & quiet(paul) & person(paul)))),
inference(rewrite,[status(thm)],[])).
tff(14,plain,
((~((brave(paul) & quiet(paul)) & person(paul))) <=> (~(brave(paul) & quiet(paul) & person(paul)))),
inference(rewrite,[status(thm)],[])).
tff(15,axiom,((~((brave(paul) & quiet(paul)) & person(paul))) & (~((((tall(paul) & creative(paul)) & old(paul)) & rich(paul)) & person(paul)))), file('/mnt/tmpfs//7885112753707158927241221.p','h6')).
tff(16,plain,
(~((brave(paul) & quiet(paul)) & person(paul))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
(~(brave(paul) & quiet(paul) & person(paul))),
inference(modus_ponens,[status(thm)],[16, 14])).
tff(18,plain,
(~(brave(paul) & quiet(paul) & person(paul))),
inference(modus_ponens,[status(thm)],[17, 13])).
tff(19,plain,
((~quiet(paul)) | (~brave(paul)) | (~person(paul))),
inference(modus_ponens,[status(thm)],[18, 12])).
tff(20,plain,
(~brave(paul)),
inference(unit_resolution,[status(thm)],[19, 8, 5])).
tff(21,plain,
(((~wise(paul)) | (~brave(paul)) | (~person(paul)) | (~tall(paul))) | brave(paul)),
inference(tautology,[status(thm)],[])).
tff(22,plain,
((~wise(paul)) | (~brave(paul)) | (~person(paul)) | (~tall(paul))),
inference(unit_resolution,[status(thm)],[21, 20])).
tff(23,plain,
((quiet(paul) | rich(paul) | wise(paul) | creative(paul) | old(paul)) | (~quiet(paul))),
inference(tautology,[status(thm)],[])).
tff(24,plain,
(quiet(paul) | rich(paul) | wise(paul) | creative(paul) | old(paul)),
inference(unit_resolution,[status(thm)],[23, 8])).
tff(25,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(26,axiom,((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))), file('/mnt/tmpfs//7885112753707158927241221.p','h0')).
tff(27,plain,
(room(mary) & room(paul)),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
(room(paul)),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[28, 25])).
tff(30,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
(room(mary)),
inference(and_elim,[status(thm)],[27])).
tff(32,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[31, 30])).
tff(33,plain,
(((~(quiet(paul) | rich(paul) | wise(paul) | creative(paul) | old(paul))) | (~((~wise(paul)) | (~brave(paul)) | (~person(paul)) | (~tall(paul)))) | (~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(quiet(paul) | rich(paul) | wise(paul) | creative(paul) | old(paul))) | (~((~wise(paul)) | (~brave(paul)) | (~person(paul)) | (~tall(paul)))))),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
((~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
((wise(paul) & brave(paul) & tall(paul) & person(paul)) <=> (~((~wise(paul)) | (~brave(paul)) | (~person(paul)) | (~tall(paul))))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) <=> (~(quiet(paul) | rich(paul) | wise(paul) | creative(paul) | old(paul)))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
((((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)) | (~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> ((~(quiet(paul) | rich(paul) | wise(paul) | creative(paul) | old(paul))) | (~((~wise(paul)) | (~brave(paul)) | (~person(paul)) | (~tall(paul)))) | (~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))),
inference(monotonicity,[status(thm)],[36, 35, 34])).
tff(38,plain,
((((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)) | (~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(quiet(paul) | rich(paul) | wise(paul) | creative(paul) | old(paul))) | (~((~wise(paul)) | (~brave(paul)) | (~person(paul)) | (~tall(paul)))))),
inference(transitivity,[status(thm)],[37, 33])).
tff(39,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))) <=> (((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)) | (~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
((((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul))) <=> (((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul))))),
inference(monotonicity,[status(thm)],[34, 40])).
tff(42,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))) <=> (((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)) | (~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))),
inference(transitivity,[status(thm)],[41, 39])).
tff(43,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul))))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))))),
inference(rewrite,[status(thm)],[])).
tff(44,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul))))))),
inference(monotonicity,[status(thm)],[43])).
tff(45,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul))))))),
inference(rewrite,[status(thm)],[])).
tff(46,plain,
((~(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((((((~wise(paul)) & (~rich(paul))) & (~quiet(paul))) & (~creative(paul))) & (~old(paul))) | (((wise(paul) & brave(paul)) & tall(paul)) & person(paul)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul))))))),
inference(rewrite,[status(thm)],[])).
tff(47,axiom,(~(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((((((~wise(paul)) & (~rich(paul))) & (~quiet(paul))) & (~creative(paul))) & (~old(paul))) | (((wise(paul) & brave(paul)) & tall(paul)) & person(paul)))))), file('/mnt/tmpfs//7885112753707158927241221.p','hypothesis')).
tff(48,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))))),
inference(modus_ponens,[status(thm)],[47, 46])).
tff(49,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))))),
inference(modus_ponens,[status(thm)],[48, 44])).
tff(50,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))))),
inference(modus_ponens,[status(thm)],[49, 45])).
tff(51,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~wise(paul)) & (~rich(paul)) & (~quiet(paul)) & (~creative(paul)) & (~old(paul))) | (wise(paul) & brave(paul) & tall(paul) & person(paul)))))),
inference(modus_ponens,[status(thm)],[50, 44])).
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!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3)))))
(a!5 (or (and (not (wise paul))
(not (rich paul))
(not (quiet paul))
(not (creative paul))
(not (old paul)))
(and (wise paul) (brave paul) (tall paul) (person paul)))))
(let ((a!6 (~ (not (and (room mary) (room paul) a!3 (not a!5)))
(or (not (room mary)) (not (room paul)) a!4 a!5))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ a!5 a!5)) a!6)))
|
Delbert is the only person in the room.
Someone who is a quiet person is taller than someone who is not quiet, not tall.
Delbert is the tallest in the room.
Delbert who is taller than Nicole, is a tall person.
Delbert is taller than Adrian.
Someone who is not a creative person is quieter than someone who is not quiet, not happy, not tall, not creative.
Delbert who is not quiet, not creative, is a happy person. | Someone who is not a creative person is taller than someone who is quieter than Nicole. | neutral | room(delbert)&(![X]:(room(X)=>(X='delbert')))&
((?[X,Y]:((quiet(X)&person(X))&(~quiet(Y)&~tall(Y))&(taller(X,Y))))&
(![X]:(taller(X,delbert)))&
((taller(nicole,delbert))&(tall(delbert)&person(delbert)))&
(taller(adrian,delbert))&
(?[X,Y]:((~(creative(X)&person(X)))&(~quiet(Y)&~happy(Y)&~tall(Y)&~creative(Y))&(quieter(X,Y))))&
((~quiet(delbert)&~creative(delbert))&(happy(delbert)&person(delbert)))) | room(delbert)&(![X]:(room(X)=>(X='delbert')))&
(?[X,Y]:((~(creative(X)&person(X)))&(quieter(nicole,Y))&(taller(X,Y)))) | contradiction | [] | null |
Ralph, Samerick are the only persons in the room.
If “someone who is not old is older than someone who is not liked by Jon” then “Ralph is the oldest in the room”.
Samerick is the least old in the room.
More than one person outside the room likes Jon.
Samerick who is a old brave person, is liked by Jon. | Ralph neither is a old person nor is liked by Jasmine. | neutral | room(ralph)&room(samerick)&(![X]:(room(X)=>(X='ralph'|X='samerick')))&
(((?[X,Y]:((~old(X))&(~like(Y,jon))&(older(X,Y))))=>(![X]:(older(X,ralph))))&
(![X]:(older(samerick,X)))&
((?[X,Y]:(~room(X)&~room(Y)&(like(jon,X)&like(jon,Y))&(X!=Y))))&
((old(samerick)&brave(samerick)&person(samerick))&(like(samerick,jon)))) | room(ralph)&room(samerick)&(![X]:(room(X)=>(X='ralph'|X='samerick')))&
(~((old(ralph)&person(ralph))|(like(ralph,jasmine)))) | contradiction | [] | null |
Ruth, Willard, Carl are the only persons in the room. If Carl is not a creative brave person and does not like Elsie then everyone in the room likes Elsie. If Carl is the least rich in the room then someone who is not a brave creative person is richer than someone who does not enjoy logic puzzles. Joan is richer than Carl only if only one person in the room is not a rich person. Willard is not happy and is a happy brave person only if no one outside the room is liked by Elsie. Joan is richer than Carl. Carl is not rich or is not a creative rich brave person or both. Ruth is not brave or is not liked by Elsie or both. Elsie is richer than Ruth. Carl is the least rich in the room. It is not the case that 'Ruth and Carl like each other'. Carl neither enjoys logic puzzles nor likes Joan. | Carl is a rich happy creative brave person and is older than Elsie. | contradiction | room(ruth)&room(willard)&room(carl)&(![X]:(room(X)=>(X='ruth'|X='willard'|X='carl')))&
((((~(creative(carl)&brave(carl)&person(carl)))&(~like(elsie,carl)))=>(![X]:(room(X)=>(like(elsie,X)))))&
((![X]:(richer(carl,X)))=>(?[X,Y]:((~(brave(X)&creative(X)&person(X)))&(does_not_enjoy_logic_puzzles(Y))&(richer(X,Y)))))&
((richer(carl,joan))=>(((?[X]:(room(X)&~(rich(X)&person(X))))&(![X,Y]:((~(rich(X)&person(X))&~(rich(Y)&person(Y)))=>(X=Y))))))&
(((~happy(willard))&(happy(willard)&brave(willard)&person(willard)))=>(~?[X]:(~room(X)=>(like(X,elsie)))))&
(richer(carl,joan))&
(((~rich(carl))|(~(creative(carl)&rich(carl)&brave(carl)&person(carl)))))&
(((~brave(ruth))|(~like(ruth,elsie))))&
(richer(ruth,elsie))&
(![X]:(richer(carl,X)))&
(~((like(ruth,carl) & like(carl,ruth))))&
(~((enjoys_logic_puzzles(carl))|(like(joan,carl))))) | room(ruth)&room(willard)&room(carl)&(![X]:(room(X)=>(X='ruth'|X='willard'|X='carl')))&
((rich(carl)&happy(carl)&creative(carl)&brave(carl)&person(carl))&(older(elsie,carl))) | neutral | [
"hypothesis",
"h6"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(rich_type, type, (
rich: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(older_type, type, (
older: ( $i * $i ) > $o)).
tff(alice_type, type, (
alice: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(mary_type, type, (
mary: $i)).
tff(1,plain,
(rich(fred) <=> rich(fred)),
inference(rewrite,[status(thm)],[])).
tff(2,axiom,((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((rich(fred) & happy(fred)) & creative(fred)) & brave(fred)) & person(fred)) & older(alice, fred))), file('/mnt/tmpfs//2139087492174152229284064.p','hypothesis')).
tff(3,plain,
(((((rich(fred) & happy(fred)) & creative(fred)) & brave(fred)) & person(fred)) & older(alice, fred)),
inference(and_elim,[status(thm)],[2])).
tff(4,plain,
((((rich(fred) & happy(fred)) & creative(fred)) & brave(fred)) & person(fred)),
inference(and_elim,[status(thm)],[3])).
tff(5,plain,
(((rich(fred) & happy(fred)) & creative(fred)) & brave(fred)),
inference(and_elim,[status(thm)],[4])).
tff(6,plain,
((rich(fred) & happy(fred)) & creative(fred)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(rich(fred) & happy(fred)),
inference(and_elim,[status(thm)],[6])).
tff(8,plain,
(rich(fred)),
inference(and_elim,[status(thm)],[7])).
tff(9,plain,
(rich(fred)),
inference(modus_ponens,[status(thm)],[8, 1])).
tff(10,plain,
(person(fred) <=> person(fred)),
inference(rewrite,[status(thm)],[])).
tff(11,plain,
(person(fred)),
inference(and_elim,[status(thm)],[4])).
tff(12,plain,
(person(fred)),
inference(modus_ponens,[status(thm)],[11, 10])).
tff(13,plain,
(creative(fred) <=> creative(fred)),
inference(rewrite,[status(thm)],[])).
tff(14,plain,
(creative(fred)),
inference(and_elim,[status(thm)],[6])).
tff(15,plain,
(creative(fred)),
inference(modus_ponens,[status(thm)],[14, 13])).
tff(16,plain,
(brave(fred) <=> brave(fred)),
inference(rewrite,[status(thm)],[])).
tff(17,plain,
(brave(fred)),
inference(and_elim,[status(thm)],[5])).
tff(18,plain,
(brave(fred)),
inference(modus_ponens,[status(thm)],[17, 16])).
tff(19,plain,
(((~rich(fred)) | ((~creative(fred)) | (~brave(fred)) | (~person(fred)))) <=> ((~rich(fred)) | (~creative(fred)) | (~brave(fred)) | (~person(fred)))),
inference(rewrite,[status(thm)],[])).
tff(20,plain,
((~(~((~creative(fred)) | (~brave(fred)) | (~person(fred))))) <=> ((~creative(fred)) | (~brave(fred)) | (~person(fred)))),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
((creative(fred) & brave(fred) & person(fred)) <=> (~((~creative(fred)) | (~brave(fred)) | (~person(fred))))),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
((~(creative(fred) & brave(fred) & person(fred))) <=> (~(~((~creative(fred)) | (~brave(fred)) | (~person(fred)))))),
inference(monotonicity,[status(thm)],[21])).
tff(23,plain,
((~(creative(fred) & brave(fred) & person(fred))) <=> ((~creative(fred)) | (~brave(fred)) | (~person(fred)))),
inference(transitivity,[status(thm)],[22, 20])).
tff(24,plain,
(((~rich(fred)) | (~(creative(fred) & brave(fred) & person(fred)))) <=> ((~rich(fred)) | ((~creative(fred)) | (~brave(fred)) | (~person(fred))))),
inference(monotonicity,[status(thm)],[23])).
tff(25,plain,
(((~rich(fred)) | (~(creative(fred) & brave(fred) & person(fred)))) <=> ((~rich(fred)) | (~creative(fred)) | (~brave(fred)) | (~person(fred)))),
inference(transitivity,[status(thm)],[24, 19])).
tff(26,plain,
(((~rich(fred)) | (~(creative(fred) & rich(fred) & brave(fred) & person(fred)))) <=> ((~rich(fred)) | (~(creative(fred) & brave(fred) & person(fred))))),
inference(rewrite,[status(thm)],[])).
tff(27,plain,
(((~rich(fred)) | (~(((creative(fred) & rich(fred)) & brave(fred)) & person(fred)))) <=> ((~rich(fred)) | (~(creative(fred) & rich(fred) & brave(fred) & person(fred))))),
inference(rewrite,[status(thm)],[])).
tff(28,axiom,((~rich(fred)) | (~(((creative(fred) & rich(fred)) & brave(fred)) & person(fred)))), file('/mnt/tmpfs//2139087492174152229284064.p','h6')).
tff(29,plain,
((~rich(fred)) | (~(creative(fred) & rich(fred) & brave(fred) & person(fred)))),
inference(modus_ponens,[status(thm)],[28, 27])).
tff(30,plain,
((~rich(fred)) | (~(creative(fred) & brave(fred) & person(fred)))),
inference(modus_ponens,[status(thm)],[29, 26])).
tff(31,plain,
((~rich(fred)) | (~creative(fred)) | (~brave(fred)) | (~person(fred))),
inference(modus_ponens,[status(thm)],[30, 25])).
tff(32,plain,
($false),
inference(unit_resolution,[status(thm)],[31, 18, 15, 12, 9])).
% SZS output end Proof
|
George, Kathleen, Jeffrey are the only persons in the room.
Either more than one person outside the room is older than Kimberley or Kathleen is not a creative person and is older than Kimberley or but not both.
Jeffrey is the least quiet in the room.
Kathleen is not a quiet happy rich old person.
Jeffrey either is older than Kimberley or is not creative.
Jeffrey either is not happy, not rich, not creative or is not rich, not quiet.
It is not the case that 'everyone outside the room who is a happy quiet person is not a quiet rich happy person'.
Kathleen and Jeffrey are respectively quiet and creative. | Someone who is quieter than Kimberley is richer than someone who is not a quiet person. | neutral | room(george)&room(kathleen)&room(jeffrey)&(![X]:(room(X)=>(X='george'|X='kathleen'|X='jeffrey')))&
((((?[X,Y]:(~room(X)&~room(Y)&(older(kimberley,X)&older(kimberley,Y))&(X!=Y))))<~>((~(creative(kathleen)&person(kathleen)))&(older(kimberley,kathleen))))&
(![X]:(quieter(jeffrey,X)))&
(~(quiet(kathleen)&happy(kathleen)&rich(kathleen)&old(kathleen)&person(kathleen)))&
(((older(kimberley,jeffrey))<~>(~creative(jeffrey))))&
(((~happy(jeffrey)&~rich(jeffrey)&~creative(jeffrey))<~>(~rich(jeffrey)&~quiet(jeffrey))))&
(~(![X]:(~room(X)=>(((happy(X)&quiet(X)&person(X))=>(~(quiet(X)&rich(X)&happy(X)&person(X))))))))&
((quiet(kathleen))&(creative(jeffrey)))) | room(george)&room(kathleen)&room(jeffrey)&(![X]:(room(X)=>(X='george'|X='kathleen'|X='jeffrey')))&
(?[X,Y]:((quieter(kimberley,X))&(~(quiet(Y)&person(Y)))&(richer(X,Y)))) | contradiction | [] | null |
Alicia is the only person in the room. Alicia who is not happy, not creative, is older than Jennifer. Alicia is the oldest in the room. Only one person in the room is a quiet person. Alicia is not tall. Alicia is the tallest in the room. | Someone who is not a happy quiet person is taller than someone who is not a creative old person. | entailment | room(alicia)&(![X]:(room(X)=>(X='alicia')))&
(((~happy(alicia)&~creative(alicia))&(older(jennifer,alicia)))&
(![X]:(older(X,alicia)))&
(((?[X]:(room(X)&quiet(X)&person(X)))&(![X,Y]:((quiet(X)&person(X)&quiet(Y)&person(Y))=>(X=Y)))))&
(~tall(alicia))&
(![X]:(taller(X,alicia)))) | room(alicia)&(![X]:(room(X)=>(X='alicia')))&
(?[X,Y]:((~(happy(X)&quiet(X)&person(X)))&(~(creative(Y)&old(Y)&person(Y)))&(taller(X,Y)))) | contradiction | [
"h3",
"h0",
"h5",
"h1",
"hypothesis"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(quiet_type, type, (
quiet: $i > $o)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(paul_type, type, (
paul: $i)).
tff(happy_type, type, (
happy: $i > $o)).
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(old_type, type, (
old: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(older_type, type, (
older: ( $i * $i ) > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(fred_type, type, (
fred: $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(1,plain,
(?[X: $i] : (room(X) & quiet(X) & person(X)) <=> ?[X: $i] : (room(X) & quiet(X) & person(X))),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
(^[X: $i] : rewrite(((room(X) & quiet(X)) & person(X)) <=> (room(X) & quiet(X) & person(X)))),
inference(bind,[status(th)],[])).
tff(3,plain,
(?[X: $i] : ((room(X) & quiet(X)) & person(X)) <=> ?[X: $i] : (room(X) & quiet(X) & person(X))),
inference(quant_intro,[status(thm)],[2])).
tff(4,axiom,(?[X: $i] : ((room(X) & quiet(X)) & person(X)) & ![X: $i, Y: $i] : ((((quiet(X) & person(X)) & quiet(Y)) & person(Y)) => (X = Y))), file('/mnt/tmpfs//222513931473946316430173.p','h3')).
tff(5,plain,
(?[X: $i] : ((room(X) & quiet(X)) & person(X))),
inference(and_elim,[status(thm)],[4])).
tff(6,plain,
(?[X: $i] : (room(X) & quiet(X) & person(X))),
inference(modus_ponens,[status(thm)],[5, 3])).
tff(7,plain,
(?[X: $i] : (room(X) & quiet(X) & person(X))),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,(
room(X!0) & quiet(X!0) & person(X!0)),
inference(skolemize,[status(sab)],[7])).
tff(9,plain,
(room(X!0)),
inference(and_elim,[status(thm)],[8])).
tff(10,plain,
(^[X: $i] : refl(((~room(X)) | (X = |'mary'|)) <=> ((~room(X)) | (X = |'mary'|)))),
inference(bind,[status(th)],[])).
tff(11,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(quant_intro,[status(thm)],[10])).
tff(12,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
(^[X: $i] : rewrite((room(X) => (X = |'mary'|)) <=> ((~room(X)) | (X = |'mary'|)))),
inference(bind,[status(th)],[])).
tff(14,plain,
(![X: $i] : (room(X) => (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(quant_intro,[status(thm)],[13])).
tff(15,axiom,(room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))), file('/mnt/tmpfs//222513931473946316430173.p','h0')).
tff(16,plain,
(![X: $i] : (room(X) => (X = |'mary'|))),
inference(and_elim,[status(thm)],[15])).
tff(17,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[16, 14])).
tff(18,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[17, 12])).
tff(19,plain,(
![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(skolemize,[status(sab)],[18])).
tff(20,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[19, 11])).
tff(21,plain,
(((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!0)) | (X!0 = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!0)) | (X!0 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(22,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!0)) | (X!0 = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(23,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!0)) | (X!0 = |'mary'|)),
inference(modus_ponens,[status(thm)],[22, 21])).
tff(24,plain,
(X!0 = |'mary'|),
inference(unit_resolution,[status(thm)],[23, 20, 9])).
tff(25,plain,
(|'mary'| = X!0),
inference(symmetry,[status(thm)],[24])).
tff(26,plain,
(quiet(|'mary'|) <=> quiet(X!0)),
inference(monotonicity,[status(thm)],[25])).
tff(27,plain,
(quiet(X!0) <=> quiet(|'mary'|)),
inference(symmetry,[status(thm)],[26])).
tff(28,plain,
(quiet(X!0)),
inference(and_elim,[status(thm)],[8])).
tff(29,plain,
(quiet(|'mary'|)),
inference(modus_ponens,[status(thm)],[28, 27])).
tff(30,plain,
(person(|'mary'|) <=> person(X!0)),
inference(monotonicity,[status(thm)],[25])).
tff(31,plain,
(person(X!0) <=> person(|'mary'|)),
inference(symmetry,[status(thm)],[30])).
tff(32,plain,
(person(X!0)),
inference(and_elim,[status(thm)],[8])).
tff(33,plain,
(person(|'mary'|)),
inference(modus_ponens,[status(thm)],[32, 31])).
tff(34,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
(room(mary)),
inference(and_elim,[status(thm)],[15])).
tff(36,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[35, 34])).
tff(37,plain,
(((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(mary)) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(38,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(39,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(mary)) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[38, 37])).
tff(40,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[39, 36, 20])).
tff(41,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[40])).
tff(42,plain,
(taller(paul, |'mary'|) <=> taller(paul, mary)),
inference(monotonicity,[status(thm)],[41])).
tff(43,plain,
(taller(paul, mary) <=> taller(paul, |'mary'|)),
inference(symmetry,[status(thm)],[42])).
tff(44,plain,
(^[X: $i] : refl(taller(X, mary) <=> taller(X, mary))),
inference(bind,[status(th)],[])).
tff(45,plain,
(![X: $i] : taller(X, mary) <=> ![X: $i] : taller(X, mary)),
inference(quant_intro,[status(thm)],[44])).
tff(46,plain,
(![X: $i] : taller(X, mary) <=> ![X: $i] : taller(X, mary)),
inference(rewrite,[status(thm)],[])).
tff(47,axiom,(![X: $i] : taller(X, mary)), file('/mnt/tmpfs//222513931473946316430173.p','h5')).
tff(48,plain,
(![X: $i] : taller(X, mary)),
inference(modus_ponens,[status(thm)],[47, 46])).
tff(49,plain,(
![X: $i] : taller(X, mary)),
inference(skolemize,[status(sab)],[48])).
tff(50,plain,
(![X: $i] : taller(X, mary)),
inference(modus_ponens,[status(thm)],[49, 45])).
tff(51,plain,
((~![X: $i] : taller(X, mary)) | taller(paul, mary)),
inference(quant_inst,[status(thm)],[])).
tff(52,plain,
(taller(paul, mary)),
inference(unit_resolution,[status(thm)],[51, 50])).
tff(53,plain,
(taller(paul, |'mary'|)),
inference(modus_ponens,[status(thm)],[52, 43])).
tff(54,plain,
(creative(|'mary'|) <=> creative(mary)),
inference(monotonicity,[status(thm)],[41])).
tff(55,plain,
(creative(mary) <=> creative(|'mary'|)),
inference(symmetry,[status(thm)],[54])).
tff(56,plain,
((~creative(mary)) <=> (~creative(|'mary'|))),
inference(monotonicity,[status(thm)],[55])).
tff(57,plain,
((~creative(mary)) <=> (~creative(mary))),
inference(rewrite,[status(thm)],[])).
tff(58,axiom,(((~happy(mary)) & (~creative(mary))) & older(paul, mary)), file('/mnt/tmpfs//222513931473946316430173.p','h1')).
tff(59,plain,
((~happy(mary)) & (~creative(mary))),
inference(and_elim,[status(thm)],[58])).
tff(60,plain,
(~creative(mary)),
inference(and_elim,[status(thm)],[59])).
tff(61,plain,
(~creative(mary)),
inference(modus_ponens,[status(thm)],[60, 57])).
tff(62,plain,
(~creative(|'mary'|)),
inference(modus_ponens,[status(thm)],[61, 56])).
tff(63,plain,
(((~creative(|'mary'|)) | (~old(|'mary'|)) | (~person(|'mary'|))) | creative(|'mary'|)),
inference(tautology,[status(thm)],[])).
tff(64,plain,
((~creative(|'mary'|)) | (~old(|'mary'|)) | (~person(|'mary'|))),
inference(unit_resolution,[status(thm)],[63, 62])).
tff(65,assumption,(~((~room(X!1)) | (X!1 = |'mary'|))), introduced(assumption)).
tff(66,plain,
(((~room(X!1)) | (X!1 = |'mary'|)) | (~(X!1 = |'mary'|))),
inference(tautology,[status(thm)],[])).
tff(67,plain,
(~(X!1 = |'mary'|)),
inference(unit_resolution,[status(thm)],[66, 65])).
tff(68,plain,
(((~room(X!1)) | (X!1 = |'mary'|)) | room(X!1)),
inference(tautology,[status(thm)],[])).
tff(69,plain,
(room(X!1)),
inference(unit_resolution,[status(thm)],[68, 65])).
tff(70,plain,
(((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!1)) | (X!1 = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!1)) | (X!1 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(71,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!1)) | (X!1 = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(72,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!1)) | (X!1 = |'mary'|)),
inference(modus_ponens,[status(thm)],[71, 70])).
tff(73,plain,
($false),
inference(unit_resolution,[status(thm)],[72, 20, 69, 67])).
tff(74,plain,((~room(X!1)) | (X!1 = |'mary'|)), inference(lemma,lemma(discharge,[]))).
tff(75,plain,
(((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | ![X: $i, Y: $i] : ((~taller(X, Y)) | (~((~quiet(X)) | (~person(X)) | (~happy(X)))) | (~((~creative(Y)) | (~old(Y)) | (~person(Y)))))) <=> ((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | ![X: $i, Y: $i] : ((~taller(X, Y)) | (~((~quiet(X)) | (~person(X)) | (~happy(X)))) | (~((~creative(Y)) | (~old(Y)) | (~person(Y))))))),
inference(rewrite,[status(thm)],[])).
tff(76,plain,
(((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | ![X: $i, Y: $i] : (~((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y)))) <=> ((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | ![X: $i, Y: $i] : ((~taller(X, Y)) | (~((~quiet(X)) | (~person(X)) | (~happy(X)))) | (~((~creative(Y)) | (~old(Y)) | (~person(Y))))))),
inference(rewrite,[status(thm)],[])).
tff(77,plain,
(((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | ![X: $i, Y: $i] : (~((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y)))) <=> ((~room(mary)) | (~((~room(X!1)) | (X!1 = |'mary'|))) | ![X: $i, Y: $i] : (~((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(78,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(79,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y))))),
inference(monotonicity,[status(thm)],[78])).
tff(80,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(81,plain,
((~((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ?[X: $i, Y: $i] : (((~((happy(X) & quiet(X)) & person(X))) & (~((creative(Y) & old(Y)) & person(Y)))) & taller(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y))))),
inference(rewrite,[status(thm)],[])).
tff(82,axiom,(~((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ?[X: $i, Y: $i] : (((~((happy(X) & quiet(X)) & person(X))) & (~((creative(Y) & old(Y)) & person(Y)))) & taller(X, Y)))), file('/mnt/tmpfs//222513931473946316430173.p','hypothesis')).
tff(83,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y)))),
inference(modus_ponens,[status(thm)],[82, 81])).
tff(84,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y)))),
inference(modus_ponens,[status(thm)],[83, 79])).
tff(85,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y)))),
inference(modus_ponens,[status(thm)],[84, 80])).
tff(86,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~(happy(X) & quiet(X) & person(X))) & (~(creative(Y) & old(Y) & person(Y))) & taller(X, Y)))),
inference(modus_ponens,[status(thm)],[85, 79])).
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!1)) (= X!1 |'mary'|))))
(a!4 (lambda ((X $i) (Y $i))
(let ((a!1 (and (not (and (happy X) (quiet X) (person X)))
(not (and (creative Y) (old Y) (person Y)))
(taller X Y))))
(refl (~ (not a!1) (not a!1))))))
(a!5 (exists ((X $i) (Y $i))
(and (not (and (happy X) (quiet X) (person X)))
(not (and (creative Y) (old Y) (person Y)))
(taller X Y))))
(a!6 (forall ((X $i) (Y $i))
(let ((a!1 (and (not (and (happy X) (quiet X) (person X)))
(not (and (creative Y) (old Y) (person Y)))
(taller X Y))))
(not a!1)))))
(let ((a!7 (~ (not (and (room mary) a!2 a!5)) (or (not (room mary)) a!3 a!6))))
(nnf-neg a!1
(sk (~ (not a!2) a!3))
(nnf-neg (proof-bind a!4) (~ (not a!5) a!6))
a!7)))
|
George, Jonathan, Mary are the only persons in the room.
Jonathan is not a drone photographer or is a drone photographer or both.
George neither plays a string instrument nor is a drone photographer.
More than one person in the room is a drone photographer. | Jonathan is a drone photographer or does not play a string instrument or both. | entailment | room(george)&room(jonathan)&room(mary)&(![X]:(room(X)=>(X='george'|X='jonathan'|X='mary')))&
((((is_not_a_drone_photographer(jonathan))|(is_a_drone_photographer(jonathan))))&
(~((plays_a_string_instrument(george))|(is_a_drone_photographer(george))))&
((?[X,Y]:(room(X)&room(Y)&(is_a_drone_photographer(X)&is_a_drone_photographer(Y))&(X!=Y))))) | room(george)&room(jonathan)&room(mary)&(![X]:(room(X)=>(X='george'|X='jonathan'|X='mary')))&
(((is_a_drone_photographer(jonathan))|(does_not_play_a_string_instrument(jonathan)))) | entailment | [
"b17",
"h2",
"h3",
"h0",
"hypothesis"
] | % 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(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(predc_type, type, (
predc: $i > $o)).
tff(tptp_fun_Y_0_type, type, (
tptp_fun_Y_0: $i)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(mary_type, type, (
mary: $i)).
tff(fred_type, type, (
fred: $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(1,plain,
((|'mary'| = Y!0) <=> (Y!0 = |'mary'|)),
inference(commutativity,[status(thm)],[])).
tff(2,assumption,(~predc(paul)), introduced(assumption)).
tff(3,assumption,(~(mary = |'fred'|)), introduced(assumption)).
tff(4,assumption,(~(X!1 = |'mary'|)), introduced(assumption)).
tff(5,assumption,(~(Y!0 = |'fred'|)), introduced(assumption)).
tff(6,assumption,(mary = |'paul'|), introduced(assumption)).
tff(7,plain,
(|'paul'| = mary),
inference(symmetry,[status(thm)],[6])).
tff(8,plain,
((paul = mary) <=> (mary = paul)),
inference(commutativity,[status(thm)],[])).
tff(9,plain,
((paul = |'paul'|) <=> (paul = mary)),
inference(monotonicity,[status(thm)],[7])).
tff(10,plain,
((paul = |'paul'|) <=> (mary = paul)),
inference(transitivity,[status(thm)],[9, 8])).
tff(11,plain,
((mary = paul) <=> (paul = |'paul'|)),
inference(symmetry,[status(thm)],[10])).
tff(12,plain,
((~(mary = paul)) <=> (~(paul = |'paul'|))),
inference(monotonicity,[status(thm)],[11])).
tff(13,plain,
((~(mary = paul)) <=> (~(mary = paul))),
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//6372852573206580908549425.p','b17')).
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,
((((((((((((((~(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(43,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)],[42])).
tff(44,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)],[43])).
tff(45,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)],[44])).
tff(46,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)],[45])).
tff(47,plain,
(((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))),
inference(and_elim,[status(thm)],[46])).
tff(48,plain,
((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))),
inference(and_elim,[status(thm)],[47])).
tff(49,plain,
(((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))),
inference(and_elim,[status(thm)],[48])).
tff(50,plain,
((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))),
inference(and_elim,[status(thm)],[49])).
tff(51,plain,
(((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))),
inference(and_elim,[status(thm)],[50])).
tff(52,plain,
((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))),
inference(and_elim,[status(thm)],[51])).
tff(53,plain,
(((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))),
inference(and_elim,[status(thm)],[52])).
tff(54,plain,
((~(mary = paul)) & (~(mary = fred))),
inference(and_elim,[status(thm)],[53])).
tff(55,plain,
(~(mary = paul)),
inference(and_elim,[status(thm)],[54])).
tff(56,plain,
(~(mary = paul)),
inference(modus_ponens,[status(thm)],[55, 13])).
tff(57,plain,
(~(paul = |'paul'|)),
inference(modus_ponens,[status(thm)],[56, 12])).
tff(58,assumption,(X!1 = |'paul'|), introduced(assumption)).
tff(59,plain,
(X!1 = mary),
inference(transitivity,[status(thm)],[58, 7])).
tff(60,plain,
(predc(X!1) <=> predc(mary)),
inference(monotonicity,[status(thm)],[59])).
tff(61,plain,
(predc(mary) <=> predc(X!1)),
inference(symmetry,[status(thm)],[60])).
tff(62,plain,
((~predc(mary)) <=> (~predc(X!1))),
inference(monotonicity,[status(thm)],[61])).
tff(63,plain,
((~predc(mary)) <=> (~predc(mary))),
inference(rewrite,[status(thm)],[])).
tff(64,axiom,(~(preda(mary) | predc(mary))), file('/mnt/tmpfs//6372852573206580908549425.p','h2')).
tff(65,plain,
(~predc(mary)),
inference(or_elim,[status(thm)],[64])).
tff(66,plain,
(~predc(mary)),
inference(modus_ponens,[status(thm)],[65, 63])).
tff(67,plain,
(~predc(X!1)),
inference(modus_ponens,[status(thm)],[66, 62])).
tff(68,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & predc(X) & predc(Y) & (~(X = Y))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & predc(X) & predc(Y) & (~(X = Y)))),
inference(rewrite,[status(thm)],[])).
tff(69,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite(((room(X) & room(Y)) & (predc(X) & predc(Y))) <=> (room(X) & room(Y) & predc(X) & predc(Y))), ((((room(X) & room(Y)) & (predc(X) & predc(Y))) & (~(X = Y))) <=> ((room(X) & room(Y) & predc(X) & predc(Y)) & (~(X = Y))))), rewrite(((room(X) & room(Y) & predc(X) & predc(Y)) & (~(X = Y))) <=> (room(X) & room(Y) & predc(X) & predc(Y) & (~(X = Y)))), ((((room(X) & room(Y)) & (predc(X) & predc(Y))) & (~(X = Y))) <=> (room(X) & room(Y) & predc(X) & predc(Y) & (~(X = Y)))))),
inference(bind,[status(th)],[])).
tff(70,plain,
(?[X: $i, Y: $i] : (((room(X) & room(Y)) & (predc(X) & predc(Y))) & (~(X = Y))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & predc(X) & predc(Y) & (~(X = Y)))),
inference(quant_intro,[status(thm)],[69])).
tff(71,axiom,(?[X: $i, Y: $i] : (((room(X) & room(Y)) & (predc(X) & predc(Y))) & (~(X = Y)))), file('/mnt/tmpfs//6372852573206580908549425.p','h3')).
tff(72,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & predc(X) & predc(Y) & (~(X = Y)))),
inference(modus_ponens,[status(thm)],[71, 70])).
tff(73,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & predc(X) & predc(Y) & (~(X = Y)))),
inference(modus_ponens,[status(thm)],[72, 68])).
tff(74,plain,(
room(X!1) & room(Y!0) & predc(X!1) & predc(Y!0) & (~(X!1 = Y!0))),
inference(skolemize,[status(sab)],[73])).
tff(75,plain,
(predc(X!1)),
inference(and_elim,[status(thm)],[74])).
tff(76,plain,
($false),
inference(unit_resolution,[status(thm)],[75, 67])).
tff(77,plain,((~(X!1 = |'paul'|)) | (~(mary = |'paul'|))), inference(lemma,lemma(discharge,[]))).
tff(78,plain,
(~(X!1 = |'paul'|)),
inference(unit_resolution,[status(thm)],[77, 6])).
tff(79,plain,
(room(X!1)),
inference(and_elim,[status(thm)],[74])).
tff(80,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(81,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)],[80])).
tff(82,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(83,plain,
(^[X: $i] : trans(monotonicity(rewrite((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) <=> ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))), ((room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|))) <=> (room(X) => ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))))), rewrite((room(X) => ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|))) <=> ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), ((room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|))) <=> ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))))),
inference(bind,[status(th)],[])).
tff(84,plain,
(![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|))) <=> ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[83])).
tff(85,axiom,(((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))), file('/mnt/tmpfs//6372852573206580908549425.p','h0')).
tff(86,plain,
(![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))),
inference(and_elim,[status(thm)],[85])).
tff(87,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[86, 84])).
tff(88,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[87, 82])).
tff(89,plain,(
![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[88])).
tff(90,plain,
(![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[89, 81])).
tff(91,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))),
inference(rewrite,[status(thm)],[])).
tff(92,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))),
inference(quant_inst,[status(thm)],[])).
tff(93,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))),
inference(modus_ponens,[status(thm)],[92, 91])).
tff(94,plain,
((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|)),
inference(unit_resolution,[status(thm)],[93, 90, 79])).
tff(95,plain,
(X!1 = |'fred'|),
inference(unit_resolution,[status(thm)],[94, 78, 4])).
tff(96,assumption,(X!1 = |'fred'|), introduced(assumption)).
tff(97,plain,
(|'fred'| = X!1),
inference(symmetry,[status(thm)],[96])).
tff(98,assumption,(paul = |'fred'|), introduced(assumption)).
tff(99,plain,
(paul = X!1),
inference(transitivity,[status(thm)],[98, 97])).
tff(100,plain,
(predc(paul) <=> predc(X!1)),
inference(monotonicity,[status(thm)],[99])).
tff(101,plain,
(predc(X!1) <=> predc(paul)),
inference(symmetry,[status(thm)],[100])).
tff(102,plain,
(predc(paul)),
inference(modus_ponens,[status(thm)],[75, 101])).
tff(103,plain,
($false),
inference(unit_resolution,[status(thm)],[2, 102])).
tff(104,plain,((~(paul = |'fred'|)) | predc(paul) | (~(X!1 = |'fred'|))), inference(lemma,lemma(discharge,[]))).
tff(105,plain,
(~(paul = |'fred'|)),
inference(unit_resolution,[status(thm)],[104, 95, 2])).
tff(106,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(107,plain,
((room(mary) & room(paul)) & room(fred)),
inference(and_elim,[status(thm)],[85])).
tff(108,plain,
(room(mary) & room(paul)),
inference(and_elim,[status(thm)],[107])).
tff(109,plain,
(room(paul)),
inference(and_elim,[status(thm)],[108])).
tff(110,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[109, 106])).
tff(111,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(112,plain,
(((paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|) | (~room(paul))) <=> ((~room(paul)) | (paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(113,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)],[112])).
tff(114,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)],[113, 111])).
tff(115,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(116,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|)),
inference(modus_ponens,[status(thm)],[115, 114])).
tff(117,plain,
((paul = |'fred'|) | (paul = |'paul'|) | (paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[116, 110, 90])).
tff(118,plain,
(paul = |'mary'|),
inference(unit_resolution,[status(thm)],[117, 105, 57])).
tff(119,assumption,(paul = |'mary'|), introduced(assumption)).
tff(120,plain,
(|'mary'| = paul),
inference(symmetry,[status(thm)],[119])).
tff(121,assumption,(Y!0 = |'mary'|), introduced(assumption)).
tff(122,plain,
(Y!0 = paul),
inference(transitivity,[status(thm)],[121, 120])).
tff(123,plain,
(predc(Y!0) <=> predc(paul)),
inference(monotonicity,[status(thm)],[122])).
tff(124,plain,
(predc(paul) <=> predc(Y!0)),
inference(symmetry,[status(thm)],[123])).
tff(125,plain,
((~predc(paul)) <=> (~predc(Y!0))),
inference(monotonicity,[status(thm)],[124])).
tff(126,plain,
(~predc(Y!0)),
inference(modus_ponens,[status(thm)],[2, 125])).
tff(127,plain,
(predc(Y!0)),
inference(and_elim,[status(thm)],[74])).
tff(128,plain,
($false),
inference(unit_resolution,[status(thm)],[127, 126])).
tff(129,plain,((~(Y!0 = |'mary'|)) | predc(paul) | (~(paul = |'mary'|))), inference(lemma,lemma(discharge,[]))).
tff(130,plain,
(~(Y!0 = |'mary'|)),
inference(unit_resolution,[status(thm)],[129, 118, 2])).
tff(131,plain,
(room(Y!0)),
inference(and_elim,[status(thm)],[74])).
tff(132,plain,
(((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((Y!0 = |'fred'|) | (Y!0 = |'paul'|) | (Y!0 = |'mary'|) | (~room(Y!0)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (Y!0 = |'fred'|) | (Y!0 = |'paul'|) | (Y!0 = |'mary'|) | (~room(Y!0)))),
inference(rewrite,[status(thm)],[])).
tff(133,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((Y!0 = |'fred'|) | (Y!0 = |'paul'|) | (Y!0 = |'mary'|) | (~room(Y!0)))),
inference(quant_inst,[status(thm)],[])).
tff(134,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (Y!0 = |'fred'|) | (Y!0 = |'paul'|) | (Y!0 = |'mary'|) | (~room(Y!0))),
inference(modus_ponens,[status(thm)],[133, 132])).
tff(135,plain,
((Y!0 = |'fred'|) | (Y!0 = |'paul'|) | (Y!0 = |'mary'|)),
inference(unit_resolution,[status(thm)],[134, 90, 131])).
tff(136,plain,
(Y!0 = |'paul'|),
inference(unit_resolution,[status(thm)],[135, 130, 5])).
tff(137,plain,
(Y!0 = mary),
inference(transitivity,[status(thm)],[136, 7])).
tff(138,plain,
(predc(Y!0) <=> predc(mary)),
inference(monotonicity,[status(thm)],[137])).
tff(139,plain,
(predc(mary) <=> predc(Y!0)),
inference(symmetry,[status(thm)],[138])).
tff(140,plain,
((~predc(mary)) <=> (~predc(Y!0))),
inference(monotonicity,[status(thm)],[139])).
tff(141,plain,
(~predc(Y!0)),
inference(modus_ponens,[status(thm)],[66, 140])).
tff(142,plain,
($false),
inference(unit_resolution,[status(thm)],[127, 141])).
tff(143,plain,((~(mary = |'paul'|)) | (Y!0 = |'fred'|) | predc(paul) | (X!1 = |'mary'|)), inference(lemma,lemma(discharge,[]))).
tff(144,plain,
(~(mary = |'paul'|)),
inference(unit_resolution,[status(thm)],[143, 5, 2, 4])).
tff(145,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(146,plain,
(room(mary)),
inference(and_elim,[status(thm)],[108])).
tff(147,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[146, 145])).
tff(148,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(149,plain,
(((mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|) | (~room(mary))) <=> ((~room(mary)) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(150,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)],[149])).
tff(151,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)],[150, 148])).
tff(152,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(153,plain,
((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[152, 151])).
tff(154,plain,
((mary = |'fred'|) | (mary = |'paul'|) | (mary = |'mary'|)),
inference(unit_resolution,[status(thm)],[153, 147, 90])).
tff(155,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[154, 144, 3])).
tff(156,assumption,(mary = |'mary'|), introduced(assumption)).
tff(157,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[156])).
tff(158,plain,
(Y!0 = mary),
inference(transitivity,[status(thm)],[121, 157])).
tff(159,plain,
(predc(Y!0) <=> predc(mary)),
inference(monotonicity,[status(thm)],[158])).
tff(160,plain,
(predc(mary) <=> predc(Y!0)),
inference(symmetry,[status(thm)],[159])).
tff(161,plain,
((~predc(mary)) <=> (~predc(Y!0))),
inference(monotonicity,[status(thm)],[160])).
tff(162,plain,
(~predc(Y!0)),
inference(modus_ponens,[status(thm)],[66, 161])).
tff(163,plain,
($false),
inference(unit_resolution,[status(thm)],[127, 162])).
tff(164,plain,((~(Y!0 = |'mary'|)) | (~(mary = |'mary'|))), inference(lemma,lemma(discharge,[]))).
tff(165,plain,
(~(Y!0 = |'mary'|)),
inference(unit_resolution,[status(thm)],[164, 155])).
tff(166,plain,
(Y!0 = |'paul'|),
inference(unit_resolution,[status(thm)],[135, 165, 5])).
tff(167,plain,
((X!1 = Y!0) <=> (X!1 = |'paul'|)),
inference(monotonicity,[status(thm)],[166])).
tff(168,plain,
((X!1 = |'paul'|) <=> (X!1 = Y!0)),
inference(symmetry,[status(thm)],[167])).
tff(169,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[155])).
tff(170,plain,
((paul = |'mary'|) <=> (paul = mary)),
inference(monotonicity,[status(thm)],[169])).
tff(171,plain,
((paul = |'mary'|) <=> (mary = paul)),
inference(transitivity,[status(thm)],[170, 8])).
tff(172,plain,
((mary = paul) <=> (paul = |'mary'|)),
inference(symmetry,[status(thm)],[171])).
tff(173,plain,
((~(mary = paul)) <=> (~(paul = |'mary'|))),
inference(monotonicity,[status(thm)],[172])).
tff(174,plain,
(~(paul = |'mary'|)),
inference(modus_ponens,[status(thm)],[56, 173])).
tff(175,assumption,(paul = |'paul'|), introduced(assumption)).
tff(176,plain,
(|'paul'| = paul),
inference(symmetry,[status(thm)],[175])).
tff(177,assumption,(Y!0 = |'paul'|), introduced(assumption)).
tff(178,plain,
(Y!0 = paul),
inference(transitivity,[status(thm)],[177, 176])).
tff(179,plain,
(predc(Y!0) <=> predc(paul)),
inference(monotonicity,[status(thm)],[178])).
tff(180,plain,
(predc(paul) <=> predc(Y!0)),
inference(symmetry,[status(thm)],[179])).
tff(181,plain,
((~predc(paul)) <=> (~predc(Y!0))),
inference(monotonicity,[status(thm)],[180])).
tff(182,plain,
(~predc(Y!0)),
inference(modus_ponens,[status(thm)],[2, 181])).
tff(183,plain,
($false),
inference(unit_resolution,[status(thm)],[127, 182])).
tff(184,plain,((~(Y!0 = |'paul'|)) | predc(paul) | (~(paul = |'paul'|))), inference(lemma,lemma(discharge,[]))).
tff(185,plain,
(~(paul = |'paul'|)),
inference(unit_resolution,[status(thm)],[184, 166, 2])).
tff(186,plain,
(paul = |'fred'|),
inference(unit_resolution,[status(thm)],[117, 185, 174])).
tff(187,plain,
(~(X!1 = |'fred'|)),
inference(unit_resolution,[status(thm)],[104, 186, 2])).
tff(188,plain,
(X!1 = |'paul'|),
inference(unit_resolution,[status(thm)],[94, 187, 4])).
tff(189,plain,
(X!1 = Y!0),
inference(modus_ponens,[status(thm)],[188, 168])).
tff(190,plain,
(~(X!1 = Y!0)),
inference(and_elim,[status(thm)],[74])).
tff(191,plain,
($false),
inference(unit_resolution,[status(thm)],[190, 189])).
tff(192,plain,((Y!0 = |'fred'|) | (X!1 = |'mary'|) | predc(paul) | (mary = |'fred'|)), inference(lemma,lemma(discharge,[]))).
tff(193,plain,
(Y!0 = |'fred'|),
inference(unit_resolution,[status(thm)],[192, 4, 2, 3])).
tff(194,plain,
(|'fred'| = Y!0),
inference(symmetry,[status(thm)],[193])).
tff(195,plain,
((X!1 = Y!0) <=> (X!1 = |'fred'|)),
inference(monotonicity,[status(thm)],[193])).
tff(196,plain,
((~(X!1 = Y!0)) <=> (~(X!1 = |'fred'|))),
inference(monotonicity,[status(thm)],[195])).
tff(197,plain,
(~(X!1 = |'fred'|)),
inference(modus_ponens,[status(thm)],[190, 196])).
tff(198,plain,
(X!1 = |'paul'|),
inference(unit_resolution,[status(thm)],[94, 197, 4])).
tff(199,plain,
(~(mary = |'paul'|)),
inference(unit_resolution,[status(thm)],[77, 198])).
tff(200,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[154, 199, 3])).
tff(201,plain,
(|'mary'| = mary),
inference(symmetry,[status(thm)],[200])).
tff(202,plain,
((paul = |'mary'|) <=> (paul = mary)),
inference(monotonicity,[status(thm)],[201])).
tff(203,plain,
((paul = |'mary'|) <=> (mary = paul)),
inference(transitivity,[status(thm)],[202, 8])).
tff(204,plain,
((mary = paul) <=> (paul = |'mary'|)),
inference(symmetry,[status(thm)],[203])).
tff(205,plain,
((~(mary = paul)) <=> (~(paul = |'mary'|))),
inference(monotonicity,[status(thm)],[204])).
tff(206,plain,
(~(paul = |'mary'|)),
inference(modus_ponens,[status(thm)],[56, 205])).
tff(207,plain,
(|'paul'| = X!1),
inference(symmetry,[status(thm)],[58])).
tff(208,plain,
(paul = X!1),
inference(transitivity,[status(thm)],[175, 207])).
tff(209,plain,
(predc(paul) <=> predc(X!1)),
inference(monotonicity,[status(thm)],[208])).
tff(210,plain,
(predc(X!1) <=> predc(paul)),
inference(symmetry,[status(thm)],[209])).
tff(211,plain,
(predc(paul)),
inference(modus_ponens,[status(thm)],[75, 210])).
tff(212,plain,
($false),
inference(unit_resolution,[status(thm)],[2, 211])).
tff(213,plain,((~(paul = |'paul'|)) | predc(paul) | (~(X!1 = |'paul'|))), inference(lemma,lemma(discharge,[]))).
tff(214,plain,
(~(paul = |'paul'|)),
inference(unit_resolution,[status(thm)],[213, 198, 2])).
tff(215,plain,
(paul = |'fred'|),
inference(unit_resolution,[status(thm)],[117, 214, 206])).
tff(216,plain,
(paul = Y!0),
inference(transitivity,[status(thm)],[215, 194])).
tff(217,plain,
(predc(paul) <=> predc(Y!0)),
inference(monotonicity,[status(thm)],[216])).
tff(218,plain,
(predc(Y!0) <=> predc(paul)),
inference(symmetry,[status(thm)],[217])).
tff(219,plain,
(predc(paul)),
inference(modus_ponens,[status(thm)],[127, 218])).
tff(220,plain,
($false),
inference(unit_resolution,[status(thm)],[2, 219])).
tff(221,plain,((X!1 = |'mary'|) | predc(paul) | (mary = |'fred'|)), inference(lemma,lemma(discharge,[]))).
tff(222,plain,
(X!1 = |'mary'|),
inference(unit_resolution,[status(thm)],[221, 3, 2])).
tff(223,assumption,(X!1 = |'mary'|), introduced(assumption)).
tff(224,plain,
(|'mary'| = X!1),
inference(symmetry,[status(thm)],[223])).
tff(225,plain,
(paul = X!1),
inference(transitivity,[status(thm)],[119, 224])).
tff(226,plain,
(predc(paul) <=> predc(X!1)),
inference(monotonicity,[status(thm)],[225])).
tff(227,plain,
(predc(X!1) <=> predc(paul)),
inference(symmetry,[status(thm)],[226])).
tff(228,plain,
(predc(paul)),
inference(modus_ponens,[status(thm)],[75, 227])).
tff(229,plain,
($false),
inference(unit_resolution,[status(thm)],[2, 228])).
tff(230,plain,((~(paul = |'mary'|)) | predc(paul) | (~(X!1 = |'mary'|))), inference(lemma,lemma(discharge,[]))).
tff(231,plain,
(~(paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[230, 222, 2])).
tff(232,plain,
(mary = X!1),
inference(transitivity,[status(thm)],[156, 224])).
tff(233,plain,
(predc(mary) <=> predc(X!1)),
inference(monotonicity,[status(thm)],[232])).
tff(234,plain,
(predc(X!1) <=> predc(mary)),
inference(symmetry,[status(thm)],[233])).
tff(235,plain,
(predc(mary)),
inference(modus_ponens,[status(thm)],[75, 234])).
tff(236,plain,
($false),
inference(unit_resolution,[status(thm)],[66, 235])).
tff(237,plain,((~(mary = |'mary'|)) | (~(X!1 = |'mary'|))), inference(lemma,lemma(discharge,[]))).
tff(238,plain,
(~(mary = |'mary'|)),
inference(unit_resolution,[status(thm)],[237, 222])).
tff(239,plain,
(mary = |'paul'|),
inference(unit_resolution,[status(thm)],[154, 238, 3])).
tff(240,plain,
(|'paul'| = mary),
inference(symmetry,[status(thm)],[239])).
tff(241,plain,
((paul = |'paul'|) <=> (paul = mary)),
inference(monotonicity,[status(thm)],[240])).
tff(242,plain,
((paul = |'paul'|) <=> (mary = paul)),
inference(transitivity,[status(thm)],[241, 8])).
tff(243,plain,
((mary = paul) <=> (paul = |'paul'|)),
inference(symmetry,[status(thm)],[242])).
tff(244,plain,
((~(mary = paul)) <=> (~(paul = |'paul'|))),
inference(monotonicity,[status(thm)],[243])).
tff(245,plain,
(~(paul = |'paul'|)),
inference(modus_ponens,[status(thm)],[56, 244])).
tff(246,plain,
(paul = |'fred'|),
inference(unit_resolution,[status(thm)],[117, 245, 231])).
tff(247,plain,
(|'fred'| = paul),
inference(symmetry,[status(thm)],[246])).
tff(248,plain,
((X!1 = Y!0) <=> (|'mary'| = Y!0)),
inference(monotonicity,[status(thm)],[222])).
tff(249,plain,
((X!1 = Y!0) <=> (Y!0 = |'mary'|)),
inference(transitivity,[status(thm)],[248, 1])).
tff(250,plain,
((~(X!1 = Y!0)) <=> (~(Y!0 = |'mary'|))),
inference(monotonicity,[status(thm)],[249])).
tff(251,plain,
(~(Y!0 = |'mary'|)),
inference(modus_ponens,[status(thm)],[190, 250])).
tff(252,plain,
(Y!0 = mary),
inference(transitivity,[status(thm)],[177, 7])).
tff(253,plain,
(predc(Y!0) <=> predc(mary)),
inference(monotonicity,[status(thm)],[252])).
tff(254,plain,
(predc(mary) <=> predc(Y!0)),
inference(symmetry,[status(thm)],[253])).
tff(255,plain,
((~predc(mary)) <=> (~predc(Y!0))),
inference(monotonicity,[status(thm)],[254])).
tff(256,plain,
(~predc(Y!0)),
inference(modus_ponens,[status(thm)],[66, 255])).
tff(257,plain,
($false),
inference(unit_resolution,[status(thm)],[127, 256])).
tff(258,plain,((~(Y!0 = |'paul'|)) | (~(mary = |'paul'|))), inference(lemma,lemma(discharge,[]))).
tff(259,plain,
(~(Y!0 = |'paul'|)),
inference(unit_resolution,[status(thm)],[258, 239])).
tff(260,plain,
(Y!0 = |'fred'|),
inference(unit_resolution,[status(thm)],[135, 259, 251])).
tff(261,plain,
(Y!0 = paul),
inference(transitivity,[status(thm)],[260, 247])).
tff(262,plain,
(predc(Y!0) <=> predc(paul)),
inference(monotonicity,[status(thm)],[261])).
tff(263,plain,
(predc(paul) <=> predc(Y!0)),
inference(symmetry,[status(thm)],[262])).
tff(264,plain,
((~predc(paul)) <=> (~predc(Y!0))),
inference(monotonicity,[status(thm)],[263])).
tff(265,plain,
(~predc(Y!0)),
inference(modus_ponens,[status(thm)],[2, 264])).
tff(266,plain,
($false),
inference(unit_resolution,[status(thm)],[127, 265])).
tff(267,plain,((mary = |'fred'|) | predc(paul)), inference(lemma,lemma(discharge,[]))).
tff(268,plain,
(mary = |'fred'|),
inference(unit_resolution,[status(thm)],[267, 2])).
tff(269,assumption,(mary = |'fred'|), introduced(assumption)).
tff(270,plain,
(|'fred'| = mary),
inference(symmetry,[status(thm)],[269])).
tff(271,plain,
(X!1 = mary),
inference(transitivity,[status(thm)],[96, 270])).
tff(272,plain,
(predc(X!1) <=> predc(mary)),
inference(monotonicity,[status(thm)],[271])).
tff(273,plain,
(predc(mary) <=> predc(X!1)),
inference(symmetry,[status(thm)],[272])).
tff(274,plain,
((~predc(mary)) <=> (~predc(X!1))),
inference(monotonicity,[status(thm)],[273])).
tff(275,plain,
(~predc(X!1)),
inference(modus_ponens,[status(thm)],[66, 274])).
tff(276,plain,
($false),
inference(unit_resolution,[status(thm)],[75, 275])).
tff(277,plain,((~(X!1 = |'fred'|)) | (~(mary = |'fred'|))), inference(lemma,lemma(discharge,[]))).
tff(278,plain,
(~(X!1 = |'fred'|)),
inference(unit_resolution,[status(thm)],[277, 268])).
tff(279,plain,
((|'paul'| = Y!0) <=> (Y!0 = |'paul'|)),
inference(commutativity,[status(thm)],[])).
tff(280,plain,
((X!1 = Y!0) <=> (|'paul'| = Y!0)),
inference(monotonicity,[status(thm)],[58])).
tff(281,plain,
((X!1 = Y!0) <=> (Y!0 = |'paul'|)),
inference(transitivity,[status(thm)],[280, 279])).
tff(282,plain,
((Y!0 = |'paul'|) <=> (X!1 = Y!0)),
inference(symmetry,[status(thm)],[281])).
tff(283,assumption,(Y!0 = |'fred'|), introduced(assumption)).
tff(284,plain,
(Y!0 = mary),
inference(transitivity,[status(thm)],[283, 270])).
tff(285,plain,
(predc(Y!0) <=> predc(mary)),
inference(monotonicity,[status(thm)],[284])).
tff(286,plain,
(predc(mary) <=> predc(Y!0)),
inference(symmetry,[status(thm)],[285])).
tff(287,plain,
((~predc(mary)) <=> (~predc(Y!0))),
inference(monotonicity,[status(thm)],[286])).
tff(288,plain,
(~predc(Y!0)),
inference(modus_ponens,[status(thm)],[66, 287])).
tff(289,plain,
($false),
inference(unit_resolution,[status(thm)],[127, 288])).
tff(290,plain,((~(Y!0 = |'fred'|)) | (~(mary = |'fred'|))), inference(lemma,lemma(discharge,[]))).
tff(291,plain,
(~(Y!0 = |'fred'|)),
inference(unit_resolution,[status(thm)],[290, 268])).
tff(292,plain,
(|'fred'| = mary),
inference(symmetry,[status(thm)],[268])).
tff(293,plain,
((paul = |'fred'|) <=> (paul = mary)),
inference(monotonicity,[status(thm)],[292])).
tff(294,plain,
((paul = |'fred'|) <=> (mary = paul)),
inference(transitivity,[status(thm)],[293, 8])).
tff(295,plain,
((mary = paul) <=> (paul = |'fred'|)),
inference(symmetry,[status(thm)],[294])).
tff(296,plain,
((~(mary = paul)) <=> (~(paul = |'fred'|))),
inference(monotonicity,[status(thm)],[295])).
tff(297,plain,
(~(paul = |'fred'|)),
inference(modus_ponens,[status(thm)],[56, 296])).
tff(298,plain,
(~(paul = |'paul'|)),
inference(unit_resolution,[status(thm)],[213, 58, 2])).
tff(299,plain,
(paul = |'mary'|),
inference(unit_resolution,[status(thm)],[117, 298, 297])).
tff(300,plain,
(~(Y!0 = |'mary'|)),
inference(unit_resolution,[status(thm)],[129, 299, 2])).
tff(301,plain,
(Y!0 = |'paul'|),
inference(unit_resolution,[status(thm)],[135, 300, 291])).
tff(302,plain,
(X!1 = Y!0),
inference(modus_ponens,[status(thm)],[301, 282])).
tff(303,plain,
($false),
inference(unit_resolution,[status(thm)],[190, 302])).
tff(304,plain,((~(X!1 = |'paul'|)) | predc(paul)), inference(lemma,lemma(discharge,[]))).
tff(305,plain,
(~(X!1 = |'paul'|)),
inference(unit_resolution,[status(thm)],[304, 2])).
tff(306,plain,
(X!1 = |'mary'|),
inference(unit_resolution,[status(thm)],[94, 305, 278])).
tff(307,plain,
((X!1 = Y!0) <=> (|'mary'| = Y!0)),
inference(monotonicity,[status(thm)],[306])).
tff(308,plain,
((X!1 = Y!0) <=> (Y!0 = |'mary'|)),
inference(transitivity,[status(thm)],[307, 1])).
tff(309,plain,
((Y!0 = |'mary'|) <=> (X!1 = Y!0)),
inference(symmetry,[status(thm)],[308])).
tff(310,plain,
(~(paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[230, 306, 2])).
tff(311,plain,
(paul = |'paul'|),
inference(unit_resolution,[status(thm)],[117, 310, 297])).
tff(312,plain,
(~(Y!0 = |'paul'|)),
inference(unit_resolution,[status(thm)],[184, 311, 2])).
tff(313,plain,
(Y!0 = |'mary'|),
inference(unit_resolution,[status(thm)],[135, 312, 291])).
tff(314,plain,
(X!1 = Y!0),
inference(modus_ponens,[status(thm)],[313, 309])).
tff(315,plain,
($false),
inference(unit_resolution,[status(thm)],[190, 314])).
tff(316,plain,(predc(paul)), inference(lemma,lemma(discharge,[]))).
tff(317,plain,
((predc(paul) | (~preda(paul))) | (~predc(paul))),
inference(tautology,[status(thm)],[])).
tff(318,plain,
(predc(paul) | (~preda(paul))),
inference(unit_resolution,[status(thm)],[317, 316])).
tff(319,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(320,plain,
(room(fred)),
inference(and_elim,[status(thm)],[107])).
tff(321,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[320, 319])).
tff(322,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(predc(paul) | (~preda(paul))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(predc(paul) | (~preda(paul)))))),
inference(rewrite,[status(thm)],[])).
tff(323,plain,
((~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))),
inference(rewrite,[status(thm)],[])).
tff(324,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(predc(paul) | (~preda(paul))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(predc(paul) | (~preda(paul)))))),
inference(monotonicity,[status(thm)],[323])).
tff(325,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(predc(paul) | (~preda(paul))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(predc(paul) | (~preda(paul)))))),
inference(transitivity,[status(thm)],[324, 322])).
tff(326,plain,
((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul))))),
inference(rewrite,[status(thm)],[])).
tff(327,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul)))))),
inference(monotonicity,[status(thm)],[326])).
tff(328,plain,
((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul)))))),
inference(rewrite,[status(thm)],[])).
tff(329,plain,
((~((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (predc(paul) | (~preda(paul))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul)))))),
inference(rewrite,[status(thm)],[])).
tff(330,axiom,(~((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (predc(paul) | (~preda(paul))))), file('/mnt/tmpfs//6372852573206580908549425.p','hypothesis')).
tff(331,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul))))),
inference(modus_ponens,[status(thm)],[330, 329])).
tff(332,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul))))),
inference(modus_ponens,[status(thm)],[331, 327])).
tff(333,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul))))),
inference(modus_ponens,[status(thm)],[332, 328])).
tff(334,plain,
(~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(paul) | (~preda(paul))))),
inference(modus_ponens,[status(thm)],[333, 327])).
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!2 |'fred'|)
(= X!2 |'paul'|)
(= X!2 |'mary'|)
(not (room X!2)))))
(a!6 (not (or (predc paul) (not (preda paul))))))
(let ((a!7 (and (room mary)
(room paul)
(room fred)
a!4
(or (predc paul) (not (preda paul))))))
(let ((a!8 (~ (not a!7)
(or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!6))))
(nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (refl (~ a!6 a!6)) a!8))))
|
Julia is the only person in the room.
At most one of the following is true:.
-Only one person outside the room cannot play the harmonica.
-Julia cannot play the harmonica or can play the harmonica or both. | It is not the case that 'more than one person in the room cannot play the harmonica'. | entailment | room(julia)&(![X]:(room(X)=>(X='julia')))&
(~(((?[X]:(~room(X)&cannot_play_the_harmonica(X)))&(![X,Y]:((cannot_play_the_harmonica(X)&cannot_play_the_harmonica(Y))=>(X=Y))))&((cannot_play_the_harmonica(julia))|(can_play_the_harmonica(julia))))) | room(julia)&(![X]:(room(X)=>(X='julia')))&
(~((?[X,Y]:(room(X)&room(Y)&(cannot_play_the_harmonica(X)&cannot_play_the_harmonica(Y))&(X!=Y))))) | entailment | [
"h0",
"hypothesis"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_Y_3_type, type, (
tptp_fun_Y_3: $i)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(preda_type, type, (
preda: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(1,assumption,(~(preda(X!4) | preda(Y!3) | (X!4 = Y!3) | (~room(X!4)) | (~room(Y!3)))), introduced(assumption)).
tff(2,plain,
((preda(X!4) | preda(Y!3) | (X!4 = Y!3) | (~room(X!4)) | (~room(Y!3))) | room(Y!3)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(room(Y!3)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
(^[X: $i] : refl(((~room(X)) | (X = |'mary'|)) <=> ((~room(X)) | (X = |'mary'|)))),
inference(bind,[status(th)],[])).
tff(5,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(quant_intro,[status(thm)],[4])).
tff(6,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(7,plain,
(^[X: $i] : rewrite((room(X) => (X = |'mary'|)) <=> ((~room(X)) | (X = |'mary'|)))),
inference(bind,[status(th)],[])).
tff(8,plain,
(![X: $i] : (room(X) => (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(quant_intro,[status(thm)],[7])).
tff(9,axiom,(room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))), file('/mnt/tmpfs//728145929767038245263371.p','h0')).
tff(10,plain,
(![X: $i] : (room(X) => (X = |'mary'|))),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[10, 8])).
tff(12,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[11, 6])).
tff(13,plain,(
![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(skolemize,[status(sab)],[12])).
tff(14,plain,
(![X: $i] : ((~room(X)) | (X = |'mary'|))),
inference(modus_ponens,[status(thm)],[13, 5])).
tff(15,plain,
(((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(Y!3)) | (Y!3 = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(Y!3)) | (Y!3 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(Y!3)) | (Y!3 = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(17,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(Y!3)) | (Y!3 = |'mary'|)),
inference(modus_ponens,[status(thm)],[16, 15])).
tff(18,plain,
(Y!3 = |'mary'|),
inference(unit_resolution,[status(thm)],[17, 14, 3])).
tff(19,plain,
((X!4 = Y!3) <=> (X!4 = |'mary'|)),
inference(monotonicity,[status(thm)],[18])).
tff(20,plain,
((X!4 = |'mary'|) <=> (X!4 = Y!3)),
inference(symmetry,[status(thm)],[19])).
tff(21,plain,
((preda(X!4) | preda(Y!3) | (X!4 = Y!3) | (~room(X!4)) | (~room(Y!3))) | room(X!4)),
inference(tautology,[status(thm)],[])).
tff(22,plain,
(room(X!4)),
inference(unit_resolution,[status(thm)],[21, 1])).
tff(23,plain,
(((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!4)) | (X!4 = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!4)) | (X!4 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(24,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!4)) | (X!4 = |'mary'|))),
inference(quant_inst,[status(thm)],[])).
tff(25,plain,
((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!4)) | (X!4 = |'mary'|)),
inference(modus_ponens,[status(thm)],[24, 23])).
tff(26,plain,
(X!4 = |'mary'|),
inference(unit_resolution,[status(thm)],[25, 14, 22])).
tff(27,plain,
(X!4 = Y!3),
inference(modus_ponens,[status(thm)],[26, 20])).
tff(28,plain,
((preda(X!4) | preda(Y!3) | (X!4 = Y!3) | (~room(X!4)) | (~room(Y!3))) | (~(X!4 = Y!3))),
inference(tautology,[status(thm)],[])).
tff(29,plain,
(~(X!4 = Y!3)),
inference(unit_resolution,[status(thm)],[28, 1])).
tff(30,plain,
($false),
inference(unit_resolution,[status(thm)],[29, 27])).
tff(31,plain,(preda(X!4) | preda(Y!3) | (X!4 = Y!3) | (~room(X!4)) | (~room(Y!3))), inference(lemma,lemma(discharge,[]))).
tff(32,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(33,plain,
(room(mary)),
inference(and_elim,[status(thm)],[9])).
tff(34,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[33, 32])).
tff(35,plain,
(((~room(mary)) | (~((~room(X!2)) | (X!2 = |'mary'|))) | (room(X!4) & room(Y!3) & (~preda(X!4)) & (~preda(Y!3)) & (~(X!4 = Y!3)))) <=> ((~room(mary)) | (~((~room(X!2)) | (X!2 = |'mary'|))) | (~(preda(X!4) | preda(Y!3) | (X!4 = Y!3) | (~room(X!4)) | (~room(Y!3)))))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y))))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y)))))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y))))))),
inference(monotonicity,[status(thm)],[36])).
tff(38,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y))))))),
inference(rewrite,[status(thm)],[])).
tff(39,plain,
((~((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (~?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~preda(X)) & (~preda(Y)))) & (~(X = Y)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y))))))),
inference(rewrite,[status(thm)],[])).
tff(40,axiom,(~((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (~?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~preda(X)) & (~preda(Y)))) & (~(X = Y)))))), file('/mnt/tmpfs//728145929767038245263371.p','hypothesis')).
tff(41,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y)))))),
inference(modus_ponens,[status(thm)],[40, 39])).
tff(42,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y)))))),
inference(modus_ponens,[status(thm)],[41, 37])).
tff(43,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y)))))),
inference(modus_ponens,[status(thm)],[42, 38])).
tff(44,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~preda(X)) & (~preda(Y)) & (~(X = Y)))))),
inference(modus_ponens,[status(thm)],[43, 37])).
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!2)) (= X!2 |'mary'|))))
(a!4 (exists ((X $i) (Y $i))
(and (room X)
(room Y)
(not (preda X))
(not (preda Y))
(not (= X Y)))))
(a!5 (and (room X!4)
(room Y!3)
(not (preda X!4))
(not (preda Y!3))
(not (= X!4 Y!3)))))
(let ((a!6 (nnf-neg (sk (~ a!4 a!5)) (~ (not (not a!4)) a!5)))
(a!7 (~ (not (and (room mary) a!2 (not a!4)))
(or (not (room mary)) a!3 a!5))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) a!6 a!7)))
|
Corey, Wendy are the only persons in the room.
Only one person in the room does not collect action figures.
Only one person outside the room does not use contact lenses.
Wendy does not play a string instrument. | Corey who plays a string instrument, does not collect action figures. | neutral | room(corey)&room(wendy)&(![X]:(room(X)=>(X='corey'|X='wendy')))&
((((?[X]:(room(X)&does_not_collect_action_figures(X)))&(![X,Y]:((does_not_collect_action_figures(X)&does_not_collect_action_figures(Y))=>(X=Y)))))&
(((?[X]:(~room(X)&does_not_use_contact_lenses(X)))&(![X,Y]:((does_not_use_contact_lenses(X)&does_not_use_contact_lenses(Y))=>(X=Y)))))&
(does_not_play_a_string_instrument(wendy))) | room(corey)&room(wendy)&(![X]:(room(X)=>(X='corey'|X='wendy')))&
((plays_a_string_instrument(corey))&(does_not_collect_action_figures(corey))) | contradiction | [] | null |
Patrick is the only person in the room.
If ''A frog does not sing opera in the swamp at night.' and 'A clock does not measure time in various colors.' and 'A clock measures time in various colors.'' then ''A clock measures time in various colors.' and 'A frog does not sing opera in the swamp at night.' and 'Mirrors do not fog permanently in one particular house.''.
Everyone in the room who is a creative person is not a creative person. | 'Mirrors fog permanently in one particular house.' and 'A frog does not sing opera in the swamp at night.' and 'A clock measures time in various colors.'. | neutral | room(patrick)&(![X]:(room(X)=>(X='patrick')))&
(((((A_frog_does_not_sing_opera_in_the_swamp_at_night.)&(A_clock_does_not_measure_time_in_various_colors.)&(A_clock_measures_time_in_various_colors.)))=>(((A_clock_measures_time_in_various_colors.)&(A_frog_does_not_sing_opera_in_the_swamp_at_night.)&(Mirrors_do_not_fog_permanently_in_one_particular_house.))))&
(![X]:(room(X)=>(((creative(X)&person(X))=>(~(creative(X)&person(X)))))))) | room(patrick)&(![X]:(room(X)=>(X='patrick')))&
(((Mirrors_fog_permanently_in_one_particular_house.)&(A_frog_does_not_sing_opera_in_the_swamp_at_night.)&(A_clock_measures_time_in_various_colors.))) | contradiction | [] | null |
Julie, Guy, Vicky are the only persons in the room.
“Everyone outside the room who is a brave person is richer than Loretta” if “someone who is a rich person is taller than someone who is taller than Loretta”.
Everyone outside the room is a creative happy rich person.
Julie is the tallest in the room.
Someone outside the room is a rich happy creative tall person.
Guy is taller than Loretta.
Someone in the room who is a rich tall person is not a brave person.
Someone who is not a tall brave person is taller than someone who is not a rich tall person.
Everyone in the room is older than Loretta. | Julie neither is not creative, not happy, not rich, not tall, not old, not brave nor is richer than Loretta. | neutral | room(julie)&room(guy)&room(vicky)&(![X]:(room(X)=>(X='julie'|X='guy'|X='vicky')))&
(((?[X,Y]:((rich(X)&person(X))&(taller(loretta,Y))&(taller(X,Y))))=>(![X]:(~room(X)=>(((brave(X)&person(X))=>(richer(loretta,X)))))))&
(![X]:(~room(X)=>(creative(X)&happy(X)&rich(X)&person(X))))&
(![X]:(taller(X,julie)))&
(?[X]:(~room(X)=>(rich(X)&happy(X)&creative(X)&tall(X)&person(X))))&
(taller(loretta,guy))&
(?[X]:(room(X)=>(((rich(X)&tall(X)&person(X))=>(~(brave(X)&person(X)))))))&
(?[X,Y]:((~(tall(X)&brave(X)&person(X)))&(~(rich(Y)&tall(Y)&person(Y)))&(taller(X,Y))))&
(![X]:(room(X)=>(older(loretta,X))))) | room(julie)&room(guy)&room(vicky)&(![X]:(room(X)=>(X='julie'|X='guy'|X='vicky')))&
(~((~creative(julie)&~happy(julie)&~rich(julie)&~tall(julie)&~old(julie)&~brave(julie))|(richer(loretta,julie)))) | contradiction | [] | null |
Scott, Robert are the only persons in the room.
Only one of the following is true:.
-Everyone outside the room who is not a creative person is not creative.
-Someone in the room is not a creative person. | Robert is a creative person or is not creative or both. | neutral | room(scott)&room(robert)&(![X]:(room(X)=>(X='scott'|X='robert')))&
(((![X]:(~room(X)=>(((~(creative(X)&person(X)))=>(~creative(X))))))<~>(?[X]:(room(X)=>(~(creative(X)&person(X))))))) | room(scott)&room(robert)&(![X]:(room(X)=>(X='scott'|X='robert')))&
(((creative(robert)&person(robert))|(~creative(robert)))) | entailment | [] | null |
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