Datasets:

unigram

/

fol-02b

like 0

Daniel is the only person in the room. 'More than one person outside the room is quieter than Polly' unless 'Daniel is the quietest in the room'. Daniel is not liked by Polly or is not a client of Google or both. Daniel is the tallest in the room. It is not the case that 'Daniel is the least tall in the room'. Dwight is a sibling of Daniel. Daniel neither is not a client of Google nor likes Polly. Chester is quieter than Daniel.

Daniel is not quiet, not tall and is a sibling of Chester.

neutral

% SZS status Satisfiable

room(daniel)&(![X]:(room(X)=>(X='daniel')))& ((~(![X]:(quieter(X,daniel)))=>((?[X,Y]:(~room(X)&~room(Y)&(quieter(polly,X)&quieter(polly,Y))&(X!=Y)))))& (((~like(daniel,polly))|(is_not_a_client_of_Google(daniel))))& (![X]:(taller(X,daniel)))& (~(![X]:(taller(daniel,X))))& (sibling(daniel,dwight))& (~((is_not_a_client_of_Google(daniel))|(like(polly,daniel))))& (quieter(daniel,chester)))

room(daniel)&(![X]:(room(X)=>(X='daniel')))& ((~quiet(daniel)&~tall(daniel))&(sibling(chester,daniel)))

contradiction

contradiction

contradiction

Willie, Regina, Ben, Shawn are the only persons in the room. "Willie is the tallest in the room" only if "more than one person in the room is taller than Kris". "Willie neither is not an amateur astronomer nor is taller than Kris" only if "Willie is hated by Kris". If "Willie is not an amateur astronomer and is not a brave person" then "Kris is a client of Willie". "Willie hates Kris or is taller than Kris or both" if "only one person in the room hates Kris". Only one person in the room is an amateur astronomer. It is not the case that 'Willie is an amateur astronomer and is hated by Kris'. Willie is hated by Kris. Willie who is not an amateur astronomer, hates Kris. Only one person in the room hates Kris. Willie who is not a tall person, is a client of Kris. More than one person in the room is hated by Kris.

Willie is not liked by Kris and is not a tall creative european.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_9_type, type, ( tptp_fun_X_9: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(european_type, type, ( european: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(person_type, type, ( person: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(predc_type, type, ( predc: $i > $o)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(lucy_type, type, ( lucy: $i)). tff(1,assumption,(~((~tall(mary)) | (~creative(mary)) | (~european(mary)))), introduced(assumption)). tff(2,plain, (((~tall(mary)) | (~creative(mary)) | (~european(mary))) | european(mary)), inference(tautology,[status(thm)],[])). tff(3,plain, (european(mary)), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, (((~tall(mary)) | (~creative(mary)) | (~european(mary))) | tall(mary)), inference(tautology,[status(thm)],[])). tff(5,plain, (tall(mary)), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, ((~(~((~person(mary)) | (~tall(mary))))) <=> ((~person(mary)) | (~tall(mary)))), inference(rewrite,[status(thm)],[])). tff(7,plain, ((tall(mary) & person(mary)) <=> (~((~person(mary)) | (~tall(mary))))), inference(rewrite,[status(thm)],[])). tff(8,plain, ((~(tall(mary) & person(mary))) <=> (~(~((~person(mary)) | (~tall(mary)))))), inference(monotonicity,[status(thm)],[7])). tff(9,plain, ((~(tall(mary) & person(mary))) <=> ((~person(mary)) | (~tall(mary)))), inference(transitivity,[status(thm)],[8, 6])). tff(10,plain, ((~(tall(mary) & person(mary))) <=> (~(tall(mary) & person(mary)))), inference(rewrite,[status(thm)],[])). tff(11,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((![X: $i] : taller(X, mary) => ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (taller(john, X) & taller(john, Y))) & (~(X = Y)))) & ((~((~predc(mary)) | taller(john, mary))) => hate(mary, john))) & (((~predc(mary)) & (~(brave(mary) & person(mary)))) => client(mary, john))) & ((?[X: $i] : (room(X) & hate(john, X)) & ![X: $i, Y: $i] : ((hate(john, X) & hate(john, Y)) => (X = Y))) => (hate(john, mary) | taller(john, mary)))) & (?[X: $i] : (room(X) & predc(X)) & ![X: $i, Y: $i] : ((predc(X) & predc(Y)) => (X = Y)))) & (~(predc(mary) & hate(mary, john)))) & hate(mary, john)) & ((~predc(mary)) & hate(john, mary))) & (?[X: $i] : (room(X) & hate(john, X)) & ![X: $i, Y: $i] : ((hate(john, X) & hate(john, Y)) => (X = Y)))) & ((~(tall(mary) & person(mary))) & client(john, mary))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (hate(X, john) & hate(Y, john))) & (~(X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~like(mary, john)) & (~((tall(mary) & creative(mary)) & european(mary))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : taller(X, mary)) | ?[X: $i, Y: $i] : (room(X) & room(Y) & taller(john, X) & taller(john, Y) & (~(X = Y)))) & ((~predc(mary)) | taller(john, mary) | hate(mary, john)) & ((~((~predc(mary)) & (~(brave(mary) & person(mary))))) | client(mary, john)) & (taller(john, mary) | hate(john, mary) | (~(?[X: $i] : (room(X) & hate(john, X)) & ![X: $i, Y: $i] : ((~(hate(john, X) & hate(john, Y))) | (X = Y))))) & ?[X: $i] : (room(X) & predc(X)) & ![X: $i, Y: $i] : ((~(predc(X) & predc(Y))) | (X = Y)) & (~(predc(mary) & hate(mary, john))) & hate(mary, john) & (~predc(mary)) & hate(john, mary) & ?[X: $i] : (room(X) & hate(john, X)) & ![X: $i, Y: $i] : ((~(hate(john, X) & hate(john, Y))) | (X = Y)) & (~(tall(mary) & person(mary))) & client(john, mary) & ?[X: $i, Y: $i] : (room(X) & room(Y) & hate(X, john) & hate(Y, john) & (~(X = Y))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary))))))), inference(rewrite,[status(thm)],[])). tff(12,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((![X: $i] : taller(X, mary) => ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (taller(john, X) & taller(john, Y))) & (~(X = Y)))) & ((~((~predc(mary)) | taller(john, mary))) => hate(mary, john))) & (((~predc(mary)) & (~(brave(mary) & person(mary)))) => client(mary, john))) & ((?[X: $i] : (room(X) & hate(john, X)) & ![X: $i, Y: $i] : ((hate(john, X) & hate(john, Y)) => (X = Y))) => (hate(john, mary) | taller(john, mary)))) & (?[X: $i] : (room(X) & predc(X)) & ![X: $i, Y: $i] : ((predc(X) & predc(Y)) => (X = Y)))) & (~(predc(mary) & hate(mary, john)))) & hate(mary, john)) & ((~predc(mary)) & hate(john, mary))) & (?[X: $i] : (room(X) & hate(john, X)) & ![X: $i, Y: $i] : ((hate(john, X) & hate(john, Y)) => (X = Y)))) & ((~(tall(mary) & person(mary))) & client(john, mary))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & (hate(X, john) & hate(Y, john))) & (~(X = Y))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~like(mary, john)) & (~((tall(mary) & creative(mary)) & european(mary))))))), file('/mnt/tmpfs//4843587835295477716997091.p','negated')). tff(13,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : taller(X, mary)) | ?[X: $i, Y: $i] : (room(X) & room(Y) & taller(john, X) & taller(john, Y) & (~(X = Y)))) & ((~predc(mary)) | taller(john, mary) | hate(mary, john)) & ((~((~predc(mary)) & (~(brave(mary) & person(mary))))) | client(mary, john)) & (taller(john, mary) | hate(john, mary) | (~(?[X: $i] : (room(X) & hate(john, X)) & ![X: $i, Y: $i] : ((~(hate(john, X) & hate(john, Y))) | (X = Y))))) & ?[X: $i] : (room(X) & predc(X)) & ![X: $i, Y: $i] : ((~(predc(X) & predc(Y))) | (X = Y)) & (~(predc(mary) & hate(mary, john))) & hate(mary, john) & (~predc(mary)) & hate(john, mary) & ?[X: $i] : (room(X) & hate(john, X)) & ![X: $i, Y: $i] : ((~(hate(john, X) & hate(john, Y))) | (X = Y)) & (~(tall(mary) & person(mary))) & client(john, mary) & ?[X: $i, Y: $i] : (room(X) & room(Y) & hate(X, john) & hate(Y, john) & (~(X = Y))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary)))))), inference(modus_ponens,[status(thm)],[12, 11])). tff(14,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : taller(X, mary)) | ?[X: $i, Y: $i] : (room(X) & room(Y) & taller(john, X) & taller(john, Y) & (~(X = Y)))) & ((~predc(mary)) | taller(john, mary) | hate(mary, john)) & ((~((~predc(mary)) & (~(brave(mary) & person(mary))))) | client(mary, john)) & (taller(john, mary) | hate(john, mary) | (~(?[X: $i] : (room(X) & hate(john, X)) & ![X: $i, Y: $i] : ((~(hate(john, X) & hate(john, Y))) | (X = Y))))) & ?[X: $i] : (room(X) & predc(X)) & ![X: $i, Y: $i] : ((~(predc(X) & predc(Y))) | (X = Y)) & (~(predc(mary) & hate(mary, john))) & hate(mary, john) & (~predc(mary)) & hate(john, mary) & ?[X: $i] : (room(X) & hate(john, X)) & ![X: $i, Y: $i] : ((~(hate(john, X) & hate(john, Y))) | (X = Y)) & (~(tall(mary) & person(mary))) & client(john, mary) & ?[X: $i, Y: $i] : (room(X) & room(Y) & hate(X, john) & hate(Y, john) & (~(X = Y)))), inference(or_elim,[status(thm)],[13])). tff(15,plain, (~(tall(mary) & person(mary))), inference(and_elim,[status(thm)],[14])). tff(16,plain, (~(tall(mary) & person(mary))), inference(modus_ponens,[status(thm)],[15, 10])). tff(17,plain, ((~person(mary)) | (~tall(mary))), inference(modus_ponens,[status(thm)],[16, 9])). tff(18,plain, (~person(mary)), inference(unit_resolution,[status(thm)],[17, 5])). tff(19,plain, (^[X: $i] : refl((person(X) | (~european(X))) <=> (person(X) | (~european(X))))), inference(bind,[status(th)],[])). tff(20,plain, (![X: $i] : (person(X) | (~european(X))) <=> ![X: $i] : (person(X) | (~european(X)))), inference(quant_intro,[status(thm)],[19])). tff(21,plain, (![X: $i] : (person(X) | (~european(X))) <=> ![X: $i] : (person(X) | (~european(X)))), inference(rewrite,[status(thm)],[])). tff(22,plain, (^[X: $i] : rewrite((european(X) => person(X)) <=> (person(X) | (~european(X))))), inference(bind,[status(th)],[])). tff(23,plain, (![X: $i] : (european(X) => person(X)) <=> ![X: $i] : (person(X) | (~european(X)))), inference(quant_intro,[status(thm)],[22])). tff(24,axiom,(![X: $i] : (european(X) => person(X))), file('/mnt/tmpfs//4843587835295477716997091.p','b2')). tff(25,plain, (![X: $i] : (person(X) | (~european(X)))), inference(modus_ponens,[status(thm)],[24, 23])). tff(26,plain, (![X: $i] : (person(X) | (~european(X)))), inference(modus_ponens,[status(thm)],[25, 21])). tff(27,plain,( ![X: $i] : (person(X) | (~european(X)))), inference(skolemize,[status(sab)],[26])). tff(28,plain, (![X: $i] : (person(X) | (~european(X)))), inference(modus_ponens,[status(thm)],[27, 20])). tff(29,plain, (((~![X: $i] : (person(X) | (~european(X)))) | (person(mary) | (~european(mary)))) <=> ((~![X: $i] : (person(X) | (~european(X)))) | person(mary) | (~european(mary)))), inference(rewrite,[status(thm)],[])). tff(30,plain, ((~![X: $i] : (person(X) | (~european(X)))) | (person(mary) | (~european(mary)))), inference(quant_inst,[status(thm)],[])). tff(31,plain, ((~![X: $i] : (person(X) | (~european(X)))) | person(mary) | (~european(mary))), inference(modus_ponens,[status(thm)],[30, 29])). tff(32,plain, ($false), inference(unit_resolution,[status(thm)],[31, 28, 18, 3])). tff(33,plain,((~tall(mary)) | (~creative(mary)) | (~european(mary))), inference(lemma,lemma(discharge,[]))). tff(34,plain, (hate(mary, john) <=> hate(mary, john)), inference(rewrite,[status(thm)],[])). tff(35,plain, (hate(mary, john)), inference(and_elim,[status(thm)],[14])). tff(36,plain, (hate(mary, john)), inference(modus_ponens,[status(thm)],[35, 34])). tff(37,plain, ((~(mary = john)) <=> (~(mary = john))), inference(rewrite,[status(thm)],[])). tff(38,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//4843587835295477716997091.p','b14')). 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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[41])). tff(43,plain, (((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = 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& (~(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)],[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))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & 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inference(and_elim,[status(thm)],[52])). tff(54,plain, ((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(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)],[53])). tff(55,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))) & 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(~(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)],[56])). tff(58,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)],[57])). tff(59,plain, (((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = 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= fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))), inference(and_elim,[status(thm)],[68])). tff(70,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)],[69])). tff(71,plain, (((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))), inference(and_elim,[status(thm)],[70])). tff(72,plain, ((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))), inference(and_elim,[status(thm)],[71])). tff(73,plain, (((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))), inference(and_elim,[status(thm)],[72])). tff(74,plain, ((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))), inference(and_elim,[status(thm)],[73])). tff(75,plain, (((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))), inference(and_elim,[status(thm)],[74])). tff(76,plain, ((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))), inference(and_elim,[status(thm)],[75])). tff(77,plain, (~(mary = john)), inference(and_elim,[status(thm)],[76])). tff(78,plain, (~(mary = john)), inference(modus_ponens,[status(thm)],[77, 37])). tff(79,plain, (^[X: $i, Y: $i] : refl(((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y))))), inference(bind,[status(th)],[])). tff(80,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(quant_intro,[status(thm)],[79])). tff(81,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(rewrite,[status(thm)],[])). tff(82,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite((like(X, Y) => (~hate(X, Y))) <=> ((~hate(X, Y)) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))))), rewrite(((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))))), inference(bind,[status(th)],[])). tff(83,plain, (![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(quant_intro,[status(thm)],[82])). tff(84,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y))))), file('/mnt/tmpfs//4843587835295477716997091.p','b0')). tff(85,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(modus_ponens,[status(thm)],[84, 83])). tff(86,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(modus_ponens,[status(thm)],[85, 81])). tff(87,plain,( ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(skolemize,[status(sab)],[86])). tff(88,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(modus_ponens,[status(thm)],[87, 80])). tff(89,plain, (((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((mary = john) | (~like(mary, john)) | (~hate(mary, john)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (mary = john) | (~like(mary, john)) | (~hate(mary, john)))), inference(rewrite,[status(thm)],[])). tff(90,plain, (((~hate(mary, john)) | (mary = john) | (~like(mary, john))) <=> ((mary = john) | (~like(mary, john)) | (~hate(mary, john)))), inference(rewrite,[status(thm)],[])). tff(91,plain, (((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(mary, john)) | (mary = john) | (~like(mary, john)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((mary = john) | (~like(mary, john)) | (~hate(mary, john))))), inference(monotonicity,[status(thm)],[90])). tff(92,plain, (((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(mary, john)) | (mary = john) | (~like(mary, john)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (mary = john) | (~like(mary, john)) | (~hate(mary, john)))), inference(transitivity,[status(thm)],[91, 89])). tff(93,plain, ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(mary, john)) | (mary = john) | (~like(mary, john)))), inference(quant_inst,[status(thm)],[])). tff(94,plain, ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (mary = john) | (~like(mary, john)) | (~hate(mary, john))), inference(modus_ponens,[status(thm)],[93, 92])). tff(95,plain, (~like(mary, john)), inference(unit_resolution,[status(thm)],[94, 88, 78, 36])). tff(96,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(97,plain, (room(alice)), inference(and_elim,[status(thm)],[14])). tff(98,plain, (room(alice)), inference(modus_ponens,[status(thm)],[97, 96])). tff(99,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(100,plain, (room(fred)), inference(and_elim,[status(thm)],[14])). tff(101,plain, (room(fred)), inference(modus_ponens,[status(thm)],[100, 99])). tff(102,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(103,plain, (room(paul)), inference(and_elim,[status(thm)],[14])). tff(104,plain, (room(paul)), inference(modus_ponens,[status(thm)],[103, 102])). tff(105,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(106,plain, (room(mary)), inference(and_elim,[status(thm)],[14])). tff(107,plain, (room(mary)), inference(modus_ponens,[status(thm)],[106, 105])). tff(108,plain, ((like(mary, john) | (~((~tall(mary)) | (~creative(mary)) | (~european(mary)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))))) <=> (like(mary, john) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~tall(mary)) | (~creative(mary)) | (~european(mary)))))), inference(rewrite,[status(thm)],[])). tff(109,plain, ((~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) <=> (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))))), inference(rewrite,[status(thm)],[])). tff(110,plain, ((tall(mary) & creative(mary) & european(mary)) <=> (~((~tall(mary)) | (~creative(mary)) | (~european(mary))))), inference(rewrite,[status(thm)],[])). tff(111,plain, ((like(mary, john) | (tall(mary) & creative(mary) & european(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))))) <=> (like(mary, john) | (~((~tall(mary)) | (~creative(mary)) | (~european(mary)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))))), inference(monotonicity,[status(thm)],[110, 109])). tff(112,plain, ((like(mary, john) | (tall(mary) & creative(mary) & european(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9))))) <=> (like(mary, john) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | (~((~tall(mary)) | (~creative(mary)) | (~european(mary)))))), inference(transitivity,[status(thm)],[111, 108])). tff(113,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | like(mary, john) | (tall(mary) & creative(mary) & european(mary))) <=> (like(mary, john) | (tall(mary) & creative(mary) & european(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))))), inference(rewrite,[status(thm)],[])). tff(114,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | like(mary, john) | (tall(mary) & creative(mary) & european(mary))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | like(mary, john) | (tall(mary) & creative(mary) & european(mary)))), inference(monotonicity,[status(thm)],[109])). tff(115,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))) | like(mary, john) | (tall(mary) & creative(mary) & european(mary))) <=> (like(mary, john) | (tall(mary) & creative(mary) & european(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!9 = |'alice'|) | (X!9 = |'fred'|) | (X!9 = |'paul'|) | (X!9 = |'mary'|) | (~room(X!9)))))), inference(transitivity,[status(thm)],[114, 113])). tff(116,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary))))), inference(rewrite,[status(thm)],[])). tff(117,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary)))))), inference(monotonicity,[status(thm)],[116])). tff(118,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary)))))), inference(rewrite,[status(thm)],[])). tff(119,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary))))), inference(or_elim,[status(thm)],[13])). tff(120,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary))))), inference(modus_ponens,[status(thm)],[119, 117])). tff(121,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary))))), inference(modus_ponens,[status(thm)],[120, 118])). tff(122,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(mary, john)) & (~(tall(mary) & creative(mary) & european(mary))))), inference(modus_ponens,[status(thm)],[121, 117])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!9 |'alice'|) (= X!9 |'fred'|) (= X!9 |'paul'|) (= X!9 |'mary'|) (not (room X!9))))) (a!7 (refl (~ (and (tall mary) (creative mary) (european mary)) (and (tall mary) (creative mary) (european mary)))))) (let ((a!8 (and (room mary) (room paul) (room fred) (room alice) a!5 (not (like mary john)) (not (and (tall mary) (creative mary) (european mary)))))) (let ((a!9 (~ (not a!8) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (like mary john) (and (tall mary) (creative mary) (european mary)))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ (like mary john) (like mary john))) a!7 a!9))))

room(willie)&room(regina)&room(ben)&room(shawn)&(![X]:(room(X)=>(X='willie'|X='regina'|X='ben'|X='shawn')))& (((![X]:(taller(X,willie)))=>((?[X,Y]:(room(X)&room(Y)&(taller(kris,X)&taller(kris,Y))&(X!=Y)))))& ((~((is_not_an_amateur_astronomer(willie))|(taller(kris,willie))))=>(hate(willie,kris)))& (((is_not_an_amateur_astronomer(willie))&(~(brave(willie)&person(willie))))=>(client(willie,kris)))& ((((?[X]:(room(X)&hate(kris,X)))&(![X,Y]:((hate(kris,X)&hate(kris,Y))=>(X=Y)))))=>(((hate(kris,willie))|(taller(kris,willie)))))& (((?[X]:(room(X)&is_an_amateur_astronomer(X)))&(![X,Y]:((is_an_amateur_astronomer(X)&is_an_amateur_astronomer(Y))=>(X=Y)))))& (~((is_an_amateur_astronomer(willie))&(hate(willie,kris))))& (hate(willie,kris))& ((is_not_an_amateur_astronomer(willie))&(hate(kris,willie)))& (((?[X]:(room(X)&hate(kris,X)))&(![X,Y]:((hate(kris,X)&hate(kris,Y))=>(X=Y)))))& ((~(tall(willie)&person(willie)))&(client(kris,willie)))& ((?[X,Y]:(room(X)&room(Y)&(hate(X,kris)&hate(Y,kris))&(X!=Y)))))

room(willie)&room(regina)&room(ben)&room(shawn)&(![X]:(room(X)=>(X='willie'|X='regina'|X='ben'|X='shawn')))& ((~like(willie,kris))&(~(tall(willie)&creative(willie)&european(willie))))

neutral

contradiction

entailment

Fannie, Tammy, Anna, Otis are the only persons in the room. Anna and Otis are respectively brave and happy only if everyone outside the room who is a happy brave tall tourist is hated by John. Otis and John like each other. Otis is the tallest in the room.

Otis is not a tall tourist or is not hated by John or both.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(tourist_type, type, ( tourist: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(mary_type, type, ( mary: $i)). tff(susan_type, type, ( susan: $i)). tff(john_type, type, ( john: $i)). tff(1,plain, (like(alice, lucy) <=> like(alice, lucy)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((brave(fred) & happy(alice)) => ![X: $i] : ((~room(X)) => ((((happy(X) & brave(X)) & tall(X)) & tourist(X)) => hate(X, lucy)))) & (like(alice, lucy) & like(lucy, alice))) & ![X: $i] : taller(X, alice))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(brave(fred) & happy(alice))) | ![X: $i] : (room(X) | hate(X, lucy) | (~(happy(X) & brave(X) & tall(X) & tourist(X))))) & like(alice, lucy) & like(lucy, alice) & ![X: $i] : taller(X, alice))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((brave(fred) & happy(alice)) => ![X: $i] : ((~room(X)) => ((((happy(X) & brave(X)) & tall(X)) & tourist(X)) => hate(X, lucy)))) & (like(alice, lucy) & like(lucy, alice))) & ![X: $i] : taller(X, alice))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))))), file('/mnt/tmpfs//2373762898973158085605156.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(brave(fred) & happy(alice))) | ![X: $i] : (room(X) | hate(X, lucy) | (~(happy(X) & brave(X) & tall(X) & tourist(X))))) & like(alice, lucy) & like(lucy, alice) & ![X: $i] : taller(X, alice))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(brave(fred) & happy(alice))) | ![X: $i] : (room(X) | hate(X, lucy) | (~(happy(X) & brave(X) & tall(X) & tourist(X))))) & like(alice, lucy) & like(lucy, alice) & ![X: $i] : taller(X, alice)), inference(or_elim,[status(thm)],[4])). tff(6,plain, (like(alice, lucy)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (like(alice, lucy)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((~(alice = lucy)) <=> (~(alice = lucy))), inference(rewrite,[status(thm)],[])). tff(9,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//2373762898973158085605156.p','b14')). tff(10,plain, (((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))), inference(and_elim,[status(thm)],[9])). tff(11,plain, ((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))), inference(and_elim,[status(thm)],[10])). tff(12,plain, (((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))), inference(and_elim,[status(thm)],[11])). tff(13,plain, ((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))), inference(and_elim,[status(thm)],[12])). tff(14,plain, (((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))), inference(and_elim,[status(thm)],[13])). tff(15,plain, ((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))), inference(and_elim,[status(thm)],[14])). tff(16,plain, (((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))), inference(and_elim,[status(thm)],[15])). tff(17,plain, ((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))), inference(and_elim,[status(thm)],[16])). tff(18,plain, (((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))), inference(and_elim,[status(thm)],[17])). tff(19,plain, ((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))), inference(and_elim,[status(thm)],[18])). tff(20,plain, (((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))), inference(and_elim,[status(thm)],[19])). tff(21,plain, ((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))), inference(and_elim,[status(thm)],[20])). tff(22,plain, (((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))), inference(and_elim,[status(thm)],[21])). tff(23,plain, ((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))), inference(and_elim,[status(thm)],[22])). tff(24,plain, (((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))), inference(and_elim,[status(thm)],[23])). tff(25,plain, ((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))), inference(and_elim,[status(thm)],[24])). tff(26,plain, (((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))), inference(and_elim,[status(thm)],[25])). tff(27,plain, ((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))), inference(and_elim,[status(thm)],[26])). tff(28,plain, (~(alice = lucy)), inference(and_elim,[status(thm)],[27])). tff(29,plain, (~(alice = lucy)), inference(modus_ponens,[status(thm)],[28, 8])). tff(30,plain, (^[X: $i, Y: $i] : refl(((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y))))), inference(bind,[status(th)],[])). tff(31,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(quant_intro,[status(thm)],[30])). tff(32,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(rewrite,[status(thm)],[])). tff(33,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite((like(X, Y) => (~hate(X, Y))) <=> ((~hate(X, Y)) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))))), rewrite(((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))))), inference(bind,[status(th)],[])). tff(34,plain, (![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(quant_intro,[status(thm)],[33])). tff(35,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y))))), file('/mnt/tmpfs//2373762898973158085605156.p','b0')). tff(36,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(modus_ponens,[status(thm)],[35, 34])). tff(37,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(modus_ponens,[status(thm)],[36, 32])). tff(38,plain,( ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(skolemize,[status(sab)],[37])). tff(39,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(modus_ponens,[status(thm)],[38, 31])). tff(40,plain, (((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((alice = lucy) | (~hate(alice, lucy)) | (~like(alice, lucy)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (alice = lucy) | (~hate(alice, lucy)) | (~like(alice, lucy)))), inference(rewrite,[status(thm)],[])). tff(41,plain, (((~hate(alice, lucy)) | (alice = lucy) | (~like(alice, lucy))) <=> ((alice = lucy) | (~hate(alice, lucy)) | (~like(alice, lucy)))), inference(rewrite,[status(thm)],[])). tff(42,plain, (((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(alice, lucy)) | (alice = lucy) | (~like(alice, lucy)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((alice = lucy) | (~hate(alice, lucy)) | (~like(alice, lucy))))), inference(monotonicity,[status(thm)],[41])). tff(43,plain, (((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(alice, lucy)) | (alice = lucy) | (~like(alice, lucy)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (alice = lucy) | (~hate(alice, lucy)) | (~like(alice, lucy)))), inference(transitivity,[status(thm)],[42, 40])). tff(44,plain, ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(alice, lucy)) | (alice = lucy) | (~like(alice, lucy)))), inference(quant_inst,[status(thm)],[])). tff(45,plain, ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (alice = lucy) | (~hate(alice, lucy)) | (~like(alice, lucy))), inference(modus_ponens,[status(thm)],[44, 43])). tff(46,plain, (~hate(alice, lucy)), inference(unit_resolution,[status(thm)],[45, 39, 29, 7])). tff(47,plain, (((~hate(alice, lucy)) | (~tall(alice)) | (~tourist(alice))) | hate(alice, lucy)), inference(tautology,[status(thm)],[])). tff(48,plain, ((~hate(alice, lucy)) | (~tall(alice)) | (~tourist(alice))), inference(unit_resolution,[status(thm)],[47, 46])). tff(49,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(50,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(51,plain, (room(alice)), inference(modus_ponens,[status(thm)],[50, 49])). tff(52,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(53,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(54,plain, (room(fred)), inference(modus_ponens,[status(thm)],[53, 52])). tff(55,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(56,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(57,plain, (room(paul)), inference(modus_ponens,[status(thm)],[56, 55])). tff(58,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(59,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(60,plain, (room(mary)), inference(modus_ponens,[status(thm)],[59, 58])). tff(61,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~hate(alice, lucy)) | (~tall(alice)) | (~tourist(alice))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~hate(alice, lucy)) | (~tall(alice)) | (~tourist(alice)))))), inference(rewrite,[status(thm)],[])). tff(62,plain, ((~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))) <=> (~((~hate(alice, lucy)) | (~tall(alice)) | (~tourist(alice))))), inference(rewrite,[status(thm)],[])). tff(63,plain, ((~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))), inference(rewrite,[status(thm)],[])). tff(64,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~hate(alice, lucy)) | (~tall(alice)) | (~tourist(alice)))))), inference(monotonicity,[status(thm)],[63, 62])). tff(65,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~hate(alice, lucy)) | (~tall(alice)) | (~tourist(alice)))))), inference(transitivity,[status(thm)],[64, 61])). tff(66,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))))), inference(rewrite,[status(thm)],[])). tff(67,plain, (((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))) <=> ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))), inference(rewrite,[status(thm)],[])). tff(68,plain, ((~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))) <=> (~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))), inference(monotonicity,[status(thm)],[67])). tff(69,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))))), inference(monotonicity,[status(thm)],[63, 68])). tff(70,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))))), inference(transitivity,[status(thm)],[69, 66])). tff(71,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))), inference(rewrite,[status(thm)],[])). tff(72,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))))), inference(monotonicity,[status(thm)],[71])). tff(73,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy)))))), inference(rewrite,[status(thm)],[])). tff(74,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))), inference(or_elim,[status(thm)],[4])). tff(75,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))), inference(modus_ponens,[status(thm)],[74, 72])). tff(76,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))), inference(modus_ponens,[status(thm)],[75, 73])). tff(77,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~(tall(alice) & tourist(alice))) | (~hate(alice, lucy))))), inference(modus_ponens,[status(thm)],[76, 72])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!0 |'alice'|) (= X!0 |'fred'|) (= X!0 |'paul'|) (= X!0 |'mary'|) (not (room X!0))))) (a!7 (or (not (and (tall alice) (tourist alice))) (not (hate alice lucy))))) (let ((a!8 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 a!7)) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (not a!7))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ (not a!7) (not a!7))) a!8)))

room(fannie)&room(tammy)&room(anna)&room(otis)&(![X]:(room(X)=>(X='fannie'|X='tammy'|X='anna'|X='otis')))& ((((brave(anna))&(happy(otis)))=>(![X]:(~room(X)=>(((happy(X)&brave(X)&tall(X)&tourist(X))=>(hate(X,john)))))))& ((like(otis,john) & like(john,otis)))& (![X]:(taller(X,otis))))

room(fannie)&room(tammy)&room(anna)&room(otis)&(![X]:(room(X)=>(X='fannie'|X='tammy'|X='anna'|X='otis')))& (((~(tall(otis)&tourist(otis)))|(~hate(otis,john))))

contradiction

entailment

entailment

Daniel, Carol, Roger are the only persons in the room. At least one of the following is true:. -Roger is the least quiet in the room. -Someone outside the room who is quieter than Patricia does not hate Maria. -Carol is not liked by Patricia and is not hated by Maria.

It is not the case that 'Daniel is quieter than Maria and is not hated by Maria'.

neutral

% SZS status Satisfiable

room(daniel)&room(carol)&room(roger)&(![X]:(room(X)=>(X='daniel'|X='carol'|X='roger')))& (((![X]:(quieter(roger,X)))| (?[X]:(~room(X)=>(((quieter(patricia,X))=>(~hate(maria,X))))))| ((~like(carol,patricia))&(~hate(carol,maria)))))

room(daniel)&room(carol)&room(roger)&(![X]:(room(X)=>(X='daniel'|X='carol'|X='roger')))& (~((quieter(maria,daniel))&(~hate(daniel,maria))))

entailment

entailment

entailment

Nathan, William, Thomas are the only persons in the room. Thomas is not William only if Eduardo is a sibling of Thomas. If Nathan is a client of Eduardo or is not hated by Paul or both then Thomas who is a brave european, is not tall otherwise it is not the case that 'only one person outside the room is not brave, not quiet'. Nathan is a client of Eduardo or is not hated by Paul or both. Nathan is not a tall brave person. William is the tallest in the room. Nathan neither is a happy brave quiet european nor is hated by Eduardo. William and Nathan are respectively quiet and tall.

Thomas neither is not hated by Adele nor is a sibling of Eduardo.

contradiction

-

room(nathan)&room(william)&room(thomas)&(![X]:(room(X)=>(X='nathan'|X='william'|X='thomas')))& (((thomas!=william)=>(sibling(thomas,eduardo)))& (((((client(eduardo,nathan))|(~hate(nathan,paul))))=>((brave(thomas)&european(thomas))&(~tall(thomas))))|((~(((client(eduardo,nathan))|(~hate(nathan,paul)))))=>(~(((?[X]:(~room(X)&~brave(X)&~quiet(X)))&(![X,Y]:((~brave(X)&~quiet(X)&~brave(Y)&~quiet(Y))=>(X=Y))))))))& (((client(eduardo,nathan))|(~hate(nathan,paul))))& (~(tall(nathan)&brave(nathan)&person(nathan)))& (![X]:(taller(X,william)))& (~((happy(nathan)&brave(nathan)&quiet(nathan)&european(nathan))|(hate(nathan,eduardo))))& ((quiet(william))&(tall(nathan))))

room(nathan)&room(william)&room(thomas)&(![X]:(room(X)=>(X='nathan'|X='william'|X='thomas')))& (~((~hate(thomas,adele))|(sibling(eduardo,thomas))))

neutral

neutral

neutral

Diana, Filomena, Thelma, Kathleen are the only persons in the room. If "Thelma is the quietest in the room" then "Thelma neither does not hate David nor is not Diana". Thelma neither is not a rich person nor is a quiet rich tourist. Someone in the room does not hate Lakisha. Barbara is a sibling of Kathleen.

Kathleen is a sibling of Barbara or is not a quiet person or both.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_2_type, type, ( tptp_fun_X_2: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(person_type, type, ( person: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(quiet_type, type, ( quiet: $i > $o)). tff(sibling_type, type, ( sibling: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(john_type, type, ( john: $i)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(mary_type, type, ( mary: $i)). tff(lucy_type, type, ( lucy: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(1,plain, ((~(alice = susan)) <=> (~(alice = susan))), inference(rewrite,[status(thm)],[])). tff(2,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//23367342890495230713756.p','b14')). tff(3,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)],[2])). tff(4,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)],[3])). tff(5,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)],[4])). tff(6,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)],[5])). tff(7,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)],[6])). tff(8,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)],[7])). tff(9,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)],[8])). tff(10,plain, ((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))), inference(and_elim,[status(thm)],[9])). tff(11,plain, (((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))), inference(and_elim,[status(thm)],[10])). tff(12,plain, ((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))), inference(and_elim,[status(thm)],[11])). tff(13,plain, (((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))), inference(and_elim,[status(thm)],[12])). tff(14,plain, ((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))), inference(and_elim,[status(thm)],[13])). tff(15,plain, (((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))), 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))), 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))), 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))), 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))), 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))), 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))), inference(and_elim,[status(thm)],[20])). tff(22,plain, (~(alice = susan)), inference(and_elim,[status(thm)],[21])). tff(23,plain, (~(alice = susan)), inference(modus_ponens,[status(thm)],[22, 1])). tff(24,plain, (^[X: $i, Y: $i] : refl(((X = Y) | (sibling(X, Y) <=> sibling(Y, X))) <=> ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))))), inference(bind,[status(th)],[])). tff(25,plain, (![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(quant_intro,[status(thm)],[24])). tff(26,plain, (![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(rewrite,[status(thm)],[])). tff(27,plain, (^[X: $i, Y: $i] : rewrite(((~(X = Y)) => (sibling(X, Y) <=> sibling(Y, X))) <=> ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))))), inference(bind,[status(th)],[])). tff(28,plain, (![X: $i, Y: $i] : ((~(X = Y)) => (sibling(X, Y) <=> sibling(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(quant_intro,[status(thm)],[27])). tff(29,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (sibling(X, Y) <=> sibling(Y, X)))), file('/mnt/tmpfs//23367342890495230713756.p','b4')). tff(30,plain, (![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(modus_ponens,[status(thm)],[29, 28])). tff(31,plain, (![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(modus_ponens,[status(thm)],[30, 26])). tff(32,plain,( ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(skolemize,[status(sab)],[31])). tff(33,plain, (![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(modus_ponens,[status(thm)],[32, 25])). tff(34,plain, (((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | ((alice = susan) | (sibling(alice, susan) <=> sibling(susan, alice)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | (alice = susan) | (sibling(alice, susan) <=> sibling(susan, alice)))), inference(rewrite,[status(thm)],[])). tff(35,plain, ((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | ((alice = susan) | (sibling(alice, susan) <=> sibling(susan, alice)))), inference(quant_inst,[status(thm)],[])). tff(36,plain, ((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | (alice = susan) | (sibling(alice, susan) <=> sibling(susan, alice))), inference(modus_ponens,[status(thm)],[35, 34])). tff(37,plain, (sibling(alice, susan) <=> sibling(susan, alice)), inference(unit_resolution,[status(thm)],[36, 33, 23])). tff(38,plain, (sibling(alice, susan) <=> sibling(alice, susan)), inference(rewrite,[status(thm)],[])). tff(39,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((![X: $i] : quieter(X, fred) => (~((~hate(john, fred)) | (~(fred = mary))))) & (~((~(rich(fred) & person(fred))) | ((quiet(fred) & rich(fred)) & tourist(fred))))) & ?[X: $i] : (room(X) => (~hate(lucy, X)))) & sibling(alice, susan))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : quieter(X, fred)) | (~((~(fred = mary)) | (~hate(john, fred))))) & (~((~(rich(fred) & person(fred))) | (quiet(fred) & rich(fred) & tourist(fred)))) & ?[X: $i] : ((~room(X)) | (~hate(lucy, X))) & sibling(alice, susan))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice)))))))), inference(rewrite,[status(thm)],[])). tff(40,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((![X: $i] : quieter(X, fred) => (~((~hate(john, fred)) | (~(fred = mary))))) & (~((~(rich(fred) & person(fred))) | ((quiet(fred) & rich(fred)) & tourist(fred))))) & ?[X: $i] : (room(X) => (~hate(lucy, X)))) & sibling(alice, susan))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice))))))), file('/mnt/tmpfs//23367342890495230713756.p','negated')). tff(41,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : quieter(X, fred)) | (~((~(fred = mary)) | (~hate(john, fred))))) & (~((~(rich(fred) & person(fred))) | (quiet(fred) & rich(fred) & tourist(fred)))) & ?[X: $i] : ((~room(X)) | (~hate(lucy, X))) & sibling(alice, susan))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice))))))), inference(modus_ponens,[status(thm)],[40, 39])). tff(42,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : quieter(X, fred)) | (~((~(fred = mary)) | (~hate(john, fred))))) & (~((~(rich(fred) & person(fred))) | (quiet(fred) & rich(fred) & tourist(fred)))) & ?[X: $i] : ((~room(X)) | (~hate(lucy, X))) & sibling(alice, susan)), inference(or_elim,[status(thm)],[41])). tff(43,plain, (sibling(alice, susan)), inference(and_elim,[status(thm)],[42])). tff(44,plain, (sibling(alice, susan)), inference(modus_ponens,[status(thm)],[43, 38])). tff(45,plain, ((~(sibling(alice, susan) <=> sibling(susan, alice))) | (~sibling(alice, susan)) | sibling(susan, alice)), inference(tautology,[status(thm)],[])). tff(46,plain, ((~(sibling(alice, susan) <=> sibling(susan, alice))) | sibling(susan, alice)), inference(unit_resolution,[status(thm)],[45, 44])). tff(47,plain, (sibling(susan, alice)), inference(unit_resolution,[status(thm)],[46, 37])). tff(48,plain, ((sibling(susan, alice) | (~quiet(alice)) | (~person(alice))) | (~sibling(susan, alice))), inference(tautology,[status(thm)],[])). tff(49,plain, (sibling(susan, alice) | (~quiet(alice)) | (~person(alice))), inference(unit_resolution,[status(thm)],[48, 47])). tff(50,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(51,plain, (room(alice)), inference(and_elim,[status(thm)],[42])). tff(52,plain, (room(alice)), inference(modus_ponens,[status(thm)],[51, 50])). tff(53,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(54,plain, (room(fred)), inference(and_elim,[status(thm)],[42])). tff(55,plain, (room(fred)), inference(modus_ponens,[status(thm)],[54, 53])). tff(56,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(57,plain, (room(paul)), inference(and_elim,[status(thm)],[42])). tff(58,plain, (room(paul)), inference(modus_ponens,[status(thm)],[57, 56])). tff(59,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(60,plain, (room(mary)), inference(and_elim,[status(thm)],[42])). tff(61,plain, (room(mary)), inference(modus_ponens,[status(thm)],[60, 59])). tff(62,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~quiet(alice)) | (~person(alice))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~quiet(alice)) | (~person(alice)))))), inference(rewrite,[status(thm)],[])). tff(63,plain, ((~(sibling(susan, alice) | (~(quiet(alice) & person(alice))))) <=> (~(sibling(susan, alice) | (~quiet(alice)) | (~person(alice))))), inference(rewrite,[status(thm)],[])). tff(64,plain, ((~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))), inference(rewrite,[status(thm)],[])). tff(65,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~(quiet(alice) & person(alice)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~quiet(alice)) | (~person(alice)))))), inference(monotonicity,[status(thm)],[64, 63])). tff(66,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~(quiet(alice) & person(alice)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~quiet(alice)) | (~person(alice)))))), inference(transitivity,[status(thm)],[65, 62])). tff(67,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~(quiet(alice) & person(alice)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~(quiet(alice) & person(alice))))))), inference(rewrite,[status(thm)],[])). tff(68,plain, ((sibling(susan, alice) | (~(quiet(alice) & person(alice)))) <=> (sibling(susan, alice) | (~(quiet(alice) & person(alice))))), inference(rewrite,[status(thm)],[])). tff(69,plain, ((~(sibling(susan, alice) | (~(quiet(alice) & person(alice))))) <=> (~(sibling(susan, alice) | (~(quiet(alice) & person(alice)))))), inference(monotonicity,[status(thm)],[68])). tff(70,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~(quiet(alice) & person(alice)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~(quiet(alice) & person(alice))))))), inference(monotonicity,[status(thm)],[64, 69])). tff(71,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~(quiet(alice) & person(alice)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | (~(sibling(susan, alice) | (~(quiet(alice) & person(alice))))))), inference(transitivity,[status(thm)],[70, 67])). tff(72,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice))))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice)))))), inference(rewrite,[status(thm)],[])). tff(73,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice))))))), inference(monotonicity,[status(thm)],[72])). tff(74,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice))))))), inference(rewrite,[status(thm)],[])). tff(75,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice)))))), inference(or_elim,[status(thm)],[41])). tff(76,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice)))))), inference(modus_ponens,[status(thm)],[75, 73])). tff(77,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice)))))), inference(modus_ponens,[status(thm)],[76, 74])). tff(78,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (sibling(susan, alice) | (~(quiet(alice) & person(alice)))))), inference(modus_ponens,[status(thm)],[77, 73])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!2 |'alice'|) (= X!2 |'fred'|) (= X!2 |'paul'|) (= X!2 |'mary'|) (not (room X!2))))) (a!7 (or (sibling susan alice) (not (and (quiet alice) (person alice)))))) (let ((a!8 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 a!7)) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (not a!7))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ (not a!7) (not a!7))) a!8)))

room(diana)&room(filomena)&room(thelma)&room(kathleen)&(![X]:(room(X)=>(X='diana'|X='filomena'|X='thelma'|X='kathleen')))& (((![X]:(quieter(X,thelma)))=>(~((~hate(david,thelma))|(thelma!=diana))))& (~((~(rich(thelma)&person(thelma)))|(quiet(thelma)&rich(thelma)&tourist(thelma))))& (?[X]:(room(X)=>(~hate(lakisha,X))))& (sibling(kathleen,barbara)))

room(diana)&room(filomena)&room(thelma)&room(kathleen)&(![X]:(room(X)=>(X='diana'|X='filomena'|X='thelma'|X='kathleen')))& (((sibling(barbara,kathleen))|(~(quiet(kathleen)&person(kathleen)))))

neutral

entailment

entailment

Nanette, Myrtis, Edmund, Kelly are the only persons in the room. "Nanette and Myrtis are respectively brave and happy" if "someone outside the room is not liked by Bernadette". Nanette who collect rare sneakers, is hated by Mary. Everyone in the room is a brave tourist. Myrtis is not a brave tourist or is not liked by Bernadette or both.

Nanette who is a creative happy european, is not hated by Mary.

contradiction

-

room(nanette)&room(myrtis)&room(edmund)&room(kelly)&(![X]:(room(X)=>(X='nanette'|X='myrtis'|X='edmund'|X='kelly')))& (((?[X]:(~room(X)=>(~like(X,bernadette))))=>((brave(nanette))&(happy(myrtis))))& ((collect_rare_sneakers(nanette))&(hate(nanette,mary)))& (![X]:(room(X)=>(brave(X)&tourist(X))))& (((~(brave(myrtis)&tourist(myrtis)))|(~like(myrtis,bernadette)))))

room(nanette)&room(myrtis)&room(edmund)&room(kelly)&(![X]:(room(X)=>(X='nanette'|X='myrtis'|X='edmund'|X='kelly')))& ((creative(nanette)&happy(nanette)&european(nanette))&(~hate(nanette,mary)))

contradiction

contradiction

contradiction

Willie, Thomas, Margaret, Wendell are the only persons in the room. Wendell is the richest in the room if Teri is taller than Margaret. Tracy and Thomas hate each other if Thomas who has a tattoo, is liked by Tracy and vice versa. If more than one person outside the room is not Wendell then Teri is taller than Thomas. Someone who hates Tracy is richer than someone who is not liked by Tracy. Willie is the tallest in the room. Margaret is not hated by Tracy and is a rich tall person. Wendell is the least rich in the room. Only one person outside the room is not a rich tall person. Margaret and Willie like each other. Only one person outside the room is richer than Tracy. Wendell who is not Thomas, is not a rich happy tall person.

Wendell neither is not happy, not rich nor is a happy rich tall person.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(person_type, type, ( person: $i > $o)). tff(tptp_fun_X_2_type, type, ( tptp_fun_X_2: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(room_type, type, ( room: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(mary_type, type, ( mary: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(1,assumption,((~rich(X!2)) | (~tall(X!2)) | (~person(X!2))), introduced(assumption)). tff(2,assumption,(X!2 = alice), introduced(assumption)). tff(3,plain, (room(X!2) <=> room(alice)), inference(monotonicity,[status(thm)],[2])). tff(4,plain, (room(alice) <=> room(X!2)), inference(symmetry,[status(thm)],[3])). tff(5,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(6,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((taller(fred, lucy) => ![X: $i] : richer(X, alice)) & ((preda(paul) & like(paul, susan)) <=> (hate(susan, paul) & hate(paul, susan)))) & (?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = alice)) & (~(Y = alice)))) & (~(X = Y))) => taller(paul, lucy))) & ?[X: $i, Y: $i] : ((hate(susan, X) & (~like(Y, susan))) & richer(X, Y))) & ![X: $i] : taller(X, mary)) & ((~hate(fred, susan)) & ((rich(fred) & tall(fred)) & person(fred)))) & ![X: $i] : richer(alice, X)) & (?[X: $i] : ((~room(X)) & (~((rich(X) & tall(X)) & person(X)))) & ![X: $i, Y: $i] : (((~((rich(X) & tall(X)) & person(X))) & (~((rich(Y) & tall(Y)) & person(Y)))) => (X = Y)))) & (like(fred, mary) & like(mary, fred))) & (?[X: $i] : ((~room(X)) & richer(susan, X)) & ![X: $i, Y: $i] : ((richer(susan, X) & richer(susan, Y)) => (X = Y)))) & ((~(alice = paul)) & (~(((rich(alice) & happy(alice)) & tall(alice)) & person(alice)))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(((~happy(alice)) & (~rich(alice))) | (((happy(alice) & rich(alice)) & tall(alice)) & person(alice))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~taller(fred, lucy)) | ![X: $i] : richer(X, alice)) & ((preda(paul) & like(paul, susan)) <=> (hate(susan, paul) & hate(paul, susan))) & ((~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))) | taller(paul, lucy)) & ?[X: $i, Y: $i] : (hate(susan, X) & (~like(Y, susan)) & richer(X, Y)) & ![X: $i] : taller(X, mary) & (~hate(fred, susan)) & rich(fred) & tall(fred) & person(fred) & ![X: $i] : richer(alice, X) & ?[X: $i] : ((~room(X)) & (~(rich(X) & tall(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(rich(X) & tall(X) & person(X))) & (~(rich(Y) & tall(Y) & person(Y))))) | (X = Y)) & like(fred, mary) & like(mary, fred) & ?[X: $i] : ((~room(X)) & richer(susan, X)) & ![X: $i, Y: $i] : ((~(richer(susan, X) & richer(susan, Y))) | (X = Y)) & (~(alice = paul)) & (~(rich(alice) & happy(alice) & tall(alice) & person(alice))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))))))), inference(rewrite,[status(thm)],[])). tff(7,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((taller(fred, lucy) => ![X: $i] : richer(X, alice)) & ((preda(paul) & like(paul, susan)) <=> (hate(susan, paul) & hate(paul, susan)))) & (?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = alice)) & (~(Y = alice)))) & (~(X = Y))) => taller(paul, lucy))) & ?[X: $i, Y: $i] : ((hate(susan, X) & (~like(Y, susan))) & richer(X, Y))) & ![X: $i] : taller(X, mary)) & ((~hate(fred, susan)) & ((rich(fred) & tall(fred)) & person(fred)))) & ![X: $i] : richer(alice, X)) & (?[X: $i] : ((~room(X)) & (~((rich(X) & tall(X)) & person(X)))) & ![X: $i, Y: $i] : (((~((rich(X) & tall(X)) & person(X))) & (~((rich(Y) & tall(Y)) & person(Y)))) => (X = Y)))) & (like(fred, mary) & like(mary, fred))) & (?[X: $i] : ((~room(X)) & richer(susan, X)) & ![X: $i, Y: $i] : ((richer(susan, X) & richer(susan, Y)) => (X = Y)))) & ((~(alice = paul)) & (~(((rich(alice) & happy(alice)) & tall(alice)) & person(alice)))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(((~happy(alice)) & (~rich(alice))) | (((happy(alice) & rich(alice)) & tall(alice)) & person(alice))))))), file('/mnt/tmpfs//216366430804513979661433.p','negated')). tff(8,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~taller(fred, lucy)) | ![X: $i] : richer(X, alice)) & ((preda(paul) & like(paul, susan)) <=> (hate(susan, paul) & hate(paul, susan))) & ((~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))) | taller(paul, lucy)) & ?[X: $i, Y: $i] : (hate(susan, X) & (~like(Y, susan)) & richer(X, Y)) & ![X: $i] : taller(X, mary) & (~hate(fred, susan)) & rich(fred) & tall(fred) & person(fred) & ![X: $i] : richer(alice, X) & ?[X: $i] : ((~room(X)) & (~(rich(X) & tall(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(rich(X) & tall(X) & person(X))) & (~(rich(Y) & tall(Y) & person(Y))))) | (X = Y)) & like(fred, mary) & like(mary, fred) & ?[X: $i] : ((~room(X)) & richer(susan, X)) & ![X: $i, Y: $i] : ((~(richer(susan, X) & richer(susan, Y))) | (X = Y)) & (~(alice = paul)) & (~(rich(alice) & happy(alice) & tall(alice) & person(alice))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice))))))), inference(modus_ponens,[status(thm)],[7, 6])). tff(9,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~taller(fred, lucy)) | ![X: $i] : richer(X, alice)) & ((preda(paul) & like(paul, susan)) <=> (hate(susan, paul) & hate(paul, susan))) & ((~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))) | taller(paul, lucy)) & ?[X: $i, Y: $i] : (hate(susan, X) & (~like(Y, susan)) & richer(X, Y)) & ![X: $i] : taller(X, mary) & (~hate(fred, susan)) & rich(fred) & tall(fred) & person(fred) & ![X: $i] : richer(alice, X) & ?[X: $i] : ((~room(X)) & (~(rich(X) & tall(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(rich(X) & tall(X) & person(X))) & (~(rich(Y) & tall(Y) & person(Y))))) | (X = Y)) & like(fred, mary) & like(mary, fred) & ?[X: $i] : ((~room(X)) & richer(susan, X)) & ![X: $i, Y: $i] : ((~(richer(susan, X) & richer(susan, Y))) | (X = Y)) & (~(alice = paul)) & (~(rich(alice) & happy(alice) & tall(alice) & person(alice)))), inference(or_elim,[status(thm)],[8])). tff(10,plain, (room(alice)), inference(and_elim,[status(thm)],[9])). tff(11,plain, (room(alice)), inference(modus_ponens,[status(thm)],[10, 5])). tff(12,plain, (room(X!2)), inference(modus_ponens,[status(thm)],[11, 4])). tff(13,plain, (?[X: $i] : ((~room(X)) & (~(rich(X) & tall(X) & person(X)))) <=> ?[X: $i] : ((~room(X)) & (~(rich(X) & tall(X) & person(X))))), inference(rewrite,[status(thm)],[])). tff(14,plain, (?[X: $i] : ((~room(X)) & (~(rich(X) & tall(X) & person(X))))), inference(and_elim,[status(thm)],[9])). tff(15,plain, (?[X: $i] : ((~room(X)) & (~(rich(X) & tall(X) & person(X))))), inference(modus_ponens,[status(thm)],[14, 13])). tff(16,plain,( (~room(X!2)) & (~(rich(X!2) & tall(X!2) & person(X!2)))), inference(skolemize,[status(sab)],[15])). tff(17,plain, (~room(X!2)), inference(and_elim,[status(thm)],[16])). tff(18,plain, ($false), inference(unit_resolution,[status(thm)],[17, 12])). tff(19,plain,(~(X!2 = alice)), inference(lemma,lemma(discharge,[]))). tff(20,assumption,(~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))), introduced(assumption)). tff(21,plain, (((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | room(X!4)), inference(tautology,[status(thm)],[])). tff(22,plain, (room(X!4)), inference(unit_resolution,[status(thm)],[21, 20])). tff(23,plain, (((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(24,plain, (~(X!4 = |'mary'|)), inference(unit_resolution,[status(thm)],[23, 20])). tff(25,plain, (((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'paul'|))), inference(tautology,[status(thm)],[])). tff(26,plain, (~(X!4 = |'paul'|)), inference(unit_resolution,[status(thm)],[25, 20])). tff(27,plain, (((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'fred'|))), inference(tautology,[status(thm)],[])). tff(28,plain, (~(X!4 = |'fred'|)), inference(unit_resolution,[status(thm)],[27, 20])). tff(29,plain, (((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'alice'|))), inference(tautology,[status(thm)],[])). tff(30,plain, (~(X!4 = |'alice'|)), inference(unit_resolution,[status(thm)],[29, 20])). tff(31,plain, (^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(bind,[status(th)],[])). tff(32,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(quant_intro,[status(thm)],[31])). tff(33,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(rewrite,[status(thm)],[])). tff(34,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(and_elim,[status(thm)],[9])). tff(35,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[34, 33])). tff(36,plain,( ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(skolemize,[status(sab)],[35])). tff(37,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[36, 32])). tff(38,plain, (((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))), inference(rewrite,[status(thm)],[])). tff(39,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))), inference(quant_inst,[status(thm)],[])). tff(40,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))), inference(modus_ponens,[status(thm)],[39, 38])). tff(41,plain, ($false), inference(unit_resolution,[status(thm)],[40, 37, 30, 28, 26, 24, 22])). tff(42,plain,((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))), inference(lemma,lemma(discharge,[]))). tff(43,assumption,(~((~rich(alice)) | (~tall(alice)) | (~person(alice)))), introduced(assumption)). tff(44,plain, (((~rich(alice)) | (~tall(alice)) | (~person(alice))) | rich(alice)), inference(tautology,[status(thm)],[])). tff(45,plain, (rich(alice)), inference(unit_resolution,[status(thm)],[44, 43])). tff(46,plain, ((happy(alice) | rich(alice)) | (~rich(alice))), inference(tautology,[status(thm)],[])). tff(47,plain, (happy(alice) | rich(alice)), inference(unit_resolution,[status(thm)],[46, 45])). tff(48,plain, (((~rich(alice)) | (~tall(alice)) | (~person(alice))) | person(alice)), inference(tautology,[status(thm)],[])). tff(49,plain, (person(alice)), inference(unit_resolution,[status(thm)],[48, 43])). tff(50,plain, (((~rich(alice)) | (~tall(alice)) | (~person(alice))) | tall(alice)), inference(tautology,[status(thm)],[])). tff(51,plain, (tall(alice)), inference(unit_resolution,[status(thm)],[50, 43])). tff(52,plain, ((~(~((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice))))) <=> ((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice)))), inference(rewrite,[status(thm)],[])). tff(53,plain, ((rich(alice) & happy(alice) & tall(alice) & person(alice)) <=> (~((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice))))), inference(rewrite,[status(thm)],[])). tff(54,plain, ((~(rich(alice) & happy(alice) & tall(alice) & person(alice))) <=> (~(~((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice)))))), inference(monotonicity,[status(thm)],[53])). tff(55,plain, ((~(rich(alice) & happy(alice) & tall(alice) & person(alice))) <=> ((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice)))), inference(transitivity,[status(thm)],[54, 52])). tff(56,plain, ((~(rich(alice) & happy(alice) & tall(alice) & person(alice))) <=> (~(rich(alice) & happy(alice) & tall(alice) & person(alice)))), inference(rewrite,[status(thm)],[])). tff(57,plain, (~(rich(alice) & happy(alice) & tall(alice) & person(alice))), inference(and_elim,[status(thm)],[9])). tff(58,plain, (~(rich(alice) & happy(alice) & tall(alice) & person(alice))), inference(modus_ponens,[status(thm)],[57, 56])). tff(59,plain, ((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice))), inference(modus_ponens,[status(thm)],[58, 55])). tff(60,plain, (~happy(alice)), inference(unit_resolution,[status(thm)],[59, 45, 51, 49])). tff(61,plain, (((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice))) | happy(alice)), inference(tautology,[status(thm)],[])). tff(62,plain, ((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice))), inference(unit_resolution,[status(thm)],[61, 60])). tff(63,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(64,plain, (room(fred)), inference(and_elim,[status(thm)],[9])). tff(65,plain, (room(fred)), inference(modus_ponens,[status(thm)],[64, 63])). tff(66,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(67,plain, (room(paul)), inference(and_elim,[status(thm)],[9])). tff(68,plain, (room(paul)), inference(modus_ponens,[status(thm)],[67, 66])). tff(69,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(70,plain, (room(mary)), inference(and_elim,[status(thm)],[9])). tff(71,plain, (room(mary)), inference(modus_ponens,[status(thm)],[70, 69])). tff(72,plain, (((~(happy(alice) | rich(alice))) | (~((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice)))) | (~(happy(alice) | rich(alice))))), inference(rewrite,[status(thm)],[])). tff(73,plain, ((~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))), inference(rewrite,[status(thm)],[])). tff(74,plain, ((happy(alice) & rich(alice) & tall(alice) & person(alice)) <=> (~((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice))))), inference(rewrite,[status(thm)],[])). tff(75,plain, (((~happy(alice)) & (~rich(alice))) <=> (~(happy(alice) | rich(alice)))), inference(rewrite,[status(thm)],[])). tff(76,plain, ((((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~(happy(alice) | rich(alice))) | (~((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))), inference(monotonicity,[status(thm)],[75, 74, 73])). tff(77,plain, ((((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~happy(alice)) | (~rich(alice)) | (~tall(alice)) | (~person(alice)))) | (~(happy(alice) | rich(alice))))), inference(transitivity,[status(thm)],[76, 72])). tff(78,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))) <=> (((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))), inference(rewrite,[status(thm)],[])). tff(79,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice))))), inference(monotonicity,[status(thm)],[73])). tff(80,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))) <=> (((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))), inference(transitivity,[status(thm)],[79, 78])). tff(81,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice))))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))))), inference(rewrite,[status(thm)],[])). tff(82,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice))))))), inference(monotonicity,[status(thm)],[81])). tff(83,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice))))))), inference(rewrite,[status(thm)],[])). tff(84,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))))), inference(or_elim,[status(thm)],[8])). tff(85,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))))), inference(modus_ponens,[status(thm)],[84, 82])). tff(86,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))))), inference(modus_ponens,[status(thm)],[85, 83])). tff(87,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~happy(alice)) & (~rich(alice))) | (happy(alice) & rich(alice) & tall(alice) & person(alice)))))), inference(modus_ponens,[status(thm)],[86, 82])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!4 |'alice'|) (= X!4 |'fred'|) (= X!4 |'paul'|) (= X!4 |'mary'|) (not (room X!4))))) (a!7 (or (and (not (happy alice)) (not (rich alice))) (and (happy alice) (rich alice) (tall alice) (person alice))))) (let ((a!8 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 (not a!7))) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 a!7)))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ a!7 a!7)) a!8)))

room(willie)&room(thomas)&room(margaret)&room(wendell)&(![X]:(room(X)=>(X='willie'|X='thomas'|X='margaret'|X='wendell')))& (((taller(margaret,teri))=>(![X]:(richer(X,wendell))))& (((has_a_tattoo(thomas))&(like(thomas,tracy)))<=>((hate(tracy,thomas) & hate(thomas,tracy))))& (((?[X,Y]:(~room(X)&~room(Y)&(X!=wendell&Y!=wendell)&(X!=Y))))=>(taller(thomas,teri)))& (?[X,Y]:((hate(tracy,X))&(~like(Y,tracy))&(richer(X,Y))))& (![X]:(taller(X,willie)))& ((~hate(margaret,tracy))&(rich(margaret)&tall(margaret)&person(margaret)))& (![X]:(richer(wendell,X)))& (((?[X]:(~room(X)&~(rich(X)&tall(X)&person(X))))&(![X,Y]:((~(rich(X)&tall(X)&person(X))&~(rich(Y)&tall(Y)&person(Y)))=>(X=Y)))))& ((like(margaret,willie) & like(willie,margaret)))& (((?[X]:(~room(X)&richer(tracy,X)))&(![X,Y]:((richer(tracy,X)&richer(tracy,Y))=>(X=Y)))))& ((wendell!=thomas)&(~(rich(wendell)&happy(wendell)&tall(wendell)&person(wendell)))))

room(willie)&room(thomas)&room(margaret)&room(wendell)&(![X]:(room(X)=>(X='willie'|X='thomas'|X='margaret'|X='wendell')))& (~((~happy(wendell)&~rich(wendell))|(happy(wendell)&rich(wendell)&tall(wendell)&person(wendell))))

neutral

contradiction

neutral

Sharon, Ellen, Richard, Charmaine are the only persons in the room. If "Ellen neither is not liked by Lynn nor does not like Lynn" then "Lynn is richer than Sharon" otherwise "Sharon is not liked by Lynn". Everyone in the room who likes Lynn does practice yoga. Only one person outside the room is not a creative rich person. Lynn is a client of Charmaine. Sharon is liked by Lynn.

Ellen is a creative rich person.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun_X_1_type, type, ( tptp_fun_X_1: $i)). tff(room_type, type, ( room: $i > $o)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(person_type, type, ( person: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(rich_type, type, ( rich: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(mary_type, type, ( mary: $i)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(predc_type, type, ( predc: $i > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(1,assumption,(~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))), introduced(assumption)). tff(2,plain, (((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))) | person(X!0)), inference(tautology,[status(thm)],[])). tff(3,plain, (person(X!0)), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, (((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))) | creative(X!0)), inference(tautology,[status(thm)],[])). tff(5,plain, (creative(X!0)), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, (((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))) | rich(X!0)), inference(tautology,[status(thm)],[])). tff(7,plain, (rich(X!0)), inference(unit_resolution,[status(thm)],[6, 1])). tff(8,plain, ((~(~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))))) <=> ((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))), inference(rewrite,[status(thm)],[])). tff(9,plain, ((creative(X!0) & rich(X!0) & person(X!0)) <=> (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))))), inference(rewrite,[status(thm)],[])). tff(10,plain, ((~(creative(X!0) & rich(X!0) & person(X!0))) <=> (~(~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))))), inference(monotonicity,[status(thm)],[9])). tff(11,plain, ((~(creative(X!0) & rich(X!0) & person(X!0))) <=> ((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))), inference(transitivity,[status(thm)],[10, 8])). tff(12,plain, (?[X: $i] : ((~room(X)) & (~(creative(X) & rich(X) & person(X)))) <=> ?[X: $i] : ((~room(X)) & (~(creative(X) & rich(X) & person(X))))), inference(rewrite,[status(thm)],[])). tff(13,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((~((~like(paul, susan)) | (~like(susan, paul)))) => richer(mary, susan)) | ((~(~((~like(paul, susan)) | (~like(susan, paul))))) => (~like(mary, susan)))) & ![X: $i] : (room(X) => (like(susan, X) => predc(X)))) & (?[X: $i] : ((~room(X)) & (~((creative(X) & rich(X)) & person(X)))) & ![X: $i, Y: $i] : (((~((creative(X) & rich(X)) & person(X))) & (~((creative(Y) & rich(Y)) & person(Y)))) => (X = Y)))) & client(alice, susan)) & like(mary, susan))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((creative(paul) & rich(paul)) & person(paul))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, susan)) | (~like(susan, paul)) | (~((~like(paul, susan)) | (~like(susan, paul)))) | richer(mary, susan) | (~like(mary, susan))) & ![X: $i] : (predc(X) | (~room(X)) | (~like(susan, X))) & ?[X: $i] : ((~room(X)) & (~(creative(X) & rich(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y)) & client(alice, susan) & like(mary, susan))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul))))), inference(rewrite,[status(thm)],[])). tff(14,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((~((~like(paul, susan)) | (~like(susan, paul)))) => richer(mary, susan)) | ((~(~((~like(paul, susan)) | (~like(susan, paul))))) => (~like(mary, susan)))) & ![X: $i] : (room(X) => (like(susan, X) => predc(X)))) & (?[X: $i] : ((~room(X)) & (~((creative(X) & rich(X)) & person(X)))) & ![X: $i, Y: $i] : (((~((creative(X) & rich(X)) & person(X))) & (~((creative(Y) & rich(Y)) & person(Y)))) => (X = Y)))) & client(alice, susan)) & like(mary, susan))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((creative(paul) & rich(paul)) & person(paul))))), file('/mnt/tmpfs//1430801639208878138953519.p','negated')). tff(15,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, susan)) | (~like(susan, paul)) | (~((~like(paul, susan)) | (~like(susan, paul)))) | richer(mary, susan) | (~like(mary, susan))) & ![X: $i] : (predc(X) | (~room(X)) | (~like(susan, X))) & ?[X: $i] : ((~room(X)) & (~(creative(X) & rich(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y)) & client(alice, susan) & like(mary, susan))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul)))), inference(modus_ponens,[status(thm)],[14, 13])). tff(16,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~like(paul, susan)) | (~like(susan, paul)) | (~((~like(paul, susan)) | (~like(susan, paul)))) | richer(mary, susan) | (~like(mary, susan))) & ![X: $i] : (predc(X) | (~room(X)) | (~like(susan, X))) & ?[X: $i] : ((~room(X)) & (~(creative(X) & rich(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y)) & client(alice, susan) & like(mary, susan)), inference(or_elim,[status(thm)],[15])). tff(17,plain, (?[X: $i] : ((~room(X)) & (~(creative(X) & rich(X) & person(X))))), inference(and_elim,[status(thm)],[16])). tff(18,plain, (?[X: $i] : ((~room(X)) & (~(creative(X) & rich(X) & person(X))))), inference(modus_ponens,[status(thm)],[17, 12])). tff(19,plain,( (~room(X!0)) & (~(creative(X!0) & rich(X!0) & person(X!0)))), inference(skolemize,[status(sab)],[18])). tff(20,plain, (~(creative(X!0) & rich(X!0) & person(X!0))), inference(and_elim,[status(thm)],[19])). tff(21,plain, ((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))), inference(modus_ponens,[status(thm)],[20, 11])). tff(22,plain, ($false), inference(unit_resolution,[status(thm)],[21, 7, 5, 3])). tff(23,plain,((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))), inference(lemma,lemma(discharge,[]))). tff(24,assumption,(paul = X!0), introduced(assumption)). tff(25,plain, (room(paul) <=> room(X!0)), inference(monotonicity,[status(thm)],[24])). tff(26,plain, (room(X!0) <=> room(paul)), inference(symmetry,[status(thm)],[25])). tff(27,plain, ((~room(X!0)) <=> (~room(paul))), inference(monotonicity,[status(thm)],[26])). tff(28,plain, (~room(X!0)), inference(and_elim,[status(thm)],[19])). tff(29,plain, (~room(paul)), inference(modus_ponens,[status(thm)],[28, 27])). tff(30,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(31,plain, (room(paul)), inference(and_elim,[status(thm)],[16])). tff(32,plain, (room(paul)), inference(modus_ponens,[status(thm)],[31, 30])). tff(33,plain, ($false), inference(unit_resolution,[status(thm)],[32, 29])). tff(34,plain,(~(paul = X!0)), inference(lemma,lemma(discharge,[]))). tff(35,plain, (^[X: $i, Y: $i] : refl(((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y))))) <=> ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y))))))), inference(bind,[status(th)],[])). tff(36,plain, (![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y))))) <=> ![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))), inference(quant_intro,[status(thm)],[35])). tff(37,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((creative(X) & rich(X) & person(X)) <=> (~((~rich(X)) | (~creative(X)) | (~person(X))))), ((~(creative(X) & rich(X) & person(X))) <=> (~(~((~rich(X)) | (~creative(X)) | (~person(X))))))), rewrite((~(~((~rich(X)) | (~creative(X)) | (~person(X))))) <=> ((~rich(X)) | (~creative(X)) | (~person(X)))), ((~(creative(X) & rich(X) & person(X))) <=> ((~rich(X)) | (~creative(X)) | (~person(X))))), trans(monotonicity(rewrite((creative(Y) & rich(Y) & person(Y)) <=> (~((~creative(Y)) | (~rich(Y)) | (~person(Y))))), ((~(creative(Y) & rich(Y) & person(Y))) <=> (~(~((~creative(Y)) | (~rich(Y)) | (~person(Y))))))), rewrite((~(~((~creative(Y)) | (~rich(Y)) | (~person(Y))))) <=> ((~creative(Y)) | (~rich(Y)) | (~person(Y)))), ((~(creative(Y) & rich(Y) & person(Y))) <=> ((~creative(Y)) | (~rich(Y)) | (~person(Y))))), (((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y)))) <=> (((~rich(X)) | (~creative(X)) | (~person(X))) & ((~creative(Y)) | (~rich(Y)) | (~person(Y)))))), rewrite((((~rich(X)) | (~creative(X)) | (~person(X))) & ((~creative(Y)) | (~rich(Y)) | (~person(Y)))) <=> (~((~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y))))))), (((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y)))) <=> (~((~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))))), ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) <=> (~(~((~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y))))))))), rewrite((~(~((~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y))))))) <=> ((~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))), ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) <=> ((~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y))))))), (((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y)) <=> (((~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y))))) | (X = Y)))), rewrite((((~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y))))) | (X = Y)) <=> ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))), (((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y)) <=> ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))))), inference(bind,[status(th)],[])). tff(38,plain, (![X: $i, Y: $i] : ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))), inference(quant_intro,[status(thm)],[37])). tff(39,plain, (![X: $i, Y: $i] : ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y))), inference(rewrite,[status(thm)],[])). tff(40,plain, (![X: $i, Y: $i] : ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y))), inference(and_elim,[status(thm)],[16])). tff(41,plain, (![X: $i, Y: $i] : ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y))), inference(modus_ponens,[status(thm)],[40, 39])). tff(42,plain,( ![X: $i, Y: $i] : ((~((~(creative(X) & rich(X) & person(X))) & (~(creative(Y) & rich(Y) & person(Y))))) | (X = Y))), inference(skolemize,[status(sab)],[41])). tff(43,plain, (![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))), inference(modus_ponens,[status(thm)],[42, 38])). tff(44,plain, (![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))), inference(modus_ponens,[status(thm)],[43, 36])). tff(45,plain, (((~![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))) | ((~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))) | (paul = X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))) | (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))) | (paul = X!0))), inference(rewrite,[status(thm)],[])). tff(46,plain, (((paul = X!0) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))) | (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))))) <=> ((~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))) | (paul = X!0))), inference(rewrite,[status(thm)],[])). tff(47,plain, ((~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))) <=> (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))))), inference(rewrite,[status(thm)],[])). tff(48,plain, ((~((~rich(paul)) | (~creative(paul)) | (~person(paul)))) <=> (~((~creative(paul)) | (~rich(paul)) | (~person(paul))))), inference(rewrite,[status(thm)],[])). tff(49,plain, (((paul = X!0) | (~((~rich(paul)) | (~creative(paul)) | (~person(paul)))) | (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))))) <=> ((paul = X!0) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))) | (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))))), inference(monotonicity,[status(thm)],[48, 47])). tff(50,plain, (((paul = X!0) | (~((~rich(paul)) | (~creative(paul)) | (~person(paul)))) | (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0))))) <=> ((~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))) | (paul = X!0))), inference(transitivity,[status(thm)],[49, 46])). tff(51,plain, (((~![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))) | ((paul = X!0) | (~((~rich(paul)) | (~creative(paul)) | (~person(paul)))) | (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))) | ((~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))) | (paul = X!0)))), inference(monotonicity,[status(thm)],[50])). tff(52,plain, (((~![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))) | ((paul = X!0) | (~((~rich(paul)) | (~creative(paul)) | (~person(paul)))) | (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))) | (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))) | (paul = X!0))), inference(transitivity,[status(thm)],[51, 45])). tff(53,plain, ((~![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))) | ((paul = X!0) | (~((~rich(paul)) | (~creative(paul)) | (~person(paul)))) | (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))))), inference(quant_inst,[status(thm)],[])). tff(54,plain, ((~![X: $i, Y: $i] : ((X = Y) | (~((~rich(X)) | (~creative(X)) | (~person(X)))) | (~((~creative(Y)) | (~rich(Y)) | (~person(Y)))))) | (~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))) | (paul = X!0)), inference(modus_ponens,[status(thm)],[53, 52])). tff(55,plain, ((~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))) | (paul = X!0)), inference(unit_resolution,[status(thm)],[54, 44])). tff(56,plain, ((~((~creative(X!0)) | (~rich(X!0)) | (~person(X!0)))) | (~((~creative(paul)) | (~rich(paul)) | (~person(paul))))), inference(unit_resolution,[status(thm)],[55, 34])). tff(57,plain, (~((~creative(paul)) | (~rich(paul)) | (~person(paul)))), inference(unit_resolution,[status(thm)],[56, 23])). tff(58,plain, (((~creative(paul)) | (~rich(paul)) | (~person(paul))) | person(paul)), inference(tautology,[status(thm)],[])). tff(59,plain, (person(paul)), inference(unit_resolution,[status(thm)],[58, 57])). tff(60,plain, (((~creative(paul)) | (~rich(paul)) | (~person(paul))) | creative(paul)), inference(tautology,[status(thm)],[])). tff(61,plain, (creative(paul)), inference(unit_resolution,[status(thm)],[60, 57])). tff(62,plain, (((~creative(paul)) | (~rich(paul)) | (~person(paul))) | rich(paul)), inference(tautology,[status(thm)],[])). tff(63,plain, (rich(paul)), inference(unit_resolution,[status(thm)],[62, 57])). tff(64,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(65,plain, (room(alice)), inference(and_elim,[status(thm)],[16])). tff(66,plain, (room(alice)), inference(modus_ponens,[status(thm)],[65, 64])). tff(67,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(68,plain, (room(fred)), inference(and_elim,[status(thm)],[16])). tff(69,plain, (room(fred)), inference(modus_ponens,[status(thm)],[68, 67])). tff(70,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(71,plain, (room(mary)), inference(and_elim,[status(thm)],[16])). tff(72,plain, (room(mary)), inference(modus_ponens,[status(thm)],[71, 70])). tff(73,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~creative(paul)) | (~rich(paul)) | (~person(paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~creative(paul)) | (~rich(paul)) | (~person(paul)))), inference(rewrite,[status(thm)],[])). tff(74,plain, ((~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))), inference(rewrite,[status(thm)],[])). tff(75,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~creative(paul)) | (~rich(paul)) | (~person(paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~creative(paul)) | (~rich(paul)) | (~person(paul)))), inference(monotonicity,[status(thm)],[74])). tff(76,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~creative(paul)) | (~rich(paul)) | (~person(paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~creative(paul)) | (~rich(paul)) | (~person(paul)))), inference(transitivity,[status(thm)],[75, 73])). tff(77,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul)) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul))), inference(rewrite,[status(thm)],[])). tff(78,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul)))), inference(monotonicity,[status(thm)],[77])). tff(79,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul)))), inference(rewrite,[status(thm)],[])). tff(80,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul))), inference(or_elim,[status(thm)],[15])). tff(81,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul))), inference(modus_ponens,[status(thm)],[80, 78])). tff(82,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul))), inference(modus_ponens,[status(thm)],[81, 79])). tff(83,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & creative(paul) & rich(paul) & person(paul))), inference(modus_ponens,[status(thm)],[82, 78])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!1 |'alice'|) (= X!1 |'fred'|) (= X!1 |'paul'|) (= X!1 |'mary'|) (not (room X!1))))) (a!7 (refl (~ (not (creative paul)) (not (creative paul))))) (a!8 (refl (~ (not (rich paul)) (not (rich paul))))) (a!9 (refl (~ (not (person paul)) (not (person paul)))))) (let ((a!10 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 (creative paul) (rich paul) (person paul))) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (not (creative paul)) (not (rich paul)) (not (person paul)))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!7 a!8 a!9 a!10)))

room(sharon)&room(ellen)&room(richard)&room(charmaine)&(![X]:(room(X)=>(X='sharon'|X='ellen'|X='richard'|X='charmaine')))& ((((~((~like(ellen,lynn))|(~like(lynn,ellen))))=>(richer(sharon,lynn)))|((~(~((~like(ellen,lynn))|(~like(lynn,ellen)))))=>(~like(sharon,lynn))))& (![X]:(room(X)=>(((like(lynn,X))=>(does_practice_yoga(X))))))& (((?[X]:(~room(X)&~(creative(X)&rich(X)&person(X))))&(![X,Y]:((~(creative(X)&rich(X)&person(X))&~(creative(Y)&rich(Y)&person(Y)))=>(X=Y)))))& (client(charmaine,lynn))& (like(sharon,lynn)))

room(sharon)&room(ellen)&room(richard)&room(charmaine)&(![X]:(room(X)=>(X='sharon'|X='ellen'|X='richard'|X='charmaine')))& (creative(ellen)&rich(ellen)&person(ellen))

entailment

contradiction

neutral

Jose, Samuel, David are the only persons in the room. 'Jose is the tallest in the room' if 'Samuel and Jose are rich creative brave quiet tourist' and vice versa. Jose is the tallest in the room. Jose who is a quiet rich creative tall tourist, is not Samuel. Someone outside the room is a rich tourist.

Samuel is not quiet, not brave, not tall, not creative or is not creative, not quiet, not brave or both.

contradiction

-

room(jose)&room(samuel)&room(david)&(![X]:(room(X)=>(X='jose'|X='samuel'|X='david')))& (((rich(samuel)&creative(samuel)&brave(samuel)&quiet(samuel)&tourist(samuel)&rich(jose)&creative(jose)&brave(jose)&quiet(jose)&tourist(jose))<=>(![X]:(taller(X,jose))))& (![X]:(taller(X,jose)))& ((quiet(jose)&rich(jose)&creative(jose)&tall(jose)&tourist(jose))&(jose!=samuel))& (?[X]:(~room(X)=>(rich(X)&tourist(X)))))

room(jose)&room(samuel)&room(david)&(![X]:(room(X)=>(X='jose'|X='samuel'|X='david')))& (((~quiet(samuel)&~brave(samuel)&~tall(samuel)&~creative(samuel))|(~creative(samuel)&~quiet(samuel)&~brave(samuel))))

entailment

neutral

neutral

Danny is the only person in the room. Only one of the following is true:. -Danny is a creative person. -Someone outside the room who is not Danny is a creative tourist.

Danny neither is not a creative tourist nor is not a rich tourist.

contradiction

-

room(danny)&(![X]:(room(X)=>(X='danny')))& (((creative(danny)&person(danny))|(?[X]:(~room(X)=>(((X!=danny)=>(creative(X)&tourist(X)))))))&~(creative(danny)&person(danny)&?[X]:(~room(X)=>(((X!=danny)=>(creative(X)&tourist(X)))))))

room(danny)&(![X]:(room(X)=>(X='danny')))& (~((~(creative(danny)&tourist(danny)))|(~(rich(danny)&tourist(danny)))))

contradiction

neutral

neutral

Russell, Phyllis, Joshua are the only persons in the room. If "no one outside the room who does not hate Arthur is a tall person" then "Phyllis who is taller than Robin, does not enjoy hiking". Only one person in the room is not hated by Robin. It is not the case that 'Phyllis neither is not hated by Arthur nor does not hate Robin'. Phyllis who is not hated by Robin, is hated by Arthur. Phyllis is the least tall in the room. Phyllis is a client of Robin and does not hate Steven.

Someone who does not hate Robin is a client of someone who does not hate Steven.

neutral

% SZS status Satisfiable

room(russell)&room(phyllis)&room(joshua)&(![X]:(room(X)=>(X='russell'|X='phyllis'|X='joshua')))& (((~?[X]:(~room(X)=>(((~hate(arthur,X))=>(tall(X)&person(X))))))=>((taller(robin,phyllis))&(does_not_enjoy_hiking(phyllis))))& (((?[X]:(room(X)&~hate(X,robin)))&(![X,Y]:((~hate(X,robin)&~hate(Y,robin))=>(X=Y)))))& (~(~((~hate(phyllis,arthur))|(~hate(robin,phyllis)))))& ((~hate(phyllis,robin))&(hate(phyllis,arthur)))& (![X]:(taller(phyllis,X)))& ((client(robin,phyllis))&(~hate(steven,phyllis))))

room(russell)&room(phyllis)&room(joshua)&(![X]:(room(X)=>(X='russell'|X='phyllis'|X='joshua')))& (?[X,Y]:((~hate(robin,X))&(~hate(steven,Y))&(client(X,Y))))

entailment

entailment

entailment

Cynthia is the only person in the room. 'Cynthia is not a tall creative person' if 'Cynthia does not enjoy logic puzzles' and vice versa. Cynthia is the least rich in the room. Only one person outside the room is not a creative european. Everyone outside the room who is not creative is a client of Leroy.

It is not the case that 'Cynthia is a creative person or does not like Era or both'.

contradiction

-

room(cynthia)&(![X]:(room(X)=>(X='cynthia')))& (((does_not_enjoy_logic_puzzles(cynthia))<=>(~(tall(cynthia)&creative(cynthia)&person(cynthia))))& (![X]:(richer(cynthia,X)))& (((?[X]:(~room(X)&~(creative(X)&european(X))))&(![X,Y]:((~(creative(X)&european(X))&~(creative(Y)&european(Y)))=>(X=Y)))))& (![X]:(~room(X)=>(((~creative(X))=>(client(leroy,X)))))))

room(cynthia)&(![X]:(room(X)=>(X='cynthia')))& (~(((creative(cynthia)&person(cynthia))|(~like(era,cynthia)))))

entailment

entailment

entailment

Janet is the only person in the room. It is not the case that 'more than one person outside the room does not enjoy hiking'.

It is not the case that 'more than one person in the room does not practice calligraphy'.

entailment

% SZS status Unsatisfiable % SZS output start Proof 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(tptp_fun_Y_1_type, type, ( tptp_fun_Y_1: $i)). tff(tptp_fun_X_2_type, type, ( tptp_fun_X_2: $i)). tff(predc_type, type, ( predc: $i > $o)). tff(preda_type, type, ( preda: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(1,assumption,(~(predc(X!2) | predc(Y!1) | (X!2 = Y!1) | (~room(X!2)) | (~room(Y!1)))), introduced(assumption)). tff(2,plain, ((predc(X!2) | predc(Y!1) | (X!2 = Y!1) | (~room(X!2)) | (~room(Y!1))) | room(Y!1)), inference(tautology,[status(thm)],[])). tff(3,plain, (room(Y!1)), 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, ((~(((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)) & ((~predc(X)) & (~predc(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)))))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~predc(X)) & (~predc(Y)) & (~(X = Y)))))))), inference(rewrite,[status(thm)],[])). tff(8,axiom,(~(((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)) & ((~predc(X)) & (~predc(Y)))) & (~(X = Y))))))), file('/mnt/tmpfs//9165806904072871122952738.p','negated')). tff(9,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) & (~predc(X)) & (~predc(Y)) & (~(X = Y))))))), inference(modus_ponens,[status(thm)],[8, 7])). tff(10,plain, (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~preda(X)) & (~preda(Y)) & (~(X = Y))))), inference(or_elim,[status(thm)],[9])). tff(11,plain, (![X: $i] : ((~room(X)) | (X = |'mary'|))), inference(and_elim,[status(thm)],[10])). 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!1)) | (Y!1 = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(Y!1)) | (Y!1 = |'mary'|))), inference(rewrite,[status(thm)],[])). tff(16,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(Y!1)) | (Y!1 = |'mary'|))), inference(quant_inst,[status(thm)],[])). tff(17,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(Y!1)) | (Y!1 = |'mary'|)), inference(modus_ponens,[status(thm)],[16, 15])). tff(18,plain, (Y!1 = |'mary'|), inference(unit_resolution,[status(thm)],[17, 14, 3])). tff(19,plain, ((X!2 = Y!1) <=> (X!2 = |'mary'|)), inference(monotonicity,[status(thm)],[18])). tff(20,plain, ((X!2 = |'mary'|) <=> (X!2 = Y!1)), inference(symmetry,[status(thm)],[19])). tff(21,plain, ((predc(X!2) | predc(Y!1) | (X!2 = Y!1) | (~room(X!2)) | (~room(Y!1))) | room(X!2)), inference(tautology,[status(thm)],[])). tff(22,plain, (room(X!2)), inference(unit_resolution,[status(thm)],[21, 1])). tff(23,plain, (((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!2)) | (X!2 = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!2)) | (X!2 = |'mary'|))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!2)) | (X!2 = |'mary'|))), inference(quant_inst,[status(thm)],[])). tff(25,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!2)) | (X!2 = |'mary'|)), inference(modus_ponens,[status(thm)],[24, 23])). tff(26,plain, (X!2 = |'mary'|), inference(unit_resolution,[status(thm)],[25, 14, 22])). tff(27,plain, (X!2 = Y!1), inference(modus_ponens,[status(thm)],[26, 20])). tff(28,plain, ((predc(X!2) | predc(Y!1) | (X!2 = Y!1) | (~room(X!2)) | (~room(Y!1))) | (~(X!2 = Y!1))), inference(tautology,[status(thm)],[])). tff(29,plain, (~(X!2 = Y!1)), inference(unit_resolution,[status(thm)],[28, 1])). tff(30,plain, ($false), inference(unit_resolution,[status(thm)],[29, 27])). tff(31,plain,(predc(X!2) | predc(Y!1) | (X!2 = Y!1) | (~room(X!2)) | (~room(Y!1))), 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)],[10])). tff(34,plain, (room(mary)), inference(modus_ponens,[status(thm)],[33, 32])). tff(35,plain, (((~room(mary)) | (~((~room(X!0)) | (X!0 = |'mary'|))) | (room(X!2) & room(Y!1) & (~predc(X!2)) & (~predc(Y!1)) & (~(X!2 = Y!1)))) <=> ((~room(mary)) | (~((~room(X!0)) | (X!0 = |'mary'|))) | (~(predc(X!2) | predc(Y!1) | (X!2 = Y!1) | (~room(X!2)) | (~room(Y!1)))))), inference(rewrite,[status(thm)],[])). tff(36,plain, ((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~predc(X)) & (~predc(Y)) & (~(X = Y))))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~predc(X)) & (~predc(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) & (~predc(X)) & (~predc(Y)) & (~(X = Y)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~predc(X)) & (~predc(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) & (~predc(X)) & (~predc(Y)) & (~(X = Y)))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~predc(X)) & (~predc(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) & (~predc(X)) & (~predc(Y)) & (~(X = Y)))))), inference(or_elim,[status(thm)],[9])). tff(40,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~predc(X)) & (~predc(Y)) & (~(X = Y)))))), inference(modus_ponens,[status(thm)],[39, 37])). tff(41,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~predc(X)) & (~predc(Y)) & (~(X = Y)))))), inference(modus_ponens,[status(thm)],[40, 38])). tff(42,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~?[X: $i, Y: $i] : (room(X) & room(Y) & (~predc(X)) & (~predc(Y)) & (~(X = Y)))))), inference(modus_ponens,[status(thm)],[41, 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!0)) (= X!0 |'mary'|)))) (a!4 (exists ((X $i) (Y $i)) (and (room X) (room Y) (not (predc X)) (not (predc Y)) (not (= X Y))))) (a!5 (and (room X!2) (room Y!1) (not (predc X!2)) (not (predc Y!1)) (not (= X!2 Y!1))))) (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)))

room(janet)&(![X]:(room(X)=>(X='janet')))& (~((?[X,Y]:(~room(X)&~room(Y)&(does_not_enjoy_hiking(X)&does_not_enjoy_hiking(Y))&(X!=Y)))))

room(janet)&(![X]:(room(X)=>(X='janet')))& (~((?[X,Y]:(room(X)&room(Y)&(does_not_practice_calligraphy(X)&does_not_practice_calligraphy(Y))&(X!=Y)))))

contradiction

neutral

neutral

Michael, Omar are the only persons in the room. None of the following is true:. -Michael is the least rich in the room. -Michael and Omar are not rich.

Michael and Omar are not rich.

contradiction

-

room(michael)&room(omar)&(![X]:(room(X)=>(X='michael'|X='omar')))& (~((![X]:(richer(michael,X)))|(~rich(michael)&~rich(omar))))

room(michael)&room(omar)&(![X]:(room(X)=>(X='michael'|X='omar')))& (~rich(michael)&~rich(omar))

entailment

neutral

entailment

Matthew, Rhonda are the only persons in the room. 'Rhonda is a client of Cordelia and is not Matthew' only if 'it is not the case that 'only one person in the room is not hated by Alphonso''. 'Rhonda is not hated by Cordelia and does not have lived in exactly three countries' only if 'Matthew who is a rich person, does not hate Cordelia'. More than one person in the room has lived in exactly three countries. Rhonda is not Matthew or does not hate Cordelia or both. More than one person in the room is a client of Alphonso. Matthew and Rhonda hate each other. Rhonda who does not hate Cordelia, is hated by Alphonso. It is not the case that 'only one person in the room is not hated by Alphonso'. Only one person in the room is a client of Cordelia. Someone in the room who does enjoy trail running is not hated by Cordelia. It is not the case that 'Matthew neither is not rich, not quiet nor is hated by Cordelia'.

Rhonda is a quiet person and collect rare sneakers.

neutral

% SZS status Satisfiable

room(matthew)&room(rhonda)&(![X]:(room(X)=>(X='matthew'|X='rhonda')))& ((((client(cordelia,rhonda))&(rhonda!=matthew))=>(~(((?[X]:(room(X)&~hate(X,alphonso)))&(![X,Y]:((~hate(X,alphonso)&~hate(Y,alphonso))=>(X=Y)))))))& (((~hate(rhonda,cordelia))&(does_not_have_lived_in_exactly_three_countries(rhonda)))=>((rich(matthew)&person(matthew))&(~hate(cordelia,matthew))))& ((?[X,Y]:(room(X)&room(Y)&(has_lived_in_exactly_three_countries(X)&has_lived_in_exactly_three_countries(Y))&(X!=Y))))& (((rhonda!=matthew)|(~hate(cordelia,rhonda))))& ((?[X,Y]:(room(X)&room(Y)&(client(alphonso,X)&client(alphonso,Y))&(X!=Y))))& ((hate(matthew,rhonda) & hate(rhonda,matthew)))& ((~hate(cordelia,rhonda))&(hate(rhonda,alphonso)))& (~(((?[X]:(room(X)&~hate(X,alphonso)))&(![X,Y]:((~hate(X,alphonso)&~hate(Y,alphonso))=>(X=Y))))))& (((?[X]:(room(X)&client(cordelia,X)))&(![X,Y]:((client(cordelia,X)&client(cordelia,Y))=>(X=Y)))))& (?[X]:(room(X)=>(((does_enjoy_trail_running(X))=>(~hate(X,cordelia))))))& (~(~((~rich(matthew)&~quiet(matthew))|(hate(matthew,cordelia))))))

room(matthew)&room(rhonda)&(![X]:(room(X)=>(X='matthew'|X='rhonda')))& ((quiet(rhonda)&person(rhonda))&(collect_rare_sneakers(rhonda)))

neutral

contradiction

contradiction

Michael is the only person in the room. Michael is the tallest in the room. More than one person outside the room is taller than Miguel. Everyone outside the room does not like Miguel. Someone who is taller than Miguel is taller than someone who is liked by Miguel.

Someone who is taller than Miguel like someone who does not like Miguel.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(tptp_fun_Y_2_type, type, ( tptp_fun_Y_2: $i)). tff(fred_type, type, ( fred: $i)). tff(tptp_fun_X_3_type, type, ( tptp_fun_X_3: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(room_type, type, ( room: $i > $o)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(mary_type, type, ( mary: $i)). tff(paul_type, type, ( paul: $i)). tff(alice_type, type, ( alice: $i)). tff(john_type, type, ( john: $i)). tff(susan_type, type, ( susan: $i)). tff(lucy_type, type, ( lucy: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(1,assumption,(X!3 = Y!2), introduced(assumption)). tff(2,plain, (taller(fred, X!3) <=> taller(fred, Y!2)), inference(monotonicity,[status(thm)],[1])). tff(3,plain, (taller(fred, Y!2) <=> taller(fred, X!3)), inference(symmetry,[status(thm)],[2])). tff(4,plain, ((~taller(fred, Y!2)) <=> (~taller(fred, X!3))), inference(monotonicity,[status(thm)],[3])). tff(5,assumption,(room(fred)), introduced(assumption)). tff(6,assumption,(fred = |'mary'|), introduced(assumption)). tff(7,plain, (|'mary'| = fred), inference(symmetry,[status(thm)],[6])). tff(8,plain, (^[X: $i] : refl(((~room(X)) | (X = |'mary'|)) <=> ((~room(X)) | (X = |'mary'|)))), inference(bind,[status(th)],[])). tff(9,plain, (![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))), inference(quant_intro,[status(thm)],[8])). tff(10,plain, (![X: $i] : ((~room(X)) | (X = |'mary'|)) <=> ![X: $i] : ((~room(X)) | (X = |'mary'|))), inference(rewrite,[status(thm)],[])). tff(11,plain, ((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (taller(fred, X) & taller(fred, Y))) & (~(X = Y)))) & ![X: $i] : ((~room(X)) => (~like(fred, X)))) & ?[X: $i, Y: $i] : ((taller(fred, X) & like(Y, fred)) & taller(X, Y)))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ?[X: $i, Y: $i] : ((taller(fred, X) & (~like(fred, Y))) & like(X, Y))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & taller(fred, X) & taller(fred, Y) & (~(X = Y))) & ![X: $i] : (room(X) | (~like(fred, X))) & ?[X: $i, Y: $i] : (taller(fred, X) & like(Y, fred) & taller(X, Y)))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(12,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (taller(fred, X) & taller(fred, Y))) & (~(X = Y)))) & ![X: $i] : ((~room(X)) => (~like(fred, X)))) & ?[X: $i, Y: $i] : ((taller(fred, X) & like(Y, fred)) & taller(X, Y)))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ?[X: $i, Y: $i] : ((taller(fred, X) & (~like(fred, Y))) & like(X, Y))))), file('/mnt/tmpfs//21337710477640378606193.p','negated')). tff(13,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & taller(fred, X) & taller(fred, Y) & (~(X = Y))) & ![X: $i] : (room(X) | (~like(fred, X))) & ?[X: $i, Y: $i] : (taller(fred, X) & like(Y, fred) & taller(X, Y)))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y))))), inference(modus_ponens,[status(thm)],[12, 11])). tff(14,plain, (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ![X: $i] : taller(X, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & taller(fred, X) & taller(fred, Y) & (~(X = Y))) & ![X: $i] : (room(X) | (~like(fred, X))) & ?[X: $i, Y: $i] : (taller(fred, X) & like(Y, fred) & taller(X, Y))), inference(or_elim,[status(thm)],[13])). tff(15,plain, (![X: $i] : ((~room(X)) | (X = |'mary'|))), inference(and_elim,[status(thm)],[14])). tff(16,plain, (![X: $i] : ((~room(X)) | (X = |'mary'|))), inference(modus_ponens,[status(thm)],[15, 10])). tff(17,plain,( ![X: $i] : ((~room(X)) | (X = |'mary'|))), inference(skolemize,[status(sab)],[16])). tff(18,plain, (![X: $i] : ((~room(X)) | (X = |'mary'|))), inference(modus_ponens,[status(thm)],[17, 9])). tff(19,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(20,plain, (room(mary)), inference(and_elim,[status(thm)],[14])). tff(21,plain, (room(mary)), inference(modus_ponens,[status(thm)],[20, 19])). tff(22,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(23,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(mary)) | (mary = |'mary'|))), inference(quant_inst,[status(thm)],[])). tff(24,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(mary)) | (mary = |'mary'|)), inference(modus_ponens,[status(thm)],[23, 22])). tff(25,plain, (mary = |'mary'|), inference(unit_resolution,[status(thm)],[24, 21, 18])). tff(26,plain, (mary = fred), inference(transitivity,[status(thm)],[25, 7])). tff(27,plain, ((~(mary = fred)) <=> (~(mary = fred))), inference(rewrite,[status(thm)],[])). tff(28,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//21337710477640378606193.p','b14')). 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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[44])). tff(46,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)],[45])). tff(47,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)],[46])). tff(48,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)],[47])). tff(49,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)],[48])). tff(50,plain, ((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))), inference(and_elim,[status(thm)],[49])). tff(51,plain, (((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))), inference(and_elim,[status(thm)],[50])). tff(52,plain, ((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))), inference(and_elim,[status(thm)],[51])). tff(53,plain, (((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))), inference(and_elim,[status(thm)],[52])). tff(54,plain, ((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))), inference(and_elim,[status(thm)],[53])). tff(55,plain, (((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))), inference(and_elim,[status(thm)],[54])). tff(56,plain, ((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))), inference(and_elim,[status(thm)],[55])). tff(57,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)],[56])). tff(58,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)],[57])). tff(59,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)],[58])). tff(60,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)],[59])). tff(61,plain, (((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))), inference(and_elim,[status(thm)],[60])). tff(62,plain, ((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))), inference(and_elim,[status(thm)],[61])). tff(63,plain, (((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))), inference(and_elim,[status(thm)],[62])). tff(64,plain, ((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))), inference(and_elim,[status(thm)],[63])). tff(65,plain, (((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))), inference(and_elim,[status(thm)],[64])). tff(66,plain, ((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))), inference(and_elim,[status(thm)],[65])). tff(67,plain, (((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))), inference(and_elim,[status(thm)],[66])). tff(68,plain, ((~(mary = paul)) & (~(mary = fred))), inference(and_elim,[status(thm)],[67])). tff(69,plain, (~(mary = fred)), inference(and_elim,[status(thm)],[68])). tff(70,plain, (~(mary = fred)), inference(modus_ponens,[status(thm)],[69, 27])). tff(71,plain, ($false), inference(unit_resolution,[status(thm)],[70, 26])). tff(72,plain,(~(fred = |'mary'|)), inference(lemma,lemma(discharge,[]))). tff(73,plain, (((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(fred)) | (fred = |'mary'|))) <=> ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(fred)) | (fred = |'mary'|))), inference(rewrite,[status(thm)],[])). tff(74,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(fred)) | (fred = |'mary'|))), inference(quant_inst,[status(thm)],[])). tff(75,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(fred)) | (fred = |'mary'|)), inference(modus_ponens,[status(thm)],[74, 73])). tff(76,plain, ($false), inference(unit_resolution,[status(thm)],[75, 18, 72, 5])). tff(77,plain,(~room(fred)), inference(lemma,lemma(discharge,[]))). tff(78,plain, (^[X: $i] : refl((room(X) | (~like(fred, X))) <=> (room(X) | (~like(fred, X))))), inference(bind,[status(th)],[])). tff(79,plain, (![X: $i] : (room(X) | (~like(fred, X))) <=> ![X: $i] : (room(X) | (~like(fred, X)))), inference(quant_intro,[status(thm)],[78])). tff(80,plain, (![X: $i] : (room(X) | (~like(fred, X))) <=> ![X: $i] : (room(X) | (~like(fred, X)))), inference(rewrite,[status(thm)],[])). tff(81,plain, (![X: $i] : (room(X) | (~like(fred, X)))), inference(and_elim,[status(thm)],[14])). tff(82,plain, (![X: $i] : (room(X) | (~like(fred, X)))), inference(modus_ponens,[status(thm)],[81, 80])). tff(83,plain,( ![X: $i] : (room(X) | (~like(fred, X)))), inference(skolemize,[status(sab)],[82])). tff(84,plain, (![X: $i] : (room(X) | (~like(fred, X)))), inference(modus_ponens,[status(thm)],[83, 79])). tff(85,plain, (((~![X: $i] : (room(X) | (~like(fred, X)))) | (room(fred) | (~like(fred, fred)))) <=> ((~![X: $i] : (room(X) | (~like(fred, X)))) | room(fred) | (~like(fred, fred)))), inference(rewrite,[status(thm)],[])). tff(86,plain, ((~![X: $i] : (room(X) | (~like(fred, X)))) | (room(fred) | (~like(fred, fred)))), inference(quant_inst,[status(thm)],[])). tff(87,plain, ((~![X: $i] : (room(X) | (~like(fred, X)))) | room(fred) | (~like(fred, fred))), inference(modus_ponens,[status(thm)],[86, 85])). tff(88,plain, (~like(fred, fred)), inference(unit_resolution,[status(thm)],[87, 84, 77])). tff(89,assumption,(~((~room(X!4)) | (X!4 = |'mary'|))), introduced(assumption)). tff(90,plain, (((~room(X!4)) | (X!4 = |'mary'|)) | (~(X!4 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(91,plain, (~(X!4 = |'mary'|)), inference(unit_resolution,[status(thm)],[90, 89])). tff(92,plain, (((~room(X!4)) | (X!4 = |'mary'|)) | room(X!4)), inference(tautology,[status(thm)],[])). tff(93,plain, (room(X!4)), inference(unit_resolution,[status(thm)],[92, 89])). tff(94,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(95,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!4)) | (X!4 = |'mary'|))), inference(quant_inst,[status(thm)],[])). tff(96,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!4)) | (X!4 = |'mary'|)), inference(modus_ponens,[status(thm)],[95, 94])). tff(97,plain, ($false), inference(unit_resolution,[status(thm)],[96, 18, 93, 91])). tff(98,plain,((~room(X!4)) | (X!4 = |'mary'|)), inference(lemma,lemma(discharge,[]))). tff(99,plain, (((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : ((~like(X, Y)) | like(fred, Y) | (~taller(fred, X)))) <=> ((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : ((~like(X, Y)) | like(fred, Y) | (~taller(fred, X))))), inference(rewrite,[status(thm)],[])). tff(100,plain, (((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~(taller(fred, X) & (~like(fred, Y)) & like(X, Y)))) <=> ((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : ((~like(X, Y)) | like(fred, Y) | (~taller(fred, X))))), inference(rewrite,[status(thm)],[])). tff(101,plain, (((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~(taller(fred, X) & (~like(fred, Y)) & like(X, Y)))) <=> ((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~(taller(fred, X) & (~like(fred, Y)) & like(X, Y))))), inference(rewrite,[status(thm)],[])). tff(102,plain, ((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y)))), inference(rewrite,[status(thm)],[])). tff(103,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y))))), inference(monotonicity,[status(thm)],[102])). tff(104,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y))))), inference(rewrite,[status(thm)],[])). tff(105,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y)))), inference(or_elim,[status(thm)],[13])). tff(106,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y)))), inference(modus_ponens,[status(thm)],[105, 103])). tff(107,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y)))), inference(modus_ponens,[status(thm)],[106, 104])). tff(108,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : (taller(fred, X) & (~like(fred, Y)) & like(X, Y)))), inference(modus_ponens,[status(thm)],[107, 103])). 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!4)) (= X!4 |'mary'|)))) (a!4 (lambda ((X $i) (Y $i)) (let ((a!1 (and (taller fred X) (not (like fred Y)) (like X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!5 (exists ((X $i) (Y $i)) (and (taller fred X) (not (like fred Y)) (like X Y)))) (a!6 (forall ((X $i) (Y $i)) (let ((a!1 (and (taller fred X) (not (like fred Y)) (like 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)))

room(michael)&(![X]:(room(X)=>(X='michael')))& ((![X]:(taller(X,michael)))& ((?[X,Y]:(~room(X)&~room(Y)&(taller(miguel,X)&taller(miguel,Y))&(X!=Y))))& (![X]:(~room(X)=>(~like(miguel,X))))& (?[X,Y]:((taller(miguel,X))&(like(Y,miguel))&(taller(X,Y)))))

room(michael)&(![X]:(room(X)=>(X='michael')))& (?[X,Y]:((taller(miguel,X))&(~like(miguel,Y))&(like(X,Y))))

contradiction

neutral

entailment

Sharon, Theresa are the only persons in the room. “No one outside the room who is not Sharon is a tall tourist” if “Theresa neither is not tall nor is not liked by Gloria” and vice versa. Only one person outside the room likes Deanna. Sharon and Gloria like each other.

Sharon who does not like Gloria, is a rich tourist.

contradiction

-

room(sharon)&room(theresa)&(![X]:(room(X)=>(X='sharon'|X='theresa')))& (((~((~tall(theresa))|(~like(theresa,gloria))))<=>(~?[X]:(~room(X)=>(((X!=sharon)=>(tall(X)&tourist(X)))))))& (((?[X]:(~room(X)&like(deanna,X)))&(![X,Y]:((like(deanna,X)&like(deanna,Y))=>(X=Y)))))& ((like(sharon,gloria) & like(gloria,sharon))))

room(sharon)&room(theresa)&(![X]:(room(X)=>(X='sharon'|X='theresa')))& ((~like(gloria,sharon))&(rich(sharon)&tourist(sharon)))

neutral

neutral

contradiction

Carolina, Michael, Johanna, Glenda are the only persons in the room. Only one person outside the room does not hate Delores. Gladys is quieter than Glenda. Michael who is not hated by Delores, is a client of Gladys. Glenda and Michael hate each other.

Glenda who is a quiet person, is a client of Gladys.

neutral

% SZS status Satisfiable

room(carolina)&room(michael)&room(johanna)&room(glenda)&(![X]:(room(X)=>(X='carolina'|X='michael'|X='johanna'|X='glenda')))& ((((?[X]:(~room(X)&~hate(delores,X)))&(![X,Y]:((~hate(delores,X)&~hate(delores,Y))=>(X=Y)))))& (quieter(glenda,gladys))& ((~hate(michael,delores))&(client(gladys,michael)))& ((hate(glenda,michael) & hate(michael,glenda))))

room(carolina)&room(michael)&room(johanna)&room(glenda)&(![X]:(room(X)=>(X='carolina'|X='michael'|X='johanna'|X='glenda')))& ((quiet(glenda)&person(glenda))&(client(gladys,glenda)))

contradiction

contradiction

contradiction

Manuel, Jessie, Richard, Lori are the only persons in the room. Manuel is the quietest in the room if more than one person outside the room enjoys spelunking and vice versa. Manuel who does not like Joseph, is not liked by Joseph. Manuel is quieter than Joseph. More than one person outside the room enjoys spelunking. Only one person outside the room does not enjoy pottery. Manuel is not a coffee connoisseur or does not enjoy pottery or both.

Manuel is not a coffee connoisseur or is not liked by Joseph or both.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(mary_type, type, ( mary: $i)). tff(predb_type, type, ( predb: $i > $o)). tff(predc_type, type, ( predc: $i > $o)). tff(preda_type, type, ( preda: $i > $o)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(1,plain, ((~like(mary, john)) <=> (~like(mary, john))), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (preda(X) & preda(Y))) & (~(X = Y))) <=> ![X: $i] : quieter(X, mary)) & ((~like(john, mary)) & (~like(mary, john)))) & quieter(john, mary)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (preda(X) & preda(Y))) & (~(X = Y)))) & (?[X: $i] : ((~room(X)) & (~predc(X))) & ![X: $i, Y: $i] : (((~predc(X)) & (~predc(Y))) => (X = Y)))) & ((~predb(mary)) | (~predc(mary))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~predb(mary)) | (~like(mary, john)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & preda(X) & preda(Y) & (~(X = Y))) <=> ![X: $i] : quieter(X, mary)) & (~like(john, mary)) & (~like(mary, john)) & quieter(john, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & preda(X) & preda(Y) & (~(X = Y))) & ?[X: $i] : ((~room(X)) & (~predc(X))) & ![X: $i, Y: $i] : ((~((~predc(X)) & (~predc(Y)))) | (X = Y)) & ((~predb(mary)) | (~predc(mary))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (preda(X) & preda(Y))) & (~(X = Y))) <=> ![X: $i] : quieter(X, mary)) & ((~like(john, mary)) & (~like(mary, john)))) & quieter(john, mary)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & (preda(X) & preda(Y))) & (~(X = Y)))) & (?[X: $i] : ((~room(X)) & (~predc(X))) & ![X: $i, Y: $i] : (((~predc(X)) & (~predc(Y))) => (X = Y)))) & ((~predb(mary)) | (~predc(mary))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~predb(mary)) | (~like(mary, john)))))), file('/mnt/tmpfs//8144370291588534845427393.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & preda(X) & preda(Y) & (~(X = Y))) <=> ![X: $i] : quieter(X, mary)) & (~like(john, mary)) & (~like(mary, john)) & quieter(john, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & preda(X) & preda(Y) & (~(X = Y))) & ?[X: $i] : ((~room(X)) & (~predc(X))) & ![X: $i, Y: $i] : ((~((~predc(X)) & (~predc(Y)))) | (X = Y)) & ((~predb(mary)) | (~predc(mary))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & preda(X) & preda(Y) & (~(X = Y))) <=> ![X: $i] : quieter(X, mary)) & (~like(john, mary)) & (~like(mary, john)) & quieter(john, mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & preda(X) & preda(Y) & (~(X = Y))) & ?[X: $i] : ((~room(X)) & (~predc(X))) & ![X: $i, Y: $i] : ((~((~predc(X)) & (~predc(Y)))) | (X = Y)) & ((~predb(mary)) | (~predc(mary)))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~like(mary, john)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (~like(mary, john)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (((~predb(mary)) | (~like(mary, john))) | like(mary, john)), inference(tautology,[status(thm)],[])). tff(9,plain, ((~predb(mary)) | (~like(mary, john))), inference(unit_resolution,[status(thm)],[8, 7])). tff(10,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(11,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(12,plain, (room(alice)), inference(modus_ponens,[status(thm)],[11, 10])). tff(13,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(14,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(15,plain, (room(fred)), inference(modus_ponens,[status(thm)],[14, 13])). tff(16,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(17,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(18,plain, (room(paul)), inference(modus_ponens,[status(thm)],[17, 16])). tff(19,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(20,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(21,plain, (room(mary)), inference(modus_ponens,[status(thm)],[20, 19])). tff(22,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~predb(mary)) | (~like(mary, john))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~predb(mary)) | (~like(mary, john)))))), inference(rewrite,[status(thm)],[])). tff(23,plain, ((~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))), inference(rewrite,[status(thm)],[])). tff(24,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~predb(mary)) | (~like(mary, john))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~predb(mary)) | (~like(mary, john)))))), inference(monotonicity,[status(thm)],[23])). tff(25,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~predb(mary)) | (~like(mary, john))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~((~predb(mary)) | (~like(mary, john)))))), inference(transitivity,[status(thm)],[24, 22])). tff(26,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john))))), inference(rewrite,[status(thm)],[])). tff(27,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john)))))), inference(monotonicity,[status(thm)],[26])). tff(28,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john)))))), inference(rewrite,[status(thm)],[])). tff(29,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john))))), inference(or_elim,[status(thm)],[4])). tff(30,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john))))), inference(modus_ponens,[status(thm)],[29, 27])). tff(31,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john))))), inference(modus_ponens,[status(thm)],[30, 28])). tff(32,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | (~like(mary, john))))), inference(modus_ponens,[status(thm)],[31, 27])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!4 |'alice'|) (= X!4 |'fred'|) (= X!4 |'paul'|) (= X!4 |'mary'|) (not (room X!4))))) (a!7 (not (or (not (predb mary)) (not (like mary john)))))) (let ((a!8 (and (room mary) (room paul) (room fred) (room alice) a!5 (or (not (predb mary)) (not (like mary john)))))) (let ((a!9 (~ (not a!8) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 a!7)))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ a!7 a!7)) a!9))))

room(manuel)&room(jessie)&room(richard)&room(lori)&(![X]:(room(X)=>(X='manuel'|X='jessie'|X='richard'|X='lori')))& ((((?[X,Y]:(~room(X)&~room(Y)&(enjoys_spelunking(X)&enjoys_spelunking(Y))&(X!=Y))))<=>(![X]:(quieter(X,manuel))))& ((~like(joseph,manuel))&(~like(manuel,joseph)))& (quieter(joseph,manuel))& ((?[X,Y]:(~room(X)&~room(Y)&(enjoys_spelunking(X)&enjoys_spelunking(Y))&(X!=Y))))& (((?[X]:(~room(X)&does_not_enjoy_pottery(X)))&(![X,Y]:((does_not_enjoy_pottery(X)&does_not_enjoy_pottery(Y))=>(X=Y)))))& (((is_not_a_coffee_connoisseur(manuel))|(does_not_enjoy_pottery(manuel)))))

room(manuel)&room(jessie)&room(richard)&room(lori)&(![X]:(room(X)=>(X='manuel'|X='jessie'|X='richard'|X='lori')))& (((is_not_a_coffee_connoisseur(manuel))|(~like(manuel,joseph))))

entailment

entailment

entailment

Alma who is not hated by Deborah, hates Deborah.

Alma does not hate Deborah or hates Deborah or both.

entailment

% SZS status Unsatisfiable % SZS output start Proof 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(mary_type, type, ( mary: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(1,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~hate(mary, paul)) & hate(paul, mary))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~hate(paul, mary)) | hate(paul, mary))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~hate(mary, paul)) & hate(paul, mary))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~hate(mary, paul)) & hate(paul, mary))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((~hate(paul, mary)) | hate(paul, mary))))), file('/mnt/tmpfs//6301874665188961233201683.p','negated')). tff(4,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~hate(mary, paul)) & hate(paul, mary))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~hate(mary, paul)) & hate(paul, mary)), inference(or_elim,[status(thm)],[4])). tff(6,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (room(mary)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))), inference(rewrite,[status(thm)],[])). tff(9,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|))))), inference(monotonicity,[status(thm)],[8])). tff(10,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|))))), inference(rewrite,[status(thm)],[])). tff(11,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))), inference(or_elim,[status(thm)],[4])). tff(12,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))), inference(modus_ponens,[status(thm)],[11, 9])). tff(13,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))), inference(modus_ponens,[status(thm)],[12, 10])). tff(14,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)))), inference(modus_ponens,[status(thm)],[13, 9])). 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!0)) (= X!0 |'mary'|))))) (let ((a!4 (~ (not (and (room mary) a!2)) (or (not (room mary)) a!3)))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) a!4)))

room(alma)&(![X]:(room(X)=>(X='alma')))& ((~hate(alma,deborah))&(hate(deborah,alma)))

room(alma)&(![X]:(room(X)=>(X='alma')))& (((~hate(deborah,alma))|(hate(deborah,alma))))

contradiction

entailment

contradiction

George is the only person in the room. 'George either is a happy creative person or is not a tall european' if 'someone who does not practice kickboxing hate someone who is not liked by Mary'. 'More than one person outside the room likes Mary' only if 'someone who does not like Robert hate someone who practices kickboxing'. More than one person outside the room is not creative. George is not a tall person or is taller than Fernando or both. Someone who is not a tall creative happy tourist is taller than someone who does not hate Armando. George is the tallest in the room. Only one person outside the room is liked by Robert. More than one person outside the room likes Mary.

Someone who is not a tall european is taller than someone who is liked by Mary.

neutral

% SZS status Satisfiable

room(george)&(![X]:(room(X)=>(X='george')))& (((?[X,Y]:((does_not_practice_kickboxing(X))&(~like(Y,mary))&(hate(X,Y))))=>((((happy(george)&creative(george)&person(george))|(~(tall(george)&european(george))))&(~((happy(george)&creative(george)&person(george))|(~(tall(george)&european(george))))))))& (((?[X,Y]:(~room(X)&~room(Y)&(like(mary,X)&like(mary,Y))&(X!=Y))))=>(?[X,Y]:((~like(robert,X))&(practices_kickboxing(Y))&(hate(X,Y)))))& ((?[X,Y]:(~room(X)&~room(Y)&(~creative(X)&~creative(Y))&(X!=Y))))& (((~(tall(george)&person(george)))|(taller(fernando,george))))& (?[X,Y]:((~(tall(X)&creative(X)&happy(X)&tourist(X)))&(~hate(armando,Y))&(taller(X,Y))))& (![X]:(taller(X,george)))& (((?[X]:(~room(X)&like(X,robert)))&(![X,Y]:((like(X,robert)&like(Y,robert))=>(X=Y)))))& ((?[X,Y]:(~room(X)&~room(Y)&(like(mary,X)&like(mary,Y))&(X!=Y)))))

room(george)&(![X]:(room(X)=>(X='george')))& (?[X,Y]:((~(tall(X)&european(X)))&(like(Y,mary))&(taller(X,Y))))

contradiction

entailment

neutral

Ronnie, Guadalupe are the only persons in the room. "Someone who owns a vinyl record player is quieter than someone who does not hate Sarah" if "Ronnie is the quietest in the room". "Ronnie is the quietest in the room" if "Ronnie and Chantelle hate each other" and vice versa. Everyone outside the room who is a tall tourist is a tall happy person. Ronnie is the least tall in the room. Ronnie hates Sarah or owns a vinyl record player or both. Someone who is not tall, not quiet, not brave is a client of someone who is not happy, not quiet, not tall, not brave. Only one person outside the room does not hate Chantelle. Ronnie does not own a vinyl record player.

It is not the case that 'Ronnie is a quiet tall person or hates Chantelle or both'.

contradiction

-

room(ronnie)&room(guadalupe)&(![X]:(room(X)=>(X='ronnie'|X='guadalupe')))& (((![X]:(quieter(X,ronnie)))=>(?[X,Y]:((owns_a_vinyl_record_player(X))&(~hate(sarah,Y))&(quieter(X,Y)))))& (((hate(ronnie,chantelle) & hate(chantelle,ronnie)))<=>(![X]:(quieter(X,ronnie))))& (![X]:(~room(X)=>(((tall(X)&tourist(X))=>(tall(X)&happy(X)&person(X))))))& (![X]:(taller(ronnie,X)))& (((hate(sarah,ronnie))|(owns_a_vinyl_record_player(ronnie))))& (?[X,Y]:((~tall(X)&~quiet(X)&~brave(X))&(~happy(Y)&~quiet(Y)&~tall(Y)&~brave(Y))&(client(X,Y))))& (((?[X]:(~room(X)&~hate(chantelle,X)))&(![X,Y]:((~hate(chantelle,X)&~hate(chantelle,Y))=>(X=Y)))))& (does_not_own_a_vinyl_record_player(ronnie)))

room(ronnie)&room(guadalupe)&(![X]:(room(X)=>(X='ronnie'|X='guadalupe')))& (~(((quiet(ronnie)&tall(ronnie)&person(ronnie))|(hate(chantelle,ronnie)))))

entailment

entailment

contradiction

Despina is the only person in the room. Someone outside the room who can play the harmonica does not like Johnathan if Devorah is a client of Despina. Despina neither is not liked by Olga nor is not liked by Johnathan. Only one person outside the room does not hate Olga. More than one person outside the room is a client of Devorah. Despina is the least quiet in the room. More than one person outside the room is a happy creative person.

Despina likes Olga and is not a creative european.

contradiction

-

room(despina)&(![X]:(room(X)=>(X='despina')))& (((client(despina,devorah))=>(?[X]:(~room(X)=>(((can_play_the_harmonica(X))=>(~like(johnathanathan,X)))))))& (~((~like(despina,olga))|(~like(despina,johnathanathan))))& (((?[X]:(~room(X)&~hate(olga,X)))&(![X,Y]:((~hate(olga,X)&~hate(olga,Y))=>(X=Y)))))& ((?[X,Y]:(~room(X)&~room(Y)&(client(devorah,X)&client(devorah,Y))&(X!=Y))))& (![X]:(quieter(despina,X)))& ((?[X,Y]:(~room(X)&~room(Y)&(happy(X)&creative(X)&person(X)&happy(Y)&creative(Y)&person(Y))&(X!=Y)))))

room(despina)&(![X]:(room(X)=>(X='despina')))& ((like(olga,despina))&(~(creative(despina)&european(despina))))

contradiction

contradiction

neutral

Kim, Barbara, Cheryl, Juliane are the only persons in the room. Cheryl and Kim do not like Jorge. Cheryl who is a quiet person, is hated by Jorge. Someone who does not like Jorge is quieter than someone who is not liked by John. Everyone in the room who is not Cheryl does not like John. Someone in the room who is hated by Jorge is not a happy brave tall person. Juliane who is a client of Jorge, is taller than John.

Cheryl neither is liked by Jorge nor is not brave, not quiet, not tall.

entailment

% 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(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(fred_type, type, ( fred: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(lucy_type, type, ( lucy: $i)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(person_type, type, ( person: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(paul_type, type, ( paul: $i)). tff(john_type, type, ( john: $i)). tff(1,plain, (hate(fred, susan) <=> hate(fred, susan)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((~like(susan, fred)) & (~like(susan, mary))) & ((quiet(fred) & person(fred)) & hate(fred, susan))) & ?[X: $i, Y: $i] : (((~like(susan, X)) & (~like(Y, lucy))) & quieter(X, Y))) & ![X: $i] : (room(X) => ((~(X = fred)) => (~like(lucy, X))))) & ?[X: $i] : (room(X) => (hate(X, susan) => (~(((happy(X) & brave(X)) & tall(X)) & person(X)))))) & (client(susan, alice) & taller(lucy, alice)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(like(fred, susan) | (((~brave(fred)) & (~quiet(fred))) & (~tall(fred)))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(susan, fred)) & (~like(susan, mary)) & quiet(fred) & person(fred) & hate(fred, susan) & ?[X: $i, Y: $i] : ((~like(susan, X)) & (~like(Y, lucy)) & quieter(X, Y)) & ![X: $i] : ((~like(lucy, X)) | (X = fred) | (~room(X))) & ?[X: $i] : ((~room(X)) | (~hate(X, susan)) | (~(happy(X) & brave(X) & tall(X) & person(X)))) & client(susan, alice) & taller(lucy, alice))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((~like(susan, fred)) & (~like(susan, mary))) & ((quiet(fred) & person(fred)) & hate(fred, susan))) & ?[X: $i, Y: $i] : (((~like(susan, X)) & (~like(Y, lucy))) & quieter(X, Y))) & ![X: $i] : (room(X) => ((~(X = fred)) => (~like(lucy, X))))) & ?[X: $i] : (room(X) => (hate(X, susan) => (~(((happy(X) & brave(X)) & tall(X)) & person(X)))))) & (client(susan, alice) & taller(lucy, alice)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(like(fred, susan) | (((~brave(fred)) & (~quiet(fred))) & (~tall(fred)))))))), file('/mnt/tmpfs//8272841622497688283376948.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(susan, fred)) & (~like(susan, mary)) & quiet(fred) & person(fred) & hate(fred, susan) & ?[X: $i, Y: $i] : ((~like(susan, X)) & (~like(Y, lucy)) & quieter(X, Y)) & ![X: $i] : ((~like(lucy, X)) | (X = fred) | (~room(X))) & ?[X: $i] : ((~room(X)) | (~hate(X, susan)) | (~(happy(X) & brave(X) & tall(X) & person(X)))) & client(susan, alice) & taller(lucy, alice))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred)))))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~like(susan, fred)) & (~like(susan, mary)) & quiet(fred) & person(fred) & hate(fred, susan) & ?[X: $i, Y: $i] : ((~like(susan, X)) & (~like(Y, lucy)) & quieter(X, Y)) & ![X: $i] : ((~like(lucy, X)) | (X = fred) | (~room(X))) & ?[X: $i] : ((~room(X)) | (~hate(X, susan)) | (~(happy(X) & brave(X) & tall(X) & person(X)))) & client(susan, alice) & taller(lucy, alice)), inference(or_elim,[status(thm)],[4])). tff(6,plain, (hate(fred, susan)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (hate(fred, susan)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((~(fred = susan)) <=> (~(fred = susan))), inference(rewrite,[status(thm)],[])). tff(9,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//8272841622497688283376948.p','b14')). tff(10,plain, (((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))), inference(and_elim,[status(thm)],[9])). tff(11,plain, ((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))), inference(and_elim,[status(thm)],[10])). tff(12,plain, (((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))), inference(and_elim,[status(thm)],[11])). tff(13,plain, ((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))), inference(and_elim,[status(thm)],[12])). tff(14,plain, (((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))), inference(and_elim,[status(thm)],[13])). tff(15,plain, ((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))), inference(and_elim,[status(thm)],[14])). tff(16,plain, (((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))), inference(and_elim,[status(thm)],[15])). tff(17,plain, ((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))), inference(and_elim,[status(thm)],[16])). tff(18,plain, (((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))), inference(and_elim,[status(thm)],[17])). tff(19,plain, ((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))), inference(and_elim,[status(thm)],[18])). tff(20,plain, (((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))), inference(and_elim,[status(thm)],[19])). tff(21,plain, ((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))), inference(and_elim,[status(thm)],[20])). tff(22,plain, (((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))), inference(and_elim,[status(thm)],[21])). tff(23,plain, ((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))), inference(and_elim,[status(thm)],[22])). tff(24,plain, (((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))), inference(and_elim,[status(thm)],[23])). tff(25,plain, ((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))), inference(and_elim,[status(thm)],[24])). tff(26,plain, (((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))), inference(and_elim,[status(thm)],[25])). tff(27,plain, ((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))), inference(and_elim,[status(thm)],[26])). tff(28,plain, (((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))), inference(and_elim,[status(thm)],[27])). tff(29,plain, ((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))), inference(and_elim,[status(thm)],[28])). tff(30,plain, (((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))), inference(and_elim,[status(thm)],[29])). tff(31,plain, ((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))), inference(and_elim,[status(thm)],[30])). tff(32,plain, (((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))), inference(and_elim,[status(thm)],[31])). tff(33,plain, ((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))), inference(and_elim,[status(thm)],[32])). tff(34,plain, (((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))), inference(and_elim,[status(thm)],[33])). tff(35,plain, (~(fred = susan)), inference(and_elim,[status(thm)],[34])). tff(36,plain, (~(fred = susan)), inference(modus_ponens,[status(thm)],[35, 8])). tff(37,plain, (^[X: $i, Y: $i] : refl(((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y))))), inference(bind,[status(th)],[])). tff(38,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(quant_intro,[status(thm)],[37])). tff(39,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(rewrite,[status(thm)],[])). tff(40,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite((like(X, Y) => (~hate(X, Y))) <=> ((~hate(X, Y)) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))))), rewrite(((~(X = Y)) => ((~hate(X, Y)) | (~like(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), (((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))))), inference(bind,[status(th)],[])). tff(41,plain, (![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y)))) <=> ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(quant_intro,[status(thm)],[40])). tff(42,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (like(X, Y) => (~hate(X, Y))))), file('/mnt/tmpfs//8272841622497688283376948.p','b0')). tff(43,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(modus_ponens,[status(thm)],[42, 41])). tff(44,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(modus_ponens,[status(thm)],[43, 39])). tff(45,plain,( ![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(skolemize,[status(sab)],[44])). tff(46,plain, (![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))), inference(modus_ponens,[status(thm)],[45, 38])). tff(47,plain, (((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((fred = susan) | (~hate(fred, susan)) | (~like(fred, susan)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (fred = susan) | (~hate(fred, susan)) | (~like(fred, susan)))), inference(rewrite,[status(thm)],[])). tff(48,plain, (((~hate(fred, susan)) | (fred = susan) | (~like(fred, susan))) <=> ((fred = susan) | (~hate(fred, susan)) | (~like(fred, susan)))), inference(rewrite,[status(thm)],[])). tff(49,plain, (((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(fred, susan)) | (fred = susan) | (~like(fred, susan)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((fred = susan) | (~hate(fred, susan)) | (~like(fred, susan))))), inference(monotonicity,[status(thm)],[48])). tff(50,plain, (((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(fred, susan)) | (fred = susan) | (~like(fred, susan)))) <=> ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (fred = susan) | (~hate(fred, susan)) | (~like(fred, susan)))), inference(transitivity,[status(thm)],[49, 47])). tff(51,plain, ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | ((~hate(fred, susan)) | (fred = susan) | (~like(fred, susan)))), inference(quant_inst,[status(thm)],[])). tff(52,plain, ((~![X: $i, Y: $i] : ((~hate(X, Y)) | (X = Y) | (~like(X, Y)))) | (fred = susan) | (~hate(fred, susan)) | (~like(fred, susan))), inference(modus_ponens,[status(thm)],[51, 50])). tff(53,plain, (~like(fred, susan)), inference(unit_resolution,[status(thm)],[52, 46, 36, 7])). tff(54,plain, (quiet(fred) <=> quiet(fred)), inference(rewrite,[status(thm)],[])). tff(55,plain, (quiet(fred)), inference(and_elim,[status(thm)],[5])). tff(56,plain, (quiet(fred)), inference(modus_ponens,[status(thm)],[55, 54])). tff(57,plain, ((brave(fred) | quiet(fred) | tall(fred)) | (~quiet(fred))), inference(tautology,[status(thm)],[])). tff(58,plain, (brave(fred) | quiet(fred) | tall(fred)), inference(unit_resolution,[status(thm)],[57, 56])). tff(59,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(60,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(61,plain, (room(alice)), inference(modus_ponens,[status(thm)],[60, 59])). tff(62,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(63,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(64,plain, (room(fred)), inference(modus_ponens,[status(thm)],[63, 62])). tff(65,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(66,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(67,plain, (room(paul)), inference(modus_ponens,[status(thm)],[66, 65])). tff(68,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(69,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(70,plain, (room(mary)), inference(modus_ponens,[status(thm)],[69, 68])). tff(71,plain, ((like(fred, susan) | (~(brave(fred) | quiet(fred) | tall(fred))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> (like(fred, susan) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(brave(fred) | quiet(fred) | tall(fred))))), inference(rewrite,[status(thm)],[])). tff(72,plain, ((~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))), inference(rewrite,[status(thm)],[])). tff(73,plain, (((~brave(fred)) & (~quiet(fred)) & (~tall(fred))) <=> (~(brave(fred) | quiet(fred) | tall(fred)))), inference(rewrite,[status(thm)],[])). tff(74,plain, ((like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> (like(fred, susan) | (~(brave(fred) | quiet(fred) | tall(fred))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))), inference(monotonicity,[status(thm)],[73, 72])). tff(75,plain, ((like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> (like(fred, susan) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(brave(fred) | quiet(fred) | tall(fred))))), inference(transitivity,[status(thm)],[74, 71])). tff(76,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))) <=> (like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))), inference(rewrite,[status(thm)],[])). tff(77,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred)))))), inference(monotonicity,[status(thm)],[72])). tff(78,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))) <=> (like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))), inference(transitivity,[status(thm)],[77, 76])). tff(79,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred)))))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))))), inference(rewrite,[status(thm)],[])). tff(80,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred)))))))), inference(monotonicity,[status(thm)],[79])). tff(81,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred)))))))), inference(rewrite,[status(thm)],[])). tff(82,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))))), inference(or_elim,[status(thm)],[4])). tff(83,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))))), inference(modus_ponens,[status(thm)],[82, 80])). tff(84,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))))), inference(modus_ponens,[status(thm)],[83, 81])). tff(85,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(like(fred, susan) | ((~brave(fred)) & (~quiet(fred)) & (~tall(fred))))))), inference(modus_ponens,[status(thm)],[84, 80])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!3 |'alice'|) (= X!3 |'fred'|) (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3))))) (a!7 (or (like fred susan) (and (not (brave fred)) (not (quiet fred)) (not (tall fred)))))) (let ((a!8 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 (not a!7))) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 a!7)))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ a!7 a!7)) a!8)))

room(kim)&room(barbara)&room(cheryl)&room(juliane)&(![X]:(room(X)=>(X='kim'|X='barbara'|X='cheryl'|X='juliane')))& ((~like(jorge,cheryl)&~like(jorge,kim))& ((quiet(cheryl)&person(cheryl))&(hate(cheryl,jorge)))& (?[X,Y]:((~like(jorge,X))&(~like(Y,john))&(quieter(X,Y))))& (![X]:(room(X)=>(((X!=cheryl)=>(~like(john,X))))))& (?[X]:(room(X)=>(((hate(X,jorge))=>(~(happy(X)&brave(X)&tall(X)&person(X)))))))& ((client(jorge,juliane))&(taller(john,juliane))))

room(kim)&room(barbara)&room(cheryl)&room(juliane)&(![X]:(room(X)=>(X='kim'|X='barbara'|X='cheryl'|X='juliane')))& (~((like(cheryl,jorge))|(~brave(cheryl)&~quiet(cheryl)&~tall(cheryl))))

contradiction

contradiction

contradiction

Jennifer, Tina are the only persons in the room. "More than one person in the room is not liked by Orville" unless "Jennifer is a quiet happy rich tourist or does not play a musical instrument or both". "It is not the case that 'only one person outside the room is hated by Orville'" if "Tina either does not enjoy macrame or is not liked by Erin" and vice versa. "More than one person outside the room does not hate Erin" if "more than one person in the room is not Jennifer". "Jennifer is not a quiet person" unless "Tina neither is quieter than Orville nor is a rich person". Tina and Jennifer are respectively quiet and rich. Tina is a rich tourist or does not like Orville or both. Jennifer and Tina are respectively happy and quiet. It is not the case that 'Tina is the least quiet in the room'. Tina is the least rich in the room. Jennifer is a quiet happy rich tourist or is richer than Erin or both.

More than one person in the room is a quiet rich creative happy tourist.

contradiction

-

room(jennifer)&room(tina)&(![X]:(room(X)=>(X='jennifer'|X='tina')))& ((~(((quiet(jennifer)&happy(jennifer)&rich(jennifer)&tourist(jennifer))|(does_not_play_a_musical_instrument(jennifer))))=>((?[X,Y]:(room(X)&room(Y)&(~like(X,orville)&~like(Y,orville))&(X!=Y)))))& (((((does_not_enjoy_macrame(tina))|(~like(tina,erin)))&(~((does_not_enjoy_macrame(tina))|(~like(tina,erin))))))<=>(~(((?[X]:(~room(X)&hate(X,orville)))&(![X,Y]:((hate(X,orville)&hate(Y,orville))=>(X=Y)))))))& (((?[X,Y]:(room(X)&room(Y)&(X!=jennifer&Y!=jennifer)&(X!=Y))))=>((?[X,Y]:(~room(X)&~room(Y)&(~hate(erin,X)&~hate(erin,Y))&(X!=Y)))))& (~(~((quieter(orville,tina))|(rich(tina)&person(tina))))=>(~(quiet(jennifer)&person(jennifer))))& ((quiet(tina))&(rich(jennifer)))& (((rich(tina)&tourist(tina))|(~like(orville,tina))))& ((happy(jennifer))&(quiet(tina)))& (~(![X]:(quieter(tina,X))))& (![X]:(richer(tina,X)))& (((quiet(jennifer)&happy(jennifer)&rich(jennifer)&tourist(jennifer))|(richer(erin,jennifer)))))

room(jennifer)&room(tina)&(![X]:(room(X)=>(X='jennifer'|X='tina')))& ((?[X,Y]:(room(X)&room(Y)&(quiet(X)&rich(X)&creative(X)&happy(X)&tourist(X)&quiet(Y)&rich(Y)&creative(Y)&happy(Y)&tourist(Y))&(X!=Y))))

neutral

neutral

entailment

Nathan, Teddy, Gabrielle, Joann are the only persons in the room. “Teddy and Joann are respectively tall and creative” unless “everyone outside the room is taller than Willard”. If “someone who does not hate Arthur is a client of someone who hates Willard” then “Joann is not tall and is not a creative european” otherwise “Joann neither is hated by Arthur nor is hated by Willard”. Nathan and Joann are respectively creative and tall. Nathan is a tall european and does not hate Arthur. More than one person outside the room hates Willard. Nathan is the tallest in the room. Only one person outside the room does not read mystery novels. Joann does not hate Arthur. Nathan who is hated by Arthur, is a creative european. It is not the case that 'Teddy who is taller than Arthur, does not hate Arthur'. Teddy is not tall, not creative and is not hated by Willard.

Teddy is hated by Willard or is a quiet happy creative tall european or both.

contradiction

-

room(nathan)&room(teddy)&room(gabrielle)&room(joann)&(![X]:(room(X)=>(X='nathan'|X='teddy'|X='gabrielle'|X='joann')))& ((~(![X]:(~room(X)=>(taller(willard,X))))=>((tall(teddy))&(creative(joann))))& (((?[X,Y]:((~hate(arthur,X))&(hate(willard,Y))&(client(X,Y))))=>((~tall(joann))&(~(creative(joann)&european(joann)))))|((~(?[X,Y]:((~hate(arthur,X))&(hate(willard,Y))&(client(X,Y)))))=>(~((hate(joann,arthur))|(hate(joann,willard))))))& ((creative(nathan))&(tall(joann)))& ((tall(nathan)&european(nathan))&(~hate(arthur,nathan)))& ((?[X,Y]:(~room(X)&~room(Y)&(hate(willard,X)&hate(willard,Y))&(X!=Y))))& (![X]:(taller(X,nathan)))& (((?[X]:(~room(X)&does_not_read_mystery_novels(X)))&(![X,Y]:((does_not_read_mystery_novels(X)&does_not_read_mystery_novels(Y))=>(X=Y)))))& (~hate(arthur,joann))& ((hate(nathan,arthur))&(creative(nathan)&european(nathan)))& (~((taller(arthur,teddy))&(~hate(arthur,teddy))))& ((~tall(teddy)&~creative(teddy))&(~hate(teddy,willard))))

room(nathan)&room(teddy)&room(gabrielle)&room(joann)&(![X]:(room(X)=>(X='nathan'|X='teddy'|X='gabrielle'|X='joann')))& (((hate(teddy,willard))|(quiet(teddy)&happy(teddy)&creative(teddy)&tall(teddy)&european(teddy))))

entailment

entailment

contradiction

Willie, Michael, Sharon are the only persons in the room. "No one in the room is taller than Deneen" only if "Sharon and Michael hate each other". If "Michael is not a tall brave happy person or hates Deneen or both" then "someone who hates Deneen is taller than someone who is hated by Deneen" otherwise "someone in the room is not Sharon". Michael is the tallest in the room. Only one person outside the room is a brave person. Michael enjoys snowboarding or is not hated by Deneen or both. Michael and Willie are not happy. Sharon is the least tall in the room. Michael is not a tall happy person or is not Willie or both. More than one person in the room is taller than Deneen. Someone who is not tall hate someone who enjoys snowboarding.

Willie is a tall brave creative happy person or is a brave tall creative person or both.

contradiction

-

room(willie)&room(michael)&room(sharon)&(![X]:(room(X)=>(X='willie'|X='michael'|X='sharon')))& (((~?[X]:(room(X)=>(taller(deneen,X))))=>((hate(sharon,michael) & hate(michael,sharon))))& (((((~(tall(michael)&brave(michael)&happy(michael)&person(michael)))|(hate(deneen,michael))))=>(?[X,Y]:((hate(deneen,X))&(hate(Y,deneen))&(taller(X,Y)))))|((~(((~(tall(michael)&brave(michael)&happy(michael)&person(michael)))|(hate(deneen,michael)))))=>(?[X]:(room(X)=>(X!=sharon)))))& (![X]:(taller(X,michael)))& (((?[X]:(~room(X)&brave(X)&person(X)))&(![X,Y]:((brave(X)&person(X)&brave(Y)&person(Y))=>(X=Y)))))& (((enjoys_snowboarding(michael))|(~hate(michael,deneen))))& (~happy(michael)&~happy(willie))& (![X]:(taller(sharon,X)))& (((~(tall(michael)&happy(michael)&person(michael)))|(michael!=willie)))& ((?[X,Y]:(room(X)&room(Y)&(taller(deneen,X)&taller(deneen,Y))&(X!=Y))))& (?[X,Y]:((~tall(X))&(enjoys_snowboarding(Y))&(hate(X,Y)))))

room(willie)&room(michael)&room(sharon)&(![X]:(room(X)=>(X='willie'|X='michael'|X='sharon')))& (((tall(willie)&brave(willie)&creative(willie)&happy(willie)&person(willie))|(brave(willie)&tall(willie)&creative(willie)&person(willie))))

neutral

neutral

neutral

Rose, Kayla, Tiffany, Diane are the only persons in the room. 'Everyone outside the room who is liked by Dennis likes Jesse' if 'everyone outside the room who is not Tiffany likes Jesse'. Kayla owns a telescope. Rose likes Jesse or owns a telescope or both. Kayla owns a telescope or is liked by Dennis or both. Someone who owns a telescope like someone who is not creative.

Kayla is not liked by Dennis or owns a telescope or both.

entailment

% 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(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(paul_type, type, ( paul: $i)). tff(predb_type, type, ( predb: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(lucy_type, type, ( lucy: $i)). tff(fred_type, type, ( fred: $i)). tff(alice_type, type, ( alice: $i)). tff(1,plain, (predb(paul) <=> predb(paul)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((![X: $i] : ((~room(X)) => ((~(X = fred)) => like(lucy, X))) => ![X: $i] : ((~room(X)) => (like(X, john) => like(lucy, X)))) & predb(paul)) & (like(lucy, mary) | predb(mary))) & (predb(paul) | like(paul, john))) & ?[X: $i, Y: $i] : ((predb(X) & (~creative(Y))) & like(X, Y)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~like(paul, john)) | predb(paul))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : (like(lucy, X) | room(X) | (X = fred))) | ![X: $i] : (like(lucy, X) | room(X) | (~like(X, john)))) & predb(paul) & (like(lucy, mary) | predb(mary)) & (predb(paul) | like(paul, john)) & ?[X: $i, Y: $i] : (predb(X) & (~creative(Y)) & like(X, Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((![X: $i] : ((~room(X)) => ((~(X = fred)) => like(lucy, X))) => ![X: $i] : ((~room(X)) => (like(X, john) => like(lucy, X)))) & predb(paul)) & (like(lucy, mary) | predb(mary))) & (predb(paul) | like(paul, john))) & ?[X: $i, Y: $i] : ((predb(X) & (~creative(Y))) & like(X, Y)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~like(paul, john)) | predb(paul))))), file('/mnt/tmpfs//6325452485085062563457542.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : (like(lucy, X) | room(X) | (X = fred))) | ![X: $i] : (like(lucy, X) | room(X) | (~like(X, john)))) & predb(paul) & (like(lucy, mary) | predb(mary)) & (predb(paul) | like(paul, john)) & ?[X: $i, Y: $i] : (predb(X) & (~creative(Y)) & like(X, Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : (like(lucy, X) | room(X) | (X = fred))) | ![X: $i] : (like(lucy, X) | room(X) | (~like(X, john)))) & predb(paul) & (like(lucy, mary) | predb(mary)) & (predb(paul) | like(paul, john)) & ?[X: $i, Y: $i] : (predb(X) & (~creative(Y)) & like(X, Y))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (predb(paul)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (predb(paul)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((predb(paul) | (~like(paul, john))) | (~predb(paul))), inference(tautology,[status(thm)],[])). tff(9,plain, (predb(paul) | (~like(paul, john))), inference(unit_resolution,[status(thm)],[8, 7])). tff(10,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(11,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(12,plain, (room(alice)), inference(modus_ponens,[status(thm)],[11, 10])). tff(13,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(14,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(15,plain, (room(fred)), inference(modus_ponens,[status(thm)],[14, 13])). tff(16,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(17,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(18,plain, (room(paul)), inference(modus_ponens,[status(thm)],[17, 16])). tff(19,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(20,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(21,plain, (room(mary)), inference(modus_ponens,[status(thm)],[20, 19])). tff(22,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(predb(paul) | (~like(paul, john))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(predb(paul) | (~like(paul, john)))))), inference(rewrite,[status(thm)],[])). tff(23,plain, ((~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))), inference(rewrite,[status(thm)],[])). tff(24,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(predb(paul) | (~like(paul, john))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(predb(paul) | (~like(paul, john)))))), inference(monotonicity,[status(thm)],[23])). tff(25,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(predb(paul) | (~like(paul, john))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(predb(paul) | (~like(paul, john)))))), inference(transitivity,[status(thm)],[24, 22])). tff(26,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john))))), inference(rewrite,[status(thm)],[])). tff(27,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john)))))), inference(monotonicity,[status(thm)],[26])). tff(28,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john)))))), inference(rewrite,[status(thm)],[])). tff(29,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john))))), inference(or_elim,[status(thm)],[4])). tff(30,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john))))), inference(modus_ponens,[status(thm)],[29, 27])). tff(31,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john))))), inference(modus_ponens,[status(thm)],[30, 28])). tff(32,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predb(paul) | (~like(paul, john))))), inference(modus_ponens,[status(thm)],[31, 27])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!3 |'alice'|) (= X!3 |'fred'|) (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3))))) (a!7 (not (or (predb paul) (not (like paul john)))))) (let ((a!8 (and (room mary) (room paul) (room fred) (room alice) a!5 (or (predb paul) (not (like paul john)))))) (let ((a!9 (~ (not a!8) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 a!7)))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ a!7 a!7)) a!9))))

room(rose)&room(kayla)&room(tiffany)&room(diane)&(![X]:(room(X)=>(X='rose'|X='kayla'|X='tiffany'|X='diane')))& (((![X]:(~room(X)=>(((X!=tiffany)=>(like(jesse,X))))))=>(![X]:(~room(X)=>(((like(X,dennis))=>(like(jesse,X)))))))& (owns_a_telescope(kayla))& (((like(jesse,rose))|(owns_a_telescope(rose))))& (((owns_a_telescope(kayla))|(like(kayla,dennis))))& (?[X,Y]:((owns_a_telescope(X))&(~creative(Y))&(like(X,Y)))))

room(rose)&room(kayla)&room(tiffany)&room(diane)&(![X]:(room(X)=>(X='rose'|X='kayla'|X='tiffany'|X='diane')))& (((~like(kayla,dennis))|(owns_a_telescope(kayla))))

contradiction

contradiction

entailment

Adelaide, Thomas are the only persons in the room. 'Sara and Nicolas hate each other' if 'someone who is not happy is taller than someone who is not Adelaide' and vice versa. 'Adelaide is a tall quiet happy tourist and is not a quiet european' if 'only one person in the room is not a rich tall european'. Adelaide is the richest in the room. Someone who is hated by Nicolas is quieter than someone who hates Sara. Sara and Nicolas hate each other. Only one person outside the room hates Nicolas. More than one person in the room is richer than Sara. More than one person outside the room is not hated by Nicolas. Adelaide enjoys origami or does not watche fantasy movies or both.

Adelaide who is richer than Nicolas, is not a quiet happy european.

neutral

% SZS status Satisfiable

room(adelaide)&room(thomas)&(![X]:(room(X)=>(X='adelaide'|X='thomas')))& (((?[X,Y]:((~happy(X))&(Y!=adelaide)&(taller(X,Y))))<=>((hate(sara,nicolas) & hate(nicolas,sara))))& ((((?[X]:(room(X)&~(rich(X)&tall(X)&european(X))))&(![X,Y]:((~(rich(X)&tall(X)&european(X))&~(rich(Y)&tall(Y)&european(Y)))=>(X=Y)))))=>((tall(adelaide)&quiet(adelaide)&happy(adelaide)&tourist(adelaide))&(~(quiet(adelaide)&european(adelaide)))))& (![X]:(richer(X,adelaide)))& (?[X,Y]:((hate(X,nicolas))&(hate(sara,Y))&(quieter(X,Y))))& ((hate(sara,nicolas) & hate(nicolas,sara)))& (((?[X]:(~room(X)&hate(nicolas,X)))&(![X,Y]:((hate(nicolas,X)&hate(nicolas,Y))=>(X=Y)))))& ((?[X,Y]:(room(X)&room(Y)&(richer(sara,X)&richer(sara,Y))&(X!=Y))))& ((?[X,Y]:(~room(X)&~room(Y)&(~hate(X,nicolas)&~hate(Y,nicolas))&(X!=Y))))& (((enjoys_origami(adelaide))|(does_not_watche_fantasy_movies(adelaide)))))

room(adelaide)&room(thomas)&(![X]:(room(X)=>(X='adelaide'|X='thomas')))& ((richer(nicolas,adelaide))&(~(quiet(adelaide)&happy(adelaide)&european(adelaide))))

contradiction

contradiction

entailment

Peter, Shasta, Owen, Gary are the only persons in the room. It is not the case that 'Owen either does not like Lawrence or is not brave'. Gary is liked by Lawrence. It is not the case that 'someone who is not Gary like someone who is not a happy brave european'. Owen who is not Shasta, is not happy, not brave, not rich. Someone who is richer than Lawrence is richer than someone who does not own a vinyl record player. Shasta is a rich european or is not a brave european or both. Shasta is not liked by Lawrence.

Owen neither is not rich, not creative, not happy nor owns a vinyl record player.

neutral

% SZS status Satisfiable

room(peter)&room(shasta)&room(owen)&room(gary)&(![X]:(room(X)=>(X='peter'|X='shasta'|X='owen'|X='gary')))& ((~((((~like(lawrence,owen))|(~brave(owen)))&(~((~like(lawrence,owen))|(~brave(owen)))))))& (like(gary,lawrence))& (~(?[X,Y]:((X!=gary)&(~(happy(Y)&brave(Y)&european(Y)))&(like(X,Y)))))& ((owen!=shasta)&(~happy(owen)&~brave(owen)&~rich(owen)))& (?[X,Y]:((richer(lawrence,X))&(does_not_own_a_vinyl_record_player(Y))&(richer(X,Y))))& (((rich(shasta)&european(shasta))|(~(brave(shasta)&european(shasta)))))& (~like(shasta,lawrence)))

room(peter)&room(shasta)&room(owen)&room(gary)&(![X]:(room(X)=>(X='peter'|X='shasta'|X='owen'|X='gary')))& (~((~rich(owen)&~creative(owen)&~happy(owen))|(owns_a_vinyl_record_player(owen))))

neutral

contradiction

contradiction

Sherri is the only person in the room. Sherri is the least quiet in the room. Marco is taller than Sherri. Sherri does not like Marco or is quieter than Marco or both. It is not the case that 'Marco is a client of Sherri'. Someone who is not liked by Marco like someone who does not like Marco.

Sherri neither is liked by Marco nor is quieter than William.

neutral

% SZS status Satisfiable

room(sherri)&(![X]:(room(X)=>(X='sherri')))& ((![X]:(quieter(sherri,X)))& (taller(sherri,marco))& (((~like(marco,sherri))|(quieter(marco,sherri))))& (~(client(sherri,marco)))& (?[X,Y]:((~like(X,marco))&(~like(marco,Y))&(like(X,Y)))))

room(sherri)&(![X]:(room(X)=>(X='sherri')))& (~((like(sherri,marco))|(quieter(william,sherri))))

neutral

neutral

contradiction

Meghan, Edna, Annie are the only persons in the room. Only one of the following is true:. -Douglas and Edna hate each other. -No one outside the room who is not Edna is hated by Douglas.

Edna hates Douglas.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(mary_type, type, ( mary: $i)). tff(paul_type, type, ( paul: $i)). tff(room_type, type, ( room: $i > $o)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(fred_type, type, ( fred: $i)). tff(tptp_fun_X_1_type, type, ( tptp_fun_X_1: $i)). tff(1,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((hate(john, paul) & hate(paul, john)) | (~?[X: $i] : ((~room(X)) => ((~(X = paul)) => hate(X, john))))) & (~((hate(john, paul) & hate(paul, john)) & (~?[X: $i] : ((~room(X)) => ((~(X = paul)) => hate(X, john)))))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & hate(john, paul)))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((hate(john, paul) & hate(paul, john)) | (~?[X: $i] : (room(X) | hate(X, john) | (X = paul)))) & (~(hate(john, paul) & hate(paul, john) & (~?[X: $i] : (room(X) | hate(X, john) | (X = paul))))))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((hate(john, paul) & hate(paul, john)) | (~?[X: $i] : ((~room(X)) => ((~(X = paul)) => hate(X, john))))) & (~((hate(john, paul) & hate(paul, john)) & (~?[X: $i] : ((~room(X)) => ((~(X = paul)) => hate(X, john)))))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & hate(john, paul)))), file('/mnt/tmpfs//7427770750229403500654854.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((hate(john, paul) & hate(paul, john)) | (~?[X: $i] : (room(X) | hate(X, john) | (X = paul)))) & (~(hate(john, paul) & hate(paul, john) & (~?[X: $i] : (room(X) | hate(X, john) | (X = paul))))))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul)))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((hate(john, paul) & hate(paul, john)) | (~?[X: $i] : (room(X) | hate(X, john) | (X = paul)))) & (~(hate(john, paul) & hate(paul, john) & (~?[X: $i] : (room(X) | hate(X, john) | (X = paul)))))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (room(mary)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((room(mary) | (mary = paul) | hate(mary, john)) | (~room(mary))), inference(tautology,[status(thm)],[])). tff(9,plain, (room(mary) | (mary = paul) | hate(mary, john)), inference(unit_resolution,[status(thm)],[8, 7])). tff(10,assumption,(~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))), introduced(assumption)). tff(11,plain, (((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | room(X!1)), inference(tautology,[status(thm)],[])). tff(12,plain, (room(X!1)), inference(unit_resolution,[status(thm)],[11, 10])). tff(13,plain, (((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(14,plain, (~(X!1 = |'mary'|)), inference(unit_resolution,[status(thm)],[13, 10])). tff(15,plain, (((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'paul'|))), inference(tautology,[status(thm)],[])). tff(16,plain, (~(X!1 = |'paul'|)), inference(unit_resolution,[status(thm)],[15, 10])). tff(17,plain, (((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'fred'|))), inference(tautology,[status(thm)],[])). tff(18,plain, (~(X!1 = |'fred'|)), inference(unit_resolution,[status(thm)],[17, 10])). tff(19,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(20,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)],[19])). tff(21,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(22,plain, (![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(and_elim,[status(thm)],[5])). tff(23,plain, (![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[22, 21])). tff(24,plain,( ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(skolemize,[status(sab)],[23])). tff(25,plain, (![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[24, 20])). tff(26,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(27,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(28,plain, ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))), inference(modus_ponens,[status(thm)],[27, 26])). tff(29,plain, ($false), inference(unit_resolution,[status(thm)],[28, 25, 18, 16, 14, 12])). tff(30,plain,((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))), inference(lemma,lemma(discharge,[]))). tff(31,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(32,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(33,plain, (room(fred)), inference(modus_ponens,[status(thm)],[32, 31])). tff(34,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(35,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(36,plain, (room(paul)), inference(modus_ponens,[status(thm)],[35, 34])). tff(37,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~hate(john, paul))) <=> ((~hate(john, paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))), inference(rewrite,[status(thm)],[])). tff(38,plain, ((~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))), inference(rewrite,[status(thm)],[])). tff(39,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~hate(john, paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~hate(john, paul)))), inference(monotonicity,[status(thm)],[38])). tff(40,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~hate(john, paul))) <=> ((~hate(john, paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))), inference(transitivity,[status(thm)],[39, 37])). tff(41,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul)) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul))), inference(rewrite,[status(thm)],[])). tff(42,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul)))), inference(monotonicity,[status(thm)],[41])). tff(43,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul)))), inference(rewrite,[status(thm)],[])). tff(44,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul))), inference(or_elim,[status(thm)],[4])). tff(45,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul))), inference(modus_ponens,[status(thm)],[44, 42])). tff(46,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul))), inference(modus_ponens,[status(thm)],[45, 43])). tff(47,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & hate(john, paul))), inference(modus_ponens,[status(thm)],[46, 42])). 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!1 |'fred'|) (= X!1 |'paul'|) (= X!1 |'mary'|) (not (room X!1))))) (a!6 (refl (~ (not (hate john paul)) (not (hate john paul)))))) (let ((a!7 (~ (not (and (room mary) (room paul) (room fred) a!4 (hate john paul))) (or (not (room mary)) (not (room paul)) (not (room fred)) a!5 (not (hate john paul)))))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) a!6 a!7)))

room(meghan)&room(edna)&room(annie)&(![X]:(room(X)=>(X='meghan'|X='edna'|X='annie')))& ((((hate(douglas,edna) & hate(edna,douglas)))|(~?[X]:(~room(X)=>(((X!=edna)=>(hate(X,douglas)))))))&~((hate(douglas,edna) & hate(edna,douglas))&~?[X]:(~room(X)=>(((X!=edna)=>(hate(X,douglas)))))))

room(meghan)&room(edna)&room(annie)&(![X]:(room(X)=>(X='meghan'|X='edna'|X='annie')))& (hate(douglas,edna))

entailment

neutral

contradiction

Sonya, Sonja, Shelly are the only persons in the room. Someone who is not Sonya is quieter than someone who is a rich tourist only if someone who is a rich tourist like someone who is not quiet. Shelly is a client of Jacqueline and likes Donald only if Sonya who is not a quiet rich tall tourist, is a rich tourist. Jacqueline is a client of Sonja only if more than one person outside the room is not Shelly. Sonja neither does not hate Jacqueline nor is not rich, not quiet. Sonja is the richest in the room. Only one person outside the room is not quiet, not tall, not rich. Everyone outside the room is a sibling of Donald. Only one person outside the room is not quiet.

Someone who is not tall, not quiet, not rich is a sibling of someone who is a sibling of John.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(lucy_type, type, ( lucy: $i)). tff(mary_type, type, ( mary: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(room_type, type, ( room: $i > $o)). tff(sibling_type, type, ( sibling: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(alice_type, type, ( alice: $i)). tff(susan_type, type, ( susan: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(quiet_type, type, ( quiet: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun_X_6_type, type, ( tptp_fun_X_6: $i)). tff(1,plain, ((lucy = mary) <=> (mary = lucy)), inference(commutativity,[status(thm)],[])). tff(2,plain, ((lucy = paul) <=> (paul = lucy)), inference(commutativity,[status(thm)],[])). tff(3,plain, ((paul = mary) <=> (mary = paul)), inference(commutativity,[status(thm)],[])). tff(4,assumption,(~(fred = |'fred'|)), introduced(assumption)). tff(5,plain, ((~(lucy = john)) <=> (~(lucy = john))), inference(rewrite,[status(thm)],[])). tff(6,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//56140497792547829147278.p','b14')). tff(7,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)],[6])). tff(8,plain, (~(lucy = john)), inference(and_elim,[status(thm)],[7])). tff(9,plain, (~(lucy = john)), inference(modus_ponens,[status(thm)],[8, 5])). tff(10,plain, (^[X: $i, Y: $i] : refl(((X = Y) | (sibling(X, Y) <=> sibling(Y, X))) <=> ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))))), inference(bind,[status(th)],[])). tff(11,plain, (![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(quant_intro,[status(thm)],[10])). tff(12,plain, (![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(rewrite,[status(thm)],[])). tff(13,plain, (^[X: $i, Y: $i] : rewrite(((~(X = Y)) => (sibling(X, Y) <=> sibling(Y, X))) <=> ((X = Y) | (sibling(X, Y) <=> sibling(Y, X))))), inference(bind,[status(th)],[])). tff(14,plain, (![X: $i, Y: $i] : ((~(X = Y)) => (sibling(X, Y) <=> sibling(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(quant_intro,[status(thm)],[13])). tff(15,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (sibling(X, Y) <=> sibling(Y, X)))), file('/mnt/tmpfs//56140497792547829147278.p','b4')). tff(16,plain, (![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(modus_ponens,[status(thm)],[15, 14])). tff(17,plain, (![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(modus_ponens,[status(thm)],[16, 12])). tff(18,plain,( ![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(skolemize,[status(sab)],[17])). tff(19,plain, (![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))), inference(modus_ponens,[status(thm)],[18, 11])). tff(20,plain, (((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | ((lucy = john) | (sibling(lucy, john) <=> sibling(john, lucy)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | (lucy = john) | (sibling(lucy, john) <=> sibling(john, lucy)))), inference(rewrite,[status(thm)],[])). tff(21,plain, ((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | ((lucy = john) | (sibling(lucy, john) <=> sibling(john, lucy)))), inference(quant_inst,[status(thm)],[])). tff(22,plain, ((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | (lucy = john) | (sibling(lucy, john) <=> sibling(john, lucy))), inference(modus_ponens,[status(thm)],[21, 20])). tff(23,plain, (sibling(lucy, john) <=> sibling(john, lucy)), inference(unit_resolution,[status(thm)],[22, 19, 9])). tff(24,assumption,(~sibling(X!4, john)), introduced(assumption)). tff(25,plain, (^[X: $i] : refl((room(X) | sibling(john, X)) <=> (room(X) | sibling(john, X)))), inference(bind,[status(th)],[])). tff(26,plain, (![X: $i] : (room(X) | sibling(john, X)) <=> ![X: $i] : (room(X) | sibling(john, X))), inference(quant_intro,[status(thm)],[25])). tff(27,plain, (![X: $i] : (room(X) | sibling(john, X)) <=> ![X: $i] : (room(X) | sibling(john, X))), inference(rewrite,[status(thm)],[])). tff(28,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((?[X: $i, Y: $i] : (((~(X = mary)) & (rich(Y) & tourist(Y))) & quieter(X, Y)) => ?[X: $i, Y: $i] : (((rich(X) & tourist(X)) & (~quiet(Y))) & like(X, Y))) & ((client(alice, fred) & like(john, fred)) => ((~(((quiet(mary) & rich(mary)) & tall(mary)) & tourist(mary))) & (rich(mary) & tourist(mary))))) & (client(paul, alice) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = fred)) & (~(Y = fred)))) & (~(X = Y))))) & (~((~hate(alice, paul)) | ((~rich(paul)) & (~quiet(paul)))))) & ![X: $i] : richer(X, paul)) & (?[X: $i] : ((((~room(X)) & (~quiet(X))) & (~tall(X))) & (~rich(X))) & ![X: $i, Y: $i] : (((((((~quiet(X)) & (~tall(X))) & (~rich(X))) & (~quiet(Y))) & (~tall(Y))) & (~rich(Y))) => (X = Y)))) & ![X: $i] : ((~room(X)) => sibling(john, X))) & (?[X: $i] : ((~room(X)) & (~quiet(X))) & ![X: $i, Y: $i] : (((~quiet(X)) & (~quiet(Y))) => (X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ?[X: $i, Y: $i] : (((((~tall(X)) & (~quiet(X))) & (~rich(X))) & sibling(lucy, Y)) & sibling(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : ((~(X = mary)) & rich(Y) & tourist(Y) & quieter(X, Y))) | ?[X: $i, Y: $i] : (rich(X) & tourist(X) & (~quiet(Y)) & like(X, Y))) & ((~(client(alice, fred) & like(john, fred))) | ((~(quiet(mary) & rich(mary) & tall(mary) & tourist(mary))) & rich(mary) & tourist(mary))) & ((~client(paul, alice)) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = fred)) & (~(Y = fred)) & (~(X = Y)))) & (~((~hate(alice, paul)) | ((~rich(paul)) & (~quiet(paul))))) & ![X: $i] : richer(X, paul) & ?[X: $i] : ((~room(X)) & (~quiet(X)) & (~tall(X)) & (~rich(X))) & ![X: $i, Y: $i] : ((~((~quiet(X)) & (~tall(X)) & (~rich(X)) & (~quiet(Y)) & (~tall(Y)) & (~rich(Y)))) | (X = Y)) & ![X: $i] : (room(X) | sibling(john, X)) & ?[X: $i] : ((~room(X)) & (~quiet(X))) & ![X: $i, Y: $i] : ((~((~quiet(X)) & (~quiet(Y)))) | (X = Y)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(29,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((?[X: $i, Y: $i] : (((~(X = mary)) & (rich(Y) & tourist(Y))) & quieter(X, Y)) => ?[X: $i, Y: $i] : (((rich(X) & tourist(X)) & (~quiet(Y))) & like(X, Y))) & ((client(alice, fred) & like(john, fred)) => ((~(((quiet(mary) & rich(mary)) & tall(mary)) & tourist(mary))) & (rich(mary) & tourist(mary))))) & (client(paul, alice) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = fred)) & (~(Y = fred)))) & (~(X = Y))))) & (~((~hate(alice, paul)) | ((~rich(paul)) & (~quiet(paul)))))) & ![X: $i] : richer(X, paul)) & (?[X: $i] : ((((~room(X)) & (~quiet(X))) & (~tall(X))) & (~rich(X))) & ![X: $i, Y: $i] : (((((((~quiet(X)) & (~tall(X))) & (~rich(X))) & (~quiet(Y))) & (~tall(Y))) & (~rich(Y))) => (X = Y)))) & ![X: $i] : ((~room(X)) => sibling(john, X))) & (?[X: $i] : ((~room(X)) & (~quiet(X))) & ![X: $i, Y: $i] : (((~quiet(X)) & (~quiet(Y))) => (X = Y))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ?[X: $i, Y: $i] : (((((~tall(X)) & (~quiet(X))) & (~rich(X))) & sibling(lucy, Y)) & sibling(X, Y))))), file('/mnt/tmpfs//56140497792547829147278.p','negated')). tff(30,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : ((~(X = mary)) & rich(Y) & tourist(Y) & quieter(X, Y))) | ?[X: $i, Y: $i] : (rich(X) & tourist(X) & (~quiet(Y)) & like(X, Y))) & ((~(client(alice, fred) & like(john, fred))) | ((~(quiet(mary) & rich(mary) & tall(mary) & tourist(mary))) & rich(mary) & tourist(mary))) & ((~client(paul, alice)) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = fred)) & (~(Y = fred)) & (~(X = Y)))) & (~((~hate(alice, paul)) | ((~rich(paul)) & (~quiet(paul))))) & ![X: $i] : richer(X, paul) & ?[X: $i] : ((~room(X)) & (~quiet(X)) & (~tall(X)) & (~rich(X))) & ![X: $i, Y: $i] : ((~((~quiet(X)) & (~tall(X)) & (~rich(X)) & (~quiet(Y)) & (~tall(Y)) & (~rich(Y)))) | (X = Y)) & ![X: $i] : (room(X) | sibling(john, X)) & ?[X: $i] : ((~room(X)) & (~quiet(X))) & ![X: $i, Y: $i] : ((~((~quiet(X)) & (~quiet(Y)))) | (X = Y)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y))))), inference(modus_ponens,[status(thm)],[29, 28])). tff(31,plain, (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : ((~(X = mary)) & rich(Y) & tourist(Y) & quieter(X, Y))) | ?[X: $i, Y: $i] : (rich(X) & tourist(X) & (~quiet(Y)) & like(X, Y))) & ((~(client(alice, fred) & like(john, fred))) | ((~(quiet(mary) & rich(mary) & tall(mary) & tourist(mary))) & rich(mary) & tourist(mary))) & ((~client(paul, alice)) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = fred)) & (~(Y = fred)) & (~(X = Y)))) & (~((~hate(alice, paul)) | ((~rich(paul)) & (~quiet(paul))))) & ![X: $i] : richer(X, paul) & ?[X: $i] : ((~room(X)) & (~quiet(X)) & (~tall(X)) & (~rich(X))) & ![X: $i, Y: $i] : ((~((~quiet(X)) & (~tall(X)) & (~rich(X)) & (~quiet(Y)) & (~tall(Y)) & (~rich(Y)))) | (X = Y)) & ![X: $i] : (room(X) | sibling(john, X)) & ?[X: $i] : ((~room(X)) & (~quiet(X))) & ![X: $i, Y: $i] : ((~((~quiet(X)) & (~quiet(Y)))) | (X = Y))), inference(or_elim,[status(thm)],[30])). tff(32,plain, (![X: $i] : (room(X) | sibling(john, X))), inference(and_elim,[status(thm)],[31])). tff(33,plain, (![X: $i] : (room(X) | sibling(john, X))), inference(modus_ponens,[status(thm)],[32, 27])). tff(34,plain,( ![X: $i] : (room(X) | sibling(john, X))), inference(skolemize,[status(sab)],[33])). tff(35,plain, (![X: $i] : (room(X) | sibling(john, X))), inference(modus_ponens,[status(thm)],[34, 26])). tff(36,plain, (?[X: $i] : ((~room(X)) & (~quiet(X)) & (~tall(X)) & (~rich(X))) <=> ?[X: $i] : ((~room(X)) & (~quiet(X)) & (~tall(X)) & (~rich(X)))), inference(rewrite,[status(thm)],[])). tff(37,plain, (?[X: $i] : ((~room(X)) & (~quiet(X)) & (~tall(X)) & (~rich(X)))), inference(and_elim,[status(thm)],[31])). tff(38,plain, (?[X: $i] : ((~room(X)) & (~quiet(X)) & (~tall(X)) & (~rich(X)))), inference(modus_ponens,[status(thm)],[37, 36])). tff(39,plain,( (~room(X!4)) & (~quiet(X!4)) & (~tall(X!4)) & (~rich(X!4))), inference(skolemize,[status(sab)],[38])). tff(40,plain, (~room(X!4)), inference(and_elim,[status(thm)],[39])). tff(41,plain, (((~![X: $i] : (room(X) | sibling(john, X))) | (room(X!4) | sibling(john, X!4))) <=> ((~![X: $i] : (room(X) | sibling(john, X))) | room(X!4) | sibling(john, X!4))), inference(rewrite,[status(thm)],[])). tff(42,plain, ((~![X: $i] : (room(X) | sibling(john, X))) | (room(X!4) | sibling(john, X!4))), inference(quant_inst,[status(thm)],[])). tff(43,plain, ((~![X: $i] : (room(X) | sibling(john, X))) | room(X!4) | sibling(john, X!4)), inference(modus_ponens,[status(thm)],[42, 41])). tff(44,plain, (sibling(john, X!4)), inference(unit_resolution,[status(thm)],[43, 40, 35])). tff(45,plain, ((~(sibling(john, X!4) <=> sibling(X!4, john))) | (~sibling(john, X!4)) | sibling(X!4, john)), inference(tautology,[status(thm)],[])). tff(46,plain, ((~(sibling(john, X!4) <=> sibling(X!4, john))) | sibling(X!4, john)), inference(unit_resolution,[status(thm)],[45, 44])). tff(47,plain, (~(sibling(john, X!4) <=> sibling(X!4, john))), inference(unit_resolution,[status(thm)],[46, 24])). tff(48,plain, (((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | ((john = X!4) | (sibling(john, X!4) <=> sibling(X!4, john)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | (john = X!4) | (sibling(john, X!4) <=> sibling(X!4, john)))), inference(rewrite,[status(thm)],[])). tff(49,plain, ((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | ((john = X!4) | (sibling(john, X!4) <=> sibling(X!4, john)))), inference(quant_inst,[status(thm)],[])). tff(50,plain, ((~![X: $i, Y: $i] : ((X = Y) | (sibling(X, Y) <=> sibling(Y, X)))) | (john = X!4) | (sibling(john, X!4) <=> sibling(X!4, john))), inference(modus_ponens,[status(thm)],[49, 48])). tff(51,plain, ((john = X!4) | (sibling(john, X!4) <=> sibling(X!4, john))), inference(unit_resolution,[status(thm)],[50, 19])). tff(52,plain, (john = X!4), inference(unit_resolution,[status(thm)],[51, 47])). tff(53,plain, (X!4 = john), inference(symmetry,[status(thm)],[52])). tff(54,plain, (sibling(X!4, john) <=> sibling(john, X!4)), inference(monotonicity,[status(thm)],[53, 52])). tff(55,plain, (sibling(john, X!4) <=> sibling(X!4, john)), inference(symmetry,[status(thm)],[54])). tff(56,plain, (sibling(X!4, john)), inference(modus_ponens,[status(thm)],[44, 55])). tff(57,plain, ($false), inference(unit_resolution,[status(thm)],[24, 56])). tff(58,plain,(sibling(X!4, john)), inference(lemma,lemma(discharge,[]))). tff(59,assumption,(sibling(lucy, john)), introduced(assumption)). tff(60,assumption,(sibling(X!4, john)), introduced(assumption)). tff(61,assumption,(~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))), introduced(assumption)). tff(62,plain, (((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6))) | room(X!6)), inference(tautology,[status(thm)],[])). tff(63,plain, (room(X!6)), inference(unit_resolution,[status(thm)],[62, 61])). tff(64,plain, (((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6))) | (~(X!6 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(65,plain, (~(X!6 = |'mary'|)), inference(unit_resolution,[status(thm)],[64, 61])). tff(66,plain, (((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6))) | (~(X!6 = |'paul'|))), inference(tautology,[status(thm)],[])). tff(67,plain, (~(X!6 = |'paul'|)), inference(unit_resolution,[status(thm)],[66, 61])). tff(68,plain, (((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6))) | (~(X!6 = |'fred'|))), inference(tautology,[status(thm)],[])). tff(69,plain, (~(X!6 = |'fred'|)), inference(unit_resolution,[status(thm)],[68, 61])). tff(70,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(71,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)],[70])). tff(72,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(73,plain, (![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(and_elim,[status(thm)],[31])). tff(74,plain, (![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[73, 72])). tff(75,plain,( ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(skolemize,[status(sab)],[74])). tff(76,plain, (![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[75, 71])). tff(77,plain, (((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) <=> ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))), inference(rewrite,[status(thm)],[])). tff(78,plain, ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))), inference(quant_inst,[status(thm)],[])). tff(79,plain, ((~![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6))), inference(modus_ponens,[status(thm)],[78, 77])). tff(80,plain, ($false), inference(unit_resolution,[status(thm)],[79, 76, 69, 67, 65, 63])). tff(81,plain,((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6))), inference(lemma,lemma(discharge,[]))). tff(82,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(83,plain, (room(fred)), inference(and_elim,[status(thm)],[31])). tff(84,plain, (room(fred)), inference(modus_ponens,[status(thm)],[83, 82])). tff(85,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(86,plain, (room(paul)), inference(and_elim,[status(thm)],[31])). tff(87,plain, (room(paul)), inference(modus_ponens,[status(thm)],[86, 85])). tff(88,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(89,plain, (room(mary)), inference(and_elim,[status(thm)],[31])). tff(90,plain, (room(mary)), inference(modus_ponens,[status(thm)],[89, 88])). tff(91,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y))))), inference(rewrite,[status(thm)],[])). tff(92,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y))))), inference(rewrite,[status(thm)],[])). tff(93,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)) <=> (~(rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y))))), ((~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y))) <=> (~(~(rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y))))))), rewrite((~(~(rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y))))) <=> (rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y)))), ((~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y))) <=> (rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y)))))), inference(bind,[status(th)],[])). tff(94,plain, (![X: $i, Y: $i] : (~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y))) <=> ![X: $i, Y: $i] : (rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y)))), inference(quant_intro,[status(thm)],[93])). tff(95,plain, ((~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) <=> (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6))))), inference(rewrite,[status(thm)],[])). tff(96,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y))))), inference(monotonicity,[status(thm)],[95, 94])). tff(97,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (rich(X) | tall(X) | quiet(X) | (~sibling(lucy, Y)) | (~sibling(X, Y))))), inference(transitivity,[status(thm)],[96, 92])). tff(98,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y))))), inference(rewrite,[status(thm)],[])). tff(99,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y))))), inference(monotonicity,[status(thm)],[95])). tff(100,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!6 = |'fred'|) | (X!6 = |'paul'|) | (X!6 = |'mary'|) | (~room(X!6)))) | ![X: $i, Y: $i] : (~((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y))))), inference(transitivity,[status(thm)],[99, 98])). tff(101,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))), inference(rewrite,[status(thm)],[])). tff(102,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y))))), inference(monotonicity,[status(thm)],[101])). tff(103,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y))))), inference(rewrite,[status(thm)],[])). tff(104,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))), inference(or_elim,[status(thm)],[30])). tff(105,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))), inference(modus_ponens,[status(thm)],[104, 102])). tff(106,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))), inference(modus_ponens,[status(thm)],[105, 103])). tff(107,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~quiet(X)) & (~rich(X)) & sibling(lucy, Y) & sibling(X, Y)))), inference(modus_ponens,[status(thm)],[106, 102])). 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!6 |'fred'|) (= X!6 |'paul'|) (= X!6 |'mary'|) (not (room X!6))))) (a!6 (lambda ((X $i) (Y $i)) (let ((a!1 (and (not (tall X)) (not (quiet X)) (not (rich X)) (sibling lucy Y) (sibling X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!7 (exists ((X $i) (Y $i)) (and (not (tall X)) (not (quiet X)) (not (rich X)) (sibling lucy Y) (sibling X Y)))) (a!8 (forall ((X $i) (Y $i)) (let ((a!1 (and (not (tall X)) (not (quiet X)) (not (rich X)) (sibling lucy Y) (sibling X Y)))) (not a!1))))) (let ((a!9 (~ (not (and (room mary) (room paul) (room fred) a!4 a!7)) (or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!8)))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (nnf-neg (proof-bind a!6) (~ (not a!7) a!8)) a!9)))

room(sonya)&room(sonja)&room(shelly)&(![X]:(room(X)=>(X='sonya'|X='sonja'|X='shelly')))& (((?[X,Y]:((X!=sonya)&(rich(Y)&tourist(Y))&(quieter(X,Y))))=>(?[X,Y]:((rich(X)&tourist(X))&(~quiet(Y))&(like(X,Y)))))& (((client(jacqueline,shelly))&(like(donald,shelly)))=>((~(quiet(sonya)&rich(sonya)&tall(sonya)&tourist(sonya)))&(rich(sonya)&tourist(sonya))))& ((client(sonja,jacqueline))=>((?[X,Y]:(~room(X)&~room(Y)&(X!=shelly&Y!=shelly)&(X!=Y)))))& (~((~hate(jacqueline,sonja))|(~rich(sonja)&~quiet(sonja))))& (![X]:(richer(X,sonja)))& (((?[X]:(~room(X)&~quiet(X)&~tall(X)&~rich(X)))&(![X,Y]:((~quiet(X)&~tall(X)&~rich(X)&~quiet(Y)&~tall(Y)&~rich(Y))=>(X=Y)))))& (![X]:(~room(X)=>(sibling(donald,X))))& (((?[X]:(~room(X)&~quiet(X)))&(![X,Y]:((~quiet(X)&~quiet(Y))=>(X=Y))))))

room(sonya)&room(sonja)&room(shelly)&(![X]:(room(X)=>(X='sonya'|X='sonja'|X='shelly')))& (?[X,Y]:((~tall(X)&~quiet(X)&~rich(X))&(sibling(john,Y))&(sibling(X,Y))))

neutral

neutral

contradiction

Gregory, Ricky, Dennis, Mildred are the only persons in the room. Only one person outside the room is not a brave tall european.

It is not the case that 'Ricky who is not a tall brave european, does not use an ios phone'.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(european_type, type, ( european: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(room_type, type, ( room: $i > $o)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(alice_type, type, ( alice: $i)). tff(fred_type, type, ( fred: $i)). tff(mary_type, type, ( mary: $i)). tff(predb_type, type, ( predb: $i > $o)). tff(tptp_fun_X_1_type, type, ( tptp_fun_X_1: $i)). tff(1,assumption,(paul = X!0), introduced(assumption)). tff(2,plain, (room(paul) <=> room(X!0)), inference(monotonicity,[status(thm)],[1])). tff(3,plain, (room(X!0) <=> room(paul)), inference(symmetry,[status(thm)],[2])). tff(4,plain, ((~room(X!0)) <=> (~room(paul))), inference(monotonicity,[status(thm)],[3])). tff(5,plain, (?[X: $i] : ((~room(X)) & (~(brave(X) & tall(X) & european(X)))) <=> ?[X: $i] : ((~room(X)) & (~(brave(X) & tall(X) & european(X))))), inference(rewrite,[status(thm)],[])). tff(6,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (?[X: $i] : ((~room(X)) & (~((brave(X) & tall(X)) & european(X)))) & ![X: $i, Y: $i] : (((~((brave(X) & tall(X)) & european(X))) & (~((brave(Y) & tall(Y)) & european(Y)))) => (X = Y)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~((~((tall(paul) & brave(paul)) & european(paul))) & (~predb(paul))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i] : ((~room(X)) & (~(brave(X) & tall(X) & european(X)))) & ![X: $i, Y: $i] : ((~((~(brave(X) & tall(X) & european(X))) & (~(brave(Y) & tall(Y) & european(Y))))) | (X = Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))))))), inference(rewrite,[status(thm)],[])). tff(7,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (?[X: $i] : ((~room(X)) & (~((brave(X) & tall(X)) & european(X)))) & ![X: $i, Y: $i] : (((~((brave(X) & tall(X)) & european(X))) & (~((brave(Y) & tall(Y)) & european(Y)))) => (X = Y)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~((~((tall(paul) & brave(paul)) & european(paul))) & (~predb(paul))))))), file('/mnt/tmpfs//5989032895324849624180768.p','negated')). tff(8,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i] : ((~room(X)) & (~(brave(X) & tall(X) & european(X)))) & ![X: $i, Y: $i] : ((~((~(brave(X) & tall(X) & european(X))) & (~(brave(Y) & tall(Y) & european(Y))))) | (X = Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))))))), inference(modus_ponens,[status(thm)],[7, 6])). tff(9,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i] : ((~room(X)) & (~(brave(X) & tall(X) & european(X)))) & ![X: $i, Y: $i] : ((~((~(brave(X) & tall(X) & european(X))) & (~(brave(Y) & tall(Y) & european(Y))))) | (X = Y))), inference(or_elim,[status(thm)],[8])). tff(10,plain, (?[X: $i] : ((~room(X)) & (~(brave(X) & tall(X) & european(X))))), inference(and_elim,[status(thm)],[9])). tff(11,plain, (?[X: $i] : ((~room(X)) & (~(brave(X) & tall(X) & european(X))))), inference(modus_ponens,[status(thm)],[10, 5])). tff(12,plain,( (~room(X!0)) & (~(brave(X!0) & tall(X!0) & european(X!0)))), inference(skolemize,[status(sab)],[11])). tff(13,plain, (~room(X!0)), inference(and_elim,[status(thm)],[12])). tff(14,plain, (~room(paul)), inference(modus_ponens,[status(thm)],[13, 4])). tff(15,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(16,plain, (room(paul)), inference(and_elim,[status(thm)],[9])). tff(17,plain, (room(paul)), inference(modus_ponens,[status(thm)],[16, 15])). tff(18,plain, ($false), inference(unit_resolution,[status(thm)],[17, 14])). tff(19,plain,(~(paul = X!0)), inference(lemma,lemma(discharge,[]))). tff(20,assumption,(~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))), introduced(assumption)). tff(21,plain, (((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | room(X!1)), inference(tautology,[status(thm)],[])). tff(22,plain, (room(X!1)), inference(unit_resolution,[status(thm)],[21, 20])). tff(23,plain, (((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(24,plain, (~(X!1 = |'mary'|)), inference(unit_resolution,[status(thm)],[23, 20])). tff(25,plain, (((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'paul'|))), inference(tautology,[status(thm)],[])). tff(26,plain, (~(X!1 = |'paul'|)), inference(unit_resolution,[status(thm)],[25, 20])). tff(27,plain, (((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'fred'|))), inference(tautology,[status(thm)],[])). tff(28,plain, (~(X!1 = |'fred'|)), inference(unit_resolution,[status(thm)],[27, 20])). tff(29,plain, (((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))) | (~(X!1 = |'alice'|))), inference(tautology,[status(thm)],[])). tff(30,plain, (~(X!1 = |'alice'|)), inference(unit_resolution,[status(thm)],[29, 20])). tff(31,plain, (^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(bind,[status(th)],[])). tff(32,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(quant_intro,[status(thm)],[31])). tff(33,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(rewrite,[status(thm)],[])). tff(34,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(and_elim,[status(thm)],[9])). tff(35,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[34, 33])). tff(36,plain,( ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(skolemize,[status(sab)],[35])). tff(37,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[36, 32])). tff(38,plain, (((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))), inference(rewrite,[status(thm)],[])). tff(39,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))), inference(quant_inst,[status(thm)],[])). tff(40,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))), inference(modus_ponens,[status(thm)],[39, 38])). tff(41,plain, ($false), inference(unit_resolution,[status(thm)],[40, 37, 30, 28, 26, 24, 22])). tff(42,plain,((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))), inference(lemma,lemma(discharge,[]))). tff(43,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(44,plain, (room(alice)), inference(and_elim,[status(thm)],[9])). tff(45,plain, (room(alice)), inference(modus_ponens,[status(thm)],[44, 43])). tff(46,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(47,plain, (room(fred)), inference(and_elim,[status(thm)],[9])). tff(48,plain, (room(fred)), inference(modus_ponens,[status(thm)],[47, 46])). tff(49,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(50,plain, (room(mary)), inference(and_elim,[status(thm)],[9])). tff(51,plain, (room(mary)), inference(modus_ponens,[status(thm)],[50, 49])). tff(52,plain, (((~(predb(paul) | (~((~tall(paul)) | (~brave(paul)) | (~european(paul)))))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~(predb(paul) | (~((~tall(paul)) | (~brave(paul)) | (~european(paul)))))))), inference(rewrite,[status(thm)],[])). tff(53,plain, ((~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))), inference(rewrite,[status(thm)],[])). tff(54,plain, ((((~tall(paul)) | (~brave(paul)) | (~european(paul))) & (~predb(paul))) <=> (~(predb(paul) | (~((~tall(paul)) | (~brave(paul)) | (~european(paul))))))), inference(rewrite,[status(thm)],[])). tff(55,plain, ((~(~((~tall(paul)) | (~brave(paul)) | (~european(paul))))) <=> ((~tall(paul)) | (~brave(paul)) | (~european(paul)))), inference(rewrite,[status(thm)],[])). tff(56,plain, ((tall(paul) & brave(paul) & european(paul)) <=> (~((~tall(paul)) | (~brave(paul)) | (~european(paul))))), inference(rewrite,[status(thm)],[])). tff(57,plain, ((~(tall(paul) & brave(paul) & european(paul))) <=> (~(~((~tall(paul)) | (~brave(paul)) | (~european(paul)))))), inference(monotonicity,[status(thm)],[56])). tff(58,plain, ((~(tall(paul) & brave(paul) & european(paul))) <=> ((~tall(paul)) | (~brave(paul)) | (~european(paul)))), inference(transitivity,[status(thm)],[57, 55])). tff(59,plain, (((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))) <=> (((~tall(paul)) | (~brave(paul)) | (~european(paul))) & (~predb(paul)))), inference(monotonicity,[status(thm)],[58])). tff(60,plain, (((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))) <=> (~(predb(paul) | (~((~tall(paul)) | (~brave(paul)) | (~european(paul))))))), inference(transitivity,[status(thm)],[59, 54])). tff(61,plain, ((((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))) <=> ((~(predb(paul) | (~((~tall(paul)) | (~brave(paul)) | (~european(paul)))))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))), inference(monotonicity,[status(thm)],[60, 53])). tff(62,plain, ((((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~(predb(paul) | (~((~tall(paul)) | (~brave(paul)) | (~european(paul)))))))), inference(transitivity,[status(thm)],[61, 52])). tff(63,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))) <=> (((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))), inference(rewrite,[status(thm)],[])). tff(64,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))))), inference(monotonicity,[status(thm)],[53])). tff(65,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | ((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))) <=> (((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))))), inference(transitivity,[status(thm)],[64, 63])). tff(66,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))))), inference(rewrite,[status(thm)],[])). tff(67,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))))))), inference(monotonicity,[status(thm)],[66])). tff(68,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul))))))), inference(rewrite,[status(thm)],[])). tff(69,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))))), inference(or_elim,[status(thm)],[8])). tff(70,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))))), inference(modus_ponens,[status(thm)],[69, 67])). tff(71,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))))), inference(modus_ponens,[status(thm)],[70, 68])). tff(72,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~(tall(paul) & brave(paul) & european(paul))) & (~predb(paul)))))), inference(modus_ponens,[status(thm)],[71, 67])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!1 |'alice'|) (= X!1 |'fred'|) (= X!1 |'paul'|) (= X!1 |'mary'|) (not (room X!1))))) (a!7 (and (not (and (tall paul) (brave paul) (european paul))) (not (predb paul))))) (let ((a!8 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 (not a!7))) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 a!7)))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ a!7 a!7)) a!8)))

room(gregory)&room(ricky)&room(dennis)&room(mildred)&(![X]:(room(X)=>(X='gregory'|X='ricky'|X='dennis'|X='mildred')))& (((?[X]:(~room(X)&~(brave(X)&tall(X)&european(X))))&(![X,Y]:((~(brave(X)&tall(X)&european(X))&~(brave(Y)&tall(Y)&european(Y)))=>(X=Y)))))

room(gregory)&room(ricky)&room(dennis)&room(mildred)&(![X]:(room(X)=>(X='gregory'|X='ricky'|X='dennis'|X='mildred')))& (~((~(tall(ricky)&brave(ricky)&european(ricky)))&(does_not_use_an_ios_phone(ricky))))

entailment

entailment

neutral

Wayne, Debra, George are the only persons in the room. Someone in the room who is not liked by Vicki collects first edition books. Someone in the room is not Debra. Everyone outside the room collects first edition books. George who is liked by Vicki, likes Elizabeth. Wayne and Vicki like each other.

Someone who is not liked by Elizabeth like someone who does not collect first edition books.

neutral

% SZS status Satisfiable

room(wayne)&room(debra)&room(george)&(![X]:(room(X)=>(X='wayne'|X='debra'|X='george')))& ((?[X]:(room(X)=>(((~like(X,vicki))=>(collects_first_edition_books(X))))))& (?[X]:(room(X)=>(X!=debra)))& (![X]:(~room(X)=>(collects_first_edition_books(X))))& ((like(george,vicki))&(like(elizabeth,george)))& ((like(wayne,vicki) & like(vicki,wayne))))

room(wayne)&room(debra)&room(george)&(![X]:(room(X)=>(X='wayne'|X='debra'|X='george')))& (?[X,Y]:((~like(X,elizabeth))&(does_not_collect_first_edition_books(Y))&(like(X,Y))))

contradiction

entailment

contradiction

Gerald, Jennifer, James, Benjamin are the only persons in the room. 'Benjamin who does not hate Judith, is not happy' only if 'Jennifer is the least quiet in the room'. 'Benjamin is not Jennifer or is not hated by Judith or both' if 'someone who is a happy person is a client of someone who is quieter than Judith' and vice versa. 'Gerald is the least quiet in the room' if 'Jennifer and Gerald are respectively quiet and happy'. More than one person outside the room likes Judith. Gerald is the least quiet in the room. Gerald and Benjamin hate Judith. Gerald does not hate Judith or can play the guitar or both. Someone outside the room who is not liked by Judith is not happy. It is not the case that 'Gerald and Jennifer are respectively happy and quiet'. Gerald and Jennifer are respectively quiet and happy. Everyone outside the room is not hated by Judith.

Someone who is not quiet hate someone who does not collect foreign coins.

contradiction

-

room(gerald)&room(jennifer)&room(james)&room(benjamin)&(![X]:(room(X)=>(X='gerald'|X='jennifer'|X='james'|X='benjamin')))& ((((~hate(judith,benjamin))&(~happy(benjamin)))=>(![X]:(quieter(jennifer,X))))& ((?[X,Y]:((happy(X)&person(X))&(quieter(judith,Y))&(client(X,Y))))<=>(((benjamin!=jennifer)|(~hate(benjamin,judith)))))& (((quiet(jennifer))&(happy(gerald)))=>(![X]:(quieter(gerald,X))))& ((?[X,Y]:(~room(X)&~room(Y)&(like(judith,X)&like(judith,Y))&(X!=Y))))& (![X]:(quieter(gerald,X)))& (hate(judith,gerald)&hate(judith,benjamin))& (((~hate(judith,gerald))|(can_play_the_guitar(gerald))))& (?[X]:(~room(X)=>(((~like(X,judith))=>(~happy(X))))))& (~((happy(gerald))&(quiet(jennifer))))& ((quiet(gerald))&(happy(jennifer)))& (![X]:(~room(X)=>(~hate(X,judith)))))

room(gerald)&room(jennifer)&room(james)&room(benjamin)&(![X]:(room(X)=>(X='gerald'|X='jennifer'|X='james'|X='benjamin')))& (?[X,Y]:((~quiet(X))&(does_not_collect_foreign_coins(Y))&(hate(X,Y))))

neutral

neutral

neutral

Tammy is the only person in the room. Tammy neither is hated by Manuel nor does not hate Audra. Someone who is a creative quiet european is quieter than someone who is quieter than Manuel. Tammy is a quiet european.

Tammy does not hate Audra or is a quiet tall european or both.

neutral

% SZS status Satisfiable

room(tammy)&(![X]:(room(X)=>(X='tammy')))& ((~((hate(tammy,manuel))|(~hate(audra,tammy))))& (?[X,Y]:((creative(X)&quiet(X)&european(X))&(quieter(manuel,Y))&(quieter(X,Y))))& (quiet(tammy)&european(tammy)))

room(tammy)&(![X]:(room(X)=>(X='tammy')))& (((~hate(audra,tammy))|(quiet(tammy)&tall(tammy)&european(tammy))))

neutral

entailment

contradiction

Sharon, Jessie, Karen, Travis are the only persons in the room. Sharon who does not like Abraham, likes Julia. Julia is richer than Jessie. Jessie and Sharon are respectively rich and creative. Jessie neither likes Julia nor does not can play the guitar. Sharon and Jessie are respectively creative and rich. Someone who is not Sharon is richer than someone who is liked by Abraham. It is not the case that 'Abraham is a client of Jessie'.

Jessie neither is richer than Julia nor is a rich creative person.

neutral

% SZS status Satisfiable

room(sharon)&room(jessie)&room(karen)&room(travis)&(![X]:(room(X)=>(X='sharon'|X='jessie'|X='karen'|X='travis')))& (((~like(abraham,sharon))&(like(julia,sharon)))& (richer(jessie,julia))& ((rich(jessie))&(creative(sharon)))& (~((like(julia,jessie))|(does_not_can_play_the_guitar(jessie))))& ((creative(sharon))&(rich(jessie)))& (?[X,Y]:((X!=sharon)&(like(Y,abraham))&(richer(X,Y))))& (~(client(jessie,abraham))))

room(sharon)&room(jessie)&room(karen)&room(travis)&(![X]:(room(X)=>(X='sharon'|X='jessie'|X='karen'|X='travis')))& (~((richer(julia,jessie))|(rich(jessie)&creative(jessie)&person(jessie))))

entailment

contradiction

contradiction

Emma, Christine, Hubert are the only persons in the room. “Christine likes Gayle” if “someone in the room does not hate Diane”. Emma does not collect comic books. Hubert and Emma do not hate Diane. Christine and Hubert like Diane. Emma neither collects comic books nor is not hated by Gayle. Emma neither does not hate Gayle nor is a creative person. Hubert is not a quiet person or does not collect comic books or both. Everyone in the room is not creative, not tall. Someone in the room does not hate Diane. Christine is the quietest in the room.

Hubert hates Diane or is not quiet or both.

neutral

% SZS status Satisfiable

room(emma)&room(christine)&room(hubert)&(![X]:(room(X)=>(X='emma'|X='christine'|X='hubert')))& (((?[X]:(room(X)=>(~hate(diane,X))))=>(like(gayle,christine)))& (does_not_collect_comic_books(emma))& (~hate(diane,hubert)&~hate(diane,emma))& (like(diane,christine)&like(diane,hubert))& (~((collects_comic_books(emma))|(~hate(emma,gayle))))& (~((~hate(gayle,emma))|(creative(emma)&person(emma))))& (((~(quiet(hubert)&person(hubert)))|(does_not_collect_comic_books(hubert))))& (![X]:(room(X)=>(~creative(X)&~tall(X))))& (?[X]:(room(X)=>(~hate(diane,X))))& (![X]:(quieter(X,christine))))

room(emma)&room(christine)&room(hubert)&(![X]:(room(X)=>(X='emma'|X='christine'|X='hubert')))& (((hate(diane,hubert))|(~quiet(hubert))))

neutral

entailment

entailment

Rachel, Ryan, Christopher are the only persons in the room. "Rachel neither own a television nor likes Veda" if "Rachel is a rich brave tourist and does enjoy trail running" and vice versa. If "someone outside the room who is not liked by Veda is not a quiet brave creative tourist" then "Ryan is not a quiet brave rich creative tourist or is not a quiet rich tourist or both" otherwise "Christopher is the least rich in the room". If "Rachel is not a rich creative brave tourist and is not liked by Robert" then "more than one person outside the room is not Christopher". Christopher neither is liked by Robert nor likes Robert. Only one person outside the room does enjoy trail running. Christopher neither is liked by Robert nor is not a brave quiet tourist. Ryan who does not enjoy trail running, own a television. Christopher is not a brave quiet rich tourist and is a brave quiet tourist. Ryan is not a quiet brave rich creative tourist or is not a quiet rich tourist or both.

Ryan and Christopher are not a creative happy rich brave quiet tourist.

entailment

% 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(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(happy_type, type, ( happy: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(predb_type, type, ( predb: $i > $o)). tff(preda_type, type, ( preda: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(mary_type, type, ( mary: $i)). tff(susan_type, type, ( susan: $i)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(1,assumption,(~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul)))), introduced(assumption)). tff(2,plain, (((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul))) | creative(paul)), inference(tautology,[status(thm)],[])). tff(3,plain, (creative(paul)), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, (((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul))) | brave(paul)), inference(tautology,[status(thm)],[])). tff(5,plain, (brave(paul)), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, (((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul))) | tourist(paul)), inference(tautology,[status(thm)],[])). tff(7,plain, (tourist(paul)), inference(unit_resolution,[status(thm)],[6, 1])). tff(8,plain, (((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul))) | quiet(paul)), inference(tautology,[status(thm)],[])). tff(9,plain, (quiet(paul)), inference(unit_resolution,[status(thm)],[8, 1])). tff(10,plain, (((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul))) | rich(paul)), inference(tautology,[status(thm)],[])). tff(11,plain, (rich(paul)), inference(unit_resolution,[status(thm)],[10, 1])). tff(12,plain, ((((~quiet(paul)) | (~rich(paul)) | (~tourist(paul))) | ((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)))) <=> ((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)))), inference(rewrite,[status(thm)],[])). tff(13,plain, ((~(~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul))))) <=> ((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)))), inference(rewrite,[status(thm)],[])). tff(14,plain, ((quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul)) <=> (~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul))))), inference(rewrite,[status(thm)],[])). tff(15,plain, ((~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul))) <=> (~(~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)))))), inference(monotonicity,[status(thm)],[14])). tff(16,plain, ((~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul))) <=> ((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)))), inference(transitivity,[status(thm)],[15, 13])). tff(17,plain, ((~(~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul))))) <=> ((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)))), inference(rewrite,[status(thm)],[])). tff(18,plain, ((quiet(paul) & rich(paul) & tourist(paul)) <=> (~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul))))), inference(rewrite,[status(thm)],[])). tff(19,plain, ((~(quiet(paul) & rich(paul) & tourist(paul))) <=> (~(~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)))))), inference(monotonicity,[status(thm)],[18])). tff(20,plain, ((~(quiet(paul) & rich(paul) & tourist(paul))) <=> ((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)))), inference(transitivity,[status(thm)],[19, 17])). tff(21,plain, (((~(quiet(paul) & rich(paul) & tourist(paul))) | (~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul)))) <=> (((~quiet(paul)) | (~rich(paul)) | (~tourist(paul))) | ((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul))))), inference(monotonicity,[status(thm)],[20, 16])). tff(22,plain, (((~(quiet(paul) & rich(paul) & tourist(paul))) | (~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul)))) <=> ((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)))), inference(transitivity,[status(thm)],[21, 12])). tff(23,plain, (((~(quiet(paul) & rich(paul) & tourist(paul))) | (~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul)))) <=> ((~(quiet(paul) & rich(paul) & tourist(paul))) | (~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul))))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((((((rich(mary) & brave(mary)) & tourist(mary)) & preda(mary)) <=> (~(predb(mary) | like(susan, mary)))) & ((?[X: $i] : ((~room(X)) => ((~like(X, susan)) => (~(((quiet(X) & brave(X)) & creative(X)) & tourist(X))))) => ((~((((quiet(paul) & brave(paul)) & rich(paul)) & creative(paul)) & tourist(paul))) | (~((quiet(paul) & rich(paul)) & tourist(paul))))) | ((~?[X: $i] : ((~room(X)) => ((~like(X, susan)) => (~(((quiet(X) & brave(X)) & creative(X)) & tourist(X)))))) => ![X: $i] : richer(fred, X)))) & (((~(((rich(mary) & creative(mary)) & brave(mary)) & tourist(mary))) & (~like(mary, alice))) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = fred)) & (~(Y = fred)))) & (~(X = Y))))) & (~(like(fred, alice) | like(alice, fred)))) & (?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((preda(X) & preda(Y)) => (X = Y)))) & (~(like(fred, alice) | (~((brave(fred) & quiet(fred)) & tourist(fred)))))) & ((~preda(paul)) & predb(paul))) & ((~(((brave(fred) & quiet(fred)) & rich(fred)) & tourist(fred))) & ((brave(fred) & quiet(fred)) & tourist(fred)))) & ((~((((quiet(paul) & brave(paul)) & rich(paul)) & creative(paul)) & tourist(paul))) | (~((quiet(paul) & rich(paul)) & tourist(paul)))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((~(((((creative(paul) & happy(paul)) & rich(paul)) & brave(paul)) & quiet(paul)) & tourist(paul))) & (~(((((creative(fred) & happy(fred)) & rich(fred)) & brave(fred)) & quiet(fred)) & tourist(fred))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((predb(mary) | like(susan, mary)) <=> (rich(mary) & brave(mary) & tourist(mary) & preda(mary)))) & ((~((~(rich(mary) & creative(mary) & brave(mary) & tourist(mary))) & (~like(mary, alice)))) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = fred)) & (~(Y = fred)) & (~(X = Y)))) & (~(like(alice, fred) | like(fred, alice))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)) & (~(like(fred, alice) | (~(brave(fred) & quiet(fred) & tourist(fred))))) & (~preda(paul)) & predb(paul) & (~(brave(fred) & quiet(fred) & rich(fred) & tourist(fred))) & brave(fred) & quiet(fred) & tourist(fred) & ((~(quiet(paul) & rich(paul) & tourist(paul))) | (~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul)))))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))))))), inference(rewrite,[status(thm)],[])). tff(25,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((((((((rich(mary) & brave(mary)) & tourist(mary)) & preda(mary)) <=> (~(predb(mary) | like(susan, mary)))) & ((?[X: $i] : ((~room(X)) => ((~like(X, susan)) => (~(((quiet(X) & brave(X)) & creative(X)) & tourist(X))))) => ((~((((quiet(paul) & brave(paul)) & rich(paul)) & creative(paul)) & tourist(paul))) | (~((quiet(paul) & rich(paul)) & tourist(paul))))) | ((~?[X: $i] : ((~room(X)) => ((~like(X, susan)) => (~(((quiet(X) & brave(X)) & creative(X)) & tourist(X)))))) => ![X: $i] : richer(fred, X)))) & (((~(((rich(mary) & creative(mary)) & brave(mary)) & tourist(mary))) & (~like(mary, alice))) => ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = fred)) & (~(Y = fred)))) & (~(X = Y))))) & (~(like(fred, alice) | like(alice, fred)))) & (?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((preda(X) & preda(Y)) => (X = Y)))) & (~(like(fred, alice) | (~((brave(fred) & quiet(fred)) & tourist(fred)))))) & ((~preda(paul)) & predb(paul))) & ((~(((brave(fred) & quiet(fred)) & rich(fred)) & tourist(fred))) & ((brave(fred) & quiet(fred)) & tourist(fred)))) & ((~((((quiet(paul) & brave(paul)) & rich(paul)) & creative(paul)) & tourist(paul))) | (~((quiet(paul) & rich(paul)) & tourist(paul)))))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((~(((((creative(paul) & happy(paul)) & rich(paul)) & brave(paul)) & quiet(paul)) & tourist(paul))) & (~(((((creative(fred) & happy(fred)) & rich(fred)) & brave(fred)) & quiet(fred)) & tourist(fred))))))), file('/mnt/tmpfs//701662956551891781488331.p','negated')). tff(26,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((predb(mary) | like(susan, mary)) <=> (rich(mary) & brave(mary) & tourist(mary) & preda(mary)))) & ((~((~(rich(mary) & creative(mary) & brave(mary) & tourist(mary))) & (~like(mary, alice)))) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = fred)) & (~(Y = fred)) & (~(X = Y)))) & (~(like(alice, fred) | like(fred, alice))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)) & (~(like(fred, alice) | (~(brave(fred) & quiet(fred) & tourist(fred))))) & (~preda(paul)) & predb(paul) & (~(brave(fred) & quiet(fred) & rich(fred) & tourist(fred))) & brave(fred) & quiet(fred) & tourist(fred) & ((~(quiet(paul) & rich(paul) & tourist(paul))) | (~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul)))))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)))))), inference(modus_ponens,[status(thm)],[25, 24])). tff(27,plain, (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((predb(mary) | like(susan, mary)) <=> (rich(mary) & brave(mary) & tourist(mary) & preda(mary)))) & ((~((~(rich(mary) & creative(mary) & brave(mary) & tourist(mary))) & (~like(mary, alice)))) | ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = fred)) & (~(Y = fred)) & (~(X = Y)))) & (~(like(alice, fred) | like(fred, alice))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)) & (~(like(fred, alice) | (~(brave(fred) & quiet(fred) & tourist(fred))))) & (~preda(paul)) & predb(paul) & (~(brave(fred) & quiet(fred) & rich(fred) & tourist(fred))) & brave(fred) & quiet(fred) & tourist(fred) & ((~(quiet(paul) & rich(paul) & tourist(paul))) | (~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul))))), inference(or_elim,[status(thm)],[26])). tff(28,plain, ((~(quiet(paul) & rich(paul) & tourist(paul))) | (~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul)))), inference(and_elim,[status(thm)],[27])). tff(29,plain, ((~(quiet(paul) & rich(paul) & tourist(paul))) | (~(quiet(paul) & brave(paul) & rich(paul) & creative(paul) & tourist(paul)))), inference(modus_ponens,[status(thm)],[28, 23])). tff(30,plain, ((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul))), inference(modus_ponens,[status(thm)],[29, 22])). tff(31,plain, ($false), inference(unit_resolution,[status(thm)],[30, 11, 9, 7, 5, 3])). tff(32,plain,((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul))), inference(lemma,lemma(discharge,[]))). tff(33,plain, (tourist(fred) <=> tourist(fred)), inference(rewrite,[status(thm)],[])). tff(34,plain, (~(like(fred, alice) | (~(brave(fred) & quiet(fred) & tourist(fred))))), inference(and_elim,[status(thm)],[27])). tff(35,plain, (brave(fred) & quiet(fred) & tourist(fred)), inference(or_elim,[status(thm)],[34])). tff(36,plain, (tourist(fred)), inference(and_elim,[status(thm)],[35])). tff(37,plain, (tourist(fred)), inference(modus_ponens,[status(thm)],[36, 33])). tff(38,plain, (quiet(fred) <=> quiet(fred)), inference(rewrite,[status(thm)],[])). tff(39,plain, (quiet(fred)), inference(and_elim,[status(thm)],[35])). tff(40,plain, (quiet(fred)), inference(modus_ponens,[status(thm)],[39, 38])). tff(41,plain, (brave(fred) <=> brave(fred)), inference(rewrite,[status(thm)],[])). tff(42,plain, (brave(fred)), inference(and_elim,[status(thm)],[35])). tff(43,plain, (brave(fred)), inference(modus_ponens,[status(thm)],[42, 41])). tff(44,plain, ((~(~((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred))))) <=> ((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred)))), inference(rewrite,[status(thm)],[])). tff(45,plain, ((brave(fred) & quiet(fred) & rich(fred) & tourist(fred)) <=> (~((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred))))), inference(rewrite,[status(thm)],[])). tff(46,plain, ((~(brave(fred) & quiet(fred) & rich(fred) & tourist(fred))) <=> (~(~((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred)))))), inference(monotonicity,[status(thm)],[45])). tff(47,plain, ((~(brave(fred) & quiet(fred) & rich(fred) & tourist(fred))) <=> ((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred)))), inference(transitivity,[status(thm)],[46, 44])). tff(48,plain, ((~(brave(fred) & quiet(fred) & rich(fred) & tourist(fred))) <=> (~(brave(fred) & quiet(fred) & rich(fred) & tourist(fred)))), inference(rewrite,[status(thm)],[])). tff(49,plain, (~(brave(fred) & quiet(fred) & rich(fred) & tourist(fred))), inference(and_elim,[status(thm)],[27])). tff(50,plain, (~(brave(fred) & quiet(fred) & rich(fred) & tourist(fred))), inference(modus_ponens,[status(thm)],[49, 48])). tff(51,plain, ((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred))), inference(modus_ponens,[status(thm)],[50, 47])). tff(52,plain, (~rich(fred)), inference(unit_resolution,[status(thm)],[51, 43, 40, 37])). tff(53,plain, (((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred)) | (~creative(fred)) | (~happy(fred))) | rich(fred)), inference(tautology,[status(thm)],[])). tff(54,plain, ((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred)) | (~creative(fred)) | (~happy(fred))), inference(unit_resolution,[status(thm)],[53, 52])). tff(55,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(56,plain, (room(fred)), inference(and_elim,[status(thm)],[27])). tff(57,plain, (room(fred)), inference(modus_ponens,[status(thm)],[56, 55])). tff(58,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(59,plain, (room(paul)), inference(and_elim,[status(thm)],[27])). tff(60,plain, (room(paul)), inference(modus_ponens,[status(thm)],[59, 58])). tff(61,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(62,plain, (room(mary)), inference(and_elim,[status(thm)],[27])). tff(63,plain, (room(mary)), inference(modus_ponens,[status(thm)],[62, 61])). tff(64,plain, (((~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul)))) | (~((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred)) | (~creative(fred)) | (~happy(fred)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul)))) | (~((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred)) | (~creative(fred)) | (~happy(fred)))))), inference(rewrite,[status(thm)],[])). tff(65,plain, ((~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))), inference(rewrite,[status(thm)],[])). tff(66,plain, ((creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)) <=> (~((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred)) | (~creative(fred)) | (~happy(fred))))), inference(rewrite,[status(thm)],[])). tff(67,plain, ((creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul)) <=> (~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul))))), inference(rewrite,[status(thm)],[])). tff(68,plain, (((creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul)) | (creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> ((~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul)))) | (~((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred)) | (~creative(fred)) | (~happy(fred)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))), inference(monotonicity,[status(thm)],[67, 66, 65])). tff(69,plain, (((creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul)) | (creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~((~quiet(paul)) | (~rich(paul)) | (~tourist(paul)) | (~brave(paul)) | (~creative(paul)) | (~happy(paul)))) | (~((~brave(fred)) | (~quiet(fred)) | (~rich(fred)) | (~tourist(fred)) | (~creative(fred)) | (~happy(fred)))))), inference(transitivity,[status(thm)],[68, 64])). tff(70,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul)) | (creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))) <=> ((creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul)) | (creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))), inference(rewrite,[status(thm)],[])). tff(71,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul)) | (creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul)) | (creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)))), inference(monotonicity,[status(thm)],[65])). tff(72,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul)) | (creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))) <=> ((creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul)) | (creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))), inference(transitivity,[status(thm)],[71, 70])). tff(73,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))))), inference(rewrite,[status(thm)],[])). tff(74,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)))))), inference(monotonicity,[status(thm)],[73])). tff(75,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred)))))), inference(rewrite,[status(thm)],[])). tff(76,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))))), inference(or_elim,[status(thm)],[26])). tff(77,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))))), inference(modus_ponens,[status(thm)],[76, 74])). tff(78,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))))), inference(modus_ponens,[status(thm)],[77, 75])). tff(79,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(creative(paul) & happy(paul) & rich(paul) & brave(paul) & quiet(paul) & tourist(paul))) & (~(creative(fred) & happy(fred) & rich(fred) & brave(fred) & quiet(fred) & tourist(fred))))), inference(modus_ponens,[status(thm)],[78, 74])). 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!3 |'fred'|) (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3))))) (a!6 (and (creative paul) (happy paul) (rich paul) (brave paul) (quiet paul) (tourist paul))) (a!7 (and (creative fred) (happy fred) (rich fred) (brave fred) (quiet fred) (tourist fred)))) (let ((a!8 (~ (not (and (room mary) (room paul) (room fred) a!4 (not a!6) (not a!7))) (or (not (room mary)) (not (room paul)) (not (room fred)) a!5 a!6 a!7)))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (refl (~ a!6 a!6)) (refl (~ a!7 a!7)) a!8)))

room(rachel)&room(ryan)&room(christopher)&(![X]:(room(X)=>(X='rachel'|X='ryan'|X='christopher')))& ((((rich(rachel)&brave(rachel)&tourist(rachel))&(does_enjoy_trail_running(rachel)))<=>(~((own_a_television(rachel))|(like(veda,rachel)))))& (((?[X]:(~room(X)=>(((~like(X,veda))=>(~(quiet(X)&brave(X)&creative(X)&tourist(X)))))))=>(((~(quiet(ryan)&brave(ryan)&rich(ryan)&creative(ryan)&tourist(ryan)))|(~(quiet(ryan)&rich(ryan)&tourist(ryan))))))|((~(?[X]:(~room(X)=>(((~like(X,veda))=>(~(quiet(X)&brave(X)&creative(X)&tourist(X))))))))=>(![X]:(richer(christopher,X)))))& (((~(rich(rachel)&creative(rachel)&brave(rachel)&tourist(rachel)))&(~like(rachel,robert)))=>((?[X,Y]:(~room(X)&~room(Y)&(X!=christopher&Y!=christopher)&(X!=Y)))))& (~((like(christopher,robert))|(like(robert,christopher))))& (((?[X]:(~room(X)&does_enjoy_trail_running(X)))&(![X,Y]:((does_enjoy_trail_running(X)&does_enjoy_trail_running(Y))=>(X=Y)))))& (~((like(christopher,robert))|(~(brave(christopher)&quiet(christopher)&tourist(christopher)))))& ((does_not_enjoy_trail_running(ryan))&(own_a_television(ryan)))& ((~(brave(christopher)&quiet(christopher)&rich(christopher)&tourist(christopher)))&(brave(christopher)&quiet(christopher)&tourist(christopher)))& (((~(quiet(ryan)&brave(ryan)&rich(ryan)&creative(ryan)&tourist(ryan)))|(~(quiet(ryan)&rich(ryan)&tourist(ryan))))))

room(rachel)&room(ryan)&room(christopher)&(![X]:(room(X)=>(X='rachel'|X='ryan'|X='christopher')))& (~(creative(ryan)&happy(ryan)&rich(ryan)&brave(ryan)&quiet(ryan)&tourist(ryan))&~(creative(christopher)&happy(christopher)&rich(christopher)&brave(christopher)&quiet(christopher)&tourist(christopher)))

neutral

entailment

contradiction

Kassie, Elwood are the only persons in the room. Kassie is not hated by Nellie or is not rich, not creative or both. Kassie who is not Elwood, is hated by Nellie. Kassie is the richest in the room. Everyone outside the room is richer than Nellie.

Kassie is not rich, not creative.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(rich_type, type, ( rich: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(1,plain, (hate(mary, lucy) <=> hate(mary, lucy)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((~hate(mary, lucy)) | ((~rich(mary)) & (~creative(mary)))) & ((~(mary = paul)) & hate(mary, lucy))) & ![X: $i] : richer(X, mary)) & ![X: $i] : ((~room(X)) => richer(lucy, X)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~rich(mary)) & (~creative(mary)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, lucy)) | ((~rich(mary)) & (~creative(mary)))) & (~(mary = paul)) & hate(mary, lucy) & ![X: $i] : richer(X, mary) & ![X: $i] : (room(X) | richer(lucy, X)))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary)))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((~hate(mary, lucy)) | ((~rich(mary)) & (~creative(mary)))) & ((~(mary = paul)) & hate(mary, lucy))) & ![X: $i] : richer(X, mary)) & ![X: $i] : ((~room(X)) => richer(lucy, X)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~rich(mary)) & (~creative(mary)))))), file('/mnt/tmpfs//406828843615712916125314.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, lucy)) | ((~rich(mary)) & (~creative(mary)))) & (~(mary = paul)) & hate(mary, lucy) & ![X: $i] : richer(X, mary) & ![X: $i] : (room(X) | richer(lucy, X)))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, lucy)) | ((~rich(mary)) & (~creative(mary)))) & (~(mary = paul)) & hate(mary, lucy) & ![X: $i] : richer(X, mary) & ![X: $i] : (room(X) | richer(lucy, X))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (hate(mary, lucy)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (hate(mary, lucy)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (((~hate(mary, lucy)) | ((~rich(mary)) & (~creative(mary)))) <=> ((~hate(mary, lucy)) | (~(rich(mary) | creative(mary))))), inference(rewrite,[status(thm)],[])). tff(9,plain, (((~hate(mary, lucy)) | ((~rich(mary)) & (~creative(mary)))) <=> ((~hate(mary, lucy)) | ((~rich(mary)) & (~creative(mary))))), inference(rewrite,[status(thm)],[])). tff(10,plain, ((~hate(mary, lucy)) | ((~rich(mary)) & (~creative(mary)))), inference(and_elim,[status(thm)],[5])). tff(11,plain, ((~hate(mary, lucy)) | ((~rich(mary)) & (~creative(mary)))), inference(modus_ponens,[status(thm)],[10, 9])). tff(12,plain, ((~hate(mary, lucy)) | (~(rich(mary) | creative(mary)))), inference(modus_ponens,[status(thm)],[11, 8])). tff(13,plain, (~(rich(mary) | creative(mary))), inference(unit_resolution,[status(thm)],[12, 7])). tff(14,plain, ((rich(mary) | creative(mary)) | (~rich(mary))), inference(tautology,[status(thm)],[])). tff(15,plain, (~rich(mary)), inference(unit_resolution,[status(thm)],[14, 13])). tff(16,plain, ((rich(mary) | creative(mary)) | (~creative(mary))), inference(tautology,[status(thm)],[])). tff(17,plain, (~creative(mary)), inference(unit_resolution,[status(thm)],[16, 13])). tff(18,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(19,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(20,plain, (room(paul)), inference(modus_ponens,[status(thm)],[19, 18])). tff(21,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(22,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(23,plain, (room(mary)), inference(modus_ponens,[status(thm)],[22, 21])). tff(24,plain, (((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | rich(mary) | creative(mary)) <=> (rich(mary) | creative(mary) | (~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(rewrite,[status(thm)],[])). tff(25,plain, ((~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))), inference(rewrite,[status(thm)],[])). tff(26,plain, (((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | rich(mary) | creative(mary)) <=> ((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | rich(mary) | creative(mary))), inference(monotonicity,[status(thm)],[25])). tff(27,plain, (((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | rich(mary) | creative(mary)) <=> (rich(mary) | creative(mary) | (~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(transitivity,[status(thm)],[26, 24])). tff(28,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary)))), inference(rewrite,[status(thm)],[])). tff(29,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary))))), inference(monotonicity,[status(thm)],[28])). tff(30,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary))))), inference(rewrite,[status(thm)],[])). tff(31,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary)))), inference(or_elim,[status(thm)],[4])). tff(32,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary)))), inference(modus_ponens,[status(thm)],[31, 29])). tff(33,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary)))), inference(modus_ponens,[status(thm)],[32, 30])). tff(34,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~rich(mary)) & (~creative(mary)))), inference(modus_ponens,[status(thm)],[33, 29])). 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!0 |'paul'|) (= X!0 |'mary'|) (not (room X!0)))))) (let ((a!5 (not (and (room mary) (room paul) a!3 (not (rich mary)) (not (creative mary)))))) (let ((a!6 (~ a!5 (or (not (room mary)) (not (room paul)) a!4 (rich mary) (creative mary))))) (nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ (rich mary) (rich mary))) (refl (~ (creative mary) (creative mary))) a!6))))

room(kassie)&room(elwood)&(![X]:(room(X)=>(X='kassie'|X='elwood')))& ((((~hate(kassie,nellie))|(~rich(kassie)&~creative(kassie))))& ((kassie!=elwood)&(hate(kassie,nellie)))& (![X]:(richer(X,kassie)))& (![X]:(~room(X)=>(richer(nellie,X)))))

room(kassie)&room(elwood)&(![X]:(room(X)=>(X='kassie'|X='elwood')))& (~rich(kassie)&~creative(kassie))

contradiction

contradiction

contradiction

Martha, Tabitha, William are the only persons in the room. 'Martha and Guadalupe hate each other' unless 'Martha neither does not like Guadalupe nor does not enjoy wildlife photography'. If 'it is not the case that 'Martha and Caleb like each other'' then 'more than one person outside the room does not hate Guadalupe' otherwise 'Guadalupe and Martha like each other'. Martha is the least tall in the room. Martha does not enjoy wildlife photography or is not liked by Guadalupe or both. Someone outside the room who is not creative, not quiet is not creative. Martha is a quiet tourist. Caleb is taller than Martha. Martha likes Shanna or is hated by Caleb or both. Martha is the least quiet in the room. Martha is the least rich in the room. Martha is a creative quiet european and is a rich tall creative person.

Someone who is richer than Caleb is quieter than someone who is hated by Caleb.

neutral

% SZS status Satisfiable

room(martha)&room(tabitha)&room(william)&(![X]:(room(X)=>(X='martha'|X='tabitha'|X='william')))& ((~(~((~like(guadalupe,martha))|(does_not_enjoy_wildlife_photography(martha))))=>((hate(martha,guadalupe) & hate(guadalupe,martha))))& (((~((like(martha,caleb) & like(caleb,martha))))=>((?[X,Y]:(~room(X)&~room(Y)&(~hate(guadalupe,X)&~hate(guadalupe,Y))&(X!=Y)))))|((~(~((like(martha,caleb) & like(caleb,martha)))))=>((like(guadalupe,martha) & like(martha,guadalupe)))))& (![X]:(taller(martha,X)))& (((does_not_enjoy_wildlife_photography(martha))|(~like(martha,guadalupe))))& (?[X]:(~room(X)=>(((~creative(X)&~quiet(X))=>(~creative(X))))))& (quiet(martha)&tourist(martha))& (taller(martha,caleb))& (((like(shanna,martha))|(hate(martha,caleb))))& (![X]:(quieter(martha,X)))& (![X]:(richer(martha,X)))& ((creative(martha)&quiet(martha)&european(martha))&(rich(martha)&tall(martha)&creative(martha)&person(martha))))

room(martha)&room(tabitha)&room(william)&(![X]:(room(X)=>(X='martha'|X='tabitha'|X='william')))& (?[X,Y]:((richer(caleb,X))&(hate(Y,caleb))&(quieter(X,Y))))

contradiction

neutral

contradiction

Danny, Betty, Charles, Thomas are the only persons in the room. Betty writes a travel blog. Betty is the least quiet in the room.

It is not the case that 'Charles is the least quiet in the room'.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(fred_type, type, ( fred: $i)). tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(mary_type, type, ( mary: $i)). tff(lucy_type, type, ( lucy: $i)). tff(susan_type, type, ( susan: $i)). tff(john_type, type, ( john: $i)). tff(1,assumption,(~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))), introduced(assumption)). tff(2,plain, (((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | room(X!0)), inference(tautology,[status(thm)],[])). tff(3,plain, (room(X!0)), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, (((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | (~(X!0 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(5,plain, (~(X!0 = |'mary'|)), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, (((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | (~(X!0 = |'paul'|))), inference(tautology,[status(thm)],[])). tff(7,plain, (~(X!0 = |'paul'|)), inference(unit_resolution,[status(thm)],[6, 1])). tff(8,plain, (((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | (~(X!0 = |'fred'|))), inference(tautology,[status(thm)],[])). tff(9,plain, (~(X!0 = |'fred'|)), inference(unit_resolution,[status(thm)],[8, 1])). tff(10,plain, (((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | (~(X!0 = |'alice'|))), inference(tautology,[status(thm)],[])). tff(11,plain, (~(X!0 = |'alice'|)), inference(unit_resolution,[status(thm)],[10, 1])). tff(12,plain, (^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(bind,[status(th)],[])). tff(13,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(quant_intro,[status(thm)],[12])). tff(14,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(rewrite,[status(thm)],[])). tff(15,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (preda(paul) & ![X: $i] : quieter(paul, X))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~![X: $i] : quieter(fred, X))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & preda(paul) & ![X: $i] : quieter(paul, X))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X)))))), inference(rewrite,[status(thm)],[])). tff(16,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (preda(paul) & ![X: $i] : quieter(paul, X))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~![X: $i] : quieter(fred, X))))), file('/mnt/tmpfs//1583526120957783189432857.p','negated')). tff(17,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & preda(paul) & ![X: $i] : quieter(paul, X))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X))))), inference(modus_ponens,[status(thm)],[16, 15])). tff(18,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & preda(paul) & ![X: $i] : quieter(paul, X)), inference(or_elim,[status(thm)],[17])). tff(19,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(and_elim,[status(thm)],[18])). tff(20,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[19, 14])). tff(21,plain,( ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(skolemize,[status(sab)],[20])). tff(22,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[21, 13])). tff(23,plain, (((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))), inference(quant_inst,[status(thm)],[])). tff(25,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))), inference(modus_ponens,[status(thm)],[24, 23])). tff(26,plain, ($false), inference(unit_resolution,[status(thm)],[25, 22, 11, 9, 7, 5, 3])). tff(27,plain,((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))), inference(lemma,lemma(discharge,[]))). tff(28,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(29,plain, (room(alice)), inference(and_elim,[status(thm)],[18])). tff(30,plain, (room(alice)), inference(modus_ponens,[status(thm)],[29, 28])). tff(31,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(32,plain, (room(fred)), inference(and_elim,[status(thm)],[18])). tff(33,plain, (room(fred)), inference(modus_ponens,[status(thm)],[32, 31])). tff(34,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(35,plain, (room(paul)), inference(and_elim,[status(thm)],[18])). tff(36,plain, (room(paul)), inference(modus_ponens,[status(thm)],[35, 34])). tff(37,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(38,plain, (room(mary)), inference(and_elim,[status(thm)],[18])). tff(39,plain, (room(mary)), inference(modus_ponens,[status(thm)],[38, 37])). tff(40,plain, ((![X: $i] : quieter(fred, X) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i] : quieter(fred, X))), inference(rewrite,[status(thm)],[])). tff(41,plain, ((~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))), inference(rewrite,[status(thm)],[])). tff(42,plain, ((![X: $i] : quieter(fred, X) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))) <=> (![X: $i] : quieter(fred, X) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(monotonicity,[status(thm)],[41])). tff(43,plain, ((![X: $i] : quieter(fred, X) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i] : quieter(fred, X))), inference(transitivity,[status(thm)],[42, 40])). tff(44,plain, ((![X: $i] : quieter(fred, X) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))) <=> (![X: $i] : quieter(fred, X) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(rewrite,[status(thm)],[])). tff(45,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i] : quieter(fred, X)) <=> (![X: $i] : quieter(fred, X) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(rewrite,[status(thm)],[])). tff(46,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i] : quieter(fred, X)) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i] : quieter(fred, X))), inference(monotonicity,[status(thm)],[41])). tff(47,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i] : quieter(fred, X)) <=> (![X: $i] : quieter(fred, X) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(transitivity,[status(thm)],[46, 45])). tff(48,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X)))), inference(rewrite,[status(thm)],[])). tff(49,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X))))), inference(monotonicity,[status(thm)],[48])). tff(50,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X))))), inference(rewrite,[status(thm)],[])). tff(51,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X)))), inference(or_elim,[status(thm)],[17])). tff(52,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X)))), inference(modus_ponens,[status(thm)],[51, 49])). tff(53,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X)))), inference(modus_ponens,[status(thm)],[52, 50])). tff(54,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~![X: $i] : quieter(fred, X)))), inference(modus_ponens,[status(thm)],[53, 49])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!0 |'alice'|) (= X!0 |'fred'|) (= X!0 |'paul'|) (= X!0 |'mary'|) (not (room X!0))))) (a!7 (lambda ((X $i)) (refl (~ (quieter fred X) (quieter fred X))))) (a!8 (forall ((X $i)) (quieter fred X)))) (let ((a!9 (nnf-neg (nnf-pos (proof-bind a!7) (~ a!8 a!8)) (~ (not (not a!8)) a!8))) (a!10 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 (not a!8))) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 a!8)))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!9 a!10)))

room(danny)&room(betty)&room(charles)&room(thomas)&(![X]:(room(X)=>(X='danny'|X='betty'|X='charles'|X='thomas')))& ((writes_a_travel_blog(betty))& (![X]:(quieter(betty,X))))

room(danny)&room(betty)&room(charles)&room(thomas)&(![X]:(room(X)=>(X='danny'|X='betty'|X='charles'|X='thomas')))& (~(![X]:(quieter(charles,X))))

entailment

entailment

entailment

Lorena, Edna, Charles, Vanessa are the only persons in the room. Charles either hates Miquel or does not have lived in exactly three countries if Charles does not hate Miquel and does not have lived in exactly three countries. If someone outside the room is a tall person then only one person outside the room does not hate Miquel otherwise Charles hates Miquel or is a brave person or both. If Charles and Edna are respectively tall and brave then Lorena is the least tall in the room otherwise Miquel is taller than Lorena. Lorena has lived in exactly three countries unless Charles and Miquel hate each other. Edna and Charles are not a tall brave tourist. Edna and Lorena hate each other. Lorena is not Edna and is a brave tourist. Edna has lived in exactly three countries or is not brave or both. Charles is not a tall brave person and does not have lived in exactly three countries. Charles is not tall.

Lorena neither is not a tall happy brave tourist nor has lived in exactly three countries.

neutral

% SZS status Satisfiable

room(lorena)&room(edna)&room(charles)&room(vanessa)&(![X]:(room(X)=>(X='lorena'|X='edna'|X='charles'|X='vanessa')))& ((((~hate(miquel,charles))&(does_not_have_lived_in_exactly_three_countries(charles)))=>((((hate(miquel,charles))|(does_not_have_lived_in_exactly_three_countries(charles)))&(~((hate(miquel,charles))|(does_not_have_lived_in_exactly_three_countries(charles)))))))& (((?[X]:(~room(X)=>(tall(X)&person(X))))=>(((?[X]:(~room(X)&~hate(miquel,X)))&(![X,Y]:((~hate(miquel,X)&~hate(miquel,Y))=>(X=Y))))))|((~(?[X]:(~room(X)=>(tall(X)&person(X)))))=>(((hate(miquel,charles))|(brave(charles)&person(charles))))))& ((((tall(charles))&(brave(edna)))=>(![X]:(taller(lorena,X))))|((~((tall(charles))&(brave(edna))))=>(taller(lorena,miquel))))& (~((hate(charles,miquel) & hate(miquel,charles)))=>(has_lived_in_exactly_three_countries(lorena)))& (~(tall(edna)&brave(edna)&tourist(edna))&~(tall(charles)&brave(charles)&tourist(charles)))& ((hate(edna,lorena) & hate(lorena,edna)))& ((lorena!=edna)&(brave(lorena)&tourist(lorena)))& (((has_lived_in_exactly_three_countries(edna))|(~brave(edna))))& ((~(tall(charles)&brave(charles)&person(charles)))&(does_not_have_lived_in_exactly_three_countries(charles)))& (~tall(charles)))

room(lorena)&room(edna)&room(charles)&room(vanessa)&(![X]:(room(X)=>(X='lorena'|X='edna'|X='charles'|X='vanessa')))& (~((~(tall(lorena)&happy(lorena)&brave(lorena)&tourist(lorena)))|(has_lived_in_exactly_three_countries(lorena))))

entailment

contradiction

contradiction

Elmer is the only person in the room. Only one person outside the room is hated by Christopher.

It is not the case that 'Elmer does not hate Christopher and is not hated by Christopher'.

neutral

% SZS status Satisfiable

room(elmer)&(![X]:(room(X)=>(X='elmer')))& (((?[X]:(~room(X)&hate(X,christopher)))&(![X,Y]:((hate(X,christopher)&hate(Y,christopher))=>(X=Y)))))

room(elmer)&(![X]:(room(X)=>(X='elmer')))& (~((~hate(christopher,elmer))&(~hate(elmer,christopher))))

contradiction

entailment

contradiction

Leslie, Alma are the only persons in the room. "Alma who does not own a television, is not creative, not quiet" only if "Charles and Zachary like each other". "Leslie is not Alma or is a sibling of Zachary or both" only if "Alma is not creative or is not liked by Ronald or both". Everyone outside the room is not Alma. Only one person in the room is a quiet creative person. Someone outside the room own a television. Zachary is a sibling of Leslie.

Someone who is not a quiet person is a sibling of someone who own a television.

neutral

% SZS status Satisfiable

room(leslie)&room(alma)&(![X]:(room(X)=>(X='leslie'|X='alma')))& ((((does_not_own_a_television(alma))&(~creative(alma)&~quiet(alma)))=>((like(charles,zachary) & like(zachary,charles))))& ((((leslie!=alma)|(sibling(zachary,leslie))))=>(((~creative(alma))|(~like(alma,ronald)))))& (![X]:(~room(X)=>(X!=alma)))& (((?[X]:(room(X)&quiet(X)&creative(X)&person(X)))&(![X,Y]:((quiet(X)&creative(X)&person(X)&quiet(Y)&creative(Y)&person(Y))=>(X=Y)))))& (?[X]:(~room(X)=>(own_a_television(X))))& (sibling(leslie,zachary)))

room(leslie)&room(alma)&(![X]:(room(X)=>(X='leslie'|X='alma')))& (?[X,Y]:((~(quiet(X)&person(X)))&(own_a_television(Y))&(sibling(X,Y))))

neutral

neutral

entailment

Evelyn, Roger are the only persons in the room. "Stacy is richer than Evelyn" if "Stacy and Evelyn hate each other" and vice versa. Stacy is a sibling of Evelyn. Everyone outside the room who is a happy person is a sibling of Stacy. Someone outside the room who enjoys hiking does not hate Stacy. More than one person outside the room is a brave rich happy person. Stacy is richer than Evelyn.

Evelyn does not enjoy hiking or is not a rich tall happy creative person or both.

neutral

% SZS status Satisfiable

room(evelyn)&room(roger)&(![X]:(room(X)=>(X='evelyn'|X='roger')))& ((((hate(stacy,evelyn) & hate(evelyn,stacy)))<=>(richer(evelyn,stacy)))& (sibling(evelyn,stacy))& (![X]:(~room(X)=>(((happy(X)&person(X))=>(sibling(stacy,X))))))& (?[X]:(~room(X)=>(((enjoys_hiking(X))=>(~hate(stacy,X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(brave(X)&rich(X)&happy(X)&person(X)&brave(Y)&rich(Y)&happy(Y)&person(Y))&(X!=Y))))& (richer(evelyn,stacy)))

room(evelyn)&room(roger)&(![X]:(room(X)=>(X='evelyn'|X='roger')))& (((does_not_enjoy_hiking(evelyn))|(~(rich(evelyn)&tall(evelyn)&happy(evelyn)&creative(evelyn)&person(evelyn)))))

entailment

neutral

neutral

Michael, Stephen are the only persons in the room. Iola is a sibling of Michael unless it is not the case that 'Michael is not hated by Nathaniel or does enjoy trail running or both'. Only one person outside the room hates Nathaniel if Michael does not hate Melinda and is a quiet tourist. James is quieter than Michael if it is not the case that 'Michael either is a happy person or hates Melinda' and vice versa. If more than one person outside the room is not tall then someone outside the room does not use an ios phone. Only one person outside the room does not hate Virginia. Nathaniel is taller than Michael. Stephen does not enjoy trail running or is not hated by Melinda or both. Only one person outside the room uses an ios phone. Stephen and Michael are not a quiet person. Iola is a sibling of Stephen.

Michael is not a tall quiet creative person or enjoys pottery or both.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(person_type, type, ( person: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(predc_type, type, ( predc: $i > $o)). tff(sibling_type, type, ( sibling: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(paul_type, type, ( paul: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(predb_type, type, ( predb: $i > $o)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(susan_type, type, ( susan: $i)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(tourist_type, type, ( tourist: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(1,assumption,(~(predc(mary) | (~quiet(mary)) | (~person(mary)) | (~tall(mary)) | (~creative(mary)))), introduced(assumption)). tff(2,plain, ((predc(mary) | (~quiet(mary)) | (~person(mary)) | (~tall(mary)) | (~creative(mary))) | quiet(mary)), inference(tautology,[status(thm)],[])). tff(3,plain, (quiet(mary)), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, ((predc(mary) | (~quiet(mary)) | (~person(mary)) | (~tall(mary)) | (~creative(mary))) | person(mary)), inference(tautology,[status(thm)],[])). tff(5,plain, (person(mary)), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, ((~(~((~quiet(mary)) | (~person(mary))))) <=> ((~quiet(mary)) | (~person(mary)))), inference(rewrite,[status(thm)],[])). tff(7,plain, ((quiet(mary) & person(mary)) <=> (~((~quiet(mary)) | (~person(mary))))), inference(rewrite,[status(thm)],[])). tff(8,plain, ((~(quiet(mary) & person(mary))) <=> (~(~((~quiet(mary)) | (~person(mary)))))), inference(monotonicity,[status(thm)],[7])). tff(9,plain, ((~(quiet(mary) & person(mary))) <=> ((~quiet(mary)) | (~person(mary)))), inference(transitivity,[status(thm)],[8, 6])). tff(10,plain, ((~(quiet(mary) & person(mary))) <=> (~(quiet(mary) & person(mary)))), inference(rewrite,[status(thm)],[])). tff(11,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((((~(~((~hate(mary, lucy)) | predb(mary)))) => sibling(mary, alice)) & (((~hate(fred, mary)) & (quiet(mary) & tourist(mary))) => (?[X: $i] : ((~room(X)) & hate(lucy, X)) & ![X: $i, Y: $i] : ((hate(lucy, X) & hate(lucy, Y)) => (X = Y))))) & ((~(((happy(mary) & person(mary)) | hate(fred, mary)) & (~((happy(mary) & person(mary)) | hate(fred, mary))))) <=> quieter(mary, john))) & (?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~tall(X)) & (~tall(Y)))) & (~(X = Y))) => ?[X: $i] : ((~room(X)) => (~preda(X))))) & (?[X: $i] : ((~room(X)) & (~hate(susan, X))) & ![X: $i, Y: $i] : (((~hate(susan, X)) & (~hate(susan, Y))) => (X = Y)))) & taller(mary, lucy)) & ((~predb(paul)) | (~hate(paul, fred)))) & (?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((preda(X) & preda(Y)) => (X = Y)))) & ((~(quiet(paul) & person(paul))) & (~(quiet(mary) & person(mary))))) & sibling(paul, alice))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~(((tall(mary) & quiet(mary)) & creative(mary)) & person(mary))) | predc(mary))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~((~hate(mary, lucy)) | predb(mary))) | sibling(mary, alice)) & ((~((~hate(fred, mary)) & quiet(mary) & tourist(mary))) | (?[X: $i] : ((~room(X)) & hate(lucy, X)) & ![X: $i, Y: $i] : ((~(hate(lucy, X) & hate(lucy, Y))) | (X = Y)))) & quieter(mary, john) & ((~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~tall(X)) & (~tall(Y)) & (~(X = Y)))) | ?[X: $i] : (room(X) | (~preda(X)))) & ?[X: $i] : ((~room(X)) & (~hate(susan, X))) & ![X: $i, Y: $i] : ((~((~hate(susan, X)) & (~hate(susan, Y)))) | (X = Y)) & taller(mary, lucy) & ((~predb(paul)) | (~hate(paul, fred))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)) & (~(quiet(paul) & person(paul))) & (~(quiet(mary) & person(mary))) & sibling(paul, alice))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary)))))))), inference(rewrite,[status(thm)],[])). tff(12,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((((((((((~(~((~hate(mary, lucy)) | predb(mary)))) => sibling(mary, alice)) & (((~hate(fred, mary)) & (quiet(mary) & tourist(mary))) => (?[X: $i] : ((~room(X)) & hate(lucy, X)) & ![X: $i, Y: $i] : ((hate(lucy, X) & hate(lucy, Y)) => (X = Y))))) & ((~(((happy(mary) & person(mary)) | hate(fred, mary)) & (~((happy(mary) & person(mary)) | hate(fred, mary))))) <=> quieter(mary, john))) & (?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~tall(X)) & (~tall(Y)))) & (~(X = Y))) => ?[X: $i] : ((~room(X)) => (~preda(X))))) & (?[X: $i] : ((~room(X)) & (~hate(susan, X))) & ![X: $i, Y: $i] : (((~hate(susan, X)) & (~hate(susan, Y))) => (X = Y)))) & taller(mary, lucy)) & ((~predb(paul)) | (~hate(paul, fred)))) & (?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((preda(X) & preda(Y)) => (X = Y)))) & ((~(quiet(paul) & person(paul))) & (~(quiet(mary) & person(mary))))) & sibling(paul, alice))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~(((tall(mary) & quiet(mary)) & creative(mary)) & person(mary))) | predc(mary))))), file('/mnt/tmpfs//8472486908566593987971794.p','negated')). tff(13,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~((~hate(mary, lucy)) | predb(mary))) | sibling(mary, alice)) & ((~((~hate(fred, mary)) & quiet(mary) & tourist(mary))) | (?[X: $i] : ((~room(X)) & hate(lucy, X)) & ![X: $i, Y: $i] : ((~(hate(lucy, X) & hate(lucy, Y))) | (X = Y)))) & quieter(mary, john) & ((~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~tall(X)) & (~tall(Y)) & (~(X = Y)))) | ?[X: $i] : (room(X) | (~preda(X)))) & ?[X: $i] : ((~room(X)) & (~hate(susan, X))) & ![X: $i, Y: $i] : ((~((~hate(susan, X)) & (~hate(susan, Y)))) | (X = Y)) & taller(mary, lucy) & ((~predb(paul)) | (~hate(paul, fred))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)) & (~(quiet(paul) & person(paul))) & (~(quiet(mary) & person(mary))) & sibling(paul, alice))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary))))))), inference(modus_ponens,[status(thm)],[12, 11])). tff(14,plain, (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~((~hate(mary, lucy)) | predb(mary))) | sibling(mary, alice)) & ((~((~hate(fred, mary)) & quiet(mary) & tourist(mary))) | (?[X: $i] : ((~room(X)) & hate(lucy, X)) & ![X: $i, Y: $i] : ((~(hate(lucy, X) & hate(lucy, Y))) | (X = Y)))) & quieter(mary, john) & ((~?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~tall(X)) & (~tall(Y)) & (~(X = Y)))) | ?[X: $i] : (room(X) | (~preda(X)))) & ?[X: $i] : ((~room(X)) & (~hate(susan, X))) & ![X: $i, Y: $i] : ((~((~hate(susan, X)) & (~hate(susan, Y)))) | (X = Y)) & taller(mary, lucy) & ((~predb(paul)) | (~hate(paul, fred))) & ?[X: $i] : ((~room(X)) & preda(X)) & ![X: $i, Y: $i] : ((~(preda(X) & preda(Y))) | (X = Y)) & (~(quiet(paul) & person(paul))) & (~(quiet(mary) & person(mary))) & sibling(paul, alice)), inference(or_elim,[status(thm)],[13])). tff(15,plain, (~(quiet(mary) & person(mary))), inference(and_elim,[status(thm)],[14])). tff(16,plain, (~(quiet(mary) & person(mary))), inference(modus_ponens,[status(thm)],[15, 10])). tff(17,plain, ((~quiet(mary)) | (~person(mary))), inference(modus_ponens,[status(thm)],[16, 9])). tff(18,plain, ($false), inference(unit_resolution,[status(thm)],[17, 5, 3])). tff(19,plain,(predc(mary) | (~quiet(mary)) | (~person(mary)) | (~tall(mary)) | (~creative(mary))), inference(lemma,lemma(discharge,[]))). tff(20,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(21,plain, (room(paul)), inference(and_elim,[status(thm)],[14])). tff(22,plain, (room(paul)), inference(modus_ponens,[status(thm)],[21, 20])). tff(23,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(24,plain, (room(mary)), inference(and_elim,[status(thm)],[14])). tff(25,plain, (room(mary)), inference(modus_ponens,[status(thm)],[24, 23])). tff(26,plain, (((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary)))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(predc(mary) | (~quiet(mary)) | (~person(mary)) | (~tall(mary)) | (~creative(mary)))))), inference(rewrite,[status(thm)],[])). tff(27,plain, ((~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))), inference(rewrite,[status(thm)],[])). tff(28,plain, (((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary)))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | (~(predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary))))))), inference(monotonicity,[status(thm)],[27])). tff(29,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary))))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary)))))), inference(rewrite,[status(thm)],[])). tff(30,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary))))))), inference(monotonicity,[status(thm)],[29])). tff(31,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary))))))), inference(rewrite,[status(thm)],[])). tff(32,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary)))))), inference(or_elim,[status(thm)],[13])). tff(33,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary)))))), inference(modus_ponens,[status(thm)],[32, 30])). tff(34,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary)))))), inference(modus_ponens,[status(thm)],[33, 31])). tff(35,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (predc(mary) | (~(tall(mary) & quiet(mary) & creative(mary) & person(mary)))))), inference(modus_ponens,[status(thm)],[34, 30])). 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!4 |'paul'|) (= X!4 |'mary'|) (not (room X!4))))) (a!5 (or (predc mary) (not (and (tall mary) (quiet mary) (creative mary) (person mary)))))) (let ((a!6 (~ (not (and (room mary) (room paul) a!3 a!5)) (or (not (room mary)) (not (room paul)) a!4 (not a!5))))) (nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ (not a!5) (not a!5))) a!6)))

room(michael)&room(stephen)&(![X]:(room(X)=>(X='michael'|X='stephen')))& ((~(~(((~hate(michael,nathaniel))|(does_enjoy_trail_running(michael)))))=>(sibling(michael,iola)))& (((~hate(melinda,michael))&(quiet(michael)&tourist(michael)))=>(((?[X]:(~room(X)&hate(nathaniel,X)))&(![X,Y]:((hate(nathaniel,X)&hate(nathaniel,Y))=>(X=Y))))))& ((~((((happy(michael)&person(michael))|(hate(melinda,michael)))&(~((happy(michael)&person(michael))|(hate(melinda,michael)))))))<=>(quieter(michael,james)))& (((?[X,Y]:(~room(X)&~room(Y)&(~tall(X)&~tall(Y))&(X!=Y))))=>(?[X]:(~room(X)=>(does_not_use_an_ios_phone(X)))))& (((?[X]:(~room(X)&~hate(virginia,X)))&(![X,Y]:((~hate(virginia,X)&~hate(virginia,Y))=>(X=Y)))))& (taller(michael,nathaniel))& (((does_not_enjoy_trail_running(stephen))|(~hate(stephen,melinda))))& (((?[X]:(~room(X)&uses_an_ios_phone(X)))&(![X,Y]:((uses_an_ios_phone(X)&uses_an_ios_phone(Y))=>(X=Y)))))& (~(quiet(stephen)&person(stephen))&~(quiet(michael)&person(michael)))& (sibling(stephen,iola)))

room(michael)&room(stephen)&(![X]:(room(X)=>(X='michael'|X='stephen')))& (((~(tall(michael)&quiet(michael)&creative(michael)&person(michael)))|(enjoys_pottery(michael))))

neutral

neutral

entailment

Brent, Daniel, Earl, Joe are the only persons in the room. "Brent neither does not practice yoga nor hates Karen" only if "Brent and Joe are respectively creative and brave". "Someone outside the room is not brave, not creative" only if "Joe is the richest in the room". "Only one person outside the room is hated by Karen" only if "Joe does practice yoga and hates Karen". "Joe and Brent are respectively creative and brave" if "someone outside the room is richer than Karen" and vice versa. Brent and Joe are respectively brave and rich. Only one person outside the room is hated by Karen. Someone who does not hate Karen hate someone who is hated by Karen. Only one person outside the room is not creative. Daniel is richer than Karen or does practice yoga or both. Daniel and Brent hate each other.

Someone who does practice yoga is richer than someone who hates Karen.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(room_type, type, ( room: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(john_type, type, ( john: $i)). tff(predb_type, type, ( predb: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(fred_type, type, ( fred: $i)). tff(tptp_fun_X_7_type, type, ( tptp_fun_X_7: $i)). tff(tptp_fun_X_3_type, type, ( tptp_fun_X_3: $i)). 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(1,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((~((~predb(mary)) | hate(john, mary))) => (creative(mary) & brave(alice))) & (?[X: $i] : ((~room(X)) => ((~brave(X)) & (~creative(X)))) => ![X: $i] : richer(X, alice))) & ((?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((hate(X, john) & hate(Y, john)) => (X = Y))) => (predb(alice) & hate(john, alice)))) & (?[X: $i] : ((~room(X)) => richer(john, X)) <=> (creative(alice) & brave(mary)))) & (brave(mary) & rich(alice))) & (?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((hate(X, john) & hate(Y, john)) => (X = Y)))) & ?[X: $i, Y: $i] : (((~hate(john, X)) & hate(Y, john)) & hate(X, Y))) & (?[X: $i] : ((~room(X)) & (~creative(X))) & ![X: $i, Y: $i] : (((~creative(X)) & (~creative(Y))) => (X = Y)))) & (richer(john, paul) | predb(paul))) & (hate(paul, mary) & hate(mary, paul)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : ((predb(X) & hate(john, Y)) & richer(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | hate(john, mary) | (creative(mary) & brave(alice))) & ((~?[X: $i] : (room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice)) & ((~(?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)))) | (predb(alice) & hate(john, alice))) & (?[X: $i] : (room(X) | richer(john, X)) <=> (creative(alice) & brave(mary))) & brave(mary) & rich(alice) & ?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)) & ?[X: $i, Y: $i] : ((~hate(john, X)) & hate(Y, john) & hate(X, Y)) & ?[X: $i] : ((~room(X)) & (~creative(X))) & ![X: $i, Y: $i] : ((~((~creative(X)) & (~creative(Y)))) | (X = Y)) & (predb(paul) | richer(john, paul)) & hate(paul, mary) & hate(mary, paul))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (predb(X) & hate(john, Y) & richer(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((~((~predb(mary)) | hate(john, mary))) => (creative(mary) & brave(alice))) & (?[X: $i] : ((~room(X)) => ((~brave(X)) & (~creative(X)))) => ![X: $i] : richer(X, alice))) & ((?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((hate(X, john) & hate(Y, john)) => (X = Y))) => (predb(alice) & hate(john, alice)))) & (?[X: $i] : ((~room(X)) => richer(john, X)) <=> (creative(alice) & brave(mary)))) & (brave(mary) & rich(alice))) & (?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((hate(X, john) & hate(Y, john)) => (X = Y)))) & ?[X: $i, Y: $i] : (((~hate(john, X)) & hate(Y, john)) & hate(X, Y))) & (?[X: $i] : ((~room(X)) & (~creative(X))) & ![X: $i, Y: $i] : (((~creative(X)) & (~creative(Y))) => (X = Y)))) & (richer(john, paul) | predb(paul))) & (hate(paul, mary) & hate(mary, paul)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : ((predb(X) & hate(john, Y)) & richer(X, Y))))), file('/mnt/tmpfs//8058759009349513279430468.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | hate(john, mary) | (creative(mary) & brave(alice))) & ((~?[X: $i] : (room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice)) & ((~(?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)))) | (predb(alice) & hate(john, alice))) & (?[X: $i] : (room(X) | richer(john, X)) <=> (creative(alice) & brave(mary))) & brave(mary) & rich(alice) & ?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)) & ?[X: $i, Y: $i] : ((~hate(john, X)) & hate(Y, john) & hate(X, Y)) & ?[X: $i] : ((~room(X)) & (~creative(X))) & ![X: $i, Y: $i] : ((~((~creative(X)) & (~creative(Y)))) | (X = Y)) & (predb(paul) | richer(john, paul)) & hate(paul, mary) & hate(mary, paul))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (predb(X) & hate(john, Y) & richer(X, Y))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~predb(mary)) | hate(john, mary) | (creative(mary) & brave(alice))) & ((~?[X: $i] : (room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice)) & ((~(?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)))) | (predb(alice) & hate(john, alice))) & (?[X: $i] : (room(X) | richer(john, X)) <=> (creative(alice) & brave(mary))) & brave(mary) & rich(alice) & ?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)) & ?[X: $i, Y: $i] : ((~hate(john, X)) & hate(Y, john) & hate(X, Y)) & ?[X: $i] : ((~room(X)) & (~creative(X))) & ![X: $i, Y: $i] : ((~((~creative(X)) & (~creative(Y)))) | (X = Y)) & (predb(paul) | richer(john, paul)) & hate(paul, mary) & hate(mary, paul)), inference(or_elim,[status(thm)],[4])). tff(6,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (room(mary)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((room(mary) | (~(brave(mary) | creative(mary)))) | (~room(mary))), inference(tautology,[status(thm)],[])). tff(9,plain, (room(mary) | (~(brave(mary) | creative(mary)))), inference(unit_resolution,[status(thm)],[8, 7])). tff(10,assumption,(![X: $i] : (~(room(X) | (~(brave(X) | creative(X)))))), introduced(assumption)). tff(11,plain, ((~![X: $i] : (~(room(X) | (~(brave(X) | creative(X)))))) | (~(room(mary) | (~(brave(mary) | creative(mary)))))), inference(quant_inst,[status(thm)],[])). tff(12,plain, ($false), inference(unit_resolution,[status(thm)],[11, 10, 9])). tff(13,plain,(~![X: $i] : (~(room(X) | (~(brave(X) | creative(X)))))), inference(lemma,lemma(discharge,[]))). tff(14,plain, ((![X: $i] : (~(room(X) | (~(brave(X) | creative(X))))) | ![X: $i] : richer(X, alice)) <=> (![X: $i] : (~(room(X) | (~(brave(X) | creative(X))))) | ![X: $i] : richer(X, alice))), inference(rewrite,[status(thm)],[])). tff(15,plain, ((![X: $i] : (~(room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice)) <=> (![X: $i] : (~(room(X) | (~(brave(X) | creative(X))))) | ![X: $i] : richer(X, alice))), inference(rewrite,[status(thm)],[])). tff(16,plain, ((![X: $i] : (~(room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice)) <=> (![X: $i] : (~(room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice))), inference(rewrite,[status(thm)],[])). tff(17,plain, (((~?[X: $i] : (room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice)) <=> ((~?[X: $i] : (room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice))), inference(rewrite,[status(thm)],[])). tff(18,plain, ((~?[X: $i] : (room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice)), inference(and_elim,[status(thm)],[5])). tff(19,plain, ((~?[X: $i] : (room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice)), inference(modus_ponens,[status(thm)],[18, 17])). tff(20,plain, ((~?[X: $i] : (room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice)), inference(modus_ponens,[status(thm)],[19, 17])). tff(21,plain, ((~?[X: $i] : (room(X) | ((~brave(X)) & (~creative(X))))) | ![X: $i] : richer(X, alice)), inference(modus_ponens,[status(thm)],[20, 17])).

room(brent)&room(daniel)&room(earl)&room(joe)&(![X]:(room(X)=>(X='brent'|X='daniel'|X='earl'|X='joe')))& (((~((does_not_practice_yoga(brent))|(hate(karen,brent))))=>((creative(brent))&(brave(joe))))& ((?[X]:(~room(X)=>(~brave(X)&~creative(X))))=>(![X]:(richer(X,joe))))& ((((?[X]:(~room(X)&hate(X,karen)))&(![X,Y]:((hate(X,karen)&hate(Y,karen))=>(X=Y)))))=>((does_practice_yoga(joe))&(hate(karen,joe))))& ((?[X]:(~room(X)=>(richer(karen,X))))<=>((creative(joe))&(brave(brent))))& ((brave(brent))&(rich(joe)))& (((?[X]:(~room(X)&hate(X,karen)))&(![X,Y]:((hate(X,karen)&hate(Y,karen))=>(X=Y)))))& (?[X,Y]:((~hate(karen,X))&(hate(Y,karen))&(hate(X,Y))))& (((?[X]:(~room(X)&~creative(X)))&(![X,Y]:((~creative(X)&~creative(Y))=>(X=Y)))))& (((richer(karen,daniel))|(does_practice_yoga(daniel))))& ((hate(daniel,brent) & hate(brent,daniel))))

room(brent)&room(daniel)&room(earl)&room(joe)&(![X]:(room(X)=>(X='brent'|X='daniel'|X='earl'|X='joe')))& (?[X,Y]:((does_practice_yoga(X))&(hate(karen,Y))&(richer(X,Y))))

neutral

neutral

neutral

Willie, Deborah, Thomas are the only persons in the room. If Willie is the richest in the room then only one person outside the room is not rich, not creative. Someone who is richer than Anthony like someone who likes Lisa if Willie is liked by Lisa or likes Anthony or both. No one in the room is not Thomas unless Thomas is taller than Golda. If Deborah is the tallest in the room then Willie is not happy. Willie is liked by Lisa or likes Anthony or both. Thomas is a creative rich tourist or is not liked by Golda or both. Golda and Deborah like each other. Deborah is not rich, not happy, not creative. Someone outside the room who is taller than Lisa makes homemade pastries. Someone who does not like Golda like someone who is liked by Lisa.

Willie who is not a rich tall person, is hated by Anthony.

neutral

% SZS status Satisfiable

room(willie)&room(deborah)&room(thomas)&(![X]:(room(X)=>(X='willie'|X='deborah'|X='thomas')))& (((![X]:(richer(X,willie)))=>(((?[X]:(~room(X)&~rich(X)&~creative(X)))&(![X,Y]:((~rich(X)&~creative(X)&~rich(Y)&~creative(Y))=>(X=Y))))))& ((((like(willie,lisa))|(like(anthony,willie))))=>(?[X,Y]:((richer(anthony,X))&(like(lisa,Y))&(like(X,Y)))))& (~(taller(golda,thomas))=>(~?[X]:(room(X)=>(X!=thomas))))& ((![X]:(taller(X,deborah)))=>(~happy(willie)))& (((like(willie,lisa))|(like(anthony,willie))))& (((creative(thomas)&rich(thomas)&tourist(thomas))|(~like(thomas,golda))))& ((like(golda,deborah) & like(deborah,golda)))& (~rich(deborah)&~happy(deborah)&~creative(deborah))& (?[X]:(~room(X)=>(((taller(lisa,X))=>(makes_homemade_pastries(X))))))& (?[X,Y]:((~like(golda,X))&(like(Y,lisa))&(like(X,Y)))))

room(willie)&room(deborah)&room(thomas)&(![X]:(room(X)=>(X='willie'|X='deborah'|X='thomas')))& ((~(rich(willie)&tall(willie)&person(willie)))&(hate(willie,anthony)))

neutral

neutral

contradiction

Raymond is the only person in the room. Raymond who is not rich, does not like Karen. Karen is richer than Raymond. Someone who is liked by Patricia like someone who is not Raymond. Only one person outside the room is not liked by Patricia. Raymond who is liked by Karen, is richer than Patricia. It is not the case that 'Raymond who is richer than Patricia, likes Karen'. Everyone outside the room who does not like Karen is not Raymond.

Raymond is a rich european and likes Patricia.

contradiction

-

room(raymond)&(![X]:(room(X)=>(X='raymond')))& (((~rich(raymond))&(~like(karen,raymond)))& (richer(raymond,karen))& (?[X,Y]:((like(X,patricia))&(Y!=raymond)&(like(X,Y))))& (((?[X]:(~room(X)&~like(X,patricia)))&(![X,Y]:((~like(X,patricia)&~like(Y,patricia))=>(X=Y)))))& ((like(raymond,karen))&(richer(patricia,raymond)))& (~((richer(patricia,raymond))&(like(karen,raymond))))& (![X]:(~room(X)=>(((~like(karen,X))=>(X!=raymond))))))

room(raymond)&(![X]:(room(X)=>(X='raymond')))& ((rich(raymond)&european(raymond))&(like(patricia,raymond)))

contradiction

contradiction

contradiction

Michael, Gayla, Evelyn, Anneliese are the only persons in the room. If 'more than one person in the room drives a hybrid car' then 'Michael who is not hated by Kathryn, is hated by Paul'. 'Only one person in the room hates Kathryn' only if 'Gayla neither is hated by Paul nor is not tall, not rich'. Michael is the richest in the room. Only one person in the room is not rich. Gayla and Kathryn hate each other. Evelyn and Michael do not hate Paul. More than one person outside the room does not drive a hybrid car. Someone who is not tall, not rich hate someone who is richer than Paul. Only one person in the room is not hated by Kathryn. Gayla is hated by Kathryn and is not rich, not tall, not happy. Michael who is not happy, does not have a piercing.

It is not the case that 'Michael is hated by Paul and has a piercing'.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_8_type, type, ( tptp_fun_X_8: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(mary_type, type, ( mary: $i)). tff(predc_type, type, ( predc: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(susan_type, type, ( susan: $i)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(preda_type, type, ( preda: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(alice_type, type, ( alice: $i)). tff(1,plain, ((~predc(mary)) <=> (~predc(mary))), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((?[X: $i, Y: $i] : (((room(X) & room(Y)) & (preda(X) & preda(Y))) & (~(X = Y))) => ((~hate(mary, susan)) & hate(mary, lucy))) & ((?[X: $i] : (room(X) & hate(susan, X)) & ![X: $i, Y: $i] : ((hate(susan, X) & hate(susan, Y)) => (X = Y))) => (~(hate(paul, lucy) | ((~tall(paul)) & (~rich(paul))))))) & ![X: $i] : richer(X, mary)) & (?[X: $i] : (room(X) & (~rich(X))) & ![X: $i, Y: $i] : (((~rich(X)) & (~rich(Y))) => (X = Y)))) & (hate(paul, susan) & hate(susan, paul))) & ((~hate(lucy, fred)) & (~hate(lucy, mary)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~preda(X)) & (~preda(Y)))) & (~(X = Y)))) & ?[X: $i, Y: $i] : ((((~tall(X)) & (~rich(X))) & richer(lucy, Y)) & hate(X, Y))) & (?[X: $i] : (room(X) & (~hate(X, susan))) & ![X: $i, Y: $i] : (((~hate(X, susan)) & (~hate(Y, susan))) => (X = Y)))) & (hate(paul, susan) & (((~rich(paul)) & (~tall(paul))) & (~happy(paul))))) & ((~happy(mary)) & (~predc(mary))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(hate(mary, lucy) & predc(mary)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : (room(X) & room(Y) & preda(X) & preda(Y) & (~(X = Y)))) | ((~hate(mary, susan)) & hate(mary, lucy))) & ((~(hate(paul, lucy) | ((~tall(paul)) & (~rich(paul))))) | (~(?[X: $i] : (room(X) & hate(susan, X)) & ![X: $i, Y: $i] : ((~(hate(susan, X) & hate(susan, Y))) | (X = Y))))) & ![X: $i] : richer(X, mary) & ?[X: $i] : (room(X) & (~rich(X))) & ![X: $i, Y: $i] : ((~((~rich(X)) & (~rich(Y)))) | (X = Y)) & hate(paul, susan) & hate(susan, paul) & (~hate(lucy, fred)) & (~hate(lucy, mary)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~preda(X)) & (~preda(Y)) & (~(X = Y))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~rich(X)) & richer(lucy, Y) & hate(X, Y)) & ?[X: $i] : (room(X) & (~hate(X, susan))) & ![X: $i, Y: $i] : ((~((~hate(X, susan)) & (~hate(Y, susan)))) | (X = Y)) & (~rich(paul)) & (~tall(paul)) & (~happy(paul)) & (~happy(mary)) & (~predc(mary)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((((((?[X: $i, Y: $i] : (((room(X) & room(Y)) & (preda(X) & preda(Y))) & (~(X = Y))) => ((~hate(mary, susan)) & hate(mary, lucy))) & ((?[X: $i] : (room(X) & hate(susan, X)) & ![X: $i, Y: $i] : ((hate(susan, X) & hate(susan, Y)) => (X = Y))) => (~(hate(paul, lucy) | ((~tall(paul)) & (~rich(paul))))))) & ![X: $i] : richer(X, mary)) & (?[X: $i] : (room(X) & (~rich(X))) & ![X: $i, Y: $i] : (((~rich(X)) & (~rich(Y))) => (X = Y)))) & (hate(paul, susan) & hate(susan, paul))) & ((~hate(lucy, fred)) & (~hate(lucy, mary)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~preda(X)) & (~preda(Y)))) & (~(X = Y)))) & ?[X: $i, Y: $i] : ((((~tall(X)) & (~rich(X))) & richer(lucy, Y)) & hate(X, Y))) & (?[X: $i] : (room(X) & (~hate(X, susan))) & ![X: $i, Y: $i] : (((~hate(X, susan)) & (~hate(Y, susan))) => (X = Y)))) & (hate(paul, susan) & (((~rich(paul)) & (~tall(paul))) & (~happy(paul))))) & ((~happy(mary)) & (~predc(mary))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(hate(mary, lucy) & predc(mary)))))), file('/mnt/tmpfs//8046543469315409281438289.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : (room(X) & room(Y) & preda(X) & preda(Y) & (~(X = Y)))) | ((~hate(mary, susan)) & hate(mary, lucy))) & ((~(hate(paul, lucy) | ((~tall(paul)) & (~rich(paul))))) | (~(?[X: $i] : (room(X) & hate(susan, X)) & ![X: $i, Y: $i] : ((~(hate(susan, X) & hate(susan, Y))) | (X = Y))))) & ![X: $i] : richer(X, mary) & ?[X: $i] : (room(X) & (~rich(X))) & ![X: $i, Y: $i] : ((~((~rich(X)) & (~rich(Y)))) | (X = Y)) & hate(paul, susan) & hate(susan, paul) & (~hate(lucy, fred)) & (~hate(lucy, mary)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~preda(X)) & (~preda(Y)) & (~(X = Y))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~rich(X)) & richer(lucy, Y) & hate(X, Y)) & ?[X: $i] : (room(X) & (~hate(X, susan))) & ![X: $i, Y: $i] : ((~((~hate(X, susan)) & (~hate(Y, susan)))) | (X = Y)) & (~rich(paul)) & (~tall(paul)) & (~happy(paul)) & (~happy(mary)) & (~predc(mary)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : (room(X) & room(Y) & preda(X) & preda(Y) & (~(X = Y)))) | ((~hate(mary, susan)) & hate(mary, lucy))) & ((~(hate(paul, lucy) | ((~tall(paul)) & (~rich(paul))))) | (~(?[X: $i] : (room(X) & hate(susan, X)) & ![X: $i, Y: $i] : ((~(hate(susan, X) & hate(susan, Y))) | (X = Y))))) & ![X: $i] : richer(X, mary) & ?[X: $i] : (room(X) & (~rich(X))) & ![X: $i, Y: $i] : ((~((~rich(X)) & (~rich(Y)))) | (X = Y)) & hate(paul, susan) & hate(susan, paul) & (~hate(lucy, fred)) & (~hate(lucy, mary)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~preda(X)) & (~preda(Y)) & (~(X = Y))) & ?[X: $i, Y: $i] : ((~tall(X)) & (~rich(X)) & richer(lucy, Y) & hate(X, Y)) & ?[X: $i] : (room(X) & (~hate(X, susan))) & ![X: $i, Y: $i] : ((~((~hate(X, susan)) & (~hate(Y, susan)))) | (X = Y)) & (~rich(paul)) & (~tall(paul)) & (~happy(paul)) & (~happy(mary)) & (~predc(mary))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~predc(mary)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (~predc(mary)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (((~predc(mary)) | (~hate(mary, lucy))) | predc(mary)), inference(tautology,[status(thm)],[])). tff(9,plain, ((~predc(mary)) | (~hate(mary, lucy))), inference(unit_resolution,[status(thm)],[8, 7])). tff(10,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(11,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(12,plain, (room(alice)), inference(modus_ponens,[status(thm)],[11, 10])). tff(13,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(14,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(15,plain, (room(fred)), inference(modus_ponens,[status(thm)],[14, 13])). tff(16,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(17,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(18,plain, (room(paul)), inference(modus_ponens,[status(thm)],[17, 16])). tff(19,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(20,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(21,plain, (room(mary)), inference(modus_ponens,[status(thm)],[20, 19])). tff(22,plain, (((~((~predc(mary)) | (~hate(mary, lucy)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (~((~predc(mary)) | (~hate(mary, lucy)))))), inference(rewrite,[status(thm)],[])). tff(23,plain, ((~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) <=> (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8))))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((hate(mary, lucy) & predc(mary)) <=> (~((~predc(mary)) | (~hate(mary, lucy))))), inference(rewrite,[status(thm)],[])). tff(25,plain, (((hate(mary, lucy) & predc(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8))))) <=> ((~((~predc(mary)) | (~hate(mary, lucy)))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))))), inference(monotonicity,[status(thm)],[24, 23])). tff(26,plain, (((hate(mary, lucy) & predc(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (~((~predc(mary)) | (~hate(mary, lucy)))))), inference(transitivity,[status(thm)],[25, 22])). tff(27,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (hate(mary, lucy) & predc(mary))) <=> ((hate(mary, lucy) & predc(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))))), inference(rewrite,[status(thm)],[])). tff(28,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (hate(mary, lucy) & predc(mary))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (hate(mary, lucy) & predc(mary)))), inference(monotonicity,[status(thm)],[23])). tff(29,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (hate(mary, lucy) & predc(mary))) <=> ((hate(mary, lucy) & predc(mary)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!8 = |'alice'|) | (X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))))), inference(transitivity,[status(thm)],[28, 27])). tff(30,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary))))), inference(rewrite,[status(thm)],[])). tff(31,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary)))))), inference(monotonicity,[status(thm)],[30])). tff(32,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary)))))), inference(rewrite,[status(thm)],[])). tff(33,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary))))), inference(or_elim,[status(thm)],[4])). tff(34,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary))))), inference(modus_ponens,[status(thm)],[33, 31])). tff(35,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary))))), inference(modus_ponens,[status(thm)],[34, 32])). tff(36,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(hate(mary, lucy) & predc(mary))))), inference(modus_ponens,[status(thm)],[35, 31])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!8 |'alice'|) (= X!8 |'fred'|) (= X!8 |'paul'|) (= X!8 |'mary'|) (not (room X!8))))) (a!7 (refl (~ (and (hate mary lucy) (predc mary)) (and (hate mary lucy) (predc mary)))))) (let ((a!8 (and (room mary) (room paul) (room fred) (room alice) a!5 (not (and (hate mary lucy) (predc mary)))))) (let ((a!9 (~ (not a!8) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (and (hate mary lucy) (predc mary)))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!7 a!9))))

room(michael)&room(gayla)&room(evelyn)&room(anneliese)&(![X]:(room(X)=>(X='michael'|X='gayla'|X='evelyn'|X='anneliese')))& ((((?[X,Y]:(room(X)&room(Y)&(drives_a_hybrid_car(X)&drives_a_hybrid_car(Y))&(X!=Y))))=>((~hate(michael,kathryn))&(hate(michael,paul))))& ((((?[X]:(room(X)&hate(kathryn,X)))&(![X,Y]:((hate(kathryn,X)&hate(kathryn,Y))=>(X=Y)))))=>(~((hate(gayla,paul))|(~tall(gayla)&~rich(gayla)))))& (![X]:(richer(X,michael)))& (((?[X]:(room(X)&~rich(X)))&(![X,Y]:((~rich(X)&~rich(Y))=>(X=Y)))))& ((hate(gayla,kathryn) & hate(kathryn,gayla)))& (~hate(paul,evelyn)&~hate(paul,michael))& ((?[X,Y]:(~room(X)&~room(Y)&(does_not_drive_a_hybrid_car(X)&does_not_drive_a_hybrid_car(Y))&(X!=Y))))& (?[X,Y]:((~tall(X)&~rich(X))&(richer(paul,Y))&(hate(X,Y))))& (((?[X]:(room(X)&~hate(X,kathryn)))&(![X,Y]:((~hate(X,kathryn)&~hate(Y,kathryn))=>(X=Y)))))& ((hate(gayla,kathryn))&(~rich(gayla)&~tall(gayla)&~happy(gayla)))& ((~happy(michael))&(does_not_have_a_piercing(michael))))

room(michael)&room(gayla)&room(evelyn)&room(anneliese)&(![X]:(room(X)=>(X='michael'|X='gayla'|X='evelyn'|X='anneliese')))& (~((hate(michael,paul))&(has_a_piercing(michael))))

entailment

entailment

entailment

Michael, Wilbur, Sylvia, Mary are the only persons in the room. 'James is richer than Mary' unless 'no one outside the room who likes Carroll is not hated by James'. 'Someone who is not hated by Carroll is quieter than someone who is a client of Peggy' if 'Michael either does not collect first edition books or is quieter than Carroll' and vice versa. Someone who does not collect first edition books hate someone who is not creative. Someone who is a client of Carroll is richer than someone who is liked by Peggy. Only one person outside the room hates Carroll. It is not the case that 'Mary and Michael are respectively quiet and creative'. Mary and Wilbur like each other. Wilbur does not like James. It is not the case that 'more than one person outside the room is liked by Peggy'.

Mary is a client of Carroll and is not creative, not tall, not quiet, not happy.

neutral

% SZS status Satisfiable

room(michael)&room(wilbur)&room(sylvia)&room(mary)&(![X]:(room(X)=>(X='michael'|X='wilbur'|X='sylvia'|X='mary')))& ((~(~?[X]:(~room(X)=>(((like(carroll,X))=>(~hate(X,james))))))=>(richer(mary,james)))& (((((does_not_collect_first_edition_books(michael))|(quieter(carroll,michael)))&(~((does_not_collect_first_edition_books(michael))|(quieter(carroll,michael))))))<=>(?[X,Y]:((~hate(X,carroll))&(client(peggy,Y))&(quieter(X,Y)))))& (?[X,Y]:((does_not_collect_first_edition_books(X))&(~creative(Y))&(hate(X,Y))))& (?[X,Y]:((client(carroll,X))&(like(Y,peggy))&(richer(X,Y))))& (((?[X]:(~room(X)&hate(carroll,X)))&(![X,Y]:((hate(carroll,X)&hate(carroll,Y))=>(X=Y)))))& (~((quiet(mary))&(creative(michael))))& ((like(mary,wilbur) & like(wilbur,mary)))& (~like(james,wilbur))& (~((?[X,Y]:(~room(X)&~room(Y)&(like(X,peggy)&like(Y,peggy))&(X!=Y))))))

room(michael)&room(wilbur)&room(sylvia)&room(mary)&(![X]:(room(X)=>(X='michael'|X='wilbur'|X='sylvia'|X='mary')))& ((client(carroll,mary))&(~creative(mary)&~tall(mary)&~quiet(mary)&~happy(mary)))

neutral

contradiction

contradiction

Thomas and Raul are not happy, not tall, not brave.

Raul who is not tall, not brave, not happy, is not a tall european.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(brave_type, type, ( brave: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(fred_type, type, ( fred: $i)). tff(european_type, type, ( european: $i > $o)). tff(1,plain, ((~brave(mary)) <=> (~brave(mary))), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((~happy(paul)) & (~tall(paul))) & (~brave(paul))) & (~happy(mary))) & (~tall(mary))) & (~brave(mary)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((~tall(mary)) & (~brave(mary))) & (~happy(mary))) & (~(tall(mary) & european(mary))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~happy(paul)) & (~tall(paul)) & (~brave(paul)) & (~happy(mary)) & (~tall(mary)) & (~brave(mary)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)) & (~(tall(mary) & european(mary))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((((~happy(paul)) & (~tall(paul))) & (~brave(paul))) & (~happy(mary))) & (~tall(mary))) & (~brave(mary)))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & ((((~tall(mary)) & (~brave(mary))) & (~happy(mary))) & (~(tall(mary) & european(mary))))))), file('/mnt/tmpfs//395514228631728705640684.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~happy(paul)) & (~tall(paul)) & (~brave(paul)) & (~happy(mary)) & (~tall(mary)) & (~brave(mary)))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)) & (~(tall(mary) & european(mary)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~happy(paul)) & (~tall(paul)) & (~brave(paul)) & (~happy(mary)) & (~tall(mary)) & (~brave(mary))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~brave(mary)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (~brave(mary)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((~tall(mary)) <=> (~tall(mary))), inference(rewrite,[status(thm)],[])). tff(9,plain, (~tall(mary)), inference(and_elim,[status(thm)],[5])). tff(10,plain, (~tall(mary)), inference(modus_ponens,[status(thm)],[9, 8])). tff(11,plain, ((~happy(mary)) <=> (~happy(mary))), inference(rewrite,[status(thm)],[])). tff(12,plain, (~happy(mary)), inference(and_elim,[status(thm)],[5])). tff(13,plain, (~happy(mary)), inference(modus_ponens,[status(thm)],[12, 11])). tff(14,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(15,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(16,plain, (room(fred)), inference(modus_ponens,[status(thm)],[15, 14])). tff(17,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(18,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(19,plain, (room(paul)), inference(modus_ponens,[status(thm)],[18, 17])). tff(20,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(21,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(22,plain, (room(mary)), inference(modus_ponens,[status(thm)],[21, 20])). tff(23,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | tall(mary) | brave(mary) | happy(mary)) <=> (happy(mary) | tall(mary) | brave(mary) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))), inference(rewrite,[status(thm)],[])). tff(25,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | tall(mary) | brave(mary) | happy(mary)) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | tall(mary) | brave(mary) | happy(mary))), inference(monotonicity,[status(thm)],[24])). tff(26,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | tall(mary) | brave(mary) | happy(mary)) <=> (happy(mary) | tall(mary) | brave(mary) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(transitivity,[status(thm)],[25, 23])). tff(27,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)))), inference(rewrite,[status(thm)],[])). tff(28,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary))))), inference(monotonicity,[status(thm)],[27])). tff(29,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)) & (~(tall(mary) & european(mary))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary))))), inference(rewrite,[status(thm)],[])). tff(30,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)) & (~(tall(mary) & european(mary)))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)) & (~(tall(mary) & european(mary))))), inference(rewrite,[status(thm)],[])). tff(31,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)) & (~(tall(mary) & european(mary))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)) & (~(tall(mary) & european(mary)))))), inference(monotonicity,[status(thm)],[30])). tff(32,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)) & (~(tall(mary) & european(mary))))), inference(or_elim,[status(thm)],[4])). tff(33,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)) & (~(tall(mary) & european(mary))))), inference(modus_ponens,[status(thm)],[32, 31])). tff(34,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)))), inference(modus_ponens,[status(thm)],[33, 29])). tff(35,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~tall(mary)) & (~brave(mary)) & (~happy(mary)))), inference(modus_ponens,[status(thm)],[34, 28])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (forall ((X $i)) (or (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!5 (not (or (= X!0 |'fred'|) (= X!0 |'paul'|) (= X!0 |'mary'|) (not (room X!0)))))) (let ((a!6 (not (and (room mary) (room paul) (room fred) a!4 (not (tall mary)) (not (brave mary)) (not (happy mary)))))) (let ((a!7 (~ a!6 (or (not (room mary)) (not (room paul)) (not (room fred)) a!5 (tall mary) (brave mary) (happy mary))))) (nnf-neg a!1 a!2 a!3 (sk (~ (not a!4) a!5)) (refl (~ (tall mary) (tall mary))) (refl (~ (brave mary) (brave mary))) (refl (~ (happy mary) (happy mary))) a!7))))

room(raul)&room(thomas)&room(lorraine)&(![X]:(room(X)=>(X='raul'|X='thomas'|X='lorraine')))& (~happy(thomas)&~tall(thomas)&~brave(thomas)&~happy(raul)&~tall(raul)&~brave(raul))

room(raul)&room(thomas)&room(lorraine)&(![X]:(room(X)=>(X='raul'|X='thomas'|X='lorraine')))& ((~tall(raul)&~brave(raul)&~happy(raul))&(~(tall(raul)&european(raul))))

neutral

neutral

entailment

Ricardo who does not play the drums, hates Audry.

It is not the case that 'Duane who does not hate Audry, hates Audry'.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(paul_type, type, ( paul: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(fred_type, type, ( fred: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(1,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~preda(mary)) & hate(fred, mary))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((~hate(fred, paul)) & hate(fred, paul)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~preda(mary)) & hate(fred, mary))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~preda(mary)) & hate(fred, mary))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((~hate(fred, paul)) & hate(fred, paul)))))), file('/mnt/tmpfs//2507698193959921080185206.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~preda(mary)) & hate(fred, mary))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~preda(mary)) & hate(fred, mary)), inference(or_elim,[status(thm)],[4])). tff(6,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (room(paul)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(9,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(10,plain, (room(mary)), inference(modus_ponens,[status(thm)],[9, 8])). tff(11,plain, ((~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))), inference(rewrite,[status(thm)],[])). tff(12,plain, (((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(monotonicity,[status(thm)],[11])). tff(13,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(rewrite,[status(thm)],[])). tff(14,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(monotonicity,[status(thm)],[13])). tff(15,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(rewrite,[status(thm)],[])). tff(16,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(or_elim,[status(thm)],[4])). tff(17,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[16, 14])). tff(18,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[17, 15])). tff(19,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[18, 14])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!4 (not (or (= X!0 |'paul'|) (= X!0 |'mary'|) (not (room X!0)))))) (let ((a!5 (~ (not (and (room mary) (room paul) a!3)) (or (not (room mary)) (not (room paul)) a!4)))) (nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) a!5)))

room(ricardo)&room(duane)&(![X]:(room(X)=>(X='ricardo'|X='duane')))& ((does_not_play_the_drums(ricardo))&(hate(audry,ricardo)))

room(ricardo)&room(duane)&(![X]:(room(X)=>(X='ricardo'|X='duane')))& (~((~hate(audry,duane))&(hate(audry,duane))))

entailment

entailment

contradiction

Luther, Tracey, Andy, Jason are the only persons in the room. If “Luther who does not play video games, is a client of William” then “Jason is the richest in the room” otherwise “Tracey is the tallest in the room”. Jason is the richest in the room. Jason is the richest in the room. Someone who plays video games hate someone who is hated by Nicolas. Jason is not hated by Nicolas and is not rich, not creative. More than one person in the room is not rich, not creative. More than one person in the room hates William. More than one person in the room is hated by Nicolas. Luther who is taller than William, is not rich, not creative. Someone who is hated by William is a client of someone who plays video games. William is a client of Jason.

Someone who is not a tall rich person is richer than someone who is a tall person.

neutral

% SZS status Satisfiable

room(luther)&room(tracey)&room(andy)&room(jason)&(![X]:(room(X)=>(X='luther'|X='tracey'|X='andy'|X='jason')))& (((((does_not_play_video_games(luther))&(client(william,luther)))=>(![X]:(richer(X,jason))))|((~((does_not_play_video_games(luther))&(client(william,luther))))=>(![X]:(taller(X,tracey)))))& (![X]:(richer(X,jason)))& (![X]:(richer(X,jason)))& (?[X,Y]:((plays_video_games(X))&(hate(Y,nicolas))&(hate(X,Y))))& ((~hate(jason,nicolas))&(~rich(jason)&~creative(jason)))& ((?[X,Y]:(room(X)&room(Y)&(~rich(X)&~creative(X)&~rich(Y)&~creative(Y))&(X!=Y))))& ((?[X,Y]:(room(X)&room(Y)&(hate(william,X)&hate(william,Y))&(X!=Y))))& ((?[X,Y]:(room(X)&room(Y)&(hate(X,nicolas)&hate(Y,nicolas))&(X!=Y))))& ((taller(william,luther))&(~rich(luther)&~creative(luther)))& (?[X,Y]:((hate(X,william))&(plays_video_games(Y))&(client(X,Y))))& (client(jason,william)))

room(luther)&room(tracey)&room(andy)&room(jason)&(![X]:(room(X)=>(X='luther'|X='tracey'|X='andy'|X='jason')))& (?[X,Y]:((~(tall(X)&rich(X)&person(X)))&(tall(Y)&person(Y))&(richer(X,Y))))

entailment

entailment

entailment

Martha, Daniel, Demetrice, David are the only persons in the room. Someone who is a brave creative tourist is a sibling of someone who is not brave. Demetrice and Martha are respectively creative and brave. Jamie is a sibling of Martha. David who does not collect foreign coins, does not like Kimberley. Everyone outside the room is not a brave tourist. Daniel neither does not like Jamie nor is a sibling of Samual.

Someone who is a brave person is a sibling of someone who is not a brave person.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(person_type, type, ( person: $i > $o)). tff(tptp_fun_Y_0_type, type, ( tptp_fun_Y_0: $i)). tff(brave_type, type, ( brave: $i > $o)). tff(sibling_type, type, ( sibling: ( $i * $i ) > $o)). tff(tptp_fun_X_1_type, type, ( tptp_fun_X_1: $i)). tff(tourist_type, type, ( tourist: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(john_type, type, ( john: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(room_type, type, ( room: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(susan_type, type, ( susan: $i)). tff(predb_type, type, ( predb: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(fred_type, type, ( fred: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(tptp_fun_X_2_type, type, ( tptp_fun_X_2: $i)). tff(1,plain, (?[X: $i, Y: $i] : (brave(X) & creative(X) & tourist(X) & (~brave(Y)) & sibling(X, Y)) <=> ?[X: $i, Y: $i] : (brave(X) & creative(X) & tourist(X) & (~brave(Y)) & sibling(X, Y))), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((?[X: $i, Y: $i] : ((((brave(X) & creative(X)) & tourist(X)) & (~brave(Y))) & sibling(X, Y)) & (creative(fred) & brave(mary))) & sibling(mary, lucy)) & ((~predb(alice)) & (~like(susan, alice)))) & ![X: $i] : ((~room(X)) => (~(brave(X) & tourist(X))))) & (~((~like(lucy, paul)) | sibling(john, paul))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : (((brave(X) & person(X)) & (~(brave(Y) & person(Y)))) & sibling(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & creative(X) & tourist(X) & (~brave(Y)) & sibling(X, Y)) & creative(fred) & brave(mary) & sibling(mary, lucy) & (~predb(alice)) & (~like(susan, alice)) & ![X: $i] : (room(X) | (~(brave(X) & tourist(X)))) & (~((~like(lucy, paul)) | sibling(john, paul))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((?[X: $i, Y: $i] : ((((brave(X) & creative(X)) & tourist(X)) & (~brave(Y))) & sibling(X, Y)) & (creative(fred) & brave(mary))) & sibling(mary, lucy)) & ((~predb(alice)) & (~like(susan, alice)))) & ![X: $i] : ((~room(X)) => (~(brave(X) & tourist(X))))) & (~((~like(lucy, paul)) | sibling(john, paul))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : (((brave(X) & person(X)) & (~(brave(Y) & person(Y)))) & sibling(X, Y))))), file('/mnt/tmpfs//555495327205994912936827.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & creative(X) & tourist(X) & (~brave(Y)) & sibling(X, Y)) & creative(fred) & brave(mary) & sibling(mary, lucy) & (~predb(alice)) & (~like(susan, alice)) & ![X: $i] : (room(X) | (~(brave(X) & tourist(X)))) & (~((~like(lucy, paul)) | sibling(john, paul))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & creative(X) & tourist(X) & (~brave(Y)) & sibling(X, Y)) & creative(fred) & brave(mary) & sibling(mary, lucy) & (~predb(alice)) & (~like(susan, alice)) & ![X: $i] : (room(X) | (~(brave(X) & tourist(X)))) & (~((~like(lucy, paul)) | sibling(john, paul)))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (?[X: $i, Y: $i] : (brave(X) & creative(X) & tourist(X) & (~brave(Y)) & sibling(X, Y))), inference(and_elim,[status(thm)],[5])). tff(7,plain, (?[X: $i, Y: $i] : (brave(X) & creative(X) & tourist(X) & (~brave(Y)) & sibling(X, Y))), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain,( brave(X!1) & creative(X!1) & tourist(X!1) & (~brave(Y!0)) & sibling(X!1, Y!0)), inference(skolemize,[status(sab)],[7])). tff(9,plain, (~brave(Y!0)), inference(and_elim,[status(thm)],[8])). tff(10,plain, (((~brave(Y!0)) | (~person(Y!0))) | brave(Y!0)), inference(tautology,[status(thm)],[])). tff(11,plain, ((~brave(Y!0)) | (~person(Y!0))), inference(unit_resolution,[status(thm)],[10, 9])). tff(12,plain, (tourist(X!1)), inference(and_elim,[status(thm)],[8])). tff(13,plain, (^[X: $i] : refl((person(X) | (~tourist(X))) <=> (person(X) | (~tourist(X))))), inference(bind,[status(th)],[])). tff(14,plain, (![X: $i] : (person(X) | (~tourist(X))) <=> ![X: $i] : (person(X) | (~tourist(X)))), inference(quant_intro,[status(thm)],[13])). tff(15,plain, (![X: $i] : (person(X) | (~tourist(X))) <=> ![X: $i] : (person(X) | (~tourist(X)))), inference(rewrite,[status(thm)],[])). tff(16,plain, (^[X: $i] : rewrite((tourist(X) => person(X)) <=> (person(X) | (~tourist(X))))), inference(bind,[status(th)],[])). tff(17,plain, (![X: $i] : (tourist(X) => person(X)) <=> ![X: $i] : (person(X) | (~tourist(X)))), inference(quant_intro,[status(thm)],[16])). tff(18,axiom,(![X: $i] : (tourist(X) => person(X))), file('/mnt/tmpfs//555495327205994912936827.p','b3')). tff(19,plain, (![X: $i] : (person(X) | (~tourist(X)))), inference(modus_ponens,[status(thm)],[18, 17])). tff(20,plain, (![X: $i] : (person(X) | (~tourist(X)))), inference(modus_ponens,[status(thm)],[19, 15])). tff(21,plain,( ![X: $i] : (person(X) | (~tourist(X)))), inference(skolemize,[status(sab)],[20])). tff(22,plain, (![X: $i] : (person(X) | (~tourist(X)))), inference(modus_ponens,[status(thm)],[21, 14])). tff(23,plain, (((~![X: $i] : (person(X) | (~tourist(X)))) | (person(X!1) | (~tourist(X!1)))) <=> ((~![X: $i] : (person(X) | (~tourist(X)))) | person(X!1) | (~tourist(X!1)))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((~![X: $i] : (person(X) | (~tourist(X)))) | (person(X!1) | (~tourist(X!1)))), inference(quant_inst,[status(thm)],[])). tff(25,plain, ((~![X: $i] : (person(X) | (~tourist(X)))) | person(X!1) | (~tourist(X!1))), inference(modus_ponens,[status(thm)],[24, 23])). tff(26,plain, (person(X!1)), inference(unit_resolution,[status(thm)],[25, 22, 12])). tff(27,assumption,(~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))), introduced(assumption)). tff(28,plain, (((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))) | room(X!2)), inference(tautology,[status(thm)],[])). tff(29,plain, (room(X!2)), inference(unit_resolution,[status(thm)],[28, 27])). tff(30,plain, (((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))) | (~(X!2 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(31,plain, (~(X!2 = |'mary'|)), inference(unit_resolution,[status(thm)],[30, 27])). tff(32,plain, (((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))) | (~(X!2 = |'paul'|))), inference(tautology,[status(thm)],[])). tff(33,plain, (~(X!2 = |'paul'|)), inference(unit_resolution,[status(thm)],[32, 27])). tff(34,plain, (((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))) | (~(X!2 = |'fred'|))), inference(tautology,[status(thm)],[])). tff(35,plain, (~(X!2 = |'fred'|)), inference(unit_resolution,[status(thm)],[34, 27])). tff(36,plain, (((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))) | (~(X!2 = |'alice'|))), inference(tautology,[status(thm)],[])). tff(37,plain, (~(X!2 = |'alice'|)), inference(unit_resolution,[status(thm)],[36, 27])). tff(38,plain, (^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(bind,[status(th)],[])). tff(39,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(quant_intro,[status(thm)],[38])). tff(40,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(rewrite,[status(thm)],[])). tff(41,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(and_elim,[status(thm)],[5])). tff(42,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[41, 40])). tff(43,plain,( ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(skolemize,[status(sab)],[42])). tff(44,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[43, 39])). tff(45,plain, (((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))), inference(rewrite,[status(thm)],[])). tff(46,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))), inference(quant_inst,[status(thm)],[])). tff(47,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))), inference(modus_ponens,[status(thm)],[46, 45])). tff(48,plain, ($false), inference(unit_resolution,[status(thm)],[47, 44, 37, 35, 33, 31, 29])). tff(49,plain,((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))), inference(lemma,lemma(discharge,[]))). tff(50,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(51,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(52,plain, (room(alice)), inference(modus_ponens,[status(thm)],[51, 50])). tff(53,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(54,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(55,plain, (room(fred)), inference(modus_ponens,[status(thm)],[54, 53])). tff(56,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(57,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(58,plain, (room(paul)), inference(modus_ponens,[status(thm)],[57, 56])). tff(59,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(60,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(61,plain, (room(mary)), inference(modus_ponens,[status(thm)],[60, 59])). tff(62,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : ((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : ((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y))))), inference(rewrite,[status(thm)],[])). tff(63,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : ((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : ((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y))))), inference(rewrite,[status(thm)],[])). tff(64,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((brave(Y) & person(Y)) <=> (~((~brave(Y)) | (~person(Y))))), ((~(brave(Y) & person(Y))) <=> (~(~((~brave(Y)) | (~person(Y))))))), rewrite((~(~((~brave(Y)) | (~person(Y))))) <=> ((~brave(Y)) | (~person(Y)))), ((~(brave(Y) & person(Y))) <=> ((~brave(Y)) | (~person(Y))))), ((brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)) <=> (brave(X) & person(X) & ((~brave(Y)) | (~person(Y))) & sibling(X, Y)))), rewrite((brave(X) & person(X) & ((~brave(Y)) | (~person(Y))) & sibling(X, Y)) <=> (~((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y))))), ((brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)) <=> (~((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y)))))), ((~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y))) <=> (~(~((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y))))))), rewrite((~(~((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y))))) <=> ((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y)))), ((~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y))) <=> ((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y)))))), inference(bind,[status(th)],[])). tff(65,plain, (![X: $i, Y: $i] : (~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y))) <=> ![X: $i, Y: $i] : ((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y)))), inference(quant_intro,[status(thm)],[64])). tff(66,plain, ((~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))), inference(rewrite,[status(thm)],[])). tff(67,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : ((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y))))), inference(monotonicity,[status(thm)],[66, 65])). tff(68,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : ((~((~brave(Y)) | (~person(Y)))) | (~brave(X)) | (~person(X)) | (~sibling(X, Y))))), inference(transitivity,[status(thm)],[67, 63])). tff(69,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y))))), inference(rewrite,[status(thm)],[])). tff(70,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y))))), inference(monotonicity,[status(thm)],[66])). tff(71,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!2 = |'alice'|) | (X!2 = |'fred'|) | (X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) | ![X: $i, Y: $i] : (~(brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y))))), inference(transitivity,[status(thm)],[70, 69])). tff(72,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))), inference(rewrite,[status(thm)],[])). tff(73,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y))))), inference(monotonicity,[status(thm)],[72])). tff(74,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y))))), inference(rewrite,[status(thm)],[])). tff(75,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))), inference(or_elim,[status(thm)],[4])). tff(76,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))), inference(modus_ponens,[status(thm)],[75, 73])). tff(77,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))), inference(modus_ponens,[status(thm)],[76, 74])). tff(78,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & person(X) & (~(brave(Y) & person(Y))) & sibling(X, Y)))), inference(modus_ponens,[status(thm)],[77, 73])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!2 |'alice'|) (= X!2 |'fred'|) (= X!2 |'paul'|) (= X!2 |'mary'|) (not (room X!2))))) (a!7 (lambda ((X $i) (Y $i)) (let ((a!1 (and (brave X) (person X) (not (and (brave Y) (person Y))) (sibling X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!8 (exists ((X $i) (Y $i)) (and (brave X) (person X) (not (and (brave Y) (person Y))) (sibling X Y)))) (a!9 (forall ((X $i) (Y $i)) (let ((a!1 (and (brave X) (person X) (not (and (brave Y) (person Y))) (sibling X Y)))) (not a!1))))) (let ((a!10 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 a!8)) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 a!9)))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (nnf-neg (proof-bind a!7) (~ (not a!8) a!9)) a!10)))

room(martha)&room(daniel)&room(demetrice)&room(david)&(![X]:(room(X)=>(X='martha'|X='daniel'|X='demetrice'|X='david')))& ((?[X,Y]:((brave(X)&creative(X)&tourist(X))&(~brave(Y))&(sibling(X,Y))))& ((creative(demetrice))&(brave(martha)))& (sibling(martha,jamie))& ((does_not_collect_foreign_coins(david))&(~like(kimberley,david)))& (![X]:(~room(X)=>(~(brave(X)&tourist(X)))))& (~((~like(jamie,daniel))|(sibling(samual,daniel)))))

room(martha)&room(daniel)&room(demetrice)&room(david)&(![X]:(room(X)=>(X='martha'|X='daniel'|X='demetrice'|X='david')))& (?[X,Y]:((brave(X)&person(X))&(~(brave(Y)&person(Y)))&(sibling(X,Y))))

entailment

entailment

entailment

Carolyn, Donald, Maura, Mary are the only persons in the room. 'Someone who is hated by Brenda hate someone who hates Brenda' if 'no one outside the room is not a rich tourist'. Carolyn neither is a sibling of Josh nor has a saltwater aquarium. Maura and Donald are brave european. Someone who is not hated by Brenda hate someone who hates Josh. Someone outside the room who is a happy european does not have a saltwater aquarium. Maura is not hated by Josh. Donald who is hated by Josh, is not a brave rich tourist. Someone in the room does not sketche as a hobby.

Carolyn is hated by Josh and is a rich european.

neutral

% SZS status Satisfiable

room(carolyn)&room(donald)&room(maura)&room(mary)&(![X]:(room(X)=>(X='carolyn'|X='donald'|X='maura'|X='mary')))& (((~?[X]:(~room(X)=>(~(rich(X)&tourist(X)))))=>(?[X,Y]:((hate(X,brenda))&(hate(brenda,Y))&(hate(X,Y)))))& (~((sibling(josh,carolyn))|(has_a_saltwater_aquarium(carolyn))))& (brave(maura)&european(maura)&brave(donald)&european(donald))& (?[X,Y]:((~hate(X,brenda))&(hate(josh,Y))&(hate(X,Y))))& (?[X]:(~room(X)=>(((happy(X)&european(X))=>(does_not_have_a_saltwater_aquarium(X))))))& (~hate(maura,josh))& ((hate(donald,josh))&(~(brave(donald)&rich(donald)&tourist(donald))))& (?[X]:(room(X)=>(does_not_sketche_as_a_hobby(X)))))

room(carolyn)&room(donald)&room(maura)&room(mary)&(![X]:(room(X)=>(X='carolyn'|X='donald'|X='maura'|X='mary')))& ((hate(carolyn,josh))&(rich(carolyn)&european(carolyn)))

neutral

contradiction

contradiction

Scott is not creative or is not tall or both.

It is not the case that 'Scott is not a tall creative european'.

contradiction

-

room(leslie)&room(scott)&(![X]:(room(X)=>(X='leslie'|X='scott')))& (((~creative(scott))|(~tall(scott))))

room(leslie)&room(scott)&(![X]:(room(X)=>(X='leslie'|X='scott')))& (~(~(tall(scott)&creative(scott)&european(scott))))

neutral

entailment

entailment

Cleveland, Michael, Nancy are the only persons in the room. If 'more than one person in the room is not a tall person' then 'Melissa is taller than Nancy'. 'Only one person outside the room likes Lisa' if 'more than one person outside the room is not liked by Leroy'. Nancy is the least tall in the room. Melissa and Leroy like each other. More than one person outside the room is not a brave quiet person. Leroy is quieter than Cleveland.

Cleveland who is a quiet tall happy person, is taller than Melissa.

neutral

% SZS status Satisfiable

room(cleveland)&room(michael)&room(nancy)&(![X]:(room(X)=>(X='cleveland'|X='michael'|X='nancy')))& ((((?[X,Y]:(room(X)&room(Y)&(~(tall(X)&person(X))&~(tall(Y)&person(Y)))&(X!=Y))))=>(taller(nancy,melissa)))& (((?[X,Y]:(~room(X)&~room(Y)&(~like(X,leroy)&~like(Y,leroy))&(X!=Y))))=>(((?[X]:(~room(X)&like(lisa,X)))&(![X,Y]:((like(lisa,X)&like(lisa,Y))=>(X=Y))))))& (![X]:(taller(nancy,X)))& ((like(melissa,leroy) & like(leroy,melissa)))& ((?[X,Y]:(~room(X)&~room(Y)&(~(brave(X)&quiet(X)&person(X))&~(brave(Y)&quiet(Y)&person(Y)))&(X!=Y))))& (quieter(cleveland,leroy)))

room(cleveland)&room(michael)&room(nancy)&(![X]:(room(X)=>(X='cleveland'|X='michael'|X='nancy')))& ((quiet(cleveland)&tall(cleveland)&happy(cleveland)&person(cleveland))&(taller(melissa,cleveland)))

neutral

contradiction

contradiction

Manuel, Paula are the only persons in the room. If someone who is richer than Stanley like someone who likes Stanley then Paula is not liked by Stanley and does not have lived in exactly three countries otherwise someone who is not Manuel like someone who is not liked by Stanley. Paula is not liked by Stanley and does not have lived in exactly three countries. Manuel and Stanley like each other. Paula is the least rich in the room. More than one person outside the room has lived in exactly three countries.

Paula who is richer than Stanley, likes Stanley.

contradiction

-

room(manuel)&room(paulaa)&(![X]:(room(X)=>(X='manuel'|X='paulaa')))& ((((?[X,Y]:((richer(stanley,X))&(like(stanley,Y))&(like(X,Y))))=>((~like(paulaa,stanley))&(does_not_have_lived_in_exactly_three_countries(paulaa))))|((~(?[X,Y]:((richer(stanley,X))&(like(stanley,Y))&(like(X,Y)))))=>(?[X,Y]:((X!=manuel)&(~like(Y,stanley))&(like(X,Y))))))& ((~like(paulaa,stanley))&(does_not_have_lived_in_exactly_three_countries(paulaa)))& ((like(manuel,stanley) & like(stanley,manuel)))& (![X]:(richer(paulaa,X)))& ((?[X,Y]:(~room(X)&~room(Y)&(has_lived_in_exactly_three_countries(X)&has_lived_in_exactly_three_countries(Y))&(X!=Y)))))

room(manuel)&room(paulaa)&(![X]:(room(X)=>(X='manuel'|X='paulaa')))& ((richer(stanley,paulaa))&(like(stanley,paulaa)))

contradiction

contradiction

contradiction

Mireya, Dalia are the only persons in the room. If "everyone outside the room is a sibling of Nichole" then "only one person outside the room is not a rich quiet person". "Mireya who is a client of Nichole, does not hate Michelle" if "Nichole and Dalia hate each other" and vice versa. "Dalia who is not a quiet person, is not tall, not rich" only if "Dalia and Nichole hate each other". Mireya is the least quiet in the room. Only one person outside the room is not a rich quiet person. Mireya is a client of Michelle or is not hated by Michelle or both.

Someone who is not quiet, not happy is a sibling of someone who is quieter than Frederick.

contradiction

-

room(mireya)&room(dalia)&(![X]:(room(X)=>(X='mireya'|X='dalia')))& (((![X]:(~room(X)=>(sibling(nichole,X))))=>(((?[X]:(~room(X)&~(rich(X)&quiet(X)&person(X))))&(![X,Y]:((~(rich(X)&quiet(X)&person(X))&~(rich(Y)&quiet(Y)&person(Y)))=>(X=Y))))))& (((hate(nichole,dalia) & hate(dalia,nichole)))<=>((client(nichole,mireya))&(~hate(michelle,mireya))))& (((~(quiet(dalia)&person(dalia)))&(~tall(dalia)&~rich(dalia)))=>((hate(dalia,nichole) & hate(nichole,dalia))))& (![X]:(quieter(mireya,X)))& (((?[X]:(~room(X)&~(rich(X)&quiet(X)&person(X))))&(![X,Y]:((~(rich(X)&quiet(X)&person(X))&~(rich(Y)&quiet(Y)&person(Y)))=>(X=Y)))))& (((client(michelle,mireya))|(~hate(mireya,michelle)))))

room(mireya)&room(dalia)&(![X]:(room(X)=>(X='mireya'|X='dalia')))& (?[X,Y]:((~quiet(X)&~happy(X))&(quieter(frederick,Y))&(sibling(X,Y))))

neutral

neutral

neutral

Alonzo is the only person in the room. Alonzo does not hate Tina. More than one person outside the room is not quiet, not tall. Alonzo is not tall and is a creative person. It is not the case that 'it is not the case that 'more than one person outside the room is not a creative european''. Alonzo is the least quiet in the room.

Someone who is not tall is quieter than someone who is a creative person.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(mary_type, type, ( mary: $i)). tff(room_type, type, ( room: $i > $o)). tff(european_type, type, ( european: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(person_type, type, ( person: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(paul_type, type, ( paul: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). 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, ((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((~hate(paul, mary)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((((~quiet(X)) & (~tall(X))) & (~quiet(Y))) & (~tall(Y)))) & (~(X = Y)))) & ((~tall(mary)) & (creative(mary) & person(mary)))) & (~(~?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(creative(X) & european(X))) & (~(creative(Y) & european(Y))))) & (~(X = Y)))))) & ![X: $i] : quieter(mary, X))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ?[X: $i, Y: $i] : (((~tall(X)) & (creative(Y) & person(Y))) & quieter(X, Y))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~hate(paul, mary)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~quiet(X)) & (~tall(X)) & (~quiet(Y)) & (~tall(Y)) & (~(X = Y))) & (~tall(mary)) & creative(mary) & person(mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(creative(X) & european(X))) & (~(creative(Y) & european(Y))) & (~(X = Y))) & ![X: $i] : quieter(mary, X))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(5,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (((((~hate(paul, mary)) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((((~quiet(X)) & (~tall(X))) & (~quiet(Y))) & (~tall(Y)))) & (~(X = Y)))) & ((~tall(mary)) & (creative(mary) & person(mary)))) & (~(~?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(creative(X) & european(X))) & (~(creative(Y) & european(Y))))) & (~(X = Y)))))) & ![X: $i] : quieter(mary, X))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ?[X: $i, Y: $i] : (((~tall(X)) & (creative(Y) & person(Y))) & quieter(X, Y))))), file('/mnt/tmpfs//1773659851701387806988666.p','negated')). tff(6,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~hate(paul, mary)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~quiet(X)) & (~tall(X)) & (~quiet(Y)) & (~tall(Y)) & (~(X = Y))) & (~tall(mary)) & creative(mary) & person(mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(creative(X) & european(X))) & (~(creative(Y) & european(Y))) & (~(X = Y))) & ![X: $i] : quieter(mary, X))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y))))), inference(modus_ponens,[status(thm)],[5, 4])). tff(7,plain, (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~hate(paul, mary)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~quiet(X)) & (~tall(X)) & (~quiet(Y)) & (~tall(Y)) & (~(X = Y))) & (~tall(mary)) & creative(mary) & person(mary) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(creative(X) & european(X))) & (~(creative(Y) & european(Y))) & (~(X = Y))) & ![X: $i] : quieter(mary, X)), inference(or_elim,[status(thm)],[6])). tff(8,plain, (![X: $i] : ((~room(X)) | (X = |'mary'|))), inference(and_elim,[status(thm)],[7])). 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)],[7])). 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, (quieter(mary, |'mary'|) <=> quieter(|'mary'|, |'mary'|)), inference(monotonicity,[status(thm)],[18])). tff(20,plain, (quieter(|'mary'|, |'mary'|) <=> quieter(mary, |'mary'|)), inference(symmetry,[status(thm)],[19])). tff(21,plain, ((~quieter(|'mary'|, |'mary'|)) <=> (~quieter(mary, |'mary'|))), inference(monotonicity,[status(thm)],[20])). tff(22,plain, (|'mary'| = mary), inference(symmetry,[status(thm)],[18])). tff(23,plain, (creative(|'mary'|) <=> creative(mary)), inference(monotonicity,[status(thm)],[22])). tff(24,plain, (creative(mary) <=> creative(|'mary'|)), inference(symmetry,[status(thm)],[23])). tff(25,plain, (creative(mary) <=> creative(mary)), inference(rewrite,[status(thm)],[])). tff(26,plain, (creative(mary)), inference(and_elim,[status(thm)],[7])). tff(27,plain, (creative(mary)), inference(modus_ponens,[status(thm)],[26, 25])). tff(28,plain, (creative(|'mary'|)), inference(modus_ponens,[status(thm)],[27, 24])). tff(29,plain, (person(|'mary'|) <=> person(mary)), inference(monotonicity,[status(thm)],[22])). tff(30,plain, (person(mary) <=> person(|'mary'|)), inference(symmetry,[status(thm)],[29])). tff(31,plain, (person(mary) <=> person(mary)), inference(rewrite,[status(thm)],[])). tff(32,plain, (person(mary)), inference(and_elim,[status(thm)],[7])). tff(33,plain, (person(mary)), inference(modus_ponens,[status(thm)],[32, 31])). tff(34,plain, (person(|'mary'|)), inference(modus_ponens,[status(thm)],[33, 30])). tff(35,plain, (tall(|'mary'|) <=> tall(mary)), inference(monotonicity,[status(thm)],[22])). tff(36,plain, (tall(mary) <=> tall(|'mary'|)), inference(symmetry,[status(thm)],[35])). tff(37,plain, ((~tall(mary)) <=> (~tall(|'mary'|))), inference(monotonicity,[status(thm)],[36])). tff(38,plain, ((~tall(mary)) <=> (~tall(mary))), inference(rewrite,[status(thm)],[])). tff(39,plain, (~tall(mary)), inference(and_elim,[status(thm)],[7])). tff(40,plain, (~tall(mary)), inference(modus_ponens,[status(thm)],[39, 38])). tff(41,plain, (~tall(|'mary'|)), inference(modus_ponens,[status(thm)],[40, 37])). tff(42,assumption,(~((~room(X!4)) | (X!4 = |'mary'|))), introduced(assumption)). tff(43,plain, (((~room(X!4)) | (X!4 = |'mary'|)) | (~(X!4 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(44,plain, (~(X!4 = |'mary'|)), inference(unit_resolution,[status(thm)],[43, 42])). tff(45,plain, (((~room(X!4)) | (X!4 = |'mary'|)) | room(X!4)), inference(tautology,[status(thm)],[])). tff(46,plain, (room(X!4)), inference(unit_resolution,[status(thm)],[45, 42])). tff(47,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(48,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!4)) | (X!4 = |'mary'|))), inference(quant_inst,[status(thm)],[])). tff(49,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!4)) | (X!4 = |'mary'|)), inference(modus_ponens,[status(thm)],[48, 47])). tff(50,plain, ($false), inference(unit_resolution,[status(thm)],[49, 11, 46, 44])). tff(51,plain,((~room(X!4)) | (X!4 = |'mary'|)), inference(lemma,lemma(discharge,[]))). tff(52,plain, (((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (tall(X) | (~creative(Y)) | (~person(Y)) | (~quieter(X, Y)))) <=> ((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (tall(X) | (~creative(Y)) | (~person(Y)) | (~quieter(X, Y))))), inference(rewrite,[status(thm)],[])). tff(53,plain, (((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y)))) <=> ((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (tall(X) | (~creative(Y)) | (~person(Y)) | (~quieter(X, Y))))), inference(rewrite,[status(thm)],[])). tff(54,plain, (((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y)))) <=> ((~room(mary)) | (~((~room(X!4)) | (X!4 = |'mary'|))) | ![X: $i, Y: $i] : (~((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y))))), inference(rewrite,[status(thm)],[])). tff(55,plain, ((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y)))), inference(rewrite,[status(thm)],[])). tff(56,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y))))), inference(monotonicity,[status(thm)],[55])). tff(57,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y))))), inference(rewrite,[status(thm)],[])). tff(58,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y)))), inference(or_elim,[status(thm)],[6])). tff(59,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y)))), inference(modus_ponens,[status(thm)],[58, 56])). tff(60,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y)))), inference(modus_ponens,[status(thm)],[59, 57])). tff(61,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ?[X: $i, Y: $i] : ((~tall(X)) & creative(Y) & person(Y) & quieter(X, Y)))), inference(modus_ponens,[status(thm)],[60, 56])). 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!4)) (= X!4 |'mary'|)))) (a!4 (lambda ((X $i) (Y $i)) (let ((a!1 (and (not (tall X)) (creative Y) (person Y) (quieter X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!5 (exists ((X $i) (Y $i)) (and (not (tall X)) (creative Y) (person Y) (quieter X Y)))) (a!6 (forall ((X $i) (Y $i)) (let ((a!1 (and (not (tall X)) (creative Y) (person Y) (quieter 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)))

room(alonzo)&(![X]:(room(X)=>(X='alonzo')))& ((~hate(tina,alonzo))& ((?[X,Y]:(~room(X)&~room(Y)&(~quiet(X)&~tall(X)&~quiet(Y)&~tall(Y))&(X!=Y))))& ((~tall(alonzo))&(creative(alonzo)&person(alonzo)))& (~(~((?[X,Y]:(~room(X)&~room(Y)&(~(creative(X)&european(X))&~(creative(Y)&european(Y)))&(X!=Y))))))& (![X]:(quieter(alonzo,X))))

room(alonzo)&(![X]:(room(X)=>(X='alonzo')))& (?[X,Y]:((~tall(X))&(creative(Y)&person(Y))&(quieter(X,Y))))

contradiction

contradiction

contradiction

None of the following is true:. -It is not the case that 'Debra is quieter than Norma'. -Alana is not Alan and is a creative person.

Debra is quieter than Norma.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(fred_type, type, ( fred: $i)). tff(person_type, type, ( person: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(alice_type, type, ( alice: $i)). tff(1,plain, (quieter(fred, john) <=> quieter(fred, john)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~((~quieter(fred, john)) | ((~(mary = paul)) & (creative(mary) & person(mary)))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & quieter(fred, john)))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~quieter(fred, john)) | ((~(mary = paul)) & creative(mary) & person(mary)))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~((~quieter(fred, john)) | ((~(mary = paul)) & (creative(mary) & person(mary)))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & quieter(fred, john)))), file('/mnt/tmpfs//4043702591556257563745561.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~quieter(fred, john)) | ((~(mary = paul)) & creative(mary) & person(mary)))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john)))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~((~quieter(fred, john)) | ((~(mary = paul)) & creative(mary) & person(mary))))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~((~quieter(fred, john)) | ((~(mary = paul)) & creative(mary) & person(mary)))), inference(and_elim,[status(thm)],[5])). tff(7,plain, (quieter(fred, john)), inference(or_elim,[status(thm)],[6])). tff(8,plain, (quieter(fred, john)), inference(modus_ponens,[status(thm)],[7, 1])). tff(9,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(10,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(11,plain, (room(alice)), inference(modus_ponens,[status(thm)],[10, 9])). tff(12,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(13,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(14,plain, (room(fred)), inference(modus_ponens,[status(thm)],[13, 12])). tff(15,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(16,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(17,plain, (room(paul)), inference(modus_ponens,[status(thm)],[16, 15])). tff(18,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(19,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(20,plain, (room(mary)), inference(modus_ponens,[status(thm)],[19, 18])). tff(21,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~quieter(fred, john))) <=> ((~quieter(fred, john)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(rewrite,[status(thm)],[])). tff(22,plain, ((~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))), inference(rewrite,[status(thm)],[])). tff(23,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~quieter(fred, john))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~quieter(fred, john)))), inference(monotonicity,[status(thm)],[22])). tff(24,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | (~quieter(fred, john))) <=> ((~quieter(fred, john)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))))), inference(transitivity,[status(thm)],[23, 21])). tff(25,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john)) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john))), inference(rewrite,[status(thm)],[])). tff(26,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john)))), inference(monotonicity,[status(thm)],[25])). tff(27,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john)))), inference(rewrite,[status(thm)],[])). tff(28,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john))), inference(or_elim,[status(thm)],[4])). tff(29,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john))), inference(modus_ponens,[status(thm)],[28, 26])). tff(30,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john))), inference(modus_ponens,[status(thm)],[29, 27])). tff(31,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quieter(fred, john))), inference(modus_ponens,[status(thm)],[30, 26])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!0 |'alice'|) (= X!0 |'fred'|) (= X!0 |'paul'|) (= X!0 |'mary'|) (not (room X!0))))) (a!7 (refl (~ (not (quieter fred john)) (not (quieter fred john)))))) (let ((a!8 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 (quieter fred john))) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (not (quieter fred john)))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!7 a!8)))

room(alana)&room(alan)&room(norma)&room(agustina)&(![X]:(room(X)=>(X='alana'|X='alan'|X='norma'|X='agustina')))& (~((~(quieter(norma,debra)))|((alana!=alan)&(creative(alana)&person(alana)))))

room(alana)&room(alan)&room(norma)&room(agustina)&(![X]:(room(X)=>(X='alana'|X='alan'|X='norma'|X='agustina')))& (quieter(norma,debra))

contradiction

neutral

contradiction

Melvin, Sharon, Robert are the only persons in the room. If 'someone who is not hated by Randy hate someone who hates Edwin' then 'someone who is not Robert is quieter than someone who does not hate Kimberly'. Someone who is not hated by Randy hate someone who hates Edwin. Someone who hates Kimberly hate someone who is not Robert. Robert neither is not hated by Kimberly nor does not hate Randy. Edwin and Sharon hate each other. Melvin is the richest in the room. Sharon is the least quiet in the room. Everyone in the room hates Randy. Someone who is not a quiet brave person is quieter than someone who is hated by Edwin. Robert who hates Kimberly, is a rich person. Robert is the least rich in the room.

Sharon neither is not quiet, not rich nor does not hate Randy.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_8_type, type, ( tptp_fun_X_8: $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(rich_type, type, ( rich: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(quiet_type, type, ( quiet: $i > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(person_type, type, ( person: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(brave_type, type, ( brave: $i > $o)). tff(susan_type, type, ( susan: $i)). tff(mary_type, type, ( mary: $i)). tff(lucy_type, type, ( lucy: $i)). tff(1,assumption,(~richer(fred, paul)), introduced(assumption)). tff(2,plain, (^[X: $i] : refl(richer(fred, X) <=> richer(fred, X))), inference(bind,[status(th)],[])). tff(3,plain, (![X: $i] : richer(fred, X) <=> ![X: $i] : richer(fred, X)), inference(quant_intro,[status(thm)],[2])). tff(4,plain, (![X: $i] : richer(fred, X) <=> ![X: $i] : richer(fred, X)), inference(rewrite,[status(thm)],[])). tff(5,plain, ((~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((((?[X: $i, Y: $i] : (((~hate(X, susan)) & hate(alice, Y)) & hate(X, Y)) => ?[X: $i, Y: $i] : (((~(X = fred)) & (~hate(john, Y))) & quieter(X, Y))) & ?[X: $i, Y: $i] : (((~hate(X, susan)) & hate(alice, Y)) & hate(X, Y))) & ?[X: $i, Y: $i] : ((hate(john, X) & (~(Y = fred))) & hate(X, Y))) & (~((~hate(fred, john)) | (~hate(susan, fred))))) & (hate(alice, paul) & hate(paul, alice))) & ![X: $i] : richer(X, mary)) & ![X: $i] : quieter(paul, X)) & ![X: $i] : (room(X) => hate(susan, X))) & ?[X: $i, Y: $i] : (((~((quiet(X) & brave(X)) & person(X))) & hate(Y, alice)) & quieter(X, Y))) & (hate(john, fred) & (rich(fred) & person(fred)))) & ![X: $i] : richer(fred, X))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : ((~hate(X, susan)) & hate(alice, Y) & hate(X, Y))) | ?[X: $i, Y: $i] : ((~(X = fred)) & (~hate(john, Y)) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((~hate(X, susan)) & hate(alice, Y) & hate(X, Y)) & ?[X: $i, Y: $i] : (hate(john, X) & (~(Y = fred)) & hate(X, Y)) & (~((~hate(fred, john)) | (~hate(susan, fred)))) & hate(alice, paul) & hate(paul, alice) & ![X: $i] : richer(X, mary) & ![X: $i] : quieter(paul, X) & ![X: $i] : ((~room(X)) | hate(susan, X)) & ?[X: $i, Y: $i] : ((~(quiet(X) & brave(X) & person(X))) & hate(Y, alice) & quieter(X, Y)) & hate(john, fred) & rich(fred) & person(fred) & ![X: $i] : richer(fred, X))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))))))), inference(rewrite,[status(thm)],[])). tff(6,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (((((((((((?[X: $i, Y: $i] : (((~hate(X, susan)) & hate(alice, Y)) & hate(X, Y)) => ?[X: $i, Y: $i] : (((~(X = fred)) & (~hate(john, Y))) & quieter(X, Y))) & ?[X: $i, Y: $i] : (((~hate(X, susan)) & hate(alice, Y)) & hate(X, Y))) & ?[X: $i, Y: $i] : ((hate(john, X) & (~(Y = fred))) & hate(X, Y))) & (~((~hate(fred, john)) | (~hate(susan, fred))))) & (hate(alice, paul) & hate(paul, alice))) & ![X: $i] : richer(X, mary)) & ![X: $i] : quieter(paul, X)) & ![X: $i] : (room(X) => hate(susan, X))) & ?[X: $i, Y: $i] : (((~((quiet(X) & brave(X)) & person(X))) & hate(Y, alice)) & quieter(X, Y))) & (hate(john, fred) & (rich(fred) & person(fred)))) & ![X: $i] : richer(fred, X))) => ((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul))))))), file('/mnt/tmpfs//283267947183139035772798.p','negated')). tff(7,plain, (~((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : ((~hate(X, susan)) & hate(alice, Y) & hate(X, Y))) | ?[X: $i, Y: $i] : ((~(X = fred)) & (~hate(john, Y)) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((~hate(X, susan)) & hate(alice, Y) & hate(X, Y)) & ?[X: $i, Y: $i] : (hate(john, X) & (~(Y = fred)) & hate(X, Y)) & (~((~hate(fred, john)) | (~hate(susan, fred)))) & hate(alice, paul) & hate(paul, alice) & ![X: $i] : richer(X, mary) & ![X: $i] : quieter(paul, X) & ![X: $i] : ((~room(X)) | hate(susan, X)) & ?[X: $i, Y: $i] : ((~(quiet(X) & brave(X) & person(X))) & hate(Y, alice) & quieter(X, Y)) & hate(john, fred) & rich(fred) & person(fred) & ![X: $i] : richer(fred, X))) | (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul))))))), inference(modus_ponens,[status(thm)],[6, 5])). tff(8,plain, (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~?[X: $i, Y: $i] : ((~hate(X, susan)) & hate(alice, Y) & hate(X, Y))) | ?[X: $i, Y: $i] : ((~(X = fred)) & (~hate(john, Y)) & quieter(X, Y))) & ?[X: $i, Y: $i] : ((~hate(X, susan)) & hate(alice, Y) & hate(X, Y)) & ?[X: $i, Y: $i] : (hate(john, X) & (~(Y = fred)) & hate(X, Y)) & (~((~hate(fred, john)) | (~hate(susan, fred)))) & hate(alice, paul) & hate(paul, alice) & ![X: $i] : richer(X, mary) & ![X: $i] : quieter(paul, X) & ![X: $i] : ((~room(X)) | hate(susan, X)) & ?[X: $i, Y: $i] : ((~(quiet(X) & brave(X) & person(X))) & hate(Y, alice) & quieter(X, Y)) & hate(john, fred) & rich(fred) & person(fred) & ![X: $i] : richer(fred, X)), inference(or_elim,[status(thm)],[7])). tff(9,plain, (![X: $i] : richer(fred, X)), inference(and_elim,[status(thm)],[8])). tff(10,plain, (![X: $i] : richer(fred, X)), inference(modus_ponens,[status(thm)],[9, 4])). tff(11,plain,( ![X: $i] : richer(fred, X)), inference(skolemize,[status(sab)],[10])). tff(12,plain, (![X: $i] : richer(fred, X)), inference(modus_ponens,[status(thm)],[11, 3])). tff(13,plain, ((~![X: $i] : richer(fred, X)) | richer(fred, paul)), inference(quant_inst,[status(thm)],[])). tff(14,plain, ($false), inference(unit_resolution,[status(thm)],[13, 12, 1])). tff(15,plain,(richer(fred, paul)), inference(lemma,lemma(discharge,[]))). tff(16,plain, (rich(fred) <=> rich(fred)), inference(rewrite,[status(thm)],[])). tff(17,plain, (rich(fred)), inference(and_elim,[status(thm)],[8])). tff(18,plain, (rich(fred)), inference(modus_ponens,[status(thm)],[17, 16])). tff(19,plain, ((~(fred = paul)) <=> (~(fred = paul))), inference(rewrite,[status(thm)],[])). tff(20,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//283267947183139035772798.p','b14')). 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))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = 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))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = 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))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = 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))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = 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))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = 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))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = 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))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))), 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))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = 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))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = 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))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = 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))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = 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))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = 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))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = 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))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))), 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))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = 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))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = 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))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = 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))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = 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))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = 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))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = 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))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))), 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))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = 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))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = 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))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = 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))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = 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))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = 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))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = 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))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))), inference(and_elim,[status(thm)],[47])). tff(49,plain, (~(fred = paul)), inference(and_elim,[status(thm)],[48])). tff(50,plain, (~(fred = paul)), inference(modus_ponens,[status(thm)],[49, 19])). tff(51,plain, (^[X: $i, Y: $i] : refl(((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X))) <=> ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X))))), inference(bind,[status(th)],[])). tff(52,plain, (![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X))) <=> ![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))), inference(quant_intro,[status(thm)],[51])). tff(53,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((richer(X, Y) & rich(X)) <=> (~((~richer(X, Y)) | (~rich(X))))), ((~(richer(X, Y) & rich(X))) <=> (~(~((~richer(X, Y)) | (~rich(X))))))), rewrite((~(~((~richer(X, Y)) | (~rich(X))))) <=> ((~richer(X, Y)) | (~rich(X)))), ((~(richer(X, Y) & rich(X))) <=> ((~richer(X, Y)) | (~rich(X))))), (((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X)))) <=> ((X = Y) | rich(Y) | ((~richer(X, Y)) | (~rich(X)))))), rewrite(((X = Y) | rich(Y) | ((~richer(X, Y)) | (~rich(X)))) <=> ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))), (((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X)))) <=> ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))))), inference(bind,[status(th)],[])). tff(54,plain, (![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X)))) <=> ![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))), inference(quant_intro,[status(thm)],[53])). tff(55,plain, (![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X)))) <=> ![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X))))), inference(rewrite,[status(thm)],[])). tff(56,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((richer(X, Y) & rich(X)) => rich(Y)) <=> (rich(Y) | (~(richer(X, Y) & rich(X))))), (((~(X = Y)) => ((richer(X, Y) & rich(X)) => rich(Y))) <=> ((~(X = Y)) => (rich(Y) | (~(richer(X, Y) & rich(X))))))), rewrite(((~(X = Y)) => (rich(Y) | (~(richer(X, Y) & rich(X))))) <=> ((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X))))), (((~(X = Y)) => ((richer(X, Y) & rich(X)) => rich(Y))) <=> ((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X))))))), inference(bind,[status(th)],[])). tff(57,plain, (![X: $i, Y: $i] : ((~(X = Y)) => ((richer(X, Y) & rich(X)) => rich(Y))) <=> ![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X))))), inference(quant_intro,[status(thm)],[56])). tff(58,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => ((richer(X, Y) & rich(X)) => rich(Y)))), file('/mnt/tmpfs//283267947183139035772798.p','b6')). tff(59,plain, (![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X))))), inference(modus_ponens,[status(thm)],[58, 57])). tff(60,plain, (![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X))))), inference(modus_ponens,[status(thm)],[59, 55])). tff(61,plain,( ![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~(richer(X, Y) & rich(X))))), inference(skolemize,[status(sab)],[60])). tff(62,plain, (![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))), inference(modus_ponens,[status(thm)],[61, 54])). tff(63,plain, (![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))), inference(modus_ponens,[status(thm)],[62, 52])). tff(64,plain, (((~![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))) | ((fred = paul) | rich(paul) | (~rich(fred)) | (~richer(fred, paul)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))) | (fred = paul) | rich(paul) | (~rich(fred)) | (~richer(fred, paul)))), inference(rewrite,[status(thm)],[])). tff(65,plain, (((fred = paul) | rich(paul) | (~richer(fred, paul)) | (~rich(fred))) <=> ((fred = paul) | rich(paul) | (~rich(fred)) | (~richer(fred, paul)))), inference(rewrite,[status(thm)],[])). tff(66,plain, (((~![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))) | ((fred = paul) | rich(paul) | (~richer(fred, paul)) | (~rich(fred)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))) | ((fred = paul) | rich(paul) | (~rich(fred)) | (~richer(fred, paul))))), inference(monotonicity,[status(thm)],[65])). tff(67,plain, (((~![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))) | ((fred = paul) | rich(paul) | (~richer(fred, paul)) | (~rich(fred)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))) | (fred = paul) | rich(paul) | (~rich(fred)) | (~richer(fred, paul)))), inference(transitivity,[status(thm)],[66, 64])). tff(68,plain, ((~![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))) | ((fred = paul) | rich(paul) | (~richer(fred, paul)) | (~rich(fred)))), inference(quant_inst,[status(thm)],[])). tff(69,plain, ((~![X: $i, Y: $i] : ((X = Y) | rich(Y) | (~richer(X, Y)) | (~rich(X)))) | (fred = paul) | rich(paul) | (~rich(fred)) | (~richer(fred, paul))), inference(modus_ponens,[status(thm)],[68, 67])). tff(70,plain, (rich(paul) | (~richer(fred, paul))), inference(unit_resolution,[status(thm)],[69, 63, 50, 18])). tff(71,plain, (rich(paul)), inference(unit_resolution,[status(thm)],[70, 15])). tff(72,plain, ((quiet(paul) | rich(paul)) | (~rich(paul))), inference(tautology,[status(thm)],[])). tff(73,plain, (quiet(paul) | rich(paul)), inference(unit_resolution,[status(thm)],[72, 71])). tff(74,plain, (^[X: $i] : refl(((~room(X)) | hate(susan, X)) <=> ((~room(X)) | hate(susan, X)))), inference(bind,[status(th)],[])). tff(75,plain, (![X: $i] : ((~room(X)) | hate(susan, X)) <=> ![X: $i] : ((~room(X)) | hate(susan, X))), inference(quant_intro,[status(thm)],[74])). tff(76,plain, (![X: $i] : ((~room(X)) | hate(susan, X)) <=> ![X: $i] : ((~room(X)) | hate(susan, X))), inference(rewrite,[status(thm)],[])). tff(77,plain, (![X: $i] : ((~room(X)) | hate(susan, X))), inference(and_elim,[status(thm)],[8])). tff(78,plain, (![X: $i] : ((~room(X)) | hate(susan, X))), inference(modus_ponens,[status(thm)],[77, 76])). tff(79,plain,( ![X: $i] : ((~room(X)) | hate(susan, X))), inference(skolemize,[status(sab)],[78])). tff(80,plain, (![X: $i] : ((~room(X)) | hate(susan, X))), inference(modus_ponens,[status(thm)],[79, 75])). tff(81,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(82,plain, (room(paul)), inference(and_elim,[status(thm)],[8])). tff(83,plain, (room(paul)), inference(modus_ponens,[status(thm)],[82, 81])). tff(84,plain, (((~![X: $i] : ((~room(X)) | hate(susan, X))) | ((~room(paul)) | hate(susan, paul))) <=> ((~![X: $i] : ((~room(X)) | hate(susan, X))) | (~room(paul)) | hate(susan, paul))), inference(rewrite,[status(thm)],[])). tff(85,plain, ((~![X: $i] : ((~room(X)) | hate(susan, X))) | ((~room(paul)) | hate(susan, paul))), inference(quant_inst,[status(thm)],[])). tff(86,plain, ((~![X: $i] : ((~room(X)) | hate(susan, X))) | (~room(paul)) | hate(susan, paul)), inference(modus_ponens,[status(thm)],[85, 84])). tff(87,plain, (hate(susan, paul)), inference(unit_resolution,[status(thm)],[86, 83, 80])). tff(88,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(89,plain, (room(fred)), inference(and_elim,[status(thm)],[8])). tff(90,plain, (room(fred)), inference(modus_ponens,[status(thm)],[89, 88])). tff(91,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(92,plain, (room(mary)), inference(and_elim,[status(thm)],[8])). tff(93,plain, (room(mary)), inference(modus_ponens,[status(thm)],[92, 91])). tff(94,plain, (((~(quiet(paul) | rich(paul))) | (~hate(susan, paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8))))) <=> ((~hate(susan, paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (~(quiet(paul) | rich(paul))))), inference(rewrite,[status(thm)],[])). tff(95,plain, ((~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) <=> (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8))))), inference(rewrite,[status(thm)],[])). tff(96,plain, (((~quiet(paul)) & (~rich(paul))) <=> (~(quiet(paul) | rich(paul)))), inference(rewrite,[status(thm)],[])). tff(97,plain, ((((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8))))) <=> ((~(quiet(paul) | rich(paul))) | (~hate(susan, paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))))), inference(monotonicity,[status(thm)],[96, 95])). tff(98,plain, ((((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8))))) <=> ((~hate(susan, paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (~(quiet(paul) | rich(paul))))), inference(transitivity,[status(thm)],[97, 94])). tff(99,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))) <=> (((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))))), inference(rewrite,[status(thm)],[])). tff(100,plain, ((((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul))) <=> (((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))), inference(rewrite,[status(thm)],[])). tff(101,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul))))), inference(monotonicity,[status(thm)],[95, 100])). tff(102,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))) <=> (((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~((X!8 = |'fred'|) | (X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))))), inference(transitivity,[status(thm)],[101, 99])). tff(103,plain, ((room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul))))) <=> (room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))))), inference(rewrite,[status(thm)],[])). tff(104,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul))))))), inference(monotonicity,[status(thm)],[103])). tff(105,plain, ((~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))))) <=> (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul))))))), inference(rewrite,[status(thm)],[])). tff(106,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))))), inference(or_elim,[status(thm)],[7])). tff(107,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))))), inference(modus_ponens,[status(thm)],[106, 104])). tff(108,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))))), inference(modus_ponens,[status(thm)],[107, 105])). tff(109,plain, (~(room(mary) & room(paul) & room(fred) & ![X: $i] : ((X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(((~quiet(paul)) & (~rich(paul))) | (~hate(susan, paul)))))), inference(modus_ponens,[status(thm)],[108, 104])). 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!8 |'fred'|) (= X!8 |'paul'|) (= X!8 |'mary'|) (not (room X!8))))) (a!6 (or (and (not (quiet paul)) (not (rich paul))) (not (hate susan paul))))) (let ((a!7 (~ (not (and (room mary) (room paul) (room fred) a!4 (not a!6))) (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!7)))

room(melvin)&room(sharon)&room(robert)&(![X]:(room(X)=>(X='melvin'|X='sharon'|X='robert')))& (((?[X,Y]:((~hate(X,randy))&(hate(edwin,Y))&(hate(X,Y))))=>(?[X,Y]:((X!=robert)&(~hate(kimberly,Y))&(quieter(X,Y)))))& (?[X,Y]:((~hate(X,randy))&(hate(edwin,Y))&(hate(X,Y))))& (?[X,Y]:((hate(kimberly,X))&(Y!=robert)&(hate(X,Y))))& (~((~hate(robert,kimberly))|(~hate(randy,robert))))& ((hate(edwin,sharon) & hate(sharon,edwin)))& (![X]:(richer(X,melvin)))& (![X]:(quieter(sharon,X)))& (![X]:(room(X)=>(hate(randy,X))))& (?[X,Y]:((~(quiet(X)&brave(X)&person(X)))&(hate(Y,edwin))&(quieter(X,Y))))& ((hate(kimberly,robert))&(rich(robert)&person(robert)))& (![X]:(richer(robert,X))))

room(melvin)&room(sharon)&room(robert)&(![X]:(room(X)=>(X='melvin'|X='sharon'|X='robert')))& (~((~quiet(sharon)&~rich(sharon))|(~hate(randy,sharon))))

entailment

contradiction

contradiction

Christi, Jacques, Karen are the only persons in the room. If Jacques and Karen are richer than Lynn then someone who hates Lynn hate someone who does not collect classic novels otherwise Lynn is a client of Karen. Christi who does not hate Lynn, does not own a television if Karen and Jacques are respectively quiet and rich and vice versa. Karen is the richest in the room. Someone who does not collect classic novels hate someone who is a quiet rich tourist. Christi and Lynn hate each other. More than one person outside the room is not Jacques. Lynn is a client of Karen.

It is not the case that 'Karen who is not a quiet creative tourist, is not a quiet rich creative european'.

neutral

% SZS status Satisfiable

room(christi)&room(jacques)&room(karen)&(![X]:(room(X)=>(X='christi'|X='jacques'|X='karen')))& ((((richer(lynn,jacques)&richer(lynn,karen))=>(?[X,Y]:((hate(lynn,X))&(does_not_collect_classic_novels(Y))&(hate(X,Y)))))|((~(richer(lynn,jacques)&richer(lynn,karen)))=>(client(karen,lynn))))& (((quiet(karen))&(rich(jacques)))<=>((~hate(lynn,christi))&(does_not_own_a_television(christi))))& (![X]:(richer(X,karen)))& (?[X,Y]:((does_not_collect_classic_novels(X))&(quiet(Y)&rich(Y)&tourist(Y))&(hate(X,Y))))& ((hate(christi,lynn) & hate(lynn,christi)))& ((?[X,Y]:(~room(X)&~room(Y)&(X!=jacques&Y!=jacques)&(X!=Y))))& (client(karen,lynn)))

room(christi)&room(jacques)&room(karen)&(![X]:(room(X)=>(X='christi'|X='jacques'|X='karen')))& (~((~(quiet(karen)&creative(karen)&tourist(karen)))&(~(quiet(karen)&rich(karen)&creative(karen)&european(karen)))))

entailment

entailment

entailment

Merle, Nancy, Pauline, Robert are the only persons in the room. Robert who builds model airplanes, is not hated by Lizzie. Pauline who is not a brave rich creative person, is a sibling of James. Pauline is not hated by Ellen and is hated by James. Only one person outside the room is not a brave happy rich person. More than one person in the room is not hated by James. Everyone in the room who is a happy brave person is not hated by Lizzie.

Nancy is a brave happy rich person.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(person_type, type, ( person: $i > $o)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(rich_type, type, ( rich: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(paul_type, type, ( paul: $i)). 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(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(susan_type, type, ( susan: $i)). tff(fred_type, type, ( fred: $i)). tff(john_type, type, ( john: $i)). tff(sibling_type, type, ( sibling: ( $i * $i ) > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(predb_type, type, ( predb: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(1,assumption,(~((~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul)))), introduced(assumption)). tff(2,plain, (((~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul))) | person(paul)), inference(tautology,[status(thm)],[])). tff(3,plain, (person(paul)), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, (((~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul))) | rich(paul)), inference(tautology,[status(thm)],[])). tff(5,plain, (rich(paul)), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, (((~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul))) | brave(paul)), inference(tautology,[status(thm)],[])). tff(7,plain, (brave(paul)), inference(unit_resolution,[status(thm)],[6, 1])). tff(8,plain, (((~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul))) | happy(paul)), inference(tautology,[status(thm)],[])). tff(9,plain, (happy(paul)), inference(unit_resolution,[status(thm)],[8, 1])). tff(10,assumption,(~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))), introduced(assumption)). tff(11,plain, (((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | room(X!3)), inference(tautology,[status(thm)],[])). tff(12,plain, (room(X!3)), inference(unit_resolution,[status(thm)],[11, 10])). tff(13,plain, (((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(14,plain, (~(X!3 = |'mary'|)), inference(unit_resolution,[status(thm)],[13, 10])). tff(15,plain, (((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'paul'|))), inference(tautology,[status(thm)],[])). tff(16,plain, (~(X!3 = |'paul'|)), inference(unit_resolution,[status(thm)],[15, 10])). tff(17,plain, (((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'fred'|))), inference(tautology,[status(thm)],[])). tff(18,plain, (~(X!3 = |'fred'|)), inference(unit_resolution,[status(thm)],[17, 10])). tff(19,plain, (((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))) | (~(X!3 = |'alice'|))), inference(tautology,[status(thm)],[])). tff(20,plain, (~(X!3 = |'alice'|)), inference(unit_resolution,[status(thm)],[19, 10])). tff(21,plain, (^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(bind,[status(th)],[])). tff(22,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(quant_intro,[status(thm)],[21])). tff(23,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((predb(alice) & (~hate(alice, lucy))) & ((~(((brave(fred) & rich(fred)) & creative(fred)) & person(fred))) & sibling(susan, fred))) & ((~hate(fred, john)) & hate(fred, susan))) & (?[X: $i] : ((~room(X)) & (~(((brave(X) & happy(X)) & rich(X)) & person(X)))) & ![X: $i, Y: $i] : (((~(((brave(X) & happy(X)) & rich(X)) & person(X))) & (~(((brave(Y) & happy(Y)) & rich(Y)) & person(Y)))) => (X = Y)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~hate(X, susan)) & (~hate(Y, susan)))) & (~(X = Y)))) & ![X: $i] : (room(X) => (((happy(X) & brave(X)) & person(X)) => (~hate(X, lucy)))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((brave(paul) & happy(paul)) & rich(paul)) & person(paul))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & predb(alice) & (~hate(alice, lucy)) & (~(brave(fred) & rich(fred) & creative(fred) & person(fred))) & sibling(susan, fred) & (~hate(fred, john)) & hate(fred, susan) & ?[X: $i] : ((~room(X)) & (~(brave(X) & happy(X) & rich(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(brave(X) & happy(X) & rich(X) & person(X))) & (~(brave(Y) & happy(Y) & rich(Y) & person(Y))))) | (X = Y)) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~hate(X, susan)) & (~hate(Y, susan)) & (~(X = Y))) & ![X: $i] : ((~room(X)) | (~hate(X, lucy)) | (~(happy(X) & brave(X) & person(X)))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul))))), inference(rewrite,[status(thm)],[])). tff(25,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((predb(alice) & (~hate(alice, lucy))) & ((~(((brave(fred) & rich(fred)) & creative(fred)) & person(fred))) & sibling(susan, fred))) & ((~hate(fred, john)) & hate(fred, susan))) & (?[X: $i] : ((~room(X)) & (~(((brave(X) & happy(X)) & rich(X)) & person(X)))) & ![X: $i, Y: $i] : (((~(((brave(X) & happy(X)) & rich(X)) & person(X))) & (~(((brave(Y) & happy(Y)) & rich(Y)) & person(Y)))) => (X = Y)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~hate(X, susan)) & (~hate(Y, susan)))) & (~(X = Y)))) & ![X: $i] : (room(X) => (((happy(X) & brave(X)) & person(X)) => (~hate(X, lucy)))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((brave(paul) & happy(paul)) & rich(paul)) & person(paul))))), file('/mnt/tmpfs//1611209173052247998158598.p','negated')). tff(26,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & predb(alice) & (~hate(alice, lucy)) & (~(brave(fred) & rich(fred) & creative(fred) & person(fred))) & sibling(susan, fred) & (~hate(fred, john)) & hate(fred, susan) & ?[X: $i] : ((~room(X)) & (~(brave(X) & happy(X) & rich(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(brave(X) & happy(X) & rich(X) & person(X))) & (~(brave(Y) & happy(Y) & rich(Y) & person(Y))))) | (X = Y)) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~hate(X, susan)) & (~hate(Y, susan)) & (~(X = Y))) & ![X: $i] : ((~room(X)) | (~hate(X, lucy)) | (~(happy(X) & brave(X) & person(X)))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul)))), inference(modus_ponens,[status(thm)],[25, 24])). tff(27,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & predb(alice) & (~hate(alice, lucy)) & (~(brave(fred) & rich(fred) & creative(fred) & person(fred))) & sibling(susan, fred) & (~hate(fred, john)) & hate(fred, susan) & ?[X: $i] : ((~room(X)) & (~(brave(X) & happy(X) & rich(X) & person(X)))) & ![X: $i, Y: $i] : ((~((~(brave(X) & happy(X) & rich(X) & person(X))) & (~(brave(Y) & happy(Y) & rich(Y) & person(Y))))) | (X = Y)) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~hate(X, susan)) & (~hate(Y, susan)) & (~(X = Y))) & ![X: $i] : ((~room(X)) | (~hate(X, lucy)) | (~(happy(X) & brave(X) & person(X))))), inference(or_elim,[status(thm)],[26])). tff(28,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(and_elim,[status(thm)],[27])). tff(29,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[28, 23])). tff(30,plain,( ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(skolemize,[status(sab)],[29])). tff(31,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[30, 22])). tff(32,plain, (((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))), inference(rewrite,[status(thm)],[])). tff(33,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))), inference(quant_inst,[status(thm)],[])). tff(34,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))), inference(modus_ponens,[status(thm)],[33, 32])). tff(35,plain, ($false), inference(unit_resolution,[status(thm)],[34, 31, 20, 18, 16, 14, 12])). tff(36,plain,((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))), inference(lemma,lemma(discharge,[]))). tff(37,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(38,plain, (room(alice)), inference(and_elim,[status(thm)],[27])). tff(39,plain, (room(alice)), inference(modus_ponens,[status(thm)],[38, 37])). tff(40,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(41,plain, (room(fred)), inference(and_elim,[status(thm)],[27])). tff(42,plain, (room(fred)), inference(modus_ponens,[status(thm)],[41, 40])). tff(43,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(44,plain, (room(paul)), inference(and_elim,[status(thm)],[27])). tff(45,plain, (room(paul)), inference(modus_ponens,[status(thm)],[44, 43])). tff(46,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(47,plain, (room(mary)), inference(and_elim,[status(thm)],[27])). tff(48,plain, (room(mary)), inference(modus_ponens,[status(thm)],[47, 46])). tff(49,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul)))), inference(rewrite,[status(thm)],[])). tff(50,plain, ((~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))), inference(rewrite,[status(thm)],[])). tff(51,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul)))), inference(monotonicity,[status(thm)],[50])). tff(52,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~brave(paul)) | (~happy(paul)) | (~rich(paul)) | (~person(paul)))), inference(transitivity,[status(thm)],[51, 49])). tff(53,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul)) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul))), inference(rewrite,[status(thm)],[])). tff(54,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul)))), inference(monotonicity,[status(thm)],[53])). tff(55,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul)))), inference(rewrite,[status(thm)],[])). tff(56,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul))), inference(or_elim,[status(thm)],[26])). tff(57,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul))), inference(modus_ponens,[status(thm)],[56, 54])). tff(58,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul))), inference(modus_ponens,[status(thm)],[57, 55])). tff(59,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & brave(paul) & happy(paul) & rich(paul) & person(paul))), inference(modus_ponens,[status(thm)],[58, 54])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!3 |'alice'|) (= X!3 |'fred'|) (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3))))) (a!7 (refl (~ (not (brave paul)) (not (brave paul))))) (a!8 (refl (~ (not (happy paul)) (not (happy paul))))) (a!9 (refl (~ (not (rich paul)) (not (rich paul))))) (a!10 (refl (~ (not (person paul)) (not (person paul)))))) (let ((a!11 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 (brave paul) (happy paul) (rich paul) (person paul))) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (not (brave paul)) (not (happy paul)) (not (rich paul)) (not (person paul)))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!7 a!8 a!9 a!10 a!11)))

room(merle)&room(nancy)&room(pauline)&room(robert)&(![X]:(room(X)=>(X='merle'|X='nancy'|X='pauline'|X='robert')))& (((builds_model_airplanes(robert))&(~hate(robert,lizzie)))& ((~(brave(pauline)&rich(pauline)&creative(pauline)&person(pauline)))&(sibling(james,pauline)))& ((~hate(pauline,ellen))&(hate(pauline,james)))& (((?[X]:(~room(X)&~(brave(X)&happy(X)&rich(X)&person(X))))&(![X,Y]:((~(brave(X)&happy(X)&rich(X)&person(X))&~(brave(Y)&happy(Y)&rich(Y)&person(Y)))=>(X=Y)))))& ((?[X,Y]:(room(X)&room(Y)&(~hate(X,james)&~hate(Y,james))&(X!=Y))))& (![X]:(room(X)=>(((happy(X)&brave(X)&person(X))=>(~hate(X,lizzie)))))))

room(merle)&room(nancy)&room(pauline)&room(robert)&(![X]:(room(X)=>(X='merle'|X='nancy'|X='pauline'|X='robert')))& (brave(nancy)&happy(nancy)&rich(nancy)&person(nancy))

contradiction

neutral

neutral

Andrew, Berta, Lucas are the only persons in the room. More than one person outside the room does not hate Wendi if Andrew is not hated by Wendi or is taller than Eugene or both and vice versa. Lucas is the tallest in the room unless it is not the case that 'Lucas is not a tall tourist and does not collect antique clocks'. Everyone in the room is not happy, not tall, not rich. Everyone in the room collects antique clocks. Andrew neither is taller than Eugene nor hates Wendi. It is not the case that 'Lucas is not a tall tourist and does not collect antique clocks'.

Berta who hates Eugene, is a tall person.

contradiction

-

room(andrew)&room(berta)&room(lucas)&(![X]:(room(X)=>(X='andrew'|X='berta'|X='lucas')))& (((((~hate(andrew,wendi))|(taller(eugene,andrew))))<=>((?[X,Y]:(~room(X)&~room(Y)&(~hate(wendi,X)&~hate(wendi,Y))&(X!=Y)))))& (~(~((~(tall(lucas)&tourist(lucas)))&(does_not_collect_antique_clocks(lucas))))=>(![X]:(taller(X,lucas))))& (![X]:(room(X)=>(~happy(X)&~tall(X)&~rich(X))))& (![X]:(room(X)=>(collects_antique_clocks(X))))& (~((taller(eugene,andrew))|(hate(wendi,andrew))))& (~((~(tall(lucas)&tourist(lucas)))&(does_not_collect_antique_clocks(lucas)))))

room(andrew)&room(berta)&room(lucas)&(![X]:(room(X)=>(X='andrew'|X='berta'|X='lucas')))& ((hate(eugene,berta))&(tall(berta)&person(berta)))

contradiction

neutral

neutral

At most one of the following is true:. -Mark either is not Richard or is not Agnes. -Mark and Richard are not Richard.

More than one person in the room is not Richard.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(fred_type, type, ( fred: $i)). tff(paul_type, type, ( paul: $i)). tff(mary_type, type, ( mary: $i)). tff(lucy_type, type, ( lucy: $i)). tff(susan_type, type, ( susan: $i)). tff(john_type, type, ( john: $i)). tff(1,assumption,(~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))), introduced(assumption)). tff(2,plain, (((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | room(X!0)), inference(tautology,[status(thm)],[])). tff(3,plain, (room(X!0)), inference(unit_resolution,[status(thm)],[2, 1])). tff(4,plain, (((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | (~(X!0 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(5,plain, (~(X!0 = |'mary'|)), inference(unit_resolution,[status(thm)],[4, 1])). tff(6,plain, (((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | (~(X!0 = |'paul'|))), inference(tautology,[status(thm)],[])). tff(7,plain, (~(X!0 = |'paul'|)), inference(unit_resolution,[status(thm)],[6, 1])). tff(8,plain, (((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | (~(X!0 = |'fred'|))), inference(tautology,[status(thm)],[])). tff(9,plain, (~(X!0 = |'fred'|)), inference(unit_resolution,[status(thm)],[8, 1])). tff(10,plain, (((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) | (~(X!0 = |'alice'|))), inference(tautology,[status(thm)],[])). tff(11,plain, (~(X!0 = |'alice'|)), inference(unit_resolution,[status(thm)],[10, 1])). tff(12,plain, (^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(bind,[status(th)],[])). tff(13,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(quant_intro,[status(thm)],[12])). tff(14,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(rewrite,[status(thm)],[])). tff(15,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(((((~(paul = alice)) | (~(paul = mary))) & (~((~(paul = alice)) | (~(paul = mary))))) & (~(paul = alice))) & (~(alice = alice))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~(X = alice)) & (~(Y = alice)))) & (~(X = Y)))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))))), inference(rewrite,[status(thm)],[])). tff(16,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(((((~(paul = alice)) | (~(paul = mary))) & (~((~(paul = alice)) | (~(paul = mary))))) & (~(paul = alice))) & (~(alice = alice))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : (((room(X) & room(Y)) & ((~(X = alice)) & (~(Y = alice)))) & (~(X = Y)))))), file('/mnt/tmpfs//8679184743559148884233913.p','negated')). tff(17,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))))), inference(modus_ponens,[status(thm)],[16, 15])). tff(18,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(or_elim,[status(thm)],[17])). tff(19,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(and_elim,[status(thm)],[18])). tff(20,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[19, 14])). tff(21,plain,( ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(skolemize,[status(sab)],[20])). tff(22,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[21, 13])). tff(23,plain, (((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))), inference(quant_inst,[status(thm)],[])). tff(25,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))), inference(modus_ponens,[status(thm)],[24, 23])). tff(26,plain, ($false), inference(unit_resolution,[status(thm)],[25, 22, 11, 9, 7, 5, 3])). tff(27,plain,((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))), inference(lemma,lemma(discharge,[]))). tff(28,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(29,plain, (room(alice)), inference(and_elim,[status(thm)],[18])). tff(30,plain, (room(alice)), inference(modus_ponens,[status(thm)],[29, 28])). tff(31,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(32,plain, (room(fred)), inference(and_elim,[status(thm)],[18])). tff(33,plain, (room(fred)), inference(modus_ponens,[status(thm)],[32, 31])). tff(34,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(35,plain, (room(paul)), inference(and_elim,[status(thm)],[18])). tff(36,plain, (room(paul)), inference(modus_ponens,[status(thm)],[35, 34])). tff(37,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(38,plain, (room(mary)), inference(and_elim,[status(thm)],[18])). tff(39,plain, (room(mary)), inference(modus_ponens,[status(thm)],[38, 37])). tff(40,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : ((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : ((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X))))), inference(rewrite,[status(thm)],[])). tff(41,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : ((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : ((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X))))), inference(rewrite,[status(thm)],[])). tff(42,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite((room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))) <=> (~((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X))))), ((~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))) <=> (~(~((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X))))))), rewrite((~(~((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X))))) <=> ((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X)))), ((~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))) <=> ((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X)))))), inference(bind,[status(th)],[])). tff(43,plain, (![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))) <=> ![X: $i, Y: $i] : ((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X)))), inference(quant_intro,[status(thm)],[42])). tff(44,plain, ((~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))))), inference(rewrite,[status(thm)],[])). tff(45,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : ((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X))))), inference(monotonicity,[status(thm)],[44, 43])). tff(46,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : ((X = Y) | (Y = alice) | (X = alice) | (~room(Y)) | (~room(X))))), inference(transitivity,[status(thm)],[45, 41])). tff(47,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))))), inference(rewrite,[status(thm)],[])). tff(48,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))))), inference(monotonicity,[status(thm)],[44])). tff(49,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!0 = |'alice'|) | (X!0 = |'fred'|) | (X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) | ![X: $i, Y: $i] : (~(room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))))), inference(transitivity,[status(thm)],[48, 47])). tff(50,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))), inference(rewrite,[status(thm)],[])). tff(51,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))))), inference(monotonicity,[status(thm)],[50])). tff(52,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y)))))), inference(rewrite,[status(thm)],[])). tff(53,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))), inference(or_elim,[status(thm)],[17])). tff(54,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))), inference(modus_ponens,[status(thm)],[53, 51])). tff(55,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))), inference(modus_ponens,[status(thm)],[54, 52])). tff(56,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (room(X) & room(Y) & (~(X = alice)) & (~(Y = alice)) & (~(X = Y))))), inference(modus_ponens,[status(thm)],[55, 51])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!0 |'alice'|) (= X!0 |'fred'|) (= X!0 |'paul'|) (= X!0 |'mary'|) (not (room X!0))))) (a!7 (lambda ((X $i) (Y $i)) (let ((a!1 (and (room X) (room Y) (not (= X alice)) (not (= Y alice)) (not (= X Y))))) (refl (~ (not a!1) (not a!1)))))) (a!8 (exists ((X $i) (Y $i)) (and (room X) (room Y) (not (= X alice)) (not (= Y alice)) (not (= X Y))))) (a!9 (forall ((X $i) (Y $i)) (let ((a!1 (and (room X) (room Y) (not (= X alice)) (not (= Y alice)) (not (= X Y))))) (not a!1))))) (let ((a!10 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 a!8)) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 a!9)))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (nnf-neg (proof-bind a!7) (~ (not a!8) a!9)) a!10)))

room(agnes)&room(mark)&room(ellen)&room(richard)&(![X]:(room(X)=>(X='agnes'|X='mark'|X='ellen'|X='richard')))& (~((((mark!=richard)|(mark!=agnes))&(~((mark!=richard)|(mark!=agnes))))&mark!=richard&richard!=richard))

room(agnes)&room(mark)&room(ellen)&room(richard)&(![X]:(room(X)=>(X='agnes'|X='mark'|X='ellen'|X='richard')))& ((?[X,Y]:(room(X)&room(Y)&(X!=richard&Y!=richard)&(X!=Y))))

neutral

neutral

entailment

Jennifer is the only person in the room. Jennifer who is not quiet, is not hated by Ellsworth unless only one person outside the room is not rich. Jennifer neither is a client of Chad nor is not a happy creative quiet european if everyone outside the room is richer than Ellsworth. More than one person outside the room does not collect luxury watches. Only one person outside the room is not a happy rich european. Jennifer is the least quiet in the room. It is not the case that 'it is not the case that 'someone who hates Chad hate someone who is taller than Ronald''. Jennifer neither is hated by Ronald nor does not collect luxury watches. Someone outside the room who is a client of Ellsworth is not liked by Ellsworth.

Jennifer neither is liked by Ruth nor is a rich creative european.

neutral

% SZS status Satisfiable

room(jennifer)&(![X]:(room(X)=>(X='jennifer')))& ((~(((?[X]:(~room(X)&~rich(X)))&(![X,Y]:((~rich(X)&~rich(Y))=>(X=Y)))))=>((~quiet(jennifer))&(~hate(jennifer,ellsworth))))& ((![X]:(~room(X)=>(richer(ellsworth,X))))=>(~((client(chad,jennifer))|(~(happy(jennifer)&creative(jennifer)&quiet(jennifer)&european(jennifer))))))& ((?[X,Y]:(~room(X)&~room(Y)&(does_not_collect_luxury_watches(X)&does_not_collect_luxury_watches(Y))&(X!=Y))))& (((?[X]:(~room(X)&~(happy(X)&rich(X)&european(X))))&(![X,Y]:((~(happy(X)&rich(X)&european(X))&~(happy(Y)&rich(Y)&european(Y)))=>(X=Y)))))& (![X]:(quieter(jennifer,X)))& (~(~(?[X,Y]:((hate(chad,X))&(taller(ronald,Y))&(hate(X,Y))))))& (~((hate(jennifer,ronald))|(does_not_collect_luxury_watches(jennifer))))& (?[X]:(~room(X)=>(((client(ellsworth,X))=>(~like(X,ellsworth)))))))

room(jennifer)&(![X]:(room(X)=>(X='jennifer')))& (~((like(jennifer,ruth))|(rich(jennifer)&creative(jennifer)&european(jennifer))))

neutral

neutral

contradiction

Geneva, Willie are the only persons in the room. Everyone outside the room who is not Geneva is a rich european. Geneva who collects rare minerals, is richer than Robert. Someone who is a quiet person hate someone who does not hate Robert. More than one person outside the room is not hated by Robert.

It is not the case that 'Willie either collects rare minerals or is not a rich happy quiet european'.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(paul_type, type, ( paul: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(person_type, type, ( person: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(european_type, type, ( european: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(1,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((![X: $i] : ((~room(X)) => ((~(X = mary)) => (rich(X) & european(X)))) & (preda(mary) & richer(john, mary))) & ?[X: $i, Y: $i] : (((quiet(X) & person(X)) & (~hate(john, Y))) & hate(X, Y))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~hate(X, john)) & (~hate(Y, john)))) & (~(X = Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((preda(paul) | (~(((rich(paul) & happy(paul)) & quiet(paul)) & european(paul)))) & (~(preda(paul) | (~(((rich(paul) & happy(paul)) & quiet(paul)) & european(paul)))))))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (room(X) | (rich(X) & european(X)) | (X = mary)) & preda(mary) & richer(john, mary) & ?[X: $i, Y: $i] : (quiet(X) & person(X) & (~hate(john, Y)) & hate(X, Y)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(X, john)) & (~hate(Y, john)) & (~(X = Y))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (((![X: $i] : ((~room(X)) => ((~(X = mary)) => (rich(X) & european(X)))) & (preda(mary) & richer(john, mary))) & ?[X: $i, Y: $i] : (((quiet(X) & person(X)) & (~hate(john, Y))) & hate(X, Y))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~hate(X, john)) & (~hate(Y, john)))) & (~(X = Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((preda(paul) | (~(((rich(paul) & happy(paul)) & quiet(paul)) & european(paul)))) & (~(preda(paul) | (~(((rich(paul) & happy(paul)) & quiet(paul)) & european(paul)))))))))), file('/mnt/tmpfs//4980249524642187305621422.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (room(X) | (rich(X) & european(X)) | (X = mary)) & preda(mary) & richer(john, mary) & ?[X: $i, Y: $i] : (quiet(X) & person(X) & (~hate(john, Y)) & hate(X, Y)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(X, john)) & (~hate(Y, john)) & (~(X = Y))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (room(X) | (rich(X) & european(X)) | (X = mary)) & preda(mary) & richer(john, mary) & ?[X: $i, Y: $i] : (quiet(X) & person(X) & (~hate(john, Y)) & hate(X, Y)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~hate(X, john)) & (~hate(Y, john)) & (~(X = Y)))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (room(paul)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(9,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(10,plain, (room(mary)), inference(modus_ponens,[status(thm)],[9, 8])). tff(11,plain, ((~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))), inference(rewrite,[status(thm)],[])). tff(12,plain, (((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))))), inference(monotonicity,[status(thm)],[11])). tff(13,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(rewrite,[status(thm)],[])). tff(14,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(monotonicity,[status(thm)],[13])). tff(15,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(rewrite,[status(thm)],[])). tff(16,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(or_elim,[status(thm)],[4])). tff(17,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[16, 14])). tff(18,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[17, 15])). tff(19,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[18, 14])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!4 (not (or (= X!4 |'paul'|) (= X!4 |'mary'|) (not (room X!4)))))) (let ((a!5 (~ (not (and (room mary) (room paul) a!3)) (or (not (room mary)) (not (room paul)) a!4)))) (nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) a!5)))

room(geneva)&room(willie)&(![X]:(room(X)=>(X='geneva'|X='willie')))& ((![X]:(~room(X)=>(((X!=geneva)=>(rich(X)&european(X))))))& ((collects_rare_minerals(geneva))&(richer(robert,geneva)))& (?[X,Y]:((quiet(X)&person(X))&(~hate(robert,Y))&(hate(X,Y))))& ((?[X,Y]:(~room(X)&~room(Y)&(~hate(X,robert)&~hate(Y,robert))&(X!=Y)))))

room(geneva)&room(willie)&(![X]:(room(X)=>(X='geneva'|X='willie')))& (~((((collects_rare_minerals(willie))|(~(rich(willie)&happy(willie)&quiet(willie)&european(willie))))&(~((collects_rare_minerals(willie))|(~(rich(willie)&happy(willie)&quiet(willie)&european(willie))))))))

entailment

entailment

entailment

Vicki, Lynda, Aaron, James are the only persons in the room. “Someone who is not liked by Mario like someone who likes Mario” unless “Aaron and Vicki like Mario”. “Lynda and Aaron are brave tourist” if “someone who is not creative is quieter than someone who is not Aaron”. Someone who is not creative is quieter than someone who is not Aaron. Mario is a client of Aaron. Mario is taller than Vicki. Aaron and Vicki like each other.

Someone who is a brave tourist is a client of someone who is not James.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(tptp_fun_Y_2_type, type, ( tptp_fun_Y_2: $i)). tff(tptp_fun_X_3_type, type, ( tptp_fun_X_3: $i)). tff(fred_type, type, ( fred: $i)). tff(creative_type, type, ( creative: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(susan_type, type, ( susan: $i)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(room_type, type, ( room: $i > $o)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(alice_type, type, ( alice: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(lucy_type, type, ( lucy: $i)). tff(john_type, type, ( john: $i)). tff(1,plain, (?[X: $i, Y: $i] : ((~creative(X)) & (~(Y = fred)) & quieter(X, Y)) <=> ?[X: $i, Y: $i] : ((~creative(X)) & (~(Y = fred)) & quieter(X, Y))), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((~(like(susan, fred) & like(susan, mary))) => ?[X: $i, Y: $i] : (((~like(X, susan)) & like(susan, Y)) & like(X, Y))) & (?[X: $i, Y: $i] : (((~creative(X)) & (~(Y = fred))) & quieter(X, Y)) => (((brave(paul) & tourist(paul)) & brave(fred)) & tourist(fred)))) & ?[X: $i, Y: $i] : (((~creative(X)) & (~(Y = fred))) & quieter(X, Y))) & client(fred, susan)) & taller(mary, susan)) & (like(fred, mary) & like(mary, fred)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : (((brave(X) & tourist(X)) & (~(Y = alice))) & client(X, Y))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((like(susan, fred) & like(susan, mary)) | ?[X: $i, Y: $i] : ((~like(X, susan)) & like(susan, Y) & like(X, Y))) & ((~?[X: $i, Y: $i] : ((~creative(X)) & (~(Y = fred)) & quieter(X, Y))) | (brave(paul) & tourist(paul) & brave(fred) & tourist(fred))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(Y = fred)) & quieter(X, Y)) & client(fred, susan) & taller(mary, susan) & like(fred, mary) & like(mary, fred))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((((((~(like(susan, fred) & like(susan, mary))) => ?[X: $i, Y: $i] : (((~like(X, susan)) & like(susan, Y)) & like(X, Y))) & (?[X: $i, Y: $i] : (((~creative(X)) & (~(Y = fred))) & quieter(X, Y)) => (((brave(paul) & tourist(paul)) & brave(fred)) & tourist(fred)))) & ?[X: $i, Y: $i] : (((~creative(X)) & (~(Y = fred))) & quieter(X, Y))) & client(fred, susan)) & taller(mary, susan)) & (like(fred, mary) & like(mary, fred)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ?[X: $i, Y: $i] : (((brave(X) & tourist(X)) & (~(Y = alice))) & client(X, Y))))), file('/mnt/tmpfs//5184718287858863649141753.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((like(susan, fred) & like(susan, mary)) | ?[X: $i, Y: $i] : ((~like(X, susan)) & like(susan, Y) & like(X, Y))) & ((~?[X: $i, Y: $i] : ((~creative(X)) & (~(Y = fred)) & quieter(X, Y))) | (brave(paul) & tourist(paul) & brave(fred) & tourist(fred))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(Y = fred)) & quieter(X, Y)) & client(fred, susan) & taller(mary, susan) & like(fred, mary) & like(mary, fred))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((like(susan, fred) & like(susan, mary)) | ?[X: $i, Y: $i] : ((~like(X, susan)) & like(susan, Y) & like(X, Y))) & ((~?[X: $i, Y: $i] : ((~creative(X)) & (~(Y = fred)) & quieter(X, Y))) | (brave(paul) & tourist(paul) & brave(fred) & tourist(fred))) & ?[X: $i, Y: $i] : ((~creative(X)) & (~(Y = fred)) & quieter(X, Y)) & client(fred, susan) & taller(mary, susan) & like(fred, mary) & like(mary, fred)), inference(or_elim,[status(thm)],[4])). tff(6,plain, (?[X: $i, Y: $i] : ((~creative(X)) & (~(Y = fred)) & quieter(X, Y))), inference(and_elim,[status(thm)],[5])). tff(7,plain, (?[X: $i, Y: $i] : ((~creative(X)) & (~(Y = fred)) & quieter(X, Y))), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain,( (~creative(X!3)) & (~(Y!2 = fred)) & quieter(X!3, Y!2)), inference(skolemize,[status(sab)],[7])). tff(9,plain, (quieter(X!3, Y!2)), inference(and_elim,[status(thm)],[8])). tff(10,plain, (~(Y!2 = fred)), inference(and_elim,[status(thm)],[8])). tff(11,plain, (~creative(X!3)), inference(and_elim,[status(thm)],[8])). tff(12,assumption,(~((~brave(paul)) | (~tourist(paul)) | (~brave(fred)) | (~tourist(fred)))), introduced(assumption)). tff(13,plain, (((~brave(paul)) | (~tourist(paul)) | (~brave(fred)) | (~tourist(fred))) | brave(fred)), inference(tautology,[status(thm)],[])). tff(14,plain, (brave(fred)), inference(unit_resolution,[status(thm)],[13, 12])). tff(15,plain, (((~brave(paul)) | (~tourist(paul)) | (~brave(fred)) | (~tourist(fred))) | tourist(fred)), inference(tautology,[status(thm)],[])). tff(16,plain, (tourist(fred)), inference(unit_resolution,[status(thm)],[15, 12])). tff(17,assumption,(~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))), introduced(assumption)). tff(18,plain, (((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | room(X!4)), inference(tautology,[status(thm)],[])). tff(19,plain, (room(X!4)), inference(unit_resolution,[status(thm)],[18, 17])). tff(20,plain, (((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(21,plain, (~(X!4 = |'mary'|)), inference(unit_resolution,[status(thm)],[20, 17])). tff(22,plain, (((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'paul'|))), inference(tautology,[status(thm)],[])). tff(23,plain, (~(X!4 = |'paul'|)), inference(unit_resolution,[status(thm)],[22, 17])). tff(24,plain, (((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'fred'|))), inference(tautology,[status(thm)],[])). tff(25,plain, (~(X!4 = |'fred'|)), inference(unit_resolution,[status(thm)],[24, 17])). tff(26,plain, (((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) | (~(X!4 = |'alice'|))), inference(tautology,[status(thm)],[])). tff(27,plain, (~(X!4 = |'alice'|)), inference(unit_resolution,[status(thm)],[26, 17])). tff(28,plain, (^[X: $i] : refl(((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(bind,[status(th)],[])). tff(29,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(quant_intro,[status(thm)],[28])). tff(30,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(rewrite,[status(thm)],[])). tff(31,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(and_elim,[status(thm)],[5])). tff(32,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[31, 30])). tff(33,plain,( ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(skolemize,[status(sab)],[32])). tff(34,plain, (![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(modus_ponens,[status(thm)],[33, 29])). tff(35,plain, (((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))), inference(rewrite,[status(thm)],[])). tff(36,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))), inference(quant_inst,[status(thm)],[])). tff(37,plain, ((~![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))), inference(modus_ponens,[status(thm)],[36, 35])). tff(38,plain, ($false), inference(unit_resolution,[status(thm)],[37, 34, 27, 25, 23, 21, 19])). tff(39,plain,((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))), inference(lemma,lemma(discharge,[]))). tff(40,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(41,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(42,plain, (room(alice)), inference(modus_ponens,[status(thm)],[41, 40])). tff(43,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(44,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(45,plain, (room(fred)), inference(modus_ponens,[status(thm)],[44, 43])). tff(46,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(47,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(48,plain, (room(paul)), inference(modus_ponens,[status(thm)],[47, 46])). tff(49,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(50,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(51,plain, (room(mary)), inference(modus_ponens,[status(thm)],[50, 49])). tff(52,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y))))), inference(rewrite,[status(thm)],[])). tff(53,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y))))), inference(rewrite,[status(thm)],[])). tff(54,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite((brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)) <=> (~((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y))))), ((~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y))) <=> (~(~((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y))))))), rewrite((~(~((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y))))) <=> ((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y)))), ((~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y))) <=> ((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y)))))), inference(bind,[status(th)],[])). tff(55,plain, (![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y))) <=> ![X: $i, Y: $i] : ((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y)))), inference(quant_intro,[status(thm)],[54])). tff(56,plain, ((~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))))), inference(rewrite,[status(thm)],[])). tff(57,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y))))), inference(monotonicity,[status(thm)],[56, 55])). tff(58,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : ((Y = alice) | (~brave(X)) | (~tourist(X)) | (~client(X, Y))))), inference(transitivity,[status(thm)],[57, 53])). tff(59,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y))))), inference(rewrite,[status(thm)],[])). tff(60,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y))))), inference(monotonicity,[status(thm)],[56])). tff(61,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!4 = |'alice'|) | (X!4 = |'fred'|) | (X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) | ![X: $i, Y: $i] : (~(brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y))))), inference(transitivity,[status(thm)],[60, 59])). tff(62,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))), inference(rewrite,[status(thm)],[])). tff(63,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y))))), inference(monotonicity,[status(thm)],[62])). tff(64,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y))))), inference(rewrite,[status(thm)],[])). tff(65,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))), inference(or_elim,[status(thm)],[4])). tff(66,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))), inference(modus_ponens,[status(thm)],[65, 63])). tff(67,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))), inference(modus_ponens,[status(thm)],[66, 64])). tff(68,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (brave(X) & tourist(X) & (~(Y = alice)) & client(X, Y)))), inference(modus_ponens,[status(thm)],[67, 63])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!4 |'alice'|) (= X!4 |'fred'|) (= X!4 |'paul'|) (= X!4 |'mary'|) (not (room X!4))))) (a!7 (lambda ((X $i) (Y $i)) (let ((a!1 (and (brave X) (tourist X) (not (= Y alice)) (client X Y)))) (refl (~ (not a!1) (not a!1)))))) (a!8 (exists ((X $i) (Y $i)) (and (brave X) (tourist X) (not (= Y alice)) (client X Y)))) (a!9 (forall ((X $i) (Y $i)) (let ((a!1 (and (brave X) (tourist X) (not (= Y alice)) (client X Y)))) (not a!1))))) (let ((a!10 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 a!8)) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 a!9)))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (nnf-neg (proof-bind a!7) (~ (not a!8) a!9)) a!10)))

room(vicki)&room(lynda)&room(aaron)&room(james)&(![X]:(room(X)=>(X='vicki'|X='lynda'|X='aaron'|X='james')))& ((~(like(mario,aaron)&like(mario,vicki))=>(?[X,Y]:((~like(X,mario))&(like(mario,Y))&(like(X,Y)))))& ((?[X,Y]:((~creative(X))&(Y!=aaron)&(quieter(X,Y))))=>(brave(lynda)&tourist(lynda)&brave(aaron)&tourist(aaron)))& (?[X,Y]:((~creative(X))&(Y!=aaron)&(quieter(X,Y))))& (client(aaron,mario))& (taller(vicki,mario))& ((like(aaron,vicki) & like(vicki,aaron))))

room(vicki)&room(lynda)&room(aaron)&room(james)&(![X]:(room(X)=>(X='vicki'|X='lynda'|X='aaron'|X='james')))& (?[X,Y]:((brave(X)&tourist(X))&(Y!=james)&(client(X,Y))))

neutral

neutral

entailment

Dawn, Matthew, Bobby, Jimmy are the only persons in the room. Katie is taller than Dawn. Dawn likes Katie. Bobby and Matthew are respectively happy and quiet. Only one person outside the room is not tall. Katie and Matthew like each other.

Dawn and Matthew are respectively tall and quiet.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_1_type, type, ( tptp_fun_X_1: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(paul_type, type, ( paul: $i)). tff(quiet_type, type, ( quiet: $i > $o)). tff(happy_type, type, ( happy: $i > $o)). tff(fred_type, type, ( fred: $i)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(1,assumption,(X!0 = mary), introduced(assumption)). tff(2,plain, (room(X!0) <=> room(mary)), inference(monotonicity,[status(thm)],[1])). tff(3,plain, (room(mary) <=> room(X!0)), inference(symmetry,[status(thm)],[2])). tff(4,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(5,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((taller(mary, lucy) & like(lucy, mary)) & (happy(fred) & quiet(paul))) & (?[X: $i] : ((~room(X)) & (~tall(X))) & ![X: $i, Y: $i] : (((~tall(X)) & (~tall(Y))) => (X = Y)))) & (like(lucy, paul) & like(paul, lucy)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (tall(mary) & quiet(paul))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & taller(mary, lucy) & like(lucy, mary) & happy(fred) & quiet(paul) & ?[X: $i] : ((~room(X)) & (~tall(X))) & ![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y)) & like(lucy, paul) & like(paul, lucy))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul))))), inference(rewrite,[status(thm)],[])). tff(6,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((taller(mary, lucy) & like(lucy, mary)) & (happy(fred) & quiet(paul))) & (?[X: $i] : ((~room(X)) & (~tall(X))) & ![X: $i, Y: $i] : (((~tall(X)) & (~tall(Y))) => (X = Y)))) & (like(lucy, paul) & like(paul, lucy)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (tall(mary) & quiet(paul))))), file('/mnt/tmpfs//8472991374276665792618252.p','negated')). tff(7,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & taller(mary, lucy) & like(lucy, mary) & happy(fred) & quiet(paul) & ?[X: $i] : ((~room(X)) & (~tall(X))) & ![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y)) & like(lucy, paul) & like(paul, lucy))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul)))), inference(modus_ponens,[status(thm)],[6, 5])). tff(8,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & taller(mary, lucy) & like(lucy, mary) & happy(fred) & quiet(paul) & ?[X: $i] : ((~room(X)) & (~tall(X))) & ![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y)) & like(lucy, paul) & like(paul, lucy)), inference(or_elim,[status(thm)],[7])). tff(9,plain, (room(mary)), inference(and_elim,[status(thm)],[8])). tff(10,plain, (room(mary)), inference(modus_ponens,[status(thm)],[9, 4])). tff(11,plain, (room(X!0)), inference(modus_ponens,[status(thm)],[10, 3])). tff(12,plain, (?[X: $i] : ((~room(X)) & (~tall(X))) <=> ?[X: $i] : ((~room(X)) & (~tall(X)))), inference(rewrite,[status(thm)],[])). tff(13,plain, (?[X: $i] : ((~room(X)) & (~tall(X)))), inference(and_elim,[status(thm)],[8])). tff(14,plain, (?[X: $i] : ((~room(X)) & (~tall(X)))), inference(modus_ponens,[status(thm)],[13, 12])). tff(15,plain,( (~room(X!0)) & (~tall(X!0))), inference(skolemize,[status(sab)],[14])). tff(16,plain, (~room(X!0)), inference(and_elim,[status(thm)],[15])). tff(17,plain, ($false), inference(unit_resolution,[status(thm)],[16, 11])). tff(18,plain,(~(X!0 = mary)), inference(lemma,lemma(discharge,[]))). tff(19,assumption,(~tall(mary)), introduced(assumption)). tff(20,plain, (^[X: $i, Y: $i] : refl(((X = Y) | tall(Y) | tall(X)) <=> ((X = Y) | tall(Y) | tall(X)))), inference(bind,[status(th)],[])). tff(21,plain, (![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X)) <=> ![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))), inference(quant_intro,[status(thm)],[20])). tff(22,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tall(X)) & (~tall(Y))) <=> (~(tall(Y) | tall(X)))), ((~((~tall(X)) & (~tall(Y)))) <=> (~(~(tall(Y) | tall(X)))))), rewrite((~(~(tall(Y) | tall(X)))) <=> (tall(Y) | tall(X))), ((~((~tall(X)) & (~tall(Y)))) <=> (tall(Y) | tall(X)))), (((~((~tall(X)) & (~tall(Y)))) | (X = Y)) <=> ((tall(Y) | tall(X)) | (X = Y)))), rewrite(((tall(Y) | tall(X)) | (X = Y)) <=> ((X = Y) | tall(Y) | tall(X))), (((~((~tall(X)) & (~tall(Y)))) | (X = Y)) <=> ((X = Y) | tall(Y) | tall(X))))), inference(bind,[status(th)],[])). tff(23,plain, (![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))), inference(quant_intro,[status(thm)],[22])). tff(24,plain, (![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y))), inference(rewrite,[status(thm)],[])). tff(25,plain, (![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y))), inference(and_elim,[status(thm)],[8])). tff(26,plain, (![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y))), inference(modus_ponens,[status(thm)],[25, 24])). tff(27,plain,( ![X: $i, Y: $i] : ((~((~tall(X)) & (~tall(Y)))) | (X = Y))), inference(skolemize,[status(sab)],[26])). tff(28,plain, (![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))), inference(modus_ponens,[status(thm)],[27, 23])). tff(29,plain, (![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))), inference(modus_ponens,[status(thm)],[28, 21])). tff(30,plain, (~tall(X!0)), inference(and_elim,[status(thm)],[15])). tff(31,plain, (((~![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))) | (tall(mary) | tall(X!0) | (X!0 = mary))) <=> ((~![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))) | tall(mary) | tall(X!0) | (X!0 = mary))), inference(rewrite,[status(thm)],[])). tff(32,plain, (((X!0 = mary) | tall(mary) | tall(X!0)) <=> (tall(mary) | tall(X!0) | (X!0 = mary))), inference(rewrite,[status(thm)],[])). tff(33,plain, (((~![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))) | ((X!0 = mary) | tall(mary) | tall(X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))) | (tall(mary) | tall(X!0) | (X!0 = mary)))), inference(monotonicity,[status(thm)],[32])). tff(34,plain, (((~![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))) | ((X!0 = mary) | tall(mary) | tall(X!0))) <=> ((~![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))) | tall(mary) | tall(X!0) | (X!0 = mary))), inference(transitivity,[status(thm)],[33, 31])). tff(35,plain, ((~![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))) | ((X!0 = mary) | tall(mary) | tall(X!0))), inference(quant_inst,[status(thm)],[])). tff(36,plain, ((~![X: $i, Y: $i] : ((X = Y) | tall(Y) | tall(X))) | tall(mary) | tall(X!0) | (X!0 = mary)), inference(modus_ponens,[status(thm)],[35, 34])). tff(37,plain, ($false), inference(unit_resolution,[status(thm)],[36, 30, 29, 19, 18])). tff(38,plain,(tall(mary)), inference(lemma,lemma(discharge,[]))). tff(39,plain, (quiet(paul) <=> quiet(paul)), inference(rewrite,[status(thm)],[])). tff(40,plain, (quiet(paul)), inference(and_elim,[status(thm)],[8])). tff(41,plain, (quiet(paul)), inference(modus_ponens,[status(thm)],[40, 39])). tff(42,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(43,plain, (room(alice)), inference(and_elim,[status(thm)],[8])). tff(44,plain, (room(alice)), inference(modus_ponens,[status(thm)],[43, 42])). tff(45,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(46,plain, (room(fred)), inference(and_elim,[status(thm)],[8])). tff(47,plain, (room(fred)), inference(modus_ponens,[status(thm)],[46, 45])). tff(48,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(49,plain, (room(paul)), inference(and_elim,[status(thm)],[8])). tff(50,plain, (room(paul)), inference(modus_ponens,[status(thm)],[49, 48])). tff(51,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~tall(mary)) | (~quiet(paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~tall(mary)) | (~quiet(paul)))), inference(rewrite,[status(thm)],[])). tff(52,plain, ((~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))), inference(rewrite,[status(thm)],[])). tff(53,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~tall(mary)) | (~quiet(paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~tall(mary)) | (~quiet(paul)))), inference(monotonicity,[status(thm)],[52])). tff(54,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~tall(mary)) | (~quiet(paul))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~tall(mary)) | (~quiet(paul)))), inference(transitivity,[status(thm)],[53, 51])). tff(55,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul)) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul))), inference(rewrite,[status(thm)],[])). tff(56,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul)))), inference(monotonicity,[status(thm)],[55])). tff(57,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul)))), inference(rewrite,[status(thm)],[])). tff(58,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul))), inference(or_elim,[status(thm)],[7])). tff(59,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul))), inference(modus_ponens,[status(thm)],[58, 56])). tff(60,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul))), inference(modus_ponens,[status(thm)],[59, 57])). tff(61,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & tall(mary) & quiet(paul))), inference(modus_ponens,[status(thm)],[60, 56])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!1 |'alice'|) (= X!1 |'fred'|) (= X!1 |'paul'|) (= X!1 |'mary'|) (not (room X!1))))) (a!7 (refl (~ (not (tall mary)) (not (tall mary))))) (a!8 (refl (~ (not (quiet paul)) (not (quiet paul)))))) (let ((a!9 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 (tall mary) (quiet paul))) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (not (tall mary)) (not (quiet paul)))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!7 a!8 a!9)))

room(dawn)&room(matthew)&room(bobby)&room(jimmy)&(![X]:(room(X)=>(X='dawn'|X='matthew'|X='bobby'|X='jimmy')))& ((taller(dawn,katie))& (like(katie,dawn))& ((happy(bobby))&(quiet(matthew)))& (((?[X]:(~room(X)&~tall(X)))&(![X,Y]:((~tall(X)&~tall(Y))=>(X=Y)))))& ((like(katie,matthew) & like(matthew,katie))))

room(dawn)&room(matthew)&room(bobby)&room(jimmy)&(![X]:(room(X)=>(X='dawn'|X='matthew'|X='bobby'|X='jimmy')))& ((tall(dawn))&(quiet(matthew)))

contradiction

entailment

contradiction

Rachel, Sadie are the only persons in the room. Rachel who does not like Norman, is not Sadie. Rachel and Sadie are respectively creative and quiet. Rachel and Sadie are respectively creative and rich. Rachel is liked by Robert. More than one person in the room does not collect luxury watches. Rachel is not a creative quiet tourist and is liked by Robert.

Rachel collects luxury watches or is a quiet creative tourist or both.

contradiction

-

room(rachel)&room(sadie)&(![X]:(room(X)=>(X='rachel'|X='sadie')))& (((~like(norman,rachel))&(rachel!=sadie))& ((creative(rachel))&(quiet(sadie)))& ((creative(rachel))&(rich(sadie)))& (like(rachel,robert))& ((?[X,Y]:(room(X)&room(Y)&(does_not_collect_luxury_watches(X)&does_not_collect_luxury_watches(Y))&(X!=Y))))& ((~(creative(rachel)&quiet(rachel)&tourist(rachel)))&(like(rachel,robert))))

room(rachel)&room(sadie)&(![X]:(room(X)=>(X='rachel'|X='sadie')))& (((collects_luxury_watches(rachel))|(quiet(rachel)&creative(rachel)&tourist(rachel))))

contradiction

entailment

neutral

Nicole, Bill are the only persons in the room. Someone who is a quiet tourist hate someone who is not a creative tourist.

Nicole is not a creative tourist or is a creative tourist or both.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_2_type, type, ( tptp_fun_X_2: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(paul_type, type, ( paul: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(tourist_type, type, ( tourist: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(1,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : (((quiet(X) & tourist(X)) & (~(creative(Y) & tourist(Y)))) & hate(X, Y))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~(creative(mary) & tourist(mary))) | (creative(mary) & tourist(mary)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (quiet(X) & tourist(X) & (~(creative(Y) & tourist(Y))) & hate(X, Y)))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ?[X: $i, Y: $i] : (((quiet(X) & tourist(X)) & (~(creative(Y) & tourist(Y)))) & hate(X, Y))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((~(creative(mary) & tourist(mary))) | (creative(mary) & tourist(mary)))))), file('/mnt/tmpfs//7250763912294257845171490.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (quiet(X) & tourist(X) & (~(creative(Y) & tourist(Y))) & hate(X, Y)))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i, Y: $i] : (quiet(X) & tourist(X) & (~(creative(Y) & tourist(Y))) & hate(X, Y))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (room(paul)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(9,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(10,plain, (room(mary)), inference(modus_ponens,[status(thm)],[9, 8])). tff(11,plain, ((~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))), inference(rewrite,[status(thm)],[])). tff(12,plain, (((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))))), inference(monotonicity,[status(thm)],[11])). tff(13,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(rewrite,[status(thm)],[])). tff(14,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(monotonicity,[status(thm)],[13])). tff(15,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(rewrite,[status(thm)],[])). tff(16,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(or_elim,[status(thm)],[4])). tff(17,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[16, 14])). tff(18,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[17, 15])). tff(19,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[18, 14])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!4 (not (or (= X!2 |'paul'|) (= X!2 |'mary'|) (not (room X!2)))))) (let ((a!5 (~ (not (and (room mary) (room paul) a!3)) (or (not (room mary)) (not (room paul)) a!4)))) (nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) a!5)))

room(nicole)&room(bill)&(![X]:(room(X)=>(X='nicole'|X='bill')))& (?[X,Y]:((quiet(X)&tourist(X))&(~(creative(Y)&tourist(Y)))&(hate(X,Y))))

room(nicole)&room(bill)&(![X]:(room(X)=>(X='nicole'|X='bill')))& (((~(creative(nicole)&tourist(nicole)))|(creative(nicole)&tourist(nicole))))

neutral

neutral

neutral

Stephen is the only person in the room. Someone who is not tall is taller than someone who is not a happy rich tall european. Someone outside the room is richer than Debra. Stephen is the tallest in the room. Everyone in the room is not rich.

Stephen neither is a tea enthusiast nor is not a rich happy tall european.

contradiction

-

room(stephen)&(![X]:(room(X)=>(X='stephen')))& ((?[X,Y]:((~tall(X))&(~(happy(Y)&rich(Y)&tall(Y)&european(Y)))&(taller(X,Y))))& (?[X]:(~room(X)=>(richer(debra,X))))& (![X]:(taller(X,stephen)))& (![X]:(room(X)=>(~rich(X)))))

room(stephen)&(![X]:(room(X)=>(X='stephen')))& (~((is_a_tea_enthusiast(stephen))|(~(rich(stephen)&happy(stephen)&tall(stephen)&european(stephen)))))

neutral

neutral

contradiction

Eddie is the only person in the room. At most one of the following is true:. -No one outside the room who is not hated by Henrietta is not a creative rich person. -Only one person outside the room hates Daphne.

It is not the case that 'Eddie who is richer than Daphne, is not a happy creative person'.

neutral

% SZS status Satisfiable

room(eddie)&(![X]:(room(X)=>(X='eddie')))& (~(~?[X]:(~room(X)=>(((~hate(X,henrietta))=>(~(creative(X)&rich(X)&person(X))))))&((?[X]:(~room(X)&hate(daphne,X)))&(![X,Y]:((hate(daphne,X)&hate(daphne,Y))=>(X=Y))))))

room(eddie)&(![X]:(room(X)=>(X='eddie')))& (~((richer(daphne,eddie))&(~(happy(eddie)&creative(eddie)&person(eddie)))))

entailment

entailment

neutral

Michael is the only person in the room. Someone who is not a creative happy rich tourist is richer than someone who is not creative. Jon is richer than Michael. Everyone in the room is not a creative rich happy tourist.

It is not the case that 'Michael who is richer than Laura, is not a happy creative person'.

neutral

% SZS status Satisfiable

room(michael)&(![X]:(room(X)=>(X='michael')))& ((?[X,Y]:((~(creative(X)&happy(X)&rich(X)&tourist(X)))&(~creative(Y))&(richer(X,Y))))& (richer(michael,jon))& (![X]:(room(X)=>(~(creative(X)&rich(X)&happy(X)&tourist(X))))))

room(michael)&(![X]:(room(X)=>(X='michael')))& (~((richer(laura,michael))&(~(happy(michael)&creative(michael)&person(michael)))))

entailment

entailment

contradiction

Lonnie, Shirley, Jarrod are the only persons in the room. “No one in the room does not hate Wendy” if “Jarrod and Lonnie are brave quiet person” and vice versa. If “everyone outside the room who is not hated by Louis is hated by Wendy” then “someone who is not a quiet person hate someone who does not hate Louis” otherwise “Shirley who is a quiet rich person, is not a rich brave quiet person”. “Shirley and Lonnie are respectively rich and quiet” unless “only one person in the room is not Jarrod”. Shirley neither does not hate Louis nor is a rich quiet person. Shirley is the least rich in the room. Lonnie is hated by Wendy or is a brave rich quiet person or both. Jarrod and Shirley are respectively brave and rich. More than one person outside the room hates Louis.

Someone who is a rich brave person hate someone who is not rich.

contradiction

-

room(lonnie)&room(shirley)&room(jarrod)&(![X]:(room(X)=>(X='lonnie'|X='shirley'|X='jarrod')))& (((brave(jarrod)&quiet(jarrod)&person(jarrod)&brave(lonnie)&quiet(lonnie)&person(lonnie))<=>(~?[X]:(room(X)=>(~hate(wendy,X)))))& (((![X]:(~room(X)=>(((~hate(X,louis))=>(hate(X,wendy))))))=>(?[X,Y]:((~(quiet(X)&person(X)))&(~hate(louis,Y))&(hate(X,Y)))))|((~(![X]:(~room(X)=>(((~hate(X,louis))=>(hate(X,wendy)))))))=>((quiet(shirley)&rich(shirley)&person(shirley))&(~(rich(shirley)&brave(shirley)&quiet(shirley)&person(shirley))))))& (~(((?[X]:(room(X)&X!=jarrod))&(![X,Y]:((X!=jarrod&Y!=jarrod)=>(X=Y)))))=>((rich(shirley))&(quiet(lonnie))))& (~((~hate(louis,shirley))|(rich(shirley)&quiet(shirley)&person(shirley))))& (![X]:(richer(shirley,X)))& (((hate(lonnie,wendy))|(brave(lonnie)&rich(lonnie)&quiet(lonnie)&person(lonnie))))& ((brave(jarrod))&(rich(shirley)))& ((?[X,Y]:(~room(X)&~room(Y)&(hate(louis,X)&hate(louis,Y))&(X!=Y)))))

room(lonnie)&room(shirley)&room(jarrod)&(![X]:(room(X)=>(X='lonnie'|X='shirley'|X='jarrod')))& (?[X,Y]:((rich(X)&brave(X)&person(X))&(~rich(Y))&(hate(X,Y))))

entailment

neutral

neutral

Geneva, Morgan, Faye, Thomasine are the only persons in the room. If "Geneva who is a brave creative person, can play the harmonica" then "Morgan who likes Elizabeth, does not can play the harmonica" otherwise "Geneva is not rich". Morgan who is not a brave rich person, is not brave. Everyone outside the room is not brave. Only one person outside the room likes Larry. Morgan is not a creative rich person or is not Geneva or both.

Thomasine likes Elizabeth and is a brave person.

neutral

% SZS status Satisfiable

room(geneva)&room(morgan)&room(faye)&room(thomasine)&(![X]:(room(X)=>(X='geneva'|X='morgan'|X='faye'|X='thomasine')))& (((((brave(geneva)&creative(geneva)&person(geneva))&(can_play_the_harmonica(geneva)))=>((like(elizabeth,morgan))&(does_not_can_play_the_harmonica(morgan))))|((~((brave(geneva)&creative(geneva)&person(geneva))&(can_play_the_harmonica(geneva))))=>(~rich(geneva))))& ((~(brave(morgan)&rich(morgan)&person(morgan)))&(~brave(morgan)))& (![X]:(~room(X)=>(~brave(X))))& (((?[X]:(~room(X)&like(larry,X)))&(![X,Y]:((like(larry,X)&like(larry,Y))=>(X=Y)))))& (((~(creative(morgan)&rich(morgan)&person(morgan)))|(morgan!=geneva))))

room(geneva)&room(morgan)&room(faye)&room(thomasine)&(![X]:(room(X)=>(X='geneva'|X='morgan'|X='faye'|X='thomasine')))& ((like(elizabeth,thomasine))&(brave(thomasine)&person(thomasine)))

neutral

contradiction

contradiction

Wayne, Jason, Joe, Valarie are the only persons in the room. More than one person outside the room is not hated by Laurie. Jason is the least rich in the room. Only one person outside the room is not a rich person. Everyone in the room is not hated by Laurie.

Wayne is hated by Laurie or is not rich or both.

contradiction

-

room(wayne)&room(jason)&room(joe)&room(valarie)&(![X]:(room(X)=>(X='wayne'|X='jason'|X='joe'|X='valarie')))& (((?[X,Y]:(~room(X)&~room(Y)&(~hate(X,laurie)&~hate(Y,laurie))&(X!=Y))))& (![X]:(richer(jason,X)))& (((?[X]:(~room(X)&~(rich(X)&person(X))))&(![X,Y]:((~(rich(X)&person(X))&~(rich(Y)&person(Y)))=>(X=Y)))))& (![X]:(room(X)=>(~hate(X,laurie)))))

room(wayne)&room(jason)&room(joe)&room(valarie)&(![X]:(room(X)=>(X='wayne'|X='jason'|X='joe'|X='valarie')))& (((hate(wayne,laurie))|(~rich(wayne))))

contradiction

entailment

entailment

Michael, Matthew, Jerry, Tami are the only persons in the room. “Matthew and Joseph hate each other” unless “only one person outside the room is quieter than Joseph”. Matthew neither is quieter than Joseph nor is not hated by Joseph. Michael and Matthew are respectively rich and quiet. Joseph is quieter than Matthew. Michael is not quiet. More than one person outside the room is not rich, not quiet. More than one person outside the room is not Michael.

Michael and Matthew are respectively quiet and rich.

contradiction

-

room(michael)&room(matthew)&room(jerry)&room(tami)&(![X]:(room(X)=>(X='michael'|X='matthew'|X='jerry'|X='tami')))& ((~(((?[X]:(~room(X)&quieter(joseph,X)))&(![X,Y]:((quieter(joseph,X)&quieter(joseph,Y))=>(X=Y)))))=>((hate(matthew,joseph) & hate(joseph,matthew))))& (~((quieter(joseph,matthew))|(~hate(matthew,joseph))))& ((rich(michael))&(quiet(matthew)))& (quieter(matthew,joseph))& (~quiet(michael))& ((?[X,Y]:(~room(X)&~room(Y)&(~rich(X)&~quiet(X)&~rich(Y)&~quiet(Y))&(X!=Y))))& ((?[X,Y]:(~room(X)&~room(Y)&(X!=michael&Y!=michael)&(X!=Y)))))

room(michael)&room(matthew)&room(jerry)&room(tami)&(![X]:(room(X)=>(X='michael'|X='matthew'|X='jerry'|X='tami')))& ((quiet(michael))&(rich(matthew)))

entailment

entailment

contradiction

Jeffery, Daniel are the only persons in the room. Daniel does not like Gertrude and does not have a piercing. Jeffery is not rich. Someone in the room is not Jeffery. Margaret and Gertrude like each other. Daniel and Jeffery are respectively happy and quiet. Jeffery who does not like Lindsay, is quieter than Gertrude.

Daniel who is not happy, not quiet, not tall, not rich, plays a string instrument.

contradiction

-

room(jeffery)&room(daniel)&(![X]:(room(X)=>(X='jeffery'|X='daniel')))& (((~like(gertrude,daniel))&(does_not_have_a_piercing(daniel)))& (~rich(jeffery))& (?[X]:(room(X)=>(X!=jeffery)))& ((like(margaret,gertrude) & like(gertrude,margaret)))& ((happy(daniel))&(quiet(jeffery)))& ((~like(lindsay,jeffery))&(quieter(gertrude,jeffery))))

room(jeffery)&room(daniel)&(![X]:(room(X)=>(X='jeffery'|X='daniel')))& ((~happy(daniel)&~quiet(daniel)&~tall(daniel)&~rich(daniel))&(plays_a_string_instrument(daniel)))

neutral

neutral

contradiction

Christine, Margaret are the only persons in the room. Margaret is not Christine. Margaret and Randall like each other. Only one person outside the room is not liked by Paul. Margaret does not practice pilates. Margaret is liked by Paul and likes Randall.

Margaret does not like Randall or does not like Larry or both.

neutral

% SZS status Satisfiable

room(christine)&room(margaret)&(![X]:(room(X)=>(X='christine'|X='margaret')))& ((margaret!=christine)& ((like(margaret,randall) & like(randall,margaret)))& (((?[X]:(~room(X)&~like(X,paul)))&(![X,Y]:((~like(X,paul)&~like(Y,paul))=>(X=Y)))))& (does_not_practice_pilates(margaret))& ((like(margaret,paul))&(like(randall,margaret))))

room(christine)&room(margaret)&(![X]:(room(X)=>(X='christine'|X='margaret')))& (((~like(randall,margaret))|(~like(larry,margaret))))

contradiction

entailment

contradiction

Raul, Robert, Frederick are the only persons in the room. If 'Frederick does not hate Kim' then 'Frederick and Robert hate each other'. 'Raul either is a client of Justin or does not hate Kim' if 'Robert is the tallest in the room'. If 'only one person outside the room is not a brave tourist' then 'Raul is not a quiet tourist'. Only one person outside the room is not a brave tourist. Justin is taller than Robert. Robert and Frederick hate each other. It is not the case that 'Kim is a client of Raul'. More than one person outside the room is a client of Justin. Raul is not hated by Justin. It is not the case that 'Frederick does not hate Justin'.

It is not the case that 'it is not the case that 'Frederick who is not a quiet tourist, does not hate Justin''.

contradiction

-

room(raul)&room(robert)&room(frederickerick)&(![X]:(room(X)=>(X='raul'|X='robert'|X='frederickerick')))& (((~hate(kim,frederickerick))=>((hate(frederickerick,robert) & hate(robert,frederickerick))))& ((![X]:(taller(X,robert)))=>((((client(justin,raul))|(~hate(kim,raul)))&(~((client(justin,raul))|(~hate(kim,raul)))))))& ((((?[X]:(~room(X)&~(brave(X)&tourist(X))))&(![X,Y]:((~(brave(X)&tourist(X))&~(brave(Y)&tourist(Y)))=>(X=Y)))))=>(~(quiet(raul)&tourist(raul))))& (((?[X]:(~room(X)&~(brave(X)&tourist(X))))&(![X,Y]:((~(brave(X)&tourist(X))&~(brave(Y)&tourist(Y)))=>(X=Y)))))& (taller(robert,justin))& ((hate(robert,frederickerick) & hate(frederickerick,robert)))& (~(client(raul,kim)))& ((?[X,Y]:(~room(X)&~room(Y)&(client(justin,X)&client(justin,Y))&(X!=Y))))& (~hate(raul,justin))& (~(~hate(justin,frederickerick))))

room(raul)&room(robert)&room(frederickerick)&(![X]:(room(X)=>(X='raul'|X='robert'|X='frederickerick')))& (~(~((~(quiet(frederickerick)&tourist(frederickerick)))&(~hate(justin,frederickerick)))))

neutral

entailment

entailment

Kiana is the only person in the room. Kiana is the least quiet in the room. Jamie is quieter than Kiana.

Kiana neither is quieter than Kay nor is quieter than Jamie.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $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(susan_type, type, ( susan: $i)). tff(john_type, type, ( john: $i)). tff(alice_type, type, ( alice: $i)). tff(paul_type, type, ( paul: $i)). tff(lucy_type, type, ( lucy: $i)). tff(tptp_fun_X_0_type, type, ( tptp_fun_X_0: $i)). 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, ((~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (![X: $i] : quieter(mary, X) & quieter(mary, susan))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (~(quieter(fred, mary) | quieter(susan, mary)))))) <=> (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ![X: $i] : quieter(mary, X) & quieter(mary, susan))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary))))))), inference(rewrite,[status(thm)],[])). tff(5,axiom,(~(((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (![X: $i] : quieter(mary, X) & quieter(mary, susan))) => ((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & (~(quieter(fred, mary) | quieter(susan, mary)))))), file('/mnt/tmpfs//4994928091810481580897227.p','negated')). tff(6,plain, (~((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ![X: $i] : quieter(mary, X) & quieter(mary, susan))) | (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary)))))), inference(modus_ponens,[status(thm)],[5, 4])). tff(7,plain, (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & ![X: $i] : quieter(mary, X) & quieter(mary, susan)), inference(or_elim,[status(thm)],[6])). tff(8,plain, (![X: $i] : ((~room(X)) | (X = |'mary'|))), inference(and_elim,[status(thm)],[7])). 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)],[7])). 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, (quieter(mary, fred) <=> quieter(|'mary'|, fred)), inference(monotonicity,[status(thm)],[18])). tff(20,plain, (quieter(|'mary'|, fred) <=> quieter(mary, fred)), inference(symmetry,[status(thm)],[19])). tff(21,plain, ((~quieter(|'mary'|, fred)) <=> (~quieter(mary, fred))), inference(monotonicity,[status(thm)],[20])). tff(22,plain, (|'mary'| = mary), inference(symmetry,[status(thm)],[18])). tff(23,plain, (quieter(fred, |'mary'|) <=> quieter(fred, mary)), inference(monotonicity,[status(thm)],[22])). tff(24,plain, (quieter(fred, mary) <=> quieter(fred, |'mary'|)), inference(symmetry,[status(thm)],[23])). tff(25,plain, (quieter(susan, |'mary'|) <=> quieter(susan, mary)), inference(monotonicity,[status(thm)],[22])). tff(26,plain, ((~quieter(susan, |'mary'|)) <=> (~quieter(susan, mary))), inference(monotonicity,[status(thm)],[25])). tff(27,plain, (quieter(|'mary'|, susan) <=> quieter(mary, susan)), inference(monotonicity,[status(thm)],[22])). tff(28,plain, (quieter(mary, susan) <=> quieter(|'mary'|, susan)), inference(symmetry,[status(thm)],[27])). tff(29,plain, (quieter(mary, susan) <=> quieter(mary, susan)), inference(rewrite,[status(thm)],[])). tff(30,plain, (quieter(mary, susan)), inference(and_elim,[status(thm)],[7])). tff(31,plain, (quieter(mary, susan)), inference(modus_ponens,[status(thm)],[30, 29])). tff(32,plain, (quieter(|'mary'|, susan)), inference(modus_ponens,[status(thm)],[31, 28])). tff(33,plain, ((|'mary'| = susan) <=> (mary = susan)), inference(monotonicity,[status(thm)],[22])). tff(34,plain, ((mary = susan) <=> (|'mary'| = susan)), inference(symmetry,[status(thm)],[33])). tff(35,plain, ((~(mary = susan)) <=> (~(|'mary'| = susan))), inference(monotonicity,[status(thm)],[34])). tff(36,plain, ((~(mary = susan)) <=> (~(mary = susan))), inference(rewrite,[status(thm)],[])). tff(37,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//4994928091810481580897227.p','b14')). 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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[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))) & (~(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)],[44])). tff(46,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)],[45])). tff(47,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)],[46])). tff(48,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)],[47])). tff(49,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)],[48])). tff(50,plain, (((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(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)],[49])). tff(51,plain, ((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(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)],[50])). tff(52,plain, (((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(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)],[51])). tff(53,plain, ((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(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)],[52])). tff(54,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)],[53])). tff(55,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)],[54])). tff(56,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)],[55])). tff(57,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)],[56])). tff(58,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)],[57])). tff(59,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)],[58])). tff(60,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)],[59])). tff(61,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)],[60])). tff(62,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)],[61])). tff(63,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)],[62])). tff(64,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)],[63])). tff(65,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)],[64])). tff(66,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)],[65])). tff(67,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)],[66])). tff(68,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)],[67])). tff(69,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)],[68])). tff(70,plain, (((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))), inference(and_elim,[status(thm)],[69])). tff(71,plain, ((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))), inference(and_elim,[status(thm)],[70])). tff(72,plain, (((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))), inference(and_elim,[status(thm)],[71])). tff(73,plain, ((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))), inference(and_elim,[status(thm)],[72])). tff(74,plain, (((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))), inference(and_elim,[status(thm)],[73])). tff(75,plain, (~(mary = susan)), inference(and_elim,[status(thm)],[74])). tff(76,plain, (~(mary = susan)), inference(modus_ponens,[status(thm)],[75, 36])). tff(77,plain, (~(|'mary'| = susan)), inference(modus_ponens,[status(thm)],[76, 35])). tff(78,plain, (![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))), inference(rewrite,[status(thm)],[])). tff(79,plain, (![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))), inference(rewrite,[status(thm)],[])). tff(80,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite((quieter(X, Y) => (~quieter(Y, X))) <=> ((~quieter(Y, X)) | (~quieter(X, Y)))), (((~(X = Y)) => (quieter(X, Y) => (~quieter(Y, X)))) <=> ((~(X = Y)) => ((~quieter(Y, X)) | (~quieter(X, Y)))))), rewrite(((~(X = Y)) => ((~quieter(Y, X)) | (~quieter(X, Y)))) <=> ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))), (((~(X = Y)) => (quieter(X, Y) => (~quieter(Y, X)))) <=> ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))))), inference(bind,[status(th)],[])). tff(81,plain, (![X: $i, Y: $i] : ((~(X = Y)) => (quieter(X, Y) => (~quieter(Y, X)))) <=> ![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))), inference(quant_intro,[status(thm)],[80])). tff(82,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (quieter(X, Y) => (~quieter(Y, X))))), file('/mnt/tmpfs//4994928091810481580897227.p','b13')). tff(83,plain, (![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))), inference(modus_ponens,[status(thm)],[82, 81])). tff(84,plain, (![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))), inference(modus_ponens,[status(thm)],[83, 79])). tff(85,plain,( ![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))), inference(skolemize,[status(sab)],[84])). tff(86,plain, (![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))), inference(modus_ponens,[status(thm)],[85, 78])). tff(87,plain, (((~![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))) | ((~quieter(susan, |'mary'|)) | (|'mary'| = susan) | (~quieter(|'mary'|, susan)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))) | (~quieter(susan, |'mary'|)) | (|'mary'| = susan) | (~quieter(|'mary'|, susan)))), inference(rewrite,[status(thm)],[])). tff(88,plain, (((|'mary'| = susan) | (~quieter(susan, |'mary'|)) | (~quieter(|'mary'|, susan))) <=> ((~quieter(susan, |'mary'|)) | (|'mary'| = susan) | (~quieter(|'mary'|, susan)))), inference(rewrite,[status(thm)],[])). tff(89,plain, (((~![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))) | ((|'mary'| = susan) | (~quieter(susan, |'mary'|)) | (~quieter(|'mary'|, susan)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))) | ((~quieter(susan, |'mary'|)) | (|'mary'| = susan) | (~quieter(|'mary'|, susan))))), inference(monotonicity,[status(thm)],[88])). tff(90,plain, (((~![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))) | ((|'mary'| = susan) | (~quieter(susan, |'mary'|)) | (~quieter(|'mary'|, susan)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))) | (~quieter(susan, |'mary'|)) | (|'mary'| = susan) | (~quieter(|'mary'|, susan)))), inference(transitivity,[status(thm)],[89, 87])). tff(91,plain, ((~![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))) | ((|'mary'| = susan) | (~quieter(susan, |'mary'|)) | (~quieter(|'mary'|, susan)))), inference(quant_inst,[status(thm)],[])). tff(92,plain, ((~![X: $i, Y: $i] : ((X = Y) | (~quieter(Y, X)) | (~quieter(X, Y)))) | (~quieter(susan, |'mary'|)) | (|'mary'| = susan) | (~quieter(|'mary'|, susan))), inference(modus_ponens,[status(thm)],[91, 90])). tff(93,plain, ((~quieter(susan, |'mary'|)) | (|'mary'| = susan) | (~quieter(|'mary'|, susan))), inference(unit_resolution,[status(thm)],[92, 86])). tff(94,plain, (~quieter(susan, |'mary'|)), inference(unit_resolution,[status(thm)],[93, 77, 32])). tff(95,plain, (~quieter(susan, mary)), inference(modus_ponens,[status(thm)],[94, 26])). tff(96,assumption,(~((~room(X!0)) | (X!0 = |'mary'|))), introduced(assumption)). tff(97,plain, (((~room(X!0)) | (X!0 = |'mary'|)) | (~(X!0 = |'mary'|))), inference(tautology,[status(thm)],[])). tff(98,plain, (~(X!0 = |'mary'|)), inference(unit_resolution,[status(thm)],[97, 96])). tff(99,plain, (((~room(X!0)) | (X!0 = |'mary'|)) | room(X!0)), inference(tautology,[status(thm)],[])). tff(100,plain, (room(X!0)), inference(unit_resolution,[status(thm)],[99, 96])). tff(101,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(102,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | ((~room(X!0)) | (X!0 = |'mary'|))), inference(quant_inst,[status(thm)],[])). tff(103,plain, ((~![X: $i] : ((~room(X)) | (X = |'mary'|))) | (~room(X!0)) | (X!0 = |'mary'|)), inference(modus_ponens,[status(thm)],[102, 101])). tff(104,plain, ($false), inference(unit_resolution,[status(thm)],[103, 11, 100, 98])). tff(105,plain,((~room(X!0)) | (X!0 = |'mary'|)), inference(lemma,lemma(discharge,[]))). tff(106,plain, (((~room(mary)) | (~((~room(X!0)) | (X!0 = |'mary'|))) | (quieter(fred, mary) | quieter(susan, mary))) <=> (quieter(fred, mary) | quieter(susan, mary) | (~room(mary)) | (~((~room(X!0)) | (X!0 = |'mary'|))))), inference(rewrite,[status(thm)],[])). tff(107,plain, ((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary)))) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary))))), inference(rewrite,[status(thm)],[])). tff(108,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary)))))), inference(monotonicity,[status(thm)],[107])). tff(109,plain, ((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary))))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary)))))), inference(rewrite,[status(thm)],[])). tff(110,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary))))), inference(or_elim,[status(thm)],[6])). tff(111,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary))))), inference(modus_ponens,[status(thm)],[110, 108])). tff(112,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary))))), inference(modus_ponens,[status(thm)],[111, 109])). tff(113,plain, (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & (~(quieter(fred, mary) | quieter(susan, mary))))), inference(modus_ponens,[status(thm)],[112, 108])). 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!0)) (= X!0 |'mary'|)))) (a!4 (refl (~ (or (quieter fred mary) (quieter susan mary)) (or (quieter fred mary) (quieter susan mary)))))) (let ((a!5 (and (room mary) a!2 (not (or (quieter fred mary) (quieter susan mary)))))) (let ((a!6 (~ (not a!5) (or (not (room mary)) a!3 (or (quieter fred mary) (quieter susan mary)))))) (nnf-neg a!1 (sk (~ (not a!2) a!3)) a!4 a!6))))

room(kiana)&(![X]:(room(X)=>(X='kiana')))& ((![X]:(quieter(kiana,X)))& (quieter(kiana,jamie)))

room(kiana)&(![X]:(room(X)=>(X='kiana')))& (~((quieter(kay,kiana))|(quieter(jamie,kiana))))

neutral

contradiction

entailment

Kandice, Sergio are the only persons in the room. If no one outside the room is not Sergio then Kandice is not quiet otherwise Kandice is not a quiet european or is not creative or both. Sergio is the least rich in the room only if Sergio is a rich european and is not creative. Kandice is the least rich in the room if only one person outside the room is not hated by Anthony and vice versa. Kandice is a rich quiet creative european if it is not the case that 'Sergio does not hate Walter' and vice versa. It is not the case that 'Sergio is not hated by Walter'. Kandice is right-handed or is hated by Anthony or both. Kandice is the least quiet in the room. It is not the case that 'only one person outside the room does not collect vintage stamps'. Kandice who is not right-handed, is not a creative european. Sergio neither hates Walter nor is not right-handed. Someone outside the room who is not quiet collects vintage stamps. It is not the case that 'Kandice is the least rich in the room'.

Sergio is hated by Walter or is not rich, not creative, not quiet, not happy or both.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_8_type, type, ( tptp_fun_X_8: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(happy_type, type, ( happy: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(quiet_type, type, ( quiet: $i > $o)). tff(creative_type, type, ( creative: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(richer_type, type, ( richer: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(preda_type, type, ( preda: $i > $o)). tff(predc_type, type, ( predc: $i > $o)). tff(european_type, type, ( european: $i > $o)). tff(quieter_type, type, ( quieter: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $i)). tff(1,plain, (hate(paul, fred) <=> hate(paul, fred)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((((((((((~?[X: $i] : ((~room(X)) => (~(X = paul)))) => (~quiet(mary))) | ((~(~?[X: $i] : ((~room(X)) => (~(X = paul))))) => ((~(quiet(mary) & european(mary))) | (~creative(mary))))) & (![X: $i] : richer(paul, X) => ((rich(paul) & european(paul)) & (~creative(paul))))) & ((?[X: $i] : ((~room(X)) & (~hate(X, alice))) & ![X: $i, Y: $i] : (((~hate(X, alice)) & (~hate(Y, alice))) => (X = Y))) <=> ![X: $i] : richer(mary, X))) & ((~(~hate(fred, paul))) <=> (((rich(mary) & quiet(mary)) & creative(mary)) & european(mary)))) & (~(~hate(paul, fred)))) & (predc(mary) | hate(mary, alice))) & ![X: $i] : quieter(mary, X)) & (~(?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))))) & ((~predc(mary)) & (~(creative(mary) & european(mary))))) & (~(hate(fred, paul) | (~predc(paul))))) & ?[X: $i] : ((~room(X)) => ((~quiet(X)) => preda(X)))) & (~![X: $i] : richer(mary, X)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (hate(paul, fred) | ((((~rich(paul)) & (~creative(paul))) & (~quiet(paul))) & (~happy(paul))))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : richer(paul, X)) | (rich(paul) & european(paul) & (~creative(paul)))) & ((?[X: $i] : ((~room(X)) & (~hate(X, alice))) & ![X: $i, Y: $i] : ((~((~hate(X, alice)) & (~hate(Y, alice)))) | (X = Y))) <=> ![X: $i] : richer(mary, X)) & (hate(fred, paul) <=> (rich(mary) & quiet(mary) & creative(mary) & european(mary))) & hate(paul, fred) & (predc(mary) | hate(mary, alice)) & ![X: $i] : quieter(mary, X) & (~(?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) | (X = Y)))) & (~predc(mary)) & (~(creative(mary) & european(mary))) & (~(hate(fred, paul) | (~predc(paul)))) & ?[X: $i] : (quiet(X) | room(X) | preda(X)) & (~![X: $i] : richer(mary, X)))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul)))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((((((((((((((~?[X: $i] : ((~room(X)) => (~(X = paul)))) => (~quiet(mary))) | ((~(~?[X: $i] : ((~room(X)) => (~(X = paul))))) => ((~(quiet(mary) & european(mary))) | (~creative(mary))))) & (![X: $i] : richer(paul, X) => ((rich(paul) & european(paul)) & (~creative(paul))))) & ((?[X: $i] : ((~room(X)) & (~hate(X, alice))) & ![X: $i, Y: $i] : (((~hate(X, alice)) & (~hate(Y, alice))) => (X = Y))) <=> ![X: $i] : richer(mary, X))) & ((~(~hate(fred, paul))) <=> (((rich(mary) & quiet(mary)) & creative(mary)) & european(mary)))) & (~(~hate(paul, fred)))) & (predc(mary) | hate(mary, alice))) & ![X: $i] : quieter(mary, X)) & (~(?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : (((~preda(X)) & (~preda(Y))) => (X = Y))))) & ((~predc(mary)) & (~(creative(mary) & european(mary))))) & (~(hate(fred, paul) | (~predc(paul))))) & ?[X: $i] : ((~room(X)) => ((~quiet(X)) => preda(X)))) & (~![X: $i] : richer(mary, X)))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (hate(paul, fred) | ((((~rich(paul)) & (~creative(paul))) & (~quiet(paul))) & (~happy(paul))))))), file('/mnt/tmpfs//6069389933582722736377717.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : richer(paul, X)) | (rich(paul) & european(paul) & (~creative(paul)))) & ((?[X: $i] : ((~room(X)) & (~hate(X, alice))) & ![X: $i, Y: $i] : ((~((~hate(X, alice)) & (~hate(Y, alice)))) | (X = Y))) <=> ![X: $i] : richer(mary, X)) & (hate(fred, paul) <=> (rich(mary) & quiet(mary) & creative(mary) & european(mary))) & hate(paul, fred) & (predc(mary) | hate(mary, alice)) & ![X: $i] : quieter(mary, X) & (~(?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) | (X = Y)))) & (~predc(mary)) & (~(creative(mary) & european(mary))) & (~(hate(fred, paul) | (~predc(paul)))) & ?[X: $i] : (quiet(X) | room(X) | preda(X)) & (~![X: $i] : richer(mary, X)))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul))))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~![X: $i] : richer(paul, X)) | (rich(paul) & european(paul) & (~creative(paul)))) & ((?[X: $i] : ((~room(X)) & (~hate(X, alice))) & ![X: $i, Y: $i] : ((~((~hate(X, alice)) & (~hate(Y, alice)))) | (X = Y))) <=> ![X: $i] : richer(mary, X)) & (hate(fred, paul) <=> (rich(mary) & quiet(mary) & creative(mary) & european(mary))) & hate(paul, fred) & (predc(mary) | hate(mary, alice)) & ![X: $i] : quieter(mary, X) & (~(?[X: $i] : ((~room(X)) & (~preda(X))) & ![X: $i, Y: $i] : ((~((~preda(X)) & (~preda(Y)))) | (X = Y)))) & (~predc(mary)) & (~(creative(mary) & european(mary))) & (~(hate(fred, paul) | (~predc(paul)))) & ?[X: $i] : (quiet(X) | room(X) | preda(X)) & (~![X: $i] : richer(mary, X))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (hate(paul, fred)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (hate(paul, fred)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, ((hate(paul, fred) | (~(rich(paul) | creative(paul) | quiet(paul) | happy(paul)))) | (~hate(paul, fred))), inference(tautology,[status(thm)],[])). tff(9,plain, (hate(paul, fred) | (~(rich(paul) | creative(paul) | quiet(paul) | happy(paul)))), inference(unit_resolution,[status(thm)],[8, 7])). tff(10,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(11,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(12,plain, (room(paul)), inference(modus_ponens,[status(thm)],[11, 10])). tff(13,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(14,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(15,plain, (room(mary)), inference(modus_ponens,[status(thm)],[14, 13])). tff(16,plain, (((~room(mary)) | (~room(paul)) | (~((X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (~(hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul)))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (~(hate(paul, fred) | (~(rich(paul) | creative(paul) | quiet(paul) | happy(paul))))))), inference(rewrite,[status(thm)],[])). tff(17,plain, ((~((X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) <=> (~((X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8))))), inference(rewrite,[status(thm)],[])). tff(18,plain, (((~room(mary)) | (~room(paul)) | (~((X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (~(hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul)))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!8 = |'paul'|) | (X!8 = |'mary'|) | (~room(X!8)))) | (~(hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul))))))), inference(monotonicity,[status(thm)],[17])). tff(19,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul))))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul)))))), inference(rewrite,[status(thm)],[])). tff(20,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul))))))), inference(monotonicity,[status(thm)],[19])). tff(21,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul)))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul))))))), inference(rewrite,[status(thm)],[])). tff(22,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul)))))), inference(or_elim,[status(thm)],[4])). tff(23,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul)))))), inference(modus_ponens,[status(thm)],[22, 20])). tff(24,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul)))))), inference(modus_ponens,[status(thm)],[23, 21])). tff(25,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (hate(paul, fred) | ((~rich(paul)) & (~creative(paul)) & (~quiet(paul)) & (~happy(paul)))))), inference(modus_ponens,[status(thm)],[24, 20])). 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!8 |'paul'|) (= X!8 |'mary'|) (not (room X!8))))) (a!5 (or (hate paul fred) (and (not (rich paul)) (not (creative paul)) (not (quiet paul)) (not (happy paul)))))) (let ((a!6 (~ (not (and (room mary) (room paul) a!3 a!5)) (or (not (room mary)) (not (room paul)) a!4 (not a!5))))) (nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (refl (~ (not a!5) (not a!5))) a!6)))

room(kandice)&room(sergio)&(![X]:(room(X)=>(X='kandice'|X='sergio')))& ((((~?[X]:(~room(X)=>(X!=sergio)))=>(~quiet(kandice)))|((~(~?[X]:(~room(X)=>(X!=sergio))))=>(((~(quiet(kandice)&european(kandice)))|(~creative(kandice))))))& ((![X]:(richer(sergio,X)))=>((rich(sergio)&european(sergio))&(~creative(sergio))))& ((((?[X]:(~room(X)&~hate(X,anthony)))&(![X,Y]:((~hate(X,anthony)&~hate(Y,anthony))=>(X=Y)))))<=>(![X]:(richer(kandice,X))))& ((~(~hate(walter,sergio)))<=>(rich(kandice)&quiet(kandice)&creative(kandice)&european(kandice)))& (~(~hate(sergio,walter)))& (((is_right-handed(kandice))|(hate(kandice,anthony))))& (![X]:(quieter(kandice,X)))& (~(((?[X]:(~room(X)&does_not_collect_vintage_stamps(X)))&(![X,Y]:((does_not_collect_vintage_stamps(X)&does_not_collect_vintage_stamps(Y))=>(X=Y))))))& ((is_not_right-handed(kandice))&(~(creative(kandice)&european(kandice))))& (~((hate(walter,sergio))|(is_not_right-handed(sergio))))& (?[X]:(~room(X)=>(((~quiet(X))=>(collects_vintage_stamps(X))))))& (~(![X]:(richer(kandice,X)))))

room(kandice)&room(sergio)&(![X]:(room(X)=>(X='kandice'|X='sergio')))& (((hate(sergio,walter))|(~rich(sergio)&~creative(sergio)&~quiet(sergio)&~happy(sergio))))

entailment

neutral

neutral

Ruth, Emily, Dagmar, Lola are the only persons in the room. Stacy and Emily like each other if Emily and Dagmar like each other and vice versa. Everyone outside the room who is not a happy tall tourist does not collect antique jewelry. Someone who collects antique jewelry like someone who is hated by James. Someone who is taller than James like someone who does not collect antique jewelry. Emily hates James or is not a happy european or both. Only one person outside the room is hated by James. Emily and James like each other. Someone who is not hated by James is a client of someone who does not like Stacy. Someone outside the room collects antique jewelry. Emily and Dagmar are respectively happy and tall. Someone who is a tall european is a client of someone who is taller than James.

Ruth is not hated by James or is not a tall european or both.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(room_type, type, ( room: $i > $o)). tff(tptp_fun_X_10_type, type, ( tptp_fun_X_10: $i)). tff(tptp_fun__mary__type, type, ( tptp_fun__mary_: $i)). tff(tptp_fun__paul__type, type, ( tptp_fun__paul_: $i)). tff(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(european_type, type, ( european: $i > $o)). tff(mary_type, type, ( mary: $i)). tff(tall_type, type, ( tall: $i > $o)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(tptp_fun_X_4_type, type, ( tptp_fun_X_4: $i)). tff(client_type, type, ( client: ( $i * $i ) > $o)). tff(taller_type, type, ( taller: ( $i * $i ) > $o)). tff(fred_type, type, ( fred: $i)). tff(happy_type, type, ( happy: $i > $o)). tff(paul_type, type, ( paul: $i)). tff(predc_type, type, ( predc: $i > $o)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(lucy_type, type, ( lucy: $i)). tff(tourist_type, type, ( tourist: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(1,assumption,(mary = X!4), introduced(assumption)). tff(2,plain, (room(mary) <=> room(X!4)), inference(monotonicity,[status(thm)],[1])). tff(3,plain, (room(X!4) <=> room(mary)), inference(symmetry,[status(thm)],[2])). tff(4,plain, ((~room(X!4)) <=> (~room(mary))), inference(monotonicity,[status(thm)],[3])). tff(5,plain, (?[X: $i] : ((~room(X)) & hate(X, john)) <=> ?[X: $i] : ((~room(X)) & hate(X, john))), inference(rewrite,[status(thm)],[])). tff(6,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((((((((like(paul, fred) & like(fred, paul)) <=> (like(lucy, paul) & like(paul, lucy))) & ![X: $i] : ((~room(X)) => ((~((happy(X) & tall(X)) & tourist(X))) => (~predc(X))))) & ?[X: $i, Y: $i] : ((predc(X) & hate(Y, john)) & like(X, Y))) & ?[X: $i, Y: $i] : ((taller(john, X) & (~predc(Y))) & like(X, Y))) & (hate(john, paul) | (~(happy(paul) & european(paul))))) & (?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((hate(X, john) & hate(Y, john)) => (X = Y)))) & (like(paul, john) & like(john, paul))) & ?[X: $i, Y: $i] : (((~hate(X, john)) & (~like(lucy, Y))) & client(X, Y))) & ?[X: $i] : ((~room(X)) => predc(X))) & (happy(paul) & tall(fred))) & ?[X: $i, Y: $i] : (((tall(X) & european(X)) & taller(john, Y)) & client(X, Y)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((like(paul, fred) & like(fred, paul)) <=> (like(lucy, paul) & like(paul, lucy))) & ![X: $i] : (room(X) | (~predc(X)) | (happy(X) & tall(X) & tourist(X))) & ?[X: $i, Y: $i] : (predc(X) & hate(Y, john) & like(X, Y)) & ?[X: $i, Y: $i] : (taller(john, X) & (~predc(Y)) & like(X, Y)) & (hate(john, paul) | (~(happy(paul) & european(paul)))) & ?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)) & like(paul, john) & like(john, paul) & ?[X: $i, Y: $i] : ((~hate(X, john)) & (~like(lucy, Y)) & client(X, Y)) & ?[X: $i] : (room(X) | predc(X)) & happy(paul) & tall(fred) & ?[X: $i, Y: $i] : (tall(X) & european(X) & taller(john, Y) & client(X, Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary)))))))), inference(rewrite,[status(thm)],[])). tff(7,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((((((((((((like(paul, fred) & like(fred, paul)) <=> (like(lucy, paul) & like(paul, lucy))) & ![X: $i] : ((~room(X)) => ((~((happy(X) & tall(X)) & tourist(X))) => (~predc(X))))) & ?[X: $i, Y: $i] : ((predc(X) & hate(Y, john)) & like(X, Y))) & ?[X: $i, Y: $i] : ((taller(john, X) & (~predc(Y))) & like(X, Y))) & (hate(john, paul) | (~(happy(paul) & european(paul))))) & (?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((hate(X, john) & hate(Y, john)) => (X = Y)))) & (like(paul, john) & like(john, paul))) & ?[X: $i, Y: $i] : (((~hate(X, john)) & (~like(lucy, Y))) & client(X, Y))) & ?[X: $i] : ((~room(X)) => predc(X))) & (happy(paul) & tall(fred))) & ?[X: $i, Y: $i] : (((tall(X) & european(X)) & taller(john, Y)) & client(X, Y)))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary))))))), file('/mnt/tmpfs//5756489372580522303612152.p','negated')). tff(8,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((like(paul, fred) & like(fred, paul)) <=> (like(lucy, paul) & like(paul, lucy))) & ![X: $i] : (room(X) | (~predc(X)) | (happy(X) & tall(X) & tourist(X))) & ?[X: $i, Y: $i] : (predc(X) & hate(Y, john) & like(X, Y)) & ?[X: $i, Y: $i] : (taller(john, X) & (~predc(Y)) & like(X, Y)) & (hate(john, paul) | (~(happy(paul) & european(paul)))) & ?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)) & like(paul, john) & like(john, paul) & ?[X: $i, Y: $i] : ((~hate(X, john)) & (~like(lucy, Y)) & client(X, Y)) & ?[X: $i] : (room(X) | predc(X)) & happy(paul) & tall(fred) & ?[X: $i, Y: $i] : (tall(X) & european(X) & taller(john, Y) & client(X, Y)))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary))))))), inference(modus_ponens,[status(thm)],[7, 6])). tff(9,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((like(paul, fred) & like(fred, paul)) <=> (like(lucy, paul) & like(paul, lucy))) & ![X: $i] : (room(X) | (~predc(X)) | (happy(X) & tall(X) & tourist(X))) & ?[X: $i, Y: $i] : (predc(X) & hate(Y, john) & like(X, Y)) & ?[X: $i, Y: $i] : (taller(john, X) & (~predc(Y)) & like(X, Y)) & (hate(john, paul) | (~(happy(paul) & european(paul)))) & ?[X: $i] : ((~room(X)) & hate(X, john)) & ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)) & like(paul, john) & like(john, paul) & ?[X: $i, Y: $i] : ((~hate(X, john)) & (~like(lucy, Y)) & client(X, Y)) & ?[X: $i] : (room(X) | predc(X)) & happy(paul) & tall(fred) & ?[X: $i, Y: $i] : (tall(X) & european(X) & taller(john, Y) & client(X, Y))), inference(or_elim,[status(thm)],[8])). tff(10,plain, (?[X: $i] : ((~room(X)) & hate(X, john))), inference(and_elim,[status(thm)],[9])). tff(11,plain, (?[X: $i] : ((~room(X)) & hate(X, john))), inference(modus_ponens,[status(thm)],[10, 5])). tff(12,plain,( (~room(X!4)) & hate(X!4, john)), inference(skolemize,[status(sab)],[11])). tff(13,plain, (~room(X!4)), inference(and_elim,[status(thm)],[12])). tff(14,plain, (~room(mary)), inference(modus_ponens,[status(thm)],[13, 4])). tff(15,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(16,plain, (room(mary)), inference(and_elim,[status(thm)],[9])). tff(17,plain, (room(mary)), inference(modus_ponens,[status(thm)],[16, 15])). tff(18,plain, ($false), inference(unit_resolution,[status(thm)],[17, 14])). tff(19,plain,(~(mary = X!4)), inference(lemma,lemma(discharge,[]))). tff(20,assumption,(hate(mary, john)), introduced(assumption)). tff(21,plain, (^[X: $i, Y: $i] : refl(((X = Y) | (~hate(X, john)) | (~hate(Y, john))) <=> ((X = Y) | (~hate(X, john)) | (~hate(Y, john))))), inference(bind,[status(th)],[])). tff(22,plain, (![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john))) <=> ![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))), inference(quant_intro,[status(thm)],[21])). tff(23,plain, (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((hate(X, john) & hate(Y, john)) <=> (~((~hate(X, john)) | (~hate(Y, john))))), ((~(hate(X, john) & hate(Y, john))) <=> (~(~((~hate(X, john)) | (~hate(Y, john))))))), rewrite((~(~((~hate(X, john)) | (~hate(Y, john))))) <=> ((~hate(X, john)) | (~hate(Y, john)))), ((~(hate(X, john) & hate(Y, john))) <=> ((~hate(X, john)) | (~hate(Y, john))))), (((~(hate(X, john) & hate(Y, john))) | (X = Y)) <=> (((~hate(X, john)) | (~hate(Y, john))) | (X = Y)))), rewrite((((~hate(X, john)) | (~hate(Y, john))) | (X = Y)) <=> ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))), (((~(hate(X, john) & hate(Y, john))) | (X = Y)) <=> ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))))), inference(bind,[status(th)],[])). tff(24,plain, (![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))), inference(quant_intro,[status(thm)],[23])). tff(25,plain, (![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y))), inference(rewrite,[status(thm)],[])). tff(26,plain, (![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y))), inference(and_elim,[status(thm)],[9])). tff(27,plain, (![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y))), inference(modus_ponens,[status(thm)],[26, 25])). tff(28,plain,( ![X: $i, Y: $i] : ((~(hate(X, john) & hate(Y, john))) | (X = Y))), inference(skolemize,[status(sab)],[27])). tff(29,plain, (![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))), inference(modus_ponens,[status(thm)],[28, 24])). tff(30,plain, (![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))), inference(modus_ponens,[status(thm)],[29, 22])). tff(31,plain, (hate(X!4, john)), inference(and_elim,[status(thm)],[12])). tff(32,plain, (((~![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))) | ((~hate(mary, john)) | (~hate(X!4, john)) | (mary = X!4))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))) | (~hate(mary, john)) | (~hate(X!4, john)) | (mary = X!4))), inference(rewrite,[status(thm)],[])). tff(33,plain, (((mary = X!4) | (~hate(mary, john)) | (~hate(X!4, john))) <=> ((~hate(mary, john)) | (~hate(X!4, john)) | (mary = X!4))), inference(rewrite,[status(thm)],[])). tff(34,plain, (((~![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))) | ((mary = X!4) | (~hate(mary, john)) | (~hate(X!4, john)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))) | ((~hate(mary, john)) | (~hate(X!4, john)) | (mary = X!4)))), inference(monotonicity,[status(thm)],[33])). tff(35,plain, (((~![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))) | ((mary = X!4) | (~hate(mary, john)) | (~hate(X!4, john)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))) | (~hate(mary, john)) | (~hate(X!4, john)) | (mary = X!4))), inference(transitivity,[status(thm)],[34, 32])). tff(36,plain, ((~![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))) | ((mary = X!4) | (~hate(mary, john)) | (~hate(X!4, john)))), inference(quant_inst,[status(thm)],[])). tff(37,plain, ((~![X: $i, Y: $i] : ((X = Y) | (~hate(X, john)) | (~hate(Y, john)))) | (~hate(mary, john)) | (~hate(X!4, john)) | (mary = X!4)), inference(modus_ponens,[status(thm)],[36, 35])). tff(38,plain, ($false), inference(unit_resolution,[status(thm)],[37, 31, 30, 20, 19])). tff(39,plain,(~hate(mary, john)), inference(lemma,lemma(discharge,[]))). tff(40,plain, (((~hate(mary, john)) | (~tall(mary)) | (~european(mary))) | hate(mary, john)), inference(tautology,[status(thm)],[])). tff(41,plain, ((~hate(mary, john)) | (~tall(mary)) | (~european(mary))), inference(unit_resolution,[status(thm)],[40, 39])). tff(42,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(43,plain, (room(alice)), inference(and_elim,[status(thm)],[9])). tff(44,plain, (room(alice)), inference(modus_ponens,[status(thm)],[43, 42])). tff(45,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(46,plain, (room(fred)), inference(and_elim,[status(thm)],[9])). tff(47,plain, (room(fred)), inference(modus_ponens,[status(thm)],[46, 45])). tff(48,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(49,plain, (room(paul)), inference(and_elim,[status(thm)],[9])). tff(50,plain, (room(paul)), inference(modus_ponens,[status(thm)],[49, 48])). tff(51,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~tall(mary)) | (~european(mary))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~tall(mary)) | (~european(mary)))))), inference(rewrite,[status(thm)],[])). tff(52,plain, ((~((~hate(mary, john)) | (~(tall(mary) & european(mary))))) <=> (~((~hate(mary, john)) | (~tall(mary)) | (~european(mary))))), inference(rewrite,[status(thm)],[])). tff(53,plain, ((~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) <=> (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10))))), inference(rewrite,[status(thm)],[])). tff(54,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~(tall(mary) & european(mary)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~tall(mary)) | (~european(mary)))))), inference(monotonicity,[status(thm)],[53, 52])). tff(55,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~(tall(mary) & european(mary)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~tall(mary)) | (~european(mary)))))), inference(transitivity,[status(thm)],[54, 51])). tff(56,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~(tall(mary) & european(mary)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~(tall(mary) & european(mary))))))), inference(rewrite,[status(thm)],[])). tff(57,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~(tall(mary) & european(mary)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~(tall(mary) & european(mary))))))), inference(monotonicity,[status(thm)],[53])). tff(58,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~(tall(mary) & european(mary)))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!10 = |'alice'|) | (X!10 = |'fred'|) | (X!10 = |'paul'|) | (X!10 = |'mary'|) | (~room(X!10)))) | (~((~hate(mary, john)) | (~(tall(mary) & european(mary))))))), inference(transitivity,[status(thm)],[57, 56])). tff(59,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary))))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary)))))), inference(rewrite,[status(thm)],[])). tff(60,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary))))))), inference(monotonicity,[status(thm)],[59])). tff(61,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary))))))), inference(rewrite,[status(thm)],[])). tff(62,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary)))))), inference(or_elim,[status(thm)],[8])). tff(63,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary)))))), inference(modus_ponens,[status(thm)],[62, 60])). tff(64,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary)))))), inference(modus_ponens,[status(thm)],[63, 61])). tff(65,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ((~hate(mary, john)) | (~(tall(mary) & european(mary)))))), inference(modus_ponens,[status(thm)],[64, 60])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!10 |'alice'|) (= X!10 |'fred'|) (= X!10 |'paul'|) (= X!10 |'mary'|) (not (room X!10))))) (a!7 (or (not (hate mary john)) (not (and (tall mary) (european mary)))))) (let ((a!8 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 a!7)) (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (not a!7))))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl (~ (not a!7) (not a!7))) a!8)))

room(ruth)&room(emily)&room(dagmar)&room(lola)&(![X]:(room(X)=>(X='ruth'|X='emily'|X='dagmar'|X='lola')))& ((((like(emily,dagmar) & like(dagmar,emily)))<=>((like(stacy,emily) & like(emily,stacy))))& (![X]:(~room(X)=>(((~(happy(X)&tall(X)&tourist(X)))=>(does_not_collect_antique_jewelry(X))))))& (?[X,Y]:((collects_antique_jewelry(X))&(hate(Y,james))&(like(X,Y))))& (?[X,Y]:((taller(james,X))&(does_not_collect_antique_jewelry(Y))&(like(X,Y))))& (((hate(james,emily))|(~(happy(emily)&european(emily)))))& (((?[X]:(~room(X)&hate(X,james)))&(![X,Y]:((hate(X,james)&hate(Y,james))=>(X=Y)))))& ((like(emily,james) & like(james,emily)))& (?[X,Y]:((~hate(X,james))&(~like(stacy,Y))&(client(X,Y))))& (?[X]:(~room(X)=>(collects_antique_jewelry(X))))& ((happy(emily))&(tall(dagmar)))& (?[X,Y]:((tall(X)&european(X))&(taller(james,Y))&(client(X,Y)))))

room(ruth)&room(emily)&room(dagmar)&room(lola)&(![X]:(room(X)=>(X='ruth'|X='emily'|X='dagmar'|X='lola')))& (((~hate(ruth,james))|(~(tall(ruth)&european(ruth)))))

entailment

neutral

entailment

Sheila is the only person in the room. If "Sheila neither hates Elaine nor is a client of Earl" then "Sheila is not a quiet brave person and is not a brave person". Sheila neither is taller than Elaine nor is not a night owl. Sheila is not a quiet person. Only one person in the room is not hated by Earl. Sheila is not a quiet brave person and is not a brave person. Sheila is the quietest in the room. Sheila does not hate Earl or is hated by Earl or both.

It is not the case that 'Sheila who does not hate Earl, is quieter than Elaine'.

contradiction

-

room(sheila)&(![X]:(room(X)=>(X='sheila')))& (((~((hate(elaine,sheila))|(client(earl,sheila))))=>((~(quiet(sheila)&brave(sheila)&person(sheila)))&(~(brave(sheila)&person(sheila)))))& (~((taller(elaine,sheila))|(is_not_a_night_owl(sheila))))& (~(quiet(sheila)&person(sheila)))& (((?[X]:(room(X)&~hate(X,earl)))&(![X,Y]:((~hate(X,earl)&~hate(Y,earl))=>(X=Y)))))& ((~(quiet(sheila)&brave(sheila)&person(sheila)))&(~(brave(sheila)&person(sheila))))& (![X]:(quieter(X,sheila)))& (((~hate(earl,sheila))|(hate(sheila,earl)))))

room(sheila)&(![X]:(room(X)=>(X='sheila')))& (~((~hate(earl,sheila))&(quieter(elaine,sheila))))

entailment

entailment

contradiction

Ines, Carla, Jessica, Julie are the only persons in the room. Carla is the tallest in the room if Ines who is a tall person, is not a tall tourist. Ines and Carla are respectively tall and happy if Brenda is a sibling of Ines. If Carla uses an ios phone or is not liked by Douglas or both then Ines is the least tall in the room. Carla does not like Douglas or owns a microscope or both. It is not the case that 'Jessica likes Brenda or is a happy brave person or both'. Douglas is a sibling of Jessica. Douglas is a sibling of Carla. Someone outside the room who is a happy brave tourist is not brave. Carla who does not use an ios phone, is liked by Douglas. Carla and Jessica are respectively tall and happy. Only one person outside the room is liked by Brenda. Only one person outside the room owns a microscope.

Ines is not a quiet brave rich tall person and owns a microscope.

contradiction

-

room(ines)&room(carla)&room(jessica)&room(julie)&(![X]:(room(X)=>(X='ines'|X='carla'|X='jessica'|X='julie')))& ((((tall(ines)&person(ines))&(~(tall(ines)&tourist(ines))))=>(![X]:(taller(X,carla))))& ((sibling(ines,brenda))=>((tall(ines))&(happy(carla))))& ((((uses_an_ios_phone(carla))|(~like(carla,douglas))))=>(![X]:(taller(ines,X))))& (((~like(douglas,carla))|(owns_a_microscope(carla))))& (~(((like(brenda,jessica))|(happy(jessica)&brave(jessica)&person(jessica)))))& (sibling(jessica,douglas))& (sibling(carla,douglas))& (?[X]:(~room(X)=>(((happy(X)&brave(X)&tourist(X))=>(~brave(X))))))& ((does_not_use_an_ios_phone(carla))&(like(carla,douglas)))& ((tall(carla))&(happy(jessica)))& (((?[X]:(~room(X)&like(X,brenda)))&(![X,Y]:((like(X,brenda)&like(Y,brenda))=>(X=Y)))))& (((?[X]:(~room(X)&owns_a_microscope(X)))&(![X,Y]:((owns_a_microscope(X)&owns_a_microscope(Y))=>(X=Y))))))

room(ines)&room(carla)&room(jessica)&room(julie)&(![X]:(room(X)=>(X='ines'|X='carla'|X='jessica'|X='julie')))& ((~(quiet(ines)&brave(ines)&rich(ines)&tall(ines)&person(ines)))&(owns_a_microscope(ines)))

neutral

neutral

contradiction

Sandy, Lora, Evelyn, Alvin are the only persons in the room. Someone outside the room who is not hated by Michelle does not can play the harmonica. More than one person outside the room is not Lora. Lora is not quiet, not brave and does not hate Michelle. Lora neither hates Michelle nor is hated by Michelle.

It is not the case that 'Lora is a brave european and is not hated by Michelle'.

entailment

% 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(tptp_fun__fred__type, type, ( tptp_fun__fred_: $i)). tff(tptp_fun__alice__type, type, ( tptp_fun__alice_: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(paul_type, type, ( paul: $i)). tff(european_type, type, ( european: $i > $o)). tff(brave_type, type, ( brave: $i > $o)). tff(quiet_type, type, ( quiet: $i > $o)). tff(predb_type, type, ( predb: $i > $o)). tff(alice_type, type, ( alice: $i)). tff(fred_type, type, ( fred: $i)). tff(mary_type, type, ( mary: $i)). tff(1,plain, ((~brave(paul)) <=> (~brave(paul))), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((?[X: $i] : ((~room(X)) => ((~hate(X, john)) => (~predb(X)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = paul)) & (~(Y = paul)))) & (~(X = Y)))) & (((~quiet(paul)) & (~brave(paul))) & (~hate(john, paul)))) & (~(hate(john, paul) | hate(paul, john))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~((brave(paul) & european(paul)) & (~hate(paul, john))))))) <=> (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i] : (room(X) | (~predb(X)) | hate(X, john)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = paul)) & (~(Y = paul)) & (~(X = Y))) & (~quiet(paul)) & (~brave(paul)) & (~hate(john, paul)) & (~(hate(john, paul) | hate(paul, john))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john)))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (((?[X: $i] : ((~room(X)) => ((~hate(X, john)) => (~predb(X)))) & ?[X: $i, Y: $i] : ((((~room(X)) & (~room(Y))) & ((~(X = paul)) & (~(Y = paul)))) & (~(X = Y)))) & (((~quiet(paul)) & (~brave(paul))) & (~hate(john, paul)))) & (~(hate(john, paul) | hate(paul, john))))) => (((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~((brave(paul) & european(paul)) & (~hate(paul, john))))))), file('/mnt/tmpfs//6155042308039695550776554.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i] : (room(X) | (~predb(X)) | hate(X, john)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = paul)) & (~(Y = paul)) & (~(X = Y))) & (~quiet(paul)) & (~brave(paul)) & (~hate(john, paul)) & (~(hate(john, paul) | hate(paul, john))))) | (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john))))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ?[X: $i] : (room(X) | (~predb(X)) | hate(X, john)) & ?[X: $i, Y: $i] : ((~room(X)) & (~room(Y)) & (~(X = paul)) & (~(Y = paul)) & (~(X = Y))) & (~quiet(paul)) & (~brave(paul)) & (~hate(john, paul)) & (~(hate(john, paul) | hate(paul, john)))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (~brave(paul)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (~brave(paul)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (((~brave(paul)) | (~european(paul)) | hate(paul, john)) | brave(paul)), inference(tautology,[status(thm)],[])). tff(9,plain, ((~brave(paul)) | (~european(paul)) | hate(paul, john)), inference(unit_resolution,[status(thm)],[8, 7])). tff(10,plain, (room(alice) <=> room(alice)), inference(rewrite,[status(thm)],[])). tff(11,plain, (room(alice)), inference(and_elim,[status(thm)],[5])). tff(12,plain, (room(alice)), inference(modus_ponens,[status(thm)],[11, 10])). tff(13,plain, (room(fred) <=> room(fred)), inference(rewrite,[status(thm)],[])). tff(14,plain, (room(fred)), inference(and_elim,[status(thm)],[5])). tff(15,plain, (room(fred)), inference(modus_ponens,[status(thm)],[14, 13])). tff(16,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(17,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(18,plain, (room(paul)), inference(modus_ponens,[status(thm)],[17, 16])). tff(19,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(20,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(21,plain, (room(mary)), inference(modus_ponens,[status(thm)],[20, 19])). tff(22,plain, (((~((~brave(paul)) | (~european(paul)) | hate(paul, john))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~((~brave(paul)) | (~european(paul)) | hate(paul, john))))), inference(rewrite,[status(thm)],[])). tff(23,plain, ((~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))), inference(rewrite,[status(thm)],[])). tff(24,plain, ((brave(paul) & european(paul) & (~hate(paul, john))) <=> (~((~brave(paul)) | (~european(paul)) | hate(paul, john)))), inference(rewrite,[status(thm)],[])). tff(25,plain, (((brave(paul) & european(paul) & (~hate(paul, john))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> ((~((~brave(paul)) | (~european(paul)) | hate(paul, john))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))), inference(monotonicity,[status(thm)],[24, 23])). tff(26,plain, (((brave(paul) & european(paul) & (~hate(paul, john))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~((~brave(paul)) | (~european(paul)) | hate(paul, john))))), inference(transitivity,[status(thm)],[25, 22])). tff(27,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (brave(paul) & european(paul) & (~hate(paul, john)))) <=> ((brave(paul) & european(paul) & (~hate(paul, john))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))), inference(rewrite,[status(thm)],[])). tff(28,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (brave(paul) & european(paul) & (~hate(paul, john)))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (brave(paul) & european(paul) & (~hate(paul, john))))), inference(monotonicity,[status(thm)],[23])). tff(29,plain, (((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (brave(paul) & european(paul) & (~hate(paul, john)))) <=> ((brave(paul) & european(paul) & (~hate(paul, john))) | (~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!3 = |'alice'|) | (X!3 = |'fred'|) | (X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))))), inference(transitivity,[status(thm)],[28, 27])). tff(30,plain, ((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john))))) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john)))))), inference(rewrite,[status(thm)],[])). tff(31,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john))))))), inference(monotonicity,[status(thm)],[30])). tff(32,plain, ((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john)))))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john))))))), inference(rewrite,[status(thm)],[])). tff(33,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john)))))), inference(or_elim,[status(thm)],[4])). tff(34,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john)))))), inference(modus_ponens,[status(thm)],[33, 31])). tff(35,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john)))))), inference(modus_ponens,[status(thm)],[34, 32])). tff(36,plain, (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (~(brave(paul) & european(paul) & (~hate(paul, john)))))), inference(modus_ponens,[status(thm)],[35, 31])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (refl (~ (not (room fred)) (not (room fred))))) (a!4 (refl (~ (not (room alice)) (not (room alice))))) (a!5 (forall ((X $i)) (or (= X |'alice'|) (= X |'fred'|) (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!6 (not (or (= X!3 |'alice'|) (= X!3 |'fred'|) (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3))))) (a!7 (~ (and (brave paul) (european paul) (not (hate paul john))) (and (brave paul) (european paul) (not (hate paul john))))) (a!8 (not (and (brave paul) (european paul) (not (hate paul john)))))) (let ((a!9 (or (not (room mary)) (not (room paul)) (not (room fred)) (not (room alice)) a!6 (and (brave paul) (european paul) (not (hate paul john)))))) (let ((a!10 (~ (not (and (room mary) (room paul) (room fred) (room alice) a!5 a!8)) a!9))) (nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) (refl a!7) a!10))))

room(sandy)&room(lora)&room(evelyn)&room(alvin)&(![X]:(room(X)=>(X='sandy'|X='lora'|X='evelyn'|X='alvin')))& ((?[X]:(~room(X)=>(((~hate(X,michelle))=>(does_not_can_play_the_harmonica(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(X!=lora&Y!=lora)&(X!=Y))))& ((~quiet(lora)&~brave(lora))&(~hate(michelle,lora)))& (~((hate(michelle,lora))|(hate(lora,michelle)))))

room(sandy)&room(lora)&room(evelyn)&room(alvin)&(![X]:(room(X)=>(X='sandy'|X='lora'|X='evelyn'|X='alvin')))& (~((brave(lora)&european(lora))&(~hate(lora,michelle))))

entailment

entailment

contradiction

Michael, Danny are the only persons in the room. Not all of the following are true:. -Michael either is not tall or likes Ronald. -Danny either owns an Android phone or is not liked by Ronald. -Someone who does not own an Android phone like someone who is not rich, not happy.

It is not the case that 'Michael either hates Dorothy or does not like Ronald'.

entailment

% SZS status Unsatisfiable % SZS output start Proof tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(mary_type, type, ( mary: $i)). tff(fred_type, type, ( fred: $i)). tff(hate_type, type, ( hate: ( $i * $i ) > $o)). tff(alice_type, type, ( alice: $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(happy_type, type, ( happy: $i > $o)). tff(rich_type, type, ( rich: $i > $o)). tff(preda_type, type, ( preda: $i > $o)). tff(tall_type, type, ( tall: $i > $o)). tff(1,plain, ((~$true) <=> $false), inference(rewrite,[status(thm)],[])). tff(2,plain, (((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) => (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> $true), inference(rewrite,[status(thm)],[])). tff(3,plain, (((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) & $true) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(rewrite,[status(thm)],[])). tff(4,plain, ((~$false) <=> $true), inference(rewrite,[status(thm)],[])). tff(5,plain, ((((~like(fred, mary)) | hate(alice, mary)) & (~((~like(fred, mary)) | hate(alice, mary)))) <=> $false), inference(rewrite,[status(thm)],[])). tff(6,plain, ((~(hate(alice, mary) | (~like(fred, mary)))) <=> (~((~like(fred, mary)) | hate(alice, mary)))), inference(rewrite,[status(thm)],[])). tff(7,plain, ((hate(alice, mary) | (~like(fred, mary))) <=> ((~like(fred, mary)) | hate(alice, mary))), inference(rewrite,[status(thm)],[])). tff(8,plain, (((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary))))) <=> (((~like(fred, mary)) | hate(alice, mary)) & (~((~like(fred, mary)) | hate(alice, mary))))), inference(monotonicity,[status(thm)],[7, 6])). tff(9,plain, (((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary))))) <=> $false), inference(transitivity,[status(thm)],[8, 5])). tff(10,plain, ((~((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary)))))) <=> (~$false)), inference(monotonicity,[status(thm)],[9])). tff(11,plain, ((~((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary)))))) <=> $true), inference(transitivity,[status(thm)],[10, 4])). tff(12,plain, (((room(mary) & room(paul)) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(rewrite,[status(thm)],[])). tff(13,plain, (^[X: $i] : rewrite((room(X) => ((X = |'mary'|) | (X = |'paul'|))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(bind,[status(th)],[])). tff(14,plain, (![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))), inference(quant_intro,[status(thm)],[13])). tff(15,plain, (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) <=> ((room(mary) & room(paul)) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(monotonicity,[status(thm)],[14])). tff(16,plain, (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(transitivity,[status(thm)],[15, 12])). tff(17,plain, ((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary))))))) <=> ((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) & $true)), inference(monotonicity,[status(thm)],[16, 11])). tff(18,plain, ((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary))))))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(transitivity,[status(thm)],[17, 3])). tff(19,plain, (($false & ?[X: $i, Y: $i] : ((~preda(X)) & (~rich(Y)) & (~happy(Y)) & like(X, Y))) <=> $false), inference(rewrite,[status(thm)],[])). tff(20,plain, (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) <=> ((~preda(X)) & (~rich(Y)) & (~happy(Y)))), ((((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y)) <=> (((~preda(X)) & (~rich(Y)) & (~happy(Y))) & like(X, Y)))), rewrite((((~preda(X)) & (~rich(Y)) & (~happy(Y))) & like(X, Y)) <=> ((~preda(X)) & (~rich(Y)) & (~happy(Y)) & like(X, Y))), ((((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y)) <=> ((~preda(X)) & (~rich(Y)) & (~happy(Y)) & like(X, Y))))), inference(bind,[status(th)],[])). tff(21,plain, (?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y)) <=> ?[X: $i, Y: $i] : ((~preda(X)) & (~rich(Y)) & (~happy(Y)) & like(X, Y))), inference(quant_intro,[status(thm)],[20])). tff(22,plain, (($false & $false) <=> $false), inference(rewrite,[status(thm)],[])). tff(23,plain, (((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred))))) <=> $false), inference(rewrite,[status(thm)],[])). tff(24,plain, ((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) <=> $false), inference(rewrite,[status(thm)],[])). tff(25,plain, (((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) <=> ($false & $false)), inference(monotonicity,[status(thm)],[24, 23])). tff(26,plain, (((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) <=> $false), inference(transitivity,[status(thm)],[25, 22])). tff(27,plain, ((((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y))) <=> ($false & ?[X: $i, Y: $i] : ((~preda(X)) & (~rich(Y)) & (~happy(Y)) & like(X, Y)))), inference(monotonicity,[status(thm)],[26, 21])). tff(28,plain, ((((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y))) <=> $false), inference(transitivity,[status(thm)],[27, 19])). tff(29,plain, ((~(((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y)))) <=> (~$false)), inference(monotonicity,[status(thm)],[28])). tff(30,plain, ((~(((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y)))) <=> $true), inference(transitivity,[status(thm)],[29, 4])). tff(31,plain, ((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y))))) <=> ((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) & $true)), inference(monotonicity,[status(thm)],[16, 30])). tff(32,plain, ((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y))))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(transitivity,[status(thm)],[31, 3])). tff(33,plain, (((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary)))))))) <=> ((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) => (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(monotonicity,[status(thm)],[32, 18])). tff(34,plain, (((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary)))))))) <=> $true), inference(transitivity,[status(thm)],[33, 2])). tff(35,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary))))))))) <=> (~$true)), inference(monotonicity,[status(thm)],[34])). tff(36,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary))))))))) <=> $false), inference(transitivity,[status(thm)],[35, 1])). tff(37,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(((((~tall(mary)) | like(fred, mary)) & (~((~tall(mary)) | like(fred, mary)))) & ((preda(paul) | (~like(paul, fred))) & (~(preda(paul) | (~like(paul, fred)))))) & ?[X: $i, Y: $i] : (((~preda(X)) & ((~rich(Y)) & (~happy(Y)))) & like(X, Y))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~((hate(alice, mary) | (~like(fred, mary))) & (~(hate(alice, mary) | (~like(fred, mary))))))))), file('/mnt/tmpfs//4363027830490086470380789.p','negated')). tff(38,plain, ($false), inference(modus_ponens,[status(thm)],[37, 36])). % SZS output end Proof

room(michael)&room(danny)&(![X]:(room(X)=>(X='michael'|X='danny')))& (~((((~tall(michael))|(like(ronald,michael)))&(~((~tall(michael))|(like(ronald,michael)))))&(((owns_an_Android_phone(danny))|(~like(danny,ronald)))&(~((owns_an_Android_phone(danny))|(~like(danny,ronald)))))&?[X,Y]:((does_not_own_an_Android_phone(X))&(~rich(Y)&~happy(Y))&(like(X,Y)))))

room(michael)&room(danny)&(![X]:(room(X)=>(X='michael'|X='danny')))& (~((((hate(dorothy,michael))|(~like(ronald,michael)))&(~((hate(dorothy,michael))|(~like(ronald,michael)))))))

entailment

entailment

neutral

Malcolm, Richard are the only persons in the room. Only one of the following is true:. -Someone who is not Richard like someone who is liked by Luisa. -Someone outside the room is liked by Luisa.

Malcolm likes Luisa or does not like Luisa or both.

entailment

% 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(paul_type, type, ( paul: $i)). tff(like_type, type, ( like: ( $i * $i ) > $o)). tff(john_type, type, ( john: $i)). tff(mary_type, type, ( mary: $i)). tff(1,plain, (room(paul) <=> room(paul)), inference(rewrite,[status(thm)],[])). tff(2,plain, ((~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((?[X: $i, Y: $i] : (((~(X = paul)) & like(Y, john)) & like(X, Y)) | ?[X: $i] : ((~room(X)) => like(X, john))) & (~(?[X: $i, Y: $i] : (((~(X = paul)) & like(Y, john)) & like(X, Y)) & ?[X: $i] : ((~room(X)) => like(X, john)))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (like(john, mary) | (~like(john, mary)))))) <=> (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i, Y: $i] : ((~(X = paul)) & like(Y, john) & like(X, Y)) | ?[X: $i] : (room(X) | like(X, john))) & (~(?[X: $i, Y: $i] : ((~(X = paul)) & like(Y, john) & like(X, Y)) & ?[X: $i] : (room(X) | like(X, john)))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))))), inference(rewrite,[status(thm)],[])). tff(3,axiom,(~((((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ((?[X: $i, Y: $i] : (((~(X = paul)) & like(Y, john)) & like(X, Y)) | ?[X: $i] : ((~room(X)) => like(X, john))) & (~(?[X: $i, Y: $i] : (((~(X = paul)) & like(Y, john)) & like(X, Y)) & ?[X: $i] : ((~room(X)) => like(X, john)))))) => (((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (like(john, mary) | (~like(john, mary)))))), file('/mnt/tmpfs//7956073661818693772864969.p','negated')). tff(4,plain, (~((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i, Y: $i] : ((~(X = paul)) & like(Y, john) & like(X, Y)) | ?[X: $i] : (room(X) | like(X, john))) & (~(?[X: $i, Y: $i] : ((~(X = paul)) & like(Y, john) & like(X, Y)) & ?[X: $i] : (room(X) | like(X, john)))))) | (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(modus_ponens,[status(thm)],[3, 2])). tff(5,plain, (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & (?[X: $i, Y: $i] : ((~(X = paul)) & like(Y, john) & like(X, Y)) | ?[X: $i] : (room(X) | like(X, john))) & (~(?[X: $i, Y: $i] : ((~(X = paul)) & like(Y, john) & like(X, Y)) & ?[X: $i] : (room(X) | like(X, john))))), inference(or_elim,[status(thm)],[4])). tff(6,plain, (room(paul)), inference(and_elim,[status(thm)],[5])). tff(7,plain, (room(paul)), inference(modus_ponens,[status(thm)],[6, 1])). tff(8,plain, (room(mary) <=> room(mary)), inference(rewrite,[status(thm)],[])). tff(9,plain, (room(mary)), inference(and_elim,[status(thm)],[5])). tff(10,plain, (room(mary)), inference(modus_ponens,[status(thm)],[9, 8])). tff(11,plain, ((~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))), inference(rewrite,[status(thm)],[])). tff(12,plain, (((~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)))))), inference(monotonicity,[status(thm)],[11])). tff(13,plain, ((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(rewrite,[status(thm)],[])). tff(14,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(monotonicity,[status(thm)],[13])). tff(15,plain, ((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))))), inference(rewrite,[status(thm)],[])). tff(16,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(or_elim,[status(thm)],[4])). tff(17,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[16, 14])). tff(18,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[17, 15])). tff(19,plain, (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))), inference(modus_ponens,[status(thm)],[18, 14])). unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary))))) (a!2 (refl (~ (not (room paul)) (not (room paul))))) (a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X))))) (a!4 (not (or (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3)))))) (let ((a!5 (~ (not (and (room mary) (room paul) a!3)) (or (not (room mary)) (not (room paul)) a!4)))) (nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) a!5)))

room(malcolm)&room(richard)&(![X]:(room(X)=>(X='malcolm'|X='richard')))& (((?[X,Y]:((X!=richard)&(like(Y,luisa))&(like(X,Y))))|(?[X]:(~room(X)=>(like(X,luisa)))))&~(?[X,Y]:((X!=richard)&(like(Y,luisa))&(like(X,Y)))&?[X]:(~room(X)=>(like(X,luisa)))))

room(malcolm)&room(richard)&(![X]:(room(X)=>(X='malcolm'|X='richard')))& (((like(luisa,malcolm))|(~like(luisa,malcolm))))

entailment

entailment

neutral

Russell, Rolf, Muriel are the only persons in the room. Russell is the tallest in the room. Only one person outside the room plays the violin. Russell is the least quiet in the room. Only one person outside the room does not collect antique jewelry. Russell is not liked by Mary and likes Mary.

Russell is quieter than Joseph or plays the violin or both.

contradiction

-

room(russell)&room(rolf)&room(muriel)&(![X]:(room(X)=>(X='russell'|X='rolf'|X='muriel')))& ((![X]:(taller(X,russell)))& (((?[X]:(~room(X)&plays_the_violin(X)))&(![X,Y]:((plays_the_violin(X)&plays_the_violin(Y))=>(X=Y)))))& (![X]:(quieter(russell,X)))& (((?[X]:(~room(X)&does_not_collect_antique_jewelry(X)))&(![X,Y]:((does_not_collect_antique_jewelry(X)&does_not_collect_antique_jewelry(Y))=>(X=Y)))))& ((~like(russell,mary))&(like(mary,russell))))

room(russell)&room(rolf)&room(muriel)&(![X]:(room(X)=>(X='russell'|X='rolf'|X='muriel')))& (((quieter(joseph,russell))|(plays_the_violin(russell))))

contradiction

entailment

contradiction

Clyde, Jennifer, William, Becky are the only persons in the room. Clyde is quieter than Heather and is hated by Heather if only one person in the room does not like Heather and vice versa. Clyde is the tallest in the room. It is not the case that 'William who is not liked by Heather, is not Jennifer'.

Becky is quieter than Heather or is liked by Heather or both.

neutral

% SZS status Satisfiable

room(clyde)&room(jennifer)&room(william)&room(becky)&(![X]:(room(X)=>(X='clyde'|X='jennifer'|X='william'|X='becky')))& (((((?[X]:(room(X)&~like(heather,X)))&(![X,Y]:((~like(heather,X)&~like(heather,Y))=>(X=Y)))))<=>((quieter(heather,clyde))&(hate(clyde,heather))))& (![X]:(taller(X,clyde)))& (~((~like(william,heather))&(william!=jennifer))))

room(clyde)&room(jennifer)&room(william)&room(becky)&(![X]:(room(X)=>(X='clyde'|X='jennifer'|X='william'|X='becky')))& (((quieter(heather,becky))|(like(becky,heather))))

entailment

entailment

entailment

Daniel, Margaret are the only persons in the room. "Margaret is not a creative quiet brave european and does not hate Gregg" if "someone outside the room is not a creative tourist" and vice versa. Daniel who is not creative, not brave, is a sibling of Jeanette. Daniel and Jim hate each other. Someone who is not a quiet european is quieter than someone who is quieter than Josie.

Margaret is not a tall creative person or is a creative quiet tall tourist or both.

neutral

% SZS status Satisfiable

room(daniel)&room(margaret)&(![X]:(room(X)=>(X='daniel'|X='margaret')))& (((?[X]:(~room(X)=>(~(creative(X)&tourist(X)))))<=>((~(creative(margaret)&quiet(margaret)&brave(margaret)&european(margaret)))&(~hate(gregg,margaret))))& ((~creative(daniel)&~brave(daniel))&(sibling(jeanette,daniel)))& ((hate(daniel,jim) & hate(jim,daniel)))& (?[X,Y]:((~(quiet(X)&european(X)))&(quieter(josie,Y))&(quieter(X,Y)))))

room(daniel)&room(margaret)&(![X]:(room(X)=>(X='daniel'|X='margaret')))& (((~(tall(margaret)&creative(margaret)&person(margaret)))|(creative(margaret)&quiet(margaret)&tall(margaret)&tourist(margaret))))

neutral

entailment

entailment

Michael, Gary, Tiffany are the only persons in the room. More than one person outside the room is not Gary. Someone who is a quiet tourist is a sibling of someone who is not Gary. Michael neither does not like Shirley nor is not rich. Michael is the least rich in the room. Michael does not enjoy jogging and is a sibling of Gary.

Gary is a rich tourist and is richer than Gary.

neutral

% SZS status Satisfiable

room(michael)&room(gary)&room(tiffany)&(![X]:(room(X)=>(X='michael'|X='gary'|X='tiffany')))& (((?[X,Y]:(~room(X)&~room(Y)&(X!=gary&Y!=gary)&(X!=Y))))& (?[X,Y]:((quiet(X)&tourist(X))&(Y!=gary)&(sibling(X,Y))))& (~((~like(shirley,michael))|(~rich(michael))))& (![X]:(richer(michael,X)))& ((does_not_enjoy_jogging(michael))&(sibling(gary,michael))))

room(michael)&room(gary)&room(tiffany)&(![X]:(room(X)=>(X='michael'|X='gary'|X='tiffany')))& ((rich(gary)&tourist(gary))&(richer(gary,gary)))

contradiction

contradiction

contradiction

Nancy, George, Joseph, Jeanette are the only persons in the room. Only one person outside the room is a creative person. Nancy and George are respectively rich and creative. Nancy is the richest in the room. Only one person in the room does not own a telescope.

Someone who is not rich, not creative is richer than someone who is not Joseph.

neutral

% SZS status Satisfiable

room(nancy)&room(george)&room(joseph)&room(jeanette)&(![X]:(room(X)=>(X='nancy'|X='george'|X='joseph'|X='jeanette')))& ((((?[X]:(~room(X)&creative(X)&person(X)))&(![X,Y]:((creative(X)&person(X)&creative(Y)&person(Y))=>(X=Y)))))& ((rich(nancy))&(creative(george)))& (![X]:(richer(X,nancy)))& (((?[X]:(room(X)&does_not_own_a_telescope(X)))&(![X,Y]:((does_not_own_a_telescope(X)&does_not_own_a_telescope(Y))=>(X=Y))))))

room(nancy)&room(george)&room(joseph)&room(jeanette)&(![X]:(room(X)=>(X='nancy'|X='george'|X='joseph'|X='jeanette')))& (?[X,Y]:((~rich(X)&~creative(X))&(Y!=joseph)&(richer(X,Y))))

neutral

entailment

contradiction

Stephanie, Helen, Autumn are the only persons in the room. Stephanie does not play a string instrument and is not a creative person unless Autumn either does not hate Alice or collect rare sneakers. If Stephanie collect rare sneakers or does not hate Sarah or both then Autumn is hated by Alice. Autumn hates Alice or is a sibling of Sarah or both. Stephanie neither does not hate Sarah nor is not tall. Someone who collect rare sneakers is a client of someone who is hated by Alice. Autumn neither is not hated by Sarah nor does not collect rare sneakers. Stephanie is the tallest in the room. Autumn is a tall creative quiet person and collect rare sneakers. It is not the case that 'Alice is a client of Autumn'.

Someone who hates Alice is a sibling of someone who is not a rich european.

neutral

% SZS status Satisfiable

room(stephanie)&room(helen)&room(autumn)&(![X]:(room(X)=>(X='stephanie'|X='helen'|X='autumn')))& ((~((((~hate(alice,autumn))|(collect_rare_sneakers(autumn)))&(~((~hate(alice,autumn))|(collect_rare_sneakers(autumn))))))=>((does_not_play_a_string_instrument(stephanie))&(~(creative(stephanie)&person(stephanie)))))& ((((collect_rare_sneakers(stephanie))|(~hate(sarah,stephanie))))=>(hate(autumn,alice)))& (((hate(alice,autumn))|(sibling(sarah,autumn))))& (~((~hate(sarah,stephanie))|(~tall(stephanie))))& (?[X,Y]:((collect_rare_sneakers(X))&(hate(Y,alice))&(client(X,Y))))& (~((~hate(autumn,sarah))|(does_not_collect_rare_sneakers(autumn))))& (![X]:(taller(X,stephanie)))& ((tall(autumn)&creative(autumn)&quiet(autumn)&person(autumn))&(collect_rare_sneakers(autumn)))& (~(client(autumn,alice))))

room(stephanie)&room(helen)&room(autumn)&(![X]:(room(X)=>(X='stephanie'|X='helen'|X='autumn')))& (?[X,Y]:((hate(alice,X))&(~(rich(Y)&european(Y)))&(sibling(X,Y))))

neutral

neutral

entailment